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# -*- coding: utf-8 -*-
"""app.py
Automatically generated by Colab.
Original file is located at
https://colab.research.google.com/drive/1QIEwA7FDPNIgdUKfLyRF4K3Im9CjkadN
Logistic Map Equation: x
n+1
β
=rβ
x
n
β
β
(1βx
n
β
)
- x_n is the current state (a number between 0 and 1).
- x_{n+1} is the next value in the sequence.
- r is the growth rate parameter.
This block:
- Introduces the logistic map function
- Lets us generate sequences with different r values
- Plots them to visually understand convergence, cycles, and chaos
"""
import numpy as np
import matplotlib.pyplot as plt
import random
# Define the logistic map function
def logistic_map(x0: float, r: float, n: int = 100) -> np.ndarray:
"""
Generates a logistic map sequence.
Args:
x0 (float): Initial value (between 0 and 1).
r (float): Growth rate parameter (between 0 and 4).
n (int): Number of time steps.
Returns:
np.ndarray: Sequence of logistic map values.
"""
seq = np.zeros(n)
seq[0] = x0
for i in range(1, n):
seq[i] = r * seq[i - 1] * (1 - seq[i - 1])
return seq
# Plot logistic map sequences for different r values
def plot_logistic_map_examples(x0: float = 0.51, n: int = 100):
"""
Plots logistic map sequences for several r values to visualize behavior.
Args:
x0 (float): Initial value.
n (int): Number of iterations.
"""
r_values = [2.5, 3.2, 3.5, 3.9, 4.0]
plt.figure(figsize=(12, 8))
for i, r in enumerate(r_values, 1):
x0_safe = random.uniform(0.11, 0.89)
seq = logistic_map(x0, r, n)
plt.subplot(3, 2, i)
plt.plot(seq, label=f"r = {r}")
plt.title(f"Logistic Map (r = {r})")
plt.xlabel("Time Step")
plt.ylabel("x")
plt.grid(True)
plt.legend()
plt.tight_layout()
plt.show()
# π Run the plot function to see different behaviors
plot_logistic_map_examples()
"""- Low r (e.g., 2.5) = stable
- Mid r (e.g., 3.3) = periodic
- High r (e.g., 3.8 β 4.0) = chaotic
Generate synthetic sequences using random r values
Label each sequence as:
- 0 = stable (low r)
- 1 = periodic (mid r)
- 2 = chaotic (high r)
Create a full dataset we can later feed into a classifier
"""
import random
from typing import Tuple, List
# Label assignment based on r value
def label_from_r(r: float) -> int:
"""
Assigns a regime label based on the value of r.
Args:
r (float): Growth rate.
Returns:
int: Label (0 = stable, 1 = periodic, 2 = chaotic)
"""
if r < 3.0:
return 0 # Stable regime
elif 3.0 <= r < 3.57:
return 1 # Periodic regime
else:
return 2 # Chaotic regime
# Create one labeled sequence
def generate_labeled_sequence(n: int = 100) -> Tuple[np.ndarray, int]:
"""
Generates a single logistic map sequence and its regime label.
Args:
n (int): Sequence length.
Returns:
Tuple: (sequence, label)
"""
r = round(random.uniform(2.5, 4.0), 4)
x0 = random.uniform(0.1, 0.9)
sequence = logistic_map(x0, r, n)
label = label_from_r(r)
return sequence, label
# Generate a full dataset
def generate_dataset(num_samples: int = 1000, n: int = 100) -> Tuple[np.ndarray, np.ndarray]:
"""
Generates a dataset of logistic sequences with regime labels.
Args:
num_samples (int): Number of sequences to generate.
n (int): Length of each sequence.
Returns:
Tuple[np.ndarray, np.ndarray]: X (sequences), y (labels)
"""
X, y = [], []
for _ in range(num_samples):
sequence, label = generate_labeled_sequence(n)
X.append(sequence)
y.append(label)
return np.array(X), np.array(y)
# Example: Generate small dataset and view label counts
X, y = generate_dataset(num_samples=500, n=100)
# Check class distribution
import collections
print("Label distribution:", collections.Counter(y))
"""Used controlled r ranges to simulate different market regimes
Created 500 synthetic sequences (X) and regime labels (y)
Now we can visualize, split, and train on this dataset
Visualize:
- Randomly samples from X, y
- Plots sequences grouped by class (0 = stable, 1 = periodic, 2 = chaotic)
Helps us verify that the labels match the visual behavior
"""
import matplotlib.pyplot as plt
import numpy as np
# Helper: Plot N random sequences for a given class
def plot_class_samples(X: np.ndarray, y: np.ndarray, target_label: int, n_samples: int = 5):
"""
Plots sample sequences from a specified class.
Args:
X (np.ndarray): Dataset of sequences.
y (np.ndarray): Labels (0=stable, 1=periodic, 2=chaotic).
target_label (int): Class to visualize.
n_samples (int): Number of sequences to plot.
"""
indices = np.where(y == target_label)[0]
chosen = np.random.choice(indices, n_samples, replace=False)
plt.figure(figsize=(12, 6))
for i, idx in enumerate(chosen):
plt.plot(X[idx], label=f"Sample {i+1}")
regime_name = ["Stable", "Periodic", "Chaotic"][target_label]
plt.title(f"{regime_name} Regime Samples (Label = {target_label})")
plt.xlabel("Time Step")
plt.ylabel("x")
plt.grid(True)
plt.legend()
plt.show()
# View class 0 (stable)
plot_class_samples(X, y, target_label=0)
# View class 1 (periodic)
plot_class_samples(X, y, target_label=1)
# View class 2 (chaotic)
plot_class_samples(X, y, target_label=2)
"""Stable: Sequences that flatten out
Periodic: Repeating waveforms (2, 4, 8 points)
Chaotic: No repeating pattern, jittery
Each of these sequences looks completely different β even though they're all generated by the same equation.
No fixed pattern. No periodic rhythm. Just deterministic unpredictability.
But it's not random β it's chaotic: sensitive to initial conditions, governed by internal structure (nonlinear dynamics).
Split X, y into training and testing sets
Normalize (optional, but improves convergence)
Convert to PyTorch tensors
Create DataLoaders for training
"""
import torch
from torch.utils.data import TensorDataset, DataLoader
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
# Step 1: Split the dataset
X_train, X_test, y_train, y_test = train_test_split(
X, y, test_size=0.2, stratify=y, random_state=42
)
# Step 2: Normalize sequences (standardization: mean=0, std=1)
scaler = StandardScaler()
X_train_scaled = scaler.fit_transform(X_train) # Fit only on train
X_test_scaled = scaler.transform(X_test)
# Step 3: Convert to PyTorch tensors
X_train_tensor = torch.tensor(X_train_scaled, dtype=torch.float32)
y_train_tensor = torch.tensor(y_train, dtype=torch.long)
X_test_tensor = torch.tensor(X_test_scaled, dtype=torch.float32)
y_test_tensor = torch.tensor(y_test, dtype=torch.long)
# Step 4: Create TensorDatasets and DataLoaders
batch_size = 64
train_dataset = TensorDataset(X_train_tensor, y_train_tensor)
test_dataset = TensorDataset(X_test_tensor, y_test_tensor)
train_loader = DataLoader(train_dataset, batch_size=batch_size, shuffle=True)
test_loader = DataLoader(test_dataset, batch_size=batch_size)
"""This CNN will:
- Take a 1D time series (length 100)
- Apply temporal convolutions to learn patterns
- Use global pooling to summarize features
- Output one of 3 regime classes
"""
import torch.nn as nn
import torch.nn.functional as F
# 1D CNN model for sequence classification
class ChaosCNN(nn.Module):
def __init__(self, input_length=100, num_classes=3):
super(ChaosCNN, self).__init__()
# Feature extractors
self.conv1 = nn.Conv1d(in_channels=1, out_channels=32, kernel_size=5, padding=2)
self.bn1 = nn.BatchNorm1d(32)
self.conv2 = nn.Conv1d(in_channels=32, out_channels=64, kernel_size=5, padding=2)
self.bn2 = nn.BatchNorm1d(64)
# Global average pooling
self.global_pool = nn.AdaptiveAvgPool1d(1) # Outputs shape: (batch_size, channels, 1)
# Final classifier
self.fc = nn.Linear(64, num_classes)
def forward(self, x):
# x shape: (batch_size, sequence_length)
x = x.unsqueeze(1) # Add channel dim (batch_size, 1, sequence_length)
x = F.relu(self.bn1(self.conv1(x))) # (batch_size, 32, seq_len)
x = F.relu(self.bn2(self.conv2(x))) # (batch_size, 64, seq_len)
x = self.global_pool(x).squeeze(2) # (batch_size, 64)
out = self.fc(x) # (batch_size, num_classes)
return out
"""Conv1d: Extracts local patterns across the time dimension
BatchNorm1d: Stabilizes training and speeds up convergence
AdaptiveAvgPool1d: Summarizes the sequence into global stats
Linear: Final decision layer for 3-class classification
"""
device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
model = ChaosCNN().to(device)
# Define loss and optimizer
criterion = nn.CrossEntropyLoss()
optimizer = torch.optim.Adam(model.parameters(), lr=0.001)
from sklearn.metrics import accuracy_score, classification_report, confusion_matrix
import seaborn as sns
import matplotlib.pyplot as plt
# Training function
def train_model(model, train_loader, test_loader, criterion, optimizer, device, epochs=15):
train_losses, test_accuracies = [], []
for epoch in range(epochs):
model.train()
running_loss = 0.0
for X_batch, y_batch in train_loader:
X_batch, y_batch = X_batch.to(device), y_batch.to(device)
optimizer.zero_grad()
outputs = model(X_batch)
loss = criterion(outputs, y_batch)
loss.backward()
optimizer.step()
running_loss += loss.item() * X_batch.size(0)
avg_loss = running_loss / len(train_loader.dataset)
train_losses.append(avg_loss)
# Evaluation after each epoch
model.eval()
all_preds, all_labels = [], []
with torch.no_grad():
for X_batch, y_batch in test_loader:
X_batch = X_batch.to(device)
outputs = model(X_batch)
preds = outputs.argmax(dim=1).cpu().numpy()
all_preds.extend(preds)
all_labels.extend(y_batch.numpy())
acc = accuracy_score(all_labels, all_preds)
test_accuracies.append(acc)
print(f"Epoch {epoch+1}/{epochs} - Loss: {avg_loss:.4f} - Test Accuracy: {acc:.4f}")
return train_losses, test_accuracies
# Train the model
train_losses, test_accuracies = train_model(
model, train_loader, test_loader, criterion, optimizer, device, epochs=15
)
plt.figure(figsize=(12, 4))
plt.subplot(1, 2, 1)
plt.plot(train_losses, label="Train Loss")
plt.xlabel("Epoch")
plt.ylabel("Loss")
plt.title("Training Loss Over Time")
plt.grid(True)
plt.subplot(1, 2, 2)
plt.plot(test_accuracies, label="Test Accuracy", color='green')
plt.xlabel("Epoch")
plt.ylabel("Accuracy")
plt.title("Test Accuracy Over Time")
plt.grid(True)
plt.tight_layout()
plt.show()
# Final performance evaluation
model.eval()
y_true, y_pred = [], []
with torch.no_grad():
for X_batch, y_batch in test_loader:
X_batch = X_batch.to(device)
outputs = model(X_batch)
preds = outputs.argmax(dim=1).cpu().numpy()
y_pred.extend(preds)
y_true.extend(y_batch.numpy())
# Confusion matrix
cm = confusion_matrix(y_true, y_pred)
labels = ["Stable", "Periodic", "Chaotic"]
plt.figure(figsize=(6, 5))
sns.heatmap(cm, annot=True, fmt="d", cmap="Blues", xticklabels=labels, yticklabels=labels)
plt.title("Confusion Matrix")
plt.xlabel("Predicted")
plt.ylabel("Actual")
plt.show()
# Classification report
print(classification_report(y_true, y_pred, target_names=labels))
"""Input an r value (between 2.5 and 4.0)
Generate a logistic map sequence
Feed it to your trained model
Predict the regime
Plot the sequence and overlay the prediction
"""
# Label map for decoding
label_map = {0: "Stable", 1: "Periodic", 2: "Chaotic"}
def predict_regime(r_value: float, model, scaler, device, sequence_length=100):
"""
Generates a logistic sequence for a given r, feeds to model, and predicts regime.
"""
assert 2.5 <= r_value <= 4.0, "r must be between 2.5 and 4.0"
# Generate sequence
x0 = np.random.uniform(0.1, 0.9)
sequence = logistic_map(x0, r_value, sequence_length).reshape(1, -1)
# Standardize using training scaler
sequence_scaled = scaler.transform(sequence)
# Convert to tensor
sequence_tensor = torch.tensor(sequence_scaled, dtype=torch.float32).to(device)
# Model inference
model.eval()
with torch.no_grad():
output = model(sequence_tensor)
pred_class = torch.argmax(output, dim=1).item()
# Plot
plt.figure(figsize=(10, 4))
plt.plot(sequence.flatten(), label=f"r = {r_value}")
plt.title(f"Predicted Regime: {label_map[pred_class]} (Class {pred_class})")
plt.xlabel("Time Step")
plt.ylabel("x")
plt.grid(True)
plt.legend()
plt.show()
return label_map[pred_class]
predict_regime(2.6, model, scaler, device)
predict_regime(3.3, model, scaler, device)
predict_regime(3.95, model, scaler, device)
import gradio as gr
# Prediction function for Gradio
def classify_sequence(r_value):
x0 = np.random.uniform(0.1, 0.9)
sequence = logistic_map(x0, r_value, 100).reshape(1, -1)
sequence_scaled = scaler.transform(sequence)
sequence_tensor = torch.tensor(sequence_scaled, dtype=torch.float32).to(device)
model.eval()
with torch.no_grad():
output = model(sequence_tensor)
pred_class = torch.argmax(output, dim=1).item()
# Plot the sequence
fig, ax = plt.subplots(figsize=(6, 3))
ax.plot(sequence.flatten())
ax.set_title(f"Logistic Map Sequence (r = {r_value})")
ax.set_xlabel("Time Step")
ax.set_ylabel("x")
ax.grid(True)
return fig, label_map[pred_class]
# Gradio UI
interface = gr.Interface(
fn=classify_sequence,
inputs=gr.Slider(2.5, 4.0, step=0.01, label="r (growth parameter)"),
outputs=[
gr.Plot(label="Sequence Plot"),
gr.Label(label="Predicted Regime")
],
title="π Chaos Classifier: Logistic Map Regime Detector",
description="Move the slider to choose an r-value and visualize the predicted regime: Stable, Periodic, or Chaotic."
)
# Launch locally or in HF Space
interface.launch(share=True) |