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"""
Calculation Handler Component
This module provides mathematical calculation capabilities for the GAIA agent,
handling numeric questions, expressions, and table-based calculations.
"""
import re
import logging
import math
import operator
from typing import Dict, Any, List, Optional, Union, Tuple
import traceback
import numpy as np
from collections import defaultdict
logger = logging.getLogger("gaia_agent.components.calculation_handler")
class CalculationHandler:
"""
Handles mathematical calculations, expression parsing, and numeric operations.
Provides capabilities for answering numerical questions.
"""
def __init__(self):
"""Initialize the calculation handler with supported operations."""
# Map operators to their functions
self.binary_ops = {
'+': operator.add,
'-': operator.sub,
'*': operator.mul,
'/': operator.truediv,
'**': operator.pow,
'^': operator.pow,
'%': operator.mod,
'//': operator.floordiv
}
# Functions that can be called in expressions
self.math_functions = {
'sqrt': math.sqrt,
'sin': math.sin,
'cos': math.cos,
'tan': math.tan,
'abs': abs,
'log': math.log,
'log10': math.log10,
'exp': math.exp,
'ceil': math.ceil,
'floor': math.floor,
'round': round,
'sum': sum,
'mean': lambda x: sum(x) / len(x) if x else 0,
'median': lambda x: sorted(x)[len(x) // 2] if x else 0,
'min': min,
'max': max
}
logger.info("CalculationHandler initialized")
def extract_expression(self, text: str) -> Optional[str]:
"""
Extract mathematical expressions from text input.
Args:
text: Input text containing potential mathematical expressions
Returns:
Extracted mathematical expression or None if not found
"""
# Try to extract expressions in various formats
patterns = [
r'calculate\s+([\d\+\-\*\/\(\)\^\.\s]+)',
r'compute\s+([\d\+\-\*\/\(\)\^\.\s]+)',
r'evaluate\s+([\d\+\-\*\/\(\)\^\.\s]+)',
r'what is\s+([\d\+\-\*\/\(\)\^\.\s]+)',
r'(\d+[\d\+\-\*\/\(\)\^\.\s]+\d+)'
]
for pattern in patterns:
match = re.search(pattern, text, re.IGNORECASE)
if match:
return match.group(1).strip()
# Try to find equations
equation_match = re.search(r'([\d\+\-\*\/\(\)\^\.\s]+\=[\d\+\-\*\/\(\)\^\.\s]+)', text)
if equation_match:
return equation_match.group(1).strip()
return None
def parse_expression(self, expression: str) -> float:
"""
Parse and evaluate a mathematical expression.
Args:
expression: Mathematical expression as a string
Returns:
Calculated result
Raises:
ValueError: If expression parsing fails
"""
try:
# Improved and more secure parser
# First, normalize and sanitize the expression
expression = self._normalize_expression(expression)
# Handle special functions
for func_name, func in self.math_functions.items():
pattern = fr'{func_name}\(([^)]+)\)'
for match in re.finditer(pattern, expression):
args_str = match.group(1)
# Recursively parse arguments
if ',' in args_str:
args = [self.parse_expression(arg.strip()) for arg in args_str.split(',')]
result = func(args)
else:
arg = self.parse_expression(args_str.strip())
result = func(arg)
expression = expression.replace(match.group(0), str(result))
# For security, parse and evaluate the expression manually
# rather than using eval() directly
return self._recursive_parse(expression)
except Exception as e:
logger.error(f"Error parsing expression '{expression}': {str(e)}")
raise ValueError(f"Could not parse mathematical expression: {str(e)}")
def _normalize_expression(self, expression: str) -> str:
"""
Normalize a mathematical expression by handling different formats and notations.
Args:
expression: The raw expression string
Returns:
Normalized expression string
"""
# Remove whitespace
expression = expression.strip()
# Replace ^ with ** for exponentiation
expression = expression.replace('^', '**')
# Convert × to * and ÷ to /
expression = expression.replace('×', '*').replace('÷', '/')
# Handle implied multiplication (e.g., 2(3+4) → 2*(3+4))
expression = re.sub(r'(\d+)(\()', r'\1*\2', expression)
# Handle percentage expressions
expression = re.sub(r'(\d+)%', r'(\1/100)', expression)
# Replace common mathematical constants
expression = expression.replace('pi', str(math.pi))
expression = expression.replace('e', str(math.e))
return expression
def _recursive_parse(self, expression: str) -> float:
"""
Recursively parse and evaluate an expression using operator precedence.
Args:
expression: The normalized expression string
Returns:
Evaluated result
Raises:
ValueError: If parsing fails
"""
# Remove all whitespace
expression = re.sub(r'\s', '', expression)
# Handle parentheses first (highest precedence)
paren_pattern = r'\(([^()]+)\)'
while '(' in expression:
match = re.search(paren_pattern, expression)
if not match:
raise ValueError(f"Mismatched parentheses in expression: {expression}")
# Recursively evaluate the parenthesized sub-expression
sub_expr = match.group(1)
sub_result = self._recursive_parse(sub_expr)
# Replace the entire parenthesized expression with its result
expression = expression.replace(f"({sub_expr})", str(sub_result))
# Handle addition and subtraction (lowest precedence)
terms = self._split_by_operators(expression, ['+', '-'])
if len(terms) > 1:
# Parse the first term
result = self._recursive_parse(terms[0])
# Process each operator and subsequent term
i = 1
while i < len(terms):
op = terms[i]
next_term = terms[i+1]
# Perform the operation
if op == '+':
result += self._recursive_parse(next_term)
elif op == '-':
result -= self._recursive_parse(next_term)
i += 2
return result
# Handle multiplication and division (medium precedence)
factors = self._split_by_operators(expression, ['*', '/', '**', '//'])
if len(factors) > 1:
# Parse the first factor
result = self._recursive_parse(factors[0])
# Process each operator and subsequent factor
i = 1
while i < len(factors):
op = factors[i]
next_factor = factors[i+1]
# Perform the operation
if op == '*':
result *= self._recursive_parse(next_factor)
elif op == '/':
divisor = self._recursive_parse(next_factor)
if divisor == 0:
raise ValueError("Division by zero")
result /= divisor
elif op == '**':
result = pow(result, self._recursive_parse(next_factor))
elif op == '//':
divisor = self._recursive_parse(next_factor)
if divisor == 0:
raise ValueError("Division by zero")
result //= divisor
i += 2
return result
# Base case: just a number
try:
return float(expression)
except ValueError:
# If it's not a simple number, check if it's a constant
safe_constants = {
'pi': math.pi,
'e': math.e
}
if expression in safe_constants:
return safe_constants[expression]
raise ValueError(f"Cannot parse expression part: {expression}")
def _split_by_operators(self, expression: str, operators: List[str]) -> List[str]:
"""
Split an expression by specified operators, preserving their positions.
Args:
expression: Expression string to split
operators: List of operators to split by
Returns:
List alternating between terms and operators
"""
if not expression:
return []
# Combine operators into a regex pattern, escaping special chars
op_pattern = '|'.join(re.escape(op) for op in sorted(operators, key=len, reverse=True))
# Split the expression, keeping the operators
parts = re.split(f'({op_pattern})', expression)
# Filter out empty parts
return [p for p in parts if p]
def extract_numbers(self, text: str) -> List[float]:
"""
Extract all numbers from a text string.
Args:
text: Text to extract numbers from
Returns:
List of extracted numbers
"""
# Extract numbers (including decimals and negative numbers)
number_pattern = r'-?\d+(?:\.\d+)?'
return [float(match) for match in re.findall(number_pattern, text)]
def check_commutative_property(self, operation: str, values: List[float]) -> bool:
"""
Check if the given operation is commutative for the provided values.
Args:
operation: Operation to check ('+', '*', etc.)
values: List of numeric values to test
Returns:
True if commutative, False otherwise
"""
if len(values) < 2:
return True
if operation not in self.binary_ops:
return False
op_func = self.binary_ops[operation]
# Test commutativity: a op b == b op a
for i in range(len(values)):
for j in range(i + 1, len(values)):
a, b = values[i], values[j]
if abs(op_func(a, b) - op_func(b, a)) > 1e-10:
return False
return True
def create_frequency_table(self, data: List[Any]) -> Dict[Any, int]:
"""
Create a frequency table from a list of data.
Args:
data: List of values
Returns:
Dictionary mapping values to their frequencies
"""
freq_table = defaultdict(int)
for item in data:
freq_table[item] += 1
return dict(freq_table)
def parse_table_data(self, table_text: str) -> Tuple[List[str], List[List[Any]]]:
"""
Parse tabular data from text representation.
Args:
table_text: Text containing table data
Returns:
Tuple of (column_headers, rows)
"""
lines = table_text.strip().split('\n')
# Extract headers (first line)
if '|' in lines[0]:
# Markdown table format
headers = [h.strip() for h in lines[0].split('|')]
# Remove empty entries at start/end from the pipe chars
headers = [h for h in headers if h]
# Skip separator line if present
start_idx = 1
if len(lines) > 1 and all(c == '-' or c == '|' or c == ' ' for c in lines[1]):
start_idx = 2
# Extract rows
rows = []
for i in range(start_idx, len(lines)):
if '|' in lines[i]:
row_values = [cell.strip() for cell in lines[i].split('|')]
# Remove empty entries at start/end
row_values = [cell for cell in row_values if cell != '']
# Convert numeric values
converted_values = []
for val in row_values:
try:
# Try to convert to number if possible
if '.' in val:
converted_values.append(float(val))
else:
converted_values.append(int(val))
except ValueError:
converted_values.append(val)
rows.append(converted_values)
else:
# CSV or space-delimited format
delimiter = ',' if ',' in lines[0] else None
headers = [h.strip() for h in lines[0].split(delimiter)]
# Extract rows
rows = []
for i in range(1, len(lines)):
row_values = [cell.strip() for cell in lines[i].split(delimiter)]
# Convert numeric values
converted_values = []
for val in row_values:
try:
# Try to convert to number if possible
if '.' in val:
converted_values.append(float(val))
else:
converted_values.append(int(val))
except ValueError:
converted_values.append(val)
rows.append(converted_values)
return headers, rows
def perform_set_operation(self, table_data: Tuple[List[str], List[List[Any]]], operation: str) -> Any:
"""
Perform set operations on table data.
Args:
table_data: Table data as (headers, rows)
operation: Operation to perform (union, intersection, etc.)
Returns:
Result of the operation
"""
headers, rows = table_data
# Extract columns as sets
columns = {}
for i, header in enumerate(headers):
if i < len(rows[0]): # Ensure column index is valid
column_data = [row[i] for row in rows if i < len(row)]
columns[header] = set(column_data)
if operation == "union":
# Union of all sets
result = set()
for column_set in columns.values():
result = result.union(column_set)
return result
elif operation == "intersection":
# Intersection of all sets
sets = list(columns.values())
if not sets:
return set()
result = sets[0].copy()
for s in sets[1:]:
result = result.intersection(s)
return result
elif operation == "difference":
# Difference between first set and all others
sets = list(columns.values())
if not sets:
return set()
result = sets[0].copy()
for s in sets[1:]:
result = result.difference(s)
return result
elif operation == "symmetric_difference":
# Symmetric difference (elements in either set but not both)
sets = list(columns.values())
if not sets:
return set()
result = sets[0].copy()
for s in sets[1:]:
result = result.symmetric_difference(s)
return result
raise ValueError(f"Unsupported set operation: {operation}")
def analyze_question(self, question: str) -> Dict[str, Any]:
"""
Analyze a question to determine if it requires calculation.
Args:
question: The question to analyze
Returns:
Dict containing analysis results, including:
- requires_calculation: Whether question requires calculation
- calculation_type: Type of calculation needed (expression, numeric, table)
- expression: Extracted expression if found
- answer: Calculated answer if possible
- confidence: Confidence in the answer
"""
result = {
"question": question,
"requires_calculation": False,
"calculation_type": None,
"expression": None,
"numbers": [],
"answer": None,
"confidence": 0.0
}
# Check for mathematical expressions
expression = self.extract_expression(question)
if expression:
result["requires_calculation"] = True
result["calculation_type"] = "expression"
result["expression"] = expression
try:
calculated_result = self.parse_expression(expression)
formatted_result = f"{calculated_result:.4f}".rstrip('0').rstrip('.') if '.' in f"{calculated_result}" else f"{calculated_result}"
result["answer"] = formatted_result
result["confidence"] = 0.95
except ValueError as e:
logger.warning(f"Failed to calculate expression: {str(e)}")
result["answer"] = f"I couldn't calculate that expression: {str(e)}"
result["confidence"] = 0.0
return result
# Check for commutative property questions
if "commutative" in question.lower():
result["requires_calculation"] = True
result["calculation_type"] = "property_check"
# Determine the operation being asked about
if "addition" in question.lower() or "+" in question:
operation = "+"
elif "multiplication" in question.lower() or "*" in question or "×" in question:
operation = "*"
elif "subtraction" in question.lower() or "-" in question:
operation = "-"
elif "division" in question.lower() or "/" in question or "÷" in question:
operation = "/"
else:
operation = None
# Extract numbers if present
numbers = self.extract_numbers(question)
result["numbers"] = numbers
if operation and numbers:
is_commutative = self.check_commutative_property(operation, numbers)
result["answer"] = "Yes" if is_commutative else "No"
result["confidence"] = 0.9
result["explanation"] = f"Testing commutativity of {operation} with values {', '.join(str(n) for n in numbers)}: {'commutative' if is_commutative else 'not commutative'}"
elif operation:
# If operation is known but no specific numbers provided
is_commutative = operation in ["+", "*"] # Only + and * are commutative
result["answer"] = "Yes" if is_commutative else "No"
result["confidence"] = 0.85
result["explanation"] = f"The {'addition' if operation == '+' else 'multiplication' if operation == '*' else 'subtraction' if operation == '-' else 'division'} operation is {'' if is_commutative else 'not '}commutative."
return result
# Check for numeric questions (e.g., sum, average, etc.)
numeric_indicators = [
"sum", "add", "total", "average", "mean", "median",
"minimum", "maximum", "min", "max", "count", "how many"
]
if any(indicator in question.lower() for indicator in numeric_indicators):
result["requires_calculation"] = True
# Extract numbers if present
numbers = self.extract_numbers(question)
result["numbers"] = numbers
if numbers:
result["calculation_type"] = "numeric"
if "sum" in question.lower() or "add" in question.lower() or "total" in question.lower():
result["answer"] = str(sum(numbers))
result["confidence"] = 0.9
elif "average" in question.lower() or "mean" in question.lower():
result["answer"] = str(sum(numbers) / len(numbers))
result["confidence"] = 0.9
elif "median" in question.lower():
sorted_nums = sorted(numbers)
mid = len(sorted_nums) // 2
if len(sorted_nums) % 2 == 0:
result["answer"] = str((sorted_nums[mid-1] + sorted_nums[mid]) / 2)
else:
result["answer"] = str(sorted_nums[mid])
result["confidence"] = 0.9
elif "min" in question.lower() or "minimum" in question.lower():
result["answer"] = str(min(numbers))
result["confidence"] = 0.9
elif "max" in question.lower() or "maximum" in question.lower():
result["answer"] = str(max(numbers))
result["confidence"] = 0.9
elif "count" in question.lower() or "how many" in question.lower():
result["answer"] = str(len(numbers))
result["confidence"] = 0.9
return result
# If no calculation pattern detected
return result
def process_table_calculation(self, question: str, table_data: str) -> Dict[str, Any]:
"""
Process calculations on tabular data.
Args:
question: Question about the table
table_data: String representation of the table
Returns:
Dict containing analysis results
"""
result = {
"question": question,
"requires_calculation": True,
"calculation_type": "table",
"answer": None,
"confidence": 0.0,
"explanation": None,
"operations_performed": []
}
try:
parsed_table = self.parse_table_data(table_data)
headers, rows = parsed_table
# Extract numeric columns
numeric_columns = {}
for i, header in enumerate(headers):
if i < len(rows[0]): # Ensure column index is valid
column_data = [row[i] for row in rows if i < len(row)]
if all(isinstance(val, (int, float)) for val in column_data):
numeric_columns[header] = column_data
# Determine what calculation to perform based on the question
question_lower = question.lower()
# Find which column is being asked about
target_column = None
for header in headers:
if header.lower() in question_lower:
target_column = header
break
if "sum" in question_lower or "total" in question_lower:
if target_column and target_column in numeric_columns:
result["answer"] = str(sum(numeric_columns[target_column]))
result["confidence"] = 0.9
else:
# Sum of all numeric values
all_nums = [val for col in numeric_columns.values() for val in col]
result["answer"] = str(sum(all_nums))
result["confidence"] = 0.7
elif "average" in question_lower or "mean" in question_lower:
if target_column and target_column in numeric_columns:
values = numeric_columns[target_column]
avg_value = sum(values) / len(values)
result["answer"] = f"{avg_value:.2f}"
result["confidence"] = 0.9
result["explanation"] = f"Calculated the average of {len(values)} values in column '{target_column}'"
result["operations_performed"].append({"operation": "average", "column": target_column, "result": avg_value})
else:
# Handle case where no target column is found or it's not numeric
pass
elif "commutative" in question_lower:
# Try to identify which operation to test
operation = None
if "add" in question_lower or "sum" in question_lower or "addition" in question_lower or "+" in question_lower:
operation = "+"
elif "multipl" in question_lower or "product" in question_lower or "*" in question_lower or "×" in question_lower:
operation = "*"
if operation and numeric_columns:
# Identify columns to test commutativity on
columns_to_test = []
# Check if specific columns are mentioned
for header in numeric_columns.keys():
if header.lower() in question_lower:
columns_to_test.append(header)
# If no specific columns found, use all numeric columns
if not columns_to_test and len(numeric_columns) >= 2:
columns_to_test = list(numeric_columns.keys())[:2] # Use first two columns
if len(columns_to_test) >= 2:
col1, col2 = columns_to_test[0], columns_to_test[1]
values1 = numeric_columns[col1]
values2 = numeric_columns[col2]
# Test commutativity
all_commutative = True
test_pairs = []
# Get operation function
op_func = self.binary_ops.get(operation)
# Only test on first 5 pairs for efficiency
max_tests = min(5, len(values1), len(values2))
for i in range(max_tests):
a, b = values1[i], values2[i]
result1 = op_func(a, b)
result2 = op_func(b, a)
is_equal = abs(result1 - result2) < 1e-10
test_pairs.append({
"a": a,
"b": b,
"a_op_b": result1,
"b_op_a": result2,
"equal": is_equal
})
if not is_equal:
all_commutative = False
result["answer"] = "Yes" if all_commutative else "No"
result["confidence"] = 0.95
result["explanation"] = f"Tested commutativity of {operation} between columns '{col1}' and '{col2}'"
result["operations_performed"].append({
"operation": "commutativity_check",
"columns": [col1, col2],
"test_operation": operation,
"result": all_commutative,
"test_pairs": test_pairs
})
else:
result["answer"] = "Cannot check commutativity without at least two numeric columns"
result["confidence"] = 0.7
else:
# Average of all numeric values
all_nums = [val for col in numeric_columns.values() for val in col]
result["answer"] = str(sum(all_nums) / len(all_nums))
result["confidence"] = 0.7
elif "maximum" in question_lower or "max" in question_lower:
if target_column and target_column in numeric_columns:
result["answer"] = str(max(numeric_columns[target_column]))
result["confidence"] = 0.9
else:
# Maximum of all numeric values
all_nums = [val for col in numeric_columns.values() for val in col]
result["answer"] = str(max(all_nums))
result["confidence"] = 0.7
elif "minimum" in question_lower or "min" in question_lower:
if target_column and target_column in numeric_columns:
result["answer"] = str(min(numeric_columns[target_column]))
result["confidence"] = 0.9
else:
# Minimum of all numeric values
all_nums = [val for col in numeric_columns.values() for val in col]
result["answer"] = str(min(all_nums))
result["confidence"] = 0.7
elif "count" in question_lower or "how many" in question_lower:
if "rows" in question_lower:
result["answer"] = str(len(rows))
result["confidence"] = 0.95
elif "columns" in question_lower:
result["answer"] = str(len(headers))
result["confidence"] = 0.95
elif target_column:
# Count values in the column
column_idx = headers.index(target_column)
column_values = [row[column_idx] for row in rows if column_idx < len(row)]
result["answer"] = str(len(column_values))
result["confidence"] = 0.9
elif "set" in question_lower or "union" in question_lower or "intersection" in question_lower:
# Determine set operation
if "union" in question_lower:
operation = "union"
elif "intersection" in question_lower or "common" in question_lower:
operation = "intersection"
elif "difference" in question_lower:
operation = "difference"
elif "symmetric" in question_lower and "difference" in question_lower:
operation = "symmetric_difference"
else:
operation = None
if operation:
set_result = self.perform_set_operation(parsed_table, operation)
result["answer"] = str(set_result)
result["confidence"] = 0.85
# If no specific calculation identified
if result["answer"] is None:
# Default to returning basic table statistics
result["answer"] = (f"Table has {len(headers)} columns and {len(rows)} rows. "
f"Columns: {', '.join(headers)}.")
result["confidence"] = 0.5
except Exception as e:
logger.error(f"Error processing table calculation: {str(e)}")
logger.debug(traceback.format_exc())
result["answer"] = f"Could not process table calculation: {str(e)}"
result["confidence"] = 0.0
return result |