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cba-pipeline-public
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cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/calculus/quadrature.py
|
import math
from ..libmp.backend import xrange
class QuadratureRule(object):
"""
Quadrature rules are implemented using this class, in order to
simplify the code and provide a common infrastructure
for tasks such as error estimation and node caching.
You can implement a custom quadrature rule by subclassing
:class:`QuadratureRule` and implementing the appropriate
methods. The subclass can then be used by :func:`~mpmath.quad` by
passing it as the *method* argument.
:class:`QuadratureRule` instances are supposed to be singletons.
:class:`QuadratureRule` therefore implements instance caching
in :func:`~mpmath.__new__`.
"""
def __init__(self, ctx):
self.ctx = ctx
self.standard_cache = {}
self.transformed_cache = {}
self.interval_count = {}
def clear(self):
"""
Delete cached node data.
"""
self.standard_cache = {}
self.transformed_cache = {}
self.interval_count = {}
def calc_nodes(self, degree, prec, verbose=False):
r"""
Compute nodes for the standard interval `[-1, 1]`. Subclasses
should probably implement only this method, and use
:func:`~mpmath.get_nodes` method to retrieve the nodes.
"""
raise NotImplementedError
def get_nodes(self, a, b, degree, prec, verbose=False):
"""
Return nodes for given interval, degree and precision. The
nodes are retrieved from a cache if already computed;
otherwise they are computed by calling :func:`~mpmath.calc_nodes`
and are then cached.
Subclasses should probably not implement this method,
but just implement :func:`~mpmath.calc_nodes` for the actual
node computation.
"""
key = (a, b, degree, prec)
if key in self.transformed_cache:
return self.transformed_cache[key]
orig = self.ctx.prec
try:
self.ctx.prec = prec+20
# Get nodes on standard interval
if (degree, prec) in self.standard_cache:
nodes = self.standard_cache[degree, prec]
else:
nodes = self.calc_nodes(degree, prec, verbose)
self.standard_cache[degree, prec] = nodes
# Transform to general interval
nodes = self.transform_nodes(nodes, a, b, verbose)
if key in self.interval_count:
self.transformed_cache[key] = nodes
else:
self.interval_count[key] = True
finally:
self.ctx.prec = orig
return nodes
def transform_nodes(self, nodes, a, b, verbose=False):
r"""
Rescale standardized nodes (for `[-1, 1]`) to a general
interval `[a, b]`. For a finite interval, a simple linear
change of variables is used. Otherwise, the following
transformations are used:
.. math ::
\lbrack a, \infty \rbrack : t = \frac{1}{x} + (a-1)
\lbrack -\infty, b \rbrack : t = (b+1) - \frac{1}{x}
\lbrack -\infty, \infty \rbrack : t = \frac{x}{\sqrt{1-x^2}}
"""
ctx = self.ctx
a = ctx.convert(a)
b = ctx.convert(b)
one = ctx.one
if (a, b) == (-one, one):
return nodes
half = ctx.mpf(0.5)
new_nodes = []
if ctx.isinf(a) or ctx.isinf(b):
if (a, b) == (ctx.ninf, ctx.inf):
p05 = -half
for x, w in nodes:
x2 = x*x
px1 = one-x2
spx1 = px1**p05
x = x*spx1
w *= spx1/px1
new_nodes.append((x, w))
elif a == ctx.ninf:
b1 = b+1
for x, w in nodes:
u = 2/(x+one)
x = b1-u
w *= half*u**2
new_nodes.append((x, w))
elif b == ctx.inf:
a1 = a-1
for x, w in nodes:
u = 2/(x+one)
x = a1+u
w *= half*u**2
new_nodes.append((x, w))
elif a == ctx.inf or b == ctx.ninf:
return [(x,-w) for (x,w) in self.transform_nodes(nodes, b, a, verbose)]
else:
raise NotImplementedError
else:
# Simple linear change of variables
C = (b-a)/2
D = (b+a)/2
for x, w in nodes:
new_nodes.append((D+C*x, C*w))
return new_nodes
def guess_degree(self, prec):
"""
Given a desired precision `p` in bits, estimate the degree `m`
of the quadrature required to accomplish full accuracy for
typical integrals. By default, :func:`~mpmath.quad` will perform up
to `m` iterations. The value of `m` should be a slight
overestimate, so that "slightly bad" integrals can be dealt
with automatically using a few extra iterations. On the
other hand, it should not be too big, so :func:`~mpmath.quad` can
quit within a reasonable amount of time when it is given
an "unsolvable" integral.
The default formula used by :func:`~mpmath.guess_degree` is tuned
for both :class:`TanhSinh` and :class:`GaussLegendre`.
The output is roughly as follows:
+---------+---------+
| `p` | `m` |
+=========+=========+
| 50 | 6 |
+---------+---------+
| 100 | 7 |
+---------+---------+
| 500 | 10 |
+---------+---------+
| 3000 | 12 |
+---------+---------+
This formula is based purely on a limited amount of
experimentation and will sometimes be wrong.
"""
# Expected degree
# XXX: use mag
g = int(4 + max(0, self.ctx.log(prec/30.0, 2)))
# Reasonable "worst case"
g += 2
return g
def estimate_error(self, results, prec, epsilon):
r"""
Given results from integrations `[I_1, I_2, \ldots, I_k]` done
with a quadrature of rule of degree `1, 2, \ldots, k`, estimate
the error of `I_k`.
For `k = 2`, we estimate `|I_{\infty}-I_2|` as `|I_2-I_1|`.
For `k > 2`, we extrapolate `|I_{\infty}-I_k| \approx |I_{k+1}-I_k|`
from `|I_k-I_{k-1}|` and `|I_k-I_{k-2}|` under the assumption
that each degree increment roughly doubles the accuracy of
the quadrature rule (this is true for both :class:`TanhSinh`
and :class:`GaussLegendre`). The extrapolation formula is given
by Borwein, Bailey & Girgensohn. Although not very conservative,
this method seems to be very robust in practice.
"""
if len(results) == 2:
return abs(results[0]-results[1])
try:
if results[-1] == results[-2] == results[-3]:
return self.ctx.zero
D1 = self.ctx.log(abs(results[-1]-results[-2]), 10)
D2 = self.ctx.log(abs(results[-1]-results[-3]), 10)
except ValueError:
return epsilon
D3 = -prec
D4 = min(0, max(D1**2/D2, 2*D1, D3))
return self.ctx.mpf(10) ** int(D4)
def summation(self, f, points, prec, epsilon, max_degree, verbose=False):
"""
Main integration function. Computes the 1D integral over
the interval specified by *points*. For each subinterval,
performs quadrature of degree from 1 up to *max_degree*
until :func:`~mpmath.estimate_error` signals convergence.
:func:`~mpmath.summation` transforms each subintegration to
the standard interval and then calls :func:`~mpmath.sum_next`.
"""
ctx = self.ctx
I = err = ctx.zero
for i in xrange(len(points)-1):
a, b = points[i], points[i+1]
if a == b:
continue
# XXX: we could use a single variable transformation,
# but this is not good in practice. We get better accuracy
# by having 0 as an endpoint.
if (a, b) == (ctx.ninf, ctx.inf):
_f = f
f = lambda x: _f(-x) + _f(x)
a, b = (ctx.zero, ctx.inf)
results = []
for degree in xrange(1, max_degree+1):
nodes = self.get_nodes(a, b, degree, prec, verbose)
if verbose:
print("Integrating from %s to %s (degree %s of %s)" % \
(ctx.nstr(a), ctx.nstr(b), degree, max_degree))
results.append(self.sum_next(f, nodes, degree, prec, results, verbose))
if degree > 1:
err = self.estimate_error(results, prec, epsilon)
if err <= epsilon:
break
if verbose:
print("Estimated error:", ctx.nstr(err))
I += results[-1]
if err > epsilon:
if verbose:
print("Failed to reach full accuracy. Estimated error:", ctx.nstr(err))
return I, err
def sum_next(self, f, nodes, degree, prec, previous, verbose=False):
r"""
Evaluates the step sum `\sum w_k f(x_k)` where the *nodes* list
contains the `(w_k, x_k)` pairs.
:func:`~mpmath.summation` will supply the list *results* of
values computed by :func:`~mpmath.sum_next` at previous degrees, in
case the quadrature rule is able to reuse them.
"""
return self.ctx.fdot((w, f(x)) for (x,w) in nodes)
class TanhSinh(QuadratureRule):
r"""
This class implements "tanh-sinh" or "doubly exponential"
quadrature. This quadrature rule is based on the Euler-Maclaurin
integral formula. By performing a change of variables involving
nested exponentials / hyperbolic functions (hence the name), the
derivatives at the endpoints vanish rapidly. Since the error term
in the Euler-Maclaurin formula depends on the derivatives at the
endpoints, a simple step sum becomes extremely accurate. In
practice, this means that doubling the number of evaluation
points roughly doubles the number of accurate digits.
Comparison to Gauss-Legendre:
* Initial computation of nodes is usually faster
* Handles endpoint singularities better
* Handles infinite integration intervals better
* Is slower for smooth integrands once nodes have been computed
The implementation of the tanh-sinh algorithm is based on the
description given in Borwein, Bailey & Girgensohn, "Experimentation
in Mathematics - Computational Paths to Discovery", A K Peters,
2003, pages 312-313. In the present implementation, a few
improvements have been made:
* A more efficient scheme is used to compute nodes (exploiting
recurrence for the exponential function)
* The nodes are computed successively instead of all at once
Various documents describing the algorithm are available online, e.g.:
* http://crd.lbl.gov/~dhbailey/dhbpapers/dhb-tanh-sinh.pdf
* http://users.cs.dal.ca/~jborwein/tanh-sinh.pdf
"""
def sum_next(self, f, nodes, degree, prec, previous, verbose=False):
"""
Step sum for tanh-sinh quadrature of degree `m`. We exploit the
fact that half of the abscissas at degree `m` are precisely the
abscissas from degree `m-1`. Thus reusing the result from
the previous level allows a 2x speedup.
"""
h = self.ctx.mpf(2)**(-degree)
# Abscissas overlap, so reusing saves half of the time
if previous:
S = previous[-1]/(h*2)
else:
S = self.ctx.zero
S += self.ctx.fdot((w,f(x)) for (x,w) in nodes)
return h*S
def calc_nodes(self, degree, prec, verbose=False):
r"""
The abscissas and weights for tanh-sinh quadrature of degree
`m` are given by
.. math::
x_k = \tanh(\pi/2 \sinh(t_k))
w_k = \pi/2 \cosh(t_k) / \cosh(\pi/2 \sinh(t_k))^2
where `t_k = t_0 + hk` for a step length `h \sim 2^{-m}`. The
list of nodes is actually infinite, but the weights die off so
rapidly that only a few are needed.
"""
ctx = self.ctx
nodes = []
extra = 20
ctx.prec += extra
tol = ctx.ldexp(1, -prec-10)
pi4 = ctx.pi/4
# For simplicity, we work in steps h = 1/2^n, with the first point
# offset so that we can reuse the sum from the previous degree
# We define degree 1 to include the "degree 0" steps, including
# the point x = 0. (It doesn't work well otherwise; not sure why.)
t0 = ctx.ldexp(1, -degree)
if degree == 1:
#nodes.append((mpf(0), pi4))
#nodes.append((-mpf(0), pi4))
nodes.append((ctx.zero, ctx.pi/2))
h = t0
else:
h = t0*2
# Since h is fixed, we can compute the next exponential
# by simply multiplying by exp(h)
expt0 = ctx.exp(t0)
a = pi4 * expt0
b = pi4 / expt0
udelta = ctx.exp(h)
urdelta = 1/udelta
for k in xrange(0, 20*2**degree+1):
# Reference implementation:
# t = t0 + k*h
# x = tanh(pi/2 * sinh(t))
# w = pi/2 * cosh(t) / cosh(pi/2 * sinh(t))**2
# Fast implementation. Note that c = exp(pi/2 * sinh(t))
c = ctx.exp(a-b)
d = 1/c
co = (c+d)/2
si = (c-d)/2
x = si / co
w = (a+b) / co**2
diff = abs(x-1)
if diff <= tol:
break
nodes.append((x, w))
nodes.append((-x, w))
a *= udelta
b *= urdelta
if verbose and k % 300 == 150:
# Note: the number displayed is rather arbitrary. Should
# figure out how to print something that looks more like a
# percentage
print("Calculating nodes:", ctx.nstr(-ctx.log(diff, 10) / prec))
ctx.prec -= extra
return nodes
class GaussLegendre(QuadratureRule):
"""
This class implements Gauss-Legendre quadrature, which is
exceptionally efficient for polynomials and polynomial-like (i.e.
very smooth) integrands.
The abscissas and weights are given by roots and values of
Legendre polynomials, which are the orthogonal polynomials
on `[-1, 1]` with respect to the unit weight
(see :func:`~mpmath.legendre`).
In this implementation, we take the "degree" `m` of the quadrature
to denote a Gauss-Legendre rule of degree `3 \cdot 2^m` (following
Borwein, Bailey & Girgensohn). This way we get quadratic, rather
than linear, convergence as the degree is incremented.
Comparison to tanh-sinh quadrature:
* Is faster for smooth integrands once nodes have been computed
* Initial computation of nodes is usually slower
* Handles endpoint singularities worse
* Handles infinite integration intervals worse
"""
def calc_nodes(self, degree, prec, verbose=False):
"""
Calculates the abscissas and weights for Gauss-Legendre
quadrature of degree of given degree (actually `3 \cdot 2^m`).
"""
ctx = self.ctx
# It is important that the epsilon is set lower than the
# "real" epsilon
epsilon = ctx.ldexp(1, -prec-8)
# Fairly high precision might be required for accurate
# evaluation of the roots
orig = ctx.prec
ctx.prec = int(prec*1.5)
if degree == 1:
x = ctx.sqrt(ctx.mpf(3)/5)
w = ctx.mpf(5)/9
nodes = [(-x,w),(ctx.zero,ctx.mpf(8)/9),(x,w)]
ctx.prec = orig
return nodes
nodes = []
n = 3*2**(degree-1)
upto = n//2 + 1
for j in xrange(1, upto):
# Asymptotic formula for the roots
r = ctx.mpf(math.cos(math.pi*(j-0.25)/(n+0.5)))
# Newton iteration
while 1:
t1, t2 = 1, 0
# Evaluates the Legendre polynomial using its defining
# recurrence relation
for j1 in xrange(1,n+1):
t3, t2, t1 = t2, t1, ((2*j1-1)*r*t1 - (j1-1)*t2)/j1
t4 = n*(r*t1- t2)/(r**2-1)
t5 = r
a = t1/t4
r = r - a
if abs(a) < epsilon:
break
x = r
w = 2/((1-r**2)*t4**2)
if verbose and j % 30 == 15:
print("Computing nodes (%i of %i)" % (j, upto))
nodes.append((x, w))
nodes.append((-x, w))
ctx.prec = orig
return nodes
class QuadratureMethods(object):
def __init__(ctx, *args, **kwargs):
ctx._gauss_legendre = GaussLegendre(ctx)
ctx._tanh_sinh = TanhSinh(ctx)
def quad(ctx, f, *points, **kwargs):
r"""
Computes a single, double or triple integral over a given
1D interval, 2D rectangle, or 3D cuboid. A basic example::
>>> from mpmath import *
>>> mp.dps = 15; mp.pretty = True
>>> quad(sin, [0, pi])
2.0
A basic 2D integral::
>>> f = lambda x, y: cos(x+y/2)
>>> quad(f, [-pi/2, pi/2], [0, pi])
4.0
**Interval format**
The integration range for each dimension may be specified
using a list or tuple. Arguments are interpreted as follows:
``quad(f, [x1, x2])`` -- calculates
`\int_{x_1}^{x_2} f(x) \, dx`
``quad(f, [x1, x2], [y1, y2])`` -- calculates
`\int_{x_1}^{x_2} \int_{y_1}^{y_2} f(x,y) \, dy \, dx`
``quad(f, [x1, x2], [y1, y2], [z1, z2])`` -- calculates
`\int_{x_1}^{x_2} \int_{y_1}^{y_2} \int_{z_1}^{z_2} f(x,y,z)
\, dz \, dy \, dx`
Endpoints may be finite or infinite. An interval descriptor
may also contain more than two points. In this
case, the integration is split into subintervals, between
each pair of consecutive points. This is useful for
dealing with mid-interval discontinuities, or integrating
over large intervals where the function is irregular or
oscillates.
**Options**
:func:`~mpmath.quad` recognizes the following keyword arguments:
*method*
Chooses integration algorithm (described below).
*error*
If set to true, :func:`~mpmath.quad` returns `(v, e)` where `v` is the
integral and `e` is the estimated error.
*maxdegree*
Maximum degree of the quadrature rule to try before
quitting.
*verbose*
Print details about progress.
**Algorithms**
Mpmath presently implements two integration algorithms: tanh-sinh
quadrature and Gauss-Legendre quadrature. These can be selected
using *method='tanh-sinh'* or *method='gauss-legendre'* or by
passing the classes *method=TanhSinh*, *method=GaussLegendre*.
The functions :func:`~mpmath.quadts` and :func:`~mpmath.quadgl` are also available
as shortcuts.
Both algorithms have the property that doubling the number of
evaluation points roughly doubles the accuracy, so both are ideal
for high precision quadrature (hundreds or thousands of digits).
At high precision, computing the nodes and weights for the
integration can be expensive (more expensive than computing the
function values). To make repeated integrations fast, nodes
are automatically cached.
The advantages of the tanh-sinh algorithm are that it tends to
handle endpoint singularities well, and that the nodes are cheap
to compute on the first run. For these reasons, it is used by
:func:`~mpmath.quad` as the default algorithm.
Gauss-Legendre quadrature often requires fewer function
evaluations, and is therefore often faster for repeated use, but
the algorithm does not handle endpoint singularities as well and
the nodes are more expensive to compute. Gauss-Legendre quadrature
can be a better choice if the integrand is smooth and repeated
integrations are required (e.g. for multiple integrals).
See the documentation for :class:`TanhSinh` and
:class:`GaussLegendre` for additional details.
**Examples of 1D integrals**
Intervals may be infinite or half-infinite. The following two
examples evaluate the limits of the inverse tangent function
(`\int 1/(1+x^2) = \tan^{-1} x`), and the Gaussian integral
`\int_{\infty}^{\infty} \exp(-x^2)\,dx = \sqrt{\pi}`::
>>> mp.dps = 15
>>> quad(lambda x: 2/(x**2+1), [0, inf])
3.14159265358979
>>> quad(lambda x: exp(-x**2), [-inf, inf])**2
3.14159265358979
Integrals can typically be resolved to high precision.
The following computes 50 digits of `\pi` by integrating the
area of the half-circle defined by `x^2 + y^2 \le 1`,
`-1 \le x \le 1`, `y \ge 0`::
>>> mp.dps = 50
>>> 2*quad(lambda x: sqrt(1-x**2), [-1, 1])
3.1415926535897932384626433832795028841971693993751
One can just as well compute 1000 digits (output truncated)::
>>> mp.dps = 1000
>>> 2*quad(lambda x: sqrt(1-x**2), [-1, 1]) #doctest:+ELLIPSIS
3.141592653589793238462643383279502884...216420198
Complex integrals are supported. The following computes
a residue at `z = 0` by integrating counterclockwise along the
diamond-shaped path from `1` to `+i` to `-1` to `-i` to `1`::
>>> mp.dps = 15
>>> chop(quad(lambda z: 1/z, [1,j,-1,-j,1]))
(0.0 + 6.28318530717959j)
**Examples of 2D and 3D integrals**
Here are several nice examples of analytically solvable
2D integrals (taken from MathWorld [1]) that can be evaluated
to high precision fairly rapidly by :func:`~mpmath.quad`::
>>> mp.dps = 30
>>> f = lambda x, y: (x-1)/((1-x*y)*log(x*y))
>>> quad(f, [0, 1], [0, 1])
0.577215664901532860606512090082
>>> +euler
0.577215664901532860606512090082
>>> f = lambda x, y: 1/sqrt(1+x**2+y**2)
>>> quad(f, [-1, 1], [-1, 1])
3.17343648530607134219175646705
>>> 4*log(2+sqrt(3))-2*pi/3
3.17343648530607134219175646705
>>> f = lambda x, y: 1/(1-x**2 * y**2)
>>> quad(f, [0, 1], [0, 1])
1.23370055013616982735431137498
>>> pi**2 / 8
1.23370055013616982735431137498
>>> quad(lambda x, y: 1/(1-x*y), [0, 1], [0, 1])
1.64493406684822643647241516665
>>> pi**2 / 6
1.64493406684822643647241516665
Multiple integrals may be done over infinite ranges::
>>> mp.dps = 15
>>> print(quad(lambda x,y: exp(-x-y), [0, inf], [1, inf]))
0.367879441171442
>>> print(1/e)
0.367879441171442
For nonrectangular areas, one can call :func:`~mpmath.quad` recursively.
For example, we can replicate the earlier example of calculating
`\pi` by integrating over the unit-circle, and actually use double
quadrature to actually measure the area circle::
>>> f = lambda x: quad(lambda y: 1, [-sqrt(1-x**2), sqrt(1-x**2)])
>>> quad(f, [-1, 1])
3.14159265358979
Here is a simple triple integral::
>>> mp.dps = 15
>>> f = lambda x,y,z: x*y/(1+z)
>>> quad(f, [0,1], [0,1], [1,2], method='gauss-legendre')
0.101366277027041
>>> (log(3)-log(2))/4
0.101366277027041
**Singularities**
Both tanh-sinh and Gauss-Legendre quadrature are designed to
integrate smooth (infinitely differentiable) functions. Neither
algorithm copes well with mid-interval singularities (such as
mid-interval discontinuities in `f(x)` or `f'(x)`).
The best solution is to split the integral into parts::
>>> mp.dps = 15
>>> quad(lambda x: abs(sin(x)), [0, 2*pi]) # Bad
3.99900894176779
>>> quad(lambda x: abs(sin(x)), [0, pi, 2*pi]) # Good
4.0
The tanh-sinh rule often works well for integrands having a
singularity at one or both endpoints::
>>> mp.dps = 15
>>> quad(log, [0, 1], method='tanh-sinh') # Good
-1.0
>>> quad(log, [0, 1], method='gauss-legendre') # Bad
-0.999932197413801
However, the result may still be inaccurate for some functions::
>>> quad(lambda x: 1/sqrt(x), [0, 1], method='tanh-sinh')
1.99999999946942
This problem is not due to the quadrature rule per se, but to
numerical amplification of errors in the nodes. The problem can be
circumvented by temporarily increasing the precision::
>>> mp.dps = 30
>>> a = quad(lambda x: 1/sqrt(x), [0, 1], method='tanh-sinh')
>>> mp.dps = 15
>>> +a
2.0
**Highly variable functions**
For functions that are smooth (in the sense of being infinitely
differentiable) but contain sharp mid-interval peaks or many
"bumps", :func:`~mpmath.quad` may fail to provide full accuracy. For
example, with default settings, :func:`~mpmath.quad` is able to integrate
`\sin(x)` accurately over an interval of length 100 but not over
length 1000::
>>> quad(sin, [0, 100]); 1-cos(100) # Good
0.137681127712316
0.137681127712316
>>> quad(sin, [0, 1000]); 1-cos(1000) # Bad
-37.8587612408485
0.437620923709297
One solution is to break the integration into 10 intervals of
length 100::
>>> quad(sin, linspace(0, 1000, 10)) # Good
0.437620923709297
Another is to increase the degree of the quadrature::
>>> quad(sin, [0, 1000], maxdegree=10) # Also good
0.437620923709297
Whether splitting the interval or increasing the degree is
more efficient differs from case to case. Another example is the
function `1/(1+x^2)`, which has a sharp peak centered around
`x = 0`::
>>> f = lambda x: 1/(1+x**2)
>>> quad(f, [-100, 100]) # Bad
3.64804647105268
>>> quad(f, [-100, 100], maxdegree=10) # Good
3.12159332021646
>>> quad(f, [-100, 0, 100]) # Also good
3.12159332021646
**References**
1. http://mathworld.wolfram.com/DoubleIntegral.html
"""
rule = kwargs.get('method', 'tanh-sinh')
if type(rule) is str:
if rule == 'tanh-sinh':
rule = ctx._tanh_sinh
elif rule == 'gauss-legendre':
rule = ctx._gauss_legendre
else:
raise ValueError("unknown quadrature rule: %s" % rule)
else:
rule = rule(ctx)
verbose = kwargs.get('verbose')
dim = len(points)
orig = prec = ctx.prec
epsilon = ctx.eps/8
m = kwargs.get('maxdegree') or rule.guess_degree(prec)
points = [ctx._as_points(p) for p in points]
try:
ctx.prec += 20
if dim == 1:
v, err = rule.summation(f, points[0], prec, epsilon, m, verbose)
elif dim == 2:
v, err = rule.summation(lambda x: \
rule.summation(lambda y: f(x,y), \
points[1], prec, epsilon, m)[0],
points[0], prec, epsilon, m, verbose)
elif dim == 3:
v, err = rule.summation(lambda x: \
rule.summation(lambda y: \
rule.summation(lambda z: f(x,y,z), \
points[2], prec, epsilon, m)[0],
points[1], prec, epsilon, m)[0],
points[0], prec, epsilon, m, verbose)
else:
raise NotImplementedError("quadrature must have dim 1, 2 or 3")
finally:
ctx.prec = orig
if kwargs.get("error"):
return +v, err
return +v
def quadts(ctx, *args, **kwargs):
"""
Performs tanh-sinh quadrature. The call
quadts(func, *points, ...)
is simply a shortcut for:
quad(func, *points, ..., method=TanhSinh)
For example, a single integral and a double integral:
quadts(lambda x: exp(cos(x)), [0, 1])
quadts(lambda x, y: exp(cos(x+y)), [0, 1], [0, 1])
See the documentation for quad for information about how points
arguments and keyword arguments are parsed.
See documentation for TanhSinh for algorithmic information about
tanh-sinh quadrature.
"""
kwargs['method'] = 'tanh-sinh'
return ctx.quad(*args, **kwargs)
def quadgl(ctx, *args, **kwargs):
"""
Performs Gauss-Legendre quadrature. The call
quadgl(func, *points, ...)
is simply a shortcut for:
quad(func, *points, ..., method=GaussLegendre)
For example, a single integral and a double integral:
quadgl(lambda x: exp(cos(x)), [0, 1])
quadgl(lambda x, y: exp(cos(x+y)), [0, 1], [0, 1])
See the documentation for quad for information about how points
arguments and keyword arguments are parsed.
See documentation for TanhSinh for algorithmic information about
tanh-sinh quadrature.
"""
kwargs['method'] = 'gauss-legendre'
return ctx.quad(*args, **kwargs)
def quadosc(ctx, f, interval, omega=None, period=None, zeros=None):
r"""
Calculates
.. math ::
I = \int_a^b f(x) dx
where at least one of `a` and `b` is infinite and where
`f(x) = g(x) \cos(\omega x + \phi)` for some slowly
decreasing function `g(x)`. With proper input, :func:`~mpmath.quadosc`
can also handle oscillatory integrals where the oscillation
rate is different from a pure sine or cosine wave.
In the standard case when `|a| < \infty, b = \infty`,
:func:`~mpmath.quadosc` works by evaluating the infinite series
.. math ::
I = \int_a^{x_1} f(x) dx +
\sum_{k=1}^{\infty} \int_{x_k}^{x_{k+1}} f(x) dx
where `x_k` are consecutive zeros (alternatively
some other periodic reference point) of `f(x)`.
Accordingly, :func:`~mpmath.quadosc` requires information about the
zeros of `f(x)`. For a periodic function, you can specify
the zeros by either providing the angular frequency `\omega`
(*omega*) or the *period* `2 \pi/\omega`. In general, you can
specify the `n`-th zero by providing the *zeros* arguments.
Below is an example of each::
>>> from mpmath import *
>>> mp.dps = 15; mp.pretty = True
>>> f = lambda x: sin(3*x)/(x**2+1)
>>> quadosc(f, [0,inf], omega=3)
0.37833007080198
>>> quadosc(f, [0,inf], period=2*pi/3)
0.37833007080198
>>> quadosc(f, [0,inf], zeros=lambda n: pi*n/3)
0.37833007080198
>>> (ei(3)*exp(-3)-exp(3)*ei(-3))/2 # Computed by Mathematica
0.37833007080198
Note that *zeros* was specified to multiply `n` by the
*half-period*, not the full period. In theory, it does not matter
whether each partial integral is done over a half period or a full
period. However, if done over half-periods, the infinite series
passed to :func:`~mpmath.nsum` becomes an *alternating series* and this
typically makes the extrapolation much more efficient.
Here is an example of an integration over the entire real line,
and a half-infinite integration starting at `-\infty`::
>>> quadosc(lambda x: cos(x)/(1+x**2), [-inf, inf], omega=1)
1.15572734979092
>>> pi/e
1.15572734979092
>>> quadosc(lambda x: cos(x)/x**2, [-inf, -1], period=2*pi)
-0.0844109505595739
>>> cos(1)+si(1)-pi/2
-0.0844109505595738
Of course, the integrand may contain a complex exponential just as
well as a real sine or cosine::
>>> quadosc(lambda x: exp(3*j*x)/(1+x**2), [-inf,inf], omega=3)
(0.156410688228254 + 0.0j)
>>> pi/e**3
0.156410688228254
>>> quadosc(lambda x: exp(3*j*x)/(2+x+x**2), [-inf,inf], omega=3)
(0.00317486988463794 - 0.0447701735209082j)
>>> 2*pi/sqrt(7)/exp(3*(j+sqrt(7))/2)
(0.00317486988463794 - 0.0447701735209082j)
**Non-periodic functions**
If `f(x) = g(x) h(x)` for some function `h(x)` that is not
strictly periodic, *omega* or *period* might not work, and it might
be necessary to use *zeros*.
A notable exception can be made for Bessel functions which, though not
periodic, are "asymptotically periodic" in a sufficiently strong sense
that the sum extrapolation will work out::
>>> quadosc(j0, [0, inf], period=2*pi)
1.0
>>> quadosc(j1, [0, inf], period=2*pi)
1.0
More properly, one should provide the exact Bessel function zeros::
>>> j0zero = lambda n: findroot(j0, pi*(n-0.25))
>>> quadosc(j0, [0, inf], zeros=j0zero)
1.0
For an example where *zeros* becomes necessary, consider the
complete Fresnel integrals
.. math ::
\int_0^{\infty} \cos x^2\,dx = \int_0^{\infty} \sin x^2\,dx
= \sqrt{\frac{\pi}{8}}.
Although the integrands do not decrease in magnitude as
`x \to \infty`, the integrals are convergent since the oscillation
rate increases (causing consecutive periods to asymptotically
cancel out). These integrals are virtually impossible to calculate
to any kind of accuracy using standard quadrature rules. However,
if one provides the correct asymptotic distribution of zeros
(`x_n \sim \sqrt{n}`), :func:`~mpmath.quadosc` works::
>>> mp.dps = 30
>>> f = lambda x: cos(x**2)
>>> quadosc(f, [0,inf], zeros=lambda n:sqrt(pi*n))
0.626657068657750125603941321203
>>> f = lambda x: sin(x**2)
>>> quadosc(f, [0,inf], zeros=lambda n:sqrt(pi*n))
0.626657068657750125603941321203
>>> sqrt(pi/8)
0.626657068657750125603941321203
(Interestingly, these integrals can still be evaluated if one
places some other constant than `\pi` in the square root sign.)
In general, if `f(x) \sim g(x) \cos(h(x))`, the zeros follow
the inverse-function distribution `h^{-1}(x)`::
>>> mp.dps = 15
>>> f = lambda x: sin(exp(x))
>>> quadosc(f, [1,inf], zeros=lambda n: log(n))
-0.25024394235267
>>> pi/2-si(e)
-0.250243942352671
**Non-alternating functions**
If the integrand oscillates around a positive value, without
alternating signs, the extrapolation might fail. A simple trick
that sometimes works is to multiply or divide the frequency by 2::
>>> f = lambda x: 1/x**2+sin(x)/x**4
>>> quadosc(f, [1,inf], omega=1) # Bad
1.28642190869861
>>> quadosc(f, [1,inf], omega=0.5) # Perfect
1.28652953559617
>>> 1+(cos(1)+ci(1)+sin(1))/6
1.28652953559617
**Fast decay**
:func:`~mpmath.quadosc` is primarily useful for slowly decaying
integrands. If the integrand decreases exponentially or faster,
:func:`~mpmath.quad` will likely handle it without trouble (and generally be
much faster than :func:`~mpmath.quadosc`)::
>>> quadosc(lambda x: cos(x)/exp(x), [0, inf], omega=1)
0.5
>>> quad(lambda x: cos(x)/exp(x), [0, inf])
0.5
"""
a, b = ctx._as_points(interval)
a = ctx.convert(a)
b = ctx.convert(b)
if [omega, period, zeros].count(None) != 2:
raise ValueError( \
"must specify exactly one of omega, period, zeros")
if a == ctx.ninf and b == ctx.inf:
s1 = ctx.quadosc(f, [a, 0], omega=omega, zeros=zeros, period=period)
s2 = ctx.quadosc(f, [0, b], omega=omega, zeros=zeros, period=period)
return s1 + s2
if a == ctx.ninf:
if zeros:
return ctx.quadosc(lambda x:f(-x), [-b,-a], lambda n: zeros(-n))
else:
return ctx.quadosc(lambda x:f(-x), [-b,-a], omega=omega, period=period)
if b != ctx.inf:
raise ValueError("quadosc requires an infinite integration interval")
if not zeros:
if omega:
period = 2*ctx.pi/omega
zeros = lambda n: n*period/2
#for n in range(1,10):
# p = zeros(n)
# if p > a:
# break
#if n >= 9:
# raise ValueError("zeros do not appear to be correctly indexed")
n = 1
s = ctx.quadgl(f, [a, zeros(n)])
def term(k):
return ctx.quadgl(f, [zeros(k), zeros(k+1)])
s += ctx.nsum(term, [n, ctx.inf])
return s
if __name__ == '__main__':
import doctest
doctest.testmod()
| 38,334 | 36.955446 | 90 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/calculus/odes.py
|
from bisect import bisect
from ..libmp.backend import xrange
class ODEMethods(object):
pass
def ode_taylor(ctx, derivs, x0, y0, tol_prec, n):
h = tol = ctx.ldexp(1, -tol_prec)
dim = len(y0)
xs = [x0]
ys = [y0]
x = x0
y = y0
orig = ctx.prec
try:
ctx.prec = orig*(1+n)
# Use n steps with Euler's method to get
# evaluation points for derivatives
for i in range(n):
fxy = derivs(x, y)
y = [y[i]+h*fxy[i] for i in xrange(len(y))]
x += h
xs.append(x)
ys.append(y)
# Compute derivatives
ser = [[] for d in range(dim)]
for j in range(n+1):
s = [0]*dim
b = (-1) ** (j & 1)
k = 1
for i in range(j+1):
for d in range(dim):
s[d] += b * ys[i][d]
b = (b * (j-k+1)) // (-k)
k += 1
scale = h**(-j) / ctx.fac(j)
for d in range(dim):
s[d] = s[d] * scale
ser[d].append(s[d])
finally:
ctx.prec = orig
# Estimate radius for which we can get full accuracy.
# XXX: do this right for zeros
radius = ctx.one
for ts in ser:
if ts[-1]:
radius = min(radius, ctx.nthroot(tol/abs(ts[-1]), n))
radius /= 2 # XXX
return ser, x0+radius
def odefun(ctx, F, x0, y0, tol=None, degree=None, method='taylor', verbose=False):
r"""
Returns a function `y(x) = [y_0(x), y_1(x), \ldots, y_n(x)]`
that is a numerical solution of the `n+1`-dimensional first-order
ordinary differential equation (ODE) system
.. math ::
y_0'(x) = F_0(x, [y_0(x), y_1(x), \ldots, y_n(x)])
y_1'(x) = F_1(x, [y_0(x), y_1(x), \ldots, y_n(x)])
\vdots
y_n'(x) = F_n(x, [y_0(x), y_1(x), \ldots, y_n(x)])
The derivatives are specified by the vector-valued function
*F* that evaluates
`[y_0', \ldots, y_n'] = F(x, [y_0, \ldots, y_n])`.
The initial point `x_0` is specified by the scalar argument *x0*,
and the initial value `y(x_0) = [y_0(x_0), \ldots, y_n(x_0)]` is
specified by the vector argument *y0*.
For convenience, if the system is one-dimensional, you may optionally
provide just a scalar value for *y0*. In this case, *F* should accept
a scalar *y* argument and return a scalar. The solution function
*y* will return scalar values instead of length-1 vectors.
Evaluation of the solution function `y(x)` is permitted
for any `x \ge x_0`.
A high-order ODE can be solved by transforming it into first-order
vector form. This transformation is described in standard texts
on ODEs. Examples will also be given below.
**Options, speed and accuracy**
By default, :func:`~mpmath.odefun` uses a high-order Taylor series
method. For reasonably well-behaved problems, the solution will
be fully accurate to within the working precision. Note that
*F* must be possible to evaluate to very high precision
for the generation of Taylor series to work.
To get a faster but less accurate solution, you can set a large
value for *tol* (which defaults roughly to *eps*). If you just
want to plot the solution or perform a basic simulation,
*tol = 0.01* is likely sufficient.
The *degree* argument controls the degree of the solver (with
*method='taylor'*, this is the degree of the Taylor series
expansion). A higher degree means that a longer step can be taken
before a new local solution must be generated from *F*,
meaning that fewer steps are required to get from `x_0` to a given
`x_1`. On the other hand, a higher degree also means that each
local solution becomes more expensive (i.e., more evaluations of
*F* are required per step, and at higher precision).
The optimal setting therefore involves a tradeoff. Generally,
decreasing the *degree* for Taylor series is likely to give faster
solution at low precision, while increasing is likely to be better
at higher precision.
The function
object returned by :func:`~mpmath.odefun` caches the solutions at all step
points and uses polynomial interpolation between step points.
Therefore, once `y(x_1)` has been evaluated for some `x_1`,
`y(x)` can be evaluated very quickly for any `x_0 \le x \le x_1`.
and continuing the evaluation up to `x_2 > x_1` is also fast.
**Examples of first-order ODEs**
We will solve the standard test problem `y'(x) = y(x), y(0) = 1`
which has explicit solution `y(x) = \exp(x)`::
>>> from mpmath import *
>>> mp.dps = 15; mp.pretty = True
>>> f = odefun(lambda x, y: y, 0, 1)
>>> for x in [0, 1, 2.5]:
... print((f(x), exp(x)))
...
(1.0, 1.0)
(2.71828182845905, 2.71828182845905)
(12.1824939607035, 12.1824939607035)
The solution with high precision::
>>> mp.dps = 50
>>> f = odefun(lambda x, y: y, 0, 1)
>>> f(1)
2.7182818284590452353602874713526624977572470937
>>> exp(1)
2.7182818284590452353602874713526624977572470937
Using the more general vectorized form, the test problem
can be input as (note that *f* returns a 1-element vector)::
>>> mp.dps = 15
>>> f = odefun(lambda x, y: [y[0]], 0, [1])
>>> f(1)
[2.71828182845905]
:func:`~mpmath.odefun` can solve nonlinear ODEs, which are generally
impossible (and at best difficult) to solve analytically. As
an example of a nonlinear ODE, we will solve `y'(x) = x \sin(y(x))`
for `y(0) = \pi/2`. An exact solution happens to be known
for this problem, and is given by
`y(x) = 2 \tan^{-1}\left(\exp\left(x^2/2\right)\right)`::
>>> f = odefun(lambda x, y: x*sin(y), 0, pi/2)
>>> for x in [2, 5, 10]:
... print((f(x), 2*atan(exp(mpf(x)**2/2))))
...
(2.87255666284091, 2.87255666284091)
(3.14158520028345, 3.14158520028345)
(3.14159265358979, 3.14159265358979)
If `F` is independent of `y`, an ODE can be solved using direct
integration. We can therefore obtain a reference solution with
:func:`~mpmath.quad`::
>>> f = lambda x: (1+x**2)/(1+x**3)
>>> g = odefun(lambda x, y: f(x), pi, 0)
>>> g(2*pi)
0.72128263801696
>>> quad(f, [pi, 2*pi])
0.72128263801696
**Examples of second-order ODEs**
We will solve the harmonic oscillator equation `y''(x) + y(x) = 0`.
To do this, we introduce the helper functions `y_0 = y, y_1 = y_0'`
whereby the original equation can be written as `y_1' + y_0' = 0`. Put
together, we get the first-order, two-dimensional vector ODE
.. math ::
\begin{cases}
y_0' = y_1 \\
y_1' = -y_0
\end{cases}
To get a well-defined IVP, we need two initial values. With
`y(0) = y_0(0) = 1` and `-y'(0) = y_1(0) = 0`, the problem will of
course be solved by `y(x) = y_0(x) = \cos(x)` and
`-y'(x) = y_1(x) = \sin(x)`. We check this::
>>> f = odefun(lambda x, y: [-y[1], y[0]], 0, [1, 0])
>>> for x in [0, 1, 2.5, 10]:
... nprint(f(x), 15)
... nprint([cos(x), sin(x)], 15)
... print("---")
...
[1.0, 0.0]
[1.0, 0.0]
---
[0.54030230586814, 0.841470984807897]
[0.54030230586814, 0.841470984807897]
---
[-0.801143615546934, 0.598472144103957]
[-0.801143615546934, 0.598472144103957]
---
[-0.839071529076452, -0.54402111088937]
[-0.839071529076452, -0.54402111088937]
---
Note that we get both the sine and the cosine solutions
simultaneously.
**TODO**
* Better automatic choice of degree and step size
* Make determination of Taylor series convergence radius
more robust
* Allow solution for `x < x_0`
* Allow solution for complex `x`
* Test for difficult (ill-conditioned) problems
* Implement Runge-Kutta and other algorithms
"""
if tol:
tol_prec = int(-ctx.log(tol, 2))+10
else:
tol_prec = ctx.prec+10
degree = degree or (3 + int(3*ctx.dps/2.))
workprec = ctx.prec + 40
try:
len(y0)
return_vector = True
except TypeError:
F_ = F
F = lambda x, y: [F_(x, y[0])]
y0 = [y0]
return_vector = False
ser, xb = ode_taylor(ctx, F, x0, y0, tol_prec, degree)
series_boundaries = [x0, xb]
series_data = [(ser, x0, xb)]
# We will be working with vectors of Taylor series
def mpolyval(ser, a):
return [ctx.polyval(s[::-1], a) for s in ser]
# Find nearest expansion point; compute if necessary
def get_series(x):
if x < x0:
raise ValueError
n = bisect(series_boundaries, x)
if n < len(series_boundaries):
return series_data[n-1]
while 1:
ser, xa, xb = series_data[-1]
if verbose:
print("Computing Taylor series for [%f, %f]" % (xa, xb))
y = mpolyval(ser, xb-xa)
xa = xb
ser, xb = ode_taylor(ctx, F, xb, y, tol_prec, degree)
series_boundaries.append(xb)
series_data.append((ser, xa, xb))
if x <= xb:
return series_data[-1]
# Evaluation function
def interpolant(x):
x = ctx.convert(x)
orig = ctx.prec
try:
ctx.prec = workprec
ser, xa, xb = get_series(x)
y = mpolyval(ser, x-xa)
finally:
ctx.prec = orig
if return_vector:
return [+yk for yk in y]
else:
return +y[0]
return interpolant
ODEMethods.odefun = odefun
if __name__ == "__main__":
import doctest
doctest.testmod()
| 9,908 | 33.287197 | 82 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/calculus/__init__.py
|
from . import calculus
# XXX: hack to set methods
from . import approximation
from . import differentiation
from . import extrapolation
from . import polynomials
| 162 | 22.285714 | 29 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/calculus/inverselaplace.py
|
# contributed to mpmath by Kristopher L. Kuhlman, February 2017
class InverseLaplaceTransform(object):
r"""
Inverse Laplace transform methods are implemented using this
class, in order to simplify the code and provide a common
infrastructure.
Implement a custom inverse Laplace transform algorithm by
subclassing :class:`InverseLaplaceTransform` and implementing the
appropriate methods. The subclass can then be used by
:func:`~mpmath.invertlaplace` by passing it as the *method*
argument.
"""
def __init__(self,ctx):
self.ctx = ctx
def calc_laplace_parameter(self,t,**kwargs):
r"""
Determine the vector of Laplace parameter values needed for an
algorithm, this will depend on the choice of algorithm (de
Hoog is default), the algorithm-specific parameters passed (or
default ones), and desired time.
"""
raise NotImplementedError
def calc_time_domain_solution(self,fp):
r"""
Compute the time domain solution, after computing the
Laplace-space function evaluations at the abscissa required
for the algorithm. Abscissa computed for one algorithm are
typically not useful for another algorithm.
"""
raise NotImplementedError
class FixedTalbot(InverseLaplaceTransform):
def calc_laplace_parameter(self,t,**kwargs):
r"""The "fixed" Talbot method deforms the Bromwich contour towards
`-\infty` in the shape of a parabola. Traditionally the Talbot
algorithm has adjustable parameters, but the "fixed" version
does not. The `r` parameter could be passed in as a parameter,
if you want to override the default given by (Abate & Valko,
2004).
The Laplace parameter is sampled along a parabola opening
along the negative imaginary axis, with the base of the
parabola along the real axis at
`p=\frac{r}{t_\mathrm{max}}`. As the number of terms used in
the approximation (degree) grows, the abscissa required for
function evaluation tend towards `-\infty`, requiring high
precision to prevent overflow. If any poles, branch cuts or
other singularities exist such that the deformed Bromwich
contour lies to the left of the singularity, the method will
fail.
**Optional arguments**
:class:`~mpmath.calculus.inverselaplace.FixedTalbot.calc_laplace_parameter`
recognizes the following keywords
*tmax*
maximum time associated with vector of times
(typically just the time requested)
*degree*
integer order of approximation (M = number of terms)
*r*
abscissa for `p_0` (otherwise computed using rule
of thumb `2M/5`)
The working precision will be increased according to a rule of
thumb. If 'degree' is not specified, the working precision and
degree are chosen to hopefully achieve the dps of the calling
context. If 'degree' is specified, the working precision is
chosen to achieve maximum resulting precision for the
specified degree.
.. math ::
p_0=\frac{r}{t}
.. math ::
p_i=\frac{i r \pi}{Mt_\mathrm{max}}\left[\cot\left(
\frac{i\pi}{M}\right) + j \right] \qquad 1\le i <M
where `j=\sqrt{-1}`, `r=2M/5`, and `t_\mathrm{max}` is the
maximum specified time.
"""
# required
# ------------------------------
# time of desired approximation
self.t = self.ctx.convert(t)
# optional
# ------------------------------
# maximum time desired (used for scaling) default is requested
# time.
self.tmax = self.ctx.convert(kwargs.get('tmax',self.t))
# empirical relationships used here based on a linear fit of
# requested and delivered dps for exponentially decaying time
# functions for requested dps up to 512.
if 'degree' in kwargs:
self.degree = kwargs['degree']
self.dps_goal = self.degree
else:
self.dps_goal = int(1.72*self.ctx.dps)
self.degree = max(12,int(1.38*self.dps_goal))
M = self.degree
# this is adjusting the dps of the calling context hopefully
# the caller doesn't monkey around with it between calling
# this routine and calc_time_domain_solution()
self.dps_orig = self.ctx.dps
self.ctx.dps = self.dps_goal
# Abate & Valko rule of thumb for r parameter
self.r = kwargs.get('r',self.ctx.fraction(2,5)*M)
self.theta = self.ctx.linspace(0.0, self.ctx.pi, M+1)
self.cot_theta = self.ctx.matrix(M,1)
self.cot_theta[0] = 0 # not used
# all but time-dependent part of p
self.delta = self.ctx.matrix(M,1)
self.delta[0] = self.r
for i in range(1,M):
self.cot_theta[i] = self.ctx.cot(self.theta[i])
self.delta[i] = self.r*self.theta[i]*(self.cot_theta[i] + 1j)
self.p = self.ctx.matrix(M,1)
self.p = self.delta/self.tmax
# NB: p is complex (mpc)
def calc_time_domain_solution(self,fp,t,manual_prec=False):
r"""The fixed Talbot time-domain solution is computed from the
Laplace-space function evaluations using
.. math ::
f(t,M)=\frac{2}{5t}\sum_{k=0}^{M-1}\Re \left[
\gamma_k \bar{f}(p_k)\right]
where
.. math ::
\gamma_0 = \frac{1}{2}e^{r}\bar{f}(p_0)
.. math ::
\gamma_k = e^{tp_k}\left\lbrace 1 + \frac{jk\pi}{M}\left[1 +
\cot \left( \frac{k \pi}{M} \right)^2 \right] - j\cot\left(
\frac{k \pi}{M}\right)\right \rbrace \qquad 1\le k<M.
Again, `j=\sqrt{-1}`.
Before calling this function, call
:class:`~mpmath.calculus.inverselaplace.FixedTalbot.calc_laplace_parameter`
to set the parameters and compute the required coefficients.
**References**
1. Abate, J., P. Valko (2004). Multi-precision Laplace
transform inversion. *International Journal for Numerical
Methods in Engineering* 60:979-993,
http://dx.doi.org/10.1002/nme.995
2. Talbot, A. (1979). The accurate numerical inversion of
Laplace transforms. *IMA Journal of Applied Mathematics*
23(1):97, http://dx.doi.org/10.1093/imamat/23.1.97
"""
# required
# ------------------------------
self.t = self.ctx.convert(t)
# assume fp was computed from p matrix returned from
# calc_laplace_parameter(), so is already a list or matrix of
# mpmath 'mpc' types
# these were computed in previous call to
# calc_laplace_parameter()
theta = self.theta
delta = self.delta
M = self.degree
p = self.p
r = self.r
ans = self.ctx.matrix(M,1)
ans[0] = self.ctx.exp(delta[0])*fp[0]/2
for i in range(1,M):
ans[i] = self.ctx.exp(delta[i])*fp[i]*(
1 + 1j*theta[i]*(1 + self.cot_theta[i]**2) -
1j*self.cot_theta[i])
result = self.ctx.fraction(2,5)*self.ctx.fsum(ans)/self.t
# setting dps back to value when calc_laplace_parameter was
# called, unless flag is set.
if not manual_prec:
self.ctx.dps = self.dps_orig
return result.real
# ****************************************
class Stehfest(InverseLaplaceTransform):
def calc_laplace_parameter(self,t,**kwargs):
r"""
The Gaver-Stehfest method is a discrete approximation of the
Widder-Post inversion algorithm, rather than a direct
approximation of the Bromwich contour integral.
The method abscissa along the real axis, and therefore has
issues inverting oscillatory functions (which have poles in
pairs away from the real axis).
The working precision will be increased according to a rule of
thumb. If 'degree' is not specified, the working precision and
degree are chosen to hopefully achieve the dps of the calling
context. If 'degree' is specified, the working precision is
chosen to achieve maximum resulting precision for the
specified degree.
.. math ::
p_k = \frac{k \log 2}{t} \qquad 1 \le k \le M
"""
# required
# ------------------------------
# time of desired approximation
self.t = self.ctx.convert(t)
# optional
# ------------------------------
# empirical relationships used here based on a linear fit of
# requested and delivered dps for exponentially decaying time
# functions for requested dps up to 512.
if 'degree' in kwargs:
self.degree = kwargs['degree']
self.dps_goal = int(1.38*self.degree)
else:
self.dps_goal = int(2.93*self.ctx.dps)
self.degree = max(16,self.dps_goal)
# _coeff routine requires even degree
if self.degree%2 > 0:
self.degree += 1
M = self.degree
# this is adjusting the dps of the calling context
# hopefully the caller doesn't monkey around with it
# between calling this routine and calc_time_domain_solution()
self.dps_orig = self.ctx.dps
self.ctx.dps = self.dps_goal
self.V = self._coeff()
self.p = self.ctx.matrix(self.ctx.arange(1,M+1))*self.ctx.ln2/self.t
# NB: p is real (mpf)
def _coeff(self):
r"""Salzer summation weights (aka, "Stehfest coefficients")
only depend on the approximation order (M) and the precision"""
M = self.degree
M2 = int(M/2) # checked earlier that M is even
V = self.ctx.matrix(M,1)
# Salzer summation weights
# get very large in magnitude and oscillate in sign,
# if the precision is not high enough, there will be
# catastrophic cancellation
for k in range(1,M+1):
z = self.ctx.matrix(min(k,M2)+1,1)
for j in range(int((k+1)/2),min(k,M2)+1):
z[j] = (self.ctx.power(j,M2)*self.ctx.fac(2*j)/
(self.ctx.fac(M2-j)*self.ctx.fac(j)*
self.ctx.fac(j-1)*self.ctx.fac(k-j)*
self.ctx.fac(2*j-k)))
V[k-1] = self.ctx.power(-1,k+M2)*self.ctx.fsum(z)
return V
def calc_time_domain_solution(self,fp,t,manual_prec=False):
r"""Compute time-domain Stehfest algorithm solution.
.. math ::
f(t,M) = \frac{\log 2}{t} \sum_{k=1}^{M} V_k \bar{f}\left(
p_k \right)
where
.. math ::
V_k = (-1)^{k + N/2} \sum^{\min(k,N/2)}_{i=\lfloor(k+1)/2 \rfloor}
\frac{i^{\frac{N}{2}}(2i)!}{\left(\frac{N}{2}-i \right)! \, i! \,
\left(i-1 \right)! \, \left(k-i\right)! \, \left(2i-k \right)!}
As the degree increases, the abscissa (`p_k`) only increase
linearly towards `\infty`, but the Stehfest coefficients
(`V_k`) alternate in sign and increase rapidly in sign,
requiring high precision to prevent overflow or loss of
significance when evaluating the sum.
**References**
1. Widder, D. (1941). *The Laplace Transform*. Princeton.
2. Stehfest, H. (1970). Algorithm 368: numerical inversion of
Laplace transforms. *Communications of the ACM* 13(1):47-49,
http://dx.doi.org/10.1145/361953.361969
"""
# required
self.t = self.ctx.convert(t)
# assume fp was computed from p matrix returned from
# calc_laplace_parameter(), so is already
# a list or matrix of mpmath 'mpf' types
result = self.ctx.fdot(self.V,fp)*self.ctx.ln2/self.t
# setting dps back to value when calc_laplace_parameter was called
if not manual_prec:
self.ctx.dps = self.dps_orig
# ignore any small imaginary part
return result.real
# ****************************************
class deHoog(InverseLaplaceTransform):
def calc_laplace_parameter(self,t,**kwargs):
r"""the de Hoog, Knight & Stokes algorithm is an
accelerated form of the Fourier series numerical
inverse Laplace transform algorithms.
.. math ::
p_k = \gamma + \frac{jk}{T} \qquad 0 \le k < 2M+1
where
.. math ::
\gamma = \alpha - \frac{\log \mathrm{tol}}{2T},
`j=\sqrt{-1}`, `T = 2t_\mathrm{max}` is a scaled time,
`\alpha=10^{-\mathrm{dps\_goal}}` is the real part of the
rightmost pole or singularity, which is chosen based on the
desired accuracy (assuming the rightmost singularity is 0),
and `\mathrm{tol}=10\alpha` is the desired tolerance, which is
chosen in relation to `\alpha`.`
When increasing the degree, the abscissa increase towards
`j\infty`, but more slowly than the fixed Talbot
algorithm. The de Hoog et al. algorithm typically does better
with oscillatory functions of time, and less well-behaved
functions. The method tends to be slower than the Talbot and
Stehfest algorithsm, especially so at very high precision
(e.g., `>500` digits precision).
"""
# required
# ------------------------------
self.t = self.ctx.convert(t)
# optional
# ------------------------------
self.tmax = kwargs.get('tmax',self.t)
# empirical relationships used here based on a linear fit of
# requested and delivered dps for exponentially decaying time
# functions for requested dps up to 512.
if 'degree' in kwargs:
self.degree = kwargs['degree']
self.dps_goal = int(1.38*self.degree)
else:
self.dps_goal = int(self.ctx.dps*1.36)
self.degree = max(10,self.dps_goal)
# 2*M+1 terms in approximation
M = self.degree
# adjust alpha component of abscissa of convergence for higher
# precision
tmp = self.ctx.power(10.0,-self.dps_goal)
self.alpha = self.ctx.convert(kwargs.get('alpha',tmp))
# desired tolerance (here simply related to alpha)
self.tol = self.ctx.convert(kwargs.get('tol',self.alpha*10.0))
self.np = 2*self.degree+1 # number of terms in approximation
# this is adjusting the dps of the calling context
# hopefully the caller doesn't monkey around with it
# between calling this routine and calc_time_domain_solution()
self.dps_orig = self.ctx.dps
self.ctx.dps = self.dps_goal
# scaling factor (likely tun-able, but 2 is typical)
self.scale = kwargs.get('scale',2)
self.T = self.ctx.convert(kwargs.get('T',self.scale*self.tmax))
self.p = self.ctx.matrix(2*M+1,1)
self.gamma = self.alpha - self.ctx.log(self.tol)/(self.scale*self.T)
self.p = (self.gamma + self.ctx.pi*
self.ctx.matrix(self.ctx.arange(self.np))/self.T*1j)
# NB: p is complex (mpc)
def calc_time_domain_solution(self,fp,t,manual_prec=False):
r"""Calculate time-domain solution for
de Hoog, Knight & Stokes algorithm.
The un-accelerated Fourier series approach is:
.. math ::
f(t,2M+1) = \frac{e^{\gamma t}}{T} \sum_{k=0}^{2M}{}^{'}
\Re\left[\bar{f}\left( p_k \right)
e^{i\pi t/T} \right],
where the prime on the summation indicates the first term is halved.
This simplistic approach requires so many function evaluations
that it is not practical. Non-linear acceleration is
accomplished via Pade-approximation and an analytic expression
for the remainder of the continued fraction. See the original
paper (reference 2 below) a detailed description of the
numerical approach.
**References**
1. Davies, B. (2005). *Integral Transforms and their
Applications*, Third Edition. Springer.
2. de Hoog, F., J. Knight, A. Stokes (1982). An improved
method for numerical inversion of Laplace transforms. *SIAM
Journal of Scientific and Statistical Computing* 3:357-366,
http://dx.doi.org/10.1137/0903022
"""
M = self.degree
np = self.np
T = self.T
self.t = self.ctx.convert(t)
# would it be useful to try re-using
# space between e&q and A&B?
e = self.ctx.zeros(np,M+1)
q = self.ctx.matrix(np,M)
d = self.ctx.matrix(np,1)
A = self.ctx.zeros(np+2,1)
B = self.ctx.ones(np+2,1)
# initialize Q-D table
# e[0:2*M,0] = 0.0 + 0.0j
q[0,0] = fp[1]/(fp[0]/2)
for i in range(1,2*M):
q[i,0] = fp[i+1]/fp[i]
# rhombus rule for filling triangular Q-D table (e & q)
for r in range(1,M+1):
# start with e, column 1, 0:2*M-2
mr = 2*(M-r)
e[0:mr,r] = q[1:mr+1,r-1] - q[0:mr,r-1] + e[1:mr+1,r-1]
if not r == M:
rq = r+1
mr = 2*(M-rq)+1
for i in range(mr):
q[i,rq-1] = q[i+1,rq-2]*e[i+1,rq-1]/e[i,rq-1]
# build up continued fraction coefficients (d)
d[0] = fp[0]/2
for r in range(1,M+1):
d[2*r-1] = -q[0,r-1] # even terms
d[2*r] = -e[0,r] # odd terms
# seed A and B for recurrence
#A[0] = 0.0 + 0.0j
A[1] = d[0]
#B[0:2] = 1.0 + 0.0j
# base of the power series
z = self.ctx.expjpi(self.t/T) # i*pi is already in fcn
# coefficients of Pade approximation (A & B)
# using recurrence for all but last term
for i in range(1,2*M):
A[i+1] = A[i] + d[i]*A[i-1]*z
B[i+1] = B[i] + d[i]*B[i-1]*z
# "improved remainder" to continued fraction
brem = (1 + (d[2*M-1] - d[2*M])*z)/2
# powm1(x,y) computes x^y - 1 more accurately near zero
rem = brem*self.ctx.powm1(1 + d[2*M]*z/brem,
self.ctx.fraction(1,2))
# last term of recurrence using new remainder
A[np] = A[2*M] + rem*A[2*M-1]
B[np] = B[2*M] + rem*B[2*M-1]
# diagonal Pade approximation
# F=A/B represents accelerated trapezoid rule
result = self.ctx.exp(self.gamma*self.t)/T*(A[np]/B[np]).real
# setting dps back to value when calc_laplace_parameter was called
if not manual_prec:
self.ctx.dps = self.dps_orig
return result
# ****************************************
class LaplaceTransformInversionMethods(object):
def __init__(ctx, *args, **kwargs):
ctx._fixed_talbot = FixedTalbot(ctx)
ctx._stehfest = Stehfest(ctx)
ctx._de_hoog = deHoog(ctx)
def invertlaplace(ctx, f, t, **kwargs):
r"""Computes the numerical inverse Laplace transform for a
Laplace-space function at a given time. The function being
evaluated is assumed to be a real-valued function of time.
The user must supply a Laplace-space function `\bar{f}(p)`,
and a desired time at which to estimate the time-domain
solution `f(t)`.
A few basic examples of Laplace-space functions with known
inverses (see references [1,2]) :
.. math ::
\mathcal{L}\left\lbrace f(t) \right\rbrace=\bar{f}(p)
.. math ::
\mathcal{L}^{-1}\left\lbrace \bar{f}(p) \right\rbrace = f(t)
.. math ::
\bar{f}(p) = \frac{1}{(p+1)^2}
.. math ::
f(t) = t e^{-t}
>>> from mpmath import *
>>> mp.dps = 15; mp.pretty = True
>>> tt = [0.001, 0.01, 0.1, 1, 10]
>>> fp = lambda p: 1/(p+1)**2
>>> ft = lambda t: t*exp(-t)
>>> ft(tt[0]),ft(tt[0])-invertlaplace(fp,tt[0],method='talbot')
(0.000999000499833375, 8.57923043561212e-20)
>>> ft(tt[1]),ft(tt[1])-invertlaplace(fp,tt[1],method='talbot')
(0.00990049833749168, 3.27007646698047e-19)
>>> ft(tt[2]),ft(tt[2])-invertlaplace(fp,tt[2],method='talbot')
(0.090483741803596, -1.75215800052168e-18)
>>> ft(tt[3]),ft(tt[3])-invertlaplace(fp,tt[3],method='talbot')
(0.367879441171442, 1.2428864009344e-17)
>>> ft(tt[4]),ft(tt[4])-invertlaplace(fp,tt[4],method='talbot')
(0.000453999297624849, 4.04513489306658e-20)
The methods also work for higher precision:
>>> mp.dps = 100; mp.pretty = True
>>> nstr(ft(tt[0]),15),nstr(ft(tt[0])-invertlaplace(fp,tt[0],method='talbot'),15)
('0.000999000499833375', '-4.96868310693356e-105')
>>> nstr(ft(tt[1]),15),nstr(ft(tt[1])-invertlaplace(fp,tt[1],method='talbot'),15)
('0.00990049833749168', '1.23032291513122e-104')
.. math ::
\bar{f}(p) = \frac{1}{p^2+1}
.. math ::
f(t) = \mathrm{J}_0(t)
>>> mp.dps = 15; mp.pretty = True
>>> fp = lambda p: 1/sqrt(p*p + 1)
>>> ft = lambda t: besselj(0,t)
>>> ft(tt[0]),ft(tt[0])-invertlaplace(fp,tt[0])
(0.999999750000016, -8.2477943034014e-18)
>>> ft(tt[1]),ft(tt[1])-invertlaplace(fp,tt[1])
(0.99997500015625, -3.69810144898872e-17)
.. math ::
\bar{f}(p) = \frac{\log p}{p}
.. math ::
f(t) = -\gamma -\log t
>>> mp.dps = 15; mp.pretty = True
>>> fp = lambda p: log(p)/p
>>> ft = lambda t: -euler-log(t)
>>> ft(tt[0]),ft(tt[0])-invertlaplace(fp,tt[0],method='stehfest')
(6.3305396140806, -1.92126634837863e-16)
>>> ft(tt[1]),ft(tt[1])-invertlaplace(fp,tt[1],method='stehfest')
(4.02795452108656, -4.81486093200704e-16)
**Options**
:func:`~mpmath.invertlaplace` recognizes the following optional keywords
valid for all methods:
*method*
Chooses numerical inverse Laplace transform algorithm
(described below).
*degree*
Number of terms used in the approximation
**Algorithms**
Mpmath implements three numerical inverse Laplace transform
algorithms, attributed to: Talbot, Stehfest, and de Hoog,
Knight and Stokes. These can be selected by using
*method='talbot'*, *method='stehfest'*, or *method='dehoog'*
or by passing the classes *method=FixedTalbot*,
*method=Stehfest*, or *method=deHoog*. The functions
:func:`~mpmath.invlaptalbot`, :func:`~mpmath.invlapstehfest`,
and :func:`~mpmath.invlapdehoog` are also available as
shortcuts.
All three algorithms implement a heuristic balance between the
requested precision and the precision used internally for the
calculations. This has been tuned for a typical exponentially
decaying function and precision up to few hundred decimal
digits.
The Laplace transform converts the variable time (i.e., along
a line) into a parameter given by the right half of the
complex `p`-plane. Singularities, poles, and branch cuts in
the complex `p`-plane contain all the information regarding
the time behavior of the corresponding function. Any numerical
method must therefore sample `p`-plane "close enough" to the
singularities to accurately characterize them, while not
getting too close to have catastrophic cancellation, overflow,
or underflow issues. Most significantly, if one or more of the
singularities in the `p`-plane is not on the left side of the
Bromwich contour, its effects will be left out of the computed
solution, and the answer will be completely wrong.
*Talbot*
The fixed Talbot method is high accuracy and fast, but the
method can catastrophically fail for certain classes of time-domain
behavior, including a Heaviside step function for positive
time (e.g., `H(t-2)`), or some oscillatory behaviors. The
Talbot method usually has adjustable parameters, but the
"fixed" variety implemented here does not. This method
deforms the Bromwich integral contour in the shape of a
parabola towards `-\infty`, which leads to problems
when the solution has a decaying exponential in it (e.g., a
Heaviside step function is equivalent to multiplying by a
decaying exponential in Laplace space).
*Stehfest*
The Stehfest algorithm only uses abscissa along the real axis
of the complex `p`-plane to estimate the time-domain
function. Oscillatory time-domain functions have poles away
from the real axis, so this method does not work well with
oscillatory functions, especially high-frequency ones. This
method also depends on summation of terms in a series that
grows very large, and will have catastrophic cancellation
during summation if the working precision is too low.
*de Hoog et al.*
The de Hoog, Knight, and Stokes method is essentially a
Fourier-series quadrature-type approximation to the Bromwich
contour integral, with non-linear series acceleration and an
analytical expression for the remainder term. This method is
typically the most robust and is therefore the default
method. This method also involves the greatest amount of
overhead, so it is typically the slowest of the three methods
at high precision.
**Singularities**
All numerical inverse Laplace transform methods have problems
at large time when the Laplace-space function has poles,
singularities, or branch cuts to the right of the origin in
the complex plane. For simple poles in `\bar{f}(p)` at the
`p`-plane origin, the time function is constant in time (e.g.,
`\mathcal{L}\left\lbrace 1 \right\rbrace=1/p` has a pole at
`p=0`). A pole in `\bar{f}(p)` to the left of the origin is a
decreasing function of time (e.g., `\mathcal{L}\left\lbrace
e^{-t/2} \right\rbrace=1/(p+1/2)` has a pole at `p=-1/2`), and
a pole to the right of the origin leads to an increasing
function in time (e.g., `\mathcal{L}\left\lbrace t e^{t/4}
\right\rbrace = 1/(p-1/4)^2` has a pole at `p=1/4`). When
singularities occur off the real `p` axis, the time-domain
function is oscillatory. For example `\mathcal{L}\left\lbrace
\mathrm{J}_0(t) \right\rbrace=1/\sqrt{p^2+1}` has a branch cut
starting at `p=j=\sqrt{-1}` and is a decaying oscillatory
function, This range of behaviors is illustrated in Duffy [3]
Figure 4.10.4, p. 228.
In general as `p \rightarrow \infty` `t \rightarrow 0` and
vice-versa. All numerical inverse Laplace transform methods
require their abscissa to shift closer to the origin for
larger times. If the abscissa shift left of the rightmost
singularity in the Laplace domain, the answer will be
completely wrong (the effect of singularities to the right of
the Bromwich contour are not included in the results).
For example, the following exponentially growing function has
a pole at `p=3`:
.. math ::
\bar{f}(p)=\frac{1}{p^2-9}
.. math ::
f(t)=\frac{1}{3}\sinh 3t
>>> mp.dps = 15; mp.pretty = True
>>> fp = lambda p: 1/(p*p-9)
>>> ft = lambda t: sinh(3*t)/3
>>> tt = [0.01,0.1,1.0,10.0]
>>> ft(tt[0]),invertlaplace(fp,tt[0],method='talbot')
(0.0100015000675014, 0.0100015000675014)
>>> ft(tt[1]),invertlaplace(fp,tt[1],method='talbot')
(0.101506764482381, 0.101506764482381)
>>> ft(tt[2]),invertlaplace(fp,tt[2],method='talbot')
(3.33929164246997, 3.33929164246997)
>>> ft(tt[3]),invertlaplace(fp,tt[3],method='talbot')
(1781079096920.74, -1.61331069624091e-14)
**References**
1. [DLMF]_ section 1.14 (http://dlmf.nist.gov/1.14T4)
2. Cohen, A.M. (2007). Numerical Methods for Laplace Transform
Inversion, Springer.
3. Duffy, D.G. (1998). Advanced Engineering Mathematics, CRC Press.
**Numerical Inverse Laplace Transform Reviews**
1. Bellman, R., R.E. Kalaba, J.A. Lockett (1966). *Numerical
inversion of the Laplace transform: Applications to Biology,
Economics, Engineering, and Physics*. Elsevier.
2. Davies, B., B. Martin (1979). Numerical inversion of the
Laplace transform: a survey and comparison of methods. *Journal
of Computational Physics* 33:1-32,
http://dx.doi.org/10.1016/0021-9991(79)90025-1
3. Duffy, D.G. (1993). On the numerical inversion of Laplace
transforms: Comparison of three new methods on characteristic
problems from applications. *ACM Transactions on Mathematical
Software* 19(3):333-359, http://dx.doi.org/10.1145/155743.155788
4. Kuhlman, K.L., (2013). Review of Inverse Laplace Transform
Algorithms for Laplace-Space Numerical Approaches, *Numerical
Algorithms*, 63(2):339-355.
http://dx.doi.org/10.1007/s11075-012-9625-3
"""
rule = kwargs.get('method','dehoog')
if type(rule) is str:
lrule = rule.lower()
if lrule == 'talbot':
rule = ctx._fixed_talbot
elif lrule == 'stehfest':
rule = ctx._stehfest
elif lrule == 'dehoog':
rule = ctx._de_hoog
else:
raise ValueError("unknown invlap algorithm: %s" % rule)
else:
rule = rule(ctx)
# determine the vector of Laplace-space parameter
# needed for the requested method and desired time
rule.calc_laplace_parameter(t,**kwargs)
# compute the Laplace-space function evalutations
# at the required abscissa.
fp = [f(p) for p in rule.p]
# compute the time-domain solution from the
# Laplace-space function evaluations
return rule.calc_time_domain_solution(fp,t)
# shortcuts for the above function for specific methods
def invlaptalbot(ctx, *args, **kwargs):
kwargs['method'] = 'talbot'
return ctx.invertlaplace(*args, **kwargs)
def invlapstehfest(ctx, *args, **kwargs):
kwargs['method'] = 'stehfest'
return ctx.invertlaplace(*args, **kwargs)
def invlapdehoog(ctx, *args, **kwargs):
kwargs['method'] = 'dehoog'
return ctx.invertlaplace(*args, **kwargs)
# ****************************************
if __name__ == '__main__':
import doctest
doctest.testmod()
| 31,135 | 36.558504 | 89 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/calculus/differentiation.py
|
from ..libmp.backend import xrange
from .calculus import defun
try:
iteritems = dict.iteritems
except AttributeError:
iteritems = dict.items
#----------------------------------------------------------------------------#
# Differentiation #
#----------------------------------------------------------------------------#
@defun
def difference(ctx, s, n):
r"""
Given a sequence `(s_k)` containing at least `n+1` items, returns the
`n`-th forward difference,
.. math ::
\Delta^n = \sum_{k=0}^{\infty} (-1)^{k+n} {n \choose k} s_k.
"""
n = int(n)
d = ctx.zero
b = (-1) ** (n & 1)
for k in xrange(n+1):
d += b * s[k]
b = (b * (k-n)) // (k+1)
return d
def hsteps(ctx, f, x, n, prec, **options):
singular = options.get('singular')
addprec = options.get('addprec', 10)
direction = options.get('direction', 0)
workprec = (prec+2*addprec) * (n+1)
orig = ctx.prec
try:
ctx.prec = workprec
h = options.get('h')
if h is None:
if options.get('relative'):
hextramag = int(ctx.mag(x))
else:
hextramag = 0
h = ctx.ldexp(1, -prec-addprec-hextramag)
else:
h = ctx.convert(h)
# Directed: steps x, x+h, ... x+n*h
direction = options.get('direction', 0)
if direction:
h *= ctx.sign(direction)
steps = xrange(n+1)
norm = h
# Central: steps x-n*h, x-(n-2)*h ..., x, ..., x+(n-2)*h, x+n*h
else:
steps = xrange(-n, n+1, 2)
norm = (2*h)
# Perturb
if singular:
x += 0.5*h
values = [f(x+k*h) for k in steps]
return values, norm, workprec
finally:
ctx.prec = orig
@defun
def diff(ctx, f, x, n=1, **options):
r"""
Numerically computes the derivative of `f`, `f'(x)`, or generally for
an integer `n \ge 0`, the `n`-th derivative `f^{(n)}(x)`.
A few basic examples are::
>>> from mpmath import *
>>> mp.dps = 15; mp.pretty = True
>>> diff(lambda x: x**2 + x, 1.0)
3.0
>>> diff(lambda x: x**2 + x, 1.0, 2)
2.0
>>> diff(lambda x: x**2 + x, 1.0, 3)
0.0
>>> nprint([diff(exp, 3, n) for n in range(5)]) # exp'(x) = exp(x)
[20.0855, 20.0855, 20.0855, 20.0855, 20.0855]
Even more generally, given a tuple of arguments `(x_1, \ldots, x_k)`
and order `(n_1, \ldots, n_k)`, the partial derivative
`f^{(n_1,\ldots,n_k)}(x_1,\ldots,x_k)` is evaluated. For example::
>>> diff(lambda x,y: 3*x*y + 2*y - x, (0.25, 0.5), (0,1))
2.75
>>> diff(lambda x,y: 3*x*y + 2*y - x, (0.25, 0.5), (1,1))
3.0
**Options**
The following optional keyword arguments are recognized:
``method``
Supported methods are ``'step'`` or ``'quad'``: derivatives may be
computed using either a finite difference with a small step
size `h` (default), or numerical quadrature.
``direction``
Direction of finite difference: can be -1 for a left
difference, 0 for a central difference (default), or +1
for a right difference; more generally can be any complex number.
``addprec``
Extra precision for `h` used to account for the function's
sensitivity to perturbations (default = 10).
``relative``
Choose `h` relative to the magnitude of `x`, rather than an
absolute value; useful for large or tiny `x` (default = False).
``h``
As an alternative to ``addprec`` and ``relative``, manually
select the step size `h`.
``singular``
If True, evaluation exactly at the point `x` is avoided; this is
useful for differentiating functions with removable singularities.
Default = False.
``radius``
Radius of integration contour (with ``method = 'quad'``).
Default = 0.25. A larger radius typically is faster and more
accurate, but it must be chosen so that `f` has no
singularities within the radius from the evaluation point.
A finite difference requires `n+1` function evaluations and must be
performed at `(n+1)` times the target precision. Accordingly, `f` must
support fast evaluation at high precision.
With integration, a larger number of function evaluations is
required, but not much extra precision is required. For high order
derivatives, this method may thus be faster if f is very expensive to
evaluate at high precision.
**Further examples**
The direction option is useful for computing left- or right-sided
derivatives of nonsmooth functions::
>>> diff(abs, 0, direction=0)
0.0
>>> diff(abs, 0, direction=1)
1.0
>>> diff(abs, 0, direction=-1)
-1.0
More generally, if the direction is nonzero, a right difference
is computed where the step size is multiplied by sign(direction).
For example, with direction=+j, the derivative from the positive
imaginary direction will be computed::
>>> diff(abs, 0, direction=j)
(0.0 - 1.0j)
With integration, the result may have a small imaginary part
even even if the result is purely real::
>>> diff(sqrt, 1, method='quad') # doctest:+ELLIPSIS
(0.5 - 4.59...e-26j)
>>> chop(_)
0.5
Adding precision to obtain an accurate value::
>>> diff(cos, 1e-30)
0.0
>>> diff(cos, 1e-30, h=0.0001)
-9.99999998328279e-31
>>> diff(cos, 1e-30, addprec=100)
-1.0e-30
"""
partial = False
try:
orders = list(n)
x = list(x)
partial = True
except TypeError:
pass
if partial:
x = [ctx.convert(_) for _ in x]
return _partial_diff(ctx, f, x, orders, options)
method = options.get('method', 'step')
if n == 0 and method != 'quad' and not options.get('singular'):
return f(ctx.convert(x))
prec = ctx.prec
try:
if method == 'step':
values, norm, workprec = hsteps(ctx, f, x, n, prec, **options)
ctx.prec = workprec
v = ctx.difference(values, n) / norm**n
elif method == 'quad':
ctx.prec += 10
radius = ctx.convert(options.get('radius', 0.25))
def g(t):
rei = radius*ctx.expj(t)
z = x + rei
return f(z) / rei**n
d = ctx.quadts(g, [0, 2*ctx.pi])
v = d * ctx.factorial(n) / (2*ctx.pi)
else:
raise ValueError("unknown method: %r" % method)
finally:
ctx.prec = prec
return +v
def _partial_diff(ctx, f, xs, orders, options):
if not orders:
return f()
if not sum(orders):
return f(*xs)
i = 0
for i in range(len(orders)):
if orders[i]:
break
order = orders[i]
def fdiff_inner(*f_args):
def inner(t):
return f(*(f_args[:i] + (t,) + f_args[i+1:]))
return ctx.diff(inner, f_args[i], order, **options)
orders[i] = 0
return _partial_diff(ctx, fdiff_inner, xs, orders, options)
@defun
def diffs(ctx, f, x, n=None, **options):
r"""
Returns a generator that yields the sequence of derivatives
.. math ::
f(x), f'(x), f''(x), \ldots, f^{(k)}(x), \ldots
With ``method='step'``, :func:`~mpmath.diffs` uses only `O(k)`
function evaluations to generate the first `k` derivatives,
rather than the roughly `O(k^2)` evaluations
required if one calls :func:`~mpmath.diff` `k` separate times.
With `n < \infty`, the generator stops as soon as the
`n`-th derivative has been generated. If the exact number of
needed derivatives is known in advance, this is further
slightly more efficient.
Options are the same as for :func:`~mpmath.diff`.
**Examples**
>>> from mpmath import *
>>> mp.dps = 15
>>> nprint(list(diffs(cos, 1, 5)))
[0.540302, -0.841471, -0.540302, 0.841471, 0.540302, -0.841471]
>>> for i, d in zip(range(6), diffs(cos, 1)):
... print("%s %s" % (i, d))
...
0 0.54030230586814
1 -0.841470984807897
2 -0.54030230586814
3 0.841470984807897
4 0.54030230586814
5 -0.841470984807897
"""
if n is None:
n = ctx.inf
else:
n = int(n)
if options.get('method', 'step') != 'step':
k = 0
while k < n + 1:
yield ctx.diff(f, x, k, **options)
k += 1
return
singular = options.get('singular')
if singular:
yield ctx.diff(f, x, 0, singular=True)
else:
yield f(ctx.convert(x))
if n < 1:
return
if n == ctx.inf:
A, B = 1, 2
else:
A, B = 1, n+1
while 1:
callprec = ctx.prec
y, norm, workprec = hsteps(ctx, f, x, B, callprec, **options)
for k in xrange(A, B):
try:
ctx.prec = workprec
d = ctx.difference(y, k) / norm**k
finally:
ctx.prec = callprec
yield +d
if k >= n:
return
A, B = B, int(A*1.4+1)
B = min(B, n)
def iterable_to_function(gen):
gen = iter(gen)
data = []
def f(k):
for i in xrange(len(data), k+1):
data.append(next(gen))
return data[k]
return f
@defun
def diffs_prod(ctx, factors):
r"""
Given a list of `N` iterables or generators yielding
`f_k(x), f'_k(x), f''_k(x), \ldots` for `k = 1, \ldots, N`,
generate `g(x), g'(x), g''(x), \ldots` where
`g(x) = f_1(x) f_2(x) \cdots f_N(x)`.
At high precision and for large orders, this is typically more efficient
than numerical differentiation if the derivatives of each `f_k(x)`
admit direct computation.
Note: This function does not increase the working precision internally,
so guard digits may have to be added externally for full accuracy.
**Examples**
>>> from mpmath import *
>>> mp.dps = 15; mp.pretty = True
>>> f = lambda x: exp(x)*cos(x)*sin(x)
>>> u = diffs(f, 1)
>>> v = mp.diffs_prod([diffs(exp,1), diffs(cos,1), diffs(sin,1)])
>>> next(u); next(v)
1.23586333600241
1.23586333600241
>>> next(u); next(v)
0.104658952245596
0.104658952245596
>>> next(u); next(v)
-5.96999877552086
-5.96999877552086
>>> next(u); next(v)
-12.4632923122697
-12.4632923122697
"""
N = len(factors)
if N == 1:
for c in factors[0]:
yield c
else:
u = iterable_to_function(ctx.diffs_prod(factors[:N//2]))
v = iterable_to_function(ctx.diffs_prod(factors[N//2:]))
n = 0
while 1:
#yield sum(binomial(n,k)*u(n-k)*v(k) for k in xrange(n+1))
s = u(n) * v(0)
a = 1
for k in xrange(1,n+1):
a = a * (n-k+1) // k
s += a * u(n-k) * v(k)
yield s
n += 1
def dpoly(n, _cache={}):
"""
nth differentiation polynomial for exp (Faa di Bruno's formula).
TODO: most exponents are zero, so maybe a sparse representation
would be better.
"""
if n in _cache:
return _cache[n]
if not _cache:
_cache[0] = {(0,):1}
R = dpoly(n-1)
R = dict((c+(0,),v) for (c,v) in iteritems(R))
Ra = {}
for powers, count in iteritems(R):
powers1 = (powers[0]+1,) + powers[1:]
if powers1 in Ra:
Ra[powers1] += count
else:
Ra[powers1] = count
for powers, count in iteritems(R):
if not sum(powers):
continue
for k,p in enumerate(powers):
if p:
powers2 = powers[:k] + (p-1,powers[k+1]+1) + powers[k+2:]
if powers2 in Ra:
Ra[powers2] += p*count
else:
Ra[powers2] = p*count
_cache[n] = Ra
return _cache[n]
@defun
def diffs_exp(ctx, fdiffs):
r"""
Given an iterable or generator yielding `f(x), f'(x), f''(x), \ldots`
generate `g(x), g'(x), g''(x), \ldots` where `g(x) = \exp(f(x))`.
At high precision and for large orders, this is typically more efficient
than numerical differentiation if the derivatives of `f(x)`
admit direct computation.
Note: This function does not increase the working precision internally,
so guard digits may have to be added externally for full accuracy.
**Examples**
The derivatives of the gamma function can be computed using
logarithmic differentiation::
>>> from mpmath import *
>>> mp.dps = 15; mp.pretty = True
>>>
>>> def diffs_loggamma(x):
... yield loggamma(x)
... i = 0
... while 1:
... yield psi(i,x)
... i += 1
...
>>> u = diffs_exp(diffs_loggamma(3))
>>> v = diffs(gamma, 3)
>>> next(u); next(v)
2.0
2.0
>>> next(u); next(v)
1.84556867019693
1.84556867019693
>>> next(u); next(v)
2.49292999190269
2.49292999190269
>>> next(u); next(v)
3.44996501352367
3.44996501352367
"""
fn = iterable_to_function(fdiffs)
f0 = ctx.exp(fn(0))
yield f0
i = 1
while 1:
s = ctx.mpf(0)
for powers, c in iteritems(dpoly(i)):
s += c*ctx.fprod(fn(k+1)**p for (k,p) in enumerate(powers) if p)
yield s * f0
i += 1
@defun
def differint(ctx, f, x, n=1, x0=0):
r"""
Calculates the Riemann-Liouville differintegral, or fractional
derivative, defined by
.. math ::
\,_{x_0}{\mathbb{D}}^n_xf(x) = \frac{1}{\Gamma(m-n)} \frac{d^m}{dx^m}
\int_{x_0}^{x}(x-t)^{m-n-1}f(t)dt
where `f` is a given (presumably well-behaved) function,
`x` is the evaluation point, `n` is the order, and `x_0` is
the reference point of integration (`m` is an arbitrary
parameter selected automatically).
With `n = 1`, this is just the standard derivative `f'(x)`; with `n = 2`,
the second derivative `f''(x)`, etc. With `n = -1`, it gives
`\int_{x_0}^x f(t) dt`, with `n = -2`
it gives `\int_{x_0}^x \left( \int_{x_0}^t f(u) du \right) dt`, etc.
As `n` is permitted to be any number, this operator generalizes
iterated differentiation and iterated integration to a single
operator with a continuous order parameter.
**Examples**
There is an exact formula for the fractional derivative of a
monomial `x^p`, which may be used as a reference. For example,
the following gives a half-derivative (order 0.5)::
>>> from mpmath import *
>>> mp.dps = 15; mp.pretty = True
>>> x = mpf(3); p = 2; n = 0.5
>>> differint(lambda t: t**p, x, n)
7.81764019044672
>>> gamma(p+1)/gamma(p-n+1) * x**(p-n)
7.81764019044672
Another useful test function is the exponential function, whose
integration / differentiation formula easy generalizes
to arbitrary order. Here we first compute a third derivative,
and then a triply nested integral. (The reference point `x_0`
is set to `-\infty` to avoid nonzero endpoint terms.)::
>>> differint(lambda x: exp(pi*x), -1.5, 3)
0.278538406900792
>>> exp(pi*-1.5) * pi**3
0.278538406900792
>>> differint(lambda x: exp(pi*x), 3.5, -3, -inf)
1922.50563031149
>>> exp(pi*3.5) / pi**3
1922.50563031149
However, for noninteger `n`, the differentiation formula for the
exponential function must be modified to give the same result as the
Riemann-Liouville differintegral::
>>> x = mpf(3.5)
>>> c = pi
>>> n = 1+2*j
>>> differint(lambda x: exp(c*x), x, n)
(-123295.005390743 + 140955.117867654j)
>>> x**(-n) * exp(c)**x * (x*c)**n * gammainc(-n, 0, x*c) / gamma(-n)
(-123295.005390743 + 140955.117867654j)
"""
m = max(int(ctx.ceil(ctx.re(n)))+1, 1)
r = m-n-1
g = lambda x: ctx.quad(lambda t: (x-t)**r * f(t), [x0, x])
return ctx.diff(g, x, m) / ctx.gamma(m-n)
@defun
def diffun(ctx, f, n=1, **options):
r"""
Given a function `f`, returns a function `g(x)` that evaluates the nth
derivative `f^{(n)}(x)`::
>>> from mpmath import *
>>> mp.dps = 15; mp.pretty = True
>>> cos2 = diffun(sin)
>>> sin2 = diffun(sin, 4)
>>> cos(1.3), cos2(1.3)
(0.267498828624587, 0.267498828624587)
>>> sin(1.3), sin2(1.3)
(0.963558185417193, 0.963558185417193)
The function `f` must support arbitrary precision evaluation.
See :func:`~mpmath.diff` for additional details and supported
keyword options.
"""
if n == 0:
return f
def g(x):
return ctx.diff(f, x, n, **options)
return g
@defun
def taylor(ctx, f, x, n, **options):
r"""
Produces a degree-`n` Taylor polynomial around the point `x` of the
given function `f`. The coefficients are returned as a list.
>>> from mpmath import *
>>> mp.dps = 15; mp.pretty = True
>>> nprint(chop(taylor(sin, 0, 5)))
[0.0, 1.0, 0.0, -0.166667, 0.0, 0.00833333]
The coefficients are computed using high-order numerical
differentiation. The function must be possible to evaluate
to arbitrary precision. See :func:`~mpmath.diff` for additional details
and supported keyword options.
Note that to evaluate the Taylor polynomial as an approximation
of `f`, e.g. with :func:`~mpmath.polyval`, the coefficients must be reversed,
and the point of the Taylor expansion must be subtracted from
the argument:
>>> p = taylor(exp, 2.0, 10)
>>> polyval(p[::-1], 2.5 - 2.0)
12.1824939606092
>>> exp(2.5)
12.1824939607035
"""
gen = enumerate(ctx.diffs(f, x, n, **options))
if options.get("chop", True):
return [ctx.chop(d)/ctx.factorial(i) for i, d in gen]
else:
return [d/ctx.factorial(i) for i, d in gen]
@defun
def pade(ctx, a, L, M):
r"""
Computes a Pade approximation of degree `(L, M)` to a function.
Given at least `L+M+1` Taylor coefficients `a` approximating
a function `A(x)`, :func:`~mpmath.pade` returns coefficients of
polynomials `P, Q` satisfying
.. math ::
P = \sum_{k=0}^L p_k x^k
Q = \sum_{k=0}^M q_k x^k
Q_0 = 1
A(x) Q(x) = P(x) + O(x^{L+M+1})
`P(x)/Q(x)` can provide a good approximation to an analytic function
beyond the radius of convergence of its Taylor series (example
from G.A. Baker 'Essentials of Pade Approximants' Academic Press,
Ch.1A)::
>>> from mpmath import *
>>> mp.dps = 15; mp.pretty = True
>>> one = mpf(1)
>>> def f(x):
... return sqrt((one + 2*x)/(one + x))
...
>>> a = taylor(f, 0, 6)
>>> p, q = pade(a, 3, 3)
>>> x = 10
>>> polyval(p[::-1], x)/polyval(q[::-1], x)
1.38169105566806
>>> f(x)
1.38169855941551
"""
# To determine L+1 coefficients of P and M coefficients of Q
# L+M+1 coefficients of A must be provided
if len(a) < L+M+1:
raise ValueError("L+M+1 Coefficients should be provided")
if M == 0:
if L == 0:
return [ctx.one], [ctx.one]
else:
return a[:L+1], [ctx.one]
# Solve first
# a[L]*q[1] + ... + a[L-M+1]*q[M] = -a[L+1]
# ...
# a[L+M-1]*q[1] + ... + a[L]*q[M] = -a[L+M]
A = ctx.matrix(M)
for j in range(M):
for i in range(min(M, L+j+1)):
A[j, i] = a[L+j-i]
v = -ctx.matrix(a[(L+1):(L+M+1)])
x = ctx.lu_solve(A, v)
q = [ctx.one] + list(x)
# compute p
p = [0]*(L+1)
for i in range(L+1):
s = a[i]
for j in range(1, min(M,i) + 1):
s += q[j]*a[i-j]
p[i] = s
return p, q
| 20,226 | 30.214506 | 81 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/tests/test_str.py
|
from mpmath import nstr, matrix, inf
def test_nstr():
m = matrix([[0.75, 0.190940654, -0.0299195971],
[0.190940654, 0.65625, 0.205663228],
[-0.0299195971, 0.205663228, 0.64453125e-20]])
assert nstr(m, 4, min_fixed=-inf) == \
'''[ 0.75 0.1909 -0.02992]
[ 0.1909 0.6563 0.2057]
[-0.02992 0.2057 0.000000000000000000006445]'''
assert nstr(m, 4) == \
'''[ 0.75 0.1909 -0.02992]
[ 0.1909 0.6563 0.2057]
[-0.02992 0.2057 6.445e-21]'''
| 544 | 35.333333 | 62 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/tests/test_functions.py
|
from mpmath.libmp import *
from mpmath import *
import random
import time
import math
import cmath
def mpc_ae(a, b, eps=eps):
res = True
res = res and a.real.ae(b.real, eps)
res = res and a.imag.ae(b.imag, eps)
return res
#----------------------------------------------------------------------------
# Constants and functions
#
tpi = "3.1415926535897932384626433832795028841971693993751058209749445923078\
1640628620899862803482534211706798"
te = "2.71828182845904523536028747135266249775724709369995957496696762772407\
663035354759457138217852516642743"
tdegree = "0.017453292519943295769236907684886127134428718885417254560971914\
4017100911460344944368224156963450948221"
teuler = "0.5772156649015328606065120900824024310421593359399235988057672348\
84867726777664670936947063291746749516"
tln2 = "0.693147180559945309417232121458176568075500134360255254120680009493\
393621969694715605863326996418687542"
tln10 = "2.30258509299404568401799145468436420760110148862877297603332790096\
757260967735248023599720508959829834"
tcatalan = "0.91596559417721901505460351493238411077414937428167213426649811\
9621763019776254769479356512926115106249"
tkhinchin = "2.6854520010653064453097148354817956938203822939944629530511523\
4555721885953715200280114117493184769800"
tglaisher = "1.2824271291006226368753425688697917277676889273250011920637400\
2174040630885882646112973649195820237439420646"
tapery = "1.2020569031595942853997381615114499907649862923404988817922715553\
4183820578631309018645587360933525815"
tphi = "1.618033988749894848204586834365638117720309179805762862135448622705\
26046281890244970720720418939113748475"
tmertens = "0.26149721284764278375542683860869585905156664826119920619206421\
3924924510897368209714142631434246651052"
ttwinprime = "0.660161815846869573927812110014555778432623360284733413319448\
423335405642304495277143760031413839867912"
def test_constants():
for prec in [3, 7, 10, 15, 20, 37, 80, 100, 29]:
mp.dps = prec
assert pi == mpf(tpi)
assert e == mpf(te)
assert degree == mpf(tdegree)
assert euler == mpf(teuler)
assert ln2 == mpf(tln2)
assert ln10 == mpf(tln10)
assert catalan == mpf(tcatalan)
assert khinchin == mpf(tkhinchin)
assert glaisher == mpf(tglaisher)
assert phi == mpf(tphi)
if prec < 50:
assert mertens == mpf(tmertens)
assert twinprime == mpf(ttwinprime)
mp.dps = 15
assert pi >= -1
assert pi > 2
assert pi > 3
assert pi < 4
def test_exact_sqrts():
for i in range(20000):
assert sqrt(mpf(i*i)) == i
random.seed(1)
for prec in [100, 300, 1000, 10000]:
mp.dps = prec
for i in range(20):
A = random.randint(10**(prec//2-2), 10**(prec//2-1))
assert sqrt(mpf(A*A)) == A
mp.dps = 15
for i in range(100):
for a in [1, 8, 25, 112307]:
assert sqrt(mpf((a*a, 2*i))) == mpf((a, i))
assert sqrt(mpf((a*a, -2*i))) == mpf((a, -i))
def test_sqrt_rounding():
for i in [2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15]:
i = from_int(i)
for dps in [7, 15, 83, 106, 2000]:
mp.dps = dps
a = mpf_pow_int(mpf_sqrt(i, mp.prec, round_down), 2, mp.prec, round_down)
b = mpf_pow_int(mpf_sqrt(i, mp.prec, round_up), 2, mp.prec, round_up)
assert mpf_lt(a, i)
assert mpf_gt(b, i)
random.seed(1234)
prec = 100
for rnd in [round_down, round_nearest, round_ceiling]:
for i in range(100):
a = mpf_rand(prec)
b = mpf_mul(a, a)
assert mpf_sqrt(b, prec, rnd) == a
# Test some extreme cases
mp.dps = 100
a = mpf(9) + 1e-90
b = mpf(9) - 1e-90
mp.dps = 15
assert sqrt(a, rounding='d') == 3
assert sqrt(a, rounding='n') == 3
assert sqrt(a, rounding='u') > 3
assert sqrt(b, rounding='d') < 3
assert sqrt(b, rounding='n') == 3
assert sqrt(b, rounding='u') == 3
# A worst case, from the MPFR test suite
assert sqrt(mpf('7.0503726185518891')) == mpf('2.655253776675949')
def test_float_sqrt():
mp.dps = 15
# These should round identically
for x in [0, 1e-7, 0.1, 0.5, 1, 2, 3, 4, 5, 0.333, 76.19]:
assert sqrt(mpf(x)) == float(x)**0.5
assert sqrt(-1) == 1j
assert sqrt(-2).ae(cmath.sqrt(-2))
assert sqrt(-3).ae(cmath.sqrt(-3))
assert sqrt(-100).ae(cmath.sqrt(-100))
assert sqrt(1j).ae(cmath.sqrt(1j))
assert sqrt(-1j).ae(cmath.sqrt(-1j))
assert sqrt(math.pi + math.e*1j).ae(cmath.sqrt(math.pi + math.e*1j))
assert sqrt(math.pi - math.e*1j).ae(cmath.sqrt(math.pi - math.e*1j))
def test_hypot():
assert hypot(0, 0) == 0
assert hypot(0, 0.33) == mpf(0.33)
assert hypot(0.33, 0) == mpf(0.33)
assert hypot(-0.33, 0) == mpf(0.33)
assert hypot(3, 4) == mpf(5)
def test_exact_cbrt():
for i in range(0, 20000, 200):
assert cbrt(mpf(i*i*i)) == i
random.seed(1)
for prec in [100, 300, 1000, 10000]:
mp.dps = prec
A = random.randint(10**(prec//2-2), 10**(prec//2-1))
assert cbrt(mpf(A*A*A)) == A
mp.dps = 15
def test_exp():
assert exp(0) == 1
assert exp(10000).ae(mpf('8.8068182256629215873e4342'))
assert exp(-10000).ae(mpf('1.1354838653147360985e-4343'))
a = exp(mpf((1, 8198646019315405, -53, 53)))
assert(a.bc == bitcount(a.man))
mp.prec = 67
a = exp(mpf((1, 1781864658064754565, -60, 61)))
assert(a.bc == bitcount(a.man))
mp.prec = 53
assert exp(ln2 * 10).ae(1024)
assert exp(2+2j).ae(cmath.exp(2+2j))
def test_issue_73():
mp.dps = 512
a = exp(-1)
b = exp(1)
mp.dps = 15
assert (+a).ae(0.36787944117144233)
assert (+b).ae(2.7182818284590451)
def test_log():
mp.dps = 15
assert log(1) == 0
for x in [0.5, 1.5, 2.0, 3.0, 100, 10**50, 1e-50]:
assert log(x).ae(math.log(x))
assert log(x, x) == 1
assert log(1024, 2) == 10
assert log(10**1234, 10) == 1234
assert log(2+2j).ae(cmath.log(2+2j))
# Accuracy near 1
assert (log(0.6+0.8j).real*10**17).ae(2.2204460492503131)
assert (log(0.6-0.8j).real*10**17).ae(2.2204460492503131)
assert (log(0.8-0.6j).real*10**17).ae(2.2204460492503131)
assert (log(1+1e-8j).real*10**16).ae(0.5)
assert (log(1-1e-8j).real*10**16).ae(0.5)
assert (log(-1+1e-8j).real*10**16).ae(0.5)
assert (log(-1-1e-8j).real*10**16).ae(0.5)
assert (log(1j+1e-8).real*10**16).ae(0.5)
assert (log(1j-1e-8).real*10**16).ae(0.5)
assert (log(-1j+1e-8).real*10**16).ae(0.5)
assert (log(-1j-1e-8).real*10**16).ae(0.5)
assert (log(1+1e-40j).real*10**80).ae(0.5)
assert (log(1j+1e-40).real*10**80).ae(0.5)
# Huge
assert log(ldexp(1.234,10**20)).ae(log(2)*1e20)
assert log(ldexp(1.234,10**200)).ae(log(2)*1e200)
# Some special values
assert log(mpc(0,0)) == mpc(-inf,0)
assert isnan(log(mpc(nan,0)).real)
assert isnan(log(mpc(nan,0)).imag)
assert isnan(log(mpc(0,nan)).real)
assert isnan(log(mpc(0,nan)).imag)
assert isnan(log(mpc(nan,1)).real)
assert isnan(log(mpc(nan,1)).imag)
assert isnan(log(mpc(1,nan)).real)
assert isnan(log(mpc(1,nan)).imag)
def test_trig_hyperb_basic():
for x in (list(range(100)) + list(range(-100,0))):
t = x / 4.1
assert cos(mpf(t)).ae(math.cos(t))
assert sin(mpf(t)).ae(math.sin(t))
assert tan(mpf(t)).ae(math.tan(t))
assert cosh(mpf(t)).ae(math.cosh(t))
assert sinh(mpf(t)).ae(math.sinh(t))
assert tanh(mpf(t)).ae(math.tanh(t))
assert sin(1+1j).ae(cmath.sin(1+1j))
assert sin(-4-3.6j).ae(cmath.sin(-4-3.6j))
assert cos(1+1j).ae(cmath.cos(1+1j))
assert cos(-4-3.6j).ae(cmath.cos(-4-3.6j))
def test_degrees():
assert cos(0*degree) == 1
assert cos(90*degree).ae(0)
assert cos(180*degree).ae(-1)
assert cos(270*degree).ae(0)
assert cos(360*degree).ae(1)
assert sin(0*degree) == 0
assert sin(90*degree).ae(1)
assert sin(180*degree).ae(0)
assert sin(270*degree).ae(-1)
assert sin(360*degree).ae(0)
def random_complexes(N):
random.seed(1)
a = []
for i in range(N):
x1 = random.uniform(-10, 10)
y1 = random.uniform(-10, 10)
x2 = random.uniform(-10, 10)
y2 = random.uniform(-10, 10)
z1 = complex(x1, y1)
z2 = complex(x2, y2)
a.append((z1, z2))
return a
def test_complex_powers():
for dps in [15, 30, 100]:
# Check accuracy for complex square root
mp.dps = dps
a = mpc(1j)**0.5
assert a.real == a.imag == mpf(2)**0.5 / 2
mp.dps = 15
random.seed(1)
for (z1, z2) in random_complexes(100):
assert (mpc(z1)**mpc(z2)).ae(z1**z2, 1e-12)
assert (e**(-pi*1j)).ae(-1)
mp.dps = 50
assert (e**(-pi*1j)).ae(-1)
mp.dps = 15
def test_complex_sqrt_accuracy():
def test_mpc_sqrt(lst):
for a, b in lst:
z = mpc(a + j*b)
assert mpc_ae(sqrt(z*z), z)
z = mpc(-a + j*b)
assert mpc_ae(sqrt(z*z), -z)
z = mpc(a - j*b)
assert mpc_ae(sqrt(z*z), z)
z = mpc(-a - j*b)
assert mpc_ae(sqrt(z*z), -z)
random.seed(2)
N = 10
mp.dps = 30
dps = mp.dps
test_mpc_sqrt([(random.uniform(0, 10),random.uniform(0, 10)) for i in range(N)])
test_mpc_sqrt([(i + 0.1, (i + 0.2)*10**i) for i in range(N)])
mp.dps = 15
def test_atan():
mp.dps = 15
assert atan(-2.3).ae(math.atan(-2.3))
assert atan(1e-50) == 1e-50
assert atan(1e50).ae(pi/2)
assert atan(-1e-50) == -1e-50
assert atan(-1e50).ae(-pi/2)
assert atan(10**1000).ae(pi/2)
for dps in [25, 70, 100, 300, 1000]:
mp.dps = dps
assert (4*atan(1)).ae(pi)
mp.dps = 15
pi2 = pi/2
assert atan(mpc(inf,-1)).ae(pi2)
assert atan(mpc(inf,0)).ae(pi2)
assert atan(mpc(inf,1)).ae(pi2)
assert atan(mpc(1,inf)).ae(pi2)
assert atan(mpc(0,inf)).ae(pi2)
assert atan(mpc(-1,inf)).ae(-pi2)
assert atan(mpc(-inf,1)).ae(-pi2)
assert atan(mpc(-inf,0)).ae(-pi2)
assert atan(mpc(-inf,-1)).ae(-pi2)
assert atan(mpc(-1,-inf)).ae(-pi2)
assert atan(mpc(0,-inf)).ae(-pi2)
assert atan(mpc(1,-inf)).ae(pi2)
def test_atan2():
mp.dps = 15
assert atan2(1,1).ae(pi/4)
assert atan2(1,-1).ae(3*pi/4)
assert atan2(-1,-1).ae(-3*pi/4)
assert atan2(-1,1).ae(-pi/4)
assert atan2(-1,0).ae(-pi/2)
assert atan2(1,0).ae(pi/2)
assert atan2(0,0) == 0
assert atan2(inf,0).ae(pi/2)
assert atan2(-inf,0).ae(-pi/2)
assert isnan(atan2(inf,inf))
assert isnan(atan2(-inf,inf))
assert isnan(atan2(inf,-inf))
assert isnan(atan2(3,nan))
assert isnan(atan2(nan,3))
assert isnan(atan2(0,nan))
assert isnan(atan2(nan,0))
assert atan2(0,inf) == 0
assert atan2(0,-inf).ae(pi)
assert atan2(10,inf) == 0
assert atan2(-10,inf) == 0
assert atan2(-10,-inf).ae(-pi)
assert atan2(10,-inf).ae(pi)
assert atan2(inf,10).ae(pi/2)
assert atan2(inf,-10).ae(pi/2)
assert atan2(-inf,10).ae(-pi/2)
assert atan2(-inf,-10).ae(-pi/2)
def test_areal_inverses():
assert asin(mpf(0)) == 0
assert asinh(mpf(0)) == 0
assert acosh(mpf(1)) == 0
assert isinstance(asin(mpf(0.5)), mpf)
assert isinstance(asin(mpf(2.0)), mpc)
assert isinstance(acos(mpf(0.5)), mpf)
assert isinstance(acos(mpf(2.0)), mpc)
assert isinstance(atanh(mpf(0.1)), mpf)
assert isinstance(atanh(mpf(1.1)), mpc)
random.seed(1)
for i in range(50):
x = random.uniform(0, 1)
assert asin(mpf(x)).ae(math.asin(x))
assert acos(mpf(x)).ae(math.acos(x))
x = random.uniform(-10, 10)
assert asinh(mpf(x)).ae(cmath.asinh(x).real)
assert isinstance(asinh(mpf(x)), mpf)
x = random.uniform(1, 10)
assert acosh(mpf(x)).ae(cmath.acosh(x).real)
assert isinstance(acosh(mpf(x)), mpf)
x = random.uniform(-10, 0.999)
assert isinstance(acosh(mpf(x)), mpc)
x = random.uniform(-1, 1)
assert atanh(mpf(x)).ae(cmath.atanh(x).real)
assert isinstance(atanh(mpf(x)), mpf)
dps = mp.dps
mp.dps = 300
assert isinstance(asin(0.5), mpf)
mp.dps = 1000
assert asin(1).ae(pi/2)
assert asin(-1).ae(-pi/2)
mp.dps = dps
def test_invhyperb_inaccuracy():
mp.dps = 15
assert (asinh(1e-5)*10**5).ae(0.99999999998333333)
assert (asinh(1e-10)*10**10).ae(1)
assert (asinh(1e-50)*10**50).ae(1)
assert (asinh(-1e-5)*10**5).ae(-0.99999999998333333)
assert (asinh(-1e-10)*10**10).ae(-1)
assert (asinh(-1e-50)*10**50).ae(-1)
assert asinh(10**20).ae(46.744849040440862)
assert asinh(-10**20).ae(-46.744849040440862)
assert (tanh(1e-10)*10**10).ae(1)
assert (tanh(-1e-10)*10**10).ae(-1)
assert (atanh(1e-10)*10**10).ae(1)
assert (atanh(-1e-10)*10**10).ae(-1)
def test_complex_functions():
for x in (list(range(10)) + list(range(-10,0))):
for y in (list(range(10)) + list(range(-10,0))):
z = complex(x, y)/4.3 + 0.01j
assert exp(mpc(z)).ae(cmath.exp(z))
assert log(mpc(z)).ae(cmath.log(z))
assert cos(mpc(z)).ae(cmath.cos(z))
assert sin(mpc(z)).ae(cmath.sin(z))
assert tan(mpc(z)).ae(cmath.tan(z))
assert sinh(mpc(z)).ae(cmath.sinh(z))
assert cosh(mpc(z)).ae(cmath.cosh(z))
assert tanh(mpc(z)).ae(cmath.tanh(z))
def test_complex_inverse_functions():
mp.dps = 15
iv.dps = 15
for (z1, z2) in random_complexes(30):
# apparently cmath uses a different branch, so we
# can't use it for comparison
assert sinh(asinh(z1)).ae(z1)
#
assert acosh(z1).ae(cmath.acosh(z1))
assert atanh(z1).ae(cmath.atanh(z1))
assert atan(z1).ae(cmath.atan(z1))
# the reason we set a big eps here is that the cmath
# functions are inaccurate
assert asin(z1).ae(cmath.asin(z1), rel_eps=1e-12)
assert acos(z1).ae(cmath.acos(z1), rel_eps=1e-12)
one = mpf(1)
for i in range(-9, 10, 3):
for k in range(-9, 10, 3):
a = 0.9*j*10**k + 0.8*one*10**i
b = cos(acos(a))
assert b.ae(a)
b = sin(asin(a))
assert b.ae(a)
one = mpf(1)
err = 2*10**-15
for i in range(-9, 9, 3):
for k in range(-9, 9, 3):
a = -0.9*10**k + j*0.8*one*10**i
b = cosh(acosh(a))
assert b.ae(a, err)
b = sinh(asinh(a))
assert b.ae(a, err)
def test_reciprocal_functions():
assert sec(3).ae(-1.01010866590799375)
assert csc(3).ae(7.08616739573718592)
assert cot(3).ae(-7.01525255143453347)
assert sech(3).ae(0.0993279274194332078)
assert csch(3).ae(0.0998215696688227329)
assert coth(3).ae(1.00496982331368917)
assert asec(3).ae(1.23095941734077468)
assert acsc(3).ae(0.339836909454121937)
assert acot(3).ae(0.321750554396642193)
assert asech(0.5).ae(1.31695789692481671)
assert acsch(3).ae(0.327450150237258443)
assert acoth(3).ae(0.346573590279972655)
assert acot(0).ae(1.5707963267948966192)
assert acoth(0).ae(1.5707963267948966192j)
def test_ldexp():
mp.dps = 15
assert ldexp(mpf(2.5), 0) == 2.5
assert ldexp(mpf(2.5), -1) == 1.25
assert ldexp(mpf(2.5), 2) == 10
assert ldexp(mpf('inf'), 3) == mpf('inf')
def test_frexp():
mp.dps = 15
assert frexp(0) == (0.0, 0)
assert frexp(9) == (0.5625, 4)
assert frexp(1) == (0.5, 1)
assert frexp(0.2) == (0.8, -2)
assert frexp(1000) == (0.9765625, 10)
def test_aliases():
assert ln(7) == log(7)
assert log10(3.75) == log(3.75,10)
assert degrees(5.6) == 5.6 / degree
assert radians(5.6) == 5.6 * degree
assert power(-1,0.5) == j
assert fmod(25,7) == 4.0 and isinstance(fmod(25,7), mpf)
def test_arg_sign():
assert arg(3) == 0
assert arg(-3).ae(pi)
assert arg(j).ae(pi/2)
assert arg(-j).ae(-pi/2)
assert arg(0) == 0
assert isnan(atan2(3,nan))
assert isnan(atan2(nan,3))
assert isnan(atan2(0,nan))
assert isnan(atan2(nan,0))
assert isnan(atan2(nan,nan))
assert arg(inf) == 0
assert arg(-inf).ae(pi)
assert isnan(arg(nan))
#assert arg(inf*j).ae(pi/2)
assert sign(0) == 0
assert sign(3) == 1
assert sign(-3) == -1
assert sign(inf) == 1
assert sign(-inf) == -1
assert isnan(sign(nan))
assert sign(j) == j
assert sign(-3*j) == -j
assert sign(1+j).ae((1+j)/sqrt(2))
def test_misc_bugs():
# test that this doesn't raise an exception
mp.dps = 1000
log(1302)
mp.dps = 15
def test_arange():
assert arange(10) == [mpf('0.0'), mpf('1.0'), mpf('2.0'), mpf('3.0'),
mpf('4.0'), mpf('5.0'), mpf('6.0'), mpf('7.0'),
mpf('8.0'), mpf('9.0')]
assert arange(-5, 5) == [mpf('-5.0'), mpf('-4.0'), mpf('-3.0'),
mpf('-2.0'), mpf('-1.0'), mpf('0.0'),
mpf('1.0'), mpf('2.0'), mpf('3.0'), mpf('4.0')]
assert arange(0, 1, 0.1) == [mpf('0.0'), mpf('0.10000000000000001'),
mpf('0.20000000000000001'),
mpf('0.30000000000000004'),
mpf('0.40000000000000002'),
mpf('0.5'), mpf('0.60000000000000009'),
mpf('0.70000000000000007'),
mpf('0.80000000000000004'),
mpf('0.90000000000000002')]
assert arange(17, -9, -3) == [mpf('17.0'), mpf('14.0'), mpf('11.0'),
mpf('8.0'), mpf('5.0'), mpf('2.0'),
mpf('-1.0'), mpf('-4.0'), mpf('-7.0')]
assert arange(0.2, 0.1, -0.1) == [mpf('0.20000000000000001')]
assert arange(0) == []
assert arange(1000, -1) == []
assert arange(-1.23, 3.21, -0.0000001) == []
def test_linspace():
assert linspace(2, 9, 7) == [mpf('2.0'), mpf('3.166666666666667'),
mpf('4.3333333333333339'), mpf('5.5'), mpf('6.666666666666667'),
mpf('7.8333333333333339'), mpf('9.0')]
assert linspace(2, 9, 7, endpoint=0) == [mpf('2.0'), mpf('3.0'), mpf('4.0'),
mpf('5.0'), mpf('6.0'), mpf('7.0'), mpf('8.0')]
assert linspace(2, 7, 1) == [mpf(2)]
def test_float_cbrt():
mp.dps = 30
for a in arange(0,10,0.1):
assert cbrt(a*a*a).ae(a, eps)
assert cbrt(-1).ae(0.5 + j*sqrt(3)/2)
one_third = mpf(1)/3
for a in arange(0,10,2.7) + [0.1 + 10**5]:
a = mpc(a + 1.1j)
r1 = cbrt(a)
mp.dps += 10
r2 = pow(a, one_third)
mp.dps -= 10
assert r1.ae(r2, eps)
mp.dps = 100
for n in range(100, 301, 100):
w = 10**n + j*10**-3
z = w*w*w
r = cbrt(z)
assert mpc_ae(r, w, eps)
mp.dps = 15
def test_root():
mp.dps = 30
random.seed(1)
a = random.randint(0, 10000)
p = a*a*a
r = nthroot(mpf(p), 3)
assert r == a
for n in range(4, 10):
p = p*a
assert nthroot(mpf(p), n) == a
mp.dps = 40
for n in range(10, 5000, 100):
for a in [random.random()*10000, random.random()*10**100]:
r = nthroot(a, n)
r1 = pow(a, mpf(1)/n)
assert r.ae(r1)
r = nthroot(a, -n)
r1 = pow(a, -mpf(1)/n)
assert r.ae(r1)
# XXX: this is broken right now
# tests for nthroot rounding
for rnd in ['nearest', 'up', 'down']:
mp.rounding = rnd
for n in [-5, -3, 3, 5]:
prec = 50
for i in range(10):
mp.prec = prec
a = rand()
mp.prec = 2*prec
b = a**n
mp.prec = prec
r = nthroot(b, n)
assert r == a
mp.dps = 30
for n in range(3, 21):
a = (random.random() + j*random.random())
assert nthroot(a, n).ae(pow(a, mpf(1)/n))
assert mpc_ae(nthroot(a, n), pow(a, mpf(1)/n))
a = (random.random()*10**100 + j*random.random())
r = nthroot(a, n)
mp.dps += 4
r1 = pow(a, mpf(1)/n)
mp.dps -= 4
assert r.ae(r1)
assert mpc_ae(r, r1, eps)
r = nthroot(a, -n)
mp.dps += 4
r1 = pow(a, -mpf(1)/n)
mp.dps -= 4
assert r.ae(r1)
assert mpc_ae(r, r1, eps)
mp.dps = 15
assert nthroot(4, 1) == 4
assert nthroot(4, 0) == 1
assert nthroot(4, -1) == 0.25
assert nthroot(inf, 1) == inf
assert nthroot(inf, 2) == inf
assert nthroot(inf, 3) == inf
assert nthroot(inf, -1) == 0
assert nthroot(inf, -2) == 0
assert nthroot(inf, -3) == 0
assert nthroot(j, 1) == j
assert nthroot(j, 0) == 1
assert nthroot(j, -1) == -j
assert isnan(nthroot(nan, 1))
assert isnan(nthroot(nan, 0))
assert isnan(nthroot(nan, -1))
assert isnan(nthroot(inf, 0))
assert root(2,3) == nthroot(2,3)
assert root(16,4,0) == 2
assert root(16,4,1) == 2j
assert root(16,4,2) == -2
assert root(16,4,3) == -2j
assert root(16,4,4) == 2
assert root(-125,3,1) == -5
def test_issue_136():
for dps in [20, 80]:
mp.dps = dps
r = nthroot(mpf('-1e-20'), 4)
assert r.ae(mpf(10)**(-5) * (1 + j) * mpf(2)**(-0.5))
mp.dps = 80
assert nthroot('-1e-3', 4).ae(mpf(10)**(-3./4) * (1 + j)/sqrt(2))
assert nthroot('-1e-6', 4).ae((1 + j)/(10 * sqrt(20)))
# Check that this doesn't take eternity to compute
mp.dps = 20
assert nthroot('-1e100000000', 4).ae((1+j)*mpf('1e25000000')/sqrt(2))
mp.dps = 15
def test_mpcfun_real_imag():
mp.dps = 15
x = mpf(0.3)
y = mpf(0.4)
assert exp(mpc(x,0)) == exp(x)
assert exp(mpc(0,y)) == mpc(cos(y),sin(y))
assert cos(mpc(x,0)) == cos(x)
assert sin(mpc(x,0)) == sin(x)
assert cos(mpc(0,y)) == cosh(y)
assert sin(mpc(0,y)) == mpc(0,sinh(y))
assert cospi(mpc(x,0)) == cospi(x)
assert sinpi(mpc(x,0)) == sinpi(x)
assert cospi(mpc(0,y)).ae(cosh(pi*y))
assert sinpi(mpc(0,y)).ae(mpc(0,sinh(pi*y)))
c, s = cospi_sinpi(mpc(x,0))
assert c == cospi(x)
assert s == sinpi(x)
c, s = cospi_sinpi(mpc(0,y))
assert c.ae(cosh(pi*y))
assert s.ae(mpc(0,sinh(pi*y)))
c, s = cos_sin(mpc(x,0))
assert c == cos(x)
assert s == sin(x)
c, s = cos_sin(mpc(0,y))
assert c == cosh(y)
assert s == mpc(0,sinh(y))
def test_perturbation_rounding():
mp.dps = 100
a = pi/10**50
b = -pi/10**50
c = 1 + a
d = 1 + b
mp.dps = 15
assert exp(a) == 1
assert exp(a, rounding='c') > 1
assert exp(b, rounding='c') == 1
assert exp(a, rounding='f') == 1
assert exp(b, rounding='f') < 1
assert cos(a) == 1
assert cos(a, rounding='c') == 1
assert cos(b, rounding='c') == 1
assert cos(a, rounding='f') < 1
assert cos(b, rounding='f') < 1
for f in [sin, atan, asinh, tanh]:
assert f(a) == +a
assert f(a, rounding='c') > a
assert f(a, rounding='f') < a
assert f(b) == +b
assert f(b, rounding='c') > b
assert f(b, rounding='f') < b
for f in [asin, tan, sinh, atanh]:
assert f(a) == +a
assert f(b) == +b
assert f(a, rounding='c') > a
assert f(b, rounding='c') > b
assert f(a, rounding='f') < a
assert f(b, rounding='f') < b
assert ln(c) == +a
assert ln(d) == +b
assert ln(c, rounding='c') > a
assert ln(c, rounding='f') < a
assert ln(d, rounding='c') > b
assert ln(d, rounding='f') < b
assert cosh(a) == 1
assert cosh(b) == 1
assert cosh(a, rounding='c') > 1
assert cosh(b, rounding='c') > 1
assert cosh(a, rounding='f') == 1
assert cosh(b, rounding='f') == 1
def test_integer_parts():
assert floor(3.2) == 3
assert ceil(3.2) == 4
assert floor(3.2+5j) == 3+5j
assert ceil(3.2+5j) == 4+5j
def test_complex_parts():
assert fabs('3') == 3
assert fabs(3+4j) == 5
assert re(3) == 3
assert re(1+4j) == 1
assert im(3) == 0
assert im(1+4j) == 4
assert conj(3) == 3
assert conj(3+4j) == 3-4j
assert mpf(3).conjugate() == 3
def test_cospi_sinpi():
assert sinpi(0) == 0
assert sinpi(0.5) == 1
assert sinpi(1) == 0
assert sinpi(1.5) == -1
assert sinpi(2) == 0
assert sinpi(2.5) == 1
assert sinpi(-0.5) == -1
assert cospi(0) == 1
assert cospi(0.5) == 0
assert cospi(1) == -1
assert cospi(1.5) == 0
assert cospi(2) == 1
assert cospi(2.5) == 0
assert cospi(-0.5) == 0
assert cospi(100000000000.25).ae(sqrt(2)/2)
a = cospi(2+3j)
assert a.real.ae(cos((2+3j)*pi).real)
assert a.imag == 0
b = sinpi(2+3j)
assert b.imag.ae(sin((2+3j)*pi).imag)
assert b.real == 0
mp.dps = 35
x1 = mpf(10000) - mpf('1e-15')
x2 = mpf(10000) + mpf('1e-15')
x3 = mpf(10000.5) - mpf('1e-15')
x4 = mpf(10000.5) + mpf('1e-15')
x5 = mpf(10001) - mpf('1e-15')
x6 = mpf(10001) + mpf('1e-15')
x7 = mpf(10001.5) - mpf('1e-15')
x8 = mpf(10001.5) + mpf('1e-15')
mp.dps = 15
M = 10**15
assert (sinpi(x1)*M).ae(-pi)
assert (sinpi(x2)*M).ae(pi)
assert (cospi(x3)*M).ae(pi)
assert (cospi(x4)*M).ae(-pi)
assert (sinpi(x5)*M).ae(pi)
assert (sinpi(x6)*M).ae(-pi)
assert (cospi(x7)*M).ae(-pi)
assert (cospi(x8)*M).ae(pi)
assert 0.999 < cospi(x1, rounding='d') < 1
assert 0.999 < cospi(x2, rounding='d') < 1
assert 0.999 < sinpi(x3, rounding='d') < 1
assert 0.999 < sinpi(x4, rounding='d') < 1
assert -1 < cospi(x5, rounding='d') < -0.999
assert -1 < cospi(x6, rounding='d') < -0.999
assert -1 < sinpi(x7, rounding='d') < -0.999
assert -1 < sinpi(x8, rounding='d') < -0.999
assert (sinpi(1e-15)*M).ae(pi)
assert (sinpi(-1e-15)*M).ae(-pi)
assert cospi(1e-15) == 1
assert cospi(1e-15, rounding='d') < 1
def test_expj():
assert expj(0) == 1
assert expj(1).ae(exp(j))
assert expj(j).ae(exp(-1))
assert expj(1+j).ae(exp(j*(1+j)))
assert expjpi(0) == 1
assert expjpi(1).ae(exp(j*pi))
assert expjpi(j).ae(exp(-pi))
assert expjpi(1+j).ae(exp(j*pi*(1+j)))
assert expjpi(-10**15 * j).ae('2.22579818340535731e+1364376353841841')
def test_sinc():
assert sinc(0) == sincpi(0) == 1
assert sinc(inf) == sincpi(inf) == 0
assert sinc(-inf) == sincpi(-inf) == 0
assert sinc(2).ae(0.45464871341284084770)
assert sinc(2+3j).ae(0.4463290318402435457-2.7539470277436474940j)
assert sincpi(2) == 0
assert sincpi(1.5).ae(-0.212206590789193781)
def test_fibonacci():
mp.dps = 15
assert [fibonacci(n) for n in range(-5, 10)] == \
[5, -3, 2, -1, 1, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34]
assert fib(2.5).ae(1.4893065462657091)
assert fib(3+4j).ae(-5248.51130728372 - 14195.962288353j)
assert fib(1000).ae(4.3466557686937455e+208)
assert str(fib(10**100)) == '6.24499112864607e+2089876402499787337692720892375554168224592399182109535392875613974104853496745963277658556235103534'
mp.dps = 2100
a = fib(10000)
assert a % 10**10 == 9947366875
mp.dps = 15
assert fibonacci(inf) == inf
assert fib(3+0j) == 2
def test_call_with_dps():
mp.dps = 15
assert abs(exp(1, dps=30)-e(dps=35)) < 1e-29
def test_tanh():
mp.dps = 15
assert tanh(0) == 0
assert tanh(inf) == 1
assert tanh(-inf) == -1
assert isnan(tanh(nan))
assert tanh(mpc('inf', '0')) == 1
def test_atanh():
mp.dps = 15
assert atanh(0) == 0
assert atanh(0.5).ae(0.54930614433405484570)
assert atanh(-0.5).ae(-0.54930614433405484570)
assert atanh(1) == inf
assert atanh(-1) == -inf
assert isnan(atanh(nan))
assert isinstance(atanh(1), mpf)
assert isinstance(atanh(-1), mpf)
# Limits at infinity
jpi2 = j*pi/2
assert atanh(inf).ae(-jpi2)
assert atanh(-inf).ae(jpi2)
assert atanh(mpc(inf,-1)).ae(-jpi2)
assert atanh(mpc(inf,0)).ae(-jpi2)
assert atanh(mpc(inf,1)).ae(jpi2)
assert atanh(mpc(1,inf)).ae(jpi2)
assert atanh(mpc(0,inf)).ae(jpi2)
assert atanh(mpc(-1,inf)).ae(jpi2)
assert atanh(mpc(-inf,1)).ae(jpi2)
assert atanh(mpc(-inf,0)).ae(jpi2)
assert atanh(mpc(-inf,-1)).ae(-jpi2)
assert atanh(mpc(-1,-inf)).ae(-jpi2)
assert atanh(mpc(0,-inf)).ae(-jpi2)
assert atanh(mpc(1,-inf)).ae(-jpi2)
def test_expm1():
mp.dps = 15
assert expm1(0) == 0
assert expm1(3).ae(exp(3)-1)
assert expm1(inf) == inf
assert expm1(1e-10)*1e10
assert expm1(1e-50).ae(1e-50)
assert (expm1(1e-10)*1e10).ae(1.00000000005)
def test_powm1():
mp.dps = 15
assert powm1(2,3) == 7
assert powm1(-1,2) == 0
assert powm1(-1,0) == 0
assert powm1(-2,0) == 0
assert powm1(3+4j,0) == 0
assert powm1(0,1) == -1
assert powm1(0,0) == 0
assert powm1(1,0) == 0
assert powm1(1,2) == 0
assert powm1(1,3+4j) == 0
assert powm1(1,5) == 0
assert powm1(j,4) == 0
assert powm1(-j,4) == 0
assert (powm1(2,1e-100)*1e100).ae(ln2)
assert powm1(2,'1e-100000000000') != 0
assert (powm1(fadd(1,1e-100,exact=True), 5)*1e100).ae(5)
def test_unitroots():
assert unitroots(1) == [1]
assert unitroots(2) == [1, -1]
a, b, c = unitroots(3)
assert a == 1
assert b.ae(-0.5 + 0.86602540378443864676j)
assert c.ae(-0.5 - 0.86602540378443864676j)
assert unitroots(1, primitive=True) == [1]
assert unitroots(2, primitive=True) == [-1]
assert unitroots(3, primitive=True) == unitroots(3)[1:]
assert unitroots(4, primitive=True) == [j, -j]
assert len(unitroots(17, primitive=True)) == 16
assert len(unitroots(16, primitive=True)) == 8
def test_cyclotomic():
mp.dps = 15
assert [cyclotomic(n,1) for n in range(31)] == [1,0,2,3,2,5,1,7,2,3,1,11,1,13,1,1,2,17,1,19,1,1,1,23,1,5,1,3,1,29,1]
assert [cyclotomic(n,-1) for n in range(31)] == [1,-2,0,1,2,1,3,1,2,1,5,1,1,1,7,1,2,1,3,1,1,1,11,1,1,1,13,1,1,1,1]
assert [cyclotomic(n,j) for n in range(21)] == [1,-1+j,1+j,j,0,1,-j,j,2,-j,1,j,3,1,-j,1,2,1,j,j,5]
assert [cyclotomic(n,-j) for n in range(21)] == [1,-1-j,1-j,-j,0,1,j,-j,2,j,1,-j,3,1,j,1,2,1,-j,-j,5]
assert cyclotomic(1624,j) == 1
assert cyclotomic(33600,j) == 1
u = sqrt(j, prec=500)
assert cyclotomic(8, u).ae(0)
assert cyclotomic(30, u).ae(5.8284271247461900976)
assert cyclotomic(2040, u).ae(1)
assert cyclotomic(0,2.5) == 1
assert cyclotomic(1,2.5) == 2.5-1
assert cyclotomic(2,2.5) == 2.5+1
assert cyclotomic(3,2.5) == 2.5**2 + 2.5 + 1
assert cyclotomic(7,2.5) == 406.234375
| 30,779 | 32.676149 | 152 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/tests/test_levin.py
|
#!/usr/bin/python
# -*- coding: utf-8 -*-
from mpmath import mp
from mpmath import libmp
xrange = libmp.backend.xrange
# Attention:
# These tests run with 15-20 decimal digits precision. For higher precision the
# working precision must be raised.
def test_levin_0():
mp.dps = 17
eps = mp.mpf(mp.eps)
with mp.extraprec(2 * mp.prec):
L = mp.levin(method = "levin", variant = "u")
S, s, n = [], 0, 1
while 1:
s += mp.one / (n * n)
n += 1
S.append(s)
v, e = L.update_psum(S)
if e < eps:
break
if n > 1000: raise RuntimeError("iteration limit exceeded")
eps = mp.exp(0.9 * mp.log(eps))
err = abs(v - mp.pi ** 2 / 6)
assert err < eps
w = mp.nsum(lambda n: 1/(n * n), [1, mp.inf], method = "levin", levin_variant = "u")
err = abs(v - w)
assert err < eps
def test_levin_1():
mp.dps = 17
eps = mp.mpf(mp.eps)
with mp.extraprec(2 * mp.prec):
L = mp.levin(method = "levin", variant = "v")
A, n = [], 1
while 1:
s = mp.mpf(n) ** (2 + 3j)
n += 1
A.append(s)
v, e = L.update(A)
if e < eps:
break
if n > 1000: raise RuntimeError("iteration limit exceeded")
eps = mp.exp(0.9 * mp.log(eps))
err = abs(v - mp.zeta(-2-3j))
assert err < eps
w = mp.nsum(lambda n: n ** (2 + 3j), [1, mp.inf], method = "levin", levin_variant = "v")
err = abs(v - w)
assert err < eps
def test_levin_2():
# [2] A. Sidi - "Pratical Extrapolation Methods" p.373
mp.dps = 17
z=mp.mpf(10)
eps = mp.mpf(mp.eps)
with mp.extraprec(2 * mp.prec):
L = mp.levin(method = "sidi", variant = "t")
n = 0
while 1:
s = (-1)**n * mp.fac(n) * z ** (-n)
v, e = L.step(s)
n += 1
if e < eps:
break
if n > 1000: raise RuntimeError("iteration limit exceeded")
eps = mp.exp(0.9 * mp.log(eps))
exact = mp.quad(lambda x: mp.exp(-x)/(1+x/z),[0,mp.inf])
# there is also a symbolic expression for the integral:
# exact = z * mp.exp(z) * mp.expint(1,z)
err = abs(v - exact)
assert err < eps
w = mp.nsum(lambda n: (-1) ** n * mp.fac(n) * z ** (-n), [0, mp.inf], method = "sidi", levin_variant = "t")
assert err < eps
def test_levin_3():
mp.dps = 17
z=mp.mpf(2)
eps = mp.mpf(mp.eps)
with mp.extraprec(7*mp.prec): # we need copious amount of precision to sum this highly divergent series
L = mp.levin(method = "levin", variant = "t")
n, s = 0, 0
while 1:
s += (-z)**n * mp.fac(4 * n) / (mp.fac(n) * mp.fac(2 * n) * (4 ** n))
n += 1
v, e = L.step_psum(s)
if e < eps:
break
if n > 1000: raise RuntimeError("iteration limit exceeded")
eps = mp.exp(0.8 * mp.log(eps))
exact = mp.quad(lambda x: mp.exp( -x * x / 2 - z * x ** 4), [0,mp.inf]) * 2 / mp.sqrt(2 * mp.pi)
# there is also a symbolic expression for the integral:
# exact = mp.exp(mp.one / (32 * z)) * mp.besselk(mp.one / 4, mp.one / (32 * z)) / (4 * mp.sqrt(z * mp.pi))
err = abs(v - exact)
assert err < eps
w = mp.nsum(lambda n: (-z)**n * mp.fac(4 * n) / (mp.fac(n) * mp.fac(2 * n) * (4 ** n)), [0, mp.inf], method = "levin", levin_variant = "t", workprec = 8*mp.prec, steps = [2] + [1 for x in xrange(1000)])
err = abs(v - w)
assert err < eps
def test_levin_nsum():
mp.dps = 17
with mp.extraprec(mp.prec):
z = mp.mpf(10) ** (-10)
a = mp.nsum(lambda n: n**(-(1+z)), [1, mp.inf], method = "l") - 1 / z
assert abs(a - mp.euler) < 1e-10
eps = mp.exp(0.8 * mp.log(mp.eps))
a = mp.nsum(lambda n: (-1)**(n-1) / n, [1, mp.inf], method = "sidi")
assert abs(a - mp.log(2)) < eps
z = 2 + 1j
f = lambda n: mp.rf(2 / mp.mpf(3), n) * mp.rf(4 / mp.mpf(3), n) * z**n / (mp.rf(1 / mp.mpf(3), n) * mp.fac(n))
v = mp.nsum(f, [0, mp.inf], method = "levin", steps = [10 for x in xrange(1000)])
exact = mp.hyp2f1(2 / mp.mpf(3), 4 / mp.mpf(3), 1 / mp.mpf(3), z)
assert abs(exact - v) < eps
def test_cohen_alt_0():
mp.dps = 17
AC = mp.cohen_alt()
S, s, n = [], 0, 1
while 1:
s += -((-1) ** n) * mp.one / (n * n)
n += 1
S.append(s)
v, e = AC.update_psum(S)
if e < mp.eps:
break
if n > 1000: raise RuntimeError("iteration limit exceeded")
eps = mp.exp(0.9 * mp.log(mp.eps))
err = abs(v - mp.pi ** 2 / 12)
assert err < eps
def test_cohen_alt_1():
mp.dps = 17
A = []
AC = mp.cohen_alt()
n = 1
while 1:
A.append( mp.loggamma(1 + mp.one / (2 * n - 1)))
A.append(-mp.loggamma(1 + mp.one / (2 * n)))
n += 1
v, e = AC.update(A)
if e < mp.eps:
break
if n > 1000: raise RuntimeError("iteration limit exceeded")
v = mp.exp(v)
err = abs(v - 1.06215090557106)
assert err < 1e-12
| 5,090 | 32.058442 | 206 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/tests/test_gammazeta.py
|
from mpmath import *
from mpmath.libmp import round_up, from_float, mpf_zeta_int
def test_zeta_int_bug():
assert mpf_zeta_int(0, 10) == from_float(-0.5)
def test_bernoulli():
assert bernfrac(0) == (1,1)
assert bernfrac(1) == (-1,2)
assert bernfrac(2) == (1,6)
assert bernfrac(3) == (0,1)
assert bernfrac(4) == (-1,30)
assert bernfrac(5) == (0,1)
assert bernfrac(6) == (1,42)
assert bernfrac(8) == (-1,30)
assert bernfrac(10) == (5,66)
assert bernfrac(12) == (-691,2730)
assert bernfrac(18) == (43867,798)
p, q = bernfrac(228)
assert p % 10**10 == 164918161
assert q == 625170
p, q = bernfrac(1000)
assert p % 10**10 == 7950421099
assert q == 342999030
mp.dps = 15
assert bernoulli(0) == 1
assert bernoulli(1) == -0.5
assert bernoulli(2).ae(1./6)
assert bernoulli(3) == 0
assert bernoulli(4).ae(-1./30)
assert bernoulli(5) == 0
assert bernoulli(6).ae(1./42)
assert str(bernoulli(10)) == '0.0757575757575758'
assert str(bernoulli(234)) == '7.62772793964344e+267'
assert str(bernoulli(10**5)) == '-5.82229431461335e+376755'
assert str(bernoulli(10**8+2)) == '1.19570355039953e+676752584'
mp.dps = 50
assert str(bernoulli(10)) == '0.075757575757575757575757575757575757575757575757576'
assert str(bernoulli(234)) == '7.6277279396434392486994969020496121553385863373331e+267'
assert str(bernoulli(10**5)) == '-5.8222943146133508236497045360612887555320691004308e+376755'
assert str(bernoulli(10**8+2)) == '1.1957035503995297272263047884604346914602088317782e+676752584'
mp.dps = 1000
assert bernoulli(10).ae(mpf(5)/66)
mp.dps = 50000
assert bernoulli(10).ae(mpf(5)/66)
mp.dps = 15
def test_bernpoly_eulerpoly():
mp.dps = 15
assert bernpoly(0,-1).ae(1)
assert bernpoly(0,0).ae(1)
assert bernpoly(0,'1/2').ae(1)
assert bernpoly(0,'3/4').ae(1)
assert bernpoly(0,1).ae(1)
assert bernpoly(0,2).ae(1)
assert bernpoly(1,-1).ae('-3/2')
assert bernpoly(1,0).ae('-1/2')
assert bernpoly(1,'1/2').ae(0)
assert bernpoly(1,'3/4').ae('1/4')
assert bernpoly(1,1).ae('1/2')
assert bernpoly(1,2).ae('3/2')
assert bernpoly(2,-1).ae('13/6')
assert bernpoly(2,0).ae('1/6')
assert bernpoly(2,'1/2').ae('-1/12')
assert bernpoly(2,'3/4').ae('-1/48')
assert bernpoly(2,1).ae('1/6')
assert bernpoly(2,2).ae('13/6')
assert bernpoly(3,-1).ae(-3)
assert bernpoly(3,0).ae(0)
assert bernpoly(3,'1/2').ae(0)
assert bernpoly(3,'3/4').ae('-3/64')
assert bernpoly(3,1).ae(0)
assert bernpoly(3,2).ae(3)
assert bernpoly(4,-1).ae('119/30')
assert bernpoly(4,0).ae('-1/30')
assert bernpoly(4,'1/2').ae('7/240')
assert bernpoly(4,'3/4').ae('7/3840')
assert bernpoly(4,1).ae('-1/30')
assert bernpoly(4,2).ae('119/30')
assert bernpoly(5,-1).ae(-5)
assert bernpoly(5,0).ae(0)
assert bernpoly(5,'1/2').ae(0)
assert bernpoly(5,'3/4').ae('25/1024')
assert bernpoly(5,1).ae(0)
assert bernpoly(5,2).ae(5)
assert bernpoly(10,-1).ae('665/66')
assert bernpoly(10,0).ae('5/66')
assert bernpoly(10,'1/2').ae('-2555/33792')
assert bernpoly(10,'3/4').ae('-2555/34603008')
assert bernpoly(10,1).ae('5/66')
assert bernpoly(10,2).ae('665/66')
assert bernpoly(11,-1).ae(-11)
assert bernpoly(11,0).ae(0)
assert bernpoly(11,'1/2').ae(0)
assert bernpoly(11,'3/4').ae('-555731/4194304')
assert bernpoly(11,1).ae(0)
assert bernpoly(11,2).ae(11)
assert eulerpoly(0,-1).ae(1)
assert eulerpoly(0,0).ae(1)
assert eulerpoly(0,'1/2').ae(1)
assert eulerpoly(0,'3/4').ae(1)
assert eulerpoly(0,1).ae(1)
assert eulerpoly(0,2).ae(1)
assert eulerpoly(1,-1).ae('-3/2')
assert eulerpoly(1,0).ae('-1/2')
assert eulerpoly(1,'1/2').ae(0)
assert eulerpoly(1,'3/4').ae('1/4')
assert eulerpoly(1,1).ae('1/2')
assert eulerpoly(1,2).ae('3/2')
assert eulerpoly(2,-1).ae(2)
assert eulerpoly(2,0).ae(0)
assert eulerpoly(2,'1/2').ae('-1/4')
assert eulerpoly(2,'3/4').ae('-3/16')
assert eulerpoly(2,1).ae(0)
assert eulerpoly(2,2).ae(2)
assert eulerpoly(3,-1).ae('-9/4')
assert eulerpoly(3,0).ae('1/4')
assert eulerpoly(3,'1/2').ae(0)
assert eulerpoly(3,'3/4').ae('-11/64')
assert eulerpoly(3,1).ae('-1/4')
assert eulerpoly(3,2).ae('9/4')
assert eulerpoly(4,-1).ae(2)
assert eulerpoly(4,0).ae(0)
assert eulerpoly(4,'1/2').ae('5/16')
assert eulerpoly(4,'3/4').ae('57/256')
assert eulerpoly(4,1).ae(0)
assert eulerpoly(4,2).ae(2)
assert eulerpoly(5,-1).ae('-3/2')
assert eulerpoly(5,0).ae('-1/2')
assert eulerpoly(5,'1/2').ae(0)
assert eulerpoly(5,'3/4').ae('361/1024')
assert eulerpoly(5,1).ae('1/2')
assert eulerpoly(5,2).ae('3/2')
assert eulerpoly(10,-1).ae(2)
assert eulerpoly(10,0).ae(0)
assert eulerpoly(10,'1/2').ae('-50521/1024')
assert eulerpoly(10,'3/4').ae('-36581523/1048576')
assert eulerpoly(10,1).ae(0)
assert eulerpoly(10,2).ae(2)
assert eulerpoly(11,-1).ae('-699/4')
assert eulerpoly(11,0).ae('691/4')
assert eulerpoly(11,'1/2').ae(0)
assert eulerpoly(11,'3/4').ae('-512343611/4194304')
assert eulerpoly(11,1).ae('-691/4')
assert eulerpoly(11,2).ae('699/4')
# Potential accuracy issues
assert bernpoly(10000,10000).ae('5.8196915936323387117e+39999')
assert bernpoly(200,17.5).ae(3.8048418524583064909e244)
assert eulerpoly(200,17.5).ae(-3.7309911582655785929e275)
def test_gamma():
mp.dps = 15
assert gamma(0.25).ae(3.6256099082219083119)
assert gamma(0.0001).ae(9999.4228832316241908)
assert gamma(300).ae('1.0201917073881354535e612')
assert gamma(-0.5).ae(-3.5449077018110320546)
assert gamma(-7.43).ae(0.00026524416464197007186)
#assert gamma(Rational(1,2)) == gamma(0.5)
#assert gamma(Rational(-7,3)).ae(gamma(mpf(-7)/3))
assert gamma(1+1j).ae(0.49801566811835604271 - 0.15494982830181068512j)
assert gamma(-1+0.01j).ae(-0.422733904013474115 + 99.985883082635367436j)
assert gamma(20+30j).ae(-1453876687.5534810 + 1163777777.8031573j)
# Should always give exact factorials when they can
# be represented as mpfs under the current working precision
fact = 1
for i in range(1, 18):
assert gamma(i) == fact
fact *= i
for dps in [170, 600]:
fact = 1
mp.dps = dps
for i in range(1, 105):
assert gamma(i) == fact
fact *= i
mp.dps = 100
assert gamma(0.5).ae(sqrt(pi))
mp.dps = 15
assert factorial(0) == fac(0) == 1
assert factorial(3) == 6
assert isnan(gamma(nan))
assert gamma(1100).ae('4.8579168073569433667e2866')
assert rgamma(0) == 0
assert rgamma(-1) == 0
assert rgamma(2) == 1.0
assert rgamma(3) == 0.5
assert loggamma(2+8j).ae(-8.5205176753667636926 + 10.8569497125597429366j)
assert loggamma('1e10000').ae('2.302485092994045684017991e10004')
assert loggamma('1e10000j').ae(mpc('-1.570796326794896619231322e10000','2.302485092994045684017991e10004'))
def test_fac2():
mp.dps = 15
assert [fac2(n) for n in range(10)] == [1,1,2,3,8,15,48,105,384,945]
assert fac2(-5).ae(1./3)
assert fac2(-11).ae(-1./945)
assert fac2(50).ae(5.20469842636666623e32)
assert fac2(0.5+0.75j).ae(0.81546769394688069176-0.34901016085573266889j)
assert fac2(inf) == inf
assert isnan(fac2(-inf))
def test_gamma_quotients():
mp.dps = 15
h = 1e-8
ep = 1e-4
G = gamma
assert gammaprod([-1],[-3,-4]) == 0
assert gammaprod([-1,0],[-5]) == inf
assert abs(gammaprod([-1],[-2]) - G(-1+h)/G(-2+h)) < 1e-4
assert abs(gammaprod([-4,-3],[-2,0]) - G(-4+h)*G(-3+h)/G(-2+h)/G(0+h)) < 1e-4
assert rf(3,0) == 1
assert rf(2.5,1) == 2.5
assert rf(-5,2) == 20
assert rf(j,j).ae(gamma(2*j)/gamma(j))
assert ff(-2,0) == 1
assert ff(-2,1) == -2
assert ff(4,3) == 24
assert ff(3,4) == 0
assert binomial(0,0) == 1
assert binomial(1,0) == 1
assert binomial(0,-1) == 0
assert binomial(3,2) == 3
assert binomial(5,2) == 10
assert binomial(5,3) == 10
assert binomial(5,5) == 1
assert binomial(-1,0) == 1
assert binomial(-2,-4) == 3
assert binomial(4.5, 1.5) == 6.5625
assert binomial(1100,1) == 1100
assert binomial(1100,2) == 604450
assert beta(1,1) == 1
assert beta(0,0) == inf
assert beta(3,0) == inf
assert beta(-1,-1) == inf
assert beta(1.5,1).ae(2/3.)
assert beta(1.5,2.5).ae(pi/16)
assert (10**15*beta(10,100)).ae(2.3455339739604649879)
assert beta(inf,inf) == 0
assert isnan(beta(-inf,inf))
assert isnan(beta(-3,inf))
assert isnan(beta(0,inf))
assert beta(inf,0.5) == beta(0.5,inf) == 0
assert beta(inf,-1.5) == inf
assert beta(inf,-0.5) == -inf
assert beta(1+2j,-1-j/2).ae(1.16396542451069943086+0.08511695947832914640j)
assert beta(-0.5,0.5) == 0
assert beta(-3,3).ae(-1/3.)
def test_zeta():
mp.dps = 15
assert zeta(2).ae(pi**2 / 6)
assert zeta(2.0).ae(pi**2 / 6)
assert zeta(mpc(2)).ae(pi**2 / 6)
assert zeta(100).ae(1)
assert zeta(0).ae(-0.5)
assert zeta(0.5).ae(-1.46035450880958681)
assert zeta(-1).ae(-mpf(1)/12)
assert zeta(-2) == 0
assert zeta(-3).ae(mpf(1)/120)
assert zeta(-4) == 0
assert zeta(-100) == 0
assert isnan(zeta(nan))
assert zeta(1e-30).ae(-0.5)
assert zeta(-1e-30).ae(-0.5)
# Zeros in the critical strip
assert zeta(mpc(0.5, 14.1347251417346937904)).ae(0)
assert zeta(mpc(0.5, 21.0220396387715549926)).ae(0)
assert zeta(mpc(0.5, 25.0108575801456887632)).ae(0)
assert zeta(mpc(1e-30,1e-40)).ae(-0.5)
assert zeta(mpc(-1e-30,1e-40)).ae(-0.5)
mp.dps = 50
im = '236.5242296658162058024755079556629786895294952121891237'
assert zeta(mpc(0.5, im)).ae(0, 1e-46)
mp.dps = 15
# Complex reflection formula
assert (zeta(-60+3j) / 10**34).ae(8.6270183987866146+15.337398548226238j)
# issue #358
assert zeta(0,0.5) == 0
assert zeta(0,0) == 0.5
assert zeta(0,0.5,1).ae(-0.34657359027997265)
def test_altzeta():
mp.dps = 15
assert altzeta(-2) == 0
assert altzeta(-4) == 0
assert altzeta(-100) == 0
assert altzeta(0) == 0.5
assert altzeta(-1) == 0.25
assert altzeta(-3) == -0.125
assert altzeta(-5) == 0.25
assert altzeta(-21) == 1180529130.25
assert altzeta(1).ae(log(2))
assert altzeta(2).ae(pi**2/12)
assert altzeta(10).ae(73*pi**10/6842880)
assert altzeta(50) < 1
assert altzeta(60, rounding='d') < 1
assert altzeta(60, rounding='u') == 1
assert altzeta(10000, rounding='d') < 1
assert altzeta(10000, rounding='u') == 1
assert altzeta(3+0j) == altzeta(3)
s = 3+4j
assert altzeta(s).ae((1-2**(1-s))*zeta(s))
s = -3+4j
assert altzeta(s).ae((1-2**(1-s))*zeta(s))
assert altzeta(-100.5).ae(4.58595480083585913e+108)
assert altzeta(1.3).ae(0.73821404216623045)
assert altzeta(1e-30).ae(0.5)
assert altzeta(-1e-30).ae(0.5)
assert altzeta(mpc(1e-30,1e-40)).ae(0.5)
assert altzeta(mpc(-1e-30,1e-40)).ae(0.5)
def test_zeta_huge():
mp.dps = 15
assert zeta(inf) == 1
mp.dps = 50
assert zeta(100).ae('1.0000000000000000000000000000007888609052210118073522')
assert zeta(40*pi).ae('1.0000000000000000000000000000000000000148407238666182')
mp.dps = 10000
v = zeta(33000)
mp.dps = 15
assert str(v-1) == '1.02363019598118e-9934'
assert zeta(pi*1000, rounding=round_up) > 1
assert zeta(3000, rounding=round_up) > 1
assert zeta(pi*1000) == 1
assert zeta(3000) == 1
def test_zeta_negative():
mp.dps = 150
a = -pi*10**40
mp.dps = 15
assert str(zeta(a)) == '2.55880492708712e+1233536161668617575553892558646631323374078'
mp.dps = 50
assert str(zeta(a)) == '2.5588049270871154960875033337384432038436330847333e+1233536161668617575553892558646631323374078'
mp.dps = 15
def test_polygamma():
mp.dps = 15
psi0 = lambda z: psi(0,z)
psi1 = lambda z: psi(1,z)
assert psi0(3) == psi(0,3) == digamma(3)
#assert psi2(3) == psi(2,3) == tetragamma(3)
#assert psi3(3) == psi(3,3) == pentagamma(3)
assert psi0(pi).ae(0.97721330794200673)
assert psi0(-pi).ae(7.8859523853854902)
assert psi0(-pi+1).ae(7.5676424992016996)
assert psi0(pi+j).ae(1.04224048313859376 + 0.35853686544063749j)
assert psi0(-pi-j).ae(1.3404026194821986 - 2.8824392476809402j)
assert findroot(psi0, 1).ae(1.4616321449683622)
assert psi0(inf) == inf
assert psi1(inf) == 0
assert psi(2,inf) == 0
assert psi1(pi).ae(0.37424376965420049)
assert psi1(-pi).ae(53.030438740085385)
assert psi1(pi+j).ae(0.32935710377142464 - 0.12222163911221135j)
assert psi1(-pi-j).ae(-0.30065008356019703 + 0.01149892486928227j)
assert (10**6*psi(4,1+10*pi*j)).ae(-6.1491803479004446 - 0.3921316371664063j)
assert psi0(1+10*pi*j).ae(3.4473994217222650 + 1.5548808324857071j)
assert isnan(psi0(nan))
assert isnan(psi0(-inf))
assert psi0(-100.5).ae(4.615124601338064)
assert psi0(3+0j).ae(psi0(3))
assert psi0(-100+3j).ae(4.6106071768714086321+3.1117510556817394626j)
assert isnan(psi(2,mpc(0,inf)))
assert isnan(psi(2,mpc(0,nan)))
assert isnan(psi(2,mpc(0,-inf)))
assert isnan(psi(2,mpc(1,inf)))
assert isnan(psi(2,mpc(1,nan)))
assert isnan(psi(2,mpc(1,-inf)))
assert isnan(psi(2,mpc(inf,inf)))
assert isnan(psi(2,mpc(nan,nan)))
assert isnan(psi(2,mpc(-inf,-inf)))
def test_polygamma_high_prec():
mp.dps = 100
assert str(psi(0,pi)) == "0.9772133079420067332920694864061823436408346099943256380095232865318105924777141317302075654362928734"
assert str(psi(10,pi)) == "-12.98876181434889529310283769414222588307175962213707170773803550518307617769657562747174101900659238"
def test_polygamma_identities():
mp.dps = 15
psi0 = lambda z: psi(0,z)
psi1 = lambda z: psi(1,z)
psi2 = lambda z: psi(2,z)
assert psi0(0.5).ae(-euler-2*log(2))
assert psi0(1).ae(-euler)
assert psi1(0.5).ae(0.5*pi**2)
assert psi1(1).ae(pi**2/6)
assert psi1(0.25).ae(pi**2 + 8*catalan)
assert psi2(1).ae(-2*apery)
mp.dps = 20
u = -182*apery+4*sqrt(3)*pi**3
mp.dps = 15
assert psi(2,5/6.).ae(u)
assert psi(3,0.5).ae(pi**4)
def test_foxtrot_identity():
# A test of the complex digamma function.
# See http://mathworld.wolfram.com/FoxTrotSeries.html and
# http://mathworld.wolfram.com/DigammaFunction.html
psi0 = lambda z: psi(0,z)
mp.dps = 50
a = (-1)**fraction(1,3)
b = (-1)**fraction(2,3)
x = -psi0(0.5*a) - psi0(-0.5*b) + psi0(0.5*(1+a)) + psi0(0.5*(1-b))
y = 2*pi*sech(0.5*sqrt(3)*pi)
assert x.ae(y)
mp.dps = 15
def test_polygamma_high_order():
mp.dps = 100
assert str(psi(50, pi)) == "-1344100348958402765749252447726432491812.641985273160531055707095989227897753035823152397679626136483"
assert str(psi(50, pi + 14*e)) == "-0.00000000000000000189793739550804321623512073101895801993019919886375952881053090844591920308111549337295143780341396"
assert str(psi(50, pi + 14*e*j)) == ("(-0.0000000000000000522516941152169248975225472155683565752375889510631513244785"
"9377385233700094871256507814151956624433 - 0.00000000000000001813157041407010184"
"702414110218205348527862196327980417757665282244728963891298080199341480881811613j)")
mp.dps = 15
assert str(psi(50, pi)) == "-1.34410034895841e+39"
assert str(psi(50, pi + 14*e)) == "-1.89793739550804e-18"
assert str(psi(50, pi + 14*e*j)) == "(-5.2251694115217e-17 - 1.81315704140701e-17j)"
def test_harmonic():
mp.dps = 15
assert harmonic(0) == 0
assert harmonic(1) == 1
assert harmonic(2) == 1.5
assert harmonic(3).ae(1. + 1./2 + 1./3)
assert harmonic(10**10).ae(23.603066594891989701)
assert harmonic(10**1000).ae(2303.162308658947)
assert harmonic(0.5).ae(2-2*log(2))
assert harmonic(inf) == inf
assert harmonic(2+0j) == 1.5+0j
assert harmonic(1+2j).ae(1.4918071802755104+0.92080728264223022j)
def test_gamma_huge_1():
mp.dps = 500
x = mpf(10**10) / 7
mp.dps = 15
assert str(gamma(x)) == "6.26075321389519e+12458010678"
mp.dps = 50
assert str(gamma(x)) == "6.2607532138951929201303779291707455874010420783933e+12458010678"
mp.dps = 15
def test_gamma_huge_2():
mp.dps = 500
x = mpf(10**100) / 19
mp.dps = 15
assert str(gamma(x)) == (\
"1.82341134776679e+5172997469323364168990133558175077136829182824042201886051511"
"9656908623426021308685461258226190190661")
mp.dps = 50
assert str(gamma(x)) == (\
"1.82341134776678875374414910350027596939980412984e+5172997469323364168990133558"
"1750771368291828240422018860515119656908623426021308685461258226190190661")
def test_gamma_huge_3():
mp.dps = 500
x = 10**80 // 3 + 10**70*j / 7
mp.dps = 15
y = gamma(x)
assert str(y.real) == (\
"-6.82925203918106e+2636286142112569524501781477865238132302397236429627932441916"
"056964386399485392600")
assert str(y.imag) == (\
"8.54647143678418e+26362861421125695245017814778652381323023972364296279324419160"
"56964386399485392600")
mp.dps = 50
y = gamma(x)
assert str(y.real) == (\
"-6.8292520391810548460682736226799637356016538421817e+26362861421125695245017814"
"77865238132302397236429627932441916056964386399485392600")
assert str(y.imag) == (\
"8.5464714367841748507479306948130687511711420234015e+263628614211256952450178147"
"7865238132302397236429627932441916056964386399485392600")
def test_gamma_huge_4():
x = 3200+11500j
mp.dps = 15
assert str(gamma(x)) == \
"(8.95783268539713e+5164 - 1.94678798329735e+5164j)"
mp.dps = 50
assert str(gamma(x)) == (\
"(8.9578326853971339570292952697675570822206567327092e+5164"
" - 1.9467879832973509568895402139429643650329524144794e+51"
"64j)")
mp.dps = 15
def test_gamma_huge_5():
mp.dps = 500
x = 10**60 * j / 3
mp.dps = 15
y = gamma(x)
assert str(y.real) == "-3.27753899634941e-227396058973640224580963937571892628368354580620654233316839"
assert str(y.imag) == "-7.1519888950416e-227396058973640224580963937571892628368354580620654233316841"
mp.dps = 50
y = gamma(x)
assert str(y.real) == (\
"-3.2775389963494132168950056995974690946983219123935e-22739605897364022458096393"
"7571892628368354580620654233316839")
assert str(y.imag) == (\
"-7.1519888950415979749736749222530209713136588885897e-22739605897364022458096393"
"7571892628368354580620654233316841")
mp.dps = 15
def test_gamma_huge_6():
return
mp.dps = 500
x = -10**10 + mpf(10)**(-175)*j
mp.dps = 15
assert str(gamma(x)) == \
"(1.86729378905343e-95657055178 - 4.29960285282433e-95657055002j)"
mp.dps = 50
assert str(gamma(x)) == (\
"(1.8672937890534298925763143275474177736153484820662e-9565705517"
"8 - 4.2996028528243336966001185406200082244961757496106e-9565705"
"5002j)")
mp.dps = 15
def test_gamma_huge_7():
mp.dps = 100
a = 3 + j/mpf(10)**1000
mp.dps = 15
y = gamma(a)
assert str(y.real) == "2.0"
# wrong
#assert str(y.imag) == "2.16735365342606e-1000"
assert str(y.imag) == "1.84556867019693e-1000"
mp.dps = 50
y = gamma(a)
assert str(y.real) == "2.0"
#assert str(y.imag) == "2.1673536534260596065418805612488708028522563689298e-1000"
assert str(y.imag) == "1.8455686701969342787869758198351951379156813281202e-1000"
def test_stieltjes():
mp.dps = 15
assert stieltjes(0).ae(+euler)
mp.dps = 25
assert stieltjes(1).ae('-0.07281584548367672486058637587')
assert stieltjes(2).ae('-0.009690363192872318484530386035')
assert stieltjes(3).ae('0.002053834420303345866160046543')
assert stieltjes(4).ae('0.002325370065467300057468170178')
mp.dps = 15
assert stieltjes(1).ae(-0.07281584548367672486058637587)
assert stieltjes(2).ae(-0.009690363192872318484530386035)
assert stieltjes(3).ae(0.002053834420303345866160046543)
assert stieltjes(4).ae(0.0023253700654673000574681701775)
def test_barnesg():
mp.dps = 15
assert barnesg(0) == barnesg(-1) == 0
assert [superfac(i) for i in range(8)] == [1, 1, 2, 12, 288, 34560, 24883200, 125411328000]
assert str(superfac(1000)) == '3.24570818422368e+1177245'
assert isnan(barnesg(nan))
assert isnan(superfac(nan))
assert isnan(hyperfac(nan))
assert barnesg(inf) == inf
assert superfac(inf) == inf
assert hyperfac(inf) == inf
assert isnan(superfac(-inf))
assert barnesg(0.7).ae(0.8068722730141471)
assert barnesg(2+3j).ae(-0.17810213864082169+0.04504542715447838j)
assert [hyperfac(n) for n in range(7)] == [1, 1, 4, 108, 27648, 86400000, 4031078400000]
assert [hyperfac(n) for n in range(0,-7,-1)] == [1,1,-1,-4,108,27648,-86400000]
a = barnesg(-3+0j)
assert a == 0 and isinstance(a, mpc)
a = hyperfac(-3+0j)
assert a == -4 and isinstance(a, mpc)
def test_polylog():
mp.dps = 15
zs = [mpmathify(z) for z in [0, 0.5, 0.99, 4, -0.5, -4, 1j, 3+4j]]
for z in zs: assert polylog(1, z).ae(-log(1-z))
for z in zs: assert polylog(0, z).ae(z/(1-z))
for z in zs: assert polylog(-1, z).ae(z/(1-z)**2)
for z in zs: assert polylog(-2, z).ae(z*(1+z)/(1-z)**3)
for z in zs: assert polylog(-3, z).ae(z*(1+4*z+z**2)/(1-z)**4)
assert polylog(3, 7).ae(5.3192579921456754382-5.9479244480803301023j)
assert polylog(3, -7).ae(-4.5693548977219423182)
assert polylog(2, 0.9).ae(1.2997147230049587252)
assert polylog(2, -0.9).ae(-0.75216317921726162037)
assert polylog(2, 0.9j).ae(-0.17177943786580149299+0.83598828572550503226j)
assert polylog(2, 1.1).ae(1.9619991013055685931-0.2994257606855892575j)
assert polylog(2, -1.1).ae(-0.89083809026228260587)
assert polylog(2, 1.1*sqrt(j)).ae(0.58841571107611387722+1.09962542118827026011j)
assert polylog(-2, 0.9).ae(1710)
assert polylog(-2, -0.9).ae(-90/6859.)
assert polylog(3, 0.9).ae(1.0496589501864398696)
assert polylog(-3, 0.9).ae(48690)
assert polylog(-3, -4).ae(-0.0064)
assert polylog(0.5+j/3, 0.5+j/2).ae(0.31739144796565650535 + 0.99255390416556261437j)
assert polylog(3+4j,1).ae(zeta(3+4j))
assert polylog(3+4j,-1).ae(-altzeta(3+4j))
def test_bell_polyexp():
mp.dps = 15
# TODO: more tests for polyexp
assert (polyexp(0,1e-10)*10**10).ae(1.00000000005)
assert (polyexp(1,1e-10)*10**10).ae(1.0000000001)
assert polyexp(5,3j).ae(-607.7044517476176454+519.962786482001476087j)
assert polyexp(-1,3.5).ae(12.09537536175543444)
# bell(0,x) = 1
assert bell(0,0) == 1
assert bell(0,1) == 1
assert bell(0,2) == 1
assert bell(0,inf) == 1
assert bell(0,-inf) == 1
assert isnan(bell(0,nan))
# bell(1,x) = x
assert bell(1,4) == 4
assert bell(1,0) == 0
assert bell(1,inf) == inf
assert bell(1,-inf) == -inf
assert isnan(bell(1,nan))
# bell(2,x) = x*(1+x)
assert bell(2,-1) == 0
assert bell(2,0) == 0
# large orders / arguments
assert bell(10) == 115975
assert bell(10,1) == 115975
assert bell(10, -8) == 11054008
assert bell(5,-50) == -253087550
assert bell(50,-50).ae('3.4746902914629720259e74')
mp.dps = 80
assert bell(50,-50) == 347469029146297202586097646631767227177164818163463279814268368579055777450
assert bell(40,50) == 5575520134721105844739265207408344706846955281965031698187656176321717550
assert bell(74) == 5006908024247925379707076470957722220463116781409659160159536981161298714301202
mp.dps = 15
assert bell(10,20j) == 7504528595600+15649605360020j
# continuity of the generalization
assert bell(0.5,0).ae(sinc(pi*0.5))
def test_primezeta():
mp.dps = 15
assert primezeta(0.9).ae(1.8388316154446882243 + 3.1415926535897932385j)
assert primezeta(4).ae(0.076993139764246844943)
assert primezeta(1) == inf
assert primezeta(inf) == 0
assert isnan(primezeta(nan))
def test_rs_zeta():
mp.dps = 15
assert zeta(0.5+100000j).ae(1.0730320148577531321 + 5.7808485443635039843j)
assert zeta(0.75+100000j).ae(1.837852337251873704 + 1.9988492668661145358j)
assert zeta(0.5+1000000j, derivative=3).ae(1647.7744105852674733 - 1423.1270943036622097j)
assert zeta(1+1000000j, derivative=3).ae(3.4085866124523582894 - 18.179184721525947301j)
assert zeta(1+1000000j, derivative=1).ae(-0.10423479366985452134 - 0.74728992803359056244j)
assert zeta(0.5-1000000j, derivative=1).ae(11.636804066002521459 + 17.127254072212996004j)
# Additional sanity tests using fp arithmetic.
# Some more high-precision tests are found in the docstrings
def ae(x, y, tol=1e-6):
return abs(x-y) < tol*abs(y)
assert ae(fp.zeta(0.5-100000j), 1.0730320148577531321 - 5.7808485443635039843j)
assert ae(fp.zeta(0.75-100000j), 1.837852337251873704 - 1.9988492668661145358j)
assert ae(fp.zeta(0.5+1e6j), 0.076089069738227100006 + 2.8051021010192989554j)
assert ae(fp.zeta(0.5+1e6j, derivative=1), 11.636804066002521459 - 17.127254072212996004j)
assert ae(fp.zeta(1+1e6j), 0.94738726251047891048 + 0.59421999312091832833j)
assert ae(fp.zeta(1+1e6j, derivative=1), -0.10423479366985452134 - 0.74728992803359056244j)
assert ae(fp.zeta(0.5+100000j, derivative=1), 10.766962036817482375 - 30.92705282105996714j)
assert ae(fp.zeta(0.5+100000j, derivative=2), -119.40515625740538429 + 217.14780631141830251j)
assert ae(fp.zeta(0.5+100000j, derivative=3), 1129.7550282628460881 - 1685.4736895169690346j)
assert ae(fp.zeta(0.5+100000j, derivative=4), -10407.160819314958615 + 13777.786698628045085j)
assert ae(fp.zeta(0.75+100000j, derivative=1), -0.41742276699594321475 - 6.4453816275049955949j)
assert ae(fp.zeta(0.75+100000j, derivative=2), -9.214314279161977266 + 35.07290795337967899j)
assert ae(fp.zeta(0.75+100000j, derivative=3), 110.61331857820103469 - 236.87847130518129926j)
assert ae(fp.zeta(0.75+100000j, derivative=4), -1054.334275898559401 + 1769.9177890161596383j)
def test_siegelz():
mp.dps = 15
assert siegelz(100000).ae(5.87959246868176504171)
assert siegelz(100000, derivative=2).ae(-54.1172711010126452832)
assert siegelz(100000, derivative=3).ae(-278.930831343966552538)
assert siegelz(100000+j,derivative=1).ae(678.214511857070283307-379.742160779916375413j)
def test_zeta_near_1():
# Test for a former bug in mpf_zeta and mpc_zeta
mp.dps = 15
s1 = fadd(1, '1e-10', exact=True)
s2 = fadd(1, '-1e-10', exact=True)
s3 = fadd(1, '1e-10j', exact=True)
assert zeta(s1).ae(1.000000000057721566490881444e10)
assert zeta(s2).ae(-9.99999999942278433510574872e9)
z = zeta(s3)
assert z.real.ae(0.57721566490153286060)
assert z.imag.ae(-9.9999999999999999999927184e9)
mp.dps = 30
s1 = fadd(1, '1e-50', exact=True)
s2 = fadd(1, '-1e-50', exact=True)
s3 = fadd(1, '1e-50j', exact=True)
assert zeta(s1).ae('1e50')
assert zeta(s2).ae('-1e50')
z = zeta(s3)
assert z.real.ae('0.57721566490153286060651209008240243104215933593992')
assert z.imag.ae('-1e50')
| 27,387 | 38.350575 | 159 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/tests/test_pickle.py
|
import os
import tempfile
import pickle
from mpmath import *
def pickler(obj):
fn = tempfile.mktemp()
f = open(fn, 'wb')
pickle.dump(obj, f)
f.close()
f = open(fn, 'rb')
obj2 = pickle.load(f)
f.close()
os.remove(fn)
return obj2
def test_pickle():
obj = mpf('0.5')
assert obj == pickler(obj)
obj = mpc('0.5','0.2')
assert obj == pickler(obj)
| 401 | 13.357143 | 30 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/tests/test_special.py
|
from mpmath import *
def test_special():
assert inf == inf
assert inf != -inf
assert -inf == -inf
assert inf != nan
assert nan != nan
assert isnan(nan)
assert --inf == inf
assert abs(inf) == inf
assert abs(-inf) == inf
assert abs(nan) != abs(nan)
assert isnan(inf - inf)
assert isnan(inf + (-inf))
assert isnan(-inf - (-inf))
assert isnan(inf + nan)
assert isnan(-inf + nan)
assert mpf(2) + inf == inf
assert 2 + inf == inf
assert mpf(2) - inf == -inf
assert 2 - inf == -inf
assert inf > 3
assert 3 < inf
assert 3 > -inf
assert -inf < 3
assert inf > mpf(3)
assert mpf(3) < inf
assert mpf(3) > -inf
assert -inf < mpf(3)
assert not (nan < 3)
assert not (nan > 3)
assert isnan(inf * 0)
assert isnan(-inf * 0)
assert inf * 3 == inf
assert inf * -3 == -inf
assert -inf * 3 == -inf
assert -inf * -3 == inf
assert inf * inf == inf
assert -inf * -inf == inf
assert isnan(nan / 3)
assert inf / -3 == -inf
assert inf / 3 == inf
assert 3 / inf == 0
assert -3 / inf == 0
assert 0 / inf == 0
assert isnan(inf / inf)
assert isnan(inf / -inf)
assert isnan(inf / nan)
assert mpf('inf') == mpf('+inf') == inf
assert mpf('-inf') == -inf
assert isnan(mpf('nan'))
assert isinf(inf)
assert isinf(-inf)
assert not isinf(mpf(0))
assert not isinf(nan)
def test_special_powers():
assert inf**3 == inf
assert isnan(inf**0)
assert inf**-3 == 0
assert (-inf)**2 == inf
assert (-inf)**3 == -inf
assert isnan((-inf)**0)
assert (-inf)**-2 == 0
assert (-inf)**-3 == 0
assert isnan(nan**5)
assert isnan(nan**0)
def test_functions_special():
assert exp(inf) == inf
assert exp(-inf) == 0
assert isnan(exp(nan))
assert log(inf) == inf
assert isnan(log(nan))
assert isnan(sin(inf))
assert isnan(sin(nan))
assert atan(inf).ae(pi/2)
assert atan(-inf).ae(-pi/2)
assert isnan(sqrt(nan))
assert sqrt(inf) == inf
def test_convert_special():
float_inf = 1e300 * 1e300
float_ninf = -float_inf
float_nan = float_inf/float_ninf
assert mpf(3) * float_inf == inf
assert mpf(3) * float_ninf == -inf
assert isnan(mpf(3) * float_nan)
assert not (mpf(3) < float_nan)
assert not (mpf(3) > float_nan)
assert not (mpf(3) <= float_nan)
assert not (mpf(3) >= float_nan)
assert float(mpf('1e1000')) == float_inf
assert float(mpf('-1e1000')) == float_ninf
assert float(mpf('1e100000000000000000')) == float_inf
assert float(mpf('-1e100000000000000000')) == float_ninf
assert float(mpf('1e-100000000000000000')) == 0.0
def test_div_bug():
assert isnan(nan/1)
assert isnan(nan/2)
assert inf/2 == inf
assert (-inf)/2 == -inf
| 2,848 | 23.991228 | 60 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/tests/test_diff.py
|
from mpmath import *
def test_diff():
mp.dps = 15
assert diff(log, 2.0, n=0).ae(log(2))
assert diff(cos, 1.0).ae(-sin(1))
assert diff(abs, 0.0) == 0
assert diff(abs, 0.0, direction=1) == 1
assert diff(abs, 0.0, direction=-1) == -1
assert diff(exp, 1.0).ae(e)
assert diff(exp, 1.0, n=5).ae(e)
assert diff(exp, 2.0, n=5, direction=3*j).ae(e**2)
assert diff(lambda x: x**2, 3.0, method='quad').ae(6)
assert diff(lambda x: 3+x**5, 3.0, n=2, method='quad').ae(540)
assert diff(lambda x: 3+x**5, 3.0, n=2, method='step').ae(540)
assert diffun(sin)(2).ae(cos(2))
assert diffun(sin, n=2)(2).ae(-sin(2))
def test_diffs():
mp.dps = 15
assert [chop(d) for d in diffs(sin, 0, 1)] == [0, 1]
assert [chop(d) for d in diffs(sin, 0, 1, method='quad')] == [0, 1]
assert [chop(d) for d in diffs(sin, 0, 2)] == [0, 1, 0]
assert [chop(d) for d in diffs(sin, 0, 2, method='quad')] == [0, 1, 0]
def test_taylor():
mp.dps = 15
# Easy to test since the coefficients are exact in floating-point
assert taylor(sqrt, 1, 4) == [1, 0.5, -0.125, 0.0625, -0.0390625]
def test_diff_partial():
mp.dps = 15
x,y,z = xyz = 2,3,7
f = lambda x,y,z: 3*x**2 * (y+2)**3 * z**5
assert diff(f, xyz, (0,0,0)).ae(25210500)
assert diff(f, xyz, (0,0,1)).ae(18007500)
assert diff(f, xyz, (0,0,2)).ae(10290000)
assert diff(f, xyz, (0,1,0)).ae(15126300)
assert diff(f, xyz, (0,1,1)).ae(10804500)
assert diff(f, xyz, (0,1,2)).ae(6174000)
assert diff(f, xyz, (0,2,0)).ae(6050520)
assert diff(f, xyz, (0,2,1)).ae(4321800)
assert diff(f, xyz, (0,2,2)).ae(2469600)
assert diff(f, xyz, (1,0,0)).ae(25210500)
assert diff(f, xyz, (1,0,1)).ae(18007500)
assert diff(f, xyz, (1,0,2)).ae(10290000)
assert diff(f, xyz, (1,1,0)).ae(15126300)
assert diff(f, xyz, (1,1,1)).ae(10804500)
assert diff(f, xyz, (1,1,2)).ae(6174000)
assert diff(f, xyz, (1,2,0)).ae(6050520)
assert diff(f, xyz, (1,2,1)).ae(4321800)
assert diff(f, xyz, (1,2,2)).ae(2469600)
assert diff(f, xyz, (2,0,0)).ae(12605250)
assert diff(f, xyz, (2,0,1)).ae(9003750)
assert diff(f, xyz, (2,0,2)).ae(5145000)
assert diff(f, xyz, (2,1,0)).ae(7563150)
assert diff(f, xyz, (2,1,1)).ae(5402250)
assert diff(f, xyz, (2,1,2)).ae(3087000)
assert diff(f, xyz, (2,2,0)).ae(3025260)
assert diff(f, xyz, (2,2,1)).ae(2160900)
assert diff(f, xyz, (2,2,2)).ae(1234800)
| 2,466 | 38.790323 | 74 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/tests/torture.py
|
"""
Torture tests for asymptotics and high precision evaluation of
special functions.
(Other torture tests may also be placed here.)
Running this file (gmpy and psyco recommended!) takes several CPU minutes.
With Python 2.6+, multiprocessing is used automatically to run tests
in parallel if many cores are available. (A single test may take between
a second and several minutes; possibly more.)
The idea:
* We evaluate functions at positive, negative, imaginary, 45- and 135-degree
complex values with magnitudes between 10^-20 to 10^20, at precisions between
5 and 150 digits (we can go even higher for fast functions).
* Comparing the result from two different precision levels provides
a strong consistency check (particularly for functions that use
different algorithms at different precision levels).
* That the computation finishes at all (without failure), within reasonable
time, provides a check that evaluation works at all: that the code runs,
that it doesn't get stuck in an infinite loop, and that it doesn't use
some extremely slowly algorithm where it could use a faster one.
TODO:
* Speed up those functions that take long to finish!
* Generalize to test more cases; more options.
* Implement a timeout mechanism.
* Some functions are notably absent, including the following:
* inverse trigonometric functions (some become inaccurate for complex arguments)
* ci, si (not implemented properly for large complex arguments)
* zeta functions (need to modify test not to try too large imaginary values)
* and others...
"""
import sys, os
from timeit import default_timer as clock
if "-psyco" in sys.argv:
sys.argv.remove('-psyco')
import psyco
psyco.full()
if "-nogmpy" in sys.argv:
sys.argv.remove('-nogmpy')
os.environ['MPMATH_NOGMPY'] = 'Y'
filt = ''
if not sys.argv[-1].endswith(".py"):
filt = sys.argv[-1]
from mpmath import *
from mpmath.libmp.backend import exec_
def test_asymp(f, maxdps=150, verbose=False, huge_range=False):
dps = [5,15,25,50,90,150,500,1500,5000,10000]
dps = [p for p in dps if p <= maxdps]
def check(x,y,p,inpt):
if abs(x-y)/abs(y) < workprec(20)(power)(10, -p+1):
return
print()
print("Error!")
print("Input:", inpt)
print("dps =", p)
print("Result 1:", x)
print("Result 2:", y)
print("Absolute error:", abs(x-y))
print("Relative error:", abs(x-y)/abs(y))
raise AssertionError
exponents = range(-20,20)
if huge_range:
exponents += [-1000, -100, -50, 50, 100, 1000]
for n in exponents:
if verbose:
sys.stdout.write(". ")
mp.dps = 25
xpos = mpf(10)**n / 1.1287
xneg = -xpos
ximag = xpos*j
xcomplex1 = xpos*(1+j)
xcomplex2 = xpos*(-1+j)
for i in range(len(dps)):
if verbose:
print("Testing dps = %s" % dps[i])
mp.dps = dps[i]
new = f(xpos), f(xneg), f(ximag), f(xcomplex1), f(xcomplex2)
if i != 0:
p = dps[i-1]
check(prev[0], new[0], p, xpos)
check(prev[1], new[1], p, xneg)
check(prev[2], new[2], p, ximag)
check(prev[3], new[3], p, xcomplex1)
check(prev[4], new[4], p, xcomplex2)
prev = new
if verbose:
print()
a1, a2, a3, a4, a5 = 1.5, -2.25, 3.125, 4, 2
def test_bernoulli_huge():
p, q = bernfrac(9000)
assert p % 10**10 == 9636701091
assert q == 4091851784687571609141381951327092757255270
mp.dps = 15
assert str(bernoulli(10**100)) == '-2.58183325604736e+987675256497386331227838638980680030172857347883537824464410652557820800494271520411283004120790908623'
mp.dps = 50
assert str(bernoulli(10**100)) == '-2.5818332560473632073252488656039475548106223822913e+987675256497386331227838638980680030172857347883537824464410652557820800494271520411283004120790908623'
mp.dps = 15
cases = """\
test_bernoulli_huge()
test_asymp(lambda z: +pi, maxdps=10000)
test_asymp(lambda z: +e, maxdps=10000)
test_asymp(lambda z: +ln2, maxdps=10000)
test_asymp(lambda z: +ln10, maxdps=10000)
test_asymp(lambda z: +phi, maxdps=10000)
test_asymp(lambda z: +catalan, maxdps=5000)
test_asymp(lambda z: +euler, maxdps=5000)
test_asymp(lambda z: +glaisher, maxdps=1000)
test_asymp(lambda z: +khinchin, maxdps=1000)
test_asymp(lambda z: +twinprime, maxdps=150)
test_asymp(lambda z: stieltjes(2), maxdps=150)
test_asymp(lambda z: +mertens, maxdps=150)
test_asymp(lambda z: +apery, maxdps=5000)
test_asymp(sqrt, maxdps=10000, huge_range=True)
test_asymp(cbrt, maxdps=5000, huge_range=True)
test_asymp(lambda z: root(z,4), maxdps=5000, huge_range=True)
test_asymp(lambda z: root(z,-5), maxdps=5000, huge_range=True)
test_asymp(exp, maxdps=5000, huge_range=True)
test_asymp(expm1, maxdps=1500)
test_asymp(ln, maxdps=5000, huge_range=True)
test_asymp(cosh, maxdps=5000)
test_asymp(sinh, maxdps=5000)
test_asymp(tanh, maxdps=1500)
test_asymp(sin, maxdps=5000, huge_range=True)
test_asymp(cos, maxdps=5000, huge_range=True)
test_asymp(tan, maxdps=1500)
test_asymp(agm, maxdps=1500, huge_range=True)
test_asymp(ellipk, maxdps=1500)
test_asymp(ellipe, maxdps=1500)
test_asymp(lambertw, huge_range=True)
test_asymp(lambda z: lambertw(z,-1))
test_asymp(lambda z: lambertw(z,1))
test_asymp(lambda z: lambertw(z,4))
test_asymp(gamma)
test_asymp(loggamma) # huge_range=True ?
test_asymp(ei)
test_asymp(e1)
test_asymp(li, huge_range=True)
test_asymp(ci)
test_asymp(si)
test_asymp(chi)
test_asymp(shi)
test_asymp(erf)
test_asymp(erfc)
test_asymp(erfi)
test_asymp(lambda z: besselj(2, z))
test_asymp(lambda z: bessely(2, z))
test_asymp(lambda z: besseli(2, z))
test_asymp(lambda z: besselk(2, z))
test_asymp(lambda z: besselj(-2.25, z))
test_asymp(lambda z: bessely(-2.25, z))
test_asymp(lambda z: besseli(-2.25, z))
test_asymp(lambda z: besselk(-2.25, z))
test_asymp(airyai)
test_asymp(airybi)
test_asymp(lambda z: hyp0f1(a1, z))
test_asymp(lambda z: hyp1f1(a1, a2, z))
test_asymp(lambda z: hyp1f2(a1, a2, a3, z))
test_asymp(lambda z: hyp2f0(a1, a2, z))
test_asymp(lambda z: hyperu(a1, a2, z))
test_asymp(lambda z: hyp2f1(a1, a2, a3, z))
test_asymp(lambda z: hyp2f2(a1, a2, a3, a4, z))
test_asymp(lambda z: hyp2f3(a1, a2, a3, a4, a5, z))
test_asymp(lambda z: coulombf(a1, a2, z))
test_asymp(lambda z: coulombg(a1, a2, z))
test_asymp(lambda z: polylog(2,z))
test_asymp(lambda z: polylog(3,z))
test_asymp(lambda z: polylog(-2,z))
test_asymp(lambda z: expint(4, z))
test_asymp(lambda z: expint(-4, z))
test_asymp(lambda z: expint(2.25, z))
test_asymp(lambda z: gammainc(2.5, z, 5))
test_asymp(lambda z: gammainc(2.5, 5, z))
test_asymp(lambda z: hermite(3, z))
test_asymp(lambda z: hermite(2.5, z))
test_asymp(lambda z: legendre(3, z))
test_asymp(lambda z: legendre(4, z))
test_asymp(lambda z: legendre(2.5, z))
test_asymp(lambda z: legenp(a1, a2, z))
test_asymp(lambda z: legenq(a1, a2, z), maxdps=90) # abnormally slow
test_asymp(lambda z: jtheta(1, z, 0.5))
test_asymp(lambda z: jtheta(2, z, 0.5))
test_asymp(lambda z: jtheta(3, z, 0.5))
test_asymp(lambda z: jtheta(4, z, 0.5))
test_asymp(lambda z: jtheta(1, z, 0.5, 1))
test_asymp(lambda z: jtheta(2, z, 0.5, 1))
test_asymp(lambda z: jtheta(3, z, 0.5, 1))
test_asymp(lambda z: jtheta(4, z, 0.5, 1))
test_asymp(barnesg, maxdps=90)
"""
def testit(line):
if filt in line:
print(line)
t1 = clock()
exec_(line, globals(), locals())
t2 = clock()
elapsed = t2-t1
print("Time:", elapsed, "for", line, "(OK)")
if __name__ == '__main__':
try:
from multiprocessing import Pool
mapf = Pool(None).map
print("Running tests with multiprocessing")
except ImportError:
print("Not using multiprocessing")
mapf = map
t1 = clock()
tasks = cases.splitlines()
mapf(testit, tasks)
t2 = clock()
print("Cumulative wall time:", t2-t1)
| 7,968 | 33.647826 | 196 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/tests/test_convert.py
|
import random
from mpmath import *
from mpmath.libmp import *
def test_basic_string():
"""
Test basic string conversion
"""
mp.dps = 15
assert mpf('3') == mpf('3.0') == mpf('0003.') == mpf('0.03e2') == mpf(3.0)
assert mpf('30') == mpf('30.0') == mpf('00030.') == mpf(30.0)
for i in range(10):
for j in range(10):
assert mpf('%ie%i' % (i,j)) == i * 10**j
assert str(mpf('25000.0')) == '25000.0'
assert str(mpf('2500.0')) == '2500.0'
assert str(mpf('250.0')) == '250.0'
assert str(mpf('25.0')) == '25.0'
assert str(mpf('2.5')) == '2.5'
assert str(mpf('0.25')) == '0.25'
assert str(mpf('0.025')) == '0.025'
assert str(mpf('0.0025')) == '0.0025'
assert str(mpf('0.00025')) == '0.00025'
assert str(mpf('0.000025')) == '2.5e-5'
assert str(mpf(0)) == '0.0'
assert str(mpf('2.5e1000000000000000000000')) == '2.5e+1000000000000000000000'
assert str(mpf('2.6e-1000000000000000000000')) == '2.6e-1000000000000000000000'
assert str(mpf(1.23402834e-15)) == '1.23402834e-15'
assert str(mpf(-1.23402834e-15)) == '-1.23402834e-15'
assert str(mpf(-1.2344e-15)) == '-1.2344e-15'
assert repr(mpf(-1.2344e-15)) == "mpf('-1.2343999999999999e-15')"
def test_pretty():
mp.pretty = True
assert repr(mpf(2.5)) == '2.5'
assert repr(mpc(2.5,3.5)) == '(2.5 + 3.5j)'
mp.pretty = False
iv.pretty = True
assert repr(mpi(2.5,3.5)) == '[2.5, 3.5]'
iv.pretty = False
def test_str_whitespace():
assert mpf('1.26 ') == 1.26
def test_unicode():
mp.dps = 15
try:
unicode = unicode
except NameError:
unicode = str
assert mpf(unicode('2.76')) == 2.76
assert mpf(unicode('inf')) == inf
def test_str_format():
assert to_str(from_float(0.1),15,strip_zeros=False) == '0.100000000000000'
assert to_str(from_float(0.0),15,show_zero_exponent=True) == '0.0e+0'
assert to_str(from_float(0.0),0,show_zero_exponent=True) == '.0e+0'
assert to_str(from_float(0.0),0,show_zero_exponent=False) == '.0'
assert to_str(from_float(0.0),1,show_zero_exponent=True) == '0.0e+0'
assert to_str(from_float(0.0),1,show_zero_exponent=False) == '0.0'
assert to_str(from_float(1.23),3,show_zero_exponent=True) == '1.23e+0'
assert to_str(from_float(1.23456789000000e-2),15,strip_zeros=False,min_fixed=0,max_fixed=0) == '1.23456789000000e-2'
assert to_str(from_float(1.23456789000000e+2),15,strip_zeros=False,min_fixed=0,max_fixed=0) == '1.23456789000000e+2'
assert to_str(from_float(2.1287e14), 15, max_fixed=1000) == '212870000000000.0'
assert to_str(from_float(2.1287e15), 15, max_fixed=1000) == '2128700000000000.0'
assert to_str(from_float(2.1287e16), 15, max_fixed=1000) == '21287000000000000.0'
assert to_str(from_float(2.1287e30), 15, max_fixed=1000) == '2128700000000000000000000000000.0'
def test_tight_string_conversion():
mp.dps = 15
# In an old version, '0.5' wasn't recognized as representing
# an exact binary number and was erroneously rounded up or down
assert from_str('0.5', 10, round_floor) == fhalf
assert from_str('0.5', 10, round_ceiling) == fhalf
def test_eval_repr_invariant():
"""Test that eval(repr(x)) == x"""
random.seed(123)
for dps in [10, 15, 20, 50, 100]:
mp.dps = dps
for i in range(1000):
a = mpf(random.random())**0.5 * 10**random.randint(-100, 100)
assert eval(repr(a)) == a
mp.dps = 15
def test_str_bugs():
mp.dps = 15
# Decimal rounding used to give the wrong exponent in some cases
assert str(mpf('1e600')) == '1.0e+600'
assert str(mpf('1e10000')) == '1.0e+10000'
def test_str_prec0():
assert to_str(from_float(1.234), 0) == '.0e+0'
assert to_str(from_float(1e-15), 0) == '.0e-15'
assert to_str(from_float(1e+15), 0) == '.0e+15'
assert to_str(from_float(-1e-15), 0) == '-.0e-15'
assert to_str(from_float(-1e+15), 0) == '-.0e+15'
def test_convert_rational():
mp.dps = 15
assert from_rational(30, 5, 53, round_nearest) == (0, 3, 1, 2)
assert from_rational(-7, 4, 53, round_nearest) == (1, 7, -2, 3)
assert to_rational((0, 1, -1, 1)) == (1, 2)
def test_custom_class():
class mympf:
@property
def _mpf_(self):
return mpf(3.5)._mpf_
class mympc:
@property
def _mpc_(self):
return mpf(3.5)._mpf_, mpf(2.5)._mpf_
assert mpf(2) + mympf() == 5.5
assert mympf() + mpf(2) == 5.5
assert mpf(mympf()) == 3.5
assert mympc() + mpc(2) == mpc(5.5, 2.5)
assert mpc(2) + mympc() == mpc(5.5, 2.5)
assert mpc(mympc()) == (3.5+2.5j)
def test_conversion_methods():
class SomethingRandom:
pass
class SomethingReal:
def _mpmath_(self, prec, rounding):
return mp.make_mpf(from_str('1.3', prec, rounding))
class SomethingComplex:
def _mpmath_(self, prec, rounding):
return mp.make_mpc((from_str('1.3', prec, rounding), \
from_str('1.7', prec, rounding)))
x = mpf(3)
z = mpc(3)
a = SomethingRandom()
y = SomethingReal()
w = SomethingComplex()
for d in [15, 45]:
mp.dps = d
assert (x+y).ae(mpf('4.3'))
assert (y+x).ae(mpf('4.3'))
assert (x+w).ae(mpc('4.3', '1.7'))
assert (w+x).ae(mpc('4.3', '1.7'))
assert (z+y).ae(mpc('4.3'))
assert (y+z).ae(mpc('4.3'))
assert (z+w).ae(mpc('4.3', '1.7'))
assert (w+z).ae(mpc('4.3', '1.7'))
x-y; y-x; x-w; w-x; z-y; y-z; z-w; w-z
x*y; y*x; x*w; w*x; z*y; y*z; z*w; w*z
x/y; y/x; x/w; w/x; z/y; y/z; z/w; w/z
x**y; y**x; x**w; w**x; z**y; y**z; z**w; w**z
x==y; y==x; x==w; w==x; z==y; y==z; z==w; w==z
mp.dps = 15
assert x.__add__(a) is NotImplemented
assert x.__radd__(a) is NotImplemented
assert x.__lt__(a) is NotImplemented
assert x.__gt__(a) is NotImplemented
assert x.__le__(a) is NotImplemented
assert x.__ge__(a) is NotImplemented
assert x.__eq__(a) is NotImplemented
assert x.__ne__(a) is NotImplemented
# implementation detail
if hasattr(x, "__cmp__"):
assert x.__cmp__(a) is NotImplemented
assert x.__sub__(a) is NotImplemented
assert x.__rsub__(a) is NotImplemented
assert x.__mul__(a) is NotImplemented
assert x.__rmul__(a) is NotImplemented
assert x.__div__(a) is NotImplemented
assert x.__rdiv__(a) is NotImplemented
assert x.__mod__(a) is NotImplemented
assert x.__rmod__(a) is NotImplemented
assert x.__pow__(a) is NotImplemented
assert x.__rpow__(a) is NotImplemented
assert z.__add__(a) is NotImplemented
assert z.__radd__(a) is NotImplemented
assert z.__eq__(a) is NotImplemented
assert z.__ne__(a) is NotImplemented
assert z.__sub__(a) is NotImplemented
assert z.__rsub__(a) is NotImplemented
assert z.__mul__(a) is NotImplemented
assert z.__rmul__(a) is NotImplemented
assert z.__div__(a) is NotImplemented
assert z.__rdiv__(a) is NotImplemented
assert z.__pow__(a) is NotImplemented
assert z.__rpow__(a) is NotImplemented
def test_mpmathify():
assert mpmathify('1/2') == 0.5
assert mpmathify('(1.0+1.0j)') == mpc(1, 1)
assert mpmathify('(1.2e-10 - 3.4e5j)') == mpc('1.2e-10', '-3.4e5')
assert mpmathify('1j') == mpc(1j)
| 7,352 | 37.296875 | 120 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/tests/test_visualization.py
|
"""
Limited tests of the visualization module. Right now it just makes
sure that passing custom Axes works.
"""
from mpmath import mp, fp
def test_axes():
try:
import matplotlib
version = matplotlib.__version__.split("-")[0]
version = version.split(".")[:2]
if [int(_) for _ in version] < [0,99]:
raise ImportError
import pylab
except ImportError:
print("\nSkipping test (pylab not available or too old version)\n")
return
fig = pylab.figure()
axes = fig.add_subplot(111)
for ctx in [mp, fp]:
ctx.plot(lambda x: x**2, [0, 3], axes=axes)
assert axes.get_xlabel() == 'x'
assert axes.get_ylabel() == 'f(x)'
fig = pylab.figure()
axes = fig.add_subplot(111)
for ctx in [mp, fp]:
ctx.cplot(lambda z: z, [-2, 2], [-10, 10], axes=axes)
assert axes.get_xlabel() == 'Re(z)'
assert axes.get_ylabel() == 'Im(z)'
| 944 | 27.636364 | 75 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/tests/test_ode.py
|
#from mpmath.calculus import ODE_step_euler, ODE_step_rk4, odeint, arange
from mpmath import odefun, cos, sin, mpf, sinc, mp
'''
solvers = [ODE_step_euler, ODE_step_rk4]
def test_ode1():
"""
Let's solve:
x'' + w**2 * x = 0
i.e. x1 = x, x2 = x1':
x1' = x2
x2' = -x1
"""
def derivs((x1, x2), t):
return x2, -x1
for solver in solvers:
t = arange(0, 3.1415926, 0.005)
sol = odeint(derivs, (0., 1.), t, solver)
x1 = [a[0] for a in sol]
x2 = [a[1] for a in sol]
# the result is x1 = sin(t), x2 = cos(t)
# let's just check the end points for t = pi
assert abs(x1[-1]) < 1e-2
assert abs(x2[-1] - (-1)) < 1e-2
def test_ode2():
"""
Let's solve:
x' - x = 0
i.e. x = exp(x)
"""
def derivs((x), t):
return x
for solver in solvers:
t = arange(0, 1, 1e-3)
sol = odeint(derivs, (1.,), t, solver)
x = [a[0] for a in sol]
# the result is x = exp(t)
# let's just check the end point for t = 1, i.e. x = e
assert abs(x[-1] - 2.718281828) < 1e-2
'''
def test_odefun_rational():
mp.dps = 15
# A rational function
f = lambda t: 1/(1+mpf(t)**2)
g = odefun(lambda x, y: [-2*x*y[0]**2], 0, [f(0)])
assert f(2).ae(g(2)[0])
def test_odefun_sinc_large():
mp.dps = 15
# Sinc function; test for large x
f = sinc
g = odefun(lambda x, y: [(cos(x)-y[0])/x], 1, [f(1)], tol=0.01, degree=5)
assert abs(f(100) - g(100)[0])/f(100) < 0.01
def test_odefun_harmonic():
mp.dps = 15
# Harmonic oscillator
f = odefun(lambda x, y: [-y[1], y[0]], 0, [1, 0])
for x in [0, 1, 2.5, 8, 3.7]: # we go back to 3.7 to check caching
c, s = f(x)
assert c.ae(cos(x))
assert s.ae(sin(x))
| 1,822 | 23.635135 | 77 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/tests/test_compatibility.py
|
from mpmath import *
from random import seed, randint, random
import math
# Test compatibility with Python floats, which are
# IEEE doubles (53-bit)
N = 5000
seed(1)
# Choosing exponents between roughly -140, 140 ensures that
# the Python floats don't overflow or underflow
xs = [(random()-1) * 10**randint(-140, 140) for x in range(N)]
ys = [(random()-1) * 10**randint(-140, 140) for x in range(N)]
# include some equal values
ys[int(N*0.8):] = xs[int(N*0.8):]
# Detect whether Python is compiled to use 80-bit floating-point
# instructions, in which case the double compatibility test breaks
uses_x87 = -4.1974624032366689e+117 / -8.4657370748010221e-47 \
== 4.9581771393902231e+163
def test_double_compatibility():
mp.prec = 53
for x, y in zip(xs, ys):
mpx = mpf(x)
mpy = mpf(y)
assert mpf(x) == x
assert (mpx < mpy) == (x < y)
assert (mpx > mpy) == (x > y)
assert (mpx == mpy) == (x == y)
assert (mpx != mpy) == (x != y)
assert (mpx <= mpy) == (x <= y)
assert (mpx >= mpy) == (x >= y)
assert mpx == mpx
if uses_x87:
mp.prec = 64
a = mpx + mpy
b = mpx * mpy
c = mpx / mpy
d = mpx % mpy
mp.prec = 53
assert +a == x + y
assert +b == x * y
assert +c == x / y
assert +d == x % y
else:
assert mpx + mpy == x + y
assert mpx * mpy == x * y
assert mpx / mpy == x / y
assert mpx % mpy == x % y
assert abs(mpx) == abs(x)
assert mpf(repr(x)) == x
assert ceil(mpx) == math.ceil(x)
assert floor(mpx) == math.floor(x)
def test_sqrt():
# this fails quite often. it appers to be float
# that rounds the wrong way, not mpf
fail = 0
mp.prec = 53
for x in xs:
x = abs(x)
mp.prec = 100
mp_high = mpf(x)**0.5
mp.prec = 53
mp_low = mpf(x)**0.5
fp = x**0.5
assert abs(mp_low-mp_high) <= abs(fp-mp_high)
fail += mp_low != fp
assert fail < N/10
def test_bugs():
# particular bugs
assert mpf(4.4408920985006262E-16) < mpf(1.7763568394002505E-15)
assert mpf(-4.4408920985006262E-16) > mpf(-1.7763568394002505E-15)
| 2,306 | 28.576923 | 70 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/tests/test_bitwise.py
|
"""
Test bit-level integer and mpf operations
"""
from mpmath import *
from mpmath.libmp import *
def test_bitcount():
assert bitcount(0) == 0
assert bitcount(1) == 1
assert bitcount(7) == 3
assert bitcount(8) == 4
assert bitcount(2**100) == 101
assert bitcount(2**100-1) == 100
def test_trailing():
assert trailing(0) == 0
assert trailing(1) == 0
assert trailing(2) == 1
assert trailing(7) == 0
assert trailing(8) == 3
assert trailing(2**100) == 100
assert trailing(2**100-1) == 0
def test_round_down():
assert from_man_exp(0, -4, 4, round_down)[:3] == (0, 0, 0)
assert from_man_exp(0xf0, -4, 4, round_down)[:3] == (0, 15, 0)
assert from_man_exp(0xf1, -4, 4, round_down)[:3] == (0, 15, 0)
assert from_man_exp(0xff, -4, 4, round_down)[:3] == (0, 15, 0)
assert from_man_exp(-0xf0, -4, 4, round_down)[:3] == (1, 15, 0)
assert from_man_exp(-0xf1, -4, 4, round_down)[:3] == (1, 15, 0)
assert from_man_exp(-0xff, -4, 4, round_down)[:3] == (1, 15, 0)
def test_round_up():
assert from_man_exp(0, -4, 4, round_up)[:3] == (0, 0, 0)
assert from_man_exp(0xf0, -4, 4, round_up)[:3] == (0, 15, 0)
assert from_man_exp(0xf1, -4, 4, round_up)[:3] == (0, 1, 4)
assert from_man_exp(0xff, -4, 4, round_up)[:3] == (0, 1, 4)
assert from_man_exp(-0xf0, -4, 4, round_up)[:3] == (1, 15, 0)
assert from_man_exp(-0xf1, -4, 4, round_up)[:3] == (1, 1, 4)
assert from_man_exp(-0xff, -4, 4, round_up)[:3] == (1, 1, 4)
def test_round_floor():
assert from_man_exp(0, -4, 4, round_floor)[:3] == (0, 0, 0)
assert from_man_exp(0xf0, -4, 4, round_floor)[:3] == (0, 15, 0)
assert from_man_exp(0xf1, -4, 4, round_floor)[:3] == (0, 15, 0)
assert from_man_exp(0xff, -4, 4, round_floor)[:3] == (0, 15, 0)
assert from_man_exp(-0xf0, -4, 4, round_floor)[:3] == (1, 15, 0)
assert from_man_exp(-0xf1, -4, 4, round_floor)[:3] == (1, 1, 4)
assert from_man_exp(-0xff, -4, 4, round_floor)[:3] == (1, 1, 4)
def test_round_ceiling():
assert from_man_exp(0, -4, 4, round_ceiling)[:3] == (0, 0, 0)
assert from_man_exp(0xf0, -4, 4, round_ceiling)[:3] == (0, 15, 0)
assert from_man_exp(0xf1, -4, 4, round_ceiling)[:3] == (0, 1, 4)
assert from_man_exp(0xff, -4, 4, round_ceiling)[:3] == (0, 1, 4)
assert from_man_exp(-0xf0, -4, 4, round_ceiling)[:3] == (1, 15, 0)
assert from_man_exp(-0xf1, -4, 4, round_ceiling)[:3] == (1, 15, 0)
assert from_man_exp(-0xff, -4, 4, round_ceiling)[:3] == (1, 15, 0)
def test_round_nearest():
assert from_man_exp(0, -4, 4, round_nearest)[:3] == (0, 0, 0)
assert from_man_exp(0xf0, -4, 4, round_nearest)[:3] == (0, 15, 0)
assert from_man_exp(0xf7, -4, 4, round_nearest)[:3] == (0, 15, 0)
assert from_man_exp(0xf8, -4, 4, round_nearest)[:3] == (0, 1, 4) # 1111.1000 -> 10000.0
assert from_man_exp(0xf9, -4, 4, round_nearest)[:3] == (0, 1, 4) # 1111.1001 -> 10000.0
assert from_man_exp(0xe8, -4, 4, round_nearest)[:3] == (0, 7, 1) # 1110.1000 -> 1110.0
assert from_man_exp(0xe9, -4, 4, round_nearest)[:3] == (0, 15, 0) # 1110.1001 -> 1111.0
assert from_man_exp(-0xf0, -4, 4, round_nearest)[:3] == (1, 15, 0)
assert from_man_exp(-0xf7, -4, 4, round_nearest)[:3] == (1, 15, 0)
assert from_man_exp(-0xf8, -4, 4, round_nearest)[:3] == (1, 1, 4)
assert from_man_exp(-0xf9, -4, 4, round_nearest)[:3] == (1, 1, 4)
assert from_man_exp(-0xe8, -4, 4, round_nearest)[:3] == (1, 7, 1)
assert from_man_exp(-0xe9, -4, 4, round_nearest)[:3] == (1, 15, 0)
def test_rounding_bugs():
# 1 less than power-of-two cases
assert from_man_exp(72057594037927935, -56, 53, round_up) == (0, 1, 0, 1)
assert from_man_exp(73786976294838205979, -65, 53, round_nearest) == (0, 1, 1, 1)
assert from_man_exp(31, 0, 4, round_up) == (0, 1, 5, 1)
assert from_man_exp(-31, 0, 4, round_floor) == (1, 1, 5, 1)
assert from_man_exp(255, 0, 7, round_up) == (0, 1, 8, 1)
assert from_man_exp(-255, 0, 7, round_floor) == (1, 1, 8, 1)
def test_rounding_issue_200():
a = from_man_exp(9867,-100)
b = from_man_exp(9867,-200)
c = from_man_exp(-1,0)
z = (1, 1023, -10, 10)
assert mpf_add(a, c, 10, 'd') == z
assert mpf_add(b, c, 10, 'd') == z
assert mpf_add(c, a, 10, 'd') == z
assert mpf_add(c, b, 10, 'd') == z
def test_perturb():
a = fone
b = from_float(0.99999999999999989)
c = from_float(1.0000000000000002)
assert mpf_perturb(a, 0, 53, round_nearest) == a
assert mpf_perturb(a, 1, 53, round_nearest) == a
assert mpf_perturb(a, 0, 53, round_up) == c
assert mpf_perturb(a, 0, 53, round_ceiling) == c
assert mpf_perturb(a, 0, 53, round_down) == a
assert mpf_perturb(a, 0, 53, round_floor) == a
assert mpf_perturb(a, 1, 53, round_up) == a
assert mpf_perturb(a, 1, 53, round_ceiling) == a
assert mpf_perturb(a, 1, 53, round_down) == b
assert mpf_perturb(a, 1, 53, round_floor) == b
a = mpf_neg(a)
b = mpf_neg(b)
c = mpf_neg(c)
assert mpf_perturb(a, 0, 53, round_nearest) == a
assert mpf_perturb(a, 1, 53, round_nearest) == a
assert mpf_perturb(a, 0, 53, round_up) == a
assert mpf_perturb(a, 0, 53, round_floor) == a
assert mpf_perturb(a, 0, 53, round_down) == b
assert mpf_perturb(a, 0, 53, round_ceiling) == b
assert mpf_perturb(a, 1, 53, round_up) == c
assert mpf_perturb(a, 1, 53, round_floor) == c
assert mpf_perturb(a, 1, 53, round_down) == a
assert mpf_perturb(a, 1, 53, round_ceiling) == a
def test_add_exact():
ff = from_float
assert mpf_add(ff(3.0), ff(2.5)) == ff(5.5)
assert mpf_add(ff(3.0), ff(-2.5)) == ff(0.5)
assert mpf_add(ff(-3.0), ff(2.5)) == ff(-0.5)
assert mpf_add(ff(-3.0), ff(-2.5)) == ff(-5.5)
assert mpf_sub(mpf_add(fone, ff(1e-100)), fone) == ff(1e-100)
assert mpf_sub(mpf_add(ff(1e-100), fone), fone) == ff(1e-100)
assert mpf_sub(mpf_add(fone, ff(-1e-100)), fone) == ff(-1e-100)
assert mpf_sub(mpf_add(ff(-1e-100), fone), fone) == ff(-1e-100)
assert mpf_add(fone, fzero) == fone
assert mpf_add(fzero, fone) == fone
assert mpf_add(fzero, fzero) == fzero
def test_long_exponent_shifts():
mp.dps = 15
# Check for possible bugs due to exponent arithmetic overflow
# in a C implementation
x = mpf(1)
for p in [32, 64]:
a = ldexp(1,2**(p-1))
b = ldexp(1,2**p)
c = ldexp(1,2**(p+1))
d = ldexp(1,-2**(p-1))
e = ldexp(1,-2**p)
f = ldexp(1,-2**(p+1))
assert (x+a) == a
assert (x+b) == b
assert (x+c) == c
assert (x+d) == x
assert (x+e) == x
assert (x+f) == x
assert (a+x) == a
assert (b+x) == b
assert (c+x) == c
assert (d+x) == x
assert (e+x) == x
assert (f+x) == x
assert (x-a) == -a
assert (x-b) == -b
assert (x-c) == -c
assert (x-d) == x
assert (x-e) == x
assert (x-f) == x
assert (a-x) == a
assert (b-x) == b
assert (c-x) == c
assert (d-x) == -x
assert (e-x) == -x
assert (f-x) == -x
def test_float_rounding():
mp.prec = 64
for x in [mpf(1), mpf(1)+eps, mpf(1)-eps, -mpf(1)+eps, -mpf(1)-eps]:
fa = float(x)
fb = float(fadd(x,0,prec=53,rounding='n'))
assert fa == fb
z = mpc(x,x)
ca = complex(z)
cb = complex(fadd(z,0,prec=53,rounding='n'))
assert ca == cb
for rnd in ['n', 'd', 'u', 'f', 'c']:
fa = to_float(x._mpf_, rnd=rnd)
fb = to_float(fadd(x,0,prec=53,rounding=rnd)._mpf_, rnd=rnd)
assert fa == fb
mp.prec = 53
| 7,686 | 39.671958 | 95 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/tests/test_division.py
|
from mpmath.libmp import *
from mpmath import mpf, mp
from random import randint, choice, seed
all_modes = [round_floor, round_ceiling, round_down, round_up, round_nearest]
fb = from_bstr
fi = from_int
ff = from_float
def test_div_1_3():
a = fi(1)
b = fi(3)
c = fi(-1)
# floor rounds down, ceiling rounds up
assert mpf_div(a, b, 7, round_floor) == fb('0.01010101')
assert mpf_div(a, b, 7, round_ceiling) == fb('0.01010110')
assert mpf_div(a, b, 7, round_down) == fb('0.01010101')
assert mpf_div(a, b, 7, round_up) == fb('0.01010110')
assert mpf_div(a, b, 7, round_nearest) == fb('0.01010101')
# floor rounds up, ceiling rounds down
assert mpf_div(c, b, 7, round_floor) == fb('-0.01010110')
assert mpf_div(c, b, 7, round_ceiling) == fb('-0.01010101')
assert mpf_div(c, b, 7, round_down) == fb('-0.01010101')
assert mpf_div(c, b, 7, round_up) == fb('-0.01010110')
assert mpf_div(c, b, 7, round_nearest) == fb('-0.01010101')
def test_mpf_divi_1_3():
a = 1
b = fi(3)
c = -1
assert mpf_rdiv_int(a, b, 7, round_floor) == fb('0.01010101')
assert mpf_rdiv_int(a, b, 7, round_ceiling) == fb('0.01010110')
assert mpf_rdiv_int(a, b, 7, round_down) == fb('0.01010101')
assert mpf_rdiv_int(a, b, 7, round_up) == fb('0.01010110')
assert mpf_rdiv_int(a, b, 7, round_nearest) == fb('0.01010101')
assert mpf_rdiv_int(c, b, 7, round_floor) == fb('-0.01010110')
assert mpf_rdiv_int(c, b, 7, round_ceiling) == fb('-0.01010101')
assert mpf_rdiv_int(c, b, 7, round_down) == fb('-0.01010101')
assert mpf_rdiv_int(c, b, 7, round_up) == fb('-0.01010110')
assert mpf_rdiv_int(c, b, 7, round_nearest) == fb('-0.01010101')
def test_div_300():
q = fi(1000000)
a = fi(300499999) # a/q is a little less than a half-integer
b = fi(300500000) # b/q exactly a half-integer
c = fi(300500001) # c/q is a little more than a half-integer
# Check nearest integer rounding (prec=9 as 2**8 < 300 < 2**9)
assert mpf_div(a, q, 9, round_down) == fi(300)
assert mpf_div(b, q, 9, round_down) == fi(300)
assert mpf_div(c, q, 9, round_down) == fi(300)
assert mpf_div(a, q, 9, round_up) == fi(301)
assert mpf_div(b, q, 9, round_up) == fi(301)
assert mpf_div(c, q, 9, round_up) == fi(301)
# Nearest even integer is down
assert mpf_div(a, q, 9, round_nearest) == fi(300)
assert mpf_div(b, q, 9, round_nearest) == fi(300)
assert mpf_div(c, q, 9, round_nearest) == fi(301)
# Nearest even integer is up
a = fi(301499999)
b = fi(301500000)
c = fi(301500001)
assert mpf_div(a, q, 9, round_nearest) == fi(301)
assert mpf_div(b, q, 9, round_nearest) == fi(302)
assert mpf_div(c, q, 9, round_nearest) == fi(302)
def test_tight_integer_division():
# Test that integer division at tightest possible precision is exact
N = 100
seed(1)
for i in range(N):
a = choice([1, -1]) * randint(1, 1<<randint(10, 100))
b = choice([1, -1]) * randint(1, 1<<randint(10, 100))
p = a * b
width = bitcount(abs(b)) - trailing(b)
a = fi(a); b = fi(b); p = fi(p)
for mode in all_modes:
assert mpf_div(p, a, width, mode) == b
def test_epsilon_rounding():
# Verify that mpf_div uses infinite precision; this result will
# appear to be exactly 0.101 to a near-sighted algorithm
a = fb('0.101' + ('0'*200) + '1')
b = fb('1.10101')
c = mpf_mul(a, b, 250, round_floor) # exact
assert mpf_div(c, b, bitcount(a[1]), round_floor) == a # exact
assert mpf_div(c, b, 2, round_down) == fb('0.10')
assert mpf_div(c, b, 3, round_down) == fb('0.101')
assert mpf_div(c, b, 2, round_up) == fb('0.11')
assert mpf_div(c, b, 3, round_up) == fb('0.110')
assert mpf_div(c, b, 2, round_floor) == fb('0.10')
assert mpf_div(c, b, 3, round_floor) == fb('0.101')
assert mpf_div(c, b, 2, round_ceiling) == fb('0.11')
assert mpf_div(c, b, 3, round_ceiling) == fb('0.110')
# The same for negative numbers
a = fb('-0.101' + ('0'*200) + '1')
b = fb('1.10101')
c = mpf_mul(a, b, 250, round_floor)
assert mpf_div(c, b, bitcount(a[1]), round_floor) == a
assert mpf_div(c, b, 2, round_down) == fb('-0.10')
assert mpf_div(c, b, 3, round_up) == fb('-0.110')
# Floor goes up, ceiling goes down
assert mpf_div(c, b, 2, round_floor) == fb('-0.11')
assert mpf_div(c, b, 3, round_floor) == fb('-0.110')
assert mpf_div(c, b, 2, round_ceiling) == fb('-0.10')
assert mpf_div(c, b, 3, round_ceiling) == fb('-0.101')
def test_mod():
mp.dps = 15
assert mpf(234) % 1 == 0
assert mpf(-3) % 256 == 253
assert mpf(0.25) % 23490.5 == 0.25
assert mpf(0.25) % -23490.5 == -23490.25
assert mpf(-0.25) % 23490.5 == 23490.25
assert mpf(-0.25) % -23490.5 == -0.25
# Check that these cases are handled efficiently
assert mpf('1e10000000000') % 1 == 0
assert mpf('1.23e-1000000000') % 1 == mpf('1.23e-1000000000')
# test __rmod__
assert 3 % mpf('1.75') == 1.25
def test_div_negative_rnd_bug():
mp.dps = 15
assert (-3) / mpf('0.1531879017645047') == mpf('-19.583791966887116')
assert mpf('-2.6342475750861301') / mpf('0.35126216427941814') == mpf('-7.4993775104985909')
| 5,340 | 36.090278 | 96 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/tests/extratest_zeta.py
|
from mpmath import zetazero
from timeit import default_timer as clock
def test_zetazero():
cases = [\
(399999999, 156762524.6750591511),
(241389216, 97490234.2276711795),
(526196239, 202950727.691229534),
(542964976, 209039046.578535272),
(1048449112, 388858885.231056486),
(1048449113, 388858885.384337406),
(1048449114, 388858886.002285122),
(1048449115, 388858886.00239369),
(1048449116, 388858886.690745053)
]
for n, v in cases:
print(n, v)
t1 = clock()
ok = zetazero(n).ae(complex(0.5,v))
t2 = clock()
print("ok =", ok, ("(time = %s)" % round(t2-t1,3)))
print("Now computing two huge zeros (this may take hours)")
print("Computing zetazero(8637740722917)")
ok = zetazero(8637740722917).ae(complex(0.5,2124447368584.39296466152))
print("ok =", ok)
ok = zetazero(8637740722918).ae(complex(0.5,2124447368584.39298170604))
print("ok =", ok)
if __name__ == "__main__":
try:
import psyco
psyco.full()
except ImportError:
pass
test_zetazero()
| 1,091 | 29.333333 | 75 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/tests/test_power.py
|
from mpmath import *
from mpmath.libmp import *
import random
def test_fractional_pow():
mp.dps = 15
assert mpf(16) ** 2.5 == 1024
assert mpf(64) ** 0.5 == 8
assert mpf(64) ** -0.5 == 0.125
assert mpf(16) ** -2.5 == 0.0009765625
assert (mpf(10) ** 0.5).ae(3.1622776601683791)
assert (mpf(10) ** 2.5).ae(316.2277660168379)
assert (mpf(10) ** -0.5).ae(0.31622776601683794)
assert (mpf(10) ** -2.5).ae(0.0031622776601683794)
assert (mpf(10) ** 0.3).ae(1.9952623149688795)
assert (mpf(10) ** -0.3).ae(0.50118723362727224)
def test_pow_integer_direction():
"""
Test that inexact integer powers are rounded in the right
direction.
"""
random.seed(1234)
for prec in [10, 53, 200]:
for i in range(50):
a = random.randint(1<<(prec-1), 1<<prec)
b = random.randint(2, 100)
ab = a**b
# note: could actually be exact, but that's very unlikely!
assert to_int(mpf_pow(from_int(a), from_int(b), prec, round_down)) < ab
assert to_int(mpf_pow(from_int(a), from_int(b), prec, round_up)) > ab
def test_pow_epsilon_rounding():
"""
Stress test directed rounding for powers with integer exponents.
Basically, we look at the following cases:
>>> 1.0001 ** -5 # doctest: +SKIP
0.99950014996500702
>>> 0.9999 ** -5 # doctest: +SKIP
1.000500150035007
>>> (-1.0001) ** -5 # doctest: +SKIP
-0.99950014996500702
>>> (-0.9999) ** -5 # doctest: +SKIP
-1.000500150035007
>>> 1.0001 ** -6 # doctest: +SKIP
0.99940020994401269
>>> 0.9999 ** -6 # doctest: +SKIP
1.0006002100560125
>>> (-1.0001) ** -6 # doctest: +SKIP
0.99940020994401269
>>> (-0.9999) ** -6 # doctest: +SKIP
1.0006002100560125
etc.
We run the tests with values a very small epsilon away from 1:
small enough that the result is indistinguishable from 1 when
rounded to nearest at the output precision. We check that the
result is not erroneously rounded to 1 in cases where the
rounding should be done strictly away from 1.
"""
def powr(x, n, r):
return make_mpf(mpf_pow_int(x._mpf_, n, mp.prec, r))
for (inprec, outprec) in [(100, 20), (5000, 3000)]:
mp.prec = inprec
pos10001 = mpf(1) + mpf(2)**(-inprec+5)
pos09999 = mpf(1) - mpf(2)**(-inprec+5)
neg10001 = -pos10001
neg09999 = -pos09999
mp.prec = outprec
r = round_up
assert powr(pos10001, 5, r) > 1
assert powr(pos09999, 5, r) == 1
assert powr(neg10001, 5, r) < -1
assert powr(neg09999, 5, r) == -1
assert powr(pos10001, 6, r) > 1
assert powr(pos09999, 6, r) == 1
assert powr(neg10001, 6, r) > 1
assert powr(neg09999, 6, r) == 1
assert powr(pos10001, -5, r) == 1
assert powr(pos09999, -5, r) > 1
assert powr(neg10001, -5, r) == -1
assert powr(neg09999, -5, r) < -1
assert powr(pos10001, -6, r) == 1
assert powr(pos09999, -6, r) > 1
assert powr(neg10001, -6, r) == 1
assert powr(neg09999, -6, r) > 1
r = round_down
assert powr(pos10001, 5, r) == 1
assert powr(pos09999, 5, r) < 1
assert powr(neg10001, 5, r) == -1
assert powr(neg09999, 5, r) > -1
assert powr(pos10001, 6, r) == 1
assert powr(pos09999, 6, r) < 1
assert powr(neg10001, 6, r) == 1
assert powr(neg09999, 6, r) < 1
assert powr(pos10001, -5, r) < 1
assert powr(pos09999, -5, r) == 1
assert powr(neg10001, -5, r) > -1
assert powr(neg09999, -5, r) == -1
assert powr(pos10001, -6, r) < 1
assert powr(pos09999, -6, r) == 1
assert powr(neg10001, -6, r) < 1
assert powr(neg09999, -6, r) == 1
r = round_ceiling
assert powr(pos10001, 5, r) > 1
assert powr(pos09999, 5, r) == 1
assert powr(neg10001, 5, r) == -1
assert powr(neg09999, 5, r) > -1
assert powr(pos10001, 6, r) > 1
assert powr(pos09999, 6, r) == 1
assert powr(neg10001, 6, r) > 1
assert powr(neg09999, 6, r) == 1
assert powr(pos10001, -5, r) == 1
assert powr(pos09999, -5, r) > 1
assert powr(neg10001, -5, r) > -1
assert powr(neg09999, -5, r) == -1
assert powr(pos10001, -6, r) == 1
assert powr(pos09999, -6, r) > 1
assert powr(neg10001, -6, r) == 1
assert powr(neg09999, -6, r) > 1
r = round_floor
assert powr(pos10001, 5, r) == 1
assert powr(pos09999, 5, r) < 1
assert powr(neg10001, 5, r) < -1
assert powr(neg09999, 5, r) == -1
assert powr(pos10001, 6, r) == 1
assert powr(pos09999, 6, r) < 1
assert powr(neg10001, 6, r) == 1
assert powr(neg09999, 6, r) < 1
assert powr(pos10001, -5, r) < 1
assert powr(pos09999, -5, r) == 1
assert powr(neg10001, -5, r) == -1
assert powr(neg09999, -5, r) < -1
assert powr(pos10001, -6, r) < 1
assert powr(pos09999, -6, r) == 1
assert powr(neg10001, -6, r) < 1
assert powr(neg09999, -6, r) == 1
mp.dps = 15
| 5,227 | 32.299363 | 83 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/tests/test_functions2.py
|
import math
from mpmath import *
def test_bessel():
mp.dps = 15
assert j0(1).ae(0.765197686557966551)
assert j0(pi).ae(-0.304242177644093864)
assert j0(1000).ae(0.0247866861524201746)
assert j0(-25).ae(0.0962667832759581162)
assert j1(1).ae(0.440050585744933516)
assert j1(pi).ae(0.284615343179752757)
assert j1(1000).ae(0.00472831190708952392)
assert j1(-25).ae(0.125350249580289905)
assert besselj(5,1).ae(0.000249757730211234431)
assert besselj(5+0j,1).ae(0.000249757730211234431)
assert besselj(5,pi).ae(0.0521411843671184747)
assert besselj(5,1000).ae(0.00502540694523318607)
assert besselj(5,-25).ae(0.0660079953984229934)
assert besselj(-3,2).ae(-0.128943249474402051)
assert besselj(-4,2).ae(0.0339957198075684341)
assert besselj(3,3+2j).ae(0.424718794929639595942 + 0.625665327745785804812j)
assert besselj(0.25,4).ae(-0.374760630804249715)
assert besselj(1+2j,3+4j).ae(0.319247428741872131 - 0.669557748880365678j)
assert (besselj(3, 10**10) * 10**5).ae(0.76765081748139204023)
assert bessely(-0.5, 0) == 0
assert bessely(0.5, 0) == -inf
assert bessely(1.5, 0) == -inf
assert bessely(0,0) == -inf
assert bessely(-0.4, 0) == -inf
assert bessely(-0.6, 0) == inf
assert bessely(-1, 0) == inf
assert bessely(-1.4, 0) == inf
assert bessely(-1.6, 0) == -inf
assert bessely(-1, 0) == inf
assert bessely(-2, 0) == -inf
assert bessely(-3, 0) == inf
assert bessely(0.5, 0) == -inf
assert bessely(1, 0) == -inf
assert bessely(1.5, 0) == -inf
assert bessely(2, 0) == -inf
assert bessely(2.5, 0) == -inf
assert bessely(3, 0) == -inf
assert bessely(0,0.5).ae(-0.44451873350670655715)
assert bessely(1,0.5).ae(-1.4714723926702430692)
assert bessely(-1,0.5).ae(1.4714723926702430692)
assert bessely(3.5,0.5).ae(-138.86400867242488443)
assert bessely(0,3+4j).ae(4.6047596915010138655-8.8110771408232264208j)
assert bessely(0,j).ae(-0.26803248203398854876+1.26606587775200833560j)
assert (bessely(3, 10**10) * 10**5).ae(0.21755917537013204058)
assert besseli(0,0) == 1
assert besseli(1,0) == 0
assert besseli(2,0) == 0
assert besseli(-1,0) == 0
assert besseli(-2,0) == 0
assert besseli(0,0.5).ae(1.0634833707413235193)
assert besseli(1,0.5).ae(0.25789430539089631636)
assert besseli(-1,0.5).ae(0.25789430539089631636)
assert besseli(3.5,0.5).ae(0.00068103597085793815863)
assert besseli(0,3+4j).ae(-3.3924877882755196097-1.3239458916287264815j)
assert besseli(0,j).ae(besselj(0,1))
assert (besseli(3, 10**10) * mpf(10)**(-4342944813)).ae(4.2996028505491271875)
assert besselk(0,0) == inf
assert besselk(1,0) == inf
assert besselk(2,0) == inf
assert besselk(-1,0) == inf
assert besselk(-2,0) == inf
assert besselk(0,0.5).ae(0.92441907122766586178)
assert besselk(1,0.5).ae(1.6564411200033008937)
assert besselk(-1,0.5).ae(1.6564411200033008937)
assert besselk(3.5,0.5).ae(207.48418747548460607)
assert besselk(0,3+4j).ae(-0.007239051213570155013+0.026510418350267677215j)
assert besselk(0,j).ae(-0.13863371520405399968-1.20196971531720649914j)
assert (besselk(3, 10**10) * mpf(10)**4342944824).ae(1.1628981033356187851)
# test for issue 331, bug reported by Michael Hartmann
for n in range(10,100,10):
mp.dps = n
assert besseli(91.5,24.7708).ae("4.00830632138673963619656140653537080438462342928377020695738635559218797348548092636896796324190271316137982810144874264e-41")
def test_bessel_zeros():
mp.dps = 15
assert besseljzero(0,1).ae(2.40482555769577276869)
assert besseljzero(2,1).ae(5.1356223018406825563)
assert besseljzero(1,50).ae(157.86265540193029781)
assert besseljzero(10,1).ae(14.475500686554541220)
assert besseljzero(0.5,3).ae(9.4247779607693797153)
assert besseljzero(2,1,1).ae(3.0542369282271403228)
assert besselyzero(0,1).ae(0.89357696627916752158)
assert besselyzero(2,1).ae(3.3842417671495934727)
assert besselyzero(1,50).ae(156.29183520147840108)
assert besselyzero(10,1).ae(12.128927704415439387)
assert besselyzero(0.5,3).ae(7.8539816339744830962)
assert besselyzero(2,1,1).ae(5.0025829314460639452)
def test_hankel():
mp.dps = 15
assert hankel1(0,0.5).ae(0.93846980724081290423-0.44451873350670655715j)
assert hankel1(1,0.5).ae(0.2422684576748738864-1.4714723926702430692j)
assert hankel1(-1,0.5).ae(-0.2422684576748738864+1.4714723926702430692j)
assert hankel1(1.5,0.5).ae(0.0917016996256513026-2.5214655504213378514j)
assert hankel1(1.5,3+4j).ae(0.0066806866476728165382-0.0036684231610839127106j)
assert hankel2(0,0.5).ae(0.93846980724081290423+0.44451873350670655715j)
assert hankel2(1,0.5).ae(0.2422684576748738864+1.4714723926702430692j)
assert hankel2(-1,0.5).ae(-0.2422684576748738864-1.4714723926702430692j)
assert hankel2(1.5,0.5).ae(0.0917016996256513026+2.5214655504213378514j)
assert hankel2(1.5,3+4j).ae(14.783528526098567526-7.397390270853446512j)
def test_struve():
mp.dps = 15
assert struveh(2,3).ae(0.74238666967748318564)
assert struveh(-2.5,3).ae(0.41271003220971599344)
assert struvel(2,3).ae(1.7476573277362782744)
assert struvel(-2.5,3).ae(1.5153394466819651377)
def test_whittaker():
mp.dps = 15
assert whitm(2,3,4).ae(49.753745589025246591)
assert whitw(2,3,4).ae(14.111656223052932215)
def test_kelvin():
mp.dps = 15
assert ber(2,3).ae(0.80836846563726819091)
assert ber(3,4).ae(-0.28262680167242600233)
assert ber(-3,2).ae(-0.085611448496796363669)
assert bei(2,3).ae(-0.89102236377977331571)
assert bei(-3,2).ae(-0.14420994155731828415)
assert ker(2,3).ae(0.12839126695733458928)
assert ker(-3,2).ae(-0.29802153400559142783)
assert ker(0.5,3).ae(-0.085662378535217097524)
assert kei(2,3).ae(0.036804426134164634000)
assert kei(-3,2).ae(0.88682069845786731114)
assert kei(0.5,3).ae(0.013633041571314302948)
def test_hyper_misc():
mp.dps = 15
assert hyp0f1(1,0) == 1
assert hyp1f1(1,2,0) == 1
assert hyp1f2(1,2,3,0) == 1
assert hyp2f1(1,2,3,0) == 1
assert hyp2f2(1,2,3,4,0) == 1
assert hyp2f3(1,2,3,4,5,0) == 1
# Degenerate case: 0F0
assert hyper([],[],0) == 1
assert hyper([],[],-2).ae(exp(-2))
# Degenerate case: 1F0
assert hyper([2],[],1.5) == 4
#
assert hyp2f1((1,3),(2,3),(5,6),mpf(27)/32).ae(1.6)
assert hyp2f1((1,4),(1,2),(3,4),mpf(80)/81).ae(1.8)
assert hyp2f1((2,3),(1,1),(3,2),(2+j)/3).ae(1.327531603558679093+0.439585080092769253j)
mp.dps = 25
v = mpc('1.2282306665029814734863026', '-0.1225033830118305184672133')
assert hyper([(3,4),2+j,1],[1,5,j/3],mpf(1)/5+j/8).ae(v)
mp.dps = 15
def test_elliptic_integrals():
mp.dps = 15
assert ellipk(0).ae(pi/2)
assert ellipk(0.5).ae(gamma(0.25)**2/(4*sqrt(pi)))
assert ellipk(1) == inf
assert ellipk(1+0j) == inf
assert ellipk(-1).ae('1.3110287771460599052')
assert ellipk(-2).ae('1.1714200841467698589')
assert isinstance(ellipk(-2), mpf)
assert isinstance(ellipe(-2), mpf)
assert ellipk(-50).ae('0.47103424540873331679')
mp.dps = 30
n1 = +fraction(99999,100000)
n2 = +fraction(100001,100000)
mp.dps = 15
assert ellipk(n1).ae('7.1427724505817781901')
assert ellipk(n2).ae(mpc('7.1427417367963090109', '-1.5707923998261688019'))
assert ellipe(n1).ae('1.0000332138990829170')
v = ellipe(n2)
assert v.real.ae('0.999966786328145474069137')
assert (v.imag*10**6).ae('7.853952181727432')
assert ellipk(2).ae(mpc('1.3110287771460599052', '-1.3110287771460599052'))
assert ellipk(50).ae(mpc('0.22326753950210985451', '-0.47434723226254522087'))
assert ellipk(3+4j).ae(mpc('0.91119556380496500866', '0.63133428324134524388'))
assert ellipk(3-4j).ae(mpc('0.91119556380496500866', '-0.63133428324134524388'))
assert ellipk(-3+4j).ae(mpc('0.95357894880405122483', '0.23093044503746114444'))
assert ellipk(-3-4j).ae(mpc('0.95357894880405122483', '-0.23093044503746114444'))
assert isnan(ellipk(nan))
assert isnan(ellipe(nan))
assert ellipk(inf) == 0
assert isinstance(ellipk(inf), mpc)
assert ellipk(-inf) == 0
assert ellipk(1+0j) == inf
assert ellipe(0).ae(pi/2)
assert ellipe(0.5).ae(pi**(mpf(3)/2)/gamma(0.25)**2 +gamma(0.25)**2/(8*sqrt(pi)))
assert ellipe(1) == 1
assert ellipe(1+0j) == 1
assert ellipe(inf) == mpc(0,inf)
assert ellipe(-inf) == inf
assert ellipe(3+4j).ae(1.4995535209333469543-1.5778790079127582745j)
assert ellipe(3-4j).ae(1.4995535209333469543+1.5778790079127582745j)
assert ellipe(-3+4j).ae(2.5804237855343377803-0.8306096791000413778j)
assert ellipe(-3-4j).ae(2.5804237855343377803+0.8306096791000413778j)
assert ellipe(2).ae(0.59907011736779610372+0.59907011736779610372j)
assert ellipe('1e-1000000000').ae(pi/2)
assert ellipk('1e-1000000000').ae(pi/2)
assert ellipe(-pi).ae(2.4535865983838923)
mp.dps = 50
assert ellipk(1/pi).ae('1.724756270009501831744438120951614673874904182624739673')
assert ellipe(1/pi).ae('1.437129808135123030101542922290970050337425479058225712')
assert ellipk(-10*pi).ae('0.5519067523886233967683646782286965823151896970015484512')
assert ellipe(-10*pi).ae('5.926192483740483797854383268707108012328213431657645509')
v = ellipk(pi)
assert v.real.ae('0.973089521698042334840454592642137667227167622330325225')
assert v.imag.ae('-1.156151296372835303836814390793087600271609993858798016')
v = ellipe(pi)
assert v.real.ae('0.4632848917264710404078033487934663562998345622611263332')
assert v.imag.ae('1.0637961621753130852473300451583414489944099504180510966')
mp.dps = 15
def test_exp_integrals():
mp.dps = 15
x = +e
z = e + sqrt(3)*j
assert ei(x).ae(8.21168165538361560)
assert li(x).ae(1.89511781635593676)
assert si(x).ae(1.82104026914756705)
assert ci(x).ae(0.213958001340379779)
assert shi(x).ae(4.11520706247846193)
assert chi(x).ae(4.09647459290515367)
assert fresnels(x).ae(0.437189718149787643)
assert fresnelc(x).ae(0.401777759590243012)
assert airyai(x).ae(0.0108502401568586681)
assert airybi(x).ae(8.98245748585468627)
assert ei(z).ae(3.72597969491314951 + 7.34213212314224421j)
assert li(z).ae(2.28662658112562502 + 1.50427225297269364j)
assert si(z).ae(2.48122029237669054 + 0.12684703275254834j)
assert ci(z).ae(0.169255590269456633 - 0.892020751420780353j)
assert shi(z).ae(1.85810366559344468 + 3.66435842914920263j)
assert chi(z).ae(1.86787602931970484 + 3.67777369399304159j)
assert fresnels(z/3).ae(0.034534397197008182 + 0.754859844188218737j)
assert fresnelc(z/3).ae(1.261581645990027372 + 0.417949198775061893j)
assert airyai(z).ae(-0.0162552579839056062 - 0.0018045715700210556j)
assert airybi(z).ae(-4.98856113282883371 + 2.08558537872180623j)
assert li(0) == 0.0
assert li(1) == -inf
assert li(inf) == inf
assert isinstance(li(0.7), mpf)
assert si(inf).ae(pi/2)
assert si(-inf).ae(-pi/2)
assert ci(inf) == 0
assert ci(0) == -inf
assert isinstance(ei(-0.7), mpf)
assert airyai(inf) == 0
assert airybi(inf) == inf
assert airyai(-inf) == 0
assert airybi(-inf) == 0
assert fresnels(inf) == 0.5
assert fresnelc(inf) == 0.5
assert fresnels(-inf) == -0.5
assert fresnelc(-inf) == -0.5
assert shi(0) == 0
assert shi(inf) == inf
assert shi(-inf) == -inf
assert chi(0) == -inf
assert chi(inf) == inf
def test_ei():
mp.dps = 15
assert ei(0) == -inf
assert ei(inf) == inf
assert ei(-inf) == -0.0
assert ei(20+70j).ae(6.1041351911152984397e6 - 2.7324109310519928872e6j)
# tests for the asymptotic expansion
# values checked with Mathematica ExpIntegralEi
mp.dps = 50
r = ei(20000)
s = '3.8781962825045010930273870085501819470698476975019e+8681'
assert str(r) == s
r = ei(-200)
s = '-6.8852261063076355977108174824557929738368086933303e-90'
assert str(r) == s
r =ei(20000 + 10*j)
sre = '-3.255138234032069402493850638874410725961401274106e+8681'
sim = '-2.1081929993474403520785942429469187647767369645423e+8681'
assert str(r.real) == sre and str(r.imag) == sim
mp.dps = 15
# More asymptotic expansions
assert chi(-10**6+100j).ae('1.3077239389562548386e+434288 + 7.6808956999707408158e+434287j')
assert shi(-10**6+100j).ae('-1.3077239389562548386e+434288 - 7.6808956999707408158e+434287j')
mp.dps = 15
assert ei(10j).ae(-0.0454564330044553726+3.2291439210137706686j)
assert ei(100j).ae(-0.0051488251426104921+3.1330217936839529126j)
u = ei(fmul(10**20, j, exact=True))
assert u.real.ae(-6.4525128526578084421345e-21, abs_eps=0, rel_eps=8*eps)
assert u.imag.ae(pi)
assert ei(-10j).ae(-0.0454564330044553726-3.2291439210137706686j)
assert ei(-100j).ae(-0.0051488251426104921-3.1330217936839529126j)
u = ei(fmul(-10**20, j, exact=True))
assert u.real.ae(-6.4525128526578084421345e-21, abs_eps=0, rel_eps=8*eps)
assert u.imag.ae(-pi)
assert ei(10+10j).ae(-1576.1504265768517448+436.9192317011328140j)
u = ei(-10+10j)
assert u.real.ae(7.6698978415553488362543e-7, abs_eps=0, rel_eps=8*eps)
assert u.imag.ae(3.141595611735621062025)
def test_e1():
mp.dps = 15
assert e1(0) == inf
assert e1(inf) == 0
assert e1(-inf) == mpc(-inf, -pi)
assert e1(10j).ae(0.045456433004455372635 + 0.087551267423977430100j)
assert e1(100j).ae(0.0051488251426104921444 - 0.0085708599058403258790j)
assert e1(fmul(10**20, j, exact=True)).ae(6.4525128526578084421e-21 - 7.6397040444172830039e-21j, abs_eps=0, rel_eps=8*eps)
assert e1(-10j).ae(0.045456433004455372635 - 0.087551267423977430100j)
assert e1(-100j).ae(0.0051488251426104921444 + 0.0085708599058403258790j)
assert e1(fmul(-10**20, j, exact=True)).ae(6.4525128526578084421e-21 + 7.6397040444172830039e-21j, abs_eps=0, rel_eps=8*eps)
def test_expint():
mp.dps = 15
assert expint(0,0) == inf
assert expint(0,1).ae(1/e)
assert expint(0,1.5).ae(2/exp(1.5)/3)
assert expint(1,1).ae(-ei(-1))
assert expint(2,0).ae(1)
assert expint(3,0).ae(1/2.)
assert expint(4,0).ae(1/3.)
assert expint(-2, 0.5).ae(26/sqrt(e))
assert expint(-1,-1) == 0
assert expint(-2,-1).ae(-e)
assert expint(5.5, 0).ae(2/9.)
assert expint(2.00000001,0).ae(100000000./100000001)
assert expint(2+3j,4-j).ae(0.0023461179581675065414+0.0020395540604713669262j)
assert expint('1.01', '1e-1000').ae(99.9999999899412802)
assert expint('1.000000000001', 3.5).ae(0.00697013985754701819446)
assert expint(2,3).ae(3*ei(-3)+exp(-3))
assert (expint(10,20)*10**10).ae(0.694439055541231353)
assert expint(3,inf) == 0
assert expint(3.2,inf) == 0
assert expint(3.2+2j,inf) == 0
assert expint(1,3j).ae(-0.11962978600800032763 + 0.27785620120457163717j)
assert expint(1,3).ae(0.013048381094197037413)
assert expint(1,-3).ae(-ei(3)-pi*j)
#assert expint(3) == expint(1,3)
assert expint(1,-20).ae(-25615652.66405658882 - 3.1415926535897932385j)
assert expint(1000000,0).ae(1./999999)
assert expint(0,2+3j).ae(-0.025019798357114678171 + 0.027980439405104419040j)
assert expint(-1,2+3j).ae(-0.022411973626262070419 + 0.038058922011377716932j)
assert expint(-1.5,0) == inf
def test_trig_integrals():
mp.dps = 30
assert si(mpf(1)/1000000).ae('0.000000999999999999944444444444446111')
assert ci(mpf(1)/1000000).ae('-13.2382948930629912435014366276')
assert si(10**10).ae('1.5707963267075846569685111517747537')
assert ci(10**10).ae('-4.87506025174822653785729773959e-11')
assert si(10**100).ae(pi/2)
assert (ci(10**100)*10**100).ae('-0.372376123661276688262086695553')
assert si(-3) == -si(3)
assert ci(-3).ae(ci(3) + pi*j)
# Test complex structure
mp.dps = 15
assert mp.ci(50).ae(-0.0056283863241163054402)
assert mp.ci(50+2j).ae(-0.018378282946133067149+0.070352808023688336193j)
assert mp.ci(20j).ae(1.28078263320282943611e7+1.5707963267949j)
assert mp.ci(-2+20j).ae(-4.050116856873293505e6+1.207476188206989909e7j)
assert mp.ci(-50+2j).ae(-0.0183782829461330671+3.0712398455661049023j)
assert mp.ci(-50).ae(-0.0056283863241163054+3.1415926535897932385j)
assert mp.ci(-50-2j).ae(-0.0183782829461330671-3.0712398455661049023j)
assert mp.ci(-2-20j).ae(-4.050116856873293505e6-1.207476188206989909e7j)
assert mp.ci(-20j).ae(1.28078263320282943611e7-1.5707963267949j)
assert mp.ci(50-2j).ae(-0.018378282946133067149-0.070352808023688336193j)
assert mp.si(50).ae(1.5516170724859358947)
assert mp.si(50+2j).ae(1.497884414277228461-0.017515007378437448j)
assert mp.si(20j).ae(1.2807826332028294459e7j)
assert mp.si(-2+20j).ae(-1.20747603112735722103e7-4.050116856873293554e6j)
assert mp.si(-50+2j).ae(-1.497884414277228461-0.017515007378437448j)
assert mp.si(-50).ae(-1.5516170724859358947)
assert mp.si(-50-2j).ae(-1.497884414277228461+0.017515007378437448j)
assert mp.si(-2-20j).ae(-1.20747603112735722103e7+4.050116856873293554e6j)
assert mp.si(-20j).ae(-1.2807826332028294459e7j)
assert mp.si(50-2j).ae(1.497884414277228461+0.017515007378437448j)
assert mp.chi(50j).ae(-0.0056283863241163054+1.5707963267948966192j)
assert mp.chi(-2+50j).ae(-0.0183782829461330671+1.6411491348185849554j)
assert mp.chi(-20).ae(1.28078263320282943611e7+3.1415926535898j)
assert mp.chi(-20-2j).ae(-4.050116856873293505e6+1.20747571696809187053e7j)
assert mp.chi(-2-50j).ae(-0.0183782829461330671-1.6411491348185849554j)
assert mp.chi(-50j).ae(-0.0056283863241163054-1.5707963267948966192j)
assert mp.chi(2-50j).ae(-0.0183782829461330671-1.500443518771208283j)
assert mp.chi(20-2j).ae(-4.050116856873293505e6-1.20747603112735722951e7j)
assert mp.chi(20).ae(1.2807826332028294361e7)
assert mp.chi(2+50j).ae(-0.0183782829461330671+1.500443518771208283j)
assert mp.shi(50j).ae(1.5516170724859358947j)
assert mp.shi(-2+50j).ae(0.017515007378437448+1.497884414277228461j)
assert mp.shi(-20).ae(-1.2807826332028294459e7)
assert mp.shi(-20-2j).ae(4.050116856873293554e6-1.20747603112735722103e7j)
assert mp.shi(-2-50j).ae(0.017515007378437448-1.497884414277228461j)
assert mp.shi(-50j).ae(-1.5516170724859358947j)
assert mp.shi(2-50j).ae(-0.017515007378437448-1.497884414277228461j)
assert mp.shi(20-2j).ae(-4.050116856873293554e6-1.20747603112735722103e7j)
assert mp.shi(20).ae(1.2807826332028294459e7)
assert mp.shi(2+50j).ae(-0.017515007378437448+1.497884414277228461j)
def ae(x,y,tol=1e-12):
return abs(x-y) <= abs(y)*tol
assert fp.ci(fp.inf) == 0
assert ae(fp.ci(fp.ninf), fp.pi*1j)
assert ae(fp.si(fp.inf), fp.pi/2)
assert ae(fp.si(fp.ninf), -fp.pi/2)
assert fp.si(0) == 0
assert ae(fp.ci(50), -0.0056283863241163054402)
assert ae(fp.ci(50+2j), -0.018378282946133067149+0.070352808023688336193j)
assert ae(fp.ci(20j), 1.28078263320282943611e7+1.5707963267949j)
assert ae(fp.ci(-2+20j), -4.050116856873293505e6+1.207476188206989909e7j)
assert ae(fp.ci(-50+2j), -0.0183782829461330671+3.0712398455661049023j)
assert ae(fp.ci(-50), -0.0056283863241163054+3.1415926535897932385j)
assert ae(fp.ci(-50-2j), -0.0183782829461330671-3.0712398455661049023j)
assert ae(fp.ci(-2-20j), -4.050116856873293505e6-1.207476188206989909e7j)
assert ae(fp.ci(-20j), 1.28078263320282943611e7-1.5707963267949j)
assert ae(fp.ci(50-2j), -0.018378282946133067149-0.070352808023688336193j)
assert ae(fp.si(50), 1.5516170724859358947)
assert ae(fp.si(50+2j), 1.497884414277228461-0.017515007378437448j)
assert ae(fp.si(20j), 1.2807826332028294459e7j)
assert ae(fp.si(-2+20j), -1.20747603112735722103e7-4.050116856873293554e6j)
assert ae(fp.si(-50+2j), -1.497884414277228461-0.017515007378437448j)
assert ae(fp.si(-50), -1.5516170724859358947)
assert ae(fp.si(-50-2j), -1.497884414277228461+0.017515007378437448j)
assert ae(fp.si(-2-20j), -1.20747603112735722103e7+4.050116856873293554e6j)
assert ae(fp.si(-20j), -1.2807826332028294459e7j)
assert ae(fp.si(50-2j), 1.497884414277228461+0.017515007378437448j)
assert ae(fp.chi(50j), -0.0056283863241163054+1.5707963267948966192j)
assert ae(fp.chi(-2+50j), -0.0183782829461330671+1.6411491348185849554j)
assert ae(fp.chi(-20), 1.28078263320282943611e7+3.1415926535898j)
assert ae(fp.chi(-20-2j), -4.050116856873293505e6+1.20747571696809187053e7j)
assert ae(fp.chi(-2-50j), -0.0183782829461330671-1.6411491348185849554j)
assert ae(fp.chi(-50j), -0.0056283863241163054-1.5707963267948966192j)
assert ae(fp.chi(2-50j), -0.0183782829461330671-1.500443518771208283j)
assert ae(fp.chi(20-2j), -4.050116856873293505e6-1.20747603112735722951e7j)
assert ae(fp.chi(20), 1.2807826332028294361e7)
assert ae(fp.chi(2+50j), -0.0183782829461330671+1.500443518771208283j)
assert ae(fp.shi(50j), 1.5516170724859358947j)
assert ae(fp.shi(-2+50j), 0.017515007378437448+1.497884414277228461j)
assert ae(fp.shi(-20), -1.2807826332028294459e7)
assert ae(fp.shi(-20-2j), 4.050116856873293554e6-1.20747603112735722103e7j)
assert ae(fp.shi(-2-50j), 0.017515007378437448-1.497884414277228461j)
assert ae(fp.shi(-50j), -1.5516170724859358947j)
assert ae(fp.shi(2-50j), -0.017515007378437448-1.497884414277228461j)
assert ae(fp.shi(20-2j), -4.050116856873293554e6-1.20747603112735722103e7j)
assert ae(fp.shi(20), 1.2807826332028294459e7)
assert ae(fp.shi(2+50j), -0.017515007378437448+1.497884414277228461j)
def test_airy():
mp.dps = 15
assert (airyai(10)*10**10).ae(1.1047532552898687)
assert (airybi(10)/10**9).ae(0.45564115354822515)
assert (airyai(1000)*10**9158).ae(9.306933063179556004)
assert (airybi(1000)/10**9154).ae(5.4077118391949465477)
assert airyai(-1000).ae(0.055971895773019918842)
assert airybi(-1000).ae(-0.083264574117080633012)
assert (airyai(100+100j)*10**188).ae(2.9099582462207032076 + 2.353013591706178756j)
assert (airybi(100+100j)/10**185).ae(1.7086751714463652039 - 3.1416590020830804578j)
def test_hyper_0f1():
mp.dps = 15
v = 8.63911136507950465
assert hyper([],[(1,3)],1.5).ae(v)
assert hyper([],[1/3.],1.5).ae(v)
assert hyp0f1(1/3.,1.5).ae(v)
assert hyp0f1((1,3),1.5).ae(v)
# Asymptotic expansion
assert hyp0f1(3,1e9).ae('4.9679055380347771271e+27455')
assert hyp0f1(3,1e9j).ae('-2.1222788784457702157e+19410 + 5.0840597555401854116e+19410j')
def test_hyper_1f1():
mp.dps = 15
v = 1.2917526488617656673
assert hyper([(1,2)],[(3,2)],0.7).ae(v)
assert hyper([(1,2)],[(3,2)],0.7+0j).ae(v)
assert hyper([0.5],[(3,2)],0.7).ae(v)
assert hyper([0.5],[1.5],0.7).ae(v)
assert hyper([0.5],[(3,2)],0.7+0j).ae(v)
assert hyper([0.5],[1.5],0.7+0j).ae(v)
assert hyper([(1,2)],[1.5+0j],0.7).ae(v)
assert hyper([0.5+0j],[1.5],0.7).ae(v)
assert hyper([0.5+0j],[1.5+0j],0.7+0j).ae(v)
assert hyp1f1(0.5,1.5,0.7).ae(v)
assert hyp1f1((1,2),1.5,0.7).ae(v)
# Asymptotic expansion
assert hyp1f1(2,3,1e10).ae('2.1555012157015796988e+4342944809')
assert (hyp1f1(2,3,1e10j)*10**10).ae(-0.97501205020039745852 - 1.7462392454512132074j)
# Shouldn't use asymptotic expansion
assert hyp1f1(-2, 1, 10000).ae(49980001)
# Bug
assert hyp1f1(1j,fraction(1,3),0.415-69.739j).ae(25.857588206024346592 + 15.738060264515292063j)
def test_hyper_2f1():
mp.dps = 15
v = 1.0652207633823291032
assert hyper([(1,2), (3,4)], [2], 0.3).ae(v)
assert hyper([(1,2), 0.75], [2], 0.3).ae(v)
assert hyper([0.5, 0.75], [2.0], 0.3).ae(v)
assert hyper([0.5, 0.75], [2.0], 0.3+0j).ae(v)
assert hyper([0.5+0j, (3,4)], [2.0], 0.3+0j).ae(v)
assert hyper([0.5+0j, (3,4)], [2.0], 0.3).ae(v)
assert hyper([0.5, (3,4)], [2.0+0j], 0.3).ae(v)
assert hyper([0.5+0j, 0.75+0j], [2.0+0j], 0.3+0j).ae(v)
v = 1.09234681096223231717 + 0.18104859169479360380j
assert hyper([(1,2),0.75+j], [2], 0.5).ae(v)
assert hyper([0.5,0.75+j], [2.0], 0.5).ae(v)
assert hyper([0.5,0.75+j], [2.0], 0.5+0j).ae(v)
assert hyper([0.5,0.75+j], [2.0+0j], 0.5+0j).ae(v)
v = 0.9625 - 0.125j
assert hyper([(3,2),-1],[4], 0.1+j/3).ae(v)
assert hyper([1.5,-1.0],[4], 0.1+j/3).ae(v)
assert hyper([1.5,-1.0],[4+0j], 0.1+j/3).ae(v)
assert hyper([1.5+0j,-1.0+0j],[4+0j], 0.1+j/3).ae(v)
v = 1.02111069501693445001 - 0.50402252613466859521j
assert hyper([(2,10),(3,10)],[(4,10)],1.5).ae(v)
assert hyper([0.2,(3,10)],[0.4+0j],1.5).ae(v)
assert hyper([0.2,(3,10)],[0.4+0j],1.5+0j).ae(v)
v = 0.76922501362865848528 + 0.32640579593235886194j
assert hyper([(2,10),(3,10)],[(4,10)],4+2j).ae(v)
assert hyper([0.2,(3,10)],[0.4+0j],4+2j).ae(v)
assert hyper([0.2,(3,10)],[(4,10)],4+2j).ae(v)
def test_hyper_2f1_hard():
mp.dps = 15
# Singular cases
assert hyp2f1(2,-1,-1,3).ae(7)
assert hyp2f1(2,-1,-1,3,eliminate_all=True).ae(0.25)
assert hyp2f1(2,-2,-2,3).ae(34)
assert hyp2f1(2,-2,-2,3,eliminate_all=True).ae(0.25)
assert hyp2f1(2,-2,-3,3) == 14
assert hyp2f1(2,-3,-2,3) == inf
assert hyp2f1(2,-1.5,-1.5,3) == 0.25
assert hyp2f1(1,2,3,0) == 1
assert hyp2f1(0,1,0,0) == 1
assert hyp2f1(0,0,0,0) == 1
assert isnan(hyp2f1(1,1,0,0))
assert hyp2f1(2,-1,-5, 0.25+0.25j).ae(1.1+0.1j)
assert hyp2f1(2,-5,-5, 0.25+0.25j, eliminate=False).ae(163./128 + 125./128*j)
assert hyp2f1(0.7235, -1, -5, 0.3).ae(1.04341)
assert hyp2f1(0.7235, -5, -5, 0.3, eliminate=False).ae(1.2939225017815903812)
assert hyp2f1(-1,-2,4,1) == 1.5
assert hyp2f1(1,2,-3,1) == inf
assert hyp2f1(-2,-2,1,1) == 6
assert hyp2f1(1,-2,-4,1).ae(5./3)
assert hyp2f1(0,-6,-4,1) == 1
assert hyp2f1(0,-3,-4,1) == 1
assert hyp2f1(0,0,0,1) == 1
assert hyp2f1(1,0,0,1,eliminate=False) == 1
assert hyp2f1(1,1,0,1) == inf
assert hyp2f1(1,-6,-4,1) == inf
assert hyp2f1(-7.2,-0.5,-4.5,1) == 0
assert hyp2f1(-7.2,-1,-2,1).ae(-2.6)
assert hyp2f1(1,-0.5,-4.5, 1) == inf
assert hyp2f1(1,0.5,-4.5, 1) == -inf
# Check evaluation on / close to unit circle
z = exp(j*pi/3)
w = (nthroot(2,3)+1)*exp(j*pi/12)/nthroot(3,4)**3
assert hyp2f1('1/2','1/6','1/3', z).ae(w)
assert hyp2f1('1/2','1/6','1/3', z.conjugate()).ae(w.conjugate())
assert hyp2f1(0.25, (1,3), 2, '0.999').ae(1.06826449496030635)
assert hyp2f1(0.25, (1,3), 2, '1.001').ae(1.06867299254830309446-0.00001446586793975874j)
assert hyp2f1(0.25, (1,3), 2, -1).ae(0.96656584492524351673)
assert hyp2f1(0.25, (1,3), 2, j).ae(0.99041766248982072266+0.03777135604180735522j)
assert hyp2f1(2,3,5,'0.99').ae(27.699347904322690602)
assert hyp2f1((3,2),-0.5,3,'0.99').ae(0.68403036843911661388)
assert hyp2f1(2,3,5,1j).ae(0.37290667145974386127+0.59210004902748285917j)
assert fsum([hyp2f1((7,10),(2,3),(-1,2), 0.95*exp(j*k)) for k in range(1,15)]).ae(52.851400204289452922+6.244285013912953225j)
assert fsum([hyp2f1((7,10),(2,3),(-1,2), 1.05*exp(j*k)) for k in range(1,15)]).ae(54.506013786220655330-3.000118813413217097j)
assert fsum([hyp2f1((7,10),(2,3),(-1,2), exp(j*k)) for k in range(1,15)]).ae(55.792077935955314887+1.731986485778500241j)
assert hyp2f1(2,2.5,-3.25,0.999).ae(218373932801217082543180041.33)
# Branches
assert hyp2f1(1,1,2,1.01).ae(4.5595744415723676911-3.1104877758314784539j)
assert hyp2f1(1,1,2,1.01+0.1j).ae(2.4149427480552782484+1.4148224796836938829j)
assert hyp2f1(1,1,2,3+4j).ae(0.14576709331407297807+0.48379185417980360773j)
assert hyp2f1(1,1,2,4).ae(-0.27465307216702742285 - 0.78539816339744830962j)
assert hyp2f1(1,1,2,-4).ae(0.40235947810852509365)
# Other:
# Cancellation with a large parameter involved (bug reported on sage-devel)
assert hyp2f1(112, (51,10), (-9,10), -0.99999).ae(-1.6241361047970862961e-24, abs_eps=0, rel_eps=eps*16)
def test_hyper_3f2_etc():
assert hyper([1,2,3],[1.5,8],-1).ae(0.67108992351533333030)
assert hyper([1,2,3,4],[5,6,7], -1).ae(0.90232988035425506008)
assert hyper([1,2,3],[1.25,5], 1).ae(28.924181329701905701)
assert hyper([1,2,3,4],[5,6,7],5).ae(1.5192307344006649499-1.1529845225075537461j)
assert hyper([1,2,3,4,5],[6,7,8,9],-1).ae(0.96288759462882357253)
assert hyper([1,2,3,4,5],[6,7,8,9],1).ae(1.0428697385885855841)
assert hyper([1,2,3,4,5],[6,7,8,9],5).ae(1.33980653631074769423-0.07143405251029226699j)
assert hyper([1,2.79,3.08,4.37],[5.2,6.1,7.3],5).ae(1.0996321464692607231-1.7748052293979985001j)
assert hyper([1,1,1],[1,2],1) == inf
assert hyper([1,1,1],[2,(101,100)],1).ae(100.01621213528313220)
# slow -- covered by doctests
#assert hyper([1,1,1],[2,3],0.9999).ae(1.2897972005319693905)
def test_hyper_u():
mp.dps = 15
assert hyperu(2,-3,0).ae(0.05)
assert hyperu(2,-3.5,0).ae(4./99)
assert hyperu(2,0,0) == 0.5
assert hyperu(-5,1,0) == -120
assert hyperu(-5,2,0) == inf
assert hyperu(-5,-2,0) == 0
assert hyperu(7,7,3).ae(0.00014681269365593503986) #exp(3)*gammainc(-6,3)
assert hyperu(2,-3,4).ae(0.011836478100271995559)
assert hyperu(3,4,5).ae(1./125)
assert hyperu(2,3,0.0625) == 256
assert hyperu(-1,2,0.25+0.5j) == -1.75+0.5j
assert hyperu(0.5,1.5,7.25).ae(2/sqrt(29))
assert hyperu(2,6,pi).ae(0.55804439825913399130)
assert (hyperu((3,2),8,100+201j)*10**4).ae(-0.3797318333856738798 - 2.9974928453561707782j)
assert (hyperu((5,2),(-1,2),-5000)*10**10).ae(-5.6681877926881664678j)
# XXX: fails because of undetected cancellation in low level series code
# Alternatively: could use asymptotic series here, if convergence test
# tweaked back to recognize this one
#assert (hyperu((5,2),(-1,2),-500)*10**7).ae(-1.82526906001593252847j)
def test_hyper_2f0():
mp.dps = 15
assert hyper([1,2],[],3) == hyp2f0(1,2,3)
assert hyp2f0(2,3,7).ae(0.0116108068639728714668 - 0.0073727413865865802130j)
assert hyp2f0(2,3,0) == 1
assert hyp2f0(0,0,0) == 1
assert hyp2f0(-1,-1,1).ae(2)
assert hyp2f0(-4,1,1.5).ae(62.5)
assert hyp2f0(-4,1,50).ae(147029801)
assert hyp2f0(-4,1,0.0001).ae(0.99960011997600240000)
assert hyp2f0(0.5,0.25,0.001).ae(1.0001251174078538115)
assert hyp2f0(0.5,0.25,3+4j).ae(0.85548875824755163518 + 0.21636041283392292973j)
# Important: cancellation check
assert hyp2f0((1,6),(5,6),-0.02371708245126284498).ae(0.996785723120804309)
# Should be exact; polynomial case
assert hyp2f0(-2,1,0.5+0.5j,zeroprec=200) == 0
assert hyp2f0(1,-2,0.5+0.5j,zeroprec=200) == 0
# There used to be a bug in thresholds that made one of the following hang
for d in [15, 50, 80]:
mp.dps = d
assert hyp2f0(1.5, 0.5, 0.009).ae('1.006867007239309717945323585695344927904000945829843527398772456281301440034218290443367270629519483 + 1.238277162240704919639384945859073461954721356062919829456053965502443570466701567100438048602352623e-46j')
def test_hyper_1f2():
mp.dps = 15
assert hyper([1],[2,3],4) == hyp1f2(1,2,3,4)
a1,b1,b2 = (1,10),(2,3),1./16
assert hyp1f2(a1,b1,b2,10).ae(298.7482725554557568)
assert hyp1f2(a1,b1,b2,100).ae(224128961.48602947604)
assert hyp1f2(a1,b1,b2,1000).ae(1.1669528298622675109e+27)
assert hyp1f2(a1,b1,b2,10000).ae(2.4780514622487212192e+86)
assert hyp1f2(a1,b1,b2,100000).ae(1.3885391458871523997e+274)
assert hyp1f2(a1,b1,b2,1000000).ae('9.8851796978960318255e+867')
assert hyp1f2(a1,b1,b2,10**7).ae('1.1505659189516303646e+2746')
assert hyp1f2(a1,b1,b2,10**8).ae('1.4672005404314334081e+8685')
assert hyp1f2(a1,b1,b2,10**20).ae('3.6888217332150976493e+8685889636')
assert hyp1f2(a1,b1,b2,10*j).ae(-16.163252524618572878 - 44.321567896480184312j)
assert hyp1f2(a1,b1,b2,100*j).ae(61938.155294517848171 + 637349.45215942348739j)
assert hyp1f2(a1,b1,b2,1000*j).ae(8455057657257695958.7 + 6261969266997571510.6j)
assert hyp1f2(a1,b1,b2,10000*j).ae(-8.9771211184008593089e+60 + 4.6550528111731631456e+59j)
assert hyp1f2(a1,b1,b2,100000*j).ae(2.6398091437239324225e+193 + 4.1658080666870618332e+193j)
assert hyp1f2(a1,b1,b2,1000000*j).ae('3.5999042951925965458e+613 + 1.5026014707128947992e+613j')
assert hyp1f2(a1,b1,b2,10**7*j).ae('-8.3208715051623234801e+1939 - 3.6752883490851869429e+1941j')
assert hyp1f2(a1,b1,b2,10**8*j).ae('2.0724195707891484454e+6140 - 1.3276619482724266387e+6141j')
assert hyp1f2(a1,b1,b2,10**20*j).ae('-1.1734497974795488504e+6141851462 + 1.1498106965385471542e+6141851462j')
def test_hyper_2f3():
mp.dps = 15
assert hyper([1,2],[3,4,5],6) == hyp2f3(1,2,3,4,5,6)
a1,a2,b1,b2,b3 = (1,10),(2,3),(3,10), 2, 1./16
# Check asymptotic expansion
assert hyp2f3(a1,a2,b1,b2,b3,10).ae(128.98207160698659976)
assert hyp2f3(a1,a2,b1,b2,b3,1000).ae(6.6309632883131273141e25)
assert hyp2f3(a1,a2,b1,b2,b3,10000).ae(4.6863639362713340539e84)
assert hyp2f3(a1,a2,b1,b2,b3,100000).ae(8.6632451236103084119e271)
assert hyp2f3(a1,a2,b1,b2,b3,10**6).ae('2.0291718386574980641e865')
assert hyp2f3(a1,a2,b1,b2,b3,10**7).ae('7.7639836665710030977e2742')
assert hyp2f3(a1,a2,b1,b2,b3,10**8).ae('3.2537462584071268759e8681')
assert hyp2f3(a1,a2,b1,b2,b3,10**20).ae('1.2966030542911614163e+8685889627')
assert hyp2f3(a1,a2,b1,b2,b3,10*j).ae(-18.551602185587547854 - 13.348031097874113552j)
assert hyp2f3(a1,a2,b1,b2,b3,100*j).ae(78634.359124504488695 + 74459.535945281973996j)
assert hyp2f3(a1,a2,b1,b2,b3,1000*j).ae(597682550276527901.59 - 65136194809352613.078j)
assert hyp2f3(a1,a2,b1,b2,b3,10000*j).ae(-1.1779696326238582496e+59 + 1.2297607505213133872e+59j)
assert hyp2f3(a1,a2,b1,b2,b3,100000*j).ae(2.9844228969804380301e+191 + 7.5587163231490273296e+190j)
assert hyp2f3(a1,a2,b1,b2,b3,1000000*j).ae('7.4859161049322370311e+610 - 2.8467477015940090189e+610j')
assert hyp2f3(a1,a2,b1,b2,b3,10**7*j).ae('-1.7477645579418800826e+1938 - 1.7606522995808116405e+1938j')
assert hyp2f3(a1,a2,b1,b2,b3,10**8*j).ae('-1.6932731942958401784e+6137 - 2.4521909113114629368e+6137j')
assert hyp2f3(a1,a2,b1,b2,b3,10**20*j).ae('-2.0988815677627225449e+6141851451 + 5.7708223542739208681e+6141851452j')
def test_hyper_2f2():
mp.dps = 15
assert hyper([1,2],[3,4],5) == hyp2f2(1,2,3,4,5)
a1,a2,b1,b2 = (3,10),4,(1,2),1./16
assert hyp2f2(a1,a2,b1,b2,10).ae(448225936.3377556696)
assert hyp2f2(a1,a2,b1,b2,10000).ae('1.2012553712966636711e+4358')
assert hyp2f2(a1,a2,b1,b2,-20000).ae(-0.04182343755661214626)
assert hyp2f2(a1,a2,b1,b2,10**20).ae('1.1148680024303263661e+43429448190325182840')
def test_orthpoly():
mp.dps = 15
assert jacobi(-4,2,3,0.7).ae(22800./4913)
assert jacobi(3,2,4,5.5) == 4133.125
assert jacobi(1.5,5/6.,4,0).ae(-1.0851951434075508417)
assert jacobi(-2, 1, 2, 4).ae(-0.16)
assert jacobi(2, -1, 2.5, 4).ae(34.59375)
#assert jacobi(2, -1, 2, 4) == 28.5
assert legendre(5, 7) == 129367
assert legendre(0.5,0).ae(0.53935260118837935667)
assert legendre(-1,-1) == 1
assert legendre(0,-1) == 1
assert legendre(0, 1) == 1
assert legendre(1, -1) == -1
assert legendre(7, 1) == 1
assert legendre(7, -1) == -1
assert legendre(8,1.5).ae(15457523./32768)
assert legendre(j,-j).ae(2.4448182735671431011 + 0.6928881737669934843j)
assert chebyu(5,1) == 6
assert chebyt(3,2) == 26
assert legendre(3.5,-1) == inf
assert legendre(4.5,-1) == -inf
assert legendre(3.5+1j,-1) == mpc(inf,inf)
assert legendre(4.5+1j,-1) == mpc(-inf,-inf)
assert laguerre(4, -2, 3).ae(-1.125)
assert laguerre(3, 1+j, 0.5).ae(0.2291666666666666667 + 2.5416666666666666667j)
def test_hermite():
mp.dps = 15
assert hermite(-2, 0).ae(0.5)
assert hermite(-1, 0).ae(0.88622692545275801365)
assert hermite(0, 0).ae(1)
assert hermite(1, 0) == 0
assert hermite(2, 0).ae(-2)
assert hermite(0, 2).ae(1)
assert hermite(1, 2).ae(4)
assert hermite(1, -2).ae(-4)
assert hermite(2, -2).ae(14)
assert hermite(0.5, 0).ae(0.69136733903629335053)
assert hermite(9, 0) == 0
assert hermite(4,4).ae(3340)
assert hermite(3,4).ae(464)
assert hermite(-4,4).ae(0.00018623860287512396181)
assert hermite(-3,4).ae(0.0016540169879668766270)
assert hermite(9, 2.5j).ae(13638725j)
assert hermite(9, -2.5j).ae(-13638725j)
assert hermite(9, 100).ae(511078883759363024000)
assert hermite(9, -100).ae(-511078883759363024000)
assert hermite(9, 100j).ae(512922083920643024000j)
assert hermite(9, -100j).ae(-512922083920643024000j)
assert hermite(-9.5, 2.5j).ae(-2.9004951258126778174e-6 + 1.7601372934039951100e-6j)
assert hermite(-9.5, -2.5j).ae(-2.9004951258126778174e-6 - 1.7601372934039951100e-6j)
assert hermite(-9.5, 100).ae(1.3776300722767084162e-22, abs_eps=0, rel_eps=eps)
assert hermite(-9.5, -100).ae('1.3106082028470671626e4355')
assert hermite(-9.5, 100j).ae(-9.7900218581864768430e-23 - 9.7900218581864768430e-23j, abs_eps=0, rel_eps=eps)
assert hermite(-9.5, -100j).ae(-9.7900218581864768430e-23 + 9.7900218581864768430e-23j, abs_eps=0, rel_eps=eps)
assert hermite(2+3j, -1-j).ae(851.3677063883687676 - 1496.4373467871007997j)
def test_gegenbauer():
mp.dps = 15
assert gegenbauer(1,2,3).ae(12)
assert gegenbauer(2,3,4).ae(381)
assert gegenbauer(0,0,0) == 0
assert gegenbauer(2,-1,3) == 0
assert gegenbauer(-7, 0.5, 3).ae(8989)
assert gegenbauer(1, -0.5, 3).ae(-3)
assert gegenbauer(1, -1.5, 3).ae(-9)
assert gegenbauer(1, -0.5, 3).ae(-3)
assert gegenbauer(-0.5, -0.5, 3).ae(-2.6383553159023906245)
assert gegenbauer(2+3j, 1-j, 3+4j).ae(14.880536623203696780 + 20.022029711598032898j)
#assert gegenbauer(-2, -0.5, 3).ae(-12)
def test_legenp():
mp.dps = 15
assert legenp(2,0,4) == legendre(2,4)
assert legenp(-2, -1, 0.5).ae(0.43301270189221932338)
assert legenp(-2, -1, 0.5, type=3).ae(0.43301270189221932338j)
assert legenp(-2, 1, 0.5).ae(-0.86602540378443864676)
assert legenp(2+j, 3+4j, -j).ae(134742.98773236786148 + 429782.72924463851745j)
assert legenp(2+j, 3+4j, -j, type=3).ae(802.59463394152268507 - 251.62481308942906447j)
assert legenp(2,4,3).ae(0)
assert legenp(2,4,3,type=3).ae(0)
assert legenp(2,1,0.5).ae(-1.2990381056766579701)
assert legenp(2,1,0.5,type=3).ae(1.2990381056766579701j)
assert legenp(3,2,3).ae(-360)
assert legenp(3,3,3).ae(240j*2**0.5)
assert legenp(3,4,3).ae(0)
assert legenp(0,0.5,2).ae(0.52503756790433198939 - 0.52503756790433198939j)
assert legenp(-1,-0.5,2).ae(0.60626116232846498110 + 0.60626116232846498110j)
assert legenp(-2,0.5,2).ae(1.5751127037129959682 - 1.5751127037129959682j)
assert legenp(-2,0.5,-0.5).ae(-0.85738275810499171286)
def test_legenq():
mp.dps = 15
f = legenq
# Evaluation at poles
assert isnan(f(3,2,1))
assert isnan(f(3,2,-1))
assert isnan(f(3,2,1,type=3))
assert isnan(f(3,2,-1,type=3))
# Evaluation at 0
assert f(0,1,0,type=2).ae(-1)
assert f(-2,2,0,type=2,zeroprec=200).ae(0)
assert f(1.5,3,0,type=2).ae(-2.2239343475841951023)
assert f(0,1,0,type=3).ae(j)
assert f(-2,2,0,type=3,zeroprec=200).ae(0)
assert f(1.5,3,0,type=3).ae(2.2239343475841951022*(1-1j))
# Standard case, degree 0
assert f(0,0,-1.5).ae(-0.8047189562170501873 + 1.5707963267948966192j)
assert f(0,0,-0.5).ae(-0.54930614433405484570)
assert f(0,0,0,zeroprec=200).ae(0)
assert f(0,0,0.5).ae(0.54930614433405484570)
assert f(0,0,1.5).ae(0.8047189562170501873 - 1.5707963267948966192j)
assert f(0,0,-1.5,type=3).ae(-0.80471895621705018730)
assert f(0,0,-0.5,type=3).ae(-0.5493061443340548457 - 1.5707963267948966192j)
assert f(0,0,0,type=3).ae(-1.5707963267948966192j)
assert f(0,0,0.5,type=3).ae(0.5493061443340548457 - 1.5707963267948966192j)
assert f(0,0,1.5,type=3).ae(0.80471895621705018730)
# Standard case, degree 1
assert f(1,0,-1.5).ae(0.2070784343255752810 - 2.3561944901923449288j)
assert f(1,0,-0.5).ae(-0.72534692783297257715)
assert f(1,0,0).ae(-1)
assert f(1,0,0.5).ae(-0.72534692783297257715)
assert f(1,0,1.5).ae(0.2070784343255752810 - 2.3561944901923449288j)
# Standard case, degree 2
assert f(2,0,-1.5).ae(-0.0635669991240192885 + 4.5160394395353277803j)
assert f(2,0,-0.5).ae(0.81866326804175685571)
assert f(2,0,0,zeroprec=200).ae(0)
assert f(2,0,0.5).ae(-0.81866326804175685571)
assert f(2,0,1.5).ae(0.0635669991240192885 - 4.5160394395353277803j)
# Misc orders and degrees
assert f(2,3,1.5,type=2).ae(-5.7243340223994616228j)
assert f(2,3,1.5,type=3).ae(-5.7243340223994616228)
assert f(2,3,0.5,type=2).ae(-12.316805742712016310)
assert f(2,3,0.5,type=3).ae(-12.316805742712016310j)
assert f(2,3,-1.5,type=2).ae(-5.7243340223994616228j)
assert f(2,3,-1.5,type=3).ae(5.7243340223994616228)
assert f(2,3,-0.5,type=2).ae(-12.316805742712016310)
assert f(2,3,-0.5,type=3).ae(-12.316805742712016310j)
assert f(2+3j, 3+4j, 0.5, type=3).ae(0.0016119404873235186807 - 0.0005885900510718119836j)
assert f(2+3j, 3+4j, -1.5, type=3).ae(0.008451400254138808670 + 0.020645193304593235298j)
assert f(-2.5,1,-1.5).ae(3.9553395527435335749j)
assert f(-2.5,1,-0.5).ae(1.9290561746445456908)
assert f(-2.5,1,0).ae(1.2708196271909686299)
assert f(-2.5,1,0.5).ae(-0.31584812990742202869)
assert f(-2.5,1,1.5).ae(-3.9553395527435335742 + 0.2993235655044701706j)
assert f(-2.5,1,-1.5,type=3).ae(0.29932356550447017254j)
assert f(-2.5,1,-0.5,type=3).ae(-0.3158481299074220287 - 1.9290561746445456908j)
assert f(-2.5,1,0,type=3).ae(1.2708196271909686292 - 1.2708196271909686299j)
assert f(-2.5,1,0.5,type=3).ae(1.9290561746445456907 + 0.3158481299074220287j)
assert f(-2.5,1,1.5,type=3).ae(-0.29932356550447017254)
def test_agm():
mp.dps = 15
assert agm(0,0) == 0
assert agm(0,1) == 0
assert agm(1,1) == 1
assert agm(7,7) == 7
assert agm(j,j) == j
assert (1/agm(1,sqrt(2))).ae(0.834626841674073186)
assert agm(1,2).ae(1.4567910310469068692)
assert agm(1,3).ae(1.8636167832448965424)
assert agm(1,j).ae(0.599070117367796104+0.599070117367796104j)
assert agm(2) == agm(1,2)
assert agm(-3,4).ae(0.63468509766550907+1.3443087080896272j)
def test_gammainc():
mp.dps = 15
assert gammainc(2,5).ae(6*exp(-5))
assert gammainc(2,0,5).ae(1-6*exp(-5))
assert gammainc(2,3,5).ae(-6*exp(-5)+4*exp(-3))
assert gammainc(-2.5,-0.5).ae(-0.9453087204829418812-5.3164237738936178621j)
assert gammainc(0,2,4).ae(0.045121158298212213088)
assert gammainc(0,3).ae(0.013048381094197037413)
assert gammainc(0,2+j,1-j).ae(0.00910653685850304839-0.22378752918074432574j)
assert gammainc(0,1-j).ae(0.00028162445198141833+0.17932453503935894015j)
assert gammainc(3,4,5,True).ae(0.11345128607046320253)
assert gammainc(3.5,0,inf).ae(gamma(3.5))
assert gammainc(-150.5,500).ae('6.9825435345798951153e-627')
assert gammainc(-150.5,800).ae('4.6885137549474089431e-788')
assert gammainc(-3.5, -20.5).ae(0.27008820585226911 - 1310.31447140574997636j)
assert gammainc(-3.5, -200.5).ae(0.27008820585226911 - 5.3264597096208368435e76j) # XXX real part
assert gammainc(0,0,2) == inf
assert gammainc(1,b=1).ae(0.6321205588285576784)
assert gammainc(3,2,2) == 0
assert gammainc(2,3+j,3-j).ae(-0.28135485191849314194j)
assert gammainc(4+0j,1).ae(5.8860710587430771455)
# GH issue #301
assert gammainc(-1,-1).ae(-0.8231640121031084799 + 3.1415926535897932385j)
assert gammainc(-2,-1).ae(1.7707229202810768576 - 1.5707963267948966192j)
assert gammainc(-3,-1).ae(-1.4963349162467073643 + 0.5235987755982988731j)
assert gammainc(-4,-1).ae(1.05365418617643814992 - 0.13089969389957471827j)
# Regularized upper gamma
assert isnan(gammainc(0, 0, regularized=True))
assert gammainc(-1, 0, regularized=True) == inf
assert gammainc(1, 0, regularized=True) == 1
assert gammainc(0, 5, regularized=True) == 0
assert gammainc(0, 2+3j, regularized=True) == 0
assert gammainc(0, 5000, regularized=True) == 0
assert gammainc(0, 10**30, regularized=True) == 0
assert gammainc(-1, 5, regularized=True) == 0
assert gammainc(-1, 5000, regularized=True) == 0
assert gammainc(-1, 10**30, regularized=True) == 0
assert gammainc(-1, -5, regularized=True) == 0
assert gammainc(-1, -5000, regularized=True) == 0
assert gammainc(-1, -10**30, regularized=True) == 0
assert gammainc(-1, 3+4j, regularized=True) == 0
assert gammainc(1, 5, regularized=True).ae(exp(-5))
assert gammainc(1, 5000, regularized=True).ae(exp(-5000))
assert gammainc(1, 10**30, regularized=True).ae(exp(-10**30))
assert gammainc(1, 3+4j, regularized=True).ae(exp(-3-4j))
assert gammainc(-1000000,2).ae('1.3669297209397347754e-301037', abs_eps=0, rel_eps=8*eps)
assert gammainc(-1000000,2,regularized=True) == 0
assert gammainc(-1000000,3+4j).ae('-1.322575609404222361e-698979 - 4.9274570591854533273e-698978j', abs_eps=0, rel_eps=8*eps)
assert gammainc(-1000000,3+4j,regularized=True) == 0
assert gammainc(2+3j, 4+5j, regularized=True).ae(0.085422013530993285774-0.052595379150390078503j)
assert gammainc(1000j, 1000j, regularized=True).ae(0.49702647628921131761 + 0.00297355675013575341j)
# Generalized
assert gammainc(3,4,2) == -gammainc(3,2,4)
assert gammainc(4, 2, 3).ae(1.2593494302978947396)
assert gammainc(4, 2, 3, regularized=True).ae(0.20989157171631578993)
assert gammainc(0, 2, 3).ae(0.035852129613864082155)
assert gammainc(0, 2, 3, regularized=True) == 0
assert gammainc(-1, 2, 3).ae(0.015219822548487616132)
assert gammainc(-1, 2, 3, regularized=True) == 0
assert gammainc(0, 2, 3).ae(0.035852129613864082155)
assert gammainc(0, 2, 3, regularized=True) == 0
# Should use upper gammas
assert gammainc(5, 10000, 12000).ae('1.1359381951461801687e-4327', abs_eps=0, rel_eps=8*eps)
# Should use lower gammas
assert gammainc(10000, 2, 3).ae('8.1244514125995785934e4765')
# GH issue 306
assert gammainc(3,-1-1j) == 0
assert gammainc(3,-1+1j) == 0
assert gammainc(2,-1) == 0
assert gammainc(2,-1+0j) == 0
assert gammainc(2+0j,-1) == 0
def test_gammainc_expint_n():
# These tests are intended to check all cases of the low-level code
# for upper gamma and expint with small integer index.
# Need to cover positive/negative arguments; small/large/huge arguments
# for both positive and negative indices, as well as indices 0 and 1
# which may be special-cased
mp.dps = 15
assert expint(-3,3.5).ae(0.021456366563296693987)
assert expint(-2,3.5).ae(0.014966633183073309405)
assert expint(-1,3.5).ae(0.011092916359219041088)
assert expint(0,3.5).ae(0.0086278238349481430685)
assert expint(1,3.5).ae(0.0069701398575483929193)
assert expint(2,3.5).ae(0.0058018939208991255223)
assert expint(3,3.5).ae(0.0049453773495857807058)
assert expint(-3,-3.5).ae(-4.6618170604073311319)
assert expint(-2,-3.5).ae(-5.5996974157555515963)
assert expint(-1,-3.5).ae(-6.7582555017739415818)
assert expint(0,-3.5).ae(-9.4615577024835182145)
assert expint(1,-3.5).ae(-13.925353995152335292 - 3.1415926535897932385j)
assert expint(2,-3.5).ae(-15.62328702434085977 - 10.995574287564276335j)
assert expint(3,-3.5).ae(-10.783026313250347722 - 19.242255003237483586j)
assert expint(-3,350).ae(2.8614825451252838069e-155, abs_eps=0, rel_eps=8*eps)
assert expint(-2,350).ae(2.8532837224504675901e-155, abs_eps=0, rel_eps=8*eps)
assert expint(-1,350).ae(2.8451316155828634555e-155, abs_eps=0, rel_eps=8*eps)
assert expint(0,350).ae(2.8370258275042797989e-155, abs_eps=0, rel_eps=8*eps)
assert expint(1,350).ae(2.8289659656701459404e-155, abs_eps=0, rel_eps=8*eps)
assert expint(2,350).ae(2.8209516419468505006e-155, abs_eps=0, rel_eps=8*eps)
assert expint(3,350).ae(2.8129824725501272171e-155, abs_eps=0, rel_eps=8*eps)
assert expint(-3,-350).ae(-2.8528796154044839443e+149)
assert expint(-2,-350).ae(-2.8610072121701264351e+149)
assert expint(-1,-350).ae(-2.8691813842677537647e+149)
assert expint(0,-350).ae(-2.8774025343659421709e+149)
u = expint(1,-350)
assert u.ae(-2.8856710698020863568e+149)
assert u.imag.ae(-3.1415926535897932385)
u = expint(2,-350)
assert u.ae(-2.8939874026504650534e+149)
assert u.imag.ae(-1099.5574287564276335)
u = expint(3,-350)
assert u.ae(-2.9023519497915044349e+149)
assert u.imag.ae(-192422.55003237483586)
assert expint(-3,350000000000000000000000).ae('2.1592908471792544286e-152003068666138139677919', abs_eps=0, rel_eps=8*eps)
assert expint(-2,350000000000000000000000).ae('2.1592908471792544286e-152003068666138139677919', abs_eps=0, rel_eps=8*eps)
assert expint(-1,350000000000000000000000).ae('2.1592908471792544286e-152003068666138139677919', abs_eps=0, rel_eps=8*eps)
assert expint(0,350000000000000000000000).ae('2.1592908471792544286e-152003068666138139677919', abs_eps=0, rel_eps=8*eps)
assert expint(1,350000000000000000000000).ae('2.1592908471792544286e-152003068666138139677919', abs_eps=0, rel_eps=8*eps)
assert expint(2,350000000000000000000000).ae('2.1592908471792544286e-152003068666138139677919', abs_eps=0, rel_eps=8*eps)
assert expint(3,350000000000000000000000).ae('2.1592908471792544286e-152003068666138139677919', abs_eps=0, rel_eps=8*eps)
assert expint(-3,-350000000000000000000000).ae('-3.7805306852415755699e+152003068666138139677871')
assert expint(-2,-350000000000000000000000).ae('-3.7805306852415755699e+152003068666138139677871')
assert expint(-1,-350000000000000000000000).ae('-3.7805306852415755699e+152003068666138139677871')
assert expint(0,-350000000000000000000000).ae('-3.7805306852415755699e+152003068666138139677871')
u = expint(1,-350000000000000000000000)
assert u.ae('-3.7805306852415755699e+152003068666138139677871')
assert u.imag.ae(-3.1415926535897932385)
u = expint(2,-350000000000000000000000)
assert u.imag.ae(-1.0995574287564276335e+24)
assert u.ae('-3.7805306852415755699e+152003068666138139677871')
u = expint(3,-350000000000000000000000)
assert u.imag.ae(-1.9242255003237483586e+47)
assert u.ae('-3.7805306852415755699e+152003068666138139677871')
# Small case; no branch cut
assert gammainc(-3,3.5).ae(0.00010020262545203707109)
assert gammainc(-2,3.5).ae(0.00040370427343557393517)
assert gammainc(-1,3.5).ae(0.0016576839773997501492)
assert gammainc(0,3.5).ae(0.0069701398575483929193)
assert gammainc(1,3.5).ae(0.03019738342231850074)
assert gammainc(2,3.5).ae(0.13588822540043325333)
assert gammainc(3,3.5).ae(0.64169439772426814072)
# Small case; with branch cut
assert gammainc(-3,-3.5).ae(0.03595832954467563286 + 0.52359877559829887308j)
assert gammainc(-2,-3.5).ae(-0.88024704597962022221 - 1.5707963267948966192j)
assert gammainc(-1,-3.5).ae(4.4637962926688170771 + 3.1415926535897932385j)
assert gammainc(0,-3.5).ae(-13.925353995152335292 - 3.1415926535897932385j)
assert gammainc(1,-3.5).ae(33.115451958692313751)
assert gammainc(2,-3.5).ae(-82.788629896730784377)
assert gammainc(3,-3.5).ae(240.08702670051927469)
# Asymptotic case; no branch cut
assert gammainc(-3,350).ae(6.5424095113340358813e-163, abs_eps=0, rel_eps=8*eps)
assert gammainc(-2,350).ae(2.296312222489899769e-160, abs_eps=0, rel_eps=8*eps)
assert gammainc(-1,350).ae(8.059861834133858573e-158, abs_eps=0, rel_eps=8*eps)
assert gammainc(0,350).ae(2.8289659656701459404e-155, abs_eps=0, rel_eps=8*eps)
assert gammainc(1,350).ae(9.9295903962649792963e-153, abs_eps=0, rel_eps=8*eps)
assert gammainc(2,350).ae(3.485286229089007733e-150, abs_eps=0, rel_eps=8*eps)
assert gammainc(3,350).ae(1.2233453960006379793e-147, abs_eps=0, rel_eps=8*eps)
# Asymptotic case; branch cut
u = gammainc(-3,-350)
assert u.ae(6.7889565783842895085e+141)
assert u.imag.ae(0.52359877559829887308)
u = gammainc(-2,-350)
assert u.ae(-2.3692668977889832121e+144)
assert u.imag.ae(-1.5707963267948966192)
u = gammainc(-1,-350)
assert u.ae(8.2685354361441858669e+146)
assert u.imag.ae(3.1415926535897932385)
u = gammainc(0,-350)
assert u.ae(-2.8856710698020863568e+149)
assert u.imag.ae(-3.1415926535897932385)
u = gammainc(1,-350)
assert u.ae(1.0070908870280797598e+152)
assert u.imag == 0
u = gammainc(2,-350)
assert u.ae(-3.5147471957279983618e+154)
assert u.imag == 0
u = gammainc(3,-350)
assert u.ae(1.2266568422179417091e+157)
assert u.imag == 0
# Extreme asymptotic case
assert gammainc(-3,350000000000000000000000).ae('5.0362468738874738859e-152003068666138139677990', abs_eps=0, rel_eps=8*eps)
assert gammainc(-2,350000000000000000000000).ae('1.7626864058606158601e-152003068666138139677966', abs_eps=0, rel_eps=8*eps)
assert gammainc(-1,350000000000000000000000).ae('6.1694024205121555102e-152003068666138139677943', abs_eps=0, rel_eps=8*eps)
assert gammainc(0,350000000000000000000000).ae('2.1592908471792544286e-152003068666138139677919', abs_eps=0, rel_eps=8*eps)
assert gammainc(1,350000000000000000000000).ae('7.5575179651273905e-152003068666138139677896', abs_eps=0, rel_eps=8*eps)
assert gammainc(2,350000000000000000000000).ae('2.645131287794586675e-152003068666138139677872', abs_eps=0, rel_eps=8*eps)
assert gammainc(3,350000000000000000000000).ae('9.2579595072810533625e-152003068666138139677849', abs_eps=0, rel_eps=8*eps)
u = gammainc(-3,-350000000000000000000000)
assert u.ae('8.8175642804468234866e+152003068666138139677800')
assert u.imag.ae(0.52359877559829887308)
u = gammainc(-2,-350000000000000000000000)
assert u.ae('-3.0861474981563882203e+152003068666138139677824')
assert u.imag.ae(-1.5707963267948966192)
u = gammainc(-1,-350000000000000000000000)
assert u.ae('1.0801516243547358771e+152003068666138139677848')
assert u.imag.ae(3.1415926535897932385)
u = gammainc(0,-350000000000000000000000)
assert u.ae('-3.7805306852415755699e+152003068666138139677871')
assert u.imag.ae(-3.1415926535897932385)
assert gammainc(1,-350000000000000000000000).ae('1.3231857398345514495e+152003068666138139677895')
assert gammainc(2,-350000000000000000000000).ae('-4.6311500894209300731e+152003068666138139677918')
assert gammainc(3,-350000000000000000000000).ae('1.6209025312973255256e+152003068666138139677942')
def test_incomplete_beta():
mp.dps = 15
assert betainc(-2,-3,0.5,0.75).ae(63.4305673311255413583969)
assert betainc(4.5,0.5+2j,2.5,6).ae(0.2628801146130621387903065 + 0.5162565234467020592855378j)
assert betainc(4,5,0,6).ae(90747.77142857142857142857)
def test_erf():
mp.dps = 15
assert erf(0) == 0
assert erf(1).ae(0.84270079294971486934)
assert erf(3+4j).ae(-120.186991395079444098 - 27.750337293623902498j)
assert erf(-4-3j).ae(-0.99991066178539168236 + 0.00004972026054496604j)
assert erf(pi).ae(0.99999112385363235839)
assert erf(1j).ae(1.6504257587975428760j)
assert erf(-1j).ae(-1.6504257587975428760j)
assert isinstance(erf(1), mpf)
assert isinstance(erf(-1), mpf)
assert isinstance(erf(0), mpf)
assert isinstance(erf(0j), mpc)
assert erf(inf) == 1
assert erf(-inf) == -1
assert erfi(0) == 0
assert erfi(1/pi).ae(0.371682698493894314)
assert erfi(inf) == inf
assert erfi(-inf) == -inf
assert erf(1+0j) == erf(1)
assert erfc(1+0j) == erfc(1)
assert erf(0.2+0.5j).ae(1 - erfc(0.2+0.5j))
assert erfc(0) == 1
assert erfc(1).ae(1-erf(1))
assert erfc(-1).ae(1-erf(-1))
assert erfc(1/pi).ae(1-erf(1/pi))
assert erfc(-10) == 2
assert erfc(-1000000) == 2
assert erfc(-inf) == 2
assert erfc(inf) == 0
assert isnan(erfc(nan))
assert (erfc(10**4)*mpf(10)**43429453).ae('3.63998738656420')
assert erf(8+9j).ae(-1072004.2525062051158 + 364149.91954310255423j)
assert erfc(8+9j).ae(1072005.2525062051158 - 364149.91954310255423j)
assert erfc(-8-9j).ae(-1072003.2525062051158 + 364149.91954310255423j)
mp.dps = 50
# This one does not use the asymptotic series
assert (erfc(10)*10**45).ae('2.0884875837625447570007862949577886115608181193212')
# This one does
assert (erfc(50)*10**1088).ae('2.0709207788416560484484478751657887929322509209954')
mp.dps = 15
assert str(erfc(10**50)) == '3.66744826532555e-4342944819032518276511289189166050822943970058036665661144537831658646492088707747292249493384317534'
assert erfinv(0) == 0
assert erfinv(0.5).ae(0.47693627620446987338)
assert erfinv(-0.5).ae(-0.47693627620446987338)
assert erfinv(1) == inf
assert erfinv(-1) == -inf
assert erf(erfinv(0.95)).ae(0.95)
assert erf(erfinv(0.999999999995)).ae(0.999999999995)
assert erf(erfinv(-0.999999999995)).ae(-0.999999999995)
mp.dps = 50
assert erf(erfinv('0.99999999999999999999999999999995')).ae('0.99999999999999999999999999999995')
assert erf(erfinv('0.999999999999999999999999999999995')).ae('0.999999999999999999999999999999995')
assert erf(erfinv('-0.999999999999999999999999999999995')).ae('-0.999999999999999999999999999999995')
mp.dps = 15
# Complex asymptotic expansions
v = erfc(50j)
assert v.real == 1
assert v.imag.ae('-6.1481820666053078736e+1083')
assert erfc(-100+5j).ae(2)
assert (erfc(100+5j)*10**4335).ae(2.3973567853824133572 - 3.9339259530609420597j)
assert erfc(100+100j).ae(0.00065234366376857698698 - 0.0039357263629214118437j)
def test_pdf():
mp.dps = 15
assert npdf(-inf) == 0
assert npdf(inf) == 0
assert npdf(5,0,2).ae(npdf(5+4,4,2))
assert quadts(lambda x: npdf(x,-0.5,0.8), [-inf, inf]) == 1
assert ncdf(0) == 0.5
assert ncdf(3,3) == 0.5
assert ncdf(-inf) == 0
assert ncdf(inf) == 1
assert ncdf(10) == 1
# Verify that this is computed accurately
assert (ncdf(-10)*10**24).ae(7.619853024160526)
def test_lambertw():
mp.dps = 15
assert lambertw(0) == 0
assert lambertw(0+0j) == 0
assert lambertw(inf) == inf
assert isnan(lambertw(nan))
assert lambertw(inf,1).real == inf
assert lambertw(inf,1).imag.ae(2*pi)
assert lambertw(-inf,1).real == inf
assert lambertw(-inf,1).imag.ae(3*pi)
assert lambertw(0,-1) == -inf
assert lambertw(0,1) == -inf
assert lambertw(0,3) == -inf
assert lambertw(e).ae(1)
assert lambertw(1).ae(0.567143290409783873)
assert lambertw(-pi/2).ae(j*pi/2)
assert lambertw(-log(2)/2).ae(-log(2))
assert lambertw(0.25).ae(0.203888354702240164)
assert lambertw(-0.25).ae(-0.357402956181388903)
assert lambertw(-1./10000,0).ae(-0.000100010001500266719)
assert lambertw(-0.25,-1).ae(-2.15329236411034965)
assert lambertw(0.25,-1).ae(-3.00899800997004620-4.07652978899159763j)
assert lambertw(-0.25,-1).ae(-2.15329236411034965)
assert lambertw(0.25,1).ae(-3.00899800997004620+4.07652978899159763j)
assert lambertw(-0.25,1).ae(-3.48973228422959210+7.41405453009603664j)
assert lambertw(-4).ae(0.67881197132094523+1.91195078174339937j)
assert lambertw(-4,1).ae(-0.66743107129800988+7.76827456802783084j)
assert lambertw(-4,-1).ae(0.67881197132094523-1.91195078174339937j)
assert lambertw(1000).ae(5.24960285240159623)
assert lambertw(1000,1).ae(4.91492239981054535+5.44652615979447070j)
assert lambertw(1000,-1).ae(4.91492239981054535-5.44652615979447070j)
assert lambertw(1000,5).ae(3.5010625305312892+29.9614548941181328j)
assert lambertw(3+4j).ae(1.281561806123775878+0.533095222020971071j)
assert lambertw(-0.4+0.4j).ae(-0.10396515323290657+0.61899273315171632j)
assert lambertw(3+4j,1).ae(-0.11691092896595324+5.61888039871282334j)
assert lambertw(3+4j,-1).ae(0.25856740686699742-3.85211668616143559j)
assert lambertw(-0.5,-1).ae(-0.794023632344689368-0.770111750510379110j)
assert lambertw(-1./10000,1).ae(-11.82350837248724344+6.80546081842002101j)
assert lambertw(-1./10000,-1).ae(-11.6671145325663544)
assert lambertw(-1./10000,-2).ae(-11.82350837248724344-6.80546081842002101j)
assert lambertw(-1./100000,4).ae(-14.9186890769540539+26.1856750178782046j)
assert lambertw(-1./100000,5).ae(-15.0931437726379218666+32.5525721210262290086j)
assert lambertw((2+j)/10).ae(0.173704503762911669+0.071781336752835511j)
assert lambertw((2+j)/10,1).ae(-3.21746028349820063+4.56175438896292539j)
assert lambertw((2+j)/10,-1).ae(-3.03781405002993088-3.53946629633505737j)
assert lambertw((2+j)/10,4).ae(-4.6878509692773249+23.8313630697683291j)
assert lambertw(-(2+j)/10).ae(-0.226933772515757933-0.164986470020154580j)
assert lambertw(-(2+j)/10,1).ae(-2.43569517046110001+0.76974067544756289j)
assert lambertw(-(2+j)/10,-1).ae(-3.54858738151989450-6.91627921869943589j)
assert lambertw(-(2+j)/10,4).ae(-4.5500846928118151+20.6672982215434637j)
mp.dps = 50
assert lambertw(pi).ae('1.073658194796149172092178407024821347547745350410314531')
mp.dps = 15
# Former bug in generated branch
assert lambertw(-0.5+0.002j).ae(-0.78917138132659918344 + 0.76743539379990327749j)
assert lambertw(-0.5-0.002j).ae(-0.78917138132659918344 - 0.76743539379990327749j)
assert lambertw(-0.448+0.4j).ae(-0.11855133765652382241 + 0.66570534313583423116j)
assert lambertw(-0.448-0.4j).ae(-0.11855133765652382241 - 0.66570534313583423116j)
assert lambertw(-0.65475+0.0001j).ae(-0.61053421111385310898+1.0396534993944097723803j)
# Huge branch index
w = lambertw(1,10**20)
assert w.real.ae(-47.889578926290259164)
assert w.imag.ae(6.2831853071795864769e+20)
def test_lambertw_hard():
def check(x,y):
y = convert(y)
type_ok = True
if isinstance(y, mpf):
type_ok = isinstance(x, mpf)
real_ok = abs(x.real-y.real) <= abs(y.real)*8*eps
imag_ok = abs(x.imag-y.imag) <= abs(y.imag)*8*eps
#print x, y, abs(x.real-y.real), abs(x.imag-y.imag)
return real_ok and imag_ok
# Evaluation near 0
mp.dps = 15
assert check(lambertw(1e-10), 9.999999999000000000e-11)
assert check(lambertw(-1e-10), -1.000000000100000000e-10)
assert check(lambertw(1e-10j), 9.999999999999999999733e-21 + 9.99999999999999999985e-11j)
assert check(lambertw(-1e-10j), 9.999999999999999999733e-21 - 9.99999999999999999985e-11j)
assert check(lambertw(1e-10,1), -26.303186778379041559 + 3.265093911703828397j)
assert check(lambertw(-1e-10,1), -26.326236166739163892 + 6.526183280686333315j)
assert check(lambertw(1e-10j,1), -26.312931726911421551 + 4.896366881798013421j)
assert check(lambertw(-1e-10j,1), -26.297238779529035066 + 1.632807161345576513j)
assert check(lambertw(1e-10,-1), -26.303186778379041559 - 3.265093911703828397j)
assert check(lambertw(-1e-10,-1), -26.295238819246925694)
assert check(lambertw(1e-10j,-1), -26.297238779529035028 - 1.6328071613455765135j)
assert check(lambertw(-1e-10j,-1), -26.312931726911421551 - 4.896366881798013421j)
# Test evaluation very close to the branch point -1/e
# on the -1, 0, and 1 branches
add = lambda x, y: fadd(x,y,exact=True)
sub = lambda x, y: fsub(x,y,exact=True)
addj = lambda x, y: fadd(x,fmul(y,1j,exact=True),exact=True)
subj = lambda x, y: fadd(x,fmul(y,-1j,exact=True),exact=True)
mp.dps = 1500
a = -1/e + 10*eps
d3 = mpf('1e-3')
d10 = mpf('1e-10')
d20 = mpf('1e-20')
d40 = mpf('1e-40')
d80 = mpf('1e-80')
d300 = mpf('1e-300')
d1000 = mpf('1e-1000')
mp.dps = 15
# ---- Branch 0 ----
# -1/e + eps
assert check(lambertw(add(a,d3)), -0.92802015005456704876)
assert check(lambertw(add(a,d10)), -0.99997668374140088071)
assert check(lambertw(add(a,d20)), -0.99999999976683560186)
assert lambertw(add(a,d40)) == -1
assert lambertw(add(a,d80)) == -1
assert lambertw(add(a,d300)) == -1
assert lambertw(add(a,d1000)) == -1
# -1/e - eps
assert check(lambertw(sub(a,d3)), -0.99819016149860989001+0.07367191188934638577j)
assert check(lambertw(sub(a,d10)), -0.9999999998187812114595992+0.0000233164398140346109194j)
assert check(lambertw(sub(a,d20)), -0.99999999999999999998187+2.331643981597124203344e-10j)
assert check(lambertw(sub(a,d40)), -1.0+2.33164398159712420336e-20j)
assert check(lambertw(sub(a,d80)), -1.0+2.33164398159712420336e-40j)
assert check(lambertw(sub(a,d300)), -1.0+2.33164398159712420336e-150j)
assert check(lambertw(sub(a,d1000)), mpc(-1,'2.33164398159712420336e-500'))
# -1/e + eps*j
assert check(lambertw(addj(a,d3)), -0.94790387486938526634+0.05036819639190132490j)
assert check(lambertw(addj(a,d10)), -0.9999835127872943680999899+0.0000164870314895821225256j)
assert check(lambertw(addj(a,d20)), -0.999999999835127872929987+1.64872127051890935830e-10j)
assert check(lambertw(addj(a,d40)), -0.9999999999999999999835+1.6487212707001281468305e-20j)
assert check(lambertw(addj(a,d80)), -1.0 + 1.64872127070012814684865e-40j)
assert check(lambertw(addj(a,d300)), -1.0 + 1.64872127070012814684865e-150j)
assert check(lambertw(addj(a,d1000)), mpc(-1.0,'1.64872127070012814684865e-500'))
# -1/e - eps*j
assert check(lambertw(subj(a,d3)), -0.94790387486938526634-0.05036819639190132490j)
assert check(lambertw(subj(a,d10)), -0.9999835127872943680999899-0.0000164870314895821225256j)
assert check(lambertw(subj(a,d20)), -0.999999999835127872929987-1.64872127051890935830e-10j)
assert check(lambertw(subj(a,d40)), -0.9999999999999999999835-1.6487212707001281468305e-20j)
assert check(lambertw(subj(a,d80)), -1.0 - 1.64872127070012814684865e-40j)
assert check(lambertw(subj(a,d300)), -1.0 - 1.64872127070012814684865e-150j)
assert check(lambertw(subj(a,d1000)), mpc(-1.0,'-1.64872127070012814684865e-500'))
# ---- Branch 1 ----
assert check(lambertw(addj(a,d3),1), -3.088501303219933378005990 + 7.458676867597474813950098j)
assert check(lambertw(addj(a,d80),1), -3.088843015613043855957087 + 7.461489285654254556906117j)
assert check(lambertw(addj(a,d300),1), -3.088843015613043855957087 + 7.461489285654254556906117j)
assert check(lambertw(addj(a,d1000),1), -3.088843015613043855957087 + 7.461489285654254556906117j)
assert check(lambertw(subj(a,d3),1), -1.0520914180450129534365906 + 0.0539925638125450525673175j)
assert check(lambertw(subj(a,d10),1), -1.0000164872127056318529390 + 0.000016487393927159250398333077j)
assert check(lambertw(subj(a,d20),1), -1.0000000001648721270700128 + 1.64872127088134693542628e-10j)
assert check(lambertw(subj(a,d40),1), -1.000000000000000000016487 + 1.64872127070012814686677e-20j)
assert check(lambertw(subj(a,d80),1), -1.0 + 1.64872127070012814684865e-40j)
assert check(lambertw(subj(a,d300),1), -1.0 + 1.64872127070012814684865e-150j)
assert check(lambertw(subj(a,d1000),1), mpc(-1.0, '1.64872127070012814684865e-500'))
# ---- Branch -1 ----
# -1/e + eps
assert check(lambertw(add(a,d3),-1), -1.075608941186624989414945)
assert check(lambertw(add(a,d10),-1), -1.000023316621036696460620)
assert check(lambertw(add(a,d20),-1), -1.000000000233164398177834)
assert lambertw(add(a,d40),-1) == -1
assert lambertw(add(a,d80),-1) == -1
assert lambertw(add(a,d300),-1) == -1
assert lambertw(add(a,d1000),-1) == -1
# -1/e - eps
assert check(lambertw(sub(a,d3),-1), -0.99819016149860989001-0.07367191188934638577j)
assert check(lambertw(sub(a,d10),-1), -0.9999999998187812114595992-0.0000233164398140346109194j)
assert check(lambertw(sub(a,d20),-1), -0.99999999999999999998187-2.331643981597124203344e-10j)
assert check(lambertw(sub(a,d40),-1), -1.0-2.33164398159712420336e-20j)
assert check(lambertw(sub(a,d80),-1), -1.0-2.33164398159712420336e-40j)
assert check(lambertw(sub(a,d300),-1), -1.0-2.33164398159712420336e-150j)
assert check(lambertw(sub(a,d1000),-1), mpc(-1,'-2.33164398159712420336e-500'))
# -1/e + eps*j
assert check(lambertw(addj(a,d3),-1), -1.0520914180450129534365906 - 0.0539925638125450525673175j)
assert check(lambertw(addj(a,d10),-1), -1.0000164872127056318529390 - 0.0000164873939271592503983j)
assert check(lambertw(addj(a,d20),-1), -1.0000000001648721270700 - 1.64872127088134693542628e-10j)
assert check(lambertw(addj(a,d40),-1), -1.00000000000000000001648 - 1.6487212707001281468667726e-20j)
assert check(lambertw(addj(a,d80),-1), -1.0 - 1.64872127070012814684865e-40j)
assert check(lambertw(addj(a,d300),-1), -1.0 - 1.64872127070012814684865e-150j)
assert check(lambertw(addj(a,d1000),-1), mpc(-1.0,'-1.64872127070012814684865e-500'))
# -1/e - eps*j
assert check(lambertw(subj(a,d3),-1), -3.088501303219933378005990-7.458676867597474813950098j)
assert check(lambertw(subj(a,d10),-1), -3.088843015579260686911033-7.461489285372968780020716j)
assert check(lambertw(subj(a,d20),-1), -3.088843015613043855953708-7.461489285654254556877988j)
assert check(lambertw(subj(a,d40),-1), -3.088843015613043855957087-7.461489285654254556906117j)
assert check(lambertw(subj(a,d80),-1), -3.088843015613043855957087 - 7.461489285654254556906117j)
assert check(lambertw(subj(a,d300),-1), -3.088843015613043855957087 - 7.461489285654254556906117j)
assert check(lambertw(subj(a,d1000),-1), -3.088843015613043855957087 - 7.461489285654254556906117j)
# One more case, testing higher precision
mp.dps = 500
x = -1/e + mpf('1e-13')
ans = "-0.99999926266961377166355784455394913638782494543377383"\
"744978844374498153493943725364881490261187530235150668593869563"\
"168276697689459394902153960200361935311512317183678882"
mp.dps = 15
assert lambertw(x).ae(ans)
mp.dps = 50
assert lambertw(x).ae(ans)
mp.dps = 150
assert lambertw(x).ae(ans)
def test_meijerg():
mp.dps = 15
assert meijerg([[2,3],[1]],[[0.5,2],[3,4]], 2.5).ae(4.2181028074787439386)
assert meijerg([[],[1+j]],[[1],[1]], 3+4j).ae(271.46290321152464592 - 703.03330399954820169j)
assert meijerg([[0.25],[1]],[[0.5],[2]],0) == 0
assert meijerg([[0],[]],[[0,0,'1/3','2/3'], []], '2/27').ae(2.2019391389653314120)
# Verify 1/z series being used
assert meijerg([[-3],[-0.5]], [[-1],[-2.5]], -0.5).ae(-1.338096165935754898687431)
assert meijerg([[1-(-1)],[1-(-2.5)]], [[1-(-3)],[1-(-0.5)]], -2.0).ae(-1.338096165935754898687431)
assert meijerg([[-3],[-0.5]], [[-1],[-2.5]], -1).ae(-(pi+4)/(4*pi))
a = 2.5
b = 1.25
for z in [mpf(0.25), mpf(2)]:
x1 = hyp1f1(a,b,z)
x2 = gamma(b)/gamma(a)*meijerg([[1-a],[]],[[0],[1-b]],-z)
x3 = gamma(b)/gamma(a)*meijerg([[1-0],[1-(1-b)]],[[1-(1-a)],[]],-1/z)
assert x1.ae(x2)
assert x1.ae(x3)
def test_appellf1():
mp.dps = 15
assert appellf1(2,-2,1,1,2,3).ae(-1.75)
assert appellf1(2,1,-2,1,2,3).ae(-8)
assert appellf1(2,1,-2,1,0.5,0.25).ae(1.5)
assert appellf1(-2,1,3,2,3,3).ae(19)
assert appellf1(1,2,3,4,0.5,0.125).ae( 1.53843285792549786518)
def test_coulomb():
# Note: most tests are doctests
# Test for a bug:
mp.dps = 15
assert coulombg(mpc(-5,0),2,3).ae(20.087729487721430394)
def test_hyper_param_accuracy():
mp.dps = 15
As = [n+1e-10 for n in range(-5,-1)]
Bs = [n+1e-10 for n in range(-12,-5)]
assert hyper(As,Bs,10).ae(-381757055858.652671927)
assert legenp(0.5, 100, 0.25).ae(-2.4124576567211311755e+144)
assert (hyp1f1(1000,1,-100)*10**24).ae(5.2589445437370169113)
assert (hyp2f1(10, -900, 10.5, 0.99)*10**24).ae(1.9185370579660768203)
assert (hyp2f1(1000,1.5,-3.5,-1.5)*10**385).ae(-2.7367529051334000764)
assert hyp2f1(-5, 10, 3, 0.5, zeroprec=500) == 0
assert (hyp1f1(-10000, 1000, 100)*10**424).ae(-3.1046080515824859974)
assert (hyp2f1(1000,1.5,-3.5,-0.75,maxterms=100000)*10**231).ae(-4.0534790813913998643)
assert legenp(2, 3, 0.25) == 0
try:
hypercomb(lambda a: [([],[],[],[],[a],[-a],0.5)], [3])
assert 0
except ValueError:
pass
assert hypercomb(lambda a: [([],[],[],[],[a],[-a],0.5)], [3], infprec=200) == inf
assert meijerg([[],[]],[[0,0,0,0],[]],0.1).ae(1.5680822343832351418)
assert (besselk(400,400)*10**94).ae(1.4387057277018550583)
mp.dps = 5
(hyp1f1(-5000.5, 1500, 100)*10**185).ae(8.5185229673381935522)
(hyp1f1(-5000, 1500, 100)*10**185).ae(9.1501213424563944311)
mp.dps = 15
(hyp1f1(-5000.5, 1500, 100)*10**185).ae(8.5185229673381935522)
(hyp1f1(-5000, 1500, 100)*10**185).ae(9.1501213424563944311)
assert hyp0f1(fadd(-20,'1e-100',exact=True), 0.25).ae(1.85014429040102783e+49)
assert hyp0f1((-20*10**100+1, 10**100), 0.25).ae(1.85014429040102783e+49)
def test_hypercomb_zero_pow():
# check that 0^0 = 1
assert hypercomb(lambda a: (([0],[a],[],[],[],[],0),), [0]) == 1
assert meijerg([[-1.5],[]],[[0],[-0.75]],0).ae(1.4464090846320771425)
def test_spherharm():
mp.dps = 15
t = 0.5; r = 0.25
assert spherharm(0,0,t,r).ae(0.28209479177387814347)
assert spherharm(1,-1,t,r).ae(0.16048941205971996369 - 0.04097967481096344271j)
assert spherharm(1,0,t,r).ae(0.42878904414183579379)
assert spherharm(1,1,t,r).ae(-0.16048941205971996369 - 0.04097967481096344271j)
assert spherharm(2,-2,t,r).ae(0.077915886919031181734 - 0.042565643022253962264j)
assert spherharm(2,-1,t,r).ae(0.31493387233497459884 - 0.08041582001959297689j)
assert spherharm(2,0,t,r).ae(0.41330596756220761898)
assert spherharm(2,1,t,r).ae(-0.31493387233497459884 - 0.08041582001959297689j)
assert spherharm(2,2,t,r).ae(0.077915886919031181734 + 0.042565643022253962264j)
assert spherharm(3,-3,t,r).ae(0.033640236589690881646 - 0.031339125318637082197j)
assert spherharm(3,-2,t,r).ae(0.18091018743101461963 - 0.09883168583167010241j)
assert spherharm(3,-1,t,r).ae(0.42796713930907320351 - 0.10927795157064962317j)
assert spherharm(3,0,t,r).ae(0.27861659336351639787)
assert spherharm(3,1,t,r).ae(-0.42796713930907320351 - 0.10927795157064962317j)
assert spherharm(3,2,t,r).ae(0.18091018743101461963 + 0.09883168583167010241j)
assert spherharm(3,3,t,r).ae(-0.033640236589690881646 - 0.031339125318637082197j)
assert spherharm(0,-1,t,r) == 0
assert spherharm(0,-2,t,r) == 0
assert spherharm(0,1,t,r) == 0
assert spherharm(0,2,t,r) == 0
assert spherharm(1,2,t,r) == 0
assert spherharm(1,3,t,r) == 0
assert spherharm(1,-2,t,r) == 0
assert spherharm(1,-3,t,r) == 0
assert spherharm(2,3,t,r) == 0
assert spherharm(2,4,t,r) == 0
assert spherharm(2,-3,t,r) == 0
assert spherharm(2,-4,t,r) == 0
assert spherharm(3,4.5,0.5,0.25).ae(-22.831053442240790148 + 10.910526059510013757j)
assert spherharm(2+3j, 1-j, 1+j, 3+4j).ae(-2.6582752037810116935 - 1.0909214905642160211j)
assert spherharm(-6,2.5,t,r).ae(0.39383644983851448178 + 0.28414687085358299021j)
assert spherharm(-3.5, 3, 0.5, 0.25).ae(0.014516852987544698924 - 0.015582769591477628495j)
assert spherharm(-3, 3, 0.5, 0.25) == 0
assert spherharm(-6, 3, 0.5, 0.25).ae(-0.16544349818782275459 - 0.15412657723253924562j)
assert spherharm(-6, 1.5, 0.5, 0.25).ae(0.032208193499767402477 + 0.012678000924063664921j)
assert spherharm(3,0,0,1).ae(0.74635266518023078283)
assert spherharm(3,-2,0,1) == 0
assert spherharm(3,-2,1,1).ae(-0.16270707338254028971 - 0.35552144137546777097j)
def test_qfunctions():
mp.dps = 15
assert qp(2,3,100).ae('2.7291482267247332183e2391')
def test_issue_239():
mp.prec = 150
x = ldexp(2476979795053773,-52)
assert betainc(206, 385, 0, 0.55, 1).ae('0.99999999999999999999996570910644857895771110649954')
mp.dps = 15
try:
u = hyp2f1(-5,5,0.5,0.5)
raise AssertionError("hyp2f1(-5,5,0.5,0.5) (failed zero detection)")
except (mp.NoConvergence, ValueError):
pass
| 76,413 | 51.302533 | 255 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/tests/test_eigen_symmetric.py
|
#!/usr/bin/python
# -*- coding: utf-8 -*-
from mpmath import mp
from mpmath import libmp
xrange = libmp.backend.xrange
def run_eigsy(A, verbose = False):
if verbose:
print("original matrix:\n", str(A))
D, Q = mp.eigsy(A)
B = Q * mp.diag(D) * Q.transpose()
C = A - B
E = Q * Q.transpose() - mp.eye(A.rows)
if verbose:
print("eigenvalues:\n", D)
print("eigenvectors:\n", Q)
NC = mp.mnorm(C)
NE = mp.mnorm(E)
if verbose:
print("difference:", NC, "\n", C, "\n")
print("difference:", NE, "\n", E, "\n")
eps = mp.exp( 0.8 * mp.log(mp.eps))
assert NC < eps
assert NE < eps
return NC
def run_eighe(A, verbose = False):
if verbose:
print("original matrix:\n", str(A))
D, Q = mp.eighe(A)
B = Q * mp.diag(D) * Q.transpose_conj()
C = A - B
E = Q * Q.transpose_conj() - mp.eye(A.rows)
if verbose:
print("eigenvalues:\n", D)
print("eigenvectors:\n", Q)
NC = mp.mnorm(C)
NE = mp.mnorm(E)
if verbose:
print("difference:", NC, "\n", C, "\n")
print("difference:", NE, "\n", E, "\n")
eps = mp.exp( 0.8 * mp.log(mp.eps))
assert NC < eps
assert NE < eps
return NC
def run_svd_r(A, full_matrices = False, verbose = True):
m, n = A.rows, A.cols
eps = mp.exp(0.8 * mp.log(mp.eps))
if verbose:
print("original matrix:\n", str(A))
print("full", full_matrices)
U, S0, V = mp.svd_r(A, full_matrices = full_matrices)
S = mp.zeros(U.cols, V.rows)
for j in xrange(min(m, n)):
S[j,j] = S0[j]
if verbose:
print("U:\n", str(U))
print("S:\n", str(S0))
print("V:\n", str(V))
C = U * S * V - A
err = mp.mnorm(C)
if verbose:
print("C\n", str(C), "\n", err)
assert err < eps
D = V * V.transpose() - mp.eye(V.rows)
err = mp.mnorm(D)
if verbose:
print("D:\n", str(D), "\n", err)
assert err < eps
E = U.transpose() * U - mp.eye(U.cols)
err = mp.mnorm(E)
if verbose:
print("E:\n", str(E), "\n", err)
assert err < eps
def run_svd_c(A, full_matrices = False, verbose = True):
m, n = A.rows, A.cols
eps = mp.exp(0.8 * mp.log(mp.eps))
if verbose:
print("original matrix:\n", str(A))
print("full", full_matrices)
U, S0, V = mp.svd_c(A, full_matrices = full_matrices)
S = mp.zeros(U.cols, V.rows)
for j in xrange(min(m, n)):
S[j,j] = S0[j]
if verbose:
print("U:\n", str(U))
print("S:\n", str(S0))
print("V:\n", str(V))
C = U * S * V - A
err = mp.mnorm(C)
if verbose:
print("C\n", str(C), "\n", err)
assert err < eps
D = V * V.transpose_conj() - mp.eye(V.rows)
err = mp.mnorm(D)
if verbose:
print("D:\n", str(D), "\n", err)
assert err < eps
E = U.transpose_conj() * U - mp.eye(U.cols)
err = mp.mnorm(E)
if verbose:
print("E:\n", str(E), "\n", err)
assert err < eps
def run_gauss(qtype, a, b):
eps = 1e-5
d, e = mp.gauss_quadrature(len(a), qtype)
d -= mp.matrix(a)
e -= mp.matrix(b)
assert mp.mnorm(d) < eps
assert mp.mnorm(e) < eps
def irandmatrix(n, range = 10):
"""
random matrix with integer entries
"""
A = mp.matrix(n, n)
for i in xrange(n):
for j in xrange(n):
A[i,j]=int( (2 * mp.rand() - 1) * range)
return A
#######################
def test_eighe_fixed_matrix():
A = mp.matrix([[2, 3], [3, 5]])
run_eigsy(A)
run_eighe(A)
A = mp.matrix([[7, -11], [-11, 13]])
run_eigsy(A)
run_eighe(A)
A = mp.matrix([[2, 11, 7], [11, 3, 13], [7, 13, 5]])
run_eigsy(A)
run_eighe(A)
A = mp.matrix([[2, 0, 7], [0, 3, 1], [7, 1, 5]])
run_eigsy(A)
run_eighe(A)
#
A = mp.matrix([[2, 3+7j], [3-7j, 5]])
run_eighe(A)
A = mp.matrix([[2, -11j, 0], [+11j, 3, 29j], [0, -29j, 5]])
run_eighe(A)
A = mp.matrix([[2, 11 + 17j, 7 + 19j], [11 - 17j, 3, -13 + 23j], [7 - 19j, -13 - 23j, 5]])
run_eighe(A)
def test_eigsy_randmatrix():
N = 5
for a in xrange(10):
A = 2 * mp.randmatrix(N, N) - 1
for i in xrange(0, N):
for j in xrange(i + 1, N):
A[j,i] = A[i,j]
run_eigsy(A)
def test_eighe_randmatrix():
N = 5
for a in xrange(10):
A = (2 * mp.randmatrix(N, N) - 1) + 1j * (2 * mp.randmatrix(N, N) - 1)
for i in xrange(0, N):
A[i,i] = mp.re(A[i,i])
for j in xrange(i + 1, N):
A[j,i] = mp.conj(A[i,j])
run_eighe(A)
def test_eigsy_irandmatrix():
N = 4
R = 4
for a in xrange(10):
A=irandmatrix(N, R)
for i in xrange(0, N):
for j in xrange(i + 1, N):
A[j,i] = A[i,j]
run_eigsy(A)
def test_eighe_irandmatrix():
N = 4
R = 4
for a in xrange(10):
A=irandmatrix(N, R) + 1j * irandmatrix(N, R)
for i in xrange(0, N):
A[i,i] = mp.re(A[i,i])
for j in xrange(i + 1, N):
A[j,i] = mp.conj(A[i,j])
run_eighe(A)
def test_svd_r_rand():
for i in xrange(5):
full = mp.rand() > 0.5
m = 1 + int(mp.rand() * 10)
n = 1 + int(mp.rand() * 10)
A = 2 * mp.randmatrix(m, n) - 1
if mp.rand() > 0.5:
A *= 10
for x in xrange(m):
for y in xrange(n):
A[x,y]=int(A[x,y])
run_svd_r(A, full_matrices = full, verbose = False)
def test_svd_c_rand():
for i in xrange(5):
full = mp.rand() > 0.5
m = 1 + int(mp.rand() * 10)
n = 1 + int(mp.rand() * 10)
A = (2 * mp.randmatrix(m, n) - 1) + 1j * (2 * mp.randmatrix(m, n) - 1)
if mp.rand() > 0.5:
A *= 10
for x in xrange(m):
for y in xrange(n):
A[x,y]=int(mp.re(A[x,y])) + 1j * int(mp.im(A[x,y]))
run_svd_c(A, full_matrices=full, verbose=False)
def test_svd_test_case():
# a test case from Golub and Reinsch
# (see wilkinson/reinsch: handbook for auto. comp., vol ii-linear algebra, 134-151(1971).)
eps = mp.exp(0.8 * mp.log(mp.eps))
a = [[22, 10, 2, 3, 7],
[14, 7, 10, 0, 8],
[-1, 13, -1, -11, 3],
[-3, -2, 13, -2, 4],
[ 9, 8, 1, -2, 4],
[ 9, 1, -7, 5, -1],
[ 2, -6, 6, 5, 1],
[ 4, 5, 0, -2, 2]]
a = mp.matrix(a)
b = mp.matrix([mp.sqrt(1248), 20, mp.sqrt(384), 0, 0])
S = mp.svd_r(a, compute_uv = False)
S -= b
assert mp.mnorm(S) < eps
S = mp.svd_c(a, compute_uv = False)
S -= b
assert mp.mnorm(S) < eps
def test_gauss_quadrature_static():
a = [-0.57735027, 0.57735027]
b = [ 1, 1]
run_gauss("legendre", a , b)
a = [ -0.906179846, -0.538469310, 0, 0.538469310, 0.906179846]
b = [ 0.23692689, 0.47862867, 0.56888889, 0.47862867, 0.23692689]
run_gauss("legendre", a , b)
a = [ 0.06943184, 0.33000948, 0.66999052, 0.93056816]
b = [ 0.17392742, 0.32607258, 0.32607258, 0.17392742]
run_gauss("legendre01", a , b)
a = [-0.70710678, 0.70710678]
b = [ 0.88622693, 0.88622693]
run_gauss("hermite", a , b)
a = [ -2.02018287, -0.958572465, 0, 0.958572465, 2.02018287]
b = [ 0.01995324, 0.39361932, 0.94530872, 0.39361932, 0.01995324]
run_gauss("hermite", a , b)
a = [ 0.41577456, 2.29428036, 6.28994508]
b = [ 0.71109301, 0.27851773, 0.01038926]
run_gauss("laguerre", a , b)
def test_gauss_quadrature_dynamic(verbose = False):
n = 5
A = mp.randmatrix(2 * n, 1)
def F(x):
r = 0
for i in xrange(len(A) - 1, -1, -1):
r = r * x + A[i]
return r
def run(qtype, FW, R, alpha = 0, beta = 0):
X, W = mp.gauss_quadrature(n, qtype, alpha = alpha, beta = beta)
a = 0
for i in xrange(len(X)):
a += W[i] * F(X[i])
b = mp.quad(lambda x: FW(x) * F(x), R)
c = mp.fabs(a - b)
if verbose:
print(qtype, c, a, b)
assert c < 1e-5
run("legendre", lambda x: 1, [-1, 1])
run("legendre01", lambda x: 1, [0, 1])
run("hermite", lambda x: mp.exp(-x*x), [-mp.inf, mp.inf])
run("laguerre", lambda x: mp.exp(-x), [0, mp.inf])
run("glaguerre", lambda x: mp.sqrt(x)*mp.exp(-x), [0, mp.inf], alpha = 1 / mp.mpf(2))
run("chebyshev1", lambda x: 1/mp.sqrt(1-x*x), [-1, 1])
run("chebyshev2", lambda x: mp.sqrt(1-x*x), [-1, 1])
run("jacobi", lambda x: (1-x)**(1/mp.mpf(3)) * (1+x)**(1/mp.mpf(5)), [-1, 1], alpha = 1 / mp.mpf(3), beta = 1 / mp.mpf(5) )
| 8,778 | 23.522346 | 127 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/tests/extratest_gamma.py
|
from mpmath import *
from mpmath.libmp import ifac
import sys
if "-dps" in sys.argv:
maxdps = int(sys.argv[sys.argv.index("-dps")+1])
else:
maxdps = 1000
raise_ = "-raise" in sys.argv
errcount = 0
def check(name, func, z, y):
global errcount
try:
x = func(z)
except:
errcount += 1
if raise_:
raise
print()
print(name)
print("EXCEPTION")
import traceback
traceback.print_tb(sys.exc_info()[2])
print()
return
xre = x.real
xim = x.imag
yre = y.real
yim = y.imag
tol = eps*8
err = 0
if abs(xre-yre) > abs(yre)*tol:
err = 1
print()
print("Error! %s (re = %s, wanted %s, err=%s)" % (name, nstr(xre,10), nstr(yre,10), nstr(abs(xre-yre))))
errcount += 1
if raise_:
raise SystemExit
if abs(xim-yim) > abs(yim)*tol:
err = 1
print()
print("Error! %s (im = %s, wanted %s, err=%s)" % (name, nstr(xim,10), nstr(yim,10), nstr(abs(xim-yim))))
errcount += 1
if raise_:
raise SystemExit
if not err:
sys.stdout.write("%s ok; " % name)
def testcase(case):
z, result = case
print("Testing z =", z)
mp.dps = 1010
z = eval(z)
mp.dps = maxdps + 50
if result is None:
gamma_val = gamma(z)
loggamma_val = loggamma(z)
factorial_val = factorial(z)
rgamma_val = rgamma(z)
else:
loggamma_val = eval(result)
gamma_val = exp(loggamma_val)
factorial_val = z * gamma_val
rgamma_val = 1/gamma_val
for dps in [5, 10, 15, 25, 40, 60, 90, 120, 250, 600, 1000, 1800, 3600]:
if dps > maxdps:
break
mp.dps = dps
print("dps = %s" % dps)
check("gamma", gamma, z, gamma_val)
check("rgamma", rgamma, z, rgamma_val)
check("loggamma", loggamma, z, loggamma_val)
check("factorial", factorial, z, factorial_val)
print()
mp.dps = 15
testcases = []
# Basic values
for n in list(range(1,200)) + list(range(201,2000,17)):
testcases.append(["%s" % n, None])
for n in range(-200,200):
testcases.append(["%s+0.5" % n, None])
testcases.append(["%s+0.37" % n, None])
testcases += [\
["(0.1+1j)", None],
["(-0.1+1j)", None],
["(0.1-1j)", None],
["(-0.1-1j)", None],
["10j", None],
["-10j", None],
["100j", None],
["10000j", None],
["-10000000j", None],
["(10**100)*j", None],
["125+(10**100)*j", None],
["-125+(10**100)*j", None],
["(10**10)*(1+j)", None],
["(10**10)*(-1+j)", None],
["(10**100)*(1+j)", None],
["(10**100)*(-1+j)", None],
["(1.5-1j)", None],
["(6+4j)", None],
["(4+1j)", None],
["(3.5+2j)", None],
["(1.5-1j)", None],
["(-6-4j)", None],
["(-2-3j)", None],
["(-2.5-2j)", None],
["(4+1j)", None],
["(3+3j)", None],
["(2-2j)", None],
["1", "0"],
["2", "0"],
["3", "log(2)"],
["4", "log(6)"],
["5", "log(24)"],
["0.5", "log(pi)/2"],
["1.5", "log(sqrt(pi)/2)"],
["2.5", "log(3*sqrt(pi)/4)"],
["mpf('0.37')", None],
["0.25", "log(sqrt(2*sqrt(2*pi**3)/agm(1,sqrt(2))))"],
["-0.4", None],
["mpf('-1.9')", None],
["mpf('12.8')", None],
["mpf('33.7')", None],
["mpf('95.2')", None],
["mpf('160.3')", None],
["mpf('2057.8')", None],
["25", "log(ifac(24))"],
["80", "log(ifac(79))"],
["500", "log(ifac(500-1))"],
["8000", "log(ifac(8000-1))"],
["8000.5", None],
["mpf('8000.1')", None],
["mpf('1.37e10')", None],
["mpf('1.37e10')*(1+j)", None],
["mpf('1.37e10')*(-1+j)", None],
["mpf('1.37e10')*(-1-j)", None],
["mpf('1.37e10')*(-1+j)", None],
["mpf('1.37e100')", None],
["mpf('1.37e100')*(1+j)", None],
["mpf('1.37e100')*(-1+j)", None],
["mpf('1.37e100')*(-1-j)", None],
["mpf('1.37e100')*(-1+j)", None],
["3+4j",
"mpc('"
"-1.7566267846037841105306041816232757851567066070613445016197619371316057169"
"4723618263960834804618463052988607348289672535780644470689771115236512106002"
"5970873471563240537307638968509556191696167970488390423963867031934333890838"
"8009531786948197210025029725361069435208930363494971027388382086721660805397"
"9163230643216054580167976201709951509519218635460317367338612500626714783631"
"7498317478048447525674016344322545858832610325861086336204591943822302971823"
"5161814175530618223688296232894588415495615809337292518431903058265147109853"
"1710568942184987827643886816200452860853873815413367529829631430146227470517"
"6579967222200868632179482214312673161276976117132204633283806161971389519137"
"1243359764435612951384238091232760634271570950240717650166551484551654327989"
"9360285030081716934130446150245110557038117075172576825490035434069388648124"
"6678152254554001586736120762641422590778766100376515737713938521275749049949"
"1284143906816424244705094759339932733567910991920631339597278805393743140853"
"391550313363278558195609260225928','"
"4.74266443803465792819488940755002274088830335171164611359052405215840070271"
"5906813009373171139767051863542508136875688550817670379002790304870822775498"
"2809996675877564504192565392367259119610438951593128982646945990372179860613"
"4294436498090428077839141927485901735557543641049637962003652638924845391650"
"9546290137755550107224907606529385248390667634297183361902055842228798984200"
"9591180450211798341715874477629099687609819466457990642030707080894518168924"
"6805549314043258530272479246115112769957368212585759640878745385160943755234"
"9398036774908108204370323896757543121853650025529763655312360354244898913463"
"7115955702828838923393113618205074162812089732064414530813087483533203244056"
"0546577484241423134079056537777170351934430586103623577814746004431994179990"
"5318522939077992613855205801498201930221975721246498720895122345420698451980"
"0051215797310305885845964334761831751370672996984756815410977750799748813563"
"8784405288158432214886648743541773208808731479748217023665577802702269468013"
"673719173759245720489020315779001')"],
]
for z in [4, 14, 34, 64]:
testcases.append(["(2+j)*%s/3" % z, None])
testcases.append(["(-2+j)*%s/3" % z, None])
testcases.append(["(1+2*j)*%s/3" % z, None])
testcases.append(["(2-j)*%s/3" % z, None])
testcases.append(["(20+j)*%s/3" % z, None])
testcases.append(["(-20+j)*%s/3" % z, None])
testcases.append(["(1+20*j)*%s/3" % z, None])
testcases.append(["(20-j)*%s/3" % z, None])
testcases.append(["(200+j)*%s/3" % z, None])
testcases.append(["(-200+j)*%s/3" % z, None])
testcases.append(["(1+200*j)*%s/3" % z, None])
testcases.append(["(200-j)*%s/3" % z, None])
# Poles
for n in [0,1,2,3,4,25,-1,-2,-3,-4,-20,-21,-50,-51,-200,-201,-20000,-20001]:
for t in ['1e-5', '1e-20', '1e-100', '1e-10000']:
testcases.append(["fadd(%s,'%s',exact=True)" % (n, t), None])
testcases.append(["fsub(%s,'%s',exact=True)" % (n, t), None])
testcases.append(["fadd(%s,'%sj',exact=True)" % (n, t), None])
testcases.append(["fsub(%s,'%sj',exact=True)" % (n, t), None])
if __name__ == "__main__":
from timeit import default_timer as clock
tot_time = 0.0
for case in testcases:
t1 = clock()
testcase(case)
t2 = clock()
print("Test time:", t2-t1)
print()
tot_time += (t2-t1)
print("Total time:", tot_time)
print("Errors:", errcount)
| 7,228 | 32.467593 | 112 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/tests/test_interval.py
|
from mpmath import *
def test_interval_identity():
iv.dps = 15
assert mpi(2) == mpi(2, 2)
assert mpi(2) != mpi(-2, 2)
assert not (mpi(2) != mpi(2, 2))
assert mpi(-1, 1) == mpi(-1, 1)
assert str(mpi('0.1')) == "[0.099999999999999991673, 0.10000000000000000555]"
assert repr(mpi('0.1')) == "mpi('0.099999999999999992', '0.10000000000000001')"
u = mpi(-1, 3)
assert -1 in u
assert 2 in u
assert 3 in u
assert -1.1 not in u
assert 3.1 not in u
assert mpi(-1, 3) in u
assert mpi(0, 1) in u
assert mpi(-1.1, 2) not in u
assert mpi(2.5, 3.1) not in u
w = mpi(-inf, inf)
assert mpi(-5, 5) in w
assert mpi(2, inf) in w
assert mpi(0, 2) in mpi(0, 10)
assert not (3 in mpi(-inf, 0))
def test_interval_hash():
assert hash(mpi(3)) == hash(3)
assert hash(mpi(3.25)) == hash(3.25)
assert hash(mpi(3,4)) == hash(mpi(3,4))
assert hash(iv.mpc(3)) == hash(3)
assert hash(iv.mpc(3,4)) == hash(3+4j)
assert hash(iv.mpc((1,3),(2,4))) == hash(iv.mpc((1,3),(2,4)))
def test_interval_arithmetic():
iv.dps = 15
assert mpi(2) + mpi(3,4) == mpi(5,6)
assert mpi(1, 2)**2 == mpi(1, 4)
assert mpi(1) + mpi(0, 1e-50) == mpi(1, mpf('1.0000000000000002'))
x = 1 / (1 / mpi(3))
assert x.a < 3 < x.b
x = mpi(2) ** mpi(0.5)
iv.dps += 5
sq = iv.sqrt(2)
iv.dps -= 5
assert x.a < sq < x.b
assert mpi(1) / mpi(1, inf)
assert mpi(2, 3) / inf == mpi(0, 0)
assert mpi(0) / inf == 0
assert mpi(0) / 0 == mpi(-inf, inf)
assert mpi(inf) / 0 == mpi(-inf, inf)
assert mpi(0) * inf == mpi(-inf, inf)
assert 1 / mpi(2, inf) == mpi(0, 0.5)
assert str((mpi(50, 50) * mpi(-10, -10)) / 3) == \
'[-166.66666666666668561, -166.66666666666665719]'
assert mpi(0, 4) ** 3 == mpi(0, 64)
assert mpi(2,4).mid == 3
iv.dps = 30
a = mpi(iv.pi)
iv.dps = 15
b = +a
assert b.a < a.a
assert b.b > a.b
a = mpi(iv.pi)
assert a == +a
assert abs(mpi(-1,2)) == mpi(0,2)
assert abs(mpi(0.5,2)) == mpi(0.5,2)
assert abs(mpi(-3,2)) == mpi(0,3)
assert abs(mpi(-3,-0.5)) == mpi(0.5,3)
assert mpi(0) * mpi(2,3) == mpi(0)
assert mpi(2,3) * mpi(0) == mpi(0)
assert mpi(1,3).delta == 2
assert mpi(1,2) - mpi(3,4) == mpi(-3,-1)
assert mpi(-inf,0) - mpi(0,inf) == mpi(-inf,0)
assert mpi(-inf,0) - mpi(-inf,inf) == mpi(-inf,inf)
assert mpi(0,inf) - mpi(-inf,1) == mpi(-1,inf)
def test_interval_mul():
assert mpi(-1, 0) * inf == mpi(-inf, 0)
assert mpi(-1, 0) * -inf == mpi(0, inf)
assert mpi(0, 1) * inf == mpi(0, inf)
assert mpi(0, 1) * mpi(0, inf) == mpi(0, inf)
assert mpi(-1, 1) * inf == mpi(-inf, inf)
assert mpi(-1, 1) * mpi(0, inf) == mpi(-inf, inf)
assert mpi(-1, 1) * mpi(-inf, inf) == mpi(-inf, inf)
assert mpi(-inf, 0) * mpi(0, 1) == mpi(-inf, 0)
assert mpi(-inf, 0) * mpi(0, 0) * mpi(-inf, 0)
assert mpi(-inf, 0) * mpi(-inf, inf) == mpi(-inf, inf)
assert mpi(-5,0)*mpi(-32,28) == mpi(-140,160)
assert mpi(2,3) * mpi(-1,2) == mpi(-3,6)
# Should be undefined?
assert mpi(inf, inf) * 0 == mpi(-inf, inf)
assert mpi(-inf, -inf) * 0 == mpi(-inf, inf)
assert mpi(0) * mpi(-inf,2) == mpi(-inf,inf)
assert mpi(0) * mpi(-2,inf) == mpi(-inf,inf)
assert mpi(-2,inf) * mpi(0) == mpi(-inf,inf)
assert mpi(-inf,2) * mpi(0) == mpi(-inf,inf)
def test_interval_pow():
assert mpi(3)**2 == mpi(9, 9)
assert mpi(-3)**2 == mpi(9, 9)
assert mpi(-3, 1)**2 == mpi(0, 9)
assert mpi(-3, -1)**2 == mpi(1, 9)
assert mpi(-3, -1)**3 == mpi(-27, -1)
assert mpi(-3, 1)**3 == mpi(-27, 1)
assert mpi(-2, 3)**2 == mpi(0, 9)
assert mpi(-3, 2)**2 == mpi(0, 9)
assert mpi(4) ** -1 == mpi(0.25, 0.25)
assert mpi(-4) ** -1 == mpi(-0.25, -0.25)
assert mpi(4) ** -2 == mpi(0.0625, 0.0625)
assert mpi(-4) ** -2 == mpi(0.0625, 0.0625)
assert mpi(0, 1) ** inf == mpi(0, 1)
assert mpi(0, 1) ** -inf == mpi(1, inf)
assert mpi(0, inf) ** inf == mpi(0, inf)
assert mpi(0, inf) ** -inf == mpi(0, inf)
assert mpi(1, inf) ** inf == mpi(1, inf)
assert mpi(1, inf) ** -inf == mpi(0, 1)
assert mpi(2, 3) ** 1 == mpi(2, 3)
assert mpi(2, 3) ** 0 == 1
assert mpi(1,3) ** mpi(2) == mpi(1,9)
def test_interval_sqrt():
assert mpi(4) ** 0.5 == mpi(2)
def test_interval_div():
assert mpi(0.5, 1) / mpi(-1, 0) == mpi(-inf, -0.5)
assert mpi(0, 1) / mpi(0, 1) == mpi(0, inf)
assert mpi(inf, inf) / mpi(inf, inf) == mpi(0, inf)
assert mpi(inf, inf) / mpi(2, inf) == mpi(0, inf)
assert mpi(inf, inf) / mpi(2, 2) == mpi(inf, inf)
assert mpi(0, inf) / mpi(2, inf) == mpi(0, inf)
assert mpi(0, inf) / mpi(2, 2) == mpi(0, inf)
assert mpi(2, inf) / mpi(2, 2) == mpi(1, inf)
assert mpi(2, inf) / mpi(2, inf) == mpi(0, inf)
assert mpi(-4, 8) / mpi(1, inf) == mpi(-4, 8)
assert mpi(-4, 8) / mpi(0.5, inf) == mpi(-8, 16)
assert mpi(-inf, 8) / mpi(0.5, inf) == mpi(-inf, 16)
assert mpi(-inf, inf) / mpi(0.5, inf) == mpi(-inf, inf)
assert mpi(8, inf) / mpi(0.5, inf) == mpi(0, inf)
assert mpi(-8, inf) / mpi(0.5, inf) == mpi(-16, inf)
assert mpi(-4, 8) / mpi(inf, inf) == mpi(0, 0)
assert mpi(0, 8) / mpi(inf, inf) == mpi(0, 0)
assert mpi(0, 0) / mpi(inf, inf) == mpi(0, 0)
assert mpi(-inf, 0) / mpi(inf, inf) == mpi(-inf, 0)
assert mpi(-inf, 8) / mpi(inf, inf) == mpi(-inf, 0)
assert mpi(-inf, inf) / mpi(inf, inf) == mpi(-inf, inf)
assert mpi(-8, inf) / mpi(inf, inf) == mpi(0, inf)
assert mpi(0, inf) / mpi(inf, inf) == mpi(0, inf)
assert mpi(8, inf) / mpi(inf, inf) == mpi(0, inf)
assert mpi(inf, inf) / mpi(inf, inf) == mpi(0, inf)
assert mpi(-1, 2) / mpi(0, 1) == mpi(-inf, +inf)
assert mpi(0, 1) / mpi(0, 1) == mpi(0.0, +inf)
assert mpi(-1, 0) / mpi(0, 1) == mpi(-inf, 0.0)
assert mpi(-0.5, -0.25) / mpi(0, 1) == mpi(-inf, -0.25)
assert mpi(0.5, 1) / mpi(0, 1) == mpi(0.5, +inf)
assert mpi(0.5, 4) / mpi(0, 1) == mpi(0.5, +inf)
assert mpi(-1, -0.5) / mpi(0, 1) == mpi(-inf, -0.5)
assert mpi(-4, -0.5) / mpi(0, 1) == mpi(-inf, -0.5)
assert mpi(-1, 2) / mpi(-2, 0.5) == mpi(-inf, +inf)
assert mpi(0, 1) / mpi(-2, 0.5) == mpi(-inf, +inf)
assert mpi(-1, 0) / mpi(-2, 0.5) == mpi(-inf, +inf)
assert mpi(-0.5, -0.25) / mpi(-2, 0.5) == mpi(-inf, +inf)
assert mpi(0.5, 1) / mpi(-2, 0.5) == mpi(-inf, +inf)
assert mpi(0.5, 4) / mpi(-2, 0.5) == mpi(-inf, +inf)
assert mpi(-1, -0.5) / mpi(-2, 0.5) == mpi(-inf, +inf)
assert mpi(-4, -0.5) / mpi(-2, 0.5) == mpi(-inf, +inf)
assert mpi(-1, 2) / mpi(-1, 0) == mpi(-inf, +inf)
assert mpi(0, 1) / mpi(-1, 0) == mpi(-inf, 0.0)
assert mpi(-1, 0) / mpi(-1, 0) == mpi(0.0, +inf)
assert mpi(-0.5, -0.25) / mpi(-1, 0) == mpi(0.25, +inf)
assert mpi(0.5, 1) / mpi(-1, 0) == mpi(-inf, -0.5)
assert mpi(0.5, 4) / mpi(-1, 0) == mpi(-inf, -0.5)
assert mpi(-1, -0.5) / mpi(-1, 0) == mpi(0.5, +inf)
assert mpi(-4, -0.5) / mpi(-1, 0) == mpi(0.5, +inf)
assert mpi(-1, 2) / mpi(0.5, 1) == mpi(-2.0, 4.0)
assert mpi(0, 1) / mpi(0.5, 1) == mpi(0.0, 2.0)
assert mpi(-1, 0) / mpi(0.5, 1) == mpi(-2.0, 0.0)
assert mpi(-0.5, -0.25) / mpi(0.5, 1) == mpi(-1.0, -0.25)
assert mpi(0.5, 1) / mpi(0.5, 1) == mpi(0.5, 2.0)
assert mpi(0.5, 4) / mpi(0.5, 1) == mpi(0.5, 8.0)
assert mpi(-1, -0.5) / mpi(0.5, 1) == mpi(-2.0, -0.5)
assert mpi(-4, -0.5) / mpi(0.5, 1) == mpi(-8.0, -0.5)
assert mpi(-1, 2) / mpi(-2, -0.5) == mpi(-4.0, 2.0)
assert mpi(0, 1) / mpi(-2, -0.5) == mpi(-2.0, 0.0)
assert mpi(-1, 0) / mpi(-2, -0.5) == mpi(0.0, 2.0)
assert mpi(-0.5, -0.25) / mpi(-2, -0.5) == mpi(0.125, 1.0)
assert mpi(0.5, 1) / mpi(-2, -0.5) == mpi(-2.0, -0.25)
assert mpi(0.5, 4) / mpi(-2, -0.5) == mpi(-8.0, -0.25)
assert mpi(-1, -0.5) / mpi(-2, -0.5) == mpi(0.25, 2.0)
assert mpi(-4, -0.5) / mpi(-2, -0.5) == mpi(0.25, 8.0)
# Should be undefined?
assert mpi(0, 0) / mpi(0, 0) == mpi(-inf, inf)
assert mpi(0, 0) / mpi(0, 1) == mpi(-inf, inf)
def test_interval_cos_sin():
iv.dps = 15
cos = iv.cos
sin = iv.sin
tan = iv.tan
pi = iv.pi
# Around 0
assert cos(mpi(0)) == 1
assert sin(mpi(0)) == 0
assert cos(mpi(0,1)) == mpi(0.54030230586813965399, 1.0)
assert sin(mpi(0,1)) == mpi(0, 0.8414709848078966159)
assert cos(mpi(1,2)) == mpi(-0.4161468365471424069, 0.54030230586813976501)
assert sin(mpi(1,2)) == mpi(0.84147098480789650488, 1.0)
assert sin(mpi(1,2.5)) == mpi(0.59847214410395643824, 1.0)
assert cos(mpi(-1, 1)) == mpi(0.54030230586813965399, 1.0)
assert cos(mpi(-1, 0.5)) == mpi(0.54030230586813965399, 1.0)
assert cos(mpi(-1, 1.5)) == mpi(0.070737201667702906405, 1.0)
assert sin(mpi(-1,1)) == mpi(-0.8414709848078966159, 0.8414709848078966159)
assert sin(mpi(-1,0.5)) == mpi(-0.8414709848078966159, 0.47942553860420300538)
assert mpi(-0.8414709848078966159, 1.00000000000000002e-100) in sin(mpi(-1,1e-100))
assert mpi(-2.00000000000000004e-100, 1.00000000000000002e-100) in sin(mpi(-2e-100,1e-100))
# Same interval
assert cos(mpi(2, 2.5))
assert cos(mpi(3.5, 4)) == mpi(-0.93645668729079634129, -0.65364362086361182946)
assert cos(mpi(5, 5.5)) == mpi(0.28366218546322624627, 0.70866977429126010168)
assert mpi(0.59847214410395654927, 0.90929742682568170942) in sin(mpi(2, 2.5))
assert sin(mpi(3.5, 4)) == mpi(-0.75680249530792831347, -0.35078322768961983646)
assert sin(mpi(5, 5.5)) == mpi(-0.95892427466313856499, -0.70554032557039181306)
# Higher roots
iv.dps = 55
w = 4*10**50 + mpi(0.5)
for p in [15, 40, 80]:
iv.dps = p
assert 0 in sin(4*mpi(pi))
assert 0 in sin(4*10**50*mpi(pi))
assert 0 in cos((4+0.5)*mpi(pi))
assert 0 in cos(w*mpi(pi))
assert 1 in cos(4*mpi(pi))
assert 1 in cos(4*10**50*mpi(pi))
iv.dps = 15
assert cos(mpi(2,inf)) == mpi(-1,1)
assert sin(mpi(2,inf)) == mpi(-1,1)
assert cos(mpi(-inf,2)) == mpi(-1,1)
assert sin(mpi(-inf,2)) == mpi(-1,1)
u = tan(mpi(0.5,1))
assert mpf(u.a).ae(mp.tan(0.5))
assert mpf(u.b).ae(mp.tan(1))
v = iv.cot(mpi(0.5,1))
assert mpf(v.a).ae(mp.cot(1))
assert mpf(v.b).ae(mp.cot(0.5))
# Sanity check of evaluation at n*pi and (n+1/2)*pi
for n in range(-5,7,2):
x = iv.cos(n*iv.pi)
assert -1 in x
assert x >= -1
assert x != -1
x = iv.sin((n+0.5)*iv.pi)
assert -1 in x
assert x >= -1
assert x != -1
for n in range(-6,8,2):
x = iv.cos(n*iv.pi)
assert 1 in x
assert x <= 1
if n:
assert x != 1
x = iv.sin((n+0.5)*iv.pi)
assert 1 in x
assert x <= 1
assert x != 1
for n in range(-6,7):
x = iv.cos((n+0.5)*iv.pi)
assert x.a < 0 < x.b
x = iv.sin(n*iv.pi)
if n:
assert x.a < 0 < x.b
def test_interval_complex():
# TODO: many more tests
iv.dps = 15
mp.dps = 15
assert iv.mpc(2,3) == 2+3j
assert iv.mpc(2,3) != 2+4j
assert iv.mpc(2,3) != 1+3j
assert 1+3j in iv.mpc([1,2],[3,4])
assert 2+5j not in iv.mpc([1,2],[3,4])
assert iv.mpc(1,2) + 1j == 1+3j
assert iv.mpc([1,2],[2,3]) + 2+3j == iv.mpc([3,4],[5,6])
assert iv.mpc([2,4],[4,8]) / 2 == iv.mpc([1,2],[2,4])
assert iv.mpc([1,2],[2,4]) * 2j == iv.mpc([-8,-4],[2,4])
assert iv.mpc([2,4],[4,8]) / 2j == iv.mpc([2,4],[-2,-1])
assert iv.exp(2+3j).ae(mp.exp(2+3j))
assert iv.log(2+3j).ae(mp.log(2+3j))
assert (iv.mpc(2,3) ** iv.mpc(0.5,2)).ae(mp.mpc(2,3) ** mp.mpc(0.5,2))
assert 1j in (iv.mpf(-1) ** 0.5)
assert 1j in (iv.mpc(-1) ** 0.5)
assert abs(iv.mpc(0)) == 0
assert abs(iv.mpc(inf)) == inf
assert abs(iv.mpc(3,4)) == 5
assert abs(iv.mpc(4)) == 4
assert abs(iv.mpc(0,4)) == 4
assert abs(iv.mpc(0,[2,3])) == iv.mpf([2,3])
assert abs(iv.mpc(0,[-3,2])) == iv.mpf([0,3])
assert abs(iv.mpc([3,5],[4,12])) == iv.mpf([5,13])
assert abs(iv.mpc([3,5],[-4,12])) == iv.mpf([3,13])
assert iv.mpc(2,3) ** 0 == 1
assert iv.mpc(2,3) ** 1 == (2+3j)
assert iv.mpc(2,3) ** 2 == (2+3j)**2
assert iv.mpc(2,3) ** 3 == (2+3j)**3
assert iv.mpc(2,3) ** 4 == (2+3j)**4
assert iv.mpc(2,3) ** 5 == (2+3j)**5
assert iv.mpc(2,2) ** (-1) == (2+2j) ** (-1)
assert iv.mpc(2,2) ** (-2) == (2+2j) ** (-2)
assert iv.cos(2).ae(mp.cos(2))
assert iv.sin(2).ae(mp.sin(2))
assert iv.cos(2+3j).ae(mp.cos(2+3j))
assert iv.sin(2+3j).ae(mp.sin(2+3j))
def test_interval_complex_arg():
mp.dps = 15
iv.dps = 15
assert iv.arg(3) == 0
assert iv.arg(0) == 0
assert iv.arg([0,3]) == 0
assert iv.arg(-3).ae(pi)
assert iv.arg(2+3j).ae(iv.arg(2+3j))
z = iv.mpc([-2,-1],[3,4])
t = iv.arg(z)
assert t.a.ae(mp.arg(-1+4j))
assert t.b.ae(mp.arg(-2+3j))
z = iv.mpc([-2,1],[3,4])
t = iv.arg(z)
assert t.a.ae(mp.arg(1+3j))
assert t.b.ae(mp.arg(-2+3j))
z = iv.mpc([1,2],[3,4])
t = iv.arg(z)
assert t.a.ae(mp.arg(2+3j))
assert t.b.ae(mp.arg(1+4j))
z = iv.mpc([1,2],[-2,3])
t = iv.arg(z)
assert t.a.ae(mp.arg(1-2j))
assert t.b.ae(mp.arg(1+3j))
z = iv.mpc([1,2],[-4,-3])
t = iv.arg(z)
assert t.a.ae(mp.arg(1-4j))
assert t.b.ae(mp.arg(2-3j))
z = iv.mpc([-1,2],[-4,-3])
t = iv.arg(z)
assert t.a.ae(mp.arg(-1-3j))
assert t.b.ae(mp.arg(2-3j))
z = iv.mpc([-2,-1],[-4,-3])
t = iv.arg(z)
assert t.a.ae(mp.arg(-2-3j))
assert t.b.ae(mp.arg(-1-4j))
z = iv.mpc([-2,-1],[-3,3])
t = iv.arg(z)
assert t.a.ae(-mp.pi)
assert t.b.ae(mp.pi)
z = iv.mpc([-2,2],[-3,3])
t = iv.arg(z)
assert t.a.ae(-mp.pi)
assert t.b.ae(mp.pi)
def test_interval_ae():
iv.dps = 15
x = iv.mpf([1,2])
assert x.ae(1) is None
assert x.ae(1.5) is None
assert x.ae(2) is None
assert x.ae(2.01) is False
assert x.ae(0.99) is False
x = iv.mpf(3.5)
assert x.ae(3.5) is True
assert x.ae(3.5+1e-15) is True
assert x.ae(3.5-1e-15) is True
assert x.ae(3.501) is False
assert x.ae(3.499) is False
assert x.ae(iv.mpf([3.5,3.501])) is None
assert x.ae(iv.mpf([3.5,4.5+1e-15])) is None
def test_interval_nstr():
iv.dps = n = 30
x = mpi(1, 2)
# FIXME: error_dps should not be necessary
assert iv.nstr(x, n, mode='plusminus', error_dps=6) == '1.5 +- 0.5'
assert iv.nstr(x, n, mode='plusminus', use_spaces=False, error_dps=6) == '1.5+-0.5'
assert iv.nstr(x, n, mode='percent') == '1.5 (33.33%)'
assert iv.nstr(x, n, mode='brackets', use_spaces=False) == '[1.0,2.0]'
assert iv.nstr(x, n, mode='brackets' , brackets=('<', '>')) == '<1.0, 2.0>'
x = mpi('5.2582327113062393041', '5.2582327113062749951')
assert iv.nstr(x, n, mode='diff') == '5.2582327113062[393041, 749951]'
assert iv.nstr(iv.cos(mpi(1)), n, mode='diff', use_spaces=False) == '0.54030230586813971740093660744[2955,3053]'
assert iv.nstr(mpi('1e123', '1e129'), n, mode='diff') == '[1.0e+123, 1.0e+129]'
exp = iv.exp
assert iv.nstr(iv.exp(mpi('5000.1')), n, mode='diff') == '3.2797365856787867069110487[0926, 1191]e+2171'
iv.dps = 15
def test_mpi_from_str():
iv.dps = 15
assert iv.convert('1.5 +- 0.5') == mpi(mpf('1.0'), mpf('2.0'))
assert mpi(1, 2) in iv.convert('1.5 (33.33333333333333333333333333333%)')
assert iv.convert('[1, 2]') == mpi(1, 2)
assert iv.convert('1[2, 3]') == mpi(12, 13)
assert iv.convert('1.[23,46]e-8') == mpi('1.23e-8', '1.46e-8')
assert iv.convert('12[3.4,5.9]e4') == mpi('123.4e+4', '125.9e4')
def test_interval_gamma():
mp.dps = 15
iv.dps = 15
# TODO: need many more tests
assert iv.rgamma(0) == 0
assert iv.fac(0) == 1
assert iv.fac(1) == 1
assert iv.fac(2) == 2
assert iv.fac(3) == 6
assert iv.gamma(0) == [-inf,inf]
assert iv.gamma(1) == 1
assert iv.gamma(2) == 1
assert iv.gamma(3) == 2
assert -3.5449077018110320546 in iv.gamma(-0.5)
assert iv.loggamma(1) == 0
assert iv.loggamma(2) == 0
assert 0.69314718055994530942 in iv.loggamma(3)
# Test tight log-gamma endpoints based on monotonicity
xs = [iv.mpc([2,3],[1,4]),
iv.mpc([2,3],[-4,-1]),
iv.mpc([2,3],[-1,4]),
iv.mpc([2,3],[-4,1]),
iv.mpc([2,3],[-4,4]),
iv.mpc([-3,-2],[2,4]),
iv.mpc([-3,-2],[-4,-2])]
for x in xs:
ys = [mp.loggamma(mp.mpc(x.a,x.c)),
mp.loggamma(mp.mpc(x.b,x.c)),
mp.loggamma(mp.mpc(x.a,x.d)),
mp.loggamma(mp.mpc(x.b,x.d))]
if 0 in x.imag:
ys += [mp.loggamma(x.a), mp.loggamma(x.b)]
min_real = min([y.real for y in ys])
max_real = max([y.real for y in ys])
min_imag = min([y.imag for y in ys])
max_imag = max([y.imag for y in ys])
z = iv.loggamma(x)
assert z.a.ae(min_real)
assert z.b.ae(max_real)
assert z.c.ae(min_imag)
assert z.d.ae(max_imag)
| 17,133 | 37.764706 | 116 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/tests/test_calculus.py
|
from mpmath import *
def test_approximation():
mp.dps = 15
f = lambda x: cos(2-2*x)/x
p, err = chebyfit(f, [2, 4], 8, error=True)
assert err < 1e-5
for i in range(10):
x = 2 + i/5.
assert abs(polyval(p, x) - f(x)) < err
def test_limits():
mp.dps = 15
assert limit(lambda x: (x-sin(x))/x**3, 0).ae(mpf(1)/6)
assert limit(lambda n: (1+1/n)**n, inf).ae(e)
def test_polyval():
assert polyval([], 3) == 0
assert polyval([0], 3) == 0
assert polyval([5], 3) == 5
# 4x^3 - 2x + 5
p = [4, 0, -2, 5]
assert polyval(p,4) == 253
assert polyval(p,4,derivative=True) == (253, 190)
def test_polyroots():
p = polyroots([1,-4])
assert p[0].ae(4)
p, q = polyroots([1,2,3])
assert p.ae(-1 - sqrt(2)*j)
assert q.ae(-1 + sqrt(2)*j)
#this is not a real test, it only tests a specific case
assert polyroots([1]) == []
try:
polyroots([0])
assert False
except ValueError:
pass
def test_polyroots_legendre():
n = 64
coeffs = [11975573020964041433067793888190275875, 0,
-190100434726484311252477736051902332000, 0,
1437919688271127330313741595496589239248, 0,
-6897338342113537600691931230430793911840, 0,
23556405536185284408974715545252277554280, 0,
-60969520211303089058522793175947071316960, 0,
124284021969194758465450309166353645376880, 0,
-204721258548015217049921875719981284186016, 0,
277415422258095841688223780704620656114900, 0,
-313237834141273382807123548182995095192800, 0,
297432255354328395601259515935229287637200, 0,
-239057700565161140389797367947941296605600, 0,
163356095386193445933028201431093219347160, 0,
-95158890516229191805647495979277603503200, 0,
47310254620162038075933656063247634556400, 0,
-20071017111583894941305187420771723751200, 0,
7255051932731034189479516844750603752850, 0,
-2228176940331017311443863996901733412640, 0,
579006552594977616773047095969088431600, 0,
-126584428502545713788439446082310831200, 0,
23112325428835593809686977515028663000, 0,
-3491517141958743235617737161547844000, 0,
431305058712550634988073414073557200, 0,
-42927166660756742088912492757452000, 0,
3378527005707706553294038781836500, 0,
-205277590220215081719131470288800, 0,
9330799555464321896324157740400, 0,
-304114948474392713657972548576, 0,
6695289961520387531608984680, 0,
-91048139350447232095702560, 0,
659769125727878493447120, 0,
-1905929106580294155360, 0,
916312070471295267]
with mp.workdps(3):
try:
roots = polyroots(coeffs, maxsteps=5, cleanup=True, error=False,
extraprec=n*10)
raise AssertionError("polyroots() didn't raise NoConvergence")
except (mp.NoConvergence):
pass
roots = polyroots(coeffs, maxsteps=50, cleanup=True, error=False,
extraprec=n*10)
roots = [str(r) for r in roots]
assert roots == \
['-0.999', '-0.996', '-0.991', '-0.983', '-0.973', '-0.961',
'-0.946', '-0.93', '-0.911', '-0.889', '-0.866', '-0.841',
'-0.813', '-0.784', '-0.753', '-0.72', '-0.685', '-0.649',
'-0.611', '-0.572', '-0.531', '-0.489', '-0.446', '-0.402',
'-0.357', '-0.311', '-0.265', '-0.217', '-0.17', '-0.121',
'-0.073', '-0.0243', '0.0243', '0.073', '0.121', '0.17', '0.217',
'0.265', '0.311', '0.357', '0.402', '0.446', '0.489', '0.531',
'0.572', '0.611', '0.649', '0.685', '0.72', '0.753', '0.784',
'0.813', '0.841', '0.866', '0.889', '0.911', '0.93', '0.946',
'0.961', '0.973', '0.983', '0.991', '0.996', '0.999']
def test_polyroots_legendre_init():
extra_prec = 100
coeffs = [11975573020964041433067793888190275875, 0,
-190100434726484311252477736051902332000, 0,
1437919688271127330313741595496589239248, 0,
-6897338342113537600691931230430793911840, 0,
23556405536185284408974715545252277554280, 0,
-60969520211303089058522793175947071316960, 0,
124284021969194758465450309166353645376880, 0,
-204721258548015217049921875719981284186016, 0,
277415422258095841688223780704620656114900, 0,
-313237834141273382807123548182995095192800, 0,
297432255354328395601259515935229287637200, 0,
-239057700565161140389797367947941296605600, 0,
163356095386193445933028201431093219347160, 0,
-95158890516229191805647495979277603503200, 0,
47310254620162038075933656063247634556400, 0,
-20071017111583894941305187420771723751200, 0,
7255051932731034189479516844750603752850, 0,
-2228176940331017311443863996901733412640, 0,
579006552594977616773047095969088431600, 0,
-126584428502545713788439446082310831200, 0,
23112325428835593809686977515028663000, 0,
-3491517141958743235617737161547844000, 0,
431305058712550634988073414073557200, 0,
-42927166660756742088912492757452000, 0,
3378527005707706553294038781836500, 0,
-205277590220215081719131470288800, 0,
9330799555464321896324157740400, 0,
-304114948474392713657972548576, 0,
6695289961520387531608984680, 0,
-91048139350447232095702560, 0,
659769125727878493447120, 0,
-1905929106580294155360, 0,
916312070471295267]
roots_init = matrix(['-0.999', '-0.996', '-0.991', '-0.983', '-0.973',
'-0.961', '-0.946', '-0.93', '-0.911', '-0.889',
'-0.866', '-0.841', '-0.813', '-0.784', '-0.753',
'-0.72', '-0.685', '-0.649', '-0.611', '-0.572',
'-0.531', '-0.489', '-0.446', '-0.402', '-0.357',
'-0.311', '-0.265', '-0.217', '-0.17', '-0.121',
'-0.073', '-0.0243', '0.0243', '0.073', '0.121',
'0.17', '0.217', '0.265', ' 0.311', '0.357',
'0.402', '0.446', '0.489', '0.531', '0.572',
'0.611', '0.649', '0.685', '0.72', '0.753',
'0.784', '0.813', '0.841', '0.866', '0.889',
'0.911', '0.93', '0.946', '0.961', '0.973',
'0.983', '0.991', '0.996', '0.999', '1.0'])
with mp.workdps(2*mp.dps):
roots_exact = polyroots(coeffs, maxsteps=50, cleanup=True, error=False,
extraprec=2*extra_prec)
try:
roots = polyroots(coeffs, maxsteps=5, cleanup=True, error=False,
extraprec=extra_prec)
raise AssertionError("polyroots() didn't raise NoConvergence")
except (mp.NoConvergence):
pass
roots,err = polyroots(coeffs, maxsteps=5, cleanup=True, error=True,
extraprec=extra_prec,roots_init=roots_init)
assert max(matrix(roots_exact)-matrix(roots).apply(abs)) < err
roots1,err1 = polyroots(coeffs, maxsteps=25, cleanup=True, error=True,
extraprec=extra_prec,roots_init=roots_init[:60])
assert max(matrix(roots_exact)-matrix(roots1).apply(abs)) < err1
def test_pade():
one = mpf(1)
mp.dps = 20
N = 10
a = [one]
k = 1
for i in range(1, N+1):
k *= i
a.append(one/k)
p, q = pade(a, N//2, N//2)
for x in arange(0, 1, 0.1):
r = polyval(p[::-1], x)/polyval(q[::-1], x)
assert(r.ae(exp(x), 1.0e-10))
mp.dps = 15
def test_fourier():
mp.dps = 15
c, s = fourier(lambda x: x+1, [-1, 2], 2)
#plot([lambda x: x+1, lambda x: fourierval((c, s), [-1, 2], x)], [-1, 2])
assert c[0].ae(1.5)
assert c[1].ae(-3*sqrt(3)/(2*pi))
assert c[2].ae(3*sqrt(3)/(4*pi))
assert s[0] == 0
assert s[1].ae(3/(2*pi))
assert s[2].ae(3/(4*pi))
assert fourierval((c, s), [-1, 2], 1).ae(1.9134966715663442)
def test_differint():
mp.dps = 15
assert differint(lambda t: t, 2, -0.5).ae(8*sqrt(2/pi)/3)
def test_invlap():
mp.dps = 15
t = 0.01
fp = lambda p: 1/(p+1)**2
ft = lambda t: t*exp(-t)
ftt = ft(t)
assert invertlaplace(fp,t,method='talbot').ae(ftt)
assert invertlaplace(fp,t,method='stehfest').ae(ftt)
assert invertlaplace(fp,t,method='dehoog').ae(ftt)
t = 1.0
ftt = ft(t)
assert invertlaplace(fp,t,method='talbot').ae(ftt)
assert invertlaplace(fp,t,method='stehfest').ae(ftt)
assert invertlaplace(fp,t,method='dehoog').ae(ftt)
t = 0.01
fp = lambda p: log(p)/p
ft = lambda t: -euler-log(t)
ftt = ft(t)
assert invertlaplace(fp,t,method='talbot').ae(ftt)
assert invertlaplace(fp,t,method='stehfest').ae(ftt)
assert invertlaplace(fp,t,method='dehoog').ae(ftt)
t = 1.0
ftt = ft(t)
assert invertlaplace(fp,t,method='talbot').ae(ftt)
assert invertlaplace(fp,t,method='stehfest').ae(ftt)
assert invertlaplace(fp,t,method='dehoog').ae(ftt)
| 9,194 | 40.418919 | 79 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/tests/extratest_bessel.py
|
# Extra stress testing for Bessel functions
# Reference zeros generated with the aid of scipy.special
# jn_zero, jnp_zero, yn_zero, ynp_zero
from mpmath import *
V = 15
M = 15
jn_small_zeros = \
[[2.4048255576957728,
5.5200781102863106,
8.6537279129110122,
11.791534439014282,
14.930917708487786,
18.071063967910923,
21.211636629879259,
24.352471530749303,
27.493479132040255,
30.634606468431975,
33.775820213573569,
36.917098353664044,
40.058425764628239,
43.19979171317673,
46.341188371661814],
[3.8317059702075123,
7.0155866698156188,
10.173468135062722,
13.323691936314223,
16.470630050877633,
19.615858510468242,
22.760084380592772,
25.903672087618383,
29.046828534916855,
32.189679910974404,
35.332307550083865,
38.474766234771615,
41.617094212814451,
44.759318997652822,
47.901460887185447],
[5.1356223018406826,
8.4172441403998649,
11.619841172149059,
14.795951782351261,
17.959819494987826,
21.116997053021846,
24.270112313573103,
27.420573549984557,
30.569204495516397,
33.7165195092227,
36.86285651128381,
40.008446733478192,
43.153453778371463,
46.297996677236919,
49.442164110416873],
[6.3801618959239835,
9.7610231299816697,
13.015200721698434,
16.223466160318768,
19.409415226435012,
22.582729593104442,
25.748166699294978,
28.908350780921758,
32.064852407097709,
35.218670738610115,
38.370472434756944,
41.520719670406776,
44.669743116617253,
47.817785691533302,
50.965029906205183],
[7.5883424345038044,
11.064709488501185,
14.37253667161759,
17.615966049804833,
20.826932956962388,
24.01901952477111,
27.199087765981251,
30.371007667117247,
33.537137711819223,
36.699001128744649,
39.857627302180889,
43.01373772335443,
46.167853512924375,
49.320360686390272,
52.471551398458023],
[8.771483815959954,
12.338604197466944,
15.700174079711671,
18.980133875179921,
22.217799896561268,
25.430341154222704,
28.626618307291138,
31.811716724047763,
34.988781294559295,
38.159868561967132,
41.326383254047406,
44.489319123219673,
47.649399806697054,
50.80716520300633,
53.963026558378149],
[9.9361095242176849,
13.589290170541217,
17.003819667816014,
20.320789213566506,
23.58608443558139,
26.820151983411405,
30.033722386570469,
33.233041762847123,
36.422019668258457,
39.603239416075404,
42.778481613199507,
45.949015998042603,
49.11577372476426,
52.279453903601052,
55.440592068853149],
[11.086370019245084,
14.821268727013171,
18.287582832481726,
21.641541019848401,
24.934927887673022,
28.191188459483199,
31.42279419226558,
34.637089352069324,
37.838717382853611,
41.030773691585537,
44.21540850526126,
47.394165755570512,
50.568184679795566,
53.738325371963291,
56.905249991978781],
[12.225092264004655,
16.037774190887709,
19.554536430997055,
22.94517313187462,
26.266814641176644,
29.54565967099855,
32.795800037341462,
36.025615063869571,
39.240447995178135,
42.443887743273558,
45.638444182199141,
48.825930381553857,
52.007691456686903,
55.184747939289049,
58.357889025269694],
[13.354300477435331,
17.241220382489128,
20.807047789264107,
24.233885257750552,
27.583748963573006,
30.885378967696675,
34.154377923855096,
37.400099977156589,
40.628553718964528,
43.843801420337347,
47.048700737654032,
50.245326955305383,
53.435227157042058,
56.619580266508436,
59.799301630960228],
[14.475500686554541,
18.433463666966583,
22.046985364697802,
25.509450554182826,
28.887375063530457,
32.211856199712731,
35.499909205373851,
38.761807017881651,
42.004190236671805,
45.231574103535045,
48.447151387269394,
51.653251668165858,
54.851619075963349,
58.043587928232478,
61.230197977292681],
[15.589847884455485,
19.61596690396692,
23.275853726263409,
26.773322545509539,
30.17906117878486,
33.526364075588624,
36.833571341894905,
40.111823270954241,
43.368360947521711,
46.608132676274944,
49.834653510396724,
53.050498959135054,
56.257604715114484,
59.457456908388002,
62.651217388202912],
[16.698249933848246,
20.789906360078443,
24.494885043881354,
28.026709949973129,
31.45996003531804,
34.829986990290238,
38.156377504681354,
41.451092307939681,
44.721943543191147,
47.974293531269048,
51.211967004101068,
54.437776928325074,
57.653844811906946,
60.8618046824805,
64.062937824850136],
[17.801435153282442,
21.95624406783631,
25.705103053924724,
29.270630441874802,
32.731053310978403,
36.123657666448762,
39.469206825243883,
42.780439265447158,
46.06571091157561,
49.330780096443524,
52.579769064383396,
55.815719876305778,
59.040934037249271,
62.257189393731728,
65.465883797232125],
[18.899997953174024,
23.115778347252756,
26.907368976182104,
30.505950163896036,
33.993184984781542,
37.408185128639695,
40.772827853501868,
44.100590565798301,
47.400347780543231,
50.678236946479898,
53.93866620912693,
57.184898598119301,
60.419409852130297,
63.644117508962281,
66.860533012260103]]
jnp_small_zeros = \
[[0.0,
3.8317059702075123,
7.0155866698156188,
10.173468135062722,
13.323691936314223,
16.470630050877633,
19.615858510468242,
22.760084380592772,
25.903672087618383,
29.046828534916855,
32.189679910974404,
35.332307550083865,
38.474766234771615,
41.617094212814451,
44.759318997652822],
[1.8411837813406593,
5.3314427735250326,
8.5363163663462858,
11.706004902592064,
14.863588633909033,
18.015527862681804,
21.16436985918879,
24.311326857210776,
27.457050571059246,
30.601922972669094,
33.746182898667383,
36.889987409236811,
40.033444053350675,
43.176628965448822,
46.319597561173912],
[3.0542369282271403,
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16.347522318321783,
19.512912782488205,
22.671581772477426,
25.826037141785263,
28.977672772993679,
32.127327020443474,
35.275535050674691,
38.422654817555906,
41.568934936074314,
44.714553532819734,
47.859641607992093],
[4.2011889412105285,
8.0152365983759522,
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14.585848286167028,
17.78874786606647,
20.9724769365377,
24.144897432909265,
27.310057930204349,
30.470268806290424,
33.626949182796679,
36.781020675464386,
39.933108623659488,
43.083652662375079,
46.232971081836478,
49.381300092370349],
[5.3175531260839944,
9.2823962852416123,
12.681908442638891,
15.964107037731551,
19.196028800048905,
22.401032267689004,
25.589759681386733,
28.767836217666503,
31.938539340972783,
35.103916677346764,
38.265316987088158,
41.423666498500732,
44.579623137359257,
47.733667523865744,
50.886159153182682],
[6.4156163757002403,
10.519860873772308,
13.9871886301403,
17.312842487884625,
20.575514521386888,
23.803581476593863,
27.01030789777772,
30.20284907898166,
33.385443901010121,
36.560777686880356,
39.730640230067416,
42.896273163494417,
46.058566273567043,
49.218174614666636,
52.375591529563596],
[7.501266144684147,
11.734935953042708,
15.268181461097873,
18.637443009666202,
21.931715017802236,
25.183925599499626,
28.409776362510085,
31.617875716105035,
34.81339298429743,
37.999640897715301,
41.178849474321413,
44.352579199070217,
47.521956905768113,
50.687817781723741,
53.85079463676896],
[8.5778364897140741,
12.932386237089576,
16.529365884366944,
19.941853366527342,
23.268052926457571,
26.545032061823576,
29.790748583196614,
33.015178641375142,
36.224380548787162,
39.422274578939259,
42.611522172286684,
45.793999658055002,
48.971070951900596,
52.143752969301988,
55.312820330403446],
[9.6474216519972168,
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21.229062622853124,
24.587197486317681,
27.889269427955092,
31.155326556188325,
34.39662855427218,
37.620078044197086,
40.830178681822041,
44.030010337966153,
47.221758471887113,
50.407020967034367,
53.586995435398319,
56.762598475105272],
[10.711433970699945,
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22.501398726777283,
25.891277276839136,
29.218563499936081,
32.505247352375523,
35.763792928808799,
39.001902811514218,
42.224638430753279,
45.435483097475542,
48.636922645305525,
51.830783925834728,
55.01844255063594,
58.200955824859509],
[11.770876674955582,
16.447852748486498,
20.223031412681701,
23.760715860327448,
27.182021527190532,
30.534504754007074,
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37.118000423665604,
40.371068905333891,
43.606764901379516,
46.828959446564562,
50.040428970943456,
53.243223214220535,
56.438892058982552,
59.628631306921512],
[12.826491228033465,
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38.460388720328256,
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44.977526250903469,
48.211333836373288,
51.433105171422278,
54.645106240447105,
57.849056857839799,
61.046288512821078],
[13.878843069697276,
18.745090916814406,
22.629300302835503,
26.246047773946584,
29.72897816891134,
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36.480548302231658,
39.791940718940855,
43.075486800191012,
46.337772104541405,
49.583396417633095,
52.815686826850452,
56.037118687012179,
59.249577075517968,
62.454525995970462],
[14.928374492964716,
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30.987394331665278,
34.414545662167183,
37.784378506209499,
41.113512376883377,
44.412454519229281,
47.688252845993366,
50.945849245830813,
54.188831071035124,
57.419876154678179,
60.641030026538746,
63.853885828967512],
[15.975438807484321,
21.015404934568315,
25.001971500138194,
28.694271223110755,
32.236969407878118,
35.688544091185301,
39.078998185245057,
42.425854432866141,
45.740236776624833,
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52.299319390331728,
55.553127779547459,
58.793933759028134,
62.02393848337554,
65.244860767043859]]
yn_small_zeros = \
[[0.89357696627916752,
3.9576784193148579,
7.0860510603017727,
10.222345043496417,
13.361097473872763,
16.500922441528091,
19.64130970088794,
22.782028047291559,
25.922957653180923,
29.064030252728398,
32.205204116493281,
35.346452305214321,
38.487756653081537,
41.629104466213808,
44.770486607221993],
[2.197141326031017,
5.4296810407941351,
8.5960058683311689,
11.749154830839881,
14.897442128336725,
18.043402276727856,
21.188068934142213,
24.331942571356912,
27.475294980449224,
30.618286491641115,
33.761017796109326,
36.90355531614295,
40.045944640266876,
43.188218097393211,
46.330399250701687],
[3.3842417671495935,
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13.209986710206416,
16.378966558947457,
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22.69395593890929,
25.845613720902269,
28.995080395650151,
32.143002257627551,
35.289793869635804,
38.435733485446343,
41.581014867297885,
44.725777117640461,
47.870122696676504],
[4.5270246611496439,
8.0975537628604907,
11.396466739595867,
14.623077742393873,
17.81845523294552,
20.997284754187761,
24.166235758581828,
27.328799850405162,
30.486989604098659,
33.642049384702463,
36.794791029185579,
39.945767226378749,
43.095367507846703,
46.2438744334407,
49.391498015725107],
[5.6451478942208959,
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19.22442895931681,
22.424810599698521,
25.610267054939328,
28.785893657666548,
31.954686680031668,
35.118529525584828,
38.278668089521758,
41.435960629910073,
44.591018225353424,
47.744288086361052,
50.896105199722123],
[6.7471838248710219,
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14.033804104911233,
17.347086393228382,
20.602899017175335,
23.826536030287532,
27.030134937138834,
30.220335654231385,
33.401105611047908,
36.574972486670962,
39.743627733020277,
42.908248189569535,
46.069679073215439,
49.228543693445843,
52.385312123112282],
[7.8377378223268716,
11.811037107609447,
15.313615118517857,
18.670704965906724,
21.958290897126571,
25.206207715021249,
28.429037095235496,
31.634879502950644,
34.828638524084437,
38.013473399691765,
41.19151880917741,
44.364272633271975,
47.53281875312084,
50.697961822183806,
53.860312300118388],
[8.919605734873789,
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19.974342312352426,
23.293972585596648,
26.5667563757203,
29.809531451608321,
33.031769327150685,
36.239265816598239,
39.435790312675323,
42.623910919472727,
45.805442883111651,
48.981708325514764,
52.153694518185572,
55.322154420959698],
[9.9946283820824834,
14.190361295800141,
17.817887841179873,
21.26093227125945,
24.612576377421522,
27.910524883974868,
31.173701563441602,
34.412862242025045,
37.634648706110989,
40.843415321050884,
44.04214994542435,
47.232978012841169,
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53.596753874948731,
56.771765754432457],
[11.064090256031013,
15.361301343575925,
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22.532765416313869,
25.91620496332662,
29.2394205079349,
32.523270869465881,
35.779715464475261,
39.016196664616095,
42.237627509803703,
45.4474001519274,
48.647941127433196,
51.841036928216499,
55.028034667184916,
58.209970905250097],
[12.128927704415439,
16.522284394784426,
20.265984501212254,
23.791669719454272,
27.206568881574774,
30.555020011020762,
33.859683872746356,
37.133649760307504,
40.385117593813002,
43.619533085646856,
46.840676630553575,
50.051265851897857,
53.253310556711732,
56.448332488918971,
59.637507005589829],
[13.189846995683845,
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21.473493977824902,
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35.184165245422787,
38.475796636190897,
41.742455848758449,
44.990096293791186,
48.222870660068338,
51.443777308699826,
54.655042589416311,
57.858358441436511,
61.055036135780528],
[14.247395665073945,
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22.671697117872794,
26.276375544903892,
29.752925495549038,
33.151412708998983,
36.497763772987645,
39.807134090704376,
43.089121522203808,
46.350163579538652,
49.594769786270069,
52.82620892320143,
56.046916910756961,
59.258751140598783,
62.463155567737854],
[15.30200785858925,
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41.128514139788358,
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50.957073905278458,
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57.429547607017405,
60.65008661807661,
63.862406280068586],
[16.354034360047551,
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25.044040298785627,
28.724161640881914,
32.260472459522644,
35.708083982611664,
39.095820003878235,
42.440684315990936,
45.75353669045622,
49.041718113283529,
52.310408280968073,
55.56338698149062,
58.803488508906895,
62.032886550960831,
65.253280088312461]]
ynp_small_zeros = \
[[2.197141326031017,
5.4296810407941351,
8.5960058683311689,
11.749154830839881,
14.897442128336725,
18.043402276727856,
21.188068934142213,
24.331942571356912,
27.475294980449224,
30.618286491641115,
33.761017796109326,
36.90355531614295,
40.045944640266876,
43.188218097393211,
46.330399250701687],
[3.6830228565851777,
6.9414999536541757,
10.123404655436613,
13.285758156782854,
16.440058007293282,
19.590241756629495,
22.738034717396327,
25.884314618788867,
29.029575819372535,
32.174118233366201,
35.318134458192094,
38.461753870997549,
41.605066618873108,
44.74813744908079,
47.891014070791065],
[5.0025829314460639,
8.3507247014130795,
11.574195465217647,
14.760909306207676,
17.931285939466855,
21.092894504412739,
24.249231678519058,
27.402145837145258,
30.552708880564553,
33.70158627151572,
36.849213419846257,
39.995887376143356,
43.141817835750686,
46.287157097544201,
49.432018469138281],
[6.2536332084598136,
9.6987879841487711,
12.972409052292216,
16.19044719506921,
19.38238844973613,
22.559791857764261,
25.728213194724094,
28.890678419054777,
32.048984005266337,
35.204266606440635,
38.357281675961019,
41.508551443818436,
44.658448731963676,
47.807246956681162,
50.95515126455207],
[7.4649217367571329,
11.005169149809189,
14.3317235192331,
17.58443601710272,
20.801062338411128,
23.997004122902644,
27.179886689853435,
30.353960608554323,
33.521797098666792,
36.685048382072301,
39.844826969405863,
43.001910515625288,
46.15685955107263,
49.310088614282257,
52.461911043685864],
[8.6495562436971983,
12.280868725807848,
15.660799304540377,
18.949739756016503,
22.192841809428241,
25.409072788867674,
28.608039283077593,
31.795195353138159,
34.973890634255288,
38.14630522169358,
41.313923188794905,
44.477791768537617,
47.638672065035628,
50.797131066967842,
53.953600129601663],
[9.8147970120105779,
13.532811875789828,
16.965526446046053,
20.291285512443867,
23.56186260680065,
26.799499736027237,
30.015665481543419,
33.216968050039509,
36.407516858984748,
39.590015243560459,
42.766320595957378,
45.937754257017323,
49.105283450953203,
52.269633324547373,
55.431358715604255],
[10.965152105242974,
14.765687379508912,
18.250123150217555,
21.612750053384621,
24.911310600813573,
28.171051927637585,
31.40518108895689,
34.621401012564177,
37.824552065973114,
41.017847386464902,
44.203512240871601,
47.3831408366063,
50.557907466622796,
53.728697478957026,
56.896191727313342],
[12.103641941939539,
15.982840905145284,
19.517731005559611,
22.916962141504605,
26.243700855690533,
29.525960140695407,
32.778568197561124,
36.010261572392516,
39.226578757802172,
42.43122493258747,
45.626783824134354,
48.815117837929515,
51.997606404328863,
55.175294723956816,
58.348990221754937],
[13.232403808592215,
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20.770762917490496,
24.206152448722253,
27.561059462697153,
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34.137476603379774,
37.385039772270268,
40.614946085165892,
43.831373184731238,
47.037251786726299,
50.234705848765229,
53.425316228549359,
56.610286079882087,
59.790548623216652],
[14.35301374369987,
18.379337301642568,
22.011118775283494,
25.482116178696707,
28.865046588695164,
32.192853922166294,
35.483296655830277,
38.747005493021857,
41.990815194320955,
45.219355876831731,
48.435892856078888,
51.642803925173029,
54.84186659475857,
58.034439083840155,
61.221578745109862],
[15.466672066554263,
19.562077985759503,
23.240325531101082,
26.746322986645901,
30.157042415639891,
33.507642948240263,
36.817212798512775,
40.097251300178642,
43.355193847719752,
46.596103410173672,
49.823567279972794,
53.040208868780832,
56.247996968470062,
59.448441365714251,
62.642721301357187],
[16.574317035530872,
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27.999993668839644,
31.438208790267783,
34.811512070805535,
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41.436725143893739,
44.708963264433333,
47.962435051891027,
51.201037321915983,
54.427630745992975,
57.644369734615238,
60.852911791989989,
64.054555435720397],
[17.676697936439624,
21.9026148697762,
25.670073356263225,
29.244155124266438,
32.709534477396028,
36.105399554497548,
39.453272918267025,
42.766255701958017,
46.052899215578358,
49.319076602061401,
52.568982147952547,
55.805705507386287,
59.031580956740466,
62.248409689597653,
65.457606670836759],
[18.774423978290318,
23.06220035979272,
26.872520985976736,
30.479680663499762,
33.971869047372436,
37.390118854896324,
40.757072537673599,
44.086572292170345,
47.387688809191869,
50.66667461073936,
53.928009929563275,
57.175005343085052,
60.410169281219877,
63.635442539153021,
66.85235358587768]]
def test_bessel_zeros():
mp.dps = 15
for v in range(V):
for m in range(1,M+1):
print(v, m, "of", V, M)
# Twice to test cache (if used)
assert besseljzero(v,m).ae(jn_small_zeros[v][m-1])
assert besseljzero(v,m).ae(jn_small_zeros[v][m-1])
assert besseljzero(v,m,1).ae(jnp_small_zeros[v][m-1])
assert besseljzero(v,m,1).ae(jnp_small_zeros[v][m-1])
assert besselyzero(v,m).ae(yn_small_zeros[v][m-1])
assert besselyzero(v,m).ae(yn_small_zeros[v][m-1])
assert besselyzero(v,m,1).ae(ynp_small_zeros[v][m-1])
assert besselyzero(v,m,1).ae(ynp_small_zeros[v][m-1])
if __name__ == "__main__":
test_bessel_zeros()
| 20,758 | 21.202139 | 65 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/tests/test_matrices.py
|
from mpmath import *
def test_matrix_basic():
A1 = matrix(3)
for i in range(3):
A1[i,i] = 1
assert A1 == eye(3)
assert A1 == matrix(A1)
A2 = matrix(3, 2)
assert not A2._matrix__data
A3 = matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
assert list(A3) == list(range(1, 10))
A3[1,1] = 0
assert not (1, 1) in A3._matrix__data
A4 = matrix([[1, 2, 3], [4, 5, 6]])
A5 = matrix([[6, -1], [3, 2], [0, -3]])
assert A4 * A5 == matrix([[12, -6], [39, -12]])
assert A1 * A3 == A3 * A1 == A3
try:
A2 * A2
assert False
except ValueError:
pass
l = [[10, 20, 30], [40, 0, 60], [70, 80, 90]]
A6 = matrix(l)
assert A6.tolist() == l
assert A6 == eval(repr(A6))
A6 = matrix(A6, force_type=float)
assert A6 == eval(repr(A6))
assert A6*1j == eval(repr(A6*1j))
assert A3 * 10 == 10 * A3 == A6
assert A2.rows == 3
assert A2.cols == 2
A3.rows = 2
A3.cols = 2
assert len(A3._matrix__data) == 3
assert A4 + A4 == 2*A4
try:
A4 + A2
except ValueError:
pass
assert sum(A1 - A1) == 0
A7 = matrix([[1, 2], [3, 4], [5, 6], [7, 8]])
x = matrix([10, -10])
assert A7*x == matrix([-10, -10, -10, -10])
A8 = ones(5)
assert sum((A8 + 1) - (2 - zeros(5))) == 0
assert (1 + ones(4)) / 2 - 1 == zeros(4)
assert eye(3)**10 == eye(3)
try:
A7**2
assert False
except ValueError:
pass
A9 = randmatrix(3)
A10 = matrix(A9)
A9[0,0] = -100
assert A9 != A10
assert nstr(A9)
def test_matrix_slices():
A = matrix([ [1, 2, 3],
[4, 5 ,6],
[7, 8 ,9]])
V = matrix([1,2,3,4,5])
# Get slice
assert A[:,:] == A
assert A[:,1] == matrix([[2],[5],[8]])
assert A[2,:] == matrix([[7, 8 ,9]])
assert A[1:3,1:3] == matrix([[5,6],[8,9]])
assert V[2:4] == matrix([3,4])
try:
A6 = A[:,1:6]
assert False
except IndexError:
pass
# Assign slice with matrix
A1 = matrix(3)
A1[:,:] = A
assert A1[:,:] == matrix([[1, 2, 3],
[4, 5 ,6],
[7, 8 ,9]])
A1[0,:] = matrix([[10, 11, 12]])
assert A1 == matrix([ [10, 11, 12],
[4, 5 ,6],
[7, 8 ,9]])
A1[:,2] = matrix([[13], [14], [15]])
assert A1 == matrix([ [10, 11, 13],
[4, 5 ,14],
[7, 8 ,15]])
A1[:2,:2] = matrix([[16, 17], [18 , 19]])
assert A1 == matrix([ [16, 17, 13],
[18, 19 ,14],
[7, 8 ,15]])
V[1:3] = 10
assert V == matrix([1,10,10,4,5])
try:
A1[2,:] = A[:,1]
assert False
except ValueError:
pass
try:
A1[2,1:20] = A[:,:]
assert False
except IndexError:
pass
# Assign slice with scalar
A1[:,2] = 10
assert A1 == matrix([ [16, 17, 10],
[18, 19 ,10],
[7, 8 ,10]])
A1[:,:] = 40
for x in A1:
assert x == 40
def test_matrix_power():
A = matrix([[1, 2], [3, 4]])
assert A**2 == A*A
assert A**3 == A*A*A
assert A**-1 == inverse(A)
assert A**-2 == inverse(A*A)
def test_matrix_transform():
A = matrix([[1, 2], [3, 4], [5, 6]])
assert A.T == A.transpose() == matrix([[1, 3, 5], [2, 4, 6]])
swap_row(A, 1, 2)
assert A == matrix([[1, 2], [5, 6], [3, 4]])
l = [1, 2]
swap_row(l, 0, 1)
assert l == [2, 1]
assert extend(eye(3), [1,2,3]) == matrix([[1,0,0,1],[0,1,0,2],[0,0,1,3]])
def test_matrix_conjugate():
A = matrix([[1 + j, 0], [2, j]])
assert A.conjugate() == matrix([[mpc(1, -1), 0], [2, mpc(0, -1)]])
assert A.transpose_conj() == A.H == matrix([[mpc(1, -1), 2],
[0, mpc(0, -1)]])
def test_matrix_creation():
assert diag([1, 2, 3]) == matrix([[1, 0, 0], [0, 2, 0], [0, 0, 3]])
A1 = ones(2, 3)
assert A1.rows == 2 and A1.cols == 3
for a in A1:
assert a == 1
A2 = zeros(3, 2)
assert A2.rows == 3 and A2.cols == 2
for a in A2:
assert a == 0
assert randmatrix(10) != randmatrix(10)
one = mpf(1)
assert hilbert(3) == matrix([[one, one/2, one/3],
[one/2, one/3, one/4],
[one/3, one/4, one/5]])
def test_norms():
# matrix norms
A = matrix([[1, -2], [-3, -1], [2, 1]])
assert mnorm(A,1) == 6
assert mnorm(A,inf) == 4
assert mnorm(A,'F') == sqrt(20)
# vector norms
assert norm(-3) == 3
x = [1, -2, 7, -12]
assert norm(x, 1) == 22
assert round(norm(x, 2), 10) == 14.0712472795
assert round(norm(x, 10), 10) == 12.0054633727
assert norm(x, inf) == 12
def test_vector():
x = matrix([0, 1, 2, 3, 4])
assert x == matrix([[0], [1], [2], [3], [4]])
assert x[3] == 3
assert len(x._matrix__data) == 4
assert list(x) == list(range(5))
x[0] = -10
x[4] = 0
assert x[0] == -10
assert len(x) == len(x.T) == 5
assert x.T*x == matrix([[114]])
def test_matrix_copy():
A = ones(6)
B = A.copy()
assert A == B
B[0,0] = 0
assert A != B
def test_matrix_numpy():
try:
import numpy
except ImportError:
return
l = [[1, 2], [3, 4], [5, 6]]
a = numpy.matrix(l)
assert matrix(l) == matrix(a)
| 5,591 | 26.820896 | 77 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/tests/test_summation.py
|
from mpmath import *
def test_sumem():
mp.dps = 15
assert sumem(lambda k: 1/k**2.5, [50, 100]).ae(0.0012524505324784962)
assert sumem(lambda k: k**4 + 3*k + 1, [10, 100]).ae(2050333103)
def test_nsum():
mp.dps = 15
assert nsum(lambda x: x**2, [1, 3]) == 14
assert nsum(lambda k: 1/factorial(k), [0, inf]).ae(e)
assert nsum(lambda k: (-1)**(k+1) / k, [1, inf]).ae(log(2))
assert nsum(lambda k: (-1)**(k+1) / k**2, [1, inf]).ae(pi**2 / 12)
assert nsum(lambda k: (-1)**k / log(k), [2, inf]).ae(0.9242998972229388)
assert nsum(lambda k: 1/k**2, [1, inf]).ae(pi**2 / 6)
assert nsum(lambda k: 2**k/fac(k), [0, inf]).ae(exp(2))
assert nsum(lambda k: 1/k**2, [4, inf], method='e').ae(0.2838229557371153)
def test_nprod():
mp.dps = 15
assert nprod(lambda k: exp(1/k**2), [1,inf], method='r').ae(exp(pi**2/6))
assert nprod(lambda x: x**2, [1, 3]) == 36
def test_fsum():
mp.dps = 15
assert fsum([]) == 0
assert fsum([-4]) == -4
assert fsum([2,3]) == 5
assert fsum([1e-100,1]) == 1
assert fsum([1,1e-100]) == 1
assert fsum([1e100,1]) == 1e100
assert fsum([1,1e100]) == 1e100
assert fsum([1e-100,0]) == 1e-100
assert fsum([1e-100,1e100,1e-100]) == 1e100
assert fsum([2,1+1j,1]) == 4+1j
assert fsum([2,inf,3]) == inf
assert fsum([2,-1], absolute=1) == 3
assert fsum([2,-1], squared=1) == 5
assert fsum([1,1+j], squared=1) == 1+2j
assert fsum([1,3+4j], absolute=1) == 6
assert fsum([1,2+3j], absolute=1, squared=1) == 14
assert isnan(fsum([inf,-inf]))
assert fsum([inf,-inf], absolute=1) == inf
assert fsum([inf,-inf], squared=1) == inf
assert fsum([inf,-inf], absolute=1, squared=1) == inf
assert iv.fsum([1,mpi(2,3)]) == mpi(3,4)
def test_fprod():
mp.dps = 15
assert fprod([]) == 1
assert fprod([2,3]) == 6
| 1,859 | 34.769231 | 78 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/tests/test_eigen.py
|
#!/usr/bin/python
# -*- coding: utf-8 -*-
from mpmath import mp
from mpmath import libmp
xrange = libmp.backend.xrange
def run_hessenberg(A, verbose = 0):
if verbose > 1:
print("original matrix (hessenberg):\n", A)
n = A.rows
Q, H = mp.hessenberg(A)
if verbose > 1:
print("Q:\n",Q)
print("H:\n",H)
B = Q * H * Q.transpose_conj()
eps = mp.exp(0.8 * mp.log(mp.eps))
err0 = 0
for x in xrange(n):
for y in xrange(n):
err0 += abs(A[y,x] - B[y,x])
err0 /= n * n
err1 = 0
for x in xrange(n):
for y in xrange(x + 2, n):
err1 += abs(H[y,x])
if verbose > 0:
print("difference (H):", err0, err1)
if verbose > 1:
print("B:\n", B)
assert err0 < eps
assert err1 == 0
def run_schur(A, verbose = 0):
if verbose > 1:
print("original matrix (schur):\n", A)
n = A.rows
Q, R = mp.schur(A)
if verbose > 1:
print("Q:\n", Q)
print("R:\n", R)
B = Q * R * Q.transpose_conj()
C = Q * Q.transpose_conj()
eps = mp.exp(0.8 * mp.log(mp.eps))
err0 = 0
for x in xrange(n):
for y in xrange(n):
err0 += abs(A[y,x] - B[y,x])
err0 /= n * n
err1 = 0
for x in xrange(n):
for y in xrange(n):
if x == y:
C[y,x] -= 1
err1 += abs(C[y,x])
err1 /= n * n
err2 = 0
for x in xrange(n):
for y in xrange(x + 1, n):
err2 += abs(R[y,x])
if verbose > 0:
print("difference (S):", err0, err1, err2)
if verbose > 1:
print("B:\n", B)
assert err0 < eps
assert err1 < eps
assert err2 == 0
def run_eig(A, verbose = 0):
if verbose > 1:
print("original matrix (eig):\n", A)
n = A.rows
E, EL, ER = mp.eig(A, left = True, right = True)
if verbose > 1:
print("E:\n", E)
print("EL:\n", EL)
print("ER:\n", ER)
eps = mp.exp(0.8 * mp.log(mp.eps))
err0 = 0
for i in xrange(n):
B = A * ER[:,i] - E[i] * ER[:,i]
err0 = max(err0, mp.mnorm(B))
B = EL[i,:] * A - EL[i,:] * E[i]
err0 = max(err0, mp.mnorm(B))
err0 /= n * n
if verbose > 0:
print("difference (E):", err0)
assert err0 < eps
#####################
def test_eig_dyn():
v = 0
for i in xrange(5):
n = 1 + int(mp.rand() * 5)
if mp.rand() > 0.5:
# real
A = 2 * mp.randmatrix(n, n) - 1
if mp.rand() > 0.5:
A *= 10
for x in xrange(n):
for y in xrange(n):
A[x,y] = int(A[x,y])
else:
A = (2 * mp.randmatrix(n, n) - 1) + 1j * (2 * mp.randmatrix(n, n) - 1)
if mp.rand() > 0.5:
A *= 10
for x in xrange(n):
for y in xrange(n):
A[x,y] = int(mp.re(A[x,y])) + 1j * int(mp.im(A[x,y]))
run_hessenberg(A, verbose = v)
run_schur(A, verbose = v)
run_eig(A, verbose = v)
def test_eig():
v = 0
AS = []
A = mp.matrix([[2, 1, 0], # jordan block of size 3
[0, 2, 1],
[0, 0, 2]])
AS.append(A)
AS.append(A.transpose())
A = mp.matrix([[2, 0, 0], # jordan block of size 2
[0, 2, 1],
[0, 0, 2]])
AS.append(A)
AS.append(A.transpose())
A = mp.matrix([[2, 0, 1], # jordan block of size 2
[0, 2, 0],
[0, 0, 2]])
AS.append(A)
AS.append(A.transpose())
A= mp.matrix([[0, 0, 1], # cyclic
[1, 0, 0],
[0, 1, 0]])
AS.append(A)
AS.append(A.transpose())
for A in AS:
run_hessenberg(A, verbose = v)
run_schur(A, verbose = v)
run_eig(A, verbose = v)
| 3,905 | 20.7 | 82 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/tests/test_linalg.py
|
# TODO: don't use round
from __future__ import division
from mpmath import *
xrange = libmp.backend.xrange
# XXX: these shouldn't be visible(?)
LU_decomp = mp.LU_decomp
L_solve = mp.L_solve
U_solve = mp.U_solve
householder = mp.householder
improve_solution = mp.improve_solution
A1 = matrix([[3, 1, 6],
[2, 1, 3],
[1, 1, 1]])
b1 = [2, 7, 4]
A2 = matrix([[ 2, -1, -1, 2],
[ 6, -2, 3, -1],
[-4, 2, 3, -2],
[ 2, 0, 4, -3]])
b2 = [3, -3, -2, -1]
A3 = matrix([[ 1, 0, -1, -1, 0],
[ 0, 1, 1, 0, -1],
[ 4, -5, 2, 0, 0],
[ 0, 0, -2, 9,-12],
[ 0, 5, 0, 0, 12]])
b3 = [0, 0, 0, 0, 50]
A4 = matrix([[10.235, -4.56, 0., -0.035, 5.67],
[-2.463, 1.27, 3.97, -8.63, 1.08],
[-6.58, 0.86, -0.257, 9.32, -43.6 ],
[ 9.83, 7.39, -17.25, 0.036, 24.86],
[-9.31, 34.9, 78.56, 1.07, 65.8 ]])
b4 = [8.95, 20.54, 7.42, 5.60, 58.43]
A5 = matrix([[ 1, 2, -4],
[-2, -3, 5],
[ 3, 5, -8]])
A6 = matrix([[ 1.377360, 2.481400, 5.359190],
[ 2.679280, -1.229560, 25.560210],
[-1.225280+1.e6, 9.910180, -35.049900-1.e6]])
b6 = [23.500000, -15.760000, 2.340000]
A7 = matrix([[1, -0.5],
[2, 1],
[-2, 6]])
b7 = [3, 2, -4]
A8 = matrix([[1, 2, 3],
[-1, 0, 1],
[-1, -2, -1],
[1, 0, -1]])
b8 = [1, 2, 3, 4]
A9 = matrix([[ 4, 2, -2],
[ 2, 5, -4],
[-2, -4, 5.5]])
b9 = [10, 16, -15.5]
A10 = matrix([[1.0 + 1.0j, 2.0, 2.0],
[4.0, 5.0, 6.0],
[7.0, 8.0, 9.0]])
b10 = [1.0, 1.0 + 1.0j, 1.0]
def test_LU_decomp():
A = A3.copy()
b = b3
A, p = LU_decomp(A)
y = L_solve(A, b, p)
x = U_solve(A, y)
assert p == [2, 1, 2, 3]
assert [round(i, 14) for i in x] == [3.78953107960742, 2.9989094874591098,
-0.081788440567070006, 3.8713195201744801, 2.9171210468920399]
A = A4.copy()
b = b4
A, p = LU_decomp(A)
y = L_solve(A, b, p)
x = U_solve(A, y)
assert p == [0, 3, 4, 3]
assert [round(i, 14) for i in x] == [2.6383625899619201, 2.6643834462368399,
0.79208015947958998, -2.5088376454101899, -1.0567657691375001]
A = randmatrix(3)
bak = A.copy()
LU_decomp(A, overwrite=1)
assert A != bak
def test_inverse():
for A in [A1, A2, A5]:
inv = inverse(A)
assert mnorm(A*inv - eye(A.rows), 1) < 1.e-14
def test_householder():
mp.dps = 15
A, b = A8, b8
H, p, x, r = householder(extend(A, b))
assert H == matrix(
[[mpf('3.0'), mpf('-2.0'), mpf('-1.0'), 0],
[-1.0,mpf('3.333333333333333'),mpf('-2.9999999999999991'),mpf('2.0')],
[-1.0, mpf('-0.66666666666666674'),mpf('2.8142135623730948'),
mpf('-2.8284271247461898')],
[1.0, mpf('-1.3333333333333333'),mpf('-0.20000000000000018'),
mpf('4.2426406871192857')]])
assert p == [-2, -2, mpf('-1.4142135623730949')]
assert round(norm(r, 2), 10) == 4.2426406870999998
y = [102.102, 58.344, 36.463, 24.310, 17.017, 12.376, 9.282, 7.140, 5.610,
4.488, 3.6465, 3.003]
def coeff(n):
# similiar to Hilbert matrix
A = []
for i in range(1, 13):
A.append([1. / (i + j - 1) for j in range(1, n + 1)])
return matrix(A)
residuals = []
refres = []
for n in range(2, 7):
A = coeff(n)
H, p, x, r = householder(extend(A, y))
x = matrix(x)
y = matrix(y)
residuals.append(norm(r, 2))
refres.append(norm(residual(A, x, y), 2))
assert [round(res, 10) for res in residuals] == [15.1733888877,
0.82378073210000002, 0.302645887, 0.0260109244,
0.00058653999999999998]
assert norm(matrix(residuals) - matrix(refres), inf) < 1.e-13
def test_factorization():
A = randmatrix(5)
P, L, U = lu(A)
assert mnorm(P*A - L*U, 1) < 1.e-15
def test_solve():
assert norm(residual(A6, lu_solve(A6, b6), b6), inf) < 1.e-10
assert norm(residual(A7, lu_solve(A7, b7), b7), inf) < 1.5
assert norm(residual(A8, lu_solve(A8, b8), b8), inf) <= 3 + 1.e-10
assert norm(residual(A6, qr_solve(A6, b6)[0], b6), inf) < 1.e-10
assert norm(residual(A7, qr_solve(A7, b7)[0], b7), inf) < 1.5
assert norm(residual(A8, qr_solve(A8, b8)[0], b8), 2) <= 4.3
assert norm(residual(A10, lu_solve(A10, b10), b10), 2) < 1.e-10
assert norm(residual(A10, qr_solve(A10, b10)[0], b10), 2) < 1.e-10
def test_solve_overdet_complex():
A = matrix([[1, 2j], [3, 4j], [5, 6]])
b = matrix([1 + j, 2, -j])
assert norm(residual(A, lu_solve(A, b), b)) < 1.0208
def test_singular():
mp.dps = 15
A = [[5.6, 1.2], [7./15, .1]]
B = repr(zeros(2))
b = [1, 2]
def _assert_ZeroDivisionError(statement):
try:
eval(statement)
assert False
except (ZeroDivisionError, ValueError):
pass
for i in ['lu_solve(%s, %s)' % (A, b), 'lu_solve(%s, %s)' % (B, b),
'qr_solve(%s, %s)' % (A, b), 'qr_solve(%s, %s)' % (B, b)]:
_assert_ZeroDivisionError(i)
def test_cholesky():
assert fp.cholesky(fp.matrix(A9)) == fp.matrix([[2, 0, 0], [1, 2, 0], [-1, -3/2, 3/2]])
x = fp.cholesky_solve(A9, b9)
assert fp.norm(fp.residual(A9, x, b9), fp.inf) == 0
def test_det():
assert det(A1) == 1
assert round(det(A2), 14) == 8
assert round(det(A3)) == 1834
assert round(det(A4)) == 4443376
assert det(A5) == 1
assert round(det(A6)) == 78356463
assert det(zeros(3)) == 0
def test_cond():
mp.dps = 15
A = matrix([[1.2969, 0.8648], [0.2161, 0.1441]])
assert cond(A, lambda x: mnorm(x,1)) == mpf('327065209.73817754')
assert cond(A, lambda x: mnorm(x,inf)) == mpf('327065209.73817754')
assert cond(A, lambda x: mnorm(x,'F')) == mpf('249729266.80008656')
@extradps(50)
def test_precision():
A = randmatrix(10, 10)
assert mnorm(inverse(inverse(A)) - A, 1) < 1.e-45
def test_interval_matrix():
mp.dps = 15
iv.dps = 15
a = iv.matrix([['0.1','0.3','1.0'],['7.1','5.5','4.8'],['3.2','4.4','5.6']])
b = iv.matrix(['4','0.6','0.5'])
c = iv.lu_solve(a, b)
assert c[0].delta < 1e-13
assert c[1].delta < 1e-13
assert c[2].delta < 1e-13
assert 5.25823271130625686059275 in c[0]
assert -13.155049396267837541163 in c[1]
assert 7.42069154774972557628979 in c[2]
def test_LU_cache():
A = randmatrix(3)
LU = LU_decomp(A)
assert A._LU == LU_decomp(A)
A[0,0] = -1000
assert A._LU is None
def test_improve_solution():
A = randmatrix(5, min=1e-20, max=1e20)
b = randmatrix(5, 1, min=-1000, max=1000)
x1 = lu_solve(A, b) + randmatrix(5, 1, min=-1e-5, max=1.e-5)
x2 = improve_solution(A, x1, b)
assert norm(residual(A, x2, b), 2) < norm(residual(A, x1, b), 2)
def test_exp_pade():
for i in range(3):
dps = 15
extra = 15
mp.dps = dps + extra
dm = 0
N = 3
dg = range(1,N+1)
a = diag(dg)
expa = diag([exp(x) for x in dg])
# choose a random matrix not close to be singular
# to avoid adding too much extra precision in computing
# m**-1 * M * m
while abs(dm) < 0.01:
m = randmatrix(N)
dm = det(m)
m = m/dm
a1 = m**-1 * a * m
e2 = m**-1 * expa * m
mp.dps = dps
e1 = expm(a1, method='pade')
mp.dps = dps + extra
d = e2 - e1
#print d
mp.dps = dps
assert norm(d, inf).ae(0)
mp.dps = 15
def test_qr():
mp.dps = 15 # used default value for dps
lowlimit = -9 # lower limit of matrix element value
uplimit = 9 # uppter limit of matrix element value
maxm = 4 # max matrix size
flg = False # toggle to create real vs complex matrix
zero = mpf('0.0')
for k in xrange(0,10):
exdps = 0
mode = 'full'
flg = bool(k % 2)
# generate arbitrary matrix size (2 to maxm)
num1 = nint(2 + (maxm-2)*rand())
num2 = nint(2 + (maxm-2)*rand())
m = int(max(num1, num2))
n = int(min(num1, num2))
# create matrix
A = mp.matrix(m,n)
# populate matrix values with arbitrary integers
if flg:
flg = False
dtype = 'complex'
for j in xrange(0,n):
for i in xrange(0,m):
val = nint(lowlimit + (uplimit-lowlimit)*rand())
val2 = nint(lowlimit + (uplimit-lowlimit)*rand())
A[i,j] = mpc(val, val2)
else:
flg = True
dtype = 'real'
for j in xrange(0,n):
for i in xrange(0,m):
val = nint(lowlimit + (uplimit-lowlimit)*rand())
A[i,j] = mpf(val)
# perform A -> QR decomposition
Q, R = qr(A, mode, edps = exdps)
#print('\n\n A = \n', nstr(A, 4))
#print('\n Q = \n', nstr(Q, 4))
#print('\n R = \n', nstr(R, 4))
#print('\n Q*R = \n', nstr(Q*R, 4))
maxnorm = mpf('1.0E-11')
n1 = norm(A - Q * R)
#print '\n Norm of A - Q * R = ', n1
if n1 > maxnorm:
raise ValueError('Excessive norm value')
if dtype == 'real':
n1 = norm(eye(m) - Q.T * Q)
#print ' Norm of I - Q.T * Q = ', n1
if n1 > maxnorm:
raise ValueError('Excessive norm value')
n1 = norm(eye(m) - Q * Q.T)
#print ' Norm of I - Q * Q.T = ', n1
if n1 > maxnorm:
raise ValueError('Excessive norm value')
if dtype == 'complex':
n1 = norm(eye(m) - Q.T * Q.conjugate())
#print ' Norm of I - Q.T * Q.conjugate() = ', n1
if n1 > maxnorm:
raise ValueError('Excessive norm value')
n1 = norm(eye(m) - Q.conjugate() * Q.T)
#print ' Norm of I - Q.conjugate() * Q.T = ', n1
if n1 > maxnorm:
raise ValueError('Excessive norm value')
| 10,263 | 30.484663 | 91 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/tests/__init__.py
| 0 | 0 | 0 |
py
|
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/tests/test_trig.py
|
from mpmath import *
from mpmath.libmp import *
def test_trig_misc_hard():
mp.prec = 53
# Worst-case input for an IEEE double, from a paper by Kahan
x = ldexp(6381956970095103,797)
assert cos(x) == mpf('-4.6871659242546277e-19')
assert sin(x) == 1
mp.prec = 150
a = mpf(10**50)
mp.prec = 53
assert sin(a).ae(-0.7896724934293100827)
assert cos(a).ae(-0.6135286082336635622)
# Check relative accuracy close to x = zero
assert sin(1e-100) == 1e-100 # when rounding to nearest
assert sin(1e-6).ae(9.999999999998333e-007, rel_eps=2e-15, abs_eps=0)
assert sin(1e-6j).ae(1.0000000000001666e-006j, rel_eps=2e-15, abs_eps=0)
assert sin(-1e-6j).ae(-1.0000000000001666e-006j, rel_eps=2e-15, abs_eps=0)
assert cos(1e-100) == 1
assert cos(1e-6).ae(0.9999999999995)
assert cos(-1e-6j).ae(1.0000000000005)
assert tan(1e-100) == 1e-100
assert tan(1e-6).ae(1.0000000000003335e-006, rel_eps=2e-15, abs_eps=0)
assert tan(1e-6j).ae(9.9999999999966644e-007j, rel_eps=2e-15, abs_eps=0)
assert tan(-1e-6j).ae(-9.9999999999966644e-007j, rel_eps=2e-15, abs_eps=0)
def test_trig_near_zero():
mp.dps = 15
for r in [round_nearest, round_down, round_up, round_floor, round_ceiling]:
assert sin(0, rounding=r) == 0
assert cos(0, rounding=r) == 1
a = mpf('1e-100')
b = mpf('-1e-100')
assert sin(a, rounding=round_nearest) == a
assert sin(a, rounding=round_down) < a
assert sin(a, rounding=round_floor) < a
assert sin(a, rounding=round_up) >= a
assert sin(a, rounding=round_ceiling) >= a
assert sin(b, rounding=round_nearest) == b
assert sin(b, rounding=round_down) > b
assert sin(b, rounding=round_floor) <= b
assert sin(b, rounding=round_up) <= b
assert sin(b, rounding=round_ceiling) > b
assert cos(a, rounding=round_nearest) == 1
assert cos(a, rounding=round_down) < 1
assert cos(a, rounding=round_floor) < 1
assert cos(a, rounding=round_up) == 1
assert cos(a, rounding=round_ceiling) == 1
assert cos(b, rounding=round_nearest) == 1
assert cos(b, rounding=round_down) < 1
assert cos(b, rounding=round_floor) < 1
assert cos(b, rounding=round_up) == 1
assert cos(b, rounding=round_ceiling) == 1
def test_trig_near_n_pi():
mp.dps = 15
a = [n*pi for n in [1, 2, 6, 11, 100, 1001, 10000, 100001]]
mp.dps = 135
a.append(10**100 * pi)
mp.dps = 15
assert sin(a[0]) == mpf('1.2246467991473531772e-16')
assert sin(a[1]) == mpf('-2.4492935982947063545e-16')
assert sin(a[2]) == mpf('-7.3478807948841190634e-16')
assert sin(a[3]) == mpf('4.8998251578625894243e-15')
assert sin(a[4]) == mpf('1.9643867237284719452e-15')
assert sin(a[5]) == mpf('-8.8632615209684813458e-15')
assert sin(a[6]) == mpf('-4.8568235395684898392e-13')
assert sin(a[7]) == mpf('3.9087342299491231029e-11')
assert sin(a[8]) == mpf('-1.369235466754566993528e-36')
r = round_nearest
assert cos(a[0], rounding=r) == -1
assert cos(a[1], rounding=r) == 1
assert cos(a[2], rounding=r) == 1
assert cos(a[3], rounding=r) == -1
assert cos(a[4], rounding=r) == 1
assert cos(a[5], rounding=r) == -1
assert cos(a[6], rounding=r) == 1
assert cos(a[7], rounding=r) == -1
assert cos(a[8], rounding=r) == 1
r = round_up
assert cos(a[0], rounding=r) == -1
assert cos(a[1], rounding=r) == 1
assert cos(a[2], rounding=r) == 1
assert cos(a[3], rounding=r) == -1
assert cos(a[4], rounding=r) == 1
assert cos(a[5], rounding=r) == -1
assert cos(a[6], rounding=r) == 1
assert cos(a[7], rounding=r) == -1
assert cos(a[8], rounding=r) == 1
r = round_down
assert cos(a[0], rounding=r) > -1
assert cos(a[1], rounding=r) < 1
assert cos(a[2], rounding=r) < 1
assert cos(a[3], rounding=r) > -1
assert cos(a[4], rounding=r) < 1
assert cos(a[5], rounding=r) > -1
assert cos(a[6], rounding=r) < 1
assert cos(a[7], rounding=r) > -1
assert cos(a[8], rounding=r) < 1
r = round_floor
assert cos(a[0], rounding=r) == -1
assert cos(a[1], rounding=r) < 1
assert cos(a[2], rounding=r) < 1
assert cos(a[3], rounding=r) == -1
assert cos(a[4], rounding=r) < 1
assert cos(a[5], rounding=r) == -1
assert cos(a[6], rounding=r) < 1
assert cos(a[7], rounding=r) == -1
assert cos(a[8], rounding=r) < 1
r = round_ceiling
assert cos(a[0], rounding=r) > -1
assert cos(a[1], rounding=r) == 1
assert cos(a[2], rounding=r) == 1
assert cos(a[3], rounding=r) > -1
assert cos(a[4], rounding=r) == 1
assert cos(a[5], rounding=r) > -1
assert cos(a[6], rounding=r) == 1
assert cos(a[7], rounding=r) > -1
assert cos(a[8], rounding=r) == 1
mp.dps = 15
if __name__ == '__main__':
for f in globals().keys():
if f.startswith("test_"):
print(f)
globals()[f]()
| 4,940 | 33.552448 | 79 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/tests/test_mpmath.py
|
from mpmath.libmp import *
from mpmath import *
def test_newstyle_classes():
for cls in [mp, fp, iv, mpf, mpc]:
for s in cls.__class__.__mro__:
assert isinstance(s, type)
| 196 | 23.625 | 39 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/tests/test_fp.py
|
"""
Easy-to-use test-generating code:
cases = '''
exp 2.25
log 2.25
'''
from mpmath import *
mp.dps = 20
for test in cases.splitlines():
if not test:
continue
words = test.split()
fname = words[0]
args = words[1:]
argstr = ", ".join(args)
testline = "%s(%s)" % (fname, argstr)
ans = str(eval(testline))
print " assert ae(fp.%s, %s)" % (testline, ans)
"""
from mpmath import fp
def ae(x, y, tol=1e-12):
if x == y:
return True
return abs(x-y) <= tol*abs(y)
def test_conj():
assert fp.conj(4) == 4
assert fp.conj(3+4j) == 3-4j
assert fp.fdot([1,2],[3,2+1j], conjugate=True) == 7-2j
def test_fp_number_parts():
assert ae(fp.arg(3), 0.0)
assert ae(fp.arg(-3), 3.1415926535897932385)
assert ae(fp.arg(3j), 1.5707963267948966192)
assert ae(fp.arg(-3j), -1.5707963267948966192)
assert ae(fp.arg(2+3j), 0.98279372324732906799)
assert ae(fp.arg(-1-1j), -2.3561944901923449288)
assert ae(fp.re(2.5), 2.5)
assert ae(fp.re(2.5+3j), 2.5)
assert ae(fp.im(2.5), 0.0)
assert ae(fp.im(2.5+3j), 3.0)
assert ae(fp.floor(2.5), 2.0)
assert ae(fp.floor(2), 2.0)
assert ae(fp.floor(2.0+0j), (2.0 + 0.0j))
assert ae(fp.floor(-1.5-0.5j), (-2.0 - 1.0j))
assert ae(fp.ceil(2.5), 3.0)
assert ae(fp.ceil(2), 2.0)
assert ae(fp.ceil(2.0+0j), (2.0 + 0.0j))
assert ae(fp.ceil(-1.5-0.5j), (-1.0 + 0.0j))
def test_fp_cospi_sinpi():
assert ae(fp.sinpi(0), 0.0)
assert ae(fp.sinpi(0.25), 0.7071067811865475244)
assert ae(fp.sinpi(0.5), 1.0)
assert ae(fp.sinpi(0.75), 0.7071067811865475244)
assert ae(fp.sinpi(1), 0.0)
assert ae(fp.sinpi(1.25), -0.7071067811865475244)
assert ae(fp.sinpi(1.5), -1.0)
assert ae(fp.sinpi(1.75), -0.7071067811865475244)
assert ae(fp.sinpi(2), 0.0)
assert ae(fp.sinpi(2.25), 0.7071067811865475244)
assert ae(fp.sinpi(0+3j), (0.0 + 6195.8238636085899556j))
assert ae(fp.sinpi(0.25+3j), (4381.1091260582448033 + 4381.1090689950686908j))
assert ae(fp.sinpi(0.5+3j), (6195.8239443081075259 + 0.0j))
assert ae(fp.sinpi(0.75+3j), (4381.1091260582448033 - 4381.1090689950686908j))
assert ae(fp.sinpi(1+3j), (0.0 - 6195.8238636085899556j))
assert ae(fp.sinpi(1.25+3j), (-4381.1091260582448033 - 4381.1090689950686908j))
assert ae(fp.sinpi(1.5+3j), (-6195.8239443081075259 + 0.0j))
assert ae(fp.sinpi(1.75+3j), (-4381.1091260582448033 + 4381.1090689950686908j))
assert ae(fp.sinpi(2+3j), (0.0 + 6195.8238636085899556j))
assert ae(fp.sinpi(2.25+3j), (4381.1091260582448033 + 4381.1090689950686908j))
assert ae(fp.sinpi(-0.75), -0.7071067811865475244)
assert ae(fp.sinpi(-1e-10), -3.1415926535897933529e-10)
assert ae(fp.sinpi(1e-10), 3.1415926535897933529e-10)
assert ae(fp.sinpi(1e-10+1e-10j), (3.141592653589793353e-10 + 3.1415926535897933528e-10j))
assert ae(fp.sinpi(1e-10-1e-10j), (3.141592653589793353e-10 - 3.1415926535897933528e-10j))
assert ae(fp.sinpi(-1e-10+1e-10j), (-3.141592653589793353e-10 + 3.1415926535897933528e-10j))
assert ae(fp.sinpi(-1e-10-1e-10j), (-3.141592653589793353e-10 - 3.1415926535897933528e-10j))
assert ae(fp.cospi(0), 1.0)
assert ae(fp.cospi(0.25), 0.7071067811865475244)
assert ae(fp.cospi(0.5), 0.0)
assert ae(fp.cospi(0.75), -0.7071067811865475244)
assert ae(fp.cospi(1), -1.0)
assert ae(fp.cospi(1.25), -0.7071067811865475244)
assert ae(fp.cospi(1.5), 0.0)
assert ae(fp.cospi(1.75), 0.7071067811865475244)
assert ae(fp.cospi(2), 1.0)
assert ae(fp.cospi(2.25), 0.7071067811865475244)
assert ae(fp.cospi(0+3j), (6195.8239443081075259 + 0.0j))
assert ae(fp.cospi(0.25+3j), (4381.1091260582448033 - 4381.1090689950686908j))
assert ae(fp.cospi(0.5+3j), (0.0 - 6195.8238636085899556j))
assert ae(fp.cospi(0.75+3j), (-4381.1091260582448033 - 4381.1090689950686908j))
assert ae(fp.cospi(1+3j), (-6195.8239443081075259 + 0.0j))
assert ae(fp.cospi(1.25+3j), (-4381.1091260582448033 + 4381.1090689950686908j))
assert ae(fp.cospi(1.5+3j), (0.0 + 6195.8238636085899556j))
assert ae(fp.cospi(1.75+3j), (4381.1091260582448033 + 4381.1090689950686908j))
assert ae(fp.cospi(2+3j), (6195.8239443081075259 + 0.0j))
assert ae(fp.cospi(2.25+3j), (4381.1091260582448033 - 4381.1090689950686908j))
assert ae(fp.cospi(-0.75), -0.7071067811865475244)
assert ae(fp.sinpi(-0.7), -0.80901699437494750611)
assert ae(fp.cospi(-0.7), -0.5877852522924730163)
assert ae(fp.cospi(-3+2j), (-267.74676148374822225 + 0.0j))
assert ae(fp.sinpi(-3+2j), (0.0 - 267.74489404101651426j))
assert ae(fp.sinpi(-0.7+2j), (-216.6116802292079471 - 157.37650009392034693j))
assert ae(fp.cospi(-0.7+2j), (-157.37759774921754565 + 216.61016943630197336j))
def test_fp_expj():
assert ae(fp.expj(0), (1.0 + 0.0j))
assert ae(fp.expj(1), (0.5403023058681397174 + 0.84147098480789650665j))
assert ae(fp.expj(2), (-0.416146836547142387 + 0.9092974268256816954j))
assert ae(fp.expj(0.75), (0.73168886887382088631 + 0.68163876002333416673j))
assert ae(fp.expj(2+3j), (-0.020718731002242879378 + 0.045271253156092975488j))
assert ae(fp.expjpi(0), (1.0 + 0.0j))
assert ae(fp.expjpi(1), (-1.0 + 0.0j))
assert ae(fp.expjpi(2), (1.0 + 0.0j))
assert ae(fp.expjpi(0.75), (-0.7071067811865475244 + 0.7071067811865475244j))
assert ae(fp.expjpi(2+3j), (0.000080699517570304599239 + 0.0j))
def test_fp_bernoulli():
assert ae(fp.bernoulli(0), 1.0)
assert ae(fp.bernoulli(1), -0.5)
assert ae(fp.bernoulli(2), 0.16666666666666666667)
assert ae(fp.bernoulli(10), 0.075757575757575757576)
assert ae(fp.bernoulli(11), 0.0)
def test_fp_gamma():
assert ae(fp.gamma(1), 1.0)
assert ae(fp.gamma(1.5), 0.88622692545275801365)
assert ae(fp.gamma(10), 362880.0)
assert ae(fp.gamma(-0.5), -3.5449077018110320546)
assert ae(fp.gamma(-7.1), 0.0016478244570263333622)
assert ae(fp.gamma(12.3), 83385367.899970000963)
assert ae(fp.gamma(2+0j), (1.0 + 0.0j))
assert ae(fp.gamma(-2.5+0j), (-0.94530872048294188123 + 0.0j))
assert ae(fp.gamma(3+4j), (0.0052255384713692141947 - 0.17254707929430018772j))
assert ae(fp.gamma(-3-4j), (0.00001460997305874775607 - 0.000020760733311509070396j))
assert ae(fp.fac(0), 1.0)
assert ae(fp.fac(1), 1.0)
assert ae(fp.fac(20), 2432902008176640000.0)
assert ae(fp.fac(-3.5), -0.94530872048294188123)
assert ae(fp.fac(2+3j), (-0.44011340763700171113 - 0.06363724312631702183j))
assert ae(fp.loggamma(1.0), 0.0)
assert ae(fp.loggamma(2.0), 0.0)
assert ae(fp.loggamma(3.0), 0.69314718055994530942)
assert ae(fp.loggamma(7.25), 7.0521854507385394449)
assert ae(fp.loggamma(1000.0), 5905.2204232091812118)
assert ae(fp.loggamma(1e50), 1.1412925464970229298e+52)
assert ae(fp.loggamma(1e25+1e25j), (5.6125802751733671621e+26 + 5.7696599078528568383e+26j))
assert ae(fp.loggamma(3+4j), (-1.7566267846037841105 + 4.7426644380346579282j))
assert ae(fp.loggamma(-0.5), (1.2655121234846453965 - 3.1415926535897932385j))
assert ae(fp.loggamma(-1.25), (1.3664317612369762346 - 6.2831853071795864769j))
assert ae(fp.loggamma(-2.75), (0.0044878975359557733115 - 9.4247779607693797154j))
assert ae(fp.loggamma(-3.5), (-1.3090066849930420464 - 12.566370614359172954j))
assert ae(fp.loggamma(-4.5), (-2.8130840817693161197 - 15.707963267948966192j))
assert ae(fp.loggamma(-2+3j), (-6.776523813485657093 - 4.568791367260286402j))
assert ae(fp.loggamma(-1000.3), (-5912.8440347785205041 - 3144.7342462433830317j))
assert ae(fp.loggamma(-100-100j), (-632.35117666833135562 - 158.37641469650352462j))
assert ae(fp.loggamma(1e-10), 23.025850929882735237)
assert ae(fp.loggamma(-1e-10), (23.02585092999817837 - 3.1415926535897932385j))
assert ae(fp.loggamma(1e-10j), (23.025850929940456804 - 1.5707963268526181857j))
assert ae(fp.loggamma(1e-10j-1e-10), (22.679277339718205716 - 2.3561944902500664954j))
def test_fp_psi():
assert ae(fp.psi(0, 3.7), 1.1671535393615114409)
assert ae(fp.psi(0, 0.5), -1.9635100260214234794)
assert ae(fp.psi(0, 1), -0.57721566490153286061)
assert ae(fp.psi(0, -2.5), 1.1031566406452431872)
assert ae(fp.psi(0, 12.9), 2.5179671503279156347)
assert ae(fp.psi(0, 100), 4.6001618527380874002)
assert ae(fp.psi(0, 2500.3), 7.8239660143238547877)
assert ae(fp.psi(0, 1e40), 92.103403719761827391)
assert ae(fp.psi(0, 1e200), 460.51701859880913677)
assert ae(fp.psi(0, 3.7+0j), (1.1671535393615114409 + 0.0j))
assert ae(fp.psi(1, 3), 0.39493406684822643647)
assert ae(fp.psi(3, 2+3j), (-0.05383196209159972116 + 0.0076890935247364805218j))
assert ae(fp.psi(4, -0.5+1j), (1.2719531355492328195 - 18.211833410936276774j))
assert ae(fp.harmonic(0), 0.0)
assert ae(fp.harmonic(1), 1.0)
assert ae(fp.harmonic(2), 1.5)
assert ae(fp.harmonic(100), 5.1873775176396202608)
assert ae(fp.harmonic(-2.5), 1.2803723055467760478)
assert ae(fp.harmonic(2+3j), (1.9390425294578375875 + 0.87336044981834544043j))
assert ae(fp.harmonic(-5-4j), (2.3725754822349437733 - 2.4160904444801621j))
def test_fp_zeta():
assert ae(fp.zeta(1e100), 1.0)
assert ae(fp.zeta(3), 1.2020569031595942854)
assert ae(fp.zeta(2+0j), (1.6449340668482264365 + 0.0j))
assert ae(fp.zeta(0.93), -13.713619351638164784)
assert ae(fp.zeta(1.74), 1.9796863545771774095)
assert ae(fp.zeta(0.0), -0.5)
assert ae(fp.zeta(-1.0), -0.083333333333333333333)
assert ae(fp.zeta(-2.0), 0.0)
assert ae(fp.zeta(-3.0), 0.0083333333333333333333)
assert ae(fp.zeta(-500.0), 0.0)
assert ae(fp.zeta(-7.4), 0.0036537321227995882447)
assert ae(fp.zeta(2.1), 1.5602165335033620158)
assert ae(fp.zeta(26.9), 1.0000000079854809935)
assert ae(fp.zeta(26), 1.0000000149015548284)
assert ae(fp.zeta(27), 1.0000000074507117898)
assert ae(fp.zeta(28), 1.0000000037253340248)
assert ae(fp.zeta(27.1), 1.000000006951755045)
assert ae(fp.zeta(32.7), 1.0000000001433243232)
assert ae(fp.zeta(100), 1.0)
assert ae(fp.altzeta(3.5), 0.92755357777394803511)
assert ae(fp.altzeta(1), 0.69314718055994530942)
assert ae(fp.altzeta(2), 0.82246703342411321824)
assert ae(fp.altzeta(0), 0.5)
assert ae(fp.zeta(-2+3j, 1), (0.13297115587929864827 + 0.12305330040458776494j))
assert ae(fp.zeta(-2+3j, 5), (18.384866151867576927 - 11.377015110597711009j))
assert ae(fp.zeta(1.0000000001), 9999999173.1735741337)
assert ae(fp.zeta(0.9999999999), -9999999172.0191428039)
assert ae(fp.zeta(1+0.000000001j), (0.57721566490153286061 - 999999999.99999993765j))
assert ae(fp.primezeta(2.5+4j), (-0.16922458243438033385 - 0.010847965298387727811j))
assert ae(fp.primezeta(4), 0.076993139764246844943)
assert ae(fp.riemannr(3.7), 2.3034079839110855717)
assert ae(fp.riemannr(8), 3.9011860449341499474)
assert ae(fp.riemannr(3+4j), (2.2369653314259991796 + 1.6339943856990281694j))
def test_fp_hyp2f1():
assert ae(fp.hyp2f1(1, (3,2), 3.25, 5.0), (-0.46600275923108143059 - 0.74393667908854842325j))
assert ae(fp.hyp2f1(1+1j, (3,2), 3.25, 5.0), (-5.9208875603806515987 - 2.3813557707889590686j))
assert ae(fp.hyp2f1(1+1j, (3,2), 3.25, 2+3j), (0.17174552030925080445 + 0.19589781970539389999j))
def test_fp_erf():
assert fp.erf(2) == fp.erf(2.0) == fp.erf(2.0+0.0j)
assert fp.erf(fp.inf) == 1.0
assert fp.erf(fp.ninf) == -1.0
assert ae(fp.erf(0), 0.0)
assert ae(fp.erf(-0), -0.0)
assert ae(fp.erf(0.3), 0.32862675945912741619)
assert ae(fp.erf(-0.3), -0.32862675945912741619)
assert ae(fp.erf(0.9), 0.79690821242283213966)
assert ae(fp.erf(-0.9), -0.79690821242283213966)
assert ae(fp.erf(1.0), 0.84270079294971486934)
assert ae(fp.erf(-1.0), -0.84270079294971486934)
assert ae(fp.erf(1.1), 0.88020506957408172966)
assert ae(fp.erf(-1.1), -0.88020506957408172966)
assert ae(fp.erf(8.5), 1.0)
assert ae(fp.erf(-8.5), -1.0)
assert ae(fp.erf(9.1), 1.0)
assert ae(fp.erf(-9.1), -1.0)
assert ae(fp.erf(20.0), 1.0)
assert ae(fp.erf(-20.0), -1.0)
assert ae(fp.erf(10000.0), 1.0)
assert ae(fp.erf(-10000.0), -1.0)
assert ae(fp.erf(1e+50), 1.0)
assert ae(fp.erf(-1e+50), -1.0)
assert ae(fp.erf(1j), 1.650425758797542876j)
assert ae(fp.erf(-1j), -1.650425758797542876j)
assert ae(fp.erf((2+3j)), (-20.829461427614568389 + 8.6873182714701631444j))
assert ae(fp.erf(-(2+3j)), -(-20.829461427614568389 + 8.6873182714701631444j))
assert ae(fp.erf((8+9j)), (-1072004.2525062051158 + 364149.91954310255423j))
assert ae(fp.erf(-(8+9j)), -(-1072004.2525062051158 + 364149.91954310255423j))
assert fp.erfc(fp.inf) == 0.0
assert fp.erfc(fp.ninf) == 2.0
assert fp.erfc(0) == 1
assert fp.erfc(-0.0) == 1
assert fp.erfc(0+0j) == 1
assert ae(fp.erfc(0.3), 0.67137324054087258381)
assert ae(fp.erfc(-0.3), 1.3286267594591274162)
assert ae(fp.erfc(0.9), 0.20309178757716786034)
assert ae(fp.erfc(-0.9), 1.7969082124228321397)
assert ae(fp.erfc(1.0), 0.15729920705028513066)
assert ae(fp.erfc(-1.0), 1.8427007929497148693)
assert ae(fp.erfc(1.1), 0.11979493042591827034)
assert ae(fp.erfc(-1.1), 1.8802050695740817297)
assert ae(fp.erfc(8.5), 2.7623240713337714461e-33)
assert ae(fp.erfc(-8.5), 2.0)
assert ae(fp.erfc(9.1), 6.6969004279886077452e-38)
assert ae(fp.erfc(-9.1), 2.0)
assert ae(fp.erfc(20.0), 5.3958656116079009289e-176)
assert ae(fp.erfc(-20.0), 2.0)
assert ae(fp.erfc(10000.0), 0.0)
assert ae(fp.erfc(-10000.0), 2.0)
assert ae(fp.erfc(1e+50), 0.0)
assert ae(fp.erfc(-1e+50), 2.0)
assert ae(fp.erfc(1j), (1.0 - 1.650425758797542876j))
assert ae(fp.erfc(-1j), (1.0 + 1.650425758797542876j))
assert ae(fp.erfc((2+3j)), (21.829461427614568389 - 8.6873182714701631444j), 1e-13)
assert ae(fp.erfc(-(2+3j)), (-19.829461427614568389 + 8.6873182714701631444j), 1e-13)
assert ae(fp.erfc((8+9j)), (1072005.2525062051158 - 364149.91954310255423j))
assert ae(fp.erfc(-(8+9j)), (-1072003.2525062051158 + 364149.91954310255423j))
assert ae(fp.erfc(20+0j), (5.3958656116079009289e-176 + 0.0j))
def test_fp_lambertw():
assert ae(fp.lambertw(0.0), 0.0)
assert ae(fp.lambertw(1.0), 0.567143290409783873)
assert ae(fp.lambertw(7.5), 1.5662309537823875394)
assert ae(fp.lambertw(-0.25), -0.35740295618138890307)
assert ae(fp.lambertw(-10.0), (1.3699809685212708156 + 2.140194527074713196j))
assert ae(fp.lambertw(0+0j), (0.0 + 0.0j))
assert ae(fp.lambertw(4+0j), (1.2021678731970429392 + 0.0j))
assert ae(fp.lambertw(1000.5), 5.2500227450408980127)
assert ae(fp.lambertw(1e100), 224.84310644511850156)
assert ae(fp.lambertw(-1000.0), (5.1501630246362515223 + 2.6641981432905204596j))
assert ae(fp.lambertw(1e-10), 9.9999999990000003645e-11)
assert ae(fp.lambertw(1e-10j), (1.0000000000000000728e-20 + 1.0000000000000000364e-10j))
assert ae(fp.lambertw(3+4j), (1.2815618061237758782 + 0.53309522202097107131j))
assert ae(fp.lambertw(-3-4j), (1.0750730665692549276 - 1.3251023817343588823j))
assert ae(fp.lambertw(10000+1000j), (7.2361526563371602186 + 0.087567810943839352034j))
assert ae(fp.lambertw(0.0, -1), -fp.inf)
assert ae(fp.lambertw(1.0, -1), (-1.5339133197935745079 - 4.3751851530618983855j))
assert ae(fp.lambertw(7.5, -1), (0.44125668415098614999 - 4.8039842008452390179j))
assert ae(fp.lambertw(-0.25, -1), -2.1532923641103496492)
assert ae(fp.lambertw(-10.0, -1), (1.3699809685212708156 - 2.140194527074713196j))
assert ae(fp.lambertw(0+0j, -1), -fp.inf)
assert ae(fp.lambertw(4+0j, -1), (-0.15730793189620765317 - 4.6787800704666656212j))
assert ae(fp.lambertw(1000.5, -1), (4.9153765415404024736 - 5.4465682700815159569j))
assert ae(fp.lambertw(1e100, -1), (224.84272130101601052 - 6.2553713838167244141j))
assert ae(fp.lambertw(-1000.0, -1), (5.1501630246362515223 - 2.6641981432905204596j))
assert ae(fp.lambertw(1e-10, -1), (-26.303186778379041521 - 3.2650939117038283975j))
assert ae(fp.lambertw(1e-10j, -1), (-26.297238779529035028 - 1.6328071613455765135j))
assert ae(fp.lambertw(3+4j, -1), (0.25856740686699741676 - 3.8521166861614355895j))
assert ae(fp.lambertw(-3-4j, -1), (-0.32028750204310768396 - 6.8801677192091972343j))
assert ae(fp.lambertw(10000+1000j, -1), (7.0255308742285435567 - 5.5177506835734067601j))
assert ae(fp.lambertw(0.0, 2), -fp.inf)
assert ae(fp.lambertw(1.0, 2), (-2.4015851048680028842 + 10.776299516115070898j))
assert ae(fp.lambertw(7.5, 2), (-0.38003357962843791529 + 10.960916473368746184j))
assert ae(fp.lambertw(-0.25, 2), (-4.0558735269061511898 + 13.852334658567271386j))
assert ae(fp.lambertw(-10.0, 2), (-0.34479123764318858696 + 14.112740596763592363j))
assert ae(fp.lambertw(0+0j, 2), -fp.inf)
assert ae(fp.lambertw(4+0j, 2), (-1.0070343323804262788 + 10.903476551861683082j))
assert ae(fp.lambertw(1000.5, 2), (4.4076185165459395295 + 11.365524591091402177j))
assert ae(fp.lambertw(1e100, 2), (224.84156762724875878 + 12.510785262632255672j))
assert ae(fp.lambertw(-1000.0, 2), (4.1984245610246530756 + 14.420478573754313845j))
assert ae(fp.lambertw(1e-10, 2), (-26.362258095445866488 + 9.7800247407031482519j))
assert ae(fp.lambertw(1e-10j, 2), (-26.384250801683084252 + 11.403535950607739763j))
assert ae(fp.lambertw(3+4j, 2), (-0.86554679943333993562 + 11.849956798331992027j))
assert ae(fp.lambertw(-3-4j, 2), (-0.55792273874679112639 + 8.7173627024159324811j))
assert ae(fp.lambertw(10000+1000j, 2), (6.6223802254585662734 + 11.61348646825020766j))
def test_fp_stress_ei_e1():
# Can be tightened on recent Pythons with more accurate math/cmath
ATOL = 1e-13
PTOL = 1e-12
v = fp.e1(1.1641532182693481445e-10)
assert ae(v, 22.296641293693077672, tol=ATOL)
assert type(v) is float
v = fp.e1(0.25)
assert ae(v, 1.0442826344437381945, tol=ATOL)
assert type(v) is float
v = fp.e1(1.0)
assert ae(v, 0.21938393439552027368, tol=ATOL)
assert type(v) is float
v = fp.e1(2.0)
assert ae(v, 0.048900510708061119567, tol=ATOL)
assert type(v) is float
v = fp.e1(5.0)
assert ae(v, 0.0011482955912753257973, tol=ATOL)
assert type(v) is float
v = fp.e1(20.0)
assert ae(v, 9.8355252906498816904e-11, tol=ATOL)
assert type(v) is float
v = fp.e1(30.0)
assert ae(v, 3.0215520106888125448e-15, tol=ATOL)
assert type(v) is float
v = fp.e1(40.0)
assert ae(v, 1.0367732614516569722e-19, tol=ATOL)
assert type(v) is float
v = fp.e1(50.0)
assert ae(v, 3.7832640295504590187e-24, tol=ATOL)
assert type(v) is float
v = fp.e1(80.0)
assert ae(v, 2.2285432586884729112e-37, tol=ATOL)
assert type(v) is float
v = fp.e1((1.1641532182693481445e-10 + 0.0j))
assert ae(v, (22.296641293693077672 + 0.0j), tol=ATOL)
assert ae(v.real, 22.296641293693077672, tol=PTOL)
assert v.imag == 0
v = fp.e1((0.25 + 0.0j))
assert ae(v, (1.0442826344437381945 + 0.0j), tol=ATOL)
assert ae(v.real, 1.0442826344437381945, tol=PTOL)
assert v.imag == 0
v = fp.e1((1.0 + 0.0j))
assert ae(v, (0.21938393439552027368 + 0.0j), tol=ATOL)
assert ae(v.real, 0.21938393439552027368, tol=PTOL)
assert v.imag == 0
v = fp.e1((2.0 + 0.0j))
assert ae(v, (0.048900510708061119567 + 0.0j), tol=ATOL)
assert ae(v.real, 0.048900510708061119567, tol=PTOL)
assert v.imag == 0
v = fp.e1((5.0 + 0.0j))
assert ae(v, (0.0011482955912753257973 + 0.0j), tol=ATOL)
assert ae(v.real, 0.0011482955912753257973, tol=PTOL)
assert v.imag == 0
v = fp.e1((20.0 + 0.0j))
assert ae(v, (9.8355252906498816904e-11 + 0.0j), tol=ATOL)
assert ae(v.real, 9.8355252906498816904e-11, tol=PTOL)
assert v.imag == 0
v = fp.e1((30.0 + 0.0j))
assert ae(v, (3.0215520106888125448e-15 + 0.0j), tol=ATOL)
assert ae(v.real, 3.0215520106888125448e-15, tol=PTOL)
assert v.imag == 0
v = fp.e1((40.0 + 0.0j))
assert ae(v, (1.0367732614516569722e-19 + 0.0j), tol=ATOL)
assert ae(v.real, 1.0367732614516569722e-19, tol=PTOL)
assert v.imag == 0
v = fp.e1((50.0 + 0.0j))
assert ae(v, (3.7832640295504590187e-24 + 0.0j), tol=ATOL)
assert ae(v.real, 3.7832640295504590187e-24, tol=PTOL)
assert v.imag == 0
v = fp.e1((80.0 + 0.0j))
assert ae(v, (2.2285432586884729112e-37 + 0.0j), tol=ATOL)
assert ae(v.real, 2.2285432586884729112e-37, tol=PTOL)
assert v.imag == 0
v = fp.e1((4.6566128730773925781e-10 + 1.1641532182693481445e-10j))
assert ae(v, (20.880034622014215597 - 0.24497866301044883237j), tol=ATOL)
assert ae(v.real, 20.880034622014215597, tol=PTOL)
assert ae(v.imag, -0.24497866301044883237, tol=PTOL)
v = fp.e1((1.0 + 0.25j))
assert ae(v, (0.19731063945004229095 - 0.087366045774299963672j), tol=ATOL)
assert ae(v.real, 0.19731063945004229095, tol=PTOL)
assert ae(v.imag, -0.087366045774299963672, tol=PTOL)
v = fp.e1((4.0 + 1.0j))
assert ae(v, (0.0013106173980145506944 - 0.0034542480199350626699j), tol=ATOL)
assert ae(v.real, 0.0013106173980145506944, tol=PTOL)
assert ae(v.imag, -0.0034542480199350626699, tol=PTOL)
v = fp.e1((8.0 + 2.0j))
assert ae(v, (-0.000022278049065270225945 - 0.000029191940456521555288j), tol=ATOL)
assert ae(v.real, -0.000022278049065270225945, tol=PTOL)
assert ae(v.imag, -0.000029191940456521555288, tol=PTOL)
v = fp.e1((20.0 + 5.0j))
assert ae(v, (4.7711374515765346894e-11 + 8.2902652405126947359e-11j), tol=ATOL)
assert ae(v.real, 4.7711374515765346894e-11, tol=PTOL)
assert ae(v.imag, 8.2902652405126947359e-11, tol=PTOL)
v = fp.e1((80.0 + 20.0j))
assert ae(v, (3.8353473865788235787e-38 - 2.129247592349605139e-37j), tol=ATOL)
assert ae(v.real, 3.8353473865788235787e-38, tol=PTOL)
assert ae(v.imag, -2.129247592349605139e-37, tol=PTOL)
v = fp.e1((120.0 + 30.0j))
assert ae(v, (2.3836002337480334716e-55 + 5.6704043587126198306e-55j), tol=ATOL)
assert ae(v.real, 2.3836002337480334716e-55, tol=PTOL)
assert ae(v.imag, 5.6704043587126198306e-55, tol=PTOL)
v = fp.e1((160.0 + 40.0j))
assert ae(v, (-1.6238022898654510661e-72 - 1.104172355572287367e-72j), tol=ATOL)
assert ae(v.real, -1.6238022898654510661e-72, tol=PTOL)
assert ae(v.imag, -1.104172355572287367e-72, tol=PTOL)
v = fp.e1((200.0 + 50.0j))
assert ae(v, (6.6800061461666228487e-90 + 1.4473816083541016115e-91j), tol=ATOL)
assert ae(v.real, 6.6800061461666228487e-90, tol=PTOL)
assert ae(v.imag, 1.4473816083541016115e-91, tol=PTOL)
v = fp.e1((320.0 + 80.0j))
assert ae(v, (4.2737871527778786157e-143 + 3.1789935525785660314e-142j), tol=ATOL)
assert ae(v.real, 4.2737871527778786157e-143, tol=PTOL)
assert ae(v.imag, 3.1789935525785660314e-142, tol=PTOL)
v = fp.e1((1.1641532182693481445e-10 + 1.1641532182693481445e-10j))
assert ae(v, (21.950067703413105017 - 0.7853981632810329878j), tol=ATOL)
assert ae(v.real, 21.950067703413105017, tol=PTOL)
assert ae(v.imag, -0.7853981632810329878, tol=PTOL)
v = fp.e1((0.25 + 0.25j))
assert ae(v, (0.71092525792923287894 - 0.56491812441304194711j), tol=ATOL)
assert ae(v.real, 0.71092525792923287894, tol=PTOL)
assert ae(v.imag, -0.56491812441304194711, tol=PTOL)
v = fp.e1((1.0 + 1.0j))
assert ae(v, (0.00028162445198141832551 - 0.17932453503935894015j), tol=ATOL)
assert ae(v.real, 0.00028162445198141832551, tol=PTOL)
assert ae(v.imag, -0.17932453503935894015, tol=PTOL)
v = fp.e1((2.0 + 2.0j))
assert ae(v, (-0.033767089606562004246 - 0.018599414169750541925j), tol=ATOL)
assert ae(v.real, -0.033767089606562004246, tol=PTOL)
assert ae(v.imag, -0.018599414169750541925, tol=PTOL)
v = fp.e1((5.0 + 5.0j))
assert ae(v, (0.0007266506660356393891 + 0.00047102780163522245054j), tol=ATOL)
assert ae(v.real, 0.0007266506660356393891, tol=PTOL)
assert ae(v.imag, 0.00047102780163522245054, tol=PTOL)
v = fp.e1((20.0 + 20.0j))
assert ae(v, (-2.3824537449367396579e-11 - 6.6969873156525615158e-11j), tol=ATOL)
assert ae(v.real, -2.3824537449367396579e-11, tol=PTOL)
assert ae(v.imag, -6.6969873156525615158e-11, tol=PTOL)
v = fp.e1((30.0 + 30.0j))
assert ae(v, (1.7316045841744061617e-15 + 1.3065678019487308689e-15j), tol=ATOL)
assert ae(v.real, 1.7316045841744061617e-15, tol=PTOL)
assert ae(v.imag, 1.3065678019487308689e-15, tol=PTOL)
v = fp.e1((40.0 + 40.0j))
assert ae(v, (-7.4001043002899232182e-20 - 4.991847855336816304e-21j), tol=ATOL)
assert ae(v.real, -7.4001043002899232182e-20, tol=PTOL)
assert ae(v.imag, -4.991847855336816304e-21, tol=PTOL)
v = fp.e1((50.0 + 50.0j))
assert ae(v, (2.3566128324644641219e-24 - 1.3188326726201614778e-24j), tol=ATOL)
assert ae(v.real, 2.3566128324644641219e-24, tol=PTOL)
assert ae(v.imag, -1.3188326726201614778e-24, tol=PTOL)
v = fp.e1((80.0 + 80.0j))
assert ae(v, (9.8279750572186526673e-38 + 1.243952841288868831e-37j), tol=ATOL)
assert ae(v.real, 9.8279750572186526673e-38, tol=PTOL)
assert ae(v.imag, 1.243952841288868831e-37, tol=PTOL)
v = fp.e1((1.1641532182693481445e-10 + 4.6566128730773925781e-10j))
assert ae(v, (20.880034621664969632 - 1.3258176632023711778j), tol=ATOL)
assert ae(v.real, 20.880034621664969632, tol=PTOL)
assert ae(v.imag, -1.3258176632023711778, tol=PTOL)
v = fp.e1((0.25 + 1.0j))
assert ae(v, (-0.16868306393667788761 - 0.4858011885947426971j), tol=ATOL)
assert ae(v.real, -0.16868306393667788761, tol=PTOL)
assert ae(v.imag, -0.4858011885947426971, tol=PTOL)
v = fp.e1((1.0 + 4.0j))
assert ae(v, (0.03373591813926547318 + 0.073523452241083821877j), tol=ATOL)
assert ae(v.real, 0.03373591813926547318, tol=PTOL)
assert ae(v.imag, 0.073523452241083821877, tol=PTOL)
v = fp.e1((2.0 + 8.0j))
assert ae(v, (-0.015392833434733785143 - 0.0031747121557605415914j), tol=ATOL)
assert ae(v.real, -0.015392833434733785143, tol=PTOL)
assert ae(v.imag, -0.0031747121557605415914, tol=PTOL)
v = fp.e1((5.0 + 20.0j))
assert ae(v, (-0.00024419662286542966525 - 0.00021008322966152755674j), tol=ATOL)
assert ae(v.real, -0.00024419662286542966525, tol=PTOL)
assert ae(v.imag, -0.00021008322966152755674, tol=PTOL)
v = fp.e1((20.0 + 80.0j))
assert ae(v, (2.3255552781051330088e-11 + 8.9463918891349438007e-12j), tol=ATOL)
assert ae(v.real, 2.3255552781051330088e-11, tol=PTOL)
assert ae(v.imag, 8.9463918891349438007e-12, tol=PTOL)
v = fp.e1((30.0 + 120.0j))
assert ae(v, (-2.7068919097124652332e-16 - 7.0477762411705130239e-16j), tol=ATOL)
assert ae(v.real, -2.7068919097124652332e-16, tol=PTOL)
assert ae(v.imag, -7.0477762411705130239e-16, tol=PTOL)
v = fp.e1((40.0 + 160.0j))
assert ae(v, (-1.1695597827678024687e-20 + 2.2907401455645736661e-20j), tol=ATOL)
assert ae(v.real, -1.1695597827678024687e-20, tol=PTOL)
assert ae(v.imag, 2.2907401455645736661e-20, tol=PTOL)
v = fp.e1((50.0 + 200.0j))
assert ae(v, (9.0323746914410162531e-25 - 2.3950601790033530935e-25j), tol=ATOL)
assert ae(v.real, 9.0323746914410162531e-25, tol=PTOL)
assert ae(v.imag, -2.3950601790033530935e-25, tol=PTOL)
v = fp.e1((80.0 + 320.0j))
assert ae(v, (3.4819106748728063576e-38 - 4.215653005615772724e-38j), tol=ATOL)
assert ae(v.real, 3.4819106748728063576e-38, tol=PTOL)
assert ae(v.imag, -4.215653005615772724e-38, tol=PTOL)
v = fp.e1((0.0 + 1.1641532182693481445e-10j))
assert ae(v, (22.29664129357666235 - 1.5707963266784812974j), tol=ATOL)
assert ae(v.real, 22.29664129357666235, tol=PTOL)
assert ae(v.imag, -1.5707963266784812974, tol=PTOL)
v = fp.e1((0.0 + 0.25j))
assert ae(v, (0.82466306258094565309 - 1.3216627564751394551j), tol=ATOL)
assert ae(v.real, 0.82466306258094565309, tol=PTOL)
assert ae(v.imag, -1.3216627564751394551, tol=PTOL)
v = fp.e1((0.0 + 1.0j))
assert ae(v, (-0.33740392290096813466 - 0.62471325642771360429j), tol=ATOL)
assert ae(v.real, -0.33740392290096813466, tol=PTOL)
assert ae(v.imag, -0.62471325642771360429, tol=PTOL)
v = fp.e1((0.0 + 2.0j))
assert ae(v, (-0.4229808287748649957 + 0.034616650007798229345j), tol=ATOL)
assert ae(v.real, -0.4229808287748649957, tol=PTOL)
assert ae(v.imag, 0.034616650007798229345, tol=PTOL)
v = fp.e1((0.0 + 5.0j))
assert ae(v, (0.19002974965664387862 - 0.020865081850222481957j), tol=ATOL)
assert ae(v.real, 0.19002974965664387862, tol=PTOL)
assert ae(v.imag, -0.020865081850222481957, tol=PTOL)
v = fp.e1((0.0 + 20.0j))
assert ae(v, (-0.04441982084535331654 - 0.022554625751456779068j), tol=ATOL)
assert ae(v.real, -0.04441982084535331654, tol=PTOL)
assert ae(v.imag, -0.022554625751456779068, tol=PTOL)
v = fp.e1((0.0 + 30.0j))
assert ae(v, (0.033032417282071143779 - 0.0040397867645455082476j), tol=ATOL)
assert ae(v.real, 0.033032417282071143779, tol=PTOL)
assert ae(v.imag, -0.0040397867645455082476, tol=PTOL)
v = fp.e1((0.0 + 40.0j))
assert ae(v, (-0.019020007896208766962 + 0.016188792559887887544j), tol=ATOL)
assert ae(v.real, -0.019020007896208766962, tol=PTOL)
assert ae(v.imag, 0.016188792559887887544, tol=PTOL)
v = fp.e1((0.0 + 50.0j))
assert ae(v, (0.0056283863241163054402 - 0.019179254308960724503j), tol=ATOL)
assert ae(v.real, 0.0056283863241163054402, tol=PTOL)
assert ae(v.imag, -0.019179254308960724503, tol=PTOL)
v = fp.e1((0.0 + 80.0j))
assert ae(v, (0.012402501155070958192 + 0.0015345601175906961199j), tol=ATOL)
assert ae(v.real, 0.012402501155070958192, tol=PTOL)
assert ae(v.imag, 0.0015345601175906961199, tol=PTOL)
v = fp.e1((-1.1641532182693481445e-10 + 4.6566128730773925781e-10j))
assert ae(v, (20.880034621432138988 - 1.8157749894560994861j), tol=ATOL)
assert ae(v.real, 20.880034621432138988, tol=PTOL)
assert ae(v.imag, -1.8157749894560994861, tol=PTOL)
v = fp.e1((-0.25 + 1.0j))
assert ae(v, (-0.59066621214766308594 - 0.74474454765205036972j), tol=ATOL)
assert ae(v.real, -0.59066621214766308594, tol=PTOL)
assert ae(v.imag, -0.74474454765205036972, tol=PTOL)
v = fp.e1((-1.0 + 4.0j))
assert ae(v, (0.49739047283060471093 + 0.41543605404038863174j), tol=ATOL)
assert ae(v.real, 0.49739047283060471093, tol=PTOL)
assert ae(v.imag, 0.41543605404038863174, tol=PTOL)
v = fp.e1((-2.0 + 8.0j))
assert ae(v, (-0.8705211147733730969 + 0.24099328498605539667j), tol=ATOL)
assert ae(v.real, -0.8705211147733730969, tol=PTOL)
assert ae(v.imag, 0.24099328498605539667, tol=PTOL)
v = fp.e1((-5.0 + 20.0j))
assert ae(v, (-7.0789514293925893007 - 1.6102177171960790536j), tol=ATOL)
assert ae(v.real, -7.0789514293925893007, tol=PTOL)
assert ae(v.imag, -1.6102177171960790536, tol=PTOL)
v = fp.e1((-20.0 + 80.0j))
assert ae(v, (5855431.4907298084434 - 720920.93315409165707j), tol=ATOL)
assert ae(v.real, 5855431.4907298084434, tol=PTOL)
assert ae(v.imag, -720920.93315409165707, tol=PTOL)
v = fp.e1((-30.0 + 120.0j))
assert ae(v, (-65402491644.703470747 - 56697658399.657460294j), tol=ATOL)
assert ae(v.real, -65402491644.703470747, tol=PTOL)
assert ae(v.imag, -56697658399.657460294, tol=PTOL)
v = fp.e1((-40.0 + 160.0j))
assert ae(v, (25504929379604.776769 + 1429035198630573.2463j), tol=ATOL)
assert ae(v.real, 25504929379604.776769, tol=PTOL)
assert ae(v.imag, 1429035198630573.2463, tol=PTOL)
v = fp.e1((-50.0 + 200.0j))
assert ae(v, (18437746526988116954.0 - 17146362239046152345.0j), tol=ATOL)
assert ae(v.real, 18437746526988116954.0, tol=PTOL)
assert ae(v.imag, -17146362239046152345.0, tol=PTOL)
v = fp.e1((-80.0 + 320.0j))
assert ae(v, (3.3464697299634526706e+31 - 1.6473152633843023919e+32j), tol=ATOL)
assert ae(v.real, 3.3464697299634526706e+31, tol=PTOL)
assert ae(v.imag, -1.6473152633843023919e+32, tol=PTOL)
v = fp.e1((-4.6566128730773925781e-10 + 1.1641532182693481445e-10j))
assert ae(v, (20.880034621082893023 - 2.8966139903465137624j), tol=ATOL)
assert ae(v.real, 20.880034621082893023, tol=PTOL)
assert ae(v.imag, -2.8966139903465137624, tol=PTOL)
v = fp.e1((-1.0 + 0.25j))
assert ae(v, (-1.8942716983721074932 - 2.4689102827070540799j), tol=ATOL)
assert ae(v.real, -1.8942716983721074932, tol=PTOL)
assert ae(v.imag, -2.4689102827070540799, tol=PTOL)
v = fp.e1((-4.0 + 1.0j))
assert ae(v, (-14.806699492675420438 + 9.1384225230837893776j), tol=ATOL)
assert ae(v.real, -14.806699492675420438, tol=PTOL)
assert ae(v.imag, 9.1384225230837893776, tol=PTOL)
v = fp.e1((-8.0 + 2.0j))
assert ae(v, (54.633252667426386294 + 413.20318163814670688j), tol=ATOL)
assert ae(v.real, 54.633252667426386294, tol=PTOL)
assert ae(v.imag, 413.20318163814670688, tol=PTOL)
v = fp.e1((-20.0 + 5.0j))
assert ae(v, (-711836.97165402624643 - 24745250.939695900956j), tol=ATOL)
assert ae(v.real, -711836.97165402624643, tol=PTOL)
assert ae(v.imag, -24745250.939695900956, tol=PTOL)
v = fp.e1((-80.0 + 20.0j))
assert ae(v, (-4.2139911108612653091e+32 + 5.3367124741918251637e+32j), tol=ATOL)
assert ae(v.real, -4.2139911108612653091e+32, tol=PTOL)
assert ae(v.imag, 5.3367124741918251637e+32, tol=PTOL)
v = fp.e1((-120.0 + 30.0j))
assert ae(v, (9.7760616203707508892e+48 - 1.058257682317195792e+50j), tol=ATOL)
assert ae(v.real, 9.7760616203707508892e+48, tol=PTOL)
assert ae(v.imag, -1.058257682317195792e+50, tol=PTOL)
v = fp.e1((-160.0 + 40.0j))
assert ae(v, (8.7065541466623638861e+66 + 1.6577106725141739889e+67j), tol=ATOL)
assert ae(v.real, 8.7065541466623638861e+66, tol=PTOL)
assert ae(v.imag, 1.6577106725141739889e+67, tol=PTOL)
v = fp.e1((-200.0 + 50.0j))
assert ae(v, (-3.070744996327018106e+84 - 1.7243244846769415903e+84j), tol=ATOL)
assert ae(v.real, -3.070744996327018106e+84, tol=PTOL)
assert ae(v.imag, -1.7243244846769415903e+84, tol=PTOL)
v = fp.e1((-320.0 + 80.0j))
assert ae(v, (9.9960598637998647276e+135 - 2.6855081527595608863e+136j), tol=ATOL)
assert ae(v.real, 9.9960598637998647276e+135, tol=PTOL)
assert ae(v.imag, -2.6855081527595608863e+136, tol=PTOL)
v = fp.e1(-1.1641532182693481445e-10)
assert ae(v, (22.296641293460247028 - 3.1415926535897932385j), tol=ATOL)
assert ae(v.real, 22.296641293460247028, tol=PTOL)
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
v = fp.e1(-0.25)
assert ae(v, (0.54254326466191372953 - 3.1415926535897932385j), tol=ATOL)
assert ae(v.real, 0.54254326466191372953, tol=PTOL)
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
v = fp.e1(-1.0)
assert ae(v, (-1.8951178163559367555 - 3.1415926535897932385j), tol=ATOL)
assert ae(v.real, -1.8951178163559367555, tol=PTOL)
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
v = fp.e1(-2.0)
assert ae(v, (-4.9542343560018901634 - 3.1415926535897932385j), tol=ATOL)
assert ae(v.real, -4.9542343560018901634, tol=PTOL)
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
v = fp.e1(-5.0)
assert ae(v, (-40.185275355803177455 - 3.1415926535897932385j), tol=ATOL)
assert ae(v.real, -40.185275355803177455, tol=PTOL)
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
v = fp.e1(-20.0)
assert ae(v, (-25615652.66405658882 - 3.1415926535897932385j), tol=ATOL)
assert ae(v.real, -25615652.66405658882, tol=PTOL)
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
v = fp.e1(-30.0)
assert ae(v, (-368973209407.27419706 - 3.1415926535897932385j), tol=ATOL)
assert ae(v.real, -368973209407.27419706, tol=PTOL)
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
v = fp.e1(-40.0)
assert ae(v, (-6039718263611241.5784 - 3.1415926535897932385j), tol=ATOL)
assert ae(v.real, -6039718263611241.5784, tol=PTOL)
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
v = fp.e1(-50.0)
assert ae(v, (-1.0585636897131690963e+20 - 3.1415926535897932385j), tol=ATOL)
assert ae(v.real, -1.0585636897131690963e+20, tol=PTOL)
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
v = fp.e1(-80.0)
assert ae(v, (-7.0146000049047999696e+32 - 3.1415926535897932385j), tol=ATOL)
assert ae(v.real, -7.0146000049047999696e+32, tol=PTOL)
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
v = fp.e1((-1.1641532182693481445e-10 + 0.0j))
assert ae(v, (22.296641293460247028 - 3.1415926535897932385j), tol=ATOL)
assert ae(v.real, 22.296641293460247028, tol=PTOL)
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
v = fp.e1((-0.25 + 0.0j))
assert ae(v, (0.54254326466191372953 - 3.1415926535897932385j), tol=ATOL)
assert ae(v.real, 0.54254326466191372953, tol=PTOL)
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
v = fp.e1((-1.0 + 0.0j))
assert ae(v, (-1.8951178163559367555 - 3.1415926535897932385j), tol=ATOL)
assert ae(v.real, -1.8951178163559367555, tol=PTOL)
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
v = fp.e1((-2.0 + 0.0j))
assert ae(v, (-4.9542343560018901634 - 3.1415926535897932385j), tol=ATOL)
assert ae(v.real, -4.9542343560018901634, tol=PTOL)
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
v = fp.e1((-5.0 + 0.0j))
assert ae(v, (-40.185275355803177455 - 3.1415926535897932385j), tol=ATOL)
assert ae(v.real, -40.185275355803177455, tol=PTOL)
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
v = fp.e1((-20.0 + 0.0j))
assert ae(v, (-25615652.66405658882 - 3.1415926535897932385j), tol=ATOL)
assert ae(v.real, -25615652.66405658882, tol=PTOL)
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
v = fp.e1((-30.0 + 0.0j))
assert ae(v, (-368973209407.27419706 - 3.1415926535897932385j), tol=ATOL)
assert ae(v.real, -368973209407.27419706, tol=PTOL)
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
v = fp.e1((-40.0 + 0.0j))
assert ae(v, (-6039718263611241.5784 - 3.1415926535897932385j), tol=ATOL)
assert ae(v.real, -6039718263611241.5784, tol=PTOL)
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
v = fp.e1((-50.0 + 0.0j))
assert ae(v, (-1.0585636897131690963e+20 - 3.1415926535897932385j), tol=ATOL)
assert ae(v.real, -1.0585636897131690963e+20, tol=PTOL)
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
v = fp.e1((-80.0 + 0.0j))
assert ae(v, (-7.0146000049047999696e+32 - 3.1415926535897932385j), tol=ATOL)
assert ae(v.real, -7.0146000049047999696e+32, tol=PTOL)
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
v = fp.e1((-4.6566128730773925781e-10 - 1.1641532182693481445e-10j))
assert ae(v, (20.880034621082893023 + 2.8966139903465137624j), tol=ATOL)
assert ae(v.real, 20.880034621082893023, tol=PTOL)
assert ae(v.imag, 2.8966139903465137624, tol=PTOL)
v = fp.e1((-1.0 - 0.25j))
assert ae(v, (-1.8942716983721074932 + 2.4689102827070540799j), tol=ATOL)
assert ae(v.real, -1.8942716983721074932, tol=PTOL)
assert ae(v.imag, 2.4689102827070540799, tol=PTOL)
v = fp.e1((-4.0 - 1.0j))
assert ae(v, (-14.806699492675420438 - 9.1384225230837893776j), tol=ATOL)
assert ae(v.real, -14.806699492675420438, tol=PTOL)
assert ae(v.imag, -9.1384225230837893776, tol=PTOL)
v = fp.e1((-8.0 - 2.0j))
assert ae(v, (54.633252667426386294 - 413.20318163814670688j), tol=ATOL)
assert ae(v.real, 54.633252667426386294, tol=PTOL)
assert ae(v.imag, -413.20318163814670688, tol=PTOL)
v = fp.e1((-20.0 - 5.0j))
assert ae(v, (-711836.97165402624643 + 24745250.939695900956j), tol=ATOL)
assert ae(v.real, -711836.97165402624643, tol=PTOL)
assert ae(v.imag, 24745250.939695900956, tol=PTOL)
v = fp.e1((-80.0 - 20.0j))
assert ae(v, (-4.2139911108612653091e+32 - 5.3367124741918251637e+32j), tol=ATOL)
assert ae(v.real, -4.2139911108612653091e+32, tol=PTOL)
assert ae(v.imag, -5.3367124741918251637e+32, tol=PTOL)
v = fp.e1((-120.0 - 30.0j))
assert ae(v, (9.7760616203707508892e+48 + 1.058257682317195792e+50j), tol=ATOL)
assert ae(v.real, 9.7760616203707508892e+48, tol=PTOL)
assert ae(v.imag, 1.058257682317195792e+50, tol=PTOL)
v = fp.e1((-160.0 - 40.0j))
assert ae(v, (8.7065541466623638861e+66 - 1.6577106725141739889e+67j), tol=ATOL)
assert ae(v.real, 8.7065541466623638861e+66, tol=PTOL)
assert ae(v.imag, -1.6577106725141739889e+67, tol=PTOL)
v = fp.e1((-200.0 - 50.0j))
assert ae(v, (-3.070744996327018106e+84 + 1.7243244846769415903e+84j), tol=ATOL)
assert ae(v.real, -3.070744996327018106e+84, tol=PTOL)
assert ae(v.imag, 1.7243244846769415903e+84, tol=PTOL)
v = fp.e1((-320.0 - 80.0j))
assert ae(v, (9.9960598637998647276e+135 + 2.6855081527595608863e+136j), tol=ATOL)
assert ae(v.real, 9.9960598637998647276e+135, tol=PTOL)
assert ae(v.imag, 2.6855081527595608863e+136, tol=PTOL)
v = fp.e1((-1.1641532182693481445e-10 - 1.1641532182693481445e-10j))
assert ae(v, (21.950067703180274374 + 2.356194490075929607j), tol=ATOL)
assert ae(v.real, 21.950067703180274374, tol=PTOL)
assert ae(v.imag, 2.356194490075929607, tol=PTOL)
v = fp.e1((-0.25 - 0.25j))
assert ae(v, (0.21441047326710323254 + 2.0732153554307936389j), tol=ATOL)
assert ae(v.real, 0.21441047326710323254, tol=PTOL)
assert ae(v.imag, 2.0732153554307936389, tol=PTOL)
v = fp.e1((-1.0 - 1.0j))
assert ae(v, (-1.7646259855638540684 + 0.7538228020792708192j), tol=ATOL)
assert ae(v.real, -1.7646259855638540684, tol=PTOL)
assert ae(v.imag, 0.7538228020792708192, tol=PTOL)
v = fp.e1((-2.0 - 2.0j))
assert ae(v, (-1.8920781621855474089 - 2.1753697842428647236j), tol=ATOL)
assert ae(v.real, -1.8920781621855474089, tol=PTOL)
assert ae(v.imag, -2.1753697842428647236, tol=PTOL)
v = fp.e1((-5.0 - 5.0j))
assert ae(v, (13.470936071475245856 + 18.464085049321024206j), tol=ATOL)
assert ae(v.real, 13.470936071475245856, tol=PTOL)
assert ae(v.imag, 18.464085049321024206, tol=PTOL)
v = fp.e1((-20.0 - 20.0j))
assert ae(v, (-16589317.398788971896 - 5831702.3296441771206j), tol=ATOL)
assert ae(v.real, -16589317.398788971896, tol=PTOL)
assert ae(v.imag, -5831702.3296441771206, tol=PTOL)
v = fp.e1((-30.0 - 30.0j))
assert ae(v, (154596484273.69322527 + 204179357837.41389696j), tol=ATOL)
assert ae(v.real, 154596484273.69322527, tol=PTOL)
assert ae(v.imag, 204179357837.41389696, tol=PTOL)
v = fp.e1((-40.0 - 40.0j))
assert ae(v, (-287512180321448.45408 - 4203502407932314.974j), tol=ATOL)
assert ae(v.real, -287512180321448.45408, tol=PTOL)
assert ae(v.imag, -4203502407932314.974, tol=PTOL)
v = fp.e1((-50.0 - 50.0j))
assert ae(v, (-36128528616649268826.0 + 64648801861338741963.0j), tol=ATOL)
assert ae(v.real, -36128528616649268826.0, tol=PTOL)
assert ae(v.imag, 64648801861338741963.0, tol=PTOL)
v = fp.e1((-80.0 - 80.0j))
assert ae(v, (3.8674816337930010217e+32 + 3.0540709639658071041e+32j), tol=ATOL)
assert ae(v.real, 3.8674816337930010217e+32, tol=PTOL)
assert ae(v.imag, 3.0540709639658071041e+32, tol=PTOL)
v = fp.e1((-1.1641532182693481445e-10 - 4.6566128730773925781e-10j))
assert ae(v, (20.880034621432138988 + 1.8157749894560994861j), tol=ATOL)
assert ae(v.real, 20.880034621432138988, tol=PTOL)
assert ae(v.imag, 1.8157749894560994861, tol=PTOL)
v = fp.e1((-0.25 - 1.0j))
assert ae(v, (-0.59066621214766308594 + 0.74474454765205036972j), tol=ATOL)
assert ae(v.real, -0.59066621214766308594, tol=PTOL)
assert ae(v.imag, 0.74474454765205036972, tol=PTOL)
v = fp.e1((-1.0 - 4.0j))
assert ae(v, (0.49739047283060471093 - 0.41543605404038863174j), tol=ATOL)
assert ae(v.real, 0.49739047283060471093, tol=PTOL)
assert ae(v.imag, -0.41543605404038863174, tol=PTOL)
v = fp.e1((-2.0 - 8.0j))
assert ae(v, (-0.8705211147733730969 - 0.24099328498605539667j), tol=ATOL)
assert ae(v.real, -0.8705211147733730969, tol=PTOL)
assert ae(v.imag, -0.24099328498605539667, tol=PTOL)
v = fp.e1((-5.0 - 20.0j))
assert ae(v, (-7.0789514293925893007 + 1.6102177171960790536j), tol=ATOL)
assert ae(v.real, -7.0789514293925893007, tol=PTOL)
assert ae(v.imag, 1.6102177171960790536, tol=PTOL)
v = fp.e1((-20.0 - 80.0j))
assert ae(v, (5855431.4907298084434 + 720920.93315409165707j), tol=ATOL)
assert ae(v.real, 5855431.4907298084434, tol=PTOL)
assert ae(v.imag, 720920.93315409165707, tol=PTOL)
v = fp.e1((-30.0 - 120.0j))
assert ae(v, (-65402491644.703470747 + 56697658399.657460294j), tol=ATOL)
assert ae(v.real, -65402491644.703470747, tol=PTOL)
assert ae(v.imag, 56697658399.657460294, tol=PTOL)
v = fp.e1((-40.0 - 160.0j))
assert ae(v, (25504929379604.776769 - 1429035198630573.2463j), tol=ATOL)
assert ae(v.real, 25504929379604.776769, tol=PTOL)
assert ae(v.imag, -1429035198630573.2463, tol=PTOL)
v = fp.e1((-50.0 - 200.0j))
assert ae(v, (18437746526988116954.0 + 17146362239046152345.0j), tol=ATOL)
assert ae(v.real, 18437746526988116954.0, tol=PTOL)
assert ae(v.imag, 17146362239046152345.0, tol=PTOL)
v = fp.e1((-80.0 - 320.0j))
assert ae(v, (3.3464697299634526706e+31 + 1.6473152633843023919e+32j), tol=ATOL)
assert ae(v.real, 3.3464697299634526706e+31, tol=PTOL)
assert ae(v.imag, 1.6473152633843023919e+32, tol=PTOL)
v = fp.e1((0.0 - 1.1641532182693481445e-10j))
assert ae(v, (22.29664129357666235 + 1.5707963266784812974j), tol=ATOL)
assert ae(v.real, 22.29664129357666235, tol=PTOL)
assert ae(v.imag, 1.5707963266784812974, tol=PTOL)
v = fp.e1((0.0 - 0.25j))
assert ae(v, (0.82466306258094565309 + 1.3216627564751394551j), tol=ATOL)
assert ae(v.real, 0.82466306258094565309, tol=PTOL)
assert ae(v.imag, 1.3216627564751394551, tol=PTOL)
v = fp.e1((0.0 - 1.0j))
assert ae(v, (-0.33740392290096813466 + 0.62471325642771360429j), tol=ATOL)
assert ae(v.real, -0.33740392290096813466, tol=PTOL)
assert ae(v.imag, 0.62471325642771360429, tol=PTOL)
v = fp.e1((0.0 - 2.0j))
assert ae(v, (-0.4229808287748649957 - 0.034616650007798229345j), tol=ATOL)
assert ae(v.real, -0.4229808287748649957, tol=PTOL)
assert ae(v.imag, -0.034616650007798229345, tol=PTOL)
v = fp.e1((0.0 - 5.0j))
assert ae(v, (0.19002974965664387862 + 0.020865081850222481957j), tol=ATOL)
assert ae(v.real, 0.19002974965664387862, tol=PTOL)
assert ae(v.imag, 0.020865081850222481957, tol=PTOL)
v = fp.e1((0.0 - 20.0j))
assert ae(v, (-0.04441982084535331654 + 0.022554625751456779068j), tol=ATOL)
assert ae(v.real, -0.04441982084535331654, tol=PTOL)
assert ae(v.imag, 0.022554625751456779068, tol=PTOL)
v = fp.e1((0.0 - 30.0j))
assert ae(v, (0.033032417282071143779 + 0.0040397867645455082476j), tol=ATOL)
assert ae(v.real, 0.033032417282071143779, tol=PTOL)
assert ae(v.imag, 0.0040397867645455082476, tol=PTOL)
v = fp.e1((0.0 - 40.0j))
assert ae(v, (-0.019020007896208766962 - 0.016188792559887887544j), tol=ATOL)
assert ae(v.real, -0.019020007896208766962, tol=PTOL)
assert ae(v.imag, -0.016188792559887887544, tol=PTOL)
v = fp.e1((0.0 - 50.0j))
assert ae(v, (0.0056283863241163054402 + 0.019179254308960724503j), tol=ATOL)
assert ae(v.real, 0.0056283863241163054402, tol=PTOL)
assert ae(v.imag, 0.019179254308960724503, tol=PTOL)
v = fp.e1((0.0 - 80.0j))
assert ae(v, (0.012402501155070958192 - 0.0015345601175906961199j), tol=ATOL)
assert ae(v.real, 0.012402501155070958192, tol=PTOL)
assert ae(v.imag, -0.0015345601175906961199, tol=PTOL)
v = fp.e1((1.1641532182693481445e-10 - 4.6566128730773925781e-10j))
assert ae(v, (20.880034621664969632 + 1.3258176632023711778j), tol=ATOL)
assert ae(v.real, 20.880034621664969632, tol=PTOL)
assert ae(v.imag, 1.3258176632023711778, tol=PTOL)
v = fp.e1((0.25 - 1.0j))
assert ae(v, (-0.16868306393667788761 + 0.4858011885947426971j), tol=ATOL)
assert ae(v.real, -0.16868306393667788761, tol=PTOL)
assert ae(v.imag, 0.4858011885947426971, tol=PTOL)
v = fp.e1((1.0 - 4.0j))
assert ae(v, (0.03373591813926547318 - 0.073523452241083821877j), tol=ATOL)
assert ae(v.real, 0.03373591813926547318, tol=PTOL)
assert ae(v.imag, -0.073523452241083821877, tol=PTOL)
v = fp.e1((2.0 - 8.0j))
assert ae(v, (-0.015392833434733785143 + 0.0031747121557605415914j), tol=ATOL)
assert ae(v.real, -0.015392833434733785143, tol=PTOL)
assert ae(v.imag, 0.0031747121557605415914, tol=PTOL)
v = fp.e1((5.0 - 20.0j))
assert ae(v, (-0.00024419662286542966525 + 0.00021008322966152755674j), tol=ATOL)
assert ae(v.real, -0.00024419662286542966525, tol=PTOL)
assert ae(v.imag, 0.00021008322966152755674, tol=PTOL)
v = fp.e1((20.0 - 80.0j))
assert ae(v, (2.3255552781051330088e-11 - 8.9463918891349438007e-12j), tol=ATOL)
assert ae(v.real, 2.3255552781051330088e-11, tol=PTOL)
assert ae(v.imag, -8.9463918891349438007e-12, tol=PTOL)
v = fp.e1((30.0 - 120.0j))
assert ae(v, (-2.7068919097124652332e-16 + 7.0477762411705130239e-16j), tol=ATOL)
assert ae(v.real, -2.7068919097124652332e-16, tol=PTOL)
assert ae(v.imag, 7.0477762411705130239e-16, tol=PTOL)
v = fp.e1((40.0 - 160.0j))
assert ae(v, (-1.1695597827678024687e-20 - 2.2907401455645736661e-20j), tol=ATOL)
assert ae(v.real, -1.1695597827678024687e-20, tol=PTOL)
assert ae(v.imag, -2.2907401455645736661e-20, tol=PTOL)
v = fp.e1((50.0 - 200.0j))
assert ae(v, (9.0323746914410162531e-25 + 2.3950601790033530935e-25j), tol=ATOL)
assert ae(v.real, 9.0323746914410162531e-25, tol=PTOL)
assert ae(v.imag, 2.3950601790033530935e-25, tol=PTOL)
v = fp.e1((80.0 - 320.0j))
assert ae(v, (3.4819106748728063576e-38 + 4.215653005615772724e-38j), tol=ATOL)
assert ae(v.real, 3.4819106748728063576e-38, tol=PTOL)
assert ae(v.imag, 4.215653005615772724e-38, tol=PTOL)
v = fp.e1((1.1641532182693481445e-10 - 1.1641532182693481445e-10j))
assert ae(v, (21.950067703413105017 + 0.7853981632810329878j), tol=ATOL)
assert ae(v.real, 21.950067703413105017, tol=PTOL)
assert ae(v.imag, 0.7853981632810329878, tol=PTOL)
v = fp.e1((0.25 - 0.25j))
assert ae(v, (0.71092525792923287894 + 0.56491812441304194711j), tol=ATOL)
assert ae(v.real, 0.71092525792923287894, tol=PTOL)
assert ae(v.imag, 0.56491812441304194711, tol=PTOL)
v = fp.e1((1.0 - 1.0j))
assert ae(v, (0.00028162445198141832551 + 0.17932453503935894015j), tol=ATOL)
assert ae(v.real, 0.00028162445198141832551, tol=PTOL)
assert ae(v.imag, 0.17932453503935894015, tol=PTOL)
v = fp.e1((2.0 - 2.0j))
assert ae(v, (-0.033767089606562004246 + 0.018599414169750541925j), tol=ATOL)
assert ae(v.real, -0.033767089606562004246, tol=PTOL)
assert ae(v.imag, 0.018599414169750541925, tol=PTOL)
v = fp.e1((5.0 - 5.0j))
assert ae(v, (0.0007266506660356393891 - 0.00047102780163522245054j), tol=ATOL)
assert ae(v.real, 0.0007266506660356393891, tol=PTOL)
assert ae(v.imag, -0.00047102780163522245054, tol=PTOL)
v = fp.e1((20.0 - 20.0j))
assert ae(v, (-2.3824537449367396579e-11 + 6.6969873156525615158e-11j), tol=ATOL)
assert ae(v.real, -2.3824537449367396579e-11, tol=PTOL)
assert ae(v.imag, 6.6969873156525615158e-11, tol=PTOL)
v = fp.e1((30.0 - 30.0j))
assert ae(v, (1.7316045841744061617e-15 - 1.3065678019487308689e-15j), tol=ATOL)
assert ae(v.real, 1.7316045841744061617e-15, tol=PTOL)
assert ae(v.imag, -1.3065678019487308689e-15, tol=PTOL)
v = fp.e1((40.0 - 40.0j))
assert ae(v, (-7.4001043002899232182e-20 + 4.991847855336816304e-21j), tol=ATOL)
assert ae(v.real, -7.4001043002899232182e-20, tol=PTOL)
assert ae(v.imag, 4.991847855336816304e-21, tol=PTOL)
v = fp.e1((50.0 - 50.0j))
assert ae(v, (2.3566128324644641219e-24 + 1.3188326726201614778e-24j), tol=ATOL)
assert ae(v.real, 2.3566128324644641219e-24, tol=PTOL)
assert ae(v.imag, 1.3188326726201614778e-24, tol=PTOL)
v = fp.e1((80.0 - 80.0j))
assert ae(v, (9.8279750572186526673e-38 - 1.243952841288868831e-37j), tol=ATOL)
assert ae(v.real, 9.8279750572186526673e-38, tol=PTOL)
assert ae(v.imag, -1.243952841288868831e-37, tol=PTOL)
v = fp.e1((4.6566128730773925781e-10 - 1.1641532182693481445e-10j))
assert ae(v, (20.880034622014215597 + 0.24497866301044883237j), tol=ATOL)
assert ae(v.real, 20.880034622014215597, tol=PTOL)
assert ae(v.imag, 0.24497866301044883237, tol=PTOL)
v = fp.e1((1.0 - 0.25j))
assert ae(v, (0.19731063945004229095 + 0.087366045774299963672j), tol=ATOL)
assert ae(v.real, 0.19731063945004229095, tol=PTOL)
assert ae(v.imag, 0.087366045774299963672, tol=PTOL)
v = fp.e1((4.0 - 1.0j))
assert ae(v, (0.0013106173980145506944 + 0.0034542480199350626699j), tol=ATOL)
assert ae(v.real, 0.0013106173980145506944, tol=PTOL)
assert ae(v.imag, 0.0034542480199350626699, tol=PTOL)
v = fp.e1((8.0 - 2.0j))
assert ae(v, (-0.000022278049065270225945 + 0.000029191940456521555288j), tol=ATOL)
assert ae(v.real, -0.000022278049065270225945, tol=PTOL)
assert ae(v.imag, 0.000029191940456521555288, tol=PTOL)
v = fp.e1((20.0 - 5.0j))
assert ae(v, (4.7711374515765346894e-11 - 8.2902652405126947359e-11j), tol=ATOL)
assert ae(v.real, 4.7711374515765346894e-11, tol=PTOL)
assert ae(v.imag, -8.2902652405126947359e-11, tol=PTOL)
v = fp.e1((80.0 - 20.0j))
assert ae(v, (3.8353473865788235787e-38 + 2.129247592349605139e-37j), tol=ATOL)
assert ae(v.real, 3.8353473865788235787e-38, tol=PTOL)
assert ae(v.imag, 2.129247592349605139e-37, tol=PTOL)
v = fp.e1((120.0 - 30.0j))
assert ae(v, (2.3836002337480334716e-55 - 5.6704043587126198306e-55j), tol=ATOL)
assert ae(v.real, 2.3836002337480334716e-55, tol=PTOL)
assert ae(v.imag, -5.6704043587126198306e-55, tol=PTOL)
v = fp.e1((160.0 - 40.0j))
assert ae(v, (-1.6238022898654510661e-72 + 1.104172355572287367e-72j), tol=ATOL)
assert ae(v.real, -1.6238022898654510661e-72, tol=PTOL)
assert ae(v.imag, 1.104172355572287367e-72, tol=PTOL)
v = fp.e1((200.0 - 50.0j))
assert ae(v, (6.6800061461666228487e-90 - 1.4473816083541016115e-91j), tol=ATOL)
assert ae(v.real, 6.6800061461666228487e-90, tol=PTOL)
assert ae(v.imag, -1.4473816083541016115e-91, tol=PTOL)
v = fp.e1((320.0 - 80.0j))
assert ae(v, (4.2737871527778786157e-143 - 3.1789935525785660314e-142j), tol=ATOL)
assert ae(v.real, 4.2737871527778786157e-143, tol=PTOL)
assert ae(v.imag, -3.1789935525785660314e-142, tol=PTOL)
v = fp.ei(1.1641532182693481445e-10)
assert ae(v, -22.296641293460247028, tol=ATOL)
assert type(v) is float
v = fp.ei(0.25)
assert ae(v, -0.54254326466191372953, tol=ATOL)
assert type(v) is float
v = fp.ei(1.0)
assert ae(v, 1.8951178163559367555, tol=ATOL)
assert type(v) is float
v = fp.ei(2.0)
assert ae(v, 4.9542343560018901634, tol=ATOL)
assert type(v) is float
v = fp.ei(5.0)
assert ae(v, 40.185275355803177455, tol=ATOL)
assert type(v) is float
v = fp.ei(20.0)
assert ae(v, 25615652.66405658882, tol=ATOL)
assert type(v) is float
v = fp.ei(30.0)
assert ae(v, 368973209407.27419706, tol=ATOL)
assert type(v) is float
v = fp.ei(40.0)
assert ae(v, 6039718263611241.5784, tol=ATOL)
assert type(v) is float
v = fp.ei(50.0)
assert ae(v, 1.0585636897131690963e+20, tol=ATOL)
assert type(v) is float
v = fp.ei(80.0)
assert ae(v, 7.0146000049047999696e+32, tol=ATOL)
assert type(v) is float
v = fp.ei((1.1641532182693481445e-10 + 0.0j))
assert ae(v, (-22.296641293460247028 + 0.0j), tol=ATOL)
assert ae(v.real, -22.296641293460247028, tol=PTOL)
assert v.imag == 0
v = fp.ei((0.25 + 0.0j))
assert ae(v, (-0.54254326466191372953 + 0.0j), tol=ATOL)
assert ae(v.real, -0.54254326466191372953, tol=PTOL)
assert v.imag == 0
v = fp.ei((1.0 + 0.0j))
assert ae(v, (1.8951178163559367555 + 0.0j), tol=ATOL)
assert ae(v.real, 1.8951178163559367555, tol=PTOL)
assert v.imag == 0
v = fp.ei((2.0 + 0.0j))
assert ae(v, (4.9542343560018901634 + 0.0j), tol=ATOL)
assert ae(v.real, 4.9542343560018901634, tol=PTOL)
assert v.imag == 0
v = fp.ei((5.0 + 0.0j))
assert ae(v, (40.185275355803177455 + 0.0j), tol=ATOL)
assert ae(v.real, 40.185275355803177455, tol=PTOL)
assert v.imag == 0
v = fp.ei((20.0 + 0.0j))
assert ae(v, (25615652.66405658882 + 0.0j), tol=ATOL)
assert ae(v.real, 25615652.66405658882, tol=PTOL)
assert v.imag == 0
v = fp.ei((30.0 + 0.0j))
assert ae(v, (368973209407.27419706 + 0.0j), tol=ATOL)
assert ae(v.real, 368973209407.27419706, tol=PTOL)
assert v.imag == 0
v = fp.ei((40.0 + 0.0j))
assert ae(v, (6039718263611241.5784 + 0.0j), tol=ATOL)
assert ae(v.real, 6039718263611241.5784, tol=PTOL)
assert v.imag == 0
v = fp.ei((50.0 + 0.0j))
assert ae(v, (1.0585636897131690963e+20 + 0.0j), tol=ATOL)
assert ae(v.real, 1.0585636897131690963e+20, tol=PTOL)
assert v.imag == 0
v = fp.ei((80.0 + 0.0j))
assert ae(v, (7.0146000049047999696e+32 + 0.0j), tol=ATOL)
assert ae(v.real, 7.0146000049047999696e+32, tol=PTOL)
assert v.imag == 0
v = fp.ei((4.6566128730773925781e-10 + 1.1641532182693481445e-10j))
assert ae(v, (-20.880034621082893023 + 0.24497866324327947603j), tol=ATOL)
assert ae(v.real, -20.880034621082893023, tol=PTOL)
assert ae(v.imag, 0.24497866324327947603, tol=PTOL)
v = fp.ei((1.0 + 0.25j))
assert ae(v, (1.8942716983721074932 + 0.67268237088273915854j), tol=ATOL)
assert ae(v.real, 1.8942716983721074932, tol=PTOL)
assert ae(v.imag, 0.67268237088273915854, tol=PTOL)
v = fp.ei((4.0 + 1.0j))
assert ae(v, (14.806699492675420438 + 12.280015176673582616j), tol=ATOL)
assert ae(v.real, 14.806699492675420438, tol=PTOL)
assert ae(v.imag, 12.280015176673582616, tol=PTOL)
v = fp.ei((8.0 + 2.0j))
assert ae(v, (-54.633252667426386294 + 416.34477429173650012j), tol=ATOL)
assert ae(v.real, -54.633252667426386294, tol=PTOL)
assert ae(v.imag, 416.34477429173650012, tol=PTOL)
v = fp.ei((20.0 + 5.0j))
assert ae(v, (711836.97165402624643 - 24745247.798103247366j), tol=ATOL)
assert ae(v.real, 711836.97165402624643, tol=PTOL)
assert ae(v.imag, -24745247.798103247366, tol=PTOL)
v = fp.ei((80.0 + 20.0j))
assert ae(v, (4.2139911108612653091e+32 + 5.3367124741918251637e+32j), tol=ATOL)
assert ae(v.real, 4.2139911108612653091e+32, tol=PTOL)
assert ae(v.imag, 5.3367124741918251637e+32, tol=PTOL)
v = fp.ei((120.0 + 30.0j))
assert ae(v, (-9.7760616203707508892e+48 - 1.058257682317195792e+50j), tol=ATOL)
assert ae(v.real, -9.7760616203707508892e+48, tol=PTOL)
assert ae(v.imag, -1.058257682317195792e+50, tol=PTOL)
v = fp.ei((160.0 + 40.0j))
assert ae(v, (-8.7065541466623638861e+66 + 1.6577106725141739889e+67j), tol=ATOL)
assert ae(v.real, -8.7065541466623638861e+66, tol=PTOL)
assert ae(v.imag, 1.6577106725141739889e+67, tol=PTOL)
v = fp.ei((200.0 + 50.0j))
assert ae(v, (3.070744996327018106e+84 - 1.7243244846769415903e+84j), tol=ATOL)
assert ae(v.real, 3.070744996327018106e+84, tol=PTOL)
assert ae(v.imag, -1.7243244846769415903e+84, tol=PTOL)
v = fp.ei((320.0 + 80.0j))
assert ae(v, (-9.9960598637998647276e+135 - 2.6855081527595608863e+136j), tol=ATOL)
assert ae(v.real, -9.9960598637998647276e+135, tol=PTOL)
assert ae(v.imag, -2.6855081527595608863e+136, tol=PTOL)
v = fp.ei((1.1641532182693481445e-10 + 1.1641532182693481445e-10j))
assert ae(v, (-21.950067703180274374 + 0.78539816351386363145j), tol=ATOL)
assert ae(v.real, -21.950067703180274374, tol=PTOL)
assert ae(v.imag, 0.78539816351386363145, tol=PTOL)
v = fp.ei((0.25 + 0.25j))
assert ae(v, (-0.21441047326710323254 + 1.0683772981589995996j), tol=ATOL)
assert ae(v.real, -0.21441047326710323254, tol=PTOL)
assert ae(v.imag, 1.0683772981589995996, tol=PTOL)
v = fp.ei((1.0 + 1.0j))
assert ae(v, (1.7646259855638540684 + 2.3877698515105224193j), tol=ATOL)
assert ae(v.real, 1.7646259855638540684, tol=PTOL)
assert ae(v.imag, 2.3877698515105224193, tol=PTOL)
v = fp.ei((2.0 + 2.0j))
assert ae(v, (1.8920781621855474089 + 5.3169624378326579621j), tol=ATOL)
assert ae(v.real, 1.8920781621855474089, tol=PTOL)
assert ae(v.imag, 5.3169624378326579621, tol=PTOL)
v = fp.ei((5.0 + 5.0j))
assert ae(v, (-13.470936071475245856 - 15.322492395731230968j), tol=ATOL)
assert ae(v.real, -13.470936071475245856, tol=PTOL)
assert ae(v.imag, -15.322492395731230968, tol=PTOL)
v = fp.ei((20.0 + 20.0j))
assert ae(v, (16589317.398788971896 + 5831705.4712368307104j), tol=ATOL)
assert ae(v.real, 16589317.398788971896, tol=PTOL)
assert ae(v.imag, 5831705.4712368307104, tol=PTOL)
v = fp.ei((30.0 + 30.0j))
assert ae(v, (-154596484273.69322527 - 204179357834.2723043j), tol=ATOL)
assert ae(v.real, -154596484273.69322527, tol=PTOL)
assert ae(v.imag, -204179357834.2723043, tol=PTOL)
v = fp.ei((40.0 + 40.0j))
assert ae(v, (287512180321448.45408 + 4203502407932318.1156j), tol=ATOL)
assert ae(v.real, 287512180321448.45408, tol=PTOL)
assert ae(v.imag, 4203502407932318.1156, tol=PTOL)
v = fp.ei((50.0 + 50.0j))
assert ae(v, (36128528616649268826.0 - 64648801861338741960.0j), tol=ATOL)
assert ae(v.real, 36128528616649268826.0, tol=PTOL)
assert ae(v.imag, -64648801861338741960.0, tol=PTOL)
v = fp.ei((80.0 + 80.0j))
assert ae(v, (-3.8674816337930010217e+32 - 3.0540709639658071041e+32j), tol=ATOL)
assert ae(v.real, -3.8674816337930010217e+32, tol=PTOL)
assert ae(v.imag, -3.0540709639658071041e+32, tol=PTOL)
v = fp.ei((1.1641532182693481445e-10 + 4.6566128730773925781e-10j))
assert ae(v, (-20.880034621432138988 + 1.3258176641336937524j), tol=ATOL)
assert ae(v.real, -20.880034621432138988, tol=PTOL)
assert ae(v.imag, 1.3258176641336937524, tol=PTOL)
v = fp.ei((0.25 + 1.0j))
assert ae(v, (0.59066621214766308594 + 2.3968481059377428687j), tol=ATOL)
assert ae(v.real, 0.59066621214766308594, tol=PTOL)
assert ae(v.imag, 2.3968481059377428687, tol=PTOL)
v = fp.ei((1.0 + 4.0j))
assert ae(v, (-0.49739047283060471093 + 3.5570287076301818702j), tol=ATOL)
assert ae(v.real, -0.49739047283060471093, tol=PTOL)
assert ae(v.imag, 3.5570287076301818702, tol=PTOL)
v = fp.ei((2.0 + 8.0j))
assert ae(v, (0.8705211147733730969 + 3.3825859385758486351j), tol=ATOL)
assert ae(v.real, 0.8705211147733730969, tol=PTOL)
assert ae(v.imag, 3.3825859385758486351, tol=PTOL)
v = fp.ei((5.0 + 20.0j))
assert ae(v, (7.0789514293925893007 + 1.5313749363937141849j), tol=ATOL)
assert ae(v.real, 7.0789514293925893007, tol=PTOL)
assert ae(v.imag, 1.5313749363937141849, tol=PTOL)
v = fp.ei((20.0 + 80.0j))
assert ae(v, (-5855431.4907298084434 - 720917.79156143806727j), tol=ATOL)
assert ae(v.real, -5855431.4907298084434, tol=PTOL)
assert ae(v.imag, -720917.79156143806727, tol=PTOL)
v = fp.ei((30.0 + 120.0j))
assert ae(v, (65402491644.703470747 - 56697658396.51586764j), tol=ATOL)
assert ae(v.real, 65402491644.703470747, tol=PTOL)
assert ae(v.imag, -56697658396.51586764, tol=PTOL)
v = fp.ei((40.0 + 160.0j))
assert ae(v, (-25504929379604.776769 + 1429035198630576.3879j), tol=ATOL)
assert ae(v.real, -25504929379604.776769, tol=PTOL)
assert ae(v.imag, 1429035198630576.3879, tol=PTOL)
v = fp.ei((50.0 + 200.0j))
assert ae(v, (-18437746526988116954.0 - 17146362239046152342.0j), tol=ATOL)
assert ae(v.real, -18437746526988116954.0, tol=PTOL)
assert ae(v.imag, -17146362239046152342.0, tol=PTOL)
v = fp.ei((80.0 + 320.0j))
assert ae(v, (-3.3464697299634526706e+31 - 1.6473152633843023919e+32j), tol=ATOL)
assert ae(v.real, -3.3464697299634526706e+31, tol=PTOL)
assert ae(v.imag, -1.6473152633843023919e+32, tol=PTOL)
v = fp.ei((0.0 + 1.1641532182693481445e-10j))
assert ae(v, (-22.29664129357666235 + 1.5707963269113119411j), tol=ATOL)
assert ae(v.real, -22.29664129357666235, tol=PTOL)
assert ae(v.imag, 1.5707963269113119411, tol=PTOL)
v = fp.ei((0.0 + 0.25j))
assert ae(v, (-0.82466306258094565309 + 1.8199298971146537833j), tol=ATOL)
assert ae(v.real, -0.82466306258094565309, tol=PTOL)
assert ae(v.imag, 1.8199298971146537833, tol=PTOL)
v = fp.ei((0.0 + 1.0j))
assert ae(v, (0.33740392290096813466 + 2.5168793971620796342j), tol=ATOL)
assert ae(v.real, 0.33740392290096813466, tol=PTOL)
assert ae(v.imag, 2.5168793971620796342, tol=PTOL)
v = fp.ei((0.0 + 2.0j))
assert ae(v, (0.4229808287748649957 + 3.1762093035975914678j), tol=ATOL)
assert ae(v.real, 0.4229808287748649957, tol=PTOL)
assert ae(v.imag, 3.1762093035975914678, tol=PTOL)
v = fp.ei((0.0 + 5.0j))
assert ae(v, (-0.19002974965664387862 + 3.1207275717395707565j), tol=ATOL)
assert ae(v.real, -0.19002974965664387862, tol=PTOL)
assert ae(v.imag, 3.1207275717395707565, tol=PTOL)
v = fp.ei((0.0 + 20.0j))
assert ae(v, (0.04441982084535331654 + 3.1190380278383364594j), tol=ATOL)
assert ae(v.real, 0.04441982084535331654, tol=PTOL)
assert ae(v.imag, 3.1190380278383364594, tol=PTOL)
v = fp.ei((0.0 + 30.0j))
assert ae(v, (-0.033032417282071143779 + 3.1375528668252477302j), tol=ATOL)
assert ae(v.real, -0.033032417282071143779, tol=PTOL)
assert ae(v.imag, 3.1375528668252477302, tol=PTOL)
v = fp.ei((0.0 + 40.0j))
assert ae(v, (0.019020007896208766962 + 3.157781446149681126j), tol=ATOL)
assert ae(v.real, 0.019020007896208766962, tol=PTOL)
assert ae(v.imag, 3.157781446149681126, tol=PTOL)
v = fp.ei((0.0 + 50.0j))
assert ae(v, (-0.0056283863241163054402 + 3.122413399280832514j), tol=ATOL)
assert ae(v.real, -0.0056283863241163054402, tol=PTOL)
assert ae(v.imag, 3.122413399280832514, tol=PTOL)
v = fp.ei((0.0 + 80.0j))
assert ae(v, (-0.012402501155070958192 + 3.1431272137073839346j), tol=ATOL)
assert ae(v.real, -0.012402501155070958192, tol=PTOL)
assert ae(v.imag, 3.1431272137073839346, tol=PTOL)
v = fp.ei((-1.1641532182693481445e-10 + 4.6566128730773925781e-10j))
assert ae(v, (-20.880034621664969632 + 1.8157749903874220607j), tol=ATOL)
assert ae(v.real, -20.880034621664969632, tol=PTOL)
assert ae(v.imag, 1.8157749903874220607, tol=PTOL)
v = fp.ei((-0.25 + 1.0j))
assert ae(v, (0.16868306393667788761 + 2.6557914649950505414j), tol=ATOL)
assert ae(v.real, 0.16868306393667788761, tol=PTOL)
assert ae(v.imag, 2.6557914649950505414, tol=PTOL)
v = fp.ei((-1.0 + 4.0j))
assert ae(v, (-0.03373591813926547318 + 3.2151161058308770603j), tol=ATOL)
assert ae(v.real, -0.03373591813926547318, tol=PTOL)
assert ae(v.imag, 3.2151161058308770603, tol=PTOL)
v = fp.ei((-2.0 + 8.0j))
assert ae(v, (0.015392833434733785143 + 3.1384179414340326969j), tol=ATOL)
assert ae(v.real, 0.015392833434733785143, tol=PTOL)
assert ae(v.imag, 3.1384179414340326969, tol=PTOL)
v = fp.ei((-5.0 + 20.0j))
assert ae(v, (0.00024419662286542966525 + 3.1413825703601317109j), tol=ATOL)
assert ae(v.real, 0.00024419662286542966525, tol=PTOL)
assert ae(v.imag, 3.1413825703601317109, tol=PTOL)
v = fp.ei((-20.0 + 80.0j))
assert ae(v, (-2.3255552781051330088e-11 + 3.1415926535987396304j), tol=ATOL)
assert ae(v.real, -2.3255552781051330088e-11, tol=PTOL)
assert ae(v.imag, 3.1415926535987396304, tol=PTOL)
v = fp.ei((-30.0 + 120.0j))
assert ae(v, (2.7068919097124652332e-16 + 3.1415926535897925337j), tol=ATOL)
assert ae(v.real, 2.7068919097124652332e-16, tol=PTOL)
assert ae(v.imag, 3.1415926535897925337, tol=PTOL)
v = fp.ei((-40.0 + 160.0j))
assert ae(v, (1.1695597827678024687e-20 + 3.1415926535897932385j), tol=ATOL)
assert ae(v.real, 1.1695597827678024687e-20, tol=PTOL)
assert ae(v.imag, 3.1415926535897932385, tol=PTOL)
v = fp.ei((-50.0 + 200.0j))
assert ae(v, (-9.0323746914410162531e-25 + 3.1415926535897932385j), tol=ATOL)
assert ae(v.real, -9.0323746914410162531e-25, tol=PTOL)
assert ae(v.imag, 3.1415926535897932385, tol=PTOL)
v = fp.ei((-80.0 + 320.0j))
assert ae(v, (-3.4819106748728063576e-38 + 3.1415926535897932385j), tol=ATOL)
assert ae(v.real, -3.4819106748728063576e-38, tol=PTOL)
assert ae(v.imag, 3.1415926535897932385, tol=PTOL)
v = fp.ei((-4.6566128730773925781e-10 + 1.1641532182693481445e-10j))
assert ae(v, (-20.880034622014215597 + 2.8966139905793444061j), tol=ATOL)
assert ae(v.real, -20.880034622014215597, tol=PTOL)
assert ae(v.imag, 2.8966139905793444061, tol=PTOL)
v = fp.ei((-1.0 + 0.25j))
assert ae(v, (-0.19731063945004229095 + 3.0542266078154932748j), tol=ATOL)
assert ae(v.real, -0.19731063945004229095, tol=PTOL)
assert ae(v.imag, 3.0542266078154932748, tol=PTOL)
v = fp.ei((-4.0 + 1.0j))
assert ae(v, (-0.0013106173980145506944 + 3.1381384055698581758j), tol=ATOL)
assert ae(v.real, -0.0013106173980145506944, tol=PTOL)
assert ae(v.imag, 3.1381384055698581758, tol=PTOL)
v = fp.ei((-8.0 + 2.0j))
assert ae(v, (0.000022278049065270225945 + 3.1415634616493367169j), tol=ATOL)
assert ae(v.real, 0.000022278049065270225945, tol=PTOL)
assert ae(v.imag, 3.1415634616493367169, tol=PTOL)
v = fp.ei((-20.0 + 5.0j))
assert ae(v, (-4.7711374515765346894e-11 + 3.1415926536726958909j), tol=ATOL)
assert ae(v.real, -4.7711374515765346894e-11, tol=PTOL)
assert ae(v.imag, 3.1415926536726958909, tol=PTOL)
v = fp.ei((-80.0 + 20.0j))
assert ae(v, (-3.8353473865788235787e-38 + 3.1415926535897932385j), tol=ATOL)
assert ae(v.real, -3.8353473865788235787e-38, tol=PTOL)
assert ae(v.imag, 3.1415926535897932385, tol=PTOL)
v = fp.ei((-120.0 + 30.0j))
assert ae(v, (-2.3836002337480334716e-55 + 3.1415926535897932385j), tol=ATOL)
assert ae(v.real, -2.3836002337480334716e-55, tol=PTOL)
assert ae(v.imag, 3.1415926535897932385, tol=PTOL)
v = fp.ei((-160.0 + 40.0j))
assert ae(v, (1.6238022898654510661e-72 + 3.1415926535897932385j), tol=ATOL)
assert ae(v.real, 1.6238022898654510661e-72, tol=PTOL)
assert ae(v.imag, 3.1415926535897932385, tol=PTOL)
v = fp.ei((-200.0 + 50.0j))
assert ae(v, (-6.6800061461666228487e-90 + 3.1415926535897932385j), tol=ATOL)
assert ae(v.real, -6.6800061461666228487e-90, tol=PTOL)
assert ae(v.imag, 3.1415926535897932385, tol=PTOL)
v = fp.ei((-320.0 + 80.0j))
assert ae(v, (-4.2737871527778786157e-143 + 3.1415926535897932385j), tol=ATOL)
assert ae(v.real, -4.2737871527778786157e-143, tol=PTOL)
assert ae(v.imag, 3.1415926535897932385, tol=PTOL)
v = fp.ei(-1.1641532182693481445e-10)
assert ae(v, -22.296641293693077672, tol=ATOL)
assert type(v) is float
v = fp.ei(-0.25)
assert ae(v, -1.0442826344437381945, tol=ATOL)
assert type(v) is float
v = fp.ei(-1.0)
assert ae(v, -0.21938393439552027368, tol=ATOL)
assert type(v) is float
v = fp.ei(-2.0)
assert ae(v, -0.048900510708061119567, tol=ATOL)
assert type(v) is float
v = fp.ei(-5.0)
assert ae(v, -0.0011482955912753257973, tol=ATOL)
assert type(v) is float
v = fp.ei(-20.0)
assert ae(v, -9.8355252906498816904e-11, tol=ATOL)
assert type(v) is float
v = fp.ei(-30.0)
assert ae(v, -3.0215520106888125448e-15, tol=ATOL)
assert type(v) is float
v = fp.ei(-40.0)
assert ae(v, -1.0367732614516569722e-19, tol=ATOL)
assert type(v) is float
v = fp.ei(-50.0)
assert ae(v, -3.7832640295504590187e-24, tol=ATOL)
assert type(v) is float
v = fp.ei(-80.0)
assert ae(v, -2.2285432586884729112e-37, tol=ATOL)
assert type(v) is float
v = fp.ei((-1.1641532182693481445e-10 + 0.0j))
assert ae(v, (-22.296641293693077672 + 0.0j), tol=ATOL)
assert ae(v.real, -22.296641293693077672, tol=PTOL)
assert v.imag == 0
v = fp.ei((-0.25 + 0.0j))
assert ae(v, (-1.0442826344437381945 + 0.0j), tol=ATOL)
assert ae(v.real, -1.0442826344437381945, tol=PTOL)
assert v.imag == 0
v = fp.ei((-1.0 + 0.0j))
assert ae(v, (-0.21938393439552027368 + 0.0j), tol=ATOL)
assert ae(v.real, -0.21938393439552027368, tol=PTOL)
assert v.imag == 0
v = fp.ei((-2.0 + 0.0j))
assert ae(v, (-0.048900510708061119567 + 0.0j), tol=ATOL)
assert ae(v.real, -0.048900510708061119567, tol=PTOL)
assert v.imag == 0
v = fp.ei((-5.0 + 0.0j))
assert ae(v, (-0.0011482955912753257973 + 0.0j), tol=ATOL)
assert ae(v.real, -0.0011482955912753257973, tol=PTOL)
assert v.imag == 0
v = fp.ei((-20.0 + 0.0j))
assert ae(v, (-9.8355252906498816904e-11 + 0.0j), tol=ATOL)
assert ae(v.real, -9.8355252906498816904e-11, tol=PTOL)
assert v.imag == 0
v = fp.ei((-30.0 + 0.0j))
assert ae(v, (-3.0215520106888125448e-15 + 0.0j), tol=ATOL)
assert ae(v.real, -3.0215520106888125448e-15, tol=PTOL)
assert v.imag == 0
v = fp.ei((-40.0 + 0.0j))
assert ae(v, (-1.0367732614516569722e-19 + 0.0j), tol=ATOL)
assert ae(v.real, -1.0367732614516569722e-19, tol=PTOL)
assert v.imag == 0
v = fp.ei((-50.0 + 0.0j))
assert ae(v, (-3.7832640295504590187e-24 + 0.0j), tol=ATOL)
assert ae(v.real, -3.7832640295504590187e-24, tol=PTOL)
assert v.imag == 0
v = fp.ei((-80.0 + 0.0j))
assert ae(v, (-2.2285432586884729112e-37 + 0.0j), tol=ATOL)
assert ae(v.real, -2.2285432586884729112e-37, tol=PTOL)
assert v.imag == 0
v = fp.ei((-4.6566128730773925781e-10 - 1.1641532182693481445e-10j))
assert ae(v, (-20.880034622014215597 - 2.8966139905793444061j), tol=ATOL)
assert ae(v.real, -20.880034622014215597, tol=PTOL)
assert ae(v.imag, -2.8966139905793444061, tol=PTOL)
v = fp.ei((-1.0 - 0.25j))
assert ae(v, (-0.19731063945004229095 - 3.0542266078154932748j), tol=ATOL)
assert ae(v.real, -0.19731063945004229095, tol=PTOL)
assert ae(v.imag, -3.0542266078154932748, tol=PTOL)
v = fp.ei((-4.0 - 1.0j))
assert ae(v, (-0.0013106173980145506944 - 3.1381384055698581758j), tol=ATOL)
assert ae(v.real, -0.0013106173980145506944, tol=PTOL)
assert ae(v.imag, -3.1381384055698581758, tol=PTOL)
v = fp.ei((-8.0 - 2.0j))
assert ae(v, (0.000022278049065270225945 - 3.1415634616493367169j), tol=ATOL)
assert ae(v.real, 0.000022278049065270225945, tol=PTOL)
assert ae(v.imag, -3.1415634616493367169, tol=PTOL)
v = fp.ei((-20.0 - 5.0j))
assert ae(v, (-4.7711374515765346894e-11 - 3.1415926536726958909j), tol=ATOL)
assert ae(v.real, -4.7711374515765346894e-11, tol=PTOL)
assert ae(v.imag, -3.1415926536726958909, tol=PTOL)
v = fp.ei((-80.0 - 20.0j))
assert ae(v, (-3.8353473865788235787e-38 - 3.1415926535897932385j), tol=ATOL)
assert ae(v.real, -3.8353473865788235787e-38, tol=PTOL)
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
v = fp.ei((-120.0 - 30.0j))
assert ae(v, (-2.3836002337480334716e-55 - 3.1415926535897932385j), tol=ATOL)
assert ae(v.real, -2.3836002337480334716e-55, tol=PTOL)
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
v = fp.ei((-160.0 - 40.0j))
assert ae(v, (1.6238022898654510661e-72 - 3.1415926535897932385j), tol=ATOL)
assert ae(v.real, 1.6238022898654510661e-72, tol=PTOL)
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
v = fp.ei((-200.0 - 50.0j))
assert ae(v, (-6.6800061461666228487e-90 - 3.1415926535897932385j), tol=ATOL)
assert ae(v.real, -6.6800061461666228487e-90, tol=PTOL)
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
v = fp.ei((-320.0 - 80.0j))
assert ae(v, (-4.2737871527778786157e-143 - 3.1415926535897932385j), tol=ATOL)
assert ae(v.real, -4.2737871527778786157e-143, tol=PTOL)
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
v = fp.ei((-1.1641532182693481445e-10 - 1.1641532182693481445e-10j))
assert ae(v, (-21.950067703413105017 - 2.3561944903087602507j), tol=ATOL)
assert ae(v.real, -21.950067703413105017, tol=PTOL)
assert ae(v.imag, -2.3561944903087602507, tol=PTOL)
v = fp.ei((-0.25 - 0.25j))
assert ae(v, (-0.71092525792923287894 - 2.5766745291767512913j), tol=ATOL)
assert ae(v.real, -0.71092525792923287894, tol=PTOL)
assert ae(v.imag, -2.5766745291767512913, tol=PTOL)
v = fp.ei((-1.0 - 1.0j))
assert ae(v, (-0.00028162445198141832551 - 2.9622681185504342983j), tol=ATOL)
assert ae(v.real, -0.00028162445198141832551, tol=PTOL)
assert ae(v.imag, -2.9622681185504342983, tol=PTOL)
v = fp.ei((-2.0 - 2.0j))
assert ae(v, (0.033767089606562004246 - 3.1229932394200426965j), tol=ATOL)
assert ae(v.real, 0.033767089606562004246, tol=PTOL)
assert ae(v.imag, -3.1229932394200426965, tol=PTOL)
v = fp.ei((-5.0 - 5.0j))
assert ae(v, (-0.0007266506660356393891 - 3.1420636813914284609j), tol=ATOL)
assert ae(v.real, -0.0007266506660356393891, tol=PTOL)
assert ae(v.imag, -3.1420636813914284609, tol=PTOL)
v = fp.ei((-20.0 - 20.0j))
assert ae(v, (2.3824537449367396579e-11 - 3.1415926535228233653j), tol=ATOL)
assert ae(v.real, 2.3824537449367396579e-11, tol=PTOL)
assert ae(v.imag, -3.1415926535228233653, tol=PTOL)
v = fp.ei((-30.0 - 30.0j))
assert ae(v, (-1.7316045841744061617e-15 - 3.141592653589794545j), tol=ATOL)
assert ae(v.real, -1.7316045841744061617e-15, tol=PTOL)
assert ae(v.imag, -3.141592653589794545, tol=PTOL)
v = fp.ei((-40.0 - 40.0j))
assert ae(v, (7.4001043002899232182e-20 - 3.1415926535897932385j), tol=ATOL)
assert ae(v.real, 7.4001043002899232182e-20, tol=PTOL)
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
v = fp.ei((-50.0 - 50.0j))
assert ae(v, (-2.3566128324644641219e-24 - 3.1415926535897932385j), tol=ATOL)
assert ae(v.real, -2.3566128324644641219e-24, tol=PTOL)
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
v = fp.ei((-80.0 - 80.0j))
assert ae(v, (-9.8279750572186526673e-38 - 3.1415926535897932385j), tol=ATOL)
assert ae(v.real, -9.8279750572186526673e-38, tol=PTOL)
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
v = fp.ei((-1.1641532182693481445e-10 - 4.6566128730773925781e-10j))
assert ae(v, (-20.880034621664969632 - 1.8157749903874220607j), tol=ATOL)
assert ae(v.real, -20.880034621664969632, tol=PTOL)
assert ae(v.imag, -1.8157749903874220607, tol=PTOL)
v = fp.ei((-0.25 - 1.0j))
assert ae(v, (0.16868306393667788761 - 2.6557914649950505414j), tol=ATOL)
assert ae(v.real, 0.16868306393667788761, tol=PTOL)
assert ae(v.imag, -2.6557914649950505414, tol=PTOL)
v = fp.ei((-1.0 - 4.0j))
assert ae(v, (-0.03373591813926547318 - 3.2151161058308770603j), tol=ATOL)
assert ae(v.real, -0.03373591813926547318, tol=PTOL)
assert ae(v.imag, -3.2151161058308770603, tol=PTOL)
v = fp.ei((-2.0 - 8.0j))
assert ae(v, (0.015392833434733785143 - 3.1384179414340326969j), tol=ATOL)
assert ae(v.real, 0.015392833434733785143, tol=PTOL)
assert ae(v.imag, -3.1384179414340326969, tol=PTOL)
v = fp.ei((-5.0 - 20.0j))
assert ae(v, (0.00024419662286542966525 - 3.1413825703601317109j), tol=ATOL)
assert ae(v.real, 0.00024419662286542966525, tol=PTOL)
assert ae(v.imag, -3.1413825703601317109, tol=PTOL)
v = fp.ei((-20.0 - 80.0j))
assert ae(v, (-2.3255552781051330088e-11 - 3.1415926535987396304j), tol=ATOL)
assert ae(v.real, -2.3255552781051330088e-11, tol=PTOL)
assert ae(v.imag, -3.1415926535987396304, tol=PTOL)
v = fp.ei((-30.0 - 120.0j))
assert ae(v, (2.7068919097124652332e-16 - 3.1415926535897925337j), tol=ATOL)
assert ae(v.real, 2.7068919097124652332e-16, tol=PTOL)
assert ae(v.imag, -3.1415926535897925337, tol=PTOL)
v = fp.ei((-40.0 - 160.0j))
assert ae(v, (1.1695597827678024687e-20 - 3.1415926535897932385j), tol=ATOL)
assert ae(v.real, 1.1695597827678024687e-20, tol=PTOL)
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
v = fp.ei((-50.0 - 200.0j))
assert ae(v, (-9.0323746914410162531e-25 - 3.1415926535897932385j), tol=ATOL)
assert ae(v.real, -9.0323746914410162531e-25, tol=PTOL)
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
v = fp.ei((-80.0 - 320.0j))
assert ae(v, (-3.4819106748728063576e-38 - 3.1415926535897932385j), tol=ATOL)
assert ae(v.real, -3.4819106748728063576e-38, tol=PTOL)
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
v = fp.ei((0.0 - 1.1641532182693481445e-10j))
assert ae(v, (-22.29664129357666235 - 1.5707963269113119411j), tol=ATOL)
assert ae(v.real, -22.29664129357666235, tol=PTOL)
assert ae(v.imag, -1.5707963269113119411, tol=PTOL)
v = fp.ei((0.0 - 0.25j))
assert ae(v, (-0.82466306258094565309 - 1.8199298971146537833j), tol=ATOL)
assert ae(v.real, -0.82466306258094565309, tol=PTOL)
assert ae(v.imag, -1.8199298971146537833, tol=PTOL)
v = fp.ei((0.0 - 1.0j))
assert ae(v, (0.33740392290096813466 - 2.5168793971620796342j), tol=ATOL)
assert ae(v.real, 0.33740392290096813466, tol=PTOL)
assert ae(v.imag, -2.5168793971620796342, tol=PTOL)
v = fp.ei((0.0 - 2.0j))
assert ae(v, (0.4229808287748649957 - 3.1762093035975914678j), tol=ATOL)
assert ae(v.real, 0.4229808287748649957, tol=PTOL)
assert ae(v.imag, -3.1762093035975914678, tol=PTOL)
v = fp.ei((0.0 - 5.0j))
assert ae(v, (-0.19002974965664387862 - 3.1207275717395707565j), tol=ATOL)
assert ae(v.real, -0.19002974965664387862, tol=PTOL)
assert ae(v.imag, -3.1207275717395707565, tol=PTOL)
v = fp.ei((0.0 - 20.0j))
assert ae(v, (0.04441982084535331654 - 3.1190380278383364594j), tol=ATOL)
assert ae(v.real, 0.04441982084535331654, tol=PTOL)
assert ae(v.imag, -3.1190380278383364594, tol=PTOL)
v = fp.ei((0.0 - 30.0j))
assert ae(v, (-0.033032417282071143779 - 3.1375528668252477302j), tol=ATOL)
assert ae(v.real, -0.033032417282071143779, tol=PTOL)
assert ae(v.imag, -3.1375528668252477302, tol=PTOL)
v = fp.ei((0.0 - 40.0j))
assert ae(v, (0.019020007896208766962 - 3.157781446149681126j), tol=ATOL)
assert ae(v.real, 0.019020007896208766962, tol=PTOL)
assert ae(v.imag, -3.157781446149681126, tol=PTOL)
v = fp.ei((0.0 - 50.0j))
assert ae(v, (-0.0056283863241163054402 - 3.122413399280832514j), tol=ATOL)
assert ae(v.real, -0.0056283863241163054402, tol=PTOL)
assert ae(v.imag, -3.122413399280832514, tol=PTOL)
v = fp.ei((0.0 - 80.0j))
assert ae(v, (-0.012402501155070958192 - 3.1431272137073839346j), tol=ATOL)
assert ae(v.real, -0.012402501155070958192, tol=PTOL)
assert ae(v.imag, -3.1431272137073839346, tol=PTOL)
v = fp.ei((1.1641532182693481445e-10 - 4.6566128730773925781e-10j))
assert ae(v, (-20.880034621432138988 - 1.3258176641336937524j), tol=ATOL)
assert ae(v.real, -20.880034621432138988, tol=PTOL)
assert ae(v.imag, -1.3258176641336937524, tol=PTOL)
v = fp.ei((0.25 - 1.0j))
assert ae(v, (0.59066621214766308594 - 2.3968481059377428687j), tol=ATOL)
assert ae(v.real, 0.59066621214766308594, tol=PTOL)
assert ae(v.imag, -2.3968481059377428687, tol=PTOL)
v = fp.ei((1.0 - 4.0j))
assert ae(v, (-0.49739047283060471093 - 3.5570287076301818702j), tol=ATOL)
assert ae(v.real, -0.49739047283060471093, tol=PTOL)
assert ae(v.imag, -3.5570287076301818702, tol=PTOL)
v = fp.ei((2.0 - 8.0j))
assert ae(v, (0.8705211147733730969 - 3.3825859385758486351j), tol=ATOL)
assert ae(v.real, 0.8705211147733730969, tol=PTOL)
assert ae(v.imag, -3.3825859385758486351, tol=PTOL)
v = fp.ei((5.0 - 20.0j))
assert ae(v, (7.0789514293925893007 - 1.5313749363937141849j), tol=ATOL)
assert ae(v.real, 7.0789514293925893007, tol=PTOL)
assert ae(v.imag, -1.5313749363937141849, tol=PTOL)
v = fp.ei((20.0 - 80.0j))
assert ae(v, (-5855431.4907298084434 + 720917.79156143806727j), tol=ATOL)
assert ae(v.real, -5855431.4907298084434, tol=PTOL)
assert ae(v.imag, 720917.79156143806727, tol=PTOL)
v = fp.ei((30.0 - 120.0j))
assert ae(v, (65402491644.703470747 + 56697658396.51586764j), tol=ATOL)
assert ae(v.real, 65402491644.703470747, tol=PTOL)
assert ae(v.imag, 56697658396.51586764, tol=PTOL)
v = fp.ei((40.0 - 160.0j))
assert ae(v, (-25504929379604.776769 - 1429035198630576.3879j), tol=ATOL)
assert ae(v.real, -25504929379604.776769, tol=PTOL)
assert ae(v.imag, -1429035198630576.3879, tol=PTOL)
v = fp.ei((50.0 - 200.0j))
assert ae(v, (-18437746526988116954.0 + 17146362239046152342.0j), tol=ATOL)
assert ae(v.real, -18437746526988116954.0, tol=PTOL)
assert ae(v.imag, 17146362239046152342.0, tol=PTOL)
v = fp.ei((80.0 - 320.0j))
assert ae(v, (-3.3464697299634526706e+31 + 1.6473152633843023919e+32j), tol=ATOL)
assert ae(v.real, -3.3464697299634526706e+31, tol=PTOL)
assert ae(v.imag, 1.6473152633843023919e+32, tol=PTOL)
v = fp.ei((1.1641532182693481445e-10 - 1.1641532182693481445e-10j))
assert ae(v, (-21.950067703180274374 - 0.78539816351386363145j), tol=ATOL)
assert ae(v.real, -21.950067703180274374, tol=PTOL)
assert ae(v.imag, -0.78539816351386363145, tol=PTOL)
v = fp.ei((0.25 - 0.25j))
assert ae(v, (-0.21441047326710323254 - 1.0683772981589995996j), tol=ATOL)
assert ae(v.real, -0.21441047326710323254, tol=PTOL)
assert ae(v.imag, -1.0683772981589995996, tol=PTOL)
v = fp.ei((1.0 - 1.0j))
assert ae(v, (1.7646259855638540684 - 2.3877698515105224193j), tol=ATOL)
assert ae(v.real, 1.7646259855638540684, tol=PTOL)
assert ae(v.imag, -2.3877698515105224193, tol=PTOL)
v = fp.ei((2.0 - 2.0j))
assert ae(v, (1.8920781621855474089 - 5.3169624378326579621j), tol=ATOL)
assert ae(v.real, 1.8920781621855474089, tol=PTOL)
assert ae(v.imag, -5.3169624378326579621, tol=PTOL)
v = fp.ei((5.0 - 5.0j))
assert ae(v, (-13.470936071475245856 + 15.322492395731230968j), tol=ATOL)
assert ae(v.real, -13.470936071475245856, tol=PTOL)
assert ae(v.imag, 15.322492395731230968, tol=PTOL)
v = fp.ei((20.0 - 20.0j))
assert ae(v, (16589317.398788971896 - 5831705.4712368307104j), tol=ATOL)
assert ae(v.real, 16589317.398788971896, tol=PTOL)
assert ae(v.imag, -5831705.4712368307104, tol=PTOL)
v = fp.ei((30.0 - 30.0j))
assert ae(v, (-154596484273.69322527 + 204179357834.2723043j), tol=ATOL)
assert ae(v.real, -154596484273.69322527, tol=PTOL)
assert ae(v.imag, 204179357834.2723043, tol=PTOL)
v = fp.ei((40.0 - 40.0j))
assert ae(v, (287512180321448.45408 - 4203502407932318.1156j), tol=ATOL)
assert ae(v.real, 287512180321448.45408, tol=PTOL)
assert ae(v.imag, -4203502407932318.1156, tol=PTOL)
v = fp.ei((50.0 - 50.0j))
assert ae(v, (36128528616649268826.0 + 64648801861338741960.0j), tol=ATOL)
assert ae(v.real, 36128528616649268826.0, tol=PTOL)
assert ae(v.imag, 64648801861338741960.0, tol=PTOL)
v = fp.ei((80.0 - 80.0j))
assert ae(v, (-3.8674816337930010217e+32 + 3.0540709639658071041e+32j), tol=ATOL)
assert ae(v.real, -3.8674816337930010217e+32, tol=PTOL)
assert ae(v.imag, 3.0540709639658071041e+32, tol=PTOL)
v = fp.ei((4.6566128730773925781e-10 - 1.1641532182693481445e-10j))
assert ae(v, (-20.880034621082893023 - 0.24497866324327947603j), tol=ATOL)
assert ae(v.real, -20.880034621082893023, tol=PTOL)
assert ae(v.imag, -0.24497866324327947603, tol=PTOL)
v = fp.ei((1.0 - 0.25j))
assert ae(v, (1.8942716983721074932 - 0.67268237088273915854j), tol=ATOL)
assert ae(v.real, 1.8942716983721074932, tol=PTOL)
assert ae(v.imag, -0.67268237088273915854, tol=PTOL)
v = fp.ei((4.0 - 1.0j))
assert ae(v, (14.806699492675420438 - 12.280015176673582616j), tol=ATOL)
assert ae(v.real, 14.806699492675420438, tol=PTOL)
assert ae(v.imag, -12.280015176673582616, tol=PTOL)
v = fp.ei((8.0 - 2.0j))
assert ae(v, (-54.633252667426386294 - 416.34477429173650012j), tol=ATOL)
assert ae(v.real, -54.633252667426386294, tol=PTOL)
assert ae(v.imag, -416.34477429173650012, tol=PTOL)
v = fp.ei((20.0 - 5.0j))
assert ae(v, (711836.97165402624643 + 24745247.798103247366j), tol=ATOL)
assert ae(v.real, 711836.97165402624643, tol=PTOL)
assert ae(v.imag, 24745247.798103247366, tol=PTOL)
v = fp.ei((80.0 - 20.0j))
assert ae(v, (4.2139911108612653091e+32 - 5.3367124741918251637e+32j), tol=ATOL)
assert ae(v.real, 4.2139911108612653091e+32, tol=PTOL)
assert ae(v.imag, -5.3367124741918251637e+32, tol=PTOL)
v = fp.ei((120.0 - 30.0j))
assert ae(v, (-9.7760616203707508892e+48 + 1.058257682317195792e+50j), tol=ATOL)
assert ae(v.real, -9.7760616203707508892e+48, tol=PTOL)
assert ae(v.imag, 1.058257682317195792e+50, tol=PTOL)
v = fp.ei((160.0 - 40.0j))
assert ae(v, (-8.7065541466623638861e+66 - 1.6577106725141739889e+67j), tol=ATOL)
assert ae(v.real, -8.7065541466623638861e+66, tol=PTOL)
assert ae(v.imag, -1.6577106725141739889e+67, tol=PTOL)
v = fp.ei((200.0 - 50.0j))
assert ae(v, (3.070744996327018106e+84 + 1.7243244846769415903e+84j), tol=ATOL)
assert ae(v.real, 3.070744996327018106e+84, tol=PTOL)
assert ae(v.imag, 1.7243244846769415903e+84, tol=PTOL)
v = fp.ei((320.0 - 80.0j))
assert ae(v, (-9.9960598637998647276e+135 + 2.6855081527595608863e+136j), tol=ATOL)
assert ae(v.real, -9.9960598637998647276e+135, tol=PTOL)
assert ae(v.imag, 2.6855081527595608863e+136, tol=PTOL)
| 89,997 | 52.826555 | 101 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/tests/test_rootfinding.py
|
from mpmath import *
from mpmath.calculus.optimization import Secant, Muller, Bisection, Illinois, \
Pegasus, Anderson, Ridder, ANewton, Newton, MNewton, MDNewton
def test_findroot():
# old tests, assuming secant
mp.dps = 15
assert findroot(lambda x: 4*x-3, mpf(5)).ae(0.75)
assert findroot(sin, mpf(3)).ae(pi)
assert findroot(sin, (mpf(3), mpf(3.14))).ae(pi)
assert findroot(lambda x: x*x+1, mpc(2+2j)).ae(1j)
# test all solvers with 1 starting point
f = lambda x: cos(x)
for solver in [Newton, Secant, MNewton, Muller, ANewton]:
x = findroot(f, 2., solver=solver)
assert abs(f(x)) < eps
# test all solvers with interval of 2 points
for solver in [Secant, Muller, Bisection, Illinois, Pegasus, Anderson,
Ridder]:
x = findroot(f, (1., 2.), solver=solver)
assert abs(f(x)) < eps
# test types
f = lambda x: (x - 2)**2
#assert isinstance(findroot(f, 1, force_type=mpf, tol=1e-10), mpf)
#assert isinstance(findroot(f, 1., force_type=None, tol=1e-10), float)
#assert isinstance(findroot(f, 1, force_type=complex, tol=1e-10), complex)
assert isinstance(fp.findroot(f, 1, tol=1e-10), float)
assert isinstance(fp.findroot(f, 1+0j, tol=1e-10), complex)
def test_bisection():
# issue 273
assert findroot(lambda x: x**2-1,(0,2),solver='bisect') == 1
def test_mnewton():
f = lambda x: polyval([1,3,3,1],x)
x = findroot(f, -0.9, solver='mnewton')
assert abs(f(x)) < eps
def test_anewton():
f = lambda x: (x - 2)**100
x = findroot(f, 1., solver=ANewton)
assert abs(f(x)) < eps
def test_muller():
f = lambda x: (2 + x)**3 + 2
x = findroot(f, 1., solver=Muller)
assert abs(f(x)) < eps
def test_multiplicity():
for i in range(1, 5):
assert multiplicity(lambda x: (x - 1)**i, 1) == i
assert multiplicity(lambda x: x**2, 1) == 0
def test_multidimensional():
def f(*x):
return [3*x[0]**2-2*x[1]**2-1, x[0]**2-2*x[0]+x[1]**2+2*x[1]-8]
assert mnorm(jacobian(f, (1,-2)) - matrix([[6,8],[0,-2]]),1) < 1.e-7
for x, error in MDNewton(mp, f, (1,-2), verbose=0,
norm=lambda x: norm(x, inf)):
pass
assert norm(f(*x), 2) < 1e-14
# The Chinese mathematician Zhu Shijie was the very first to solve this
# nonlinear system 700 years ago
f1 = lambda x, y: -x + 2*y
f2 = lambda x, y: (x**2 + x*(y**2 - 2) - 4*y) / (x + 4)
f3 = lambda x, y: sqrt(x**2 + y**2)
def f(x, y):
f1x = f1(x, y)
return (f2(x, y) - f1x, f3(x, y) - f1x)
x = findroot(f, (10, 10))
assert [int(round(i)) for i in x] == [3, 4]
def test_trivial():
assert findroot(lambda x: 0, 1) == 1
assert findroot(lambda x: x, 0) == 0
#assert findroot(lambda x, y: x + y, (1, -1)) == (1, -1)
| 2,831 | 35.307692 | 79 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/tests/test_hp.py
|
"""
Check that the output from irrational functions is accurate for
high-precision input, from 5 to 200 digits. The reference values were
verified with Mathematica.
"""
import time
from mpmath import *
precs = [5, 15, 28, 35, 57, 80, 100, 150, 200]
# sqrt(3) + pi/2
a = \
"3.302847134363773912758768033145623809041389953497933538543279275605"\
"841220051904536395163599428307109666700184672047856353516867399774243594"\
"67433521615861420725323528325327484262075464241255915238845599752675"
# e + 1/euler**2
b = \
"5.719681166601007617111261398629939965860873957353320734275716220045750"\
"31474116300529519620938123730851145473473708966080207482581266469342214"\
"824842256999042984813905047895479210702109260221361437411947323431"
# sqrt(a)
sqrt_a = \
"1.817373691447021556327498239690365674922395036495564333152483422755"\
"144321726165582817927383239308173567921345318453306994746434073691275094"\
"484777905906961689902608644112196725896908619756404253109722911487"
# sqrt(a+b*i).real
sqrt_abi_real = \
"2.225720098415113027729407777066107959851146508557282707197601407276"\
"89160998185797504198062911768240808839104987021515555650875977724230130"\
"3584116233925658621288393930286871862273400475179312570274423840384"
# sqrt(a+b*i).imag
sqrt_abi_imag = \
"1.2849057639084690902371581529110949983261182430040898147672052833653668"\
"0629534491275114877090834296831373498336559849050755848611854282001250"\
"1924311019152914021365263161630765255610885489295778894976075186"
# log(a)
log_a = \
"1.194784864491089550288313512105715261520511949410072046160598707069"\
"4336653155025770546309137440687056366757650909754708302115204338077595203"\
"83005773986664564927027147084436553262269459110211221152925732612"
# log(a+b*i).real
log_abi_real = \
"1.8877985921697018111624077550443297276844736840853590212962006811663"\
"04949387789489704203167470111267581371396245317618589339274243008242708"\
"014251531496104028712866224020066439049377679709216784954509456421"
# log(a+b*i).imag
log_abi_imag = \
"1.0471204952840802663567714297078763189256357109769672185219334169734948"\
"4265809854092437285294686651806426649541504240470168212723133326542181"\
"8300136462287639956713914482701017346851009323172531601894918640"
# exp(a)
exp_a = \
"27.18994224087168661137253262213293847994194869430518354305430976149"\
"382792035050358791398632888885200049857986258414049540376323785711941636"\
"100358982497583832083513086941635049329804685212200507288797531143"
# exp(a+b*i).real
exp_abi_real = \
"22.98606617170543596386921087657586890620262522816912505151109385026"\
"40160179326569526152851983847133513990281518417211964710397233157168852"\
"4963130831190142571659948419307628119985383887599493378056639916701"
# exp(a+b*i).imag
exp_abi_imag = \
"-14.523557450291489727214750571590272774669907424478129280902375851196283"\
"3377162379031724734050088565710975758824441845278120105728824497308303"\
"6065619788140201636218705414429933685889542661364184694108251449"
# a**b
pow_a_b = \
"928.7025342285568142947391505837660251004990092821305668257284426997"\
"361966028275685583421197860603126498884545336686124793155581311527995550"\
"580229264427202446131740932666832138634013168125809402143796691154"
# (a**(a+b*i)).real
pow_a_abi_real = \
"44.09156071394489511956058111704382592976814280267142206420038656267"\
"67707916510652790502399193109819563864568986234654864462095231138500505"\
"8197456514795059492120303477512711977915544927440682508821426093455"
# (a**(a+b*i)).imag
pow_a_abi_imag = \
"27.069371511573224750478105146737852141664955461266218367212527612279886"\
"9322304536553254659049205414427707675802193810711302947536332040474573"\
"8166261217563960235014674118610092944307893857862518964990092301"
# ((a+b*i)**(a+b*i)).real
pow_abi_abi_real = \
"-0.15171310677859590091001057734676423076527145052787388589334350524"\
"8084195882019497779202452975350579073716811284169068082670778986235179"\
"0813026562962084477640470612184016755250592698408112493759742219150452"\
# ((a+b*i)**(a+b*i)).imag
pow_abi_abi_imag = \
"1.2697592504953448936553147870155987153192995316950583150964099070426"\
"4736837932577176947632535475040521749162383347758827307504526525647759"\
"97547638617201824468382194146854367480471892602963428122896045019902"
# sin(a)
sin_a = \
"-0.16055653857469062740274792907968048154164433772938156243509084009"\
"38437090841460493108570147191289893388608611542655654723437248152535114"\
"528368009465836614227575701220612124204622383149391870684288862269631"
# sin(1000*a)
sin_1000a = \
"-0.85897040577443833776358106803777589664322997794126153477060795801"\
"09151695416961724733492511852267067419573754315098042850381158563024337"\
"216458577140500488715469780315833217177634490142748614625281171216863"
# sin(a+b*i)
sin_abi_real = \
"-24.4696999681556977743346798696005278716053366404081910969773939630"\
"7149215135459794473448465734589287491880563183624997435193637389884206"\
"02151395451271809790360963144464736839412254746645151672423256977064"
sin_abi_imag = \
"-150.42505378241784671801405965872972765595073690984080160750785565810981"\
"8314482499135443827055399655645954830931316357243750839088113122816583"\
"7169201254329464271121058839499197583056427233866320456505060735"
# cos
cos_a = \
"-0.98702664499035378399332439243967038895709261414476495730788864004"\
"05406821549361039745258003422386169330787395654908532996287293003581554"\
"257037193284199198069707141161341820684198547572456183525659969145501"
cos_1000a = \
"-0.51202523570982001856195696460663971099692261342827540426136215533"\
"52686662667660613179619804463250686852463876088694806607652218586060613"\
"951310588158830695735537073667299449753951774916401887657320950496820"
# tan
tan_a = \
"0.162666873675188117341401059858835168007137819495998960250142156848"\
"639654718809412181543343168174807985559916643549174530459883826451064966"\
"7996119428949951351938178809444268785629011625179962457123195557310"
tan_abi_real = \
"6.822696615947538488826586186310162599974827139564433912601918442911"\
"1026830824380070400102213741875804368044342309515353631134074491271890"\
"467615882710035471686578162073677173148647065131872116479947620E-6"
tan_abi_imag = \
"0.9999795833048243692245661011298447587046967777739649018690797625964167"\
"1446419978852235960862841608081413169601038230073129482874832053357571"\
"62702259309150715669026865777947502665936317953101462202542168429"
def test_hp():
for dps in precs:
mp.dps = dps + 8
aa = mpf(a)
bb = mpf(b)
a1000 = 1000*mpf(a)
abi = mpc(aa, bb)
mp.dps = dps
assert (sqrt(3) + pi/2).ae(aa)
assert (e + 1/euler**2).ae(bb)
assert sqrt(aa).ae(mpf(sqrt_a))
assert sqrt(abi).ae(mpc(sqrt_abi_real, sqrt_abi_imag))
assert log(aa).ae(mpf(log_a))
assert log(abi).ae(mpc(log_abi_real, log_abi_imag))
assert exp(aa).ae(mpf(exp_a))
assert exp(abi).ae(mpc(exp_abi_real, exp_abi_imag))
assert (aa**bb).ae(mpf(pow_a_b))
assert (aa**abi).ae(mpc(pow_a_abi_real, pow_a_abi_imag))
assert (abi**abi).ae(mpc(pow_abi_abi_real, pow_abi_abi_imag))
assert sin(a).ae(mpf(sin_a))
assert sin(a1000).ae(mpf(sin_1000a))
assert sin(abi).ae(mpc(sin_abi_real, sin_abi_imag))
assert cos(a).ae(mpf(cos_a))
assert cos(a1000).ae(mpf(cos_1000a))
assert tan(a).ae(mpf(tan_a))
assert tan(abi).ae(mpc(tan_abi_real, tan_abi_imag))
# check that complex cancellation is avoided so that both
# real and imaginary parts have high relative accuracy.
# abs_eps should be 0, but has to be set to 1e-205 to pass the
# 200-digit case, probably due to slight inaccuracy in the
# precomputed input
assert (tan(abi).real).ae(mpf(tan_abi_real), abs_eps=1e-205)
assert (tan(abi).imag).ae(mpf(tan_abi_imag), abs_eps=1e-205)
mp.dps = 460
assert str(log(3))[-20:] == '02166121184001409826'
mp.dps = 15
# Since str(a) can differ in the last digit from rounded a, and I want
# to compare the last digits of big numbers with the results in Mathematica,
# I made this hack to get the last 20 digits of rounded a
def last_digits(a):
r = repr(a)
s = str(a)
#dps = mp.dps
#mp.dps += 3
m = 10
r = r.replace(s[:-m],'')
r = r.replace("mpf('",'').replace("')",'')
num0 = 0
for c in r:
if c == '0':
num0 += 1
else:
break
b = float(int(r))/10**(len(r) - m)
if b >= 10**m - 0.5:
raise NotImplementedError
n = int(round(b))
sn = str(n)
s = s[:-m] + '0'*num0 + sn
return s[-20:]
# values checked with Mathematica
def test_log_hp():
mp.dps = 2000
a = mpf(10)**15000/3
r = log(a)
res = last_digits(r)
# Mathematica N[Log[10^15000/3], 2000]
# ...7443804441768333470331
assert res == '44380444176833347033'
# see issue 145
r = log(mpf(3)/2)
# Mathematica N[Log[3/2], 2000]
# ...69653749808140753263288
res = last_digits(r)
assert res == '53749808140753263288'
mp.dps = 10000
r = log(2)
res = last_digits(r)
# Mathematica N[Log[2], 10000]
# ...695615913401856601359655561
assert res == '91340185660135965556'
r = log(mpf(10)**10/3)
res = last_digits(r)
# Mathematica N[Log[10^10/3], 10000]
# ...587087654020631943060007154
assert res == '54020631943060007154', res
r = log(mpf(10)**100/3)
res = last_digits(r)
# Mathematica N[Log[10^100/3], 10000]
# ,,,59246336539088351652334666
assert res == '36539088351652334666', res
mp.dps += 10
a = 1 - mpf(1)/10**10
mp.dps -= 10
r = log(a)
res = last_digits(r)
# ...3310334360482956137216724048322957404
# 372167240483229574038733026370
# Mathematica N[Log[1 - 10^-10]*10^10, 10000]
# ...60482956137216724048322957404
assert res == '37216724048322957404', res
mp.dps = 10000
mp.dps += 100
a = 1 + mpf(1)/10**100
mp.dps -= 100
r = log(a)
res = last_digits(+r)
# Mathematica N[Log[1 + 10^-100]*10^10, 10030]
# ...3994733877377412241546890854692521568292338268273 10^-91
assert res == '39947338773774122415', res
mp.dps = 15
def test_exp_hp():
mp.dps = 4000
r = exp(mpf(1)/10)
# IntegerPart[N[Exp[1/10] * 10^4000, 4000]]
# ...92167105162069688129
assert int(r * 10**mp.dps) % 10**20 == 92167105162069688129
| 10,441 | 34.760274 | 76 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/tests/runtests.py
|
#!/usr/bin/env python
"""
python runtests.py -py
Use py.test to run tests (more useful for debugging)
python runtests.py -psyco
Enable psyco to make tests run about 50% faster
python runtests.py -coverage
Generate test coverage report. Statistics are written to /tmp
python runtests.py -profile
Generate profile stats (this is much slower)
python runtests.py -nogmpy
Run tests without using GMPY even if it exists
python runtests.py -strict
Enforce extra tests in normalize()
python runtests.py -local
Insert '../..' at the beginning of sys.path to use local mpmath
Additional arguments are used to filter the tests to run. Only files that have
one of the arguments in their name are executed.
"""
import sys, os, traceback
if "-psyco" in sys.argv:
sys.argv.remove('-psyco')
import psyco
psyco.full()
profile = False
if "-profile" in sys.argv:
sys.argv.remove('-profile')
profile = True
coverage = False
if "-coverage" in sys.argv:
sys.argv.remove('-coverage')
coverage = True
if "-nogmpy" in sys.argv:
sys.argv.remove('-nogmpy')
os.environ['MPMATH_NOGMPY'] = 'Y'
if "-strict" in sys.argv:
sys.argv.remove('-strict')
os.environ['MPMATH_STRICT'] = 'Y'
if "-local" in sys.argv:
sys.argv.remove('-local')
importdir = os.path.abspath(os.path.join(os.path.dirname(sys.argv[0]),
'../..'))
else:
importdir = ''
# TODO: add a flag for this
testdir = ''
def testit(importdir='', testdir=''):
"""Run all tests in testdir while importing from importdir."""
if importdir:
sys.path.insert(1, importdir)
if testdir:
sys.path.insert(1, testdir)
import os.path
import mpmath
print("mpmath imported from %s" % os.path.dirname(mpmath.__file__))
print("mpmath backend: %s" % mpmath.libmp.backend.BACKEND)
print("mpmath mp class: %s" % repr(mpmath.mp))
print("mpmath version: %s" % mpmath.__version__)
print("Python version: %s" % sys.version)
print("")
if "-py" in sys.argv:
sys.argv.remove('-py')
import py
py.test.cmdline.main()
else:
import glob
from timeit import default_timer as clock
modules = []
args = sys.argv[1:]
# search for tests in directory of this file if not otherwise specified
if not testdir:
pattern = os.path.dirname(sys.argv[0])
else:
pattern = testdir
if pattern:
pattern += '/'
pattern += 'test*.py'
# look for tests (respecting specified filter)
for f in glob.glob(pattern):
name = os.path.splitext(os.path.basename(f))[0]
# If run as a script, only run tests given as args, if any are given
if args and __name__ == "__main__":
ok = False
for arg in args:
if arg in name:
ok = True
break
if not ok:
continue
module = __import__(name)
priority = module.__dict__.get('priority', 100)
if priority == 666:
modules = [[priority, name, module]]
break
modules.append([priority, name, module])
# execute tests
modules.sort()
tstart = clock()
for priority, name, module in modules:
print(name)
for f in sorted(module.__dict__.keys()):
if f.startswith('test_'):
if coverage and ('numpy' in f):
continue
sys.stdout.write(" " + f[5:].ljust(25) + " ")
t1 = clock()
try:
module.__dict__[f]()
except:
etype, evalue, trb = sys.exc_info()
if etype in (KeyboardInterrupt, SystemExit):
raise
print("")
print("TEST FAILED!")
print("")
traceback.print_exc()
t2 = clock()
print("ok " + " " + ("%.7f" % (t2-t1)) + " s")
tend = clock()
print("")
print("finished tests in " + ("%.2f" % (tend-tstart)) + " seconds")
# clean sys.path
if importdir:
sys.path.remove(importdir)
if testdir:
sys.path.remove(testdir)
if __name__ == '__main__':
if profile:
import cProfile
cProfile.run("testit('%s', '%s')" % (importdir, testdir), sort=1)
elif coverage:
import trace
tracer = trace.Trace(ignoredirs=[sys.prefix, sys.exec_prefix],
trace=0, count=1)
tracer.run('testit(importdir, testdir)')
r = tracer.results()
r.write_results(show_missing=True, summary=True, coverdir="/tmp")
else:
testit(importdir, testdir)
| 4,985 | 30.358491 | 80 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/tests/test_elliptic.py
|
"""
Limited tests of the elliptic functions module. A full suite of
extensive testing can be found in elliptic_torture_tests.py
Author of the first version: M.T. Taschuk
References:
[1] Abramowitz & Stegun. 'Handbook of Mathematical Functions, 9th Ed.',
(Dover duplicate of 1972 edition)
[2] Whittaker 'A Course of Modern Analysis, 4th Ed.', 1946,
Cambridge University Press
"""
import mpmath
import random
from mpmath import *
def mpc_ae(a, b, eps=eps):
res = True
res = res and a.real.ae(b.real, eps)
res = res and a.imag.ae(b.imag, eps)
return res
zero = mpf(0)
one = mpf(1)
jsn = ellipfun('sn')
jcn = ellipfun('cn')
jdn = ellipfun('dn')
calculate_nome = lambda k: qfrom(k=k)
def test_ellipfun():
mp.dps = 15
assert ellipfun('ss', 0, 0) == 1
assert ellipfun('cc', 0, 0) == 1
assert ellipfun('dd', 0, 0) == 1
assert ellipfun('nn', 0, 0) == 1
assert ellipfun('sn', 0.25, 0).ae(sin(0.25))
assert ellipfun('cn', 0.25, 0).ae(cos(0.25))
assert ellipfun('dn', 0.25, 0).ae(1)
assert ellipfun('ns', 0.25, 0).ae(csc(0.25))
assert ellipfun('nc', 0.25, 0).ae(sec(0.25))
assert ellipfun('nd', 0.25, 0).ae(1)
assert ellipfun('sc', 0.25, 0).ae(tan(0.25))
assert ellipfun('sd', 0.25, 0).ae(sin(0.25))
assert ellipfun('cd', 0.25, 0).ae(cos(0.25))
assert ellipfun('cs', 0.25, 0).ae(cot(0.25))
assert ellipfun('dc', 0.25, 0).ae(sec(0.25))
assert ellipfun('ds', 0.25, 0).ae(csc(0.25))
assert ellipfun('sn', 0.25, 1).ae(tanh(0.25))
assert ellipfun('cn', 0.25, 1).ae(sech(0.25))
assert ellipfun('dn', 0.25, 1).ae(sech(0.25))
assert ellipfun('ns', 0.25, 1).ae(coth(0.25))
assert ellipfun('nc', 0.25, 1).ae(cosh(0.25))
assert ellipfun('nd', 0.25, 1).ae(cosh(0.25))
assert ellipfun('sc', 0.25, 1).ae(sinh(0.25))
assert ellipfun('sd', 0.25, 1).ae(sinh(0.25))
assert ellipfun('cd', 0.25, 1).ae(1)
assert ellipfun('cs', 0.25, 1).ae(csch(0.25))
assert ellipfun('dc', 0.25, 1).ae(1)
assert ellipfun('ds', 0.25, 1).ae(csch(0.25))
assert ellipfun('sn', 0.25, 0.5).ae(0.24615967096986145833)
assert ellipfun('cn', 0.25, 0.5).ae(0.96922928989378439337)
assert ellipfun('dn', 0.25, 0.5).ae(0.98473484156599474563)
assert ellipfun('ns', 0.25, 0.5).ae(4.0624038700573130369)
assert ellipfun('nc', 0.25, 0.5).ae(1.0317476065024692949)
assert ellipfun('nd', 0.25, 0.5).ae(1.0155017958029488665)
assert ellipfun('sc', 0.25, 0.5).ae(0.25397465134058993408)
assert ellipfun('sd', 0.25, 0.5).ae(0.24997558792415733063)
assert ellipfun('cd', 0.25, 0.5).ae(0.98425408443195497052)
assert ellipfun('cs', 0.25, 0.5).ae(3.9374008182374110826)
assert ellipfun('dc', 0.25, 0.5).ae(1.0159978158253033913)
assert ellipfun('ds', 0.25, 0.5).ae(4.0003906313579720593)
def test_calculate_nome():
mp.dps = 100
q = calculate_nome(zero)
assert(q == zero)
mp.dps = 25
# used Mathematica's EllipticNomeQ[m]
math1 = [(mpf(1)/10, mpf('0.006584651553858370274473060')),
(mpf(2)/10, mpf('0.01394285727531826872146409')),
(mpf(3)/10, mpf('0.02227743615715350822901627')),
(mpf(4)/10, mpf('0.03188334731336317755064299')),
(mpf(5)/10, mpf('0.04321391826377224977441774')),
(mpf(6)/10, mpf('0.05702025781460967637754953')),
(mpf(7)/10, mpf('0.07468994353717944761143751')),
(mpf(8)/10, mpf('0.09927369733882489703607378')),
(mpf(9)/10, mpf('0.1401731269542615524091055')),
(mpf(9)/10, mpf('0.1401731269542615524091055'))]
for i in math1:
m = i[0]
q = calculate_nome(sqrt(m))
assert q.ae(i[1])
mp.dps = 15
def test_jtheta():
mp.dps = 25
z = q = zero
for n in range(1,5):
value = jtheta(n, z, q)
assert(value == (n-1)//2)
for q in [one, mpf(2)]:
for n in range(1,5):
raised = True
try:
r = jtheta(n, z, q)
except:
pass
else:
raised = False
assert(raised)
z = one/10
q = one/11
# Mathematical N[EllipticTheta[1, 1/10, 1/11], 25]
res = mpf('0.1069552990104042681962096')
result = jtheta(1, z, q)
assert(result.ae(res))
# Mathematica N[EllipticTheta[2, 1/10, 1/11], 25]
res = mpf('1.101385760258855791140606')
result = jtheta(2, z, q)
assert(result.ae(res))
# Mathematica N[EllipticTheta[3, 1/10, 1/11], 25]
res = mpf('1.178319743354331061795905')
result = jtheta(3, z, q)
assert(result.ae(res))
# Mathematica N[EllipticTheta[4, 1/10, 1/11], 25]
res = mpf('0.8219318954665153577314573')
result = jtheta(4, z, q)
assert(result.ae(res))
# test for sin zeros for jtheta(1, z, q)
# test for cos zeros for jtheta(2, z, q)
z1 = pi
z2 = pi/2
for i in range(10):
qstring = str(random.random())
q = mpf(qstring)
result = jtheta(1, z1, q)
assert(result.ae(0))
result = jtheta(2, z2, q)
assert(result.ae(0))
mp.dps = 15
def test_jtheta_issue_79():
# near the circle of covergence |q| = 1 the convergence slows
# down; for |q| > Q_LIM the theta functions raise ValueError
mp.dps = 30
mp.dps += 30
q = mpf(6)/10 - one/10**6 - mpf(8)/10 * j
mp.dps -= 30
# Mathematica run first
# N[EllipticTheta[3, 1, 6/10 - 10^-6 - 8/10*I], 2000]
# then it works:
# N[EllipticTheta[3, 1, 6/10 - 10^-6 - 8/10*I], 30]
res = mpf('32.0031009628901652627099524264') + \
mpf('16.6153027998236087899308935624') * j
result = jtheta(3, 1, q)
# check that for abs(q) > Q_LIM a ValueError exception is raised
mp.dps += 30
q = mpf(6)/10 - one/10**7 - mpf(8)/10 * j
mp.dps -= 30
try:
result = jtheta(3, 1, q)
except ValueError:
pass
else:
assert(False)
# bug reported in issue 79
mp.dps = 100
z = (1+j)/3
q = mpf(368983957219251)/10**15 + mpf(636363636363636)/10**15 * j
# Mathematica N[EllipticTheta[1, z, q], 35]
res = mpf('2.4439389177990737589761828991467471') + \
mpf('0.5446453005688226915290954851851490') *j
mp.dps = 30
result = jtheta(1, z, q)
assert(result.ae(res))
mp.dps = 80
z = 3 + 4*j
q = 0.5 + 0.5*j
r1 = jtheta(1, z, q)
mp.dps = 15
r2 = jtheta(1, z, q)
assert r1.ae(r2)
mp.dps = 80
z = 3 + j
q1 = exp(j*3)
# longer test
# for n in range(1, 6)
for n in range(1, 2):
mp.dps = 80
q = q1*(1 - mpf(1)/10**n)
r1 = jtheta(1, z, q)
mp.dps = 15
r2 = jtheta(1, z, q)
assert r1.ae(r2)
mp.dps = 15
# issue 79 about high derivatives
assert jtheta(3, 4.5, 0.25, 9).ae(1359.04892680683)
assert jtheta(3, 4.5, 0.25, 50).ae(-6.14832772630905e+33)
mp.dps = 50
r = jtheta(3, 4.5, 0.25, 9)
assert r.ae('1359.048926806828939547859396600218966947753213803')
r = jtheta(3, 4.5, 0.25, 50)
assert r.ae('-6148327726309051673317975084654262.4119215720343656')
def test_jtheta_identities():
"""
Tests the some of the jacobi identidies found in Abramowitz,
Sec. 16.28, Pg. 576. The identities are tested to 1 part in 10^98.
"""
mp.dps = 110
eps1 = ldexp(eps, 30)
for i in range(10):
qstring = str(random.random())
q = mpf(qstring)
zstring = str(10*random.random())
z = mpf(zstring)
# Abramowitz 16.28.1
# v_1(z, q)**2 * v_4(0, q)**2 = v_3(z, q)**2 * v_2(0, q)**2
# - v_2(z, q)**2 * v_3(0, q)**2
term1 = (jtheta(1, z, q)**2) * (jtheta(4, zero, q)**2)
term2 = (jtheta(3, z, q)**2) * (jtheta(2, zero, q)**2)
term3 = (jtheta(2, z, q)**2) * (jtheta(3, zero, q)**2)
equality = term1 - term2 + term3
assert(equality.ae(0, eps1))
zstring = str(100*random.random())
z = mpf(zstring)
# Abramowitz 16.28.2
# v_2(z, q)**2 * v_4(0, q)**2 = v_4(z, q)**2 * v_2(0, q)**2
# - v_1(z, q)**2 * v_3(0, q)**2
term1 = (jtheta(2, z, q)**2) * (jtheta(4, zero, q)**2)
term2 = (jtheta(4, z, q)**2) * (jtheta(2, zero, q)**2)
term3 = (jtheta(1, z, q)**2) * (jtheta(3, zero, q)**2)
equality = term1 - term2 + term3
assert(equality.ae(0, eps1))
# Abramowitz 16.28.3
# v_3(z, q)**2 * v_4(0, q)**2 = v_4(z, q)**2 * v_3(0, q)**2
# - v_1(z, q)**2 * v_2(0, q)**2
term1 = (jtheta(3, z, q)**2) * (jtheta(4, zero, q)**2)
term2 = (jtheta(4, z, q)**2) * (jtheta(3, zero, q)**2)
term3 = (jtheta(1, z, q)**2) * (jtheta(2, zero, q)**2)
equality = term1 - term2 + term3
assert(equality.ae(0, eps1))
# Abramowitz 16.28.4
# v_4(z, q)**2 * v_4(0, q)**2 = v_3(z, q)**2 * v_3(0, q)**2
# - v_2(z, q)**2 * v_2(0, q)**2
term1 = (jtheta(4, z, q)**2) * (jtheta(4, zero, q)**2)
term2 = (jtheta(3, z, q)**2) * (jtheta(3, zero, q)**2)
term3 = (jtheta(2, z, q)**2) * (jtheta(2, zero, q)**2)
equality = term1 - term2 + term3
assert(equality.ae(0, eps1))
# Abramowitz 16.28.5
# v_2(0, q)**4 + v_4(0, q)**4 == v_3(0, q)**4
term1 = (jtheta(2, zero, q))**4
term2 = (jtheta(4, zero, q))**4
term3 = (jtheta(3, zero, q))**4
equality = term1 + term2 - term3
assert(equality.ae(0, eps1))
mp.dps = 15
def test_jtheta_complex():
mp.dps = 30
z = mpf(1)/4 + j/8
q = mpf(1)/3 + j/7
# Mathematica N[EllipticTheta[1, 1/4 + I/8, 1/3 + I/7], 35]
res = mpf('0.31618034835986160705729105731678285') + \
mpf('0.07542013825835103435142515194358975') * j
r = jtheta(1, z, q)
assert(mpc_ae(r, res))
# Mathematica N[EllipticTheta[2, 1/4 + I/8, 1/3 + I/7], 35]
res = mpf('1.6530986428239765928634711417951828') + \
mpf('0.2015344864707197230526742145361455') * j
r = jtheta(2, z, q)
assert(mpc_ae(r, res))
# Mathematica N[EllipticTheta[3, 1/4 + I/8, 1/3 + I/7], 35]
res = mpf('1.6520564411784228184326012700348340') + \
mpf('0.1998129119671271328684690067401823') * j
r = jtheta(3, z, q)
assert(mpc_ae(r, res))
# Mathematica N[EllipticTheta[4, 1/4 + I/8, 1/3 + I/7], 35]
res = mpf('0.37619082382228348252047624089973824') - \
mpf('0.15623022130983652972686227200681074') * j
r = jtheta(4, z, q)
assert(mpc_ae(r, res))
# check some theta function identities
mp.dos = 100
z = mpf(1)/4 + j/8
q = mpf(1)/3 + j/7
mp.dps += 10
a = [0,0, jtheta(2, 0, q), jtheta(3, 0, q), jtheta(4, 0, q)]
t = [0, jtheta(1, z, q), jtheta(2, z, q), jtheta(3, z, q), jtheta(4, z, q)]
r = [(t[2]*a[4])**2 - (t[4]*a[2])**2 + (t[1] *a[3])**2,
(t[3]*a[4])**2 - (t[4]*a[3])**2 + (t[1] *a[2])**2,
(t[1]*a[4])**2 - (t[3]*a[2])**2 + (t[2] *a[3])**2,
(t[4]*a[4])**2 - (t[3]*a[3])**2 + (t[2] *a[2])**2,
a[2]**4 + a[4]**4 - a[3]**4]
mp.dps -= 10
for x in r:
assert(mpc_ae(x, mpc(0)))
mp.dps = 15
def test_djtheta():
mp.dps = 30
z = one/7 + j/3
q = one/8 + j/5
# Mathematica N[EllipticThetaPrime[1, 1/7 + I/3, 1/8 + I/5], 35]
res = mpf('1.5555195883277196036090928995803201') - \
mpf('0.02439761276895463494054149673076275') * j
result = jtheta(1, z, q, 1)
assert(mpc_ae(result, res))
# Mathematica N[EllipticThetaPrime[2, 1/7 + I/3, 1/8 + I/5], 35]
res = mpf('0.19825296689470982332701283509685662') - \
mpf('0.46038135182282106983251742935250009') * j
result = jtheta(2, z, q, 1)
assert(mpc_ae(result, res))
# Mathematica N[EllipticThetaPrime[3, 1/7 + I/3, 1/8 + I/5], 35]
res = mpf('0.36492498415476212680896699407390026') - \
mpf('0.57743812698666990209897034525640369') * j
result = jtheta(3, z, q, 1)
assert(mpc_ae(result, res))
# Mathematica N[EllipticThetaPrime[4, 1/7 + I/3, 1/8 + I/5], 35]
res = mpf('-0.38936892528126996010818803742007352') + \
mpf('0.66549886179739128256269617407313625') * j
result = jtheta(4, z, q, 1)
assert(mpc_ae(result, res))
for i in range(10):
q = (one*random.random() + j*random.random())/2
# identity in Wittaker, Watson &21.41
a = jtheta(1, 0, q, 1)
b = jtheta(2, 0, q)*jtheta(3, 0, q)*jtheta(4, 0, q)
assert(a.ae(b))
# test higher derivatives
mp.dps = 20
for q,z in [(one/3, one/5), (one/3 + j/8, one/5),
(one/3, one/5 + j/8), (one/3 + j/7, one/5 + j/8)]:
for n in [1, 2, 3, 4]:
r = jtheta(n, z, q, 2)
r1 = diff(lambda zz: jtheta(n, zz, q), z, n=2)
assert r.ae(r1)
r = jtheta(n, z, q, 3)
r1 = diff(lambda zz: jtheta(n, zz, q), z, n=3)
assert r.ae(r1)
# identity in Wittaker, Watson &21.41
q = one/3
z = zero
a = [0]*5
a[1] = jtheta(1, z, q, 3)/jtheta(1, z, q, 1)
for n in [2,3,4]:
a[n] = jtheta(n, z, q, 2)/jtheta(n, z, q)
equality = a[2] + a[3] + a[4] - a[1]
assert(equality.ae(0))
mp.dps = 15
def test_jsn():
"""
Test some special cases of the sn(z, q) function.
"""
mp.dps = 100
# trival case
result = jsn(zero, zero)
assert(result == zero)
# Abramowitz Table 16.5
#
# sn(0, m) = 0
for i in range(10):
qstring = str(random.random())
q = mpf(qstring)
equality = jsn(zero, q)
assert(equality.ae(0))
# Abramowitz Table 16.6.1
#
# sn(z, 0) = sin(z), m == 0
#
# sn(z, 1) = tanh(z), m == 1
#
# It would be nice to test these, but I find that they run
# in to numerical trouble. I'm currently treating as a boundary
# case for sn function.
mp.dps = 25
arg = one/10
#N[JacobiSN[1/10, 2^-100], 25]
res = mpf('0.09983341664682815230681420')
m = ldexp(one, -100)
result = jsn(arg, m)
assert(result.ae(res))
# N[JacobiSN[1/10, 1/10], 25]
res = mpf('0.09981686718599080096451168')
result = jsn(arg, arg)
assert(result.ae(res))
mp.dps = 15
def test_jcn():
"""
Test some special cases of the cn(z, q) function.
"""
mp.dps = 100
# Abramowitz Table 16.5
# cn(0, q) = 1
qstring = str(random.random())
q = mpf(qstring)
cn = jcn(zero, q)
assert(cn.ae(one))
# Abramowitz Table 16.6.2
#
# cn(u, 0) = cos(u), m == 0
#
# cn(u, 1) = sech(z), m == 1
#
# It would be nice to test these, but I find that they run
# in to numerical trouble. I'm currently treating as a boundary
# case for cn function.
mp.dps = 25
arg = one/10
m = ldexp(one, -100)
#N[JacobiCN[1/10, 2^-100], 25]
res = mpf('0.9950041652780257660955620')
result = jcn(arg, m)
assert(result.ae(res))
# N[JacobiCN[1/10, 1/10], 25]
res = mpf('0.9950058256237368748520459')
result = jcn(arg, arg)
assert(result.ae(res))
mp.dps = 15
def test_jdn():
"""
Test some special cases of the dn(z, q) function.
"""
mp.dps = 100
# Abramowitz Table 16.5
# dn(0, q) = 1
mstring = str(random.random())
m = mpf(mstring)
dn = jdn(zero, m)
assert(dn.ae(one))
mp.dps = 25
# N[JacobiDN[1/10, 1/10], 25]
res = mpf('0.9995017055025556219713297')
arg = one/10
result = jdn(arg, arg)
assert(result.ae(res))
mp.dps = 15
def test_sn_cn_dn_identities():
"""
Tests the some of the jacobi elliptic function identities found
on Mathworld. Haven't found in Abramowitz.
"""
mp.dps = 100
N = 5
for i in range(N):
qstring = str(random.random())
q = mpf(qstring)
zstring = str(100*random.random())
z = mpf(zstring)
# MathWorld
# sn(z, q)**2 + cn(z, q)**2 == 1
term1 = jsn(z, q)**2
term2 = jcn(z, q)**2
equality = one - term1 - term2
assert(equality.ae(0))
# MathWorld
# k**2 * sn(z, m)**2 + dn(z, m)**2 == 1
for i in range(N):
mstring = str(random.random())
m = mpf(qstring)
k = m.sqrt()
zstring = str(10*random.random())
z = mpf(zstring)
term1 = k**2 * jsn(z, m)**2
term2 = jdn(z, m)**2
equality = one - term1 - term2
assert(equality.ae(0))
for i in range(N):
mstring = str(random.random())
m = mpf(mstring)
k = m.sqrt()
zstring = str(random.random())
z = mpf(zstring)
# MathWorld
# k**2 * cn(z, m)**2 + (1 - k**2) = dn(z, m)**2
term1 = k**2 * jcn(z, m)**2
term2 = 1 - k**2
term3 = jdn(z, m)**2
equality = term3 - term1 - term2
assert(equality.ae(0))
K = ellipk(k**2)
# Abramowitz Table 16.5
# sn(K, m) = 1; K is K(k), first complete elliptic integral
r = jsn(K, m)
assert(r.ae(one))
# Abramowitz Table 16.5
# cn(K, q) = 0; K is K(k), first complete elliptic integral
equality = jcn(K, m)
assert(equality.ae(0))
# Abramowitz Table 16.6.3
# dn(z, 0) = 1, m == 0
z = m
value = jdn(z, zero)
assert(value.ae(one))
mp.dps = 15
def test_sn_cn_dn_complex():
mp.dps = 30
# N[JacobiSN[1/4 + I/8, 1/3 + I/7], 35] in Mathematica
res = mpf('0.2495674401066275492326652143537') + \
mpf('0.12017344422863833381301051702823') * j
u = mpf(1)/4 + j/8
m = mpf(1)/3 + j/7
r = jsn(u, m)
assert(mpc_ae(r, res))
#N[JacobiCN[1/4 + I/8, 1/3 + I/7], 35]
res = mpf('0.9762691700944007312693721148331') - \
mpf('0.0307203994181623243583169154824')*j
r = jcn(u, m)
#assert r.real.ae(res.real)
#assert r.imag.ae(res.imag)
assert(mpc_ae(r, res))
#N[JacobiDN[1/4 + I/8, 1/3 + I/7], 35]
res = mpf('0.99639490163039577560547478589753039') - \
mpf('0.01346296520008176393432491077244994')*j
r = jdn(u, m)
assert(mpc_ae(r, res))
mp.dps = 15
def test_elliptic_integrals():
# Test cases from Carlson's paper
mp.dps = 15
assert elliprd(0,2,1).ae(1.7972103521033883112)
assert elliprd(2,3,4).ae(0.16510527294261053349)
assert elliprd(j,-j,2).ae(0.65933854154219768919)
assert elliprd(0,j,-j).ae(1.2708196271909686299 + 2.7811120159520578777j)
assert elliprd(0,j-1,j).ae(-1.8577235439239060056 - 0.96193450888838559989j)
assert elliprd(-2-j,-j,-1+j).ae(1.8249027393703805305 - 1.2218475784827035855j)
# extra test cases
assert elliprg(0,0,0) == 0
assert elliprg(0,0,16).ae(2)
assert elliprg(0,16,0).ae(2)
assert elliprg(16,0,0).ae(2)
assert elliprg(1,4,0).ae(1.2110560275684595248036)
assert elliprg(1,0,4).ae(1.2110560275684595248036)
assert elliprg(0,4,1).ae(1.2110560275684595248036)
# should be symmetric -- fixes a bug present in the paper
x,y,z = 1,1j,-1+1j
assert elliprg(x,y,z).ae(0.64139146875812627545 + 0.58085463774808290907j)
assert elliprg(x,z,y).ae(0.64139146875812627545 + 0.58085463774808290907j)
assert elliprg(y,x,z).ae(0.64139146875812627545 + 0.58085463774808290907j)
assert elliprg(y,z,x).ae(0.64139146875812627545 + 0.58085463774808290907j)
assert elliprg(z,x,y).ae(0.64139146875812627545 + 0.58085463774808290907j)
assert elliprg(z,y,x).ae(0.64139146875812627545 + 0.58085463774808290907j)
for n in [5, 15, 30, 60, 100]:
mp.dps = n
assert elliprf(1,2,0).ae('1.3110287771460599052324197949455597068413774757158115814084108519003952935352071251151477664807145467230678763')
assert elliprf(0.5,1,0).ae('1.854074677301371918433850347195260046217598823521766905585928045056021776838119978357271861650371897277771871')
assert elliprf(j,-j,0).ae('1.854074677301371918433850347195260046217598823521766905585928045056021776838119978357271861650371897277771871')
assert elliprf(j-1,j,0).ae(mpc('0.79612586584233913293056938229563057846592264089185680214929401744498956943287031832657642790719940442165621412',
'-1.2138566698364959864300942567386038975419875860741507618279563735753073152507112254567291141460317931258599889'))
assert elliprf(2,3,4).ae('0.58408284167715170669284916892566789240351359699303216166309375305508295130412919665541330837704050454472379308')
assert elliprf(j,-j,2).ae('1.0441445654064360931078658361850779139591660747973017593275012615517220315993723776182276555339288363064476126')
assert elliprf(j-1,j,1-j).ae(mpc('0.93912050218619371196624617169781141161485651998254431830645241993282941057500174238125105410055253623847335313',
'-0.53296252018635269264859303449447908970360344322834582313172115220559316331271520508208025270300138589669326136'))
assert elliprc(0,0.25).ae(+pi)
assert elliprc(2.25,2).ae(+ln2)
assert elliprc(0,j).ae(mpc('1.1107207345395915617539702475151734246536554223439225557713489017391086982748684776438317336911913093408525532',
'-1.1107207345395915617539702475151734246536554223439225557713489017391086982748684776438317336911913093408525532'))
assert elliprc(-j,j).ae(mpc('1.2260849569072198222319655083097718755633725139745941606203839524036426936825652935738621522906572884239069297',
'-0.34471136988767679699935618332997956653521218571295874986708834375026550946053920574015526038040124556716711353'))
assert elliprc(0.25,-2).ae(ln2/3)
assert elliprc(j,-1).ae(mpc('0.77778596920447389875196055840799837589537035343923012237628610795937014001905822029050288316217145443865649819',
'0.1983248499342877364755170948292130095921681309577950696116251029742793455964385947473103628983664877025779304'))
assert elliprj(0,1,2,3).ae('0.77688623778582332014190282640545501102298064276022952731669118325952563819813258230708177398475643634103990878')
assert elliprj(2,3,4,5).ae('0.14297579667156753833233879421985774801466647854232626336218889885463800128817976132826443904216546421431528308')
assert elliprj(2,3,4,-1+j).ae(mpc('0.13613945827770535203521374457913768360237593025944342652613569368333226052158214183059386307242563164036672709',
'-0.38207561624427164249600936454845112611060375760094156571007648297226090050927156176977091273224510621553615189'))
assert elliprj(j,-j,0,2).ae('1.6490011662710884518243257224860232300246792717163891216346170272567376981346412066066050103935109581019055806')
assert elliprj(-1+j,-1-j,1,2).ae('0.94148358841220238083044612133767270187474673547917988681610772381758628963408843935027667916713866133196845063')
assert elliprj(j,-j,0,1-j).ae(mpc('1.8260115229009316249372594065790946657011067182850435297162034335356430755397401849070610280860044610878657501',
'1.2290661908643471500163617732957042849283739403009556715926326841959667290840290081010472716420690899886276961'))
assert elliprj(-1+j,-1-j,1,-3+j).ae(mpc('-0.61127970812028172123588152373622636829986597243716610650831553882054127570542477508023027578037045504958619422',
'-1.0684038390006807880182112972232562745485871763154040245065581157751693730095703406209466903752930797510491155'))
assert elliprj(-1+j,-2-j,-j,-1+j).ae(mpc('1.8249027393703805304622013339009022294368078659619988943515764258335975852685224202567854526307030593012768954',
'-1.2218475784827035854568450371590419833166777535029296025352291308244564398645467465067845461070602841312456831'))
assert elliprg(0,16,16).ae(+pi)
assert elliprg(2,3,4).ae('1.7255030280692277601061148835701141842692457170470456590515892070736643637303053506944907685301315299153040991')
assert elliprg(0,j,-j).ae('0.42360654239698954330324956174109581824072295516347109253028968632986700241706737986160014699730561497106114281')
assert elliprg(j-1,j,0).ae(mpc('0.44660591677018372656731970402124510811555212083508861036067729944477855594654762496407405328607219895053798354',
'0.70768352357515390073102719507612395221369717586839400605901402910893345301718731499237159587077682267374159282'))
assert elliprg(-j,j-1,j).ae(mpc('0.36023392184473309033675652092928695596803358846377334894215349632203382573844427952830064383286995172598964266',
'0.40348623401722113740956336997761033878615232917480045914551915169013722542827052849476969199578321834819903921'))
assert elliprg(0, mpf('0.0796'), 4).ae('1.0284758090288040009838871385180217366569777284430590125081211090574701293154645750017813190805144572673802094')
mp.dps = 15
def test_issue_238():
assert isnan(qfrom(m=nan))
| 24,819 | 36.492447 | 164 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/tests/test_quad.py
|
from mpmath import *
def ae(a, b):
return abs(a-b) < 10**(-mp.dps+5)
def test_basic_integrals():
for prec in [15, 30, 100]:
mp.dps = prec
assert ae(quadts(lambda x: x**3 - 3*x**2, [-2, 4]), -12)
assert ae(quadgl(lambda x: x**3 - 3*x**2, [-2, 4]), -12)
assert ae(quadts(sin, [0, pi]), 2)
assert ae(quadts(sin, [0, 2*pi]), 0)
assert ae(quadts(exp, [-inf, -1]), 1/e)
assert ae(quadts(lambda x: exp(-x), [0, inf]), 1)
assert ae(quadts(lambda x: exp(-x*x), [-inf, inf]), sqrt(pi))
assert ae(quadts(lambda x: 1/(1+x*x), [-1, 1]), pi/2)
assert ae(quadts(lambda x: 1/(1+x*x), [-inf, inf]), pi)
assert ae(quadts(lambda x: 2*sqrt(1-x*x), [-1, 1]), pi)
mp.dps = 15
def test_quad_symmetry():
assert quadts(sin, [-1, 1]) == 0
assert quadgl(sin, [-1, 1]) == 0
def test_quad_infinite_mirror():
# Check mirrored infinite interval
assert ae(quad(lambda x: exp(-x*x), [inf,-inf]), -sqrt(pi))
assert ae(quad(lambda x: exp(x), [0,-inf]), -1)
def test_quadgl_linear():
assert quadgl(lambda x: x, [0, 1], maxdegree=1).ae(0.5)
def test_complex_integration():
assert quadts(lambda x: x, [0, 1+j]).ae(j)
def test_quadosc():
mp.dps = 15
assert quadosc(lambda x: sin(x)/x, [0, inf], period=2*pi).ae(pi/2)
# Double integrals
def test_double_trivial():
assert ae(quadts(lambda x, y: x, [0, 1], [0, 1]), 0.5)
assert ae(quadts(lambda x, y: x, [-1, 1], [-1, 1]), 0.0)
def test_double_1():
assert ae(quadts(lambda x, y: cos(x+y/2), [-pi/2, pi/2], [0, pi]), 4)
def test_double_2():
assert ae(quadts(lambda x, y: (x-1)/((1-x*y)*log(x*y)), [0, 1], [0, 1]), euler)
def test_double_3():
assert ae(quadts(lambda x, y: 1/sqrt(1+x*x+y*y), [-1, 1], [-1, 1]), 4*log(2+sqrt(3))-2*pi/3)
def test_double_4():
assert ae(quadts(lambda x, y: 1/(1-x*x * y*y), [0, 1], [0, 1]), pi**2 / 8)
def test_double_5():
assert ae(quadts(lambda x, y: 1/(1-x*y), [0, 1], [0, 1]), pi**2 / 6)
def test_double_6():
assert ae(quadts(lambda x, y: exp(-(x+y)), [0, inf], [0, inf]), 1)
# fails
def xtest_double_7():
assert ae(quadts(lambda x, y: exp(-x*x-y*y), [-inf, inf], [-inf, inf]), pi)
# Test integrals from "Experimentation in Mathematics" by Borwein,
# Bailey & Girgensohn
def test_expmath_integrals():
for prec in [15, 30, 50]:
mp.dps = prec
assert ae(quadts(lambda x: x/sinh(x), [0, inf]), pi**2 / 4)
assert ae(quadts(lambda x: log(x)**2 / (1+x**2), [0, inf]), pi**3 / 8)
assert ae(quadts(lambda x: (1+x**2)/(1+x**4), [0, inf]), pi/sqrt(2))
assert ae(quadts(lambda x: log(x)/cosh(x)**2, [0, inf]), log(pi)-2*log(2)-euler)
assert ae(quadts(lambda x: log(1+x**3)/(1-x+x**2), [0, inf]), 2*pi*log(3)/sqrt(3))
assert ae(quadts(lambda x: log(x)**2 / (x**2+x+1), [0, 1]), 8*pi**3 / (81*sqrt(3)))
assert ae(quadts(lambda x: log(cos(x))**2, [0, pi/2]), pi/2 * (log(2)**2+pi**2/12))
assert ae(quadts(lambda x: x**2 / sin(x)**2, [0, pi/2]), pi*log(2))
assert ae(quadts(lambda x: x**2/sqrt(exp(x)-1), [0, inf]), 4*pi*(log(2)**2 + pi**2/12))
assert ae(quadts(lambda x: x*exp(-x)*sqrt(1-exp(-2*x)), [0, inf]), pi*(1+2*log(2))/8)
mp.dps = 15
# Do not reach full accuracy
def xtest_expmath_fail():
assert ae(quadts(lambda x: sqrt(tan(x)), [0, pi/2]), pi*sqrt(2)/2)
assert ae(quadts(lambda x: atan(x)/(x*sqrt(1-x**2)), [0, 1]), pi*log(1+sqrt(2))/2)
assert ae(quadts(lambda x: log(1+x**2)/x**2, [0, 1]), pi/2-log(2))
assert ae(quadts(lambda x: x**2/((1+x**4)*sqrt(1-x**4)), [0, 1]), pi/8)
| 3,731 | 40.010989 | 104 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/tests/test_basic_ops.py
|
import mpmath
from mpmath import *
from mpmath.libmp import *
import random
import sys
try:
long = long
except NameError:
long = int
def test_type_compare():
assert mpf(2) == mpc(2,0)
assert mpf(0) == mpc(0)
assert mpf(2) != mpc(2, 0.00001)
assert mpf(2) == 2.0
assert mpf(2) != 3.0
assert mpf(2) == 2
assert mpf(2) != '2.0'
assert mpc(2) != '2.0'
def test_add():
assert mpf(2.5) + mpf(3) == 5.5
assert mpf(2.5) + 3 == 5.5
assert mpf(2.5) + 3.0 == 5.5
assert 3 + mpf(2.5) == 5.5
assert 3.0 + mpf(2.5) == 5.5
assert (3+0j) + mpf(2.5) == 5.5
assert mpc(2.5) + mpf(3) == 5.5
assert mpc(2.5) + 3 == 5.5
assert mpc(2.5) + 3.0 == 5.5
assert mpc(2.5) + (3+0j) == 5.5
assert 3 + mpc(2.5) == 5.5
assert 3.0 + mpc(2.5) == 5.5
assert (3+0j) + mpc(2.5) == 5.5
def test_sub():
assert mpf(2.5) - mpf(3) == -0.5
assert mpf(2.5) - 3 == -0.5
assert mpf(2.5) - 3.0 == -0.5
assert 3 - mpf(2.5) == 0.5
assert 3.0 - mpf(2.5) == 0.5
assert (3+0j) - mpf(2.5) == 0.5
assert mpc(2.5) - mpf(3) == -0.5
assert mpc(2.5) - 3 == -0.5
assert mpc(2.5) - 3.0 == -0.5
assert mpc(2.5) - (3+0j) == -0.5
assert 3 - mpc(2.5) == 0.5
assert 3.0 - mpc(2.5) == 0.5
assert (3+0j) - mpc(2.5) == 0.5
def test_mul():
assert mpf(2.5) * mpf(3) == 7.5
assert mpf(2.5) * 3 == 7.5
assert mpf(2.5) * 3.0 == 7.5
assert 3 * mpf(2.5) == 7.5
assert 3.0 * mpf(2.5) == 7.5
assert (3+0j) * mpf(2.5) == 7.5
assert mpc(2.5) * mpf(3) == 7.5
assert mpc(2.5) * 3 == 7.5
assert mpc(2.5) * 3.0 == 7.5
assert mpc(2.5) * (3+0j) == 7.5
assert 3 * mpc(2.5) == 7.5
assert 3.0 * mpc(2.5) == 7.5
assert (3+0j) * mpc(2.5) == 7.5
def test_div():
assert mpf(6) / mpf(3) == 2.0
assert mpf(6) / 3 == 2.0
assert mpf(6) / 3.0 == 2.0
assert 6 / mpf(3) == 2.0
assert 6.0 / mpf(3) == 2.0
assert (6+0j) / mpf(3.0) == 2.0
assert mpc(6) / mpf(3) == 2.0
assert mpc(6) / 3 == 2.0
assert mpc(6) / 3.0 == 2.0
assert mpc(6) / (3+0j) == 2.0
assert 6 / mpc(3) == 2.0
assert 6.0 / mpc(3) == 2.0
assert (6+0j) / mpc(3) == 2.0
def test_pow():
assert mpf(6) ** mpf(3) == 216.0
assert mpf(6) ** 3 == 216.0
assert mpf(6) ** 3.0 == 216.0
assert 6 ** mpf(3) == 216.0
assert 6.0 ** mpf(3) == 216.0
assert (6+0j) ** mpf(3.0) == 216.0
assert mpc(6) ** mpf(3) == 216.0
assert mpc(6) ** 3 == 216.0
assert mpc(6) ** 3.0 == 216.0
assert mpc(6) ** (3+0j) == 216.0
assert 6 ** mpc(3) == 216.0
assert 6.0 ** mpc(3) == 216.0
assert (6+0j) ** mpc(3) == 216.0
def test_mixed_misc():
assert 1 + mpf(3) == mpf(3) + 1 == 4
assert 1 - mpf(3) == -(mpf(3) - 1) == -2
assert 3 * mpf(2) == mpf(2) * 3 == 6
assert 6 / mpf(2) == mpf(6) / 2 == 3
assert 1.0 + mpf(3) == mpf(3) + 1.0 == 4
assert 1.0 - mpf(3) == -(mpf(3) - 1.0) == -2
assert 3.0 * mpf(2) == mpf(2) * 3.0 == 6
assert 6.0 / mpf(2) == mpf(6) / 2.0 == 3
def test_add_misc():
mp.dps = 15
assert mpf(4) + mpf(-70) == -66
assert mpf(1) + mpf(1.1)/80 == 1 + 1.1/80
assert mpf((1, 10000000000)) + mpf(3) == mpf((1, 10000000000))
assert mpf(3) + mpf((1, 10000000000)) == mpf((1, 10000000000))
assert mpf((1, -10000000000)) + mpf(3) == mpf(3)
assert mpf(3) + mpf((1, -10000000000)) == mpf(3)
assert mpf(1) + 1e-15 != 1
assert mpf(1) + 1e-20 == 1
assert mpf(1.07e-22) + 0 == mpf(1.07e-22)
assert mpf(0) + mpf(1.07e-22) == mpf(1.07e-22)
def test_complex_misc():
# many more tests needed
assert 1 + mpc(2) == 3
assert not mpc(2).ae(2 + 1e-13)
assert mpc(2+1e-15j).ae(2)
def test_complex_zeros():
for a in [0,2]:
for b in [0,3]:
for c in [0,4]:
for d in [0,5]:
assert mpc(a,b)*mpc(c,d) == complex(a,b)*complex(c,d)
def test_hash():
for i in range(-256, 256):
assert hash(mpf(i)) == hash(i)
assert hash(mpf(0.5)) == hash(0.5)
assert hash(mpc(2,3)) == hash(2+3j)
# Check that this doesn't fail
assert hash(inf)
# Check that overflow doesn't assign equal hashes to large numbers
assert hash(mpf('1e1000')) != hash('1e10000')
assert hash(mpc(100,'1e1000')) != hash(mpc(200,'1e1000'))
from mpmath.rational import mpq
assert hash(mp.mpq(1,3))
assert hash(mp.mpq(0,1)) == 0
assert hash(mp.mpq(-1,1)) == hash(-1)
assert hash(mp.mpq(1,1)) == hash(1)
assert hash(mp.mpq(5,1)) == hash(5)
assert hash(mp.mpq(1,2)) == hash(0.5)
if sys.version >= "3.2":
assert hash(mpf(1)*2**2000) == hash(2**2000)
assert hash(mpf(1)/2**2000) == hash(mpq(1,2**2000))
# Advanced rounding test
def test_add_rounding():
mp.dps = 15
a = from_float(1e-50)
assert mpf_sub(mpf_add(fone, a, 53, round_up), fone, 53, round_up) == from_float(2.2204460492503131e-16)
assert mpf_sub(fone, a, 53, round_up) == fone
assert mpf_sub(fone, mpf_sub(fone, a, 53, round_down), 53, round_down) == from_float(1.1102230246251565e-16)
assert mpf_add(fone, a, 53, round_down) == fone
def test_almost_equal():
assert mpf(1.2).ae(mpf(1.20000001), 1e-7)
assert not mpf(1.2).ae(mpf(1.20000001), 1e-9)
assert not mpf(-0.7818314824680298).ae(mpf(-0.774695868667929))
def test_arithmetic_functions():
import operator
ops = [(operator.add, fadd), (operator.sub, fsub), (operator.mul, fmul),
(operator.truediv, fdiv)]
a = mpf(0.27)
b = mpf(1.13)
c = mpc(0.51+2.16j)
d = mpc(1.08-0.99j)
for x in [a,b,c,d]:
for y in [a,b,c,d]:
for op, fop in ops:
if fop is not fdiv:
mp.prec = 200
z0 = op(x,y)
mp.prec = 60
z1 = op(x,y)
mp.prec = 53
z2 = op(x,y)
assert fop(x, y, prec=60) == z1
assert fop(x, y) == z2
if fop is not fdiv:
assert fop(x, y, prec=inf) == z0
assert fop(x, y, dps=inf) == z0
assert fop(x, y, exact=True) == z0
assert fneg(fneg(z1, exact=True), prec=inf) == z1
assert fneg(z1) == -(+z1)
mp.dps = 15
def test_exact_integer_arithmetic():
# XXX: re-fix this so that all operations are tested with all rounding modes
random.seed(0)
for prec in [6, 10, 25, 40, 100, 250, 725]:
for rounding in ['d', 'u', 'f', 'c', 'n']:
mp.dps = prec
M = 10**(prec-2)
M2 = 10**(prec//2-2)
for i in range(10):
a = random.randint(-M, M)
b = random.randint(-M, M)
assert mpf(a, rounding=rounding) == a
assert int(mpf(a, rounding=rounding)) == a
assert int(mpf(str(a), rounding=rounding)) == a
assert mpf(a) + mpf(b) == a + b
assert mpf(a) - mpf(b) == a - b
assert -mpf(a) == -a
a = random.randint(-M2, M2)
b = random.randint(-M2, M2)
assert mpf(a) * mpf(b) == a*b
assert mpf_mul(from_int(a), from_int(b), mp.prec, rounding) == from_int(a*b)
mp.dps = 15
def test_odd_int_bug():
assert to_int(from_int(3), round_nearest) == 3
def test_str_1000_digits():
mp.dps = 1001
# last digit may be wrong
assert str(mpf(2)**0.5)[-10:-1] == '9518488472'[:9]
assert str(pi)[-10:-1] == '2164201989'[:9]
mp.dps = 15
def test_str_10000_digits():
mp.dps = 10001
# last digit may be wrong
assert str(mpf(2)**0.5)[-10:-1] == '5873258351'[:9]
assert str(pi)[-10:-1] == '5256375678'[:9]
mp.dps = 15
def test_monitor():
f = lambda x: x**2
a = []
b = []
g = monitor(f, a.append, b.append)
assert g(3) == 9
assert g(4) == 16
assert a[0] == ((3,), {})
assert b[0] == 9
def test_nint_distance():
assert nint_distance(mpf(-3)) == (-3, -inf)
assert nint_distance(mpc(-3)) == (-3, -inf)
assert nint_distance(mpf(-3.1)) == (-3, -3)
assert nint_distance(mpf(-3.01)) == (-3, -6)
assert nint_distance(mpf(-3.001)) == (-3, -9)
assert nint_distance(mpf(-3.0001)) == (-3, -13)
assert nint_distance(mpf(-2.9)) == (-3, -3)
assert nint_distance(mpf(-2.99)) == (-3, -6)
assert nint_distance(mpf(-2.999)) == (-3, -9)
assert nint_distance(mpf(-2.9999)) == (-3, -13)
assert nint_distance(mpc(-3+0.1j)) == (-3, -3)
assert nint_distance(mpc(-3+0.01j)) == (-3, -6)
assert nint_distance(mpc(-3.1+0.1j)) == (-3, -3)
assert nint_distance(mpc(-3.01+0.01j)) == (-3, -6)
assert nint_distance(mpc(-3.001+0.001j)) == (-3, -9)
assert nint_distance(mpf(0)) == (0, -inf)
assert nint_distance(mpf(0.01)) == (0, -6)
assert nint_distance(mpf('1e-100')) == (0, -332)
def test_floor_ceil_nint_frac():
mp.dps = 15
for n in range(-10,10):
assert floor(n) == n
assert floor(n+0.5) == n
assert ceil(n) == n
assert ceil(n+0.5) == n+1
assert nint(n) == n
# nint rounds to even
if n % 2 == 1:
assert nint(n+0.5) == n+1
else:
assert nint(n+0.5) == n
assert floor(inf) == inf
assert floor(ninf) == ninf
assert isnan(floor(nan))
assert ceil(inf) == inf
assert ceil(ninf) == ninf
assert isnan(ceil(nan))
assert nint(inf) == inf
assert nint(ninf) == ninf
assert isnan(nint(nan))
assert floor(0.1) == 0
assert floor(0.9) == 0
assert floor(-0.1) == -1
assert floor(-0.9) == -1
assert floor(10000000000.1) == 10000000000
assert floor(10000000000.9) == 10000000000
assert floor(-10000000000.1) == -10000000000-1
assert floor(-10000000000.9) == -10000000000-1
assert floor(1e-100) == 0
assert floor(-1e-100) == -1
assert floor(1e100) == 1e100
assert floor(-1e100) == -1e100
assert ceil(0.1) == 1
assert ceil(0.9) == 1
assert ceil(-0.1) == 0
assert ceil(-0.9) == 0
assert ceil(10000000000.1) == 10000000000+1
assert ceil(10000000000.9) == 10000000000+1
assert ceil(-10000000000.1) == -10000000000
assert ceil(-10000000000.9) == -10000000000
assert ceil(1e-100) == 1
assert ceil(-1e-100) == 0
assert ceil(1e100) == 1e100
assert ceil(-1e100) == -1e100
assert nint(0.1) == 0
assert nint(0.9) == 1
assert nint(-0.1) == 0
assert nint(-0.9) == -1
assert nint(10000000000.1) == 10000000000
assert nint(10000000000.9) == 10000000000+1
assert nint(-10000000000.1) == -10000000000
assert nint(-10000000000.9) == -10000000000-1
assert nint(1e-100) == 0
assert nint(-1e-100) == 0
assert nint(1e100) == 1e100
assert nint(-1e100) == -1e100
assert floor(3.2+4.6j) == 3+4j
assert ceil(3.2+4.6j) == 4+5j
assert nint(3.2+4.6j) == 3+5j
for n in range(-10,10):
assert frac(n) == 0
assert frac(0.25) == 0.25
assert frac(1.25) == 0.25
assert frac(2.25) == 0.25
assert frac(-0.25) == 0.75
assert frac(-1.25) == 0.75
assert frac(-2.25) == 0.75
assert frac('1e100000000000000') == 0
u = mpf('1e-100000000000000')
assert frac(u) == u
assert frac(-u) == 1 # rounding!
u = mpf('1e-400')
assert frac(-u, prec=0) == fsub(1, u, exact=True)
assert frac(3.25+4.75j) == 0.25+0.75j
def test_isnan_etc():
from mpmath.rational import mpq
assert isnan(nan) == True
assert isnan(3) == False
assert isnan(mpf(3)) == False
assert isnan(inf) == False
assert isnan(mpc(2,nan)) == True
assert isnan(mpc(2,nan)) == True
assert isnan(mpc(nan,nan)) == True
assert isnan(mpc(2,2)) == False
assert isnan(mpc(nan,inf)) == True
assert isnan(mpc(inf,inf)) == False
assert isnan(mpq((3,2))) == False
assert isnan(mpq((0,1))) == False
assert isinf(inf) == True
assert isinf(-inf) == True
assert isinf(3) == False
assert isinf(nan) == False
assert isinf(3+4j) == False
assert isinf(mpc(inf)) == True
assert isinf(mpc(3,inf)) == True
assert isinf(mpc(inf,3)) == True
assert isinf(mpc(inf,inf)) == True
assert isinf(mpc(nan,inf)) == True
assert isinf(mpc(inf,nan)) == True
assert isinf(mpc(nan,nan)) == False
assert isinf(mpq((3,2))) == False
assert isinf(mpq((0,1))) == False
assert isnormal(3) == True
assert isnormal(3.5) == True
assert isnormal(mpf(3.5)) == True
assert isnormal(0) == False
assert isnormal(mpf(0)) == False
assert isnormal(0.0) == False
assert isnormal(inf) == False
assert isnormal(-inf) == False
assert isnormal(nan) == False
assert isnormal(float(inf)) == False
assert isnormal(mpc(0,0)) == False
assert isnormal(mpc(3,0)) == True
assert isnormal(mpc(0,3)) == True
assert isnormal(mpc(3,3)) == True
assert isnormal(mpc(0,nan)) == False
assert isnormal(mpc(0,inf)) == False
assert isnormal(mpc(3,nan)) == False
assert isnormal(mpc(3,inf)) == False
assert isnormal(mpc(3,-inf)) == False
assert isnormal(mpc(nan,0)) == False
assert isnormal(mpc(inf,0)) == False
assert isnormal(mpc(nan,3)) == False
assert isnormal(mpc(inf,3)) == False
assert isnormal(mpc(inf,nan)) == False
assert isnormal(mpc(nan,inf)) == False
assert isnormal(mpc(nan,nan)) == False
assert isnormal(mpc(inf,inf)) == False
assert isnormal(mpq((3,2))) == True
assert isnormal(mpq((0,1))) == False
assert isint(3) == True
assert isint(0) == True
assert isint(long(3)) == True
assert isint(long(0)) == True
assert isint(mpf(3)) == True
assert isint(mpf(0)) == True
assert isint(mpf(-3)) == True
assert isint(mpf(3.2)) == False
assert isint(3.2) == False
assert isint(nan) == False
assert isint(inf) == False
assert isint(-inf) == False
assert isint(mpc(0)) == True
assert isint(mpc(3)) == True
assert isint(mpc(3.2)) == False
assert isint(mpc(3,inf)) == False
assert isint(mpc(inf)) == False
assert isint(mpc(3,2)) == False
assert isint(mpc(0,2)) == False
assert isint(mpc(3,2),gaussian=True) == True
assert isint(mpc(3,0),gaussian=True) == True
assert isint(mpc(0,3),gaussian=True) == True
assert isint(3+4j) == False
assert isint(3+4j, gaussian=True) == True
assert isint(3+0j) == True
assert isint(mpq((3,2))) == False
assert isint(mpq((3,9))) == False
assert isint(mpq((9,3))) == True
assert isint(mpq((0,4))) == True
assert isint(mpq((1,1))) == True
assert isint(mpq((-1,1))) == True
assert mp.isnpint(0) == True
assert mp.isnpint(1) == False
assert mp.isnpint(-1) == True
assert mp.isnpint(-1.1) == False
assert mp.isnpint(-1.0) == True
assert mp.isnpint(mp.mpq(1,2)) == False
assert mp.isnpint(mp.mpq(-1,2)) == False
assert mp.isnpint(mp.mpq(-3,1)) == True
assert mp.isnpint(mp.mpq(0,1)) == True
assert mp.isnpint(mp.mpq(1,1)) == False
assert mp.isnpint(0+0j) == True
assert mp.isnpint(-1+0j) == True
assert mp.isnpint(-1.1+0j) == False
assert mp.isnpint(-1+0.1j) == False
assert mp.isnpint(0+0.1j) == False
| 15,199 | 33.080717 | 112 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/tests/test_identify.py
|
from mpmath import *
def test_pslq():
mp.dps = 15
assert pslq([3*pi+4*e/7, pi, e, log(2)]) == [7, -21, -4, 0]
assert pslq([4.9999999999999991, 1]) == [1, -5]
assert pslq([2,1]) == [1, -2]
def test_identify():
mp.dps = 20
assert identify(zeta(4), ['log(2)', 'pi**4']) == '((1/90)*pi**4)'
mp.dps = 15
assert identify(exp(5)) == 'exp(5)'
assert identify(exp(4)) == 'exp(4)'
assert identify(log(5)) == 'log(5)'
assert identify(exp(3*pi), ['pi']) == 'exp((3*pi))'
assert identify(3, full=True) == ['3', '3', '1/(1/3)', 'sqrt(9)',
'1/sqrt((1/9))', '(sqrt(12)/2)**2', '1/(sqrt(12)/6)**2']
assert identify(pi+1, {'a':+pi}) == '(1 + 1*a)'
| 692 | 33.65 | 69 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/libmp/libmpf.py
|
"""
Low-level functions for arbitrary-precision floating-point arithmetic.
"""
__docformat__ = 'plaintext'
import math
from bisect import bisect
import sys
# Importing random is slow
#from random import getrandbits
getrandbits = None
from .backend import (MPZ, MPZ_TYPE, MPZ_ZERO, MPZ_ONE, MPZ_TWO, MPZ_FIVE,
BACKEND, STRICT, HASH_MODULUS, HASH_BITS, gmpy, sage, sage_utils)
from .libintmath import (giant_steps,
trailtable, bctable, lshift, rshift, bitcount, trailing,
sqrt_fixed, numeral, isqrt, isqrt_fast, sqrtrem,
bin_to_radix)
# We don't pickle tuples directly for the following reasons:
# 1: pickle uses str() for ints, which is inefficient when they are large
# 2: pickle doesn't work for gmpy mpzs
# Both problems are solved by using hex()
if BACKEND == 'sage':
def to_pickable(x):
sign, man, exp, bc = x
return sign, hex(man), exp, bc
else:
def to_pickable(x):
sign, man, exp, bc = x
return sign, hex(man)[2:], exp, bc
def from_pickable(x):
sign, man, exp, bc = x
return (sign, MPZ(man, 16), exp, bc)
class ComplexResult(ValueError):
pass
try:
intern
except NameError:
intern = lambda x: x
# All supported rounding modes
round_nearest = intern('n')
round_floor = intern('f')
round_ceiling = intern('c')
round_up = intern('u')
round_down = intern('d')
round_fast = round_down
def prec_to_dps(n):
"""Return number of accurate decimals that can be represented
with a precision of n bits."""
return max(1, int(round(int(n)/3.3219280948873626)-1))
def dps_to_prec(n):
"""Return the number of bits required to represent n decimals
accurately."""
return max(1, int(round((int(n)+1)*3.3219280948873626)))
def repr_dps(n):
"""Return the number of decimal digits required to represent
a number with n-bit precision so that it can be uniquely
reconstructed from the representation."""
dps = prec_to_dps(n)
if dps == 15:
return 17
return dps + 3
#----------------------------------------------------------------------------#
# Some commonly needed float values #
#----------------------------------------------------------------------------#
# Regular number format:
# (-1)**sign * mantissa * 2**exponent, plus bitcount of mantissa
fzero = (0, MPZ_ZERO, 0, 0)
fnzero = (1, MPZ_ZERO, 0, 0)
fone = (0, MPZ_ONE, 0, 1)
fnone = (1, MPZ_ONE, 0, 1)
ftwo = (0, MPZ_ONE, 1, 1)
ften = (0, MPZ_FIVE, 1, 3)
fhalf = (0, MPZ_ONE, -1, 1)
# Arbitrary encoding for special numbers: zero mantissa, nonzero exponent
fnan = (0, MPZ_ZERO, -123, -1)
finf = (0, MPZ_ZERO, -456, -2)
fninf = (1, MPZ_ZERO, -789, -3)
# Was 1e1000; this is broken in Python 2.4
math_float_inf = 1e300 * 1e300
#----------------------------------------------------------------------------#
# Rounding #
#----------------------------------------------------------------------------#
# This function can be used to round a mantissa generally. However,
# we will try to do most rounding inline for efficiency.
def round_int(x, n, rnd):
if rnd == round_nearest:
if x >= 0:
t = x >> (n-1)
if t & 1 and ((t & 2) or (x & h_mask[n<300][n])):
return (t>>1)+1
else:
return t>>1
else:
return -round_int(-x, n, rnd)
if rnd == round_floor:
return x >> n
if rnd == round_ceiling:
return -((-x) >> n)
if rnd == round_down:
if x >= 0:
return x >> n
return -((-x) >> n)
if rnd == round_up:
if x >= 0:
return -((-x) >> n)
return x >> n
# These masks are used to pick out segments of numbers to determine
# which direction to round when rounding to nearest.
class h_mask_big:
def __getitem__(self, n):
return (MPZ_ONE<<(n-1))-1
h_mask_small = [0]+[((MPZ_ONE<<(_-1))-1) for _ in range(1, 300)]
h_mask = [h_mask_big(), h_mask_small]
# The >> operator rounds to floor. shifts_down[rnd][sign]
# tells whether this is the right direction to use, or if the
# number should be negated before shifting
shifts_down = {round_floor:(1,0), round_ceiling:(0,1),
round_down:(1,1), round_up:(0,0)}
#----------------------------------------------------------------------------#
# Normalization of raw mpfs #
#----------------------------------------------------------------------------#
# This function is called almost every time an mpf is created.
# It has been optimized accordingly.
def _normalize(sign, man, exp, bc, prec, rnd):
"""
Create a raw mpf tuple with value (-1)**sign * man * 2**exp and
normalized mantissa. The mantissa is rounded in the specified
direction if its size exceeds the precision. Trailing zero bits
are also stripped from the mantissa to ensure that the
representation is canonical.
Conditions on the input:
* The input must represent a regular (finite) number
* The sign bit must be 0 or 1
* The mantissa must be positive
* The exponent must be an integer
* The bitcount must be exact
If these conditions are not met, use from_man_exp, mpf_pos, or any
of the conversion functions to create normalized raw mpf tuples.
"""
if not man:
return fzero
# Cut mantissa down to size if larger than target precision
n = bc - prec
if n > 0:
if rnd == round_nearest:
t = man >> (n-1)
if t & 1 and ((t & 2) or (man & h_mask[n<300][n])):
man = (t>>1)+1
else:
man = t>>1
elif shifts_down[rnd][sign]:
man >>= n
else:
man = -((-man)>>n)
exp += n
bc = prec
# Strip trailing bits
if not man & 1:
t = trailtable[int(man & 255)]
if not t:
while not man & 255:
man >>= 8
exp += 8
bc -= 8
t = trailtable[int(man & 255)]
man >>= t
exp += t
bc -= t
# Bit count can be wrong if the input mantissa was 1 less than
# a power of 2 and got rounded up, thereby adding an extra bit.
# With trailing bits removed, all powers of two have mantissa 1,
# so this is easy to check for.
if man == 1:
bc = 1
return sign, man, exp, bc
def _normalize1(sign, man, exp, bc, prec, rnd):
"""same as normalize, but with the added condition that
man is odd or zero
"""
if not man:
return fzero
if bc <= prec:
return sign, man, exp, bc
n = bc - prec
if rnd == round_nearest:
t = man >> (n-1)
if t & 1 and ((t & 2) or (man & h_mask[n<300][n])):
man = (t>>1)+1
else:
man = t>>1
elif shifts_down[rnd][sign]:
man >>= n
else:
man = -((-man)>>n)
exp += n
bc = prec
# Strip trailing bits
if not man & 1:
t = trailtable[int(man & 255)]
if not t:
while not man & 255:
man >>= 8
exp += 8
bc -= 8
t = trailtable[int(man & 255)]
man >>= t
exp += t
bc -= t
# Bit count can be wrong if the input mantissa was 1 less than
# a power of 2 and got rounded up, thereby adding an extra bit.
# With trailing bits removed, all powers of two have mantissa 1,
# so this is easy to check for.
if man == 1:
bc = 1
return sign, man, exp, bc
try:
_exp_types = (int, long)
except NameError:
_exp_types = (int,)
def strict_normalize(sign, man, exp, bc, prec, rnd):
"""Additional checks on the components of an mpf. Enable tests by setting
the environment variable MPMATH_STRICT to Y."""
assert type(man) == MPZ_TYPE
assert type(bc) in _exp_types
assert type(exp) in _exp_types
assert bc == bitcount(man)
return _normalize(sign, man, exp, bc, prec, rnd)
def strict_normalize1(sign, man, exp, bc, prec, rnd):
"""Additional checks on the components of an mpf. Enable tests by setting
the environment variable MPMATH_STRICT to Y."""
assert type(man) == MPZ_TYPE
assert type(bc) in _exp_types
assert type(exp) in _exp_types
assert bc == bitcount(man)
assert (not man) or (man & 1)
return _normalize1(sign, man, exp, bc, prec, rnd)
if BACKEND == 'gmpy' and '_mpmath_normalize' in dir(gmpy):
_normalize = gmpy._mpmath_normalize
_normalize1 = gmpy._mpmath_normalize
if BACKEND == 'sage':
_normalize = _normalize1 = sage_utils.normalize
if STRICT:
normalize = strict_normalize
normalize1 = strict_normalize1
else:
normalize = _normalize
normalize1 = _normalize1
#----------------------------------------------------------------------------#
# Conversion functions #
#----------------------------------------------------------------------------#
def from_man_exp(man, exp, prec=None, rnd=round_fast):
"""Create raw mpf from (man, exp) pair. The mantissa may be signed.
If no precision is specified, the mantissa is stored exactly."""
man = MPZ(man)
sign = 0
if man < 0:
sign = 1
man = -man
if man < 1024:
bc = bctable[int(man)]
else:
bc = bitcount(man)
if not prec:
if not man:
return fzero
if not man & 1:
if man & 2:
return (sign, man >> 1, exp + 1, bc - 1)
t = trailtable[int(man & 255)]
if not t:
while not man & 255:
man >>= 8
exp += 8
bc -= 8
t = trailtable[int(man & 255)]
man >>= t
exp += t
bc -= t
return (sign, man, exp, bc)
return normalize(sign, man, exp, bc, prec, rnd)
int_cache = dict((n, from_man_exp(n, 0)) for n in range(-10, 257))
if BACKEND == 'gmpy' and '_mpmath_create' in dir(gmpy):
from_man_exp = gmpy._mpmath_create
if BACKEND == 'sage':
from_man_exp = sage_utils.from_man_exp
def from_int(n, prec=0, rnd=round_fast):
"""Create a raw mpf from an integer. If no precision is specified,
the mantissa is stored exactly."""
if not prec:
if n in int_cache:
return int_cache[n]
return from_man_exp(n, 0, prec, rnd)
def to_man_exp(s):
"""Return (man, exp) of a raw mpf. Raise an error if inf/nan."""
sign, man, exp, bc = s
if (not man) and exp:
raise ValueError("mantissa and exponent are undefined for %s" % man)
return man, exp
def to_int(s, rnd=None):
"""Convert a raw mpf to the nearest int. Rounding is done down by
default (same as int(float) in Python), but can be changed. If the
input is inf/nan, an exception is raised."""
sign, man, exp, bc = s
if (not man) and exp:
raise ValueError("cannot convert inf or nan to int")
if exp >= 0:
if sign:
return (-man) << exp
return man << exp
# Make default rounding fast
if not rnd:
if sign:
return -(man >> (-exp))
else:
return man >> (-exp)
if sign:
return round_int(-man, -exp, rnd)
else:
return round_int(man, -exp, rnd)
def mpf_round_int(s, rnd):
sign, man, exp, bc = s
if (not man) and exp:
return s
if exp >= 0:
return s
mag = exp+bc
if mag < 1:
if rnd == round_ceiling:
if sign: return fzero
else: return fone
elif rnd == round_floor:
if sign: return fnone
else: return fzero
elif rnd == round_nearest:
if mag < 0 or man == MPZ_ONE: return fzero
elif sign: return fnone
else: return fone
else:
raise NotImplementedError
return mpf_pos(s, min(bc, mag), rnd)
def mpf_floor(s, prec=0, rnd=round_fast):
v = mpf_round_int(s, round_floor)
if prec:
v = mpf_pos(v, prec, rnd)
return v
def mpf_ceil(s, prec=0, rnd=round_fast):
v = mpf_round_int(s, round_ceiling)
if prec:
v = mpf_pos(v, prec, rnd)
return v
def mpf_nint(s, prec=0, rnd=round_fast):
v = mpf_round_int(s, round_nearest)
if prec:
v = mpf_pos(v, prec, rnd)
return v
def mpf_frac(s, prec=0, rnd=round_fast):
return mpf_sub(s, mpf_floor(s), prec, rnd)
def from_float(x, prec=53, rnd=round_fast):
"""Create a raw mpf from a Python float, rounding if necessary.
If prec >= 53, the result is guaranteed to represent exactly the
same number as the input. If prec is not specified, use prec=53."""
# frexp only raises an exception for nan on some platforms
if x != x:
return fnan
# in Python2.5 math.frexp gives an exception for float infinity
# in Python2.6 it returns (float infinity, 0)
try:
m, e = math.frexp(x)
except:
if x == math_float_inf: return finf
if x == -math_float_inf: return fninf
return fnan
if x == math_float_inf: return finf
if x == -math_float_inf: return fninf
return from_man_exp(int(m*(1<<53)), e-53, prec, rnd)
def to_float(s, strict=False, rnd=round_fast):
"""
Convert a raw mpf to a Python float. The result is exact if the
bitcount of s is <= 53 and no underflow/overflow occurs.
If the number is too large or too small to represent as a regular
float, it will be converted to inf or 0.0. Setting strict=True
forces an OverflowError to be raised instead.
Warning: with a directed rounding mode, the correct nearest representable
floating-point number in the specified direction might not be computed
in case of overflow or (gradual) underflow.
"""
sign, man, exp, bc = s
if not man:
if s == fzero: return 0.0
if s == finf: return math_float_inf
if s == fninf: return -math_float_inf
return math_float_inf/math_float_inf
if bc > 53:
sign, man, exp, bc = normalize1(sign, man, exp, bc, 53, rnd)
if sign:
man = -man
try:
return math.ldexp(man, exp)
except OverflowError:
if strict:
raise
# Overflow to infinity
if exp + bc > 0:
if sign:
return -math_float_inf
else:
return math_float_inf
# Underflow to zero
return 0.0
def from_rational(p, q, prec, rnd=round_fast):
"""Create a raw mpf from a rational number p/q, round if
necessary."""
return mpf_div(from_int(p), from_int(q), prec, rnd)
def to_rational(s):
"""Convert a raw mpf to a rational number. Return integers (p, q)
such that s = p/q exactly."""
sign, man, exp, bc = s
if sign:
man = -man
if bc == -1:
raise ValueError("cannot convert %s to a rational number" % man)
if exp >= 0:
return man * (1<<exp), 1
else:
return man, 1<<(-exp)
def to_fixed(s, prec):
"""Convert a raw mpf to a fixed-point big integer"""
sign, man, exp, bc = s
offset = exp + prec
if sign:
if offset >= 0: return (-man) << offset
else: return (-man) >> (-offset)
else:
if offset >= 0: return man << offset
else: return man >> (-offset)
##############################################################################
##############################################################################
#----------------------------------------------------------------------------#
# Arithmetic operations, etc. #
#----------------------------------------------------------------------------#
def mpf_rand(prec):
"""Return a raw mpf chosen randomly from [0, 1), with prec bits
in the mantissa."""
global getrandbits
if not getrandbits:
import random
getrandbits = random.getrandbits
return from_man_exp(getrandbits(prec), -prec, prec, round_floor)
def mpf_eq(s, t):
"""Test equality of two raw mpfs. This is simply tuple comparison
unless either number is nan, in which case the result is False."""
if not s[1] or not t[1]:
if s == fnan or t == fnan:
return False
return s == t
def mpf_hash(s):
# Duplicate the new hash algorithm introduces in Python 3.2.
if sys.version >= "3.2":
ssign, sman, sexp, sbc = s
# Handle special numbers
if not sman:
if s == fnan: return sys.hash_info.nan
if s == finf: return sys.hash_info.inf
if s == fninf: return -sys.hash_info.inf
h = sman % HASH_MODULUS
if sexp >= 0:
sexp = sexp % HASH_BITS
else:
sexp = HASH_BITS - 1 - ((-1 - sexp) % HASH_BITS)
h = (h << sexp) % HASH_MODULUS
if ssign: h = -h
if h == -1: h == -2
return int(h)
else:
try:
# Try to be compatible with hash values for floats and ints
return hash(to_float(s, strict=1))
except OverflowError:
# We must unfortunately sacrifice compatibility with ints here.
# We could do hash(man << exp) when the exponent is positive, but
# this would cause unreasonable inefficiency for large numbers.
return hash(s)
def mpf_cmp(s, t):
"""Compare the raw mpfs s and t. Return -1 if s < t, 0 if s == t,
and 1 if s > t. (Same convention as Python's cmp() function.)"""
# In principle, a comparison amounts to determining the sign of s-t.
# A full subtraction is relatively slow, however, so we first try to
# look at the components.
ssign, sman, sexp, sbc = s
tsign, tman, texp, tbc = t
# Handle zeros and special numbers
if not sman or not tman:
if s == fzero: return -mpf_sign(t)
if t == fzero: return mpf_sign(s)
if s == t: return 0
# Follow same convention as Python's cmp for float nan
if t == fnan: return 1
if s == finf: return 1
if t == fninf: return 1
return -1
# Different sides of zero
if ssign != tsign:
if not ssign: return 1
return -1
# This reduces to direct integer comparison
if sexp == texp:
if sman == tman:
return 0
if sman > tman:
if ssign: return -1
else: return 1
else:
if ssign: return 1
else: return -1
# Check position of the highest set bit in each number. If
# different, there is certainly an inequality.
a = sbc + sexp
b = tbc + texp
if ssign:
if a < b: return 1
if a > b: return -1
else:
if a < b: return -1
if a > b: return 1
# Both numbers have the same highest bit. Subtract to find
# how the lower bits compare.
delta = mpf_sub(s, t, 5, round_floor)
if delta[0]:
return -1
return 1
def mpf_lt(s, t):
if s == fnan or t == fnan:
return False
return mpf_cmp(s, t) < 0
def mpf_le(s, t):
if s == fnan or t == fnan:
return False
return mpf_cmp(s, t) <= 0
def mpf_gt(s, t):
if s == fnan or t == fnan:
return False
return mpf_cmp(s, t) > 0
def mpf_ge(s, t):
if s == fnan or t == fnan:
return False
return mpf_cmp(s, t) >= 0
def mpf_min_max(seq):
min = max = seq[0]
for x in seq[1:]:
if mpf_lt(x, min): min = x
if mpf_gt(x, max): max = x
return min, max
def mpf_pos(s, prec=0, rnd=round_fast):
"""Calculate 0+s for a raw mpf (i.e., just round s to the specified
precision)."""
if prec:
sign, man, exp, bc = s
if (not man) and exp:
return s
return normalize1(sign, man, exp, bc, prec, rnd)
return s
def mpf_neg(s, prec=None, rnd=round_fast):
"""Negate a raw mpf (return -s), rounding the result to the
specified precision. The prec argument can be omitted to do the
operation exactly."""
sign, man, exp, bc = s
if not man:
if exp:
if s == finf: return fninf
if s == fninf: return finf
return s
if not prec:
return (1-sign, man, exp, bc)
return normalize1(1-sign, man, exp, bc, prec, rnd)
def mpf_abs(s, prec=None, rnd=round_fast):
"""Return abs(s) of the raw mpf s, rounded to the specified
precision. The prec argument can be omitted to generate an
exact result."""
sign, man, exp, bc = s
if (not man) and exp:
if s == fninf:
return finf
return s
if not prec:
if sign:
return (0, man, exp, bc)
return s
return normalize1(0, man, exp, bc, prec, rnd)
def mpf_sign(s):
"""Return -1, 0, or 1 (as a Python int, not a raw mpf) depending on
whether s is negative, zero, or positive. (Nan is taken to give 0.)"""
sign, man, exp, bc = s
if not man:
if s == finf: return 1
if s == fninf: return -1
return 0
return (-1) ** sign
def mpf_add(s, t, prec=0, rnd=round_fast, _sub=0):
"""
Add the two raw mpf values s and t.
With prec=0, no rounding is performed. Note that this can
produce a very large mantissa (potentially too large to fit
in memory) if exponents are far apart.
"""
ssign, sman, sexp, sbc = s
tsign, tman, texp, tbc = t
tsign ^= _sub
# Standard case: two nonzero, regular numbers
if sman and tman:
offset = sexp - texp
if offset:
if offset > 0:
# Outside precision range; only need to perturb
if offset > 100 and prec:
delta = sbc + sexp - tbc - texp
if delta > prec + 4:
offset = prec + 4
sman <<= offset
if tsign == ssign: sman += 1
else: sman -= 1
return normalize1(ssign, sman, sexp-offset,
bitcount(sman), prec, rnd)
# Add
if ssign == tsign:
man = tman + (sman << offset)
# Subtract
else:
if ssign: man = tman - (sman << offset)
else: man = (sman << offset) - tman
if man >= 0:
ssign = 0
else:
man = -man
ssign = 1
bc = bitcount(man)
return normalize1(ssign, man, texp, bc, prec or bc, rnd)
elif offset < 0:
# Outside precision range; only need to perturb
if offset < -100 and prec:
delta = tbc + texp - sbc - sexp
if delta > prec + 4:
offset = prec + 4
tman <<= offset
if ssign == tsign: tman += 1
else: tman -= 1
return normalize1(tsign, tman, texp-offset,
bitcount(tman), prec, rnd)
# Add
if ssign == tsign:
man = sman + (tman << -offset)
# Subtract
else:
if tsign: man = sman - (tman << -offset)
else: man = (tman << -offset) - sman
if man >= 0:
ssign = 0
else:
man = -man
ssign = 1
bc = bitcount(man)
return normalize1(ssign, man, sexp, bc, prec or bc, rnd)
# Equal exponents; no shifting necessary
if ssign == tsign:
man = tman + sman
else:
if ssign: man = tman - sman
else: man = sman - tman
if man >= 0:
ssign = 0
else:
man = -man
ssign = 1
bc = bitcount(man)
return normalize(ssign, man, texp, bc, prec or bc, rnd)
# Handle zeros and special numbers
if _sub:
t = mpf_neg(t)
if not sman:
if sexp:
if s == t or tman or not texp:
return s
return fnan
if tman:
return normalize1(tsign, tman, texp, tbc, prec or tbc, rnd)
return t
if texp:
return t
if sman:
return normalize1(ssign, sman, sexp, sbc, prec or sbc, rnd)
return s
def mpf_sub(s, t, prec=0, rnd=round_fast):
"""Return the difference of two raw mpfs, s-t. This function is
simply a wrapper of mpf_add that changes the sign of t."""
return mpf_add(s, t, prec, rnd, 1)
def mpf_sum(xs, prec=0, rnd=round_fast, absolute=False):
"""
Sum a list of mpf values efficiently and accurately
(typically no temporary roundoff occurs). If prec=0,
the final result will not be rounded either.
There may be roundoff error or cancellation if extremely
large exponent differences occur.
With absolute=True, sums the absolute values.
"""
man = 0
exp = 0
max_extra_prec = prec*2 or 1000000 # XXX
special = None
for x in xs:
xsign, xman, xexp, xbc = x
if xman:
if xsign and not absolute:
xman = -xman
delta = xexp - exp
if xexp >= exp:
# x much larger than existing sum?
# first: quick test
if (delta > max_extra_prec) and \
((not man) or delta-bitcount(abs(man)) > max_extra_prec):
man = xman
exp = xexp
else:
man += (xman << delta)
else:
delta = -delta
# x much smaller than existing sum?
if delta-xbc > max_extra_prec:
if not man:
man, exp = xman, xexp
else:
man = (man << delta) + xman
exp = xexp
elif xexp:
if absolute:
x = mpf_abs(x)
special = mpf_add(special or fzero, x, 1)
# Will be inf or nan
if special:
return special
return from_man_exp(man, exp, prec, rnd)
def gmpy_mpf_mul(s, t, prec=0, rnd=round_fast):
"""Multiply two raw mpfs"""
ssign, sman, sexp, sbc = s
tsign, tman, texp, tbc = t
sign = ssign ^ tsign
man = sman*tman
if man:
bc = bitcount(man)
if prec:
return normalize1(sign, man, sexp+texp, bc, prec, rnd)
else:
return (sign, man, sexp+texp, bc)
s_special = (not sman) and sexp
t_special = (not tman) and texp
if not s_special and not t_special:
return fzero
if fnan in (s, t): return fnan
if (not tman) and texp: s, t = t, s
if t == fzero: return fnan
return {1:finf, -1:fninf}[mpf_sign(s) * mpf_sign(t)]
def gmpy_mpf_mul_int(s, n, prec, rnd=round_fast):
"""Multiply by a Python integer."""
sign, man, exp, bc = s
if not man:
return mpf_mul(s, from_int(n), prec, rnd)
if not n:
return fzero
if n < 0:
sign ^= 1
n = -n
man *= n
return normalize(sign, man, exp, bitcount(man), prec, rnd)
def python_mpf_mul(s, t, prec=0, rnd=round_fast):
"""Multiply two raw mpfs"""
ssign, sman, sexp, sbc = s
tsign, tman, texp, tbc = t
sign = ssign ^ tsign
man = sman*tman
if man:
bc = sbc + tbc - 1
bc += int(man>>bc)
if prec:
return normalize1(sign, man, sexp+texp, bc, prec, rnd)
else:
return (sign, man, sexp+texp, bc)
s_special = (not sman) and sexp
t_special = (not tman) and texp
if not s_special and not t_special:
return fzero
if fnan in (s, t): return fnan
if (not tman) and texp: s, t = t, s
if t == fzero: return fnan
return {1:finf, -1:fninf}[mpf_sign(s) * mpf_sign(t)]
def python_mpf_mul_int(s, n, prec, rnd=round_fast):
"""Multiply by a Python integer."""
sign, man, exp, bc = s
if not man:
return mpf_mul(s, from_int(n), prec, rnd)
if not n:
return fzero
if n < 0:
sign ^= 1
n = -n
man *= n
# Generally n will be small
if n < 1024:
bc += bctable[int(n)] - 1
else:
bc += bitcount(n) - 1
bc += int(man>>bc)
return normalize(sign, man, exp, bc, prec, rnd)
if BACKEND == 'gmpy':
mpf_mul = gmpy_mpf_mul
mpf_mul_int = gmpy_mpf_mul_int
else:
mpf_mul = python_mpf_mul
mpf_mul_int = python_mpf_mul_int
def mpf_shift(s, n):
"""Quickly multiply the raw mpf s by 2**n without rounding."""
sign, man, exp, bc = s
if not man:
return s
return sign, man, exp+n, bc
def mpf_frexp(x):
"""Convert x = y*2**n to (y, n) with abs(y) in [0.5, 1) if nonzero"""
sign, man, exp, bc = x
if not man:
if x == fzero:
return (fzero, 0)
else:
raise ValueError
return mpf_shift(x, -bc-exp), bc+exp
def mpf_div(s, t, prec, rnd=round_fast):
"""Floating-point division"""
ssign, sman, sexp, sbc = s
tsign, tman, texp, tbc = t
if not sman or not tman:
if s == fzero:
if t == fzero: raise ZeroDivisionError
if t == fnan: return fnan
return fzero
if t == fzero:
raise ZeroDivisionError
s_special = (not sman) and sexp
t_special = (not tman) and texp
if s_special and t_special:
return fnan
if s == fnan or t == fnan:
return fnan
if not t_special:
if t == fzero:
return fnan
return {1:finf, -1:fninf}[mpf_sign(s) * mpf_sign(t)]
return fzero
sign = ssign ^ tsign
if tman == 1:
return normalize1(sign, sman, sexp-texp, sbc, prec, rnd)
# Same strategy as for addition: if there is a remainder, perturb
# the result a few bits outside the precision range before rounding
extra = prec - sbc + tbc + 5
if extra < 5:
extra = 5
quot, rem = divmod(sman<<extra, tman)
if rem:
quot = (quot<<1) + 1
extra += 1
return normalize1(sign, quot, sexp-texp-extra, bitcount(quot), prec, rnd)
return normalize(sign, quot, sexp-texp-extra, bitcount(quot), prec, rnd)
def mpf_rdiv_int(n, t, prec, rnd=round_fast):
"""Floating-point division n/t with a Python integer as numerator"""
sign, man, exp, bc = t
if not n or not man:
return mpf_div(from_int(n), t, prec, rnd)
if n < 0:
sign ^= 1
n = -n
extra = prec + bc + 5
quot, rem = divmod(n<<extra, man)
if rem:
quot = (quot<<1) + 1
extra += 1
return normalize1(sign, quot, -exp-extra, bitcount(quot), prec, rnd)
return normalize(sign, quot, -exp-extra, bitcount(quot), prec, rnd)
def mpf_mod(s, t, prec, rnd=round_fast):
ssign, sman, sexp, sbc = s
tsign, tman, texp, tbc = t
if ((not sman) and sexp) or ((not tman) and texp):
return fnan
# Important special case: do nothing if t is larger
if ssign == tsign and texp > sexp+sbc:
return s
# Another important special case: this allows us to do e.g. x % 1.0
# to find the fractional part of x, and it will work when x is huge.
if tman == 1 and sexp > texp+tbc:
return fzero
base = min(sexp, texp)
sman = (-1)**ssign * sman
tman = (-1)**tsign * tman
man = (sman << (sexp-base)) % (tman << (texp-base))
if man >= 0:
sign = 0
else:
man = -man
sign = 1
return normalize(sign, man, base, bitcount(man), prec, rnd)
reciprocal_rnd = {
round_down : round_up,
round_up : round_down,
round_floor : round_ceiling,
round_ceiling : round_floor,
round_nearest : round_nearest
}
negative_rnd = {
round_down : round_down,
round_up : round_up,
round_floor : round_ceiling,
round_ceiling : round_floor,
round_nearest : round_nearest
}
def mpf_pow_int(s, n, prec, rnd=round_fast):
"""Compute s**n, where s is a raw mpf and n is a Python integer."""
sign, man, exp, bc = s
if (not man) and exp:
if s == finf:
if n > 0: return s
if n == 0: return fnan
return fzero
if s == fninf:
if n > 0: return [finf, fninf][n & 1]
if n == 0: return fnan
return fzero
return fnan
n = int(n)
if n == 0: return fone
if n == 1: return mpf_pos(s, prec, rnd)
if n == 2:
_, man, exp, bc = s
if not man:
return fzero
man = man*man
if man == 1:
return (0, MPZ_ONE, exp+exp, 1)
bc = bc + bc - 2
bc += bctable[int(man>>bc)]
return normalize1(0, man, exp+exp, bc, prec, rnd)
if n == -1: return mpf_div(fone, s, prec, rnd)
if n < 0:
inverse = mpf_pow_int(s, -n, prec+5, reciprocal_rnd[rnd])
return mpf_div(fone, inverse, prec, rnd)
result_sign = sign & n
# Use exact integer power when the exact mantissa is small
if man == 1:
return (result_sign, MPZ_ONE, exp*n, 1)
if bc*n < 1000:
man **= n
return normalize1(result_sign, man, exp*n, bitcount(man), prec, rnd)
# Use directed rounding all the way through to maintain rigorous
# bounds for interval arithmetic
rounds_down = (rnd == round_nearest) or \
shifts_down[rnd][result_sign]
# Now we perform binary exponentiation. Need to estimate precision
# to avoid rounding errors from temporary operations. Roughly log_2(n)
# operations are performed.
workprec = prec + 4*bitcount(n) + 4
_, pm, pe, pbc = fone
while 1:
if n & 1:
pm = pm*man
pe = pe+exp
pbc += bc - 2
pbc = pbc + bctable[int(pm >> pbc)]
if pbc > workprec:
if rounds_down:
pm = pm >> (pbc-workprec)
else:
pm = -((-pm) >> (pbc-workprec))
pe += pbc - workprec
pbc = workprec
n -= 1
if not n:
break
man = man*man
exp = exp+exp
bc = bc + bc - 2
bc = bc + bctable[int(man >> bc)]
if bc > workprec:
if rounds_down:
man = man >> (bc-workprec)
else:
man = -((-man) >> (bc-workprec))
exp += bc - workprec
bc = workprec
n = n // 2
return normalize(result_sign, pm, pe, pbc, prec, rnd)
def mpf_perturb(x, eps_sign, prec, rnd):
"""
For nonzero x, calculate x + eps with directed rounding, where
eps < prec relatively and eps has the given sign (0 for
positive, 1 for negative).
With rounding to nearest, this is taken to simply normalize
x to the given precision.
"""
if rnd == round_nearest:
return mpf_pos(x, prec, rnd)
sign, man, exp, bc = x
eps = (eps_sign, MPZ_ONE, exp+bc-prec-1, 1)
if sign:
away = (rnd in (round_down, round_ceiling)) ^ eps_sign
else:
away = (rnd in (round_up, round_ceiling)) ^ eps_sign
if away:
return mpf_add(x, eps, prec, rnd)
else:
return mpf_pos(x, prec, rnd)
#----------------------------------------------------------------------------#
# Radix conversion #
#----------------------------------------------------------------------------#
def to_digits_exp(s, dps):
"""Helper function for representing the floating-point number s as
a decimal with dps digits. Returns (sign, string, exponent) where
sign is '' or '-', string is the digit string, and exponent is
the decimal exponent as an int.
If inexact, the decimal representation is rounded toward zero."""
# Extract sign first so it doesn't mess up the string digit count
if s[0]:
sign = '-'
s = mpf_neg(s)
else:
sign = ''
_sign, man, exp, bc = s
if not man:
return '', '0', 0
bitprec = int(dps * math.log(10,2)) + 10
# Cut down to size
# TODO: account for precision when doing this
exp_from_1 = exp + bc
if abs(exp_from_1) > 3500:
from .libelefun import mpf_ln2, mpf_ln10
# Set b = int(exp * log(2)/log(10))
# If exp is huge, we must use high-precision arithmetic to
# find the nearest power of ten
expprec = bitcount(abs(exp)) + 5
tmp = from_int(exp)
tmp = mpf_mul(tmp, mpf_ln2(expprec))
tmp = mpf_div(tmp, mpf_ln10(expprec), expprec)
b = to_int(tmp)
s = mpf_div(s, mpf_pow_int(ften, b, bitprec), bitprec)
_sign, man, exp, bc = s
exponent = b
else:
exponent = 0
# First, calculate mantissa digits by converting to a binary
# fixed-point number and then converting that number to
# a decimal fixed-point number.
fixprec = max(bitprec - exp - bc, 0)
fixdps = int(fixprec / math.log(10,2) + 0.5)
sf = to_fixed(s, fixprec)
sd = bin_to_radix(sf, fixprec, 10, fixdps)
digits = numeral(sd, base=10, size=dps)
exponent += len(digits) - fixdps - 1
return sign, digits, exponent
def to_str(s, dps, strip_zeros=True, min_fixed=None, max_fixed=None,
show_zero_exponent=False):
"""
Convert a raw mpf to a decimal floating-point literal with at
most `dps` decimal digits in the mantissa (not counting extra zeros
that may be inserted for visual purposes).
The number will be printed in fixed-point format if the position
of the leading digit is strictly between min_fixed
(default = min(-dps/3,-5)) and max_fixed (default = dps).
To force fixed-point format always, set min_fixed = -inf,
max_fixed = +inf. To force floating-point format, set
min_fixed >= max_fixed.
The literal is formatted so that it can be parsed back to a number
by to_str, float() or Decimal().
"""
# Special numbers
if not s[1]:
if s == fzero:
if dps: t = '0.0'
else: t = '.0'
if show_zero_exponent:
t += 'e+0'
return t
if s == finf: return '+inf'
if s == fninf: return '-inf'
if s == fnan: return 'nan'
raise ValueError
if min_fixed is None: min_fixed = min(-(dps//3), -5)
if max_fixed is None: max_fixed = dps
# to_digits_exp rounds to floor.
# This sometimes kills some instances of "...00001"
sign, digits, exponent = to_digits_exp(s, dps+3)
# No digits: show only .0; round exponent to nearest
if not dps:
if digits[0] in '56789':
exponent += 1
digits = ".0"
else:
# Rounding up kills some instances of "...99999"
if len(digits) > dps and digits[dps] in '56789' and \
(dps < 500 or digits[dps-4:dps] == '9999'):
digits2 = str(int(digits[:dps]) + 1)
if len(digits2) > dps:
digits2 = digits2[:dps]
exponent += 1
digits = digits2
else:
digits = digits[:dps]
# Prettify numbers close to unit magnitude
if min_fixed < exponent < max_fixed:
if exponent < 0:
digits = ("0"*int(-exponent)) + digits
split = 1
else:
split = exponent + 1
if split > dps:
digits += "0"*(split-dps)
exponent = 0
else:
split = 1
digits = (digits[:split] + "." + digits[split:])
if strip_zeros:
# Clean up trailing zeros
digits = digits.rstrip('0')
if digits[-1] == ".":
digits += "0"
if exponent == 0 and dps and not show_zero_exponent: return sign + digits
if exponent >= 0: return sign + digits + "e+" + str(exponent)
if exponent < 0: return sign + digits + "e" + str(exponent)
def str_to_man_exp(x, base=10):
"""Helper function for from_str."""
# Verify that the input is a valid float literal
float(x)
# Split into mantissa, exponent
x = x.lower()
parts = x.split('e')
if len(parts) == 1:
exp = 0
else: # == 2
x = parts[0]
exp = int(parts[1])
# Look for radix point in mantissa
parts = x.split('.')
if len(parts) == 2:
a, b = parts[0], parts[1].rstrip('0')
exp -= len(b)
x = a + b
x = MPZ(int(x, base))
return x, exp
special_str = {'inf':finf, '+inf':finf, '-inf':fninf, 'nan':fnan}
def from_str(x, prec, rnd=round_fast):
"""Create a raw mpf from a decimal literal, rounding in the
specified direction if the input number cannot be represented
exactly as a binary floating-point number with the given number of
bits. The literal syntax accepted is the same as for Python
floats.
TODO: the rounding does not work properly for large exponents.
"""
x = x.strip()
if x in special_str:
return special_str[x]
if '/' in x:
p, q = x.split('/')
return from_rational(int(p), int(q), prec, rnd)
man, exp = str_to_man_exp(x, base=10)
# XXX: appropriate cutoffs & track direction
# note no factors of 5
if abs(exp) > 400:
s = from_int(man, prec+10)
s = mpf_mul(s, mpf_pow_int(ften, exp, prec+10), prec, rnd)
else:
if exp >= 0:
s = from_int(man * 10**exp, prec, rnd)
else:
s = from_rational(man, 10**-exp, prec, rnd)
return s
# Binary string conversion. These are currently mainly used for debugging
# and could use some improvement in the future
def from_bstr(x):
man, exp = str_to_man_exp(x, base=2)
man = MPZ(man)
sign = 0
if man < 0:
man = -man
sign = 1
bc = bitcount(man)
return normalize(sign, man, exp, bc, bc, round_floor)
def to_bstr(x):
sign, man, exp, bc = x
return ['','-'][sign] + numeral(man, size=bitcount(man), base=2) + ("e%i" % exp)
#----------------------------------------------------------------------------#
# Square roots #
#----------------------------------------------------------------------------#
def mpf_sqrt(s, prec, rnd=round_fast):
"""
Compute the square root of a nonnegative mpf value. The
result is correctly rounded.
"""
sign, man, exp, bc = s
if sign:
raise ComplexResult("square root of a negative number")
if not man:
return s
if exp & 1:
exp -= 1
man <<= 1
bc += 1
elif man == 1:
return normalize1(sign, man, exp//2, bc, prec, rnd)
shift = max(4, 2*prec-bc+4)
shift += shift & 1
if rnd in 'fd':
man = isqrt(man<<shift)
else:
man, rem = sqrtrem(man<<shift)
# Perturb up
if rem:
man = (man<<1)+1
shift += 2
return from_man_exp(man, (exp-shift)//2, prec, rnd)
def mpf_hypot(x, y, prec, rnd=round_fast):
"""Compute the Euclidean norm sqrt(x**2 + y**2) of two raw mpfs
x and y."""
if y == fzero: return mpf_abs(x, prec, rnd)
if x == fzero: return mpf_abs(y, prec, rnd)
hypot2 = mpf_add(mpf_mul(x,x), mpf_mul(y,y), prec+4)
return mpf_sqrt(hypot2, prec, rnd)
if BACKEND == 'sage':
try:
import sage.libs.mpmath.ext_libmp as ext_lib
mpf_add = ext_lib.mpf_add
mpf_sub = ext_lib.mpf_sub
mpf_mul = ext_lib.mpf_mul
mpf_div = ext_lib.mpf_div
mpf_sqrt = ext_lib.mpf_sqrt
except ImportError:
pass
| 43,833 | 30.626263 | 84 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/libmp/gammazeta.py
|
"""
-----------------------------------------------------------------------
This module implements gamma- and zeta-related functions:
* Bernoulli numbers
* Factorials
* The gamma function
* Polygamma functions
* Harmonic numbers
* The Riemann zeta function
* Constants related to these functions
-----------------------------------------------------------------------
"""
import math
import sys
from .backend import xrange
from .backend import MPZ, MPZ_ZERO, MPZ_ONE, MPZ_THREE, gmpy
from .libintmath import list_primes, ifac, ifac2, moebius
from .libmpf import (\
round_floor, round_ceiling, round_down, round_up,
round_nearest, round_fast,
lshift, sqrt_fixed, isqrt_fast,
fzero, fone, fnone, fhalf, ftwo, finf, fninf, fnan,
from_int, to_int, to_fixed, from_man_exp, from_rational,
mpf_pos, mpf_neg, mpf_abs, mpf_add, mpf_sub,
mpf_mul, mpf_mul_int, mpf_div, mpf_sqrt, mpf_pow_int,
mpf_rdiv_int,
mpf_perturb, mpf_le, mpf_lt, mpf_gt, mpf_shift,
negative_rnd, reciprocal_rnd,
bitcount, to_float, mpf_floor, mpf_sign, ComplexResult
)
from .libelefun import (\
constant_memo,
def_mpf_constant,
mpf_pi, pi_fixed, ln2_fixed, log_int_fixed, mpf_ln2,
mpf_exp, mpf_log, mpf_pow, mpf_cosh,
mpf_cos_sin, mpf_cosh_sinh, mpf_cos_sin_pi, mpf_cos_pi, mpf_sin_pi,
ln_sqrt2pi_fixed, mpf_ln_sqrt2pi, sqrtpi_fixed, mpf_sqrtpi,
cos_sin_fixed, exp_fixed
)
from .libmpc import (\
mpc_zero, mpc_one, mpc_half, mpc_two,
mpc_abs, mpc_shift, mpc_pos, mpc_neg,
mpc_add, mpc_sub, mpc_mul, mpc_div,
mpc_add_mpf, mpc_mul_mpf, mpc_div_mpf, mpc_mpf_div,
mpc_mul_int, mpc_pow_int,
mpc_log, mpc_exp, mpc_pow,
mpc_cos_pi, mpc_sin_pi,
mpc_reciprocal, mpc_square,
mpc_sub_mpf
)
# Catalan's constant is computed using Lupas's rapidly convergent series
# (listed on http://mathworld.wolfram.com/CatalansConstant.html)
# oo
# ___ n-1 8n 2 3 2
# 1 \ (-1) 2 (40n - 24n + 3) [(2n)!] (n!)
# K = --- ) -----------------------------------------
# 64 /___ 3 2
# n (2n-1) [(4n)!]
# n = 1
@constant_memo
def catalan_fixed(prec):
prec = prec + 20
a = one = MPZ_ONE << prec
s, t, n = 0, 1, 1
while t:
a *= 32 * n**3 * (2*n-1)
a //= (3-16*n+16*n**2)**2
t = a * (-1)**(n-1) * (40*n**2-24*n+3) // (n**3 * (2*n-1))
s += t
n += 1
return s >> (20 + 6)
# Khinchin's constant is relatively difficult to compute. Here
# we use the rational zeta series
# oo 2*n-1
# ___ ___
# \ ` zeta(2*n)-1 \ ` (-1)^(k+1)
# log(K)*log(2) = ) ------------ ) ----------
# /___. n /___. k
# n = 1 k = 1
# which adds half a digit per term. The essential trick for achieving
# reasonable efficiency is to recycle both the values of the zeta
# function (essentially Bernoulli numbers) and the partial terms of
# the inner sum.
# An alternative might be to use K = 2*exp[1/log(2) X] where
# / 1 1 [ pi*x*(1-x^2) ]
# X = | ------ log [ ------------ ].
# / 0 x(1+x) [ sin(pi*x) ]
# and integrate numerically. In practice, this seems to be slightly
# slower than the zeta series at high precision.
@constant_memo
def khinchin_fixed(prec):
wp = int(prec + prec**0.5 + 15)
s = MPZ_ZERO
fac = from_int(4)
t = ONE = MPZ_ONE << wp
pi = mpf_pi(wp)
pipow = twopi2 = mpf_shift(mpf_mul(pi, pi, wp), 2)
n = 1
while 1:
zeta2n = mpf_abs(mpf_bernoulli(2*n, wp))
zeta2n = mpf_mul(zeta2n, pipow, wp)
zeta2n = mpf_div(zeta2n, fac, wp)
zeta2n = to_fixed(zeta2n, wp)
term = (((zeta2n - ONE) * t) // n) >> wp
if term < 100:
break
#if not n % 10:
# print n, math.log(int(abs(term)))
s += term
t += ONE//(2*n+1) - ONE//(2*n)
n += 1
fac = mpf_mul_int(fac, (2*n)*(2*n-1), wp)
pipow = mpf_mul(pipow, twopi2, wp)
s = (s << wp) // ln2_fixed(wp)
K = mpf_exp(from_man_exp(s, -wp), wp)
K = to_fixed(K, prec)
return K
# Glaisher's constant is defined as A = exp(1/2 - zeta'(-1)).
# One way to compute it would be to perform direct numerical
# differentiation, but computing arbitrary Riemann zeta function
# values at high precision is expensive. We instead use the formula
# A = exp((6 (-zeta'(2))/pi^2 + log 2 pi + gamma)/12)
# and compute zeta'(2) from the series representation
# oo
# ___
# \ log k
# -zeta'(2) = ) -----
# /___ 2
# k
# k = 2
# This series converges exceptionally slowly, but can be accelerated
# using Euler-Maclaurin formula. The important insight is that the
# E-M integral can be done in closed form and that the high order
# are given by
# n / \
# d | log x | a + b log x
# --- | ----- | = -----------
# n | 2 | 2 + n
# dx \ x / x
# where a and b are integers given by a simple recurrence. Note
# that just one logarithm is needed. However, lots of integer
# logarithms are required for the initial summation.
# This algorithm could possibly be turned into a faster algorithm
# for general evaluation of zeta(s) or zeta'(s); this should be
# looked into.
@constant_memo
def glaisher_fixed(prec):
wp = prec + 30
# Number of direct terms to sum before applying the Euler-Maclaurin
# formula to the tail. TODO: choose more intelligently
N = int(0.33*prec + 5)
ONE = MPZ_ONE << wp
# Euler-Maclaurin, step 1: sum log(k)/k**2 for k from 2 to N-1
s = MPZ_ZERO
for k in range(2, N):
#print k, N
s += log_int_fixed(k, wp) // k**2
logN = log_int_fixed(N, wp)
#logN = to_fixed(mpf_log(from_int(N), wp+20), wp)
# E-M step 2: integral of log(x)/x**2 from N to inf
s += (ONE + logN) // N
# E-M step 3: endpoint correction term f(N)/2
s += logN // (N**2 * 2)
# E-M step 4: the series of derivatives
pN = N**3
a = 1
b = -2
j = 3
fac = from_int(2)
k = 1
while 1:
# D(2*k-1) * B(2*k) / fac(2*k) [D(n) = nth derivative]
D = ((a << wp) + b*logN) // pN
D = from_man_exp(D, -wp)
B = mpf_bernoulli(2*k, wp)
term = mpf_mul(B, D, wp)
term = mpf_div(term, fac, wp)
term = to_fixed(term, wp)
if abs(term) < 100:
break
#if not k % 10:
# print k, math.log(int(abs(term)), 10)
s -= term
# Advance derivative twice
a, b, pN, j = b-a*j, -j*b, pN*N, j+1
a, b, pN, j = b-a*j, -j*b, pN*N, j+1
k += 1
fac = mpf_mul_int(fac, (2*k)*(2*k-1), wp)
# A = exp((6*s/pi**2 + log(2*pi) + euler)/12)
pi = pi_fixed(wp)
s *= 6
s = (s << wp) // (pi**2 >> wp)
s += euler_fixed(wp)
s += to_fixed(mpf_log(from_man_exp(2*pi, -wp), wp), wp)
s //= 12
A = mpf_exp(from_man_exp(s, -wp), wp)
return to_fixed(A, prec)
# Apery's constant can be computed using the very rapidly convergent
# series
# oo
# ___ 2 10
# \ n 205 n + 250 n + 77 (n!)
# zeta(3) = ) (-1) ------------------- ----------
# /___ 64 5
# n = 0 ((2n+1)!)
@constant_memo
def apery_fixed(prec):
prec += 20
d = MPZ_ONE << prec
term = MPZ(77) << prec
n = 1
s = MPZ_ZERO
while term:
s += term
d *= (n**10)
d //= (((2*n+1)**5) * (2*n)**5)
term = (-1)**n * (205*(n**2) + 250*n + 77) * d
n += 1
return s >> (20 + 6)
"""
Euler's constant (gamma) is computed using the Brent-McMillan formula,
gamma ~= I(n)/J(n) - log(n), where
I(n) = sum_{k=0,1,2,...} (n**k / k!)**2 * H(k)
J(n) = sum_{k=0,1,2,...} (n**k / k!)**2
H(k) = 1 + 1/2 + 1/3 + ... + 1/k
The error is bounded by O(exp(-4n)). Choosing n to be a power
of two, 2**p, the logarithm becomes particularly easy to calculate.[1]
We use the formulation of Algorithm 3.9 in [2] to make the summation
more efficient.
Reference:
[1] Xavier Gourdon & Pascal Sebah, The Euler constant: gamma
http://numbers.computation.free.fr/Constants/Gamma/gamma.pdf
[2] Jonathan Borwein & David Bailey, Mathematics by Experiment,
A K Peters, 2003
"""
@constant_memo
def euler_fixed(prec):
extra = 30
prec += extra
# choose p such that exp(-4*(2**p)) < 2**-n
p = int(math.log((prec/4) * math.log(2), 2)) + 1
n = 2**p
A = U = -p*ln2_fixed(prec)
B = V = MPZ_ONE << prec
k = 1
while 1:
B = B*n**2//k**2
A = (A*n**2//k + B)//k
U += A
V += B
if max(abs(A), abs(B)) < 100:
break
k += 1
return (U<<(prec-extra))//V
# Use zeta accelerated formulas for the Mertens and twin
# prime constants; see
# http://mathworld.wolfram.com/MertensConstant.html
# http://mathworld.wolfram.com/TwinPrimesConstant.html
@constant_memo
def mertens_fixed(prec):
wp = prec + 20
m = 2
s = mpf_euler(wp)
while 1:
t = mpf_zeta_int(m, wp)
if t == fone:
break
t = mpf_log(t, wp)
t = mpf_mul_int(t, moebius(m), wp)
t = mpf_div(t, from_int(m), wp)
s = mpf_add(s, t)
m += 1
return to_fixed(s, prec)
@constant_memo
def twinprime_fixed(prec):
def I(n):
return sum(moebius(d)<<(n//d) for d in xrange(1,n+1) if not n%d)//n
wp = 2*prec + 30
res = fone
primes = [from_rational(1,p,wp) for p in [2,3,5,7]]
ppowers = [mpf_mul(p,p,wp) for p in primes]
n = 2
while 1:
a = mpf_zeta_int(n, wp)
for i in range(4):
a = mpf_mul(a, mpf_sub(fone, ppowers[i]), wp)
ppowers[i] = mpf_mul(ppowers[i], primes[i], wp)
a = mpf_pow_int(a, -I(n), wp)
if mpf_pos(a, prec+10, 'n') == fone:
break
#from libmpf import to_str
#print n, to_str(mpf_sub(fone, a), 6)
res = mpf_mul(res, a, wp)
n += 1
res = mpf_mul(res, from_int(3*15*35), wp)
res = mpf_div(res, from_int(4*16*36), wp)
return to_fixed(res, prec)
mpf_euler = def_mpf_constant(euler_fixed)
mpf_apery = def_mpf_constant(apery_fixed)
mpf_khinchin = def_mpf_constant(khinchin_fixed)
mpf_glaisher = def_mpf_constant(glaisher_fixed)
mpf_catalan = def_mpf_constant(catalan_fixed)
mpf_mertens = def_mpf_constant(mertens_fixed)
mpf_twinprime = def_mpf_constant(twinprime_fixed)
#-----------------------------------------------------------------------#
# #
# Bernoulli numbers #
# #
#-----------------------------------------------------------------------#
MAX_BERNOULLI_CACHE = 3000
"""
Small Bernoulli numbers and factorials are used in numerous summations,
so it is critical for speed that sequential computation is fast and that
values are cached up to a fairly high threshold.
On the other hand, we also want to support fast computation of isolated
large numbers. Currently, no such acceleration is provided for integer
factorials (though it is for large floating-point factorials, which are
computed via gamma if the precision is low enough).
For sequential computation of Bernoulli numbers, we use Ramanujan's formula
/ n + 3 \
B = (A(n) - S(n)) / | |
n \ n /
where A(n) = (n+3)/3 when n = 0 or 2 (mod 6), A(n) = -(n+3)/6
when n = 4 (mod 6), and
[n/6]
___
\ / n + 3 \
S(n) = ) | | * B
/___ \ n - 6*k / n-6*k
k = 1
For isolated large Bernoulli numbers, we use the Riemann zeta function
to calculate a numerical value for B_n. The von Staudt-Clausen theorem
can then be used to optionally find the exact value of the
numerator and denominator.
"""
bernoulli_cache = {}
f3 = from_int(3)
f6 = from_int(6)
def bernoulli_size(n):
"""Accurately estimate the size of B_n (even n > 2 only)"""
lgn = math.log(n,2)
return int(2.326 + 0.5*lgn + n*(lgn - 4.094))
BERNOULLI_PREC_CUTOFF = bernoulli_size(MAX_BERNOULLI_CACHE)
def mpf_bernoulli(n, prec, rnd=None):
"""Computation of Bernoulli numbers (numerically)"""
if n < 2:
if n < 0:
raise ValueError("Bernoulli numbers only defined for n >= 0")
if n == 0:
return fone
if n == 1:
return mpf_neg(fhalf)
# For odd n > 1, the Bernoulli numbers are zero
if n & 1:
return fzero
# If precision is extremely high, we can save time by computing
# the Bernoulli number at a lower precision that is sufficient to
# obtain the exact fraction, round to the exact fraction, and
# convert the fraction back to an mpf value at the original precision
if prec > BERNOULLI_PREC_CUTOFF and prec > bernoulli_size(n)*1.1 + 1000:
p, q = bernfrac(n)
return from_rational(p, q, prec, rnd or round_floor)
if n > MAX_BERNOULLI_CACHE:
return mpf_bernoulli_huge(n, prec, rnd)
wp = prec + 30
# Reuse nearby precisions
wp += 32 - (prec & 31)
cached = bernoulli_cache.get(wp)
if cached:
numbers, state = cached
if n in numbers:
if not rnd:
return numbers[n]
return mpf_pos(numbers[n], prec, rnd)
m, bin, bin1 = state
if n - m > 10:
return mpf_bernoulli_huge(n, prec, rnd)
else:
if n > 10:
return mpf_bernoulli_huge(n, prec, rnd)
numbers = {0:fone}
m, bin, bin1 = state = [2, MPZ(10), MPZ_ONE]
bernoulli_cache[wp] = (numbers, state)
while m <= n:
#print m
case = m % 6
# Accurately estimate size of B_m so we can use
# fixed point math without using too much precision
szbm = bernoulli_size(m)
s = 0
sexp = max(0, szbm) - wp
if m < 6:
a = MPZ_ZERO
else:
a = bin1
for j in xrange(1, m//6+1):
usign, uman, uexp, ubc = u = numbers[m-6*j]
if usign:
uman = -uman
s += lshift(a*uman, uexp-sexp)
# Update inner binomial coefficient
j6 = 6*j
a *= ((m-5-j6)*(m-4-j6)*(m-3-j6)*(m-2-j6)*(m-1-j6)*(m-j6))
a //= ((4+j6)*(5+j6)*(6+j6)*(7+j6)*(8+j6)*(9+j6))
if case == 0: b = mpf_rdiv_int(m+3, f3, wp)
if case == 2: b = mpf_rdiv_int(m+3, f3, wp)
if case == 4: b = mpf_rdiv_int(-m-3, f6, wp)
s = from_man_exp(s, sexp, wp)
b = mpf_div(mpf_sub(b, s, wp), from_int(bin), wp)
numbers[m] = b
m += 2
# Update outer binomial coefficient
bin = bin * ((m+2)*(m+3)) // (m*(m-1))
if m > 6:
bin1 = bin1 * ((2+m)*(3+m)) // ((m-7)*(m-6))
state[:] = [m, bin, bin1]
return numbers[n]
def mpf_bernoulli_huge(n, prec, rnd=None):
wp = prec + 10
piprec = wp + int(math.log(n,2))
v = mpf_gamma_int(n+1, wp)
v = mpf_mul(v, mpf_zeta_int(n, wp), wp)
v = mpf_mul(v, mpf_pow_int(mpf_pi(piprec), -n, wp))
v = mpf_shift(v, 1-n)
if not n & 3:
v = mpf_neg(v)
return mpf_pos(v, prec, rnd or round_fast)
def bernfrac(n):
r"""
Returns a tuple of integers `(p, q)` such that `p/q = B_n` exactly,
where `B_n` denotes the `n`-th Bernoulli number. The fraction is
always reduced to lowest terms. Note that for `n > 1` and `n` odd,
`B_n = 0`, and `(0, 1)` is returned.
**Examples**
The first few Bernoulli numbers are exactly::
>>> from mpmath import *
>>> for n in range(15):
... p, q = bernfrac(n)
... print("%s %s/%s" % (n, p, q))
...
0 1/1
1 -1/2
2 1/6
3 0/1
4 -1/30
5 0/1
6 1/42
7 0/1
8 -1/30
9 0/1
10 5/66
11 0/1
12 -691/2730
13 0/1
14 7/6
This function works for arbitrarily large `n`::
>>> p, q = bernfrac(10**4)
>>> print(q)
2338224387510
>>> print(len(str(p)))
27692
>>> mp.dps = 15
>>> print(mpf(p) / q)
-9.04942396360948e+27677
>>> print(bernoulli(10**4))
-9.04942396360948e+27677
.. note ::
:func:`~mpmath.bernoulli` computes a floating-point approximation
directly, without computing the exact fraction first.
This is much faster for large `n`.
**Algorithm**
:func:`~mpmath.bernfrac` works by computing the value of `B_n` numerically
and then using the von Staudt-Clausen theorem [1] to reconstruct
the exact fraction. For large `n`, this is significantly faster than
computing `B_1, B_2, \ldots, B_2` recursively with exact arithmetic.
The implementation has been tested for `n = 10^m` up to `m = 6`.
In practice, :func:`~mpmath.bernfrac` appears to be about three times
slower than the specialized program calcbn.exe [2]
**References**
1. MathWorld, von Staudt-Clausen Theorem:
http://mathworld.wolfram.com/vonStaudt-ClausenTheorem.html
2. The Bernoulli Number Page:
http://www.bernoulli.org/
"""
n = int(n)
if n < 3:
return [(1, 1), (-1, 2), (1, 6)][n]
if n & 1:
return (0, 1)
q = 1
for k in list_primes(n+1):
if not (n % (k-1)):
q *= k
prec = bernoulli_size(n) + int(math.log(q,2)) + 20
b = mpf_bernoulli(n, prec)
p = mpf_mul(b, from_int(q))
pint = to_int(p, round_nearest)
return (pint, q)
#-----------------------------------------------------------------------#
# #
# The gamma function (OLD IMPLEMENTATION) #
# #
#-----------------------------------------------------------------------#
"""
We compute the real factorial / gamma function using Spouge's approximation
x! = (x+a)**(x+1/2) * exp(-x-a) * [c_0 + S(x) + eps]
where S(x) is the sum of c_k/(x+k) from k = 1 to a-1 and the coefficients
are given by
c_0 = sqrt(2*pi)
(-1)**(k-1)
c_k = ----------- (a-k)**(k-1/2) exp(-k+a), k = 1,2,...,a-1
(k - 1)!
As proved by Spouge, if we choose a = log(2)/log(2*pi)*n = 0.38*n, the
relative error eps is less than 2^(-n) for any x in the right complex
half-plane (assuming a > 2). In practice, it seems that a can be chosen
quite a bit lower still (30-50%); this possibility should be investigated.
For negative x, we use the reflection formula.
References:
-----------
John L. Spouge, "Computation of the gamma, digamma, and trigamma
functions", SIAM Journal on Numerical Analysis 31 (1994), no. 3, 931-944.
"""
spouge_cache = {}
def calc_spouge_coefficients(a, prec):
wp = prec + int(a*1.4)
c = [0] * a
# b = exp(a-1)
b = mpf_exp(from_int(a-1), wp)
# e = exp(1)
e = mpf_exp(fone, wp)
# sqrt(2*pi)
sq2pi = mpf_sqrt(mpf_shift(mpf_pi(wp), 1), wp)
c[0] = to_fixed(sq2pi, prec)
for k in xrange(1, a):
# c[k] = ((-1)**(k-1) * (a-k)**k) * b / sqrt(a-k)
term = mpf_mul_int(b, ((-1)**(k-1) * (a-k)**k), wp)
term = mpf_div(term, mpf_sqrt(from_int(a-k), wp), wp)
c[k] = to_fixed(term, prec)
# b = b / (e * k)
b = mpf_div(b, mpf_mul(e, from_int(k), wp), wp)
return c
# Cached lookup of coefficients
def get_spouge_coefficients(prec):
# This exact precision has been used before
if prec in spouge_cache:
return spouge_cache[prec]
for p in spouge_cache:
if 0.8 <= prec/float(p) < 1:
return spouge_cache[p]
# Here we estimate the value of a based on Spouge's inequality for
# the relative error
a = max(3, int(0.38*prec)) # 0.38 = log(2)/log(2*pi), ~= 1.26*n
coefs = calc_spouge_coefficients(a, prec)
spouge_cache[prec] = (prec, a, coefs)
return spouge_cache[prec]
def spouge_sum_real(x, prec, a, c):
x = to_fixed(x, prec)
s = c[0]
for k in xrange(1, a):
s += (c[k] << prec) // (x + (k << prec))
return from_man_exp(s, -prec, prec, round_floor)
# Unused: for fast computation of gamma(p/q)
def spouge_sum_rational(p, q, prec, a, c):
s = c[0]
for k in xrange(1, a):
s += c[k] * q // (p+q*k)
return from_man_exp(s, -prec, prec, round_floor)
# For a complex number a + b*I, we have
#
# c_k (a+k)*c_k b * c_k
# ------------- = --------- - ------- * I
# (a + b*I) + k M M
#
# 2 2 2 2 2
# where M = (a+k) + b = (a + b ) + (2*a*k + k )
def spouge_sum_complex(re, im, prec, a, c):
re = to_fixed(re, prec)
im = to_fixed(im, prec)
sre, sim = c[0], 0
mag = ((re**2)>>prec) + ((im**2)>>prec)
for k in xrange(1, a):
M = mag + re*(2*k) + ((k**2) << prec)
sre += (c[k] * (re + (k << prec))) // M
sim -= (c[k] * im) // M
re = from_man_exp(sre, -prec, prec, round_floor)
im = from_man_exp(sim, -prec, prec, round_floor)
return re, im
def mpf_gamma_int_old(n, prec, rounding=round_fast):
if n < 1000:
return from_int(ifac(n-1), prec, rounding)
# XXX: choose the cutoff less arbitrarily
size = int(n*math.log(n,2))
if prec > size/20.0:
return from_int(ifac(n-1), prec, rounding)
return mpf_gamma(from_int(n), prec, rounding)
def mpf_factorial_old(x, prec, rounding=round_fast):
return mpf_gamma_old(x, prec, rounding, p1=0)
def mpc_factorial_old(x, prec, rounding=round_fast):
return mpc_gamma_old(x, prec, rounding, p1=0)
def mpf_gamma_old(x, prec, rounding=round_fast, p1=1):
"""
Computes the gamma function of a real floating-point argument.
With p1=0, computes a factorial instead.
"""
sign, man, exp, bc = x
if not man:
if x == finf:
return finf
if x == fninf or x == fnan:
return fnan
# More precision is needed for enormous x. TODO:
# use Stirling's formula + Euler-Maclaurin summation
size = exp + bc
if size > 5:
size = int(size * math.log(size,2))
wp = prec + max(0, size) + 15
if exp >= 0:
if sign or (p1 and not man):
raise ValueError("gamma function pole")
# A direct factorial is fastest
if exp + bc <= 10:
return from_int(ifac((man<<exp)-p1), prec, rounding)
reflect = sign or exp+bc < -1
if p1:
# Should be done exactly!
x = mpf_sub(x, fone)
# x < 0.25
if reflect:
# gamma = pi / (sin(pi*x) * gamma(1-x))
wp += 15
pix = mpf_mul(x, mpf_pi(wp), wp)
t = mpf_sin_pi(x, wp)
g = mpf_gamma_old(mpf_sub(fone, x), wp)
return mpf_div(pix, mpf_mul(t, g, wp), prec, rounding)
sprec, a, c = get_spouge_coefficients(wp)
s = spouge_sum_real(x, sprec, a, c)
# gamma = exp(log(x+a)*(x+0.5) - xpa) * s
xpa = mpf_add(x, from_int(a), wp)
logxpa = mpf_log(xpa, wp)
xph = mpf_add(x, fhalf, wp)
t = mpf_sub(mpf_mul(logxpa, xph, wp), xpa, wp)
t = mpf_mul(mpf_exp(t, wp), s, prec, rounding)
return t
def mpc_gamma_old(x, prec, rounding=round_fast, p1=1):
re, im = x
if im == fzero:
return mpf_gamma_old(re, prec, rounding, p1), fzero
# More precision is needed for enormous x.
sign, man, exp, bc = re
isign, iman, iexp, ibc = im
if re == fzero:
size = iexp+ibc
else:
size = max(exp+bc, iexp+ibc)
if size > 5:
size = int(size * math.log(size,2))
reflect = sign or (exp+bc < -1)
wp = prec + max(0, size) + 25
# Near x = 0 pole (TODO: other poles)
if p1:
if size < -prec-5:
return mpc_add_mpf(mpc_div(mpc_one, x, 2*prec+10), \
mpf_neg(mpf_euler(2*prec+10)), prec, rounding)
elif size < -5:
wp += (-2*size)
if p1:
# Should be done exactly!
re_orig = re
re = mpf_sub(re, fone, bc+abs(exp)+2)
x = re, im
if reflect:
# Reflection formula
wp += 15
pi = mpf_pi(wp), fzero
pix = mpc_mul(x, pi, wp)
t = mpc_sin_pi(x, wp)
u = mpc_sub(mpc_one, x, wp)
g = mpc_gamma_old(u, wp)
w = mpc_mul(t, g, wp)
return mpc_div(pix, w, wp)
# Extremely close to the real line?
# XXX: reflection formula
if iexp+ibc < -wp:
a = mpf_gamma_old(re_orig, wp)
b = mpf_psi0(re_orig, wp)
gamma_diff = mpf_div(a, b, wp)
return mpf_pos(a, prec, rounding), mpf_mul(gamma_diff, im, prec, rounding)
sprec, a, c = get_spouge_coefficients(wp)
s = spouge_sum_complex(re, im, sprec, a, c)
# gamma = exp(log(x+a)*(x+0.5) - xpa) * s
repa = mpf_add(re, from_int(a), wp)
logxpa = mpc_log((repa, im), wp)
reph = mpf_add(re, fhalf, wp)
t = mpc_sub(mpc_mul(logxpa, (reph, im), wp), (repa, im), wp)
t = mpc_mul(mpc_exp(t, wp), s, prec, rounding)
return t
#-----------------------------------------------------------------------#
# #
# Polygamma functions #
# #
#-----------------------------------------------------------------------#
"""
For all polygamma (psi) functions, we use the Euler-Maclaurin summation
formula. It looks slightly different in the m = 0 and m > 0 cases.
For m = 0, we have
oo
___ B
(0) 1 \ 2 k -2 k
psi (z) ~ log z + --- - ) ------ z
2 z /___ (2 k)!
k = 1
Experiment shows that the minimum term of the asymptotic series
reaches 2^(-p) when Re(z) > 0.11*p. So we simply use the recurrence
for psi (equivalent, in fact, to summing to the first few terms
directly before applying E-M) to obtain z large enough.
Since, very crudely, log z ~= 1 for Re(z) > 1, we can use
fixed-point arithmetic (if z is extremely large, log(z) itself
is a sufficient approximation, so we can stop there already).
For Re(z) << 0, we could use recurrence, but this is of course
inefficient for large negative z, so there we use the
reflection formula instead.
For m > 0, we have
N - 1
___
~~~(m) [ \ 1 ] 1 1
psi (z) ~ [ ) -------- ] + ---------- + -------- +
[ /___ m+1 ] m+1 m
k = 1 (z+k) ] 2 (z+N) m (z+N)
oo
___ B
\ 2 k (m+1) (m+2) ... (m+2k-1)
+ ) ------ ------------------------
/___ (2 k)! m + 2 k
k = 1 (z+N)
where ~~~ denotes the function rescaled by 1/((-1)^(m+1) m!).
Here again N is chosen to make z+N large enough for the minimum
term in the last series to become smaller than eps.
TODO: the current estimation of N for m > 0 is *very suboptimal*.
TODO: implement the reflection formula for m > 0, Re(z) << 0.
It is generally a combination of multiple cotangents. Need to
figure out a reasonably simple way to generate these formulas
on the fly.
TODO: maybe use exact algorithms to compute psi for integral
and certain rational arguments, as this can be much more
efficient. (On the other hand, the availability of these
special values provides a convenient way to test the general
algorithm.)
"""
# Harmonic numbers are just shifted digamma functions
# We should calculate these exactly when x is an integer
# and when doing so is faster.
def mpf_harmonic(x, prec, rnd):
if x in (fzero, fnan, finf):
return x
a = mpf_psi0(mpf_add(fone, x, prec+5), prec)
return mpf_add(a, mpf_euler(prec+5, rnd), prec, rnd)
def mpc_harmonic(z, prec, rnd):
if z[1] == fzero:
return (mpf_harmonic(z[0], prec, rnd), fzero)
a = mpc_psi0(mpc_add_mpf(z, fone, prec+5), prec)
return mpc_add_mpf(a, mpf_euler(prec+5, rnd), prec, rnd)
def mpf_psi0(x, prec, rnd=round_fast):
"""
Computation of the digamma function (psi function of order 0)
of a real argument.
"""
sign, man, exp, bc = x
wp = prec + 10
if not man:
if x == finf: return x
if x == fninf or x == fnan: return fnan
if x == fzero or (exp >= 0 and sign):
raise ValueError("polygamma pole")
# Reflection formula
if sign and exp+bc > 3:
c, s = mpf_cos_sin_pi(x, wp)
q = mpf_mul(mpf_div(c, s, wp), mpf_pi(wp), wp)
p = mpf_psi0(mpf_sub(fone, x, wp), wp)
return mpf_sub(p, q, prec, rnd)
# The logarithmic term is accurate enough
if (not sign) and bc + exp > wp:
return mpf_log(mpf_sub(x, fone, wp), prec, rnd)
# Initial recurrence to obtain a large enough x
m = to_int(x)
n = int(0.11*wp) + 2
s = MPZ_ZERO
x = to_fixed(x, wp)
one = MPZ_ONE << wp
if m < n:
for k in xrange(m, n):
s -= (one << wp) // x
x += one
x -= one
# Logarithmic term
s += to_fixed(mpf_log(from_man_exp(x, -wp, wp), wp), wp)
# Endpoint term in Euler-Maclaurin expansion
s += (one << wp) // (2*x)
# Euler-Maclaurin remainder sum
x2 = (x*x) >> wp
t = one
prev = 0
k = 1
while 1:
t = (t*x2) >> wp
bsign, bman, bexp, bbc = mpf_bernoulli(2*k, wp)
offset = (bexp + 2*wp)
if offset >= 0: term = (bman << offset) // (t*(2*k))
else: term = (bman >> (-offset)) // (t*(2*k))
if k & 1: s -= term
else: s += term
if k > 2 and term >= prev:
break
prev = term
k += 1
return from_man_exp(s, -wp, wp, rnd)
def mpc_psi0(z, prec, rnd=round_fast):
"""
Computation of the digamma function (psi function of order 0)
of a complex argument.
"""
re, im = z
# Fall back to the real case
if im == fzero:
return (mpf_psi0(re, prec, rnd), fzero)
wp = prec + 20
sign, man, exp, bc = re
# Reflection formula
if sign and exp+bc > 3:
c = mpc_cos_pi(z, wp)
s = mpc_sin_pi(z, wp)
q = mpc_mul_mpf(mpc_div(c, s, wp), mpf_pi(wp), wp)
p = mpc_psi0(mpc_sub(mpc_one, z, wp), wp)
return mpc_sub(p, q, prec, rnd)
# Just the logarithmic term
if (not sign) and bc + exp > wp:
return mpc_log(mpc_sub(z, mpc_one, wp), prec, rnd)
# Initial recurrence to obtain a large enough z
w = to_int(re)
n = int(0.11*wp) + 2
s = mpc_zero
if w < n:
for k in xrange(w, n):
s = mpc_sub(s, mpc_reciprocal(z, wp), wp)
z = mpc_add_mpf(z, fone, wp)
z = mpc_sub(z, mpc_one, wp)
# Logarithmic and endpoint term
s = mpc_add(s, mpc_log(z, wp), wp)
s = mpc_add(s, mpc_div(mpc_half, z, wp), wp)
# Euler-Maclaurin remainder sum
z2 = mpc_square(z, wp)
t = mpc_one
prev = mpc_zero
k = 1
eps = mpf_shift(fone, -wp+2)
while 1:
t = mpc_mul(t, z2, wp)
bern = mpf_bernoulli(2*k, wp)
term = mpc_mpf_div(bern, mpc_mul_int(t, 2*k, wp), wp)
s = mpc_sub(s, term, wp)
szterm = mpc_abs(term, 10)
if k > 2 and mpf_le(szterm, eps):
break
prev = term
k += 1
return s
# Currently unoptimized
def mpf_psi(m, x, prec, rnd=round_fast):
"""
Computation of the polygamma function of arbitrary integer order
m >= 0, for a real argument x.
"""
if m == 0:
return mpf_psi0(x, prec, rnd=round_fast)
return mpc_psi(m, (x, fzero), prec, rnd)[0]
def mpc_psi(m, z, prec, rnd=round_fast):
"""
Computation of the polygamma function of arbitrary integer order
m >= 0, for a complex argument z.
"""
if m == 0:
return mpc_psi0(z, prec, rnd)
re, im = z
wp = prec + 20
sign, man, exp, bc = re
if not im[1]:
if im in (finf, fninf, fnan):
return (fnan, fnan)
if not man:
if re == finf and im == fzero:
return (fzero, fzero)
if re == fnan:
return (fnan, fnan)
# Recurrence
w = to_int(re)
n = int(0.4*wp + 4*m)
s = mpc_zero
if w < n:
for k in xrange(w, n):
t = mpc_pow_int(z, -m-1, wp)
s = mpc_add(s, t, wp)
z = mpc_add_mpf(z, fone, wp)
zm = mpc_pow_int(z, -m, wp)
z2 = mpc_pow_int(z, -2, wp)
# 1/m*(z+N)^m
integral_term = mpc_div_mpf(zm, from_int(m), wp)
s = mpc_add(s, integral_term, wp)
# 1/2*(z+N)^(-(m+1))
s = mpc_add(s, mpc_mul_mpf(mpc_div(zm, z, wp), fhalf, wp), wp)
a = m + 1
b = 2
k = 1
# Important: we want to sum up to the *relative* error,
# not the absolute error, because psi^(m)(z) might be tiny
magn = mpc_abs(s, 10)
magn = magn[2]+magn[3]
eps = mpf_shift(fone, magn-wp+2)
while 1:
zm = mpc_mul(zm, z2, wp)
bern = mpf_bernoulli(2*k, wp)
scal = mpf_mul_int(bern, a, wp)
scal = mpf_div(scal, from_int(b), wp)
term = mpc_mul_mpf(zm, scal, wp)
s = mpc_add(s, term, wp)
szterm = mpc_abs(term, 10)
if k > 2 and mpf_le(szterm, eps):
break
#print k, to_str(szterm, 10), to_str(eps, 10)
a *= (m+2*k)*(m+2*k+1)
b *= (2*k+1)*(2*k+2)
k += 1
# Scale and sign factor
v = mpc_mul_mpf(s, mpf_gamma(from_int(m+1), wp), prec, rnd)
if not (m & 1):
v = mpf_neg(v[0]), mpf_neg(v[1])
return v
#-----------------------------------------------------------------------#
# #
# Riemann zeta function #
# #
#-----------------------------------------------------------------------#
"""
We use zeta(s) = eta(s) / (1 - 2**(1-s)) and Borwein's approximation
n-1
___ k
-1 \ (-1) (d_k - d_n)
eta(s) ~= ---- ) ------------------
d_n /___ s
k = 0 (k + 1)
where
k
___ i
\ (n + i - 1)! 4
d_k = n ) ---------------.
/___ (n - i)! (2i)!
i = 0
If s = a + b*I, the absolute error for eta(s) is bounded by
3 (1 + 2|b|)
------------ * exp(|b| pi/2)
n
(3+sqrt(8))
Disregarding the linear term, we have approximately,
log(err) ~= log(exp(1.58*|b|)) - log(5.8**n)
log(err) ~= 1.58*|b| - log(5.8)*n
log(err) ~= 1.58*|b| - 1.76*n
log2(err) ~= 2.28*|b| - 2.54*n
So for p bits, we should choose n > (p + 2.28*|b|) / 2.54.
References:
-----------
Peter Borwein, "An Efficient Algorithm for the Riemann Zeta Function"
http://www.cecm.sfu.ca/personal/pborwein/PAPERS/P117.ps
http://en.wikipedia.org/wiki/Dirichlet_eta_function
"""
borwein_cache = {}
def borwein_coefficients(n):
if n in borwein_cache:
return borwein_cache[n]
ds = [MPZ_ZERO] * (n+1)
d = MPZ_ONE
s = ds[0] = MPZ_ONE
for i in range(1, n+1):
d = d * 4 * (n+i-1) * (n-i+1)
d //= ((2*i) * ((2*i)-1))
s += d
ds[i] = s
borwein_cache[n] = ds
return ds
ZETA_INT_CACHE_MAX_PREC = 1000
zeta_int_cache = {}
def mpf_zeta_int(s, prec, rnd=round_fast):
"""
Optimized computation of zeta(s) for an integer s.
"""
wp = prec + 20
s = int(s)
if s in zeta_int_cache and zeta_int_cache[s][0] >= wp:
return mpf_pos(zeta_int_cache[s][1], prec, rnd)
if s < 2:
if s == 1:
raise ValueError("zeta(1) pole")
if not s:
return mpf_neg(fhalf)
return mpf_div(mpf_bernoulli(-s+1, wp), from_int(s-1), prec, rnd)
# 2^-s term vanishes?
if s >= wp:
return mpf_perturb(fone, 0, prec, rnd)
# 5^-s term vanishes?
elif s >= wp*0.431:
t = one = 1 << wp
t += 1 << (wp - s)
t += one // (MPZ_THREE ** s)
t += 1 << max(0, wp - s*2)
return from_man_exp(t, -wp, prec, rnd)
else:
# Fast enough to sum directly?
# Even better, we use the Euler product (idea stolen from pari)
m = (float(wp)/(s-1) + 1)
if m < 30:
needed_terms = int(2.0**m + 1)
if needed_terms < int(wp/2.54 + 5) / 10:
t = fone
for k in list_primes(needed_terms):
#print k, needed_terms
powprec = int(wp - s*math.log(k,2))
if powprec < 2:
break
a = mpf_sub(fone, mpf_pow_int(from_int(k), -s, powprec), wp)
t = mpf_mul(t, a, wp)
return mpf_div(fone, t, wp)
# Use Borwein's algorithm
n = int(wp/2.54 + 5)
d = borwein_coefficients(n)
t = MPZ_ZERO
s = MPZ(s)
for k in xrange(n):
t += (((-1)**k * (d[k] - d[n])) << wp) // (k+1)**s
t = (t << wp) // (-d[n])
t = (t << wp) // ((1 << wp) - (1 << (wp+1-s)))
if (s in zeta_int_cache and zeta_int_cache[s][0] < wp) or (s not in zeta_int_cache):
zeta_int_cache[s] = (wp, from_man_exp(t, -wp-wp))
return from_man_exp(t, -wp-wp, prec, rnd)
def mpf_zeta(s, prec, rnd=round_fast, alt=0):
sign, man, exp, bc = s
if not man:
if s == fzero:
if alt:
return fhalf
else:
return mpf_neg(fhalf)
if s == finf:
return fone
return fnan
wp = prec + 20
# First term vanishes?
if (not sign) and (exp + bc > (math.log(wp,2) + 2)):
return mpf_perturb(fone, alt, prec, rnd)
# Optimize for integer arguments
elif exp >= 0:
if alt:
if s == fone:
return mpf_ln2(prec, rnd)
z = mpf_zeta_int(to_int(s), wp, negative_rnd[rnd])
q = mpf_sub(fone, mpf_pow(ftwo, mpf_sub(fone, s, wp), wp), wp)
return mpf_mul(z, q, prec, rnd)
else:
return mpf_zeta_int(to_int(s), prec, rnd)
# Negative: use the reflection formula
# Borwein only proves the accuracy bound for x >= 1/2. However, based on
# tests, the accuracy without reflection is quite good even some distance
# to the left of 1/2. XXX: verify this.
if sign:
# XXX: could use the separate refl. formula for Dirichlet eta
if alt:
q = mpf_sub(fone, mpf_pow(ftwo, mpf_sub(fone, s, wp), wp), wp)
return mpf_mul(mpf_zeta(s, wp), q, prec, rnd)
# XXX: -1 should be done exactly
y = mpf_sub(fone, s, 10*wp)
a = mpf_gamma(y, wp)
b = mpf_zeta(y, wp)
c = mpf_sin_pi(mpf_shift(s, -1), wp)
wp2 = wp + max(0,exp+bc)
pi = mpf_pi(wp+wp2)
d = mpf_div(mpf_pow(mpf_shift(pi, 1), s, wp2), pi, wp2)
return mpf_mul(a,mpf_mul(b,mpf_mul(c,d,wp),wp),prec,rnd)
# Near pole
r = mpf_sub(fone, s, wp)
asign, aman, aexp, abc = mpf_abs(r)
pole_dist = -2*(aexp+abc)
if pole_dist > wp:
if alt:
return mpf_ln2(prec, rnd)
else:
q = mpf_neg(mpf_div(fone, r, wp))
return mpf_add(q, mpf_euler(wp), prec, rnd)
else:
wp += max(0, pole_dist)
t = MPZ_ZERO
#wp += 16 - (prec & 15)
# Use Borwein's algorithm
n = int(wp/2.54 + 5)
d = borwein_coefficients(n)
t = MPZ_ZERO
sf = to_fixed(s, wp)
ln2 = ln2_fixed(wp)
for k in xrange(n):
u = (-sf*log_int_fixed(k+1, wp, ln2)) >> wp
#esign, eman, eexp, ebc = mpf_exp(u, wp)
#offset = eexp + wp
#if offset >= 0:
# w = ((d[k] - d[n]) * eman) << offset
#else:
# w = ((d[k] - d[n]) * eman) >> (-offset)
eman = exp_fixed(u, wp, ln2)
w = (d[k] - d[n]) * eman
if k & 1:
t -= w
else:
t += w
t = t // (-d[n])
t = from_man_exp(t, -wp, wp)
if alt:
return mpf_pos(t, prec, rnd)
else:
q = mpf_sub(fone, mpf_pow(ftwo, mpf_sub(fone, s, wp), wp), wp)
return mpf_div(t, q, prec, rnd)
def mpc_zeta(s, prec, rnd=round_fast, alt=0, force=False):
re, im = s
if im == fzero:
return mpf_zeta(re, prec, rnd, alt), fzero
# slow for large s
if (not force) and mpf_gt(mpc_abs(s, 10), from_int(prec)):
raise NotImplementedError
wp = prec + 20
# Near pole
r = mpc_sub(mpc_one, s, wp)
asign, aman, aexp, abc = mpc_abs(r, 10)
pole_dist = -2*(aexp+abc)
if pole_dist > wp:
if alt:
q = mpf_ln2(wp)
y = mpf_mul(q, mpf_euler(wp), wp)
g = mpf_shift(mpf_mul(q, q, wp), -1)
g = mpf_sub(y, g)
z = mpc_mul_mpf(r, mpf_neg(g), wp)
z = mpc_add_mpf(z, q, wp)
return mpc_pos(z, prec, rnd)
else:
q = mpc_neg(mpc_div(mpc_one, r, wp))
q = mpc_add_mpf(q, mpf_euler(wp), wp)
return mpc_pos(q, prec, rnd)
else:
wp += max(0, pole_dist)
# Reflection formula. To be rigorous, we should reflect to the left of
# re = 1/2 (see comments for mpf_zeta), but this leads to unnecessary
# slowdown for interesting values of s
if mpf_lt(re, fzero):
# XXX: could use the separate refl. formula for Dirichlet eta
if alt:
q = mpc_sub(mpc_one, mpc_pow(mpc_two, mpc_sub(mpc_one, s, wp),
wp), wp)
return mpc_mul(mpc_zeta(s, wp), q, prec, rnd)
# XXX: -1 should be done exactly
y = mpc_sub(mpc_one, s, 10*wp)
a = mpc_gamma(y, wp)
b = mpc_zeta(y, wp)
c = mpc_sin_pi(mpc_shift(s, -1), wp)
rsign, rman, rexp, rbc = re
isign, iman, iexp, ibc = im
mag = max(rexp+rbc, iexp+ibc)
wp2 = wp + max(0, mag)
pi = mpf_pi(wp+wp2)
pi2 = (mpf_shift(pi, 1), fzero)
d = mpc_div_mpf(mpc_pow(pi2, s, wp2), pi, wp2)
return mpc_mul(a,mpc_mul(b,mpc_mul(c,d,wp),wp),prec,rnd)
n = int(wp/2.54 + 5)
n += int(0.9*abs(to_int(im)))
d = borwein_coefficients(n)
ref = to_fixed(re, wp)
imf = to_fixed(im, wp)
tre = MPZ_ZERO
tim = MPZ_ZERO
one = MPZ_ONE << wp
one_2wp = MPZ_ONE << (2*wp)
critical_line = re == fhalf
ln2 = ln2_fixed(wp)
pi2 = pi_fixed(wp-1)
wp2 = wp+wp
for k in xrange(n):
log = log_int_fixed(k+1, wp, ln2)
# A square root is much cheaper than an exp
if critical_line:
w = one_2wp // isqrt_fast((k+1) << wp2)
else:
w = exp_fixed((-ref*log) >> wp, wp)
if k & 1:
w *= (d[n] - d[k])
else:
w *= (d[k] - d[n])
wre, wim = cos_sin_fixed((-imf*log)>>wp, wp, pi2)
tre += (w * wre) >> wp
tim += (w * wim) >> wp
tre //= (-d[n])
tim //= (-d[n])
tre = from_man_exp(tre, -wp, wp)
tim = from_man_exp(tim, -wp, wp)
if alt:
return mpc_pos((tre, tim), prec, rnd)
else:
q = mpc_sub(mpc_one, mpc_pow(mpc_two, r, wp), wp)
return mpc_div((tre, tim), q, prec, rnd)
def mpf_altzeta(s, prec, rnd=round_fast):
return mpf_zeta(s, prec, rnd, 1)
def mpc_altzeta(s, prec, rnd=round_fast):
return mpc_zeta(s, prec, rnd, 1)
# Not optimized currently
mpf_zetasum = None
def pow_fixed(x, n, wp):
if n == 1:
return x
y = MPZ_ONE << wp
while n:
if n & 1:
y = (y*x) >> wp
n -= 1
x = (x*x) >> wp
n //= 2
return y
# TODO: optimize / cleanup interface / unify with list_primes
sieve_cache = []
primes_cache = []
mult_cache = []
def primesieve(n):
global sieve_cache, primes_cache, mult_cache
if n < len(sieve_cache):
sieve = sieve_cache#[:n+1]
primes = primes_cache[:primes_cache.index(max(sieve))+1]
mult = mult_cache#[:n+1]
return sieve, primes, mult
sieve = [0] * (n+1)
mult = [0] * (n+1)
primes = list_primes(n)
for p in primes:
#sieve[p::p] = p
for k in xrange(p,n+1,p):
sieve[k] = p
for i, p in enumerate(sieve):
if i >= 2:
m = 1
n = i // p
while not n % p:
n //= p
m += 1
mult[i] = m
sieve_cache = sieve
primes_cache = primes
mult_cache = mult
return sieve, primes, mult
def zetasum_sieved(critical_line, sre, sim, a, n, wp):
if a < 1:
raise ValueError("a cannot be less than 1")
sieve, primes, mult = primesieve(a+n)
basic_powers = {}
one = MPZ_ONE << wp
one_2wp = MPZ_ONE << (2*wp)
wp2 = wp+wp
ln2 = ln2_fixed(wp)
pi2 = pi_fixed(wp-1)
for p in primes:
if p*2 > a+n:
break
log = log_int_fixed(p, wp, ln2)
cos, sin = cos_sin_fixed((-sim*log)>>wp, wp, pi2)
if critical_line:
u = one_2wp // isqrt_fast(p<<wp2)
else:
u = exp_fixed((-sre*log)>>wp, wp)
pre = (u*cos) >> wp
pim = (u*sin) >> wp
basic_powers[p] = [(pre, pim)]
tre, tim = pre, pim
for m in range(1,int(math.log(a+n,p)+0.01)+1):
tre, tim = ((pre*tre-pim*tim)>>wp), ((pim*tre+pre*tim)>>wp)
basic_powers[p].append((tre,tim))
xre = MPZ_ZERO
xim = MPZ_ZERO
if a == 1:
xre += one
aa = max(a,2)
for k in xrange(aa, a+n+1):
p = sieve[k]
if p in basic_powers:
m = mult[k]
tre, tim = basic_powers[p][m-1]
while 1:
k //= p**m
if k == 1:
break
p = sieve[k]
m = mult[k]
pre, pim = basic_powers[p][m-1]
tre, tim = ((pre*tre-pim*tim)>>wp), ((pim*tre+pre*tim)>>wp)
else:
log = log_int_fixed(k, wp, ln2)
cos, sin = cos_sin_fixed((-sim*log)>>wp, wp, pi2)
if critical_line:
u = one_2wp // isqrt_fast(k<<wp2)
else:
u = exp_fixed((-sre*log)>>wp, wp)
tre = (u*cos) >> wp
tim = (u*sin) >> wp
xre += tre
xim += tim
return xre, xim
# Set to something large to disable
ZETASUM_SIEVE_CUTOFF = 10
def mpc_zetasum(s, a, n, derivatives, reflect, prec):
"""
Fast version of mp._zetasum, assuming s = complex, a = integer.
"""
wp = prec + 10
derivatives = list(derivatives)
have_derivatives = derivatives != [0]
have_one_derivative = len(derivatives) == 1
# parse s
sre, sim = s
critical_line = (sre == fhalf)
sre = to_fixed(sre, wp)
sim = to_fixed(sim, wp)
if a > 0 and n > ZETASUM_SIEVE_CUTOFF and not have_derivatives \
and not reflect and (n < 4e7 or sys.maxsize > 2**32):
re, im = zetasum_sieved(critical_line, sre, sim, a, n, wp)
xs = [(from_man_exp(re, -wp, prec, 'n'), from_man_exp(im, -wp, prec, 'n'))]
return xs, []
maxd = max(derivatives)
if not have_one_derivative:
derivatives = range(maxd+1)
# x_d = 0, y_d = 0
xre = [MPZ_ZERO for d in derivatives]
xim = [MPZ_ZERO for d in derivatives]
if reflect:
yre = [MPZ_ZERO for d in derivatives]
yim = [MPZ_ZERO for d in derivatives]
else:
yre = yim = []
one = MPZ_ONE << wp
one_2wp = MPZ_ONE << (2*wp)
ln2 = ln2_fixed(wp)
pi2 = pi_fixed(wp-1)
wp2 = wp+wp
for w in xrange(a, a+n+1):
log = log_int_fixed(w, wp, ln2)
cos, sin = cos_sin_fixed((-sim*log)>>wp, wp, pi2)
if critical_line:
u = one_2wp // isqrt_fast(w<<wp2)
else:
u = exp_fixed((-sre*log)>>wp, wp)
xterm_re = (u * cos) >> wp
xterm_im = (u * sin) >> wp
if reflect:
reciprocal = (one_2wp // (u*w))
yterm_re = (reciprocal * cos) >> wp
yterm_im = (reciprocal * sin) >> wp
if have_derivatives:
if have_one_derivative:
log = pow_fixed(log, maxd, wp)
xre[0] += (xterm_re * log) >> wp
xim[0] += (xterm_im * log) >> wp
if reflect:
yre[0] += (yterm_re * log) >> wp
yim[0] += (yterm_im * log) >> wp
else:
t = MPZ_ONE << wp
for d in derivatives:
xre[d] += (xterm_re * t) >> wp
xim[d] += (xterm_im * t) >> wp
if reflect:
yre[d] += (yterm_re * t) >> wp
yim[d] += (yterm_im * t) >> wp
t = (t * log) >> wp
else:
xre[0] += xterm_re
xim[0] += xterm_im
if reflect:
yre[0] += yterm_re
yim[0] += yterm_im
if have_derivatives:
if have_one_derivative:
if maxd % 2:
xre[0] = -xre[0]
xim[0] = -xim[0]
if reflect:
yre[0] = -yre[0]
yim[0] = -yim[0]
else:
xre = [(-1)**d * xre[d] for d in derivatives]
xim = [(-1)**d * xim[d] for d in derivatives]
if reflect:
yre = [(-1)**d * yre[d] for d in derivatives]
yim = [(-1)**d * yim[d] for d in derivatives]
xs = [(from_man_exp(xa, -wp, prec, 'n'), from_man_exp(xb, -wp, prec, 'n'))
for (xa, xb) in zip(xre, xim)]
ys = [(from_man_exp(ya, -wp, prec, 'n'), from_man_exp(yb, -wp, prec, 'n'))
for (ya, yb) in zip(yre, yim)]
return xs, ys
#-----------------------------------------------------------------------#
# #
# The gamma function (NEW IMPLEMENTATION) #
# #
#-----------------------------------------------------------------------#
# Higher means faster, but more precomputation time
MAX_GAMMA_TAYLOR_PREC = 5000
# Need to derive higher bounds for Taylor series to go higher
assert MAX_GAMMA_TAYLOR_PREC < 15000
# Use Stirling's series if abs(x) > beta*prec
# Important: must be large enough for convergence!
GAMMA_STIRLING_BETA = 0.2
SMALL_FACTORIAL_CACHE_SIZE = 150
gamma_taylor_cache = {}
gamma_stirling_cache = {}
small_factorial_cache = [from_int(ifac(n)) for \
n in range(SMALL_FACTORIAL_CACHE_SIZE+1)]
def zeta_array(N, prec):
"""
zeta(n) = A * pi**n / n! + B
where A is a rational number (A = Bernoulli number
for n even) and B is an infinite sum over powers of exp(2*pi).
(B = 0 for n even).
TODO: this is currently only used for gamma, but could
be very useful elsewhere.
"""
extra = 30
wp = prec+extra
zeta_values = [MPZ_ZERO] * (N+2)
pi = pi_fixed(wp)
# STEP 1:
one = MPZ_ONE << wp
zeta_values[0] = -one//2
f_2pi = mpf_shift(mpf_pi(wp),1)
exp_2pi_k = exp_2pi = mpf_exp(f_2pi, wp)
# Compute exponential series
# Store values of 1/(exp(2*pi*k)-1),
# exp(2*pi*k)/(exp(2*pi*k)-1)**2, 1/(exp(2*pi*k)-1)**2
# pi*k*exp(2*pi*k)/(exp(2*pi*k)-1)**2
exps3 = []
k = 1
while 1:
tp = wp - 9*k
if tp < 1:
break
# 1/(exp(2*pi*k-1)
q1 = mpf_div(fone, mpf_sub(exp_2pi_k, fone, tp), tp)
# pi*k*exp(2*pi*k)/(exp(2*pi*k)-1)**2
q2 = mpf_mul(exp_2pi_k, mpf_mul(q1,q1,tp), tp)
q1 = to_fixed(q1, wp)
q2 = to_fixed(q2, wp)
q2 = (k * q2 * pi) >> wp
exps3.append((q1, q2))
# Multiply for next round
exp_2pi_k = mpf_mul(exp_2pi_k, exp_2pi, wp)
k += 1
# Exponential sum
for n in xrange(3, N+1, 2):
s = MPZ_ZERO
k = 1
for e1, e2 in exps3:
if n%4 == 3:
t = e1 // k**n
else:
U = (n-1)//4
t = (e1 + e2//U) // k**n
if not t:
break
s += t
k += 1
zeta_values[n] = -2*s
# Even zeta values
B = [mpf_abs(mpf_bernoulli(k,wp)) for k in xrange(N+2)]
pi_pow = fpi = mpf_pow_int(mpf_shift(mpf_pi(wp), 1), 2, wp)
pi_pow = mpf_div(pi_pow, from_int(4), wp)
for n in xrange(2,N+2,2):
z = mpf_mul(B[n], pi_pow, wp)
zeta_values[n] = to_fixed(z, wp)
pi_pow = mpf_mul(pi_pow, fpi, wp)
pi_pow = mpf_div(pi_pow, from_int((n+1)*(n+2)), wp)
# Zeta sum
reciprocal_pi = (one << wp) // pi
for n in xrange(3, N+1, 4):
U = (n-3)//4
s = zeta_values[4*U+4]*(4*U+7)//4
for k in xrange(1, U+1):
s -= (zeta_values[4*k] * zeta_values[4*U+4-4*k]) >> wp
zeta_values[n] += (2*s*reciprocal_pi) >> wp
for n in xrange(5, N+1, 4):
U = (n-1)//4
s = zeta_values[4*U+2]*(2*U+1)
for k in xrange(1, 2*U+1):
s += ((-1)**k*2*k* zeta_values[2*k] * zeta_values[4*U+2-2*k])>>wp
zeta_values[n] += ((s*reciprocal_pi)>>wp)//(2*U)
return [x>>extra for x in zeta_values]
def gamma_taylor_coefficients(inprec):
"""
Gives the Taylor coefficients of 1/gamma(1+x) as
a list of fixed-point numbers. Enough coefficients are returned
to ensure that the series converges to the given precision
when x is in [0.5, 1.5].
"""
# Reuse nearby cache values (small case)
if inprec < 400:
prec = inprec + (10-(inprec%10))
elif inprec < 1000:
prec = inprec + (30-(inprec%30))
else:
prec = inprec
if prec in gamma_taylor_cache:
return gamma_taylor_cache[prec], prec
# Experimentally determined bounds
if prec < 1000:
N = int(prec**0.76 + 2)
else:
# Valid to at least 15000 bits
N = int(prec**0.787 + 2)
# Reuse higher precision values
for cprec in gamma_taylor_cache:
if cprec > prec:
coeffs = [x>>(cprec-prec) for x in gamma_taylor_cache[cprec][-N:]]
if inprec < 1000:
gamma_taylor_cache[prec] = coeffs
return coeffs, prec
# Cache at a higher precision (large case)
if prec > 1000:
prec = int(prec * 1.2)
wp = prec + 20
A = [0] * N
A[0] = MPZ_ZERO
A[1] = MPZ_ONE << wp
A[2] = euler_fixed(wp)
# SLOW, reference implementation
#zeta_values = [0,0]+[to_fixed(mpf_zeta_int(k,wp),wp) for k in xrange(2,N)]
zeta_values = zeta_array(N, wp)
for k in xrange(3, N):
a = (-A[2]*A[k-1])>>wp
for j in xrange(2,k):
a += ((-1)**j * zeta_values[j] * A[k-j]) >> wp
a //= (1-k)
A[k] = a
A = [a>>20 for a in A]
A = A[::-1]
A = A[:-1]
gamma_taylor_cache[prec] = A
#return A, prec
return gamma_taylor_coefficients(inprec)
def gamma_fixed_taylor(xmpf, x, wp, prec, rnd, type):
# Determine nearest multiple of N/2
#n = int(x >> (wp-1))
#steps = (n-1)>>1
nearest_int = ((x >> (wp-1)) + MPZ_ONE) >> 1
one = MPZ_ONE << wp
coeffs, cwp = gamma_taylor_coefficients(wp)
if nearest_int > 0:
r = one
for i in xrange(nearest_int-1):
x -= one
r = (r*x) >> wp
x -= one
p = MPZ_ZERO
for c in coeffs:
p = c + ((x*p)>>wp)
p >>= (cwp-wp)
if type == 0:
return from_man_exp((r<<wp)//p, -wp, prec, rnd)
if type == 2:
return mpf_shift(from_rational(p, (r<<wp), prec, rnd), wp)
if type == 3:
return mpf_log(mpf_abs(from_man_exp((r<<wp)//p, -wp)), prec, rnd)
else:
r = one
for i in xrange(-nearest_int):
r = (r*x) >> wp
x += one
p = MPZ_ZERO
for c in coeffs:
p = c + ((x*p)>>wp)
p >>= (cwp-wp)
if wp - bitcount(abs(x)) > 10:
# pass very close to 0, so do floating-point multiply
g = mpf_add(xmpf, from_int(-nearest_int)) # exact
r = from_man_exp(p*r,-wp-wp)
r = mpf_mul(r, g, wp)
if type == 0:
return mpf_div(fone, r, prec, rnd)
if type == 2:
return mpf_pos(r, prec, rnd)
if type == 3:
return mpf_log(mpf_abs(mpf_div(fone, r, wp)), prec, rnd)
else:
r = from_man_exp(x*p*r,-3*wp)
if type == 0: return mpf_div(fone, r, prec, rnd)
if type == 2: return mpf_pos(r, prec, rnd)
if type == 3: return mpf_neg(mpf_log(mpf_abs(r), prec, rnd))
def stirling_coefficient(n):
if n in gamma_stirling_cache:
return gamma_stirling_cache[n]
p, q = bernfrac(n)
q *= MPZ(n*(n-1))
gamma_stirling_cache[n] = p, q, bitcount(abs(p)), bitcount(q)
return gamma_stirling_cache[n]
def real_stirling_series(x, prec):
"""
Sums the rational part of Stirling's expansion,
log(sqrt(2*pi)) - z + 1/(12*z) - 1/(360*z^3) + ...
"""
t = (MPZ_ONE<<(prec+prec)) // x # t = 1/x
u = (t*t)>>prec # u = 1/x**2
s = ln_sqrt2pi_fixed(prec) - x
# Add initial terms of Stirling's series
s += t//12; t = (t*u)>>prec
s -= t//360; t = (t*u)>>prec
s += t//1260; t = (t*u)>>prec
s -= t//1680; t = (t*u)>>prec
if not t: return s
s += t//1188; t = (t*u)>>prec
s -= 691*t//360360; t = (t*u)>>prec
s += t//156; t = (t*u)>>prec
if not t: return s
s -= 3617*t//122400; t = (t*u)>>prec
s += 43867*t//244188; t = (t*u)>>prec
s -= 174611*t//125400; t = (t*u)>>prec
if not t: return s
k = 22
# From here on, the coefficients are growing, so we
# have to keep t at a roughly constant size
usize = bitcount(abs(u))
tsize = bitcount(abs(t))
texp = 0
while 1:
p, q, pb, qb = stirling_coefficient(k)
term_mag = tsize + pb + texp
shift = -texp
m = pb - term_mag
if m > 0 and shift < m:
p >>= m
shift -= m
m = tsize - term_mag
if m > 0 and shift < m:
w = t >> m
shift -= m
else:
w = t
term = (t*p//q) >> shift
if not term:
break
s += term
t = (t*u) >> usize
texp -= (prec - usize)
k += 2
return s
def complex_stirling_series(x, y, prec):
# t = 1/z
_m = (x*x + y*y) >> prec
tre = (x << prec) // _m
tim = (-y << prec) // _m
# u = 1/z**2
ure = (tre*tre - tim*tim) >> prec
uim = tim*tre >> (prec-1)
# s = log(sqrt(2*pi)) - z
sre = ln_sqrt2pi_fixed(prec) - x
sim = -y
# Add initial terms of Stirling's series
sre += tre//12; sim += tim//12;
tre, tim = ((tre*ure-tim*uim)>>prec), ((tre*uim+tim*ure)>>prec)
sre -= tre//360; sim -= tim//360;
tre, tim = ((tre*ure-tim*uim)>>prec), ((tre*uim+tim*ure)>>prec)
sre += tre//1260; sim += tim//1260;
tre, tim = ((tre*ure-tim*uim)>>prec), ((tre*uim+tim*ure)>>prec)
sre -= tre//1680; sim -= tim//1680;
tre, tim = ((tre*ure-tim*uim)>>prec), ((tre*uim+tim*ure)>>prec)
if abs(tre) + abs(tim) < 5: return sre, sim
sre += tre//1188; sim += tim//1188;
tre, tim = ((tre*ure-tim*uim)>>prec), ((tre*uim+tim*ure)>>prec)
sre -= 691*tre//360360; sim -= 691*tim//360360;
tre, tim = ((tre*ure-tim*uim)>>prec), ((tre*uim+tim*ure)>>prec)
sre += tre//156; sim += tim//156;
tre, tim = ((tre*ure-tim*uim)>>prec), ((tre*uim+tim*ure)>>prec)
if abs(tre) + abs(tim) < 5: return sre, sim
sre -= 3617*tre//122400; sim -= 3617*tim//122400;
tre, tim = ((tre*ure-tim*uim)>>prec), ((tre*uim+tim*ure)>>prec)
sre += 43867*tre//244188; sim += 43867*tim//244188;
tre, tim = ((tre*ure-tim*uim)>>prec), ((tre*uim+tim*ure)>>prec)
sre -= 174611*tre//125400; sim -= 174611*tim//125400;
tre, tim = ((tre*ure-tim*uim)>>prec), ((tre*uim+tim*ure)>>prec)
if abs(tre) + abs(tim) < 5: return sre, sim
k = 22
# From here on, the coefficients are growing, so we
# have to keep t at a roughly constant size
usize = bitcount(max(abs(ure), abs(uim)))
tsize = bitcount(max(abs(tre), abs(tim)))
texp = 0
while 1:
p, q, pb, qb = stirling_coefficient(k)
term_mag = tsize + pb + texp
shift = -texp
m = pb - term_mag
if m > 0 and shift < m:
p >>= m
shift -= m
m = tsize - term_mag
if m > 0 and shift < m:
wre = tre >> m
wim = tim >> m
shift -= m
else:
wre = tre
wim = tim
termre = (tre*p//q) >> shift
termim = (tim*p//q) >> shift
if abs(termre) + abs(termim) < 5:
break
sre += termre
sim += termim
tre, tim = ((tre*ure - tim*uim)>>usize), \
((tre*uim + tim*ure)>>usize)
texp -= (prec - usize)
k += 2
return sre, sim
def mpf_gamma(x, prec, rnd='d', type=0):
"""
This function implements multipurpose evaluation of the gamma
function, G(x), as well as the following versions of the same:
type = 0 -- G(x) [standard gamma function]
type = 1 -- G(x+1) = x*G(x+1) = x! [factorial]
type = 2 -- 1/G(x) [reciprocal gamma function]
type = 3 -- log(|G(x)|) [log-gamma function, real part]
"""
# Specal values
sign, man, exp, bc = x
if not man:
if x == fzero:
if type == 1: return fone
if type == 2: return fzero
raise ValueError("gamma function pole")
if x == finf:
if type == 2: return fzero
return finf
return fnan
# First of all, for log gamma, numbers can be well beyond the fixed-point
# range, so we must take care of huge numbers before e.g. trying
# to convert x to the nearest integer
if type == 3:
wp = prec+20
if exp+bc > wp and not sign:
return mpf_sub(mpf_mul(x, mpf_log(x, wp), wp), x, prec, rnd)
# We strongly want to special-case small integers
is_integer = exp >= 0
if is_integer:
# Poles
if sign:
if type == 2:
return fzero
raise ValueError("gamma function pole")
# n = x
n = man << exp
if n < SMALL_FACTORIAL_CACHE_SIZE:
if type == 0:
return mpf_pos(small_factorial_cache[n-1], prec, rnd)
if type == 1:
return mpf_pos(small_factorial_cache[n], prec, rnd)
if type == 2:
return mpf_div(fone, small_factorial_cache[n-1], prec, rnd)
if type == 3:
return mpf_log(small_factorial_cache[n-1], prec, rnd)
else:
# floor(abs(x))
n = int(man >> (-exp))
# Estimate size and precision
# Estimate log(gamma(|x|),2) as x*log(x,2)
mag = exp + bc
gamma_size = n*mag
if type == 3:
wp = prec + 20
else:
wp = prec + bitcount(gamma_size) + 20
# Very close to 0, pole
if mag < -wp:
if type == 0:
return mpf_sub(mpf_div(fone,x, wp),mpf_shift(fone,-wp),prec,rnd)
if type == 1: return mpf_sub(fone, x, prec, rnd)
if type == 2: return mpf_add(x, mpf_shift(fone,mag-wp), prec, rnd)
if type == 3: return mpf_neg(mpf_log(mpf_abs(x), prec, rnd))
# From now on, we assume having a gamma function
if type == 1:
return mpf_gamma(mpf_add(x, fone), prec, rnd, 0)
# Special case integers (those not small enough to be caught above,
# but still small enough for an exact factorial to be faster
# than an approximate algorithm), and half-integers
if exp >= -1:
if is_integer:
if gamma_size < 10*wp:
if type == 0:
return from_int(ifac(n-1), prec, rnd)
if type == 2:
return from_rational(MPZ_ONE, ifac(n-1), prec, rnd)
if type == 3:
return mpf_log(from_int(ifac(n-1)), prec, rnd)
# half-integer
if n < 100 or gamma_size < 10*wp:
if sign:
w = sqrtpi_fixed(wp)
if n % 2: f = ifac2(2*n+1)
else: f = -ifac2(2*n+1)
if type == 0:
return mpf_shift(from_rational(w, f, prec, rnd), -wp+n+1)
if type == 2:
return mpf_shift(from_rational(f, w, prec, rnd), wp-n-1)
if type == 3:
return mpf_log(mpf_shift(from_rational(w, abs(f),
prec, rnd), -wp+n+1), prec, rnd)
elif n == 0:
if type == 0: return mpf_sqrtpi(prec, rnd)
if type == 2: return mpf_div(fone, mpf_sqrtpi(wp), prec, rnd)
if type == 3: return mpf_log(mpf_sqrtpi(wp), prec, rnd)
else:
w = sqrtpi_fixed(wp)
w = from_man_exp(w * ifac2(2*n-1), -wp-n)
if type == 0: return mpf_pos(w, prec, rnd)
if type == 2: return mpf_div(fone, w, prec, rnd)
if type == 3: return mpf_log(mpf_abs(w), prec, rnd)
# Convert to fixed point
offset = exp + wp
if offset >= 0: absxman = man << offset
else: absxman = man >> (-offset)
# For log gamma, provide accurate evaluation for x = 1+eps and 2+eps
if type == 3 and not sign:
one = MPZ_ONE << wp
one_dist = abs(absxman-one)
two_dist = abs(absxman-2*one)
cancellation = (wp - bitcount(min(one_dist, two_dist)))
if cancellation > 10:
xsub1 = mpf_sub(fone, x)
xsub2 = mpf_sub(ftwo, x)
xsub1mag = xsub1[2]+xsub1[3]
xsub2mag = xsub2[2]+xsub2[3]
if xsub1mag < -wp:
return mpf_mul(mpf_euler(wp), mpf_sub(fone, x), prec, rnd)
if xsub2mag < -wp:
return mpf_mul(mpf_sub(fone, mpf_euler(wp)),
mpf_sub(x, ftwo), prec, rnd)
# Proceed but increase precision
wp += max(-xsub1mag, -xsub2mag)
offset = exp + wp
if offset >= 0: absxman = man << offset
else: absxman = man >> (-offset)
# Use Taylor series if appropriate
n_for_stirling = int(GAMMA_STIRLING_BETA*wp)
if n < max(100, n_for_stirling) and wp < MAX_GAMMA_TAYLOR_PREC:
if sign:
absxman = -absxman
return gamma_fixed_taylor(x, absxman, wp, prec, rnd, type)
# Use Stirling's series
# First ensure that |x| is large enough for rapid convergence
xorig = x
# Argument reduction
r = 0
if n < n_for_stirling:
r = one = MPZ_ONE << wp
d = n_for_stirling - n
for k in xrange(d):
r = (r * absxman) >> wp
absxman += one
x = xabs = from_man_exp(absxman, -wp)
if sign:
x = mpf_neg(x)
else:
xabs = mpf_abs(x)
# Asymptotic series
y = real_stirling_series(absxman, wp)
u = to_fixed(mpf_log(xabs, wp), wp)
u = ((absxman - (MPZ_ONE<<(wp-1))) * u) >> wp
y += u
w = from_man_exp(y, -wp)
# Compute final value
if sign:
# Reflection formula
A = mpf_mul(mpf_sin_pi(xorig, wp), xorig, wp)
B = mpf_neg(mpf_pi(wp))
if type == 0 or type == 2:
A = mpf_mul(A, mpf_exp(w, wp))
if r:
B = mpf_mul(B, from_man_exp(r, -wp), wp)
if type == 0:
return mpf_div(B, A, prec, rnd)
if type == 2:
return mpf_div(A, B, prec, rnd)
if type == 3:
if r:
B = mpf_mul(B, from_man_exp(r, -wp), wp)
A = mpf_add(mpf_log(mpf_abs(A), wp), w, wp)
return mpf_sub(mpf_log(mpf_abs(B), wp), A, prec, rnd)
else:
if type == 0:
if r:
return mpf_div(mpf_exp(w, wp),
from_man_exp(r, -wp), prec, rnd)
return mpf_exp(w, prec, rnd)
if type == 2:
if r:
return mpf_div(from_man_exp(r, -wp),
mpf_exp(w, wp), prec, rnd)
return mpf_exp(mpf_neg(w), prec, rnd)
if type == 3:
if r:
return mpf_sub(w, mpf_log(from_man_exp(r,-wp), wp), prec, rnd)
return mpf_pos(w, prec, rnd)
def mpc_gamma(z, prec, rnd='d', type=0):
a, b = z
asign, aman, aexp, abc = a
bsign, bman, bexp, bbc = b
if b == fzero:
# Imaginary part on negative half-axis for log-gamma function
if type == 3 and asign:
re = mpf_gamma(a, prec, rnd, 3)
n = (-aman) >> (-aexp)
im = mpf_mul_int(mpf_pi(prec+10), n, prec, rnd)
return re, im
return mpf_gamma(a, prec, rnd, type), fzero
# Some kind of complex inf/nan
if (not aman and aexp) or (not bman and bexp):
return (fnan, fnan)
# Initial working precision
wp = prec + 20
amag = aexp+abc
bmag = bexp+bbc
if aman:
mag = max(amag, bmag)
else:
mag = bmag
# Close to 0
if mag < -8:
if mag < -wp:
# 1/gamma(z) = z + euler*z^2 + O(z^3)
v = mpc_add(z, mpc_mul_mpf(mpc_mul(z,z,wp),mpf_euler(wp),wp), wp)
if type == 0: return mpc_reciprocal(v, prec, rnd)
if type == 1: return mpc_div(z, v, prec, rnd)
if type == 2: return mpc_pos(v, prec, rnd)
if type == 3: return mpc_log(mpc_reciprocal(v, prec), prec, rnd)
elif type != 1:
wp += (-mag)
# Handle huge log-gamma values; must do this before converting to
# a fixed-point value. TODO: determine a precise cutoff of validity
# depending on amag and bmag
if type == 3 and mag > wp and ((not asign) or (bmag >= amag)):
return mpc_sub(mpc_mul(z, mpc_log(z, wp), wp), z, prec, rnd)
# From now on, we assume having a gamma function
if type == 1:
return mpc_gamma((mpf_add(a, fone), b), prec, rnd, 0)
an = abs(to_int(a))
bn = abs(to_int(b))
absn = max(an, bn)
gamma_size = absn*mag
if type == 3:
pass
else:
wp += bitcount(gamma_size)
# Reflect to the right half-plane. Note that Stirling's expansion
# is valid in the left half-plane too, as long as we're not too close
# to the real axis, but in order to use this argument reduction
# in the negative direction must be implemented.
#need_reflection = asign and ((bmag < 0) or (amag-bmag > 4))
need_reflection = asign
zorig = z
if need_reflection:
z = mpc_neg(z)
asign, aman, aexp, abc = a = z[0]
bsign, bman, bexp, bbc = b = z[1]
# Imaginary part very small compared to real one?
yfinal = 0
balance_prec = 0
if bmag < -10:
# Check z ~= 1 and z ~= 2 for loggamma
if type == 3:
zsub1 = mpc_sub_mpf(z, fone)
if zsub1[0] == fzero:
cancel1 = -bmag
else:
cancel1 = -max(zsub1[0][2]+zsub1[0][3], bmag)
if cancel1 > wp:
pi = mpf_pi(wp)
x = mpc_mul_mpf(zsub1, pi, wp)
x = mpc_mul(x, x, wp)
x = mpc_div_mpf(x, from_int(12), wp)
y = mpc_mul_mpf(zsub1, mpf_neg(mpf_euler(wp)), wp)
yfinal = mpc_add(x, y, wp)
if not need_reflection:
return mpc_pos(yfinal, prec, rnd)
elif cancel1 > 0:
wp += cancel1
zsub2 = mpc_sub_mpf(z, ftwo)
if zsub2[0] == fzero:
cancel2 = -bmag
else:
cancel2 = -max(zsub2[0][2]+zsub2[0][3], bmag)
if cancel2 > wp:
pi = mpf_pi(wp)
t = mpf_sub(mpf_mul(pi, pi), from_int(6))
x = mpc_mul_mpf(mpc_mul(zsub2, zsub2, wp), t, wp)
x = mpc_div_mpf(x, from_int(12), wp)
y = mpc_mul_mpf(zsub2, mpf_sub(fone, mpf_euler(wp)), wp)
yfinal = mpc_add(x, y, wp)
if not need_reflection:
return mpc_pos(yfinal, prec, rnd)
elif cancel2 > 0:
wp += cancel2
if bmag < -wp:
# Compute directly from the real gamma function.
pp = 2*(wp+10)
aabs = mpf_abs(a)
eps = mpf_shift(fone, amag-wp)
x1 = mpf_gamma(aabs, pp, type=type)
x2 = mpf_gamma(mpf_add(aabs, eps), pp, type=type)
xprime = mpf_div(mpf_sub(x2, x1, pp), eps, pp)
y = mpf_mul(b, xprime, prec, rnd)
yfinal = (x1, y)
# Note: we still need to use the reflection formula for
# near-poles, and the correct branch of the log-gamma function
if not need_reflection:
return mpc_pos(yfinal, prec, rnd)
else:
balance_prec += (-bmag)
wp += balance_prec
n_for_stirling = int(GAMMA_STIRLING_BETA*wp)
need_reduction = absn < n_for_stirling
afix = to_fixed(a, wp)
bfix = to_fixed(b, wp)
r = 0
if not yfinal:
zprered = z
# Argument reduction
if absn < n_for_stirling:
absn = complex(an, bn)
d = int((1 + n_for_stirling**2 - bn**2)**0.5 - an)
rre = one = MPZ_ONE << wp
rim = MPZ_ZERO
for k in xrange(d):
rre, rim = ((afix*rre-bfix*rim)>>wp), ((afix*rim + bfix*rre)>>wp)
afix += one
r = from_man_exp(rre, -wp), from_man_exp(rim, -wp)
a = from_man_exp(afix, -wp)
z = a, b
yre, yim = complex_stirling_series(afix, bfix, wp)
# (z-1/2)*log(z) + S
lre, lim = mpc_log(z, wp)
lre = to_fixed(lre, wp)
lim = to_fixed(lim, wp)
yre = ((lre*afix - lim*bfix)>>wp) - (lre>>1) + yre
yim = ((lre*bfix + lim*afix)>>wp) - (lim>>1) + yim
y = from_man_exp(yre, -wp), from_man_exp(yim, -wp)
if r and type == 3:
# If re(z) > 0 and abs(z) <= 4, the branches of loggamma(z)
# and log(gamma(z)) coincide. Otherwise, use the zeroth order
# Stirling expansion to compute the correct imaginary part.
y = mpc_sub(y, mpc_log(r, wp), wp)
zfa = to_float(zprered[0])
zfb = to_float(zprered[1])
zfabs = math.hypot(zfa,zfb)
#if not (zfa > 0.0 and zfabs <= 4):
yfb = to_float(y[1])
u = math.atan2(zfb, zfa)
if zfabs <= 0.5:
gi = 0.577216*zfb - u
else:
gi = -zfb - 0.5*u + zfa*u + zfb*math.log(zfabs)
n = int(math.floor((gi-yfb)/(2*math.pi)+0.5))
y = (y[0], mpf_add(y[1], mpf_mul_int(mpf_pi(wp), 2*n, wp), wp))
if need_reflection:
if type == 0 or type == 2:
A = mpc_mul(mpc_sin_pi(zorig, wp), zorig, wp)
B = (mpf_neg(mpf_pi(wp)), fzero)
if yfinal:
if type == 2:
A = mpc_div(A, yfinal, wp)
else:
A = mpc_mul(A, yfinal, wp)
else:
A = mpc_mul(A, mpc_exp(y, wp), wp)
if r:
B = mpc_mul(B, r, wp)
if type == 0: return mpc_div(B, A, prec, rnd)
if type == 2: return mpc_div(A, B, prec, rnd)
# Reflection formula for the log-gamma function with correct branch
# http://functions.wolfram.com/GammaBetaErf/LogGamma/16/01/01/0006/
# LogGamma[z] == -LogGamma[-z] - Log[-z] +
# Sign[Im[z]] Floor[Re[z]] Pi I + Log[Pi] -
# Log[Sin[Pi (z - Floor[Re[z]])]] -
# Pi I (1 - Abs[Sign[Im[z]]]) Abs[Floor[Re[z]]]
if type == 3:
if yfinal:
s1 = mpc_neg(yfinal)
else:
s1 = mpc_neg(y)
# s -= log(-z)
s1 = mpc_sub(s1, mpc_log(mpc_neg(zorig), wp), wp)
# floor(re(z))
rezfloor = mpf_floor(zorig[0])
imzsign = mpf_sign(zorig[1])
pi = mpf_pi(wp)
t = mpf_mul(pi, rezfloor)
t = mpf_mul_int(t, imzsign, wp)
s1 = (s1[0], mpf_add(s1[1], t, wp))
s1 = mpc_add_mpf(s1, mpf_log(pi, wp), wp)
t = mpc_sin_pi(mpc_sub_mpf(zorig, rezfloor), wp)
t = mpc_log(t, wp)
s1 = mpc_sub(s1, t, wp)
# Note: may actually be unused, because we fall back
# to the mpf_ function for real arguments
if not imzsign:
t = mpf_mul(pi, mpf_floor(rezfloor), wp)
s1 = (s1[0], mpf_sub(s1[1], t, wp))
return mpc_pos(s1, prec, rnd)
else:
if type == 0:
if r:
return mpc_div(mpc_exp(y, wp), r, prec, rnd)
return mpc_exp(y, prec, rnd)
if type == 2:
if r:
return mpc_div(r, mpc_exp(y, wp), prec, rnd)
return mpc_exp(mpc_neg(y), prec, rnd)
if type == 3:
return mpc_pos(y, prec, rnd)
def mpf_factorial(x, prec, rnd='d'):
return mpf_gamma(x, prec, rnd, 1)
def mpc_factorial(x, prec, rnd='d'):
return mpc_gamma(x, prec, rnd, 1)
def mpf_rgamma(x, prec, rnd='d'):
return mpf_gamma(x, prec, rnd, 2)
def mpc_rgamma(x, prec, rnd='d'):
return mpc_gamma(x, prec, rnd, 2)
def mpf_loggamma(x, prec, rnd='d'):
sign, man, exp, bc = x
if sign:
raise ComplexResult
return mpf_gamma(x, prec, rnd, 3)
def mpc_loggamma(z, prec, rnd='d'):
a, b = z
asign, aman, aexp, abc = a
bsign, bman, bexp, bbc = b
if b == fzero and asign:
re = mpf_gamma(a, prec, rnd, 3)
n = (-aman) >> (-aexp)
im = mpf_mul_int(mpf_pi(prec+10), n, prec, rnd)
return re, im
return mpc_gamma(z, prec, rnd, 3)
def mpf_gamma_int(n, prec, rnd=round_fast):
if n < SMALL_FACTORIAL_CACHE_SIZE:
return mpf_pos(small_factorial_cache[n-1], prec, rnd)
return mpf_gamma(from_int(n), prec, rnd)
| 78,727 | 32.009644 | 88 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/libmp/libhyper.py
|
"""
This module implements computation of hypergeometric and related
functions. In particular, it provides code for generic summation
of hypergeometric series. Optimized versions for various special
cases are also provided.
"""
import operator
import math
from .backend import MPZ_ZERO, MPZ_ONE, BACKEND, xrange, exec_
from .libintmath import gcd
from .libmpf import (\
ComplexResult, round_fast, round_nearest,
negative_rnd, bitcount, to_fixed, from_man_exp, from_int, to_int,
from_rational,
fzero, fone, fnone, ftwo, finf, fninf, fnan,
mpf_sign, mpf_add, mpf_abs, mpf_pos,
mpf_cmp, mpf_lt, mpf_le, mpf_gt, mpf_min_max,
mpf_perturb, mpf_neg, mpf_shift, mpf_sub, mpf_mul, mpf_div,
sqrt_fixed, mpf_sqrt, mpf_rdiv_int, mpf_pow_int,
to_rational,
)
from .libelefun import (\
mpf_pi, mpf_exp, mpf_log, pi_fixed, mpf_cos_sin, mpf_cos, mpf_sin,
mpf_sqrt, agm_fixed,
)
from .libmpc import (\
mpc_one, mpc_sub, mpc_mul_mpf, mpc_mul, mpc_neg, complex_int_pow,
mpc_div, mpc_add_mpf, mpc_sub_mpf,
mpc_log, mpc_add, mpc_pos, mpc_shift,
mpc_is_infnan, mpc_zero, mpc_sqrt, mpc_abs,
mpc_mpf_div, mpc_square, mpc_exp
)
from .libintmath import ifac
from .gammazeta import mpf_gamma_int, mpf_euler, euler_fixed
class NoConvergence(Exception):
pass
#-----------------------------------------------------------------------#
# #
# Generic hypergeometric series #
# #
#-----------------------------------------------------------------------#
"""
TODO:
1. proper mpq parsing
2. imaginary z special-cased (also: rational, integer?)
3. more clever handling of series that don't converge because of stupid
upwards rounding
4. checking for cancellation
"""
def make_hyp_summator(key):
"""
Returns a function that sums a generalized hypergeometric series,
for given parameter types (integer, rational, real, complex).
"""
p, q, param_types, ztype = key
pstring = "".join(param_types)
fname = "hypsum_%i_%i_%s_%s_%s" % (p, q, pstring[:p], pstring[p:], ztype)
#print "generating hypsum", fname
have_complex_param = 'C' in param_types
have_complex_arg = ztype == 'C'
have_complex = have_complex_param or have_complex_arg
source = []
add = source.append
aint = []
arat = []
bint = []
brat = []
areal = []
breal = []
acomplex = []
bcomplex = []
#add("wp = prec + 40")
add("MAX = kwargs.get('maxterms', wp*100)")
add("HIGH = MPZ_ONE<<epsshift")
add("LOW = -HIGH")
# Setup code
add("SRE = PRE = one = (MPZ_ONE << wp)")
if have_complex:
add("SIM = PIM = MPZ_ZERO")
if have_complex_arg:
add("xsign, xm, xe, xbc = z[0]")
add("if xsign: xm = -xm")
add("ysign, ym, ye, ybc = z[1]")
add("if ysign: ym = -ym")
else:
add("xsign, xm, xe, xbc = z")
add("if xsign: xm = -xm")
add("offset = xe + wp")
add("if offset >= 0:")
add(" ZRE = xm << offset")
add("else:")
add(" ZRE = xm >> (-offset)")
if have_complex_arg:
add("offset = ye + wp")
add("if offset >= 0:")
add(" ZIM = ym << offset")
add("else:")
add(" ZIM = ym >> (-offset)")
for i, flag in enumerate(param_types):
W = ["A", "B"][i >= p]
if flag == 'Z':
([aint,bint][i >= p]).append(i)
add("%sINT_%i = coeffs[%i]" % (W, i, i))
elif flag == 'Q':
([arat,brat][i >= p]).append(i)
add("%sP_%i, %sQ_%i = coeffs[%i]._mpq_" % (W, i, W, i, i))
elif flag == 'R':
([areal,breal][i >= p]).append(i)
add("xsign, xm, xe, xbc = coeffs[%i]._mpf_" % i)
add("if xsign: xm = -xm")
add("offset = xe + wp")
add("if offset >= 0:")
add(" %sREAL_%i = xm << offset" % (W, i))
add("else:")
add(" %sREAL_%i = xm >> (-offset)" % (W, i))
elif flag == 'C':
([acomplex,bcomplex][i >= p]).append(i)
add("__re, __im = coeffs[%i]._mpc_" % i)
add("xsign, xm, xe, xbc = __re")
add("if xsign: xm = -xm")
add("ysign, ym, ye, ybc = __im")
add("if ysign: ym = -ym")
add("offset = xe + wp")
add("if offset >= 0:")
add(" %sCRE_%i = xm << offset" % (W, i))
add("else:")
add(" %sCRE_%i = xm >> (-offset)" % (W, i))
add("offset = ye + wp")
add("if offset >= 0:")
add(" %sCIM_%i = ym << offset" % (W, i))
add("else:")
add(" %sCIM_%i = ym >> (-offset)" % (W, i))
else:
raise ValueError
l_areal = len(areal)
l_breal = len(breal)
cancellable_real = min(l_areal, l_breal)
noncancellable_real_num = areal[cancellable_real:]
noncancellable_real_den = breal[cancellable_real:]
# LOOP
add("for n in xrange(1,10**8):")
add(" if n in magnitude_check:")
add(" p_mag = bitcount(abs(PRE))")
if have_complex:
add(" p_mag = max(p_mag, bitcount(abs(PIM)))")
add(" magnitude_check[n] = wp-p_mag")
# Real factors
multiplier = " * ".join(["AINT_#".replace("#", str(i)) for i in aint] + \
["AP_#".replace("#", str(i)) for i in arat] + \
["BQ_#".replace("#", str(i)) for i in brat])
divisor = " * ".join(["BINT_#".replace("#", str(i)) for i in bint] + \
["BP_#".replace("#", str(i)) for i in brat] + \
["AQ_#".replace("#", str(i)) for i in arat] + ["n"])
if multiplier:
add(" mul = " + multiplier)
add(" div = " + divisor)
# Check for singular terms
add(" if not div:")
if multiplier:
add(" if not mul:")
add(" break")
add(" raise ZeroDivisionError")
# Update product
if have_complex:
# TODO: when there are several real parameters and just a few complex
# (maybe just the complex argument), we only need to do about
# half as many ops if we accumulate the real factor in a single real variable
for k in range(cancellable_real): add(" PRE = PRE * AREAL_%i // BREAL_%i" % (areal[k], breal[k]))
for i in noncancellable_real_num: add(" PRE = (PRE * AREAL_#) >> wp".replace("#", str(i)))
for i in noncancellable_real_den: add(" PRE = (PRE << wp) // BREAL_#".replace("#", str(i)))
for k in range(cancellable_real): add(" PIM = PIM * AREAL_%i // BREAL_%i" % (areal[k], breal[k]))
for i in noncancellable_real_num: add(" PIM = (PIM * AREAL_#) >> wp".replace("#", str(i)))
for i in noncancellable_real_den: add(" PIM = (PIM << wp) // BREAL_#".replace("#", str(i)))
if multiplier:
if have_complex_arg:
add(" PRE, PIM = (mul*(PRE*ZRE-PIM*ZIM))//div, (mul*(PIM*ZRE+PRE*ZIM))//div")
add(" PRE >>= wp")
add(" PIM >>= wp")
else:
add(" PRE = ((mul * PRE * ZRE) >> wp) // div")
add(" PIM = ((mul * PIM * ZRE) >> wp) // div")
else:
if have_complex_arg:
add(" PRE, PIM = (PRE*ZRE-PIM*ZIM)//div, (PIM*ZRE+PRE*ZIM)//div")
add(" PRE >>= wp")
add(" PIM >>= wp")
else:
add(" PRE = ((PRE * ZRE) >> wp) // div")
add(" PIM = ((PIM * ZRE) >> wp) // div")
for i in acomplex:
add(" PRE, PIM = PRE*ACRE_#-PIM*ACIM_#, PIM*ACRE_#+PRE*ACIM_#".replace("#", str(i)))
add(" PRE >>= wp")
add(" PIM >>= wp")
for i in bcomplex:
add(" mag = BCRE_#*BCRE_#+BCIM_#*BCIM_#".replace("#", str(i)))
add(" re = PRE*BCRE_# + PIM*BCIM_#".replace("#", str(i)))
add(" im = PIM*BCRE_# - PRE*BCIM_#".replace("#", str(i)))
add(" PRE = (re << wp) // mag".replace("#", str(i)))
add(" PIM = (im << wp) // mag".replace("#", str(i)))
else:
for k in range(cancellable_real): add(" PRE = PRE * AREAL_%i // BREAL_%i" % (areal[k], breal[k]))
for i in noncancellable_real_num: add(" PRE = (PRE * AREAL_#) >> wp".replace("#", str(i)))
for i in noncancellable_real_den: add(" PRE = (PRE << wp) // BREAL_#".replace("#", str(i)))
if multiplier:
add(" PRE = ((PRE * mul * ZRE) >> wp) // div")
else:
add(" PRE = ((PRE * ZRE) >> wp) // div")
# Add product to sum
if have_complex:
add(" SRE += PRE")
add(" SIM += PIM")
add(" if (HIGH > PRE > LOW) and (HIGH > PIM > LOW):")
add(" break")
else:
add(" SRE += PRE")
add(" if HIGH > PRE > LOW:")
add(" break")
#add(" from mpmath import nprint, log, ldexp")
#add(" nprint([n, log(abs(PRE),2), ldexp(PRE,-wp)])")
add(" if n > MAX:")
add(" raise NoConvergence('Hypergeometric series converges too slowly. Try increasing maxterms.')")
# +1 all parameters for next loop
for i in aint: add(" AINT_# += 1".replace("#", str(i)))
for i in bint: add(" BINT_# += 1".replace("#", str(i)))
for i in arat: add(" AP_# += AQ_#".replace("#", str(i)))
for i in brat: add(" BP_# += BQ_#".replace("#", str(i)))
for i in areal: add(" AREAL_# += one".replace("#", str(i)))
for i in breal: add(" BREAL_# += one".replace("#", str(i)))
for i in acomplex: add(" ACRE_# += one".replace("#", str(i)))
for i in bcomplex: add(" BCRE_# += one".replace("#", str(i)))
if have_complex:
add("a = from_man_exp(SRE, -wp, prec, 'n')")
add("b = from_man_exp(SIM, -wp, prec, 'n')")
add("if SRE:")
add(" if SIM:")
add(" magn = max(a[2]+a[3], b[2]+b[3])")
add(" else:")
add(" magn = a[2]+a[3]")
add("elif SIM:")
add(" magn = b[2]+b[3]")
add("else:")
add(" magn = -wp+1")
add("return (a, b), True, magn")
else:
add("a = from_man_exp(SRE, -wp, prec, 'n')")
add("if SRE:")
add(" magn = a[2]+a[3]")
add("else:")
add(" magn = -wp+1")
add("return a, False, magn")
source = "\n".join((" " + line) for line in source)
source = ("def %s(coeffs, z, prec, wp, epsshift, magnitude_check, **kwargs):\n" % fname) + source
namespace = {}
exec_(source, globals(), namespace)
#print source
return source, namespace[fname]
if BACKEND == 'sage':
def make_hyp_summator(key):
"""
Returns a function that sums a generalized hypergeometric series,
for given parameter types (integer, rational, real, complex).
"""
from sage.libs.mpmath.ext_main import hypsum_internal
p, q, param_types, ztype = key
def _hypsum(coeffs, z, prec, wp, epsshift, magnitude_check, **kwargs):
return hypsum_internal(p, q, param_types, ztype, coeffs, z,
prec, wp, epsshift, magnitude_check, kwargs)
return "(none)", _hypsum
#-----------------------------------------------------------------------#
# #
# Error functions #
# #
#-----------------------------------------------------------------------#
# TODO: mpf_erf should call mpf_erfc when appropriate (currently
# only the converse delegation is implemented)
def mpf_erf(x, prec, rnd=round_fast):
sign, man, exp, bc = x
if not man:
if x == fzero: return fzero
if x == finf: return fone
if x== fninf: return fnone
return fnan
size = exp + bc
lg = math.log
# The approximation erf(x) = 1 is accurate to > x^2 * log(e,2) bits
if size > 3 and 2*(size-1) + 0.528766 > lg(prec,2):
if sign:
return mpf_perturb(fnone, 0, prec, rnd)
else:
return mpf_perturb(fone, 1, prec, rnd)
# erf(x) ~ 2*x/sqrt(pi) close to 0
if size < -prec:
# 2*x
x = mpf_shift(x,1)
c = mpf_sqrt(mpf_pi(prec+20), prec+20)
# TODO: interval rounding
return mpf_div(x, c, prec, rnd)
wp = prec + abs(size) + 25
# Taylor series for erf, fixed-point summation
t = abs(to_fixed(x, wp))
t2 = (t*t) >> wp
s, term, k = t, 12345, 1
while term:
t = ((t * t2) >> wp) // k
term = t // (2*k+1)
if k & 1:
s -= term
else:
s += term
k += 1
s = (s << (wp+1)) // sqrt_fixed(pi_fixed(wp), wp)
if sign:
s = -s
return from_man_exp(s, -wp, prec, rnd)
# If possible, we use the asymptotic series for erfc.
# This is an alternating divergent asymptotic series, so
# the error is at most equal to the first omitted term.
# Here we check if the smallest term is small enough
# for a given x and precision
def erfc_check_series(x, prec):
n = to_int(x)
if n**2 * 1.44 > prec:
return True
return False
def mpf_erfc(x, prec, rnd=round_fast):
sign, man, exp, bc = x
if not man:
if x == fzero: return fone
if x == finf: return fzero
if x == fninf: return ftwo
return fnan
wp = prec + 20
mag = bc+exp
# Preserve full accuracy when exponent grows huge
wp += max(0, 2*mag)
regular_erf = sign or mag < 2
if regular_erf or not erfc_check_series(x, wp):
if regular_erf:
return mpf_sub(fone, mpf_erf(x, prec+10, negative_rnd[rnd]), prec, rnd)
# 1-erf(x) ~ exp(-x^2), increase prec to deal with cancellation
n = to_int(x)+1
return mpf_sub(fone, mpf_erf(x, prec + int(n**2*1.44) + 10), prec, rnd)
s = term = MPZ_ONE << wp
term_prev = 0
t = (2 * to_fixed(x, wp) ** 2) >> wp
k = 1
while 1:
term = ((term * (2*k - 1)) << wp) // t
if k > 4 and term > term_prev or not term:
break
if k & 1:
s -= term
else:
s += term
term_prev = term
#print k, to_str(from_man_exp(term, -wp, 50), 10)
k += 1
s = (s << wp) // sqrt_fixed(pi_fixed(wp), wp)
s = from_man_exp(s, -wp, wp)
z = mpf_exp(mpf_neg(mpf_mul(x,x,wp),wp),wp)
y = mpf_div(mpf_mul(z, s, wp), x, prec, rnd)
return y
#-----------------------------------------------------------------------#
# #
# Exponential integrals #
# #
#-----------------------------------------------------------------------#
def ei_taylor(x, prec):
s = t = x
k = 2
while t:
t = ((t*x) >> prec) // k
s += t // k
k += 1
return s
def complex_ei_taylor(zre, zim, prec):
_abs = abs
sre = tre = zre
sim = tim = zim
k = 2
while _abs(tre) + _abs(tim) > 5:
tre, tim = ((tre*zre-tim*zim)//k)>>prec, ((tre*zim+tim*zre)//k)>>prec
sre += tre // k
sim += tim // k
k += 1
return sre, sim
def ei_asymptotic(x, prec):
one = MPZ_ONE << prec
x = t = ((one << prec) // x)
s = one + x
k = 2
while t:
t = (k*t*x) >> prec
s += t
k += 1
return s
def complex_ei_asymptotic(zre, zim, prec):
_abs = abs
one = MPZ_ONE << prec
M = (zim*zim + zre*zre) >> prec
# 1 / z
xre = tre = (zre << prec) // M
xim = tim = ((-zim) << prec) // M
sre = one + xre
sim = xim
k = 2
while _abs(tre) + _abs(tim) > 1000:
#print tre, tim
tre, tim = ((tre*xre-tim*xim)*k)>>prec, ((tre*xim+tim*xre)*k)>>prec
sre += tre
sim += tim
k += 1
if k > prec:
raise NoConvergence
return sre, sim
def mpf_ei(x, prec, rnd=round_fast, e1=False):
if e1:
x = mpf_neg(x)
sign, man, exp, bc = x
if e1 and not sign:
if x == fzero:
return finf
raise ComplexResult("E1(x) for x < 0")
if man:
xabs = 0, man, exp, bc
xmag = exp+bc
wp = prec + 20
can_use_asymp = xmag > wp
if not can_use_asymp:
if exp >= 0:
xabsint = man << exp
else:
xabsint = man >> (-exp)
can_use_asymp = xabsint > int(wp*0.693) + 10
if can_use_asymp:
if xmag > wp:
v = fone
else:
v = from_man_exp(ei_asymptotic(to_fixed(x, wp), wp), -wp)
v = mpf_mul(v, mpf_exp(x, wp), wp)
v = mpf_div(v, x, prec, rnd)
else:
wp += 2*int(to_int(xabs))
u = to_fixed(x, wp)
v = ei_taylor(u, wp) + euler_fixed(wp)
t1 = from_man_exp(v,-wp)
t2 = mpf_log(xabs,wp)
v = mpf_add(t1, t2, prec, rnd)
else:
if x == fzero: v = fninf
elif x == finf: v = finf
elif x == fninf: v = fzero
else: v = fnan
if e1:
v = mpf_neg(v)
return v
def mpc_ei(z, prec, rnd=round_fast, e1=False):
if e1:
z = mpc_neg(z)
a, b = z
asign, aman, aexp, abc = a
bsign, bman, bexp, bbc = b
if b == fzero:
if e1:
x = mpf_neg(mpf_ei(a, prec, rnd))
if not asign:
y = mpf_neg(mpf_pi(prec, rnd))
else:
y = fzero
return x, y
else:
return mpf_ei(a, prec, rnd), fzero
if a != fzero:
if not aman or not bman:
return (fnan, fnan)
wp = prec + 40
amag = aexp+abc
bmag = bexp+bbc
zmag = max(amag, bmag)
can_use_asymp = zmag > wp
if not can_use_asymp:
zabsint = abs(to_int(a)) + abs(to_int(b))
can_use_asymp = zabsint > int(wp*0.693) + 20
try:
if can_use_asymp:
if zmag > wp:
v = fone, fzero
else:
zre = to_fixed(a, wp)
zim = to_fixed(b, wp)
vre, vim = complex_ei_asymptotic(zre, zim, wp)
v = from_man_exp(vre, -wp), from_man_exp(vim, -wp)
v = mpc_mul(v, mpc_exp(z, wp), wp)
v = mpc_div(v, z, wp)
if e1:
v = mpc_neg(v, prec, rnd)
else:
x, y = v
if bsign:
v = mpf_pos(x, prec, rnd), mpf_sub(y, mpf_pi(wp), prec, rnd)
else:
v = mpf_pos(x, prec, rnd), mpf_add(y, mpf_pi(wp), prec, rnd)
return v
except NoConvergence:
pass
#wp += 2*max(0,zmag)
wp += 2*int(to_int(mpc_abs(z, 5)))
zre = to_fixed(a, wp)
zim = to_fixed(b, wp)
vre, vim = complex_ei_taylor(zre, zim, wp)
vre += euler_fixed(wp)
v = from_man_exp(vre,-wp), from_man_exp(vim,-wp)
if e1:
u = mpc_log(mpc_neg(z),wp)
else:
u = mpc_log(z,wp)
v = mpc_add(v, u, prec, rnd)
if e1:
v = mpc_neg(v)
return v
def mpf_e1(x, prec, rnd=round_fast):
return mpf_ei(x, prec, rnd, True)
def mpc_e1(x, prec, rnd=round_fast):
return mpc_ei(x, prec, rnd, True)
def mpf_expint(n, x, prec, rnd=round_fast, gamma=False):
"""
E_n(x), n an integer, x real
With gamma=True, computes Gamma(n,x) (upper incomplete gamma function)
Returns (real, None) if real, otherwise (real, imag)
The imaginary part is an optional branch cut term
"""
sign, man, exp, bc = x
if not man:
if gamma:
if x == fzero:
# Actually gamma function pole
if n <= 0:
return finf, None
return mpf_gamma_int(n, prec, rnd), None
if x == finf:
return fzero, None
# TODO: could return finite imaginary value at -inf
return fnan, fnan
else:
if x == fzero:
if n > 1:
return from_rational(1, n-1, prec, rnd), None
else:
return finf, None
if x == finf:
return fzero, None
return fnan, fnan
n_orig = n
if gamma:
n = 1-n
wp = prec + 20
xmag = exp + bc
# Beware of near-poles
if xmag < -10:
raise NotImplementedError
nmag = bitcount(abs(n))
have_imag = n > 0 and sign
negx = mpf_neg(x)
# Skip series if direct convergence
if n == 0 or 2*nmag - xmag < -wp:
if gamma:
v = mpf_exp(negx, wp)
re = mpf_mul(v, mpf_pow_int(x, n_orig-1, wp), prec, rnd)
else:
v = mpf_exp(negx, wp)
re = mpf_div(v, x, prec, rnd)
else:
# Finite number of terms, or...
can_use_asymptotic_series = -3*wp < n <= 0
# ...large enough?
if not can_use_asymptotic_series:
xi = abs(to_int(x))
m = min(max(1, xi-n), 2*wp)
siz = -n*nmag + (m+n)*bitcount(abs(m+n)) - m*xmag - (144*m//100)
tol = -wp-10
can_use_asymptotic_series = siz < tol
if can_use_asymptotic_series:
r = ((-MPZ_ONE) << (wp+wp)) // to_fixed(x, wp)
m = n
t = r*m
s = MPZ_ONE << wp
while m and t:
s += t
m += 1
t = (m*r*t) >> wp
v = mpf_exp(negx, wp)
if gamma:
# ~ exp(-x) * x^(n-1) * (1 + ...)
v = mpf_mul(v, mpf_pow_int(x, n_orig-1, wp), wp)
else:
# ~ exp(-x)/x * (1 + ...)
v = mpf_div(v, x, wp)
re = mpf_mul(v, from_man_exp(s, -wp), prec, rnd)
elif n == 1:
re = mpf_neg(mpf_ei(negx, prec, rnd))
elif n > 0 and n < 3*wp:
T1 = mpf_neg(mpf_ei(negx, wp))
if gamma:
if n_orig & 1:
T1 = mpf_neg(T1)
else:
T1 = mpf_mul(T1, mpf_pow_int(negx, n-1, wp), wp)
r = t = to_fixed(x, wp)
facs = [1] * (n-1)
for k in range(1,n-1):
facs[k] = facs[k-1] * k
facs = facs[::-1]
s = facs[0] << wp
for k in range(1, n-1):
if k & 1:
s -= facs[k] * t
else:
s += facs[k] * t
t = (t*r) >> wp
T2 = from_man_exp(s, -wp, wp)
T2 = mpf_mul(T2, mpf_exp(negx, wp))
if gamma:
T2 = mpf_mul(T2, mpf_pow_int(x, n_orig, wp), wp)
R = mpf_add(T1, T2)
re = mpf_div(R, from_int(ifac(n-1)), prec, rnd)
else:
raise NotImplementedError
if have_imag:
M = from_int(-ifac(n-1))
if gamma:
im = mpf_div(mpf_pi(wp), M, prec, rnd)
if n_orig & 1:
im = mpf_neg(im)
else:
im = mpf_div(mpf_mul(mpf_pi(wp), mpf_pow_int(negx, n_orig-1, wp), wp), M, prec, rnd)
return re, im
else:
return re, None
def mpf_ci_si_taylor(x, wp, which=0):
"""
0 - Ci(x) - (euler+log(x))
1 - Si(x)
"""
x = to_fixed(x, wp)
x2 = -(x*x) >> wp
if which == 0:
s, t, k = 0, (MPZ_ONE<<wp), 2
else:
s, t, k = x, x, 3
while t:
t = (t*x2//(k*(k-1)))>>wp
s += t//k
k += 2
return from_man_exp(s, -wp)
def mpc_ci_si_taylor(re, im, wp, which=0):
# The following code is only designed for small arguments,
# and not too small arguments (for relative accuracy)
if re[1]:
mag = re[2]+re[3]
elif im[1]:
mag = im[2]+im[3]
if im[1]:
mag = max(mag, im[2]+im[3])
if mag > 2 or mag < -wp:
raise NotImplementedError
wp += (2-mag)
zre = to_fixed(re, wp)
zim = to_fixed(im, wp)
z2re = (zim*zim-zre*zre)>>wp
z2im = (-2*zre*zim)>>wp
tre = zre
tim = zim
one = MPZ_ONE<<wp
if which == 0:
sre, sim, tre, tim, k = 0, 0, (MPZ_ONE<<wp), 0, 2
else:
sre, sim, tre, tim, k = zre, zim, zre, zim, 3
while max(abs(tre), abs(tim)) > 2:
f = k*(k-1)
tre, tim = ((tre*z2re-tim*z2im)//f)>>wp, ((tre*z2im+tim*z2re)//f)>>wp
sre += tre//k
sim += tim//k
k += 2
return from_man_exp(sre, -wp), from_man_exp(sim, -wp)
def mpf_ci_si(x, prec, rnd=round_fast, which=2):
"""
Calculation of Ci(x), Si(x) for real x.
which = 0 -- returns (Ci(x), -)
which = 1 -- returns (Si(x), -)
which = 2 -- returns (Ci(x), Si(x))
Note: if x < 0, Ci(x) needs an additional imaginary term, pi*i.
"""
wp = prec + 20
sign, man, exp, bc = x
ci, si = None, None
if not man:
if x == fzero:
return (fninf, fzero)
if x == fnan:
return (x, x)
ci = fzero
if which != 0:
if x == finf:
si = mpf_shift(mpf_pi(prec, rnd), -1)
if x == fninf:
si = mpf_neg(mpf_shift(mpf_pi(prec, negative_rnd[rnd]), -1))
return (ci, si)
# For small x: Ci(x) ~ euler + log(x), Si(x) ~ x
mag = exp+bc
if mag < -wp:
if which != 0:
si = mpf_perturb(x, 1-sign, prec, rnd)
if which != 1:
y = mpf_euler(wp)
xabs = mpf_abs(x)
ci = mpf_add(y, mpf_log(xabs, wp), prec, rnd)
return ci, si
# For huge x: Ci(x) ~ sin(x)/x, Si(x) ~ pi/2
elif mag > wp:
if which != 0:
if sign:
si = mpf_neg(mpf_pi(prec, negative_rnd[rnd]))
else:
si = mpf_pi(prec, rnd)
si = mpf_shift(si, -1)
if which != 1:
ci = mpf_div(mpf_sin(x, wp), x, prec, rnd)
return ci, si
else:
wp += abs(mag)
# Use an asymptotic series? The smallest value of n!/x^n
# occurs for n ~ x, where the magnitude is ~ exp(-x).
asymptotic = mag-1 > math.log(wp, 2)
# Case 1: convergent series near 0
if not asymptotic:
if which != 0:
si = mpf_pos(mpf_ci_si_taylor(x, wp, 1), prec, rnd)
if which != 1:
ci = mpf_ci_si_taylor(x, wp, 0)
ci = mpf_add(ci, mpf_euler(wp), wp)
ci = mpf_add(ci, mpf_log(mpf_abs(x), wp), prec, rnd)
return ci, si
x = mpf_abs(x)
# Case 2: asymptotic series for x >> 1
xf = to_fixed(x, wp)
xr = (MPZ_ONE<<(2*wp)) // xf # 1/x
s1 = (MPZ_ONE << wp)
s2 = xr
t = xr
k = 2
while t:
t = -t
t = (t*xr*k)>>wp
k += 1
s1 += t
t = (t*xr*k)>>wp
k += 1
s2 += t
s1 = from_man_exp(s1, -wp)
s2 = from_man_exp(s2, -wp)
s1 = mpf_div(s1, x, wp)
s2 = mpf_div(s2, x, wp)
cos, sin = mpf_cos_sin(x, wp)
# Ci(x) = sin(x)*s1-cos(x)*s2
# Si(x) = pi/2-cos(x)*s1-sin(x)*s2
if which != 0:
si = mpf_add(mpf_mul(cos, s1), mpf_mul(sin, s2), wp)
si = mpf_sub(mpf_shift(mpf_pi(wp), -1), si, wp)
if sign:
si = mpf_neg(si)
si = mpf_pos(si, prec, rnd)
if which != 1:
ci = mpf_sub(mpf_mul(sin, s1), mpf_mul(cos, s2), prec, rnd)
return ci, si
def mpf_ci(x, prec, rnd=round_fast):
if mpf_sign(x) < 0:
raise ComplexResult
return mpf_ci_si(x, prec, rnd, 0)[0]
def mpf_si(x, prec, rnd=round_fast):
return mpf_ci_si(x, prec, rnd, 1)[1]
def mpc_ci(z, prec, rnd=round_fast):
re, im = z
if im == fzero:
ci = mpf_ci_si(re, prec, rnd, 0)[0]
if mpf_sign(re) < 0:
return (ci, mpf_pi(prec, rnd))
return (ci, fzero)
wp = prec + 20
cre, cim = mpc_ci_si_taylor(re, im, wp, 0)
cre = mpf_add(cre, mpf_euler(wp), wp)
ci = mpc_add((cre, cim), mpc_log(z, wp), prec, rnd)
return ci
def mpc_si(z, prec, rnd=round_fast):
re, im = z
if im == fzero:
return (mpf_ci_si(re, prec, rnd, 1)[1], fzero)
wp = prec + 20
z = mpc_ci_si_taylor(re, im, wp, 1)
return mpc_pos(z, prec, rnd)
#-----------------------------------------------------------------------#
# #
# Bessel functions #
# #
#-----------------------------------------------------------------------#
# A Bessel function of the first kind of integer order, J_n(x), is
# given by the power series
# oo
# ___ k 2 k + n
# \ (-1) / x \
# J_n(x) = ) ----------- | - |
# /___ k! (k + n)! \ 2 /
# k = 0
# Simplifying the quotient between two successive terms gives the
# ratio x^2 / (-4*k*(k+n)). Hence, we only need one full-precision
# multiplication and one division by a small integer per term.
# The complex version is very similar, the only difference being
# that the multiplication is actually 4 multiplies.
# In the general case, we have
# J_v(x) = (x/2)**v / v! * 0F1(v+1, (-1/4)*z**2)
# TODO: for extremely large x, we could use an asymptotic
# trigonometric approximation.
# TODO: recompute at higher precision if the fixed-point mantissa
# is very small
def mpf_besseljn(n, x, prec, rounding=round_fast):
prec += 50
negate = n < 0 and n & 1
mag = x[2]+x[3]
n = abs(n)
wp = prec + 20 + n*bitcount(n)
if mag < 0:
wp -= n * mag
x = to_fixed(x, wp)
x2 = (x**2) >> wp
if not n:
s = t = MPZ_ONE << wp
else:
s = t = (x**n // ifac(n)) >> ((n-1)*wp + n)
k = 1
while t:
t = ((t * x2) // (-4*k*(k+n))) >> wp
s += t
k += 1
if negate:
s = -s
return from_man_exp(s, -wp, prec, rounding)
def mpc_besseljn(n, z, prec, rounding=round_fast):
negate = n < 0 and n & 1
n = abs(n)
origprec = prec
zre, zim = z
mag = max(zre[2]+zre[3], zim[2]+zim[3])
prec += 20 + n*bitcount(n) + abs(mag)
if mag < 0:
prec -= n * mag
zre = to_fixed(zre, prec)
zim = to_fixed(zim, prec)
z2re = (zre**2 - zim**2) >> prec
z2im = (zre*zim) >> (prec-1)
if not n:
sre = tre = MPZ_ONE << prec
sim = tim = MPZ_ZERO
else:
re, im = complex_int_pow(zre, zim, n)
sre = tre = (re // ifac(n)) >> ((n-1)*prec + n)
sim = tim = (im // ifac(n)) >> ((n-1)*prec + n)
k = 1
while abs(tre) + abs(tim) > 3:
p = -4*k*(k+n)
tre, tim = tre*z2re - tim*z2im, tim*z2re + tre*z2im
tre = (tre // p) >> prec
tim = (tim // p) >> prec
sre += tre
sim += tim
k += 1
if negate:
sre = -sre
sim = -sim
re = from_man_exp(sre, -prec, origprec, rounding)
im = from_man_exp(sim, -prec, origprec, rounding)
return (re, im)
def mpf_agm(a, b, prec, rnd=round_fast):
"""
Computes the arithmetic-geometric mean agm(a,b) for
nonnegative mpf values a, b.
"""
asign, aman, aexp, abc = a
bsign, bman, bexp, bbc = b
if asign or bsign:
raise ComplexResult("agm of a negative number")
# Handle inf, nan or zero in either operand
if not (aman and bman):
if a == fnan or b == fnan:
return fnan
if a == finf:
if b == fzero:
return fnan
return finf
if b == finf:
if a == fzero:
return fnan
return finf
# agm(0,x) = agm(x,0) = 0
return fzero
wp = prec + 20
amag = aexp+abc
bmag = bexp+bbc
mag_delta = amag - bmag
# Reduce to roughly the same magnitude using floating-point AGM
abs_mag_delta = abs(mag_delta)
if abs_mag_delta > 10:
while abs_mag_delta > 10:
a, b = mpf_shift(mpf_add(a,b,wp),-1), \
mpf_sqrt(mpf_mul(a,b,wp),wp)
abs_mag_delta //= 2
asign, aman, aexp, abc = a
bsign, bman, bexp, bbc = b
amag = aexp+abc
bmag = bexp+bbc
mag_delta = amag - bmag
#print to_float(a), to_float(b)
# Use agm(a,b) = agm(x*a,x*b)/x to obtain a, b ~= 1
min_mag = min(amag,bmag)
max_mag = max(amag,bmag)
n = 0
# If too small, we lose precision when going to fixed-point
if min_mag < -8:
n = -min_mag
# If too large, we waste time using fixed-point with large numbers
elif max_mag > 20:
n = -max_mag
if n:
a = mpf_shift(a, n)
b = mpf_shift(b, n)
#print to_float(a), to_float(b)
af = to_fixed(a, wp)
bf = to_fixed(b, wp)
g = agm_fixed(af, bf, wp)
return from_man_exp(g, -wp-n, prec, rnd)
def mpf_agm1(a, prec, rnd=round_fast):
"""
Computes the arithmetic-geometric mean agm(1,a) for a nonnegative
mpf value a.
"""
return mpf_agm(fone, a, prec, rnd)
def mpc_agm(a, b, prec, rnd=round_fast):
"""
Complex AGM.
TODO:
* check that convergence works as intended
* optimize
* select a nonarbitrary branch
"""
if mpc_is_infnan(a) or mpc_is_infnan(b):
return fnan, fnan
if mpc_zero in (a, b):
return fzero, fzero
if mpc_neg(a) == b:
return fzero, fzero
wp = prec+20
eps = mpf_shift(fone, -wp+10)
while 1:
a1 = mpc_shift(mpc_add(a, b, wp), -1)
b1 = mpc_sqrt(mpc_mul(a, b, wp), wp)
a, b = a1, b1
size = mpf_min_max([mpc_abs(a,10), mpc_abs(b,10)])[1]
err = mpc_abs(mpc_sub(a, b, 10), 10)
if size == fzero or mpf_lt(err, mpf_mul(eps, size)):
return a
def mpc_agm1(a, prec, rnd=round_fast):
return mpc_agm(mpc_one, a, prec, rnd)
def mpf_ellipk(x, prec, rnd=round_fast):
if not x[1]:
if x == fzero:
return mpf_shift(mpf_pi(prec, rnd), -1)
if x == fninf:
return fzero
if x == fnan:
return x
if x == fone:
return finf
# TODO: for |x| << 1/2, one could use fall back to
# pi/2 * hyp2f1_rat((1,2),(1,2),(1,1), x)
wp = prec + 15
# Use K(x) = pi/2/agm(1,a) where a = sqrt(1-x)
# The sqrt raises ComplexResult if x > 0
a = mpf_sqrt(mpf_sub(fone, x, wp), wp)
v = mpf_agm1(a, wp)
r = mpf_div(mpf_pi(wp), v, prec, rnd)
return mpf_shift(r, -1)
def mpc_ellipk(z, prec, rnd=round_fast):
re, im = z
if im == fzero:
if re == finf:
return mpc_zero
if mpf_le(re, fone):
return mpf_ellipk(re, prec, rnd), fzero
wp = prec + 15
a = mpc_sqrt(mpc_sub(mpc_one, z, wp), wp)
v = mpc_agm1(a, wp)
r = mpc_mpf_div(mpf_pi(wp), v, prec, rnd)
return mpc_shift(r, -1)
def mpf_ellipe(x, prec, rnd=round_fast):
# http://functions.wolfram.com/EllipticIntegrals/
# EllipticK/20/01/0001/
# E = (1-m)*(K'(m)*2*m + K(m))
sign, man, exp, bc = x
if not man:
if x == fzero:
return mpf_shift(mpf_pi(prec, rnd), -1)
if x == fninf:
return finf
if x == fnan:
return x
if x == finf:
raise ComplexResult
if x == fone:
return fone
wp = prec+20
mag = exp+bc
if mag < -wp:
return mpf_shift(mpf_pi(prec, rnd), -1)
# Compute a finite difference for K'
p = max(mag, 0) - wp
h = mpf_shift(fone, p)
K = mpf_ellipk(x, 2*wp)
Kh = mpf_ellipk(mpf_sub(x, h), 2*wp)
Kdiff = mpf_shift(mpf_sub(K, Kh), -p)
t = mpf_sub(fone, x)
b = mpf_mul(Kdiff, mpf_shift(x,1), wp)
return mpf_mul(t, mpf_add(K, b), prec, rnd)
def mpc_ellipe(z, prec, rnd=round_fast):
re, im = z
if im == fzero:
if re == finf:
return (fzero, finf)
if mpf_le(re, fone):
return mpf_ellipe(re, prec, rnd), fzero
wp = prec + 15
mag = mpc_abs(z, 1)
p = max(mag[2]+mag[3], 0) - wp
h = mpf_shift(fone, p)
K = mpc_ellipk(z, 2*wp)
Kh = mpc_ellipk(mpc_add_mpf(z, h, 2*wp), 2*wp)
Kdiff = mpc_shift(mpc_sub(Kh, K, wp), -p)
t = mpc_sub(mpc_one, z, wp)
b = mpc_mul(Kdiff, mpc_shift(z,1), wp)
return mpc_mul(t, mpc_add(K, b, wp), prec, rnd)
| 36,624 | 30.820156 | 110 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/libmp/six.py
|
"""Utilities for writing code that runs on Python 2 and 3"""
# Copyright (c) 2010-2012 Benjamin Peterson
#
# Permission is hereby granted, free of charge, to any person obtaining a copy of
# this software and associated documentation files (the "Software"), to deal in
# the Software without restriction, including without limitation the rights to
# use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
# the Software, and to permit persons to whom the Software is furnished to do so,
# subject to the following conditions:
#
# The above copyright notice and this permission notice shall be included in all
# copies or substantial portions of the Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
# FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
# COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
# IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
# CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
import operator
import sys
import types
__author__ = "Benjamin Peterson <benjamin@python.org>"
__version__ = "1.2.0"
# True if we are running on Python 3.
PY3 = sys.version_info[0] == 3
if PY3:
string_types = str,
integer_types = int,
class_types = type,
text_type = str
binary_type = bytes
MAXSIZE = sys.maxsize
else:
string_types = basestring,
integer_types = (int, long)
class_types = (type, types.ClassType)
text_type = unicode
binary_type = str
if sys.platform.startswith("java"):
# Jython always uses 32 bits.
MAXSIZE = int((1 << 31) - 1)
else:
# It's possible to have sizeof(long) != sizeof(Py_ssize_t).
class X(object):
def __len__(self):
return 1 << 31
try:
len(X())
except OverflowError:
# 32-bit
MAXSIZE = int((1 << 31) - 1)
else:
# 64-bit
MAXSIZE = int((1 << 63) - 1)
del X
def _add_doc(func, doc):
"""Add documentation to a function."""
func.__doc__ = doc
def _import_module(name):
"""Import module, returning the module after the last dot."""
__import__(name)
return sys.modules[name]
class _LazyDescr(object):
def __init__(self, name):
self.name = name
def __get__(self, obj, tp):
result = self._resolve()
setattr(obj, self.name, result)
# This is a bit ugly, but it avoids running this again.
delattr(tp, self.name)
return result
class MovedModule(_LazyDescr):
def __init__(self, name, old, new=None):
super(MovedModule, self).__init__(name)
if PY3:
if new is None:
new = name
self.mod = new
else:
self.mod = old
def _resolve(self):
return _import_module(self.mod)
class MovedAttribute(_LazyDescr):
def __init__(self, name, old_mod, new_mod, old_attr=None, new_attr=None):
super(MovedAttribute, self).__init__(name)
if PY3:
if new_mod is None:
new_mod = name
self.mod = new_mod
if new_attr is None:
if old_attr is None:
new_attr = name
else:
new_attr = old_attr
self.attr = new_attr
else:
self.mod = old_mod
if old_attr is None:
old_attr = name
self.attr = old_attr
def _resolve(self):
module = _import_module(self.mod)
return getattr(module, self.attr)
class _MovedItems(types.ModuleType):
"""Lazy loading of moved objects"""
_moved_attributes = [
MovedAttribute("cStringIO", "cStringIO", "io", "StringIO"),
MovedAttribute("filter", "itertools", "builtins", "ifilter", "filter"),
MovedAttribute("input", "__builtin__", "builtins", "raw_input", "input"),
MovedAttribute("map", "itertools", "builtins", "imap", "map"),
MovedAttribute("reload_module", "__builtin__", "imp", "reload"),
MovedAttribute("reduce", "__builtin__", "functools"),
MovedAttribute("StringIO", "StringIO", "io"),
MovedAttribute("xrange", "__builtin__", "builtins", "xrange", "range"),
MovedAttribute("zip", "itertools", "builtins", "izip", "zip"),
MovedModule("builtins", "__builtin__"),
MovedModule("configparser", "ConfigParser"),
MovedModule("copyreg", "copy_reg"),
MovedModule("http_cookiejar", "cookielib", "http.cookiejar"),
MovedModule("http_cookies", "Cookie", "http.cookies"),
MovedModule("html_entities", "htmlentitydefs", "html.entities"),
MovedModule("html_parser", "HTMLParser", "html.parser"),
MovedModule("http_client", "httplib", "http.client"),
MovedModule("email_mime_multipart", "email.MIMEMultipart", "email.mime.multipart"),
MovedModule("email_mime_text", "email.MIMEText", "email.mime.text"),
MovedModule("email_mime_base", "email.MIMEBase", "email.mime.base"),
MovedModule("BaseHTTPServer", "BaseHTTPServer", "http.server"),
MovedModule("CGIHTTPServer", "CGIHTTPServer", "http.server"),
MovedModule("SimpleHTTPServer", "SimpleHTTPServer", "http.server"),
MovedModule("cPickle", "cPickle", "pickle"),
MovedModule("queue", "Queue"),
MovedModule("reprlib", "repr"),
MovedModule("socketserver", "SocketServer"),
MovedModule("tkinter", "Tkinter"),
MovedModule("tkinter_dialog", "Dialog", "tkinter.dialog"),
MovedModule("tkinter_filedialog", "FileDialog", "tkinter.filedialog"),
MovedModule("tkinter_scrolledtext", "ScrolledText", "tkinter.scrolledtext"),
MovedModule("tkinter_simpledialog", "SimpleDialog", "tkinter.simpledialog"),
MovedModule("tkinter_tix", "Tix", "tkinter.tix"),
MovedModule("tkinter_constants", "Tkconstants", "tkinter.constants"),
MovedModule("tkinter_dnd", "Tkdnd", "tkinter.dnd"),
MovedModule("tkinter_colorchooser", "tkColorChooser",
"tkinter.colorchooser"),
MovedModule("tkinter_commondialog", "tkCommonDialog",
"tkinter.commondialog"),
MovedModule("tkinter_tkfiledialog", "tkFileDialog", "tkinter.filedialog"),
MovedModule("tkinter_font", "tkFont", "tkinter.font"),
MovedModule("tkinter_messagebox", "tkMessageBox", "tkinter.messagebox"),
MovedModule("tkinter_tksimpledialog", "tkSimpleDialog",
"tkinter.simpledialog"),
MovedModule("urllib_robotparser", "robotparser", "urllib.robotparser"),
MovedModule("winreg", "_winreg"),
]
for attr in _moved_attributes:
setattr(_MovedItems, attr.name, attr)
del attr
moves = sys.modules[__name__ + ".moves"] = _MovedItems("moves")
def add_move(move):
"""Add an item to six.moves."""
setattr(_MovedItems, move.name, move)
def remove_move(name):
"""Remove item from six.moves."""
try:
delattr(_MovedItems, name)
except AttributeError:
try:
del moves.__dict__[name]
except KeyError:
raise AttributeError("no such move, %r" % (name,))
if PY3:
_meth_func = "__func__"
_meth_self = "__self__"
_func_code = "__code__"
_func_defaults = "__defaults__"
_iterkeys = "keys"
_itervalues = "values"
_iteritems = "items"
else:
_meth_func = "im_func"
_meth_self = "im_self"
_func_code = "func_code"
_func_defaults = "func_defaults"
_iterkeys = "iterkeys"
_itervalues = "itervalues"
_iteritems = "iteritems"
try:
advance_iterator = next
except NameError:
def advance_iterator(it):
return it.next()
next = advance_iterator
if PY3:
def get_unbound_function(unbound):
return unbound
Iterator = object
def callable(obj):
return any("__call__" in klass.__dict__ for klass in type(obj).__mro__)
else:
def get_unbound_function(unbound):
return unbound.im_func
class Iterator(object):
def next(self):
return type(self).__next__(self)
callable = callable
_add_doc(get_unbound_function,
"""Get the function out of a possibly unbound function""")
get_method_function = operator.attrgetter(_meth_func)
get_method_self = operator.attrgetter(_meth_self)
get_function_code = operator.attrgetter(_func_code)
get_function_defaults = operator.attrgetter(_func_defaults)
def iterkeys(d):
"""Return an iterator over the keys of a dictionary."""
return iter(getattr(d, _iterkeys)())
def itervalues(d):
"""Return an iterator over the values of a dictionary."""
return iter(getattr(d, _itervalues)())
def iteritems(d):
"""Return an iterator over the (key, value) pairs of a dictionary."""
return iter(getattr(d, _iteritems)())
if PY3:
def b(s):
return s.encode("latin-1")
def u(s):
return s
if sys.version_info[1] <= 1:
def int2byte(i):
return bytes((i,))
else:
# This is about 2x faster than the implementation above on 3.2+
int2byte = operator.methodcaller("to_bytes", 1, "big")
import io
StringIO = io.StringIO
BytesIO = io.BytesIO
else:
def b(s):
return s
def u(s):
return unicode(s, "unicode_escape")
int2byte = chr
import StringIO
StringIO = BytesIO = StringIO.StringIO
_add_doc(b, """Byte literal""")
_add_doc(u, """Text literal""")
if PY3:
import builtins
exec_ = getattr(builtins, "exec")
def reraise(tp, value, tb=None):
if value.__traceback__ is not tb:
raise value.with_traceback(tb)
raise value
print_ = getattr(builtins, "print")
del builtins
else:
def exec_(code, globs=None, locs=None):
"""Execute code in a namespace."""
if globs is None:
frame = sys._getframe(1)
globs = frame.f_globals
if locs is None:
locs = frame.f_locals
del frame
elif locs is None:
locs = globs
exec("""exec code in globs, locs""")
exec_("""def reraise(tp, value, tb=None):
raise tp, value, tb
""")
def print_(*args, **kwargs):
"""The new-style print function."""
fp = kwargs.pop("file", sys.stdout)
if fp is None:
return
def write(data):
if not isinstance(data, basestring):
data = str(data)
fp.write(data)
want_unicode = False
sep = kwargs.pop("sep", None)
if sep is not None:
if isinstance(sep, unicode):
want_unicode = True
elif not isinstance(sep, str):
raise TypeError("sep must be None or a string")
end = kwargs.pop("end", None)
if end is not None:
if isinstance(end, unicode):
want_unicode = True
elif not isinstance(end, str):
raise TypeError("end must be None or a string")
if kwargs:
raise TypeError("invalid keyword arguments to print()")
if not want_unicode:
for arg in args:
if isinstance(arg, unicode):
want_unicode = True
break
if want_unicode:
newline = unicode("\n")
space = unicode(" ")
else:
newline = "\n"
space = " "
if sep is None:
sep = space
if end is None:
end = newline
for i, arg in enumerate(args):
if i:
write(sep)
write(arg)
write(end)
_add_doc(reraise, """Reraise an exception.""")
def with_metaclass(meta, base=object):
"""Create a base class with a metaclass."""
return meta("NewBase", (base,), {})
| 11,855 | 29.478149 | 87 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/libmp/libelefun.py
|
"""
This module implements computation of elementary transcendental
functions (powers, logarithms, trigonometric and hyperbolic
functions, inverse trigonometric and hyperbolic) for real
floating-point numbers.
For complex and interval implementations of the same functions,
see libmpc and libmpi.
"""
import math
from bisect import bisect
from .backend import xrange
from .backend import MPZ, MPZ_ZERO, MPZ_ONE, MPZ_TWO, MPZ_FIVE, BACKEND
from .libmpf import (
round_floor, round_ceiling, round_down, round_up,
round_nearest, round_fast,
ComplexResult,
bitcount, bctable, lshift, rshift, giant_steps, sqrt_fixed,
from_int, to_int, from_man_exp, to_fixed, to_float, from_float,
from_rational, normalize,
fzero, fone, fnone, fhalf, finf, fninf, fnan,
mpf_cmp, mpf_sign, mpf_abs,
mpf_pos, mpf_neg, mpf_add, mpf_sub, mpf_mul, mpf_div, mpf_shift,
mpf_rdiv_int, mpf_pow_int, mpf_sqrt,
reciprocal_rnd, negative_rnd, mpf_perturb,
isqrt_fast
)
from .libintmath import ifib
#-------------------------------------------------------------------------------
# Tuning parameters
#-------------------------------------------------------------------------------
# Cutoff for computing exp from cosh+sinh. This reduces the
# number of terms by half, but also requires a square root which
# is expensive with the pure-Python square root code.
if BACKEND == 'python':
EXP_COSH_CUTOFF = 600
else:
EXP_COSH_CUTOFF = 400
# Cutoff for using more than 2 series
EXP_SERIES_U_CUTOFF = 1500
# Also basically determined by sqrt
if BACKEND == 'python':
COS_SIN_CACHE_PREC = 400
else:
COS_SIN_CACHE_PREC = 200
COS_SIN_CACHE_STEP = 8
cos_sin_cache = {}
# Number of integer logarithms to cache (for zeta sums)
MAX_LOG_INT_CACHE = 2000
log_int_cache = {}
LOG_TAYLOR_PREC = 2500 # Use Taylor series with caching up to this prec
LOG_TAYLOR_SHIFT = 9 # Cache log values in steps of size 2^-N
log_taylor_cache = {}
# prec/size ratio of x for fastest convergence in AGM formula
LOG_AGM_MAG_PREC_RATIO = 20
ATAN_TAYLOR_PREC = 3000 # Same as for log
ATAN_TAYLOR_SHIFT = 7 # steps of size 2^-N
atan_taylor_cache = {}
# ~= next power of two + 20
cache_prec_steps = [22,22]
for k in xrange(1, bitcount(LOG_TAYLOR_PREC)+1):
cache_prec_steps += [min(2**k,LOG_TAYLOR_PREC)+20] * 2**(k-1)
#----------------------------------------------------------------------------#
# #
# Elementary mathematical constants #
# #
#----------------------------------------------------------------------------#
def constant_memo(f):
"""
Decorator for caching computed values of mathematical
constants. This decorator should be applied to a
function taking a single argument prec as input and
returning a fixed-point value with the given precision.
"""
f.memo_prec = -1
f.memo_val = None
def g(prec, **kwargs):
memo_prec = f.memo_prec
if prec <= memo_prec:
return f.memo_val >> (memo_prec-prec)
newprec = int(prec*1.05+10)
f.memo_val = f(newprec, **kwargs)
f.memo_prec = newprec
return f.memo_val >> (newprec-prec)
g.__name__ = f.__name__
g.__doc__ = f.__doc__
return g
def def_mpf_constant(fixed):
"""
Create a function that computes the mpf value for a mathematical
constant, given a function that computes the fixed-point value.
Assumptions: the constant is positive and has magnitude ~= 1;
the fixed-point function rounds to floor.
"""
def f(prec, rnd=round_fast):
wp = prec + 20
v = fixed(wp)
if rnd in (round_up, round_ceiling):
v += 1
return normalize(0, v, -wp, bitcount(v), prec, rnd)
f.__doc__ = fixed.__doc__
return f
def bsp_acot(q, a, b, hyperbolic):
if b - a == 1:
a1 = MPZ(2*a + 3)
if hyperbolic or a&1:
return MPZ_ONE, a1 * q**2, a1
else:
return -MPZ_ONE, a1 * q**2, a1
m = (a+b)//2
p1, q1, r1 = bsp_acot(q, a, m, hyperbolic)
p2, q2, r2 = bsp_acot(q, m, b, hyperbolic)
return q2*p1 + r1*p2, q1*q2, r1*r2
# the acoth(x) series converges like the geometric series for x^2
# N = ceil(p*log(2)/(2*log(x)))
def acot_fixed(a, prec, hyperbolic):
"""
Compute acot(a) or acoth(a) for an integer a with binary splitting; see
http://numbers.computation.free.fr/Constants/Algorithms/splitting.html
"""
N = int(0.35 * prec/math.log(a) + 20)
p, q, r = bsp_acot(a, 0,N, hyperbolic)
return ((p+q)<<prec)//(q*a)
def machin(coefs, prec, hyperbolic=False):
"""
Evaluate a Machin-like formula, i.e., a linear combination of
acot(n) or acoth(n) for specific integer values of n, using fixed-
point arithmetic. The input should be a list [(c, n), ...], giving
c*acot[h](n) + ...
"""
extraprec = 10
s = MPZ_ZERO
for a, b in coefs:
s += MPZ(a) * acot_fixed(MPZ(b), prec+extraprec, hyperbolic)
return (s >> extraprec)
# Logarithms of integers are needed for various computations involving
# logarithms, powers, radix conversion, etc
@constant_memo
def ln2_fixed(prec):
"""
Computes ln(2). This is done with a hyperbolic Machin-type formula,
with binary splitting at high precision.
"""
return machin([(18, 26), (-2, 4801), (8, 8749)], prec, True)
@constant_memo
def ln10_fixed(prec):
"""
Computes ln(10). This is done with a hyperbolic Machin-type formula.
"""
return machin([(46, 31), (34, 49), (20, 161)], prec, True)
"""
For computation of pi, we use the Chudnovsky series:
oo
___ k
1 \ (-1) (6 k)! (A + B k)
----- = ) -----------------------
12 pi /___ 3 3k+3/2
(3 k)! (k!) C
k = 0
where A, B, and C are certain integer constants. This series adds roughly
14 digits per term. Note that C^(3/2) can be extracted so that the
series contains only rational terms. This makes binary splitting very
efficient.
The recurrence formulas for the binary splitting were taken from
ftp://ftp.gmplib.org/pub/src/gmp-chudnovsky.c
Previously, Machin's formula was used at low precision and the AGM iteration
was used at high precision. However, the Chudnovsky series is essentially as
fast as the Machin formula at low precision and in practice about 3x faster
than the AGM at high precision (despite theoretically having a worse
asymptotic complexity), so there is no reason not to use it in all cases.
"""
# Constants in Chudnovsky's series
CHUD_A = MPZ(13591409)
CHUD_B = MPZ(545140134)
CHUD_C = MPZ(640320)
CHUD_D = MPZ(12)
def bs_chudnovsky(a, b, level, verbose):
"""
Computes the sum from a to b of the series in the Chudnovsky
formula. Returns g, p, q where p/q is the sum as an exact
fraction and g is a temporary value used to save work
for recursive calls.
"""
if b-a == 1:
g = MPZ((6*b-5)*(2*b-1)*(6*b-1))
p = b**3 * CHUD_C**3 // 24
q = (-1)**b * g * (CHUD_A+CHUD_B*b)
else:
if verbose and level < 4:
print(" binary splitting", a, b)
mid = (a+b)//2
g1, p1, q1 = bs_chudnovsky(a, mid, level+1, verbose)
g2, p2, q2 = bs_chudnovsky(mid, b, level+1, verbose)
p = p1*p2
g = g1*g2
q = q1*p2 + q2*g1
return g, p, q
@constant_memo
def pi_fixed(prec, verbose=False, verbose_base=None):
"""
Compute floor(pi * 2**prec) as a big integer.
This is done using Chudnovsky's series (see comments in
libelefun.py for details).
"""
# The Chudnovsky series gives 14.18 digits per term
N = int(prec/3.3219280948/14.181647462 + 2)
if verbose:
print("binary splitting with N =", N)
g, p, q = bs_chudnovsky(0, N, 0, verbose)
sqrtC = isqrt_fast(CHUD_C<<(2*prec))
v = p*CHUD_C*sqrtC//((q+CHUD_A*p)*CHUD_D)
return v
def degree_fixed(prec):
return pi_fixed(prec)//180
def bspe(a, b):
"""
Sum series for exp(1)-1 between a, b, returning the result
as an exact fraction (p, q).
"""
if b-a == 1:
return MPZ_ONE, MPZ(b)
m = (a+b)//2
p1, q1 = bspe(a, m)
p2, q2 = bspe(m, b)
return p1*q2+p2, q1*q2
@constant_memo
def e_fixed(prec):
"""
Computes exp(1). This is done using the ordinary Taylor series for
exp, with binary splitting. For a description of the algorithm,
see:
http://numbers.computation.free.fr/Constants/
Algorithms/splitting.html
"""
# Slight overestimate of N needed for 1/N! < 2**(-prec)
# This could be tightened for large N.
N = int(1.1*prec/math.log(prec) + 20)
p, q = bspe(0,N)
return ((p+q)<<prec)//q
@constant_memo
def phi_fixed(prec):
"""
Computes the golden ratio, (1+sqrt(5))/2
"""
prec += 10
a = isqrt_fast(MPZ_FIVE<<(2*prec)) + (MPZ_ONE << prec)
return a >> 11
mpf_phi = def_mpf_constant(phi_fixed)
mpf_pi = def_mpf_constant(pi_fixed)
mpf_e = def_mpf_constant(e_fixed)
mpf_degree = def_mpf_constant(degree_fixed)
mpf_ln2 = def_mpf_constant(ln2_fixed)
mpf_ln10 = def_mpf_constant(ln10_fixed)
@constant_memo
def ln_sqrt2pi_fixed(prec):
wp = prec + 10
# ln(sqrt(2*pi)) = ln(2*pi)/2
return to_fixed(mpf_log(mpf_shift(mpf_pi(wp), 1), wp), prec-1)
@constant_memo
def sqrtpi_fixed(prec):
return sqrt_fixed(pi_fixed(prec), prec)
mpf_sqrtpi = def_mpf_constant(sqrtpi_fixed)
mpf_ln_sqrt2pi = def_mpf_constant(ln_sqrt2pi_fixed)
#----------------------------------------------------------------------------#
# #
# Powers #
# #
#----------------------------------------------------------------------------#
def mpf_pow(s, t, prec, rnd=round_fast):
"""
Compute s**t. Raises ComplexResult if s is negative and t is
fractional.
"""
ssign, sman, sexp, sbc = s
tsign, tman, texp, tbc = t
if ssign and texp < 0:
raise ComplexResult("negative number raised to a fractional power")
if texp >= 0:
return mpf_pow_int(s, (-1)**tsign * (tman<<texp), prec, rnd)
# s**(n/2) = sqrt(s)**n
if texp == -1:
if tman == 1:
if tsign:
return mpf_div(fone, mpf_sqrt(s, prec+10,
reciprocal_rnd[rnd]), prec, rnd)
return mpf_sqrt(s, prec, rnd)
else:
if tsign:
return mpf_pow_int(mpf_sqrt(s, prec+10,
reciprocal_rnd[rnd]), -tman, prec, rnd)
return mpf_pow_int(mpf_sqrt(s, prec+10, rnd), tman, prec, rnd)
# General formula: s**t = exp(t*log(s))
# TODO: handle rnd direction of the logarithm carefully
c = mpf_log(s, prec+10, rnd)
return mpf_exp(mpf_mul(t, c), prec, rnd)
def int_pow_fixed(y, n, prec):
"""n-th power of a fixed point number with precision prec
Returns the power in the form man, exp,
man * 2**exp ~= y**n
"""
if n == 2:
return (y*y), 0
bc = bitcount(y)
exp = 0
workprec = 2 * (prec + 4*bitcount(n) + 4)
_, pm, pe, pbc = fone
while 1:
if n & 1:
pm = pm*y
pe = pe+exp
pbc += bc - 2
pbc = pbc + bctable[int(pm >> pbc)]
if pbc > workprec:
pm = pm >> (pbc-workprec)
pe += pbc - workprec
pbc = workprec
n -= 1
if not n:
break
y = y*y
exp = exp+exp
bc = bc + bc - 2
bc = bc + bctable[int(y >> bc)]
if bc > workprec:
y = y >> (bc-workprec)
exp += bc - workprec
bc = workprec
n = n // 2
return pm, pe
# froot(s, n, prec, rnd) computes the real n-th root of a
# positive mpf tuple s.
# To compute the root we start from a 50-bit estimate for r
# generated with ordinary floating-point arithmetic, and then refine
# the value to full accuracy using the iteration
# 1 / y \
# r = --- | (n-1) * r + ---------- |
# n+1 n \ n r_n**(n-1) /
# which is simply Newton's method applied to the equation r**n = y.
# With giant_steps(start, prec+extra) = [p0,...,pm, prec+extra]
# and y = man * 2**-shift one has
# (man * 2**exp)**(1/n) =
# y**(1/n) * 2**(start-prec/n) * 2**(p0-start) * ... * 2**(prec+extra-pm) *
# 2**((exp+shift-(n-1)*prec)/n -extra))
# The last factor is accounted for in the last line of froot.
def nthroot_fixed(y, n, prec, exp1):
start = 50
try:
y1 = rshift(y, prec - n*start)
r = MPZ(int(y1**(1.0/n)))
except OverflowError:
y1 = from_int(y1, start)
fn = from_int(n)
fn = mpf_rdiv_int(1, fn, start)
r = mpf_pow(y1, fn, start)
r = to_int(r)
extra = 10
extra1 = n
prevp = start
for p in giant_steps(start, prec+extra):
pm, pe = int_pow_fixed(r, n-1, prevp)
r2 = rshift(pm, (n-1)*prevp - p - pe - extra1)
B = lshift(y, 2*p-prec+extra1)//r2
r = (B + (n-1) * lshift(r, p-prevp))//n
prevp = p
return r
def mpf_nthroot(s, n, prec, rnd=round_fast):
"""nth-root of a positive number
Use the Newton method when faster, otherwise use x**(1/n)
"""
sign, man, exp, bc = s
if sign:
raise ComplexResult("nth root of a negative number")
if not man:
if s == fnan:
return fnan
if s == fzero:
if n > 0:
return fzero
if n == 0:
return fone
return finf
# Infinity
if not n:
return fnan
if n < 0:
return fzero
return finf
flag_inverse = False
if n < 2:
if n == 0:
return fone
if n == 1:
return mpf_pos(s, prec, rnd)
if n == -1:
return mpf_div(fone, s, prec, rnd)
# n < 0
rnd = reciprocal_rnd[rnd]
flag_inverse = True
extra_inverse = 5
prec += extra_inverse
n = -n
if n > 20 and (n >= 20000 or prec < int(233 + 28.3 * n**0.62)):
prec2 = prec + 10
fn = from_int(n)
nth = mpf_rdiv_int(1, fn, prec2)
r = mpf_pow(s, nth, prec2, rnd)
s = normalize(r[0], r[1], r[2], r[3], prec, rnd)
if flag_inverse:
return mpf_div(fone, s, prec-extra_inverse, rnd)
else:
return s
# Convert to a fixed-point number with prec2 bits.
prec2 = prec + 2*n - (prec%n)
# a few tests indicate that
# for 10 < n < 10**4 a bit more precision is needed
if n > 10:
prec2 += prec2//10
prec2 = prec2 - prec2%n
# Mantissa may have more bits than we need. Trim it down.
shift = bc - prec2
# Adjust exponents to make prec2 and exp+shift multiples of n.
sign1 = 0
es = exp+shift
if es < 0:
sign1 = 1
es = -es
if sign1:
shift += es%n
else:
shift -= es%n
man = rshift(man, shift)
extra = 10
exp1 = ((exp+shift-(n-1)*prec2)//n) - extra
rnd_shift = 0
if flag_inverse:
if rnd == 'u' or rnd == 'c':
rnd_shift = 1
else:
if rnd == 'd' or rnd == 'f':
rnd_shift = 1
man = nthroot_fixed(man+rnd_shift, n, prec2, exp1)
s = from_man_exp(man, exp1, prec, rnd)
if flag_inverse:
return mpf_div(fone, s, prec-extra_inverse, rnd)
else:
return s
def mpf_cbrt(s, prec, rnd=round_fast):
"""cubic root of a positive number"""
return mpf_nthroot(s, 3, prec, rnd)
#----------------------------------------------------------------------------#
# #
# Logarithms #
# #
#----------------------------------------------------------------------------#
def log_int_fixed(n, prec, ln2=None):
"""
Fast computation of log(n), caching the value for small n,
intended for zeta sums.
"""
if n in log_int_cache:
value, vprec = log_int_cache[n]
if vprec >= prec:
return value >> (vprec - prec)
wp = prec + 10
if wp <= LOG_TAYLOR_SHIFT:
if ln2 is None:
ln2 = ln2_fixed(wp)
r = bitcount(n)
x = n << (wp-r)
v = log_taylor_cached(x, wp) + r*ln2
else:
v = to_fixed(mpf_log(from_int(n), wp+5), wp)
if n < MAX_LOG_INT_CACHE:
log_int_cache[n] = (v, wp)
return v >> (wp-prec)
def agm_fixed(a, b, prec):
"""
Fixed-point computation of agm(a,b), assuming
a, b both close to unit magnitude.
"""
i = 0
while 1:
anew = (a+b)>>1
if i > 4 and abs(a-anew) < 8:
return a
b = isqrt_fast(a*b)
a = anew
i += 1
return a
def log_agm(x, prec):
"""
Fixed-point computation of -log(x) = log(1/x), suitable
for large precision. It is required that 0 < x < 1. The
algorithm used is the Sasaki-Kanada formula
-log(x) = pi/agm(theta2(x)^2,theta3(x)^2). [1]
For faster convergence in the theta functions, x should
be chosen closer to 0.
Guard bits must be added by the caller.
HYPOTHESIS: if x = 2^(-n), n bits need to be added to
account for the truncation to a fixed-point number,
and this is the only significant cancellation error.
The number of bits lost to roundoff is small and can be
considered constant.
[1] Richard P. Brent, "Fast Algorithms for High-Precision
Computation of Elementary Functions (extended abstract)",
http://wwwmaths.anu.edu.au/~brent/pd/RNC7-Brent.pdf
"""
x2 = (x*x) >> prec
# Compute jtheta2(x)**2
s = a = b = x2
while a:
b = (b*x2) >> prec
a = (a*b) >> prec
s += a
s += (MPZ_ONE<<prec)
s = (s*s)>>(prec-2)
s = (s*isqrt_fast(x<<prec))>>prec
# Compute jtheta3(x)**2
t = a = b = x
while a:
b = (b*x2) >> prec
a = (a*b) >> prec
t += a
t = (MPZ_ONE<<prec) + (t<<1)
t = (t*t)>>prec
# Final formula
p = agm_fixed(s, t, prec)
return (pi_fixed(prec) << prec) // p
def log_taylor(x, prec, r=0):
"""
Fixed-point calculation of log(x). It is assumed that x is close
enough to 1 for the Taylor series to converge quickly. Convergence
can be improved by specifying r > 0 to compute
log(x^(1/2^r))*2^r, at the cost of performing r square roots.
The caller must provide sufficient guard bits.
"""
for i in xrange(r):
x = isqrt_fast(x<<prec)
one = MPZ_ONE << prec
v = ((x-one)<<prec)//(x+one)
sign = v < 0
if sign:
v = -v
v2 = (v*v) >> prec
v4 = (v2*v2) >> prec
s0 = v
s1 = v//3
v = (v*v4) >> prec
k = 5
while v:
s0 += v // k
k += 2
s1 += v // k
v = (v*v4) >> prec
k += 2
s1 = (s1*v2) >> prec
s = (s0+s1) << (1+r)
if sign:
return -s
return s
def log_taylor_cached(x, prec):
"""
Fixed-point computation of log(x), assuming x in (0.5, 2)
and prec <= LOG_TAYLOR_PREC.
"""
n = x >> (prec-LOG_TAYLOR_SHIFT)
cached_prec = cache_prec_steps[prec]
dprec = cached_prec - prec
if (n, cached_prec) in log_taylor_cache:
a, log_a = log_taylor_cache[n, cached_prec]
else:
a = n << (cached_prec - LOG_TAYLOR_SHIFT)
log_a = log_taylor(a, cached_prec, 8)
log_taylor_cache[n, cached_prec] = (a, log_a)
a >>= dprec
log_a >>= dprec
u = ((x - a) << prec) // a
v = (u << prec) // ((MPZ_TWO << prec) + u)
v2 = (v*v) >> prec
v4 = (v2*v2) >> prec
s0 = v
s1 = v//3
v = (v*v4) >> prec
k = 5
while v:
s0 += v//k
k += 2
s1 += v//k
v = (v*v4) >> prec
k += 2
s1 = (s1*v2) >> prec
s = (s0+s1) << 1
return log_a + s
def mpf_log(x, prec, rnd=round_fast):
"""
Compute the natural logarithm of the mpf value x. If x is negative,
ComplexResult is raised.
"""
sign, man, exp, bc = x
#------------------------------------------------------------------
# Handle special values
if not man:
if x == fzero: return fninf
if x == finf: return finf
if x == fnan: return fnan
if sign:
raise ComplexResult("logarithm of a negative number")
wp = prec + 20
#------------------------------------------------------------------
# Handle log(2^n) = log(n)*2.
# Here we catch the only possible exact value, log(1) = 0
if man == 1:
if not exp:
return fzero
return from_man_exp(exp*ln2_fixed(wp), -wp, prec, rnd)
mag = exp+bc
abs_mag = abs(mag)
#------------------------------------------------------------------
# Handle x = 1+eps, where log(x) ~ x. We need to check for
# cancellation when moving to fixed-point math and compensate
# by increasing the precision. Note that abs_mag in (0, 1) <=>
# 0.5 < x < 2 and x != 1
if abs_mag <= 1:
# Calculate t = x-1 to measure distance from 1 in bits
tsign = 1-abs_mag
if tsign:
tman = (MPZ_ONE<<bc) - man
else:
tman = man - (MPZ_ONE<<(bc-1))
tbc = bitcount(tman)
cancellation = bc - tbc
if cancellation > wp:
t = normalize(tsign, tman, abs_mag-bc, tbc, tbc, 'n')
return mpf_perturb(t, tsign, prec, rnd)
else:
wp += cancellation
# TODO: if close enough to 1, we could use Taylor series
# even in the AGM precision range, since the Taylor series
# converges rapidly
#------------------------------------------------------------------
# Another special case:
# n*log(2) is a good enough approximation
if abs_mag > 10000:
if bitcount(abs_mag) > wp:
return from_man_exp(exp*ln2_fixed(wp), -wp, prec, rnd)
#------------------------------------------------------------------
# General case.
# Perform argument reduction using log(x) = log(x*2^n) - n*log(2):
# If we are in the Taylor precision range, choose magnitude 0 or 1.
# If we are in the AGM precision range, choose magnitude -m for
# some large m; benchmarking on one machine showed m = prec/20 to be
# optimal between 1000 and 100,000 digits.
if wp <= LOG_TAYLOR_PREC:
m = log_taylor_cached(lshift(man, wp-bc), wp)
if mag:
m += mag*ln2_fixed(wp)
else:
optimal_mag = -wp//LOG_AGM_MAG_PREC_RATIO
n = optimal_mag - mag
x = mpf_shift(x, n)
wp += (-optimal_mag)
m = -log_agm(to_fixed(x, wp), wp)
m -= n*ln2_fixed(wp)
return from_man_exp(m, -wp, prec, rnd)
def mpf_log_hypot(a, b, prec, rnd):
"""
Computes log(sqrt(a^2+b^2)) accurately.
"""
# If either a or b is inf/nan/0, assume it to be a
if not b[1]:
a, b = b, a
# a is inf/nan/0
if not a[1]:
# both are inf/nan/0
if not b[1]:
if a == b == fzero:
return fninf
if fnan in (a, b):
return fnan
# at least one term is (+/- inf)^2
return finf
# only a is inf/nan/0
if a == fzero:
# log(sqrt(0+b^2)) = log(|b|)
return mpf_log(mpf_abs(b), prec, rnd)
if a == fnan:
return fnan
return finf
# Exact
a2 = mpf_mul(a,a)
b2 = mpf_mul(b,b)
extra = 20
# Not exact
h2 = mpf_add(a2, b2, prec+extra)
cancelled = mpf_add(h2, fnone, 10)
mag_cancelled = cancelled[2]+cancelled[3]
# Just redo the sum exactly if necessary (could be smarter
# and avoid memory allocation when a or b is precisely 1
# and the other is tiny...)
if cancelled == fzero or mag_cancelled < -extra//2:
h2 = mpf_add(a2, b2, prec+extra-min(a2[2],b2[2]))
return mpf_shift(mpf_log(h2, prec, rnd), -1)
#----------------------------------------------------------------------
# Inverse tangent
#
def atan_newton(x, prec):
if prec >= 100:
r = math.atan(int((x>>(prec-53)))/2.0**53)
else:
r = math.atan(int(x)/2.0**prec)
prevp = 50
r = MPZ(int(r * 2.0**53) >> (53-prevp))
extra_p = 50
for wp in giant_steps(prevp, prec):
wp += extra_p
r = r << (wp-prevp)
cos, sin = cos_sin_fixed(r, wp)
tan = (sin << wp) // cos
a = ((tan-rshift(x, prec-wp)) << wp) // ((MPZ_ONE<<wp) + ((tan**2)>>wp))
r = r - a
prevp = wp
return rshift(r, prevp-prec)
def atan_taylor_get_cached(n, prec):
# Taylor series with caching wins up to huge precisions
# To avoid unnecessary precomputation at low precision, we
# do it in steps
# Round to next power of 2
prec2 = (1<<(bitcount(prec-1))) + 20
dprec = prec2 - prec
if (n, prec2) in atan_taylor_cache:
a, atan_a = atan_taylor_cache[n, prec2]
else:
a = n << (prec2 - ATAN_TAYLOR_SHIFT)
atan_a = atan_newton(a, prec2)
atan_taylor_cache[n, prec2] = (a, atan_a)
return (a >> dprec), (atan_a >> dprec)
def atan_taylor(x, prec):
n = (x >> (prec-ATAN_TAYLOR_SHIFT))
a, atan_a = atan_taylor_get_cached(n, prec)
d = x - a
s0 = v = (d << prec) // ((a**2 >> prec) + (a*d >> prec) + (MPZ_ONE << prec))
v2 = (v**2 >> prec)
v4 = (v2 * v2) >> prec
s1 = v//3
v = (v * v4) >> prec
k = 5
while v:
s0 += v // k
k += 2
s1 += v // k
v = (v * v4) >> prec
k += 2
s1 = (s1 * v2) >> prec
s = s0 - s1
return atan_a + s
def atan_inf(sign, prec, rnd):
if not sign:
return mpf_shift(mpf_pi(prec, rnd), -1)
return mpf_neg(mpf_shift(mpf_pi(prec, negative_rnd[rnd]), -1))
def mpf_atan(x, prec, rnd=round_fast):
sign, man, exp, bc = x
if not man:
if x == fzero: return fzero
if x == finf: return atan_inf(0, prec, rnd)
if x == fninf: return atan_inf(1, prec, rnd)
return fnan
mag = exp + bc
# Essentially infinity
if mag > prec+20:
return atan_inf(sign, prec, rnd)
# Essentially ~ x
if -mag > prec+20:
return mpf_perturb(x, 1-sign, prec, rnd)
wp = prec + 30 + abs(mag)
# For large x, use atan(x) = pi/2 - atan(1/x)
if mag >= 2:
x = mpf_rdiv_int(1, x, wp)
reciprocal = True
else:
reciprocal = False
t = to_fixed(x, wp)
if sign:
t = -t
if wp < ATAN_TAYLOR_PREC:
a = atan_taylor(t, wp)
else:
a = atan_newton(t, wp)
if reciprocal:
a = ((pi_fixed(wp)>>1)+1) - a
if sign:
a = -a
return from_man_exp(a, -wp, prec, rnd)
# TODO: cleanup the special cases
def mpf_atan2(y, x, prec, rnd=round_fast):
xsign, xman, xexp, xbc = x
ysign, yman, yexp, ybc = y
if not yman:
if y == fzero and x != fnan:
if mpf_sign(x) >= 0:
return fzero
return mpf_pi(prec, rnd)
if y in (finf, fninf):
if x in (finf, fninf):
return fnan
# pi/2
if y == finf:
return mpf_shift(mpf_pi(prec, rnd), -1)
# -pi/2
return mpf_neg(mpf_shift(mpf_pi(prec, negative_rnd[rnd]), -1))
return fnan
if ysign:
return mpf_neg(mpf_atan2(mpf_neg(y), x, prec, negative_rnd[rnd]))
if not xman:
if x == fnan:
return fnan
if x == finf:
return fzero
if x == fninf:
return mpf_pi(prec, rnd)
if y == fzero:
return fzero
return mpf_shift(mpf_pi(prec, rnd), -1)
tquo = mpf_atan(mpf_div(y, x, prec+4), prec+4)
if xsign:
return mpf_add(mpf_pi(prec+4), tquo, prec, rnd)
else:
return mpf_pos(tquo, prec, rnd)
def mpf_asin(x, prec, rnd=round_fast):
sign, man, exp, bc = x
if bc+exp > 0 and x not in (fone, fnone):
raise ComplexResult("asin(x) is real only for -1 <= x <= 1")
# asin(x) = 2*atan(x/(1+sqrt(1-x**2)))
wp = prec + 15
a = mpf_mul(x, x)
b = mpf_add(fone, mpf_sqrt(mpf_sub(fone, a, wp), wp), wp)
c = mpf_div(x, b, wp)
return mpf_shift(mpf_atan(c, prec, rnd), 1)
def mpf_acos(x, prec, rnd=round_fast):
# acos(x) = 2*atan(sqrt(1-x**2)/(1+x))
sign, man, exp, bc = x
if bc + exp > 0:
if x not in (fone, fnone):
raise ComplexResult("acos(x) is real only for -1 <= x <= 1")
if x == fnone:
return mpf_pi(prec, rnd)
wp = prec + 15
a = mpf_mul(x, x)
b = mpf_sqrt(mpf_sub(fone, a, wp), wp)
c = mpf_div(b, mpf_add(fone, x, wp), wp)
return mpf_shift(mpf_atan(c, prec, rnd), 1)
def mpf_asinh(x, prec, rnd=round_fast):
wp = prec + 20
sign, man, exp, bc = x
mag = exp+bc
if mag < -8:
if mag < -wp:
return mpf_perturb(x, 1-sign, prec, rnd)
wp += (-mag)
# asinh(x) = log(x+sqrt(x**2+1))
# use reflection symmetry to avoid cancellation
q = mpf_sqrt(mpf_add(mpf_mul(x, x), fone, wp), wp)
q = mpf_add(mpf_abs(x), q, wp)
if sign:
return mpf_neg(mpf_log(q, prec, negative_rnd[rnd]))
else:
return mpf_log(q, prec, rnd)
def mpf_acosh(x, prec, rnd=round_fast):
# acosh(x) = log(x+sqrt(x**2-1))
wp = prec + 15
if mpf_cmp(x, fone) == -1:
raise ComplexResult("acosh(x) is real only for x >= 1")
q = mpf_sqrt(mpf_add(mpf_mul(x,x), fnone, wp), wp)
return mpf_log(mpf_add(x, q, wp), prec, rnd)
def mpf_atanh(x, prec, rnd=round_fast):
# atanh(x) = log((1+x)/(1-x))/2
sign, man, exp, bc = x
if (not man) and exp:
if x in (fzero, fnan):
return x
raise ComplexResult("atanh(x) is real only for -1 <= x <= 1")
mag = bc + exp
if mag > 0:
if mag == 1 and man == 1:
return [finf, fninf][sign]
raise ComplexResult("atanh(x) is real only for -1 <= x <= 1")
wp = prec + 15
if mag < -8:
if mag < -wp:
return mpf_perturb(x, sign, prec, rnd)
wp += (-mag)
a = mpf_add(x, fone, wp)
b = mpf_sub(fone, x, wp)
return mpf_shift(mpf_log(mpf_div(a, b, wp), prec, rnd), -1)
def mpf_fibonacci(x, prec, rnd=round_fast):
sign, man, exp, bc = x
if not man:
if x == fninf:
return fnan
return x
# F(2^n) ~= 2^(2^n)
size = abs(exp+bc)
if exp >= 0:
# Exact
if size < 10 or size <= bitcount(prec):
return from_int(ifib(to_int(x)), prec, rnd)
# Use the modified Binet formula
wp = prec + size + 20
a = mpf_phi(wp)
b = mpf_add(mpf_shift(a, 1), fnone, wp)
u = mpf_pow(a, x, wp)
v = mpf_cos_pi(x, wp)
v = mpf_div(v, u, wp)
u = mpf_sub(u, v, wp)
u = mpf_div(u, b, prec, rnd)
return u
#-------------------------------------------------------------------------------
# Exponential-type functions
#-------------------------------------------------------------------------------
def exponential_series(x, prec, type=0):
"""
Taylor series for cosh/sinh or cos/sin.
type = 0 -- returns exp(x) (slightly faster than cosh+sinh)
type = 1 -- returns (cosh(x), sinh(x))
type = 2 -- returns (cos(x), sin(x))
"""
if x < 0:
x = -x
sign = 1
else:
sign = 0
r = int(0.5*prec**0.5)
xmag = bitcount(x) - prec
r = max(0, xmag + r)
extra = 10 + 2*max(r,-xmag)
wp = prec + extra
x <<= (extra - r)
one = MPZ_ONE << wp
alt = (type == 2)
if prec < EXP_SERIES_U_CUTOFF:
x2 = a = (x*x) >> wp
x4 = (x2*x2) >> wp
s0 = s1 = MPZ_ZERO
k = 2
while a:
a //= (k-1)*k; s0 += a; k += 2
a //= (k-1)*k; s1 += a; k += 2
a = (a*x4) >> wp
s1 = (x2*s1) >> wp
if alt:
c = s1 - s0 + one
else:
c = s1 + s0 + one
else:
u = int(0.3*prec**0.35)
x2 = a = (x*x) >> wp
xpowers = [one, x2]
for i in xrange(1, u):
xpowers.append((xpowers[-1]*x2)>>wp)
sums = [MPZ_ZERO] * u
k = 2
while a:
for i in xrange(u):
a //= (k-1)*k
if alt and k & 2: sums[i] -= a
else: sums[i] += a
k += 2
a = (a*xpowers[-1]) >> wp
for i in xrange(1, u):
sums[i] = (sums[i]*xpowers[i]) >> wp
c = sum(sums) + one
if type == 0:
s = isqrt_fast(c*c - (one<<wp))
if sign:
v = c - s
else:
v = c + s
for i in xrange(r):
v = (v*v) >> wp
return v >> extra
else:
# Repeatedly apply the double-angle formula
# cosh(2*x) = 2*cosh(x)^2 - 1
# cos(2*x) = 2*cos(x)^2 - 1
pshift = wp-1
for i in xrange(r):
c = ((c*c) >> pshift) - one
# With the abs, this is the same for sinh and sin
s = isqrt_fast(abs((one<<wp) - c*c))
if sign:
s = -s
return (c>>extra), (s>>extra)
def exp_basecase(x, prec):
"""
Compute exp(x) as a fixed-point number. Works for any x,
but for speed should have |x| < 1. For an arbitrary number,
use exp(x) = exp(x-m*log(2)) * 2^m where m = floor(x/log(2)).
"""
if prec > EXP_COSH_CUTOFF:
return exponential_series(x, prec, 0)
r = int(prec**0.5)
prec += r
s0 = s1 = (MPZ_ONE << prec)
k = 2
a = x2 = (x*x) >> prec
while a:
a //= k; s0 += a; k += 1
a //= k; s1 += a; k += 1
a = (a*x2) >> prec
s1 = (s1*x) >> prec
s = s0 + s1
u = r
while r:
s = (s*s) >> prec
r -= 1
return s >> u
def exp_expneg_basecase(x, prec):
"""
Computation of exp(x), exp(-x)
"""
if prec > EXP_COSH_CUTOFF:
cosh, sinh = exponential_series(x, prec, 1)
return cosh+sinh, cosh-sinh
a = exp_basecase(x, prec)
b = (MPZ_ONE << (prec+prec)) // a
return a, b
def cos_sin_basecase(x, prec):
"""
Compute cos(x), sin(x) as fixed-point numbers, assuming x
in [0, pi/2). For an arbitrary number, use x' = x - m*(pi/2)
where m = floor(x/(pi/2)) along with quarter-period symmetries.
"""
if prec > COS_SIN_CACHE_PREC:
return exponential_series(x, prec, 2)
precs = prec - COS_SIN_CACHE_STEP
t = x >> precs
n = int(t)
if n not in cos_sin_cache:
w = t<<(10+COS_SIN_CACHE_PREC-COS_SIN_CACHE_STEP)
cos_t, sin_t = exponential_series(w, 10+COS_SIN_CACHE_PREC, 2)
cos_sin_cache[n] = (cos_t>>10), (sin_t>>10)
cos_t, sin_t = cos_sin_cache[n]
offset = COS_SIN_CACHE_PREC - prec
cos_t >>= offset
sin_t >>= offset
x -= t << precs
cos = MPZ_ONE << prec
sin = x
k = 2
a = -((x*x) >> prec)
while a:
a //= k; cos += a; k += 1; a = (a*x) >> prec
a //= k; sin += a; k += 1; a = -((a*x) >> prec)
return ((cos*cos_t-sin*sin_t) >> prec), ((sin*cos_t+cos*sin_t) >> prec)
def mpf_exp(x, prec, rnd=round_fast):
sign, man, exp, bc = x
if man:
mag = bc + exp
wp = prec + 14
if sign:
man = -man
# TODO: the best cutoff depends on both x and the precision.
if prec > 600 and exp >= 0:
# Need about log2(exp(n)) ~= 1.45*mag extra precision
e = mpf_e(wp+int(1.45*mag))
return mpf_pow_int(e, man<<exp, prec, rnd)
if mag < -wp:
return mpf_perturb(fone, sign, prec, rnd)
# |x| >= 2
if mag > 1:
# For large arguments: exp(2^mag*(1+eps)) =
# exp(2^mag)*exp(2^mag*eps) = exp(2^mag)*(1 + 2^mag*eps + ...)
# so about mag extra bits is required.
wpmod = wp + mag
offset = exp + wpmod
if offset >= 0:
t = man << offset
else:
t = man >> (-offset)
lg2 = ln2_fixed(wpmod)
n, t = divmod(t, lg2)
n = int(n)
t >>= mag
else:
offset = exp + wp
if offset >= 0:
t = man << offset
else:
t = man >> (-offset)
n = 0
man = exp_basecase(t, wp)
return from_man_exp(man, n-wp, prec, rnd)
if not exp:
return fone
if x == fninf:
return fzero
return x
def mpf_cosh_sinh(x, prec, rnd=round_fast, tanh=0):
"""Simultaneously compute (cosh(x), sinh(x)) for real x"""
sign, man, exp, bc = x
if (not man) and exp:
if tanh:
if x == finf: return fone
if x == fninf: return fnone
return fnan
if x == finf: return (finf, finf)
if x == fninf: return (finf, fninf)
return fnan, fnan
mag = exp+bc
wp = prec+14
if mag < -4:
# Extremely close to 0, sinh(x) ~= x and cosh(x) ~= 1
if mag < -wp:
if tanh:
return mpf_perturb(x, 1-sign, prec, rnd)
cosh = mpf_perturb(fone, 0, prec, rnd)
sinh = mpf_perturb(x, sign, prec, rnd)
return cosh, sinh
# Fix for cancellation when computing sinh
wp += (-mag)
# Does exp(-2*x) vanish?
if mag > 10:
if 3*(1<<(mag-1)) > wp:
# XXX: rounding
if tanh:
return mpf_perturb([fone,fnone][sign], 1-sign, prec, rnd)
c = s = mpf_shift(mpf_exp(mpf_abs(x), prec, rnd), -1)
if sign:
s = mpf_neg(s)
return c, s
# |x| > 1
if mag > 1:
wpmod = wp + mag
offset = exp + wpmod
if offset >= 0:
t = man << offset
else:
t = man >> (-offset)
lg2 = ln2_fixed(wpmod)
n, t = divmod(t, lg2)
n = int(n)
t >>= mag
else:
offset = exp + wp
if offset >= 0:
t = man << offset
else:
t = man >> (-offset)
n = 0
a, b = exp_expneg_basecase(t, wp)
# TODO: optimize division precision
cosh = a + (b>>(2*n))
sinh = a - (b>>(2*n))
if sign:
sinh = -sinh
if tanh:
man = (sinh << wp) // cosh
return from_man_exp(man, -wp, prec, rnd)
else:
cosh = from_man_exp(cosh, n-wp-1, prec, rnd)
sinh = from_man_exp(sinh, n-wp-1, prec, rnd)
return cosh, sinh
def mod_pi2(man, exp, mag, wp):
# Reduce to standard interval
if mag > 0:
i = 0
while 1:
cancellation_prec = 20 << i
wpmod = wp + mag + cancellation_prec
pi2 = pi_fixed(wpmod-1)
pi4 = pi2 >> 1
offset = wpmod + exp
if offset >= 0:
t = man << offset
else:
t = man >> (-offset)
n, y = divmod(t, pi2)
if y > pi4:
small = pi2 - y
else:
small = y
if small >> (wp+mag-10):
n = int(n)
t = y >> mag
wp = wpmod - mag
break
i += 1
else:
wp += (-mag)
offset = exp + wp
if offset >= 0:
t = man << offset
else:
t = man >> (-offset)
n = 0
return t, n, wp
def mpf_cos_sin(x, prec, rnd=round_fast, which=0, pi=False):
"""
which:
0 -- return cos(x), sin(x)
1 -- return cos(x)
2 -- return sin(x)
3 -- return tan(x)
if pi=True, compute for pi*x
"""
sign, man, exp, bc = x
if not man:
if exp:
c, s = fnan, fnan
else:
c, s = fone, fzero
if which == 0: return c, s
if which == 1: return c
if which == 2: return s
if which == 3: return s
mag = bc + exp
wp = prec + 10
# Extremely small?
if mag < 0:
if mag < -wp:
if pi:
x = mpf_mul(x, mpf_pi(wp))
c = mpf_perturb(fone, 1, prec, rnd)
s = mpf_perturb(x, 1-sign, prec, rnd)
if which == 0: return c, s
if which == 1: return c
if which == 2: return s
if which == 3: return mpf_perturb(x, sign, prec, rnd)
if pi:
if exp >= -1:
if exp == -1:
c = fzero
s = (fone, fnone)[bool(man & 2) ^ sign]
elif exp == 0:
c, s = (fnone, fzero)
else:
c, s = (fone, fzero)
if which == 0: return c, s
if which == 1: return c
if which == 2: return s
if which == 3: return mpf_div(s, c, prec, rnd)
# Subtract nearest half-integer (= mod by pi/2)
n = ((man >> (-exp-2)) + 1) >> 1
man = man - (n << (-exp-1))
mag2 = bitcount(man) + exp
wp = prec + 10 - mag2
offset = exp + wp
if offset >= 0:
t = man << offset
else:
t = man >> (-offset)
t = (t*pi_fixed(wp)) >> wp
else:
t, n, wp = mod_pi2(man, exp, mag, wp)
c, s = cos_sin_basecase(t, wp)
m = n & 3
if m == 1: c, s = -s, c
elif m == 2: c, s = -c, -s
elif m == 3: c, s = s, -c
if sign:
s = -s
if which == 0:
c = from_man_exp(c, -wp, prec, rnd)
s = from_man_exp(s, -wp, prec, rnd)
return c, s
if which == 1:
return from_man_exp(c, -wp, prec, rnd)
if which == 2:
return from_man_exp(s, -wp, prec, rnd)
if which == 3:
return from_rational(s, c, prec, rnd)
def mpf_cos(x, prec, rnd=round_fast): return mpf_cos_sin(x, prec, rnd, 1)
def mpf_sin(x, prec, rnd=round_fast): return mpf_cos_sin(x, prec, rnd, 2)
def mpf_tan(x, prec, rnd=round_fast): return mpf_cos_sin(x, prec, rnd, 3)
def mpf_cos_sin_pi(x, prec, rnd=round_fast): return mpf_cos_sin(x, prec, rnd, 0, 1)
def mpf_cos_pi(x, prec, rnd=round_fast): return mpf_cos_sin(x, prec, rnd, 1, 1)
def mpf_sin_pi(x, prec, rnd=round_fast): return mpf_cos_sin(x, prec, rnd, 2, 1)
def mpf_cosh(x, prec, rnd=round_fast): return mpf_cosh_sinh(x, prec, rnd)[0]
def mpf_sinh(x, prec, rnd=round_fast): return mpf_cosh_sinh(x, prec, rnd)[1]
def mpf_tanh(x, prec, rnd=round_fast): return mpf_cosh_sinh(x, prec, rnd, tanh=1)
# Low-overhead fixed-point versions
def cos_sin_fixed(x, prec, pi2=None):
if pi2 is None:
pi2 = pi_fixed(prec-1)
n, t = divmod(x, pi2)
n = int(n)
c, s = cos_sin_basecase(t, prec)
m = n & 3
if m == 0: return c, s
if m == 1: return -s, c
if m == 2: return -c, -s
if m == 3: return s, -c
def exp_fixed(x, prec, ln2=None):
if ln2 is None:
ln2 = ln2_fixed(prec)
n, t = divmod(x, ln2)
n = int(n)
v = exp_basecase(t, prec)
if n >= 0:
return v << n
else:
return v >> (-n)
if BACKEND == 'sage':
try:
import sage.libs.mpmath.ext_libmp as _lbmp
mpf_sqrt = _lbmp.mpf_sqrt
mpf_exp = _lbmp.mpf_exp
mpf_log = _lbmp.mpf_log
mpf_cos = _lbmp.mpf_cos
mpf_sin = _lbmp.mpf_sin
mpf_pow = _lbmp.mpf_pow
exp_fixed = _lbmp.exp_fixed
cos_sin_fixed = _lbmp.cos_sin_fixed
log_int_fixed = _lbmp.log_int_fixed
except (ImportError, AttributeError):
print("Warning: Sage imports in libelefun failed")
| 43,860 | 29.693492 | 83 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/libmp/libmpi.py
|
"""
Computational functions for interval arithmetic.
"""
from .backend import xrange
from .libmpf import (
ComplexResult,
round_down, round_up, round_floor, round_ceiling, round_nearest,
prec_to_dps, repr_dps, dps_to_prec,
bitcount,
from_float,
fnan, finf, fninf, fzero, fhalf, fone, fnone,
mpf_sign, mpf_lt, mpf_le, mpf_gt, mpf_ge, mpf_eq, mpf_cmp,
mpf_min_max,
mpf_floor, from_int, to_int, to_str, from_str,
mpf_abs, mpf_neg, mpf_pos, mpf_add, mpf_sub, mpf_mul, mpf_mul_int,
mpf_div, mpf_shift, mpf_pow_int,
from_man_exp, MPZ_ONE)
from .libelefun import (
mpf_log, mpf_exp, mpf_sqrt, mpf_atan, mpf_atan2,
mpf_pi, mod_pi2, mpf_cos_sin
)
from .gammazeta import mpf_gamma, mpf_rgamma, mpf_loggamma, mpc_loggamma
def mpi_str(s, prec):
sa, sb = s
dps = prec_to_dps(prec) + 5
return "[%s, %s]" % (to_str(sa, dps), to_str(sb, dps))
#dps = prec_to_dps(prec)
#m = mpi_mid(s, prec)
#d = mpf_shift(mpi_delta(s, 20), -1)
#return "%s +/- %s" % (to_str(m, dps), to_str(d, 3))
mpi_zero = (fzero, fzero)
mpi_one = (fone, fone)
def mpi_eq(s, t):
return s == t
def mpi_ne(s, t):
return s != t
def mpi_lt(s, t):
sa, sb = s
ta, tb = t
if mpf_lt(sb, ta): return True
if mpf_ge(sa, tb): return False
return None
def mpi_le(s, t):
sa, sb = s
ta, tb = t
if mpf_le(sb, ta): return True
if mpf_gt(sa, tb): return False
return None
def mpi_gt(s, t): return mpi_lt(t, s)
def mpi_ge(s, t): return mpi_le(t, s)
def mpi_add(s, t, prec=0):
sa, sb = s
ta, tb = t
a = mpf_add(sa, ta, prec, round_floor)
b = mpf_add(sb, tb, prec, round_ceiling)
if a == fnan: a = fninf
if b == fnan: b = finf
return a, b
def mpi_sub(s, t, prec=0):
sa, sb = s
ta, tb = t
a = mpf_sub(sa, tb, prec, round_floor)
b = mpf_sub(sb, ta, prec, round_ceiling)
if a == fnan: a = fninf
if b == fnan: b = finf
return a, b
def mpi_delta(s, prec):
sa, sb = s
return mpf_sub(sb, sa, prec, round_up)
def mpi_mid(s, prec):
sa, sb = s
return mpf_shift(mpf_add(sa, sb, prec, round_nearest), -1)
def mpi_pos(s, prec):
sa, sb = s
a = mpf_pos(sa, prec, round_floor)
b = mpf_pos(sb, prec, round_ceiling)
return a, b
def mpi_neg(s, prec=0):
sa, sb = s
a = mpf_neg(sb, prec, round_floor)
b = mpf_neg(sa, prec, round_ceiling)
return a, b
def mpi_abs(s, prec=0):
sa, sb = s
sas = mpf_sign(sa)
sbs = mpf_sign(sb)
# Both points nonnegative?
if sas >= 0:
a = mpf_pos(sa, prec, round_floor)
b = mpf_pos(sb, prec, round_ceiling)
# Upper point nonnegative?
elif sbs >= 0:
a = fzero
negsa = mpf_neg(sa)
if mpf_lt(negsa, sb):
b = mpf_pos(sb, prec, round_ceiling)
else:
b = mpf_pos(negsa, prec, round_ceiling)
# Both negative?
else:
a = mpf_neg(sb, prec, round_floor)
b = mpf_neg(sa, prec, round_ceiling)
return a, b
# TODO: optimize
def mpi_mul_mpf(s, t, prec):
return mpi_mul(s, (t, t), prec)
def mpi_div_mpf(s, t, prec):
return mpi_div(s, (t, t), prec)
def mpi_mul(s, t, prec=0):
sa, sb = s
ta, tb = t
sas = mpf_sign(sa)
sbs = mpf_sign(sb)
tas = mpf_sign(ta)
tbs = mpf_sign(tb)
if sas == sbs == 0:
# Should maybe be undefined
if ta == fninf or tb == finf:
return fninf, finf
return fzero, fzero
if tas == tbs == 0:
# Should maybe be undefined
if sa == fninf or sb == finf:
return fninf, finf
return fzero, fzero
if sas >= 0:
# positive * positive
if tas >= 0:
a = mpf_mul(sa, ta, prec, round_floor)
b = mpf_mul(sb, tb, prec, round_ceiling)
if a == fnan: a = fzero
if b == fnan: b = finf
# positive * negative
elif tbs <= 0:
a = mpf_mul(sb, ta, prec, round_floor)
b = mpf_mul(sa, tb, prec, round_ceiling)
if a == fnan: a = fninf
if b == fnan: b = fzero
# positive * both signs
else:
a = mpf_mul(sb, ta, prec, round_floor)
b = mpf_mul(sb, tb, prec, round_ceiling)
if a == fnan: a = fninf
if b == fnan: b = finf
elif sbs <= 0:
# negative * positive
if tas >= 0:
a = mpf_mul(sa, tb, prec, round_floor)
b = mpf_mul(sb, ta, prec, round_ceiling)
if a == fnan: a = fninf
if b == fnan: b = fzero
# negative * negative
elif tbs <= 0:
a = mpf_mul(sb, tb, prec, round_floor)
b = mpf_mul(sa, ta, prec, round_ceiling)
if a == fnan: a = fzero
if b == fnan: b = finf
# negative * both signs
else:
a = mpf_mul(sa, tb, prec, round_floor)
b = mpf_mul(sa, ta, prec, round_ceiling)
if a == fnan: a = fninf
if b == fnan: b = finf
else:
# General case: perform all cross-multiplications and compare
# Since the multiplications can be done exactly, we need only
# do 4 (instead of 8: two for each rounding mode)
cases = [mpf_mul(sa, ta), mpf_mul(sa, tb), mpf_mul(sb, ta), mpf_mul(sb, tb)]
if fnan in cases:
a, b = (fninf, finf)
else:
a, b = mpf_min_max(cases)
a = mpf_pos(a, prec, round_floor)
b = mpf_pos(b, prec, round_ceiling)
return a, b
def mpi_square(s, prec=0):
sa, sb = s
if mpf_ge(sa, fzero):
a = mpf_mul(sa, sa, prec, round_floor)
b = mpf_mul(sb, sb, prec, round_ceiling)
elif mpf_le(sb, fzero):
a = mpf_mul(sb, sb, prec, round_floor)
b = mpf_mul(sa, sa, prec, round_ceiling)
else:
sa = mpf_neg(sa)
sa, sb = mpf_min_max([sa, sb])
a = fzero
b = mpf_mul(sb, sb, prec, round_ceiling)
return a, b
def mpi_div(s, t, prec):
sa, sb = s
ta, tb = t
sas = mpf_sign(sa)
sbs = mpf_sign(sb)
tas = mpf_sign(ta)
tbs = mpf_sign(tb)
# 0 / X
if sas == sbs == 0:
# 0 / <interval containing 0>
if (tas < 0 and tbs > 0) or (tas == 0 or tbs == 0):
return fninf, finf
return fzero, fzero
# Denominator contains both negative and positive numbers;
# this should properly be a multi-interval, but the closest
# match is the entire (extended) real line
if tas < 0 and tbs > 0:
return fninf, finf
# Assume denominator to be nonnegative
if tas < 0:
return mpi_div(mpi_neg(s), mpi_neg(t), prec)
# Division by zero
# XXX: make sure all results make sense
if tas == 0:
# Numerator contains both signs?
if sas < 0 and sbs > 0:
return fninf, finf
if tas == tbs:
return fninf, finf
# Numerator positive?
if sas >= 0:
a = mpf_div(sa, tb, prec, round_floor)
b = finf
if sbs <= 0:
a = fninf
b = mpf_div(sb, tb, prec, round_ceiling)
# Division with positive denominator
# We still have to handle nans resulting from inf/0 or inf/inf
else:
# Nonnegative numerator
if sas >= 0:
a = mpf_div(sa, tb, prec, round_floor)
b = mpf_div(sb, ta, prec, round_ceiling)
if a == fnan: a = fzero
if b == fnan: b = finf
# Nonpositive numerator
elif sbs <= 0:
a = mpf_div(sa, ta, prec, round_floor)
b = mpf_div(sb, tb, prec, round_ceiling)
if a == fnan: a = fninf
if b == fnan: b = fzero
# Numerator contains both signs?
else:
a = mpf_div(sa, ta, prec, round_floor)
b = mpf_div(sb, ta, prec, round_ceiling)
if a == fnan: a = fninf
if b == fnan: b = finf
return a, b
def mpi_pi(prec):
a = mpf_pi(prec, round_floor)
b = mpf_pi(prec, round_ceiling)
return a, b
def mpi_exp(s, prec):
sa, sb = s
# exp is monotonic
a = mpf_exp(sa, prec, round_floor)
b = mpf_exp(sb, prec, round_ceiling)
return a, b
def mpi_log(s, prec):
sa, sb = s
# log is monotonic
a = mpf_log(sa, prec, round_floor)
b = mpf_log(sb, prec, round_ceiling)
return a, b
def mpi_sqrt(s, prec):
sa, sb = s
# sqrt is monotonic
a = mpf_sqrt(sa, prec, round_floor)
b = mpf_sqrt(sb, prec, round_ceiling)
return a, b
def mpi_atan(s, prec):
sa, sb = s
a = mpf_atan(sa, prec, round_floor)
b = mpf_atan(sb, prec, round_ceiling)
return a, b
def mpi_pow_int(s, n, prec):
sa, sb = s
if n < 0:
return mpi_div((fone, fone), mpi_pow_int(s, -n, prec+20), prec)
if n == 0:
return (fone, fone)
if n == 1:
return s
if n == 2:
return mpi_square(s, prec)
# Odd -- signs are preserved
if n & 1:
a = mpf_pow_int(sa, n, prec, round_floor)
b = mpf_pow_int(sb, n, prec, round_ceiling)
# Even -- important to ensure positivity
else:
sas = mpf_sign(sa)
sbs = mpf_sign(sb)
# Nonnegative?
if sas >= 0:
a = mpf_pow_int(sa, n, prec, round_floor)
b = mpf_pow_int(sb, n, prec, round_ceiling)
# Nonpositive?
elif sbs <= 0:
a = mpf_pow_int(sb, n, prec, round_floor)
b = mpf_pow_int(sa, n, prec, round_ceiling)
# Mixed signs?
else:
a = fzero
# max(-a,b)**n
sa = mpf_neg(sa)
if mpf_ge(sa, sb):
b = mpf_pow_int(sa, n, prec, round_ceiling)
else:
b = mpf_pow_int(sb, n, prec, round_ceiling)
return a, b
def mpi_pow(s, t, prec):
ta, tb = t
if ta == tb and ta not in (finf, fninf):
if ta == from_int(to_int(ta)):
return mpi_pow_int(s, to_int(ta), prec)
if ta == fhalf:
return mpi_sqrt(s, prec)
u = mpi_log(s, prec + 20)
v = mpi_mul(u, t, prec + 20)
return mpi_exp(v, prec)
def MIN(x, y):
if mpf_le(x, y):
return x
return y
def MAX(x, y):
if mpf_ge(x, y):
return x
return y
def cos_sin_quadrant(x, wp):
sign, man, exp, bc = x
if x == fzero:
return fone, fzero, 0
# TODO: combine evaluation code to avoid duplicate modulo
c, s = mpf_cos_sin(x, wp)
t, n, wp_ = mod_pi2(man, exp, exp+bc, 15)
if sign:
n = -1-n
return c, s, n
def mpi_cos_sin(x, prec):
a, b = x
if a == b == fzero:
return (fone, fone), (fzero, fzero)
# Guaranteed to contain both -1 and 1
if (finf in x) or (fninf in x):
return (fnone, fone), (fnone, fone)
wp = prec + 20
ca, sa, na = cos_sin_quadrant(a, wp)
cb, sb, nb = cos_sin_quadrant(b, wp)
ca, cb = mpf_min_max([ca, cb])
sa, sb = mpf_min_max([sa, sb])
# Both functions are monotonic within one quadrant
if na == nb:
pass
# Guaranteed to contain both -1 and 1
elif nb - na >= 4:
return (fnone, fone), (fnone, fone)
else:
# cos has maximum between a and b
if na//4 != nb//4:
cb = fone
# cos has minimum
if (na-2)//4 != (nb-2)//4:
ca = fnone
# sin has maximum
if (na-1)//4 != (nb-1)//4:
sb = fone
# sin has minimum
if (na-3)//4 != (nb-3)//4:
sa = fnone
# Perturb to force interval rounding
more = from_man_exp((MPZ_ONE<<wp) + (MPZ_ONE<<10), -wp)
less = from_man_exp((MPZ_ONE<<wp) - (MPZ_ONE<<10), -wp)
def finalize(v, rounding):
if bool(v[0]) == (rounding == round_floor):
p = more
else:
p = less
v = mpf_mul(v, p, prec, rounding)
sign, man, exp, bc = v
if exp+bc >= 1:
if sign:
return fnone
return fone
return v
ca = finalize(ca, round_floor)
cb = finalize(cb, round_ceiling)
sa = finalize(sa, round_floor)
sb = finalize(sb, round_ceiling)
return (ca,cb), (sa,sb)
def mpi_cos(x, prec):
return mpi_cos_sin(x, prec)[0]
def mpi_sin(x, prec):
return mpi_cos_sin(x, prec)[1]
def mpi_tan(x, prec):
cos, sin = mpi_cos_sin(x, prec+20)
return mpi_div(sin, cos, prec)
def mpi_cot(x, prec):
cos, sin = mpi_cos_sin(x, prec+20)
return mpi_div(cos, sin, prec)
def mpi_from_str_a_b(x, y, percent, prec):
wp = prec + 20
xa = from_str(x, wp, round_floor)
xb = from_str(x, wp, round_ceiling)
#ya = from_str(y, wp, round_floor)
y = from_str(y, wp, round_ceiling)
assert mpf_ge(y, fzero)
if percent:
y = mpf_mul(MAX(mpf_abs(xa), mpf_abs(xb)), y, wp, round_ceiling)
y = mpf_div(y, from_int(100), wp, round_ceiling)
a = mpf_sub(xa, y, prec, round_floor)
b = mpf_add(xb, y, prec, round_ceiling)
return a, b
def mpi_from_str(s, prec):
"""
Parse an interval number given as a string.
Allowed forms are
"-1.23e-27"
Any single decimal floating-point literal.
"a +- b" or "a (b)"
a is the midpoint of the interval and b is the half-width
"a +- b%" or "a (b%)"
a is the midpoint of the interval and the half-width
is b percent of a (`a \times b / 100`).
"[a, b]"
The interval indicated directly.
"x[y,z]e"
x are shared digits, y and z are unequal digits, e is the exponent.
"""
e = ValueError("Improperly formed interval number '%s'" % s)
s = s.replace(" ", "")
wp = prec + 20
if "+-" in s:
x, y = s.split("+-")
return mpi_from_str_a_b(x, y, False, prec)
# case 2
elif "(" in s:
# Don't confuse with a complex number (x,y)
if s[0] == "(" or ")" not in s:
raise e
s = s.replace(")", "")
percent = False
if "%" in s:
if s[-1] != "%":
raise e
percent = True
s = s.replace("%", "")
x, y = s.split("(")
return mpi_from_str_a_b(x, y, percent, prec)
elif "," in s:
if ('[' not in s) or (']' not in s):
raise e
if s[0] == '[':
# case 3
s = s.replace("[", "")
s = s.replace("]", "")
a, b = s.split(",")
a = from_str(a, prec, round_floor)
b = from_str(b, prec, round_ceiling)
return a, b
else:
# case 4
x, y = s.split('[')
y, z = y.split(',')
if 'e' in s:
z, e = z.split(']')
else:
z, e = z.rstrip(']'), ''
a = from_str(x+y+e, prec, round_floor)
b = from_str(x+z+e, prec, round_ceiling)
return a, b
else:
a = from_str(s, prec, round_floor)
b = from_str(s, prec, round_ceiling)
return a, b
def mpi_to_str(x, dps, use_spaces=True, brackets='[]', mode='brackets', error_dps=4, **kwargs):
"""
Convert a mpi interval to a string.
**Arguments**
*dps*
decimal places to use for printing
*use_spaces*
use spaces for more readable output, defaults to true
*brackets*
pair of strings (or two-character string) giving left and right brackets
*mode*
mode of display: 'plusminus', 'percent', 'brackets' (default) or 'diff'
*error_dps*
limit the error to *error_dps* digits (mode 'plusminus and 'percent')
Additional keyword arguments are forwarded to the mpf-to-string conversion
for the components of the output.
**Examples**
>>> from mpmath import mpi, mp
>>> mp.dps = 30
>>> x = mpi(1, 2)._mpi_
>>> mpi_to_str(x, 2, mode='plusminus')
'1.5 +- 0.5'
>>> mpi_to_str(x, 2, mode='percent')
'1.5 (33.33%)'
>>> mpi_to_str(x, 2, mode='brackets')
'[1.0, 2.0]'
>>> mpi_to_str(x, 2, mode='brackets' , brackets=('<', '>'))
'<1.0, 2.0>'
>>> x = mpi('5.2582327113062393041', '5.2582327113062749951')._mpi_
>>> mpi_to_str(x, 15, mode='diff')
'5.2582327113062[4, 7]'
>>> mpi_to_str(mpi(0)._mpi_, 2, mode='percent')
'0.0 (0.0%)'
"""
prec = dps_to_prec(dps)
wp = prec + 20
a, b = x
mid = mpi_mid(x, prec)
delta = mpi_delta(x, prec)
a_str = to_str(a, dps, **kwargs)
b_str = to_str(b, dps, **kwargs)
mid_str = to_str(mid, dps, **kwargs)
sp = ""
if use_spaces:
sp = " "
br1, br2 = brackets
if mode == 'plusminus':
delta_str = to_str(mpf_shift(delta,-1), dps, **kwargs)
s = mid_str + sp + "+-" + sp + delta_str
elif mode == 'percent':
if mid == fzero:
p = fzero
else:
# p = 100 * delta(x) / (2*mid(x))
p = mpf_mul(delta, from_int(100))
p = mpf_div(p, mpf_mul(mid, from_int(2)), wp)
s = mid_str + sp + "(" + to_str(p, error_dps) + "%)"
elif mode == 'brackets':
s = br1 + a_str + "," + sp + b_str + br2
elif mode == 'diff':
# use more digits if str(x.a) and str(x.b) are equal
if a_str == b_str:
a_str = to_str(a, dps+3, **kwargs)
b_str = to_str(b, dps+3, **kwargs)
# separate mantissa and exponent
a = a_str.split('e')
if len(a) == 1:
a.append('')
b = b_str.split('e')
if len(b) == 1:
b.append('')
if a[1] == b[1]:
if a[0] != b[0]:
for i in xrange(len(a[0]) + 1):
if a[0][i] != b[0][i]:
break
s = (a[0][:i] + br1 + a[0][i:] + ',' + sp + b[0][i:] + br2
+ 'e'*min(len(a[1]), 1) + a[1])
else: # no difference
s = a[0] + br1 + br2 + 'e'*min(len(a[1]), 1) + a[1]
else:
s = br1 + 'e'.join(a) + ',' + sp + 'e'.join(b) + br2
else:
raise ValueError("'%s' is unknown mode for printing mpi" % mode)
return s
def mpci_add(x, y, prec):
a, b = x
c, d = y
return mpi_add(a, c, prec), mpi_add(b, d, prec)
def mpci_sub(x, y, prec):
a, b = x
c, d = y
return mpi_sub(a, c, prec), mpi_sub(b, d, prec)
def mpci_neg(x, prec=0):
a, b = x
return mpi_neg(a, prec), mpi_neg(b, prec)
def mpci_pos(x, prec):
a, b = x
return mpi_pos(a, prec), mpi_pos(b, prec)
def mpci_mul(x, y, prec):
# TODO: optimize for real/imag cases
a, b = x
c, d = y
r1 = mpi_mul(a,c)
r2 = mpi_mul(b,d)
re = mpi_sub(r1,r2,prec)
i1 = mpi_mul(a,d)
i2 = mpi_mul(b,c)
im = mpi_add(i1,i2,prec)
return re, im
def mpci_div(x, y, prec):
# TODO: optimize for real/imag cases
a, b = x
c, d = y
wp = prec+20
m1 = mpi_square(c)
m2 = mpi_square(d)
m = mpi_add(m1,m2,wp)
re = mpi_add(mpi_mul(a,c), mpi_mul(b,d), wp)
im = mpi_sub(mpi_mul(b,c), mpi_mul(a,d), wp)
re = mpi_div(re, m, prec)
im = mpi_div(im, m, prec)
return re, im
def mpci_exp(x, prec):
a, b = x
wp = prec+20
r = mpi_exp(a, wp)
c, s = mpi_cos_sin(b, wp)
a = mpi_mul(r, c, prec)
b = mpi_mul(r, s, prec)
return a, b
def mpi_shift(x, n):
a, b = x
return mpf_shift(a,n), mpf_shift(b,n)
def mpi_cosh_sinh(x, prec):
# TODO: accuracy for small x
wp = prec+20
e1 = mpi_exp(x, wp)
e2 = mpi_div(mpi_one, e1, wp)
c = mpi_add(e1, e2, prec)
s = mpi_sub(e1, e2, prec)
c = mpi_shift(c, -1)
s = mpi_shift(s, -1)
return c, s
def mpci_cos(x, prec):
a, b = x
wp = prec+10
c, s = mpi_cos_sin(a, wp)
ch, sh = mpi_cosh_sinh(b, wp)
re = mpi_mul(c, ch, prec)
im = mpi_mul(s, sh, prec)
return re, mpi_neg(im)
def mpci_sin(x, prec):
a, b = x
wp = prec+10
c, s = mpi_cos_sin(a, wp)
ch, sh = mpi_cosh_sinh(b, wp)
re = mpi_mul(s, ch, prec)
im = mpi_mul(c, sh, prec)
return re, im
def mpci_abs(x, prec):
a, b = x
if a == mpi_zero:
return mpi_abs(b)
if b == mpi_zero:
return mpi_abs(a)
# Important: nonnegative
a = mpi_square(a)
b = mpi_square(b)
t = mpi_add(a, b, prec+20)
return mpi_sqrt(t, prec)
def mpi_atan2(y, x, prec):
ya, yb = y
xa, xb = x
# Constrained to the real line
if ya == yb == fzero:
if mpf_ge(xa, fzero):
return mpi_zero
return mpi_pi(prec)
# Right half-plane
if mpf_ge(xa, fzero):
if mpf_ge(ya, fzero):
a = mpf_atan2(ya, xb, prec, round_floor)
else:
a = mpf_atan2(ya, xa, prec, round_floor)
if mpf_ge(yb, fzero):
b = mpf_atan2(yb, xa, prec, round_ceiling)
else:
b = mpf_atan2(yb, xb, prec, round_ceiling)
# Upper half-plane
elif mpf_ge(ya, fzero):
b = mpf_atan2(ya, xa, prec, round_ceiling)
if mpf_le(xb, fzero):
a = mpf_atan2(yb, xb, prec, round_floor)
else:
a = mpf_atan2(ya, xb, prec, round_floor)
# Lower half-plane
elif mpf_le(yb, fzero):
a = mpf_atan2(yb, xa, prec, round_floor)
if mpf_le(xb, fzero):
b = mpf_atan2(ya, xb, prec, round_ceiling)
else:
b = mpf_atan2(yb, xb, prec, round_ceiling)
# Covering the origin
else:
b = mpf_pi(prec, round_ceiling)
a = mpf_neg(b)
return a, b
def mpci_arg(z, prec):
x, y = z
return mpi_atan2(y, x, prec)
def mpci_log(z, prec):
x, y = z
re = mpi_log(mpci_abs(z, prec+20), prec)
im = mpci_arg(z, prec)
return re, im
def mpci_pow(x, y, prec):
# TODO: recognize/speed up real cases, integer y
yre, yim = y
if yim == mpi_zero:
ya, yb = yre
if ya == yb:
sign, man, exp, bc = yb
if man and exp >= 0:
return mpci_pow_int(x, (-1)**sign * int(man<<exp), prec)
# x^0
if yb == fzero:
return mpci_pow_int(x, 0, prec)
wp = prec+20
return mpci_exp(mpci_mul(y, mpci_log(x, wp), wp), prec)
def mpci_square(x, prec):
a, b = x
# (a+bi)^2 = (a^2-b^2) + 2abi
re = mpi_sub(mpi_square(a), mpi_square(b), prec)
im = mpi_mul(a, b, prec)
im = mpi_shift(im, 1)
return re, im
def mpci_pow_int(x, n, prec):
if n < 0:
return mpci_div((mpi_one,mpi_zero), mpci_pow_int(x, -n, prec+20), prec)
if n == 0:
return mpi_one, mpi_zero
if n == 1:
return mpci_pos(x, prec)
if n == 2:
return mpci_square(x, prec)
wp = prec + 20
result = (mpi_one, mpi_zero)
while n:
if n & 1:
result = mpci_mul(result, x, wp)
n -= 1
x = mpci_square(x, wp)
n >>= 1
return mpci_pos(result, prec)
gamma_min_a = from_float(1.46163214496)
gamma_min_b = from_float(1.46163214497)
gamma_min = (gamma_min_a, gamma_min_b)
gamma_mono_imag_a = from_float(-1.1)
gamma_mono_imag_b = from_float(1.1)
def mpi_overlap(x, y):
a, b = x
c, d = y
if mpf_lt(d, a): return False
if mpf_gt(c, b): return False
return True
# type = 0 -- gamma
# type = 1 -- factorial
# type = 2 -- 1/gamma
# type = 3 -- log-gamma
def mpi_gamma(z, prec, type=0):
a, b = z
wp = prec+20
if type == 1:
return mpi_gamma(mpi_add(z, mpi_one, wp), prec, 0)
# increasing
if mpf_gt(a, gamma_min_b):
if type == 0:
c = mpf_gamma(a, prec, round_floor)
d = mpf_gamma(b, prec, round_ceiling)
elif type == 2:
c = mpf_rgamma(b, prec, round_floor)
d = mpf_rgamma(a, prec, round_ceiling)
elif type == 3:
c = mpf_loggamma(a, prec, round_floor)
d = mpf_loggamma(b, prec, round_ceiling)
# decreasing
elif mpf_gt(a, fzero) and mpf_lt(b, gamma_min_a):
if type == 0:
c = mpf_gamma(b, prec, round_floor)
d = mpf_gamma(a, prec, round_ceiling)
elif type == 2:
c = mpf_rgamma(a, prec, round_floor)
d = mpf_rgamma(b, prec, round_ceiling)
elif type == 3:
c = mpf_loggamma(b, prec, round_floor)
d = mpf_loggamma(a, prec, round_ceiling)
else:
# TODO: reflection formula
znew = mpi_add(z, mpi_one, wp)
if type == 0: return mpi_div(mpi_gamma(znew, prec+2, 0), z, prec)
if type == 2: return mpi_mul(mpi_gamma(znew, prec+2, 2), z, prec)
if type == 3: return mpi_sub(mpi_gamma(znew, prec+2, 3), mpi_log(z, prec+2), prec)
return c, d
def mpci_gamma(z, prec, type=0):
(a1,a2), (b1,b2) = z
# Real case
if b1 == b2 == fzero and (type != 3 or mpf_gt(a1,fzero)):
return mpi_gamma(z, prec, type), mpi_zero
# Estimate precision
wp = prec+20
if type != 3:
amag = a2[2]+a2[3]
bmag = b2[2]+b2[3]
if a2 != fzero:
mag = max(amag, bmag)
else:
mag = bmag
an = abs(to_int(a2))
bn = abs(to_int(b2))
absn = max(an, bn)
gamma_size = max(0,absn*mag)
wp += bitcount(gamma_size)
# Assume type != 1
if type == 1:
(a1,a2) = mpi_add((a1,a2), mpi_one, wp); z = (a1,a2), (b1,b2)
type = 0
# Avoid non-monotonic region near the negative real axis
if mpf_lt(a1, gamma_min_b):
if mpi_overlap((b1,b2), (gamma_mono_imag_a, gamma_mono_imag_b)):
# TODO: reflection formula
#if mpf_lt(a2, mpf_shift(fone,-1)):
# znew = mpci_sub((mpi_one,mpi_zero),z,wp)
# ...
# Recurrence:
# gamma(z) = gamma(z+1)/z
znew = mpi_add((a1,a2), mpi_one, wp), (b1,b2)
if type == 0: return mpci_div(mpci_gamma(znew, prec+2, 0), z, prec)
if type == 2: return mpci_mul(mpci_gamma(znew, prec+2, 2), z, prec)
if type == 3: return mpci_sub(mpci_gamma(znew, prec+2, 3), mpci_log(z,prec+2), prec)
# Use monotonicity (except for a small region close to the
# origin and near poles)
# upper half-plane
if mpf_ge(b1, fzero):
minre = mpc_loggamma((a1,b2), wp, round_floor)
maxre = mpc_loggamma((a2,b1), wp, round_ceiling)
minim = mpc_loggamma((a1,b1), wp, round_floor)
maxim = mpc_loggamma((a2,b2), wp, round_ceiling)
# lower half-plane
elif mpf_le(b2, fzero):
minre = mpc_loggamma((a1,b1), wp, round_floor)
maxre = mpc_loggamma((a2,b2), wp, round_ceiling)
minim = mpc_loggamma((a2,b1), wp, round_floor)
maxim = mpc_loggamma((a1,b2), wp, round_ceiling)
# crosses real axis
else:
maxre = mpc_loggamma((a2,fzero), wp, round_ceiling)
# stretches more into the lower half-plane
if mpf_gt(mpf_neg(b1), b2):
minre = mpc_loggamma((a1,b1), wp, round_ceiling)
else:
minre = mpc_loggamma((a1,b2), wp, round_ceiling)
minim = mpc_loggamma((a2,b1), wp, round_floor)
maxim = mpc_loggamma((a2,b2), wp, round_floor)
w = (minre[0], maxre[0]), (minim[1], maxim[1])
if type == 3:
return mpi_pos(w[0], prec), mpi_pos(w[1], prec)
if type == 2:
w = mpci_neg(w)
return mpci_exp(w, prec)
def mpi_loggamma(z, prec): return mpi_gamma(z, prec, type=3)
def mpci_loggamma(z, prec): return mpci_gamma(z, prec, type=3)
def mpi_rgamma(z, prec): return mpi_gamma(z, prec, type=2)
def mpci_rgamma(z, prec): return mpci_gamma(z, prec, type=2)
def mpi_factorial(z, prec): return mpi_gamma(z, prec, type=1)
def mpci_factorial(z, prec): return mpci_gamma(z, prec, type=1)
| 27,622 | 28.511752 | 96 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/libmp/libmpc.py
|
"""
Low-level functions for complex arithmetic.
"""
import sys
from .backend import MPZ, MPZ_ZERO, MPZ_ONE, MPZ_TWO, BACKEND
from .libmpf import (\
round_floor, round_ceiling, round_down, round_up,
round_nearest, round_fast, bitcount,
bctable, normalize, normalize1, reciprocal_rnd, rshift, lshift, giant_steps,
negative_rnd,
to_str, to_fixed, from_man_exp, from_float, to_float, from_int, to_int,
fzero, fone, ftwo, fhalf, finf, fninf, fnan, fnone,
mpf_abs, mpf_pos, mpf_neg, mpf_add, mpf_sub, mpf_mul,
mpf_div, mpf_mul_int, mpf_shift, mpf_sqrt, mpf_hypot,
mpf_rdiv_int, mpf_floor, mpf_ceil, mpf_nint, mpf_frac,
mpf_sign, mpf_hash,
ComplexResult
)
from .libelefun import (\
mpf_pi, mpf_exp, mpf_log, mpf_cos_sin, mpf_cosh_sinh, mpf_tan, mpf_pow_int,
mpf_log_hypot,
mpf_cos_sin_pi, mpf_phi,
mpf_cos, mpf_sin, mpf_cos_pi, mpf_sin_pi,
mpf_atan, mpf_atan2, mpf_cosh, mpf_sinh, mpf_tanh,
mpf_asin, mpf_acos, mpf_acosh, mpf_nthroot, mpf_fibonacci
)
# An mpc value is a (real, imag) tuple
mpc_one = fone, fzero
mpc_zero = fzero, fzero
mpc_two = ftwo, fzero
mpc_half = (fhalf, fzero)
_infs = (finf, fninf)
_infs_nan = (finf, fninf, fnan)
def mpc_is_inf(z):
"""Check if either real or imaginary part is infinite"""
re, im = z
if re in _infs: return True
if im in _infs: return True
return False
def mpc_is_infnan(z):
"""Check if either real or imaginary part is infinite or nan"""
re, im = z
if re in _infs_nan: return True
if im in _infs_nan: return True
return False
def mpc_to_str(z, dps, **kwargs):
re, im = z
rs = to_str(re, dps)
if im[0]:
return rs + " - " + to_str(mpf_neg(im), dps, **kwargs) + "j"
else:
return rs + " + " + to_str(im, dps, **kwargs) + "j"
def mpc_to_complex(z, strict=False, rnd=round_fast):
re, im = z
return complex(to_float(re, strict, rnd), to_float(im, strict, rnd))
def mpc_hash(z):
if sys.version >= "3.2":
re, im = z
h = mpf_hash(re) + sys.hash_info.imag * mpf_hash(im)
# Need to reduce either module 2^32 or 2^64
h = h % (2**sys.hash_info.width)
return int(h)
else:
try:
return hash(mpc_to_complex(z, strict=True))
except OverflowError:
return hash(z)
def mpc_conjugate(z, prec, rnd=round_fast):
re, im = z
return re, mpf_neg(im, prec, rnd)
def mpc_is_nonzero(z):
return z != mpc_zero
def mpc_add(z, w, prec, rnd=round_fast):
a, b = z
c, d = w
return mpf_add(a, c, prec, rnd), mpf_add(b, d, prec, rnd)
def mpc_add_mpf(z, x, prec, rnd=round_fast):
a, b = z
return mpf_add(a, x, prec, rnd), b
def mpc_sub(z, w, prec=0, rnd=round_fast):
a, b = z
c, d = w
return mpf_sub(a, c, prec, rnd), mpf_sub(b, d, prec, rnd)
def mpc_sub_mpf(z, p, prec=0, rnd=round_fast):
a, b = z
return mpf_sub(a, p, prec, rnd), b
def mpc_pos(z, prec, rnd=round_fast):
a, b = z
return mpf_pos(a, prec, rnd), mpf_pos(b, prec, rnd)
def mpc_neg(z, prec=None, rnd=round_fast):
a, b = z
return mpf_neg(a, prec, rnd), mpf_neg(b, prec, rnd)
def mpc_shift(z, n):
a, b = z
return mpf_shift(a, n), mpf_shift(b, n)
def mpc_abs(z, prec, rnd=round_fast):
"""Absolute value of a complex number, |a+bi|.
Returns an mpf value."""
a, b = z
return mpf_hypot(a, b, prec, rnd)
def mpc_arg(z, prec, rnd=round_fast):
"""Argument of a complex number. Returns an mpf value."""
a, b = z
return mpf_atan2(b, a, prec, rnd)
def mpc_floor(z, prec, rnd=round_fast):
a, b = z
return mpf_floor(a, prec, rnd), mpf_floor(b, prec, rnd)
def mpc_ceil(z, prec, rnd=round_fast):
a, b = z
return mpf_ceil(a, prec, rnd), mpf_ceil(b, prec, rnd)
def mpc_nint(z, prec, rnd=round_fast):
a, b = z
return mpf_nint(a, prec, rnd), mpf_nint(b, prec, rnd)
def mpc_frac(z, prec, rnd=round_fast):
a, b = z
return mpf_frac(a, prec, rnd), mpf_frac(b, prec, rnd)
def mpc_mul(z, w, prec, rnd=round_fast):
"""
Complex multiplication.
Returns the real and imaginary part of (a+bi)*(c+di), rounded to
the specified precision. The rounding mode applies to the real and
imaginary parts separately.
"""
a, b = z
c, d = w
p = mpf_mul(a, c)
q = mpf_mul(b, d)
r = mpf_mul(a, d)
s = mpf_mul(b, c)
re = mpf_sub(p, q, prec, rnd)
im = mpf_add(r, s, prec, rnd)
return re, im
def mpc_square(z, prec, rnd=round_fast):
# (a+b*I)**2 == a**2 - b**2 + 2*I*a*b
a, b = z
p = mpf_mul(a,a)
q = mpf_mul(b,b)
r = mpf_mul(a,b, prec, rnd)
re = mpf_sub(p, q, prec, rnd)
im = mpf_shift(r, 1)
return re, im
def mpc_mul_mpf(z, p, prec, rnd=round_fast):
a, b = z
re = mpf_mul(a, p, prec, rnd)
im = mpf_mul(b, p, prec, rnd)
return re, im
def mpc_mul_imag_mpf(z, x, prec, rnd=round_fast):
"""
Multiply the mpc value z by I*x where x is an mpf value.
"""
a, b = z
re = mpf_neg(mpf_mul(b, x, prec, rnd))
im = mpf_mul(a, x, prec, rnd)
return re, im
def mpc_mul_int(z, n, prec, rnd=round_fast):
a, b = z
re = mpf_mul_int(a, n, prec, rnd)
im = mpf_mul_int(b, n, prec, rnd)
return re, im
def mpc_div(z, w, prec, rnd=round_fast):
a, b = z
c, d = w
wp = prec + 10
# mag = c*c + d*d
mag = mpf_add(mpf_mul(c, c), mpf_mul(d, d), wp)
# (a*c+b*d)/mag, (b*c-a*d)/mag
t = mpf_add(mpf_mul(a,c), mpf_mul(b,d), wp)
u = mpf_sub(mpf_mul(b,c), mpf_mul(a,d), wp)
return mpf_div(t,mag,prec,rnd), mpf_div(u,mag,prec,rnd)
def mpc_div_mpf(z, p, prec, rnd=round_fast):
"""Calculate z/p where p is real"""
a, b = z
re = mpf_div(a, p, prec, rnd)
im = mpf_div(b, p, prec, rnd)
return re, im
def mpc_reciprocal(z, prec, rnd=round_fast):
"""Calculate 1/z efficiently"""
a, b = z
m = mpf_add(mpf_mul(a,a),mpf_mul(b,b),prec+10)
re = mpf_div(a, m, prec, rnd)
im = mpf_neg(mpf_div(b, m, prec, rnd))
return re, im
def mpc_mpf_div(p, z, prec, rnd=round_fast):
"""Calculate p/z where p is real efficiently"""
a, b = z
m = mpf_add(mpf_mul(a,a),mpf_mul(b,b), prec+10)
re = mpf_div(mpf_mul(a,p), m, prec, rnd)
im = mpf_div(mpf_neg(mpf_mul(b,p)), m, prec, rnd)
return re, im
def complex_int_pow(a, b, n):
"""Complex integer power: computes (a+b*I)**n exactly for
nonnegative n (a and b must be Python ints)."""
wre = 1
wim = 0
while n:
if n & 1:
wre, wim = wre*a - wim*b, wim*a + wre*b
n -= 1
a, b = a*a - b*b, 2*a*b
n //= 2
return wre, wim
def mpc_pow(z, w, prec, rnd=round_fast):
if w[1] == fzero:
return mpc_pow_mpf(z, w[0], prec, rnd)
return mpc_exp(mpc_mul(mpc_log(z, prec+10), w, prec+10), prec, rnd)
def mpc_pow_mpf(z, p, prec, rnd=round_fast):
psign, pman, pexp, pbc = p
if pexp >= 0:
return mpc_pow_int(z, (-1)**psign * (pman<<pexp), prec, rnd)
if pexp == -1:
sqrtz = mpc_sqrt(z, prec+10)
return mpc_pow_int(sqrtz, (-1)**psign * pman, prec, rnd)
return mpc_exp(mpc_mul_mpf(mpc_log(z, prec+10), p, prec+10), prec, rnd)
def mpc_pow_int(z, n, prec, rnd=round_fast):
a, b = z
if b == fzero:
return mpf_pow_int(a, n, prec, rnd), fzero
if a == fzero:
v = mpf_pow_int(b, n, prec, rnd)
n %= 4
if n == 0:
return v, fzero
elif n == 1:
return fzero, v
elif n == 2:
return mpf_neg(v), fzero
elif n == 3:
return fzero, mpf_neg(v)
if n == 0: return mpc_one
if n == 1: return mpc_pos(z, prec, rnd)
if n == 2: return mpc_square(z, prec, rnd)
if n == -1: return mpc_reciprocal(z, prec, rnd)
if n < 0: return mpc_reciprocal(mpc_pow_int(z, -n, prec+4), prec, rnd)
asign, aman, aexp, abc = a
bsign, bman, bexp, bbc = b
if asign: aman = -aman
if bsign: bman = -bman
de = aexp - bexp
abs_de = abs(de)
exact_size = n*(abs_de + max(abc, bbc))
if exact_size < 10000:
if de > 0:
aman <<= de
aexp = bexp
else:
bman <<= (-de)
bexp = aexp
re, im = complex_int_pow(aman, bman, n)
re = from_man_exp(re, int(n*aexp), prec, rnd)
im = from_man_exp(im, int(n*bexp), prec, rnd)
return re, im
return mpc_exp(mpc_mul_int(mpc_log(z, prec+10), n, prec+10), prec, rnd)
def mpc_sqrt(z, prec, rnd=round_fast):
"""Complex square root (principal branch).
We have sqrt(a+bi) = sqrt((r+a)/2) + b/sqrt(2*(r+a))*i where
r = abs(a+bi), when a+bi is not a negative real number."""
a, b = z
if b == fzero:
if a == fzero:
return (a, b)
# When a+bi is a negative real number, we get a real sqrt times i
if a[0]:
im = mpf_sqrt(mpf_neg(a), prec, rnd)
return (fzero, im)
else:
re = mpf_sqrt(a, prec, rnd)
return (re, fzero)
wp = prec+20
if not a[0]: # case a positive
t = mpf_add(mpc_abs((a, b), wp), a, wp) # t = abs(a+bi) + a
u = mpf_shift(t, -1) # u = t/2
re = mpf_sqrt(u, prec, rnd) # re = sqrt(u)
v = mpf_shift(t, 1) # v = 2*t
w = mpf_sqrt(v, wp) # w = sqrt(v)
im = mpf_div(b, w, prec, rnd) # im = b / w
else: # case a negative
t = mpf_sub(mpc_abs((a, b), wp), a, wp) # t = abs(a+bi) - a
u = mpf_shift(t, -1) # u = t/2
im = mpf_sqrt(u, prec, rnd) # im = sqrt(u)
v = mpf_shift(t, 1) # v = 2*t
w = mpf_sqrt(v, wp) # w = sqrt(v)
re = mpf_div(b, w, prec, rnd) # re = b/w
if b[0]:
re = mpf_neg(re)
im = mpf_neg(im)
return re, im
def mpc_nthroot_fixed(a, b, n, prec):
# a, b signed integers at fixed precision prec
start = 50
a1 = int(rshift(a, prec - n*start))
b1 = int(rshift(b, prec - n*start))
try:
r = (a1 + 1j * b1)**(1.0/n)
re = r.real
im = r.imag
re = MPZ(int(re))
im = MPZ(int(im))
except OverflowError:
a1 = from_int(a1, start)
b1 = from_int(b1, start)
fn = from_int(n)
nth = mpf_rdiv_int(1, fn, start)
re, im = mpc_pow((a1, b1), (nth, fzero), start)
re = to_int(re)
im = to_int(im)
extra = 10
prevp = start
extra1 = n
for p in giant_steps(start, prec+extra):
# this is slow for large n, unlike int_pow_fixed
re2, im2 = complex_int_pow(re, im, n-1)
re2 = rshift(re2, (n-1)*prevp - p - extra1)
im2 = rshift(im2, (n-1)*prevp - p - extra1)
r4 = (re2*re2 + im2*im2) >> (p + extra1)
ap = rshift(a, prec - p)
bp = rshift(b, prec - p)
rec = (ap * re2 + bp * im2) >> p
imc = (-ap * im2 + bp * re2) >> p
reb = (rec << p) // r4
imb = (imc << p) // r4
re = (reb + (n-1)*lshift(re, p-prevp))//n
im = (imb + (n-1)*lshift(im, p-prevp))//n
prevp = p
return re, im
def mpc_nthroot(z, n, prec, rnd=round_fast):
"""
Complex n-th root.
Use Newton method as in the real case when it is faster,
otherwise use z**(1/n)
"""
a, b = z
if a[0] == 0 and b == fzero:
re = mpf_nthroot(a, n, prec, rnd)
return (re, fzero)
if n < 2:
if n == 0:
return mpc_one
if n == 1:
return mpc_pos((a, b), prec, rnd)
if n == -1:
return mpc_div(mpc_one, (a, b), prec, rnd)
inverse = mpc_nthroot((a, b), -n, prec+5, reciprocal_rnd[rnd])
return mpc_div(mpc_one, inverse, prec, rnd)
if n <= 20:
prec2 = int(1.2 * (prec + 10))
asign, aman, aexp, abc = a
bsign, bman, bexp, bbc = b
pf = mpc_abs((a,b), prec)
if pf[-2] + pf[-1] > -10 and pf[-2] + pf[-1] < prec:
af = to_fixed(a, prec2)
bf = to_fixed(b, prec2)
re, im = mpc_nthroot_fixed(af, bf, n, prec2)
extra = 10
re = from_man_exp(re, -prec2-extra, prec2, rnd)
im = from_man_exp(im, -prec2-extra, prec2, rnd)
return re, im
fn = from_int(n)
prec2 = prec+10 + 10
nth = mpf_rdiv_int(1, fn, prec2)
re, im = mpc_pow((a, b), (nth, fzero), prec2, rnd)
re = normalize(re[0], re[1], re[2], re[3], prec, rnd)
im = normalize(im[0], im[1], im[2], im[3], prec, rnd)
return re, im
def mpc_cbrt(z, prec, rnd=round_fast):
"""
Complex cubic root.
"""
return mpc_nthroot(z, 3, prec, rnd)
def mpc_exp(z, prec, rnd=round_fast):
"""
Complex exponential function.
We use the direct formula exp(a+bi) = exp(a) * (cos(b) + sin(b)*i)
for the computation. This formula is very nice because it is
pefectly stable; since we just do real multiplications, the only
numerical errors that can creep in are single-ulp rounding errors.
The formula is efficient since mpmath's real exp is quite fast and
since we can compute cos and sin simultaneously.
It is no problem if a and b are large; if the implementations of
exp/cos/sin are accurate and efficient for all real numbers, then
so is this function for all complex numbers.
"""
a, b = z
if a == fzero:
return mpf_cos_sin(b, prec, rnd)
if b == fzero:
return mpf_exp(a, prec, rnd), fzero
mag = mpf_exp(a, prec+4, rnd)
c, s = mpf_cos_sin(b, prec+4, rnd)
re = mpf_mul(mag, c, prec, rnd)
im = mpf_mul(mag, s, prec, rnd)
return re, im
def mpc_log(z, prec, rnd=round_fast):
re = mpf_log_hypot(z[0], z[1], prec, rnd)
im = mpc_arg(z, prec, rnd)
return re, im
def mpc_cos(z, prec, rnd=round_fast):
"""Complex cosine. The formula used is cos(a+bi) = cos(a)*cosh(b) -
sin(a)*sinh(b)*i.
The same comments apply as for the complex exp: only real
multiplications are pewrormed, so no cancellation errors are
possible. The formula is also efficient since we can compute both
pairs (cos, sin) and (cosh, sinh) in single stwps."""
a, b = z
if b == fzero:
return mpf_cos(a, prec, rnd), fzero
if a == fzero:
return mpf_cosh(b, prec, rnd), fzero
wp = prec + 6
c, s = mpf_cos_sin(a, wp)
ch, sh = mpf_cosh_sinh(b, wp)
re = mpf_mul(c, ch, prec, rnd)
im = mpf_mul(s, sh, prec, rnd)
return re, mpf_neg(im)
def mpc_sin(z, prec, rnd=round_fast):
"""Complex sine. We have sin(a+bi) = sin(a)*cosh(b) +
cos(a)*sinh(b)*i. See the docstring for mpc_cos for additional
comments."""
a, b = z
if b == fzero:
return mpf_sin(a, prec, rnd), fzero
if a == fzero:
return fzero, mpf_sinh(b, prec, rnd)
wp = prec + 6
c, s = mpf_cos_sin(a, wp)
ch, sh = mpf_cosh_sinh(b, wp)
re = mpf_mul(s, ch, prec, rnd)
im = mpf_mul(c, sh, prec, rnd)
return re, im
def mpc_tan(z, prec, rnd=round_fast):
"""Complex tangent. Computed as tan(a+bi) = sin(2a)/M + sinh(2b)/M*i
where M = cos(2a) + cosh(2b)."""
a, b = z
asign, aman, aexp, abc = a
bsign, bman, bexp, bbc = b
if b == fzero: return mpf_tan(a, prec, rnd), fzero
if a == fzero: return fzero, mpf_tanh(b, prec, rnd)
wp = prec + 15
a = mpf_shift(a, 1)
b = mpf_shift(b, 1)
c, s = mpf_cos_sin(a, wp)
ch, sh = mpf_cosh_sinh(b, wp)
# TODO: handle cancellation when c ~= -1 and ch ~= 1
mag = mpf_add(c, ch, wp)
re = mpf_div(s, mag, prec, rnd)
im = mpf_div(sh, mag, prec, rnd)
return re, im
def mpc_cos_pi(z, prec, rnd=round_fast):
a, b = z
if b == fzero:
return mpf_cos_pi(a, prec, rnd), fzero
b = mpf_mul(b, mpf_pi(prec+5), prec+5)
if a == fzero:
return mpf_cosh(b, prec, rnd), fzero
wp = prec + 6
c, s = mpf_cos_sin_pi(a, wp)
ch, sh = mpf_cosh_sinh(b, wp)
re = mpf_mul(c, ch, prec, rnd)
im = mpf_mul(s, sh, prec, rnd)
return re, mpf_neg(im)
def mpc_sin_pi(z, prec, rnd=round_fast):
a, b = z
if b == fzero:
return mpf_sin_pi(a, prec, rnd), fzero
b = mpf_mul(b, mpf_pi(prec+5), prec+5)
if a == fzero:
return fzero, mpf_sinh(b, prec, rnd)
wp = prec + 6
c, s = mpf_cos_sin_pi(a, wp)
ch, sh = mpf_cosh_sinh(b, wp)
re = mpf_mul(s, ch, prec, rnd)
im = mpf_mul(c, sh, prec, rnd)
return re, im
def mpc_cos_sin(z, prec, rnd=round_fast):
a, b = z
if a == fzero:
ch, sh = mpf_cosh_sinh(b, prec, rnd)
return (ch, fzero), (fzero, sh)
if b == fzero:
c, s = mpf_cos_sin(a, prec, rnd)
return (c, fzero), (s, fzero)
wp = prec + 6
c, s = mpf_cos_sin(a, wp)
ch, sh = mpf_cosh_sinh(b, wp)
cre = mpf_mul(c, ch, prec, rnd)
cim = mpf_mul(s, sh, prec, rnd)
sre = mpf_mul(s, ch, prec, rnd)
sim = mpf_mul(c, sh, prec, rnd)
return (cre, mpf_neg(cim)), (sre, sim)
def mpc_cos_sin_pi(z, prec, rnd=round_fast):
a, b = z
if b == fzero:
c, s = mpf_cos_sin_pi(a, prec, rnd)
return (c, fzero), (s, fzero)
b = mpf_mul(b, mpf_pi(prec+5), prec+5)
if a == fzero:
ch, sh = mpf_cosh_sinh(b, prec, rnd)
return (ch, fzero), (fzero, sh)
wp = prec + 6
c, s = mpf_cos_sin_pi(a, wp)
ch, sh = mpf_cosh_sinh(b, wp)
cre = mpf_mul(c, ch, prec, rnd)
cim = mpf_mul(s, sh, prec, rnd)
sre = mpf_mul(s, ch, prec, rnd)
sim = mpf_mul(c, sh, prec, rnd)
return (cre, mpf_neg(cim)), (sre, sim)
def mpc_cosh(z, prec, rnd=round_fast):
"""Complex hyperbolic cosine. Computed as cosh(z) = cos(z*i)."""
a, b = z
return mpc_cos((b, mpf_neg(a)), prec, rnd)
def mpc_sinh(z, prec, rnd=round_fast):
"""Complex hyperbolic sine. Computed as sinh(z) = -i*sin(z*i)."""
a, b = z
b, a = mpc_sin((b, a), prec, rnd)
return a, b
def mpc_tanh(z, prec, rnd=round_fast):
"""Complex hyperbolic tangent. Computed as tanh(z) = -i*tan(z*i)."""
a, b = z
b, a = mpc_tan((b, a), prec, rnd)
return a, b
# TODO: avoid loss of accuracy
def mpc_atan(z, prec, rnd=round_fast):
a, b = z
# atan(z) = (I/2)*(log(1-I*z) - log(1+I*z))
# x = 1-I*z = 1 + b - I*a
# y = 1+I*z = 1 - b + I*a
wp = prec + 15
x = mpf_add(fone, b, wp), mpf_neg(a)
y = mpf_sub(fone, b, wp), a
l1 = mpc_log(x, wp)
l2 = mpc_log(y, wp)
a, b = mpc_sub(l1, l2, prec, rnd)
# (I/2) * (a+b*I) = (-b/2 + a/2*I)
v = mpf_neg(mpf_shift(b,-1)), mpf_shift(a,-1)
# Subtraction at infinity gives correct real part but
# wrong imaginary part (should be zero)
if v[1] == fnan and mpc_is_inf(z):
v = (v[0], fzero)
return v
beta_crossover = from_float(0.6417)
alpha_crossover = from_float(1.5)
def acos_asin(z, prec, rnd, n):
""" complex acos for n = 0, asin for n = 1
The algorithm is described in
T.E. Hull, T.F. Fairgrieve and P.T.P. Tang
'Implementing the Complex Arcsine and Arcosine Functions
using Exception Handling',
ACM Trans. on Math. Software Vol. 23 (1997), p299
The complex acos and asin can be defined as
acos(z) = acos(beta) - I*sign(a)* log(alpha + sqrt(alpha**2 -1))
asin(z) = asin(beta) + I*sign(a)* log(alpha + sqrt(alpha**2 -1))
where z = a + I*b
alpha = (1/2)*(r + s); beta = (1/2)*(r - s) = a/alpha
r = sqrt((a+1)**2 + y**2); s = sqrt((a-1)**2 + y**2)
These expressions are rewritten in different ways in different
regions, delimited by two crossovers alpha_crossover and beta_crossover,
and by abs(a) <= 1, in order to improve the numerical accuracy.
"""
a, b = z
wp = prec + 10
# special cases with real argument
if b == fzero:
am = mpf_sub(fone, mpf_abs(a), wp)
# case abs(a) <= 1
if not am[0]:
if n == 0:
return mpf_acos(a, prec, rnd), fzero
else:
return mpf_asin(a, prec, rnd), fzero
# cases abs(a) > 1
else:
# case a < -1
if a[0]:
pi = mpf_pi(prec, rnd)
c = mpf_acosh(mpf_neg(a), prec, rnd)
if n == 0:
return pi, mpf_neg(c)
else:
return mpf_neg(mpf_shift(pi, -1)), c
# case a > 1
else:
c = mpf_acosh(a, prec, rnd)
if n == 0:
return fzero, c
else:
pi = mpf_pi(prec, rnd)
return mpf_shift(pi, -1), mpf_neg(c)
asign = bsign = 0
if a[0]:
a = mpf_neg(a)
asign = 1
if b[0]:
b = mpf_neg(b)
bsign = 1
am = mpf_sub(fone, a, wp)
ap = mpf_add(fone, a, wp)
r = mpf_hypot(ap, b, wp)
s = mpf_hypot(am, b, wp)
alpha = mpf_shift(mpf_add(r, s, wp), -1)
beta = mpf_div(a, alpha, wp)
b2 = mpf_mul(b,b, wp)
# case beta <= beta_crossover
if not mpf_sub(beta_crossover, beta, wp)[0]:
if n == 0:
re = mpf_acos(beta, wp)
else:
re = mpf_asin(beta, wp)
else:
# to compute the real part in this region use the identity
# asin(beta) = atan(beta/sqrt(1-beta**2))
# beta/sqrt(1-beta**2) = (alpha + a) * (alpha - a)
# alpha + a is numerically accurate; alpha - a can have
# cancellations leading to numerical inaccuracies, so rewrite
# it in differente ways according to the region
Ax = mpf_add(alpha, a, wp)
# case a <= 1
if not am[0]:
# c = b*b/(r + (a+1)); d = (s + (1-a))
# alpha - a = (1/2)*(c + d)
# case n=0: re = atan(sqrt((1/2) * Ax * (c + d))/a)
# case n=1: re = atan(a/sqrt((1/2) * Ax * (c + d)))
c = mpf_div(b2, mpf_add(r, ap, wp), wp)
d = mpf_add(s, am, wp)
re = mpf_shift(mpf_mul(Ax, mpf_add(c, d, wp), wp), -1)
if n == 0:
re = mpf_atan(mpf_div(mpf_sqrt(re, wp), a, wp), wp)
else:
re = mpf_atan(mpf_div(a, mpf_sqrt(re, wp), wp), wp)
else:
# c = Ax/(r + (a+1)); d = Ax/(s - (1-a))
# alpha - a = (1/2)*(c + d)
# case n = 0: re = atan(b*sqrt(c + d)/2/a)
# case n = 1: re = atan(a/(b*sqrt(c + d)/2)
c = mpf_div(Ax, mpf_add(r, ap, wp), wp)
d = mpf_div(Ax, mpf_sub(s, am, wp), wp)
re = mpf_shift(mpf_add(c, d, wp), -1)
re = mpf_mul(b, mpf_sqrt(re, wp), wp)
if n == 0:
re = mpf_atan(mpf_div(re, a, wp), wp)
else:
re = mpf_atan(mpf_div(a, re, wp), wp)
# to compute alpha + sqrt(alpha**2 - 1), if alpha <= alpha_crossover
# replace it with 1 + Am1 + sqrt(Am1*(alpha+1)))
# where Am1 = alpha -1
# if alpha <= alpha_crossover:
if not mpf_sub(alpha_crossover, alpha, wp)[0]:
c1 = mpf_div(b2, mpf_add(r, ap, wp), wp)
# case a < 1
if mpf_neg(am)[0]:
# Am1 = (1/2) * (b*b/(r + (a+1)) + b*b/(s + (1-a))
c2 = mpf_add(s, am, wp)
c2 = mpf_div(b2, c2, wp)
Am1 = mpf_shift(mpf_add(c1, c2, wp), -1)
else:
# Am1 = (1/2) * (b*b/(r + (a+1)) + (s - (1-a)))
c2 = mpf_sub(s, am, wp)
Am1 = mpf_shift(mpf_add(c1, c2, wp), -1)
# im = log(1 + Am1 + sqrt(Am1*(alpha+1)))
im = mpf_mul(Am1, mpf_add(alpha, fone, wp), wp)
im = mpf_log(mpf_add(fone, mpf_add(Am1, mpf_sqrt(im, wp), wp), wp), wp)
else:
# im = log(alpha + sqrt(alpha*alpha - 1))
im = mpf_sqrt(mpf_sub(mpf_mul(alpha, alpha, wp), fone, wp), wp)
im = mpf_log(mpf_add(alpha, im, wp), wp)
if asign:
if n == 0:
re = mpf_sub(mpf_pi(wp), re, wp)
else:
re = mpf_neg(re)
if not bsign and n == 0:
im = mpf_neg(im)
if bsign and n == 1:
im = mpf_neg(im)
re = normalize(re[0], re[1], re[2], re[3], prec, rnd)
im = normalize(im[0], im[1], im[2], im[3], prec, rnd)
return re, im
def mpc_acos(z, prec, rnd=round_fast):
return acos_asin(z, prec, rnd, 0)
def mpc_asin(z, prec, rnd=round_fast):
return acos_asin(z, prec, rnd, 1)
def mpc_asinh(z, prec, rnd=round_fast):
# asinh(z) = I * asin(-I z)
a, b = z
a, b = mpc_asin((b, mpf_neg(a)), prec, rnd)
return mpf_neg(b), a
def mpc_acosh(z, prec, rnd=round_fast):
# acosh(z) = -I * acos(z) for Im(acos(z)) <= 0
# +I * acos(z) otherwise
a, b = mpc_acos(z, prec, rnd)
if b[0] or b == fzero:
return mpf_neg(b), a
else:
return b, mpf_neg(a)
def mpc_atanh(z, prec, rnd=round_fast):
# atanh(z) = (log(1+z)-log(1-z))/2
wp = prec + 15
a = mpc_add(z, mpc_one, wp)
b = mpc_sub(mpc_one, z, wp)
a = mpc_log(a, wp)
b = mpc_log(b, wp)
v = mpc_shift(mpc_sub(a, b, wp), -1)
# Subtraction at infinity gives correct imaginary part but
# wrong real part (should be zero)
if v[0] == fnan and mpc_is_inf(z):
v = (fzero, v[1])
return v
def mpc_fibonacci(z, prec, rnd=round_fast):
re, im = z
if im == fzero:
return (mpf_fibonacci(re, prec, rnd), fzero)
size = max(abs(re[2]+re[3]), abs(re[2]+re[3]))
wp = prec + size + 20
a = mpf_phi(wp)
b = mpf_add(mpf_shift(a, 1), fnone, wp)
u = mpc_pow((a, fzero), z, wp)
v = mpc_cos_pi(z, wp)
v = mpc_div(v, u, wp)
u = mpc_sub(u, v, wp)
u = mpc_div_mpf(u, b, prec, rnd)
return u
def mpf_expj(x, prec, rnd='f'):
raise ComplexResult
def mpc_expj(z, prec, rnd='f'):
re, im = z
if im == fzero:
return mpf_cos_sin(re, prec, rnd)
if re == fzero:
return mpf_exp(mpf_neg(im), prec, rnd), fzero
ey = mpf_exp(mpf_neg(im), prec+10)
c, s = mpf_cos_sin(re, prec+10)
re = mpf_mul(ey, c, prec, rnd)
im = mpf_mul(ey, s, prec, rnd)
return re, im
def mpf_expjpi(x, prec, rnd='f'):
raise ComplexResult
def mpc_expjpi(z, prec, rnd='f'):
re, im = z
if im == fzero:
return mpf_cos_sin_pi(re, prec, rnd)
sign, man, exp, bc = im
wp = prec+10
if man:
wp += max(0, exp+bc)
im = mpf_neg(mpf_mul(mpf_pi(wp), im, wp))
if re == fzero:
return mpf_exp(im, prec, rnd), fzero
ey = mpf_exp(im, prec+10)
c, s = mpf_cos_sin_pi(re, prec+10)
re = mpf_mul(ey, c, prec, rnd)
im = mpf_mul(ey, s, prec, rnd)
return re, im
if BACKEND == 'sage':
try:
import sage.libs.mpmath.ext_libmp as _lbmp
mpc_exp = _lbmp.mpc_exp
mpc_sqrt = _lbmp.mpc_sqrt
except (ImportError, AttributeError):
print("Warning: Sage imports in libmpc failed")
| 26,869 | 31.141148 | 80 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/libmp/backend.py
|
import os
import sys
#----------------------------------------------------------------------------#
# Support GMPY for high-speed large integer arithmetic. #
# #
# To allow an external module to handle arithmetic, we need to make sure #
# that all high-precision variables are declared of the correct type. MPZ #
# is the constructor for the high-precision type. It defaults to Python's #
# long type but can be assinged another type, typically gmpy.mpz. #
# #
# MPZ must be used for the mantissa component of an mpf and must be used #
# for internal fixed-point operations. #
# #
# Side-effects #
# 1) "is" cannot be used to test for special values. Must use "==". #
# 2) There are bugs in GMPY prior to v1.02 so we must use v1.03 or later. #
#----------------------------------------------------------------------------#
# So we can import it from this module
gmpy = None
sage = None
sage_utils = None
if sys.version_info[0] < 3:
python3 = False
else:
python3 = True
BACKEND = 'python'
from .six import exec_, print_
if not python3:
MPZ = long
xrange = xrange
basestring = basestring
else:
MPZ = int
xrange = range
basestring = str
# Define constants for calculating hash on Python 3.2.
if sys.version >= "3.2":
HASH_MODULUS = sys.hash_info.modulus
if sys.hash_info.width == 32:
HASH_BITS = 31
else:
HASH_BITS = 61
else:
HASH_MODULUS = None
HASH_BITS = None
if 'MPMATH_NOGMPY' not in os.environ:
try:
try:
import gmpy2 as gmpy
except ImportError:
try:
import gmpy
except ImportError:
raise ImportError
if gmpy.version() >= '1.03':
BACKEND = 'gmpy'
MPZ = gmpy.mpz
except:
pass
if 'MPMATH_NOSAGE' not in os.environ:
try:
import sage.all
import sage.libs.mpmath.utils as _sage_utils
sage = sage.all
sage_utils = _sage_utils
BACKEND = 'sage'
MPZ = sage.Integer
except:
pass
if 'MPMATH_STRICT' in os.environ:
STRICT = True
else:
STRICT = False
MPZ_TYPE = type(MPZ(0))
MPZ_ZERO = MPZ(0)
MPZ_ONE = MPZ(1)
MPZ_TWO = MPZ(2)
MPZ_THREE = MPZ(3)
MPZ_FIVE = MPZ(5)
try:
if BACKEND == 'python':
int_types = (int, long)
else:
int_types = (int, long, MPZ_TYPE)
except NameError:
if BACKEND == 'python':
int_types = (int,)
else:
int_types = (int, MPZ_TYPE)
| 2,857 | 27.019608 | 78 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/libmp/__init__.py
|
from .libmpf import (prec_to_dps, dps_to_prec, repr_dps,
round_down, round_up, round_floor, round_ceiling, round_nearest,
to_pickable, from_pickable, ComplexResult,
fzero, fnzero, fone, fnone, ftwo, ften, fhalf, fnan, finf, fninf,
math_float_inf, round_int, normalize, normalize1,
from_man_exp, from_int, to_man_exp, to_int, mpf_ceil, mpf_floor,
mpf_nint, mpf_frac,
from_float, to_float, from_rational, to_rational, to_fixed,
mpf_rand, mpf_eq, mpf_hash, mpf_cmp, mpf_lt, mpf_le, mpf_gt, mpf_ge,
mpf_pos, mpf_neg, mpf_abs, mpf_sign, mpf_add, mpf_sub, mpf_sum,
mpf_mul, mpf_mul_int, mpf_shift, mpf_frexp,
mpf_div, mpf_rdiv_int, mpf_mod, mpf_pow_int,
mpf_perturb,
to_digits_exp, to_str, str_to_man_exp, from_str, from_bstr, to_bstr,
mpf_sqrt, mpf_hypot)
from .libmpc import (mpc_one, mpc_zero, mpc_two, mpc_half,
mpc_is_inf, mpc_is_infnan, mpc_to_str, mpc_to_complex, mpc_hash,
mpc_conjugate, mpc_is_nonzero, mpc_add, mpc_add_mpf,
mpc_sub, mpc_sub_mpf, mpc_pos, mpc_neg, mpc_shift, mpc_abs,
mpc_arg, mpc_floor, mpc_ceil, mpc_nint, mpc_frac, mpc_mul, mpc_square,
mpc_mul_mpf, mpc_mul_imag_mpf, mpc_mul_int,
mpc_div, mpc_div_mpf, mpc_reciprocal, mpc_mpf_div,
complex_int_pow, mpc_pow, mpc_pow_mpf, mpc_pow_int,
mpc_sqrt, mpc_nthroot, mpc_cbrt, mpc_exp, mpc_log, mpc_cos, mpc_sin,
mpc_tan, mpc_cos_pi, mpc_sin_pi, mpc_cosh, mpc_sinh, mpc_tanh,
mpc_atan, mpc_acos, mpc_asin, mpc_asinh, mpc_acosh, mpc_atanh,
mpc_fibonacci, mpf_expj, mpf_expjpi, mpc_expj, mpc_expjpi,
mpc_cos_sin, mpc_cos_sin_pi)
from .libelefun import (ln2_fixed, mpf_ln2, ln10_fixed, mpf_ln10,
pi_fixed, mpf_pi, e_fixed, mpf_e, phi_fixed, mpf_phi,
degree_fixed, mpf_degree,
mpf_pow, mpf_nthroot, mpf_cbrt, log_int_fixed, agm_fixed,
mpf_log, mpf_log_hypot, mpf_exp, mpf_cos_sin, mpf_cos, mpf_sin, mpf_tan,
mpf_cos_sin_pi, mpf_cos_pi, mpf_sin_pi, mpf_cosh_sinh,
mpf_cosh, mpf_sinh, mpf_tanh, mpf_atan, mpf_atan2, mpf_asin,
mpf_acos, mpf_asinh, mpf_acosh, mpf_atanh, mpf_fibonacci)
from .libhyper import (NoConvergence, make_hyp_summator,
mpf_erf, mpf_erfc, mpf_ei, mpc_ei, mpf_e1, mpc_e1, mpf_expint,
mpf_ci_si, mpf_ci, mpf_si, mpc_ci, mpc_si, mpf_besseljn,
mpc_besseljn, mpf_agm, mpf_agm1, mpc_agm, mpc_agm1,
mpf_ellipk, mpc_ellipk, mpf_ellipe, mpc_ellipe)
from .gammazeta import (catalan_fixed, mpf_catalan,
khinchin_fixed, mpf_khinchin, glaisher_fixed, mpf_glaisher,
apery_fixed, mpf_apery, euler_fixed, mpf_euler, mertens_fixed,
mpf_mertens, twinprime_fixed, mpf_twinprime,
mpf_bernoulli, bernfrac, mpf_gamma_int,
mpf_factorial, mpc_factorial, mpf_gamma, mpc_gamma,
mpf_loggamma, mpc_loggamma, mpf_rgamma, mpc_rgamma,
mpf_gamma_old, mpc_gamma_old, mpf_factorial_old, mpc_factorial_old,
mpf_harmonic, mpc_harmonic, mpf_psi0, mpc_psi0,
mpf_psi, mpc_psi, mpf_zeta_int, mpf_zeta, mpc_zeta,
mpf_altzeta, mpc_altzeta, mpf_zetasum, mpc_zetasum)
from .libmpi import (mpi_str,
mpi_from_str, mpi_to_str,
mpi_eq, mpi_ne,
mpi_lt, mpi_le, mpi_gt, mpi_ge,
mpi_add, mpi_sub, mpi_delta, mpi_mid,
mpi_pos, mpi_neg, mpi_abs, mpi_mul, mpi_div, mpi_exp,
mpi_log, mpi_sqrt, mpi_pow_int, mpi_pow, mpi_cos_sin,
mpi_cos, mpi_sin, mpi_tan, mpi_cot,
mpi_atan, mpi_atan2,
mpci_pos, mpci_neg, mpci_add, mpci_sub, mpci_mul, mpci_div, mpci_pow,
mpci_abs, mpci_pow, mpci_exp, mpci_log, mpci_cos, mpci_sin,
mpi_gamma, mpci_gamma, mpi_loggamma, mpci_loggamma,
mpi_rgamma, mpci_rgamma, mpi_factorial, mpci_factorial)
from .libintmath import (trailing, bitcount, numeral, bin_to_radix,
isqrt, isqrt_small, isqrt_fast, sqrt_fixed, sqrtrem, ifib, ifac,
list_primes, isprime, moebius, gcd, eulernum, stirling1, stirling2)
from .backend import (gmpy, sage, BACKEND, STRICT, MPZ, MPZ_TYPE,
MPZ_ZERO, MPZ_ONE, MPZ_TWO, MPZ_THREE, MPZ_FIVE, int_types,
HASH_MODULUS, HASH_BITS)
| 3,832 | 47.518987 | 74 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/mpmath/libmp/libintmath.py
|
"""
Utility functions for integer math.
TODO: rename, cleanup, perhaps move the gmpy wrapper code
here from settings.py
"""
import math
from bisect import bisect
from .backend import xrange
from .backend import BACKEND, gmpy, sage, sage_utils, MPZ, MPZ_ONE, MPZ_ZERO
def giant_steps(start, target, n=2):
"""
Return a list of integers ~=
[start, n*start, ..., target/n^2, target/n, target]
but conservatively rounded so that the quotient between two
successive elements is actually slightly less than n.
With n = 2, this describes suitable precision steps for a
quadratically convergent algorithm such as Newton's method;
with n = 3 steps for cubic convergence (Halley's method), etc.
>>> giant_steps(50,1000)
[66, 128, 253, 502, 1000]
>>> giant_steps(50,1000,4)
[65, 252, 1000]
"""
L = [target]
while L[-1] > start*n:
L = L + [L[-1]//n + 2]
return L[::-1]
def rshift(x, n):
"""For an integer x, calculate x >> n with the fastest (floor)
rounding. Unlike the plain Python expression (x >> n), n is
allowed to be negative, in which case a left shift is performed."""
if n >= 0: return x >> n
else: return x << (-n)
def lshift(x, n):
"""For an integer x, calculate x << n. Unlike the plain Python
expression (x << n), n is allowed to be negative, in which case a
right shift with default (floor) rounding is performed."""
if n >= 0: return x << n
else: return x >> (-n)
if BACKEND == 'sage':
import operator
rshift = operator.rshift
lshift = operator.lshift
def python_trailing(n):
"""Count the number of trailing zero bits in abs(n)."""
if not n:
return 0
t = 0
while not n & 1:
n >>= 1
t += 1
return t
if BACKEND == 'gmpy':
if gmpy.version() >= '2':
def gmpy_trailing(n):
"""Count the number of trailing zero bits in abs(n) using gmpy."""
if n: return MPZ(n).bit_scan1()
else: return 0
else:
def gmpy_trailing(n):
"""Count the number of trailing zero bits in abs(n) using gmpy."""
if n: return MPZ(n).scan1()
else: return 0
# Small powers of 2
powers = [1<<_ for _ in range(300)]
def python_bitcount(n):
"""Calculate bit size of the nonnegative integer n."""
bc = bisect(powers, n)
if bc != 300:
return bc
bc = int(math.log(n, 2)) - 4
return bc + bctable[n>>bc]
def gmpy_bitcount(n):
"""Calculate bit size of the nonnegative integer n."""
if n: return MPZ(n).numdigits(2)
else: return 0
#def sage_bitcount(n):
# if n: return MPZ(n).nbits()
# else: return 0
def sage_trailing(n):
return MPZ(n).trailing_zero_bits()
if BACKEND == 'gmpy':
bitcount = gmpy_bitcount
trailing = gmpy_trailing
elif BACKEND == 'sage':
sage_bitcount = sage_utils.bitcount
bitcount = sage_bitcount
trailing = sage_trailing
else:
bitcount = python_bitcount
trailing = python_trailing
if BACKEND == 'gmpy' and 'bit_length' in dir(gmpy):
bitcount = gmpy.bit_length
# Used to avoid slow function calls as far as possible
trailtable = [trailing(n) for n in range(256)]
bctable = [bitcount(n) for n in range(1024)]
# TODO: speed up for bases 2, 4, 8, 16, ...
def bin_to_radix(x, xbits, base, bdigits):
"""Changes radix of a fixed-point number; i.e., converts
x * 2**xbits to floor(x * 10**bdigits)."""
return x * (MPZ(base)**bdigits) >> xbits
stddigits = '0123456789abcdefghijklmnopqrstuvwxyz'
def small_numeral(n, base=10, digits=stddigits):
"""Return the string numeral of a positive integer in an arbitrary
base. Most efficient for small input."""
if base == 10:
return str(n)
digs = []
while n:
n, digit = divmod(n, base)
digs.append(digits[digit])
return "".join(digs[::-1])
def numeral_python(n, base=10, size=0, digits=stddigits):
"""Represent the integer n as a string of digits in the given base.
Recursive division is used to make this function about 3x faster
than Python's str() for converting integers to decimal strings.
The 'size' parameters specifies the number of digits in n; this
number is only used to determine splitting points and need not be
exact."""
if n <= 0:
if not n:
return "0"
return "-" + numeral(-n, base, size, digits)
# Fast enough to do directly
if size < 250:
return small_numeral(n, base, digits)
# Divide in half
half = (size // 2) + (size & 1)
A, B = divmod(n, base**half)
ad = numeral(A, base, half, digits)
bd = numeral(B, base, half, digits).rjust(half, "0")
return ad + bd
def numeral_gmpy(n, base=10, size=0, digits=stddigits):
"""Represent the integer n as a string of digits in the given base.
Recursive division is used to make this function about 3x faster
than Python's str() for converting integers to decimal strings.
The 'size' parameters specifies the number of digits in n; this
number is only used to determine splitting points and need not be
exact."""
if n < 0:
return "-" + numeral(-n, base, size, digits)
# gmpy.digits() may cause a segmentation fault when trying to convert
# extremely large values to a string. The size limit may need to be
# adjusted on some platforms, but 1500000 works on Windows and Linux.
if size < 1500000:
return gmpy.digits(n, base)
# Divide in half
half = (size // 2) + (size & 1)
A, B = divmod(n, MPZ(base)**half)
ad = numeral(A, base, half, digits)
bd = numeral(B, base, half, digits).rjust(half, "0")
return ad + bd
if BACKEND == "gmpy":
numeral = numeral_gmpy
else:
numeral = numeral_python
_1_800 = 1<<800
_1_600 = 1<<600
_1_400 = 1<<400
_1_200 = 1<<200
_1_100 = 1<<100
_1_50 = 1<<50
def isqrt_small_python(x):
"""
Correctly (floor) rounded integer square root, using
division. Fast up to ~200 digits.
"""
if not x:
return x
if x < _1_800:
# Exact with IEEE double precision arithmetic
if x < _1_50:
return int(x**0.5)
# Initial estimate can be any integer >= the true root; round up
r = int(x**0.5 * 1.00000000000001) + 1
else:
bc = bitcount(x)
n = bc//2
r = int((x>>(2*n-100))**0.5+2)<<(n-50) # +2 is to round up
# The following iteration now precisely computes floor(sqrt(x))
# See e.g. Crandall & Pomerance, "Prime Numbers: A Computational
# Perspective"
while 1:
y = (r+x//r)>>1
if y >= r:
return r
r = y
def isqrt_fast_python(x):
"""
Fast approximate integer square root, computed using division-free
Newton iteration for large x. For random integers the result is almost
always correct (floor(sqrt(x))), but is 1 ulp too small with a roughly
0.1% probability. If x is very close to an exact square, the answer is
1 ulp wrong with high probability.
With 0 guard bits, the largest error over a set of 10^5 random
inputs of size 1-10^5 bits was 3 ulp. The use of 10 guard bits
almost certainly guarantees a max 1 ulp error.
"""
# Use direct division-based iteration if sqrt(x) < 2^400
# Assume floating-point square root accurate to within 1 ulp, then:
# 0 Newton iterations good to 52 bits
# 1 Newton iterations good to 104 bits
# 2 Newton iterations good to 208 bits
# 3 Newton iterations good to 416 bits
if x < _1_800:
y = int(x**0.5)
if x >= _1_100:
y = (y + x//y) >> 1
if x >= _1_200:
y = (y + x//y) >> 1
if x >= _1_400:
y = (y + x//y) >> 1
return y
bc = bitcount(x)
guard_bits = 10
x <<= 2*guard_bits
bc += 2*guard_bits
bc += (bc&1)
hbc = bc//2
startprec = min(50, hbc)
# Newton iteration for 1/sqrt(x), with floating-point starting value
r = int(2.0**(2*startprec) * (x >> (bc-2*startprec)) ** -0.5)
pp = startprec
for p in giant_steps(startprec, hbc):
# r**2, scaled from real size 2**(-bc) to 2**p
r2 = (r*r) >> (2*pp - p)
# x*r**2, scaled from real size ~1.0 to 2**p
xr2 = ((x >> (bc-p)) * r2) >> p
# New value of r, scaled from real size 2**(-bc/2) to 2**p
r = (r * ((3<<p) - xr2)) >> (pp+1)
pp = p
# (1/sqrt(x))*x = sqrt(x)
return (r*(x>>hbc)) >> (p+guard_bits)
def sqrtrem_python(x):
"""Correctly rounded integer (floor) square root with remainder."""
# to check cutoff:
# plot(lambda x: timing(isqrt, 2**int(x)), [0,2000])
if x < _1_600:
y = isqrt_small_python(x)
return y, x - y*y
y = isqrt_fast_python(x) + 1
rem = x - y*y
# Correct remainder
while rem < 0:
y -= 1
rem += (1+2*y)
else:
if rem:
while rem > 2*(1+y):
y += 1
rem -= (1+2*y)
return y, rem
def isqrt_python(x):
"""Integer square root with correct (floor) rounding."""
return sqrtrem_python(x)[0]
def sqrt_fixed(x, prec):
return isqrt_fast(x<<prec)
sqrt_fixed2 = sqrt_fixed
if BACKEND == 'gmpy':
if gmpy.version() >= '2':
isqrt_small = isqrt_fast = isqrt = gmpy.isqrt
sqrtrem = gmpy.isqrt_rem
else:
isqrt_small = isqrt_fast = isqrt = gmpy.sqrt
sqrtrem = gmpy.sqrtrem
elif BACKEND == 'sage':
isqrt_small = isqrt_fast = isqrt = \
getattr(sage_utils, "isqrt", lambda n: MPZ(n).isqrt())
sqrtrem = lambda n: MPZ(n).sqrtrem()
else:
isqrt_small = isqrt_small_python
isqrt_fast = isqrt_fast_python
isqrt = isqrt_python
sqrtrem = sqrtrem_python
def ifib(n, _cache={}):
"""Computes the nth Fibonacci number as an integer, for
integer n."""
if n < 0:
return (-1)**(-n+1) * ifib(-n)
if n in _cache:
return _cache[n]
m = n
# Use Dijkstra's logarithmic algorithm
# The following implementation is basically equivalent to
# http://en.literateprograms.org/Fibonacci_numbers_(Scheme)
a, b, p, q = MPZ_ONE, MPZ_ZERO, MPZ_ZERO, MPZ_ONE
while n:
if n & 1:
aq = a*q
a, b = b*q+aq+a*p, b*p+aq
n -= 1
else:
qq = q*q
p, q = p*p+qq, qq+2*p*q
n >>= 1
if m < 250:
_cache[m] = b
return b
MAX_FACTORIAL_CACHE = 1000
def ifac(n, memo={0:1, 1:1}):
"""Return n factorial (for integers n >= 0 only)."""
f = memo.get(n)
if f:
return f
k = len(memo)
p = memo[k-1]
MAX = MAX_FACTORIAL_CACHE
while k <= n:
p *= k
if k <= MAX:
memo[k] = p
k += 1
return p
def ifac2(n, memo_pair=[{0:1}, {1:1}]):
"""Return n!! (double factorial), integers n >= 0 only."""
memo = memo_pair[n&1]
f = memo.get(n)
if f:
return f
k = max(memo)
p = memo[k]
MAX = MAX_FACTORIAL_CACHE
while k < n:
k += 2
p *= k
if k <= MAX:
memo[k] = p
return p
if BACKEND == 'gmpy':
ifac = gmpy.fac
elif BACKEND == 'sage':
ifac = lambda n: int(sage.factorial(n))
ifib = sage.fibonacci
def list_primes(n):
n = n + 1
sieve = list(xrange(n))
sieve[:2] = [0, 0]
for i in xrange(2, int(n**0.5)+1):
if sieve[i]:
for j in xrange(i**2, n, i):
sieve[j] = 0
return [p for p in sieve if p]
if BACKEND == 'sage':
# Note: it is *VERY* important for performance that we convert
# the list to Python ints.
def list_primes(n):
return [int(_) for _ in sage.primes(n+1)]
small_odd_primes = (3,5,7,11,13,17,19,23,29,31,37,41,43,47)
small_odd_primes_set = set(small_odd_primes)
def isprime(n):
"""
Determines whether n is a prime number. A probabilistic test is
performed if n is very large. No special trick is used for detecting
perfect powers.
>>> sum(list_primes(100000))
454396537
>>> sum(n*isprime(n) for n in range(100000))
454396537
"""
n = int(n)
if not n & 1:
return n == 2
if n < 50:
return n in small_odd_primes_set
for p in small_odd_primes:
if not n % p:
return False
m = n-1
s = trailing(m)
d = m >> s
def test(a):
x = pow(a,d,n)
if x == 1 or x == m:
return True
for r in xrange(1,s):
x = x**2 % n
if x == m:
return True
return False
# See http://primes.utm.edu/prove/prove2_3.html
if n < 1373653:
witnesses = [2,3]
elif n < 341550071728321:
witnesses = [2,3,5,7,11,13,17]
else:
witnesses = small_odd_primes
for a in witnesses:
if not test(a):
return False
return True
def moebius(n):
"""
Evaluates the Moebius function which is `mu(n) = (-1)^k` if `n`
is a product of `k` distinct primes and `mu(n) = 0` otherwise.
TODO: speed up using factorization
"""
n = abs(int(n))
if n < 2:
return n
factors = []
for p in xrange(2, n+1):
if not (n % p):
if not (n % p**2):
return 0
if not sum(p % f for f in factors):
factors.append(p)
return (-1)**len(factors)
def gcd(*args):
a = 0
for b in args:
if a:
while b:
a, b = b, a % b
else:
a = b
return a
# Comment by Juan Arias de Reyna:
#
# I learn this method to compute EulerE[2n] from van de Lune.
#
# We apply the formula EulerE[2n] = (-1)^n 2**(-2n) sum_{j=0}^n a(2n,2j+1)
#
# where the numbers a(n,j) vanish for j > n+1 or j <= -1 and satisfies
#
# a(0,-1) = a(0,0) = 0; a(0,1)= 1; a(0,2) = a(0,3) = 0
#
# a(n,j) = a(n-1,j) when n+j is even
# a(n,j) = (j-1) a(n-1,j-1) + (j+1) a(n-1,j+1) when n+j is odd
#
#
# But we can use only one array unidimensional a(j) since to compute
# a(n,j) we only need to know a(n-1,k) where k and j are of different parity
# and we have not to conserve the used values.
#
# We cached up the values of Euler numbers to sufficiently high order.
#
# Important Observation: If we pretend to use the numbers
# EulerE[1], EulerE[2], ... , EulerE[n]
# it is convenient to compute first EulerE[n], since the algorithm
# computes first all
# the previous ones, and keeps them in the CACHE
MAX_EULER_CACHE = 500
def eulernum(m, _cache={0:MPZ_ONE}):
r"""
Computes the Euler numbers `E(n)`, which can be defined as
coefficients of the Taylor expansion of `1/cosh x`:
.. math ::
\frac{1}{\cosh x} = \sum_{n=0}^\infty \frac{E_n}{n!} x^n
Example::
>>> [int(eulernum(n)) for n in range(11)]
[1, 0, -1, 0, 5, 0, -61, 0, 1385, 0, -50521]
>>> [int(eulernum(n)) for n in range(11)] # test cache
[1, 0, -1, 0, 5, 0, -61, 0, 1385, 0, -50521]
"""
# for odd m > 1, the Euler numbers are zero
if m & 1:
return MPZ_ZERO
f = _cache.get(m)
if f:
return f
MAX = MAX_EULER_CACHE
n = m
a = [MPZ(_) for _ in [0,0,1,0,0,0]]
for n in range(1, m+1):
for j in range(n+1, -1, -2):
a[j+1] = (j-1)*a[j] + (j+1)*a[j+2]
a.append(0)
suma = 0
for k in range(n+1, -1, -2):
suma += a[k+1]
if n <= MAX:
_cache[n] = ((-1)**(n//2))*(suma // 2**n)
if n == m:
return ((-1)**(n//2))*suma // 2**n
def stirling1(n, k):
"""
Stirling number of the first kind.
"""
if n < 0 or k < 0:
raise ValueError
if k >= n:
return MPZ(n == k)
if k < 1:
return MPZ_ZERO
L = [MPZ_ZERO] * (k+1)
L[1] = MPZ_ONE
for m in xrange(2, n+1):
for j in xrange(min(k, m), 0, -1):
L[j] = (m-1) * L[j] + L[j-1]
return (-1)**(n+k) * L[k]
def stirling2(n, k):
"""
Stirling number of the second kind.
"""
if n < 0 or k < 0:
raise ValueError
if k >= n:
return MPZ(n == k)
if k <= 1:
return MPZ(k == 1)
s = MPZ_ZERO
t = MPZ_ONE
for j in xrange(k+1):
if (k + j) & 1:
s -= t * MPZ(j)**n
else:
s += t * MPZ(j)**n
t = t * (k - j) // (j + 1)
return s // ifac(k)
| 16,462 | 27.532062 | 78 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/libpasteurize/main.py
|
"""
pasteurize: automatic conversion of Python 3 code to clean 2/3 code
===================================================================
``pasteurize`` attempts to convert existing Python 3 code into source-compatible
Python 2 and 3 code.
Use it like this on Python 3 code:
$ pasteurize --verbose mypython3script.py
This removes any Py3-only syntax (e.g. new metaclasses) and adds these
import lines:
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
from __future__ import unicode_literals
from future import standard_library
standard_library.install_hooks()
from builtins import *
To write changes to the files, use the -w flag.
It also adds any other wrappers needed for Py2/3 compatibility.
Note that separate stages are not available (or needed) when converting from
Python 3 with ``pasteurize`` as they are when converting from Python 2 with
``futurize``.
The --all-imports option forces adding all ``__future__`` imports,
``builtins`` imports, and standard library aliases, even if they don't
seem necessary for the current state of each module. (This can simplify
testing, and can reduce the need to think about Py2 compatibility when editing
the code further.)
"""
from __future__ import (absolute_import, print_function, unicode_literals)
import sys
import logging
import optparse
from lib2to3.main import main, warn, StdoutRefactoringTool
from lib2to3 import refactor
from future import __version__
from libpasteurize.fixes import fix_names
def main(args=None):
"""Main program.
Returns a suggested exit status (0, 1, 2).
"""
# Set up option parser
parser = optparse.OptionParser(usage="pasteurize [options] file|dir ...")
parser.add_option("-V", "--version", action="store_true",
help="Report the version number of pasteurize")
parser.add_option("-a", "--all-imports", action="store_true",
help="Adds all __future__ and future imports to each module")
parser.add_option("-f", "--fix", action="append", default=[],
help="Each FIX specifies a transformation; default: all")
parser.add_option("-j", "--processes", action="store", default=1,
type="int", help="Run 2to3 concurrently")
parser.add_option("-x", "--nofix", action="append", default=[],
help="Prevent a fixer from being run.")
parser.add_option("-l", "--list-fixes", action="store_true",
help="List available transformations")
# parser.add_option("-p", "--print-function", action="store_true",
# help="Modify the grammar so that print() is a function")
parser.add_option("-v", "--verbose", action="store_true",
help="More verbose logging")
parser.add_option("--no-diffs", action="store_true",
help="Don't show diffs of the refactoring")
parser.add_option("-w", "--write", action="store_true",
help="Write back modified files")
parser.add_option("-n", "--nobackups", action="store_true", default=False,
help="Don't write backups for modified files.")
# Parse command line arguments
refactor_stdin = False
flags = {}
options, args = parser.parse_args(args)
fixer_pkg = 'libpasteurize.fixes'
avail_fixes = fix_names
flags["print_function"] = True
if not options.write and options.no_diffs:
warn("not writing files and not printing diffs; that's not very useful")
if not options.write and options.nobackups:
parser.error("Can't use -n without -w")
if options.version:
print(__version__)
return 0
if options.list_fixes:
print("Available transformations for the -f/--fix option:")
for fixname in sorted(avail_fixes):
print(fixname)
if not args:
return 0
if not args:
print("At least one file or directory argument required.",
file=sys.stderr)
print("Use --help to show usage.", file=sys.stderr)
return 2
if "-" in args:
refactor_stdin = True
if options.write:
print("Can't write to stdin.", file=sys.stderr)
return 2
# Set up logging handler
level = logging.DEBUG if options.verbose else logging.INFO
logging.basicConfig(format='%(name)s: %(message)s', level=level)
# Initialize the refactoring tool
unwanted_fixes = set(fixer_pkg + ".fix_" + fix for fix in options.nofix)
extra_fixes = set()
if options.all_imports:
prefix = 'libpasteurize.fixes.'
extra_fixes.add(prefix + 'fix_add_all__future__imports')
extra_fixes.add(prefix + 'fix_add_future_standard_library_import')
extra_fixes.add(prefix + 'fix_add_all_future_builtins')
fixer_names = avail_fixes | extra_fixes - unwanted_fixes
rt = StdoutRefactoringTool(sorted(fixer_names), flags, set(),
options.nobackups, not options.no_diffs)
# Refactor all files and directories passed as arguments
if not rt.errors:
if refactor_stdin:
rt.refactor_stdin()
else:
try:
rt.refactor(args, options.write, None,
options.processes)
except refactor.MultiprocessingUnsupported:
assert options.processes > 1
print("Sorry, -j isn't " \
"supported on this platform.", file=sys.stderr)
return 1
rt.summarize()
# Return error status (0 if rt.errors is zero)
return int(bool(rt.errors))
| 5,705 | 37.04 | 83 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/libpasteurize/__init__.py
|
# empty to make this a package
| 31 | 15 | 30 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/libpasteurize/fixes/fix_raise.py
|
u"""Fixer for 'raise E(V).with_traceback(T)' -> 'raise E, V, T'"""
from lib2to3 import fixer_base
from lib2to3.fixer_util import Comma, Node, Leaf, token, syms
class FixRaise(fixer_base.BaseFix):
PATTERN = u"""
raise_stmt< 'raise' (power< name=any [trailer< '(' val=any* ')' >]
[trailer< '.' 'with_traceback' > trailer< '(' trc=any ')' >] > | any) ['from' chain=any] >"""
def transform(self, node, results):
name, val, trc = (results.get(u"name"), results.get(u"val"), results.get(u"trc"))
chain = results.get(u"chain")
if chain is not None:
self.warning(node, u"explicit exception chaining is not supported in Python 2")
chain.prev_sibling.remove()
chain.remove()
if trc is not None:
val = val[0] if val else Leaf(token.NAME, u"None")
val.prefix = trc.prefix = u" "
kids = [Leaf(token.NAME, u"raise"), name.clone(), Comma(),
val.clone(), Comma(), trc.clone()]
raise_stmt = Node(syms.raise_stmt, kids)
node.replace(raise_stmt)
| 1,099 | 41.307692 | 101 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/libpasteurize/fixes/fix_metaclass.py
|
u"""
Fixer for (metaclass=X) -> __metaclass__ = X
Some semantics (see PEP 3115) may be altered in the translation."""
from lib2to3 import fixer_base
from lib2to3.fixer_util import Name, syms, Node, Leaf, Newline, find_root
from lib2to3.pygram import token
from libfuturize.fixer_util import indentation, suitify
# from ..fixer_util import Name, syms, Node, Leaf, Newline, find_root, indentation, suitify
def has_metaclass(parent):
results = None
for node in parent.children:
kids = node.children
if node.type == syms.argument:
if kids[0] == Leaf(token.NAME, u"metaclass") and \
kids[1] == Leaf(token.EQUAL, u"=") and \
kids[2]:
#Hack to avoid "class X(=):" with this case.
results = [node] + kids
break
elif node.type == syms.arglist:
# Argument list... loop through it looking for:
# Node(*, [*, Leaf(token.NAME, u"metaclass"), Leaf(token.EQUAL, u"="), Leaf(*, *)]
for child in node.children:
if results: break
if child.type == token.COMMA:
#Store the last comma, which precedes the metaclass
comma = child
elif type(child) == Node:
meta = equal = name = None
for arg in child.children:
if arg == Leaf(token.NAME, u"metaclass"):
#We have the (metaclass) part
meta = arg
elif meta and arg == Leaf(token.EQUAL, u"="):
#We have the (metaclass=) part
equal = arg
elif meta and equal:
#Here we go, we have (metaclass=X)
name = arg
results = (comma, meta, equal, name)
break
return results
class FixMetaclass(fixer_base.BaseFix):
PATTERN = u"""
classdef<any*>
"""
def transform(self, node, results):
meta_results = has_metaclass(node)
if not meta_results: return
for meta in meta_results:
meta.remove()
target = Leaf(token.NAME, u"__metaclass__")
equal = Leaf(token.EQUAL, u"=", prefix=u" ")
# meta is the last item in what was returned by has_metaclass(): name
name = meta
name.prefix = u" "
stmt_node = Node(syms.atom, [target, equal, name])
suitify(node)
for item in node.children:
if item.type == syms.suite:
for stmt in item.children:
if stmt.type == token.INDENT:
# Insert, in reverse order, the statement, a newline,
# and an indent right after the first indented line
loc = item.children.index(stmt) + 1
# Keep consistent indentation form
ident = Leaf(token.INDENT, stmt.value)
item.insert_child(loc, ident)
item.insert_child(loc, Newline())
item.insert_child(loc, stmt_node)
break
| 3,268 | 40.379747 | 94 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/libpasteurize/fixes/fix_memoryview.py
|
u"""
Fixer for memoryview(s) -> buffer(s).
Explicit because some memoryview methods are invalid on buffer objects.
"""
from lib2to3 import fixer_base
from lib2to3.fixer_util import Name
class FixMemoryview(fixer_base.BaseFix):
explicit = True # User must specify that they want this.
PATTERN = u"""
power< name='memoryview' trailer< '(' [any] ')' >
rest=any* >
"""
def transform(self, node, results):
name = results[u"name"]
name.replace(Name(u"buffer", prefix=name.prefix))
| 551 | 24.090909 | 71 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/libpasteurize/fixes/fix_division.py
|
u"""
Fixer for division: from __future__ import division if needed
"""
from lib2to3 import fixer_base
from libfuturize.fixer_util import token, future_import
def match_division(node):
u"""
__future__.division redefines the meaning of a single slash for division,
so we match that and only that.
"""
slash = token.SLASH
return node.type == slash and not node.next_sibling.type == slash and \
not node.prev_sibling.type == slash
class FixDivision(fixer_base.BaseFix):
run_order = 4 # this seems to be ignored?
def match(self, node):
u"""
Since the tree needs to be fixed once and only once if and only if it
matches, then we can start discarding matches after we make the first.
"""
return match_division(node)
def transform(self, node, results):
future_import(u"division", node)
| 904 | 30.206897 | 78 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/libpasteurize/fixes/fix_annotations.py
|
u"""
Fixer to remove function annotations
"""
from lib2to3 import fixer_base
from lib2to3.pgen2 import token
from lib2to3.fixer_util import syms
warning_text = u"Removing function annotations completely."
def param_without_annotations(node):
return node.children[0]
class FixAnnotations(fixer_base.BaseFix):
warned = False
def warn_once(self, node, reason):
if not self.warned:
self.warned = True
self.warning(node, reason=reason)
PATTERN = u"""
funcdef< 'def' any parameters< '(' [params=any] ')' > ['->' ret=any] ':' any* >
"""
def transform(self, node, results):
u"""
This just strips annotations from the funcdef completely.
"""
params = results.get(u"params")
ret = results.get(u"ret")
if ret is not None:
assert ret.prev_sibling.type == token.RARROW, u"Invalid return annotation"
self.warn_once(node, reason=warning_text)
ret.prev_sibling.remove()
ret.remove()
if params is None: return
if params.type == syms.typedargslist:
# more than one param in a typedargslist
for param in params.children:
if param.type == syms.tname:
self.warn_once(node, reason=warning_text)
param.replace(param_without_annotations(param))
elif params.type == syms.tname:
# one param
self.warn_once(node, reason=warning_text)
params.replace(param_without_annotations(params))
| 1,585 | 31.367347 | 93 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/libpasteurize/fixes/fix_kwargs.py
|
u"""
Fixer for Python 3 function parameter syntax
This fixer is rather sensitive to incorrect py3k syntax.
"""
# Note: "relevant" parameters are parameters following the first STAR in the list.
from lib2to3 import fixer_base
from lib2to3.fixer_util import token, String, Newline, Comma, Name
from libfuturize.fixer_util import indentation, suitify, DoubleStar
_assign_template = u"%(name)s = %(kwargs)s['%(name)s']; del %(kwargs)s['%(name)s']"
_if_template = u"if '%(name)s' in %(kwargs)s: %(assign)s"
_else_template = u"else: %(name)s = %(default)s"
_kwargs_default_name = u"_3to2kwargs"
def gen_params(raw_params):
u"""
Generator that yields tuples of (name, default_value) for each parameter in the list
If no default is given, then it is default_value is None (not Leaf(token.NAME, 'None'))
"""
assert raw_params[0].type == token.STAR and len(raw_params) > 2
curr_idx = 2 # the first place a keyword-only parameter name can be is index 2
max_idx = len(raw_params)
while curr_idx < max_idx:
curr_item = raw_params[curr_idx]
prev_item = curr_item.prev_sibling
if curr_item.type != token.NAME:
curr_idx += 1
continue
if prev_item is not None and prev_item.type == token.DOUBLESTAR:
break
name = curr_item.value
nxt = curr_item.next_sibling
if nxt is not None and nxt.type == token.EQUAL:
default_value = nxt.next_sibling
curr_idx += 2
else:
default_value = None
yield (name, default_value)
curr_idx += 1
def remove_params(raw_params, kwargs_default=_kwargs_default_name):
u"""
Removes all keyword-only args from the params list and a bare star, if any.
Does not add the kwargs dict if needed.
Returns True if more action is needed, False if not
(more action is needed if no kwargs dict exists)
"""
assert raw_params[0].type == token.STAR
if raw_params[1].type == token.COMMA:
raw_params[0].remove()
raw_params[1].remove()
kw_params = raw_params[2:]
else:
kw_params = raw_params[3:]
for param in kw_params:
if param.type != token.DOUBLESTAR:
param.remove()
else:
return False
else:
return True
def needs_fixing(raw_params, kwargs_default=_kwargs_default_name):
u"""
Returns string with the name of the kwargs dict if the params after the first star need fixing
Otherwise returns empty string
"""
found_kwargs = False
needs_fix = False
for t in raw_params[2:]:
if t.type == token.COMMA:
# Commas are irrelevant at this stage.
continue
elif t.type == token.NAME and not found_kwargs:
# Keyword-only argument: definitely need to fix.
needs_fix = True
elif t.type == token.NAME and found_kwargs:
# Return 'foobar' of **foobar, if needed.
return t.value if needs_fix else u''
elif t.type == token.DOUBLESTAR:
# Found either '*' from **foobar.
found_kwargs = True
else:
# Never found **foobar. Return a synthetic name, if needed.
return kwargs_default if needs_fix else u''
class FixKwargs(fixer_base.BaseFix):
run_order = 7 # Run after function annotations are removed
PATTERN = u"funcdef< 'def' NAME parameters< '(' arglist=typedargslist< params=any* > ')' > ':' suite=any >"
def transform(self, node, results):
params_rawlist = results[u"params"]
for i, item in enumerate(params_rawlist):
if item.type == token.STAR:
params_rawlist = params_rawlist[i:]
break
else:
return
# params is guaranteed to be a list starting with *.
# if fixing is needed, there will be at least 3 items in this list:
# [STAR, COMMA, NAME] is the minimum that we need to worry about.
new_kwargs = needs_fixing(params_rawlist)
# new_kwargs is the name of the kwargs dictionary.
if not new_kwargs:
return
suitify(node)
# At this point, params_rawlist is guaranteed to be a list
# beginning with a star that includes at least one keyword-only param
# e.g., [STAR, NAME, COMMA, NAME, COMMA, DOUBLESTAR, NAME] or
# [STAR, COMMA, NAME], or [STAR, COMMA, NAME, COMMA, DOUBLESTAR, NAME]
# Anatomy of a funcdef: ['def', 'name', parameters, ':', suite]
# Anatomy of that suite: [NEWLINE, INDENT, first_stmt, all_other_stmts]
# We need to insert our new stuff before the first_stmt and change the
# first_stmt's prefix.
suite = node.children[4]
first_stmt = suite.children[2]
ident = indentation(first_stmt)
for name, default_value in gen_params(params_rawlist):
if default_value is None:
suite.insert_child(2, Newline())
suite.insert_child(2, String(_assign_template %{u'name':name, u'kwargs':new_kwargs}, prefix=ident))
else:
suite.insert_child(2, Newline())
suite.insert_child(2, String(_else_template %{u'name':name, u'default':default_value}, prefix=ident))
suite.insert_child(2, Newline())
suite.insert_child(2, String(_if_template %{u'assign':_assign_template %{u'name':name, u'kwargs':new_kwargs}, u'name':name, u'kwargs':new_kwargs}, prefix=ident))
first_stmt.prefix = ident
suite.children[2].prefix = u""
# Now, we need to fix up the list of params.
must_add_kwargs = remove_params(params_rawlist)
if must_add_kwargs:
arglist = results[u'arglist']
if len(arglist.children) > 0 and arglist.children[-1].type != token.COMMA:
arglist.append_child(Comma())
arglist.append_child(DoubleStar(prefix=u" "))
arglist.append_child(Name(new_kwargs))
| 6,008 | 39.328859 | 177 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/libpasteurize/fixes/fix_printfunction.py
|
u"""
Fixer for print: from __future__ import print_function.
"""
from lib2to3 import fixer_base
from libfuturize.fixer_util import future_import
class FixPrintfunction(fixer_base.BaseFix):
# explicit = True
PATTERN = u"""
power< 'print' trailer < '(' any* ')' > any* >
"""
def transform(self, node, results):
future_import(u"print_function", node)
| 401 | 21.333333 | 60 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/libpasteurize/fixes/fix_future_builtins.py
|
"""
Adds this import line:
from builtins import XYZ
for each of the functions XYZ that is used in the module.
"""
from __future__ import unicode_literals
from lib2to3 import fixer_base
from lib2to3.pygram import python_symbols as syms
from lib2to3.fixer_util import Name, Call, in_special_context
from libfuturize.fixer_util import touch_import_top
# All builtins are:
# from future.builtins.iterators import (filter, map, zip)
# from future.builtins.misc import (ascii, chr, hex, input, isinstance, oct, open, round, super)
# from future.types import (bytes, dict, int, range, str)
# We don't need isinstance any more.
replaced_builtins = '''filter map zip
ascii chr hex input next oct open round super
bytes dict int range str'''.split()
expression = '|'.join(["name='{0}'".format(name) for name in replaced_builtins])
class FixFutureBuiltins(fixer_base.BaseFix):
BM_compatible = True
run_order = 9
# Currently we only match uses as a function. This doesn't match e.g.:
# if isinstance(s, str):
# ...
PATTERN = """
power<
({0}) trailer< '(' args=[any] ')' >
rest=any* >
""".format(expression)
def transform(self, node, results):
name = results["name"]
touch_import_top(u'builtins', name.value, node)
# name.replace(Name(u"input", prefix=name.prefix))
| 1,451 | 29.25 | 100 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/libpasteurize/fixes/fix_newstyle.py
|
u"""
Fixer for "class Foo: ..." -> "class Foo(object): ..."
"""
from lib2to3 import fixer_base
from lib2to3.fixer_util import LParen, RParen, Name
from libfuturize.fixer_util import touch_import_top
def insert_object(node, idx):
node.insert_child(idx, RParen())
node.insert_child(idx, Name(u"object"))
node.insert_child(idx, LParen())
class FixNewstyle(fixer_base.BaseFix):
# Match:
# class Blah:
# and:
# class Blah():
PATTERN = u"classdef< 'class' NAME ['(' ')'] colon=':' any >"
def transform(self, node, results):
colon = results[u"colon"]
idx = node.children.index(colon)
if (node.children[idx-2].value == '(' and
node.children[idx-1].value == ')'):
del node.children[idx-2:idx]
idx -= 2
insert_object(node, idx)
touch_import_top(u'builtins', 'object', node)
| 888 | 25.147059 | 65 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/libpasteurize/fixes/fix_getcwd.py
|
u"""
Fixer for os.getcwd() -> os.getcwdu().
Also warns about "from os import getcwd", suggesting the above form.
"""
from lib2to3 import fixer_base
from lib2to3.fixer_util import Name
class FixGetcwd(fixer_base.BaseFix):
PATTERN = u"""
power< 'os' trailer< dot='.' name='getcwd' > any* >
|
import_from< 'from' 'os' 'import' bad='getcwd' >
"""
def transform(self, node, results):
if u"name" in results:
name = results[u"name"]
name.replace(Name(u"getcwdu", prefix=name.prefix))
elif u"bad" in results:
# Can't convert to getcwdu and then expect to catch every use.
self.cannot_convert(node, u"import os, use os.getcwd() instead.")
return
else:
raise ValueError(u"For some reason, the pattern matcher failed.")
| 873 | 31.37037 | 77 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/libpasteurize/fixes/fix_throw.py
|
u"""Fixer for 'g.throw(E(V).with_traceback(T))' -> 'g.throw(E, V, T)'"""
from lib2to3 import fixer_base
from lib2to3.pytree import Node, Leaf
from lib2to3.pgen2 import token
from lib2to3.fixer_util import Comma
class FixThrow(fixer_base.BaseFix):
PATTERN = u"""
power< any trailer< '.' 'throw' >
trailer< '(' args=power< exc=any trailer< '(' val=any* ')' >
trailer< '.' 'with_traceback' > trailer< '(' trc=any ')' > > ')' > >
"""
def transform(self, node, results):
syms = self.syms
exc, val, trc = (results[u"exc"], results[u"val"], results[u"trc"])
val = val[0] if val else Leaf(token.NAME, u"None")
val.prefix = trc.prefix = u" "
kids = [exc.clone(), Comma(), val.clone(), Comma(), trc.clone()]
args = results[u"args"]
args.children = kids
| 835 | 33.833333 | 76 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/libpasteurize/fixes/fix_add_all__future__imports.py
|
"""
Fixer for adding:
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
from __future__ import unicode_literals
This is done when converting from Py3 to both Py3/Py2.
"""
from lib2to3 import fixer_base
from libfuturize.fixer_util import future_import
class FixAddAllFutureImports(fixer_base.BaseFix):
BM_compatible = True
PATTERN = "file_input"
run_order = 1
def transform(self, node, results):
future_import(u"unicode_literals", node)
future_import(u"print_function", node)
future_import(u"division", node)
future_import(u"absolute_import", node)
| 677 | 25.076923 | 54 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/libpasteurize/fixes/fix_fullargspec.py
|
u"""
Fixer for getfullargspec -> getargspec
"""
from lib2to3 import fixer_base
from lib2to3.fixer_util import Name
warn_msg = u"some of the values returned by getfullargspec are not valid in Python 2 and have no equivalent."
class FixFullargspec(fixer_base.BaseFix):
PATTERN = u"'getfullargspec'"
def transform(self, node, results):
self.warning(node, warn_msg)
return Name(u"getargspec", prefix=node.prefix)
| 442 | 25.058824 | 109 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/libpasteurize/fixes/fix_add_future_standard_library_import.py
|
"""
For the ``future`` package.
Adds this import line:
from future import standard_library
after any __future__ imports but before any other imports. Doesn't actually
change the imports to Py3 style.
"""
from lib2to3 import fixer_base
from libfuturize.fixer_util import touch_import_top
class FixAddFutureStandardLibraryImport(fixer_base.BaseFix):
BM_compatible = True
PATTERN = "file_input"
run_order = 8
def transform(self, node, results):
# TODO: add a blank line between any __future__ imports and this?
touch_import_top(u'future', u'standard_library', node)
# TODO: also add standard_library.install_hooks()
| 663 | 26.666667 | 75 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/libpasteurize/fixes/fix_raise_.py
|
u"""Fixer for
raise E(V).with_traceback(T)
to:
from future.utils import raise_
...
raise_(E, V, T)
TODO: FIXME!!
"""
from lib2to3 import fixer_base
from lib2to3.fixer_util import Comma, Node, Leaf, token, syms
class FixRaise(fixer_base.BaseFix):
PATTERN = u"""
raise_stmt< 'raise' (power< name=any [trailer< '(' val=any* ')' >]
[trailer< '.' 'with_traceback' > trailer< '(' trc=any ')' >] > | any) ['from' chain=any] >"""
def transform(self, node, results):
FIXME
name, val, trc = (results.get(u"name"), results.get(u"val"), results.get(u"trc"))
chain = results.get(u"chain")
if chain is not None:
self.warning(node, u"explicit exception chaining is not supported in Python 2")
chain.prev_sibling.remove()
chain.remove()
if trc is not None:
val = val[0] if val else Leaf(token.NAME, u"None")
val.prefix = trc.prefix = u" "
kids = [Leaf(token.NAME, u"raise"), name.clone(), Comma(),
val.clone(), Comma(), trc.clone()]
raise_stmt = Node(syms.raise_stmt, kids)
node.replace(raise_stmt)
| 1,225 | 33.055556 | 101 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/libpasteurize/fixes/feature_base.py
|
u"""
Base classes for features that are backwards-incompatible.
Usage:
features = Features()
features.add(Feature("py3k_feature", "power< 'py3k' any* >", "2.7"))
PATTERN = features.PATTERN
"""
pattern_unformatted = u"%s=%s" # name=pattern, for dict lookups
message_unformatted = u"""
%s is only supported in Python %s and above."""
class Feature(object):
u"""
A feature has a name, a pattern, and a minimum version of Python 2.x
required to use the feature (or 3.x if there is no backwards-compatible
version of 2.x)
"""
def __init__(self, name, PATTERN, version):
self.name = name
self._pattern = PATTERN
self.version = version
def message_text(self):
u"""
Format the above text with the name and minimum version required.
"""
return message_unformatted % (self.name, self.version)
class Features(set):
u"""
A set of features that generates a pattern for the features it contains.
This set will act like a mapping in that we map names to patterns.
"""
mapping = {}
def update_mapping(self):
u"""
Called every time we care about the mapping of names to features.
"""
self.mapping = dict([(f.name, f) for f in iter(self)])
@property
def PATTERN(self):
u"""
Uses the mapping of names to features to return a PATTERN suitable
for using the lib2to3 patcomp.
"""
self.update_mapping()
return u" |\n".join([pattern_unformatted % (f.name, f._pattern) for f in iter(self)])
def __getitem__(self, key):
u"""
Implement a simple mapping to get patterns from names.
"""
return self.mapping[key]
| 1,727 | 28.793103 | 93 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/libpasteurize/fixes/fix_unpacking.py
|
u"""
Fixer for:
(a,)* *b (,c)* [,] = s
for (a,)* *b (,c)* [,] in d: ...
"""
from lib2to3 import fixer_base
from itertools import count
from lib2to3.fixer_util import (Assign, Comma, Call, Newline, Name,
Number, token, syms, Node, Leaf)
from libfuturize.fixer_util import indentation, suitify, commatize
# from libfuturize.fixer_util import Assign, Comma, Call, Newline, Name, Number, indentation, suitify, commatize, token, syms, Node, Leaf
def assignment_source(num_pre, num_post, LISTNAME, ITERNAME):
u"""
Accepts num_pre and num_post, which are counts of values
before and after the starg (not including the starg)
Returns a source fit for Assign() from fixer_util
"""
children = []
pre = unicode(num_pre)
post = unicode(num_post)
# This code builds the assignment source from lib2to3 tree primitives.
# It's not very readable, but it seems like the most correct way to do it.
if num_pre > 0:
pre_part = Node(syms.power, [Name(LISTNAME), Node(syms.trailer, [Leaf(token.LSQB, u"["), Node(syms.subscript, [Leaf(token.COLON, u":"), Number(pre)]), Leaf(token.RSQB, u"]")])])
children.append(pre_part)
children.append(Leaf(token.PLUS, u"+", prefix=u" "))
main_part = Node(syms.power, [Leaf(token.LSQB, u"[", prefix=u" "), Name(LISTNAME), Node(syms.trailer, [Leaf(token.LSQB, u"["), Node(syms.subscript, [Number(pre) if num_pre > 0 else Leaf(1, u""), Leaf(token.COLON, u":"), Node(syms.factor, [Leaf(token.MINUS, u"-"), Number(post)]) if num_post > 0 else Leaf(1, u"")]), Leaf(token.RSQB, u"]"), Leaf(token.RSQB, u"]")])])
children.append(main_part)
if num_post > 0:
children.append(Leaf(token.PLUS, u"+", prefix=u" "))
post_part = Node(syms.power, [Name(LISTNAME, prefix=u" "), Node(syms.trailer, [Leaf(token.LSQB, u"["), Node(syms.subscript, [Node(syms.factor, [Leaf(token.MINUS, u"-"), Number(post)]), Leaf(token.COLON, u":")]), Leaf(token.RSQB, u"]")])])
children.append(post_part)
source = Node(syms.arith_expr, children)
return source
class FixUnpacking(fixer_base.BaseFix):
PATTERN = u"""
expl=expr_stmt< testlist_star_expr<
pre=(any ',')*
star_expr< '*' name=NAME >
post=(',' any)* [','] > '=' source=any > |
impl=for_stmt< 'for' lst=exprlist<
pre=(any ',')*
star_expr< '*' name=NAME >
post=(',' any)* [','] > 'in' it=any ':' suite=any>"""
def fix_explicit_context(self, node, results):
pre, name, post, source = (results.get(n) for n in (u"pre", u"name", u"post", u"source"))
pre = [n.clone() for n in pre if n.type == token.NAME]
name.prefix = u" "
post = [n.clone() for n in post if n.type == token.NAME]
target = [n.clone() for n in commatize(pre + [name.clone()] + post)]
# to make the special-case fix for "*z, = ..." correct with the least
# amount of modification, make the left-side into a guaranteed tuple
target.append(Comma())
source.prefix = u""
setup_line = Assign(Name(self.LISTNAME), Call(Name(u"list"), [source.clone()]))
power_line = Assign(target, assignment_source(len(pre), len(post), self.LISTNAME, self.ITERNAME))
return setup_line, power_line
def fix_implicit_context(self, node, results):
u"""
Only example of the implicit context is
a for loop, so only fix that.
"""
pre, name, post, it = (results.get(n) for n in (u"pre", u"name", u"post", u"it"))
pre = [n.clone() for n in pre if n.type == token.NAME]
name.prefix = u" "
post = [n.clone() for n in post if n.type == token.NAME]
target = [n.clone() for n in commatize(pre + [name.clone()] + post)]
# to make the special-case fix for "*z, = ..." correct with the least
# amount of modification, make the left-side into a guaranteed tuple
target.append(Comma())
source = it.clone()
source.prefix = u""
setup_line = Assign(Name(self.LISTNAME), Call(Name(u"list"), [Name(self.ITERNAME)]))
power_line = Assign(target, assignment_source(len(pre), len(post), self.LISTNAME, self.ITERNAME))
return setup_line, power_line
def transform(self, node, results):
u"""
a,b,c,d,e,f,*g,h,i = range(100) changes to
_3to2list = list(range(100))
a,b,c,d,e,f,g,h,i, = _3to2list[:6] + [_3to2list[6:-2]] + _3to2list[-2:]
and
for a,b,*c,d,e in iter_of_iters: do_stuff changes to
for _3to2iter in iter_of_iters:
_3to2list = list(_3to2iter)
a,b,c,d,e, = _3to2list[:2] + [_3to2list[2:-2]] + _3to2list[-2:]
do_stuff
"""
self.LISTNAME = self.new_name(u"_3to2list")
self.ITERNAME = self.new_name(u"_3to2iter")
expl, impl = results.get(u"expl"), results.get(u"impl")
if expl is not None:
setup_line, power_line = self.fix_explicit_context(node, results)
setup_line.prefix = expl.prefix
power_line.prefix = indentation(expl.parent)
setup_line.append_child(Newline())
parent = node.parent
i = node.remove()
parent.insert_child(i, power_line)
parent.insert_child(i, setup_line)
elif impl is not None:
setup_line, power_line = self.fix_implicit_context(node, results)
suitify(node)
suite = [k for k in node.children if k.type == syms.suite][0]
setup_line.prefix = u""
power_line.prefix = suite.children[1].value
suite.children[2].prefix = indentation(suite.children[2])
suite.insert_child(2, Newline())
suite.insert_child(2, power_line)
suite.insert_child(2, Newline())
suite.insert_child(2, setup_line)
results.get(u"lst").replace(Name(self.ITERNAME, prefix=u" "))
| 5,954 | 48.214876 | 370 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/libpasteurize/fixes/fix_imports.py
|
u"""
Fixer for standard library imports renamed in Python 3
"""
from lib2to3 import fixer_base
from lib2to3.fixer_util import Name, is_probably_builtin, Newline, does_tree_import
from lib2to3.pygram import python_symbols as syms
from lib2to3.pgen2 import token
from lib2to3.pytree import Node, Leaf
from libfuturize.fixer_util import touch_import_top
# from ..fixer_util import NameImport
# used in simple_mapping_to_pattern()
MAPPING = {u"reprlib": u"repr",
u"winreg": u"_winreg",
u"configparser": u"ConfigParser",
u"copyreg": u"copy_reg",
u"queue": u"Queue",
u"socketserver": u"SocketServer",
u"_markupbase": u"markupbase",
u"test.support": u"test.test_support",
u"dbm.bsd": u"dbhash",
u"dbm.ndbm": u"dbm",
u"dbm.dumb": u"dumbdbm",
u"dbm.gnu": u"gdbm",
u"html.parser": u"HTMLParser",
u"html.entities": u"htmlentitydefs",
u"http.client": u"httplib",
u"http.cookies": u"Cookie",
u"http.cookiejar": u"cookielib",
# "tkinter": "Tkinter",
u"tkinter.dialog": u"Dialog",
u"tkinter._fix": u"FixTk",
u"tkinter.scrolledtext": u"ScrolledText",
u"tkinter.tix": u"Tix",
u"tkinter.constants": u"Tkconstants",
u"tkinter.dnd": u"Tkdnd",
u"tkinter.__init__": u"Tkinter",
u"tkinter.colorchooser": u"tkColorChooser",
u"tkinter.commondialog": u"tkCommonDialog",
u"tkinter.font": u"tkFont",
u"tkinter.ttk": u"ttk",
u"tkinter.messagebox": u"tkMessageBox",
u"tkinter.turtle": u"turtle",
u"urllib.robotparser": u"robotparser",
u"xmlrpc.client": u"xmlrpclib",
u"builtins": u"__builtin__",
}
# generic strings to help build patterns
# these variables mean (with http.client.HTTPConnection as an example):
# name = http
# attr = client
# used = HTTPConnection
# fmt_name is a formatted subpattern (simple_name_match or dotted_name_match)
# helps match 'queue', as in 'from queue import ...'
simple_name_match = u"name='%s'"
# helps match 'client', to be used if client has been imported from http
subname_match = u"attr='%s'"
# helps match 'http.client', as in 'import urllib.request'
dotted_name_match = u"dotted_name=dotted_name< %s '.' %s >"
# helps match 'queue', as in 'queue.Queue(...)'
power_onename_match = u"%s"
# helps match 'http.client', as in 'http.client.HTTPConnection(...)'
power_twoname_match = u"power< %s trailer< '.' %s > any* >"
# helps match 'client.HTTPConnection', if 'client' has been imported from http
power_subname_match = u"power< %s any* >"
# helps match 'from http.client import HTTPConnection'
from_import_match = u"from_import=import_from< 'from' %s 'import' imported=any >"
# helps match 'from http import client'
from_import_submod_match = u"from_import_submod=import_from< 'from' %s 'import' (%s | import_as_name< %s 'as' renamed=any > | import_as_names< any* (%s | import_as_name< %s 'as' renamed=any >) any* > ) >"
# helps match 'import urllib.request'
name_import_match = u"name_import=import_name< 'import' %s > | name_import=import_name< 'import' dotted_as_name< %s 'as' renamed=any > >"
# helps match 'import http.client, winreg'
multiple_name_import_match = u"name_import=import_name< 'import' dotted_as_names< names=any* > >"
def all_patterns(name):
u"""
Accepts a string and returns a pattern of possible patterns involving that name
Called by simple_mapping_to_pattern for each name in the mapping it receives.
"""
# i_ denotes an import-like node
# u_ denotes a node that appears to be a usage of the name
if u'.' in name:
name, attr = name.split(u'.', 1)
simple_name = simple_name_match % (name)
simple_attr = subname_match % (attr)
dotted_name = dotted_name_match % (simple_name, simple_attr)
i_from = from_import_match % (dotted_name)
i_from_submod = from_import_submod_match % (simple_name, simple_attr, simple_attr, simple_attr, simple_attr)
i_name = name_import_match % (dotted_name, dotted_name)
u_name = power_twoname_match % (simple_name, simple_attr)
u_subname = power_subname_match % (simple_attr)
return u' | \n'.join((i_name, i_from, i_from_submod, u_name, u_subname))
else:
simple_name = simple_name_match % (name)
i_name = name_import_match % (simple_name, simple_name)
i_from = from_import_match % (simple_name)
u_name = power_onename_match % (simple_name)
return u' | \n'.join((i_name, i_from, u_name))
class FixImports(fixer_base.BaseFix):
PATTERN = u' | \n'.join([all_patterns(name) for name in MAPPING])
PATTERN = u' | \n'.join((PATTERN, multiple_name_import_match))
def transform(self, node, results):
touch_import_top(u'future', u'standard_library', node)
| 4,945 | 42.385965 | 204 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/libpasteurize/fixes/__init__.py
|
import sys
from lib2to3 import refactor
# The original set of these fixes comes from lib3to2 (https://bitbucket.org/amentajo/lib3to2):
fix_names = set([
'libpasteurize.fixes.fix_add_all__future__imports', # from __future__ import absolute_import etc. on separate lines
'libpasteurize.fixes.fix_add_future_standard_library_import', # we force adding this import for now, even if it doesn't seem necessary to the fix_future_standard_library fixer, for ease of testing
# 'libfuturize.fixes.fix_order___future__imports', # consolidates to a single line to simplify testing -- UNFINISHED
'libpasteurize.fixes.fix_future_builtins', # adds "from future.builtins import *"
'libfuturize.fixes.fix_future_standard_library', # adds "from future import standard_library"
'libpasteurize.fixes.fix_annotations',
# 'libpasteurize.fixes.fix_bitlength', # ints have this in Py2.7
# 'libpasteurize.fixes.fix_bool', # need a decorator or Mixin
# 'libpasteurize.fixes.fix_bytes', # leave bytes as bytes
# 'libpasteurize.fixes.fix_classdecorator', # available in
# Py2.6+
# 'libpasteurize.fixes.fix_collections', hmmm ...
# 'libpasteurize.fixes.fix_dctsetcomp', # avail in Py27
'libpasteurize.fixes.fix_division', # yes
# 'libpasteurize.fixes.fix_except', # avail in Py2.6+
# 'libpasteurize.fixes.fix_features', # ?
'libpasteurize.fixes.fix_fullargspec',
# 'libpasteurize.fixes.fix_funcattrs',
'libpasteurize.fixes.fix_getcwd',
'libpasteurize.fixes.fix_imports', # adds "from future import standard_library"
'libpasteurize.fixes.fix_imports2',
# 'libpasteurize.fixes.fix_input',
# 'libpasteurize.fixes.fix_int',
# 'libpasteurize.fixes.fix_intern',
# 'libpasteurize.fixes.fix_itertools',
'libpasteurize.fixes.fix_kwargs', # yes, we want this
# 'libpasteurize.fixes.fix_memoryview',
# 'libpasteurize.fixes.fix_metaclass', # write a custom handler for
# this
# 'libpasteurize.fixes.fix_methodattrs', # __func__ and __self__ seem to be defined on Py2.7 already
'libpasteurize.fixes.fix_newstyle', # yes, we want this: explicit inheritance from object. Without new-style classes in Py2, super() will break etc.
# 'libpasteurize.fixes.fix_next', # use a decorator for this
# 'libpasteurize.fixes.fix_numliterals', # prob not
# 'libpasteurize.fixes.fix_open', # huh?
# 'libpasteurize.fixes.fix_print', # no way
'libpasteurize.fixes.fix_printfunction', # adds __future__ import print_function
# 'libpasteurize.fixes.fix_raise_', # TODO: get this working!
# 'libpasteurize.fixes.fix_range', # nope
# 'libpasteurize.fixes.fix_reduce',
# 'libpasteurize.fixes.fix_setliteral',
# 'libpasteurize.fixes.fix_str',
# 'libpasteurize.fixes.fix_super', # maybe, if our magic super() isn't robust enough
'libpasteurize.fixes.fix_throw', # yes, if Py3 supports it
# 'libpasteurize.fixes.fix_unittest',
'libpasteurize.fixes.fix_unpacking', # yes, this is useful
# 'libpasteurize.fixes.fix_with' # way out of date
])
| 3,720 | 65.446429 | 214 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/libpasteurize/fixes/fix_imports2.py
|
u"""
Fixer for complicated imports
"""
from lib2to3 import fixer_base
from lib2to3.fixer_util import Name, String, FromImport, Newline, Comma
from libfuturize.fixer_util import touch_import_top
TK_BASE_NAMES = (u'ACTIVE', u'ALL', u'ANCHOR', u'ARC',u'BASELINE', u'BEVEL', u'BOTH',
u'BOTTOM', u'BROWSE', u'BUTT', u'CASCADE', u'CENTER', u'CHAR',
u'CHECKBUTTON', u'CHORD', u'COMMAND', u'CURRENT', u'DISABLED',
u'DOTBOX', u'E', u'END', u'EW', u'EXCEPTION', u'EXTENDED', u'FALSE',
u'FIRST', u'FLAT', u'GROOVE', u'HIDDEN', u'HORIZONTAL', u'INSERT',
u'INSIDE', u'LAST', u'LEFT', u'MITER', u'MOVETO', u'MULTIPLE', u'N',
u'NE', u'NO', u'NONE', u'NORMAL', u'NS', u'NSEW', u'NUMERIC', u'NW',
u'OFF', u'ON', u'OUTSIDE', u'PAGES', u'PIESLICE', u'PROJECTING',
u'RADIOBUTTON', u'RAISED', u'READABLE', u'RIDGE', u'RIGHT',
u'ROUND', u'S', u'SCROLL', u'SE', u'SEL', u'SEL_FIRST', u'SEL_LAST',
u'SEPARATOR', u'SINGLE', u'SOLID', u'SUNKEN', u'SW', u'StringTypes',
u'TOP', u'TRUE', u'TclVersion', u'TkVersion', u'UNDERLINE',
u'UNITS', u'VERTICAL', u'W', u'WORD', u'WRITABLE', u'X', u'Y', u'YES',
u'wantobjects')
PY2MODULES = {
u'urllib2' : (
u'AbstractBasicAuthHandler', u'AbstractDigestAuthHandler',
u'AbstractHTTPHandler', u'BaseHandler', u'CacheFTPHandler',
u'FTPHandler', u'FileHandler', u'HTTPBasicAuthHandler',
u'HTTPCookieProcessor', u'HTTPDefaultErrorHandler',
u'HTTPDigestAuthHandler', u'HTTPError', u'HTTPErrorProcessor',
u'HTTPHandler', u'HTTPPasswordMgr',
u'HTTPPasswordMgrWithDefaultRealm', u'HTTPRedirectHandler',
u'HTTPSHandler', u'OpenerDirector', u'ProxyBasicAuthHandler',
u'ProxyDigestAuthHandler', u'ProxyHandler', u'Request',
u'StringIO', u'URLError', u'UnknownHandler', u'addinfourl',
u'build_opener', u'install_opener', u'parse_http_list',
u'parse_keqv_list', u'randombytes', u'request_host', u'urlopen'),
u'urllib' : (
u'ContentTooShortError', u'FancyURLopener',u'URLopener',
u'basejoin', u'ftperrors', u'getproxies',
u'getproxies_environment', u'localhost', u'pathname2url',
u'quote', u'quote_plus', u'splitattr', u'splithost',
u'splitnport', u'splitpasswd', u'splitport', u'splitquery',
u'splittag', u'splittype', u'splituser', u'splitvalue',
u'thishost', u'unquote', u'unquote_plus', u'unwrap',
u'url2pathname', u'urlcleanup', u'urlencode', u'urlopen',
u'urlretrieve',),
u'urlparse' : (
u'parse_qs', u'parse_qsl', u'urldefrag', u'urljoin',
u'urlparse', u'urlsplit', u'urlunparse', u'urlunsplit'),
u'dbm' : (
u'ndbm', u'gnu', u'dumb'),
u'anydbm' : (
u'error', u'open'),
u'whichdb' : (
u'whichdb',),
u'BaseHTTPServer' : (
u'BaseHTTPRequestHandler', u'HTTPServer'),
u'CGIHTTPServer' : (
u'CGIHTTPRequestHandler',),
u'SimpleHTTPServer' : (
u'SimpleHTTPRequestHandler',),
u'FileDialog' : TK_BASE_NAMES + (
u'FileDialog', u'LoadFileDialog', u'SaveFileDialog',
u'dialogstates', u'test'),
u'tkFileDialog' : (
u'Directory', u'Open', u'SaveAs', u'_Dialog', u'askdirectory',
u'askopenfile', u'askopenfilename', u'askopenfilenames',
u'askopenfiles', u'asksaveasfile', u'asksaveasfilename'),
u'SimpleDialog' : TK_BASE_NAMES + (
u'SimpleDialog',),
u'tkSimpleDialog' : TK_BASE_NAMES + (
u'askfloat', u'askinteger', u'askstring', u'Dialog'),
u'SimpleXMLRPCServer' : (
u'CGIXMLRPCRequestHandler', u'SimpleXMLRPCDispatcher',
u'SimpleXMLRPCRequestHandler', u'SimpleXMLRPCServer',
u'list_public_methods', u'remove_duplicates',
u'resolve_dotted_attribute'),
u'DocXMLRPCServer' : (
u'DocCGIXMLRPCRequestHandler', u'DocXMLRPCRequestHandler',
u'DocXMLRPCServer', u'ServerHTMLDoc',u'XMLRPCDocGenerator'),
}
MAPPING = { u'urllib.request' :
(u'urllib2', u'urllib'),
u'urllib.error' :
(u'urllib2', u'urllib'),
u'urllib.parse' :
(u'urllib2', u'urllib', u'urlparse'),
u'dbm.__init__' :
(u'anydbm', u'whichdb'),
u'http.server' :
(u'CGIHTTPServer', u'SimpleHTTPServer', u'BaseHTTPServer'),
u'tkinter.filedialog' :
(u'tkFileDialog', u'FileDialog'),
u'tkinter.simpledialog' :
(u'tkSimpleDialog', u'SimpleDialog'),
u'xmlrpc.server' :
(u'DocXMLRPCServer', u'SimpleXMLRPCServer'),
}
# helps match 'http', as in 'from http.server import ...'
simple_name = u"name='%s'"
# helps match 'server', as in 'from http.server import ...'
simple_attr = u"attr='%s'"
# helps match 'HTTPServer', as in 'from http.server import HTTPServer'
simple_using = u"using='%s'"
# helps match 'urllib.request', as in 'import urllib.request'
dotted_name = u"dotted_name=dotted_name< %s '.' %s >"
# helps match 'http.server', as in 'http.server.HTTPServer(...)'
power_twoname = u"pow=power< %s trailer< '.' %s > trailer< '.' using=any > any* >"
# helps match 'dbm.whichdb', as in 'dbm.whichdb(...)'
power_onename = u"pow=power< %s trailer< '.' using=any > any* >"
# helps match 'from http.server import HTTPServer'
# also helps match 'from http.server import HTTPServer, SimpleHTTPRequestHandler'
# also helps match 'from http.server import *'
from_import = u"from_import=import_from< 'from' %s 'import' (import_as_name< using=any 'as' renamed=any> | in_list=import_as_names< using=any* > | using='*' | using=NAME) >"
# helps match 'import urllib.request'
name_import = u"name_import=import_name< 'import' (%s | in_list=dotted_as_names< imp_list=any* >) >"
#############
# WON'T FIX #
#############
# helps match 'import urllib.request as name'
name_import_rename = u"name_import_rename=dotted_as_name< %s 'as' renamed=any >"
# helps match 'from http import server'
from_import_rename = u"from_import_rename=import_from< 'from' %s 'import' (%s | import_as_name< %s 'as' renamed=any > | in_list=import_as_names< any* (%s | import_as_name< %s 'as' renamed=any >) any* >) >"
def all_modules_subpattern():
u"""
Builds a pattern for all toplevel names
(urllib, http, etc)
"""
names_dot_attrs = [mod.split(u".") for mod in MAPPING]
ret = u"( " + u" | ".join([dotted_name % (simple_name % (mod[0]),
simple_attr % (mod[1])) for mod in names_dot_attrs])
ret += u" | "
ret += u" | ".join([simple_name % (mod[0]) for mod in names_dot_attrs if mod[1] == u"__init__"]) + u" )"
return ret
def build_import_pattern(mapping1, mapping2):
u"""
mapping1: A dict mapping py3k modules to all possible py2k replacements
mapping2: A dict mapping py2k modules to the things they do
This builds a HUGE pattern to match all ways that things can be imported
"""
# py3k: urllib.request, py2k: ('urllib2', 'urllib')
yield from_import % (all_modules_subpattern())
for py3k, py2k in mapping1.items():
name, attr = py3k.split(u'.')
s_name = simple_name % (name)
s_attr = simple_attr % (attr)
d_name = dotted_name % (s_name, s_attr)
yield name_import % (d_name)
yield power_twoname % (s_name, s_attr)
if attr == u'__init__':
yield name_import % (s_name)
yield power_onename % (s_name)
yield name_import_rename % (d_name)
yield from_import_rename % (s_name, s_attr, s_attr, s_attr, s_attr)
class FixImports2(fixer_base.BaseFix):
run_order = 4
PATTERN = u" | \n".join(build_import_pattern(MAPPING, PY2MODULES))
def transform(self, node, results):
touch_import_top(u'future', u'standard_library', node)
| 8,583 | 47.772727 | 205 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/libpasteurize/fixes/fix_next.py
|
u"""
Fixer for:
it.__next__() -> it.next().
next(it) -> it.next().
"""
from lib2to3.pgen2 import token
from lib2to3.pygram import python_symbols as syms
from lib2to3 import fixer_base
from lib2to3.fixer_util import Name, Call, find_binding, Attr
bind_warning = u"Calls to builtin next() possibly shadowed by global binding"
class FixNext(fixer_base.BaseFix):
PATTERN = u"""
power< base=any+ trailer< '.' attr='__next__' > any* >
|
power< head='next' trailer< '(' arg=any ')' > any* >
|
classdef< 'class' base=any+ ':'
suite< any*
funcdef< 'def'
attr='__next__'
parameters< '(' NAME ')' > any+ >
any* > >
"""
def transform(self, node, results):
assert results
base = results.get(u"base")
attr = results.get(u"attr")
head = results.get(u"head")
arg_ = results.get(u"arg")
if arg_:
arg = arg_.clone()
head.replace(Attr(Name(unicode(arg),prefix=head.prefix),
Name(u"next")))
arg_.remove()
elif base:
attr.replace(Name(u"next", prefix=attr.prefix))
| 1,233 | 27.045455 | 77 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/libpasteurize/fixes/fix_add_all_future_builtins.py
|
"""
For the ``future`` package.
Adds this import line::
from builtins import (ascii, bytes, chr, dict, filter, hex, input,
int, list, map, next, object, oct, open, pow,
range, round, str, super, zip)
to a module, irrespective of whether each definition is used.
Adds these imports after any other imports (in an initial block of them).
"""
from __future__ import unicode_literals
from lib2to3 import fixer_base
from libfuturize.fixer_util import touch_import_top
class FixAddAllFutureBuiltins(fixer_base.BaseFix):
BM_compatible = True
PATTERN = "file_input"
run_order = 1
def transform(self, node, results):
# import_str = """(ascii, bytes, chr, dict, filter, hex, input,
# int, list, map, next, object, oct, open, pow,
# range, round, str, super, zip)"""
touch_import_top(u'builtins', '*', node)
# builtins = """ascii bytes chr dict filter hex input
# int list map next object oct open pow
# range round str super zip"""
# for builtin in sorted(builtins.split(), reverse=True):
# touch_import_top(u'builtins', builtin, node)
| 1,270 | 31.589744 | 76 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/libpasteurize/fixes/fix_features.py
|
u"""
Warn about features that are not present in Python 2.5, giving a message that
points to the earliest version of Python 2.x (or 3.x, if none) that supports it
"""
from .feature_base import Feature, Features
from lib2to3 import fixer_base
FEATURES = [
#(FeatureName,
# FeaturePattern,
# FeatureMinVersion,
#),
(u"memoryview",
u"power < 'memoryview' trailer < '(' any* ')' > any* >",
u"2.7",
),
(u"numbers",
u"""import_from< 'from' 'numbers' 'import' any* > |
import_name< 'import' ('numbers' dotted_as_names< any* 'numbers' any* >) >""",
u"2.6",
),
(u"abc",
u"""import_name< 'import' ('abc' dotted_as_names< any* 'abc' any* >) > |
import_from< 'from' 'abc' 'import' any* >""",
u"2.6",
),
(u"io",
u"""import_name< 'import' ('io' dotted_as_names< any* 'io' any* >) > |
import_from< 'from' 'io' 'import' any* >""",
u"2.6",
),
(u"bin",
u"power< 'bin' trailer< '(' any* ')' > any* >",
u"2.6",
),
(u"formatting",
u"power< any trailer< '.' 'format' > trailer< '(' any* ')' > >",
u"2.6",
),
(u"nonlocal",
u"global_stmt< 'nonlocal' any* >",
u"3.0",
),
(u"with_traceback",
u"trailer< '.' 'with_traceback' >",
u"3.0",
),
]
class FixFeatures(fixer_base.BaseFix):
run_order = 9 # Wait until all other fixers have run to check for these
# To avoid spamming, we only want to warn for each feature once.
features_warned = set()
# Build features from the list above
features = Features([Feature(name, pattern, version) for \
name, pattern, version in FEATURES])
PATTERN = features.PATTERN
def match(self, node):
to_ret = super(FixFeatures, self).match(node)
# We want the mapping only to tell us the node's specific information.
try:
del to_ret[u'node']
except Exception:
# We want it to delete the 'node' from the results
# if it's there, so we don't care if it fails for normal reasons.
pass
return to_ret
def transform(self, node, results):
for feature_name in results:
if feature_name in self.features_warned:
continue
else:
curr_feature = self.features[feature_name]
if curr_feature.version >= u"3":
fail = self.cannot_convert
else:
fail = self.warning
fail(node, reason=curr_feature.message_text())
self.features_warned.add(feature_name)
| 2,679 | 29.804598 | 89 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/dateutil/easter.py
|
# -*- coding: utf-8 -*-
"""
This module offers a generic easter computing method for any given year, using
Western, Orthodox or Julian algorithms.
"""
import datetime
__all__ = ["easter", "EASTER_JULIAN", "EASTER_ORTHODOX", "EASTER_WESTERN"]
EASTER_JULIAN = 1
EASTER_ORTHODOX = 2
EASTER_WESTERN = 3
def easter(year, method=EASTER_WESTERN):
"""
This method was ported from the work done by GM Arts,
on top of the algorithm by Claus Tondering, which was
based in part on the algorithm of Ouding (1940), as
quoted in "Explanatory Supplement to the Astronomical
Almanac", P. Kenneth Seidelmann, editor.
This algorithm implements three different easter
calculation methods:
1 - Original calculation in Julian calendar, valid in
dates after 326 AD
2 - Original method, with date converted to Gregorian
calendar, valid in years 1583 to 4099
3 - Revised method, in Gregorian calendar, valid in
years 1583 to 4099 as well
These methods are represented by the constants:
* ``EASTER_JULIAN = 1``
* ``EASTER_ORTHODOX = 2``
* ``EASTER_WESTERN = 3``
The default method is method 3.
More about the algorithm may be found at:
`GM Arts: Easter Algorithms <http://www.gmarts.org/index.php?go=415>`_
and
`The Calendar FAQ: Easter <https://www.tondering.dk/claus/cal/easter.php>`_
"""
if not (1 <= method <= 3):
raise ValueError("invalid method")
# g - Golden year - 1
# c - Century
# h - (23 - Epact) mod 30
# i - Number of days from March 21 to Paschal Full Moon
# j - Weekday for PFM (0=Sunday, etc)
# p - Number of days from March 21 to Sunday on or before PFM
# (-6 to 28 methods 1 & 3, to 56 for method 2)
# e - Extra days to add for method 2 (converting Julian
# date to Gregorian date)
y = year
g = y % 19
e = 0
if method < 3:
# Old method
i = (19*g + 15) % 30
j = (y + y//4 + i) % 7
if method == 2:
# Extra dates to convert Julian to Gregorian date
e = 10
if y > 1600:
e = e + y//100 - 16 - (y//100 - 16)//4
else:
# New method
c = y//100
h = (c - c//4 - (8*c + 13)//25 + 19*g + 15) % 30
i = h - (h//28)*(1 - (h//28)*(29//(h + 1))*((21 - g)//11))
j = (y + y//4 + i + 2 - c + c//4) % 7
# p can be from -6 to 56 corresponding to dates 22 March to 23 May
# (later dates apply to method 2, although 23 May never actually occurs)
p = i - j + e
d = 1 + (p + 27 + (p + 6)//40) % 31
m = 3 + (p + 26)//30
return datetime.date(int(y), int(m), int(d))
| 2,684 | 28.833333 | 79 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/dateutil/tzwin.py
|
# tzwin has moved to dateutil.tz.win
from .tz.win import *
| 59 | 19 | 36 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/dateutil/utils.py
|
# -*- coding: utf-8 -*-
"""
This module offers general convenience and utility functions for dealing with
datetimes.
.. versionadded:: 2.7.0
"""
from __future__ import unicode_literals
from datetime import datetime, time
def today(tzinfo=None):
"""
Returns a :py:class:`datetime` representing the current day at midnight
:param tzinfo:
The time zone to attach (also used to determine the current day).
:return:
A :py:class:`datetime.datetime` object representing the current day
at midnight.
"""
dt = datetime.now(tzinfo)
return datetime.combine(dt.date(), time(0, tzinfo=tzinfo))
def default_tzinfo(dt, tzinfo):
"""
Sets the the ``tzinfo`` parameter on naive datetimes only
This is useful for example when you are provided a datetime that may have
either an implicit or explicit time zone, such as when parsing a time zone
string.
.. doctest::
>>> from dateutil.tz import tzoffset
>>> from dateutil.parser import parse
>>> from dateutil.utils import default_tzinfo
>>> dflt_tz = tzoffset("EST", -18000)
>>> print(default_tzinfo(parse('2014-01-01 12:30 UTC'), dflt_tz))
2014-01-01 12:30:00+00:00
>>> print(default_tzinfo(parse('2014-01-01 12:30'), dflt_tz))
2014-01-01 12:30:00-05:00
:param dt:
The datetime on which to replace the time zone
:param tzinfo:
The :py:class:`datetime.tzinfo` subclass instance to assign to
``dt`` if (and only if) it is naive.
:return:
Returns an aware :py:class:`datetime.datetime`.
"""
if dt.tzinfo is not None:
return dt
else:
return dt.replace(tzinfo=tzinfo)
def within_delta(dt1, dt2, delta):
"""
Useful for comparing two datetimes that may a negilible difference
to be considered equal.
"""
delta = abs(delta)
difference = dt1 - dt2
return -delta <= difference <= delta
| 1,963 | 26.277778 | 78 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/dateutil/_version.py
|
# coding: utf-8
# file generated by setuptools_scm
# don't change, don't track in version control
version = '2.7.3'
| 116 | 22.4 | 46 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/dateutil/relativedelta.py
|
# -*- coding: utf-8 -*-
import datetime
import calendar
import operator
from math import copysign
from six import integer_types
from warnings import warn
from ._common import weekday
MO, TU, WE, TH, FR, SA, SU = weekdays = tuple(weekday(x) for x in range(7))
__all__ = ["relativedelta", "MO", "TU", "WE", "TH", "FR", "SA", "SU"]
class relativedelta(object):
"""
The relativedelta type is based on the specification of the excellent
work done by M.-A. Lemburg in his
`mx.DateTime <https://www.egenix.com/products/python/mxBase/mxDateTime/>`_ extension.
However, notice that this type does *NOT* implement the same algorithm as
his work. Do *NOT* expect it to behave like mx.DateTime's counterpart.
There are two different ways to build a relativedelta instance. The
first one is passing it two date/datetime classes::
relativedelta(datetime1, datetime2)
The second one is passing it any number of the following keyword arguments::
relativedelta(arg1=x,arg2=y,arg3=z...)
year, month, day, hour, minute, second, microsecond:
Absolute information (argument is singular); adding or subtracting a
relativedelta with absolute information does not perform an arithmetic
operation, but rather REPLACES the corresponding value in the
original datetime with the value(s) in relativedelta.
years, months, weeks, days, hours, minutes, seconds, microseconds:
Relative information, may be negative (argument is plural); adding
or subtracting a relativedelta with relative information performs
the corresponding aritmetic operation on the original datetime value
with the information in the relativedelta.
weekday:
One of the weekday instances (MO, TU, etc). These
instances may receive a parameter N, specifying the Nth
weekday, which could be positive or negative (like MO(+1)
or MO(-2). Not specifying it is the same as specifying
+1. You can also use an integer, where 0=MO. Notice that
if the calculated date is already Monday, for example,
using MO(1) or MO(-1) won't change the day.
leapdays:
Will add given days to the date found, if year is a leap
year, and the date found is post 28 of february.
yearday, nlyearday:
Set the yearday or the non-leap year day (jump leap days).
These are converted to day/month/leapdays information.
There are relative and absolute forms of the keyword
arguments. The plural is relative, and the singular is
absolute. For each argument in the order below, the absolute form
is applied first (by setting each attribute to that value) and
then the relative form (by adding the value to the attribute).
The order of attributes considered when this relativedelta is
added to a datetime is:
1. Year
2. Month
3. Day
4. Hours
5. Minutes
6. Seconds
7. Microseconds
Finally, weekday is applied, using the rule described above.
For example
>>> dt = datetime(2018, 4, 9, 13, 37, 0)
>>> delta = relativedelta(hours=25, day=1, weekday=MO(1))
datetime(2018, 4, 2, 14, 37, 0)
First, the day is set to 1 (the first of the month), then 25 hours
are added, to get to the 2nd day and 14th hour, finally the
weekday is applied, but since the 2nd is already a Monday there is
no effect.
"""
def __init__(self, dt1=None, dt2=None,
years=0, months=0, days=0, leapdays=0, weeks=0,
hours=0, minutes=0, seconds=0, microseconds=0,
year=None, month=None, day=None, weekday=None,
yearday=None, nlyearday=None,
hour=None, minute=None, second=None, microsecond=None):
if dt1 and dt2:
# datetime is a subclass of date. So both must be date
if not (isinstance(dt1, datetime.date) and
isinstance(dt2, datetime.date)):
raise TypeError("relativedelta only diffs datetime/date")
# We allow two dates, or two datetimes, so we coerce them to be
# of the same type
if (isinstance(dt1, datetime.datetime) !=
isinstance(dt2, datetime.datetime)):
if not isinstance(dt1, datetime.datetime):
dt1 = datetime.datetime.fromordinal(dt1.toordinal())
elif not isinstance(dt2, datetime.datetime):
dt2 = datetime.datetime.fromordinal(dt2.toordinal())
self.years = 0
self.months = 0
self.days = 0
self.leapdays = 0
self.hours = 0
self.minutes = 0
self.seconds = 0
self.microseconds = 0
self.year = None
self.month = None
self.day = None
self.weekday = None
self.hour = None
self.minute = None
self.second = None
self.microsecond = None
self._has_time = 0
# Get year / month delta between the two
months = (dt1.year - dt2.year) * 12 + (dt1.month - dt2.month)
self._set_months(months)
# Remove the year/month delta so the timedelta is just well-defined
# time units (seconds, days and microseconds)
dtm = self.__radd__(dt2)
# If we've overshot our target, make an adjustment
if dt1 < dt2:
compare = operator.gt
increment = 1
else:
compare = operator.lt
increment = -1
while compare(dt1, dtm):
months += increment
self._set_months(months)
dtm = self.__radd__(dt2)
# Get the timedelta between the "months-adjusted" date and dt1
delta = dt1 - dtm
self.seconds = delta.seconds + delta.days * 86400
self.microseconds = delta.microseconds
else:
# Check for non-integer values in integer-only quantities
if any(x is not None and x != int(x) for x in (years, months)):
raise ValueError("Non-integer years and months are "
"ambiguous and not currently supported.")
# Relative information
self.years = int(years)
self.months = int(months)
self.days = days + weeks * 7
self.leapdays = leapdays
self.hours = hours
self.minutes = minutes
self.seconds = seconds
self.microseconds = microseconds
# Absolute information
self.year = year
self.month = month
self.day = day
self.hour = hour
self.minute = minute
self.second = second
self.microsecond = microsecond
if any(x is not None and int(x) != x
for x in (year, month, day, hour,
minute, second, microsecond)):
# For now we'll deprecate floats - later it'll be an error.
warn("Non-integer value passed as absolute information. " +
"This is not a well-defined condition and will raise " +
"errors in future versions.", DeprecationWarning)
if isinstance(weekday, integer_types):
self.weekday = weekdays[weekday]
else:
self.weekday = weekday
yday = 0
if nlyearday:
yday = nlyearday
elif yearday:
yday = yearday
if yearday > 59:
self.leapdays = -1
if yday:
ydayidx = [31, 59, 90, 120, 151, 181, 212,
243, 273, 304, 334, 366]
for idx, ydays in enumerate(ydayidx):
if yday <= ydays:
self.month = idx+1
if idx == 0:
self.day = yday
else:
self.day = yday-ydayidx[idx-1]
break
else:
raise ValueError("invalid year day (%d)" % yday)
self._fix()
def _fix(self):
if abs(self.microseconds) > 999999:
s = _sign(self.microseconds)
div, mod = divmod(self.microseconds * s, 1000000)
self.microseconds = mod * s
self.seconds += div * s
if abs(self.seconds) > 59:
s = _sign(self.seconds)
div, mod = divmod(self.seconds * s, 60)
self.seconds = mod * s
self.minutes += div * s
if abs(self.minutes) > 59:
s = _sign(self.minutes)
div, mod = divmod(self.minutes * s, 60)
self.minutes = mod * s
self.hours += div * s
if abs(self.hours) > 23:
s = _sign(self.hours)
div, mod = divmod(self.hours * s, 24)
self.hours = mod * s
self.days += div * s
if abs(self.months) > 11:
s = _sign(self.months)
div, mod = divmod(self.months * s, 12)
self.months = mod * s
self.years += div * s
if (self.hours or self.minutes or self.seconds or self.microseconds
or self.hour is not None or self.minute is not None or
self.second is not None or self.microsecond is not None):
self._has_time = 1
else:
self._has_time = 0
@property
def weeks(self):
return int(self.days / 7.0)
@weeks.setter
def weeks(self, value):
self.days = self.days - (self.weeks * 7) + value * 7
def _set_months(self, months):
self.months = months
if abs(self.months) > 11:
s = _sign(self.months)
div, mod = divmod(self.months * s, 12)
self.months = mod * s
self.years = div * s
else:
self.years = 0
def normalized(self):
"""
Return a version of this object represented entirely using integer
values for the relative attributes.
>>> relativedelta(days=1.5, hours=2).normalized()
relativedelta(days=1, hours=14)
:return:
Returns a :class:`dateutil.relativedelta.relativedelta` object.
"""
# Cascade remainders down (rounding each to roughly nearest microsecond)
days = int(self.days)
hours_f = round(self.hours + 24 * (self.days - days), 11)
hours = int(hours_f)
minutes_f = round(self.minutes + 60 * (hours_f - hours), 10)
minutes = int(minutes_f)
seconds_f = round(self.seconds + 60 * (minutes_f - minutes), 8)
seconds = int(seconds_f)
microseconds = round(self.microseconds + 1e6 * (seconds_f - seconds))
# Constructor carries overflow back up with call to _fix()
return self.__class__(years=self.years, months=self.months,
days=days, hours=hours, minutes=minutes,
seconds=seconds, microseconds=microseconds,
leapdays=self.leapdays, year=self.year,
month=self.month, day=self.day,
weekday=self.weekday, hour=self.hour,
minute=self.minute, second=self.second,
microsecond=self.microsecond)
def __add__(self, other):
if isinstance(other, relativedelta):
return self.__class__(years=other.years + self.years,
months=other.months + self.months,
days=other.days + self.days,
hours=other.hours + self.hours,
minutes=other.minutes + self.minutes,
seconds=other.seconds + self.seconds,
microseconds=(other.microseconds +
self.microseconds),
leapdays=other.leapdays or self.leapdays,
year=(other.year if other.year is not None
else self.year),
month=(other.month if other.month is not None
else self.month),
day=(other.day if other.day is not None
else self.day),
weekday=(other.weekday if other.weekday is not None
else self.weekday),
hour=(other.hour if other.hour is not None
else self.hour),
minute=(other.minute if other.minute is not None
else self.minute),
second=(other.second if other.second is not None
else self.second),
microsecond=(other.microsecond if other.microsecond
is not None else
self.microsecond))
if isinstance(other, datetime.timedelta):
return self.__class__(years=self.years,
months=self.months,
days=self.days + other.days,
hours=self.hours,
minutes=self.minutes,
seconds=self.seconds + other.seconds,
microseconds=self.microseconds + other.microseconds,
leapdays=self.leapdays,
year=self.year,
month=self.month,
day=self.day,
weekday=self.weekday,
hour=self.hour,
minute=self.minute,
second=self.second,
microsecond=self.microsecond)
if not isinstance(other, datetime.date):
return NotImplemented
elif self._has_time and not isinstance(other, datetime.datetime):
other = datetime.datetime.fromordinal(other.toordinal())
year = (self.year or other.year)+self.years
month = self.month or other.month
if self.months:
assert 1 <= abs(self.months) <= 12
month += self.months
if month > 12:
year += 1
month -= 12
elif month < 1:
year -= 1
month += 12
day = min(calendar.monthrange(year, month)[1],
self.day or other.day)
repl = {"year": year, "month": month, "day": day}
for attr in ["hour", "minute", "second", "microsecond"]:
value = getattr(self, attr)
if value is not None:
repl[attr] = value
days = self.days
if self.leapdays and month > 2 and calendar.isleap(year):
days += self.leapdays
ret = (other.replace(**repl)
+ datetime.timedelta(days=days,
hours=self.hours,
minutes=self.minutes,
seconds=self.seconds,
microseconds=self.microseconds))
if self.weekday:
weekday, nth = self.weekday.weekday, self.weekday.n or 1
jumpdays = (abs(nth) - 1) * 7
if nth > 0:
jumpdays += (7 - ret.weekday() + weekday) % 7
else:
jumpdays += (ret.weekday() - weekday) % 7
jumpdays *= -1
ret += datetime.timedelta(days=jumpdays)
return ret
def __radd__(self, other):
return self.__add__(other)
def __rsub__(self, other):
return self.__neg__().__radd__(other)
def __sub__(self, other):
if not isinstance(other, relativedelta):
return NotImplemented # In case the other object defines __rsub__
return self.__class__(years=self.years - other.years,
months=self.months - other.months,
days=self.days - other.days,
hours=self.hours - other.hours,
minutes=self.minutes - other.minutes,
seconds=self.seconds - other.seconds,
microseconds=self.microseconds - other.microseconds,
leapdays=self.leapdays or other.leapdays,
year=(self.year if self.year is not None
else other.year),
month=(self.month if self.month is not None else
other.month),
day=(self.day if self.day is not None else
other.day),
weekday=(self.weekday if self.weekday is not None else
other.weekday),
hour=(self.hour if self.hour is not None else
other.hour),
minute=(self.minute if self.minute is not None else
other.minute),
second=(self.second if self.second is not None else
other.second),
microsecond=(self.microsecond if self.microsecond
is not None else
other.microsecond))
def __abs__(self):
return self.__class__(years=abs(self.years),
months=abs(self.months),
days=abs(self.days),
hours=abs(self.hours),
minutes=abs(self.minutes),
seconds=abs(self.seconds),
microseconds=abs(self.microseconds),
leapdays=self.leapdays,
year=self.year,
month=self.month,
day=self.day,
weekday=self.weekday,
hour=self.hour,
minute=self.minute,
second=self.second,
microsecond=self.microsecond)
def __neg__(self):
return self.__class__(years=-self.years,
months=-self.months,
days=-self.days,
hours=-self.hours,
minutes=-self.minutes,
seconds=-self.seconds,
microseconds=-self.microseconds,
leapdays=self.leapdays,
year=self.year,
month=self.month,
day=self.day,
weekday=self.weekday,
hour=self.hour,
minute=self.minute,
second=self.second,
microsecond=self.microsecond)
def __bool__(self):
return not (not self.years and
not self.months and
not self.days and
not self.hours and
not self.minutes and
not self.seconds and
not self.microseconds and
not self.leapdays and
self.year is None and
self.month is None and
self.day is None and
self.weekday is None and
self.hour is None and
self.minute is None and
self.second is None and
self.microsecond is None)
# Compatibility with Python 2.x
__nonzero__ = __bool__
def __mul__(self, other):
try:
f = float(other)
except TypeError:
return NotImplemented
return self.__class__(years=int(self.years * f),
months=int(self.months * f),
days=int(self.days * f),
hours=int(self.hours * f),
minutes=int(self.minutes * f),
seconds=int(self.seconds * f),
microseconds=int(self.microseconds * f),
leapdays=self.leapdays,
year=self.year,
month=self.month,
day=self.day,
weekday=self.weekday,
hour=self.hour,
minute=self.minute,
second=self.second,
microsecond=self.microsecond)
__rmul__ = __mul__
def __eq__(self, other):
if not isinstance(other, relativedelta):
return NotImplemented
if self.weekday or other.weekday:
if not self.weekday or not other.weekday:
return False
if self.weekday.weekday != other.weekday.weekday:
return False
n1, n2 = self.weekday.n, other.weekday.n
if n1 != n2 and not ((not n1 or n1 == 1) and (not n2 or n2 == 1)):
return False
return (self.years == other.years and
self.months == other.months and
self.days == other.days and
self.hours == other.hours and
self.minutes == other.minutes and
self.seconds == other.seconds and
self.microseconds == other.microseconds and
self.leapdays == other.leapdays and
self.year == other.year and
self.month == other.month and
self.day == other.day and
self.hour == other.hour and
self.minute == other.minute and
self.second == other.second and
self.microsecond == other.microsecond)
def __hash__(self):
return hash((
self.weekday,
self.years,
self.months,
self.days,
self.hours,
self.minutes,
self.seconds,
self.microseconds,
self.leapdays,
self.year,
self.month,
self.day,
self.hour,
self.minute,
self.second,
self.microsecond,
))
def __ne__(self, other):
return not self.__eq__(other)
def __div__(self, other):
try:
reciprocal = 1 / float(other)
except TypeError:
return NotImplemented
return self.__mul__(reciprocal)
__truediv__ = __div__
def __repr__(self):
l = []
for attr in ["years", "months", "days", "leapdays",
"hours", "minutes", "seconds", "microseconds"]:
value = getattr(self, attr)
if value:
l.append("{attr}={value:+g}".format(attr=attr, value=value))
for attr in ["year", "month", "day", "weekday",
"hour", "minute", "second", "microsecond"]:
value = getattr(self, attr)
if value is not None:
l.append("{attr}={value}".format(attr=attr, value=repr(value)))
return "{classname}({attrs})".format(classname=self.__class__.__name__,
attrs=", ".join(l))
def _sign(x):
return int(copysign(1, x))
# vim:ts=4:sw=4:et
| 24,418 | 40.318105 | 89 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/dateutil/rrule.py
|
# -*- coding: utf-8 -*-
"""
The rrule module offers a small, complete, and very fast, implementation of
the recurrence rules documented in the
`iCalendar RFC <https://tools.ietf.org/html/rfc5545>`_,
including support for caching of results.
"""
import itertools
import datetime
import calendar
import re
import sys
try:
from math import gcd
except ImportError:
from fractions import gcd
from six import advance_iterator, integer_types
from six.moves import _thread, range
import heapq
from ._common import weekday as weekdaybase
from .tz import tzutc, tzlocal
# For warning about deprecation of until and count
from warnings import warn
__all__ = ["rrule", "rruleset", "rrulestr",
"YEARLY", "MONTHLY", "WEEKLY", "DAILY",
"HOURLY", "MINUTELY", "SECONDLY",
"MO", "TU", "WE", "TH", "FR", "SA", "SU"]
# Every mask is 7 days longer to handle cross-year weekly periods.
M366MASK = tuple([1]*31+[2]*29+[3]*31+[4]*30+[5]*31+[6]*30 +
[7]*31+[8]*31+[9]*30+[10]*31+[11]*30+[12]*31+[1]*7)
M365MASK = list(M366MASK)
M29, M30, M31 = list(range(1, 30)), list(range(1, 31)), list(range(1, 32))
MDAY366MASK = tuple(M31+M29+M31+M30+M31+M30+M31+M31+M30+M31+M30+M31+M31[:7])
MDAY365MASK = list(MDAY366MASK)
M29, M30, M31 = list(range(-29, 0)), list(range(-30, 0)), list(range(-31, 0))
NMDAY366MASK = tuple(M31+M29+M31+M30+M31+M30+M31+M31+M30+M31+M30+M31+M31[:7])
NMDAY365MASK = list(NMDAY366MASK)
M366RANGE = (0, 31, 60, 91, 121, 152, 182, 213, 244, 274, 305, 335, 366)
M365RANGE = (0, 31, 59, 90, 120, 151, 181, 212, 243, 273, 304, 334, 365)
WDAYMASK = [0, 1, 2, 3, 4, 5, 6]*55
del M29, M30, M31, M365MASK[59], MDAY365MASK[59], NMDAY365MASK[31]
MDAY365MASK = tuple(MDAY365MASK)
M365MASK = tuple(M365MASK)
FREQNAMES = ['YEARLY', 'MONTHLY', 'WEEKLY', 'DAILY', 'HOURLY', 'MINUTELY', 'SECONDLY']
(YEARLY,
MONTHLY,
WEEKLY,
DAILY,
HOURLY,
MINUTELY,
SECONDLY) = list(range(7))
# Imported on demand.
easter = None
parser = None
class weekday(weekdaybase):
"""
This version of weekday does not allow n = 0.
"""
def __init__(self, wkday, n=None):
if n == 0:
raise ValueError("Can't create weekday with n==0")
super(weekday, self).__init__(wkday, n)
MO, TU, WE, TH, FR, SA, SU = weekdays = tuple(weekday(x) for x in range(7))
def _invalidates_cache(f):
"""
Decorator for rruleset methods which may invalidate the
cached length.
"""
def inner_func(self, *args, **kwargs):
rv = f(self, *args, **kwargs)
self._invalidate_cache()
return rv
return inner_func
class rrulebase(object):
def __init__(self, cache=False):
if cache:
self._cache = []
self._cache_lock = _thread.allocate_lock()
self._invalidate_cache()
else:
self._cache = None
self._cache_complete = False
self._len = None
def __iter__(self):
if self._cache_complete:
return iter(self._cache)
elif self._cache is None:
return self._iter()
else:
return self._iter_cached()
def _invalidate_cache(self):
if self._cache is not None:
self._cache = []
self._cache_complete = False
self._cache_gen = self._iter()
if self._cache_lock.locked():
self._cache_lock.release()
self._len = None
def _iter_cached(self):
i = 0
gen = self._cache_gen
cache = self._cache
acquire = self._cache_lock.acquire
release = self._cache_lock.release
while gen:
if i == len(cache):
acquire()
if self._cache_complete:
break
try:
for j in range(10):
cache.append(advance_iterator(gen))
except StopIteration:
self._cache_gen = gen = None
self._cache_complete = True
break
release()
yield cache[i]
i += 1
while i < self._len:
yield cache[i]
i += 1
def __getitem__(self, item):
if self._cache_complete:
return self._cache[item]
elif isinstance(item, slice):
if item.step and item.step < 0:
return list(iter(self))[item]
else:
return list(itertools.islice(self,
item.start or 0,
item.stop or sys.maxsize,
item.step or 1))
elif item >= 0:
gen = iter(self)
try:
for i in range(item+1):
res = advance_iterator(gen)
except StopIteration:
raise IndexError
return res
else:
return list(iter(self))[item]
def __contains__(self, item):
if self._cache_complete:
return item in self._cache
else:
for i in self:
if i == item:
return True
elif i > item:
return False
return False
# __len__() introduces a large performance penality.
def count(self):
""" Returns the number of recurrences in this set. It will have go
trough the whole recurrence, if this hasn't been done before. """
if self._len is None:
for x in self:
pass
return self._len
def before(self, dt, inc=False):
""" Returns the last recurrence before the given datetime instance. The
inc keyword defines what happens if dt is an occurrence. With
inc=True, if dt itself is an occurrence, it will be returned. """
if self._cache_complete:
gen = self._cache
else:
gen = self
last = None
if inc:
for i in gen:
if i > dt:
break
last = i
else:
for i in gen:
if i >= dt:
break
last = i
return last
def after(self, dt, inc=False):
""" Returns the first recurrence after the given datetime instance. The
inc keyword defines what happens if dt is an occurrence. With
inc=True, if dt itself is an occurrence, it will be returned. """
if self._cache_complete:
gen = self._cache
else:
gen = self
if inc:
for i in gen:
if i >= dt:
return i
else:
for i in gen:
if i > dt:
return i
return None
def xafter(self, dt, count=None, inc=False):
"""
Generator which yields up to `count` recurrences after the given
datetime instance, equivalent to `after`.
:param dt:
The datetime at which to start generating recurrences.
:param count:
The maximum number of recurrences to generate. If `None` (default),
dates are generated until the recurrence rule is exhausted.
:param inc:
If `dt` is an instance of the rule and `inc` is `True`, it is
included in the output.
:yields: Yields a sequence of `datetime` objects.
"""
if self._cache_complete:
gen = self._cache
else:
gen = self
# Select the comparison function
if inc:
comp = lambda dc, dtc: dc >= dtc
else:
comp = lambda dc, dtc: dc > dtc
# Generate dates
n = 0
for d in gen:
if comp(d, dt):
if count is not None:
n += 1
if n > count:
break
yield d
def between(self, after, before, inc=False, count=1):
""" Returns all the occurrences of the rrule between after and before.
The inc keyword defines what happens if after and/or before are
themselves occurrences. With inc=True, they will be included in the
list, if they are found in the recurrence set. """
if self._cache_complete:
gen = self._cache
else:
gen = self
started = False
l = []
if inc:
for i in gen:
if i > before:
break
elif not started:
if i >= after:
started = True
l.append(i)
else:
l.append(i)
else:
for i in gen:
if i >= before:
break
elif not started:
if i > after:
started = True
l.append(i)
else:
l.append(i)
return l
class rrule(rrulebase):
"""
That's the base of the rrule operation. It accepts all the keywords
defined in the RFC as its constructor parameters (except byday,
which was renamed to byweekday) and more. The constructor prototype is::
rrule(freq)
Where freq must be one of YEARLY, MONTHLY, WEEKLY, DAILY, HOURLY, MINUTELY,
or SECONDLY.
.. note::
Per RFC section 3.3.10, recurrence instances falling on invalid dates
and times are ignored rather than coerced:
Recurrence rules may generate recurrence instances with an invalid
date (e.g., February 30) or nonexistent local time (e.g., 1:30 AM
on a day where the local time is moved forward by an hour at 1:00
AM). Such recurrence instances MUST be ignored and MUST NOT be
counted as part of the recurrence set.
This can lead to possibly surprising behavior when, for example, the
start date occurs at the end of the month:
>>> from dateutil.rrule import rrule, MONTHLY
>>> from datetime import datetime
>>> start_date = datetime(2014, 12, 31)
>>> list(rrule(freq=MONTHLY, count=4, dtstart=start_date))
... # doctest: +NORMALIZE_WHITESPACE
[datetime.datetime(2014, 12, 31, 0, 0),
datetime.datetime(2015, 1, 31, 0, 0),
datetime.datetime(2015, 3, 31, 0, 0),
datetime.datetime(2015, 5, 31, 0, 0)]
Additionally, it supports the following keyword arguments:
:param dtstart:
The recurrence start. Besides being the base for the recurrence,
missing parameters in the final recurrence instances will also be
extracted from this date. If not given, datetime.now() will be used
instead.
:param interval:
The interval between each freq iteration. For example, when using
YEARLY, an interval of 2 means once every two years, but with HOURLY,
it means once every two hours. The default interval is 1.
:param wkst:
The week start day. Must be one of the MO, TU, WE constants, or an
integer, specifying the first day of the week. This will affect
recurrences based on weekly periods. The default week start is got
from calendar.firstweekday(), and may be modified by
calendar.setfirstweekday().
:param count:
How many occurrences will be generated.
.. note::
As of version 2.5.0, the use of the ``until`` keyword together
with the ``count`` keyword is deprecated per RFC-5545 Sec. 3.3.10.
:param until:
If given, this must be a datetime instance, that will specify the
limit of the recurrence. The last recurrence in the rule is the greatest
datetime that is less than or equal to the value specified in the
``until`` parameter.
.. note::
As of version 2.5.0, the use of the ``until`` keyword together
with the ``count`` keyword is deprecated per RFC-5545 Sec. 3.3.10.
:param bysetpos:
If given, it must be either an integer, or a sequence of integers,
positive or negative. Each given integer will specify an occurrence
number, corresponding to the nth occurrence of the rule inside the
frequency period. For example, a bysetpos of -1 if combined with a
MONTHLY frequency, and a byweekday of (MO, TU, WE, TH, FR), will
result in the last work day of every month.
:param bymonth:
If given, it must be either an integer, or a sequence of integers,
meaning the months to apply the recurrence to.
:param bymonthday:
If given, it must be either an integer, or a sequence of integers,
meaning the month days to apply the recurrence to.
:param byyearday:
If given, it must be either an integer, or a sequence of integers,
meaning the year days to apply the recurrence to.
:param byeaster:
If given, it must be either an integer, or a sequence of integers,
positive or negative. Each integer will define an offset from the
Easter Sunday. Passing the offset 0 to byeaster will yield the Easter
Sunday itself. This is an extension to the RFC specification.
:param byweekno:
If given, it must be either an integer, or a sequence of integers,
meaning the week numbers to apply the recurrence to. Week numbers
have the meaning described in ISO8601, that is, the first week of
the year is that containing at least four days of the new year.
:param byweekday:
If given, it must be either an integer (0 == MO), a sequence of
integers, one of the weekday constants (MO, TU, etc), or a sequence
of these constants. When given, these variables will define the
weekdays where the recurrence will be applied. It's also possible to
use an argument n for the weekday instances, which will mean the nth
occurrence of this weekday in the period. For example, with MONTHLY,
or with YEARLY and BYMONTH, using FR(+1) in byweekday will specify the
first friday of the month where the recurrence happens. Notice that in
the RFC documentation, this is specified as BYDAY, but was renamed to
avoid the ambiguity of that keyword.
:param byhour:
If given, it must be either an integer, or a sequence of integers,
meaning the hours to apply the recurrence to.
:param byminute:
If given, it must be either an integer, or a sequence of integers,
meaning the minutes to apply the recurrence to.
:param bysecond:
If given, it must be either an integer, or a sequence of integers,
meaning the seconds to apply the recurrence to.
:param cache:
If given, it must be a boolean value specifying to enable or disable
caching of results. If you will use the same rrule instance multiple
times, enabling caching will improve the performance considerably.
"""
def __init__(self, freq, dtstart=None,
interval=1, wkst=None, count=None, until=None, bysetpos=None,
bymonth=None, bymonthday=None, byyearday=None, byeaster=None,
byweekno=None, byweekday=None,
byhour=None, byminute=None, bysecond=None,
cache=False):
super(rrule, self).__init__(cache)
global easter
if not dtstart:
if until and until.tzinfo:
dtstart = datetime.datetime.now(tz=until.tzinfo).replace(microsecond=0)
else:
dtstart = datetime.datetime.now().replace(microsecond=0)
elif not isinstance(dtstart, datetime.datetime):
dtstart = datetime.datetime.fromordinal(dtstart.toordinal())
else:
dtstart = dtstart.replace(microsecond=0)
self._dtstart = dtstart
self._tzinfo = dtstart.tzinfo
self._freq = freq
self._interval = interval
self._count = count
# Cache the original byxxx rules, if they are provided, as the _byxxx
# attributes do not necessarily map to the inputs, and this can be
# a problem in generating the strings. Only store things if they've
# been supplied (the string retrieval will just use .get())
self._original_rule = {}
if until and not isinstance(until, datetime.datetime):
until = datetime.datetime.fromordinal(until.toordinal())
self._until = until
if self._dtstart and self._until:
if (self._dtstart.tzinfo is not None) != (self._until.tzinfo is not None):
# According to RFC5545 Section 3.3.10:
# https://tools.ietf.org/html/rfc5545#section-3.3.10
#
# > If the "DTSTART" property is specified as a date with UTC
# > time or a date with local time and time zone reference,
# > then the UNTIL rule part MUST be specified as a date with
# > UTC time.
raise ValueError(
'RRULE UNTIL values must be specified in UTC when DTSTART '
'is timezone-aware'
)
if count is not None and until:
warn("Using both 'count' and 'until' is inconsistent with RFC 5545"
" and has been deprecated in dateutil. Future versions will "
"raise an error.", DeprecationWarning)
if wkst is None:
self._wkst = calendar.firstweekday()
elif isinstance(wkst, integer_types):
self._wkst = wkst
else:
self._wkst = wkst.weekday
if bysetpos is None:
self._bysetpos = None
elif isinstance(bysetpos, integer_types):
if bysetpos == 0 or not (-366 <= bysetpos <= 366):
raise ValueError("bysetpos must be between 1 and 366, "
"or between -366 and -1")
self._bysetpos = (bysetpos,)
else:
self._bysetpos = tuple(bysetpos)
for pos in self._bysetpos:
if pos == 0 or not (-366 <= pos <= 366):
raise ValueError("bysetpos must be between 1 and 366, "
"or between -366 and -1")
if self._bysetpos:
self._original_rule['bysetpos'] = self._bysetpos
if (byweekno is None and byyearday is None and bymonthday is None and
byweekday is None and byeaster is None):
if freq == YEARLY:
if bymonth is None:
bymonth = dtstart.month
self._original_rule['bymonth'] = None
bymonthday = dtstart.day
self._original_rule['bymonthday'] = None
elif freq == MONTHLY:
bymonthday = dtstart.day
self._original_rule['bymonthday'] = None
elif freq == WEEKLY:
byweekday = dtstart.weekday()
self._original_rule['byweekday'] = None
# bymonth
if bymonth is None:
self._bymonth = None
else:
if isinstance(bymonth, integer_types):
bymonth = (bymonth,)
self._bymonth = tuple(sorted(set(bymonth)))
if 'bymonth' not in self._original_rule:
self._original_rule['bymonth'] = self._bymonth
# byyearday
if byyearday is None:
self._byyearday = None
else:
if isinstance(byyearday, integer_types):
byyearday = (byyearday,)
self._byyearday = tuple(sorted(set(byyearday)))
self._original_rule['byyearday'] = self._byyearday
# byeaster
if byeaster is not None:
if not easter:
from dateutil import easter
if isinstance(byeaster, integer_types):
self._byeaster = (byeaster,)
else:
self._byeaster = tuple(sorted(byeaster))
self._original_rule['byeaster'] = self._byeaster
else:
self._byeaster = None
# bymonthday
if bymonthday is None:
self._bymonthday = ()
self._bynmonthday = ()
else:
if isinstance(bymonthday, integer_types):
bymonthday = (bymonthday,)
bymonthday = set(bymonthday) # Ensure it's unique
self._bymonthday = tuple(sorted(x for x in bymonthday if x > 0))
self._bynmonthday = tuple(sorted(x for x in bymonthday if x < 0))
# Storing positive numbers first, then negative numbers
if 'bymonthday' not in self._original_rule:
self._original_rule['bymonthday'] = tuple(
itertools.chain(self._bymonthday, self._bynmonthday))
# byweekno
if byweekno is None:
self._byweekno = None
else:
if isinstance(byweekno, integer_types):
byweekno = (byweekno,)
self._byweekno = tuple(sorted(set(byweekno)))
self._original_rule['byweekno'] = self._byweekno
# byweekday / bynweekday
if byweekday is None:
self._byweekday = None
self._bynweekday = None
else:
# If it's one of the valid non-sequence types, convert to a
# single-element sequence before the iterator that builds the
# byweekday set.
if isinstance(byweekday, integer_types) or hasattr(byweekday, "n"):
byweekday = (byweekday,)
self._byweekday = set()
self._bynweekday = set()
for wday in byweekday:
if isinstance(wday, integer_types):
self._byweekday.add(wday)
elif not wday.n or freq > MONTHLY:
self._byweekday.add(wday.weekday)
else:
self._bynweekday.add((wday.weekday, wday.n))
if not self._byweekday:
self._byweekday = None
elif not self._bynweekday:
self._bynweekday = None
if self._byweekday is not None:
self._byweekday = tuple(sorted(self._byweekday))
orig_byweekday = [weekday(x) for x in self._byweekday]
else:
orig_byweekday = ()
if self._bynweekday is not None:
self._bynweekday = tuple(sorted(self._bynweekday))
orig_bynweekday = [weekday(*x) for x in self._bynweekday]
else:
orig_bynweekday = ()
if 'byweekday' not in self._original_rule:
self._original_rule['byweekday'] = tuple(itertools.chain(
orig_byweekday, orig_bynweekday))
# byhour
if byhour is None:
if freq < HOURLY:
self._byhour = {dtstart.hour}
else:
self._byhour = None
else:
if isinstance(byhour, integer_types):
byhour = (byhour,)
if freq == HOURLY:
self._byhour = self.__construct_byset(start=dtstart.hour,
byxxx=byhour,
base=24)
else:
self._byhour = set(byhour)
self._byhour = tuple(sorted(self._byhour))
self._original_rule['byhour'] = self._byhour
# byminute
if byminute is None:
if freq < MINUTELY:
self._byminute = {dtstart.minute}
else:
self._byminute = None
else:
if isinstance(byminute, integer_types):
byminute = (byminute,)
if freq == MINUTELY:
self._byminute = self.__construct_byset(start=dtstart.minute,
byxxx=byminute,
base=60)
else:
self._byminute = set(byminute)
self._byminute = tuple(sorted(self._byminute))
self._original_rule['byminute'] = self._byminute
# bysecond
if bysecond is None:
if freq < SECONDLY:
self._bysecond = ((dtstart.second,))
else:
self._bysecond = None
else:
if isinstance(bysecond, integer_types):
bysecond = (bysecond,)
self._bysecond = set(bysecond)
if freq == SECONDLY:
self._bysecond = self.__construct_byset(start=dtstart.second,
byxxx=bysecond,
base=60)
else:
self._bysecond = set(bysecond)
self._bysecond = tuple(sorted(self._bysecond))
self._original_rule['bysecond'] = self._bysecond
if self._freq >= HOURLY:
self._timeset = None
else:
self._timeset = []
for hour in self._byhour:
for minute in self._byminute:
for second in self._bysecond:
self._timeset.append(
datetime.time(hour, minute, second,
tzinfo=self._tzinfo))
self._timeset.sort()
self._timeset = tuple(self._timeset)
def __str__(self):
"""
Output a string that would generate this RRULE if passed to rrulestr.
This is mostly compatible with RFC5545, except for the
dateutil-specific extension BYEASTER.
"""
output = []
h, m, s = [None] * 3
if self._dtstart:
output.append(self._dtstart.strftime('DTSTART:%Y%m%dT%H%M%S'))
h, m, s = self._dtstart.timetuple()[3:6]
parts = ['FREQ=' + FREQNAMES[self._freq]]
if self._interval != 1:
parts.append('INTERVAL=' + str(self._interval))
if self._wkst:
parts.append('WKST=' + repr(weekday(self._wkst))[0:2])
if self._count is not None:
parts.append('COUNT=' + str(self._count))
if self._until:
parts.append(self._until.strftime('UNTIL=%Y%m%dT%H%M%S'))
if self._original_rule.get('byweekday') is not None:
# The str() method on weekday objects doesn't generate
# RFC5545-compliant strings, so we should modify that.
original_rule = dict(self._original_rule)
wday_strings = []
for wday in original_rule['byweekday']:
if wday.n:
wday_strings.append('{n:+d}{wday}'.format(
n=wday.n,
wday=repr(wday)[0:2]))
else:
wday_strings.append(repr(wday))
original_rule['byweekday'] = wday_strings
else:
original_rule = self._original_rule
partfmt = '{name}={vals}'
for name, key in [('BYSETPOS', 'bysetpos'),
('BYMONTH', 'bymonth'),
('BYMONTHDAY', 'bymonthday'),
('BYYEARDAY', 'byyearday'),
('BYWEEKNO', 'byweekno'),
('BYDAY', 'byweekday'),
('BYHOUR', 'byhour'),
('BYMINUTE', 'byminute'),
('BYSECOND', 'bysecond'),
('BYEASTER', 'byeaster')]:
value = original_rule.get(key)
if value:
parts.append(partfmt.format(name=name, vals=(','.join(str(v)
for v in value))))
output.append('RRULE:' + ';'.join(parts))
return '\n'.join(output)
def replace(self, **kwargs):
"""Return new rrule with same attributes except for those attributes given new
values by whichever keyword arguments are specified."""
new_kwargs = {"interval": self._interval,
"count": self._count,
"dtstart": self._dtstart,
"freq": self._freq,
"until": self._until,
"wkst": self._wkst,
"cache": False if self._cache is None else True }
new_kwargs.update(self._original_rule)
new_kwargs.update(kwargs)
return rrule(**new_kwargs)
def _iter(self):
year, month, day, hour, minute, second, weekday, yearday, _ = \
self._dtstart.timetuple()
# Some local variables to speed things up a bit
freq = self._freq
interval = self._interval
wkst = self._wkst
until = self._until
bymonth = self._bymonth
byweekno = self._byweekno
byyearday = self._byyearday
byweekday = self._byweekday
byeaster = self._byeaster
bymonthday = self._bymonthday
bynmonthday = self._bynmonthday
bysetpos = self._bysetpos
byhour = self._byhour
byminute = self._byminute
bysecond = self._bysecond
ii = _iterinfo(self)
ii.rebuild(year, month)
getdayset = {YEARLY: ii.ydayset,
MONTHLY: ii.mdayset,
WEEKLY: ii.wdayset,
DAILY: ii.ddayset,
HOURLY: ii.ddayset,
MINUTELY: ii.ddayset,
SECONDLY: ii.ddayset}[freq]
if freq < HOURLY:
timeset = self._timeset
else:
gettimeset = {HOURLY: ii.htimeset,
MINUTELY: ii.mtimeset,
SECONDLY: ii.stimeset}[freq]
if ((freq >= HOURLY and
self._byhour and hour not in self._byhour) or
(freq >= MINUTELY and
self._byminute and minute not in self._byminute) or
(freq >= SECONDLY and
self._bysecond and second not in self._bysecond)):
timeset = ()
else:
timeset = gettimeset(hour, minute, second)
total = 0
count = self._count
while True:
# Get dayset with the right frequency
dayset, start, end = getdayset(year, month, day)
# Do the "hard" work ;-)
filtered = False
for i in dayset[start:end]:
if ((bymonth and ii.mmask[i] not in bymonth) or
(byweekno and not ii.wnomask[i]) or
(byweekday and ii.wdaymask[i] not in byweekday) or
(ii.nwdaymask and not ii.nwdaymask[i]) or
(byeaster and not ii.eastermask[i]) or
((bymonthday or bynmonthday) and
ii.mdaymask[i] not in bymonthday and
ii.nmdaymask[i] not in bynmonthday) or
(byyearday and
((i < ii.yearlen and i+1 not in byyearday and
-ii.yearlen+i not in byyearday) or
(i >= ii.yearlen and i+1-ii.yearlen not in byyearday and
-ii.nextyearlen+i-ii.yearlen not in byyearday)))):
dayset[i] = None
filtered = True
# Output results
if bysetpos and timeset:
poslist = []
for pos in bysetpos:
if pos < 0:
daypos, timepos = divmod(pos, len(timeset))
else:
daypos, timepos = divmod(pos-1, len(timeset))
try:
i = [x for x in dayset[start:end]
if x is not None][daypos]
time = timeset[timepos]
except IndexError:
pass
else:
date = datetime.date.fromordinal(ii.yearordinal+i)
res = datetime.datetime.combine(date, time)
if res not in poslist:
poslist.append(res)
poslist.sort()
for res in poslist:
if until and res > until:
self._len = total
return
elif res >= self._dtstart:
if count is not None:
count -= 1
if count < 0:
self._len = total
return
total += 1
yield res
else:
for i in dayset[start:end]:
if i is not None:
date = datetime.date.fromordinal(ii.yearordinal + i)
for time in timeset:
res = datetime.datetime.combine(date, time)
if until and res > until:
self._len = total
return
elif res >= self._dtstart:
if count is not None:
count -= 1
if count < 0:
self._len = total
return
total += 1
yield res
# Handle frequency and interval
fixday = False
if freq == YEARLY:
year += interval
if year > datetime.MAXYEAR:
self._len = total
return
ii.rebuild(year, month)
elif freq == MONTHLY:
month += interval
if month > 12:
div, mod = divmod(month, 12)
month = mod
year += div
if month == 0:
month = 12
year -= 1
if year > datetime.MAXYEAR:
self._len = total
return
ii.rebuild(year, month)
elif freq == WEEKLY:
if wkst > weekday:
day += -(weekday+1+(6-wkst))+self._interval*7
else:
day += -(weekday-wkst)+self._interval*7
weekday = wkst
fixday = True
elif freq == DAILY:
day += interval
fixday = True
elif freq == HOURLY:
if filtered:
# Jump to one iteration before next day
hour += ((23-hour)//interval)*interval
if byhour:
ndays, hour = self.__mod_distance(value=hour,
byxxx=self._byhour,
base=24)
else:
ndays, hour = divmod(hour+interval, 24)
if ndays:
day += ndays
fixday = True
timeset = gettimeset(hour, minute, second)
elif freq == MINUTELY:
if filtered:
# Jump to one iteration before next day
minute += ((1439-(hour*60+minute))//interval)*interval
valid = False
rep_rate = (24*60)
for j in range(rep_rate // gcd(interval, rep_rate)):
if byminute:
nhours, minute = \
self.__mod_distance(value=minute,
byxxx=self._byminute,
base=60)
else:
nhours, minute = divmod(minute+interval, 60)
div, hour = divmod(hour+nhours, 24)
if div:
day += div
fixday = True
filtered = False
if not byhour or hour in byhour:
valid = True
break
if not valid:
raise ValueError('Invalid combination of interval and ' +
'byhour resulting in empty rule.')
timeset = gettimeset(hour, minute, second)
elif freq == SECONDLY:
if filtered:
# Jump to one iteration before next day
second += (((86399 - (hour * 3600 + minute * 60 + second))
// interval) * interval)
rep_rate = (24 * 3600)
valid = False
for j in range(0, rep_rate // gcd(interval, rep_rate)):
if bysecond:
nminutes, second = \
self.__mod_distance(value=second,
byxxx=self._bysecond,
base=60)
else:
nminutes, second = divmod(second+interval, 60)
div, minute = divmod(minute+nminutes, 60)
if div:
hour += div
div, hour = divmod(hour, 24)
if div:
day += div
fixday = True
if ((not byhour or hour in byhour) and
(not byminute or minute in byminute) and
(not bysecond or second in bysecond)):
valid = True
break
if not valid:
raise ValueError('Invalid combination of interval, ' +
'byhour and byminute resulting in empty' +
' rule.')
timeset = gettimeset(hour, minute, second)
if fixday and day > 28:
daysinmonth = calendar.monthrange(year, month)[1]
if day > daysinmonth:
while day > daysinmonth:
day -= daysinmonth
month += 1
if month == 13:
month = 1
year += 1
if year > datetime.MAXYEAR:
self._len = total
return
daysinmonth = calendar.monthrange(year, month)[1]
ii.rebuild(year, month)
def __construct_byset(self, start, byxxx, base):
"""
If a `BYXXX` sequence is passed to the constructor at the same level as
`FREQ` (e.g. `FREQ=HOURLY,BYHOUR={2,4,7},INTERVAL=3`), there are some
specifications which cannot be reached given some starting conditions.
This occurs whenever the interval is not coprime with the base of a
given unit and the difference between the starting position and the
ending position is not coprime with the greatest common denominator
between the interval and the base. For example, with a FREQ of hourly
starting at 17:00 and an interval of 4, the only valid values for
BYHOUR would be {21, 1, 5, 9, 13, 17}, because 4 and 24 are not
coprime.
:param start:
Specifies the starting position.
:param byxxx:
An iterable containing the list of allowed values.
:param base:
The largest allowable value for the specified frequency (e.g.
24 hours, 60 minutes).
This does not preserve the type of the iterable, returning a set, since
the values should be unique and the order is irrelevant, this will
speed up later lookups.
In the event of an empty set, raises a :exception:`ValueError`, as this
results in an empty rrule.
"""
cset = set()
# Support a single byxxx value.
if isinstance(byxxx, integer_types):
byxxx = (byxxx, )
for num in byxxx:
i_gcd = gcd(self._interval, base)
# Use divmod rather than % because we need to wrap negative nums.
if i_gcd == 1 or divmod(num - start, i_gcd)[1] == 0:
cset.add(num)
if len(cset) == 0:
raise ValueError("Invalid rrule byxxx generates an empty set.")
return cset
def __mod_distance(self, value, byxxx, base):
"""
Calculates the next value in a sequence where the `FREQ` parameter is
specified along with a `BYXXX` parameter at the same "level"
(e.g. `HOURLY` specified with `BYHOUR`).
:param value:
The old value of the component.
:param byxxx:
The `BYXXX` set, which should have been generated by
`rrule._construct_byset`, or something else which checks that a
valid rule is present.
:param base:
The largest allowable value for the specified frequency (e.g.
24 hours, 60 minutes).
If a valid value is not found after `base` iterations (the maximum
number before the sequence would start to repeat), this raises a
:exception:`ValueError`, as no valid values were found.
This returns a tuple of `divmod(n*interval, base)`, where `n` is the
smallest number of `interval` repetitions until the next specified
value in `byxxx` is found.
"""
accumulator = 0
for ii in range(1, base + 1):
# Using divmod() over % to account for negative intervals
div, value = divmod(value + self._interval, base)
accumulator += div
if value in byxxx:
return (accumulator, value)
class _iterinfo(object):
__slots__ = ["rrule", "lastyear", "lastmonth",
"yearlen", "nextyearlen", "yearordinal", "yearweekday",
"mmask", "mrange", "mdaymask", "nmdaymask",
"wdaymask", "wnomask", "nwdaymask", "eastermask"]
def __init__(self, rrule):
for attr in self.__slots__:
setattr(self, attr, None)
self.rrule = rrule
def rebuild(self, year, month):
# Every mask is 7 days longer to handle cross-year weekly periods.
rr = self.rrule
if year != self.lastyear:
self.yearlen = 365 + calendar.isleap(year)
self.nextyearlen = 365 + calendar.isleap(year + 1)
firstyday = datetime.date(year, 1, 1)
self.yearordinal = firstyday.toordinal()
self.yearweekday = firstyday.weekday()
wday = datetime.date(year, 1, 1).weekday()
if self.yearlen == 365:
self.mmask = M365MASK
self.mdaymask = MDAY365MASK
self.nmdaymask = NMDAY365MASK
self.wdaymask = WDAYMASK[wday:]
self.mrange = M365RANGE
else:
self.mmask = M366MASK
self.mdaymask = MDAY366MASK
self.nmdaymask = NMDAY366MASK
self.wdaymask = WDAYMASK[wday:]
self.mrange = M366RANGE
if not rr._byweekno:
self.wnomask = None
else:
self.wnomask = [0]*(self.yearlen+7)
# no1wkst = firstwkst = self.wdaymask.index(rr._wkst)
no1wkst = firstwkst = (7-self.yearweekday+rr._wkst) % 7
if no1wkst >= 4:
no1wkst = 0
# Number of days in the year, plus the days we got
# from last year.
wyearlen = self.yearlen+(self.yearweekday-rr._wkst) % 7
else:
# Number of days in the year, minus the days we
# left in last year.
wyearlen = self.yearlen-no1wkst
div, mod = divmod(wyearlen, 7)
numweeks = div+mod//4
for n in rr._byweekno:
if n < 0:
n += numweeks+1
if not (0 < n <= numweeks):
continue
if n > 1:
i = no1wkst+(n-1)*7
if no1wkst != firstwkst:
i -= 7-firstwkst
else:
i = no1wkst
for j in range(7):
self.wnomask[i] = 1
i += 1
if self.wdaymask[i] == rr._wkst:
break
if 1 in rr._byweekno:
# Check week number 1 of next year as well
# TODO: Check -numweeks for next year.
i = no1wkst+numweeks*7
if no1wkst != firstwkst:
i -= 7-firstwkst
if i < self.yearlen:
# If week starts in next year, we
# don't care about it.
for j in range(7):
self.wnomask[i] = 1
i += 1
if self.wdaymask[i] == rr._wkst:
break
if no1wkst:
# Check last week number of last year as
# well. If no1wkst is 0, either the year
# started on week start, or week number 1
# got days from last year, so there are no
# days from last year's last week number in
# this year.
if -1 not in rr._byweekno:
lyearweekday = datetime.date(year-1, 1, 1).weekday()
lno1wkst = (7-lyearweekday+rr._wkst) % 7
lyearlen = 365+calendar.isleap(year-1)
if lno1wkst >= 4:
lno1wkst = 0
lnumweeks = 52+(lyearlen +
(lyearweekday-rr._wkst) % 7) % 7//4
else:
lnumweeks = 52+(self.yearlen-no1wkst) % 7//4
else:
lnumweeks = -1
if lnumweeks in rr._byweekno:
for i in range(no1wkst):
self.wnomask[i] = 1
if (rr._bynweekday and (month != self.lastmonth or
year != self.lastyear)):
ranges = []
if rr._freq == YEARLY:
if rr._bymonth:
for month in rr._bymonth:
ranges.append(self.mrange[month-1:month+1])
else:
ranges = [(0, self.yearlen)]
elif rr._freq == MONTHLY:
ranges = [self.mrange[month-1:month+1]]
if ranges:
# Weekly frequency won't get here, so we may not
# care about cross-year weekly periods.
self.nwdaymask = [0]*self.yearlen
for first, last in ranges:
last -= 1
for wday, n in rr._bynweekday:
if n < 0:
i = last+(n+1)*7
i -= (self.wdaymask[i]-wday) % 7
else:
i = first+(n-1)*7
i += (7-self.wdaymask[i]+wday) % 7
if first <= i <= last:
self.nwdaymask[i] = 1
if rr._byeaster:
self.eastermask = [0]*(self.yearlen+7)
eyday = easter.easter(year).toordinal()-self.yearordinal
for offset in rr._byeaster:
self.eastermask[eyday+offset] = 1
self.lastyear = year
self.lastmonth = month
def ydayset(self, year, month, day):
return list(range(self.yearlen)), 0, self.yearlen
def mdayset(self, year, month, day):
dset = [None]*self.yearlen
start, end = self.mrange[month-1:month+1]
for i in range(start, end):
dset[i] = i
return dset, start, end
def wdayset(self, year, month, day):
# We need to handle cross-year weeks here.
dset = [None]*(self.yearlen+7)
i = datetime.date(year, month, day).toordinal()-self.yearordinal
start = i
for j in range(7):
dset[i] = i
i += 1
# if (not (0 <= i < self.yearlen) or
# self.wdaymask[i] == self.rrule._wkst):
# This will cross the year boundary, if necessary.
if self.wdaymask[i] == self.rrule._wkst:
break
return dset, start, i
def ddayset(self, year, month, day):
dset = [None] * self.yearlen
i = datetime.date(year, month, day).toordinal() - self.yearordinal
dset[i] = i
return dset, i, i + 1
def htimeset(self, hour, minute, second):
tset = []
rr = self.rrule
for minute in rr._byminute:
for second in rr._bysecond:
tset.append(datetime.time(hour, minute, second,
tzinfo=rr._tzinfo))
tset.sort()
return tset
def mtimeset(self, hour, minute, second):
tset = []
rr = self.rrule
for second in rr._bysecond:
tset.append(datetime.time(hour, minute, second, tzinfo=rr._tzinfo))
tset.sort()
return tset
def stimeset(self, hour, minute, second):
return (datetime.time(hour, minute, second,
tzinfo=self.rrule._tzinfo),)
class rruleset(rrulebase):
""" The rruleset type allows more complex recurrence setups, mixing
multiple rules, dates, exclusion rules, and exclusion dates. The type
constructor takes the following keyword arguments:
:param cache: If True, caching of results will be enabled, improving
performance of multiple queries considerably. """
class _genitem(object):
def __init__(self, genlist, gen):
try:
self.dt = advance_iterator(gen)
genlist.append(self)
except StopIteration:
pass
self.genlist = genlist
self.gen = gen
def __next__(self):
try:
self.dt = advance_iterator(self.gen)
except StopIteration:
if self.genlist[0] is self:
heapq.heappop(self.genlist)
else:
self.genlist.remove(self)
heapq.heapify(self.genlist)
next = __next__
def __lt__(self, other):
return self.dt < other.dt
def __gt__(self, other):
return self.dt > other.dt
def __eq__(self, other):
return self.dt == other.dt
def __ne__(self, other):
return self.dt != other.dt
def __init__(self, cache=False):
super(rruleset, self).__init__(cache)
self._rrule = []
self._rdate = []
self._exrule = []
self._exdate = []
@_invalidates_cache
def rrule(self, rrule):
""" Include the given :py:class:`rrule` instance in the recurrence set
generation. """
self._rrule.append(rrule)
@_invalidates_cache
def rdate(self, rdate):
""" Include the given :py:class:`datetime` instance in the recurrence
set generation. """
self._rdate.append(rdate)
@_invalidates_cache
def exrule(self, exrule):
""" Include the given rrule instance in the recurrence set exclusion
list. Dates which are part of the given recurrence rules will not
be generated, even if some inclusive rrule or rdate matches them.
"""
self._exrule.append(exrule)
@_invalidates_cache
def exdate(self, exdate):
""" Include the given datetime instance in the recurrence set
exclusion list. Dates included that way will not be generated,
even if some inclusive rrule or rdate matches them. """
self._exdate.append(exdate)
def _iter(self):
rlist = []
self._rdate.sort()
self._genitem(rlist, iter(self._rdate))
for gen in [iter(x) for x in self._rrule]:
self._genitem(rlist, gen)
exlist = []
self._exdate.sort()
self._genitem(exlist, iter(self._exdate))
for gen in [iter(x) for x in self._exrule]:
self._genitem(exlist, gen)
lastdt = None
total = 0
heapq.heapify(rlist)
heapq.heapify(exlist)
while rlist:
ritem = rlist[0]
if not lastdt or lastdt != ritem.dt:
while exlist and exlist[0] < ritem:
exitem = exlist[0]
advance_iterator(exitem)
if exlist and exlist[0] is exitem:
heapq.heapreplace(exlist, exitem)
if not exlist or ritem != exlist[0]:
total += 1
yield ritem.dt
lastdt = ritem.dt
advance_iterator(ritem)
if rlist and rlist[0] is ritem:
heapq.heapreplace(rlist, ritem)
self._len = total
class _rrulestr(object):
_freq_map = {"YEARLY": YEARLY,
"MONTHLY": MONTHLY,
"WEEKLY": WEEKLY,
"DAILY": DAILY,
"HOURLY": HOURLY,
"MINUTELY": MINUTELY,
"SECONDLY": SECONDLY}
_weekday_map = {"MO": 0, "TU": 1, "WE": 2, "TH": 3,
"FR": 4, "SA": 5, "SU": 6}
def _handle_int(self, rrkwargs, name, value, **kwargs):
rrkwargs[name.lower()] = int(value)
def _handle_int_list(self, rrkwargs, name, value, **kwargs):
rrkwargs[name.lower()] = [int(x) for x in value.split(',')]
_handle_INTERVAL = _handle_int
_handle_COUNT = _handle_int
_handle_BYSETPOS = _handle_int_list
_handle_BYMONTH = _handle_int_list
_handle_BYMONTHDAY = _handle_int_list
_handle_BYYEARDAY = _handle_int_list
_handle_BYEASTER = _handle_int_list
_handle_BYWEEKNO = _handle_int_list
_handle_BYHOUR = _handle_int_list
_handle_BYMINUTE = _handle_int_list
_handle_BYSECOND = _handle_int_list
def _handle_FREQ(self, rrkwargs, name, value, **kwargs):
rrkwargs["freq"] = self._freq_map[value]
def _handle_UNTIL(self, rrkwargs, name, value, **kwargs):
global parser
if not parser:
from dateutil import parser
try:
rrkwargs["until"] = parser.parse(value,
ignoretz=kwargs.get("ignoretz"),
tzinfos=kwargs.get("tzinfos"))
except ValueError:
raise ValueError("invalid until date")
def _handle_WKST(self, rrkwargs, name, value, **kwargs):
rrkwargs["wkst"] = self._weekday_map[value]
def _handle_BYWEEKDAY(self, rrkwargs, name, value, **kwargs):
"""
Two ways to specify this: +1MO or MO(+1)
"""
l = []
for wday in value.split(','):
if '(' in wday:
# If it's of the form TH(+1), etc.
splt = wday.split('(')
w = splt[0]
n = int(splt[1][:-1])
elif len(wday):
# If it's of the form +1MO
for i in range(len(wday)):
if wday[i] not in '+-0123456789':
break
n = wday[:i] or None
w = wday[i:]
if n:
n = int(n)
else:
raise ValueError("Invalid (empty) BYDAY specification.")
l.append(weekdays[self._weekday_map[w]](n))
rrkwargs["byweekday"] = l
_handle_BYDAY = _handle_BYWEEKDAY
def _parse_rfc_rrule(self, line,
dtstart=None,
cache=False,
ignoretz=False,
tzinfos=None):
if line.find(':') != -1:
name, value = line.split(':')
if name != "RRULE":
raise ValueError("unknown parameter name")
else:
value = line
rrkwargs = {}
for pair in value.split(';'):
name, value = pair.split('=')
name = name.upper()
value = value.upper()
try:
getattr(self, "_handle_"+name)(rrkwargs, name, value,
ignoretz=ignoretz,
tzinfos=tzinfos)
except AttributeError:
raise ValueError("unknown parameter '%s'" % name)
except (KeyError, ValueError):
raise ValueError("invalid '%s': %s" % (name, value))
return rrule(dtstart=dtstart, cache=cache, **rrkwargs)
def _parse_rfc(self, s,
dtstart=None,
cache=False,
unfold=False,
forceset=False,
compatible=False,
ignoretz=False,
tzids=None,
tzinfos=None):
global parser
if compatible:
forceset = True
unfold = True
TZID_NAMES = dict(map(
lambda x: (x.upper(), x),
re.findall('TZID=(?P<name>[^:]+):', s)
))
s = s.upper()
if not s.strip():
raise ValueError("empty string")
if unfold:
lines = s.splitlines()
i = 0
while i < len(lines):
line = lines[i].rstrip()
if not line:
del lines[i]
elif i > 0 and line[0] == " ":
lines[i-1] += line[1:]
del lines[i]
else:
i += 1
else:
lines = s.split()
if (not forceset and len(lines) == 1 and (s.find(':') == -1 or
s.startswith('RRULE:'))):
return self._parse_rfc_rrule(lines[0], cache=cache,
dtstart=dtstart, ignoretz=ignoretz,
tzinfos=tzinfos)
else:
rrulevals = []
rdatevals = []
exrulevals = []
exdatevals = []
for line in lines:
if not line:
continue
if line.find(':') == -1:
name = "RRULE"
value = line
else:
name, value = line.split(':', 1)
parms = name.split(';')
if not parms:
raise ValueError("empty property name")
name = parms[0]
parms = parms[1:]
if name == "RRULE":
for parm in parms:
raise ValueError("unsupported RRULE parm: "+parm)
rrulevals.append(value)
elif name == "RDATE":
for parm in parms:
if parm != "VALUE=DATE-TIME":
raise ValueError("unsupported RDATE parm: "+parm)
rdatevals.append(value)
elif name == "EXRULE":
for parm in parms:
raise ValueError("unsupported EXRULE parm: "+parm)
exrulevals.append(value)
elif name == "EXDATE":
for parm in parms:
if parm != "VALUE=DATE-TIME":
raise ValueError("unsupported EXDATE parm: "+parm)
exdatevals.append(value)
elif name == "DTSTART":
# RFC 5445 3.8.2.4: The VALUE parameter is optional, but
# may be found only once.
value_found = False
TZID = None
valid_values = {"VALUE=DATE-TIME", "VALUE=DATE"}
for parm in parms:
if parm.startswith("TZID="):
try:
tzkey = TZID_NAMES[parm.split('TZID=')[-1]]
except KeyError:
continue
if tzids is None:
from . import tz
tzlookup = tz.gettz
elif callable(tzids):
tzlookup = tzids
else:
tzlookup = getattr(tzids, 'get', None)
if tzlookup is None:
msg = ('tzids must be a callable, ' +
'mapping, or None, ' +
'not %s' % tzids)
raise ValueError(msg)
TZID = tzlookup(tzkey)
continue
if parm not in valid_values:
raise ValueError("unsupported DTSTART parm: "+parm)
else:
if value_found:
msg = ("Duplicate value parameter found in " +
"DTSTART: " + parm)
raise ValueError(msg)
value_found = True
if not parser:
from dateutil import parser
dtstart = parser.parse(value, ignoretz=ignoretz,
tzinfos=tzinfos)
if TZID is not None:
if dtstart.tzinfo is None:
dtstart = dtstart.replace(tzinfo=TZID)
else:
raise ValueError('DTSTART specifies multiple timezones')
else:
raise ValueError("unsupported property: "+name)
if (forceset or len(rrulevals) > 1 or rdatevals
or exrulevals or exdatevals):
if not parser and (rdatevals or exdatevals):
from dateutil import parser
rset = rruleset(cache=cache)
for value in rrulevals:
rset.rrule(self._parse_rfc_rrule(value, dtstart=dtstart,
ignoretz=ignoretz,
tzinfos=tzinfos))
for value in rdatevals:
for datestr in value.split(','):
rset.rdate(parser.parse(datestr,
ignoretz=ignoretz,
tzinfos=tzinfos))
for value in exrulevals:
rset.exrule(self._parse_rfc_rrule(value, dtstart=dtstart,
ignoretz=ignoretz,
tzinfos=tzinfos))
for value in exdatevals:
for datestr in value.split(','):
rset.exdate(parser.parse(datestr,
ignoretz=ignoretz,
tzinfos=tzinfos))
if compatible and dtstart:
rset.rdate(dtstart)
return rset
else:
return self._parse_rfc_rrule(rrulevals[0],
dtstart=dtstart,
cache=cache,
ignoretz=ignoretz,
tzinfos=tzinfos)
def __call__(self, s, **kwargs):
return self._parse_rfc(s, **kwargs)
rrulestr = _rrulestr()
# vim:ts=4:sw=4:et
| 64,802 | 37.734608 | 87 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/dateutil/__init__.py
|
# -*- coding: utf-8 -*-
try:
from ._version import version as __version__
except ImportError:
__version__ = 'unknown'
__all__ = ['easter', 'parser', 'relativedelta', 'rrule', 'tz',
'utils', 'zoneinfo']
| 222 | 23.777778 | 62 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/dateutil/_common.py
|
"""
Common code used in multiple modules.
"""
class weekday(object):
__slots__ = ["weekday", "n"]
def __init__(self, weekday, n=None):
self.weekday = weekday
self.n = n
def __call__(self, n):
if n == self.n:
return self
else:
return self.__class__(self.weekday, n)
def __eq__(self, other):
try:
if self.weekday != other.weekday or self.n != other.n:
return False
except AttributeError:
return False
return True
def __hash__(self):
return hash((
self.weekday,
self.n,
))
def __ne__(self, other):
return not (self == other)
def __repr__(self):
s = ("MO", "TU", "WE", "TH", "FR", "SA", "SU")[self.weekday]
if not self.n:
return s
else:
return "%s(%+d)" % (s, self.n)
# vim:ts=4:sw=4:et
| 932 | 20.204545 | 68 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/dateutil/zoneinfo/rebuild.py
|
import logging
import os
import tempfile
import shutil
import json
from subprocess import check_call
from tarfile import TarFile
from dateutil.zoneinfo import METADATA_FN, ZONEFILENAME
def rebuild(filename, tag=None, format="gz", zonegroups=[], metadata=None):
"""Rebuild the internal timezone info in dateutil/zoneinfo/zoneinfo*tar*
filename is the timezone tarball from ``ftp.iana.org/tz``.
"""
tmpdir = tempfile.mkdtemp()
zonedir = os.path.join(tmpdir, "zoneinfo")
moduledir = os.path.dirname(__file__)
try:
with TarFile.open(filename) as tf:
for name in zonegroups:
tf.extract(name, tmpdir)
filepaths = [os.path.join(tmpdir, n) for n in zonegroups]
try:
check_call(["zic", "-d", zonedir] + filepaths)
except OSError as e:
_print_on_nosuchfile(e)
raise
# write metadata file
with open(os.path.join(zonedir, METADATA_FN), 'w') as f:
json.dump(metadata, f, indent=4, sort_keys=True)
target = os.path.join(moduledir, ZONEFILENAME)
with TarFile.open(target, "w:%s" % format) as tf:
for entry in os.listdir(zonedir):
entrypath = os.path.join(zonedir, entry)
tf.add(entrypath, entry)
finally:
shutil.rmtree(tmpdir)
def _print_on_nosuchfile(e):
"""Print helpful troubleshooting message
e is an exception raised by subprocess.check_call()
"""
if e.errno == 2:
logging.error(
"Could not find zic. Perhaps you need to install "
"libc-bin or some other package that provides it, "
"or it's not in your PATH?")
| 1,719 | 30.851852 | 76 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/dateutil/zoneinfo/__init__.py
|
# -*- coding: utf-8 -*-
import warnings
import json
from tarfile import TarFile
from pkgutil import get_data
from io import BytesIO
from dateutil.tz import tzfile as _tzfile
__all__ = ["get_zonefile_instance", "gettz", "gettz_db_metadata"]
ZONEFILENAME = "dateutil-zoneinfo.tar.gz"
METADATA_FN = 'METADATA'
class tzfile(_tzfile):
def __reduce__(self):
return (gettz, (self._filename,))
def getzoneinfofile_stream():
try:
return BytesIO(get_data(__name__, ZONEFILENAME))
except IOError as e: # TODO switch to FileNotFoundError?
warnings.warn("I/O error({0}): {1}".format(e.errno, e.strerror))
return None
class ZoneInfoFile(object):
def __init__(self, zonefile_stream=None):
if zonefile_stream is not None:
with TarFile.open(fileobj=zonefile_stream) as tf:
self.zones = {zf.name: tzfile(tf.extractfile(zf), filename=zf.name)
for zf in tf.getmembers()
if zf.isfile() and zf.name != METADATA_FN}
# deal with links: They'll point to their parent object. Less
# waste of memory
links = {zl.name: self.zones[zl.linkname]
for zl in tf.getmembers() if
zl.islnk() or zl.issym()}
self.zones.update(links)
try:
metadata_json = tf.extractfile(tf.getmember(METADATA_FN))
metadata_str = metadata_json.read().decode('UTF-8')
self.metadata = json.loads(metadata_str)
except KeyError:
# no metadata in tar file
self.metadata = None
else:
self.zones = {}
self.metadata = None
def get(self, name, default=None):
"""
Wrapper for :func:`ZoneInfoFile.zones.get`. This is a convenience method
for retrieving zones from the zone dictionary.
:param name:
The name of the zone to retrieve. (Generally IANA zone names)
:param default:
The value to return in the event of a missing key.
.. versionadded:: 2.6.0
"""
return self.zones.get(name, default)
# The current API has gettz as a module function, although in fact it taps into
# a stateful class. So as a workaround for now, without changing the API, we
# will create a new "global" class instance the first time a user requests a
# timezone. Ugly, but adheres to the api.
#
# TODO: Remove after deprecation period.
_CLASS_ZONE_INSTANCE = []
def get_zonefile_instance(new_instance=False):
"""
This is a convenience function which provides a :class:`ZoneInfoFile`
instance using the data provided by the ``dateutil`` package. By default, it
caches a single instance of the ZoneInfoFile object and returns that.
:param new_instance:
If ``True``, a new instance of :class:`ZoneInfoFile` is instantiated and
used as the cached instance for the next call. Otherwise, new instances
are created only as necessary.
:return:
Returns a :class:`ZoneInfoFile` object.
.. versionadded:: 2.6
"""
if new_instance:
zif = None
else:
zif = getattr(get_zonefile_instance, '_cached_instance', None)
if zif is None:
zif = ZoneInfoFile(getzoneinfofile_stream())
get_zonefile_instance._cached_instance = zif
return zif
def gettz(name):
"""
This retrieves a time zone from the local zoneinfo tarball that is packaged
with dateutil.
:param name:
An IANA-style time zone name, as found in the zoneinfo file.
:return:
Returns a :class:`dateutil.tz.tzfile` time zone object.
.. warning::
It is generally inadvisable to use this function, and it is only
provided for API compatibility with earlier versions. This is *not*
equivalent to ``dateutil.tz.gettz()``, which selects an appropriate
time zone based on the inputs, favoring system zoneinfo. This is ONLY
for accessing the dateutil-specific zoneinfo (which may be out of
date compared to the system zoneinfo).
.. deprecated:: 2.6
If you need to use a specific zoneinfofile over the system zoneinfo,
instantiate a :class:`dateutil.zoneinfo.ZoneInfoFile` object and call
:func:`dateutil.zoneinfo.ZoneInfoFile.get(name)` instead.
Use :func:`get_zonefile_instance` to retrieve an instance of the
dateutil-provided zoneinfo.
"""
warnings.warn("zoneinfo.gettz() will be removed in future versions, "
"to use the dateutil-provided zoneinfo files, instantiate a "
"ZoneInfoFile object and use ZoneInfoFile.zones.get() "
"instead. See the documentation for details.",
DeprecationWarning)
if len(_CLASS_ZONE_INSTANCE) == 0:
_CLASS_ZONE_INSTANCE.append(ZoneInfoFile(getzoneinfofile_stream()))
return _CLASS_ZONE_INSTANCE[0].zones.get(name)
def gettz_db_metadata():
""" Get the zonefile metadata
See `zonefile_metadata`_
:returns:
A dictionary with the database metadata
.. deprecated:: 2.6
See deprecation warning in :func:`zoneinfo.gettz`. To get metadata,
query the attribute ``zoneinfo.ZoneInfoFile.metadata``.
"""
warnings.warn("zoneinfo.gettz_db_metadata() will be removed in future "
"versions, to use the dateutil-provided zoneinfo files, "
"ZoneInfoFile object and query the 'metadata' attribute "
"instead. See the documentation for details.",
DeprecationWarning)
if len(_CLASS_ZONE_INSTANCE) == 0:
_CLASS_ZONE_INSTANCE.append(ZoneInfoFile(getzoneinfofile_stream()))
return _CLASS_ZONE_INSTANCE[0].metadata
| 5,889 | 34.059524 | 83 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/dateutil/parser/_parser.py
|
# -*- coding: utf-8 -*-
"""
This module offers a generic date/time string parser which is able to parse
most known formats to represent a date and/or time.
This module attempts to be forgiving with regards to unlikely input formats,
returning a datetime object even for dates which are ambiguous. If an element
of a date/time stamp is omitted, the following rules are applied:
- If AM or PM is left unspecified, a 24-hour clock is assumed, however, an hour
on a 12-hour clock (``0 <= hour <= 12``) *must* be specified if AM or PM is
specified.
- If a time zone is omitted, a timezone-naive datetime is returned.
If any other elements are missing, they are taken from the
:class:`datetime.datetime` object passed to the parameter ``default``. If this
results in a day number exceeding the valid number of days per month, the
value falls back to the end of the month.
Additional resources about date/time string formats can be found below:
- `A summary of the international standard date and time notation
<http://www.cl.cam.ac.uk/~mgk25/iso-time.html>`_
- `W3C Date and Time Formats <http://www.w3.org/TR/NOTE-datetime>`_
- `Time Formats (Planetary Rings Node) <https://pds-rings.seti.org:443/tools/time_formats.html>`_
- `CPAN ParseDate module
<http://search.cpan.org/~muir/Time-modules-2013.0912/lib/Time/ParseDate.pm>`_
- `Java SimpleDateFormat Class
<https://docs.oracle.com/javase/6/docs/api/java/text/SimpleDateFormat.html>`_
"""
from __future__ import unicode_literals
import datetime
import re
import string
import time
import warnings
from calendar import monthrange
from io import StringIO
import six
from six import binary_type, integer_types, text_type
from decimal import Decimal
from warnings import warn
from .. import relativedelta
from .. import tz
__all__ = ["parse", "parserinfo"]
# TODO: pandas.core.tools.datetimes imports this explicitly. Might be worth
# making public and/or figuring out if there is something we can
# take off their plate.
class _timelex(object):
# Fractional seconds are sometimes split by a comma
_split_decimal = re.compile("([.,])")
def __init__(self, instream):
if six.PY2:
# In Python 2, we can't duck type properly because unicode has
# a 'decode' function, and we'd be double-decoding
if isinstance(instream, (binary_type, bytearray)):
instream = instream.decode()
else:
if getattr(instream, 'decode', None) is not None:
instream = instream.decode()
if isinstance(instream, text_type):
instream = StringIO(instream)
elif getattr(instream, 'read', None) is None:
raise TypeError('Parser must be a string or character stream, not '
'{itype}'.format(itype=instream.__class__.__name__))
self.instream = instream
self.charstack = []
self.tokenstack = []
self.eof = False
def get_token(self):
"""
This function breaks the time string into lexical units (tokens), which
can be parsed by the parser. Lexical units are demarcated by changes in
the character set, so any continuous string of letters is considered
one unit, any continuous string of numbers is considered one unit.
The main complication arises from the fact that dots ('.') can be used
both as separators (e.g. "Sep.20.2009") or decimal points (e.g.
"4:30:21.447"). As such, it is necessary to read the full context of
any dot-separated strings before breaking it into tokens; as such, this
function maintains a "token stack", for when the ambiguous context
demands that multiple tokens be parsed at once.
"""
if self.tokenstack:
return self.tokenstack.pop(0)
seenletters = False
token = None
state = None
while not self.eof:
# We only realize that we've reached the end of a token when we
# find a character that's not part of the current token - since
# that character may be part of the next token, it's stored in the
# charstack.
if self.charstack:
nextchar = self.charstack.pop(0)
else:
nextchar = self.instream.read(1)
while nextchar == '\x00':
nextchar = self.instream.read(1)
if not nextchar:
self.eof = True
break
elif not state:
# First character of the token - determines if we're starting
# to parse a word, a number or something else.
token = nextchar
if self.isword(nextchar):
state = 'a'
elif self.isnum(nextchar):
state = '0'
elif self.isspace(nextchar):
token = ' '
break # emit token
else:
break # emit token
elif state == 'a':
# If we've already started reading a word, we keep reading
# letters until we find something that's not part of a word.
seenletters = True
if self.isword(nextchar):
token += nextchar
elif nextchar == '.':
token += nextchar
state = 'a.'
else:
self.charstack.append(nextchar)
break # emit token
elif state == '0':
# If we've already started reading a number, we keep reading
# numbers until we find something that doesn't fit.
if self.isnum(nextchar):
token += nextchar
elif nextchar == '.' or (nextchar == ',' and len(token) >= 2):
token += nextchar
state = '0.'
else:
self.charstack.append(nextchar)
break # emit token
elif state == 'a.':
# If we've seen some letters and a dot separator, continue
# parsing, and the tokens will be broken up later.
seenletters = True
if nextchar == '.' or self.isword(nextchar):
token += nextchar
elif self.isnum(nextchar) and token[-1] == '.':
token += nextchar
state = '0.'
else:
self.charstack.append(nextchar)
break # emit token
elif state == '0.':
# If we've seen at least one dot separator, keep going, we'll
# break up the tokens later.
if nextchar == '.' or self.isnum(nextchar):
token += nextchar
elif self.isword(nextchar) and token[-1] == '.':
token += nextchar
state = 'a.'
else:
self.charstack.append(nextchar)
break # emit token
if (state in ('a.', '0.') and (seenletters or token.count('.') > 1 or
token[-1] in '.,')):
l = self._split_decimal.split(token)
token = l[0]
for tok in l[1:]:
if tok:
self.tokenstack.append(tok)
if state == '0.' and token.count('.') == 0:
token = token.replace(',', '.')
return token
def __iter__(self):
return self
def __next__(self):
token = self.get_token()
if token is None:
raise StopIteration
return token
def next(self):
return self.__next__() # Python 2.x support
@classmethod
def split(cls, s):
return list(cls(s))
@classmethod
def isword(cls, nextchar):
""" Whether or not the next character is part of a word """
return nextchar.isalpha()
@classmethod
def isnum(cls, nextchar):
""" Whether the next character is part of a number """
return nextchar.isdigit()
@classmethod
def isspace(cls, nextchar):
""" Whether the next character is whitespace """
return nextchar.isspace()
class _resultbase(object):
def __init__(self):
for attr in self.__slots__:
setattr(self, attr, None)
def _repr(self, classname):
l = []
for attr in self.__slots__:
value = getattr(self, attr)
if value is not None:
l.append("%s=%s" % (attr, repr(value)))
return "%s(%s)" % (classname, ", ".join(l))
def __len__(self):
return (sum(getattr(self, attr) is not None
for attr in self.__slots__))
def __repr__(self):
return self._repr(self.__class__.__name__)
class parserinfo(object):
"""
Class which handles what inputs are accepted. Subclass this to customize
the language and acceptable values for each parameter.
:param dayfirst:
Whether to interpret the first value in an ambiguous 3-integer date
(e.g. 01/05/09) as the day (``True``) or month (``False``). If
``yearfirst`` is set to ``True``, this distinguishes between YDM
and YMD. Default is ``False``.
:param yearfirst:
Whether to interpret the first value in an ambiguous 3-integer date
(e.g. 01/05/09) as the year. If ``True``, the first number is taken
to be the year, otherwise the last number is taken to be the year.
Default is ``False``.
"""
# m from a.m/p.m, t from ISO T separator
JUMP = [" ", ".", ",", ";", "-", "/", "'",
"at", "on", "and", "ad", "m", "t", "of",
"st", "nd", "rd", "th"]
WEEKDAYS = [("Mon", "Monday"),
("Tue", "Tuesday"), # TODO: "Tues"
("Wed", "Wednesday"),
("Thu", "Thursday"), # TODO: "Thurs"
("Fri", "Friday"),
("Sat", "Saturday"),
("Sun", "Sunday")]
MONTHS = [("Jan", "January"),
("Feb", "February"), # TODO: "Febr"
("Mar", "March"),
("Apr", "April"),
("May", "May"),
("Jun", "June"),
("Jul", "July"),
("Aug", "August"),
("Sep", "Sept", "September"),
("Oct", "October"),
("Nov", "November"),
("Dec", "December")]
HMS = [("h", "hour", "hours"),
("m", "minute", "minutes"),
("s", "second", "seconds")]
AMPM = [("am", "a"),
("pm", "p")]
UTCZONE = ["UTC", "GMT", "Z"]
PERTAIN = ["of"]
TZOFFSET = {}
# TODO: ERA = ["AD", "BC", "CE", "BCE", "Stardate",
# "Anno Domini", "Year of Our Lord"]
def __init__(self, dayfirst=False, yearfirst=False):
self._jump = self._convert(self.JUMP)
self._weekdays = self._convert(self.WEEKDAYS)
self._months = self._convert(self.MONTHS)
self._hms = self._convert(self.HMS)
self._ampm = self._convert(self.AMPM)
self._utczone = self._convert(self.UTCZONE)
self._pertain = self._convert(self.PERTAIN)
self.dayfirst = dayfirst
self.yearfirst = yearfirst
self._year = time.localtime().tm_year
self._century = self._year // 100 * 100
def _convert(self, lst):
dct = {}
for i, v in enumerate(lst):
if isinstance(v, tuple):
for v in v:
dct[v.lower()] = i
else:
dct[v.lower()] = i
return dct
def jump(self, name):
return name.lower() in self._jump
def weekday(self, name):
try:
return self._weekdays[name.lower()]
except KeyError:
pass
return None
def month(self, name):
try:
return self._months[name.lower()] + 1
except KeyError:
pass
return None
def hms(self, name):
try:
return self._hms[name.lower()]
except KeyError:
return None
def ampm(self, name):
try:
return self._ampm[name.lower()]
except KeyError:
return None
def pertain(self, name):
return name.lower() in self._pertain
def utczone(self, name):
return name.lower() in self._utczone
def tzoffset(self, name):
if name in self._utczone:
return 0
return self.TZOFFSET.get(name)
def convertyear(self, year, century_specified=False):
"""
Converts two-digit years to year within [-50, 49]
range of self._year (current local time)
"""
# Function contract is that the year is always positive
assert year >= 0
if year < 100 and not century_specified:
# assume current century to start
year += self._century
if year >= self._year + 50: # if too far in future
year -= 100
elif year < self._year - 50: # if too far in past
year += 100
return year
def validate(self, res):
# move to info
if res.year is not None:
res.year = self.convertyear(res.year, res.century_specified)
if res.tzoffset == 0 and not res.tzname or res.tzname == 'Z':
res.tzname = "UTC"
res.tzoffset = 0
elif res.tzoffset != 0 and res.tzname and self.utczone(res.tzname):
res.tzoffset = 0
return True
class _ymd(list):
def __init__(self, *args, **kwargs):
super(self.__class__, self).__init__(*args, **kwargs)
self.century_specified = False
self.dstridx = None
self.mstridx = None
self.ystridx = None
@property
def has_year(self):
return self.ystridx is not None
@property
def has_month(self):
return self.mstridx is not None
@property
def has_day(self):
return self.dstridx is not None
def could_be_day(self, value):
if self.has_day:
return False
elif not self.has_month:
return 1 <= value <= 31
elif not self.has_year:
# Be permissive, assume leapyear
month = self[self.mstridx]
return 1 <= value <= monthrange(2000, month)[1]
else:
month = self[self.mstridx]
year = self[self.ystridx]
return 1 <= value <= monthrange(year, month)[1]
def append(self, val, label=None):
if hasattr(val, '__len__'):
if val.isdigit() and len(val) > 2:
self.century_specified = True
if label not in [None, 'Y']: # pragma: no cover
raise ValueError(label)
label = 'Y'
elif val > 100:
self.century_specified = True
if label not in [None, 'Y']: # pragma: no cover
raise ValueError(label)
label = 'Y'
super(self.__class__, self).append(int(val))
if label == 'M':
if self.has_month:
raise ValueError('Month is already set')
self.mstridx = len(self) - 1
elif label == 'D':
if self.has_day:
raise ValueError('Day is already set')
self.dstridx = len(self) - 1
elif label == 'Y':
if self.has_year:
raise ValueError('Year is already set')
self.ystridx = len(self) - 1
def _resolve_from_stridxs(self, strids):
"""
Try to resolve the identities of year/month/day elements using
ystridx, mstridx, and dstridx, if enough of these are specified.
"""
if len(self) == 3 and len(strids) == 2:
# we can back out the remaining stridx value
missing = [x for x in range(3) if x not in strids.values()]
key = [x for x in ['y', 'm', 'd'] if x not in strids]
assert len(missing) == len(key) == 1
key = key[0]
val = missing[0]
strids[key] = val
assert len(self) == len(strids) # otherwise this should not be called
out = {key: self[strids[key]] for key in strids}
return (out.get('y'), out.get('m'), out.get('d'))
def resolve_ymd(self, yearfirst, dayfirst):
len_ymd = len(self)
year, month, day = (None, None, None)
strids = (('y', self.ystridx),
('m', self.mstridx),
('d', self.dstridx))
strids = {key: val for key, val in strids if val is not None}
if (len(self) == len(strids) > 0 or
(len(self) == 3 and len(strids) == 2)):
return self._resolve_from_stridxs(strids)
mstridx = self.mstridx
if len_ymd > 3:
raise ValueError("More than three YMD values")
elif len_ymd == 1 or (mstridx is not None and len_ymd == 2):
# One member, or two members with a month string
if mstridx is not None:
month = self[mstridx]
# since mstridx is 0 or 1, self[mstridx-1] always
# looks up the other element
other = self[mstridx - 1]
else:
other = self[0]
if len_ymd > 1 or mstridx is None:
if other > 31:
year = other
else:
day = other
elif len_ymd == 2:
# Two members with numbers
if self[0] > 31:
# 99-01
year, month = self
elif self[1] > 31:
# 01-99
month, year = self
elif dayfirst and self[1] <= 12:
# 13-01
day, month = self
else:
# 01-13
month, day = self
elif len_ymd == 3:
# Three members
if mstridx == 0:
if self[1] > 31:
# Apr-2003-25
month, year, day = self
else:
month, day, year = self
elif mstridx == 1:
if self[0] > 31 or (yearfirst and self[2] <= 31):
# 99-Jan-01
year, month, day = self
else:
# 01-Jan-01
# Give precendence to day-first, since
# two-digit years is usually hand-written.
day, month, year = self
elif mstridx == 2:
# WTF!?
if self[1] > 31:
# 01-99-Jan
day, year, month = self
else:
# 99-01-Jan
year, day, month = self
else:
if (self[0] > 31 or
self.ystridx == 0 or
(yearfirst and self[1] <= 12 and self[2] <= 31)):
# 99-01-01
if dayfirst and self[2] <= 12:
year, day, month = self
else:
year, month, day = self
elif self[0] > 12 or (dayfirst and self[1] <= 12):
# 13-01-01
day, month, year = self
else:
# 01-13-01
month, day, year = self
return year, month, day
class parser(object):
def __init__(self, info=None):
self.info = info or parserinfo()
def parse(self, timestr, default=None,
ignoretz=False, tzinfos=None, **kwargs):
"""
Parse the date/time string into a :class:`datetime.datetime` object.
:param timestr:
Any date/time string using the supported formats.
:param default:
The default datetime object, if this is a datetime object and not
``None``, elements specified in ``timestr`` replace elements in the
default object.
:param ignoretz:
If set ``True``, time zones in parsed strings are ignored and a
naive :class:`datetime.datetime` object is returned.
:param tzinfos:
Additional time zone names / aliases which may be present in the
string. This argument maps time zone names (and optionally offsets
from those time zones) to time zones. This parameter can be a
dictionary with timezone aliases mapping time zone names to time
zones or a function taking two parameters (``tzname`` and
``tzoffset``) and returning a time zone.
The timezones to which the names are mapped can be an integer
offset from UTC in seconds or a :class:`tzinfo` object.
.. doctest::
:options: +NORMALIZE_WHITESPACE
>>> from dateutil.parser import parse
>>> from dateutil.tz import gettz
>>> tzinfos = {"BRST": -7200, "CST": gettz("America/Chicago")}
>>> parse("2012-01-19 17:21:00 BRST", tzinfos=tzinfos)
datetime.datetime(2012, 1, 19, 17, 21, tzinfo=tzoffset(u'BRST', -7200))
>>> parse("2012-01-19 17:21:00 CST", tzinfos=tzinfos)
datetime.datetime(2012, 1, 19, 17, 21,
tzinfo=tzfile('/usr/share/zoneinfo/America/Chicago'))
This parameter is ignored if ``ignoretz`` is set.
:param \\*\\*kwargs:
Keyword arguments as passed to ``_parse()``.
:return:
Returns a :class:`datetime.datetime` object or, if the
``fuzzy_with_tokens`` option is ``True``, returns a tuple, the
first element being a :class:`datetime.datetime` object, the second
a tuple containing the fuzzy tokens.
:raises ValueError:
Raised for invalid or unknown string format, if the provided
:class:`tzinfo` is not in a valid format, or if an invalid date
would be created.
:raises TypeError:
Raised for non-string or character stream input.
:raises OverflowError:
Raised if the parsed date exceeds the largest valid C integer on
your system.
"""
if default is None:
default = datetime.datetime.now().replace(hour=0, minute=0,
second=0, microsecond=0)
res, skipped_tokens = self._parse(timestr, **kwargs)
if res is None:
raise ValueError("Unknown string format:", timestr)
if len(res) == 0:
raise ValueError("String does not contain a date:", timestr)
ret = self._build_naive(res, default)
if not ignoretz:
ret = self._build_tzaware(ret, res, tzinfos)
if kwargs.get('fuzzy_with_tokens', False):
return ret, skipped_tokens
else:
return ret
class _result(_resultbase):
__slots__ = ["year", "month", "day", "weekday",
"hour", "minute", "second", "microsecond",
"tzname", "tzoffset", "ampm","any_unused_tokens"]
def _parse(self, timestr, dayfirst=None, yearfirst=None, fuzzy=False,
fuzzy_with_tokens=False):
"""
Private method which performs the heavy lifting of parsing, called from
``parse()``, which passes on its ``kwargs`` to this function.
:param timestr:
The string to parse.
:param dayfirst:
Whether to interpret the first value in an ambiguous 3-integer date
(e.g. 01/05/09) as the day (``True``) or month (``False``). If
``yearfirst`` is set to ``True``, this distinguishes between YDM
and YMD. If set to ``None``, this value is retrieved from the
current :class:`parserinfo` object (which itself defaults to
``False``).
:param yearfirst:
Whether to interpret the first value in an ambiguous 3-integer date
(e.g. 01/05/09) as the year. If ``True``, the first number is taken
to be the year, otherwise the last number is taken to be the year.
If this is set to ``None``, the value is retrieved from the current
:class:`parserinfo` object (which itself defaults to ``False``).
:param fuzzy:
Whether to allow fuzzy parsing, allowing for string like "Today is
January 1, 2047 at 8:21:00AM".
:param fuzzy_with_tokens:
If ``True``, ``fuzzy`` is automatically set to True, and the parser
will return a tuple where the first element is the parsed
:class:`datetime.datetime` datetimestamp and the second element is
a tuple containing the portions of the string which were ignored:
.. doctest::
>>> from dateutil.parser import parse
>>> parse("Today is January 1, 2047 at 8:21:00AM", fuzzy_with_tokens=True)
(datetime.datetime(2047, 1, 1, 8, 21), (u'Today is ', u' ', u'at '))
"""
if fuzzy_with_tokens:
fuzzy = True
info = self.info
if dayfirst is None:
dayfirst = info.dayfirst
if yearfirst is None:
yearfirst = info.yearfirst
res = self._result()
l = _timelex.split(timestr) # Splits the timestr into tokens
skipped_idxs = []
# year/month/day list
ymd = _ymd()
len_l = len(l)
i = 0
try:
while i < len_l:
# Check if it's a number
value_repr = l[i]
try:
value = float(value_repr)
except ValueError:
value = None
if value is not None:
# Numeric token
i = self._parse_numeric_token(l, i, info, ymd, res, fuzzy)
# Check weekday
elif info.weekday(l[i]) is not None:
value = info.weekday(l[i])
res.weekday = value
# Check month name
elif info.month(l[i]) is not None:
value = info.month(l[i])
ymd.append(value, 'M')
if i + 1 < len_l:
if l[i + 1] in ('-', '/'):
# Jan-01[-99]
sep = l[i + 1]
ymd.append(l[i + 2])
if i + 3 < len_l and l[i + 3] == sep:
# Jan-01-99
ymd.append(l[i + 4])
i += 2
i += 2
elif (i + 4 < len_l and l[i + 1] == l[i + 3] == ' ' and
info.pertain(l[i + 2])):
# Jan of 01
# In this case, 01 is clearly year
if l[i + 4].isdigit():
# Convert it here to become unambiguous
value = int(l[i + 4])
year = str(info.convertyear(value))
ymd.append(year, 'Y')
else:
# Wrong guess
pass
# TODO: not hit in tests
i += 4
# Check am/pm
elif info.ampm(l[i]) is not None:
value = info.ampm(l[i])
val_is_ampm = self._ampm_valid(res.hour, res.ampm, fuzzy)
if val_is_ampm:
res.hour = self._adjust_ampm(res.hour, value)
res.ampm = value
elif fuzzy:
skipped_idxs.append(i)
# Check for a timezone name
elif self._could_be_tzname(res.hour, res.tzname, res.tzoffset, l[i]):
res.tzname = l[i]
res.tzoffset = info.tzoffset(res.tzname)
# Check for something like GMT+3, or BRST+3. Notice
# that it doesn't mean "I am 3 hours after GMT", but
# "my time +3 is GMT". If found, we reverse the
# logic so that timezone parsing code will get it
# right.
if i + 1 < len_l and l[i + 1] in ('+', '-'):
l[i + 1] = ('+', '-')[l[i + 1] == '+']
res.tzoffset = None
if info.utczone(res.tzname):
# With something like GMT+3, the timezone
# is *not* GMT.
res.tzname = None
# Check for a numbered timezone
elif res.hour is not None and l[i] in ('+', '-'):
signal = (-1, 1)[l[i] == '+']
len_li = len(l[i + 1])
# TODO: check that l[i + 1] is integer?
if len_li == 4:
# -0300
hour_offset = int(l[i + 1][:2])
min_offset = int(l[i + 1][2:])
elif i + 2 < len_l and l[i + 2] == ':':
# -03:00
hour_offset = int(l[i + 1])
min_offset = int(l[i + 3]) # TODO: Check that l[i+3] is minute-like?
i += 2
elif len_li <= 2:
# -[0]3
hour_offset = int(l[i + 1][:2])
min_offset = 0
else:
raise ValueError(timestr)
res.tzoffset = signal * (hour_offset * 3600 + min_offset * 60)
# Look for a timezone name between parenthesis
if (i + 5 < len_l and
info.jump(l[i + 2]) and l[i + 3] == '(' and
l[i + 5] == ')' and
3 <= len(l[i + 4]) and
self._could_be_tzname(res.hour, res.tzname,
None, l[i + 4])):
# -0300 (BRST)
res.tzname = l[i + 4]
i += 4
i += 1
# Check jumps
elif not (info.jump(l[i]) or fuzzy):
raise ValueError(timestr)
else:
skipped_idxs.append(i)
i += 1
# Process year/month/day
year, month, day = ymd.resolve_ymd(yearfirst, dayfirst)
res.century_specified = ymd.century_specified
res.year = year
res.month = month
res.day = day
except (IndexError, ValueError):
return None, None
if not info.validate(res):
return None, None
if fuzzy_with_tokens:
skipped_tokens = self._recombine_skipped(l, skipped_idxs)
return res, tuple(skipped_tokens)
else:
return res, None
def _parse_numeric_token(self, tokens, idx, info, ymd, res, fuzzy):
# Token is a number
value_repr = tokens[idx]
try:
value = self._to_decimal(value_repr)
except Exception as e:
six.raise_from(ValueError('Unknown numeric token'), e)
len_li = len(value_repr)
len_l = len(tokens)
if (len(ymd) == 3 and len_li in (2, 4) and
res.hour is None and
(idx + 1 >= len_l or
(tokens[idx + 1] != ':' and
info.hms(tokens[idx + 1]) is None))):
# 19990101T23[59]
s = tokens[idx]
res.hour = int(s[:2])
if len_li == 4:
res.minute = int(s[2:])
elif len_li == 6 or (len_li > 6 and tokens[idx].find('.') == 6):
# YYMMDD or HHMMSS[.ss]
s = tokens[idx]
if not ymd and '.' not in tokens[idx]:
ymd.append(s[:2])
ymd.append(s[2:4])
ymd.append(s[4:])
else:
# 19990101T235959[.59]
# TODO: Check if res attributes already set.
res.hour = int(s[:2])
res.minute = int(s[2:4])
res.second, res.microsecond = self._parsems(s[4:])
elif len_li in (8, 12, 14):
# YYYYMMDD
s = tokens[idx]
ymd.append(s[:4], 'Y')
ymd.append(s[4:6])
ymd.append(s[6:8])
if len_li > 8:
res.hour = int(s[8:10])
res.minute = int(s[10:12])
if len_li > 12:
res.second = int(s[12:])
elif self._find_hms_idx(idx, tokens, info, allow_jump=True) is not None:
# HH[ ]h or MM[ ]m or SS[.ss][ ]s
hms_idx = self._find_hms_idx(idx, tokens, info, allow_jump=True)
(idx, hms) = self._parse_hms(idx, tokens, info, hms_idx)
if hms is not None:
# TODO: checking that hour/minute/second are not
# already set?
self._assign_hms(res, value_repr, hms)
elif idx + 2 < len_l and tokens[idx + 1] == ':':
# HH:MM[:SS[.ss]]
res.hour = int(value)
value = self._to_decimal(tokens[idx + 2]) # TODO: try/except for this?
(res.minute, res.second) = self._parse_min_sec(value)
if idx + 4 < len_l and tokens[idx + 3] == ':':
res.second, res.microsecond = self._parsems(tokens[idx + 4])
idx += 2
idx += 2
elif idx + 1 < len_l and tokens[idx + 1] in ('-', '/', '.'):
sep = tokens[idx + 1]
ymd.append(value_repr)
if idx + 2 < len_l and not info.jump(tokens[idx + 2]):
if tokens[idx + 2].isdigit():
# 01-01[-01]
ymd.append(tokens[idx + 2])
else:
# 01-Jan[-01]
value = info.month(tokens[idx + 2])
if value is not None:
ymd.append(value, 'M')
else:
raise ValueError()
if idx + 3 < len_l and tokens[idx + 3] == sep:
# We have three members
value = info.month(tokens[idx + 4])
if value is not None:
ymd.append(value, 'M')
else:
ymd.append(tokens[idx + 4])
idx += 2
idx += 1
idx += 1
elif idx + 1 >= len_l or info.jump(tokens[idx + 1]):
if idx + 2 < len_l and info.ampm(tokens[idx + 2]) is not None:
# 12 am
hour = int(value)
res.hour = self._adjust_ampm(hour, info.ampm(tokens[idx + 2]))
idx += 1
else:
# Year, month or day
ymd.append(value)
idx += 1
elif info.ampm(tokens[idx + 1]) is not None and (0 <= value < 24):
# 12am
hour = int(value)
res.hour = self._adjust_ampm(hour, info.ampm(tokens[idx + 1]))
idx += 1
elif ymd.could_be_day(value):
ymd.append(value)
elif not fuzzy:
raise ValueError()
return idx
def _find_hms_idx(self, idx, tokens, info, allow_jump):
len_l = len(tokens)
if idx+1 < len_l and info.hms(tokens[idx+1]) is not None:
# There is an "h", "m", or "s" label following this token. We take
# assign the upcoming label to the current token.
# e.g. the "12" in 12h"
hms_idx = idx + 1
elif (allow_jump and idx+2 < len_l and tokens[idx+1] == ' ' and
info.hms(tokens[idx+2]) is not None):
# There is a space and then an "h", "m", or "s" label.
# e.g. the "12" in "12 h"
hms_idx = idx + 2
elif idx > 0 and info.hms(tokens[idx-1]) is not None:
# There is a "h", "m", or "s" preceeding this token. Since neither
# of the previous cases was hit, there is no label following this
# token, so we use the previous label.
# e.g. the "04" in "12h04"
hms_idx = idx-1
elif (1 < idx == len_l-1 and tokens[idx-1] == ' ' and
info.hms(tokens[idx-2]) is not None):
# If we are looking at the final token, we allow for a
# backward-looking check to skip over a space.
# TODO: Are we sure this is the right condition here?
hms_idx = idx - 2
else:
hms_idx = None
return hms_idx
def _assign_hms(self, res, value_repr, hms):
# See GH issue #427, fixing float rounding
value = self._to_decimal(value_repr)
if hms == 0:
# Hour
res.hour = int(value)
if value % 1:
res.minute = int(60*(value % 1))
elif hms == 1:
(res.minute, res.second) = self._parse_min_sec(value)
elif hms == 2:
(res.second, res.microsecond) = self._parsems(value_repr)
def _could_be_tzname(self, hour, tzname, tzoffset, token):
return (hour is not None and
tzname is None and
tzoffset is None and
len(token) <= 5 and
all(x in string.ascii_uppercase for x in token))
def _ampm_valid(self, hour, ampm, fuzzy):
"""
For fuzzy parsing, 'a' or 'am' (both valid English words)
may erroneously trigger the AM/PM flag. Deal with that
here.
"""
val_is_ampm = True
# If there's already an AM/PM flag, this one isn't one.
if fuzzy and ampm is not None:
val_is_ampm = False
# If AM/PM is found and hour is not, raise a ValueError
if hour is None:
if fuzzy:
val_is_ampm = False
else:
raise ValueError('No hour specified with AM or PM flag.')
elif not 0 <= hour <= 12:
# If AM/PM is found, it's a 12 hour clock, so raise
# an error for invalid range
if fuzzy:
val_is_ampm = False
else:
raise ValueError('Invalid hour specified for 12-hour clock.')
return val_is_ampm
def _adjust_ampm(self, hour, ampm):
if hour < 12 and ampm == 1:
hour += 12
elif hour == 12 and ampm == 0:
hour = 0
return hour
def _parse_min_sec(self, value):
# TODO: Every usage of this function sets res.second to the return
# value. Are there any cases where second will be returned as None and
# we *dont* want to set res.second = None?
minute = int(value)
second = None
sec_remainder = value % 1
if sec_remainder:
second = int(60 * sec_remainder)
return (minute, second)
def _parsems(self, value):
"""Parse a I[.F] seconds value into (seconds, microseconds)."""
if "." not in value:
return int(value), 0
else:
i, f = value.split(".")
return int(i), int(f.ljust(6, "0")[:6])
def _parse_hms(self, idx, tokens, info, hms_idx):
# TODO: Is this going to admit a lot of false-positives for when we
# just happen to have digits and "h", "m" or "s" characters in non-date
# text? I guess hex hashes won't have that problem, but there's plenty
# of random junk out there.
if hms_idx is None:
hms = None
new_idx = idx
elif hms_idx > idx:
hms = info.hms(tokens[hms_idx])
new_idx = hms_idx
else:
# Looking backwards, increment one.
hms = info.hms(tokens[hms_idx]) + 1
new_idx = idx
return (new_idx, hms)
def _recombine_skipped(self, tokens, skipped_idxs):
"""
>>> tokens = ["foo", " ", "bar", " ", "19June2000", "baz"]
>>> skipped_idxs = [0, 1, 2, 5]
>>> _recombine_skipped(tokens, skipped_idxs)
["foo bar", "baz"]
"""
skipped_tokens = []
for i, idx in enumerate(sorted(skipped_idxs)):
if i > 0 and idx - 1 == skipped_idxs[i - 1]:
skipped_tokens[-1] = skipped_tokens[-1] + tokens[idx]
else:
skipped_tokens.append(tokens[idx])
return skipped_tokens
def _build_tzinfo(self, tzinfos, tzname, tzoffset):
if callable(tzinfos):
tzdata = tzinfos(tzname, tzoffset)
else:
tzdata = tzinfos.get(tzname)
# handle case where tzinfo is paased an options that returns None
# eg tzinfos = {'BRST' : None}
if isinstance(tzdata, datetime.tzinfo) or tzdata is None:
tzinfo = tzdata
elif isinstance(tzdata, text_type):
tzinfo = tz.tzstr(tzdata)
elif isinstance(tzdata, integer_types):
tzinfo = tz.tzoffset(tzname, tzdata)
return tzinfo
def _build_tzaware(self, naive, res, tzinfos):
if (callable(tzinfos) or (tzinfos and res.tzname in tzinfos)):
tzinfo = self._build_tzinfo(tzinfos, res.tzname, res.tzoffset)
aware = naive.replace(tzinfo=tzinfo)
aware = self._assign_tzname(aware, res.tzname)
elif res.tzname and res.tzname in time.tzname:
aware = naive.replace(tzinfo=tz.tzlocal())
# Handle ambiguous local datetime
aware = self._assign_tzname(aware, res.tzname)
# This is mostly relevant for winter GMT zones parsed in the UK
if (aware.tzname() != res.tzname and
res.tzname in self.info.UTCZONE):
aware = aware.replace(tzinfo=tz.tzutc())
elif res.tzoffset == 0:
aware = naive.replace(tzinfo=tz.tzutc())
elif res.tzoffset:
aware = naive.replace(tzinfo=tz.tzoffset(res.tzname, res.tzoffset))
elif not res.tzname and not res.tzoffset:
# i.e. no timezone information was found.
aware = naive
elif res.tzname:
# tz-like string was parsed but we don't know what to do
# with it
warnings.warn("tzname {tzname} identified but not understood. "
"Pass `tzinfos` argument in order to correctly "
"return a timezone-aware datetime. In a future "
"version, this will raise an "
"exception.".format(tzname=res.tzname),
category=UnknownTimezoneWarning)
aware = naive
return aware
def _build_naive(self, res, default):
repl = {}
for attr in ("year", "month", "day", "hour",
"minute", "second", "microsecond"):
value = getattr(res, attr)
if value is not None:
repl[attr] = value
if 'day' not in repl:
# If the default day exceeds the last day of the month, fall back
# to the end of the month.
cyear = default.year if res.year is None else res.year
cmonth = default.month if res.month is None else res.month
cday = default.day if res.day is None else res.day
if cday > monthrange(cyear, cmonth)[1]:
repl['day'] = monthrange(cyear, cmonth)[1]
naive = default.replace(**repl)
if res.weekday is not None and not res.day:
naive = naive + relativedelta.relativedelta(weekday=res.weekday)
return naive
def _assign_tzname(self, dt, tzname):
if dt.tzname() != tzname:
new_dt = tz.enfold(dt, fold=1)
if new_dt.tzname() == tzname:
return new_dt
return dt
def _to_decimal(self, val):
try:
decimal_value = Decimal(val)
# See GH 662, edge case, infinite value should not be converted via `_to_decimal`
if not decimal_value.is_finite():
raise ValueError("Converted decimal value is infinite or NaN")
except Exception as e:
msg = "Could not convert %s to decimal" % val
six.raise_from(ValueError(msg), e)
else:
return decimal_value
DEFAULTPARSER = parser()
def parse(timestr, parserinfo=None, **kwargs):
"""
Parse a string in one of the supported formats, using the
``parserinfo`` parameters.
:param timestr:
A string containing a date/time stamp.
:param parserinfo:
A :class:`parserinfo` object containing parameters for the parser.
If ``None``, the default arguments to the :class:`parserinfo`
constructor are used.
The ``**kwargs`` parameter takes the following keyword arguments:
:param default:
The default datetime object, if this is a datetime object and not
``None``, elements specified in ``timestr`` replace elements in the
default object.
:param ignoretz:
If set ``True``, time zones in parsed strings are ignored and a naive
:class:`datetime` object is returned.
:param tzinfos:
Additional time zone names / aliases which may be present in the
string. This argument maps time zone names (and optionally offsets
from those time zones) to time zones. This parameter can be a
dictionary with timezone aliases mapping time zone names to time
zones or a function taking two parameters (``tzname`` and
``tzoffset``) and returning a time zone.
The timezones to which the names are mapped can be an integer
offset from UTC in seconds or a :class:`tzinfo` object.
.. doctest::
:options: +NORMALIZE_WHITESPACE
>>> from dateutil.parser import parse
>>> from dateutil.tz import gettz
>>> tzinfos = {"BRST": -7200, "CST": gettz("America/Chicago")}
>>> parse("2012-01-19 17:21:00 BRST", tzinfos=tzinfos)
datetime.datetime(2012, 1, 19, 17, 21, tzinfo=tzoffset(u'BRST', -7200))
>>> parse("2012-01-19 17:21:00 CST", tzinfos=tzinfos)
datetime.datetime(2012, 1, 19, 17, 21,
tzinfo=tzfile('/usr/share/zoneinfo/America/Chicago'))
This parameter is ignored if ``ignoretz`` is set.
:param dayfirst:
Whether to interpret the first value in an ambiguous 3-integer date
(e.g. 01/05/09) as the day (``True``) or month (``False``). If
``yearfirst`` is set to ``True``, this distinguishes between YDM and
YMD. If set to ``None``, this value is retrieved from the current
:class:`parserinfo` object (which itself defaults to ``False``).
:param yearfirst:
Whether to interpret the first value in an ambiguous 3-integer date
(e.g. 01/05/09) as the year. If ``True``, the first number is taken to
be the year, otherwise the last number is taken to be the year. If
this is set to ``None``, the value is retrieved from the current
:class:`parserinfo` object (which itself defaults to ``False``).
:param fuzzy:
Whether to allow fuzzy parsing, allowing for string like "Today is
January 1, 2047 at 8:21:00AM".
:param fuzzy_with_tokens:
If ``True``, ``fuzzy`` is automatically set to True, and the parser
will return a tuple where the first element is the parsed
:class:`datetime.datetime` datetimestamp and the second element is
a tuple containing the portions of the string which were ignored:
.. doctest::
>>> from dateutil.parser import parse
>>> parse("Today is January 1, 2047 at 8:21:00AM", fuzzy_with_tokens=True)
(datetime.datetime(2047, 1, 1, 8, 21), (u'Today is ', u' ', u'at '))
:return:
Returns a :class:`datetime.datetime` object or, if the
``fuzzy_with_tokens`` option is ``True``, returns a tuple, the
first element being a :class:`datetime.datetime` object, the second
a tuple containing the fuzzy tokens.
:raises ValueError:
Raised for invalid or unknown string format, if the provided
:class:`tzinfo` is not in a valid format, or if an invalid date
would be created.
:raises OverflowError:
Raised if the parsed date exceeds the largest valid C integer on
your system.
"""
if parserinfo:
return parser(parserinfo).parse(timestr, **kwargs)
else:
return DEFAULTPARSER.parse(timestr, **kwargs)
class _tzparser(object):
class _result(_resultbase):
__slots__ = ["stdabbr", "stdoffset", "dstabbr", "dstoffset",
"start", "end"]
class _attr(_resultbase):
__slots__ = ["month", "week", "weekday",
"yday", "jyday", "day", "time"]
def __repr__(self):
return self._repr("")
def __init__(self):
_resultbase.__init__(self)
self.start = self._attr()
self.end = self._attr()
def parse(self, tzstr):
res = self._result()
l = [x for x in re.split(r'([,:.]|[a-zA-Z]+|[0-9]+)',tzstr) if x]
used_idxs = list()
try:
len_l = len(l)
i = 0
while i < len_l:
# BRST+3[BRDT[+2]]
j = i
while j < len_l and not [x for x in l[j]
if x in "0123456789:,-+"]:
j += 1
if j != i:
if not res.stdabbr:
offattr = "stdoffset"
res.stdabbr = "".join(l[i:j])
else:
offattr = "dstoffset"
res.dstabbr = "".join(l[i:j])
for ii in range(j):
used_idxs.append(ii)
i = j
if (i < len_l and (l[i] in ('+', '-') or l[i][0] in
"0123456789")):
if l[i] in ('+', '-'):
# Yes, that's right. See the TZ variable
# documentation.
signal = (1, -1)[l[i] == '+']
used_idxs.append(i)
i += 1
else:
signal = -1
len_li = len(l[i])
if len_li == 4:
# -0300
setattr(res, offattr, (int(l[i][:2]) * 3600 +
int(l[i][2:]) * 60) * signal)
elif i + 1 < len_l and l[i + 1] == ':':
# -03:00
setattr(res, offattr,
(int(l[i]) * 3600 +
int(l[i + 2]) * 60) * signal)
used_idxs.append(i)
i += 2
elif len_li <= 2:
# -[0]3
setattr(res, offattr,
int(l[i][:2]) * 3600 * signal)
else:
return None
used_idxs.append(i)
i += 1
if res.dstabbr:
break
else:
break
if i < len_l:
for j in range(i, len_l):
if l[j] == ';':
l[j] = ','
assert l[i] == ','
i += 1
if i >= len_l:
pass
elif (8 <= l.count(',') <= 9 and
not [y for x in l[i:] if x != ','
for y in x if y not in "0123456789+-"]):
# GMT0BST,3,0,30,3600,10,0,26,7200[,3600]
for x in (res.start, res.end):
x.month = int(l[i])
used_idxs.append(i)
i += 2
if l[i] == '-':
value = int(l[i + 1]) * -1
used_idxs.append(i)
i += 1
else:
value = int(l[i])
used_idxs.append(i)
i += 2
if value:
x.week = value
x.weekday = (int(l[i]) - 1) % 7
else:
x.day = int(l[i])
used_idxs.append(i)
i += 2
x.time = int(l[i])
used_idxs.append(i)
i += 2
if i < len_l:
if l[i] in ('-', '+'):
signal = (-1, 1)[l[i] == "+"]
used_idxs.append(i)
i += 1
else:
signal = 1
used_idxs.append(i)
res.dstoffset = (res.stdoffset + int(l[i]) * signal)
# This was a made-up format that is not in normal use
warn(('Parsed time zone "%s"' % tzstr) +
'is in a non-standard dateutil-specific format, which ' +
'is now deprecated; support for parsing this format ' +
'will be removed in future versions. It is recommended ' +
'that you switch to a standard format like the GNU ' +
'TZ variable format.', tz.DeprecatedTzFormatWarning)
elif (l.count(',') == 2 and l[i:].count('/') <= 2 and
not [y for x in l[i:] if x not in (',', '/', 'J', 'M',
'.', '-', ':')
for y in x if y not in "0123456789"]):
for x in (res.start, res.end):
if l[i] == 'J':
# non-leap year day (1 based)
used_idxs.append(i)
i += 1
x.jyday = int(l[i])
elif l[i] == 'M':
# month[-.]week[-.]weekday
used_idxs.append(i)
i += 1
x.month = int(l[i])
used_idxs.append(i)
i += 1
assert l[i] in ('-', '.')
used_idxs.append(i)
i += 1
x.week = int(l[i])
if x.week == 5:
x.week = -1
used_idxs.append(i)
i += 1
assert l[i] in ('-', '.')
used_idxs.append(i)
i += 1
x.weekday = (int(l[i]) - 1) % 7
else:
# year day (zero based)
x.yday = int(l[i]) + 1
used_idxs.append(i)
i += 1
if i < len_l and l[i] == '/':
used_idxs.append(i)
i += 1
# start time
len_li = len(l[i])
if len_li == 4:
# -0300
x.time = (int(l[i][:2]) * 3600 +
int(l[i][2:]) * 60)
elif i + 1 < len_l and l[i + 1] == ':':
# -03:00
x.time = int(l[i]) * 3600 + int(l[i + 2]) * 60
used_idxs.append(i)
i += 2
if i + 1 < len_l and l[i + 1] == ':':
used_idxs.append(i)
i += 2
x.time += int(l[i])
elif len_li <= 2:
# -[0]3
x.time = (int(l[i][:2]) * 3600)
else:
return None
used_idxs.append(i)
i += 1
assert i == len_l or l[i] == ','
i += 1
assert i >= len_l
except (IndexError, ValueError, AssertionError):
return None
unused_idxs = set(range(len_l)).difference(used_idxs)
res.any_unused_tokens = not {l[n] for n in unused_idxs}.issubset({",",":"})
return res
DEFAULTTZPARSER = _tzparser()
def _parsetz(tzstr):
return DEFAULTTZPARSER.parse(tzstr)
class UnknownTimezoneWarning(RuntimeWarning):
"""Raised when the parser finds a timezone it cannot parse into a tzinfo"""
# vim:ts=4:sw=4:et
| 57,607 | 35.483851 | 97 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/dateutil/parser/isoparser.py
|
# -*- coding: utf-8 -*-
"""
This module offers a parser for ISO-8601 strings
It is intended to support all valid date, time and datetime formats per the
ISO-8601 specification.
..versionadded:: 2.7.0
"""
from datetime import datetime, timedelta, time, date
import calendar
from dateutil import tz
from functools import wraps
import re
import six
__all__ = ["isoparse", "isoparser"]
def _takes_ascii(f):
@wraps(f)
def func(self, str_in, *args, **kwargs):
# If it's a stream, read the whole thing
str_in = getattr(str_in, 'read', lambda: str_in)()
# If it's unicode, turn it into bytes, since ISO-8601 only covers ASCII
if isinstance(str_in, six.text_type):
# ASCII is the same in UTF-8
try:
str_in = str_in.encode('ascii')
except UnicodeEncodeError as e:
msg = 'ISO-8601 strings should contain only ASCII characters'
six.raise_from(ValueError(msg), e)
return f(self, str_in, *args, **kwargs)
return func
class isoparser(object):
def __init__(self, sep=None):
"""
:param sep:
A single character that separates date and time portions. If
``None``, the parser will accept any single character.
For strict ISO-8601 adherence, pass ``'T'``.
"""
if sep is not None:
if (len(sep) != 1 or ord(sep) >= 128 or sep in '0123456789'):
raise ValueError('Separator must be a single, non-numeric ' +
'ASCII character')
sep = sep.encode('ascii')
self._sep = sep
@_takes_ascii
def isoparse(self, dt_str):
"""
Parse an ISO-8601 datetime string into a :class:`datetime.datetime`.
An ISO-8601 datetime string consists of a date portion, followed
optionally by a time portion - the date and time portions are separated
by a single character separator, which is ``T`` in the official
standard. Incomplete date formats (such as ``YYYY-MM``) may *not* be
combined with a time portion.
Supported date formats are:
Common:
- ``YYYY``
- ``YYYY-MM`` or ``YYYYMM``
- ``YYYY-MM-DD`` or ``YYYYMMDD``
Uncommon:
- ``YYYY-Www`` or ``YYYYWww`` - ISO week (day defaults to 0)
- ``YYYY-Www-D`` or ``YYYYWwwD`` - ISO week and day
The ISO week and day numbering follows the same logic as
:func:`datetime.date.isocalendar`.
Supported time formats are:
- ``hh``
- ``hh:mm`` or ``hhmm``
- ``hh:mm:ss`` or ``hhmmss``
- ``hh:mm:ss.sss`` or ``hh:mm:ss.ssssss`` (3-6 sub-second digits)
Midnight is a special case for `hh`, as the standard supports both
00:00 and 24:00 as a representation.
.. caution::
Support for fractional components other than seconds is part of the
ISO-8601 standard, but is not currently implemented in this parser.
Supported time zone offset formats are:
- `Z` (UTC)
- `±HH:MM`
- `±HHMM`
- `±HH`
Offsets will be represented as :class:`dateutil.tz.tzoffset` objects,
with the exception of UTC, which will be represented as
:class:`dateutil.tz.tzutc`. Time zone offsets equivalent to UTC (such
as `+00:00`) will also be represented as :class:`dateutil.tz.tzutc`.
:param dt_str:
A string or stream containing only an ISO-8601 datetime string
:return:
Returns a :class:`datetime.datetime` representing the string.
Unspecified components default to their lowest value.
.. warning::
As of version 2.7.0, the strictness of the parser should not be
considered a stable part of the contract. Any valid ISO-8601 string
that parses correctly with the default settings will continue to
parse correctly in future versions, but invalid strings that
currently fail (e.g. ``2017-01-01T00:00+00:00:00``) are not
guaranteed to continue failing in future versions if they encode
a valid date.
.. versionadded:: 2.7.0
"""
components, pos = self._parse_isodate(dt_str)
if len(dt_str) > pos:
if self._sep is None or dt_str[pos:pos + 1] == self._sep:
components += self._parse_isotime(dt_str[pos + 1:])
else:
raise ValueError('String contains unknown ISO components')
return datetime(*components)
@_takes_ascii
def parse_isodate(self, datestr):
"""
Parse the date portion of an ISO string.
:param datestr:
The string portion of an ISO string, without a separator
:return:
Returns a :class:`datetime.date` object
"""
components, pos = self._parse_isodate(datestr)
if pos < len(datestr):
raise ValueError('String contains unknown ISO ' +
'components: {}'.format(datestr))
return date(*components)
@_takes_ascii
def parse_isotime(self, timestr):
"""
Parse the time portion of an ISO string.
:param timestr:
The time portion of an ISO string, without a separator
:return:
Returns a :class:`datetime.time` object
"""
return time(*self._parse_isotime(timestr))
@_takes_ascii
def parse_tzstr(self, tzstr, zero_as_utc=True):
"""
Parse a valid ISO time zone string.
See :func:`isoparser.isoparse` for details on supported formats.
:param tzstr:
A string representing an ISO time zone offset
:param zero_as_utc:
Whether to return :class:`dateutil.tz.tzutc` for zero-offset zones
:return:
Returns :class:`dateutil.tz.tzoffset` for offsets and
:class:`dateutil.tz.tzutc` for ``Z`` and (if ``zero_as_utc`` is
specified) offsets equivalent to UTC.
"""
return self._parse_tzstr(tzstr, zero_as_utc=zero_as_utc)
# Constants
_MICROSECOND_END_REGEX = re.compile(b'[-+Z]+')
_DATE_SEP = b'-'
_TIME_SEP = b':'
_MICRO_SEP = b'.'
def _parse_isodate(self, dt_str):
try:
return self._parse_isodate_common(dt_str)
except ValueError:
return self._parse_isodate_uncommon(dt_str)
def _parse_isodate_common(self, dt_str):
len_str = len(dt_str)
components = [1, 1, 1]
if len_str < 4:
raise ValueError('ISO string too short')
# Year
components[0] = int(dt_str[0:4])
pos = 4
if pos >= len_str:
return components, pos
has_sep = dt_str[pos:pos + 1] == self._DATE_SEP
if has_sep:
pos += 1
# Month
if len_str - pos < 2:
raise ValueError('Invalid common month')
components[1] = int(dt_str[pos:pos + 2])
pos += 2
if pos >= len_str:
if has_sep:
return components, pos
else:
raise ValueError('Invalid ISO format')
if has_sep:
if dt_str[pos:pos + 1] != self._DATE_SEP:
raise ValueError('Invalid separator in ISO string')
pos += 1
# Day
if len_str - pos < 2:
raise ValueError('Invalid common day')
components[2] = int(dt_str[pos:pos + 2])
return components, pos + 2
def _parse_isodate_uncommon(self, dt_str):
if len(dt_str) < 4:
raise ValueError('ISO string too short')
# All ISO formats start with the year
year = int(dt_str[0:4])
has_sep = dt_str[4:5] == self._DATE_SEP
pos = 4 + has_sep # Skip '-' if it's there
if dt_str[pos:pos + 1] == b'W':
# YYYY-?Www-?D?
pos += 1
weekno = int(dt_str[pos:pos + 2])
pos += 2
dayno = 1
if len(dt_str) > pos:
if (dt_str[pos:pos + 1] == self._DATE_SEP) != has_sep:
raise ValueError('Inconsistent use of dash separator')
pos += has_sep
dayno = int(dt_str[pos:pos + 1])
pos += 1
base_date = self._calculate_weekdate(year, weekno, dayno)
else:
# YYYYDDD or YYYY-DDD
if len(dt_str) - pos < 3:
raise ValueError('Invalid ordinal day')
ordinal_day = int(dt_str[pos:pos + 3])
pos += 3
if ordinal_day < 1 or ordinal_day > (365 + calendar.isleap(year)):
raise ValueError('Invalid ordinal day' +
' {} for year {}'.format(ordinal_day, year))
base_date = date(year, 1, 1) + timedelta(days=ordinal_day - 1)
components = [base_date.year, base_date.month, base_date.day]
return components, pos
def _calculate_weekdate(self, year, week, day):
"""
Calculate the day of corresponding to the ISO year-week-day calendar.
This function is effectively the inverse of
:func:`datetime.date.isocalendar`.
:param year:
The year in the ISO calendar
:param week:
The week in the ISO calendar - range is [1, 53]
:param day:
The day in the ISO calendar - range is [1 (MON), 7 (SUN)]
:return:
Returns a :class:`datetime.date`
"""
if not 0 < week < 54:
raise ValueError('Invalid week: {}'.format(week))
if not 0 < day < 8: # Range is 1-7
raise ValueError('Invalid weekday: {}'.format(day))
# Get week 1 for the specific year:
jan_4 = date(year, 1, 4) # Week 1 always has January 4th in it
week_1 = jan_4 - timedelta(days=jan_4.isocalendar()[2] - 1)
# Now add the specific number of weeks and days to get what we want
week_offset = (week - 1) * 7 + (day - 1)
return week_1 + timedelta(days=week_offset)
def _parse_isotime(self, timestr):
len_str = len(timestr)
components = [0, 0, 0, 0, None]
pos = 0
comp = -1
if len(timestr) < 2:
raise ValueError('ISO time too short')
has_sep = len_str >= 3 and timestr[2:3] == self._TIME_SEP
while pos < len_str and comp < 5:
comp += 1
if timestr[pos:pos + 1] in b'-+Z':
# Detect time zone boundary
components[-1] = self._parse_tzstr(timestr[pos:])
pos = len_str
break
if comp < 3:
# Hour, minute, second
components[comp] = int(timestr[pos:pos + 2])
pos += 2
if (has_sep and pos < len_str and
timestr[pos:pos + 1] == self._TIME_SEP):
pos += 1
if comp == 3:
# Microsecond
if timestr[pos:pos + 1] != self._MICRO_SEP:
continue
pos += 1
us_str = self._MICROSECOND_END_REGEX.split(timestr[pos:pos + 6],
1)[0]
components[comp] = int(us_str) * 10**(6 - len(us_str))
pos += len(us_str)
if pos < len_str:
raise ValueError('Unused components in ISO string')
if components[0] == 24:
# Standard supports 00:00 and 24:00 as representations of midnight
if any(component != 0 for component in components[1:4]):
raise ValueError('Hour may only be 24 at 24:00:00.000')
components[0] = 0
return components
def _parse_tzstr(self, tzstr, zero_as_utc=True):
if tzstr == b'Z':
return tz.tzutc()
if len(tzstr) not in {3, 5, 6}:
raise ValueError('Time zone offset must be 1, 3, 5 or 6 characters')
if tzstr[0:1] == b'-':
mult = -1
elif tzstr[0:1] == b'+':
mult = 1
else:
raise ValueError('Time zone offset requires sign')
hours = int(tzstr[1:3])
if len(tzstr) == 3:
minutes = 0
else:
minutes = int(tzstr[(4 if tzstr[3:4] == self._TIME_SEP else 3):])
if zero_as_utc and hours == 0 and minutes == 0:
return tz.tzutc()
else:
if minutes > 59:
raise ValueError('Invalid minutes in time zone offset')
if hours > 23:
raise ValueError('Invalid hours in time zone offset')
return tz.tzoffset(None, mult * (hours * 60 + minutes) * 60)
DEFAULT_ISOPARSER = isoparser()
isoparse = DEFAULT_ISOPARSER.isoparse
| 12,899 | 30.695332 | 80 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/dateutil/parser/__init__.py
|
# -*- coding: utf-8 -*-
from ._parser import parse, parser, parserinfo
from ._parser import DEFAULTPARSER, DEFAULTTZPARSER
from ._parser import UnknownTimezoneWarning
from ._parser import __doc__
from .isoparser import isoparser, isoparse
__all__ = ['parse', 'parser', 'parserinfo',
'isoparse', 'isoparser',
'UnknownTimezoneWarning']
###
# Deprecate portions of the private interface so that downstream code that
# is improperly relying on it is given *some* notice.
def __deprecated_private_func(f):
from functools import wraps
import warnings
msg = ('{name} is a private function and may break without warning, '
'it will be moved and or renamed in future versions.')
msg = msg.format(name=f.__name__)
@wraps(f)
def deprecated_func(*args, **kwargs):
warnings.warn(msg, DeprecationWarning)
return f(*args, **kwargs)
return deprecated_func
def __deprecate_private_class(c):
import warnings
msg = ('{name} is a private class and may break without warning, '
'it will be moved and or renamed in future versions.')
msg = msg.format(name=c.__name__)
class private_class(c):
__doc__ = c.__doc__
def __init__(self, *args, **kwargs):
warnings.warn(msg, DeprecationWarning)
super(private_class, self).__init__(*args, **kwargs)
private_class.__name__ = c.__name__
return private_class
from ._parser import _timelex, _resultbase
from ._parser import _tzparser, _parsetz
_timelex = __deprecate_private_class(_timelex)
_tzparser = __deprecate_private_class(_tzparser)
_resultbase = __deprecate_private_class(_resultbase)
_parsetz = __deprecated_private_func(_parsetz)
| 1,727 | 27.327869 | 74 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/dateutil/tz/_factories.py
|
from datetime import timedelta
class _TzSingleton(type):
def __init__(cls, *args, **kwargs):
cls.__instance = None
super(_TzSingleton, cls).__init__(*args, **kwargs)
def __call__(cls):
if cls.__instance is None:
cls.__instance = super(_TzSingleton, cls).__call__()
return cls.__instance
class _TzFactory(type):
def instance(cls, *args, **kwargs):
"""Alternate constructor that returns a fresh instance"""
return type.__call__(cls, *args, **kwargs)
class _TzOffsetFactory(_TzFactory):
def __init__(cls, *args, **kwargs):
cls.__instances = {}
def __call__(cls, name, offset):
if isinstance(offset, timedelta):
key = (name, offset.total_seconds())
else:
key = (name, offset)
instance = cls.__instances.get(key, None)
if instance is None:
instance = cls.__instances.setdefault(key,
cls.instance(name, offset))
return instance
class _TzStrFactory(_TzFactory):
def __init__(cls, *args, **kwargs):
cls.__instances = {}
def __call__(cls, s, posix_offset=False):
key = (s, posix_offset)
instance = cls.__instances.get(key, None)
if instance is None:
instance = cls.__instances.setdefault(key,
cls.instance(s, posix_offset))
return instance
| 1,434 | 27.7 | 77 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/dateutil/tz/win.py
|
# This code was originally contributed by Jeffrey Harris.
import datetime
import struct
from six.moves import winreg
from six import text_type
try:
import ctypes
from ctypes import wintypes
except ValueError:
# ValueError is raised on non-Windows systems for some horrible reason.
raise ImportError("Running tzwin on non-Windows system")
from ._common import tzrangebase
__all__ = ["tzwin", "tzwinlocal", "tzres"]
ONEWEEK = datetime.timedelta(7)
TZKEYNAMENT = r"SOFTWARE\Microsoft\Windows NT\CurrentVersion\Time Zones"
TZKEYNAME9X = r"SOFTWARE\Microsoft\Windows\CurrentVersion\Time Zones"
TZLOCALKEYNAME = r"SYSTEM\CurrentControlSet\Control\TimeZoneInformation"
def _settzkeyname():
handle = winreg.ConnectRegistry(None, winreg.HKEY_LOCAL_MACHINE)
try:
winreg.OpenKey(handle, TZKEYNAMENT).Close()
TZKEYNAME = TZKEYNAMENT
except WindowsError:
TZKEYNAME = TZKEYNAME9X
handle.Close()
return TZKEYNAME
TZKEYNAME = _settzkeyname()
class tzres(object):
"""
Class for accessing `tzres.dll`, which contains timezone name related
resources.
.. versionadded:: 2.5.0
"""
p_wchar = ctypes.POINTER(wintypes.WCHAR) # Pointer to a wide char
def __init__(self, tzres_loc='tzres.dll'):
# Load the user32 DLL so we can load strings from tzres
user32 = ctypes.WinDLL('user32')
# Specify the LoadStringW function
user32.LoadStringW.argtypes = (wintypes.HINSTANCE,
wintypes.UINT,
wintypes.LPWSTR,
ctypes.c_int)
self.LoadStringW = user32.LoadStringW
self._tzres = ctypes.WinDLL(tzres_loc)
self.tzres_loc = tzres_loc
def load_name(self, offset):
"""
Load a timezone name from a DLL offset (integer).
>>> from dateutil.tzwin import tzres
>>> tzr = tzres()
>>> print(tzr.load_name(112))
'Eastern Standard Time'
:param offset:
A positive integer value referring to a string from the tzres dll.
..note:
Offsets found in the registry are generally of the form
`@tzres.dll,-114`. The offset in this case if 114, not -114.
"""
resource = self.p_wchar()
lpBuffer = ctypes.cast(ctypes.byref(resource), wintypes.LPWSTR)
nchar = self.LoadStringW(self._tzres._handle, offset, lpBuffer, 0)
return resource[:nchar]
def name_from_string(self, tzname_str):
"""
Parse strings as returned from the Windows registry into the time zone
name as defined in the registry.
>>> from dateutil.tzwin import tzres
>>> tzr = tzres()
>>> print(tzr.name_from_string('@tzres.dll,-251'))
'Dateline Daylight Time'
>>> print(tzr.name_from_string('Eastern Standard Time'))
'Eastern Standard Time'
:param tzname_str:
A timezone name string as returned from a Windows registry key.
:return:
Returns the localized timezone string from tzres.dll if the string
is of the form `@tzres.dll,-offset`, else returns the input string.
"""
if not tzname_str.startswith('@'):
return tzname_str
name_splt = tzname_str.split(',-')
try:
offset = int(name_splt[1])
except:
raise ValueError("Malformed timezone string.")
return self.load_name(offset)
class tzwinbase(tzrangebase):
"""tzinfo class based on win32's timezones available in the registry."""
def __init__(self):
raise NotImplementedError('tzwinbase is an abstract base class')
def __eq__(self, other):
# Compare on all relevant dimensions, including name.
if not isinstance(other, tzwinbase):
return NotImplemented
return (self._std_offset == other._std_offset and
self._dst_offset == other._dst_offset and
self._stddayofweek == other._stddayofweek and
self._dstdayofweek == other._dstdayofweek and
self._stdweeknumber == other._stdweeknumber and
self._dstweeknumber == other._dstweeknumber and
self._stdhour == other._stdhour and
self._dsthour == other._dsthour and
self._stdminute == other._stdminute and
self._dstminute == other._dstminute and
self._std_abbr == other._std_abbr and
self._dst_abbr == other._dst_abbr)
@staticmethod
def list():
"""Return a list of all time zones known to the system."""
with winreg.ConnectRegistry(None, winreg.HKEY_LOCAL_MACHINE) as handle:
with winreg.OpenKey(handle, TZKEYNAME) as tzkey:
result = [winreg.EnumKey(tzkey, i)
for i in range(winreg.QueryInfoKey(tzkey)[0])]
return result
def display(self):
return self._display
def transitions(self, year):
"""
For a given year, get the DST on and off transition times, expressed
always on the standard time side. For zones with no transitions, this
function returns ``None``.
:param year:
The year whose transitions you would like to query.
:return:
Returns a :class:`tuple` of :class:`datetime.datetime` objects,
``(dston, dstoff)`` for zones with an annual DST transition, or
``None`` for fixed offset zones.
"""
if not self.hasdst:
return None
dston = picknthweekday(year, self._dstmonth, self._dstdayofweek,
self._dsthour, self._dstminute,
self._dstweeknumber)
dstoff = picknthweekday(year, self._stdmonth, self._stddayofweek,
self._stdhour, self._stdminute,
self._stdweeknumber)
# Ambiguous dates default to the STD side
dstoff -= self._dst_base_offset
return dston, dstoff
def _get_hasdst(self):
return self._dstmonth != 0
@property
def _dst_base_offset(self):
return self._dst_base_offset_
class tzwin(tzwinbase):
def __init__(self, name):
self._name = name
with winreg.ConnectRegistry(None, winreg.HKEY_LOCAL_MACHINE) as handle:
tzkeyname = text_type("{kn}\\{name}").format(kn=TZKEYNAME, name=name)
with winreg.OpenKey(handle, tzkeyname) as tzkey:
keydict = valuestodict(tzkey)
self._std_abbr = keydict["Std"]
self._dst_abbr = keydict["Dlt"]
self._display = keydict["Display"]
# See http://ww_winreg.jsiinc.com/SUBA/tip0300/rh0398.htm
tup = struct.unpack("=3l16h", keydict["TZI"])
stdoffset = -tup[0]-tup[1] # Bias + StandardBias * -1
dstoffset = stdoffset-tup[2] # + DaylightBias * -1
self._std_offset = datetime.timedelta(minutes=stdoffset)
self._dst_offset = datetime.timedelta(minutes=dstoffset)
# for the meaning see the win32 TIME_ZONE_INFORMATION structure docs
# http://msdn.microsoft.com/en-us/library/windows/desktop/ms725481(v=vs.85).aspx
(self._stdmonth,
self._stddayofweek, # Sunday = 0
self._stdweeknumber, # Last = 5
self._stdhour,
self._stdminute) = tup[4:9]
(self._dstmonth,
self._dstdayofweek, # Sunday = 0
self._dstweeknumber, # Last = 5
self._dsthour,
self._dstminute) = tup[12:17]
self._dst_base_offset_ = self._dst_offset - self._std_offset
self.hasdst = self._get_hasdst()
def __repr__(self):
return "tzwin(%s)" % repr(self._name)
def __reduce__(self):
return (self.__class__, (self._name,))
class tzwinlocal(tzwinbase):
def __init__(self):
with winreg.ConnectRegistry(None, winreg.HKEY_LOCAL_MACHINE) as handle:
with winreg.OpenKey(handle, TZLOCALKEYNAME) as tzlocalkey:
keydict = valuestodict(tzlocalkey)
self._std_abbr = keydict["StandardName"]
self._dst_abbr = keydict["DaylightName"]
try:
tzkeyname = text_type('{kn}\\{sn}').format(kn=TZKEYNAME,
sn=self._std_abbr)
with winreg.OpenKey(handle, tzkeyname) as tzkey:
_keydict = valuestodict(tzkey)
self._display = _keydict["Display"]
except OSError:
self._display = None
stdoffset = -keydict["Bias"]-keydict["StandardBias"]
dstoffset = stdoffset-keydict["DaylightBias"]
self._std_offset = datetime.timedelta(minutes=stdoffset)
self._dst_offset = datetime.timedelta(minutes=dstoffset)
# For reasons unclear, in this particular key, the day of week has been
# moved to the END of the SYSTEMTIME structure.
tup = struct.unpack("=8h", keydict["StandardStart"])
(self._stdmonth,
self._stdweeknumber, # Last = 5
self._stdhour,
self._stdminute) = tup[1:5]
self._stddayofweek = tup[7]
tup = struct.unpack("=8h", keydict["DaylightStart"])
(self._dstmonth,
self._dstweeknumber, # Last = 5
self._dsthour,
self._dstminute) = tup[1:5]
self._dstdayofweek = tup[7]
self._dst_base_offset_ = self._dst_offset - self._std_offset
self.hasdst = self._get_hasdst()
def __repr__(self):
return "tzwinlocal()"
def __str__(self):
# str will return the standard name, not the daylight name.
return "tzwinlocal(%s)" % repr(self._std_abbr)
def __reduce__(self):
return (self.__class__, ())
def picknthweekday(year, month, dayofweek, hour, minute, whichweek):
""" dayofweek == 0 means Sunday, whichweek 5 means last instance """
first = datetime.datetime(year, month, 1, hour, minute)
# This will work if dayofweek is ISO weekday (1-7) or Microsoft-style (0-6),
# Because 7 % 7 = 0
weekdayone = first.replace(day=((dayofweek - first.isoweekday()) % 7) + 1)
wd = weekdayone + ((whichweek - 1) * ONEWEEK)
if (wd.month != month):
wd -= ONEWEEK
return wd
def valuestodict(key):
"""Convert a registry key's values to a dictionary."""
dout = {}
size = winreg.QueryInfoKey(key)[1]
tz_res = None
for i in range(size):
key_name, value, dtype = winreg.EnumValue(key, i)
if dtype == winreg.REG_DWORD or dtype == winreg.REG_DWORD_LITTLE_ENDIAN:
# If it's a DWORD (32-bit integer), it's stored as unsigned - convert
# that to a proper signed integer
if value & (1 << 31):
value = value - (1 << 32)
elif dtype == winreg.REG_SZ:
# If it's a reference to the tzres DLL, load the actual string
if value.startswith('@tzres'):
tz_res = tz_res or tzres()
value = tz_res.name_from_string(value)
value = value.rstrip('\x00') # Remove trailing nulls
dout[key_name] = value
return dout
| 11,318 | 33.093373 | 88 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/dateutil/tz/__init__.py
|
# -*- coding: utf-8 -*-
from .tz import *
from .tz import __doc__
#: Convenience constant providing a :class:`tzutc()` instance
#:
#: .. versionadded:: 2.7.0
UTC = tzutc()
__all__ = ["tzutc", "tzoffset", "tzlocal", "tzfile", "tzrange",
"tzstr", "tzical", "tzwin", "tzwinlocal", "gettz",
"enfold", "datetime_ambiguous", "datetime_exists",
"resolve_imaginary", "UTC", "DeprecatedTzFormatWarning"]
class DeprecatedTzFormatWarning(Warning):
"""Warning raised when time zones are parsed from deprecated formats."""
| 551 | 29.666667 | 76 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/dateutil/tz/_common.py
|
from six import PY3
from functools import wraps
from datetime import datetime, timedelta, tzinfo
ZERO = timedelta(0)
__all__ = ['tzname_in_python2', 'enfold']
def tzname_in_python2(namefunc):
"""Change unicode output into bytestrings in Python 2
tzname() API changed in Python 3. It used to return bytes, but was changed
to unicode strings
"""
def adjust_encoding(*args, **kwargs):
name = namefunc(*args, **kwargs)
if name is not None and not PY3:
name = name.encode()
return name
return adjust_encoding
# The following is adapted from Alexander Belopolsky's tz library
# https://github.com/abalkin/tz
if hasattr(datetime, 'fold'):
# This is the pre-python 3.6 fold situation
def enfold(dt, fold=1):
"""
Provides a unified interface for assigning the ``fold`` attribute to
datetimes both before and after the implementation of PEP-495.
:param fold:
The value for the ``fold`` attribute in the returned datetime. This
should be either 0 or 1.
:return:
Returns an object for which ``getattr(dt, 'fold', 0)`` returns
``fold`` for all versions of Python. In versions prior to
Python 3.6, this is a ``_DatetimeWithFold`` object, which is a
subclass of :py:class:`datetime.datetime` with the ``fold``
attribute added, if ``fold`` is 1.
.. versionadded:: 2.6.0
"""
return dt.replace(fold=fold)
else:
class _DatetimeWithFold(datetime):
"""
This is a class designed to provide a PEP 495-compliant interface for
Python versions before 3.6. It is used only for dates in a fold, so
the ``fold`` attribute is fixed at ``1``.
.. versionadded:: 2.6.0
"""
__slots__ = ()
def replace(self, *args, **kwargs):
"""
Return a datetime with the same attributes, except for those
attributes given new values by whichever keyword arguments are
specified. Note that tzinfo=None can be specified to create a naive
datetime from an aware datetime with no conversion of date and time
data.
This is reimplemented in ``_DatetimeWithFold`` because pypy3 will
return a ``datetime.datetime`` even if ``fold`` is unchanged.
"""
argnames = (
'year', 'month', 'day', 'hour', 'minute', 'second',
'microsecond', 'tzinfo'
)
for arg, argname in zip(args, argnames):
if argname in kwargs:
raise TypeError('Duplicate argument: {}'.format(argname))
kwargs[argname] = arg
for argname in argnames:
if argname not in kwargs:
kwargs[argname] = getattr(self, argname)
dt_class = self.__class__ if kwargs.get('fold', 1) else datetime
return dt_class(**kwargs)
@property
def fold(self):
return 1
def enfold(dt, fold=1):
"""
Provides a unified interface for assigning the ``fold`` attribute to
datetimes both before and after the implementation of PEP-495.
:param fold:
The value for the ``fold`` attribute in the returned datetime. This
should be either 0 or 1.
:return:
Returns an object for which ``getattr(dt, 'fold', 0)`` returns
``fold`` for all versions of Python. In versions prior to
Python 3.6, this is a ``_DatetimeWithFold`` object, which is a
subclass of :py:class:`datetime.datetime` with the ``fold``
attribute added, if ``fold`` is 1.
.. versionadded:: 2.6.0
"""
if getattr(dt, 'fold', 0) == fold:
return dt
args = dt.timetuple()[:6]
args += (dt.microsecond, dt.tzinfo)
if fold:
return _DatetimeWithFold(*args)
else:
return datetime(*args)
def _validate_fromutc_inputs(f):
"""
The CPython version of ``fromutc`` checks that the input is a ``datetime``
object and that ``self`` is attached as its ``tzinfo``.
"""
@wraps(f)
def fromutc(self, dt):
if not isinstance(dt, datetime):
raise TypeError("fromutc() requires a datetime argument")
if dt.tzinfo is not self:
raise ValueError("dt.tzinfo is not self")
return f(self, dt)
return fromutc
class _tzinfo(tzinfo):
"""
Base class for all ``dateutil`` ``tzinfo`` objects.
"""
def is_ambiguous(self, dt):
"""
Whether or not the "wall time" of a given datetime is ambiguous in this
zone.
:param dt:
A :py:class:`datetime.datetime`, naive or time zone aware.
:return:
Returns ``True`` if ambiguous, ``False`` otherwise.
.. versionadded:: 2.6.0
"""
dt = dt.replace(tzinfo=self)
wall_0 = enfold(dt, fold=0)
wall_1 = enfold(dt, fold=1)
same_offset = wall_0.utcoffset() == wall_1.utcoffset()
same_dt = wall_0.replace(tzinfo=None) == wall_1.replace(tzinfo=None)
return same_dt and not same_offset
def _fold_status(self, dt_utc, dt_wall):
"""
Determine the fold status of a "wall" datetime, given a representation
of the same datetime as a (naive) UTC datetime. This is calculated based
on the assumption that ``dt.utcoffset() - dt.dst()`` is constant for all
datetimes, and that this offset is the actual number of hours separating
``dt_utc`` and ``dt_wall``.
:param dt_utc:
Representation of the datetime as UTC
:param dt_wall:
Representation of the datetime as "wall time". This parameter must
either have a `fold` attribute or have a fold-naive
:class:`datetime.tzinfo` attached, otherwise the calculation may
fail.
"""
if self.is_ambiguous(dt_wall):
delta_wall = dt_wall - dt_utc
_fold = int(delta_wall == (dt_utc.utcoffset() - dt_utc.dst()))
else:
_fold = 0
return _fold
def _fold(self, dt):
return getattr(dt, 'fold', 0)
def _fromutc(self, dt):
"""
Given a timezone-aware datetime in a given timezone, calculates a
timezone-aware datetime in a new timezone.
Since this is the one time that we *know* we have an unambiguous
datetime object, we take this opportunity to determine whether the
datetime is ambiguous and in a "fold" state (e.g. if it's the first
occurence, chronologically, of the ambiguous datetime).
:param dt:
A timezone-aware :class:`datetime.datetime` object.
"""
# Re-implement the algorithm from Python's datetime.py
dtoff = dt.utcoffset()
if dtoff is None:
raise ValueError("fromutc() requires a non-None utcoffset() "
"result")
# The original datetime.py code assumes that `dst()` defaults to
# zero during ambiguous times. PEP 495 inverts this presumption, so
# for pre-PEP 495 versions of python, we need to tweak the algorithm.
dtdst = dt.dst()
if dtdst is None:
raise ValueError("fromutc() requires a non-None dst() result")
delta = dtoff - dtdst
dt += delta
# Set fold=1 so we can default to being in the fold for
# ambiguous dates.
dtdst = enfold(dt, fold=1).dst()
if dtdst is None:
raise ValueError("fromutc(): dt.dst gave inconsistent "
"results; cannot convert")
return dt + dtdst
@_validate_fromutc_inputs
def fromutc(self, dt):
"""
Given a timezone-aware datetime in a given timezone, calculates a
timezone-aware datetime in a new timezone.
Since this is the one time that we *know* we have an unambiguous
datetime object, we take this opportunity to determine whether the
datetime is ambiguous and in a "fold" state (e.g. if it's the first
occurance, chronologically, of the ambiguous datetime).
:param dt:
A timezone-aware :class:`datetime.datetime` object.
"""
dt_wall = self._fromutc(dt)
# Calculate the fold status given the two datetimes.
_fold = self._fold_status(dt, dt_wall)
# Set the default fold value for ambiguous dates
return enfold(dt_wall, fold=_fold)
class tzrangebase(_tzinfo):
"""
This is an abstract base class for time zones represented by an annual
transition into and out of DST. Child classes should implement the following
methods:
* ``__init__(self, *args, **kwargs)``
* ``transitions(self, year)`` - this is expected to return a tuple of
datetimes representing the DST on and off transitions in standard
time.
A fully initialized ``tzrangebase`` subclass should also provide the
following attributes:
* ``hasdst``: Boolean whether or not the zone uses DST.
* ``_dst_offset`` / ``_std_offset``: :class:`datetime.timedelta` objects
representing the respective UTC offsets.
* ``_dst_abbr`` / ``_std_abbr``: Strings representing the timezone short
abbreviations in DST and STD, respectively.
* ``_hasdst``: Whether or not the zone has DST.
.. versionadded:: 2.6.0
"""
def __init__(self):
raise NotImplementedError('tzrangebase is an abstract base class')
def utcoffset(self, dt):
isdst = self._isdst(dt)
if isdst is None:
return None
elif isdst:
return self._dst_offset
else:
return self._std_offset
def dst(self, dt):
isdst = self._isdst(dt)
if isdst is None:
return None
elif isdst:
return self._dst_base_offset
else:
return ZERO
@tzname_in_python2
def tzname(self, dt):
if self._isdst(dt):
return self._dst_abbr
else:
return self._std_abbr
def fromutc(self, dt):
""" Given a datetime in UTC, return local time """
if not isinstance(dt, datetime):
raise TypeError("fromutc() requires a datetime argument")
if dt.tzinfo is not self:
raise ValueError("dt.tzinfo is not self")
# Get transitions - if there are none, fixed offset
transitions = self.transitions(dt.year)
if transitions is None:
return dt + self.utcoffset(dt)
# Get the transition times in UTC
dston, dstoff = transitions
dston -= self._std_offset
dstoff -= self._std_offset
utc_transitions = (dston, dstoff)
dt_utc = dt.replace(tzinfo=None)
isdst = self._naive_isdst(dt_utc, utc_transitions)
if isdst:
dt_wall = dt + self._dst_offset
else:
dt_wall = dt + self._std_offset
_fold = int(not isdst and self.is_ambiguous(dt_wall))
return enfold(dt_wall, fold=_fold)
def is_ambiguous(self, dt):
"""
Whether or not the "wall time" of a given datetime is ambiguous in this
zone.
:param dt:
A :py:class:`datetime.datetime`, naive or time zone aware.
:return:
Returns ``True`` if ambiguous, ``False`` otherwise.
.. versionadded:: 2.6.0
"""
if not self.hasdst:
return False
start, end = self.transitions(dt.year)
dt = dt.replace(tzinfo=None)
return (end <= dt < end + self._dst_base_offset)
def _isdst(self, dt):
if not self.hasdst:
return False
elif dt is None:
return None
transitions = self.transitions(dt.year)
if transitions is None:
return False
dt = dt.replace(tzinfo=None)
isdst = self._naive_isdst(dt, transitions)
# Handle ambiguous dates
if not isdst and self.is_ambiguous(dt):
return not self._fold(dt)
else:
return isdst
def _naive_isdst(self, dt, transitions):
dston, dstoff = transitions
dt = dt.replace(tzinfo=None)
if dston < dstoff:
isdst = dston <= dt < dstoff
else:
isdst = not dstoff <= dt < dston
return isdst
@property
def _dst_base_offset(self):
return self._dst_offset - self._std_offset
__hash__ = None
def __ne__(self, other):
return not (self == other)
def __repr__(self):
return "%s(...)" % self.__class__.__name__
__reduce__ = object.__reduce__
| 12,892 | 29.992788 | 80 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/dateutil/tz/tz.py
|
# -*- coding: utf-8 -*-
"""
This module offers timezone implementations subclassing the abstract
:py:class:`datetime.tzinfo` type. There are classes to handle tzfile format
files (usually are in :file:`/etc/localtime`, :file:`/usr/share/zoneinfo`,
etc), TZ environment string (in all known formats), given ranges (with help
from relative deltas), local machine timezone, fixed offset timezone, and UTC
timezone.
"""
import datetime
import struct
import time
import sys
import os
import bisect
import six
from six import string_types
from six.moves import _thread
from ._common import tzname_in_python2, _tzinfo
from ._common import tzrangebase, enfold
from ._common import _validate_fromutc_inputs
from ._factories import _TzSingleton, _TzOffsetFactory
from ._factories import _TzStrFactory
try:
from .win import tzwin, tzwinlocal
except ImportError:
tzwin = tzwinlocal = None
ZERO = datetime.timedelta(0)
EPOCH = datetime.datetime.utcfromtimestamp(0)
EPOCHORDINAL = EPOCH.toordinal()
@six.add_metaclass(_TzSingleton)
class tzutc(datetime.tzinfo):
"""
This is a tzinfo object that represents the UTC time zone.
**Examples:**
.. doctest::
>>> from datetime import *
>>> from dateutil.tz import *
>>> datetime.now()
datetime.datetime(2003, 9, 27, 9, 40, 1, 521290)
>>> datetime.now(tzutc())
datetime.datetime(2003, 9, 27, 12, 40, 12, 156379, tzinfo=tzutc())
>>> datetime.now(tzutc()).tzname()
'UTC'
.. versionchanged:: 2.7.0
``tzutc()`` is now a singleton, so the result of ``tzutc()`` will
always return the same object.
.. doctest::
>>> from dateutil.tz import tzutc, UTC
>>> tzutc() is tzutc()
True
>>> tzutc() is UTC
True
"""
def utcoffset(self, dt):
return ZERO
def dst(self, dt):
return ZERO
@tzname_in_python2
def tzname(self, dt):
return "UTC"
def is_ambiguous(self, dt):
"""
Whether or not the "wall time" of a given datetime is ambiguous in this
zone.
:param dt:
A :py:class:`datetime.datetime`, naive or time zone aware.
:return:
Returns ``True`` if ambiguous, ``False`` otherwise.
.. versionadded:: 2.6.0
"""
return False
@_validate_fromutc_inputs
def fromutc(self, dt):
"""
Fast track version of fromutc() returns the original ``dt`` object for
any valid :py:class:`datetime.datetime` object.
"""
return dt
def __eq__(self, other):
if not isinstance(other, (tzutc, tzoffset)):
return NotImplemented
return (isinstance(other, tzutc) or
(isinstance(other, tzoffset) and other._offset == ZERO))
__hash__ = None
def __ne__(self, other):
return not (self == other)
def __repr__(self):
return "%s()" % self.__class__.__name__
__reduce__ = object.__reduce__
@six.add_metaclass(_TzOffsetFactory)
class tzoffset(datetime.tzinfo):
"""
A simple class for representing a fixed offset from UTC.
:param name:
The timezone name, to be returned when ``tzname()`` is called.
:param offset:
The time zone offset in seconds, or (since version 2.6.0, represented
as a :py:class:`datetime.timedelta` object).
"""
def __init__(self, name, offset):
self._name = name
try:
# Allow a timedelta
offset = offset.total_seconds()
except (TypeError, AttributeError):
pass
self._offset = datetime.timedelta(seconds=offset)
def utcoffset(self, dt):
return self._offset
def dst(self, dt):
return ZERO
@tzname_in_python2
def tzname(self, dt):
return self._name
@_validate_fromutc_inputs
def fromutc(self, dt):
return dt + self._offset
def is_ambiguous(self, dt):
"""
Whether or not the "wall time" of a given datetime is ambiguous in this
zone.
:param dt:
A :py:class:`datetime.datetime`, naive or time zone aware.
:return:
Returns ``True`` if ambiguous, ``False`` otherwise.
.. versionadded:: 2.6.0
"""
return False
def __eq__(self, other):
if not isinstance(other, tzoffset):
return NotImplemented
return self._offset == other._offset
__hash__ = None
def __ne__(self, other):
return not (self == other)
def __repr__(self):
return "%s(%s, %s)" % (self.__class__.__name__,
repr(self._name),
int(self._offset.total_seconds()))
__reduce__ = object.__reduce__
class tzlocal(_tzinfo):
"""
A :class:`tzinfo` subclass built around the ``time`` timezone functions.
"""
def __init__(self):
super(tzlocal, self).__init__()
self._std_offset = datetime.timedelta(seconds=-time.timezone)
if time.daylight:
self._dst_offset = datetime.timedelta(seconds=-time.altzone)
else:
self._dst_offset = self._std_offset
self._dst_saved = self._dst_offset - self._std_offset
self._hasdst = bool(self._dst_saved)
self._tznames = tuple(time.tzname)
def utcoffset(self, dt):
if dt is None and self._hasdst:
return None
if self._isdst(dt):
return self._dst_offset
else:
return self._std_offset
def dst(self, dt):
if dt is None and self._hasdst:
return None
if self._isdst(dt):
return self._dst_offset - self._std_offset
else:
return ZERO
@tzname_in_python2
def tzname(self, dt):
return self._tznames[self._isdst(dt)]
def is_ambiguous(self, dt):
"""
Whether or not the "wall time" of a given datetime is ambiguous in this
zone.
:param dt:
A :py:class:`datetime.datetime`, naive or time zone aware.
:return:
Returns ``True`` if ambiguous, ``False`` otherwise.
.. versionadded:: 2.6.0
"""
naive_dst = self._naive_is_dst(dt)
return (not naive_dst and
(naive_dst != self._naive_is_dst(dt - self._dst_saved)))
def _naive_is_dst(self, dt):
timestamp = _datetime_to_timestamp(dt)
return time.localtime(timestamp + time.timezone).tm_isdst
def _isdst(self, dt, fold_naive=True):
# We can't use mktime here. It is unstable when deciding if
# the hour near to a change is DST or not.
#
# timestamp = time.mktime((dt.year, dt.month, dt.day, dt.hour,
# dt.minute, dt.second, dt.weekday(), 0, -1))
# return time.localtime(timestamp).tm_isdst
#
# The code above yields the following result:
#
# >>> import tz, datetime
# >>> t = tz.tzlocal()
# >>> datetime.datetime(2003,2,15,23,tzinfo=t).tzname()
# 'BRDT'
# >>> datetime.datetime(2003,2,16,0,tzinfo=t).tzname()
# 'BRST'
# >>> datetime.datetime(2003,2,15,23,tzinfo=t).tzname()
# 'BRST'
# >>> datetime.datetime(2003,2,15,22,tzinfo=t).tzname()
# 'BRDT'
# >>> datetime.datetime(2003,2,15,23,tzinfo=t).tzname()
# 'BRDT'
#
# Here is a more stable implementation:
#
if not self._hasdst:
return False
# Check for ambiguous times:
dstval = self._naive_is_dst(dt)
fold = getattr(dt, 'fold', None)
if self.is_ambiguous(dt):
if fold is not None:
return not self._fold(dt)
else:
return True
return dstval
def __eq__(self, other):
if isinstance(other, tzlocal):
return (self._std_offset == other._std_offset and
self._dst_offset == other._dst_offset)
elif isinstance(other, tzutc):
return (not self._hasdst and
self._tznames[0] in {'UTC', 'GMT'} and
self._std_offset == ZERO)
elif isinstance(other, tzoffset):
return (not self._hasdst and
self._tznames[0] == other._name and
self._std_offset == other._offset)
else:
return NotImplemented
__hash__ = None
def __ne__(self, other):
return not (self == other)
def __repr__(self):
return "%s()" % self.__class__.__name__
__reduce__ = object.__reduce__
class _ttinfo(object):
__slots__ = ["offset", "delta", "isdst", "abbr",
"isstd", "isgmt", "dstoffset"]
def __init__(self):
for attr in self.__slots__:
setattr(self, attr, None)
def __repr__(self):
l = []
for attr in self.__slots__:
value = getattr(self, attr)
if value is not None:
l.append("%s=%s" % (attr, repr(value)))
return "%s(%s)" % (self.__class__.__name__, ", ".join(l))
def __eq__(self, other):
if not isinstance(other, _ttinfo):
return NotImplemented
return (self.offset == other.offset and
self.delta == other.delta and
self.isdst == other.isdst and
self.abbr == other.abbr and
self.isstd == other.isstd and
self.isgmt == other.isgmt and
self.dstoffset == other.dstoffset)
__hash__ = None
def __ne__(self, other):
return not (self == other)
def __getstate__(self):
state = {}
for name in self.__slots__:
state[name] = getattr(self, name, None)
return state
def __setstate__(self, state):
for name in self.__slots__:
if name in state:
setattr(self, name, state[name])
class _tzfile(object):
"""
Lightweight class for holding the relevant transition and time zone
information read from binary tzfiles.
"""
attrs = ['trans_list', 'trans_list_utc', 'trans_idx', 'ttinfo_list',
'ttinfo_std', 'ttinfo_dst', 'ttinfo_before', 'ttinfo_first']
def __init__(self, **kwargs):
for attr in self.attrs:
setattr(self, attr, kwargs.get(attr, None))
class tzfile(_tzinfo):
"""
This is a ``tzinfo`` subclass thant allows one to use the ``tzfile(5)``
format timezone files to extract current and historical zone information.
:param fileobj:
This can be an opened file stream or a file name that the time zone
information can be read from.
:param filename:
This is an optional parameter specifying the source of the time zone
information in the event that ``fileobj`` is a file object. If omitted
and ``fileobj`` is a file stream, this parameter will be set either to
``fileobj``'s ``name`` attribute or to ``repr(fileobj)``.
See `Sources for Time Zone and Daylight Saving Time Data
<https://data.iana.org/time-zones/tz-link.html>`_ for more information.
Time zone files can be compiled from the `IANA Time Zone database files
<https://www.iana.org/time-zones>`_ with the `zic time zone compiler
<https://www.freebsd.org/cgi/man.cgi?query=zic&sektion=8>`_
.. note::
Only construct a ``tzfile`` directly if you have a specific timezone
file on disk that you want to read into a Python ``tzinfo`` object.
If you want to get a ``tzfile`` representing a specific IANA zone,
(e.g. ``'America/New_York'``), you should call
:func:`dateutil.tz.gettz` with the zone identifier.
**Examples:**
Using the US Eastern time zone as an example, we can see that a ``tzfile``
provides time zone information for the standard Daylight Saving offsets:
.. testsetup:: tzfile
from dateutil.tz import gettz
from datetime import datetime
.. doctest:: tzfile
>>> NYC = gettz('America/New_York')
>>> NYC
tzfile('/usr/share/zoneinfo/America/New_York')
>>> print(datetime(2016, 1, 3, tzinfo=NYC)) # EST
2016-01-03 00:00:00-05:00
>>> print(datetime(2016, 7, 7, tzinfo=NYC)) # EDT
2016-07-07 00:00:00-04:00
The ``tzfile`` structure contains a fully history of the time zone,
so historical dates will also have the right offsets. For example, before
the adoption of the UTC standards, New York used local solar mean time:
.. doctest:: tzfile
>>> print(datetime(1901, 4, 12, tzinfo=NYC)) # LMT
1901-04-12 00:00:00-04:56
And during World War II, New York was on "Eastern War Time", which was a
state of permanent daylight saving time:
.. doctest:: tzfile
>>> print(datetime(1944, 2, 7, tzinfo=NYC)) # EWT
1944-02-07 00:00:00-04:00
"""
def __init__(self, fileobj, filename=None):
super(tzfile, self).__init__()
file_opened_here = False
if isinstance(fileobj, string_types):
self._filename = fileobj
fileobj = open(fileobj, 'rb')
file_opened_here = True
elif filename is not None:
self._filename = filename
elif hasattr(fileobj, "name"):
self._filename = fileobj.name
else:
self._filename = repr(fileobj)
if fileobj is not None:
if not file_opened_here:
fileobj = _ContextWrapper(fileobj)
with fileobj as file_stream:
tzobj = self._read_tzfile(file_stream)
self._set_tzdata(tzobj)
def _set_tzdata(self, tzobj):
""" Set the time zone data of this object from a _tzfile object """
# Copy the relevant attributes over as private attributes
for attr in _tzfile.attrs:
setattr(self, '_' + attr, getattr(tzobj, attr))
def _read_tzfile(self, fileobj):
out = _tzfile()
# From tzfile(5):
#
# The time zone information files used by tzset(3)
# begin with the magic characters "TZif" to identify
# them as time zone information files, followed by
# sixteen bytes reserved for future use, followed by
# six four-byte values of type long, written in a
# ``standard'' byte order (the high-order byte
# of the value is written first).
if fileobj.read(4).decode() != "TZif":
raise ValueError("magic not found")
fileobj.read(16)
(
# The number of UTC/local indicators stored in the file.
ttisgmtcnt,
# The number of standard/wall indicators stored in the file.
ttisstdcnt,
# The number of leap seconds for which data is
# stored in the file.
leapcnt,
# The number of "transition times" for which data
# is stored in the file.
timecnt,
# The number of "local time types" for which data
# is stored in the file (must not be zero).
typecnt,
# The number of characters of "time zone
# abbreviation strings" stored in the file.
charcnt,
) = struct.unpack(">6l", fileobj.read(24))
# The above header is followed by tzh_timecnt four-byte
# values of type long, sorted in ascending order.
# These values are written in ``standard'' byte order.
# Each is used as a transition time (as returned by
# time(2)) at which the rules for computing local time
# change.
if timecnt:
out.trans_list_utc = list(struct.unpack(">%dl" % timecnt,
fileobj.read(timecnt*4)))
else:
out.trans_list_utc = []
# Next come tzh_timecnt one-byte values of type unsigned
# char; each one tells which of the different types of
# ``local time'' types described in the file is associated
# with the same-indexed transition time. These values
# serve as indices into an array of ttinfo structures that
# appears next in the file.
if timecnt:
out.trans_idx = struct.unpack(">%dB" % timecnt,
fileobj.read(timecnt))
else:
out.trans_idx = []
# Each ttinfo structure is written as a four-byte value
# for tt_gmtoff of type long, in a standard byte
# order, followed by a one-byte value for tt_isdst
# and a one-byte value for tt_abbrind. In each
# structure, tt_gmtoff gives the number of
# seconds to be added to UTC, tt_isdst tells whether
# tm_isdst should be set by localtime(3), and
# tt_abbrind serves as an index into the array of
# time zone abbreviation characters that follow the
# ttinfo structure(s) in the file.
ttinfo = []
for i in range(typecnt):
ttinfo.append(struct.unpack(">lbb", fileobj.read(6)))
abbr = fileobj.read(charcnt).decode()
# Then there are tzh_leapcnt pairs of four-byte
# values, written in standard byte order; the
# first value of each pair gives the time (as
# returned by time(2)) at which a leap second
# occurs; the second gives the total number of
# leap seconds to be applied after the given time.
# The pairs of values are sorted in ascending order
# by time.
# Not used, for now (but seek for correct file position)
if leapcnt:
fileobj.seek(leapcnt * 8, os.SEEK_CUR)
# Then there are tzh_ttisstdcnt standard/wall
# indicators, each stored as a one-byte value;
# they tell whether the transition times associated
# with local time types were specified as standard
# time or wall clock time, and are used when
# a time zone file is used in handling POSIX-style
# time zone environment variables.
if ttisstdcnt:
isstd = struct.unpack(">%db" % ttisstdcnt,
fileobj.read(ttisstdcnt))
# Finally, there are tzh_ttisgmtcnt UTC/local
# indicators, each stored as a one-byte value;
# they tell whether the transition times associated
# with local time types were specified as UTC or
# local time, and are used when a time zone file
# is used in handling POSIX-style time zone envi-
# ronment variables.
if ttisgmtcnt:
isgmt = struct.unpack(">%db" % ttisgmtcnt,
fileobj.read(ttisgmtcnt))
# Build ttinfo list
out.ttinfo_list = []
for i in range(typecnt):
gmtoff, isdst, abbrind = ttinfo[i]
# Round to full-minutes if that's not the case. Python's
# datetime doesn't accept sub-minute timezones. Check
# http://python.org/sf/1447945 for some information.
gmtoff = 60 * ((gmtoff + 30) // 60)
tti = _ttinfo()
tti.offset = gmtoff
tti.dstoffset = datetime.timedelta(0)
tti.delta = datetime.timedelta(seconds=gmtoff)
tti.isdst = isdst
tti.abbr = abbr[abbrind:abbr.find('\x00', abbrind)]
tti.isstd = (ttisstdcnt > i and isstd[i] != 0)
tti.isgmt = (ttisgmtcnt > i and isgmt[i] != 0)
out.ttinfo_list.append(tti)
# Replace ttinfo indexes for ttinfo objects.
out.trans_idx = [out.ttinfo_list[idx] for idx in out.trans_idx]
# Set standard, dst, and before ttinfos. before will be
# used when a given time is before any transitions,
# and will be set to the first non-dst ttinfo, or to
# the first dst, if all of them are dst.
out.ttinfo_std = None
out.ttinfo_dst = None
out.ttinfo_before = None
if out.ttinfo_list:
if not out.trans_list_utc:
out.ttinfo_std = out.ttinfo_first = out.ttinfo_list[0]
else:
for i in range(timecnt-1, -1, -1):
tti = out.trans_idx[i]
if not out.ttinfo_std and not tti.isdst:
out.ttinfo_std = tti
elif not out.ttinfo_dst and tti.isdst:
out.ttinfo_dst = tti
if out.ttinfo_std and out.ttinfo_dst:
break
else:
if out.ttinfo_dst and not out.ttinfo_std:
out.ttinfo_std = out.ttinfo_dst
for tti in out.ttinfo_list:
if not tti.isdst:
out.ttinfo_before = tti
break
else:
out.ttinfo_before = out.ttinfo_list[0]
# Now fix transition times to become relative to wall time.
#
# I'm not sure about this. In my tests, the tz source file
# is setup to wall time, and in the binary file isstd and
# isgmt are off, so it should be in wall time. OTOH, it's
# always in gmt time. Let me know if you have comments
# about this.
laststdoffset = None
out.trans_list = []
for i, tti in enumerate(out.trans_idx):
if not tti.isdst:
offset = tti.offset
laststdoffset = offset
else:
if laststdoffset is not None:
# Store the DST offset as well and update it in the list
tti.dstoffset = tti.offset - laststdoffset
out.trans_idx[i] = tti
offset = laststdoffset or 0
out.trans_list.append(out.trans_list_utc[i] + offset)
# In case we missed any DST offsets on the way in for some reason, make
# a second pass over the list, looking for the /next/ DST offset.
laststdoffset = None
for i in reversed(range(len(out.trans_idx))):
tti = out.trans_idx[i]
if tti.isdst:
if not (tti.dstoffset or laststdoffset is None):
tti.dstoffset = tti.offset - laststdoffset
else:
laststdoffset = tti.offset
if not isinstance(tti.dstoffset, datetime.timedelta):
tti.dstoffset = datetime.timedelta(seconds=tti.dstoffset)
out.trans_idx[i] = tti
out.trans_idx = tuple(out.trans_idx)
out.trans_list = tuple(out.trans_list)
out.trans_list_utc = tuple(out.trans_list_utc)
return out
def _find_last_transition(self, dt, in_utc=False):
# If there's no list, there are no transitions to find
if not self._trans_list:
return None
timestamp = _datetime_to_timestamp(dt)
# Find where the timestamp fits in the transition list - if the
# timestamp is a transition time, it's part of the "after" period.
trans_list = self._trans_list_utc if in_utc else self._trans_list
idx = bisect.bisect_right(trans_list, timestamp)
# We want to know when the previous transition was, so subtract off 1
return idx - 1
def _get_ttinfo(self, idx):
# For no list or after the last transition, default to _ttinfo_std
if idx is None or (idx + 1) >= len(self._trans_list):
return self._ttinfo_std
# If there is a list and the time is before it, return _ttinfo_before
if idx < 0:
return self._ttinfo_before
return self._trans_idx[idx]
def _find_ttinfo(self, dt):
idx = self._resolve_ambiguous_time(dt)
return self._get_ttinfo(idx)
def fromutc(self, dt):
"""
The ``tzfile`` implementation of :py:func:`datetime.tzinfo.fromutc`.
:param dt:
A :py:class:`datetime.datetime` object.
:raises TypeError:
Raised if ``dt`` is not a :py:class:`datetime.datetime` object.
:raises ValueError:
Raised if this is called with a ``dt`` which does not have this
``tzinfo`` attached.
:return:
Returns a :py:class:`datetime.datetime` object representing the
wall time in ``self``'s time zone.
"""
# These isinstance checks are in datetime.tzinfo, so we'll preserve
# them, even if we don't care about duck typing.
if not isinstance(dt, datetime.datetime):
raise TypeError("fromutc() requires a datetime argument")
if dt.tzinfo is not self:
raise ValueError("dt.tzinfo is not self")
# First treat UTC as wall time and get the transition we're in.
idx = self._find_last_transition(dt, in_utc=True)
tti = self._get_ttinfo(idx)
dt_out = dt + datetime.timedelta(seconds=tti.offset)
fold = self.is_ambiguous(dt_out, idx=idx)
return enfold(dt_out, fold=int(fold))
def is_ambiguous(self, dt, idx=None):
"""
Whether or not the "wall time" of a given datetime is ambiguous in this
zone.
:param dt:
A :py:class:`datetime.datetime`, naive or time zone aware.
:return:
Returns ``True`` if ambiguous, ``False`` otherwise.
.. versionadded:: 2.6.0
"""
if idx is None:
idx = self._find_last_transition(dt)
# Calculate the difference in offsets from current to previous
timestamp = _datetime_to_timestamp(dt)
tti = self._get_ttinfo(idx)
if idx is None or idx <= 0:
return False
od = self._get_ttinfo(idx - 1).offset - tti.offset
tt = self._trans_list[idx] # Transition time
return timestamp < tt + od
def _resolve_ambiguous_time(self, dt):
idx = self._find_last_transition(dt)
# If we have no transitions, return the index
_fold = self._fold(dt)
if idx is None or idx == 0:
return idx
# If it's ambiguous and we're in a fold, shift to a different index.
idx_offset = int(not _fold and self.is_ambiguous(dt, idx))
return idx - idx_offset
def utcoffset(self, dt):
if dt is None:
return None
if not self._ttinfo_std:
return ZERO
return self._find_ttinfo(dt).delta
def dst(self, dt):
if dt is None:
return None
if not self._ttinfo_dst:
return ZERO
tti = self._find_ttinfo(dt)
if not tti.isdst:
return ZERO
# The documentation says that utcoffset()-dst() must
# be constant for every dt.
return tti.dstoffset
@tzname_in_python2
def tzname(self, dt):
if not self._ttinfo_std or dt is None:
return None
return self._find_ttinfo(dt).abbr
def __eq__(self, other):
if not isinstance(other, tzfile):
return NotImplemented
return (self._trans_list == other._trans_list and
self._trans_idx == other._trans_idx and
self._ttinfo_list == other._ttinfo_list)
__hash__ = None
def __ne__(self, other):
return not (self == other)
def __repr__(self):
return "%s(%s)" % (self.__class__.__name__, repr(self._filename))
def __reduce__(self):
return self.__reduce_ex__(None)
def __reduce_ex__(self, protocol):
return (self.__class__, (None, self._filename), self.__dict__)
class tzrange(tzrangebase):
"""
The ``tzrange`` object is a time zone specified by a set of offsets and
abbreviations, equivalent to the way the ``TZ`` variable can be specified
in POSIX-like systems, but using Python delta objects to specify DST
start, end and offsets.
:param stdabbr:
The abbreviation for standard time (e.g. ``'EST'``).
:param stdoffset:
An integer or :class:`datetime.timedelta` object or equivalent
specifying the base offset from UTC.
If unspecified, +00:00 is used.
:param dstabbr:
The abbreviation for DST / "Summer" time (e.g. ``'EDT'``).
If specified, with no other DST information, DST is assumed to occur
and the default behavior or ``dstoffset``, ``start`` and ``end`` is
used. If unspecified and no other DST information is specified, it
is assumed that this zone has no DST.
If this is unspecified and other DST information is *is* specified,
DST occurs in the zone but the time zone abbreviation is left
unchanged.
:param dstoffset:
A an integer or :class:`datetime.timedelta` object or equivalent
specifying the UTC offset during DST. If unspecified and any other DST
information is specified, it is assumed to be the STD offset +1 hour.
:param start:
A :class:`relativedelta.relativedelta` object or equivalent specifying
the time and time of year that daylight savings time starts. To
specify, for example, that DST starts at 2AM on the 2nd Sunday in
March, pass:
``relativedelta(hours=2, month=3, day=1, weekday=SU(+2))``
If unspecified and any other DST information is specified, the default
value is 2 AM on the first Sunday in April.
:param end:
A :class:`relativedelta.relativedelta` object or equivalent
representing the time and time of year that daylight savings time
ends, with the same specification method as in ``start``. One note is
that this should point to the first time in the *standard* zone, so if
a transition occurs at 2AM in the DST zone and the clocks are set back
1 hour to 1AM, set the ``hours`` parameter to +1.
**Examples:**
.. testsetup:: tzrange
from dateutil.tz import tzrange, tzstr
.. doctest:: tzrange
>>> tzstr('EST5EDT') == tzrange("EST", -18000, "EDT")
True
>>> from dateutil.relativedelta import *
>>> range1 = tzrange("EST", -18000, "EDT")
>>> range2 = tzrange("EST", -18000, "EDT", -14400,
... relativedelta(hours=+2, month=4, day=1,
... weekday=SU(+1)),
... relativedelta(hours=+1, month=10, day=31,
... weekday=SU(-1)))
>>> tzstr('EST5EDT') == range1 == range2
True
"""
def __init__(self, stdabbr, stdoffset=None,
dstabbr=None, dstoffset=None,
start=None, end=None):
global relativedelta
from dateutil import relativedelta
self._std_abbr = stdabbr
self._dst_abbr = dstabbr
try:
stdoffset = stdoffset.total_seconds()
except (TypeError, AttributeError):
pass
try:
dstoffset = dstoffset.total_seconds()
except (TypeError, AttributeError):
pass
if stdoffset is not None:
self._std_offset = datetime.timedelta(seconds=stdoffset)
else:
self._std_offset = ZERO
if dstoffset is not None:
self._dst_offset = datetime.timedelta(seconds=dstoffset)
elif dstabbr and stdoffset is not None:
self._dst_offset = self._std_offset + datetime.timedelta(hours=+1)
else:
self._dst_offset = ZERO
if dstabbr and start is None:
self._start_delta = relativedelta.relativedelta(
hours=+2, month=4, day=1, weekday=relativedelta.SU(+1))
else:
self._start_delta = start
if dstabbr and end is None:
self._end_delta = relativedelta.relativedelta(
hours=+1, month=10, day=31, weekday=relativedelta.SU(-1))
else:
self._end_delta = end
self._dst_base_offset_ = self._dst_offset - self._std_offset
self.hasdst = bool(self._start_delta)
def transitions(self, year):
"""
For a given year, get the DST on and off transition times, expressed
always on the standard time side. For zones with no transitions, this
function returns ``None``.
:param year:
The year whose transitions you would like to query.
:return:
Returns a :class:`tuple` of :class:`datetime.datetime` objects,
``(dston, dstoff)`` for zones with an annual DST transition, or
``None`` for fixed offset zones.
"""
if not self.hasdst:
return None
base_year = datetime.datetime(year, 1, 1)
start = base_year + self._start_delta
end = base_year + self._end_delta
return (start, end)
def __eq__(self, other):
if not isinstance(other, tzrange):
return NotImplemented
return (self._std_abbr == other._std_abbr and
self._dst_abbr == other._dst_abbr and
self._std_offset == other._std_offset and
self._dst_offset == other._dst_offset and
self._start_delta == other._start_delta and
self._end_delta == other._end_delta)
@property
def _dst_base_offset(self):
return self._dst_base_offset_
@six.add_metaclass(_TzStrFactory)
class tzstr(tzrange):
"""
``tzstr`` objects are time zone objects specified by a time-zone string as
it would be passed to a ``TZ`` variable on POSIX-style systems (see
the `GNU C Library: TZ Variable`_ for more details).
There is one notable exception, which is that POSIX-style time zones use an
inverted offset format, so normally ``GMT+3`` would be parsed as an offset
3 hours *behind* GMT. The ``tzstr`` time zone object will parse this as an
offset 3 hours *ahead* of GMT. If you would like to maintain the POSIX
behavior, pass a ``True`` value to ``posix_offset``.
The :class:`tzrange` object provides the same functionality, but is
specified using :class:`relativedelta.relativedelta` objects. rather than
strings.
:param s:
A time zone string in ``TZ`` variable format. This can be a
:class:`bytes` (2.x: :class:`str`), :class:`str` (2.x:
:class:`unicode`) or a stream emitting unicode characters
(e.g. :class:`StringIO`).
:param posix_offset:
Optional. If set to ``True``, interpret strings such as ``GMT+3`` or
``UTC+3`` as being 3 hours *behind* UTC rather than ahead, per the
POSIX standard.
.. caution::
Prior to version 2.7.0, this function also supported time zones
in the format:
* ``EST5EDT,4,0,6,7200,10,0,26,7200,3600``
* ``EST5EDT,4,1,0,7200,10,-1,0,7200,3600``
This format is non-standard and has been deprecated; this function
will raise a :class:`DeprecatedTZFormatWarning` until
support is removed in a future version.
.. _`GNU C Library: TZ Variable`:
https://www.gnu.org/software/libc/manual/html_node/TZ-Variable.html
"""
def __init__(self, s, posix_offset=False):
global parser
from dateutil.parser import _parser as parser
self._s = s
res = parser._parsetz(s)
if res is None or res.any_unused_tokens:
raise ValueError("unknown string format")
# Here we break the compatibility with the TZ variable handling.
# GMT-3 actually *means* the timezone -3.
if res.stdabbr in ("GMT", "UTC") and not posix_offset:
res.stdoffset *= -1
# We must initialize it first, since _delta() needs
# _std_offset and _dst_offset set. Use False in start/end
# to avoid building it two times.
tzrange.__init__(self, res.stdabbr, res.stdoffset,
res.dstabbr, res.dstoffset,
start=False, end=False)
if not res.dstabbr:
self._start_delta = None
self._end_delta = None
else:
self._start_delta = self._delta(res.start)
if self._start_delta:
self._end_delta = self._delta(res.end, isend=1)
self.hasdst = bool(self._start_delta)
def _delta(self, x, isend=0):
from dateutil import relativedelta
kwargs = {}
if x.month is not None:
kwargs["month"] = x.month
if x.weekday is not None:
kwargs["weekday"] = relativedelta.weekday(x.weekday, x.week)
if x.week > 0:
kwargs["day"] = 1
else:
kwargs["day"] = 31
elif x.day:
kwargs["day"] = x.day
elif x.yday is not None:
kwargs["yearday"] = x.yday
elif x.jyday is not None:
kwargs["nlyearday"] = x.jyday
if not kwargs:
# Default is to start on first sunday of april, and end
# on last sunday of october.
if not isend:
kwargs["month"] = 4
kwargs["day"] = 1
kwargs["weekday"] = relativedelta.SU(+1)
else:
kwargs["month"] = 10
kwargs["day"] = 31
kwargs["weekday"] = relativedelta.SU(-1)
if x.time is not None:
kwargs["seconds"] = x.time
else:
# Default is 2AM.
kwargs["seconds"] = 7200
if isend:
# Convert to standard time, to follow the documented way
# of working with the extra hour. See the documentation
# of the tzinfo class.
delta = self._dst_offset - self._std_offset
kwargs["seconds"] -= delta.seconds + delta.days * 86400
return relativedelta.relativedelta(**kwargs)
def __repr__(self):
return "%s(%s)" % (self.__class__.__name__, repr(self._s))
class _tzicalvtzcomp(object):
def __init__(self, tzoffsetfrom, tzoffsetto, isdst,
tzname=None, rrule=None):
self.tzoffsetfrom = datetime.timedelta(seconds=tzoffsetfrom)
self.tzoffsetto = datetime.timedelta(seconds=tzoffsetto)
self.tzoffsetdiff = self.tzoffsetto - self.tzoffsetfrom
self.isdst = isdst
self.tzname = tzname
self.rrule = rrule
class _tzicalvtz(_tzinfo):
def __init__(self, tzid, comps=[]):
super(_tzicalvtz, self).__init__()
self._tzid = tzid
self._comps = comps
self._cachedate = []
self._cachecomp = []
self._cache_lock = _thread.allocate_lock()
def _find_comp(self, dt):
if len(self._comps) == 1:
return self._comps[0]
dt = dt.replace(tzinfo=None)
try:
with self._cache_lock:
return self._cachecomp[self._cachedate.index(
(dt, self._fold(dt)))]
except ValueError:
pass
lastcompdt = None
lastcomp = None
for comp in self._comps:
compdt = self._find_compdt(comp, dt)
if compdt and (not lastcompdt or lastcompdt < compdt):
lastcompdt = compdt
lastcomp = comp
if not lastcomp:
# RFC says nothing about what to do when a given
# time is before the first onset date. We'll look for the
# first standard component, or the first component, if
# none is found.
for comp in self._comps:
if not comp.isdst:
lastcomp = comp
break
else:
lastcomp = comp[0]
with self._cache_lock:
self._cachedate.insert(0, (dt, self._fold(dt)))
self._cachecomp.insert(0, lastcomp)
if len(self._cachedate) > 10:
self._cachedate.pop()
self._cachecomp.pop()
return lastcomp
def _find_compdt(self, comp, dt):
if comp.tzoffsetdiff < ZERO and self._fold(dt):
dt -= comp.tzoffsetdiff
compdt = comp.rrule.before(dt, inc=True)
return compdt
def utcoffset(self, dt):
if dt is None:
return None
return self._find_comp(dt).tzoffsetto
def dst(self, dt):
comp = self._find_comp(dt)
if comp.isdst:
return comp.tzoffsetdiff
else:
return ZERO
@tzname_in_python2
def tzname(self, dt):
return self._find_comp(dt).tzname
def __repr__(self):
return "<tzicalvtz %s>" % repr(self._tzid)
__reduce__ = object.__reduce__
class tzical(object):
"""
This object is designed to parse an iCalendar-style ``VTIMEZONE`` structure
as set out in `RFC 5545`_ Section 4.6.5 into one or more `tzinfo` objects.
:param `fileobj`:
A file or stream in iCalendar format, which should be UTF-8 encoded
with CRLF endings.
.. _`RFC 5545`: https://tools.ietf.org/html/rfc5545
"""
def __init__(self, fileobj):
global rrule
from dateutil import rrule
if isinstance(fileobj, string_types):
self._s = fileobj
# ical should be encoded in UTF-8 with CRLF
fileobj = open(fileobj, 'r')
else:
self._s = getattr(fileobj, 'name', repr(fileobj))
fileobj = _ContextWrapper(fileobj)
self._vtz = {}
with fileobj as fobj:
self._parse_rfc(fobj.read())
def keys(self):
"""
Retrieves the available time zones as a list.
"""
return list(self._vtz.keys())
def get(self, tzid=None):
"""
Retrieve a :py:class:`datetime.tzinfo` object by its ``tzid``.
:param tzid:
If there is exactly one time zone available, omitting ``tzid``
or passing :py:const:`None` value returns it. Otherwise a valid
key (which can be retrieved from :func:`keys`) is required.
:raises ValueError:
Raised if ``tzid`` is not specified but there are either more
or fewer than 1 zone defined.
:returns:
Returns either a :py:class:`datetime.tzinfo` object representing
the relevant time zone or :py:const:`None` if the ``tzid`` was
not found.
"""
if tzid is None:
if len(self._vtz) == 0:
raise ValueError("no timezones defined")
elif len(self._vtz) > 1:
raise ValueError("more than one timezone available")
tzid = next(iter(self._vtz))
return self._vtz.get(tzid)
def _parse_offset(self, s):
s = s.strip()
if not s:
raise ValueError("empty offset")
if s[0] in ('+', '-'):
signal = (-1, +1)[s[0] == '+']
s = s[1:]
else:
signal = +1
if len(s) == 4:
return (int(s[:2]) * 3600 + int(s[2:]) * 60) * signal
elif len(s) == 6:
return (int(s[:2]) * 3600 + int(s[2:4]) * 60 + int(s[4:])) * signal
else:
raise ValueError("invalid offset: " + s)
def _parse_rfc(self, s):
lines = s.splitlines()
if not lines:
raise ValueError("empty string")
# Unfold
i = 0
while i < len(lines):
line = lines[i].rstrip()
if not line:
del lines[i]
elif i > 0 and line[0] == " ":
lines[i-1] += line[1:]
del lines[i]
else:
i += 1
tzid = None
comps = []
invtz = False
comptype = None
for line in lines:
if not line:
continue
name, value = line.split(':', 1)
parms = name.split(';')
if not parms:
raise ValueError("empty property name")
name = parms[0].upper()
parms = parms[1:]
if invtz:
if name == "BEGIN":
if value in ("STANDARD", "DAYLIGHT"):
# Process component
pass
else:
raise ValueError("unknown component: "+value)
comptype = value
founddtstart = False
tzoffsetfrom = None
tzoffsetto = None
rrulelines = []
tzname = None
elif name == "END":
if value == "VTIMEZONE":
if comptype:
raise ValueError("component not closed: "+comptype)
if not tzid:
raise ValueError("mandatory TZID not found")
if not comps:
raise ValueError(
"at least one component is needed")
# Process vtimezone
self._vtz[tzid] = _tzicalvtz(tzid, comps)
invtz = False
elif value == comptype:
if not founddtstart:
raise ValueError("mandatory DTSTART not found")
if tzoffsetfrom is None:
raise ValueError(
"mandatory TZOFFSETFROM not found")
if tzoffsetto is None:
raise ValueError(
"mandatory TZOFFSETFROM not found")
# Process component
rr = None
if rrulelines:
rr = rrule.rrulestr("\n".join(rrulelines),
compatible=True,
ignoretz=True,
cache=True)
comp = _tzicalvtzcomp(tzoffsetfrom, tzoffsetto,
(comptype == "DAYLIGHT"),
tzname, rr)
comps.append(comp)
comptype = None
else:
raise ValueError("invalid component end: "+value)
elif comptype:
if name == "DTSTART":
# DTSTART in VTIMEZONE takes a subset of valid RRULE
# values under RFC 5545.
for parm in parms:
if parm != 'VALUE=DATE-TIME':
msg = ('Unsupported DTSTART param in ' +
'VTIMEZONE: ' + parm)
raise ValueError(msg)
rrulelines.append(line)
founddtstart = True
elif name in ("RRULE", "RDATE", "EXRULE", "EXDATE"):
rrulelines.append(line)
elif name == "TZOFFSETFROM":
if parms:
raise ValueError(
"unsupported %s parm: %s " % (name, parms[0]))
tzoffsetfrom = self._parse_offset(value)
elif name == "TZOFFSETTO":
if parms:
raise ValueError(
"unsupported TZOFFSETTO parm: "+parms[0])
tzoffsetto = self._parse_offset(value)
elif name == "TZNAME":
if parms:
raise ValueError(
"unsupported TZNAME parm: "+parms[0])
tzname = value
elif name == "COMMENT":
pass
else:
raise ValueError("unsupported property: "+name)
else:
if name == "TZID":
if parms:
raise ValueError(
"unsupported TZID parm: "+parms[0])
tzid = value
elif name in ("TZURL", "LAST-MODIFIED", "COMMENT"):
pass
else:
raise ValueError("unsupported property: "+name)
elif name == "BEGIN" and value == "VTIMEZONE":
tzid = None
comps = []
invtz = True
def __repr__(self):
return "%s(%s)" % (self.__class__.__name__, repr(self._s))
if sys.platform != "win32":
TZFILES = ["/etc/localtime", "localtime"]
TZPATHS = ["/usr/share/zoneinfo",
"/usr/lib/zoneinfo",
"/usr/share/lib/zoneinfo",
"/etc/zoneinfo"]
else:
TZFILES = []
TZPATHS = []
def __get_gettz():
tzlocal_classes = (tzlocal,)
if tzwinlocal is not None:
tzlocal_classes += (tzwinlocal,)
class GettzFunc(object):
"""
Retrieve a time zone object from a string representation
This function is intended to retrieve the :py:class:`tzinfo` subclass
that best represents the time zone that would be used if a POSIX
`TZ variable`_ were set to the same value.
If no argument or an empty string is passed to ``gettz``, local time
is returned:
.. code-block:: python3
>>> gettz()
tzfile('/etc/localtime')
This function is also the preferred way to map IANA tz database keys
to :class:`tzfile` objects:
.. code-block:: python3
>>> gettz('Pacific/Kiritimati')
tzfile('/usr/share/zoneinfo/Pacific/Kiritimati')
On Windows, the standard is extended to include the Windows-specific
zone names provided by the operating system:
.. code-block:: python3
>>> gettz('Egypt Standard Time')
tzwin('Egypt Standard Time')
Passing a GNU ``TZ`` style string time zone specification returns a
:class:`tzstr` object:
.. code-block:: python3
>>> gettz('AEST-10AEDT-11,M10.1.0/2,M4.1.0/3')
tzstr('AEST-10AEDT-11,M10.1.0/2,M4.1.0/3')
:param name:
A time zone name (IANA, or, on Windows, Windows keys), location of
a ``tzfile(5)`` zoneinfo file or ``TZ`` variable style time zone
specifier. An empty string, no argument or ``None`` is interpreted
as local time.
:return:
Returns an instance of one of ``dateutil``'s :py:class:`tzinfo`
subclasses.
.. versionchanged:: 2.7.0
After version 2.7.0, any two calls to ``gettz`` using the same
input strings will return the same object:
.. code-block:: python3
>>> tz.gettz('America/Chicago') is tz.gettz('America/Chicago')
True
In addition to improving performance, this ensures that
`"same zone" semantics`_ are used for datetimes in the same zone.
.. _`TZ variable`:
https://www.gnu.org/software/libc/manual/html_node/TZ-Variable.html
.. _`"same zone" semantics`:
https://blog.ganssle.io/articles/2018/02/aware-datetime-arithmetic.html
"""
def __init__(self):
self.__instances = {}
self._cache_lock = _thread.allocate_lock()
def __call__(self, name=None):
with self._cache_lock:
rv = self.__instances.get(name, None)
if rv is None:
rv = self.nocache(name=name)
if not (name is None or isinstance(rv, tzlocal_classes)):
# tzlocal is slightly more complicated than the other
# time zone providers because it depends on environment
# at construction time, so don't cache that.
self.__instances[name] = rv
return rv
def cache_clear(self):
with self._cache_lock:
self.__instances = {}
@staticmethod
def nocache(name=None):
"""A non-cached version of gettz"""
tz = None
if not name:
try:
name = os.environ["TZ"]
except KeyError:
pass
if name is None or name == ":":
for filepath in TZFILES:
if not os.path.isabs(filepath):
filename = filepath
for path in TZPATHS:
filepath = os.path.join(path, filename)
if os.path.isfile(filepath):
break
else:
continue
if os.path.isfile(filepath):
try:
tz = tzfile(filepath)
break
except (IOError, OSError, ValueError):
pass
else:
tz = tzlocal()
else:
if name.startswith(":"):
name = name[1:]
if os.path.isabs(name):
if os.path.isfile(name):
tz = tzfile(name)
else:
tz = None
else:
for path in TZPATHS:
filepath = os.path.join(path, name)
if not os.path.isfile(filepath):
filepath = filepath.replace(' ', '_')
if not os.path.isfile(filepath):
continue
try:
tz = tzfile(filepath)
break
except (IOError, OSError, ValueError):
pass
else:
tz = None
if tzwin is not None:
try:
tz = tzwin(name)
except WindowsError:
tz = None
if not tz:
from dateutil.zoneinfo import get_zonefile_instance
tz = get_zonefile_instance().get(name)
if not tz:
for c in name:
# name is not a tzstr unless it has at least
# one offset. For short values of "name", an
# explicit for loop seems to be the fastest way
# To determine if a string contains a digit
if c in "0123456789":
try:
tz = tzstr(name)
except ValueError:
pass
break
else:
if name in ("GMT", "UTC"):
tz = tzutc()
elif name in time.tzname:
tz = tzlocal()
return tz
return GettzFunc()
gettz = __get_gettz()
del __get_gettz
def datetime_exists(dt, tz=None):
"""
Given a datetime and a time zone, determine whether or not a given datetime
would fall in a gap.
:param dt:
A :class:`datetime.datetime` (whose time zone will be ignored if ``tz``
is provided.)
:param tz:
A :class:`datetime.tzinfo` with support for the ``fold`` attribute. If
``None`` or not provided, the datetime's own time zone will be used.
:return:
Returns a boolean value whether or not the "wall time" exists in
``tz``.
.. versionadded:: 2.7.0
"""
if tz is None:
if dt.tzinfo is None:
raise ValueError('Datetime is naive and no time zone provided.')
tz = dt.tzinfo
dt = dt.replace(tzinfo=None)
# This is essentially a test of whether or not the datetime can survive
# a round trip to UTC.
dt_rt = dt.replace(tzinfo=tz).astimezone(tzutc()).astimezone(tz)
dt_rt = dt_rt.replace(tzinfo=None)
return dt == dt_rt
def datetime_ambiguous(dt, tz=None):
"""
Given a datetime and a time zone, determine whether or not a given datetime
is ambiguous (i.e if there are two times differentiated only by their DST
status).
:param dt:
A :class:`datetime.datetime` (whose time zone will be ignored if ``tz``
is provided.)
:param tz:
A :class:`datetime.tzinfo` with support for the ``fold`` attribute. If
``None`` or not provided, the datetime's own time zone will be used.
:return:
Returns a boolean value whether or not the "wall time" is ambiguous in
``tz``.
.. versionadded:: 2.6.0
"""
if tz is None:
if dt.tzinfo is None:
raise ValueError('Datetime is naive and no time zone provided.')
tz = dt.tzinfo
# If a time zone defines its own "is_ambiguous" function, we'll use that.
is_ambiguous_fn = getattr(tz, 'is_ambiguous', None)
if is_ambiguous_fn is not None:
try:
return tz.is_ambiguous(dt)
except Exception:
pass
# If it doesn't come out and tell us it's ambiguous, we'll just check if
# the fold attribute has any effect on this particular date and time.
dt = dt.replace(tzinfo=tz)
wall_0 = enfold(dt, fold=0)
wall_1 = enfold(dt, fold=1)
same_offset = wall_0.utcoffset() == wall_1.utcoffset()
same_dst = wall_0.dst() == wall_1.dst()
return not (same_offset and same_dst)
def resolve_imaginary(dt):
"""
Given a datetime that may be imaginary, return an existing datetime.
This function assumes that an imaginary datetime represents what the
wall time would be in a zone had the offset transition not occurred, so
it will always fall forward by the transition's change in offset.
.. doctest::
>>> from dateutil import tz
>>> from datetime import datetime
>>> NYC = tz.gettz('America/New_York')
>>> print(tz.resolve_imaginary(datetime(2017, 3, 12, 2, 30, tzinfo=NYC)))
2017-03-12 03:30:00-04:00
>>> KIR = tz.gettz('Pacific/Kiritimati')
>>> print(tz.resolve_imaginary(datetime(1995, 1, 1, 12, 30, tzinfo=KIR)))
1995-01-02 12:30:00+14:00
As a note, :func:`datetime.astimezone` is guaranteed to produce a valid,
existing datetime, so a round-trip to and from UTC is sufficient to get
an extant datetime, however, this generally "falls back" to an earlier time
rather than falling forward to the STD side (though no guarantees are made
about this behavior).
:param dt:
A :class:`datetime.datetime` which may or may not exist.
:return:
Returns an existing :class:`datetime.datetime`. If ``dt`` was not
imaginary, the datetime returned is guaranteed to be the same object
passed to the function.
.. versionadded:: 2.7.0
"""
if dt.tzinfo is not None and not datetime_exists(dt):
curr_offset = (dt + datetime.timedelta(hours=24)).utcoffset()
old_offset = (dt - datetime.timedelta(hours=24)).utcoffset()
dt += curr_offset - old_offset
return dt
def _datetime_to_timestamp(dt):
"""
Convert a :class:`datetime.datetime` object to an epoch timestamp in
seconds since January 1, 1970, ignoring the time zone.
"""
return (dt.replace(tzinfo=None) - EPOCH).total_seconds()
class _ContextWrapper(object):
"""
Class for wrapping contexts so that they are passed through in a
with statement.
"""
def __init__(self, context):
self.context = context
def __enter__(self):
return self.context
def __exit__(*args, **kwargs):
pass
# vim:ts=4:sw=4:et
| 60,472 | 32.859462 | 83 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/matplotlib/fontconfig_pattern.py
|
"""
A module for parsing and generating fontconfig patterns.
See the `fontconfig pattern specification
<https://www.freedesktop.org/software/fontconfig/fontconfig-user.html>`_ for
more information.
"""
# This class is defined here because it must be available in:
# - The old-style config framework (:file:`rcsetup.py`)
# - The font manager (:file:`font_manager.py`)
# It probably logically belongs in :file:`font_manager.py`, but placing it
# there would have created cyclical dependency problems.
from __future__ import (absolute_import, division, print_function,
unicode_literals)
import six
import re
from pyparsing import (Literal, ZeroOrMore, Optional, Regex, StringEnd,
ParseException, Suppress)
try:
from functools import lru_cache
except ImportError:
from backports.functools_lru_cache import lru_cache
family_punc = r'\\\-:,'
family_unescape = re.compile(r'\\([%s])' % family_punc).sub
family_escape = re.compile(r'([%s])' % family_punc).sub
value_punc = r'\\=_:,'
value_unescape = re.compile(r'\\([%s])' % value_punc).sub
value_escape = re.compile(r'([%s])' % value_punc).sub
class FontconfigPatternParser(object):
"""A simple pyparsing-based parser for fontconfig-style patterns.
See the `fontconfig pattern specification
<https://www.freedesktop.org/software/fontconfig/fontconfig-user.html>`_
for more information.
"""
_constants = {
'thin' : ('weight', 'light'),
'extralight' : ('weight', 'light'),
'ultralight' : ('weight', 'light'),
'light' : ('weight', 'light'),
'book' : ('weight', 'book'),
'regular' : ('weight', 'regular'),
'normal' : ('weight', 'normal'),
'medium' : ('weight', 'medium'),
'demibold' : ('weight', 'demibold'),
'semibold' : ('weight', 'semibold'),
'bold' : ('weight', 'bold'),
'extrabold' : ('weight', 'extra bold'),
'black' : ('weight', 'black'),
'heavy' : ('weight', 'heavy'),
'roman' : ('slant', 'normal'),
'italic' : ('slant', 'italic'),
'oblique' : ('slant', 'oblique'),
'ultracondensed' : ('width', 'ultra-condensed'),
'extracondensed' : ('width', 'extra-condensed'),
'condensed' : ('width', 'condensed'),
'semicondensed' : ('width', 'semi-condensed'),
'expanded' : ('width', 'expanded'),
'extraexpanded' : ('width', 'extra-expanded'),
'ultraexpanded' : ('width', 'ultra-expanded')
}
def __init__(self):
family = Regex(r'([^%s]|(\\[%s]))*' %
(family_punc, family_punc)) \
.setParseAction(self._family)
size = Regex(r"([0-9]+\.?[0-9]*|\.[0-9]+)") \
.setParseAction(self._size)
name = Regex(r'[a-z]+') \
.setParseAction(self._name)
value = Regex(r'([^%s]|(\\[%s]))*' %
(value_punc, value_punc)) \
.setParseAction(self._value)
families =(family
+ ZeroOrMore(
Literal(',')
+ family)
).setParseAction(self._families)
point_sizes =(size
+ ZeroOrMore(
Literal(',')
+ size)
).setParseAction(self._point_sizes)
property =( (name
+ Suppress(Literal('='))
+ value
+ ZeroOrMore(
Suppress(Literal(','))
+ value)
)
| name
).setParseAction(self._property)
pattern =(Optional(
families)
+ Optional(
Literal('-')
+ point_sizes)
+ ZeroOrMore(
Literal(':')
+ property)
+ StringEnd()
)
self._parser = pattern
self.ParseException = ParseException
def parse(self, pattern):
"""
Parse the given fontconfig *pattern* and return a dictionary
of key/value pairs useful for initializing a
:class:`font_manager.FontProperties` object.
"""
props = self._properties = {}
try:
self._parser.parseString(pattern)
except self.ParseException as e:
raise ValueError(
"Could not parse font string: '%s'\n%s" % (pattern, e))
self._properties = None
self._parser.resetCache()
return props
def _family(self, s, loc, tokens):
return [family_unescape(r'\1', str(tokens[0]))]
def _size(self, s, loc, tokens):
return [float(tokens[0])]
def _name(self, s, loc, tokens):
return [str(tokens[0])]
def _value(self, s, loc, tokens):
return [value_unescape(r'\1', str(tokens[0]))]
def _families(self, s, loc, tokens):
self._properties['family'] = [str(x) for x in tokens]
return []
def _point_sizes(self, s, loc, tokens):
self._properties['size'] = [str(x) for x in tokens]
return []
def _property(self, s, loc, tokens):
if len(tokens) == 1:
if tokens[0] in self._constants:
key, val = self._constants[tokens[0]]
self._properties.setdefault(key, []).append(val)
else:
key = tokens[0]
val = tokens[1:]
self._properties.setdefault(key, []).extend(val)
return []
# `parse_fontconfig_pattern` is a bottleneck during the tests because it is
# repeatedly called when the rcParams are reset (to validate the default
# fonts). In practice, the cache size doesn't grow beyond a few dozen entries
# during the test suite.
parse_fontconfig_pattern = lru_cache()(FontconfigPatternParser().parse)
def generate_fontconfig_pattern(d):
"""
Given a dictionary of key/value pairs, generates a fontconfig
pattern string.
"""
props = []
families = ''
size = ''
for key in 'family style variant weight stretch file size'.split():
val = getattr(d, 'get_' + key)()
if val is not None and val != []:
if type(val) == list:
val = [value_escape(r'\\\1', str(x)) for x in val
if x is not None]
if val != []:
val = ','.join(val)
props.append(":%s=%s" % (key, val))
return ''.join(props)
| 6,800 | 33.522843 | 78 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/matplotlib/mathtext.py
|
r"""
:mod:`~matplotlib.mathtext` is a module for parsing a subset of the
TeX math syntax and drawing them to a matplotlib backend.
For a tutorial of its usage see :ref:`sphx_glr_tutorials_text_mathtext.py`. This
document is primarily concerned with implementation details.
The module uses pyparsing_ to parse the TeX expression.
.. _pyparsing: http://pyparsing.wikispaces.com/
The Bakoma distribution of the TeX Computer Modern fonts, and STIX
fonts are supported. There is experimental support for using
arbitrary fonts, but results may vary without proper tweaking and
metrics for those fonts.
"""
from __future__ import (absolute_import, division, print_function,
unicode_literals)
import six
from six import unichr
import os
from math import ceil
import unicodedata
from warnings import warn
from numpy import inf, isinf
import numpy as np
from pyparsing import (
Combine, Empty, FollowedBy, Forward, Group, Literal, oneOf, OneOrMore,
Optional, ParseBaseException, ParseFatalException, ParserElement,
QuotedString, Regex, StringEnd, Suppress, ZeroOrMore)
ParserElement.enablePackrat()
from matplotlib import _png, colors as mcolors, get_data_path, rcParams
from matplotlib.afm import AFM
from matplotlib.cbook import Bunch, get_realpath_and_stat, maxdict
from matplotlib.ft2font import FT2Image, KERNING_DEFAULT, LOAD_NO_HINTING
from matplotlib.font_manager import findfont, FontProperties, get_font
from matplotlib._mathtext_data import (latex_to_bakoma, latex_to_standard,
tex2uni, latex_to_cmex,
stix_virtual_fonts)
####################
##############################################################################
# FONTS
def get_unicode_index(symbol, math=True):
"""get_unicode_index(symbol, [bool]) -> integer
Return the integer index (from the Unicode table) of symbol. *symbol*
can be a single unicode character, a TeX command (i.e. r'\\pi'), or a
Type1 symbol name (i.e. 'phi').
If math is False, the current symbol should be treated as a non-math symbol.
"""
# for a non-math symbol, simply return its unicode index
if not math:
return ord(symbol)
# From UTF #25: U+2212 minus sign is the preferred
# representation of the unary and binary minus sign rather than
# the ASCII-derived U+002D hyphen-minus, because minus sign is
# unambiguous and because it is rendered with a more desirable
# length, usually longer than a hyphen.
if symbol == '-':
return 0x2212
try:# This will succeed if symbol is a single unicode char
return ord(symbol)
except TypeError:
pass
try:# Is symbol a TeX symbol (i.e. \alpha)
return tex2uni[symbol.strip("\\")]
except KeyError:
message = """'%(symbol)s' is not a valid Unicode character or
TeX/Type1 symbol"""%locals()
raise ValueError(message)
def unichr_safe(index):
"""Return the Unicode character corresponding to the index,
or the replacement character if this is a narrow build of Python
and the requested character is outside the BMP."""
try:
return unichr(index)
except ValueError:
return unichr(0xFFFD)
class MathtextBackend(object):
"""
The base class for the mathtext backend-specific code. The
purpose of :class:`MathtextBackend` subclasses is to interface
between mathtext and a specific matplotlib graphics backend.
Subclasses need to override the following:
- :meth:`render_glyph`
- :meth:`render_rect_filled`
- :meth:`get_results`
And optionally, if you need to use a FreeType hinting style:
- :meth:`get_hinting_type`
"""
def __init__(self):
self.width = 0
self.height = 0
self.depth = 0
def set_canvas_size(self, w, h, d):
'Dimension the drawing canvas'
self.width = w
self.height = h
self.depth = d
def render_glyph(self, ox, oy, info):
"""
Draw a glyph described by *info* to the reference point (*ox*,
*oy*).
"""
raise NotImplementedError()
def render_rect_filled(self, x1, y1, x2, y2):
"""
Draw a filled black rectangle from (*x1*, *y1*) to (*x2*, *y2*).
"""
raise NotImplementedError()
def get_results(self, box):
"""
Return a backend-specific tuple to return to the backend after
all processing is done.
"""
raise NotImplementedError()
def get_hinting_type(self):
"""
Get the FreeType hinting type to use with this particular
backend.
"""
return LOAD_NO_HINTING
class MathtextBackendAgg(MathtextBackend):
"""
Render glyphs and rectangles to an FTImage buffer, which is later
transferred to the Agg image by the Agg backend.
"""
def __init__(self):
self.ox = 0
self.oy = 0
self.image = None
self.mode = 'bbox'
self.bbox = [0, 0, 0, 0]
MathtextBackend.__init__(self)
def _update_bbox(self, x1, y1, x2, y2):
self.bbox = [min(self.bbox[0], x1),
min(self.bbox[1], y1),
max(self.bbox[2], x2),
max(self.bbox[3], y2)]
def set_canvas_size(self, w, h, d):
MathtextBackend.set_canvas_size(self, w, h, d)
if self.mode != 'bbox':
self.image = FT2Image(ceil(w), ceil(h + max(d, 0)))
def render_glyph(self, ox, oy, info):
if self.mode == 'bbox':
self._update_bbox(ox + info.metrics.xmin,
oy - info.metrics.ymax,
ox + info.metrics.xmax,
oy - info.metrics.ymin)
else:
info.font.draw_glyph_to_bitmap(
self.image, ox, oy - info.metrics.iceberg, info.glyph,
antialiased=rcParams['text.antialiased'])
def render_rect_filled(self, x1, y1, x2, y2):
if self.mode == 'bbox':
self._update_bbox(x1, y1, x2, y2)
else:
height = max(int(y2 - y1) - 1, 0)
if height == 0:
center = (y2 + y1) / 2.0
y = int(center - (height + 1) / 2.0)
else:
y = int(y1)
self.image.draw_rect_filled(int(x1), y, ceil(x2), y + height)
def get_results(self, box, used_characters):
self.mode = 'bbox'
orig_height = box.height
orig_depth = box.depth
ship(0, 0, box)
bbox = self.bbox
bbox = [bbox[0] - 1, bbox[1] - 1, bbox[2] + 1, bbox[3] + 1]
self.mode = 'render'
self.set_canvas_size(
bbox[2] - bbox[0],
(bbox[3] - bbox[1]) - orig_depth,
(bbox[3] - bbox[1]) - orig_height)
ship(-bbox[0], -bbox[1], box)
result = (self.ox,
self.oy,
self.width,
self.height + self.depth,
self.depth,
self.image,
used_characters)
self.image = None
return result
def get_hinting_type(self):
from matplotlib.backends import backend_agg
return backend_agg.get_hinting_flag()
class MathtextBackendBitmap(MathtextBackendAgg):
def get_results(self, box, used_characters):
ox, oy, width, height, depth, image, characters = \
MathtextBackendAgg.get_results(self, box, used_characters)
return image, depth
class MathtextBackendPs(MathtextBackend):
"""
Store information to write a mathtext rendering to the PostScript
backend.
"""
def __init__(self):
self.pswriter = six.moves.cStringIO()
self.lastfont = None
def render_glyph(self, ox, oy, info):
oy = self.height - oy + info.offset
postscript_name = info.postscript_name
fontsize = info.fontsize
symbol_name = info.symbol_name
if (postscript_name, fontsize) != self.lastfont:
ps = """/%(postscript_name)s findfont
%(fontsize)s scalefont
setfont
""" % locals()
self.lastfont = postscript_name, fontsize
self.pswriter.write(ps)
ps = """%(ox)f %(oy)f moveto
/%(symbol_name)s glyphshow\n
""" % locals()
self.pswriter.write(ps)
def render_rect_filled(self, x1, y1, x2, y2):
ps = "%f %f %f %f rectfill\n" % (x1, self.height - y2, x2 - x1, y2 - y1)
self.pswriter.write(ps)
def get_results(self, box, used_characters):
ship(0, 0, box)
return (self.width,
self.height + self.depth,
self.depth,
self.pswriter,
used_characters)
class MathtextBackendPdf(MathtextBackend):
"""
Store information to write a mathtext rendering to the PDF
backend.
"""
def __init__(self):
self.glyphs = []
self.rects = []
def render_glyph(self, ox, oy, info):
filename = info.font.fname
oy = self.height - oy + info.offset
self.glyphs.append(
(ox, oy, filename, info.fontsize,
info.num, info.symbol_name))
def render_rect_filled(self, x1, y1, x2, y2):
self.rects.append((x1, self.height - y2, x2 - x1, y2 - y1))
def get_results(self, box, used_characters):
ship(0, 0, box)
return (self.width,
self.height + self.depth,
self.depth,
self.glyphs,
self.rects,
used_characters)
class MathtextBackendSvg(MathtextBackend):
"""
Store information to write a mathtext rendering to the SVG
backend.
"""
def __init__(self):
self.svg_glyphs = []
self.svg_rects = []
def render_glyph(self, ox, oy, info):
oy = self.height - oy + info.offset
self.svg_glyphs.append(
(info.font, info.fontsize, info.num, ox, oy, info.metrics))
def render_rect_filled(self, x1, y1, x2, y2):
self.svg_rects.append(
(x1, self.height - y1 + 1, x2 - x1, y2 - y1))
def get_results(self, box, used_characters):
ship(0, 0, box)
svg_elements = Bunch(svg_glyphs = self.svg_glyphs,
svg_rects = self.svg_rects)
return (self.width,
self.height + self.depth,
self.depth,
svg_elements,
used_characters)
class MathtextBackendPath(MathtextBackend):
"""
Store information to write a mathtext rendering to the text path
machinery.
"""
def __init__(self):
self.glyphs = []
self.rects = []
def render_glyph(self, ox, oy, info):
oy = self.height - oy + info.offset
thetext = info.num
self.glyphs.append(
(info.font, info.fontsize, thetext, ox, oy))
def render_rect_filled(self, x1, y1, x2, y2):
self.rects.append(
(x1, self.height-y2 , x2 - x1, y2 - y1))
def get_results(self, box, used_characters):
ship(0, 0, box)
return (self.width,
self.height + self.depth,
self.depth,
self.glyphs,
self.rects)
class MathtextBackendCairo(MathtextBackend):
"""
Store information to write a mathtext rendering to the Cairo
backend.
"""
def __init__(self):
self.glyphs = []
self.rects = []
def render_glyph(self, ox, oy, info):
oy = oy - info.offset - self.height
thetext = unichr_safe(info.num)
self.glyphs.append(
(info.font, info.fontsize, thetext, ox, oy))
def render_rect_filled(self, x1, y1, x2, y2):
self.rects.append(
(x1, y1 - self.height, x2 - x1, y2 - y1))
def get_results(self, box, used_characters):
ship(0, 0, box)
return (self.width,
self.height + self.depth,
self.depth,
self.glyphs,
self.rects)
class Fonts(object):
"""
An abstract base class for a system of fonts to use for mathtext.
The class must be able to take symbol keys and font file names and
return the character metrics. It also delegates to a backend class
to do the actual drawing.
"""
def __init__(self, default_font_prop, mathtext_backend):
"""
*default_font_prop*: A
:class:`~matplotlib.font_manager.FontProperties` object to use
for the default non-math font, or the base font for Unicode
(generic) font rendering.
*mathtext_backend*: A subclass of :class:`MathTextBackend`
used to delegate the actual rendering.
"""
self.default_font_prop = default_font_prop
self.mathtext_backend = mathtext_backend
self.used_characters = {}
def destroy(self):
"""
Fix any cyclical references before the object is about
to be destroyed.
"""
self.used_characters = None
def get_kern(self, font1, fontclass1, sym1, fontsize1,
font2, fontclass2, sym2, fontsize2, dpi):
"""
Get the kerning distance for font between *sym1* and *sym2*.
*fontX*: one of the TeX font names::
tt, it, rm, cal, sf, bf or default/regular (non-math)
*fontclassX*: TODO
*symX*: a symbol in raw TeX form. e.g., '1', 'x' or '\\sigma'
*fontsizeX*: the fontsize in points
*dpi*: the current dots-per-inch
"""
return 0.
def get_metrics(self, font, font_class, sym, fontsize, dpi, math=True):
"""
*font*: one of the TeX font names::
tt, it, rm, cal, sf, bf or default/regular (non-math)
*font_class*: TODO
*sym*: a symbol in raw TeX form. e.g., '1', 'x' or '\\sigma'
*fontsize*: font size in points
*dpi*: current dots-per-inch
*math*: whether sym is a math character
Returns an object with the following attributes:
- *advance*: The advance distance (in points) of the glyph.
- *height*: The height of the glyph in points.
- *width*: The width of the glyph in points.
- *xmin*, *xmax*, *ymin*, *ymax* - the ink rectangle of the glyph
- *iceberg* - the distance from the baseline to the top of
the glyph. This corresponds to TeX's definition of
"height".
"""
info = self._get_info(font, font_class, sym, fontsize, dpi, math)
return info.metrics
def set_canvas_size(self, w, h, d):
"""
Set the size of the buffer used to render the math expression.
Only really necessary for the bitmap backends.
"""
self.width, self.height, self.depth = ceil(w), ceil(h), ceil(d)
self.mathtext_backend.set_canvas_size(self.width, self.height, self.depth)
def render_glyph(self, ox, oy, facename, font_class, sym, fontsize, dpi):
"""
Draw a glyph at
- *ox*, *oy*: position
- *facename*: One of the TeX face names
- *font_class*:
- *sym*: TeX symbol name or single character
- *fontsize*: fontsize in points
- *dpi*: The dpi to draw at.
"""
info = self._get_info(facename, font_class, sym, fontsize, dpi)
realpath, stat_key = get_realpath_and_stat(info.font.fname)
used_characters = self.used_characters.setdefault(
stat_key, (realpath, set()))
used_characters[1].add(info.num)
self.mathtext_backend.render_glyph(ox, oy, info)
def render_rect_filled(self, x1, y1, x2, y2):
"""
Draw a filled rectangle from (*x1*, *y1*) to (*x2*, *y2*).
"""
self.mathtext_backend.render_rect_filled(x1, y1, x2, y2)
def get_xheight(self, font, fontsize, dpi):
"""
Get the xheight for the given *font* and *fontsize*.
"""
raise NotImplementedError()
def get_underline_thickness(self, font, fontsize, dpi):
"""
Get the line thickness that matches the given font. Used as a
base unit for drawing lines such as in a fraction or radical.
"""
raise NotImplementedError()
def get_used_characters(self):
"""
Get the set of characters that were used in the math
expression. Used by backends that need to subset fonts so
they know which glyphs to include.
"""
return self.used_characters
def get_results(self, box):
"""
Get the data needed by the backend to render the math
expression. The return value is backend-specific.
"""
result = self.mathtext_backend.get_results(box, self.get_used_characters())
self.destroy()
return result
def get_sized_alternatives_for_symbol(self, fontname, sym):
"""
Override if your font provides multiple sizes of the same
symbol. Should return a list of symbols matching *sym* in
various sizes. The expression renderer will select the most
appropriate size for a given situation from this list.
"""
return [(fontname, sym)]
class TruetypeFonts(Fonts):
"""
A generic base class for all font setups that use Truetype fonts
(through FT2Font).
"""
def __init__(self, default_font_prop, mathtext_backend):
Fonts.__init__(self, default_font_prop, mathtext_backend)
self.glyphd = {}
self._fonts = {}
filename = findfont(default_font_prop)
default_font = get_font(filename)
self._fonts['default'] = default_font
self._fonts['regular'] = default_font
def destroy(self):
self.glyphd = None
Fonts.destroy(self)
def _get_font(self, font):
if font in self.fontmap:
basename = self.fontmap[font]
else:
basename = font
cached_font = self._fonts.get(basename)
if cached_font is None and os.path.exists(basename):
cached_font = get_font(basename)
self._fonts[basename] = cached_font
self._fonts[cached_font.postscript_name] = cached_font
self._fonts[cached_font.postscript_name.lower()] = cached_font
return cached_font
def _get_offset(self, font, glyph, fontsize, dpi):
if font.postscript_name == 'Cmex10':
return ((glyph.height/64.0/2.0) + (fontsize/3.0 * dpi/72.0))
return 0.
def _get_info(self, fontname, font_class, sym, fontsize, dpi, math=True):
key = fontname, font_class, sym, fontsize, dpi
bunch = self.glyphd.get(key)
if bunch is not None:
return bunch
font, num, symbol_name, fontsize, slanted = \
self._get_glyph(fontname, font_class, sym, fontsize, math)
font.set_size(fontsize, dpi)
glyph = font.load_char(
num,
flags=self.mathtext_backend.get_hinting_type())
xmin, ymin, xmax, ymax = [val/64.0 for val in glyph.bbox]
offset = self._get_offset(font, glyph, fontsize, dpi)
metrics = Bunch(
advance = glyph.linearHoriAdvance/65536.0,
height = glyph.height/64.0,
width = glyph.width/64.0,
xmin = xmin,
xmax = xmax,
ymin = ymin+offset,
ymax = ymax+offset,
# iceberg is the equivalent of TeX's "height"
iceberg = glyph.horiBearingY/64.0 + offset,
slanted = slanted
)
result = self.glyphd[key] = Bunch(
font = font,
fontsize = fontsize,
postscript_name = font.postscript_name,
metrics = metrics,
symbol_name = symbol_name,
num = num,
glyph = glyph,
offset = offset
)
return result
def get_xheight(self, fontname, fontsize, dpi):
font = self._get_font(fontname)
font.set_size(fontsize, dpi)
pclt = font.get_sfnt_table('pclt')
if pclt is None:
# Some fonts don't store the xHeight, so we do a poor man's xHeight
metrics = self.get_metrics(fontname, rcParams['mathtext.default'], 'x', fontsize, dpi)
return metrics.iceberg
xHeight = (pclt['xHeight'] / 64.0) * (fontsize / 12.0) * (dpi / 100.0)
return xHeight
def get_underline_thickness(self, font, fontsize, dpi):
# This function used to grab underline thickness from the font
# metrics, but that information is just too un-reliable, so it
# is now hardcoded.
return ((0.75 / 12.0) * fontsize * dpi) / 72.0
def get_kern(self, font1, fontclass1, sym1, fontsize1,
font2, fontclass2, sym2, fontsize2, dpi):
if font1 == font2 and fontsize1 == fontsize2:
info1 = self._get_info(font1, fontclass1, sym1, fontsize1, dpi)
info2 = self._get_info(font2, fontclass2, sym2, fontsize2, dpi)
font = info1.font
return font.get_kerning(info1.num, info2.num, KERNING_DEFAULT) / 64.0
return Fonts.get_kern(self, font1, fontclass1, sym1, fontsize1,
font2, fontclass2, sym2, fontsize2, dpi)
class BakomaFonts(TruetypeFonts):
"""
Use the Bakoma TrueType fonts for rendering.
Symbols are strewn about a number of font files, each of which has
its own proprietary 8-bit encoding.
"""
_fontmap = { 'cal' : 'cmsy10',
'rm' : 'cmr10',
'tt' : 'cmtt10',
'it' : 'cmmi10',
'bf' : 'cmb10',
'sf' : 'cmss10',
'ex' : 'cmex10'
}
def __init__(self, *args, **kwargs):
self._stix_fallback = StixFonts(*args, **kwargs)
TruetypeFonts.__init__(self, *args, **kwargs)
self.fontmap = {}
for key, val in six.iteritems(self._fontmap):
fullpath = findfont(val)
self.fontmap[key] = fullpath
self.fontmap[val] = fullpath
_slanted_symbols = set(r"\int \oint".split())
def _get_glyph(self, fontname, font_class, sym, fontsize, math=True):
symbol_name = None
font = None
if fontname in self.fontmap and sym in latex_to_bakoma:
basename, num = latex_to_bakoma[sym]
slanted = (basename == "cmmi10") or sym in self._slanted_symbols
font = self._get_font(basename)
elif len(sym) == 1:
slanted = (fontname == "it")
font = self._get_font(fontname)
if font is not None:
num = ord(sym)
if font is not None:
gid = font.get_char_index(num)
if gid != 0:
symbol_name = font.get_glyph_name(gid)
if symbol_name is None:
return self._stix_fallback._get_glyph(
fontname, font_class, sym, fontsize, math)
return font, num, symbol_name, fontsize, slanted
# The Bakoma fonts contain many pre-sized alternatives for the
# delimiters. The AutoSizedChar class will use these alternatives
# and select the best (closest sized) glyph.
_size_alternatives = {
'(' : [('rm', '('), ('ex', '\xa1'), ('ex', '\xb3'),
('ex', '\xb5'), ('ex', '\xc3')],
')' : [('rm', ')'), ('ex', '\xa2'), ('ex', '\xb4'),
('ex', '\xb6'), ('ex', '\x21')],
'{' : [('cal', '{'), ('ex', '\xa9'), ('ex', '\x6e'),
('ex', '\xbd'), ('ex', '\x28')],
'}' : [('cal', '}'), ('ex', '\xaa'), ('ex', '\x6f'),
('ex', '\xbe'), ('ex', '\x29')],
# The fourth size of '[' is mysteriously missing from the BaKoMa
# font, so I've omitted it for both '[' and ']'
'[' : [('rm', '['), ('ex', '\xa3'), ('ex', '\x68'),
('ex', '\x22')],
']' : [('rm', ']'), ('ex', '\xa4'), ('ex', '\x69'),
('ex', '\x23')],
r'\lfloor' : [('ex', '\xa5'), ('ex', '\x6a'),
('ex', '\xb9'), ('ex', '\x24')],
r'\rfloor' : [('ex', '\xa6'), ('ex', '\x6b'),
('ex', '\xba'), ('ex', '\x25')],
r'\lceil' : [('ex', '\xa7'), ('ex', '\x6c'),
('ex', '\xbb'), ('ex', '\x26')],
r'\rceil' : [('ex', '\xa8'), ('ex', '\x6d'),
('ex', '\xbc'), ('ex', '\x27')],
r'\langle' : [('ex', '\xad'), ('ex', '\x44'),
('ex', '\xbf'), ('ex', '\x2a')],
r'\rangle' : [('ex', '\xae'), ('ex', '\x45'),
('ex', '\xc0'), ('ex', '\x2b')],
r'\__sqrt__' : [('ex', '\x70'), ('ex', '\x71'),
('ex', '\x72'), ('ex', '\x73')],
r'\backslash': [('ex', '\xb2'), ('ex', '\x2f'),
('ex', '\xc2'), ('ex', '\x2d')],
r'/' : [('rm', '/'), ('ex', '\xb1'), ('ex', '\x2e'),
('ex', '\xcb'), ('ex', '\x2c')],
r'\widehat' : [('rm', '\x5e'), ('ex', '\x62'), ('ex', '\x63'),
('ex', '\x64')],
r'\widetilde': [('rm', '\x7e'), ('ex', '\x65'), ('ex', '\x66'),
('ex', '\x67')],
r'<' : [('cal', 'h'), ('ex', 'D')],
r'>' : [('cal', 'i'), ('ex', 'E')]
}
for alias, target in [(r'\leftparen', '('),
(r'\rightparent', ')'),
(r'\leftbrace', '{'),
(r'\rightbrace', '}'),
(r'\leftbracket', '['),
(r'\rightbracket', ']'),
(r'\{', '{'),
(r'\}', '}'),
(r'\[', '['),
(r'\]', ']')]:
_size_alternatives[alias] = _size_alternatives[target]
def get_sized_alternatives_for_symbol(self, fontname, sym):
return self._size_alternatives.get(sym, [(fontname, sym)])
class UnicodeFonts(TruetypeFonts):
"""
An abstract base class for handling Unicode fonts.
While some reasonably complete Unicode fonts (such as DejaVu) may
work in some situations, the only Unicode font I'm aware of with a
complete set of math symbols is STIX.
This class will "fallback" on the Bakoma fonts when a required
symbol can not be found in the font.
"""
use_cmex = True
def __init__(self, *args, **kwargs):
# This must come first so the backend's owner is set correctly
if rcParams['mathtext.fallback_to_cm']:
self.cm_fallback = BakomaFonts(*args, **kwargs)
else:
self.cm_fallback = None
TruetypeFonts.__init__(self, *args, **kwargs)
self.fontmap = {}
for texfont in "cal rm tt it bf sf".split():
prop = rcParams['mathtext.' + texfont]
font = findfont(prop)
self.fontmap[texfont] = font
prop = FontProperties('cmex10')
font = findfont(prop)
self.fontmap['ex'] = font
_slanted_symbols = set(r"\int \oint".split())
def _map_virtual_font(self, fontname, font_class, uniindex):
return fontname, uniindex
def _get_glyph(self, fontname, font_class, sym, fontsize, math=True):
found_symbol = False
if self.use_cmex:
uniindex = latex_to_cmex.get(sym)
if uniindex is not None:
fontname = 'ex'
found_symbol = True
if not found_symbol:
try:
uniindex = get_unicode_index(sym, math)
found_symbol = True
except ValueError:
uniindex = ord('?')
warn("No TeX to unicode mapping for '%s'" %
sym.encode('ascii', 'backslashreplace'),
MathTextWarning)
fontname, uniindex = self._map_virtual_font(
fontname, font_class, uniindex)
new_fontname = fontname
# Only characters in the "Letter" class should be italicized in 'it'
# mode. Greek capital letters should be Roman.
if found_symbol:
if fontname == 'it':
if uniindex < 0x10000:
unistring = unichr(uniindex)
if (not unicodedata.category(unistring)[0] == "L"
or unicodedata.name(unistring).startswith("GREEK CAPITAL")):
new_fontname = 'rm'
slanted = (new_fontname == 'it') or sym in self._slanted_symbols
found_symbol = False
font = self._get_font(new_fontname)
if font is not None:
glyphindex = font.get_char_index(uniindex)
if glyphindex != 0:
found_symbol = True
if not found_symbol:
if self.cm_fallback:
if isinstance(self.cm_fallback, BakomaFonts):
warn("Substituting with a symbol from Computer Modern.",
MathTextWarning)
if (fontname in ('it', 'regular') and
isinstance(self.cm_fallback, StixFonts)):
return self.cm_fallback._get_glyph(
'rm', font_class, sym, fontsize)
else:
return self.cm_fallback._get_glyph(
fontname, font_class, sym, fontsize)
else:
if fontname in ('it', 'regular') and isinstance(self, StixFonts):
return self._get_glyph('rm', font_class, sym, fontsize)
warn("Font '%s' does not have a glyph for '%s' [U+%x]" %
(new_fontname,
sym.encode('ascii', 'backslashreplace').decode('ascii'),
uniindex),
MathTextWarning)
warn("Substituting with a dummy symbol.", MathTextWarning)
fontname = 'rm'
new_fontname = fontname
font = self._get_font(fontname)
uniindex = 0xA4 # currency character, for lack of anything better
glyphindex = font.get_char_index(uniindex)
slanted = False
symbol_name = font.get_glyph_name(glyphindex)
return font, uniindex, symbol_name, fontsize, slanted
def get_sized_alternatives_for_symbol(self, fontname, sym):
if self.cm_fallback:
return self.cm_fallback.get_sized_alternatives_for_symbol(
fontname, sym)
return [(fontname, sym)]
class DejaVuFonts(UnicodeFonts):
use_cmex = False
def __init__(self, *args, **kwargs):
# This must come first so the backend's owner is set correctly
if isinstance(self, DejaVuSerifFonts):
self.cm_fallback = StixFonts(*args, **kwargs)
else:
self.cm_fallback = StixSansFonts(*args, **kwargs)
self.bakoma = BakomaFonts(*args, **kwargs)
TruetypeFonts.__init__(self, *args, **kwargs)
self.fontmap = {}
# Include Stix sized alternatives for glyphs
self._fontmap.update({
1 : 'STIXSizeOneSym',
2 : 'STIXSizeTwoSym',
3 : 'STIXSizeThreeSym',
4 : 'STIXSizeFourSym',
5 : 'STIXSizeFiveSym'})
for key, name in six.iteritems(self._fontmap):
fullpath = findfont(name)
self.fontmap[key] = fullpath
self.fontmap[name] = fullpath
def _get_glyph(self, fontname, font_class, sym, fontsize, math=True):
""" Override prime symbol to use Bakoma """
if sym == r'\prime':
return self.bakoma._get_glyph(fontname,
font_class, sym, fontsize, math)
else:
# check whether the glyph is available in the display font
uniindex = get_unicode_index(sym)
font = self._get_font('ex')
if font is not None:
glyphindex = font.get_char_index(uniindex)
if glyphindex != 0:
return super(DejaVuFonts, self)._get_glyph('ex',
font_class, sym, fontsize, math)
# otherwise return regular glyph
return super(DejaVuFonts, self)._get_glyph(fontname,
font_class, sym, fontsize, math)
class DejaVuSerifFonts(DejaVuFonts):
"""
A font handling class for the DejaVu Serif fonts
If a glyph is not found it will fallback to Stix Serif
"""
_fontmap = { 'rm' : 'DejaVu Serif',
'it' : 'DejaVu Serif:italic',
'bf' : 'DejaVu Serif:weight=bold',
'sf' : 'DejaVu Sans',
'tt' : 'DejaVu Sans Mono',
'ex' : 'DejaVu Serif Display',
0 : 'DejaVu Serif',
}
class DejaVuSansFonts(DejaVuFonts):
"""
A font handling class for the DejaVu Sans fonts
If a glyph is not found it will fallback to Stix Sans
"""
_fontmap = { 'rm' : 'DejaVu Sans',
'it' : 'DejaVu Sans:italic',
'bf' : 'DejaVu Sans:weight=bold',
'sf' : 'DejaVu Sans',
'tt' : 'DejaVu Sans Mono',
'ex' : 'DejaVu Sans Display',
0 : 'DejaVu Sans',
}
class StixFonts(UnicodeFonts):
"""
A font handling class for the STIX fonts.
In addition to what UnicodeFonts provides, this class:
- supports "virtual fonts" which are complete alpha numeric
character sets with different font styles at special Unicode
code points, such as "Blackboard".
- handles sized alternative characters for the STIXSizeX fonts.
"""
_fontmap = { 'rm' : 'STIXGeneral',
'it' : 'STIXGeneral:italic',
'bf' : 'STIXGeneral:weight=bold',
'nonunirm' : 'STIXNonUnicode',
'nonuniit' : 'STIXNonUnicode:italic',
'nonunibf' : 'STIXNonUnicode:weight=bold',
0 : 'STIXGeneral',
1 : 'STIXSizeOneSym',
2 : 'STIXSizeTwoSym',
3 : 'STIXSizeThreeSym',
4 : 'STIXSizeFourSym',
5 : 'STIXSizeFiveSym'
}
use_cmex = False
cm_fallback = False
_sans = False
def __init__(self, *args, **kwargs):
TruetypeFonts.__init__(self, *args, **kwargs)
self.fontmap = {}
for key, name in six.iteritems(self._fontmap):
fullpath = findfont(name)
self.fontmap[key] = fullpath
self.fontmap[name] = fullpath
def _map_virtual_font(self, fontname, font_class, uniindex):
# Handle these "fonts" that are actually embedded in
# other fonts.
mapping = stix_virtual_fonts.get(fontname)
if (self._sans and mapping is None and
fontname not in ('regular', 'default')):
mapping = stix_virtual_fonts['sf']
doing_sans_conversion = True
else:
doing_sans_conversion = False
if mapping is not None:
if isinstance(mapping, dict):
try:
mapping = mapping[font_class]
except KeyError:
mapping = mapping['rm']
# Binary search for the source glyph
lo = 0
hi = len(mapping)
while lo < hi:
mid = (lo+hi)//2
range = mapping[mid]
if uniindex < range[0]:
hi = mid
elif uniindex <= range[1]:
break
else:
lo = mid + 1
if uniindex >= range[0] and uniindex <= range[1]:
uniindex = uniindex - range[0] + range[3]
fontname = range[2]
elif not doing_sans_conversion:
# This will generate a dummy character
uniindex = 0x1
fontname = rcParams['mathtext.default']
# Handle private use area glyphs
if (fontname in ('it', 'rm', 'bf') and
uniindex >= 0xe000 and uniindex <= 0xf8ff):
fontname = 'nonuni' + fontname
return fontname, uniindex
_size_alternatives = {}
def get_sized_alternatives_for_symbol(self, fontname, sym):
fixes = {'\\{': '{', '\\}': '}', '\\[': '[', '\\]': ']'}
sym = fixes.get(sym, sym)
alternatives = self._size_alternatives.get(sym)
if alternatives:
return alternatives
alternatives = []
try:
uniindex = get_unicode_index(sym)
except ValueError:
return [(fontname, sym)]
fix_ups = {
ord('<'): 0x27e8,
ord('>'): 0x27e9 }
uniindex = fix_ups.get(uniindex, uniindex)
for i in range(6):
font = self._get_font(i)
glyphindex = font.get_char_index(uniindex)
if glyphindex != 0:
alternatives.append((i, unichr_safe(uniindex)))
# The largest size of the radical symbol in STIX has incorrect
# metrics that cause it to be disconnected from the stem.
if sym == r'\__sqrt__':
alternatives = alternatives[:-1]
self._size_alternatives[sym] = alternatives
return alternatives
class StixSansFonts(StixFonts):
"""
A font handling class for the STIX fonts (that uses sans-serif
characters by default).
"""
_sans = True
class StandardPsFonts(Fonts):
"""
Use the standard postscript fonts for rendering to backend_ps
Unlike the other font classes, BakomaFont and UnicodeFont, this
one requires the Ps backend.
"""
basepath = os.path.join( get_data_path(), 'fonts', 'afm' )
fontmap = { 'cal' : 'pzcmi8a', # Zapf Chancery
'rm' : 'pncr8a', # New Century Schoolbook
'tt' : 'pcrr8a', # Courier
'it' : 'pncri8a', # New Century Schoolbook Italic
'sf' : 'phvr8a', # Helvetica
'bf' : 'pncb8a', # New Century Schoolbook Bold
None : 'psyr' # Symbol
}
def __init__(self, default_font_prop):
Fonts.__init__(self, default_font_prop, MathtextBackendPs())
self.glyphd = {}
self.fonts = {}
filename = findfont(default_font_prop, fontext='afm',
directory=self.basepath)
if filename is None:
filename = findfont('Helvetica', fontext='afm',
directory=self.basepath)
with open(filename, 'rb') as fd:
default_font = AFM(fd)
default_font.fname = filename
self.fonts['default'] = default_font
self.fonts['regular'] = default_font
self.pswriter = six.moves.cStringIO()
def _get_font(self, font):
if font in self.fontmap:
basename = self.fontmap[font]
else:
basename = font
cached_font = self.fonts.get(basename)
if cached_font is None:
fname = os.path.join(self.basepath, basename + ".afm")
with open(fname, 'rb') as fd:
cached_font = AFM(fd)
cached_font.fname = fname
self.fonts[basename] = cached_font
self.fonts[cached_font.get_fontname()] = cached_font
return cached_font
def _get_info (self, fontname, font_class, sym, fontsize, dpi, math=True):
'load the cmfont, metrics and glyph with caching'
key = fontname, sym, fontsize, dpi
tup = self.glyphd.get(key)
if tup is not None:
return tup
# Only characters in the "Letter" class should really be italicized.
# This class includes greek letters, so we're ok
if (fontname == 'it' and
(len(sym) > 1 or
not unicodedata.category(six.text_type(sym)).startswith("L"))):
fontname = 'rm'
found_symbol = False
if sym in latex_to_standard:
fontname, num = latex_to_standard[sym]
glyph = chr(num)
found_symbol = True
elif len(sym) == 1:
glyph = sym
num = ord(glyph)
found_symbol = True
else:
warn("No TeX to built-in Postscript mapping for {!r}".format(sym),
MathTextWarning)
slanted = (fontname == 'it')
font = self._get_font(fontname)
if found_symbol:
try:
symbol_name = font.get_name_char(glyph)
except KeyError:
warn("No glyph in standard Postscript font {!r} for {!r}"
.format(font.get_fontname(), sym), MathTextWarning)
found_symbol = False
if not found_symbol:
glyph = sym = '?'
num = ord(glyph)
symbol_name = font.get_name_char(glyph)
offset = 0
scale = 0.001 * fontsize
xmin, ymin, xmax, ymax = [val * scale
for val in font.get_bbox_char(glyph)]
metrics = Bunch(
advance = font.get_width_char(glyph) * scale,
width = font.get_width_char(glyph) * scale,
height = font.get_height_char(glyph) * scale,
xmin = xmin,
xmax = xmax,
ymin = ymin+offset,
ymax = ymax+offset,
# iceberg is the equivalent of TeX's "height"
iceberg = ymax + offset,
slanted = slanted
)
self.glyphd[key] = Bunch(
font = font,
fontsize = fontsize,
postscript_name = font.get_fontname(),
metrics = metrics,
symbol_name = symbol_name,
num = num,
glyph = glyph,
offset = offset
)
return self.glyphd[key]
def get_kern(self, font1, fontclass1, sym1, fontsize1,
font2, fontclass2, sym2, fontsize2, dpi):
if font1 == font2 and fontsize1 == fontsize2:
info1 = self._get_info(font1, fontclass1, sym1, fontsize1, dpi)
info2 = self._get_info(font2, fontclass2, sym2, fontsize2, dpi)
font = info1.font
return (font.get_kern_dist(info1.glyph, info2.glyph)
* 0.001 * fontsize1)
return Fonts.get_kern(self, font1, fontclass1, sym1, fontsize1,
font2, fontclass2, sym2, fontsize2, dpi)
def get_xheight(self, font, fontsize, dpi):
font = self._get_font(font)
return font.get_xheight() * 0.001 * fontsize
def get_underline_thickness(self, font, fontsize, dpi):
font = self._get_font(font)
return font.get_underline_thickness() * 0.001 * fontsize
##############################################################################
# TeX-LIKE BOX MODEL
# The following is based directly on the document 'woven' from the
# TeX82 source code. This information is also available in printed
# form:
#
# Knuth, Donald E.. 1986. Computers and Typesetting, Volume B:
# TeX: The Program. Addison-Wesley Professional.
#
# The most relevant "chapters" are:
# Data structures for boxes and their friends
# Shipping pages out (Ship class)
# Packaging (hpack and vpack)
# Data structures for math mode
# Subroutines for math mode
# Typesetting math formulas
#
# Many of the docstrings below refer to a numbered "node" in that
# book, e.g., node123
#
# Note that (as TeX) y increases downward, unlike many other parts of
# matplotlib.
# How much text shrinks when going to the next-smallest level. GROW_FACTOR
# must be the inverse of SHRINK_FACTOR.
SHRINK_FACTOR = 0.7
GROW_FACTOR = 1.0 / SHRINK_FACTOR
# The number of different sizes of chars to use, beyond which they will not
# get any smaller
NUM_SIZE_LEVELS = 6
class FontConstantsBase(object):
"""
A set of constants that controls how certain things, such as sub-
and superscripts are laid out. These are all metrics that can't
be reliably retrieved from the font metrics in the font itself.
"""
# Percentage of x-height of additional horiz. space after sub/superscripts
script_space = 0.05
# Percentage of x-height that sub/superscripts drop below the baseline
subdrop = 0.4
# Percentage of x-height that superscripts are raised from the baseline
sup1 = 0.7
# Percentage of x-height that subscripts drop below the baseline
sub1 = 0.3
# Percentage of x-height that subscripts drop below the baseline when a
# superscript is present
sub2 = 0.5
# Percentage of x-height that sub/supercripts are offset relative to the
# nucleus edge for non-slanted nuclei
delta = 0.025
# Additional percentage of last character height above 2/3 of the
# x-height that supercripts are offset relative to the subscript
# for slanted nuclei
delta_slanted = 0.2
# Percentage of x-height that supercripts and subscripts are offset for
# integrals
delta_integral = 0.1
class ComputerModernFontConstants(FontConstantsBase):
script_space = 0.075
subdrop = 0.2
sup1 = 0.45
sub1 = 0.2
sub2 = 0.3
delta = 0.075
delta_slanted = 0.3
delta_integral = 0.3
class STIXFontConstants(FontConstantsBase):
script_space = 0.1
sup1 = 0.8
sub2 = 0.6
delta = 0.05
delta_slanted = 0.3
delta_integral = 0.3
class STIXSansFontConstants(FontConstantsBase):
script_space = 0.05
sup1 = 0.8
delta_slanted = 0.6
delta_integral = 0.3
class DejaVuSerifFontConstants(FontConstantsBase):
pass
class DejaVuSansFontConstants(FontConstantsBase):
pass
# Maps font family names to the FontConstantBase subclass to use
_font_constant_mapping = {
'DejaVu Sans': DejaVuSansFontConstants,
'DejaVu Sans Mono': DejaVuSansFontConstants,
'DejaVu Serif': DejaVuSerifFontConstants,
'cmb10': ComputerModernFontConstants,
'cmex10': ComputerModernFontConstants,
'cmmi10': ComputerModernFontConstants,
'cmr10': ComputerModernFontConstants,
'cmss10': ComputerModernFontConstants,
'cmsy10': ComputerModernFontConstants,
'cmtt10': ComputerModernFontConstants,
'STIXGeneral': STIXFontConstants,
'STIXNonUnicode': STIXFontConstants,
'STIXSizeFiveSym': STIXFontConstants,
'STIXSizeFourSym': STIXFontConstants,
'STIXSizeThreeSym': STIXFontConstants,
'STIXSizeTwoSym': STIXFontConstants,
'STIXSizeOneSym': STIXFontConstants,
# Map the fonts we used to ship, just for good measure
'Bitstream Vera Sans': DejaVuSansFontConstants,
'Bitstream Vera': DejaVuSansFontConstants,
}
def _get_font_constant_set(state):
constants = _font_constant_mapping.get(
state.font_output._get_font(state.font).family_name,
FontConstantsBase)
# STIX sans isn't really its own fonts, just different code points
# in the STIX fonts, so we have to detect this one separately.
if (constants is STIXFontConstants and
isinstance(state.font_output, StixSansFonts)):
return STIXSansFontConstants
return constants
class MathTextWarning(Warning):
pass
class Node(object):
"""
A node in the TeX box model
"""
def __init__(self):
self.size = 0
def __repr__(self):
return self.__internal_repr__()
def __internal_repr__(self):
return self.__class__.__name__
def get_kerning(self, next):
return 0.0
def shrink(self):
"""
Shrinks one level smaller. There are only three levels of
sizes, after which things will no longer get smaller.
"""
self.size += 1
def grow(self):
"""
Grows one level larger. There is no limit to how big
something can get.
"""
self.size -= 1
def render(self, x, y):
pass
class Box(Node):
"""
Represents any node with a physical location.
"""
def __init__(self, width, height, depth):
Node.__init__(self)
self.width = width
self.height = height
self.depth = depth
def shrink(self):
Node.shrink(self)
if self.size < NUM_SIZE_LEVELS:
self.width *= SHRINK_FACTOR
self.height *= SHRINK_FACTOR
self.depth *= SHRINK_FACTOR
def grow(self):
Node.grow(self)
self.width *= GROW_FACTOR
self.height *= GROW_FACTOR
self.depth *= GROW_FACTOR
def render(self, x1, y1, x2, y2):
pass
class Vbox(Box):
"""
A box with only height (zero width).
"""
def __init__(self, height, depth):
Box.__init__(self, 0., height, depth)
class Hbox(Box):
"""
A box with only width (zero height and depth).
"""
def __init__(self, width):
Box.__init__(self, width, 0., 0.)
class Char(Node):
"""
Represents a single character. Unlike TeX, the font information
and metrics are stored with each :class:`Char` to make it easier
to lookup the font metrics when needed. Note that TeX boxes have
a width, height, and depth, unlike Type1 and Truetype which use a
full bounding box and an advance in the x-direction. The metrics
must be converted to the TeX way, and the advance (if different
from width) must be converted into a :class:`Kern` node when the
:class:`Char` is added to its parent :class:`Hlist`.
"""
def __init__(self, c, state, math=True):
Node.__init__(self)
self.c = c
self.font_output = state.font_output
self.font = state.font
self.font_class = state.font_class
self.fontsize = state.fontsize
self.dpi = state.dpi
self.math = math
# The real width, height and depth will be set during the
# pack phase, after we know the real fontsize
self._update_metrics()
def __internal_repr__(self):
return '`%s`' % self.c
def _update_metrics(self):
metrics = self._metrics = self.font_output.get_metrics(
self.font, self.font_class, self.c, self.fontsize, self.dpi, self.math)
if self.c == ' ':
self.width = metrics.advance
else:
self.width = metrics.width
self.height = metrics.iceberg
self.depth = -(metrics.iceberg - metrics.height)
def is_slanted(self):
return self._metrics.slanted
def get_kerning(self, next):
"""
Return the amount of kerning between this and the given
character. Called when characters are strung together into
:class:`Hlist` to create :class:`Kern` nodes.
"""
advance = self._metrics.advance - self.width
kern = 0.
if isinstance(next, Char):
kern = self.font_output.get_kern(
self.font, self.font_class, self.c, self.fontsize,
next.font, next.font_class, next.c, next.fontsize,
self.dpi)
return advance + kern
def render(self, x, y):
"""
Render the character to the canvas
"""
self.font_output.render_glyph(
x, y,
self.font, self.font_class, self.c, self.fontsize, self.dpi)
def shrink(self):
Node.shrink(self)
if self.size < NUM_SIZE_LEVELS:
self.fontsize *= SHRINK_FACTOR
self.width *= SHRINK_FACTOR
self.height *= SHRINK_FACTOR
self.depth *= SHRINK_FACTOR
def grow(self):
Node.grow(self)
self.fontsize *= GROW_FACTOR
self.width *= GROW_FACTOR
self.height *= GROW_FACTOR
self.depth *= GROW_FACTOR
class Accent(Char):
"""
The font metrics need to be dealt with differently for accents,
since they are already offset correctly from the baseline in
TrueType fonts.
"""
def _update_metrics(self):
metrics = self._metrics = self.font_output.get_metrics(
self.font, self.font_class, self.c, self.fontsize, self.dpi)
self.width = metrics.xmax - metrics.xmin
self.height = metrics.ymax - metrics.ymin
self.depth = 0
def shrink(self):
Char.shrink(self)
self._update_metrics()
def grow(self):
Char.grow(self)
self._update_metrics()
def render(self, x, y):
"""
Render the character to the canvas.
"""
self.font_output.render_glyph(
x - self._metrics.xmin, y + self._metrics.ymin,
self.font, self.font_class, self.c, self.fontsize, self.dpi)
class List(Box):
"""
A list of nodes (either horizontal or vertical).
"""
def __init__(self, elements):
Box.__init__(self, 0., 0., 0.)
self.shift_amount = 0. # An arbitrary offset
self.children = elements # The child nodes of this list
# The following parameters are set in the vpack and hpack functions
self.glue_set = 0. # The glue setting of this list
self.glue_sign = 0 # 0: normal, -1: shrinking, 1: stretching
self.glue_order = 0 # The order of infinity (0 - 3) for the glue
def __repr__(self):
return '[%s <%.02f %.02f %.02f %.02f> %s]' % (
self.__internal_repr__(),
self.width, self.height,
self.depth, self.shift_amount,
' '.join([repr(x) for x in self.children]))
def _determine_order(self, totals):
"""
A helper function to determine the highest order of glue
used by the members of this list. Used by vpack and hpack.
"""
o = 0
for i in range(len(totals) - 1, 0, -1):
if totals[i] != 0.0:
o = i
break
return o
def _set_glue(self, x, sign, totals, error_type):
o = self._determine_order(totals)
self.glue_order = o
self.glue_sign = sign
if totals[o] != 0.:
self.glue_set = x / totals[o]
else:
self.glue_sign = 0
self.glue_ratio = 0.
if o == 0:
if len(self.children):
warn("%s %s: %r" % (error_type, self.__class__.__name__, self),
MathTextWarning)
def shrink(self):
for child in self.children:
child.shrink()
Box.shrink(self)
if self.size < NUM_SIZE_LEVELS:
self.shift_amount *= SHRINK_FACTOR
self.glue_set *= SHRINK_FACTOR
def grow(self):
for child in self.children:
child.grow()
Box.grow(self)
self.shift_amount *= GROW_FACTOR
self.glue_set *= GROW_FACTOR
class Hlist(List):
"""
A horizontal list of boxes.
"""
def __init__(self, elements, w=0., m='additional', do_kern=True):
List.__init__(self, elements)
if do_kern:
self.kern()
self.hpack()
def kern(self):
"""
Insert :class:`Kern` nodes between :class:`Char` nodes to set
kerning. The :class:`Char` nodes themselves determine the
amount of kerning they need (in :meth:`~Char.get_kerning`),
and this function just creates the linked list in the correct
way.
"""
new_children = []
num_children = len(self.children)
if num_children:
for i in range(num_children):
elem = self.children[i]
if i < num_children - 1:
next = self.children[i + 1]
else:
next = None
new_children.append(elem)
kerning_distance = elem.get_kerning(next)
if kerning_distance != 0.:
kern = Kern(kerning_distance)
new_children.append(kern)
self.children = new_children
# This is a failed experiment to fake cross-font kerning.
# def get_kerning(self, next):
# if len(self.children) >= 2 and isinstance(self.children[-2], Char):
# if isinstance(next, Char):
# print "CASE A"
# return self.children[-2].get_kerning(next)
# elif isinstance(next, Hlist) and len(next.children) and isinstance(next.children[0], Char):
# print "CASE B"
# result = self.children[-2].get_kerning(next.children[0])
# print result
# return result
# return 0.0
def hpack(self, w=0., m='additional'):
"""
The main duty of :meth:`hpack` is to compute the dimensions of
the resulting boxes, and to adjust the glue if one of those
dimensions is pre-specified. The computed sizes normally
enclose all of the material inside the new box; but some items
may stick out if negative glue is used, if the box is
overfull, or if a ``\\vbox`` includes other boxes that have
been shifted left.
- *w*: specifies a width
- *m*: is either 'exactly' or 'additional'.
Thus, ``hpack(w, 'exactly')`` produces a box whose width is
exactly *w*, while ``hpack(w, 'additional')`` yields a box
whose width is the natural width plus *w*. The default values
produce a box with the natural width.
"""
# I don't know why these get reset in TeX. Shift_amount is pretty
# much useless if we do.
#self.shift_amount = 0.
h = 0.
d = 0.
x = 0.
total_stretch = [0.] * 4
total_shrink = [0.] * 4
for p in self.children:
if isinstance(p, Char):
x += p.width
h = max(h, p.height)
d = max(d, p.depth)
elif isinstance(p, Box):
x += p.width
if not np.isinf(p.height) and not np.isinf(p.depth):
s = getattr(p, 'shift_amount', 0.)
h = max(h, p.height - s)
d = max(d, p.depth + s)
elif isinstance(p, Glue):
glue_spec = p.glue_spec
x += glue_spec.width
total_stretch[glue_spec.stretch_order] += glue_spec.stretch
total_shrink[glue_spec.shrink_order] += glue_spec.shrink
elif isinstance(p, Kern):
x += p.width
self.height = h
self.depth = d
if m == 'additional':
w += x
self.width = w
x = w - x
if x == 0.:
self.glue_sign = 0
self.glue_order = 0
self.glue_ratio = 0.
return
if x > 0.:
self._set_glue(x, 1, total_stretch, "Overfull")
else:
self._set_glue(x, -1, total_shrink, "Underfull")
class Vlist(List):
"""
A vertical list of boxes.
"""
def __init__(self, elements, h=0., m='additional'):
List.__init__(self, elements)
self.vpack()
def vpack(self, h=0., m='additional', l=np.inf):
"""
The main duty of :meth:`vpack` is to compute the dimensions of
the resulting boxes, and to adjust the glue if one of those
dimensions is pre-specified.
- *h*: specifies a height
- *m*: is either 'exactly' or 'additional'.
- *l*: a maximum height
Thus, ``vpack(h, 'exactly')`` produces a box whose height is
exactly *h*, while ``vpack(h, 'additional')`` yields a box
whose height is the natural height plus *h*. The default
values produce a box with the natural width.
"""
# I don't know why these get reset in TeX. Shift_amount is pretty
# much useless if we do.
# self.shift_amount = 0.
w = 0.
d = 0.
x = 0.
total_stretch = [0.] * 4
total_shrink = [0.] * 4
for p in self.children:
if isinstance(p, Box):
x += d + p.height
d = p.depth
if not np.isinf(p.width):
s = getattr(p, 'shift_amount', 0.)
w = max(w, p.width + s)
elif isinstance(p, Glue):
x += d
d = 0.
glue_spec = p.glue_spec
x += glue_spec.width
total_stretch[glue_spec.stretch_order] += glue_spec.stretch
total_shrink[glue_spec.shrink_order] += glue_spec.shrink
elif isinstance(p, Kern):
x += d + p.width
d = 0.
elif isinstance(p, Char):
raise RuntimeError("Internal mathtext error: Char node found in Vlist.")
self.width = w
if d > l:
x += d - l
self.depth = l
else:
self.depth = d
if m == 'additional':
h += x
self.height = h
x = h - x
if x == 0:
self.glue_sign = 0
self.glue_order = 0
self.glue_ratio = 0.
return
if x > 0.:
self._set_glue(x, 1, total_stretch, "Overfull")
else:
self._set_glue(x, -1, total_shrink, "Underfull")
class Rule(Box):
"""
A :class:`Rule` node stands for a solid black rectangle; it has
*width*, *depth*, and *height* fields just as in an
:class:`Hlist`. However, if any of these dimensions is inf, the
actual value will be determined by running the rule up to the
boundary of the innermost enclosing box. This is called a "running
dimension." The width is never running in an :class:`Hlist`; the
height and depth are never running in a :class:`Vlist`.
"""
def __init__(self, width, height, depth, state):
Box.__init__(self, width, height, depth)
self.font_output = state.font_output
def render(self, x, y, w, h):
self.font_output.render_rect_filled(x, y, x + w, y + h)
class Hrule(Rule):
"""
Convenience class to create a horizontal rule.
"""
def __init__(self, state, thickness=None):
if thickness is None:
thickness = state.font_output.get_underline_thickness(
state.font, state.fontsize, state.dpi)
height = depth = thickness * 0.5
Rule.__init__(self, np.inf, height, depth, state)
class Vrule(Rule):
"""
Convenience class to create a vertical rule.
"""
def __init__(self, state):
thickness = state.font_output.get_underline_thickness(
state.font, state.fontsize, state.dpi)
Rule.__init__(self, thickness, np.inf, np.inf, state)
class Glue(Node):
"""
Most of the information in this object is stored in the underlying
:class:`GlueSpec` class, which is shared between multiple glue objects. (This
is a memory optimization which probably doesn't matter anymore, but it's
easier to stick to what TeX does.)
"""
def __init__(self, glue_type, copy=False):
Node.__init__(self)
self.glue_subtype = 'normal'
if isinstance(glue_type, six.string_types):
glue_spec = GlueSpec.factory(glue_type)
elif isinstance(glue_type, GlueSpec):
glue_spec = glue_type
else:
raise ValueError("glue_type must be a glue spec name or instance.")
if copy:
glue_spec = glue_spec.copy()
self.glue_spec = glue_spec
def shrink(self):
Node.shrink(self)
if self.size < NUM_SIZE_LEVELS:
if self.glue_spec.width != 0.:
self.glue_spec = self.glue_spec.copy()
self.glue_spec.width *= SHRINK_FACTOR
def grow(self):
Node.grow(self)
if self.glue_spec.width != 0.:
self.glue_spec = self.glue_spec.copy()
self.glue_spec.width *= GROW_FACTOR
class GlueSpec(object):
"""
See :class:`Glue`.
"""
def __init__(self, width=0., stretch=0., stretch_order=0, shrink=0., shrink_order=0):
self.width = width
self.stretch = stretch
self.stretch_order = stretch_order
self.shrink = shrink
self.shrink_order = shrink_order
def copy(self):
return GlueSpec(
self.width,
self.stretch,
self.stretch_order,
self.shrink,
self.shrink_order)
def factory(cls, glue_type):
return cls._types[glue_type]
factory = classmethod(factory)
GlueSpec._types = {
'fil': GlueSpec(0., 1., 1, 0., 0),
'fill': GlueSpec(0., 1., 2, 0., 0),
'filll': GlueSpec(0., 1., 3, 0., 0),
'neg_fil': GlueSpec(0., 0., 0, 1., 1),
'neg_fill': GlueSpec(0., 0., 0, 1., 2),
'neg_filll': GlueSpec(0., 0., 0, 1., 3),
'empty': GlueSpec(0., 0., 0, 0., 0),
'ss': GlueSpec(0., 1., 1, -1., 1)
}
# Some convenient ways to get common kinds of glue
class Fil(Glue):
def __init__(self):
Glue.__init__(self, 'fil')
class Fill(Glue):
def __init__(self):
Glue.__init__(self, 'fill')
class Filll(Glue):
def __init__(self):
Glue.__init__(self, 'filll')
class NegFil(Glue):
def __init__(self):
Glue.__init__(self, 'neg_fil')
class NegFill(Glue):
def __init__(self):
Glue.__init__(self, 'neg_fill')
class NegFilll(Glue):
def __init__(self):
Glue.__init__(self, 'neg_filll')
class SsGlue(Glue):
def __init__(self):
Glue.__init__(self, 'ss')
class HCentered(Hlist):
"""
A convenience class to create an :class:`Hlist` whose contents are
centered within its enclosing box.
"""
def __init__(self, elements):
Hlist.__init__(self, [SsGlue()] + elements + [SsGlue()],
do_kern=False)
class VCentered(Hlist):
"""
A convenience class to create a :class:`Vlist` whose contents are
centered within its enclosing box.
"""
def __init__(self, elements):
Vlist.__init__(self, [SsGlue()] + elements + [SsGlue()])
class Kern(Node):
"""
A :class:`Kern` node has a width field to specify a (normally
negative) amount of spacing. This spacing correction appears in
horizontal lists between letters like A and V when the font
designer said that it looks better to move them closer together or
further apart. A kern node can also appear in a vertical list,
when its *width* denotes additional spacing in the vertical
direction.
"""
height = 0
depth = 0
def __init__(self, width):
Node.__init__(self)
self.width = width
def __repr__(self):
return "k%.02f" % self.width
def shrink(self):
Node.shrink(self)
if self.size < NUM_SIZE_LEVELS:
self.width *= SHRINK_FACTOR
def grow(self):
Node.grow(self)
self.width *= GROW_FACTOR
class SubSuperCluster(Hlist):
"""
:class:`SubSuperCluster` is a sort of hack to get around that fact
that this code do a two-pass parse like TeX. This lets us store
enough information in the hlist itself, namely the nucleus, sub-
and super-script, such that if another script follows that needs
to be attached, it can be reconfigured on the fly.
"""
def __init__(self):
self.nucleus = None
self.sub = None
self.super = None
Hlist.__init__(self, [])
class AutoHeightChar(Hlist):
"""
:class:`AutoHeightChar` will create a character as close to the
given height and depth as possible. When using a font with
multiple height versions of some characters (such as the BaKoMa
fonts), the correct glyph will be selected, otherwise this will
always just return a scaled version of the glyph.
"""
def __init__(self, c, height, depth, state, always=False, factor=None):
alternatives = state.font_output.get_sized_alternatives_for_symbol(
state.font, c)
xHeight = state.font_output.get_xheight(
state.font, state.fontsize, state.dpi)
state = state.copy()
target_total = height + depth
for fontname, sym in alternatives:
state.font = fontname
char = Char(sym, state)
# Ensure that size 0 is chosen when the text is regular sized but
# with descender glyphs by subtracting 0.2 * xHeight
if char.height + char.depth >= target_total - 0.2 * xHeight:
break
shift = 0
if state.font != 0:
if factor is None:
factor = (target_total) / (char.height + char.depth)
state.fontsize *= factor
char = Char(sym, state)
shift = (depth - char.depth)
Hlist.__init__(self, [char])
self.shift_amount = shift
class AutoWidthChar(Hlist):
"""
:class:`AutoWidthChar` will create a character as close to the
given width as possible. When using a font with multiple width
versions of some characters (such as the BaKoMa fonts), the
correct glyph will be selected, otherwise this will always just
return a scaled version of the glyph.
"""
def __init__(self, c, width, state, always=False, char_class=Char):
alternatives = state.font_output.get_sized_alternatives_for_symbol(
state.font, c)
state = state.copy()
for fontname, sym in alternatives:
state.font = fontname
char = char_class(sym, state)
if char.width >= width:
break
factor = width / char.width
state.fontsize *= factor
char = char_class(sym, state)
Hlist.__init__(self, [char])
self.width = char.width
class Ship(object):
"""
Once the boxes have been set up, this sends them to output. Since
boxes can be inside of boxes inside of boxes, the main work of
:class:`Ship` is done by two mutually recursive routines,
:meth:`hlist_out` and :meth:`vlist_out`, which traverse the
:class:`Hlist` nodes and :class:`Vlist` nodes inside of horizontal
and vertical boxes. The global variables used in TeX to store
state as it processes have become member variables here.
"""
def __call__(self, ox, oy, box):
self.max_push = 0 # Deepest nesting of push commands so far
self.cur_s = 0
self.cur_v = 0.
self.cur_h = 0.
self.off_h = ox
self.off_v = oy + box.height
self.hlist_out(box)
def clamp(value):
if value < -1000000000.:
return -1000000000.
if value > 1000000000.:
return 1000000000.
return value
clamp = staticmethod(clamp)
def hlist_out(self, box):
cur_g = 0
cur_glue = 0.
glue_order = box.glue_order
glue_sign = box.glue_sign
base_line = self.cur_v
left_edge = self.cur_h
self.cur_s += 1
self.max_push = max(self.cur_s, self.max_push)
clamp = self.clamp
for p in box.children:
if isinstance(p, Char):
p.render(self.cur_h + self.off_h, self.cur_v + self.off_v)
self.cur_h += p.width
elif isinstance(p, Kern):
self.cur_h += p.width
elif isinstance(p, List):
# node623
if len(p.children) == 0:
self.cur_h += p.width
else:
edge = self.cur_h
self.cur_v = base_line + p.shift_amount
if isinstance(p, Hlist):
self.hlist_out(p)
else:
# p.vpack(box.height + box.depth, 'exactly')
self.vlist_out(p)
self.cur_h = edge + p.width
self.cur_v = base_line
elif isinstance(p, Box):
# node624
rule_height = p.height
rule_depth = p.depth
rule_width = p.width
if np.isinf(rule_height):
rule_height = box.height
if np.isinf(rule_depth):
rule_depth = box.depth
if rule_height > 0 and rule_width > 0:
self.cur_v = base_line + rule_depth
p.render(self.cur_h + self.off_h,
self.cur_v + self.off_v,
rule_width, rule_height)
self.cur_v = base_line
self.cur_h += rule_width
elif isinstance(p, Glue):
# node625
glue_spec = p.glue_spec
rule_width = glue_spec.width - cur_g
if glue_sign != 0: # normal
if glue_sign == 1: # stretching
if glue_spec.stretch_order == glue_order:
cur_glue += glue_spec.stretch
cur_g = np.round(clamp(float(box.glue_set) * cur_glue))
elif glue_spec.shrink_order == glue_order:
cur_glue += glue_spec.shrink
cur_g = np.round(clamp(float(box.glue_set) * cur_glue))
rule_width += cur_g
self.cur_h += rule_width
self.cur_s -= 1
def vlist_out(self, box):
cur_g = 0
cur_glue = 0.
glue_order = box.glue_order
glue_sign = box.glue_sign
self.cur_s += 1
self.max_push = max(self.max_push, self.cur_s)
left_edge = self.cur_h
self.cur_v -= box.height
top_edge = self.cur_v
clamp = self.clamp
for p in box.children:
if isinstance(p, Kern):
self.cur_v += p.width
elif isinstance(p, List):
if len(p.children) == 0:
self.cur_v += p.height + p.depth
else:
self.cur_v += p.height
self.cur_h = left_edge + p.shift_amount
save_v = self.cur_v
p.width = box.width
if isinstance(p, Hlist):
self.hlist_out(p)
else:
self.vlist_out(p)
self.cur_v = save_v + p.depth
self.cur_h = left_edge
elif isinstance(p, Box):
rule_height = p.height
rule_depth = p.depth
rule_width = p.width
if np.isinf(rule_width):
rule_width = box.width
rule_height += rule_depth
if rule_height > 0 and rule_depth > 0:
self.cur_v += rule_height
p.render(self.cur_h + self.off_h,
self.cur_v + self.off_v,
rule_width, rule_height)
elif isinstance(p, Glue):
glue_spec = p.glue_spec
rule_height = glue_spec.width - cur_g
if glue_sign != 0: # normal
if glue_sign == 1: # stretching
if glue_spec.stretch_order == glue_order:
cur_glue += glue_spec.stretch
cur_g = np.round(clamp(float(box.glue_set) * cur_glue))
elif glue_spec.shrink_order == glue_order: # shrinking
cur_glue += glue_spec.shrink
cur_g = np.round(clamp(float(box.glue_set) * cur_glue))
rule_height += cur_g
self.cur_v += rule_height
elif isinstance(p, Char):
raise RuntimeError("Internal mathtext error: Char node found in vlist")
self.cur_s -= 1
ship = Ship()
##############################################################################
# PARSER
def Error(msg):
"""
Helper class to raise parser errors.
"""
def raise_error(s, loc, toks):
raise ParseFatalException(s, loc, msg)
empty = Empty()
empty.setParseAction(raise_error)
return empty
class Parser(object):
"""
This is the pyparsing-based parser for math expressions. It
actually parses full strings *containing* math expressions, in
that raw text may also appear outside of pairs of ``$``.
The grammar is based directly on that in TeX, though it cuts a few
corners.
"""
_math_style_dict = dict(displaystyle=0, textstyle=1,
scriptstyle=2, scriptscriptstyle=3)
_binary_operators = set('''
+ * -
\\pm \\sqcap \\rhd
\\mp \\sqcup \\unlhd
\\times \\vee \\unrhd
\\div \\wedge \\oplus
\\ast \\setminus \\ominus
\\star \\wr \\otimes
\\circ \\diamond \\oslash
\\bullet \\bigtriangleup \\odot
\\cdot \\bigtriangledown \\bigcirc
\\cap \\triangleleft \\dagger
\\cup \\triangleright \\ddagger
\\uplus \\lhd \\amalg'''.split())
_relation_symbols = set('''
= < > :
\\leq \\geq \\equiv \\models
\\prec \\succ \\sim \\perp
\\preceq \\succeq \\simeq \\mid
\\ll \\gg \\asymp \\parallel
\\subset \\supset \\approx \\bowtie
\\subseteq \\supseteq \\cong \\Join
\\sqsubset \\sqsupset \\neq \\smile
\\sqsubseteq \\sqsupseteq \\doteq \\frown
\\in \\ni \\propto \\vdash
\\dashv \\dots \\dotplus \\doteqdot'''.split())
_arrow_symbols = set('''
\\leftarrow \\longleftarrow \\uparrow
\\Leftarrow \\Longleftarrow \\Uparrow
\\rightarrow \\longrightarrow \\downarrow
\\Rightarrow \\Longrightarrow \\Downarrow
\\leftrightarrow \\longleftrightarrow \\updownarrow
\\Leftrightarrow \\Longleftrightarrow \\Updownarrow
\\mapsto \\longmapsto \\nearrow
\\hookleftarrow \\hookrightarrow \\searrow
\\leftharpoonup \\rightharpoonup \\swarrow
\\leftharpoondown \\rightharpoondown \\nwarrow
\\rightleftharpoons \\leadsto'''.split())
_spaced_symbols = _binary_operators | _relation_symbols | _arrow_symbols
_punctuation_symbols = set(r', ; . ! \ldotp \cdotp'.split())
_overunder_symbols = set(r'''
\sum \prod \coprod \bigcap \bigcup \bigsqcup \bigvee
\bigwedge \bigodot \bigotimes \bigoplus \biguplus
'''.split())
_overunder_functions = set(
r"lim liminf limsup sup max min".split())
_dropsub_symbols = set(r'''\int \oint'''.split())
_fontnames = set("rm cal it tt sf bf default bb frak circled scr regular".split())
_function_names = set("""
arccos csc ker min arcsin deg lg Pr arctan det lim sec arg dim
liminf sin cos exp limsup sinh cosh gcd ln sup cot hom log tan
coth inf max tanh""".split())
_ambi_delim = set("""
| \\| / \\backslash \\uparrow \\downarrow \\updownarrow \\Uparrow
\\Downarrow \\Updownarrow . \\vert \\Vert \\\\|""".split())
_left_delim = set(r"( [ \{ < \lfloor \langle \lceil".split())
_right_delim = set(r") ] \} > \rfloor \rangle \rceil".split())
def __init__(self):
p = Bunch()
# All forward declarations are here
p.accent = Forward()
p.ambi_delim = Forward()
p.apostrophe = Forward()
p.auto_delim = Forward()
p.binom = Forward()
p.bslash = Forward()
p.c_over_c = Forward()
p.customspace = Forward()
p.end_group = Forward()
p.float_literal = Forward()
p.font = Forward()
p.frac = Forward()
p.dfrac = Forward()
p.function = Forward()
p.genfrac = Forward()
p.group = Forward()
p.int_literal = Forward()
p.latexfont = Forward()
p.lbracket = Forward()
p.left_delim = Forward()
p.lbrace = Forward()
p.main = Forward()
p.math = Forward()
p.math_string = Forward()
p.non_math = Forward()
p.operatorname = Forward()
p.overline = Forward()
p.placeable = Forward()
p.rbrace = Forward()
p.rbracket = Forward()
p.required_group = Forward()
p.right_delim = Forward()
p.right_delim_safe = Forward()
p.simple = Forward()
p.simple_group = Forward()
p.single_symbol = Forward()
p.snowflake = Forward()
p.space = Forward()
p.sqrt = Forward()
p.stackrel = Forward()
p.start_group = Forward()
p.subsuper = Forward()
p.subsuperop = Forward()
p.symbol = Forward()
p.symbol_name = Forward()
p.token = Forward()
p.unknown_symbol = Forward()
# Set names on everything -- very useful for debugging
for key, val in vars(p).items():
if not key.startswith('_'):
val.setName(key)
p.float_literal <<= Regex(r"[-+]?([0-9]+\.?[0-9]*|\.[0-9]+)")
p.int_literal <<= Regex("[-+]?[0-9]+")
p.lbrace <<= Literal('{').suppress()
p.rbrace <<= Literal('}').suppress()
p.lbracket <<= Literal('[').suppress()
p.rbracket <<= Literal(']').suppress()
p.bslash <<= Literal('\\')
p.space <<= oneOf(list(self._space_widths))
p.customspace <<= (Suppress(Literal(r'\hspace'))
- ((p.lbrace + p.float_literal + p.rbrace)
| Error(r"Expected \hspace{n}")))
unicode_range = "\U00000080-\U0001ffff"
p.single_symbol <<= Regex(r"([a-zA-Z0-9 +\-*/<>=:,.;!\?&'@()\[\]|%s])|(\\[%%${}\[\]_|])" %
unicode_range)
p.snowflake <<= Suppress(p.bslash) + oneOf(self._snowflake)
p.symbol_name <<= (Combine(p.bslash + oneOf(list(tex2uni))) +
FollowedBy(Regex("[^A-Za-z]").leaveWhitespace() | StringEnd()))
p.symbol <<= (p.single_symbol | p.symbol_name).leaveWhitespace()
p.apostrophe <<= Regex("'+")
p.c_over_c <<= Suppress(p.bslash) + oneOf(list(self._char_over_chars))
p.accent <<= Group(
Suppress(p.bslash)
+ oneOf(list(self._accent_map) + list(self._wide_accents))
- p.placeable
)
p.function <<= Suppress(p.bslash) + oneOf(list(self._function_names))
p.start_group <<= Optional(p.latexfont) + p.lbrace
p.end_group <<= p.rbrace.copy()
p.simple_group <<= Group(p.lbrace + ZeroOrMore(p.token) + p.rbrace)
p.required_group<<= Group(p.lbrace + OneOrMore(p.token) + p.rbrace)
p.group <<= Group(p.start_group + ZeroOrMore(p.token) + p.end_group)
p.font <<= Suppress(p.bslash) + oneOf(list(self._fontnames))
p.latexfont <<= Suppress(p.bslash) + oneOf(['math' + x for x in self._fontnames])
p.frac <<= Group(
Suppress(Literal(r"\frac"))
- ((p.required_group + p.required_group) | Error(r"Expected \frac{num}{den}"))
)
p.dfrac <<= Group(
Suppress(Literal(r"\dfrac"))
- ((p.required_group + p.required_group) | Error(r"Expected \dfrac{num}{den}"))
)
p.stackrel <<= Group(
Suppress(Literal(r"\stackrel"))
- ((p.required_group + p.required_group) | Error(r"Expected \stackrel{num}{den}"))
)
p.binom <<= Group(
Suppress(Literal(r"\binom"))
- ((p.required_group + p.required_group) | Error(r"Expected \binom{num}{den}"))
)
p.ambi_delim <<= oneOf(list(self._ambi_delim))
p.left_delim <<= oneOf(list(self._left_delim))
p.right_delim <<= oneOf(list(self._right_delim))
p.right_delim_safe <<= oneOf(list(self._right_delim - {'}'}) + [r'\}'])
p.genfrac <<= Group(
Suppress(Literal(r"\genfrac"))
- (((p.lbrace + Optional(p.ambi_delim | p.left_delim, default='') + p.rbrace)
+ (p.lbrace + Optional(p.ambi_delim | p.right_delim_safe, default='') + p.rbrace)
+ (p.lbrace + p.float_literal + p.rbrace)
+ p.simple_group + p.required_group + p.required_group)
| Error(r"Expected \genfrac{ldelim}{rdelim}{rulesize}{style}{num}{den}"))
)
p.sqrt <<= Group(
Suppress(Literal(r"\sqrt"))
- ((Optional(p.lbracket + p.int_literal + p.rbracket, default=None)
+ p.required_group)
| Error("Expected \\sqrt{value}"))
)
p.overline <<= Group(
Suppress(Literal(r"\overline"))
- (p.required_group | Error("Expected \\overline{value}"))
)
p.unknown_symbol<<= Combine(p.bslash + Regex("[A-Za-z]*"))
p.operatorname <<= Group(
Suppress(Literal(r"\operatorname"))
- ((p.lbrace + ZeroOrMore(p.simple | p.unknown_symbol) + p.rbrace)
| Error("Expected \\operatorname{value}"))
)
p.placeable <<= ( p.snowflake # this needs to be before accent so named symbols
# that are prefixed with an accent name work
| p.accent # Must be before symbol as all accents are symbols
| p.symbol # Must be third to catch all named symbols and single chars not in a group
| p.c_over_c
| p.function
| p.group
| p.frac
| p.dfrac
| p.stackrel
| p.binom
| p.genfrac
| p.sqrt
| p.overline
| p.operatorname
)
p.simple <<= ( p.space
| p.customspace
| p.font
| p.subsuper
)
p.subsuperop <<= oneOf(["_", "^"])
p.subsuper <<= Group(
(Optional(p.placeable) + OneOrMore(p.subsuperop - p.placeable) + Optional(p.apostrophe))
| (p.placeable + Optional(p.apostrophe))
| p.apostrophe
)
p.token <<= ( p.simple
| p.auto_delim
| p.unknown_symbol # Must be last
)
p.auto_delim <<= (Suppress(Literal(r"\left"))
- ((p.left_delim | p.ambi_delim) | Error("Expected a delimiter"))
+ Group(ZeroOrMore(p.simple | p.auto_delim))
+ Suppress(Literal(r"\right"))
- ((p.right_delim | p.ambi_delim) | Error("Expected a delimiter"))
)
p.math <<= OneOrMore(p.token)
p.math_string <<= QuotedString('$', '\\', unquoteResults=False)
p.non_math <<= Regex(r"(?:(?:\\[$])|[^$])*").leaveWhitespace()
p.main <<= (p.non_math + ZeroOrMore(p.math_string + p.non_math)) + StringEnd()
# Set actions
for key, val in vars(p).items():
if not key.startswith('_'):
if hasattr(self, key):
val.setParseAction(getattr(self, key))
self._expression = p.main
self._math_expression = p.math
def parse(self, s, fonts_object, fontsize, dpi):
"""
Parse expression *s* using the given *fonts_object* for
output, at the given *fontsize* and *dpi*.
Returns the parse tree of :class:`Node` instances.
"""
self._state_stack = [self.State(fonts_object, 'default', 'rm', fontsize, dpi)]
self._em_width_cache = {}
try:
result = self._expression.parseString(s)
except ParseBaseException as err:
raise ValueError("\n".join([
"",
err.line,
" " * (err.column - 1) + "^",
six.text_type(err)]))
self._state_stack = None
self._em_width_cache = {}
self._expression.resetCache()
return result[0]
# The state of the parser is maintained in a stack. Upon
# entering and leaving a group { } or math/non-math, the stack
# is pushed and popped accordingly. The current state always
# exists in the top element of the stack.
class State(object):
"""
Stores the state of the parser.
States are pushed and popped from a stack as necessary, and
the "current" state is always at the top of the stack.
"""
def __init__(self, font_output, font, font_class, fontsize, dpi):
self.font_output = font_output
self._font = font
self.font_class = font_class
self.fontsize = fontsize
self.dpi = dpi
def copy(self):
return Parser.State(
self.font_output,
self.font,
self.font_class,
self.fontsize,
self.dpi)
def _get_font(self):
return self._font
def _set_font(self, name):
if name in ('rm', 'it', 'bf'):
self.font_class = name
self._font = name
font = property(_get_font, _set_font)
def get_state(self):
"""
Get the current :class:`State` of the parser.
"""
return self._state_stack[-1]
def pop_state(self):
"""
Pop a :class:`State` off of the stack.
"""
self._state_stack.pop()
def push_state(self):
"""
Push a new :class:`State` onto the stack which is just a copy
of the current state.
"""
self._state_stack.append(self.get_state().copy())
def main(self, s, loc, toks):
return [Hlist(toks)]
def math_string(self, s, loc, toks):
return self._math_expression.parseString(toks[0][1:-1])
def math(self, s, loc, toks):
hlist = Hlist(toks)
self.pop_state()
return [hlist]
def non_math(self, s, loc, toks):
s = toks[0].replace(r'\$', '$')
symbols = [Char(c, self.get_state(), math=False) for c in s]
hlist = Hlist(symbols)
# We're going into math now, so set font to 'it'
self.push_state()
self.get_state().font = rcParams['mathtext.default']
return [hlist]
def _make_space(self, percentage):
# All spaces are relative to em width
state = self.get_state()
key = (state.font, state.fontsize, state.dpi)
width = self._em_width_cache.get(key)
if width is None:
metrics = state.font_output.get_metrics(
state.font, rcParams['mathtext.default'], 'm', state.fontsize, state.dpi)
width = metrics.advance
self._em_width_cache[key] = width
return Kern(width * percentage)
_space_widths = { r'\,' : 0.16667, # 3/18 em = 3 mu
r'\thinspace' : 0.16667, # 3/18 em = 3 mu
r'\/' : 0.16667, # 3/18 em = 3 mu
r'\>' : 0.22222, # 4/18 em = 4 mu
r'\:' : 0.22222, # 4/18 em = 4 mu
r'\;' : 0.27778, # 5/18 em = 5 mu
r'\ ' : 0.33333, # 6/18 em = 6 mu
r'\enspace' : 0.5, # 9/18 em = 9 mu
r'\quad' : 1, # 1 em = 18 mu
r'\qquad' : 2, # 2 em = 36 mu
r'\!' : -0.16667, # -3/18 em = -3 mu
}
def space(self, s, loc, toks):
assert len(toks)==1
num = self._space_widths[toks[0]]
box = self._make_space(num)
return [box]
def customspace(self, s, loc, toks):
return [self._make_space(float(toks[0]))]
def symbol(self, s, loc, toks):
c = toks[0]
try:
char = Char(c, self.get_state())
except ValueError:
raise ParseFatalException(s, loc, "Unknown symbol: %s" % c)
if c in self._spaced_symbols:
# iterate until we find previous character, needed for cases
# such as ${ -2}$, $ -2$, or $ -2$.
for i in six.moves.xrange(1, loc + 1):
prev_char = s[loc-i]
if prev_char != ' ':
break
# Binary operators at start of string should not be spaced
if (c in self._binary_operators and
(len(s[:loc].split()) == 0 or prev_char == '{' or
prev_char in self._left_delim)):
return [char]
else:
return [Hlist([self._make_space(0.2),
char,
self._make_space(0.2)] ,
do_kern = True)]
elif c in self._punctuation_symbols:
# Do not space commas between brackets
if c == ',':
prev_char, next_char = '', ''
for i in six.moves.xrange(1, loc + 1):
prev_char = s[loc - i]
if prev_char != ' ':
break
for i in six.moves.xrange(1, len(s) - loc):
next_char = s[loc + i]
if next_char != ' ':
break
if (prev_char == '{' and next_char == '}'):
return [char]
# Do not space dots as decimal separators
if (c == '.' and s[loc - 1].isdigit() and s[loc + 1].isdigit()):
return [char]
else:
return [Hlist([char,
self._make_space(0.2)],
do_kern = True)]
return [char]
snowflake = symbol
def unknown_symbol(self, s, loc, toks):
c = toks[0]
raise ParseFatalException(s, loc, "Unknown symbol: %s" % c)
_char_over_chars = {
# The first 2 entries in the tuple are (font, char, sizescale) for
# the two symbols under and over. The third element is the space
# (in multiples of underline height)
r'AA': (('it', 'A', 1.0), (None, '\\circ', 0.5), 0.0),
}
def c_over_c(self, s, loc, toks):
sym = toks[0]
state = self.get_state()
thickness = state.font_output.get_underline_thickness(
state.font, state.fontsize, state.dpi)
under_desc, over_desc, space = \
self._char_over_chars.get(sym, (None, None, 0.0))
if under_desc is None:
raise ParseFatalException("Error parsing symbol")
over_state = state.copy()
if over_desc[0] is not None:
over_state.font = over_desc[0]
over_state.fontsize *= over_desc[2]
over = Accent(over_desc[1], over_state)
under_state = state.copy()
if under_desc[0] is not None:
under_state.font = under_desc[0]
under_state.fontsize *= under_desc[2]
under = Char(under_desc[1], under_state)
width = max(over.width, under.width)
over_centered = HCentered([over])
over_centered.hpack(width, 'exactly')
under_centered = HCentered([under])
under_centered.hpack(width, 'exactly')
return Vlist([
over_centered,
Vbox(0., thickness * space),
under_centered
])
_accent_map = {
r'hat' : r'\circumflexaccent',
r'breve' : r'\combiningbreve',
r'bar' : r'\combiningoverline',
r'grave' : r'\combininggraveaccent',
r'acute' : r'\combiningacuteaccent',
r'tilde' : r'\combiningtilde',
r'dot' : r'\combiningdotabove',
r'ddot' : r'\combiningdiaeresis',
r'vec' : r'\combiningrightarrowabove',
r'"' : r'\combiningdiaeresis',
r"`" : r'\combininggraveaccent',
r"'" : r'\combiningacuteaccent',
r'~' : r'\combiningtilde',
r'.' : r'\combiningdotabove',
r'^' : r'\circumflexaccent',
r'overrightarrow' : r'\rightarrow',
r'overleftarrow' : r'\leftarrow',
r'mathring' : r'\circ'
}
_wide_accents = set(r"widehat widetilde widebar".split())
# make a lambda and call it to get the namespace right
_snowflake = (lambda am: [p for p in tex2uni if
any(p.startswith(a) and a != p for a in am)]
) (set(_accent_map))
def accent(self, s, loc, toks):
assert len(toks)==1
state = self.get_state()
thickness = state.font_output.get_underline_thickness(
state.font, state.fontsize, state.dpi)
if len(toks[0]) != 2:
raise ParseFatalException("Error parsing accent")
accent, sym = toks[0]
if accent in self._wide_accents:
accent_box = AutoWidthChar(
'\\' + accent, sym.width, state, char_class=Accent)
else:
accent_box = Accent(self._accent_map[accent], state)
if accent == 'mathring':
accent_box.shrink()
accent_box.shrink()
centered = HCentered([Hbox(sym.width / 4.0), accent_box])
centered.hpack(sym.width, 'exactly')
return Vlist([
centered,
Vbox(0., thickness * 2.0),
Hlist([sym])
])
def function(self, s, loc, toks):
self.push_state()
state = self.get_state()
state.font = 'rm'
hlist = Hlist([Char(c, state) for c in toks[0]])
self.pop_state()
hlist.function_name = toks[0]
return hlist
def operatorname(self, s, loc, toks):
self.push_state()
state = self.get_state()
state.font = 'rm'
# Change the font of Chars, but leave Kerns alone
for c in toks[0]:
if isinstance(c, Char):
c.font = 'rm'
c._update_metrics()
self.pop_state()
return Hlist(toks[0])
def start_group(self, s, loc, toks):
self.push_state()
# Deal with LaTeX-style font tokens
if len(toks):
self.get_state().font = toks[0][4:]
return []
def group(self, s, loc, toks):
grp = Hlist(toks[0])
return [grp]
required_group = simple_group = group
def end_group(self, s, loc, toks):
self.pop_state()
return []
def font(self, s, loc, toks):
assert len(toks)==1
name = toks[0]
self.get_state().font = name
return []
def is_overunder(self, nucleus):
if isinstance(nucleus, Char):
return nucleus.c in self._overunder_symbols
elif isinstance(nucleus, Hlist) and hasattr(nucleus, 'function_name'):
return nucleus.function_name in self._overunder_functions
return False
def is_dropsub(self, nucleus):
if isinstance(nucleus, Char):
return nucleus.c in self._dropsub_symbols
return False
def is_slanted(self, nucleus):
if isinstance(nucleus, Char):
return nucleus.is_slanted()
return False
def is_between_brackets(self, s, loc):
return False
def subsuper(self, s, loc, toks):
assert len(toks)==1
nucleus = None
sub = None
super = None
# Pick all of the apostrophes out, including first apostrophes that have
# been parsed as characters
napostrophes = 0
new_toks = []
for tok in toks[0]:
if isinstance(tok, six.string_types) and tok not in ('^', '_'):
napostrophes += len(tok)
elif isinstance(tok, Char) and tok.c == "'":
napostrophes += 1
else:
new_toks.append(tok)
toks = new_toks
if len(toks) == 0:
assert napostrophes
nucleus = Hbox(0.0)
elif len(toks) == 1:
if not napostrophes:
return toks[0] # .asList()
else:
nucleus = toks[0]
elif len(toks) in (2, 3):
# single subscript or superscript
nucleus = toks[0] if len(toks) == 3 else Hbox(0.0)
op, next = toks[-2:]
if op == '_':
sub = next
else:
super = next
elif len(toks) in (4, 5):
# subscript and superscript
nucleus = toks[0] if len(toks) == 5 else Hbox(0.0)
op1, next1, op2, next2 = toks[-4:]
if op1 == op2:
if op1 == '_':
raise ParseFatalException("Double subscript")
else:
raise ParseFatalException("Double superscript")
if op1 == '_':
sub = next1
super = next2
else:
super = next1
sub = next2
else:
raise ParseFatalException(
"Subscript/superscript sequence is too long. "
"Use braces { } to remove ambiguity.")
state = self.get_state()
rule_thickness = state.font_output.get_underline_thickness(
state.font, state.fontsize, state.dpi)
xHeight = state.font_output.get_xheight(
state.font, state.fontsize, state.dpi)
if napostrophes:
if super is None:
super = Hlist([])
for i in range(napostrophes):
super.children.extend(self.symbol(s, loc, ['\\prime']))
# kern() and hpack() needed to get the metrics right after extending
super.kern()
super.hpack()
# Handle over/under symbols, such as sum or integral
if self.is_overunder(nucleus):
vlist = []
shift = 0.
width = nucleus.width
if super is not None:
super.shrink()
width = max(width, super.width)
if sub is not None:
sub.shrink()
width = max(width, sub.width)
if super is not None:
hlist = HCentered([super])
hlist.hpack(width, 'exactly')
vlist.extend([hlist, Kern(rule_thickness * 3.0)])
hlist = HCentered([nucleus])
hlist.hpack(width, 'exactly')
vlist.append(hlist)
if sub is not None:
hlist = HCentered([sub])
hlist.hpack(width, 'exactly')
vlist.extend([Kern(rule_thickness * 3.0), hlist])
shift = hlist.height
vlist = Vlist(vlist)
vlist.shift_amount = shift + nucleus.depth
result = Hlist([vlist])
return [result]
# We remove kerning on the last character for consistency (otherwise it
# will compute kerning based on non-shrinked characters and may put them
# too close together when superscripted)
# We change the width of the last character to match the advance to
# consider some fonts with weird metrics: e.g. stix's f has a width of
# 7.75 and a kerning of -4.0 for an advance of 3.72, and we want to put
# the superscript at the advance
last_char = nucleus
if isinstance(nucleus, Hlist):
new_children = nucleus.children
if len(new_children):
# remove last kern
if (isinstance(new_children[-1],Kern) and
hasattr(new_children[-2], '_metrics')):
new_children = new_children[:-1]
last_char = new_children[-1]
if hasattr(last_char, '_metrics'):
last_char.width = last_char._metrics.advance
# create new Hlist without kerning
nucleus = Hlist(new_children, do_kern=False)
else:
if isinstance(nucleus, Char):
last_char.width = last_char._metrics.advance
nucleus = Hlist([nucleus])
# Handle regular sub/superscripts
constants = _get_font_constant_set(state)
lc_height = last_char.height
lc_baseline = 0
if self.is_dropsub(last_char):
lc_baseline = last_char.depth
# Compute kerning for sub and super
superkern = constants.delta * xHeight
subkern = constants.delta * xHeight
if self.is_slanted(last_char):
superkern += constants.delta * xHeight
superkern += (constants.delta_slanted *
(lc_height - xHeight * 2. / 3.))
if self.is_dropsub(last_char):
subkern = (3 * constants.delta -
constants.delta_integral) * lc_height
superkern = (3 * constants.delta +
constants.delta_integral) * lc_height
else:
subkern = 0
if super is None:
# node757
x = Hlist([Kern(subkern), sub])
x.shrink()
if self.is_dropsub(last_char):
shift_down = lc_baseline + constants.subdrop * xHeight
else:
shift_down = constants.sub1 * xHeight
x.shift_amount = shift_down
else:
x = Hlist([Kern(superkern), super])
x.shrink()
if self.is_dropsub(last_char):
shift_up = lc_height - constants.subdrop * xHeight
else:
shift_up = constants.sup1 * xHeight
if sub is None:
x.shift_amount = -shift_up
else: # Both sub and superscript
y = Hlist([Kern(subkern),sub])
y.shrink()
if self.is_dropsub(last_char):
shift_down = lc_baseline + constants.subdrop * xHeight
else:
shift_down = constants.sub2 * xHeight
# If sub and superscript collide, move super up
clr = (2.0 * rule_thickness -
((shift_up - x.depth) - (y.height - shift_down)))
if clr > 0.:
shift_up += clr
x = Vlist([x,
Kern((shift_up - x.depth) - (y.height - shift_down)),
y])
x.shift_amount = shift_down
if not self.is_dropsub(last_char):
x.width += constants.script_space * xHeight
result = Hlist([nucleus, x])
return [result]
def _genfrac(self, ldelim, rdelim, rule, style, num, den):
state = self.get_state()
thickness = state.font_output.get_underline_thickness(
state.font, state.fontsize, state.dpi)
rule = float(rule)
# If style != displaystyle == 0, shrink the num and den
if style != self._math_style_dict['displaystyle']:
num.shrink()
den.shrink()
cnum = HCentered([num])
cden = HCentered([den])
width = max(num.width, den.width)
cnum.hpack(width, 'exactly')
cden.hpack(width, 'exactly')
vlist = Vlist([cnum, # numerator
Vbox(0, thickness * 2.0), # space
Hrule(state, rule), # rule
Vbox(0, thickness * 2.0), # space
cden # denominator
])
# Shift so the fraction line sits in the middle of the
# equals sign
metrics = state.font_output.get_metrics(
state.font, rcParams['mathtext.default'],
'=', state.fontsize, state.dpi)
shift = (cden.height -
((metrics.ymax + metrics.ymin) / 2 -
thickness * 3.0))
vlist.shift_amount = shift
result = [Hlist([vlist, Hbox(thickness * 2.)])]
if ldelim or rdelim:
if ldelim == '':
ldelim = '.'
if rdelim == '':
rdelim = '.'
return self._auto_sized_delimiter(ldelim, result, rdelim)
return result
def genfrac(self, s, loc, toks):
assert len(toks) == 1
assert len(toks[0]) == 6
return self._genfrac(*tuple(toks[0]))
def frac(self, s, loc, toks):
assert len(toks) == 1
assert len(toks[0]) == 2
state = self.get_state()
thickness = state.font_output.get_underline_thickness(
state.font, state.fontsize, state.dpi)
num, den = toks[0]
return self._genfrac('', '', thickness,
self._math_style_dict['textstyle'], num, den)
def dfrac(self, s, loc, toks):
assert len(toks) == 1
assert len(toks[0]) == 2
state = self.get_state()
thickness = state.font_output.get_underline_thickness(
state.font, state.fontsize, state.dpi)
num, den = toks[0]
return self._genfrac('', '', thickness,
self._math_style_dict['displaystyle'], num, den)
def stackrel(self, s, loc, toks):
assert len(toks) == 1
assert len(toks[0]) == 2
num, den = toks[0]
return self._genfrac('', '', 0.0,
self._math_style_dict['textstyle'], num, den)
def binom(self, s, loc, toks):
assert len(toks) == 1
assert len(toks[0]) == 2
num, den = toks[0]
return self._genfrac('(', ')', 0.0,
self._math_style_dict['textstyle'], num, den)
def sqrt(self, s, loc, toks):
root, body = toks[0]
state = self.get_state()
thickness = state.font_output.get_underline_thickness(
state.font, state.fontsize, state.dpi)
# Determine the height of the body, and add a little extra to
# the height so it doesn't seem cramped
height = body.height - body.shift_amount + thickness * 5.0
depth = body.depth + body.shift_amount
check = AutoHeightChar(r'\__sqrt__', height, depth, state, always=True)
height = check.height - check.shift_amount
depth = check.depth + check.shift_amount
# Put a little extra space to the left and right of the body
padded_body = Hlist([Hbox(thickness * 2.0),
body,
Hbox(thickness * 2.0)])
rightside = Vlist([Hrule(state),
Fill(),
padded_body])
# Stretch the glue between the hrule and the body
rightside.vpack(height + (state.fontsize * state.dpi) / (100.0 * 12.0),
'exactly', depth)
# Add the root and shift it upward so it is above the tick.
# The value of 0.6 is a hard-coded hack ;)
if root is None:
root = Box(check.width * 0.5, 0., 0.)
else:
root = Hlist([Char(x, state) for x in root])
root.shrink()
root.shrink()
root_vlist = Vlist([Hlist([root])])
root_vlist.shift_amount = -height * 0.6
hlist = Hlist([root_vlist, # Root
# Negative kerning to put root over tick
Kern(-check.width * 0.5),
check, # Check
rightside]) # Body
return [hlist]
def overline(self, s, loc, toks):
assert len(toks)==1
assert len(toks[0])==1
body = toks[0][0]
state = self.get_state()
thickness = state.font_output.get_underline_thickness(
state.font, state.fontsize, state.dpi)
height = body.height - body.shift_amount + thickness * 3.0
depth = body.depth + body.shift_amount
# Place overline above body
rightside = Vlist([Hrule(state),
Fill(),
Hlist([body])])
# Stretch the glue between the hrule and the body
rightside.vpack(height + (state.fontsize * state.dpi) / (100.0 * 12.0),
'exactly', depth)
hlist = Hlist([rightside])
return [hlist]
def _auto_sized_delimiter(self, front, middle, back):
state = self.get_state()
if len(middle):
height = max(x.height for x in middle)
depth = max(x.depth for x in middle)
factor = None
else:
height = 0
depth = 0
factor = 1.0
parts = []
# \left. and \right. aren't supposed to produce any symbols
if front != '.':
parts.append(AutoHeightChar(front, height, depth, state, factor=factor))
parts.extend(middle)
if back != '.':
parts.append(AutoHeightChar(back, height, depth, state, factor=factor))
hlist = Hlist(parts)
return hlist
def auto_delim(self, s, loc, toks):
front, middle, back = toks
return self._auto_sized_delimiter(front, middle.asList(), back)
###
##############################################################################
# MAIN
class MathTextParser(object):
_parser = None
_backend_mapping = {
'bitmap': MathtextBackendBitmap,
'agg' : MathtextBackendAgg,
'ps' : MathtextBackendPs,
'pdf' : MathtextBackendPdf,
'svg' : MathtextBackendSvg,
'path' : MathtextBackendPath,
'cairo' : MathtextBackendCairo,
'macosx': MathtextBackendAgg,
}
_font_type_mapping = {
'cm' : BakomaFonts,
'dejavuserif' : DejaVuSerifFonts,
'dejavusans' : DejaVuSansFonts,
'stix' : StixFonts,
'stixsans' : StixSansFonts,
'custom' : UnicodeFonts
}
def __init__(self, output):
"""
Create a MathTextParser for the given backend *output*.
"""
self._output = output.lower()
self._cache = maxdict(50)
def parse(self, s, dpi = 72, prop = None):
"""
Parse the given math expression *s* at the given *dpi*. If
*prop* is provided, it is a
:class:`~matplotlib.font_manager.FontProperties` object
specifying the "default" font to use in the math expression,
used for all non-math text.
The results are cached, so multiple calls to :meth:`parse`
with the same expression should be fast.
"""
# There is a bug in Python 3.x where it leaks frame references,
# and therefore can't handle this caching
if prop is None:
prop = FontProperties()
cacheKey = (s, dpi, hash(prop))
result = self._cache.get(cacheKey)
if result is not None:
return result
if self._output == 'ps' and rcParams['ps.useafm']:
font_output = StandardPsFonts(prop)
else:
backend = self._backend_mapping[self._output]()
fontset = rcParams['mathtext.fontset']
fontset_class = self._font_type_mapping.get(fontset.lower())
if fontset_class is not None:
font_output = fontset_class(prop, backend)
else:
raise ValueError(
"mathtext.fontset must be either 'cm', 'dejavuserif', "
"'dejavusans', 'stix', 'stixsans', or 'custom'")
fontsize = prop.get_size_in_points()
# This is a class variable so we don't rebuild the parser
# with each request.
if self._parser is None:
self.__class__._parser = Parser()
box = self._parser.parse(s, font_output, fontsize, dpi)
font_output.set_canvas_size(box.width, box.height, box.depth)
result = font_output.get_results(box)
self._cache[cacheKey] = result
return result
def to_mask(self, texstr, dpi=120, fontsize=14):
"""
*texstr*
A valid mathtext string, e.g., r'IQ: $\\sigma_i=15$'
*dpi*
The dots-per-inch to render the text
*fontsize*
The font size in points
Returns a tuple (*array*, *depth*)
- *array* is an NxM uint8 alpha ubyte mask array of
rasterized tex.
- depth is the offset of the baseline from the bottom of the
image in pixels.
"""
assert self._output == "bitmap"
prop = FontProperties(size=fontsize)
ftimage, depth = self.parse(texstr, dpi=dpi, prop=prop)
x = ftimage.as_array()
return x, depth
def to_rgba(self, texstr, color='black', dpi=120, fontsize=14):
"""
*texstr*
A valid mathtext string, e.g., r'IQ: $\\sigma_i=15$'
*color*
Any matplotlib color argument
*dpi*
The dots-per-inch to render the text
*fontsize*
The font size in points
Returns a tuple (*array*, *depth*)
- *array* is an NxM uint8 alpha ubyte mask array of
rasterized tex.
- depth is the offset of the baseline from the bottom of the
image in pixels.
"""
x, depth = self.to_mask(texstr, dpi=dpi, fontsize=fontsize)
r, g, b, a = mcolors.to_rgba(color)
RGBA = np.zeros((x.shape[0], x.shape[1], 4), dtype=np.uint8)
RGBA[:, :, 0] = 255 * r
RGBA[:, :, 1] = 255 * g
RGBA[:, :, 2] = 255 * b
RGBA[:, :, 3] = x
return RGBA, depth
def to_png(self, filename, texstr, color='black', dpi=120, fontsize=14):
"""
Writes a tex expression to a PNG file.
Returns the offset of the baseline from the bottom of the
image in pixels.
*filename*
A writable filename or fileobject
*texstr*
A valid mathtext string, e.g., r'IQ: $\\sigma_i=15$'
*color*
A valid matplotlib color argument
*dpi*
The dots-per-inch to render the text
*fontsize*
The font size in points
Returns the offset of the baseline from the bottom of the
image in pixels.
"""
rgba, depth = self.to_rgba(texstr, color=color, dpi=dpi, fontsize=fontsize)
_png.write_png(rgba, filename)
return depth
def get_depth(self, texstr, dpi=120, fontsize=14):
"""
Returns the offset of the baseline from the bottom of the
image in pixels.
*texstr*
A valid mathtext string, e.g., r'IQ: $\\sigma_i=15$'
*dpi*
The dots-per-inch to render the text
*fontsize*
The font size in points
"""
assert self._output=="bitmap"
prop = FontProperties(size=fontsize)
ftimage, depth = self.parse(texstr, dpi=dpi, prop=prop)
return depth
def math_to_image(s, filename_or_obj, prop=None, dpi=None, format=None):
"""
Given a math expression, renders it in a closely-clipped bounding
box to an image file.
*s*
A math expression. The math portion should be enclosed in
dollar signs.
*filename_or_obj*
A filepath or writable file-like object to write the image data
to.
*prop*
If provided, a FontProperties() object describing the size and
style of the text.
*dpi*
Override the output dpi, otherwise use the default associated
with the output format.
*format*
The output format, e.g., 'svg', 'pdf', 'ps' or 'png'. If not
provided, will be deduced from the filename.
"""
from matplotlib import figure
# backend_agg supports all of the core output formats
from matplotlib.backends import backend_agg
if prop is None:
prop = FontProperties()
parser = MathTextParser('path')
width, height, depth, _, _ = parser.parse(s, dpi=72, prop=prop)
fig = figure.Figure(figsize=(width / 72.0, height / 72.0))
fig.text(0, depth/height, s, fontproperties=prop)
backend_agg.FigureCanvasAgg(fig)
fig.savefig(filename_or_obj, dpi=dpi, format=format)
return depth
| 122,489 | 34.54556 | 117 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/matplotlib/patches.py
|
# -*- coding: utf-8 -*-
from __future__ import (absolute_import, division, print_function,
unicode_literals)
import six
from six.moves import map, zip
import math
import warnings
import numpy as np
import matplotlib as mpl
from . import artist, cbook, colors, docstring, lines as mlines, transforms
from .bezier import (
concatenate_paths, get_cos_sin, get_intersection, get_parallels,
inside_circle, make_path_regular, make_wedged_bezier2,
split_bezier_intersecting_with_closedpath, split_path_inout)
from .path import Path
_patch_alias_map = {
'antialiased': ['aa'],
'edgecolor': ['ec'],
'facecolor': ['fc'],
'linewidth': ['lw'],
'linestyle': ['ls']
}
class Patch(artist.Artist):
"""
A patch is a 2D artist with a face color and an edge color.
If any of *edgecolor*, *facecolor*, *linewidth*, or *antialiased*
are *None*, they default to their rc params setting.
"""
zorder = 1
validCap = ('butt', 'round', 'projecting')
validJoin = ('miter', 'round', 'bevel')
# Whether to draw an edge by default. Set on a
# subclass-by-subclass basis.
_edge_default = False
def __str__(self):
return str(self.__class__).split('.')[-1]
def __init__(self,
edgecolor=None,
facecolor=None,
color=None,
linewidth=None,
linestyle=None,
antialiased=None,
hatch=None,
fill=True,
capstyle=None,
joinstyle=None,
**kwargs):
"""
The following kwarg properties are supported
%(Patch)s
"""
artist.Artist.__init__(self)
if linewidth is None:
linewidth = mpl.rcParams['patch.linewidth']
if linestyle is None:
linestyle = "solid"
if capstyle is None:
capstyle = 'butt'
if joinstyle is None:
joinstyle = 'miter'
if antialiased is None:
antialiased = mpl.rcParams['patch.antialiased']
self._hatch_color = colors.to_rgba(mpl.rcParams['hatch.color'])
self._fill = True # needed for set_facecolor call
if color is not None:
if (edgecolor is not None or facecolor is not None):
warnings.warn("Setting the 'color' property will override"
"the edgecolor or facecolor properties. ")
self.set_color(color)
else:
self.set_edgecolor(edgecolor)
self.set_facecolor(facecolor)
# unscaled dashes. Needed to scale dash patterns by lw
self._us_dashes = None
self._linewidth = 0
self.set_fill(fill)
self.set_linestyle(linestyle)
self.set_linewidth(linewidth)
self.set_antialiased(antialiased)
self.set_hatch(hatch)
self.set_capstyle(capstyle)
self.set_joinstyle(joinstyle)
self._combined_transform = transforms.IdentityTransform()
if len(kwargs):
self.update(kwargs)
def get_verts(self):
"""
Return a copy of the vertices used in this patch
If the patch contains Bezier curves, the curves will be
interpolated by line segments. To access the curves as
curves, use :meth:`get_path`.
"""
trans = self.get_transform()
path = self.get_path()
polygons = path.to_polygons(trans)
if len(polygons):
return polygons[0]
return []
def _process_radius(self, radius):
if radius is not None:
return radius
if cbook.is_numlike(self._picker):
_radius = self._picker
else:
if self.get_edgecolor()[3] == 0:
_radius = 0
else:
_radius = self.get_linewidth()
return _radius
def contains(self, mouseevent, radius=None):
"""Test whether the mouse event occurred in the patch.
Returns T/F, {}
"""
if callable(self._contains):
return self._contains(self, mouseevent)
radius = self._process_radius(radius)
inside = self.get_path().contains_point(
(mouseevent.x, mouseevent.y), self.get_transform(), radius)
return inside, {}
def contains_point(self, point, radius=None):
"""
Returns ``True`` if the given *point* is inside the path
(transformed with its transform attribute).
*radius* allows the path to be made slightly larger or smaller.
"""
radius = self._process_radius(radius)
return self.get_path().contains_point(point,
self.get_transform(),
radius)
def contains_points(self, points, radius=None):
"""
Returns a bool array which is ``True`` if the (closed) path
contains the corresponding point.
(transformed with its transform attribute).
*points* must be Nx2 array.
*radius* allows the path to be made slightly larger or smaller.
"""
radius = self._process_radius(radius)
return self.get_path().contains_points(points,
self.get_transform(),
radius)
def update_from(self, other):
"""
Updates this :class:`Patch` from the properties of *other*.
"""
artist.Artist.update_from(self, other)
# For some properties we don't need or don't want to go through the
# getters/setters, so we just copy them directly.
self._edgecolor = other._edgecolor
self._facecolor = other._facecolor
self._fill = other._fill
self._hatch = other._hatch
self._hatch_color = other._hatch_color
# copy the unscaled dash pattern
self._us_dashes = other._us_dashes
self.set_linewidth(other._linewidth) # also sets dash properties
self.set_transform(other.get_data_transform())
def get_extents(self):
"""
Return a :class:`~matplotlib.transforms.Bbox` object defining
the axis-aligned extents of the :class:`Patch`.
"""
return self.get_path().get_extents(self.get_transform())
def get_transform(self):
"""
Return the :class:`~matplotlib.transforms.Transform` applied
to the :class:`Patch`.
"""
return self.get_patch_transform() + artist.Artist.get_transform(self)
def get_data_transform(self):
"""
Return the :class:`~matplotlib.transforms.Transform` instance which
maps data coordinates to physical coordinates.
"""
return artist.Artist.get_transform(self)
def get_patch_transform(self):
"""
Return the :class:`~matplotlib.transforms.Transform` instance which
takes patch coordinates to data coordinates.
For example, one may define a patch of a circle which represents a
radius of 5 by providing coordinates for a unit circle, and a
transform which scales the coordinates (the patch coordinate) by 5.
"""
return transforms.IdentityTransform()
def get_antialiased(self):
"""
Returns True if the :class:`Patch` is to be drawn with antialiasing.
"""
return self._antialiased
get_aa = get_antialiased
def get_edgecolor(self):
"""
Return the edge color of the :class:`Patch`.
"""
return self._edgecolor
get_ec = get_edgecolor
def get_facecolor(self):
"""
Return the face color of the :class:`Patch`.
"""
return self._facecolor
get_fc = get_facecolor
def get_linewidth(self):
"""
Return the line width in points.
"""
return self._linewidth
get_lw = get_linewidth
def get_linestyle(self):
"""
Return the linestyle. Will be one of ['solid' | 'dashed' |
'dashdot' | 'dotted']
"""
return self._linestyle
get_ls = get_linestyle
def set_antialiased(self, aa):
"""
Set whether to use antialiased rendering.
Parameters
----------
b : bool or None
.. ACCEPTS: bool or None
"""
if aa is None:
aa = mpl.rcParams['patch.antialiased']
self._antialiased = aa
self.stale = True
def set_aa(self, aa):
"""alias for set_antialiased"""
return self.set_antialiased(aa)
def _set_edgecolor(self, color):
set_hatch_color = True
if color is None:
if (mpl.rcParams['patch.force_edgecolor'] or
not self._fill or self._edge_default):
color = mpl.rcParams['patch.edgecolor']
else:
color = 'none'
set_hatch_color = False
self._edgecolor = colors.to_rgba(color, self._alpha)
if set_hatch_color:
self._hatch_color = self._edgecolor
self.stale = True
def set_edgecolor(self, color):
"""
Set the patch edge color
ACCEPTS: mpl color spec, None, 'none', or 'auto'
"""
self._original_edgecolor = color
self._set_edgecolor(color)
def set_ec(self, color):
"""alias for set_edgecolor"""
return self.set_edgecolor(color)
def _set_facecolor(self, color):
if color is None:
color = mpl.rcParams['patch.facecolor']
alpha = self._alpha if self._fill else 0
self._facecolor = colors.to_rgba(color, alpha)
self.stale = True
def set_facecolor(self, color):
"""
Set the patch face color
ACCEPTS: mpl color spec, or None for default, or 'none' for no color
"""
self._original_facecolor = color
self._set_facecolor(color)
def set_fc(self, color):
"""alias for set_facecolor"""
return self.set_facecolor(color)
def set_color(self, c):
"""
Set both the edgecolor and the facecolor.
ACCEPTS: matplotlib color spec
.. seealso::
:meth:`set_facecolor`, :meth:`set_edgecolor`
For setting the edge or face color individually.
"""
self.set_facecolor(c)
self.set_edgecolor(c)
def set_alpha(self, alpha):
"""
Set the alpha tranparency of the patch.
ACCEPTS: float or None
"""
if alpha is not None:
try:
float(alpha)
except TypeError:
raise TypeError('alpha must be a float or None')
artist.Artist.set_alpha(self, alpha)
self._set_facecolor(self._original_facecolor)
self._set_edgecolor(self._original_edgecolor)
# stale is already True
def set_linewidth(self, w):
"""
Set the patch linewidth in points
ACCEPTS: float or None for default
"""
if w is None:
w = mpl.rcParams['patch.linewidth']
if w is None:
w = mpl.rcParams['axes.linewidth']
self._linewidth = float(w)
# scale the dash pattern by the linewidth
offset, ls = self._us_dashes
self._dashoffset, self._dashes = mlines._scale_dashes(
offset, ls, self._linewidth)
self.stale = True
def set_lw(self, lw):
"""alias for set_linewidth"""
return self.set_linewidth(lw)
def set_linestyle(self, ls):
"""
Set the patch linestyle
=========================== =================
linestyle description
=========================== =================
``'-'`` or ``'solid'`` solid line
``'--'`` or ``'dashed'`` dashed line
``'-.'`` or ``'dashdot'`` dash-dotted line
``':'`` or ``'dotted'`` dotted line
=========================== =================
Alternatively a dash tuple of the following form can be provided::
(offset, onoffseq),
where ``onoffseq`` is an even length tuple of on and off ink
in points.
ACCEPTS: ['solid' | 'dashed', 'dashdot', 'dotted' |
(offset, on-off-dash-seq) |
``'-'`` | ``'--'`` | ``'-.'`` | ``':'`` | ``'None'`` |
``' '`` | ``''``]
Parameters
----------
ls : { '-', '--', '-.', ':'} and more see description
The line style.
"""
if ls is None:
ls = "solid"
self._linestyle = ls
# get the unscalled dash pattern
offset, ls = self._us_dashes = mlines._get_dash_pattern(ls)
# scale the dash pattern by the linewidth
self._dashoffset, self._dashes = mlines._scale_dashes(
offset, ls, self._linewidth)
self.stale = True
def set_ls(self, ls):
"""alias for set_linestyle"""
return self.set_linestyle(ls)
def set_fill(self, b):
"""
Set whether to fill the patch.
Parameters
----------
b : bool
.. ACCEPTS: bool
"""
self._fill = bool(b)
self._set_facecolor(self._original_facecolor)
self._set_edgecolor(self._original_edgecolor)
self.stale = True
def get_fill(self):
'return whether fill is set'
return self._fill
# Make fill a property so as to preserve the long-standing
# but somewhat inconsistent behavior in which fill was an
# attribute.
fill = property(get_fill, set_fill)
def set_capstyle(self, s):
"""
Set the patch capstyle
ACCEPTS: ['butt' | 'round' | 'projecting']
"""
s = s.lower()
if s not in self.validCap:
raise ValueError('set_capstyle passed "%s";\n' % (s,) +
'valid capstyles are %s' % (self.validCap,))
self._capstyle = s
self.stale = True
def get_capstyle(self):
"Return the current capstyle"
return self._capstyle
def set_joinstyle(self, s):
"""
Set the patch joinstyle
ACCEPTS: ['miter' | 'round' | 'bevel']
"""
s = s.lower()
if s not in self.validJoin:
raise ValueError('set_joinstyle passed "%s";\n' % (s,) +
'valid joinstyles are %s' % (self.validJoin,))
self._joinstyle = s
self.stale = True
def get_joinstyle(self):
"Return the current joinstyle"
return self._joinstyle
def set_hatch(self, hatch):
"""
Set the hatching pattern
*hatch* can be one of::
/ - diagonal hatching
\\ - back diagonal
| - vertical
- - horizontal
+ - crossed
x - crossed diagonal
o - small circle
O - large circle
. - dots
* - stars
Letters can be combined, in which case all the specified
hatchings are done. If same letter repeats, it increases the
density of hatching of that pattern.
Hatching is supported in the PostScript, PDF, SVG and Agg
backends only.
ACCEPTS: ['/' | '\\\\' | '|' | '-' | '+' | 'x' | 'o' | 'O' | '.' | '*']
"""
self._hatch = hatch
self.stale = True
def get_hatch(self):
'Return the current hatching pattern'
return self._hatch
@artist.allow_rasterization
def draw(self, renderer):
'Draw the :class:`Patch` to the given *renderer*.'
if not self.get_visible():
return
renderer.open_group('patch', self.get_gid())
gc = renderer.new_gc()
gc.set_foreground(self._edgecolor, isRGBA=True)
lw = self._linewidth
if self._edgecolor[3] == 0:
lw = 0
gc.set_linewidth(lw)
gc.set_dashes(0, self._dashes)
gc.set_capstyle(self._capstyle)
gc.set_joinstyle(self._joinstyle)
gc.set_antialiased(self._antialiased)
self._set_gc_clip(gc)
gc.set_url(self._url)
gc.set_snap(self.get_snap())
rgbFace = self._facecolor
if rgbFace[3] == 0:
rgbFace = None # (some?) renderers expect this as no-fill signal
gc.set_alpha(self._alpha)
if self._hatch:
gc.set_hatch(self._hatch)
try:
gc.set_hatch_color(self._hatch_color)
except AttributeError:
# if we end up with a GC that does not have this method
warnings.warn("Your backend does not have support for "
"setting the hatch color.")
if self.get_sketch_params() is not None:
gc.set_sketch_params(*self.get_sketch_params())
path = self.get_path()
transform = self.get_transform()
tpath = transform.transform_path_non_affine(path)
affine = transform.get_affine()
if self.get_path_effects():
from matplotlib.patheffects import PathEffectRenderer
renderer = PathEffectRenderer(self.get_path_effects(), renderer)
renderer.draw_path(gc, tpath, affine, rgbFace)
gc.restore()
renderer.close_group('patch')
self.stale = False
def get_path(self):
"""
Return the path of this patch
"""
raise NotImplementedError('Derived must override')
def get_window_extent(self, renderer=None):
return self.get_path().get_extents(self.get_transform())
patchdoc = artist.kwdoc(Patch)
for k in ('Rectangle', 'Circle', 'RegularPolygon', 'Polygon', 'Wedge', 'Arrow',
'FancyArrow', 'YAArrow', 'CirclePolygon', 'Ellipse', 'Arc',
'FancyBboxPatch', 'Patch'):
docstring.interpd.update({k: patchdoc})
# define Patch.__init__ docstring after the class has been added to interpd
docstring.dedent_interpd(Patch.__init__)
class Shadow(Patch):
def __str__(self):
return "Shadow(%s)" % (str(self.patch))
@docstring.dedent_interpd
def __init__(self, patch, ox, oy, props=None, **kwargs):
"""
Create a shadow of the given *patch* offset by *ox*, *oy*.
*props*, if not *None*, is a patch property update dictionary.
If *None*, the shadow will have have the same color as the face,
but darkened.
kwargs are
%(Patch)s
"""
Patch.__init__(self)
self.patch = patch
self.props = props
self._ox, self._oy = ox, oy
self._shadow_transform = transforms.Affine2D()
self._update()
def _update(self):
self.update_from(self.patch)
# Place the shadow patch directly behind the inherited patch.
self.set_zorder(np.nextafter(self.patch.zorder, -np.inf))
if self.props is not None:
self.update(self.props)
else:
r, g, b, a = colors.to_rgba(self.patch.get_facecolor())
rho = 0.3
r = rho * r
g = rho * g
b = rho * b
self.set_facecolor((r, g, b, 0.5))
self.set_edgecolor((r, g, b, 0.5))
self.set_alpha(0.5)
def _update_transform(self, renderer):
ox = renderer.points_to_pixels(self._ox)
oy = renderer.points_to_pixels(self._oy)
self._shadow_transform.clear().translate(ox, oy)
def _get_ox(self):
return self._ox
def _set_ox(self, ox):
self._ox = ox
def _get_oy(self):
return self._oy
def _set_oy(self, oy):
self._oy = oy
def get_path(self):
return self.patch.get_path()
def get_patch_transform(self):
return self.patch.get_patch_transform() + self._shadow_transform
def draw(self, renderer):
self._update_transform(renderer)
Patch.draw(self, renderer)
class Rectangle(Patch):
"""
Draw a rectangle with lower left at *xy* = (*x*, *y*) with
specified *width*, *height* and rotation *angle*.
"""
def __str__(self):
pars = self._x0, self._y0, self._width, self._height, self.angle
fmt = "Rectangle(xy=(%g, %g), width=%g, height=%g, angle=%g)"
return fmt % pars
@docstring.dedent_interpd
def __init__(self, xy, width, height, angle=0.0, **kwargs):
"""
Parameters
----------
xy: length-2 tuple
The bottom and left rectangle coordinates
width:
Rectangle width
height:
Rectangle height
angle: float, optional
rotation in degrees anti-clockwise about *xy* (default is 0.0)
fill: bool, optional
Whether to fill the rectangle (default is ``True``)
Notes
-----
Valid kwargs are:
%(Patch)s
"""
Patch.__init__(self, **kwargs)
self._x0 = xy[0]
self._y0 = xy[1]
self._width = width
self._height = height
self._x1 = self._x0 + self._width
self._y1 = self._y0 + self._height
self.angle = float(angle)
# Note: This cannot be calculated until this is added to an Axes
self._rect_transform = transforms.IdentityTransform()
def get_path(self):
"""
Return the vertices of the rectangle
"""
return Path.unit_rectangle()
def _update_patch_transform(self):
"""NOTE: This cannot be called until after this has been added
to an Axes, otherwise unit conversion will fail. This
makes it very important to call the accessor method and
not directly access the transformation member variable.
"""
x0, y0, x1, y1 = self._convert_units()
bbox = transforms.Bbox.from_extents(x0, y0, x1, y1)
rot_trans = transforms.Affine2D()
rot_trans.rotate_deg_around(x0, y0, self.angle)
self._rect_transform = transforms.BboxTransformTo(bbox)
self._rect_transform += rot_trans
def _update_x1(self):
self._x1 = self._x0 + self._width
def _update_y1(self):
self._y1 = self._y0 + self._height
def _convert_units(self):
'''
Convert bounds of the rectangle
'''
x0 = self.convert_xunits(self._x0)
y0 = self.convert_yunits(self._y0)
x1 = self.convert_xunits(self._x1)
y1 = self.convert_yunits(self._y1)
return x0, y0, x1, y1
def get_patch_transform(self):
self._update_patch_transform()
return self._rect_transform
def get_x(self):
"Return the left coord of the rectangle"
return self._x0
def get_y(self):
"Return the bottom coord of the rectangle"
return self._y0
def get_xy(self):
"Return the left and bottom coords of the rectangle"
return self._x0, self._y0
def get_width(self):
"Return the width of the rectangle"
return self._width
def get_height(self):
"Return the height of the rectangle"
return self._height
def set_x(self, x):
"Set the left coord of the rectangle"
self._x0 = x
self._update_x1()
self.stale = True
def set_y(self, y):
"Set the bottom coord of the rectangle"
self._y0 = y
self._update_y1()
self.stale = True
def set_xy(self, xy):
"""
Set the left and bottom coords of the rectangle
ACCEPTS: 2-item sequence
"""
self._x0, self._y0 = xy
self._update_x1()
self._update_y1()
self.stale = True
def set_width(self, w):
"Set the width of the rectangle"
self._width = w
self._update_x1()
self.stale = True
def set_height(self, h):
"Set the height of the rectangle"
self._height = h
self._update_y1()
self.stale = True
def set_bounds(self, *args):
"""
Set the bounds of the rectangle: l,b,w,h
ACCEPTS: (left, bottom, width, height)
"""
if len(args) == 0:
l, b, w, h = args[0]
else:
l, b, w, h = args
self._x0 = l
self._y0 = b
self._width = w
self._height = h
self._update_x1()
self._update_y1()
self.stale = True
def get_bbox(self):
x0, y0, x1, y1 = self._convert_units()
return transforms.Bbox.from_extents(x0, y0, x1, y1)
xy = property(get_xy, set_xy)
class RegularPolygon(Patch):
"""
A regular polygon patch.
"""
def __str__(self):
return "Poly%d(%g,%g)" % (self._numVertices, self._xy[0], self._xy[1])
@docstring.dedent_interpd
def __init__(self, xy, numVertices, radius=5, orientation=0,
**kwargs):
"""
Constructor arguments:
*xy*
A length 2 tuple (*x*, *y*) of the center.
*numVertices*
the number of vertices.
*radius*
The distance from the center to each of the vertices.
*orientation*
rotates the polygon (in radians).
Valid kwargs are:
%(Patch)s
"""
self._xy = xy
self._numVertices = numVertices
self._orientation = orientation
self._radius = radius
self._path = Path.unit_regular_polygon(numVertices)
self._poly_transform = transforms.Affine2D()
self._update_transform()
Patch.__init__(self, **kwargs)
def _update_transform(self):
self._poly_transform.clear() \
.scale(self.radius) \
.rotate(self.orientation) \
.translate(*self.xy)
def _get_xy(self):
return self._xy
def _set_xy(self, xy):
self._xy = xy
self._update_transform()
xy = property(_get_xy, _set_xy)
def _get_orientation(self):
return self._orientation
def _set_orientation(self, orientation):
self._orientation = orientation
self._update_transform()
orientation = property(_get_orientation, _set_orientation)
def _get_radius(self):
return self._radius
def _set_radius(self, radius):
self._radius = radius
self._update_transform()
radius = property(_get_radius, _set_radius)
def _get_numvertices(self):
return self._numVertices
def _set_numvertices(self, numVertices):
self._numVertices = numVertices
numvertices = property(_get_numvertices, _set_numvertices)
def get_path(self):
return self._path
def get_patch_transform(self):
self._update_transform()
return self._poly_transform
class PathPatch(Patch):
"""
A general polycurve path patch.
"""
_edge_default = True
def __str__(self):
return "Poly((%g, %g) ...)" % tuple(self._path.vertices[0])
@docstring.dedent_interpd
def __init__(self, path, **kwargs):
"""
*path* is a :class:`matplotlib.path.Path` object.
Valid kwargs are:
%(Patch)s
.. seealso::
:class:`Patch`
For additional kwargs
"""
Patch.__init__(self, **kwargs)
self._path = path
def get_path(self):
return self._path
class Polygon(Patch):
"""
A general polygon patch.
"""
def __str__(self):
return "Poly((%g, %g) ...)" % tuple(self._path.vertices[0])
@docstring.dedent_interpd
def __init__(self, xy, closed=True, **kwargs):
"""
*xy* is a numpy array with shape Nx2.
If *closed* is *True*, the polygon will be closed so the
starting and ending points are the same.
Valid kwargs are:
%(Patch)s
.. seealso::
:class:`Patch`
For additional kwargs
"""
Patch.__init__(self, **kwargs)
self._closed = closed
self.set_xy(xy)
def get_path(self):
"""
Get the path of the polygon
Returns
-------
path : Path
The :class:`~matplotlib.path.Path` object for
the polygon
"""
return self._path
def get_closed(self):
"""
Returns if the polygon is closed
Returns
-------
closed : bool
If the path is closed
"""
return self._closed
def set_closed(self, closed):
"""
Set if the polygon is closed
Parameters
----------
closed : bool
True if the polygon is closed
"""
if self._closed == bool(closed):
return
self._closed = bool(closed)
self.set_xy(self.get_xy())
self.stale = True
def get_xy(self):
"""
Get the vertices of the path
Returns
-------
vertices : numpy array
The coordinates of the vertices as a Nx2
ndarray.
"""
return self._path.vertices
def set_xy(self, xy):
"""
Set the vertices of the polygon
Parameters
----------
xy : numpy array or iterable of pairs
The coordinates of the vertices as a Nx2
ndarray or iterable of pairs.
"""
xy = np.asarray(xy)
if self._closed:
if len(xy) and (xy[0] != xy[-1]).any():
xy = np.concatenate([xy, [xy[0]]])
else:
if len(xy) > 2 and (xy[0] == xy[-1]).all():
xy = xy[:-1]
self._path = Path(xy, closed=self._closed)
self.stale = True
_get_xy = get_xy
_set_xy = set_xy
xy = property(
get_xy, set_xy, None,
"""Set/get the vertices of the polygon. This property is
provided for backward compatibility with matplotlib 0.91.x
only. New code should use
:meth:`~matplotlib.patches.Polygon.get_xy` and
:meth:`~matplotlib.patches.Polygon.set_xy` instead.""")
class Wedge(Patch):
"""
Wedge shaped patch.
"""
def __str__(self):
pars = (self.center[0], self.center[1], self.r,
self.theta1, self.theta2, self.width)
fmt = "Wedge(center=(%g, %g), r=%g, theta1=%g, theta2=%g, width=%s)"
return fmt % pars
@docstring.dedent_interpd
def __init__(self, center, r, theta1, theta2, width=None, **kwargs):
"""
Draw a wedge centered at *x*, *y* center with radius *r* that
sweeps *theta1* to *theta2* (in degrees). If *width* is given,
then a partial wedge is drawn from inner radius *r* - *width*
to outer radius *r*.
Valid kwargs are:
%(Patch)s
"""
Patch.__init__(self, **kwargs)
self.center = center
self.r, self.width = r, width
self.theta1, self.theta2 = theta1, theta2
self._patch_transform = transforms.IdentityTransform()
self._recompute_path()
def _recompute_path(self):
# Inner and outer rings are connected unless the annulus is complete
if abs((self.theta2 - self.theta1) - 360) <= 1e-12:
theta1, theta2 = 0, 360
connector = Path.MOVETO
else:
theta1, theta2 = self.theta1, self.theta2
connector = Path.LINETO
# Form the outer ring
arc = Path.arc(theta1, theta2)
if self.width is not None:
# Partial annulus needs to draw the outer ring
# followed by a reversed and scaled inner ring
v1 = arc.vertices
v2 = arc.vertices[::-1] * (self.r - self.width) / self.r
v = np.vstack([v1, v2, v1[0, :], (0, 0)])
c = np.hstack([arc.codes, arc.codes, connector, Path.CLOSEPOLY])
c[len(arc.codes)] = connector
else:
# Wedge doesn't need an inner ring
v = np.vstack([arc.vertices, [(0, 0), arc.vertices[0, :], (0, 0)]])
c = np.hstack([arc.codes, [connector, connector, Path.CLOSEPOLY]])
# Shift and scale the wedge to the final location.
v *= self.r
v += np.asarray(self.center)
self._path = Path(v, c)
def set_center(self, center):
self._path = None
self.center = center
self.stale = True
def set_radius(self, radius):
self._path = None
self.r = radius
self.stale = True
def set_theta1(self, theta1):
self._path = None
self.theta1 = theta1
self.stale = True
def set_theta2(self, theta2):
self._path = None
self.theta2 = theta2
self.stale = True
def set_width(self, width):
self._path = None
self.width = width
self.stale = True
def get_path(self):
if self._path is None:
self._recompute_path()
return self._path
# COVERAGE NOTE: Not used internally or from examples
class Arrow(Patch):
"""
An arrow patch.
"""
def __str__(self):
return "Arrow()"
_path = Path([[0.0, 0.1], [0.0, -0.1],
[0.8, -0.1], [0.8, -0.3],
[1.0, 0.0], [0.8, 0.3],
[0.8, 0.1], [0.0, 0.1]],
closed=True)
@docstring.dedent_interpd
def __init__(self, x, y, dx, dy, width=1.0, **kwargs):
"""
Draws an arrow from (*x*, *y*) to (*x* + *dx*, *y* + *dy*).
The width of the arrow is scaled by *width*.
Parameters
----------
x : scalar
x coordinate of the arrow tail
y : scalar
y coordinate of the arrow tail
dx : scalar
Arrow length in the x direction
dy : scalar
Arrow length in the y direction
width : scalar, optional (default: 1)
Scale factor for the width of the arrow. With a default value of
1, the tail width is 0.2 and head width is 0.6.
**kwargs :
Keyword arguments control the :class:`~matplotlib.patches.Patch`
properties:
%(Patch)s
See Also
--------
:class:`FancyArrow` :
Patch that allows independent control of the head and tail
properties
"""
Patch.__init__(self, **kwargs)
L = np.hypot(dx, dy)
if L != 0:
cx = dx / L
sx = dy / L
else:
# Account for division by zero
cx, sx = 0, 1
trans1 = transforms.Affine2D().scale(L, width)
trans2 = transforms.Affine2D.from_values(cx, sx, -sx, cx, 0.0, 0.0)
trans3 = transforms.Affine2D().translate(x, y)
trans = trans1 + trans2 + trans3
self._patch_transform = trans.frozen()
def get_path(self):
return self._path
def get_patch_transform(self):
return self._patch_transform
class FancyArrow(Polygon):
"""
Like Arrow, but lets you set head width and head height independently.
"""
_edge_default = True
def __str__(self):
return "FancyArrow()"
@docstring.dedent_interpd
def __init__(self, x, y, dx, dy, width=0.001, length_includes_head=False,
head_width=None, head_length=None, shape='full', overhang=0,
head_starts_at_zero=False, **kwargs):
"""
Constructor arguments
*width*: float (default: 0.001)
width of full arrow tail
*length_includes_head*: bool (default: False)
True if head is to be counted in calculating the length.
*head_width*: float or None (default: 3*width)
total width of the full arrow head
*head_length*: float or None (default: 1.5 * head_width)
length of arrow head
*shape*: ['full', 'left', 'right'] (default: 'full')
draw the left-half, right-half, or full arrow
*overhang*: float (default: 0)
fraction that the arrow is swept back (0 overhang means
triangular shape). Can be negative or greater than one.
*head_starts_at_zero*: bool (default: False)
if True, the head starts being drawn at coordinate 0
instead of ending at coordinate 0.
Other valid kwargs (inherited from :class:`Patch`) are:
%(Patch)s
"""
if head_width is None:
head_width = 3 * width
if head_length is None:
head_length = 1.5 * head_width
distance = np.hypot(dx, dy)
if length_includes_head:
length = distance
else:
length = distance + head_length
if not length:
verts = [] # display nothing if empty
else:
# start by drawing horizontal arrow, point at (0,0)
hw, hl, hs, lw = head_width, head_length, overhang, width
left_half_arrow = np.array([
[0.0, 0.0], # tip
[-hl, -hw / 2.0], # leftmost
[-hl * (1 - hs), -lw / 2.0], # meets stem
[-length, -lw / 2.0], # bottom left
[-length, 0],
])
# if we're not including the head, shift up by head length
if not length_includes_head:
left_half_arrow += [head_length, 0]
# if the head starts at 0, shift up by another head length
if head_starts_at_zero:
left_half_arrow += [head_length / 2.0, 0]
# figure out the shape, and complete accordingly
if shape == 'left':
coords = left_half_arrow
else:
right_half_arrow = left_half_arrow * [1, -1]
if shape == 'right':
coords = right_half_arrow
elif shape == 'full':
# The half-arrows contain the midpoint of the stem,
# which we can omit from the full arrow. Including it
# twice caused a problem with xpdf.
coords = np.concatenate([left_half_arrow[:-1],
right_half_arrow[-2::-1]])
else:
raise ValueError("Got unknown shape: %s" % shape)
if distance != 0:
cx = dx / distance
sx = dy / distance
else:
# Account for division by zero
cx, sx = 0, 1
M = [[cx, sx], [-sx, cx]]
verts = np.dot(coords, M) + (x + dx, y + dy)
Polygon.__init__(self, list(map(tuple, verts)), closed=True, **kwargs)
docstring.interpd.update({"FancyArrow": FancyArrow.__init__.__doc__})
class YAArrow(Patch):
"""
Yet another arrow class.
This is an arrow that is defined in display space and has a tip at
*x1*, *y1* and a base at *x2*, *y2*.
"""
def __str__(self):
return "YAArrow()"
@docstring.dedent_interpd
def __init__(self, figure, xytip, xybase,
width=4, frac=0.1, headwidth=12, **kwargs):
"""
Constructor arguments:
*xytip*
(*x*, *y*) location of arrow tip
*xybase*
(*x*, *y*) location the arrow base mid point
*figure*
The :class:`~matplotlib.figure.Figure` instance
(fig.dpi)
*width*
The width of the arrow in points
*frac*
The fraction of the arrow length occupied by the head
*headwidth*
The width of the base of the arrow head in points
Valid kwargs are:
%(Patch)s
"""
self.xytip = xytip
self.xybase = xybase
self.width = width
self.frac = frac
self.headwidth = headwidth
Patch.__init__(self, **kwargs)
# Set self.figure after Patch.__init__, since it sets self.figure to
# None
self.figure = figure
def get_path(self):
# Since this is dpi dependent, we need to recompute the path
# every time.
# the base vertices
x1, y1 = self.xytip
x2, y2 = self.xybase
k1 = self.width * self.figure.dpi / 72. / 2.
k2 = self.headwidth * self.figure.dpi / 72. / 2.
xb1, yb1, xb2, yb2 = self.getpoints(x1, y1, x2, y2, k1)
# a point on the segment 20% of the distance from the tip to the base
theta = math.atan2(y2 - y1, x2 - x1)
r = math.sqrt((y2 - y1) ** 2. + (x2 - x1) ** 2.)
xm = x1 + self.frac * r * math.cos(theta)
ym = y1 + self.frac * r * math.sin(theta)
xc1, yc1, xc2, yc2 = self.getpoints(x1, y1, xm, ym, k1)
xd1, yd1, xd2, yd2 = self.getpoints(x1, y1, xm, ym, k2)
xs = self.convert_xunits([xb1, xb2, xc2, xd2, x1, xd1, xc1, xb1])
ys = self.convert_yunits([yb1, yb2, yc2, yd2, y1, yd1, yc1, yb1])
return Path(np.column_stack([xs, ys]), closed=True)
def get_patch_transform(self):
return transforms.IdentityTransform()
def getpoints(self, x1, y1, x2, y2, k):
"""
For line segment defined by (*x1*, *y1*) and (*x2*, *y2*)
return the points on the line that is perpendicular to the
line and intersects (*x2*, *y2*) and the distance from (*x2*,
*y2*) of the returned points is *k*.
"""
x1, y1, x2, y2, k = map(float, (x1, y1, x2, y2, k))
if y2 - y1 == 0:
return x2, y2 + k, x2, y2 - k
elif x2 - x1 == 0:
return x2 + k, y2, x2 - k, y2
m = (y2 - y1) / (x2 - x1)
pm = -1. / m
a = 1
b = -2 * y2
c = y2 ** 2. - k ** 2. * pm ** 2. / (1. + pm ** 2.)
y3a = (-b + math.sqrt(b ** 2 - 4 * a * c)) / (2 * a)
x3a = (y3a - y2) / pm + x2
y3b = (-b - math.sqrt(b ** 2 - 4 * a * c)) / (2 * a)
x3b = (y3b - y2) / pm + x2
return x3a, y3a, x3b, y3b
class CirclePolygon(RegularPolygon):
"""
A polygon-approximation of a circle patch.
"""
def __str__(self):
return "CirclePolygon(%d,%d)" % self.center
@docstring.dedent_interpd
def __init__(self, xy, radius=5,
resolution=20, # the number of vertices
** kwargs):
"""
Create a circle at *xy* = (*x*, *y*) with given *radius*.
This circle is approximated by a regular polygon with
*resolution* sides. For a smoother circle drawn with splines,
see :class:`~matplotlib.patches.Circle`.
Valid kwargs are:
%(Patch)s
"""
RegularPolygon.__init__(self, xy,
resolution,
radius,
orientation=0,
**kwargs)
class Ellipse(Patch):
"""
A scale-free ellipse.
"""
def __str__(self):
pars = (self.center[0], self.center[1],
self.width, self.height, self.angle)
fmt = "Ellipse(xy=(%s, %s), width=%s, height=%s, angle=%s)"
return fmt % pars
@docstring.dedent_interpd
def __init__(self, xy, width, height, angle=0.0, **kwargs):
"""
*xy*
center of ellipse
*width*
total length (diameter) of horizontal axis
*height*
total length (diameter) of vertical axis
*angle*
rotation in degrees (anti-clockwise)
Valid kwargs are:
%(Patch)s
"""
Patch.__init__(self, **kwargs)
self.center = xy
self.width, self.height = width, height
self.angle = angle
self._path = Path.unit_circle()
# Note: This cannot be calculated until this is added to an Axes
self._patch_transform = transforms.IdentityTransform()
def _recompute_transform(self):
"""NOTE: This cannot be called until after this has been added
to an Axes, otherwise unit conversion will fail. This
makes it very important to call the accessor method and
not directly access the transformation member variable.
"""
center = (self.convert_xunits(self.center[0]),
self.convert_yunits(self.center[1]))
width = self.convert_xunits(self.width)
height = self.convert_yunits(self.height)
self._patch_transform = transforms.Affine2D() \
.scale(width * 0.5, height * 0.5) \
.rotate_deg(self.angle) \
.translate(*center)
def get_path(self):
"""
Return the vertices of the rectangle
"""
return self._path
def get_patch_transform(self):
self._recompute_transform()
return self._patch_transform
class Circle(Ellipse):
"""
A circle patch.
"""
def __str__(self):
pars = self.center[0], self.center[1], self.radius
fmt = "Circle(xy=(%g, %g), radius=%g)"
return fmt % pars
@docstring.dedent_interpd
def __init__(self, xy, radius=5, **kwargs):
"""
Create true circle at center *xy* = (*x*, *y*) with given
*radius*. Unlike :class:`~matplotlib.patches.CirclePolygon`
which is a polygonal approximation, this uses Bézier splines
and is much closer to a scale-free circle.
Valid kwargs are:
%(Patch)s
"""
Ellipse.__init__(self, xy, radius * 2, radius * 2, **kwargs)
self.radius = radius
def set_radius(self, radius):
"""
Set the radius of the circle
ACCEPTS: float
"""
self.width = self.height = 2 * radius
self.stale = True
def get_radius(self):
'return the radius of the circle'
return self.width / 2.
radius = property(get_radius, set_radius)
class Arc(Ellipse):
"""
An elliptical arc. Because it performs various optimizations, it
can not be filled.
The arc must be used in an :class:`~matplotlib.axes.Axes`
instance---it can not be added directly to a
:class:`~matplotlib.figure.Figure`---because it is optimized to
only render the segments that are inside the axes bounding box
with high resolution.
"""
def __str__(self):
pars = (self.center[0], self.center[1], self.width,
self.height, self.angle, self.theta1, self.theta2)
fmt = ("Arc(xy=(%g, %g), width=%g, "
"height=%g, angle=%g, theta1=%g, theta2=%g)")
return fmt % pars
@docstring.dedent_interpd
def __init__(self, xy, width, height, angle=0.0,
theta1=0.0, theta2=360.0, **kwargs):
"""
The following args are supported:
*xy*
center of ellipse
*width*
length of horizontal axis
*height*
length of vertical axis
*angle*
rotation in degrees (anti-clockwise)
*theta1*
starting angle of the arc in degrees
*theta2*
ending angle of the arc in degrees
If *theta1* and *theta2* are not provided, the arc will form a
complete ellipse.
Valid kwargs are:
%(Patch)s
"""
fill = kwargs.setdefault('fill', False)
if fill:
raise ValueError("Arc objects can not be filled")
Ellipse.__init__(self, xy, width, height, angle, **kwargs)
self.theta1 = theta1
self.theta2 = theta2
@artist.allow_rasterization
def draw(self, renderer):
"""
Ellipses are normally drawn using an approximation that uses
eight cubic bezier splines. The error of this approximation
is 1.89818e-6, according to this unverified source:
Lancaster, Don. Approximating a Circle or an Ellipse Using
Four Bezier Cubic Splines.
http://www.tinaja.com/glib/ellipse4.pdf
There is a use case where very large ellipses must be drawn
with very high accuracy, and it is too expensive to render the
entire ellipse with enough segments (either splines or line
segments). Therefore, in the case where either radius of the
ellipse is large enough that the error of the spline
approximation will be visible (greater than one pixel offset
from the ideal), a different technique is used.
In that case, only the visible parts of the ellipse are drawn,
with each visible arc using a fixed number of spline segments
(8). The algorithm proceeds as follows:
1. The points where the ellipse intersects the axes bounding
box are located. (This is done be performing an inverse
transformation on the axes bbox such that it is relative
to the unit circle -- this makes the intersection
calculation much easier than doing rotated ellipse
intersection directly).
This uses the "line intersecting a circle" algorithm
from:
Vince, John. Geometry for Computer Graphics: Formulae,
Examples & Proofs. London: Springer-Verlag, 2005.
2. The angles of each of the intersection points are
calculated.
3. Proceeding counterclockwise starting in the positive
x-direction, each of the visible arc-segments between the
pairs of vertices are drawn using the bezier arc
approximation technique implemented in
:meth:`matplotlib.path.Path.arc`.
"""
if not hasattr(self, 'axes'):
raise RuntimeError('Arcs can only be used in Axes instances')
self._recompute_transform()
width = self.convert_xunits(self.width)
height = self.convert_yunits(self.height)
# If the width and height of ellipse are not equal, take into account
# stretching when calculating angles to draw between
def theta_stretch(theta, scale):
theta = np.deg2rad(theta)
x = np.cos(theta)
y = np.sin(theta)
return np.rad2deg(np.arctan2(scale * y, x))
theta1 = theta_stretch(self.theta1, width / height)
theta2 = theta_stretch(self.theta2, width / height)
# Get width and height in pixels
width, height = self.get_transform().transform_point((width, height))
inv_error = (1.0 / 1.89818e-6) * 0.5
if width < inv_error and height < inv_error:
self._path = Path.arc(theta1, theta2)
return Patch.draw(self, renderer)
def iter_circle_intersect_on_line(x0, y0, x1, y1):
dx = x1 - x0
dy = y1 - y0
dr2 = dx * dx + dy * dy
D = x0 * y1 - x1 * y0
D2 = D * D
discrim = dr2 - D2
# Single (tangential) intersection
if discrim == 0.0:
x = (D * dy) / dr2
y = (-D * dx) / dr2
yield x, y
elif discrim > 0.0:
# The definition of "sign" here is different from
# np.sign: we never want to get 0.0
if dy < 0.0:
sign_dy = -1.0
else:
sign_dy = 1.0
sqrt_discrim = np.sqrt(discrim)
for sign in (1., -1.):
x = (D * dy + sign * sign_dy * dx * sqrt_discrim) / dr2
y = (-D * dx + sign * np.abs(dy) * sqrt_discrim) / dr2
yield x, y
def iter_circle_intersect_on_line_seg(x0, y0, x1, y1):
epsilon = 1e-9
if x1 < x0:
x0e, x1e = x1, x0
else:
x0e, x1e = x0, x1
if y1 < y0:
y0e, y1e = y1, y0
else:
y0e, y1e = y0, y1
x0e -= epsilon
y0e -= epsilon
x1e += epsilon
y1e += epsilon
for x, y in iter_circle_intersect_on_line(x0, y0, x1, y1):
if x >= x0e and x <= x1e and y >= y0e and y <= y1e:
yield x, y
# Transforms the axes box_path so that it is relative to the unit
# circle in the same way that it is relative to the desired
# ellipse.
box_path = Path.unit_rectangle()
box_path_transform = transforms.BboxTransformTo(self.axes.bbox) + \
self.get_transform().inverted()
box_path = box_path.transformed(box_path_transform)
thetas = set()
# For each of the point pairs, there is a line segment
for p0, p1 in zip(box_path.vertices[:-1], box_path.vertices[1:]):
x0, y0 = p0
x1, y1 = p1
for x, y in iter_circle_intersect_on_line_seg(x0, y0, x1, y1):
theta = np.arccos(x)
if y < 0:
theta = 2 * np.pi - theta
# Convert radians to angles
theta = np.rad2deg(theta)
if theta1 < theta < theta2:
thetas.add(theta)
thetas = sorted(thetas) + [theta2]
last_theta = theta1
theta1_rad = np.deg2rad(theta1)
inside = box_path.contains_point((np.cos(theta1_rad),
np.sin(theta1_rad)))
# save original path
path_original = self._path
for theta in thetas:
if inside:
self._path = Path.arc(last_theta, theta, 8)
Patch.draw(self, renderer)
inside = False
else:
inside = True
last_theta = theta
# restore original path
self._path = path_original
def bbox_artist(artist, renderer, props=None, fill=True):
"""
This is a debug function to draw a rectangle around the bounding
box returned by
:meth:`~matplotlib.artist.Artist.get_window_extent` of an artist,
to test whether the artist is returning the correct bbox.
*props* is a dict of rectangle props with the additional property
'pad' that sets the padding around the bbox in points.
"""
if props is None:
props = {}
props = props.copy() # don't want to alter the pad externally
pad = props.pop('pad', 4)
pad = renderer.points_to_pixels(pad)
bbox = artist.get_window_extent(renderer)
l, b, w, h = bbox.bounds
l -= pad / 2.
b -= pad / 2.
w += pad
h += pad
r = Rectangle(xy=(l, b),
width=w,
height=h,
fill=fill,
)
r.set_transform(transforms.IdentityTransform())
r.set_clip_on(False)
r.update(props)
r.draw(renderer)
def draw_bbox(bbox, renderer, color='k', trans=None):
"""
This is a debug function to draw a rectangle around the bounding
box returned by
:meth:`~matplotlib.artist.Artist.get_window_extent` of an artist,
to test whether the artist is returning the correct bbox.
"""
l, b, w, h = bbox.bounds
r = Rectangle(xy=(l, b),
width=w,
height=h,
edgecolor=color,
fill=False,
)
if trans is not None:
r.set_transform(trans)
r.set_clip_on(False)
r.draw(renderer)
def _pprint_table(_table, leadingspace=2):
"""
Given the list of list of strings, return a string of REST table format.
"""
if leadingspace:
pad = ' ' * leadingspace
else:
pad = ''
columns = [[] for cell in _table[0]]
for row in _table:
for column, cell in zip(columns, row):
column.append(cell)
col_len = [max(len(cell) for cell in column) for column in columns]
lines = []
table_formatstr = pad + ' '.join([('=' * cl) for cl in col_len])
lines.append('')
lines.append(table_formatstr)
lines.append(pad + ' '.join([cell.ljust(cl)
for cell, cl
in zip(_table[0], col_len)]))
lines.append(table_formatstr)
lines.extend([(pad + ' '.join([cell.ljust(cl)
for cell, cl
in zip(row, col_len)]))
for row in _table[1:]])
lines.append(table_formatstr)
lines.append('')
return "\n".join(lines)
def _pprint_styles(_styles):
"""
A helper function for the _Style class. Given the dictionary of
(stylename : styleclass), return a formatted string listing all the
styles. Used to update the documentation.
"""
import inspect
_table = [["Class", "Name", "Attrs"]]
for name, cls in sorted(_styles.items()):
if six.PY2:
args, varargs, varkw, defaults = inspect.getargspec(cls.__init__)
else:
(args, varargs, varkw, defaults, kwonlyargs, kwonlydefs,
annotations) = inspect.getfullargspec(cls.__init__)
if defaults:
args = [(argname, argdefault)
for argname, argdefault in zip(args[1:], defaults)]
else:
args = None
if args is None:
argstr = 'None'
else:
argstr = ",".join([("%s=%s" % (an, av))
for an, av
in args])
# adding ``quotes`` since - and | have special meaning in reST
_table.append([cls.__name__, "``%s``" % name, argstr])
return _pprint_table(_table)
def _simpleprint_styles(_styles):
"""
A helper function for the _Style class. Given the dictionary of
(stylename : styleclass), return a string rep of the list of keys.
Used to update the documentation.
"""
return "[{}]".format("|".join(map(" '{}' ".format, sorted(_styles))))
class _Style(object):
"""
A base class for the Styles. It is meant to be a container class,
where actual styles are declared as subclass of it, and it
provides some helper functions.
"""
def __new__(self, stylename, **kw):
"""
return the instance of the subclass with the given style name.
"""
# the "class" should have the _style_list attribute, which is
# a dictionary of stylname, style class paie.
_list = stylename.replace(" ", "").split(",")
_name = _list[0].lower()
try:
_cls = self._style_list[_name]
except KeyError:
raise ValueError("Unknown style : %s" % stylename)
try:
_args_pair = [cs.split("=") for cs in _list[1:]]
_args = {k: float(v) for k, v in _args_pair}
except ValueError:
raise ValueError("Incorrect style argument : %s" % stylename)
_args.update(kw)
return _cls(**_args)
@classmethod
def get_styles(klass):
"""
A class method which returns a dictionary of available styles.
"""
return klass._style_list
@classmethod
def pprint_styles(klass):
"""
A class method which returns a string of the available styles.
"""
return _pprint_styles(klass._style_list)
@classmethod
def register(klass, name, style):
"""
Register a new style.
"""
if not issubclass(style, klass._Base):
raise ValueError("%s must be a subclass of %s" % (style,
klass._Base))
klass._style_list[name] = style
class BoxStyle(_Style):
"""
:class:`BoxStyle` is a container class which defines several
boxstyle classes, which are used for :class:`FancyBboxPatch`.
A style object can be created as::
BoxStyle.Round(pad=0.2)
or::
BoxStyle("Round", pad=0.2)
or::
BoxStyle("Round, pad=0.2")
Following boxstyle classes are defined.
%(AvailableBoxstyles)s
An instance of any boxstyle class is an callable object,
whose call signature is::
__call__(self, x0, y0, width, height, mutation_size, aspect_ratio=1.)
and returns a :class:`Path` instance. *x0*, *y0*, *width* and
*height* specify the location and size of the box to be
drawn. *mutation_scale* determines the overall size of the
mutation (by which I mean the transformation of the rectangle to
the fancy box). *mutation_aspect* determines the aspect-ratio of
the mutation.
"""
_style_list = {}
class _Base(object):
"""
:class:`BBoxTransmuterBase` and its derivatives are used to make a
fancy box around a given rectangle. The :meth:`__call__` method
returns the :class:`~matplotlib.path.Path` of the fancy box. This
class is not an artist and actual drawing of the fancy box is done
by the :class:`FancyBboxPatch` class.
"""
# The derived classes are required to be able to be initialized
# w/o arguments, i.e., all its argument (except self) must have
# the default values.
def __init__(self):
"""
initializtion.
"""
super(BoxStyle._Base, self).__init__()
def transmute(self, x0, y0, width, height, mutation_size):
"""
The transmute method is a very core of the
:class:`BboxTransmuter` class and must be overridden in the
subclasses. It receives the location and size of the
rectangle, and the mutation_size, with which the amount of
padding and etc. will be scaled. It returns a
:class:`~matplotlib.path.Path` instance.
"""
raise NotImplementedError('Derived must override')
def __call__(self, x0, y0, width, height, mutation_size,
aspect_ratio=1.):
"""
Given the location and size of the box, return the path of
the box around it.
- *x0*, *y0*, *width*, *height* : location and size of the box
- *mutation_size* : a reference scale for the mutation.
- *aspect_ratio* : aspect-ration for the mutation.
"""
# The __call__ method is a thin wrapper around the transmute method
# and take care of the aspect.
if aspect_ratio is not None:
# Squeeze the given height by the aspect_ratio
y0, height = y0 / aspect_ratio, height / aspect_ratio
# call transmute method with squeezed height.
path = self.transmute(x0, y0, width, height, mutation_size)
vertices, codes = path.vertices, path.codes
# Restore the height
vertices[:, 1] = vertices[:, 1] * aspect_ratio
return Path(vertices, codes)
else:
return self.transmute(x0, y0, width, height, mutation_size)
def __reduce__(self):
# because we have decided to nest these classes, we need to
# add some more information to allow instance pickling.
return (cbook._NestedClassGetter(),
(BoxStyle, self.__class__.__name__),
self.__dict__
)
class Square(_Base):
"""
A simple square box.
"""
def __init__(self, pad=0.3):
"""
*pad*
amount of padding
"""
self.pad = pad
super(BoxStyle.Square, self).__init__()
def transmute(self, x0, y0, width, height, mutation_size):
pad = mutation_size * self.pad
# width and height with padding added.
width, height = width + 2*pad, height + 2*pad
# boundary of the padded box
x0, y0 = x0 - pad, y0 - pad,
x1, y1 = x0 + width, y0 + height
vertices = [(x0, y0), (x1, y0), (x1, y1), (x0, y1), (x0, y0)]
codes = [Path.MOVETO] + [Path.LINETO] * 3 + [Path.CLOSEPOLY]
return Path(vertices, codes)
_style_list["square"] = Square
class Circle(_Base):
"""A simple circle box."""
def __init__(self, pad=0.3):
"""
Parameters
----------
pad : float
The amount of padding around the original box.
"""
self.pad = pad
super(BoxStyle.Circle, self).__init__()
def transmute(self, x0, y0, width, height, mutation_size):
pad = mutation_size * self.pad
width, height = width + 2 * pad, height + 2 * pad
# boundary of the padded box
x0, y0 = x0 - pad, y0 - pad,
return Path.circle((x0 + width / 2, y0 + height / 2),
max(width, height) / 2)
_style_list["circle"] = Circle
class LArrow(_Base):
"""
(left) Arrow Box
"""
def __init__(self, pad=0.3):
self.pad = pad
super(BoxStyle.LArrow, self).__init__()
def transmute(self, x0, y0, width, height, mutation_size):
# padding
pad = mutation_size * self.pad
# width and height with padding added.
width, height = width + 2. * pad, height + 2. * pad
# boundary of the padded box
x0, y0 = x0 - pad, y0 - pad,
x1, y1 = x0 + width, y0 + height
dx = (y1 - y0) / 2.
dxx = dx * .5
# adjust x0. 1.4 <- sqrt(2)
x0 = x0 + pad / 1.4
cp = [(x0 + dxx, y0), (x1, y0), (x1, y1), (x0 + dxx, y1),
(x0 + dxx, y1 + dxx), (x0 - dx, y0 + dx),
(x0 + dxx, y0 - dxx), # arrow
(x0 + dxx, y0), (x0 + dxx, y0)]
com = [Path.MOVETO, Path.LINETO, Path.LINETO, Path.LINETO,
Path.LINETO, Path.LINETO, Path.LINETO,
Path.LINETO, Path.CLOSEPOLY]
path = Path(cp, com)
return path
_style_list["larrow"] = LArrow
class RArrow(LArrow):
"""
(right) Arrow Box
"""
def __init__(self, pad=0.3):
super(BoxStyle.RArrow, self).__init__(pad)
def transmute(self, x0, y0, width, height, mutation_size):
p = BoxStyle.LArrow.transmute(self, x0, y0,
width, height, mutation_size)
p.vertices[:, 0] = 2 * x0 + width - p.vertices[:, 0]
return p
_style_list["rarrow"] = RArrow
class DArrow(_Base):
"""
(Double) Arrow Box
"""
# This source is copied from LArrow,
# modified to add a right arrow to the bbox.
def __init__(self, pad=0.3):
self.pad = pad
super(BoxStyle.DArrow, self).__init__()
def transmute(self, x0, y0, width, height, mutation_size):
# padding
pad = mutation_size * self.pad
# width and height with padding added.
# The width is padded by the arrows, so we don't need to pad it.
height = height + 2. * pad
# boundary of the padded box
x0, y0 = x0 - pad, y0 - pad
x1, y1 = x0 + width, y0 + height
dx = (y1 - y0)/2.
dxx = dx * .5
# adjust x0. 1.4 <- sqrt(2)
x0 = x0 + pad / 1.4
cp = [(x0 + dxx, y0), (x1, y0), # bot-segment
(x1, y0 - dxx), (x1 + dx + dxx, y0 + dx),
(x1, y1 + dxx), # right-arrow
(x1, y1), (x0 + dxx, y1), # top-segment
(x0 + dxx, y1 + dxx), (x0 - dx, y0 + dx),
(x0 + dxx, y0 - dxx), # left-arrow
(x0 + dxx, y0), (x0 + dxx, y0)] # close-poly
com = [Path.MOVETO, Path.LINETO,
Path.LINETO, Path.LINETO,
Path.LINETO,
Path.LINETO, Path.LINETO,
Path.LINETO, Path.LINETO,
Path.LINETO,
Path.LINETO, Path.CLOSEPOLY]
path = Path(cp, com)
return path
_style_list['darrow'] = DArrow
class Round(_Base):
"""
A box with round corners.
"""
def __init__(self, pad=0.3, rounding_size=None):
"""
*pad*
amount of padding
*rounding_size*
rounding radius of corners. *pad* if None
"""
self.pad = pad
self.rounding_size = rounding_size
super(BoxStyle.Round, self).__init__()
def transmute(self, x0, y0, width, height, mutation_size):
# padding
pad = mutation_size * self.pad
# size of the roudning corner
if self.rounding_size:
dr = mutation_size * self.rounding_size
else:
dr = pad
width, height = width + 2. * pad, height + 2. * pad
x0, y0 = x0 - pad, y0 - pad,
x1, y1 = x0 + width, y0 + height
# Round corners are implemented as quadratic bezier. e.g.,
# [(x0, y0-dr), (x0, y0), (x0+dr, y0)] for lower left corner.
cp = [(x0 + dr, y0),
(x1 - dr, y0),
(x1, y0), (x1, y0 + dr),
(x1, y1 - dr),
(x1, y1), (x1 - dr, y1),
(x0 + dr, y1),
(x0, y1), (x0, y1 - dr),
(x0, y0 + dr),
(x0, y0), (x0 + dr, y0),
(x0 + dr, y0)]
com = [Path.MOVETO,
Path.LINETO,
Path.CURVE3, Path.CURVE3,
Path.LINETO,
Path.CURVE3, Path.CURVE3,
Path.LINETO,
Path.CURVE3, Path.CURVE3,
Path.LINETO,
Path.CURVE3, Path.CURVE3,
Path.CLOSEPOLY]
path = Path(cp, com)
return path
_style_list["round"] = Round
class Round4(_Base):
"""
Another box with round edges.
"""
def __init__(self, pad=0.3, rounding_size=None):
"""
*pad*
amount of padding
*rounding_size*
rounding size of edges. *pad* if None
"""
self.pad = pad
self.rounding_size = rounding_size
super(BoxStyle.Round4, self).__init__()
def transmute(self, x0, y0, width, height, mutation_size):
# padding
pad = mutation_size * self.pad
# roudning size. Use a half of the pad if not set.
if self.rounding_size:
dr = mutation_size * self.rounding_size
else:
dr = pad / 2.
width, height = (width + 2. * pad - 2 * dr,
height + 2. * pad - 2 * dr)
x0, y0 = x0 - pad + dr, y0 - pad + dr,
x1, y1 = x0 + width, y0 + height
cp = [(x0, y0),
(x0 + dr, y0 - dr), (x1 - dr, y0 - dr), (x1, y0),
(x1 + dr, y0 + dr), (x1 + dr, y1 - dr), (x1, y1),
(x1 - dr, y1 + dr), (x0 + dr, y1 + dr), (x0, y1),
(x0 - dr, y1 - dr), (x0 - dr, y0 + dr), (x0, y0),
(x0, y0)]
com = [Path.MOVETO,
Path.CURVE4, Path.CURVE4, Path.CURVE4,
Path.CURVE4, Path.CURVE4, Path.CURVE4,
Path.CURVE4, Path.CURVE4, Path.CURVE4,
Path.CURVE4, Path.CURVE4, Path.CURVE4,
Path.CLOSEPOLY]
path = Path(cp, com)
return path
_style_list["round4"] = Round4
class Sawtooth(_Base):
"""
A sawtooth box.
"""
def __init__(self, pad=0.3, tooth_size=None):
"""
*pad*
amount of padding
*tooth_size*
size of the sawtooth. pad* if None
"""
self.pad = pad
self.tooth_size = tooth_size
super(BoxStyle.Sawtooth, self).__init__()
def _get_sawtooth_vertices(self, x0, y0, width, height, mutation_size):
# padding
pad = mutation_size * self.pad
# size of sawtooth
if self.tooth_size is None:
tooth_size = self.pad * .5 * mutation_size
else:
tooth_size = self.tooth_size * mutation_size
tooth_size2 = tooth_size / 2.
width, height = (width + 2. * pad - tooth_size,
height + 2. * pad - tooth_size)
# the sizes of the vertical and horizontal sawtooth are
# separately adjusted to fit the given box size.
dsx_n = int(np.round((width - tooth_size) / (tooth_size * 2))) * 2
dsx = (width - tooth_size) / dsx_n
dsy_n = int(np.round((height - tooth_size) / (tooth_size * 2))) * 2
dsy = (height - tooth_size) / dsy_n
x0, y0 = x0 - pad + tooth_size2, y0 - pad + tooth_size2
x1, y1 = x0 + width, y0 + height
bottom_saw_x = [x0] + \
[x0 + tooth_size2 + dsx * .5 * i
for i
in range(dsx_n * 2)] + \
[x1 - tooth_size2]
bottom_saw_y = [y0] + \
[y0 - tooth_size2, y0,
y0 + tooth_size2, y0] * dsx_n + \
[y0 - tooth_size2]
right_saw_x = [x1] + \
[x1 + tooth_size2,
x1,
x1 - tooth_size2,
x1] * dsx_n + \
[x1 + tooth_size2]
right_saw_y = [y0] + \
[y0 + tooth_size2 + dsy * .5 * i
for i
in range(dsy_n * 2)] + \
[y1 - tooth_size2]
top_saw_x = [x1] + \
[x1 - tooth_size2 - dsx * .5 * i
for i
in range(dsx_n * 2)] + \
[x0 + tooth_size2]
top_saw_y = [y1] + \
[y1 + tooth_size2,
y1,
y1 - tooth_size2,
y1] * dsx_n + \
[y1 + tooth_size2]
left_saw_x = [x0] + \
[x0 - tooth_size2,
x0,
x0 + tooth_size2,
x0] * dsy_n + \
[x0 - tooth_size2]
left_saw_y = [y1] + \
[y1 - tooth_size2 - dsy * .5 * i
for i
in range(dsy_n * 2)] + \
[y0 + tooth_size2]
saw_vertices = (list(zip(bottom_saw_x, bottom_saw_y)) +
list(zip(right_saw_x, right_saw_y)) +
list(zip(top_saw_x, top_saw_y)) +
list(zip(left_saw_x, left_saw_y)) +
[(bottom_saw_x[0], bottom_saw_y[0])])
return saw_vertices
def transmute(self, x0, y0, width, height, mutation_size):
saw_vertices = self._get_sawtooth_vertices(x0, y0, width,
height, mutation_size)
path = Path(saw_vertices, closed=True)
return path
_style_list["sawtooth"] = Sawtooth
class Roundtooth(Sawtooth):
"""A rounded tooth box."""
def __init__(self, pad=0.3, tooth_size=None):
"""
*pad*
amount of padding
*tooth_size*
size of the sawtooth. pad* if None
"""
super(BoxStyle.Roundtooth, self).__init__(pad, tooth_size)
def transmute(self, x0, y0, width, height, mutation_size):
saw_vertices = self._get_sawtooth_vertices(x0, y0,
width, height,
mutation_size)
# Add a trailing vertex to allow us to close the polygon correctly
saw_vertices = np.concatenate([np.array(saw_vertices),
[saw_vertices[0]]], axis=0)
codes = ([Path.MOVETO] +
[Path.CURVE3, Path.CURVE3] * ((len(saw_vertices)-1)//2) +
[Path.CLOSEPOLY])
return Path(saw_vertices, codes)
_style_list["roundtooth"] = Roundtooth
if __doc__: # __doc__ could be None if -OO optimization is enabled
__doc__ = cbook.dedent(__doc__) % \
{"AvailableBoxstyles": _pprint_styles(_style_list)}
docstring.interpd.update(
AvailableBoxstyles=_pprint_styles(BoxStyle._style_list),
ListBoxstyles=_simpleprint_styles(BoxStyle._style_list))
class FancyBboxPatch(Patch):
"""
Draw a fancy box around a rectangle with lower left at *xy*=(*x*,
*y*) with specified width and height.
:class:`FancyBboxPatch` class is similar to :class:`Rectangle`
class, but it draws a fancy box around the rectangle. The
transformation of the rectangle box to the fancy box is delegated
to the :class:`BoxTransmuterBase` and its derived classes.
"""
_edge_default = True
def __str__(self):
return self.__class__.__name__ \
+ "(%g,%g;%gx%g)" % (self._x, self._y,
self._width, self._height)
@docstring.dedent_interpd
def __init__(self, xy, width, height,
boxstyle="round",
bbox_transmuter=None,
mutation_scale=1.,
mutation_aspect=None,
**kwargs):
"""
*xy* = lower left corner
*width*, *height*
*boxstyle* determines what kind of fancy box will be drawn. It
can be a string of the style name with a comma separated
attribute, or an instance of :class:`BoxStyle`. Following box
styles are available.
%(AvailableBoxstyles)s
*mutation_scale* : a value with which attributes of boxstyle
(e.g., pad) will be scaled. default=1.
*mutation_aspect* : The height of the rectangle will be
squeezed by this value before the mutation and the mutated
box will be stretched by the inverse of it. default=None.
Valid kwargs are:
%(Patch)s
"""
Patch.__init__(self, **kwargs)
self._x = xy[0]
self._y = xy[1]
self._width = width
self._height = height
if boxstyle == "custom":
if bbox_transmuter is None:
raise ValueError("bbox_transmuter argument is needed with "
"custom boxstyle")
self._bbox_transmuter = bbox_transmuter
else:
self.set_boxstyle(boxstyle)
self._mutation_scale = mutation_scale
self._mutation_aspect = mutation_aspect
self.stale = True
@docstring.dedent_interpd
def set_boxstyle(self, boxstyle=None, **kw):
"""
Set the box style.
*boxstyle* can be a string with boxstyle name with optional
comma-separated attributes. Alternatively, the attrs can
be provided as keywords::
set_boxstyle("round,pad=0.2")
set_boxstyle("round", pad=0.2)
Old attrs simply are forgotten.
Without argument (or with *boxstyle* = None), it returns
available box styles.
The following boxstyles are available:
%(AvailableBoxstyles)s
ACCEPTS: %(ListBoxstyles)s
"""
if boxstyle is None:
return BoxStyle.pprint_styles()
if isinstance(boxstyle, BoxStyle._Base) or callable(boxstyle):
self._bbox_transmuter = boxstyle
else:
self._bbox_transmuter = BoxStyle(boxstyle, **kw)
self.stale = True
def set_mutation_scale(self, scale):
"""
Set the mutation scale.
ACCEPTS: float
"""
self._mutation_scale = scale
self.stale = True
def get_mutation_scale(self):
"""
Return the mutation scale.
"""
return self._mutation_scale
def set_mutation_aspect(self, aspect):
"""
Set the aspect ratio of the bbox mutation.
ACCEPTS: float
"""
self._mutation_aspect = aspect
self.stale = True
def get_mutation_aspect(self):
"""
Return the aspect ratio of the bbox mutation.
"""
return self._mutation_aspect
def get_boxstyle(self):
"Return the boxstyle object"
return self._bbox_transmuter
def get_path(self):
"""
Return the mutated path of the rectangle
"""
_path = self.get_boxstyle()(self._x, self._y,
self._width, self._height,
self.get_mutation_scale(),
self.get_mutation_aspect())
return _path
# Following methods are borrowed from the Rectangle class.
def get_x(self):
"Return the left coord of the rectangle"
return self._x
def get_y(self):
"Return the bottom coord of the rectangle"
return self._y
def get_width(self):
"Return the width of the rectangle"
return self._width
def get_height(self):
"Return the height of the rectangle"
return self._height
def set_x(self, x):
"""
Set the left coord of the rectangle
ACCEPTS: float
"""
self._x = x
self.stale = True
def set_y(self, y):
"""
Set the bottom coord of the rectangle
ACCEPTS: float
"""
self._y = y
self.stale = True
def set_width(self, w):
"""
Set the width rectangle
ACCEPTS: float
"""
self._width = w
self.stale = True
def set_height(self, h):
"""
Set the width rectangle
ACCEPTS: float
"""
self._height = h
self.stale = True
def set_bounds(self, *args):
"""
Set the bounds of the rectangle: l,b,w,h
ACCEPTS: (left, bottom, width, height)
"""
if len(args) == 0:
l, b, w, h = args[0]
else:
l, b, w, h = args
self._x = l
self._y = b
self._width = w
self._height = h
self.stale = True
def get_bbox(self):
return transforms.Bbox.from_bounds(self._x, self._y,
self._width, self._height)
class ConnectionStyle(_Style):
"""
:class:`ConnectionStyle` is a container class which defines
several connectionstyle classes, which is used to create a path
between two points. These are mainly used with
:class:`FancyArrowPatch`.
A connectionstyle object can be either created as::
ConnectionStyle.Arc3(rad=0.2)
or::
ConnectionStyle("Arc3", rad=0.2)
or::
ConnectionStyle("Arc3, rad=0.2")
The following classes are defined
%(AvailableConnectorstyles)s
An instance of any connection style class is an callable object,
whose call signature is::
__call__(self, posA, posB,
patchA=None, patchB=None,
shrinkA=2., shrinkB=2.)
and it returns a :class:`Path` instance. *posA* and *posB* are
tuples of x,y coordinates of the two points to be
connected. *patchA* (or *patchB*) is given, the returned path is
clipped so that it start (or end) from the boundary of the
patch. The path is further shrunk by *shrinkA* (or *shrinkB*)
which is given in points.
"""
_style_list = {}
class _Base(object):
"""
A base class for connectionstyle classes. The subclass needs
to implement a *connect* method whose call signature is::
connect(posA, posB)
where posA and posB are tuples of x, y coordinates to be
connected. The method needs to return a path connecting two
points. This base class defines a __call__ method, and a few
helper methods.
"""
class SimpleEvent:
def __init__(self, xy):
self.x, self.y = xy
def _clip(self, path, patchA, patchB):
"""
Clip the path to the boundary of the patchA and patchB.
The starting point of the path needed to be inside of the
patchA and the end point inside the patch B. The *contains*
methods of each patch object is utilized to test if the point
is inside the path.
"""
if patchA:
def insideA(xy_display):
xy_event = ConnectionStyle._Base.SimpleEvent(xy_display)
return patchA.contains(xy_event)[0]
try:
left, right = split_path_inout(path, insideA)
except ValueError:
right = path
path = right
if patchB:
def insideB(xy_display):
xy_event = ConnectionStyle._Base.SimpleEvent(xy_display)
return patchB.contains(xy_event)[0]
try:
left, right = split_path_inout(path, insideB)
except ValueError:
left = path
path = left
return path
def _shrink(self, path, shrinkA, shrinkB):
"""
Shrink the path by fixed size (in points) with shrinkA and shrinkB
"""
if shrinkA:
x, y = path.vertices[0]
insideA = inside_circle(x, y, shrinkA)
try:
left, right = split_path_inout(path, insideA)
path = right
except ValueError:
pass
if shrinkB:
x, y = path.vertices[-1]
insideB = inside_circle(x, y, shrinkB)
try:
left, right = split_path_inout(path, insideB)
path = left
except ValueError:
pass
return path
def __call__(self, posA, posB,
shrinkA=2., shrinkB=2., patchA=None, patchB=None):
"""
Calls the *connect* method to create a path between *posA*
and *posB*. The path is clipped and shrunken.
"""
path = self.connect(posA, posB)
clipped_path = self._clip(path, patchA, patchB)
shrunk_path = self._shrink(clipped_path, shrinkA, shrinkB)
return shrunk_path
def __reduce__(self):
# because we have decided to nest these classes, we need to
# add some more information to allow instance pickling.
return (cbook._NestedClassGetter(),
(ConnectionStyle, self.__class__.__name__),
self.__dict__
)
class Arc3(_Base):
"""
Creates a simple quadratic bezier curve between two
points. The curve is created so that the middle control point
(C1) is located at the same distance from the start (C0) and
end points(C2) and the distance of the C1 to the line
connecting C0-C2 is *rad* times the distance of C0-C2.
"""
def __init__(self, rad=0.):
"""
*rad*
curvature of the curve.
"""
self.rad = rad
def connect(self, posA, posB):
x1, y1 = posA
x2, y2 = posB
x12, y12 = (x1 + x2) / 2., (y1 + y2) / 2.
dx, dy = x2 - x1, y2 - y1
f = self.rad
cx, cy = x12 + f * dy, y12 - f * dx
vertices = [(x1, y1),
(cx, cy),
(x2, y2)]
codes = [Path.MOVETO,
Path.CURVE3,
Path.CURVE3]
return Path(vertices, codes)
_style_list["arc3"] = Arc3
class Angle3(_Base):
"""
Creates a simple quadratic bezier curve between two
points. The middle control points is placed at the
intersecting point of two lines which crosses the start (or
end) point and has a angle of angleA (or angleB).
"""
def __init__(self, angleA=90, angleB=0):
"""
*angleA*
starting angle of the path
*angleB*
ending angle of the path
"""
self.angleA = angleA
self.angleB = angleB
def connect(self, posA, posB):
x1, y1 = posA
x2, y2 = posB
cosA = math.cos(math.radians(self.angleA))
sinA = math.sin(math.radians(self.angleA))
cosB = math.cos(math.radians(self.angleB))
sinB = math.sin(math.radians(self.angleB))
cx, cy = get_intersection(x1, y1, cosA, sinA,
x2, y2, cosB, sinB)
vertices = [(x1, y1), (cx, cy), (x2, y2)]
codes = [Path.MOVETO, Path.CURVE3, Path.CURVE3]
return Path(vertices, codes)
_style_list["angle3"] = Angle3
class Angle(_Base):
"""
Creates a picewise continuous quadratic bezier path between
two points. The path has a one passing-through point placed at
the intersecting point of two lines which crosses the start
(or end) point and has a angle of angleA (or angleB). The
connecting edges are rounded with *rad*.
"""
def __init__(self, angleA=90, angleB=0, rad=0.):
"""
*angleA*
starting angle of the path
*angleB*
ending angle of the path
*rad*
rounding radius of the edge
"""
self.angleA = angleA
self.angleB = angleB
self.rad = rad
def connect(self, posA, posB):
x1, y1 = posA
x2, y2 = posB
cosA = math.cos(math.radians(self.angleA))
sinA = math.sin(math.radians(self.angleA))
cosB = math.cos(math.radians(self.angleB))
sinB = math.sin(math.radians(self.angleB))
cx, cy = get_intersection(x1, y1, cosA, sinA,
x2, y2, cosB, sinB)
vertices = [(x1, y1)]
codes = [Path.MOVETO]
if self.rad == 0.:
vertices.append((cx, cy))
codes.append(Path.LINETO)
else:
dx1, dy1 = x1 - cx, y1 - cy
d1 = (dx1 ** 2 + dy1 ** 2) ** .5
f1 = self.rad / d1
dx2, dy2 = x2 - cx, y2 - cy
d2 = (dx2 ** 2 + dy2 ** 2) ** .5
f2 = self.rad / d2
vertices.extend([(cx + dx1 * f1, cy + dy1 * f1),
(cx, cy),
(cx + dx2 * f2, cy + dy2 * f2)])
codes.extend([Path.LINETO, Path.CURVE3, Path.CURVE3])
vertices.append((x2, y2))
codes.append(Path.LINETO)
return Path(vertices, codes)
_style_list["angle"] = Angle
class Arc(_Base):
"""
Creates a picewise continuous quadratic bezier path between
two points. The path can have two passing-through points, a
point placed at the distance of armA and angle of angleA from
point A, another point with respect to point B. The edges are
rounded with *rad*.
"""
def __init__(self, angleA=0, angleB=0, armA=None, armB=None, rad=0.):
"""
*angleA* :
starting angle of the path
*angleB* :
ending angle of the path
*armA* :
length of the starting arm
*armB* :
length of the ending arm
*rad* :
rounding radius of the edges
"""
self.angleA = angleA
self.angleB = angleB
self.armA = armA
self.armB = armB
self.rad = rad
def connect(self, posA, posB):
x1, y1 = posA
x2, y2 = posB
vertices = [(x1, y1)]
rounded = []
codes = [Path.MOVETO]
if self.armA:
cosA = math.cos(math.radians(self.angleA))
sinA = math.sin(math.radians(self.angleA))
# x_armA, y_armB
d = self.armA - self.rad
rounded.append((x1 + d * cosA, y1 + d * sinA))
d = self.armA
rounded.append((x1 + d * cosA, y1 + d * sinA))
if self.armB:
cosB = math.cos(math.radians(self.angleB))
sinB = math.sin(math.radians(self.angleB))
x_armB, y_armB = x2 + self.armB * cosB, y2 + self.armB * sinB
if rounded:
xp, yp = rounded[-1]
dx, dy = x_armB - xp, y_armB - yp
dd = (dx * dx + dy * dy) ** .5
rounded.append((xp + self.rad * dx / dd,
yp + self.rad * dy / dd))
vertices.extend(rounded)
codes.extend([Path.LINETO,
Path.CURVE3,
Path.CURVE3])
else:
xp, yp = vertices[-1]
dx, dy = x_armB - xp, y_armB - yp
dd = (dx * dx + dy * dy) ** .5
d = dd - self.rad
rounded = [(xp + d * dx / dd, yp + d * dy / dd),
(x_armB, y_armB)]
if rounded:
xp, yp = rounded[-1]
dx, dy = x2 - xp, y2 - yp
dd = (dx * dx + dy * dy) ** .5
rounded.append((xp + self.rad * dx / dd,
yp + self.rad * dy / dd))
vertices.extend(rounded)
codes.extend([Path.LINETO,
Path.CURVE3,
Path.CURVE3])
vertices.append((x2, y2))
codes.append(Path.LINETO)
return Path(vertices, codes)
_style_list["arc"] = Arc
class Bar(_Base):
"""
A line with *angle* between A and B with *armA* and
*armB*. One of the arms is extended so that they are connected in
a right angle. The length of armA is determined by (*armA*
+ *fraction* x AB distance). Same for armB.
"""
def __init__(self, armA=0., armB=0., fraction=0.3, angle=None):
"""
Parameters
----------
armA : float
minimum length of armA
armB : float
minimum length of armB
fraction : float
a fraction of the distance between two points that
will be added to armA and armB.
angle : float or None
angle of the connecting line (if None, parallel
to A and B)
"""
self.armA = armA
self.armB = armB
self.fraction = fraction
self.angle = angle
def connect(self, posA, posB):
x1, y1 = posA
x20, y20 = x2, y2 = posB
theta1 = math.atan2(y2 - y1, x2 - x1)
dx, dy = x2 - x1, y2 - y1
dd = (dx * dx + dy * dy) ** .5
ddx, ddy = dx / dd, dy / dd
armA, armB = self.armA, self.armB
if self.angle is not None:
theta0 = np.deg2rad(self.angle)
dtheta = theta1 - theta0
dl = dd * math.sin(dtheta)
dL = dd * math.cos(dtheta)
x2, y2 = x1 + dL * math.cos(theta0), y1 + dL * math.sin(theta0)
armB = armB - dl
# update
dx, dy = x2 - x1, y2 - y1
dd2 = (dx * dx + dy * dy) ** .5
ddx, ddy = dx / dd2, dy / dd2
else:
dl = 0.
arm = max(armA, armB)
f = self.fraction * dd + arm
cx1, cy1 = x1 + f * ddy, y1 - f * ddx
cx2, cy2 = x2 + f * ddy, y2 - f * ddx
vertices = [(x1, y1),
(cx1, cy1),
(cx2, cy2),
(x20, y20)]
codes = [Path.MOVETO,
Path.LINETO,
Path.LINETO,
Path.LINETO]
return Path(vertices, codes)
_style_list["bar"] = Bar
if __doc__:
__doc__ = cbook.dedent(__doc__) % \
{"AvailableConnectorstyles": _pprint_styles(_style_list)}
def _point_along_a_line(x0, y0, x1, y1, d):
"""
find a point along a line connecting (x0, y0) -- (x1, y1) whose
distance from (x0, y0) is d.
"""
dx, dy = x0 - x1, y0 - y1
ff = d / (dx * dx + dy * dy) ** .5
x2, y2 = x0 - ff * dx, y0 - ff * dy
return x2, y2
class ArrowStyle(_Style):
"""
:class:`ArrowStyle` is a container class which defines several
arrowstyle classes, which is used to create an arrow path along a
given path. These are mainly used with :class:`FancyArrowPatch`.
A arrowstyle object can be either created as::
ArrowStyle.Fancy(head_length=.4, head_width=.4, tail_width=.4)
or::
ArrowStyle("Fancy", head_length=.4, head_width=.4, tail_width=.4)
or::
ArrowStyle("Fancy, head_length=.4, head_width=.4, tail_width=.4")
The following classes are defined
%(AvailableArrowstyles)s
An instance of any arrow style class is a callable object,
whose call signature is::
__call__(self, path, mutation_size, linewidth, aspect_ratio=1.)
and it returns a tuple of a :class:`Path` instance and a boolean
value. *path* is a :class:`Path` instance along which the arrow
will be drawn. *mutation_size* and *aspect_ratio* have the same
meaning as in :class:`BoxStyle`. *linewidth* is a line width to be
stroked. This is meant to be used to correct the location of the
head so that it does not overshoot the destination point, but not all
classes support it.
"""
_style_list = {}
class _Base(object):
"""
Arrow Transmuter Base class
ArrowTransmuterBase and its derivatives are used to make a fancy
arrow around a given path. The __call__ method returns a path
(which will be used to create a PathPatch instance) and a boolean
value indicating the path is open therefore is not fillable. This
class is not an artist and actual drawing of the fancy arrow is
done by the FancyArrowPatch class.
"""
# The derived classes are required to be able to be initialized
# w/o arguments, i.e., all its argument (except self) must have
# the default values.
@staticmethod
def ensure_quadratic_bezier(path):
""" Some ArrowStyle class only wokrs with a simple
quaratic bezier curve (created with Arc3Connetion or
Angle3Connector). This static method is to check if the
provided path is a simple quadratic bezier curve and returns
its control points if true.
"""
segments = list(path.iter_segments())
if (len(segments) != 2 or segments[0][1] != Path.MOVETO or
segments[1][1] != Path.CURVE3):
raise ValueError(
"'path' it's not a valid quadratic Bezier curve")
return list(segments[0][0]) + list(segments[1][0])
def transmute(self, path, mutation_size, linewidth):
"""
The transmute method is the very core of the ArrowStyle
class and must be overridden in the subclasses. It receives
the path object along which the arrow will be drawn, and
the mutation_size, with which the arrow head etc.
will be scaled. The linewidth may be used to adjust
the path so that it does not pass beyond the given
points. It returns a tuple of a Path instance and a
boolean. The boolean value indicate whether the path can
be filled or not. The return value can also be a list of paths
and list of booleans of a same length.
"""
raise NotImplementedError('Derived must override')
def __call__(self, path, mutation_size, linewidth,
aspect_ratio=1.):
"""
The __call__ method is a thin wrapper around the transmute method
and take care of the aspect ratio.
"""
path = make_path_regular(path)
if aspect_ratio is not None:
# Squeeze the given height by the aspect_ratio
vertices, codes = path.vertices[:], path.codes[:]
# Squeeze the height
vertices[:, 1] = vertices[:, 1] / aspect_ratio
path_shrunk = Path(vertices, codes)
# call transmute method with squeezed height.
path_mutated, fillable = self.transmute(path_shrunk,
linewidth,
mutation_size)
if cbook.iterable(fillable):
path_list = []
for p in zip(path_mutated):
v, c = p.vertices, p.codes
# Restore the height
v[:, 1] = v[:, 1] * aspect_ratio
path_list.append(Path(v, c))
return path_list, fillable
else:
return path_mutated, fillable
else:
return self.transmute(path, mutation_size, linewidth)
def __reduce__(self):
# because we have decided to nest these classes, we need to
# add some more information to allow instance pickling.
return (cbook._NestedClassGetter(),
(ArrowStyle, self.__class__.__name__),
self.__dict__
)
class _Curve(_Base):
"""
A simple arrow which will work with any path instance. The
returned path is simply concatenation of the original path + at
most two paths representing the arrow head at the begin point and the
at the end point. The arrow heads can be either open or closed.
"""
def __init__(self, beginarrow=None, endarrow=None,
fillbegin=False, fillend=False,
head_length=.2, head_width=.1):
"""
The arrows are drawn if *beginarrow* and/or *endarrow* are
true. *head_length* and *head_width* determines the size
of the arrow relative to the *mutation scale*. The
arrowhead at the begin (or end) is closed if fillbegin (or
fillend) is True.
"""
self.beginarrow, self.endarrow = beginarrow, endarrow
self.head_length, self.head_width = head_length, head_width
self.fillbegin, self.fillend = fillbegin, fillend
super(ArrowStyle._Curve, self).__init__()
def _get_arrow_wedge(self, x0, y0, x1, y1,
head_dist, cos_t, sin_t, linewidth
):
"""
Return the paths for arrow heads. Since arrow lines are
drawn with capstyle=projected, The arrow goes beyond the
desired point. This method also returns the amount of the path
to be shrunken so that it does not overshoot.
"""
# arrow from x0, y0 to x1, y1
dx, dy = x0 - x1, y0 - y1
cp_distance = np.hypot(dx, dy)
# pad_projected : amount of pad to account the
# overshooting of the projection of the wedge
pad_projected = (.5 * linewidth / sin_t)
# Account for division by zero
if cp_distance == 0:
cp_distance = 1
# apply pad for projected edge
ddx = pad_projected * dx / cp_distance
ddy = pad_projected * dy / cp_distance
# offset for arrow wedge
dx = dx / cp_distance * head_dist
dy = dy / cp_distance * head_dist
dx1, dy1 = cos_t * dx + sin_t * dy, -sin_t * dx + cos_t * dy
dx2, dy2 = cos_t * dx - sin_t * dy, sin_t * dx + cos_t * dy
vertices_arrow = [(x1 + ddx + dx1, y1 + ddy + dy1),
(x1 + ddx, y1 + ddy),
(x1 + ddx + dx2, y1 + ddy + dy2)]
codes_arrow = [Path.MOVETO,
Path.LINETO,
Path.LINETO]
return vertices_arrow, codes_arrow, ddx, ddy
def transmute(self, path, mutation_size, linewidth):
head_length = self.head_length * mutation_size
head_width = self.head_width * mutation_size
head_dist = math.sqrt(head_length ** 2 + head_width ** 2)
cos_t, sin_t = head_length / head_dist, head_width / head_dist
# begin arrow
x0, y0 = path.vertices[0]
x1, y1 = path.vertices[1]
# If there is no room for an arrow and a line, then skip the arrow
has_begin_arrow = self.beginarrow and not (x0 == x1 and y0 == y1)
if has_begin_arrow:
verticesA, codesA, ddxA, ddyA = \
self._get_arrow_wedge(x1, y1, x0, y0,
head_dist, cos_t, sin_t,
linewidth)
else:
verticesA, codesA = [], []
ddxA, ddyA = 0., 0.
# end arrow
x2, y2 = path.vertices[-2]
x3, y3 = path.vertices[-1]
# If there is no room for an arrow and a line, then skip the arrow
has_end_arrow = (self.endarrow and not ((x2 == x3) and (y2 == y3)))
if has_end_arrow:
verticesB, codesB, ddxB, ddyB = \
self._get_arrow_wedge(x2, y2, x3, y3,
head_dist, cos_t, sin_t,
linewidth)
else:
verticesB, codesB = [], []
ddxB, ddyB = 0., 0.
# this simple code will not work if ddx, ddy is greater than
# separation bettern vertices.
_path = [Path(np.concatenate([[(x0 + ddxA, y0 + ddyA)],
path.vertices[1:-1],
[(x3 + ddxB, y3 + ddyB)]]),
path.codes)]
_fillable = [False]
if has_begin_arrow:
if self.fillbegin:
p = np.concatenate([verticesA, [verticesA[0],
verticesA[0]], ])
c = np.concatenate([codesA, [Path.LINETO, Path.CLOSEPOLY]])
_path.append(Path(p, c))
_fillable.append(True)
else:
_path.append(Path(verticesA, codesA))
_fillable.append(False)
if has_end_arrow:
if self.fillend:
_fillable.append(True)
p = np.concatenate([verticesB, [verticesB[0],
verticesB[0]], ])
c = np.concatenate([codesB, [Path.LINETO, Path.CLOSEPOLY]])
_path.append(Path(p, c))
else:
_fillable.append(False)
_path.append(Path(verticesB, codesB))
return _path, _fillable
class Curve(_Curve):
"""
A simple curve without any arrow head.
"""
def __init__(self):
super(ArrowStyle.Curve, self).__init__(
beginarrow=False, endarrow=False)
_style_list["-"] = Curve
class CurveA(_Curve):
"""
An arrow with a head at its begin point.
"""
def __init__(self, head_length=.4, head_width=.2):
"""
Parameters
----------
head_length : float, optional, default : 0.4
Length of the arrow head
head_width : float, optional, default : 0.2
Width of the arrow head
"""
super(ArrowStyle.CurveA, self).__init__(
beginarrow=True, endarrow=False,
head_length=head_length, head_width=head_width)
_style_list["<-"] = CurveA
class CurveB(_Curve):
"""
An arrow with a head at its end point.
"""
def __init__(self, head_length=.4, head_width=.2):
"""
Parameters
----------
head_length : float, optional, default : 0.4
Length of the arrow head
head_width : float, optional, default : 0.2
Width of the arrow head
"""
super(ArrowStyle.CurveB, self).__init__(
beginarrow=False, endarrow=True,
head_length=head_length, head_width=head_width)
_style_list["->"] = CurveB
class CurveAB(_Curve):
"""
An arrow with heads both at the begin and the end point.
"""
def __init__(self, head_length=.4, head_width=.2):
"""
Parameters
----------
head_length : float, optional, default : 0.4
Length of the arrow head
head_width : float, optional, default : 0.2
Width of the arrow head
"""
super(ArrowStyle.CurveAB, self).__init__(
beginarrow=True, endarrow=True,
head_length=head_length, head_width=head_width)
_style_list["<->"] = CurveAB
class CurveFilledA(_Curve):
"""
An arrow with filled triangle head at the begin.
"""
def __init__(self, head_length=.4, head_width=.2):
"""
Parameters
----------
head_length : float, optional, default : 0.4
Length of the arrow head
head_width : float, optional, default : 0.2
Width of the arrow head
"""
super(ArrowStyle.CurveFilledA, self).__init__(
beginarrow=True, endarrow=False,
fillbegin=True, fillend=False,
head_length=head_length, head_width=head_width)
_style_list["<|-"] = CurveFilledA
class CurveFilledB(_Curve):
"""
An arrow with filled triangle head at the end.
"""
def __init__(self, head_length=.4, head_width=.2):
"""
Parameters
----------
head_length : float, optional, default : 0.4
Length of the arrow head
head_width : float, optional, default : 0.2
Width of the arrow head
"""
super(ArrowStyle.CurveFilledB, self).__init__(
beginarrow=False, endarrow=True,
fillbegin=False, fillend=True,
head_length=head_length, head_width=head_width)
_style_list["-|>"] = CurveFilledB
class CurveFilledAB(_Curve):
"""
An arrow with filled triangle heads at both ends.
"""
def __init__(self, head_length=.4, head_width=.2):
"""
Parameters
----------
head_length : float, optional, default : 0.4
Length of the arrow head
head_width : float, optional, default : 0.2
Width of the arrow head
"""
super(ArrowStyle.CurveFilledAB, self).__init__(
beginarrow=True, endarrow=True,
fillbegin=True, fillend=True,
head_length=head_length, head_width=head_width)
_style_list["<|-|>"] = CurveFilledAB
class _Bracket(_Base):
def __init__(self, bracketA=None, bracketB=None,
widthA=1., widthB=1.,
lengthA=0.2, lengthB=0.2,
angleA=None, angleB=None,
scaleA=None, scaleB=None):
self.bracketA, self.bracketB = bracketA, bracketB
self.widthA, self.widthB = widthA, widthB
self.lengthA, self.lengthB = lengthA, lengthB
self.angleA, self.angleB = angleA, angleB
self.scaleA, self.scaleB = scaleA, scaleB
def _get_bracket(self, x0, y0,
cos_t, sin_t, width, length):
# arrow from x0, y0 to x1, y1
from matplotlib.bezier import get_normal_points
x1, y1, x2, y2 = get_normal_points(x0, y0, cos_t, sin_t, width)
dx, dy = length * cos_t, length * sin_t
vertices_arrow = [(x1 + dx, y1 + dy),
(x1, y1),
(x2, y2),
(x2 + dx, y2 + dy)]
codes_arrow = [Path.MOVETO,
Path.LINETO,
Path.LINETO,
Path.LINETO]
return vertices_arrow, codes_arrow
def transmute(self, path, mutation_size, linewidth):
if self.scaleA is None:
scaleA = mutation_size
else:
scaleA = self.scaleA
if self.scaleB is None:
scaleB = mutation_size
else:
scaleB = self.scaleB
vertices_list, codes_list = [], []
if self.bracketA:
x0, y0 = path.vertices[0]
x1, y1 = path.vertices[1]
cos_t, sin_t = get_cos_sin(x1, y1, x0, y0)
verticesA, codesA = self._get_bracket(x0, y0, cos_t, sin_t,
self.widthA * scaleA,
self.lengthA * scaleA)
vertices_list.append(verticesA)
codes_list.append(codesA)
vertices_list.append(path.vertices)
codes_list.append(path.codes)
if self.bracketB:
x0, y0 = path.vertices[-1]
x1, y1 = path.vertices[-2]
cos_t, sin_t = get_cos_sin(x1, y1, x0, y0)
verticesB, codesB = self._get_bracket(x0, y0, cos_t, sin_t,
self.widthB * scaleB,
self.lengthB * scaleB)
vertices_list.append(verticesB)
codes_list.append(codesB)
vertices = np.concatenate(vertices_list)
codes = np.concatenate(codes_list)
p = Path(vertices, codes)
return p, False
class BracketAB(_Bracket):
"""
An arrow with a bracket(]) at both ends.
"""
def __init__(self,
widthA=1., lengthA=0.2, angleA=None,
widthB=1., lengthB=0.2, angleB=None):
"""
Parameters
----------
widthA : float, optional, default : 1.0
Width of the bracket
lengthA : float, optional, default : 0.2
Length of the bracket
angleA : float, optional, default : None
Angle between the bracket and the line
widthB : float, optional, default : 1.0
Width of the bracket
lengthB : float, optional, default : 0.2
Length of the bracket
angleB : float, optional, default : None
Angle between the bracket and the line
"""
super(ArrowStyle.BracketAB, self).__init__(
True, True, widthA=widthA, lengthA=lengthA,
angleA=angleA, widthB=widthB, lengthB=lengthB,
angleB=angleB)
_style_list["]-["] = BracketAB
class BracketA(_Bracket):
"""
An arrow with a bracket(]) at its end.
"""
def __init__(self, widthA=1., lengthA=0.2, angleA=None):
"""
Parameters
----------
widthA : float, optional, default : 1.0
Width of the bracket
lengthA : float, optional, default : 0.2
Length of the bracket
angleA : float, optional, default : None
Angle between the bracket and the line
"""
super(ArrowStyle.BracketA, self).__init__(True, None,
widthA=widthA,
lengthA=lengthA,
angleA=angleA)
_style_list["]-"] = BracketA
class BracketB(_Bracket):
"""
An arrow with a bracket([) at its end.
"""
def __init__(self, widthB=1., lengthB=0.2, angleB=None):
"""
Parameters
----------
widthB : float, optional, default : 1.0
Width of the bracket
lengthB : float, optional, default : 0.2
Length of the bracket
angleB : float, optional, default : None
Angle between the bracket and the line
"""
super(ArrowStyle.BracketB, self).__init__(None, True,
widthB=widthB,
lengthB=lengthB,
angleB=angleB)
_style_list["-["] = BracketB
class BarAB(_Bracket):
"""
An arrow with a bar(|) at both ends.
"""
def __init__(self,
widthA=1., angleA=None,
widthB=1., angleB=None):
"""
Parameters
----------
widthA : float, optional, default : 1.0
Width of the bracket
angleA : float, optional, default : None
Angle between the bracket and the line
widthB : float, optional, default : 1.0
Width of the bracket
angleB : float, optional, default : None
Angle between the bracket and the line
"""
super(ArrowStyle.BarAB, self).__init__(
True, True, widthA=widthA, lengthA=0, angleA=angleA,
widthB=widthB, lengthB=0, angleB=angleB)
_style_list["|-|"] = BarAB
class Simple(_Base):
"""
A simple arrow. Only works with a quadratic bezier curve.
"""
def __init__(self, head_length=.5, head_width=.5, tail_width=.2):
"""
Parameters
----------
head_length : float, optional, default : 0.5
Length of the arrow head
head_width : float, optional, default : 0.5
Width of the arrow head
tail_width : float, optional, default : 0.2
Width of the arrow tail
"""
self.head_length, self.head_width, self.tail_width = \
head_length, head_width, tail_width
super(ArrowStyle.Simple, self).__init__()
def transmute(self, path, mutation_size, linewidth):
x0, y0, x1, y1, x2, y2 = self.ensure_quadratic_bezier(path)
# divide the path into a head and a tail
head_length = self.head_length * mutation_size
in_f = inside_circle(x2, y2, head_length)
arrow_path = [(x0, y0), (x1, y1), (x2, y2)]
from .bezier import NonIntersectingPathException
try:
arrow_out, arrow_in = \
split_bezier_intersecting_with_closedpath(arrow_path,
in_f,
tolerence=0.01)
except NonIntersectingPathException:
# if this happens, make a straight line of the head_length
# long.
x0, y0 = _point_along_a_line(x2, y2, x1, y1, head_length)
x1n, y1n = 0.5 * (x0 + x2), 0.5 * (y0 + y2)
arrow_in = [(x0, y0), (x1n, y1n), (x2, y2)]
arrow_out = None
# head
head_width = self.head_width * mutation_size
head_left, head_right = make_wedged_bezier2(arrow_in,
head_width / 2., wm=.5)
# tail
if arrow_out is not None:
tail_width = self.tail_width * mutation_size
tail_left, tail_right = get_parallels(arrow_out,
tail_width / 2.)
patch_path = [(Path.MOVETO, tail_right[0]),
(Path.CURVE3, tail_right[1]),
(Path.CURVE3, tail_right[2]),
(Path.LINETO, head_right[0]),
(Path.CURVE3, head_right[1]),
(Path.CURVE3, head_right[2]),
(Path.CURVE3, head_left[1]),
(Path.CURVE3, head_left[0]),
(Path.LINETO, tail_left[2]),
(Path.CURVE3, tail_left[1]),
(Path.CURVE3, tail_left[0]),
(Path.LINETO, tail_right[0]),
(Path.CLOSEPOLY, tail_right[0]),
]
else:
patch_path = [(Path.MOVETO, head_right[0]),
(Path.CURVE3, head_right[1]),
(Path.CURVE3, head_right[2]),
(Path.CURVE3, head_left[1]),
(Path.CURVE3, head_left[0]),
(Path.CLOSEPOLY, head_left[0]),
]
path = Path([p for c, p in patch_path], [c for c, p in patch_path])
return path, True
_style_list["simple"] = Simple
class Fancy(_Base):
"""
A fancy arrow. Only works with a quadratic bezier curve.
"""
def __init__(self, head_length=.4, head_width=.4, tail_width=.4):
"""
Parameters
----------
head_length : float, optional, default : 0.4
Length of the arrow head
head_width : float, optional, default : 0.4
Width of the arrow head
tail_width : float, optional, default : 0.4
Width of the arrow tail
"""
self.head_length, self.head_width, self.tail_width = \
head_length, head_width, tail_width
super(ArrowStyle.Fancy, self).__init__()
def transmute(self, path, mutation_size, linewidth):
x0, y0, x1, y1, x2, y2 = self.ensure_quadratic_bezier(path)
# divide the path into a head and a tail
head_length = self.head_length * mutation_size
arrow_path = [(x0, y0), (x1, y1), (x2, y2)]
from .bezier import NonIntersectingPathException
# path for head
in_f = inside_circle(x2, y2, head_length)
try:
path_out, path_in = \
split_bezier_intersecting_with_closedpath(
arrow_path,
in_f,
tolerence=0.01)
except NonIntersectingPathException:
# if this happens, make a straight line of the head_length
# long.
x0, y0 = _point_along_a_line(x2, y2, x1, y1, head_length)
x1n, y1n = 0.5 * (x0 + x2), 0.5 * (y0 + y2)
arrow_path = [(x0, y0), (x1n, y1n), (x2, y2)]
path_head = arrow_path
else:
path_head = path_in
# path for head
in_f = inside_circle(x2, y2, head_length * .8)
path_out, path_in = split_bezier_intersecting_with_closedpath(
arrow_path,
in_f,
tolerence=0.01
)
path_tail = path_out
# head
head_width = self.head_width * mutation_size
head_l, head_r = make_wedged_bezier2(path_head,
head_width / 2.,
wm=.6)
# tail
tail_width = self.tail_width * mutation_size
tail_left, tail_right = make_wedged_bezier2(path_tail,
tail_width * .5,
w1=1., wm=0.6, w2=0.3)
# path for head
in_f = inside_circle(x0, y0, tail_width * .3)
path_in, path_out = split_bezier_intersecting_with_closedpath(
arrow_path,
in_f,
tolerence=0.01
)
tail_start = path_in[-1]
head_right, head_left = head_r, head_l
patch_path = [(Path.MOVETO, tail_start),
(Path.LINETO, tail_right[0]),
(Path.CURVE3, tail_right[1]),
(Path.CURVE3, tail_right[2]),
(Path.LINETO, head_right[0]),
(Path.CURVE3, head_right[1]),
(Path.CURVE3, head_right[2]),
(Path.CURVE3, head_left[1]),
(Path.CURVE3, head_left[0]),
(Path.LINETO, tail_left[2]),
(Path.CURVE3, tail_left[1]),
(Path.CURVE3, tail_left[0]),
(Path.LINETO, tail_start),
(Path.CLOSEPOLY, tail_start),
]
path = Path([p for c, p in patch_path], [c for c, p in patch_path])
return path, True
_style_list["fancy"] = Fancy
class Wedge(_Base):
"""
Wedge(?) shape. Only works with a quadratic bezier curve. The
begin point has a width of the tail_width and the end point has a
width of 0. At the middle, the width is shrink_factor*tail_width.
"""
def __init__(self, tail_width=.3, shrink_factor=0.5):
"""
Parameters
----------
tail_width : float, optional, default : 0.3
Width of the tail
shrink_factor : float, optional, default : 0.5
Fraction of the arrow width at the middle point
"""
self.tail_width = tail_width
self.shrink_factor = shrink_factor
super(ArrowStyle.Wedge, self).__init__()
def transmute(self, path, mutation_size, linewidth):
x0, y0, x1, y1, x2, y2 = self.ensure_quadratic_bezier(path)
arrow_path = [(x0, y0), (x1, y1), (x2, y2)]
b_plus, b_minus = make_wedged_bezier2(
arrow_path,
self.tail_width * mutation_size / 2.,
wm=self.shrink_factor)
patch_path = [(Path.MOVETO, b_plus[0]),
(Path.CURVE3, b_plus[1]),
(Path.CURVE3, b_plus[2]),
(Path.LINETO, b_minus[2]),
(Path.CURVE3, b_minus[1]),
(Path.CURVE3, b_minus[0]),
(Path.CLOSEPOLY, b_minus[0]),
]
path = Path([p for c, p in patch_path], [c for c, p in patch_path])
return path, True
_style_list["wedge"] = Wedge
if __doc__:
__doc__ = cbook.dedent(__doc__) % \
{"AvailableArrowstyles": _pprint_styles(_style_list)}
docstring.interpd.update(
AvailableArrowstyles=_pprint_styles(ArrowStyle._style_list),
AvailableConnectorstyles=_pprint_styles(ConnectionStyle._style_list),
)
class FancyArrowPatch(Patch):
"""
A fancy arrow patch. It draws an arrow using the :class:`ArrowStyle`.
The head and tail positions are fixed at the specified start and end points
of the arrow, but the size and shape (in display coordinates) of the arrow
does not change when the axis is moved or zoomed.
"""
_edge_default = True
def __str__(self):
if self._posA_posB is not None:
(x1, y1), (x2, y2) = self._posA_posB
return self.__class__.__name__ \
+ "(%g,%g->%g,%g)" % (x1, y1, x2, y2)
else:
return self.__class__.__name__ \
+ "(%s)" % (str(self._path_original),)
@docstring.dedent_interpd
def __init__(self, posA=None, posB=None,
path=None,
arrowstyle="simple",
arrow_transmuter=None,
connectionstyle="arc3",
connector=None,
patchA=None,
patchB=None,
shrinkA=2,
shrinkB=2,
mutation_scale=1,
mutation_aspect=None,
dpi_cor=1,
**kwargs):
"""
If *posA* and *posB* are given, a path connecting two points is
created according to *connectionstyle*. The path will be
clipped with *patchA* and *patchB* and further shrunken by
*shrinkA* and *shrinkB*. An arrow is drawn along this
resulting path using the *arrowstyle* parameter.
Alternatively if *path* is provided, an arrow is drawn along this path
and *patchA*, *patchB*, *shrinkA*, and *shrinkB* are ignored.
Parameters
----------
posA, posB : None, tuple, optional (default: None)
(x,y) coordinates of arrow tail and arrow head respectively.
path : None, Path (default: None)
:class:`matplotlib.path.Path` instance. If provided, an arrow is
drawn along this path and *patchA*, *patchB*, *shrinkA*, and
*shrinkB* are ignored.
arrowstyle : str or ArrowStyle, optional (default: 'simple')
Describes how the fancy arrow will be
drawn. It can be string of the available arrowstyle names,
with optional comma-separated attributes, or an
:class:`ArrowStyle` instance. The optional attributes are meant to
be scaled with the *mutation_scale*. The following arrow styles are
available:
%(AvailableArrowstyles)s
arrow_transmuter :
Ignored
connectionstyle : str, ConnectionStyle, or None, optional
(default: 'arc3')
Describes how *posA* and *posB* are connected. It can be an
instance of the :class:`ConnectionStyle` class or a string of the
connectionstyle name, with optional comma-separated attributes. The
following connection styles are available:
%(AvailableConnectorstyles)s
connector :
Ignored
patchA, patchB : None, Patch, optional (default: None)
Head and tail patch respectively. :class:`matplotlib.patch.Patch`
instance.
shrinkA, shrinkB : scalar, optional (default: 2)
Shrinking factor of the tail and head of the arrow respectively
mutation_scale : scalar, optional (default: 1)
Value with which attributes of *arrowstyle* (e.g., *head_length*)
will be scaled.
mutation_aspect : None, scalar, optional (default: None)
The height of the rectangle will be squeezed by this value before
the mutation and the mutated box will be stretched by the inverse
of it.
dpi_cor : scalar, optional (default: 1)
dpi_cor is currently used for linewidth-related things and shrink
factor. Mutation scale is affected by this.
Notes
-----
Valid kwargs are:
%(Patch)s
"""
Patch.__init__(self, **kwargs)
if posA is not None and posB is not None and path is None:
self._posA_posB = [posA, posB]
if connectionstyle is None:
connectionstyle = "arc3"
self.set_connectionstyle(connectionstyle)
elif posA is None and posB is None and path is not None:
self._posA_posB = None
self._connetors = None
else:
raise ValueError("either posA and posB, or path need to provided")
self.patchA = patchA
self.patchB = patchB
self.shrinkA = shrinkA
self.shrinkB = shrinkB
self._path_original = path
self.set_arrowstyle(arrowstyle)
self._mutation_scale = mutation_scale
self._mutation_aspect = mutation_aspect
self.set_dpi_cor(dpi_cor)
def set_dpi_cor(self, dpi_cor):
"""
dpi_cor is currently used for linewidth-related things and
shrink factor. Mutation scale is affected by this.
Parameters
----------
dpi_cor : scalar
"""
self._dpi_cor = dpi_cor
self.stale = True
def get_dpi_cor(self):
"""
dpi_cor is currently used for linewidth-related things and
shrink factor. Mutation scale is affected by this.
Returns
-------
dpi_cor : scalar
"""
return self._dpi_cor
def set_positions(self, posA, posB):
"""
Set the begin and end positions of the connecting path.
Parameters
----------
posA, posB : None, tuple
(x,y) coordinates of arrow tail and arrow head respectively. If
`None` use current value.
"""
if posA is not None:
self._posA_posB[0] = posA
if posB is not None:
self._posA_posB[1] = posB
self.stale = True
def set_patchA(self, patchA):
"""
Set the tail patch.
Parameters
----------
patchA : Patch
:class:`matplotlib.patch.Patch` instance.
"""
self.patchA = patchA
self.stale = True
def set_patchB(self, patchB):
"""
Set the head patch.
Parameters
----------
patchB : Patch
:class:`matplotlib.patch.Patch` instance.
"""
self.patchB = patchB
self.stale = True
def set_connectionstyle(self, connectionstyle, **kw):
"""
Set the connection style. Old attributes are forgotten.
Parameters
----------
connectionstyle : None, ConnectionStyle instance, or string
Can be a string with connectionstyle name with
optional comma-separated attributes, e.g.::
set_connectionstyle("arc,angleA=0,armA=30,rad=10")
Alternatively, the attributes can be provided as keywords, e.g.::
set_connectionstyle("arc", angleA=0,armA=30,rad=10)
Without any arguments (or with ``connectionstyle=None``), return
available styles as a list of strings.
"""
if connectionstyle is None:
return ConnectionStyle.pprint_styles()
if (isinstance(connectionstyle, ConnectionStyle._Base) or
callable(connectionstyle)):
self._connector = connectionstyle
else:
self._connector = ConnectionStyle(connectionstyle, **kw)
self.stale = True
def get_connectionstyle(self):
"""
Return the :class:`ConnectionStyle` instance.
"""
return self._connector
def set_arrowstyle(self, arrowstyle=None, **kw):
"""
Set the arrow style. Old attributes are forgotten. Without arguments
(or with ``arrowstyle=None``) returns available box styles as a list of
strings.
Parameters
----------
arrowstyle : None, ArrowStyle, str, optional (default: None)
Can be a string with arrowstyle name with optional comma-separated
attributes, e.g.::
set_arrowstyle("Fancy,head_length=0.2")
Alternatively attributes can be provided as keywords, e.g.::
set_arrowstyle("fancy", head_length=0.2)
"""
if arrowstyle is None:
return ArrowStyle.pprint_styles()
if isinstance(arrowstyle, ArrowStyle._Base):
self._arrow_transmuter = arrowstyle
else:
self._arrow_transmuter = ArrowStyle(arrowstyle, **kw)
self.stale = True
def get_arrowstyle(self):
"""
Return the arrowstyle object.
"""
return self._arrow_transmuter
def set_mutation_scale(self, scale):
"""
Set the mutation scale.
Parameters
----------
scale : scalar
"""
self._mutation_scale = scale
self.stale = True
def get_mutation_scale(self):
"""
Return the mutation scale.
Returns
-------
scale : scalar
"""
return self._mutation_scale
def set_mutation_aspect(self, aspect):
"""
Set the aspect ratio of the bbox mutation.
Parameters
----------
aspect : scalar
"""
self._mutation_aspect = aspect
self.stale = True
def get_mutation_aspect(self):
"""
Return the aspect ratio of the bbox mutation.
"""
return self._mutation_aspect
def get_path(self):
"""
Return the path of the arrow in the data coordinates. Use
get_path_in_displaycoord() method to retrieve the arrow path
in display coordinates.
"""
_path, fillable = self.get_path_in_displaycoord()
if cbook.iterable(fillable):
_path = concatenate_paths(_path)
return self.get_transform().inverted().transform_path(_path)
def get_path_in_displaycoord(self):
"""
Return the mutated path of the arrow in display coordinates.
"""
dpi_cor = self.get_dpi_cor()
if self._posA_posB is not None:
posA = self.get_transform().transform_point(self._posA_posB[0])
posB = self.get_transform().transform_point(self._posA_posB[1])
_path = self.get_connectionstyle()(posA, posB,
patchA=self.patchA,
patchB=self.patchB,
shrinkA=self.shrinkA * dpi_cor,
shrinkB=self.shrinkB * dpi_cor
)
else:
_path = self.get_transform().transform_path(self._path_original)
_path, fillable = self.get_arrowstyle()(
_path,
self.get_mutation_scale() * dpi_cor,
self.get_linewidth() * dpi_cor,
self.get_mutation_aspect())
# if not fillable:
# self._fill = False
return _path, fillable
def draw(self, renderer):
if not self.get_visible():
return
renderer.open_group('patch', self.get_gid())
gc = renderer.new_gc()
gc.set_foreground(self._edgecolor, isRGBA=True)
lw = self._linewidth
if self._edgecolor[3] == 0:
lw = 0
gc.set_linewidth(lw)
gc.set_dashes(self._dashoffset, self._dashes)
gc.set_antialiased(self._antialiased)
self._set_gc_clip(gc)
gc.set_capstyle('round')
gc.set_snap(self.get_snap())
rgbFace = self._facecolor
if rgbFace[3] == 0:
rgbFace = None # (some?) renderers expect this as no-fill signal
gc.set_alpha(self._alpha)
if self._hatch:
gc.set_hatch(self._hatch)
if self._hatch_color is not None:
try:
gc.set_hatch_color(self._hatch_color)
except AttributeError:
# if we end up with a GC that does not have this method
warnings.warn("Your backend does not support setting the "
"hatch color.")
if self.get_sketch_params() is not None:
gc.set_sketch_params(*self.get_sketch_params())
# FIXME : dpi_cor is for the dpi-dependecy of the
# linewidth. There could be room for improvement.
#
# dpi_cor = renderer.points_to_pixels(1.)
self.set_dpi_cor(renderer.points_to_pixels(1.))
path, fillable = self.get_path_in_displaycoord()
if not cbook.iterable(fillable):
path = [path]
fillable = [fillable]
affine = transforms.IdentityTransform()
if self.get_path_effects():
from matplotlib.patheffects import PathEffectRenderer
renderer = PathEffectRenderer(self.get_path_effects(), renderer)
for p, f in zip(path, fillable):
if f:
renderer.draw_path(gc, p, affine, rgbFace)
else:
renderer.draw_path(gc, p, affine, None)
gc.restore()
renderer.close_group('patch')
self.stale = False
class ConnectionPatch(FancyArrowPatch):
"""
A :class:`~matplotlib.patches.ConnectionPatch` class is to make
connecting lines between two points (possibly in different axes).
"""
def __str__(self):
return "ConnectionPatch((%g,%g),(%g,%g))" % \
(self.xy1[0], self.xy1[1], self.xy2[0], self.xy2[1])
@docstring.dedent_interpd
def __init__(self, xyA, xyB, coordsA, coordsB=None,
axesA=None, axesB=None,
arrowstyle="-",
arrow_transmuter=None,
connectionstyle="arc3",
connector=None,
patchA=None,
patchB=None,
shrinkA=0.,
shrinkB=0.,
mutation_scale=10.,
mutation_aspect=None,
clip_on=False,
dpi_cor=1.,
**kwargs):
"""
Connect point *xyA* in *coordsA* with point *xyB* in *coordsB*
Valid keys are
=============== ======================================================
Key Description
=============== ======================================================
arrowstyle the arrow style
connectionstyle the connection style
relpos default is (0.5, 0.5)
patchA default is bounding box of the text
patchB default is None
shrinkA default is 2 points
shrinkB default is 2 points
mutation_scale default is text size (in points)
mutation_aspect default is 1.
? any key for :class:`matplotlib.patches.PathPatch`
=============== ======================================================
*coordsA* and *coordsB* are strings that indicate the
coordinates of *xyA* and *xyB*.
================= ===================================================
Property Description
================= ===================================================
'figure points' points from the lower left corner of the figure
'figure pixels' pixels from the lower left corner of the figure
'figure fraction' 0,0 is lower left of figure and 1,1 is upper, right
'axes points' points from lower left corner of axes
'axes pixels' pixels from lower left corner of axes
'axes fraction' 0,1 is lower left of axes and 1,1 is upper right
'data' use the coordinate system of the object being
annotated (default)
'offset points' Specify an offset (in points) from the *xy* value
'polar' you can specify *theta*, *r* for the annotation,
even in cartesian plots. Note that if you
are using a polar axes, you do not need
to specify polar for the coordinate
system since that is the native "data" coordinate
system.
================= ===================================================
"""
if coordsB is None:
coordsB = coordsA
# we'll draw ourself after the artist we annotate by default
self.xy1 = xyA
self.xy2 = xyB
self.coords1 = coordsA
self.coords2 = coordsB
self.axesA = axesA
self.axesB = axesB
FancyArrowPatch.__init__(self,
posA=(0, 0), posB=(1, 1),
arrowstyle=arrowstyle,
arrow_transmuter=arrow_transmuter,
connectionstyle=connectionstyle,
connector=connector,
patchA=patchA,
patchB=patchB,
shrinkA=shrinkA,
shrinkB=shrinkB,
mutation_scale=mutation_scale,
mutation_aspect=mutation_aspect,
clip_on=clip_on,
dpi_cor=dpi_cor,
**kwargs)
# if True, draw annotation only if self.xy is inside the axes
self._annotation_clip = None
def _get_xy(self, x, y, s, axes=None):
"""
calculate the pixel position of given point
"""
if axes is None:
axes = self.axes
if s == 'data':
trans = axes.transData
x = float(self.convert_xunits(x))
y = float(self.convert_yunits(y))
return trans.transform_point((x, y))
elif s == 'offset points':
# convert the data point
dx, dy = self.xy
# prevent recursion
if self.xycoords == 'offset points':
return self._get_xy(dx, dy, 'data')
dx, dy = self._get_xy(dx, dy, self.xycoords)
# convert the offset
dpi = self.figure.get_dpi()
x *= dpi / 72.
y *= dpi / 72.
# add the offset to the data point
x += dx
y += dy
return x, y
elif s == 'polar':
theta, r = x, y
x = r * np.cos(theta)
y = r * np.sin(theta)
trans = axes.transData
return trans.transform_point((x, y))
elif s == 'figure points':
# points from the lower left corner of the figure
dpi = self.figure.dpi
l, b, w, h = self.figure.bbox.bounds
r = l + w
t = b + h
x *= dpi / 72.
y *= dpi / 72.
if x < 0:
x = r + x
if y < 0:
y = t + y
return x, y
elif s == 'figure pixels':
# pixels from the lower left corner of the figure
l, b, w, h = self.figure.bbox.bounds
r = l + w
t = b + h
if x < 0:
x = r + x
if y < 0:
y = t + y
return x, y
elif s == 'figure fraction':
# (0,0) is lower left, (1,1) is upper right of figure
trans = self.figure.transFigure
return trans.transform_point((x, y))
elif s == 'axes points':
# points from the lower left corner of the axes
dpi = self.figure.dpi
l, b, w, h = axes.bbox.bounds
r = l + w
t = b + h
if x < 0:
x = r + x * dpi / 72.
else:
x = l + x * dpi / 72.
if y < 0:
y = t + y * dpi / 72.
else:
y = b + y * dpi / 72.
return x, y
elif s == 'axes pixels':
#pixels from the lower left corner of the axes
l, b, w, h = axes.bbox.bounds
r = l + w
t = b + h
if x < 0:
x = r + x
else:
x = l + x
if y < 0:
y = t + y
else:
y = b + y
return x, y
elif s == 'axes fraction':
#(0,0) is lower left, (1,1) is upper right of axes
trans = axes.transAxes
return trans.transform_point((x, y))
def set_annotation_clip(self, b):
"""
set *annotation_clip* attribute.
* True: the annotation will only be drawn when self.xy is inside the
axes.
* False: the annotation will always be drawn regardless of its
position.
* None: the self.xy will be checked only if *xycoords* is "data"
"""
self._annotation_clip = b
self.stale = True
def get_annotation_clip(self):
"""
Return *annotation_clip* attribute.
See :meth:`set_annotation_clip` for the meaning of return values.
"""
return self._annotation_clip
def get_path_in_displaycoord(self):
"""
Return the mutated path of the arrow in the display coord
"""
dpi_cor = self.get_dpi_cor()
x, y = self.xy1
posA = self._get_xy(x, y, self.coords1, self.axesA)
x, y = self.xy2
posB = self._get_xy(x, y, self.coords2, self.axesB)
_path = self.get_connectionstyle()(posA, posB,
patchA=self.patchA,
patchB=self.patchB,
shrinkA=self.shrinkA * dpi_cor,
shrinkB=self.shrinkB * dpi_cor
)
_path, fillable = self.get_arrowstyle()(
_path,
self.get_mutation_scale() * dpi_cor,
self.get_linewidth() * dpi_cor,
self.get_mutation_aspect()
)
return _path, fillable
def _check_xy(self, renderer):
"""
check if the annotation need to
be drawn.
"""
b = self.get_annotation_clip()
if b or (b is None and self.coords1 == "data"):
x, y = self.xy1
xy_pixel = self._get_xy(x, y, self.coords1, self.axesA)
if not self.axes.contains_point(xy_pixel):
return False
if b or (b is None and self.coords2 == "data"):
x, y = self.xy2
xy_pixel = self._get_xy(x, y, self.coords2, self.axesB)
if self.axesB is None:
axes = self.axes
else:
axes = self.axesB
if not axes.contains_point(xy_pixel):
return False
return True
def draw(self, renderer):
"""
Draw.
"""
if renderer is not None:
self._renderer = renderer
if not self.get_visible():
return
if not self._check_xy(renderer):
return
FancyArrowPatch.draw(self, renderer)
| 153,118 | 31.433595 | 79 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/matplotlib/tight_bbox.py
|
"""
This module is to support *bbox_inches* option in savefig command.
"""
from __future__ import (absolute_import, division, print_function,
unicode_literals)
import six
from matplotlib.transforms import Bbox, TransformedBbox, Affine2D
def adjust_bbox(fig, bbox_inches, fixed_dpi=None):
"""
Temporarily adjust the figure so that only the specified area
(bbox_inches) is saved.
It modifies fig.bbox, fig.bbox_inches,
fig.transFigure._boxout, and fig.patch. While the figure size
changes, the scale of the original figure is conserved. A
function which restores the original values are returned.
"""
origBbox = fig.bbox
origBboxInches = fig.bbox_inches
_boxout = fig.transFigure._boxout
asp_list = []
locator_list = []
for ax in fig.axes:
pos = ax.get_position(original=False).frozen()
locator_list.append(ax.get_axes_locator())
asp_list.append(ax.get_aspect())
def _l(a, r, pos=pos):
return pos
ax.set_axes_locator(_l)
ax.set_aspect("auto")
def restore_bbox():
for ax, asp, loc in zip(fig.axes, asp_list, locator_list):
ax.set_aspect(asp)
ax.set_axes_locator(loc)
fig.bbox = origBbox
fig.bbox_inches = origBboxInches
fig.transFigure._boxout = _boxout
fig.transFigure.invalidate()
fig.patch.set_bounds(0, 0, 1, 1)
if fixed_dpi is not None:
tr = Affine2D().scale(fixed_dpi)
dpi_scale = fixed_dpi / fig.dpi
else:
tr = Affine2D().scale(fig.dpi)
dpi_scale = 1.
_bbox = TransformedBbox(bbox_inches, tr)
fig.bbox_inches = Bbox.from_bounds(0, 0,
bbox_inches.width, bbox_inches.height)
x0, y0 = _bbox.x0, _bbox.y0
w1, h1 = fig.bbox.width * dpi_scale, fig.bbox.height * dpi_scale
fig.transFigure._boxout = Bbox.from_bounds(-x0, -y0, w1, h1)
fig.transFigure.invalidate()
fig.bbox = TransformedBbox(fig.bbox_inches, tr)
fig.patch.set_bounds(x0 / w1, y0 / h1,
fig.bbox.width / w1, fig.bbox.height / h1)
return restore_bbox
def process_figure_for_rasterizing(fig, bbox_inches_restore, fixed_dpi=None):
"""
This need to be called when figure dpi changes during the drawing
(e.g., rasterizing). It recovers the bbox and re-adjust it with
the new dpi.
"""
bbox_inches, restore_bbox = bbox_inches_restore
restore_bbox()
r = adjust_bbox(fig, bbox_inches, fixed_dpi)
return bbox_inches, r
| 2,585 | 28.386364 | 77 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/matplotlib/ticker.py
|
"""
Tick locating and formatting
============================
This module contains classes to support completely configurable tick
locating and formatting. Although the locators know nothing about major
or minor ticks, they are used by the Axis class to support major and
minor tick locating and formatting. Generic tick locators and
formatters are provided, as well as domain specific custom ones.
Default Formatter
-----------------
The default formatter identifies when the x-data being plotted is a
small range on top of a large off set. To reduce the chances that the
ticklabels overlap the ticks are labeled as deltas from a fixed offset.
For example::
ax.plot(np.arange(2000, 2010), range(10))
will have tick of 0-9 with an offset of +2e3. If this is not desired
turn off the use of the offset on the default formatter::
ax.get_xaxis().get_major_formatter().set_useOffset(False)
set the rcParam ``axes.formatter.useoffset=False`` to turn it off
globally, or set a different formatter.
Tick locating
-------------
The Locator class is the base class for all tick locators. The locators
handle autoscaling of the view limits based on the data limits, and the
choosing of tick locations. A useful semi-automatic tick locator is
`MultipleLocator`. It is initialized with a base, e.g., 10, and it picks
axis limits and ticks that are multiples of that base.
The Locator subclasses defined here are
:class:`AutoLocator`
`MaxNLocator` with simple defaults. This is the default tick locator for
most plotting.
:class:`MaxNLocator`
Finds up to a max number of intervals with ticks at nice locations.
:class:`LinearLocator`
Space ticks evenly from min to max.
:class:`LogLocator`
Space ticks logarithmically from min to max.
:class:`MultipleLocator`
Ticks and range are a multiple of base; either integer or float.
:class:`FixedLocator`
Tick locations are fixed.
:class:`IndexLocator`
Locator for index plots (e.g., where ``x = range(len(y))``).
:class:`NullLocator`
No ticks.
:class:`SymmetricalLogLocator`
Locator for use with with the symlog norm; works like `LogLocator` for the
part outside of the threshold and adds 0 if inside the limits.
:class:`LogitLocator`
Locator for logit scaling.
:class:`OldAutoLocator`
Choose a `MultipleLocator` and dynamically reassign it for intelligent
ticking during navigation.
:class:`AutoMinorLocator`
Locator for minor ticks when the axis is linear and the
major ticks are uniformly spaced. Subdivides the major
tick interval into a specified number of minor intervals,
defaulting to 4 or 5 depending on the major interval.
There are a number of locators specialized for date locations - see
the `dates` module.
You can define your own locator by deriving from Locator. You must
override the ``__call__`` method, which returns a sequence of locations,
and you will probably want to override the autoscale method to set the
view limits from the data limits.
If you want to override the default locator, use one of the above or a custom
locator and pass it to the x or y axis instance. The relevant methods are::
ax.xaxis.set_major_locator(xmajor_locator)
ax.xaxis.set_minor_locator(xminor_locator)
ax.yaxis.set_major_locator(ymajor_locator)
ax.yaxis.set_minor_locator(yminor_locator)
The default minor locator is `NullLocator`, i.e., no minor ticks on by default.
Tick formatting
---------------
Tick formatting is controlled by classes derived from Formatter. The formatter
operates on a single tick value and returns a string to the axis.
:class:`NullFormatter`
No labels on the ticks.
:class:`IndexFormatter`
Set the strings from a list of labels.
:class:`FixedFormatter`
Set the strings manually for the labels.
:class:`FuncFormatter`
User defined function sets the labels.
:class:`StrMethodFormatter`
Use string `format` method.
:class:`FormatStrFormatter`
Use an old-style sprintf format string.
:class:`ScalarFormatter`
Default formatter for scalars: autopick the format string.
:class:`LogFormatter`
Formatter for log axes.
:class:`LogFormatterExponent`
Format values for log axis using ``exponent = log_base(value)``.
:class:`LogFormatterMathtext`
Format values for log axis using ``exponent = log_base(value)``
using Math text.
:class:`LogFormatterSciNotation`
Format values for log axis using scientific notation.
:class:`LogitFormatter`
Probability formatter.
:class:`EngFormatter`
Format labels in engineering notation
:class:`PercentFormatter`
Format labels as a percentage
You can derive your own formatter from the Formatter base class by
simply overriding the ``__call__`` method. The formatter class has
access to the axis view and data limits.
To control the major and minor tick label formats, use one of the
following methods::
ax.xaxis.set_major_formatter(xmajor_formatter)
ax.xaxis.set_minor_formatter(xminor_formatter)
ax.yaxis.set_major_formatter(ymajor_formatter)
ax.yaxis.set_minor_formatter(yminor_formatter)
See :ref:`sphx_glr_gallery_ticks_and_spines_major_minor_demo.py` for an
example of setting major and minor ticks. See the :mod:`matplotlib.dates`
module for more information and examples of using date locators and formatters.
"""
from __future__ import (absolute_import, division, print_function,
unicode_literals)
import six
import itertools
import locale
import math
import numpy as np
from matplotlib import rcParams
from matplotlib import cbook
from matplotlib import transforms as mtransforms
from matplotlib.cbook import mplDeprecation
import warnings
__all__ = ('TickHelper', 'Formatter', 'FixedFormatter',
'NullFormatter', 'FuncFormatter', 'FormatStrFormatter',
'StrMethodFormatter', 'ScalarFormatter', 'LogFormatter',
'LogFormatterExponent', 'LogFormatterMathtext',
'IndexFormatter', 'LogFormatterSciNotation',
'LogitFormatter', 'EngFormatter', 'PercentFormatter',
'Locator', 'IndexLocator', 'FixedLocator', 'NullLocator',
'LinearLocator', 'LogLocator', 'AutoLocator',
'MultipleLocator', 'MaxNLocator', 'AutoMinorLocator',
'SymmetricalLogLocator', 'LogitLocator')
if six.PY3:
long = int
# Work around numpy/numpy#6127.
def _divmod(x, y):
if isinstance(x, np.generic):
x = x.item()
if isinstance(y, np.generic):
y = y.item()
return six.moves.builtins.divmod(x, y)
def _mathdefault(s):
return '\\mathdefault{%s}' % s
class _DummyAxis(object):
def __init__(self, minpos=0):
self.dataLim = mtransforms.Bbox.unit()
self.viewLim = mtransforms.Bbox.unit()
self._minpos = minpos
def get_view_interval(self):
return self.viewLim.intervalx
def set_view_interval(self, vmin, vmax):
self.viewLim.intervalx = vmin, vmax
def get_minpos(self):
return self._minpos
def get_data_interval(self):
return self.dataLim.intervalx
def set_data_interval(self, vmin, vmax):
self.dataLim.intervalx = vmin, vmax
def get_tick_space(self):
# Just use the long-standing default of nbins==9
return 9
class TickHelper(object):
axis = None
def set_axis(self, axis):
self.axis = axis
def create_dummy_axis(self, **kwargs):
if self.axis is None:
self.axis = _DummyAxis(**kwargs)
def set_view_interval(self, vmin, vmax):
self.axis.set_view_interval(vmin, vmax)
def set_data_interval(self, vmin, vmax):
self.axis.set_data_interval(vmin, vmax)
def set_bounds(self, vmin, vmax):
self.set_view_interval(vmin, vmax)
self.set_data_interval(vmin, vmax)
class Formatter(TickHelper):
"""
Create a string based on a tick value and location.
"""
# some classes want to see all the locs to help format
# individual ones
locs = []
def __call__(self, x, pos=None):
"""
Return the format for tick value `x` at position pos.
``pos=None`` indicates an unspecified location.
"""
raise NotImplementedError('Derived must override')
def format_data(self, value):
"""
Returns the full string representation of the value with the
position unspecified.
"""
return self.__call__(value)
def format_data_short(self, value):
"""
Return a short string version of the tick value.
Defaults to the position-independent long value.
"""
return self.format_data(value)
def get_offset(self):
return ''
def set_locs(self, locs):
self.locs = locs
def fix_minus(self, s):
"""
Some classes may want to replace a hyphen for minus with the
proper unicode symbol (U+2212) for typographical correctness.
The default is to not replace it.
Note, if you use this method, e.g., in :meth:`format_data` or
call, you probably don't want to use it for
:meth:`format_data_short` since the toolbar uses this for
interactive coord reporting and I doubt we can expect GUIs
across platforms will handle the unicode correctly. So for
now the classes that override :meth:`fix_minus` should have an
explicit :meth:`format_data_short` method
"""
return s
class IndexFormatter(Formatter):
"""
Format the position x to the nearest i-th label where i=int(x+0.5)
"""
def __init__(self, labels):
self.labels = labels
self.n = len(labels)
def __call__(self, x, pos=None):
"""
Return the format for tick value `x` at position pos.
The position is ignored and the value is rounded to the nearest
integer, which is used to look up the label.
"""
i = int(x + 0.5)
if i < 0 or i >= self.n:
return ''
else:
return self.labels[i]
class NullFormatter(Formatter):
"""
Always return the empty string.
"""
def __call__(self, x, pos=None):
"""
Returns an empty string for all inputs.
"""
return ''
class FixedFormatter(Formatter):
"""
Return fixed strings for tick labels based only on position, not
value.
"""
def __init__(self, seq):
"""
Set the sequence of strings that will be used for labels.
"""
self.seq = seq
self.offset_string = ''
def __call__(self, x, pos=None):
"""
Returns the label that matches the position regardless of the
value.
For positions ``pos < len(seq)``, return `seq[i]` regardless of
`x`. Otherwise return empty string. `seq` is the sequence of
strings that this object was initialized with.
"""
if pos is None or pos >= len(self.seq):
return ''
else:
return self.seq[pos]
def get_offset(self):
return self.offset_string
def set_offset_string(self, ofs):
self.offset_string = ofs
class FuncFormatter(Formatter):
"""
Use a user-defined function for formatting.
The function should take in two inputs (a tick value ``x`` and a
position ``pos``), and return a string containing the corresponding
tick label.
"""
def __init__(self, func):
self.func = func
def __call__(self, x, pos=None):
"""
Return the value of the user defined function.
`x` and `pos` are passed through as-is.
"""
return self.func(x, pos)
class FormatStrFormatter(Formatter):
"""
Use an old-style ('%' operator) format string to format the tick.
The format string should have a single variable format (%) in it.
It will be applied to the value (not the position) of the tick.
"""
def __init__(self, fmt):
self.fmt = fmt
def __call__(self, x, pos=None):
"""
Return the formatted label string.
Only the value `x` is formatted. The position is ignored.
"""
return self.fmt % x
class StrMethodFormatter(Formatter):
"""
Use a new-style format string (as used by `str.format()`)
to format the tick.
The field used for the value must be labeled `x` and the field used
for the position must be labeled `pos`.
"""
def __init__(self, fmt):
self.fmt = fmt
def __call__(self, x, pos=None):
"""
Return the formatted label string.
`x` and `pos` are passed to `str.format` as keyword arguments
with those exact names.
"""
return self.fmt.format(x=x, pos=pos)
class OldScalarFormatter(Formatter):
"""
Tick location is a plain old number.
"""
def __call__(self, x, pos=None):
"""
Return the format for tick val `x` based on the width of the
axis.
The position `pos` is ignored.
"""
xmin, xmax = self.axis.get_view_interval()
d = abs(xmax - xmin)
return self.pprint_val(x, d)
def pprint_val(self, x, d):
"""
Formats the value `x` based on the size of the axis range `d`.
"""
#if the number is not too big and it's an int, format it as an
#int
if abs(x) < 1e4 and x == int(x):
return '%d' % x
if d < 1e-2:
fmt = '%1.3e'
elif d < 1e-1:
fmt = '%1.3f'
elif d > 1e5:
fmt = '%1.1e'
elif d > 10:
fmt = '%1.1f'
elif d > 1:
fmt = '%1.2f'
else:
fmt = '%1.3f'
s = fmt % x
tup = s.split('e')
if len(tup) == 2:
mantissa = tup[0].rstrip('0').rstrip('.')
sign = tup[1][0].replace('+', '')
exponent = tup[1][1:].lstrip('0')
s = '%se%s%s' % (mantissa, sign, exponent)
else:
s = s.rstrip('0').rstrip('.')
return s
class ScalarFormatter(Formatter):
"""
Format tick values as a number.
Tick value is interpreted as a plain old number. If
``useOffset==True`` and the data range is much smaller than the data
average, then an offset will be determined such that the tick labels
are meaningful. Scientific notation is used for ``data < 10^-n`` or
``data >= 10^m``, where ``n`` and ``m`` are the power limits set
using ``set_powerlimits((n,m))``. The defaults for these are
controlled by the ``axes.formatter.limits`` rc parameter.
"""
def __init__(self, useOffset=None, useMathText=None, useLocale=None):
# useOffset allows plotting small data ranges with large offsets: for
# example: [1+1e-9,1+2e-9,1+3e-9] useMathText will render the offset
# and scientific notation in mathtext
if useOffset is None:
useOffset = rcParams['axes.formatter.useoffset']
self._offset_threshold = rcParams['axes.formatter.offset_threshold']
self.set_useOffset(useOffset)
self._usetex = rcParams['text.usetex']
if useMathText is None:
useMathText = rcParams['axes.formatter.use_mathtext']
self.set_useMathText(useMathText)
self.orderOfMagnitude = 0
self.format = ''
self._scientific = True
self._powerlimits = rcParams['axes.formatter.limits']
if useLocale is None:
useLocale = rcParams['axes.formatter.use_locale']
self._useLocale = useLocale
def get_useOffset(self):
return self._useOffset
def set_useOffset(self, val):
if val in [True, False]:
self.offset = 0
self._useOffset = val
else:
self._useOffset = False
self.offset = val
useOffset = property(fget=get_useOffset, fset=set_useOffset)
def get_useLocale(self):
return self._useLocale
def set_useLocale(self, val):
if val is None:
self._useLocale = rcParams['axes.formatter.use_locale']
else:
self._useLocale = val
useLocale = property(fget=get_useLocale, fset=set_useLocale)
def get_useMathText(self):
return self._useMathText
def set_useMathText(self, val):
if val is None:
self._useMathText = rcParams['axes.formatter.use_mathtext']
else:
self._useMathText = val
useMathText = property(fget=get_useMathText, fset=set_useMathText)
def fix_minus(self, s):
"""
Replace hyphens with a unicode minus.
"""
if rcParams['text.usetex'] or not rcParams['axes.unicode_minus']:
return s
else:
return s.replace('-', '\N{MINUS SIGN}')
def __call__(self, x, pos=None):
"""
Return the format for tick value `x` at position `pos`.
"""
if len(self.locs) == 0:
return ''
else:
s = self.pprint_val(x)
return self.fix_minus(s)
def set_scientific(self, b):
"""
Turn scientific notation on or off.
.. seealso:: Method :meth:`set_powerlimits`
"""
self._scientific = bool(b)
def set_powerlimits(self, lims):
"""
Sets size thresholds for scientific notation.
``lims`` is a two-element sequence containing the powers of 10
that determine the switchover threshold. Numbers below
``10**lims[0]`` and above ``10**lims[1]`` will be displayed in
scientific notation.
For example, ``formatter.set_powerlimits((-3, 4))`` sets the
pre-2007 default in which scientific notation is used for
numbers less than 1e-3 or greater than 1e4.
.. seealso:: Method :meth:`set_scientific`
"""
if len(lims) != 2:
raise ValueError("'lims' must be a sequence of length 2")
self._powerlimits = lims
def format_data_short(self, value):
"""
Return a short formatted string representation of a number.
"""
if self._useLocale:
return locale.format_string('%-12g', (value,))
else:
return '%-12g' % value
def format_data(self, value):
"""
Return a formatted string representation of a number.
"""
if self._useLocale:
s = locale.format_string('%1.10e', (value,))
else:
s = '%1.10e' % value
s = self._formatSciNotation(s)
return self.fix_minus(s)
def get_offset(self):
"""
Return scientific notation, plus offset.
"""
if len(self.locs) == 0:
return ''
s = ''
if self.orderOfMagnitude or self.offset:
offsetStr = ''
sciNotStr = ''
if self.offset:
offsetStr = self.format_data(self.offset)
if self.offset > 0:
offsetStr = '+' + offsetStr
if self.orderOfMagnitude:
if self._usetex or self._useMathText:
sciNotStr = self.format_data(10 ** self.orderOfMagnitude)
else:
sciNotStr = '1e%d' % self.orderOfMagnitude
if self._useMathText:
if sciNotStr != '':
sciNotStr = r'\times%s' % _mathdefault(sciNotStr)
s = ''.join(('$', sciNotStr, _mathdefault(offsetStr), '$'))
elif self._usetex:
if sciNotStr != '':
sciNotStr = r'\times%s' % sciNotStr
s = ''.join(('$', sciNotStr, offsetStr, '$'))
else:
s = ''.join((sciNotStr, offsetStr))
return self.fix_minus(s)
def set_locs(self, locs):
"""
Set the locations of the ticks.
"""
self.locs = locs
if len(self.locs) > 0:
vmin, vmax = self.axis.get_view_interval()
d = abs(vmax - vmin)
if self._useOffset:
self._compute_offset()
self._set_orderOfMagnitude(d)
self._set_format(vmin, vmax)
def _compute_offset(self):
locs = self.locs
if locs is None or not len(locs):
self.offset = 0
return
# Restrict to visible ticks.
vmin, vmax = sorted(self.axis.get_view_interval())
locs = np.asarray(locs)
locs = locs[(vmin <= locs) & (locs <= vmax)]
if not len(locs):
self.offset = 0
return
lmin, lmax = locs.min(), locs.max()
# Only use offset if there are at least two ticks and every tick has
# the same sign.
if lmin == lmax or lmin <= 0 <= lmax:
self.offset = 0
return
# min, max comparing absolute values (we want division to round towards
# zero so we work on absolute values).
abs_min, abs_max = sorted([abs(float(lmin)), abs(float(lmax))])
sign = math.copysign(1, lmin)
# What is the smallest power of ten such that abs_min and abs_max are
# equal up to that precision?
# Note: Internally using oom instead of 10 ** oom avoids some numerical
# accuracy issues.
oom_max = np.ceil(math.log10(abs_max))
oom = 1 + next(oom for oom in itertools.count(oom_max, -1)
if abs_min // 10 ** oom != abs_max // 10 ** oom)
if (abs_max - abs_min) / 10 ** oom <= 1e-2:
# Handle the case of straddling a multiple of a large power of ten
# (relative to the span).
# What is the smallest power of ten such that abs_min and abs_max
# are no more than 1 apart at that precision?
oom = 1 + next(oom for oom in itertools.count(oom_max, -1)
if abs_max // 10 ** oom - abs_min // 10 ** oom > 1)
# Only use offset if it saves at least _offset_threshold digits.
n = self._offset_threshold - 1
self.offset = (sign * (abs_max // 10 ** oom) * 10 ** oom
if abs_max // 10 ** oom >= 10**n
else 0)
def _set_orderOfMagnitude(self, range):
# if scientific notation is to be used, find the appropriate exponent
# if using an numerical offset, find the exponent after applying the
# offset
if not self._scientific:
self.orderOfMagnitude = 0
return
locs = np.abs(self.locs)
if self.offset:
oom = math.floor(math.log10(range))
else:
if locs[0] > locs[-1]:
val = locs[0]
else:
val = locs[-1]
if val == 0:
oom = 0
else:
oom = math.floor(math.log10(val))
if oom <= self._powerlimits[0]:
self.orderOfMagnitude = oom
elif oom >= self._powerlimits[1]:
self.orderOfMagnitude = oom
else:
self.orderOfMagnitude = 0
def _set_format(self, vmin, vmax):
# set the format string to format all the ticklabels
if len(self.locs) < 2:
# Temporarily augment the locations with the axis end points.
_locs = list(self.locs) + [vmin, vmax]
else:
_locs = self.locs
locs = (np.asarray(_locs) - self.offset) / 10. ** self.orderOfMagnitude
loc_range = np.ptp(locs)
# Curvilinear coordinates can yield two identical points.
if loc_range == 0:
loc_range = np.max(np.abs(locs))
# Both points might be zero.
if loc_range == 0:
loc_range = 1
if len(self.locs) < 2:
# We needed the end points only for the loc_range calculation.
locs = locs[:-2]
loc_range_oom = int(math.floor(math.log10(loc_range)))
# first estimate:
sigfigs = max(0, 3 - loc_range_oom)
# refined estimate:
thresh = 1e-3 * 10 ** loc_range_oom
while sigfigs >= 0:
if np.abs(locs - np.round(locs, decimals=sigfigs)).max() < thresh:
sigfigs -= 1
else:
break
sigfigs += 1
self.format = '%1.' + str(sigfigs) + 'f'
if self._usetex:
self.format = '$%s$' % self.format
elif self._useMathText:
self.format = '$%s$' % _mathdefault(self.format)
def pprint_val(self, x):
xp = (x - self.offset) / (10. ** self.orderOfMagnitude)
if np.abs(xp) < 1e-8:
xp = 0
if self._useLocale:
return locale.format_string(self.format, (xp,))
else:
return self.format % xp
def _formatSciNotation(self, s):
# transform 1e+004 into 1e4, for example
if self._useLocale:
decimal_point = locale.localeconv()['decimal_point']
positive_sign = locale.localeconv()['positive_sign']
else:
decimal_point = '.'
positive_sign = '+'
tup = s.split('e')
try:
significand = tup[0].rstrip('0').rstrip(decimal_point)
sign = tup[1][0].replace(positive_sign, '')
exponent = tup[1][1:].lstrip('0')
if self._useMathText or self._usetex:
if significand == '1' and exponent != '':
# reformat 1x10^y as 10^y
significand = ''
if exponent:
exponent = '10^{%s%s}' % (sign, exponent)
if significand and exponent:
return r'%s{\times}%s' % (significand, exponent)
else:
return r'%s%s' % (significand, exponent)
else:
s = ('%se%s%s' % (significand, sign, exponent)).rstrip('e')
return s
except IndexError:
return s
class LogFormatter(Formatter):
"""
Base class for formatting ticks on a log or symlog scale.
It may be instantiated directly, or subclassed.
Parameters
----------
base : float, optional, default: 10.
Base of the logarithm used in all calculations.
labelOnlyBase : bool, optional, default: False
If True, label ticks only at integer powers of base.
This is normally True for major ticks and False for
minor ticks.
minor_thresholds : (subset, all), optional, default: (1, 0.4)
If labelOnlyBase is False, these two numbers control
the labeling of ticks that are not at integer powers of
base; normally these are the minor ticks. The controlling
parameter is the log of the axis data range. In the typical
case where base is 10 it is the number of decades spanned
by the axis, so we can call it 'numdec'. If ``numdec <= all``,
all minor ticks will be labeled. If ``all < numdec <= subset``,
then only a subset of minor ticks will be labeled, so as to
avoid crowding. If ``numdec > subset`` then no minor ticks will
be labeled.
linthresh : None or float, optional, default: None
If a symmetric log scale is in use, its ``linthresh``
parameter must be supplied here.
Notes
-----
The `set_locs` method must be called to enable the subsetting
logic controlled by the ``minor_thresholds`` parameter.
In some cases such as the colorbar, there is no distinction between
major and minor ticks; the tick locations might be set manually,
or by a locator that puts ticks at integer powers of base and
at intermediate locations. For this situation, disable the
minor_thresholds logic by using ``minor_thresholds=(np.inf, np.inf)``,
so that all ticks will be labeled.
To disable labeling of minor ticks when 'labelOnlyBase' is False,
use ``minor_thresholds=(0, 0)``. This is the default for the
"classic" style.
Examples
--------
To label a subset of minor ticks when the view limits span up
to 2 decades, and all of the ticks when zoomed in to 0.5 decades
or less, use ``minor_thresholds=(2, 0.5)``.
To label all minor ticks when the view limits span up to 1.5
decades, use ``minor_thresholds=(1.5, 1.5)``.
"""
def __init__(self, base=10.0, labelOnlyBase=False,
minor_thresholds=None,
linthresh=None):
self._base = float(base)
self.labelOnlyBase = labelOnlyBase
if minor_thresholds is None:
if rcParams['_internal.classic_mode']:
minor_thresholds = (0, 0)
else:
minor_thresholds = (1, 0.4)
self.minor_thresholds = minor_thresholds
self._sublabels = None
self._linthresh = linthresh
def base(self, base):
"""
change the `base` for labeling.
.. warning::
Should always match the base used for :class:`LogLocator`
"""
self._base = base
def label_minor(self, labelOnlyBase):
"""
Switch minor tick labeling on or off.
Parameters
----------
labelOnlyBase : bool
If True, label ticks only at integer powers of base.
"""
self.labelOnlyBase = labelOnlyBase
def set_locs(self, locs=None):
"""
Use axis view limits to control which ticks are labeled.
The ``locs`` parameter is ignored in the present algorithm.
"""
if np.isinf(self.minor_thresholds[0]):
self._sublabels = None
return
# Handle symlog case:
linthresh = self._linthresh
if linthresh is None:
try:
linthresh = self.axis.get_transform().linthresh
except AttributeError:
pass
vmin, vmax = self.axis.get_view_interval()
if vmin > vmax:
vmin, vmax = vmax, vmin
if linthresh is None and vmin <= 0:
# It's probably a colorbar with
# a format kwarg setting a LogFormatter in the manner
# that worked with 1.5.x, but that doesn't work now.
self._sublabels = set((1,)) # label powers of base
return
b = self._base
if linthresh is not None: # symlog
# Only compute the number of decades in the logarithmic part of the
# axis
numdec = 0
if vmin < -linthresh:
rhs = min(vmax, -linthresh)
numdec += math.log(vmin / rhs) / math.log(b)
if vmax > linthresh:
lhs = max(vmin, linthresh)
numdec += math.log(vmax / lhs) / math.log(b)
else:
vmin = math.log(vmin) / math.log(b)
vmax = math.log(vmax) / math.log(b)
numdec = abs(vmax - vmin)
if numdec > self.minor_thresholds[0]:
# Label only bases
self._sublabels = {1}
elif numdec > self.minor_thresholds[1]:
# Add labels between bases at log-spaced coefficients;
# include base powers in case the locations include
# "major" and "minor" points, as in colorbar.
c = np.logspace(0, 1, int(b)//2 + 1, base=b)
self._sublabels = set(np.round(c))
# For base 10, this yields (1, 2, 3, 4, 6, 10).
else:
# Label all integer multiples of base**n.
self._sublabels = set(np.arange(1, b + 1))
def _num_to_string(self, x, vmin, vmax):
if x > 10000:
s = '%1.0e' % x
elif x < 1:
s = '%1.0e' % x
else:
s = self.pprint_val(x, vmax - vmin)
return s
def __call__(self, x, pos=None):
"""
Return the format for tick val `x`.
"""
if x == 0.0: # Symlog
return '0'
x = abs(x)
b = self._base
# only label the decades
fx = math.log(x) / math.log(b)
is_x_decade = is_close_to_int(fx)
exponent = np.round(fx) if is_x_decade else np.floor(fx)
coeff = np.round(x / b ** exponent)
if self.labelOnlyBase and not is_x_decade:
return ''
if self._sublabels is not None and coeff not in self._sublabels:
return ''
vmin, vmax = self.axis.get_view_interval()
vmin, vmax = mtransforms.nonsingular(vmin, vmax, expander=0.05)
s = self._num_to_string(x, vmin, vmax)
return self.fix_minus(s)
def format_data(self, value):
b = self.labelOnlyBase
self.labelOnlyBase = False
value = cbook.strip_math(self.__call__(value))
self.labelOnlyBase = b
return value
def format_data_short(self, value):
"""
Return a short formatted string representation of a number.
"""
return '%-12g' % value
def pprint_val(self, x, d):
#if the number is not too big and it's an int, format it as an
#int
if abs(x) < 1e4 and x == int(x):
return '%d' % x
if d < 1e-2:
fmt = '%1.3e'
elif d < 1e-1:
fmt = '%1.3f'
elif d > 1e5:
fmt = '%1.1e'
elif d > 10:
fmt = '%1.1f'
elif d > 1:
fmt = '%1.2f'
else:
fmt = '%1.3f'
s = fmt % x
tup = s.split('e')
if len(tup) == 2:
mantissa = tup[0].rstrip('0').rstrip('.')
exponent = int(tup[1])
if exponent:
s = '%se%d' % (mantissa, exponent)
else:
s = mantissa
else:
s = s.rstrip('0').rstrip('.')
return s
class LogFormatterExponent(LogFormatter):
"""
Format values for log axis using ``exponent = log_base(value)``.
"""
def _num_to_string(self, x, vmin, vmax):
fx = math.log(x) / math.log(self._base)
if abs(fx) > 10000:
s = '%1.0g' % fx
elif abs(fx) < 1:
s = '%1.0g' % fx
else:
fd = math.log(vmax - vmin) / math.log(self._base)
s = self.pprint_val(fx, fd)
return s
class LogFormatterMathtext(LogFormatter):
"""
Format values for log axis using ``exponent = log_base(value)``.
"""
def _non_decade_format(self, sign_string, base, fx, usetex):
'Return string for non-decade locations'
if usetex:
return (r'$%s%s^{%.2f}$') % (sign_string, base, fx)
else:
return ('$%s$' % _mathdefault('%s%s^{%.2f}' %
(sign_string, base, fx)))
def __call__(self, x, pos=None):
"""
Return the format for tick value `x`.
The position `pos` is ignored.
"""
usetex = rcParams['text.usetex']
min_exp = rcParams['axes.formatter.min_exponent']
if x == 0: # Symlog
if usetex:
return '$0$'
else:
return '$%s$' % _mathdefault('0')
sign_string = '-' if x < 0 else ''
x = abs(x)
b = self._base
# only label the decades
fx = math.log(x) / math.log(b)
is_x_decade = is_close_to_int(fx)
exponent = np.round(fx) if is_x_decade else np.floor(fx)
coeff = np.round(x / b ** exponent)
if is_x_decade:
fx = nearest_long(fx)
if self.labelOnlyBase and not is_x_decade:
return ''
if self._sublabels is not None and coeff not in self._sublabels:
return ''
# use string formatting of the base if it is not an integer
if b % 1 == 0.0:
base = '%d' % b
else:
base = '%s' % b
if np.abs(fx) < min_exp:
if usetex:
return r'${0}{1:g}$'.format(sign_string, x)
else:
return '${0}$'.format(_mathdefault(
'{0}{1:g}'.format(sign_string, x)))
elif not is_x_decade:
return self._non_decade_format(sign_string, base, fx, usetex)
else:
if usetex:
return (r'$%s%s^{%d}$') % (sign_string,
base,
nearest_long(fx))
else:
return ('$%s$' % _mathdefault(
'%s%s^{%d}' %
(sign_string, base, nearest_long(fx))))
class LogFormatterSciNotation(LogFormatterMathtext):
"""
Format values following scientific notation in a logarithmic axis
"""
def _non_decade_format(self, sign_string, base, fx, usetex):
'Return string for non-decade locations'
b = float(base)
exponent = math.floor(fx)
coeff = b ** fx / b ** exponent
if is_close_to_int(coeff):
coeff = nearest_long(coeff)
if usetex:
return (r'$%s%g\times%s^{%d}$') % \
(sign_string, coeff, base, exponent)
else:
return ('$%s$' % _mathdefault(r'%s%g\times%s^{%d}' %
(sign_string, coeff, base, exponent)))
class LogitFormatter(Formatter):
"""
Probability formatter (using Math text).
"""
def __call__(self, x, pos=None):
s = ''
if 0.01 <= x <= 0.99:
s = '{:.2f}'.format(x)
elif x < 0.01:
if is_decade(x):
s = '$10^{{{:.0f}}}$'.format(np.log10(x))
else:
s = '${:.5f}$'.format(x)
else: # x > 0.99
if is_decade(1-x):
s = '$1-10^{{{:.0f}}}$'.format(np.log10(1-x))
else:
s = '$1-{:.5f}$'.format(1-x)
return s
def format_data_short(self, value):
'return a short formatted string representation of a number'
return '%-12g' % value
class EngFormatter(Formatter):
"""
Formats axis values using engineering prefixes to represent powers
of 1000, plus a specified unit, e.g., 10 MHz instead of 1e7.
"""
# The SI engineering prefixes
ENG_PREFIXES = {
-24: "y",
-21: "z",
-18: "a",
-15: "f",
-12: "p",
-9: "n",
-6: "\N{GREEK SMALL LETTER MU}",
-3: "m",
0: "",
3: "k",
6: "M",
9: "G",
12: "T",
15: "P",
18: "E",
21: "Z",
24: "Y"
}
def __init__(self, unit="", places=None, sep=" "):
"""
Parameters
----------
unit : str (default: "")
Unit symbol to use, suitable for use with single-letter
representations of powers of 1000. For example, 'Hz' or 'm'.
places : int (default: None)
Precision with which to display the number, specified in
digits after the decimal point (there will be between one
and three digits before the decimal point). If it is None,
the formatting falls back to the floating point format '%g',
which displays up to 6 *significant* digits, i.e. the equivalent
value for *places* varies between 0 and 5 (inclusive).
sep : str (default: " ")
Separator used between the value and the prefix/unit. For
example, one get '3.14 mV' if ``sep`` is " " (default) and
'3.14mV' if ``sep`` is "". Besides the default behavior, some
other useful options may be:
* ``sep=""`` to append directly the prefix/unit to the value;
* ``sep="\\N{THIN SPACE}"`` (``U+2009``);
* ``sep="\\N{NARROW NO-BREAK SPACE}"`` (``U+202F``);
* ``sep="\\N{NO-BREAK SPACE}"`` (``U+00A0``).
"""
self.unit = unit
self.places = places
self.sep = sep
def __call__(self, x, pos=None):
s = "%s%s" % (self.format_eng(x), self.unit)
# Remove the trailing separator when there is neither prefix nor unit
if len(self.sep) > 0 and s.endswith(self.sep):
s = s[:-len(self.sep)]
return self.fix_minus(s)
def format_eng(self, num):
"""
Formats a number in engineering notation, appending a letter
representing the power of 1000 of the original number.
Some examples:
>>> format_eng(0) # for self.places = 0
'0'
>>> format_eng(1000000) # for self.places = 1
'1.0 M'
>>> format_eng("-1e-6") # for self.places = 2
u'-1.00 \N{GREEK SMALL LETTER MU}'
`num` may be a numeric value or a string that can be converted
to a numeric value with ``float(num)``.
"""
if isinstance(num, six.string_types):
warnings.warn(
"Passing a string as *num* argument is deprecated since"
"Matplotlib 2.1, and is expected to be removed in 2.3.",
mplDeprecation)
dnum = float(num)
sign = 1
fmt = "g" if self.places is None else ".{:d}f".format(self.places)
if dnum < 0:
sign = -1
dnum = -dnum
if dnum != 0:
pow10 = int(math.floor(math.log10(dnum) / 3) * 3)
else:
pow10 = 0
# Force dnum to zero, to avoid inconsistencies like
# format_eng(-0) = "0" and format_eng(0.0) = "0"
# but format_eng(-0.0) = "-0.0"
dnum = 0.0
pow10 = np.clip(pow10, min(self.ENG_PREFIXES), max(self.ENG_PREFIXES))
mant = sign * dnum / (10.0 ** pow10)
# Taking care of the cases like 999.9..., which
# may be rounded to 1000 instead of 1 k. Beware
# of the corner case of values that are beyond
# the range of SI prefixes (i.e. > 'Y').
_fmant = float("{mant:{fmt}}".format(mant=mant, fmt=fmt))
if _fmant >= 1000 and pow10 != max(self.ENG_PREFIXES):
mant /= 1000
pow10 += 3
prefix = self.ENG_PREFIXES[int(pow10)]
formatted = "{mant:{fmt}}{sep}{prefix}".format(
mant=mant, sep=self.sep, prefix=prefix, fmt=fmt)
return formatted
class PercentFormatter(Formatter):
"""
Format numbers as a percentage.
How the number is converted into a percentage is determined by the
`xmax` parameter. `xmax` is the data value that corresponds to 100%.
Percentages are computed as ``x / xmax * 100``. So if the data is
already scaled to be percentages, `xmax` will be 100. Another common
situation is where `xmax` is 1.0.
`symbol` is a string which will be appended to the label. It may be
`None` or empty to indicate that no symbol should be used. LaTeX
special characters are escaped in `symbol` whenever latex mode is
enabled, unless `is_latex` is `True`.
`decimals` is the number of decimal places to place after the point.
If it is set to `None` (the default), the number will be computed
automatically.
"""
def __init__(self, xmax=100, decimals=None, symbol='%', is_latex=False):
self.xmax = xmax + 0.0
self.decimals = decimals
self._symbol = symbol
self._is_latex = is_latex
def __call__(self, x, pos=None):
"""
Formats the tick as a percentage with the appropriate scaling.
"""
ax_min, ax_max = self.axis.get_view_interval()
display_range = abs(ax_max - ax_min)
return self.fix_minus(self.format_pct(x, display_range))
def format_pct(self, x, display_range):
"""
Formats the number as a percentage number with the correct
number of decimals and adds the percent symbol, if any.
If `self.decimals` is `None`, the number of digits after the
decimal point is set based on the `display_range` of the axis
as follows:
+---------------+----------+------------------------+
| display_range | decimals | sample |
+---------------+----------+------------------------+
| >50 | 0 | ``x = 34.5`` => 35% |
+---------------+----------+------------------------+
| >5 | 1 | ``x = 34.5`` => 34.5% |
+---------------+----------+------------------------+
| >0.5 | 2 | ``x = 34.5`` => 34.50% |
+---------------+----------+------------------------+
| ... | ... | ... |
+---------------+----------+------------------------+
This method will not be very good for tiny axis ranges or
extremely large ones. It assumes that the values on the chart
are percentages displayed on a reasonable scale.
"""
x = self.convert_to_pct(x)
if self.decimals is None:
# conversion works because display_range is a difference
scaled_range = self.convert_to_pct(display_range)
if scaled_range <= 0:
decimals = 0
else:
# Luckily Python's built-in ceil rounds to +inf, not away from
# zero. This is very important since the equation for decimals
# starts out as `scaled_range > 0.5 * 10**(2 - decimals)`
# and ends up with `decimals > 2 - log10(2 * scaled_range)`.
decimals = math.ceil(2.0 - math.log10(2.0 * scaled_range))
if decimals > 5:
decimals = 5
elif decimals < 0:
decimals = 0
else:
decimals = self.decimals
s = '{x:0.{decimals}f}'.format(x=x, decimals=int(decimals))
return s + self.symbol
def convert_to_pct(self, x):
return 100.0 * (x / self.xmax)
@property
def symbol(self):
"""
The configured percent symbol as a string.
If LaTeX is enabled via :rc:`text.usetex`, the special characters
``{'#', '$', '%', '&', '~', '_', '^', '\\', '{', '}'}`` are
automatically escaped in the string.
"""
symbol = self._symbol
if not symbol:
symbol = ''
elif rcParams['text.usetex'] and not self._is_latex:
# Source: http://www.personal.ceu.hu/tex/specchar.htm
# Backslash must be first for this to work correctly since
# it keeps getting added in
for spec in r'\#$%&~_^{}':
symbol = symbol.replace(spec, '\\' + spec)
return symbol
@symbol.setter
def symbol(self, symbol):
self._symbol = symbol
class Locator(TickHelper):
"""
Determine the tick locations;
Note, you should not use the same locator between different
:class:`~matplotlib.axis.Axis` because the locator stores references to
the Axis data and view limits
"""
# Some automatic tick locators can generate so many ticks they
# kill the machine when you try and render them.
# This parameter is set to cause locators to raise an error if too
# many ticks are generated.
MAXTICKS = 1000
def tick_values(self, vmin, vmax):
"""
Return the values of the located ticks given **vmin** and **vmax**.
.. note::
To get tick locations with the vmin and vmax values defined
automatically for the associated :attr:`axis` simply call
the Locator instance::
>>> print((type(loc)))
<type 'Locator'>
>>> print((loc()))
[1, 2, 3, 4]
"""
raise NotImplementedError('Derived must override')
def set_params(self, **kwargs):
"""
Do nothing, and rase a warning. Any locator class not supporting the
set_params() function will call this.
"""
warnings.warn("'set_params()' not defined for locator of type " +
str(type(self)))
def __call__(self):
"""Return the locations of the ticks"""
# note: some locators return data limits, other return view limits,
# hence there is no *one* interface to call self.tick_values.
raise NotImplementedError('Derived must override')
def raise_if_exceeds(self, locs):
"""raise a RuntimeError if Locator attempts to create more than
MAXTICKS locs"""
if len(locs) >= self.MAXTICKS:
raise RuntimeError("Locator attempting to generate {} ticks from "
"{} to {}: exceeds Locator.MAXTICKS".format(
len(locs), locs[0], locs[-1]))
return locs
def view_limits(self, vmin, vmax):
"""
select a scale for the range from vmin to vmax
Normally this method is overridden by subclasses to
change locator behaviour.
"""
return mtransforms.nonsingular(vmin, vmax)
def autoscale(self):
"""autoscale the view limits"""
return self.view_limits(*self.axis.get_view_interval())
def pan(self, numsteps):
"""Pan numticks (can be positive or negative)"""
ticks = self()
numticks = len(ticks)
vmin, vmax = self.axis.get_view_interval()
vmin, vmax = mtransforms.nonsingular(vmin, vmax, expander=0.05)
if numticks > 2:
step = numsteps * abs(ticks[0] - ticks[1])
else:
d = abs(vmax - vmin)
step = numsteps * d / 6.
vmin += step
vmax += step
self.axis.set_view_interval(vmin, vmax, ignore=True)
def zoom(self, direction):
"Zoom in/out on axis; if direction is >0 zoom in, else zoom out"
vmin, vmax = self.axis.get_view_interval()
vmin, vmax = mtransforms.nonsingular(vmin, vmax, expander=0.05)
interval = abs(vmax - vmin)
step = 0.1 * interval * direction
self.axis.set_view_interval(vmin + step, vmax - step, ignore=True)
def refresh(self):
"""refresh internal information based on current lim"""
pass
class IndexLocator(Locator):
"""
Place a tick on every multiple of some base number of points
plotted, e.g., on every 5th point. It is assumed that you are doing
index plotting; i.e., the axis is 0, len(data). This is mainly
useful for x ticks.
"""
def __init__(self, base, offset):
'place ticks on the i-th data points where (i-offset)%base==0'
self._base = base
self.offset = offset
def set_params(self, base=None, offset=None):
"""Set parameters within this locator"""
if base is not None:
self._base = base
if offset is not None:
self.offset = offset
def __call__(self):
"""Return the locations of the ticks"""
dmin, dmax = self.axis.get_data_interval()
return self.tick_values(dmin, dmax)
def tick_values(self, vmin, vmax):
return self.raise_if_exceeds(
np.arange(vmin + self.offset, vmax + 1, self._base))
class FixedLocator(Locator):
"""
Tick locations are fixed. If nbins is not None,
the array of possible positions will be subsampled to
keep the number of ticks <= nbins +1.
The subsampling will be done so as to include the smallest
absolute value; for example, if zero is included in the
array of possibilities, then it is guaranteed to be one of
the chosen ticks.
"""
def __init__(self, locs, nbins=None):
self.locs = np.asarray(locs)
self.nbins = nbins
if self.nbins is not None:
self.nbins = max(self.nbins, 2)
def set_params(self, nbins=None):
"""Set parameters within this locator."""
if nbins is not None:
self.nbins = nbins
def __call__(self):
return self.tick_values(None, None)
def tick_values(self, vmin, vmax):
""""
Return the locations of the ticks.
.. note::
Because the values are fixed, vmin and vmax are not used in this
method.
"""
if self.nbins is None:
return self.locs
step = max(int(np.ceil(len(self.locs) / self.nbins)), 1)
ticks = self.locs[::step]
for i in range(1, step):
ticks1 = self.locs[i::step]
if np.abs(ticks1).min() < np.abs(ticks).min():
ticks = ticks1
return self.raise_if_exceeds(ticks)
class NullLocator(Locator):
"""
No ticks
"""
def __call__(self):
return self.tick_values(None, None)
def tick_values(self, vmin, vmax):
""""
Return the locations of the ticks.
.. note::
Because the values are Null, vmin and vmax are not used in this
method.
"""
return []
class LinearLocator(Locator):
"""
Determine the tick locations
The first time this function is called it will try to set the
number of ticks to make a nice tick partitioning. Thereafter the
number of ticks will be fixed so that interactive navigation will
be nice
"""
def __init__(self, numticks=None, presets=None):
"""
Use presets to set locs based on lom. A dict mapping vmin, vmax->locs
"""
self.numticks = numticks
if presets is None:
self.presets = {}
else:
self.presets = presets
def set_params(self, numticks=None, presets=None):
"""Set parameters within this locator."""
if presets is not None:
self.presets = presets
if numticks is not None:
self.numticks = numticks
def __call__(self):
'Return the locations of the ticks'
vmin, vmax = self.axis.get_view_interval()
return self.tick_values(vmin, vmax)
def tick_values(self, vmin, vmax):
vmin, vmax = mtransforms.nonsingular(vmin, vmax, expander=0.05)
if vmax < vmin:
vmin, vmax = vmax, vmin
if (vmin, vmax) in self.presets:
return self.presets[(vmin, vmax)]
if self.numticks is None:
self._set_numticks()
if self.numticks == 0:
return []
ticklocs = np.linspace(vmin, vmax, self.numticks)
return self.raise_if_exceeds(ticklocs)
def _set_numticks(self):
self.numticks = 11 # todo; be smart here; this is just for dev
def view_limits(self, vmin, vmax):
'Try to choose the view limits intelligently'
if vmax < vmin:
vmin, vmax = vmax, vmin
if vmin == vmax:
vmin -= 1
vmax += 1
if rcParams['axes.autolimit_mode'] == 'round_numbers':
exponent, remainder = _divmod(
math.log10(vmax - vmin), math.log10(max(self.numticks - 1, 1)))
exponent -= (remainder < .5)
scale = max(self.numticks - 1, 1) ** (-exponent)
vmin = math.floor(scale * vmin) / scale
vmax = math.ceil(scale * vmax) / scale
return mtransforms.nonsingular(vmin, vmax)
def closeto(x, y):
if abs(x - y) < 1e-10:
return True
else:
return False
class Base(object):
'this solution has some hacks to deal with floating point inaccuracies'
def __init__(self, base):
if base <= 0:
raise ValueError("'base' must be positive")
self._base = base
def lt(self, x):
'return the largest multiple of base < x'
d, m = _divmod(x, self._base)
if closeto(m, 0) and not closeto(m / self._base, 1):
return (d - 1) * self._base
return d * self._base
def le(self, x):
'return the largest multiple of base <= x'
d, m = _divmod(x, self._base)
if closeto(m / self._base, 1): # was closeto(m, self._base)
#looks like floating point error
return (d + 1) * self._base
return d * self._base
def gt(self, x):
'return the smallest multiple of base > x'
d, m = _divmod(x, self._base)
if closeto(m / self._base, 1):
#looks like floating point error
return (d + 2) * self._base
return (d + 1) * self._base
def ge(self, x):
'return the smallest multiple of base >= x'
d, m = _divmod(x, self._base)
if closeto(m, 0) and not closeto(m / self._base, 1):
return d * self._base
return (d + 1) * self._base
def get_base(self):
return self._base
class MultipleLocator(Locator):
"""
Set a tick on every integer that is multiple of base in the
view interval
"""
def __init__(self, base=1.0):
self._base = Base(base)
def set_params(self, base):
"""Set parameters within this locator."""
if base is not None:
self._base = base
def __call__(self):
'Return the locations of the ticks'
vmin, vmax = self.axis.get_view_interval()
return self.tick_values(vmin, vmax)
def tick_values(self, vmin, vmax):
if vmax < vmin:
vmin, vmax = vmax, vmin
vmin = self._base.ge(vmin)
base = self._base.get_base()
n = (vmax - vmin + 0.001 * base) // base
locs = vmin - base + np.arange(n + 3) * base
return self.raise_if_exceeds(locs)
def view_limits(self, dmin, dmax):
"""
Set the view limits to the nearest multiples of base that
contain the data
"""
if rcParams['axes.autolimit_mode'] == 'round_numbers':
vmin = self._base.le(dmin)
vmax = self._base.ge(dmax)
if vmin == vmax:
vmin -= 1
vmax += 1
else:
vmin = dmin
vmax = dmax
return mtransforms.nonsingular(vmin, vmax)
def scale_range(vmin, vmax, n=1, threshold=100):
dv = abs(vmax - vmin) # > 0 as nonsingular is called before.
meanv = (vmax + vmin) / 2
if abs(meanv) / dv < threshold:
offset = 0
else:
offset = math.copysign(10 ** (math.log10(abs(meanv)) // 1), meanv)
scale = 10 ** (math.log10(dv / n) // 1)
return scale, offset
class MaxNLocator(Locator):
"""
Select no more than N intervals at nice locations.
"""
default_params = dict(nbins=10,
steps=None,
integer=False,
symmetric=False,
prune=None,
min_n_ticks=2)
def __init__(self, *args, **kwargs):
"""
Keyword args:
*nbins*
Maximum number of intervals; one less than max number of
ticks. If the string `'auto'`, the number of bins will be
automatically determined based on the length of the axis.
*steps*
Sequence of nice numbers starting with 1 and ending with 10;
e.g., [1, 2, 4, 5, 10], where the values are acceptable
tick multiples. i.e. for the example, 20, 40, 60 would be
an acceptable set of ticks, as would 0.4, 0.6, 0.8, because
they are multiples of 2. However, 30, 60, 90 would not
be allowed because 3 does not appear in the list of steps.
*integer*
If True, ticks will take only integer values, provided
at least `min_n_ticks` integers are found within the
view limits.
*symmetric*
If True, autoscaling will result in a range symmetric
about zero.
*prune*
['lower' | 'upper' | 'both' | None]
Remove edge ticks -- useful for stacked or ganged plots where
the upper tick of one axes overlaps with the lower tick of the
axes above it, primarily when :rc:`axes.autolimit_mode` is
``'round_numbers'``. If ``prune=='lower'``, the smallest tick will
be removed. If ``prune == 'upper'``, the largest tick will be
removed. If ``prune == 'both'``, the largest and smallest ticks
will be removed. If ``prune == None``, no ticks will be removed.
*min_n_ticks*
Relax `nbins` and `integer` constraints if necessary to
obtain this minimum number of ticks.
"""
if args:
kwargs['nbins'] = args[0]
if len(args) > 1:
raise ValueError(
"Keywords are required for all arguments except 'nbins'")
self.set_params(**self.default_params)
self.set_params(**kwargs)
@staticmethod
def _validate_steps(steps):
if not np.iterable(steps):
raise ValueError('steps argument must be a sequence of numbers '
'from 1 to 10')
steps = np.asarray(steps)
if np.any(np.diff(steps) <= 0):
raise ValueError('steps argument must be uniformly increasing')
if steps[-1] > 10 or steps[0] < 1:
warnings.warn('Steps argument should be a sequence of numbers\n'
'increasing from 1 to 10, inclusive. Behavior with\n'
'values outside this range is undefined, and will\n'
'raise a ValueError in future versions of mpl.')
if steps[0] != 1:
steps = np.hstack((1, steps))
if steps[-1] != 10:
steps = np.hstack((steps, 10))
return steps
@staticmethod
def _staircase(steps):
# Make an extended staircase within which the needed
# step will be found. This is probably much larger
# than necessary.
flights = (0.1 * steps[:-1], steps, 10 * steps[1])
return np.hstack(flights)
def set_params(self, **kwargs):
"""Set parameters within this locator."""
if 'nbins' in kwargs:
self._nbins = kwargs['nbins']
if self._nbins != 'auto':
self._nbins = int(self._nbins)
if 'symmetric' in kwargs:
self._symmetric = kwargs['symmetric']
if 'prune' in kwargs:
prune = kwargs['prune']
if prune is not None and prune not in ['upper', 'lower', 'both']:
raise ValueError(
"prune must be 'upper', 'lower', 'both', or None")
self._prune = prune
if 'min_n_ticks' in kwargs:
self._min_n_ticks = max(1, kwargs['min_n_ticks'])
if 'steps' in kwargs:
steps = kwargs['steps']
if steps is None:
self._steps = np.array([1, 1.5, 2, 2.5, 3, 4, 5, 6, 8, 10])
else:
self._steps = self._validate_steps(steps)
self._extended_steps = self._staircase(self._steps)
if 'integer' in kwargs:
self._integer = kwargs['integer']
def _raw_ticks(self, vmin, vmax):
if self._nbins == 'auto':
if self.axis is not None:
nbins = np.clip(self.axis.get_tick_space(),
max(1, self._min_n_ticks - 1), 9)
else:
nbins = 9
else:
nbins = self._nbins
scale, offset = scale_range(vmin, vmax, nbins)
_vmin = vmin - offset
_vmax = vmax - offset
raw_step = (vmax - vmin) / nbins
steps = self._extended_steps * scale
if self._integer:
# For steps > 1, keep only integer values.
igood = (steps < 1) | (np.abs(steps - np.round(steps)) < 0.001)
steps = steps[igood]
istep = np.nonzero(steps >= raw_step)[0][0]
# Classic round_numbers mode may require a larger step.
if rcParams['axes.autolimit_mode'] == 'round_numbers':
for istep in range(istep, len(steps)):
step = steps[istep]
best_vmin = (_vmin // step) * step
best_vmax = best_vmin + step * nbins
if (best_vmax >= _vmax):
break
# This is an upper limit; move to smaller steps if necessary.
for i in range(istep):
step = steps[istep - i]
if (self._integer and
np.floor(_vmax) - np.ceil(_vmin) >= self._min_n_ticks - 1):
step = max(1, step)
best_vmin = (_vmin // step) * step
low = np.round(Base(step).le(_vmin - best_vmin) / step)
high = np.round(Base(step).ge(_vmax - best_vmin) / step)
ticks = np.arange(low, high + 1) * step + best_vmin + offset
nticks = ((ticks <= vmax) & (ticks >= vmin)).sum()
if nticks >= self._min_n_ticks:
break
return ticks
def __call__(self):
vmin, vmax = self.axis.get_view_interval()
return self.tick_values(vmin, vmax)
def tick_values(self, vmin, vmax):
if self._symmetric:
vmax = max(abs(vmin), abs(vmax))
vmin = -vmax
vmin, vmax = mtransforms.nonsingular(
vmin, vmax, expander=1e-13, tiny=1e-14)
locs = self._raw_ticks(vmin, vmax)
prune = self._prune
if prune == 'lower':
locs = locs[1:]
elif prune == 'upper':
locs = locs[:-1]
elif prune == 'both':
locs = locs[1:-1]
return self.raise_if_exceeds(locs)
def view_limits(self, dmin, dmax):
if self._symmetric:
dmax = max(abs(dmin), abs(dmax))
dmin = -dmax
dmin, dmax = mtransforms.nonsingular(
dmin, dmax, expander=1e-12, tiny=1e-13)
if rcParams['axes.autolimit_mode'] == 'round_numbers':
return self._raw_ticks(dmin, dmax)[[0, -1]]
else:
return dmin, dmax
def decade_down(x, base=10):
'floor x to the nearest lower decade'
if x == 0.0:
return -base
lx = np.floor(np.log(x) / np.log(base))
return base ** lx
def decade_up(x, base=10):
'ceil x to the nearest higher decade'
if x == 0.0:
return base
lx = np.ceil(np.log(x) / np.log(base))
return base ** lx
def nearest_long(x):
if x == 0:
return long(0)
elif x > 0:
return long(x + 0.5)
else:
return long(x - 0.5)
def is_decade(x, base=10):
if not np.isfinite(x):
return False
if x == 0.0:
return True
lx = np.log(np.abs(x)) / np.log(base)
return is_close_to_int(lx)
def is_close_to_int(x):
if not np.isfinite(x):
return False
return abs(x - nearest_long(x)) < 1e-10
class LogLocator(Locator):
"""
Determine the tick locations for log axes
"""
def __init__(self, base=10.0, subs=(1.0,), numdecs=4, numticks=None):
"""
Place ticks on the locations : subs[j] * base**i
Parameters
----------
subs : None, string, or sequence of float, optional, default (1.0,)
Gives the multiples of integer powers of the base at which
to place ticks. The default places ticks only at
integer powers of the base.
The permitted string values are ``'auto'`` and ``'all'``,
both of which use an algorithm based on the axis view
limits to determine whether and how to put ticks between
integer powers of the base. With ``'auto'``, ticks are
placed only between integer powers; with ``'all'``, the
integer powers are included. A value of None is
equivalent to ``'auto'``.
"""
if numticks is None:
if rcParams['_internal.classic_mode']:
numticks = 15
else:
numticks = 'auto'
self.base(base)
self.subs(subs)
self.numdecs = numdecs
self.numticks = numticks
def set_params(self, base=None, subs=None, numdecs=None, numticks=None):
"""Set parameters within this locator."""
if base is not None:
self.base(base)
if subs is not None:
self.subs(subs)
if numdecs is not None:
self.numdecs = numdecs
if numticks is not None:
self.numticks = numticks
# FIXME: these base and subs functions are contrary to our
# usual and desired API.
def base(self, base):
"""
set the base of the log scaling (major tick every base**i, i integer)
"""
self._base = float(base)
def subs(self, subs):
"""
set the minor ticks for the log scaling every base**i*subs[j]
"""
if subs is None: # consistency with previous bad API
self._subs = 'auto'
elif isinstance(subs, six.string_types):
if subs not in ('all', 'auto'):
raise ValueError("A subs string must be 'all' or 'auto'; "
"found '%s'." % subs)
self._subs = subs
else:
self._subs = np.asarray(subs, dtype=float)
def __call__(self):
'Return the locations of the ticks'
vmin, vmax = self.axis.get_view_interval()
return self.tick_values(vmin, vmax)
def tick_values(self, vmin, vmax):
if self.numticks == 'auto':
if self.axis is not None:
numticks = np.clip(self.axis.get_tick_space(), 2, 9)
else:
numticks = 9
else:
numticks = self.numticks
b = self._base
# dummy axis has no axes attribute
if hasattr(self.axis, 'axes') and self.axis.axes.name == 'polar':
vmax = math.ceil(math.log(vmax) / math.log(b))
decades = np.arange(vmax - self.numdecs, vmax)
ticklocs = b ** decades
return ticklocs
if vmin <= 0.0:
if self.axis is not None:
vmin = self.axis.get_minpos()
if vmin <= 0.0 or not np.isfinite(vmin):
raise ValueError(
"Data has no positive values, and therefore can not be "
"log-scaled.")
vmin = math.log(vmin) / math.log(b)
vmax = math.log(vmax) / math.log(b)
if vmax < vmin:
vmin, vmax = vmax, vmin
numdec = math.floor(vmax) - math.ceil(vmin)
if isinstance(self._subs, six.string_types):
_first = 2.0 if self._subs == 'auto' else 1.0
if numdec > 10 or b < 3:
if self._subs == 'auto':
return np.array([]) # no minor or major ticks
else:
subs = np.array([1.0]) # major ticks
else:
subs = np.arange(_first, b)
else:
subs = self._subs
stride = 1
if rcParams['_internal.classic_mode']:
# Leave the bug left over from the PY2-PY3 transition.
while numdec / stride + 1 > numticks:
stride += 1
else:
while numdec // stride + 1 > numticks:
stride += 1
# Does subs include anything other than 1?
have_subs = len(subs) > 1 or (len(subs == 1) and subs[0] != 1.0)
decades = np.arange(math.floor(vmin) - stride,
math.ceil(vmax) + 2 * stride, stride)
if hasattr(self, '_transform'):
ticklocs = self._transform.inverted().transform(decades)
if have_subs:
if stride == 1:
ticklocs = np.ravel(np.outer(subs, ticklocs))
else:
ticklocs = []
else:
if have_subs:
ticklocs = []
if stride == 1:
for decadeStart in b ** decades:
ticklocs.extend(subs * decadeStart)
else:
ticklocs = b ** decades
return self.raise_if_exceeds(np.asarray(ticklocs))
def view_limits(self, vmin, vmax):
'Try to choose the view limits intelligently'
b = self._base
vmin, vmax = self.nonsingular(vmin, vmax)
if self.axis.axes.name == 'polar':
vmax = math.ceil(math.log(vmax) / math.log(b))
vmin = b ** (vmax - self.numdecs)
if rcParams['axes.autolimit_mode'] == 'round_numbers':
if not is_decade(vmin, self._base):
vmin = decade_down(vmin, self._base)
if not is_decade(vmax, self._base):
vmax = decade_up(vmax, self._base)
return vmin, vmax
def nonsingular(self, vmin, vmax):
if not np.isfinite(vmin) or not np.isfinite(vmax):
return 1, 10 # initial range, no data plotted yet
if vmin > vmax:
vmin, vmax = vmax, vmin
if vmax <= 0:
warnings.warn(
"Data has no positive values, and therefore cannot be "
"log-scaled.")
return 1, 10
minpos = self.axis.get_minpos()
if not np.isfinite(minpos):
minpos = 1e-300 # This should never take effect.
if vmin <= 0:
vmin = minpos
if vmin == vmax:
vmin = decade_down(vmin, self._base)
vmax = decade_up(vmax, self._base)
return vmin, vmax
class SymmetricalLogLocator(Locator):
"""
Determine the tick locations for symmetric log axes
"""
def __init__(self, transform=None, subs=None, linthresh=None, base=None):
"""
place ticks on the location= base**i*subs[j]
"""
if transform is not None:
self._base = transform.base
self._linthresh = transform.linthresh
elif linthresh is not None and base is not None:
self._base = base
self._linthresh = linthresh
else:
raise ValueError("Either transform, or both linthresh "
"and base, must be provided.")
if subs is None:
self._subs = [1.0]
else:
self._subs = subs
self.numticks = 15
def set_params(self, subs=None, numticks=None):
"""Set parameters within this locator."""
if numticks is not None:
self.numticks = numticks
if subs is not None:
self._subs = subs
def __call__(self):
'Return the locations of the ticks'
# Note, these are untransformed coordinates
vmin, vmax = self.axis.get_view_interval()
return self.tick_values(vmin, vmax)
def tick_values(self, vmin, vmax):
b = self._base
t = self._linthresh
if vmax < vmin:
vmin, vmax = vmax, vmin
# The domain is divided into three sections, only some of
# which may actually be present.
#
# <======== -t ==0== t ========>
# aaaaaaaaa bbbbb ccccccccc
#
# a) and c) will have ticks at integral log positions. The
# number of ticks needs to be reduced if there are more
# than self.numticks of them.
#
# b) has a tick at 0 and only 0 (we assume t is a small
# number, and the linear segment is just an implementation
# detail and not interesting.)
#
# We could also add ticks at t, but that seems to usually be
# uninteresting.
#
# "simple" mode is when the range falls entirely within (-t,
# t) -- it should just display (vmin, 0, vmax)
has_a = has_b = has_c = False
if vmin < -t:
has_a = True
if vmax > -t:
has_b = True
if vmax > t:
has_c = True
elif vmin < 0:
if vmax > 0:
has_b = True
if vmax > t:
has_c = True
else:
return [vmin, vmax]
elif vmin < t:
if vmax > t:
has_b = True
has_c = True
else:
return [vmin, vmax]
else:
has_c = True
def get_log_range(lo, hi):
lo = np.floor(np.log(lo) / np.log(b))
hi = np.ceil(np.log(hi) / np.log(b))
return lo, hi
# First, calculate all the ranges, so we can determine striding
if has_a:
if has_b:
a_range = get_log_range(t, -vmin + 1)
else:
a_range = get_log_range(-vmax, -vmin + 1)
else:
a_range = (0, 0)
if has_c:
if has_b:
c_range = get_log_range(t, vmax + 1)
else:
c_range = get_log_range(vmin, vmax + 1)
else:
c_range = (0, 0)
total_ticks = (a_range[1] - a_range[0]) + (c_range[1] - c_range[0])
if has_b:
total_ticks += 1
stride = max(total_ticks // (self.numticks - 1), 1)
decades = []
if has_a:
decades.extend(-1 * (b ** (np.arange(a_range[0], a_range[1],
stride)[::-1])))
if has_b:
decades.append(0.0)
if has_c:
decades.extend(b ** (np.arange(c_range[0], c_range[1], stride)))
# Add the subticks if requested
if self._subs is None:
subs = np.arange(2.0, b)
else:
subs = np.asarray(self._subs)
if len(subs) > 1 or subs[0] != 1.0:
ticklocs = []
for decade in decades:
if decade == 0:
ticklocs.append(decade)
else:
ticklocs.extend(subs * decade)
else:
ticklocs = decades
return self.raise_if_exceeds(np.array(ticklocs))
def view_limits(self, vmin, vmax):
'Try to choose the view limits intelligently'
b = self._base
if vmax < vmin:
vmin, vmax = vmax, vmin
if rcParams['axes.autolimit_mode'] == 'round_numbers':
if not is_decade(abs(vmin), b):
if vmin < 0:
vmin = -decade_up(-vmin, b)
else:
vmin = decade_down(vmin, b)
if not is_decade(abs(vmax), b):
if vmax < 0:
vmax = -decade_down(-vmax, b)
else:
vmax = decade_up(vmax, b)
if vmin == vmax:
if vmin < 0:
vmin = -decade_up(-vmin, b)
vmax = -decade_down(-vmax, b)
else:
vmin = decade_down(vmin, b)
vmax = decade_up(vmax, b)
result = mtransforms.nonsingular(vmin, vmax)
return result
class LogitLocator(Locator):
"""
Determine the tick locations for logit axes
"""
def __init__(self, minor=False):
"""
place ticks on the logit locations
"""
self.minor = minor
def set_params(self, minor=None):
"""Set parameters within this locator."""
if minor is not None:
self.minor = minor
def __call__(self):
'Return the locations of the ticks'
vmin, vmax = self.axis.get_view_interval()
return self.tick_values(vmin, vmax)
def tick_values(self, vmin, vmax):
# dummy axis has no axes attribute
if hasattr(self.axis, 'axes') and self.axis.axes.name == 'polar':
raise NotImplementedError('Polar axis cannot be logit scaled yet')
vmin, vmax = self.nonsingular(vmin, vmax)
vmin = np.log10(vmin / (1 - vmin))
vmax = np.log10(vmax / (1 - vmax))
decade_min = np.floor(vmin)
decade_max = np.ceil(vmax)
# major ticks
if not self.minor:
ticklocs = []
if (decade_min <= -1):
expo = np.arange(decade_min, min(0, decade_max + 1))
ticklocs.extend(list(10**expo))
if (decade_min <= 0) and (decade_max >= 0):
ticklocs.append(0.5)
if (decade_max >= 1):
expo = -np.arange(max(1, decade_min), decade_max + 1)
ticklocs.extend(list(1 - 10**expo))
# minor ticks
else:
ticklocs = []
if (decade_min <= -2):
expo = np.arange(decade_min, min(-1, decade_max))
newticks = np.outer(np.arange(2, 10), 10**expo).ravel()
ticklocs.extend(list(newticks))
if (decade_min <= 0) and (decade_max >= 0):
ticklocs.extend([0.2, 0.3, 0.4, 0.6, 0.7, 0.8])
if (decade_max >= 2):
expo = -np.arange(max(2, decade_min), decade_max + 1)
newticks = 1 - np.outer(np.arange(2, 10), 10**expo).ravel()
ticklocs.extend(list(newticks))
return self.raise_if_exceeds(np.array(ticklocs))
def nonsingular(self, vmin, vmax):
initial_range = (1e-7, 1 - 1e-7)
if not np.isfinite(vmin) or not np.isfinite(vmax):
return initial_range # no data plotted yet
if vmin > vmax:
vmin, vmax = vmax, vmin
# what to do if a window beyond ]0, 1[ is chosen
if self.axis is not None:
minpos = self.axis.get_minpos()
if not np.isfinite(minpos):
return initial_range # again, no data plotted
else:
minpos = 1e-7 # should not occur in normal use
# NOTE: for vmax, we should query a property similar to get_minpos, but
# related to the maximal, less-than-one data point. Unfortunately,
# Bbox._minpos is defined very deep in the BBox and updated with data,
# so for now we use 1 - minpos as a substitute.
if vmin <= 0:
vmin = minpos
if vmax >= 1:
vmax = 1 - minpos
if vmin == vmax:
return 0.1 * vmin, 1 - 0.1 * vmin
return vmin, vmax
class AutoLocator(MaxNLocator):
"""
Dynamically find major tick positions. This is actually a subclass
of `~matplotlib.ticker.MaxNLocator`, with parameters *nbins = 'auto'*
and *steps = [1, 2, 2.5, 5, 10]*.
"""
def __init__(self):
"""
To know the values of the non-public parameters, please have a
look to the defaults of `~matplotlib.ticker.MaxNLocator`.
"""
if rcParams['_internal.classic_mode']:
nbins = 9
steps = [1, 2, 5, 10]
else:
nbins = 'auto'
steps = [1, 2, 2.5, 5, 10]
MaxNLocator.__init__(self, nbins=nbins, steps=steps)
class AutoMinorLocator(Locator):
"""
Dynamically find minor tick positions based on the positions of
major ticks. The scale must be linear with major ticks evenly spaced.
"""
def __init__(self, n=None):
"""
*n* is the number of subdivisions of the interval between
major ticks; e.g., n=2 will place a single minor tick midway
between major ticks.
If *n* is omitted or None, it will be set to 5 or 4.
"""
self.ndivs = n
def __call__(self):
'Return the locations of the ticks'
if self.axis.get_scale() == 'log':
warnings.warn('AutoMinorLocator does not work with logarithmic '
'scale')
return []
majorlocs = self.axis.get_majorticklocs()
try:
majorstep = majorlocs[1] - majorlocs[0]
except IndexError:
# Need at least two major ticks to find minor tick locations
# TODO: Figure out a way to still be able to display minor
# ticks without two major ticks visible. For now, just display
# no ticks at all.
return []
if self.ndivs is None:
x = int(np.round(10 ** (np.log10(majorstep) % 1)))
if x in [1, 5, 10]:
ndivs = 5
else:
ndivs = 4
else:
ndivs = self.ndivs
minorstep = majorstep / ndivs
vmin, vmax = self.axis.get_view_interval()
if vmin > vmax:
vmin, vmax = vmax, vmin
t0 = majorlocs[0]
tmin = ((vmin - t0) // minorstep + 1) * minorstep
tmax = ((vmax - t0) // minorstep + 1) * minorstep
locs = np.arange(tmin, tmax, minorstep) + t0
cond = np.abs((locs - t0) % majorstep) > minorstep / 10.0
locs = locs.compress(cond)
return self.raise_if_exceeds(np.array(locs))
def tick_values(self, vmin, vmax):
raise NotImplementedError('Cannot get tick locations for a '
'%s type.' % type(self))
class OldAutoLocator(Locator):
"""
On autoscale this class picks the best MultipleLocator to set the
view limits and the tick locs.
"""
def __init__(self):
self._locator = LinearLocator()
def __call__(self):
'Return the locations of the ticks'
self.refresh()
return self.raise_if_exceeds(self._locator())
def tick_values(self, vmin, vmax):
raise NotImplementedError('Cannot get tick locations for a '
'%s type.' % type(self))
def refresh(self):
'refresh internal information based on current lim'
vmin, vmax = self.axis.get_view_interval()
vmin, vmax = mtransforms.nonsingular(vmin, vmax, expander=0.05)
d = abs(vmax - vmin)
self._locator = self.get_locator(d)
def view_limits(self, vmin, vmax):
'Try to choose the view limits intelligently'
d = abs(vmax - vmin)
self._locator = self.get_locator(d)
return self._locator.view_limits(vmin, vmax)
def get_locator(self, d):
'pick the best locator based on a distance'
d = abs(d)
if d <= 0:
locator = MultipleLocator(0.2)
else:
try:
ld = math.log10(d)
except OverflowError:
raise RuntimeError('AutoLocator illegal data interval range')
fld = math.floor(ld)
base = 10 ** fld
#if ld==fld: base = 10**(fld-1)
#else: base = 10**fld
if d >= 5 * base:
ticksize = base
elif d >= 2 * base:
ticksize = base / 2.0
else:
ticksize = base / 5.0
locator = MultipleLocator(ticksize)
return locator
| 86,246 | 31.94385 | 79 |
py
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