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import numpy as np
# ------- BEGIN FUNCTIONS -------
# 2d Camel3
def testfunc_2d(x):
if len(x.shape) == 2:
N, n = x.shape
axis = 1
else:
n = len(x)
axis = 0
y = np.sum(x**2, axis=axis, keepdims=True)
return y
def camel3_2d(X):
try:
X.shape[1]
except:
X = np.array([X])
return (2*X[:, 0]**2 - 1.05*X[:, 0]**4 + (X[:, 0]**6)/6 + X[:, 0]*X[:, 1] + X[:, 1]**2).reshape(-1, 1)
# 2d Camel16
def camel16_2d(X):
try:
X.shape[1]
except:
X = np.array([X])
return (4*X[:, 0]**2 - 2.1*X[:, 0]**4 + (X[:, 0]**6)/3 + X[:, 0]*X[:, 1] - 4*X[:, 1]**2 + 4*X[:, 1]**4).reshape(-1, 1)
# 2d Treccani
def treccani_2d(X):
try:
X.shape[1]
except:
X = np.array([X])
return (X[:, 0]**4 + 4*X[:, 0]**3 + 4*X[:, 0]**2 + X[:, 1]**2).reshape(-1, 1)
# 2d Goldstein
def goldstein_2d(X):
try:
X.shape[1]
except:
X = np.array([X])
x1 = X[:, 0]
x2 = X[:, 1]
term1 = 1 + (x1 + x2 + 1)**2 * (19 - 14*x1 + 3*x1**2 - 14*x2 + 6*x1*x2 + 3*x2**2)
term2 = 30 + (2*x1 - 3*x2)**2 * (16 - 32*x1 + 12*x1**2 + 48*x2 - 36*x1*x2 + 27*x2**2)
return (term1 * term2).reshape(-1, 1)
# 2d Branin
def branin_2d(X):
try:
X.shape[1]
except:
X = np.array([X])
x1 = X[:, 0]
x2 = X[:, 1]
return ((x2 - (5.1 / (4 * np.pi**2)) * x1**2 + (5 / np.pi) * x1 - 6)**2 + (10 * (1 - (1 / (8 * np.pi))) * np.cos(x1)) + 10).reshape(-1, 1)
# 2d Rosenbrock
def rosenbrock_2d(X):
try:
X.shape[1]
except:
X = np.array([X])
return (0.5 * (X[:, 0]**2 - X[:, 1])**2 + (X[:, 0] - 1)**2).reshape(-1, 1)
# 2d Ackley
def ackley_2d(X):
try:
X.shape[1]
except:
X = np.array([X])
x1 = X[:, 0]
x2 = X[:, 1]
return (20 + np.exp(1) - 20 * np.exp(-0.2 * np.sqrt(0.5 * (x1**2 + x2**2))) - np.exp(0.5 * (np.cos(2 * np.pi * x1) + np.cos(2 * np.pi * x2)))).reshape(-1, 1)
# 10d Rosenbrock
def rosenbrock_10d(X):
try:
X.shape[1]
except:
X = np.array([X])
return (np.sum(100 * (X[:, :-1]**2 - X[:, 1:])**2 + (X[:, :-1] - 1)**2, axis=1)).reshape(-1, 1)
# 10d Griewank
def griewank_10d(X):
try:
X.shape[1]
except:
X = np.array([X])
d = X.shape[1]
sum_sq = np.sum((X[:, 1:] - 100)**2, axis=1)
prod_cos = np.prod(np.cos((X - 100) / np.sqrt(np.arange(1, d + 1))), axis=1)
return (sum_sq / 4000 - prod_cos + 1).reshape(-1, 1)
# 10d Rastrigin
def rastrigin_10d(X):
try:
X.shape[1]
except:
X = np.array([X])
return (np.sum(X**2 - 10 * np.cos(2 * np.pi * X) + 10, axis=1)).reshape(-1, 1)
# 2d Rastrigin
def rastrigin_2d(X):
try:
X.shape[1]
except:
X = np.array([X])
return (np.sum(X**2 - 10 * np.cos(2 * np.pi * X) + 10, axis=1)).reshape(-1, 1)
# ------- END FUNCTIONS -------
if __name__ == "__main__":
import sys
import matplotlib.pyplot as plt
if len(sys.argv) != 2:
print("Usage: python functions.py [function_name]")
sys.exit(1)
function_name = sys.argv[1]
# Evaluate the function based on the provided name
f = globals().get(function_name)
if f == camel3_2d or f == camel16_2d or f == treccani_2d:
x1_min = x2_min = -5
x1_max = x2_max = 5
elif f == goldstein_2d:
x1_min = x2_min = -2
x1_max = x2_max = 2
elif f == branin_2d:
x1_min, x1_max = (-5, 10)
x2_min, x2_max = (0, 15)
elif f == rosenbrock_2d or f == rosenbrock_10d:
x1_min = x2_min = -2.048
x1_max = x2_max = 2.048
elif f == ackley_2d:
# normally it was (-15, 30) but the plot was bad in that case
x1_min = x2_min = -30
x1_max = x2_max = 30
elif f == griewank_10d:
x1_min = x2_min = -600
x1_max = x2_max = 600
elif f == rastrigin_10d:
x1_min = x2_min = -5.12
x1_max = x2_max = 5.12
elif f == rastrigin_2d:
x1_min = x2_min = -5.12
x1_max = x2_max = 5.12
elif f == testfunc_2d:
x1_min = x2_min = -5
x1_max = x2_max = 5
N = 100
x1 = np.linspace(x1_min, x1_max, N)
x2 = np.linspace(x2_min, x2_max, N)
# x2 = np.random.uniform(0, 1, N) * x1
X1, X2 = np.meshgrid(x1, x2)
Y = f(np.column_stack((X1.ravel(), X2.ravel()))).reshape(X1.shape)
fig = plt.figure(figsize=(11, 7))
ax = fig.add_subplot(111, projection='3d')
ax.plot_surface(X1, X2, Y, cmap='jet')
ax.set_xlabel('x1')
ax.set_ylabel('x2')
ax.set_zlabel('y')
plt.show()
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