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functions.py
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functions.py
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import numpy as np
from profilehooks import profile
import matplotlib.pyplot
import scipy as sp
import scipy.optimize
import math
def rosenbrook_start(n):
if n % 2 != 0:
print("n must be a multiple of 2")
return []
else:
x_0 = np.array([0.0 for i in range(n)])
for i in range(n // 2):
i1 = 2 * i
i2 = 2 * i + 1
x_0[i1] = -1.2
x_0[i2] = 1
return x_0
def powell_start(n):
if n % 4 != 0:
print("n must be a multiple of 4")
return []
else:
x_0 = np.array([0.0 for i in range(n)])
for i in range(n // 4):
i1 = 4 * i
i2 = 4 * i + 1
i3 = 4 * i + 2
i4 = 4 * i + 3
x_0[i1] = 3
x_0[i2] = -1
x_0[i3] = 0
x_0[i4] = 1
return x_0
def rosenbrook_obj(x):
n = len(x)
if n % 2 != 0:
print("n must be a multiple of 2")
return []
else:
f_x = 0.0
for i in range(n // 2):
i1 = 2 * i
i2 = 2 * i + 1
f_x += (10 * (x[i2] - (x[i1] ** 2))) ** 2
f_x += (1 - x[i1]) ** 2
return f_x
def rosenbrook_grad(x):
n = len(x)
if n % 2 != 0:
print("n must be a multiple of 2")
return []
else:
g = np.array([0.0 for i in range(n)])
for i in range(n // 2):
i1 = 2 * i
i2 = 2 * i + 1
g[i1] = (
400 * (x[i1] ** 3)
+ 2 * x[i1]
- 400 * x[i2] * x[i1]
- 2
)
g[i2] = (
- 200 * (x[i1] ** 2)
+ 200 * x[i2]
)
return g
def powell_obj(x):
n = len(x)
if n % 4 != 0:
print("n must be a multiple of 4")
return []
else:
f_x = 0.0
for i in range(n // 4):
i1 = 4 * i
i2 = 4 * i + 1
i3 = 4 * i + 2
i4 = 4 * i + 3
f_x += (
10 * (x[i1]**4)
- 40 * x[i4] * (x[i1]**3)
+ 60 * (x[i4]**2) * (x[i1]**2)
+ (x[i1]**2)
- 40 * (x[i4]**3) * x[i1]
+ 20 * x[i2] * x[i1]
+ (x[i2]**4)
+ 16 * (x[i3]**4)
+ 10 * (x[i4]**4)
- 32 * x[i2] * (x[i3]**3)
+ 100 * (x[i2]**2)
+ 24 * (x[i2]**2) * (x[i3]**2)
+ 5 * (x[i3]**2)
+ 5 * (x[i4]**2)
- 8 * (x[i2]**3) * x[i3]
- 10 * x[i3] * x[i4]
)
return f_x
def powell_grad(x):
n = len(x)
if n % 4 != 0:
print("n must be a multiple of 4")
return []
else:
g = np.array([0.0 for i in range(n)])
for i in range(n // 4):
i1 = 4 * i
i2 = 4 * i + 1
i3 = 4 * i + 2
i4 = 4 * i + 3
g[i1] = 40 * (x[i1] - x[i4])**3 + 2 *(x[i1] + 10 * x[i2])
g[i2] = 4 * (x[i2] - 2*x[i3])**3 + 20 *(x[i1] + 10*x[i2])
g[i3] = 10*(x[i3] - x[i4]) - 8*(x[i2] - 2 * x[i3])**3
g[i4] = -40*(x[i1] - x[i4])**3 - 10*(x[i3] - x[i4])
return g