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"""
Common test functions for optimizers.
Also see: https://en.wikipedia.org/wiki/Test_functions_for_optimization
"""
def rosenbrock(x, y):
"""
Rosenbrock function. Minimum: f(1, 1) = 0.
https://en.wikipedia.org/wiki/Rosenbrock_function
"""
return (1 - x) ** 2 + 100 * (y - x**2) ** 2
def rosenbrock_grad(x, y):
"""Gradient of Rosenbrock function."""
return (-400 * x * (-(x**2) + y) + 2 * x - 2, -200 * x**2 + 200 * y)
def ackley(x, y):
"""
Ackley function. Minimum: f(0, 0) = 0.
https://en.wikipedia.org/wiki/Ackley_function
"""
from math import sqrt, exp, cos, pi, e
term1 = -20 * exp(-0.2 * sqrt(0.5 * (x**2 + y**2)))
term2 = -exp(0.5 * (cos(2 * pi * x) + cos(2 * pi * y)))
return term1 + term2 + 20 + e
def beale(x, y):
"""
Beale function. Minimum: f(3, 0.5) = 0.
https://en.wikipedia.org/wiki/Test_functions_for_optimization
"""
term1 = 1.5 - x + x * y
term2 = 2.25 - x + x * y**2
term3 = 2.625 - x + x * y**3
return term1 * term1 + term2 * term2 + term3 * term3
def matyas(x, y):
"""
Matyas function. Minimum: f(0, 0) = 0.
https://en.wikipedia.org/wiki/Test_functions_for_optimization
"""
return 0.26 * (x**2 + y**2) - 0.48 * x * y
def sphere_np(x):
"""
Sphere function for variable number of arguments. Minimum: f(0, ..., 0) = 0.
https://en.wikipedia.org/wiki/Test_functions_for_optimization
"""
import numpy as np
return np.sum(x**2)
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