Jonathan Rampersad
34019a67b0
This commit introduces a major enhancement to the genetic algorithm's convergence logic and refactors key parts of the API for better clarity and usability.
- **feat(ga):** Re-implements the GA solver (CPU & CUDA) to use a more robust strategy based on Elitism, Crossover, and Mutation. This replaces the previous, less efficient model and is designed to significantly improve accuracy and convergence speed.
- **feat(api):** Updates `GA_Options` to expose the new GA strategy parameters:
- Renames `mutation_percentage` to `mutation_strength` for clarity.
- Adds `elite_ratio`, `crossover_ratio`, and `mutation_ratio`.
- Includes a `__post_init__` validator to ensure ratios are valid.
- **refactor(api):** Moves `quadratic_solve` from a standalone function to a method of the `Function` class (`f1.quadratic_solve()`). This provides a cleaner, more object-oriented API.
- **docs:** Updates the README, `GA_Options` doc page, and `quadratic_solve` doc page to reflect all API changes, new parameters, and updated usage examples.
- **chore:** Bumps version to 0.4.0.
688 lines
25 KiB
Python
688 lines
25 KiB
Python
import math
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import numpy as np
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from dataclasses import dataclass
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from typing import List, Optional, Union
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import warnings
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# Attempt to import CuPy for CUDA acceleration.
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# If CuPy is not installed, the CUDA functionality will not be available.
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try:
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import cupy
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_CUPY_AVAILABLE = True
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except ImportError:
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_CUPY_AVAILABLE = False
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# The CUDA kernels for the fitness function
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_FITNESS_KERNEL_FLOAT = """
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extern "C" __global__ void fitness_kernel(
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const double* coefficients,
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int num_coefficients,
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const double* x_vals,
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double* ranks,
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int size,
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double y_val)
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{
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int idx = threadIdx.x + blockIdx.x * blockDim.x;
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if (idx < size)
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{
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double ans = coefficients[0];
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for (int i = 1; i < num_coefficients; ++i)
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{
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ans = ans * x_vals[idx] + coefficients[i];
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}
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ans -= y_val;
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ranks[idx] = (ans == 0) ? 1.7976931348623157e+308 : fabs(1.0 / ans);
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}
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}
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"""
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@dataclass
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class GA_Options:
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"""
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Configuration options for the genetic algorithm used to find function roots.
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Attributes:
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min_range (float): The minimum value for the initial random solutions.
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Default: -100.0
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max_range (float): The maximum value for the initial random solutions.
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Default: 100.0
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num_of_generations (int): The number of iterations the algorithm will run.
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Default: 10
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sample_size (int): The number of top solutions to *return* at the end.
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Default: 1000
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data_size (int): The total number of solutions (population size)
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generated in each generation. Default: 100000
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mutation_strength (float): The percentage (e.g., 0.01 for 1%) by which
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a solution is mutated. Default: 0.01
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elite_ratio (float): The percentage (e.g., 0.05 for 5%) of the *best*
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solutions to carry over to the next generation
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unchanged (elitism). Default: 0.05
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crossover_ratio (float): The percentage (e.g., 0.45 for 45%) of the next
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generation to be created by "breeding" two
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solutions from the parent pool. Default: 0.45
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mutation_ratio (float): The percentage (e.g., 0.40 for 40%) of the next
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generation to be created by mutating solutions
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from the parent pool. Default: 0.40
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"""
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min_range: float = -100.0
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max_range: float = 100.0
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num_of_generations: int = 10
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sample_size: int = 1000
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data_size: int = 100000
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mutation_strength: float = 0.01
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elite_ratio: float = 0.05
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crossover_ratio: float = 0.45
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mutation_ratio: float = 0.40
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def __post_init__(self):
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"""Validates the GA options after initialization."""
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total_ratio = self.elite_ratio + self.crossover_ratio + self.mutation_ratio
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if total_ratio > 1.0:
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raise ValueError(
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f"The sum of elite_ratio, crossover_ratio, and mutation_ratio must be <= 1.0, but got {total_ratio}"
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)
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if any(r < 0 for r in [self.elite_ratio, self.crossover_ratio, self.mutation_ratio]):
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raise ValueError("GA ratios cannot be negative.")
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if self.data_size < self.sample_size:
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warnings.warn(
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f"data_size ({self.data_size}) is less than sample_size ({self.sample_size}). "
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"The number of returned solutions will be limited to data_size."
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)
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class Function:
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"""
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Represents an exponential function (polynomial) of the form:
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c_0*x^n + c_1*x^(n-1) + ... + c_n
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"""
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def __init__(self, largest_exponent: int):
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"""
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Initializes a function with its highest degree.
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Args:
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largest_exponent (int): The largest exponent (n) in the function.
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"""
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if not isinstance(largest_exponent, int) or largest_exponent < 0:
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raise ValueError("largest_exponent must be a non-negative integer.")
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self._largest_exponent = largest_exponent
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self.coefficients: Optional[np.ndarray] = None
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self._initialized = False
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def set_coeffs(self, coefficients: List[Union[int, float]]):
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"""
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Sets the coefficients of the polynomial.
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Args:
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coefficients (List[Union[int, float]]): A list of integer or float
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coefficients. The list size
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must be largest_exponent + 1.
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Raises:
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ValueError: If the input is invalid.
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"""
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expected_size = self._largest_exponent + 1
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if len(coefficients) != expected_size:
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raise ValueError(
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f"Function with exponent {self._largest_exponent} requires {expected_size} coefficients, "
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f"but {len(coefficients)} were given."
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)
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if coefficients[0] == 0 and self._largest_exponent > 0:
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raise ValueError("The first constant (for the largest exponent) cannot be 0.")
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# Check if any coefficient is a float
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is_float = any(isinstance(c, float) for c in coefficients)
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# Choose the dtype based on the input
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target_dtype = np.float64 if is_float else np.int64
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self.coefficients = np.array(coefficients, dtype=target_dtype)
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self._initialized = True
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def _check_initialized(self):
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"""Raises a RuntimeError if the function coefficients have not been set."""
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if not self._initialized:
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raise RuntimeError("Function is not fully initialized. Call .set_coeffs() first.")
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@property
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def largest_exponent(self) -> int:
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"""Returns the largest exponent of the function."""
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return self._largest_exponent
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@property
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def degree(self) -> int:
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"""Returns the largest exponent of the function."""
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return self._largest_exponent
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def solve_y(self, x_val: float) -> float:
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"""
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Solves for y given an x value. (i.e., evaluates the polynomial at x).
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Args:
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x_val (float): The x-value to evaluate.
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Returns:
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float: The resulting y-value.
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"""
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self._check_initialized()
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return np.polyval(self.coefficients, x_val)
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def differential(self) -> 'Function':
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"""
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Calculates the derivative of the function.
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Returns:
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Function: A new Function object representing the derivative.
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"""
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warnings.warn(
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"The 'differential' function has been renamed. Please use 'derivative' instead.",
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DeprecationWarning,
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stacklevel=2
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)
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self._check_initialized()
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if self._largest_exponent == 0:
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raise ValueError("Cannot differentiate a constant (Function of degree 0).")
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return self.derivative()
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def derivative(self) -> 'Function':
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"""
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Calculates the derivative of the function.
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Returns:
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Function: A new Function object representing the derivative.
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"""
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self._check_initialized()
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if self._largest_exponent == 0:
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raise ValueError("Cannot differentiate a constant (Function of degree 0).")
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derivative_coefficients = np.polyder(self.coefficients)
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diff_func = Function(self._largest_exponent - 1)
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diff_func.set_coeffs(derivative_coefficients.tolist())
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return diff_func
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def nth_derivative(self, n: int) -> 'Function':
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"""
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Calculates the nth derivative of the function.
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Args:
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n (int): The order of the derivative to calculate.
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Returns:
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Function: A new Function object representing the nth derivative.
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"""
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self._check_initialized()
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if not isinstance(n, int) or n < 1:
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raise ValueError("Derivative order 'n' must be a positive integer.")
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if n > self.largest_exponent:
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function = Function(0)
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function.set_coeffs([0])
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return function
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if n == 1:
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return self.derivative()
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function = self
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for _ in range(n):
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function = function.derivative()
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return function
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def get_real_roots(self, options: GA_Options = GA_Options(), use_cuda: bool = False) -> np.ndarray:
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"""
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Uses a genetic algorithm to find the approximate real roots of the function (where y=0).
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Args:
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options (GA_Options): Configuration for the genetic algorithm.
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use_cuda (bool): If True, attempts to use CUDA for acceleration.
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Returns:
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np.ndarray: An array of approximate root values.
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"""
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self._check_initialized()
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return self.solve_x(0.0, options, use_cuda)
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def solve_x(self, y_val: float, options: GA_Options = GA_Options(), use_cuda: bool = False) -> np.ndarray:
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"""
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Uses a genetic algorithm to find x-values for a given y-value.
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Args:
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y_val (float): The target y-value.
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options (GA_Options): Configuration for the genetic algorithm.
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use_cuda (bool): If True, attempts to use CUDA for acceleration.
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Returns:
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np.ndarray: An array of approximate x-values.
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"""
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self._check_initialized()
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if use_cuda and _CUPY_AVAILABLE:
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return self._solve_x_cuda(y_val, options)
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else:
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if use_cuda:
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warnings.warn(
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"use_cuda=True was specified, but CuPy is not installed. "
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"Falling back to NumPy (CPU). For GPU acceleration, "
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"install with 'pip install polysolve[cuda]'.",
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UserWarning
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)
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return self._solve_x_numpy(y_val, options)
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def _solve_x_numpy(self, y_val: float, options: GA_Options) -> np.ndarray:
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"""Genetic algorithm implementation using NumPy (CPU)."""
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elite_ratio = options.elite_ratio
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crossover_ratio = options.crossover_ratio
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mutation_ratio = options.mutation_ratio
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data_size = options.data_size
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elite_size = int(data_size * elite_ratio)
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crossover_size = int(data_size * crossover_ratio)
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mutation_size = int(data_size * mutation_ratio)
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random_size = data_size - elite_size - crossover_size - mutation_size
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# Create initial random solutions
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solutions = np.random.uniform(options.min_range, options.max_range, data_size)
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for _ in range(options.num_of_generations):
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# Calculate fitness for all solutions (vectorized)
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y_calculated = np.polyval(self.coefficients, solutions)
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error = y_calculated - y_val
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ranks = np.where(error == 0, np.finfo(float).max, np.abs(1.0 / error))
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# Sort solutions by fitness (descending)
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sorted_indices = np.argsort(-ranks)
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solutions = solutions[sorted_indices]
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# --- Create the next generation ---
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# 1. Elitism: Keep the best solutions as-is
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elite_solutions = solutions[:elite_size]
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# Define a "parent pool" of the top 50% of solutions to breed from
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parent_pool = solutions[:data_size // 2]
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# 2. Crossover: Breed two parents to create a child
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parent1_indices = np.random.randint(0, parent_pool.size, crossover_size)
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parent2_indices = np.random.randint(0, parent_pool.size, crossover_size)
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parents1 = parent_pool[parent1_indices]
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parents2 = parent_pool[parent2_indices]
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# Simple "average" crossover
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crossover_solutions = (parents1 + parents2) / 2.0
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# 3. Mutation: Apply your original mutation logic
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mutation_candidates = parent_pool[np.random.randint(0, parent_pool.size, mutation_size)]
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# Use mutation_strength (the new name)
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mutation_factors = np.random.uniform(
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1 - options.mutation_strength,
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1 + options.mutation_strength,
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mutation_size
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)
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mutated_solutions = mutation_candidates * mutation_factors
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# 4. New Randoms: Add new blood to prevent getting stuck
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random_solutions = np.random.uniform(options.min_range, options.max_range, random_size)
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# Assemble the new generation
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solutions = np.concatenate([
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elite_solutions,
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crossover_solutions,
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mutated_solutions,
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random_solutions
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])
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# --- Final Step: Return the best results ---
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# After all generations, do one last ranking to find the best solutions
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y_calculated = np.polyval(self.coefficients, solutions)
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error = y_calculated - y_val
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ranks = np.where(error == 0, np.finfo(float).max, np.abs(1.0 / error))
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sorted_indices = np.argsort(-ranks)
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# Get the top 'sample_size' solutions the user asked for
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best_solutions = solutions[sorted_indices][:options.sample_size]
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return np.sort(best_solutions)
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def _solve_x_cuda(self, y_val: float, options: GA_Options) -> np.ndarray:
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"""Genetic algorithm implementation using CuPy (GPU/CUDA)."""
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elite_ratio = options.elite_ratio
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crossover_ratio = options.crossover_ratio
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mutation_ratio = options.mutation_ratio
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data_size = options.data_size
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elite_size = int(data_size * elite_ratio)
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crossover_size = int(data_size * crossover_ratio)
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mutation_size = int(data_size * mutation_ratio)
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random_size = data_size - elite_size - crossover_size - mutation_size
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# ALWAYS cast coefficients to float64 for the kernel.
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fitness_gpu = cupy.RawKernel(_FITNESS_KERNEL_FLOAT, 'fitness_kernel')
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d_coefficients = cupy.array(self.coefficients, dtype=cupy.float64)
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# Create initial random solutions on the GPU
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d_solutions = cupy.random.uniform(
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options.min_range, options.max_range, options.data_size, dtype=cupy.float64
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)
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d_ranks = cupy.empty(options.data_size, dtype=cupy.float64)
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# Configure kernel launch parameters
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threads_per_block = 512
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blocks_per_grid = (options.data_size + threads_per_block - 1) // threads_per_block
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for i in range(options.num_of_generations):
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# Run the fitness kernel on the GPU
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fitness_gpu(
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(blocks_per_grid,), (threads_per_block,),
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(d_coefficients, d_coefficients.size, d_solutions, d_ranks, d_solutions.size, y_val)
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)
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# Sort solutions by rank on the GPU
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sorted_indices = cupy.argsort(-d_ranks)
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d_solutions = d_solutions[sorted_indices]
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# --- Create the next generation ---
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# 1. Elitism
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d_elite_solutions = d_solutions[:elite_size]
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# Define a "parent pool" of the top 50% of solutions to breed from
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d_parent_pool = d_solutions[:data_size // 2]
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parent_pool_size = d_parent_pool.size
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# 2. Crossover
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parent1_indices = cupy.random.randint(0, parent_pool_size, crossover_size)
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parent2_indices = cupy.random.randint(0, parent_pool_size, crossover_size)
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d_parents1 = d_parent_pool[parent1_indices]
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d_parents2 = d_parent_pool[parent2_indices]
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d_crossover_solutions = (d_parents1 + d_parents2) / 2.0
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# 3. Mutation
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mutation_indices = cupy.random.randint(0, parent_pool_size, mutation_size)
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d_mutation_candidates = d_parent_pool[mutation_indices]
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# Use mutation_strength (the new name)
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d_mutation_factors = cupy.random.uniform(
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1 - options.mutation_strength,
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1 + options.mutation_strength,
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mutation_size
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)
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d_mutated_solutions = d_mutation_candidates * d_mutation_factors
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# 4. New Randoms
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d_random_solutions = cupy.random.uniform(
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options.min_range, options.max_range, random_size, dtype=cupy.float64
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)
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# Assemble the new generation
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d_solutions = cupy.concatenate([
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d_elite_solutions,
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d_crossover_solutions,
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d_mutated_solutions,
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d_random_solutions
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])
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# --- Final Step: Return the best results ---
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# After all generations, do one last ranking to find the best solutions
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fitness_gpu(
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(blocks_per_grid,), (threads_per_block,),
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(d_coefficients, d_coefficients.size, d_solutions, d_ranks, d_solutions.size, y_val)
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)
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sorted_indices = cupy.argsort(-d_ranks)
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# Get the top 'sample_size' solutions
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d_best_solutions = d_solutions[sorted_indices][:options.sample_size]
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# Get the final sample, sort it, and copy back to CPU
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final_solutions_gpu = cupy.sort(d_best_solutions)
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return final_solutions_gpu.get()
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def __str__(self) -> str:
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"""Returns a human-readable string representation of the function."""
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self._check_initialized()
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parts = []
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for i, c in enumerate(self.coefficients):
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if c == 0:
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continue
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power = self._largest_exponent - i
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# Coefficient part
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coeff_val = c
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if c == int(c):
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coeff_val = int(c)
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if coeff_val == 1 and power != 0:
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coeff = ""
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elif coeff_val == -1 and power != 0:
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coeff = "-"
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else:
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coeff = str(coeff_val)
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# Variable part
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if power == 0:
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var = ""
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elif power == 1:
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var = "x"
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else:
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var = f"x^{power}"
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# Add sign for non-leading terms
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sign = ""
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if i > 0:
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sign = " + " if c > 0 else " - "
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coeff = str(abs(coeff_val))
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if abs(c) == 1 and power != 0:
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|
coeff = "" # Don't show 1 for non-constant terms
|
|
|
|
parts.append(f"{sign}{coeff}{var}")
|
|
|
|
# Join parts and clean up
|
|
result = "".join(parts)
|
|
if result.startswith(" + "):
|
|
result = result[3:]
|
|
return result if result else "0"
|
|
|
|
def __repr__(self) -> str:
|
|
return f"Function(str='{self}')"
|
|
|
|
def __add__(self, other: 'Function') -> 'Function':
|
|
"""Adds two Function objects."""
|
|
self._check_initialized()
|
|
other._check_initialized()
|
|
|
|
new_coefficients = np.polyadd(self.coefficients, other.coefficients)
|
|
|
|
result_func = Function(len(new_coefficients) - 1)
|
|
result_func.set_coeffs(new_coefficients.tolist())
|
|
return result_func
|
|
|
|
def __sub__(self, other: 'Function') -> 'Function':
|
|
"""Subtracts another Function object from this one."""
|
|
self._check_initialized()
|
|
other._check_initialized()
|
|
|
|
new_coefficients = np.polysub(self.coefficients, other.coefficients)
|
|
|
|
result_func = Function(len(new_coefficients) - 1)
|
|
result_func.set_coeffs(new_coefficients.tolist())
|
|
return result_func
|
|
|
|
def _multiply_by_scalar(self, scalar: Union[int, float]) -> 'Function':
|
|
"""Helper method to multiply the function by a scalar constant."""
|
|
self._check_initialized() # It's good practice to check here too
|
|
|
|
if scalar == 0:
|
|
result_func = Function(0)
|
|
result_func.set_coeffs([0])
|
|
return result_func
|
|
|
|
new_coefficients = self.coefficients * scalar
|
|
|
|
result_func = Function(self._largest_exponent)
|
|
result_func.set_coeffs(new_coefficients.tolist())
|
|
return result_func
|
|
|
|
def _multiply_by_function(self, other: 'Function') -> 'Function':
|
|
"""Helper method for polynomial multiplication (Function * Function)."""
|
|
self._check_initialized()
|
|
other._check_initialized()
|
|
|
|
# np.polymul performs convolution of coefficients to multiply polynomials
|
|
new_coefficients = np.polymul(self.coefficients, other.coefficients)
|
|
|
|
# The degree of the resulting polynomial is derived from the new coefficients
|
|
new_degree = len(new_coefficients) - 1
|
|
|
|
result_func = Function(new_degree)
|
|
result_func.set_coeffs(new_coefficients.tolist())
|
|
return result_func
|
|
|
|
def __mul__(self, other: Union['Function', int, float]) -> 'Function':
|
|
"""Multiplies the function by a scalar constant."""
|
|
if isinstance(other, (int, float)):
|
|
return self._multiply_by_scalar(other)
|
|
elif isinstance(other, self.__class__):
|
|
return self._multiply_by_function(other)
|
|
else:
|
|
return NotImplemented
|
|
|
|
def __rmul__(self, scalar: Union[int, float]) -> 'Function':
|
|
"""Handles scalar multiplication from the right (e.g., 3 * func)."""
|
|
|
|
return self.__mul__(scalar)
|
|
|
|
def __imul__(self, other: Union['Function', int, float]) -> 'Function':
|
|
"""Performs in-place multiplication by a scalar (func *= 3)."""
|
|
|
|
self._check_initialized()
|
|
|
|
if isinstance(other, (int, float)):
|
|
if other == 0:
|
|
self.coefficients = np.array([0], dtype=self.coefficients.dtype)
|
|
self._largest_exponent = 0
|
|
else:
|
|
self.coefficients *= other
|
|
|
|
elif isinstance(other, self.__class__):
|
|
other._check_initialized()
|
|
self.coefficients = np.polymul(self.coefficients, other.coefficients)
|
|
self._largest_exponent = len(self.coefficients) - 1
|
|
|
|
else:
|
|
return NotImplemented
|
|
|
|
return self
|
|
|
|
|
|
def quadratic_solve(self) -> Optional[List[float]]:
|
|
"""
|
|
Calculates the real roots of a quadratic function using the quadratic formula.
|
|
|
|
Args:
|
|
f (Function): A Function object of degree 2.
|
|
|
|
Returns:
|
|
Optional[List[float]]: A list containing the two real roots, or None if there are no real roots.
|
|
"""
|
|
self._check_initialized()
|
|
if self.largest_exponent != 2:
|
|
raise ValueError("Input function must be quadratic (degree 2) to use quadratic_solve.")
|
|
|
|
a, b, c = self.coefficients
|
|
|
|
discriminant = (b**2) - (4*a*c)
|
|
|
|
if discriminant < 0:
|
|
return None # No real roots
|
|
|
|
sqrt_discriminant = math.sqrt(discriminant)
|
|
root1 = (-b + sqrt_discriminant) / (2 * a)
|
|
root2 = (-b - sqrt_discriminant) / (2 * a)
|
|
|
|
return [root1, root2]
|
|
|
|
# Example Usage
|
|
if __name__ == '__main__':
|
|
print("--- Demonstrating Functionality ---")
|
|
|
|
# Create a quadratic function: 2x^2 - 3x - 5
|
|
f1 = Function(2)
|
|
f1.set_coeffs([2, -3, -5])
|
|
print(f"Function f1: {f1}")
|
|
|
|
# Solve for y
|
|
y = f1.solve_y(5)
|
|
print(f"Value of f1 at x=5 is: {y}") # Expected: 2*(25) - 3*(5) - 5 = 50 - 15 - 5 = 30
|
|
|
|
# Find the derivative: 4x - 3
|
|
df1 = f1.derivative()
|
|
print(f"Derivative of f1: {df1}")
|
|
|
|
# Find the second derivative: 4
|
|
ddf1 = f1.nth_derivative(2)
|
|
print(f"Second derivative of f1: {ddf1}")
|
|
|
|
# --- Root Finding ---
|
|
# 1. Analytical solution for quadratic
|
|
roots_analytic = quadratic_solve(f1)
|
|
print(f"Analytic roots of f1: {roots_analytic}") # Expected: -1, 2.5
|
|
|
|
# 2. Genetic algorithm solution
|
|
ga_opts = GA_Options(num_of_generations=20, data_size=50000, sample_size=10)
|
|
print("\nFinding roots with Genetic Algorithm (CPU)...")
|
|
roots_ga_cpu = f1.get_real_roots(ga_opts)
|
|
print(f"Approximate roots from GA (CPU): {roots_ga_cpu}")
|
|
print("(Note: GA provides approximations around the true roots)")
|
|
|
|
# 3. CUDA accelerated genetic algorithm
|
|
if _CUPY_AVAILABLE:
|
|
print("\nFinding roots with Genetic Algorithm (CUDA)...")
|
|
# Since this PC has an RTX 4060 Ti, we can use the CUDA version.
|
|
roots_ga_gpu = f1.get_real_roots(ga_opts, use_cuda=True)
|
|
print(f"Approximate roots from GA (GPU): {roots_ga_gpu}")
|
|
else:
|
|
print("\nSkipping CUDA example: CuPy library not found or no compatible GPU.")
|
|
|
|
# --- Function Arithmetic ---
|
|
print("\n--- Function Arithmetic ---")
|
|
f2 = Function(1)
|
|
f2.set_coeffs([1, 10]) # x + 10
|
|
print(f"Function f2: {f2}")
|
|
|
|
# Addition: (2x^2 - 3x - 5) + (x + 10) = 2x^2 - 2x + 5
|
|
f_add = f1 + f2
|
|
print(f"f1 + f2 = {f_add}")
|
|
|
|
# Subtraction: (2x^2 - 3x - 5) - (x + 10) = 2x^2 - 4x - 15
|
|
f_sub = f1 - f2
|
|
print(f"f1 - f2 = {f_sub}")
|
|
|
|
# Multiplication: (x + 10) * 3 = 3x + 30
|
|
f_mul = f2 * 3
|
|
print(f"f2 * 3 = {f_mul}")
|
|
|
|
# f3 represents 2x^2 + 3x + 1
|
|
f3 = Function(2)
|
|
f3.set_coeffs([2, 3, 1])
|
|
print(f"Function f3: {f3}")
|
|
|
|
# f4 represents 5x - 4
|
|
f4 = Function(1)
|
|
f4.set_coeffs([5, -4])
|
|
print(f"Function f4: {f4}")
|
|
|
|
# Multiply the two functions
|
|
product_func = f3 * f4
|
|
print(f"f3 * f4 = {product_func}")
|