-
Notifications
You must be signed in to change notification settings - Fork 0
/
MultiD_example.py
160 lines (134 loc) · 5.64 KB
/
MultiD_example.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
from __future__ import annotations
import numpy as np
import math
import matplotlib
matplotlib.use('TKAgg')
import matplotlib.pyplot as plt
from mpl_toolkits import mplot3d
from sympy import *
class Vector3:
def __init__(self, X, Y, Z):
self.x = X
self.y = Y
self.z = Z
fig = plt.figure()
ax3 = plt.axes(projection='3d') # matplotlib projecction selection
ax3.set_proj_type('ortho')
V1 = Vector3(0, 0, 1) # z axis
V1xline = np.linspace(0,V1.x,10)
V1yline = np.linspace(0,V1.y,10)
V1zline = np.linspace(0,V1.z,10)
V2 = Vector3(0, 1, 0) # y axis
V2xline = np.linspace(0, V2.x, 10)
V2yline = np.linspace(0, V2.y, 10)
V2zline = np.linspace(0, V2.z, 10)
V3 = Vector3(1, 0, 0) # x axis
V3xline = np.linspace(0, V3.x, 10)
V3yline = np.linspace(0, V3.y, 10)
V3zline = np.linspace(0, V3.z, 10)
ax3.plot3D(V1xline, V1yline, V1zline, 'blue')
ax3.plot3D(V2xline, V2yline, V2zline, 'red')
ax3.plot3D(V3xline, V3yline, V3zline, 'orange')
domain_resolution = 100 # number of sampling points in the domain
def f(x): # single variable f : R -> R
assert type(x) == float or type(x) == int or type(x) == np.float64
return 8*math.exp(1 - x) + 7*math.log(x)
def domain(a = 0, b = 1, dom_res = 100):
iteration_val = (b + a)/dom_res
while a < b:
yield a
a += iteration_val
ax3.set_xlim3d(0,2) # setting the viewable domain area
ax3.set_ylim3d(0,10)
ax3.set_zlim3d(0,0)
a = 1
b = 2
v = Vector3(a, f(a), 0)
for i in domain(a, b, domain_resolution):
ax3.plot3D(
np.linspace(v.x,i,5),
np.linspace(v.y,f(i),5),
np.linspace(v.z,0,5),
'black')
v = Vector3(i, f(i), 0)
def GoldenSearch(f, dom, uncertainty):
assert callable(f) and type(dom) == list and type(uncertainty) == float
rho = (3 - np.sqrt(5))/2
ax3.plot3D(np.linspace(dom[1], dom[1], 5), np.linspace(0, f(dom[1]), 5), np.linspace(0,0,5), 'blue')
ax3.plot3D(np.linspace(dom[0], dom[0], 5), np.linspace(0, f(dom[0]), 5), np.linspace(0,0,5), 'purple')
#print(f'dom: {dom},\n f({dom[0]}) = {f(dom[0])}, f({dom[1]}) = {f(dom[1])}')
while (abs(dom[1] - dom[0]) > uncertainty):
if f(dom[0]) < f(dom[1]):
dom[1] = dom[1] - rho*(dom[1] - dom[0])
ax3.plot3D(np.linspace(dom[1], dom[1], 5), np.linspace(0, f(dom[1]), 5), np.linspace(0,0,5), 'blue')
else:
dom[0] = dom[0] + rho*(dom[1] - dom[0])
ax3.plot3D(np.linspace(dom[0], dom[0], 5), np.linspace(0, f(dom[0]), 5), np.linspace(0,0,5), 'purple')
#print(f'dom: {dom},\n f({dom[0]}) = {f(dom[0])}, f({dom[1]}) = {f(dom[1])}')
#print(f'dom: {dom}')
return dom
def Fibonacci(n):
assert type(n) == int
return int((1/np.sqrt(5))*(((1 + np.sqrt(5))/2)**(n) - ((1 - np.sqrt(5))/2)**(n)))
def FibSearch(f, dom, uncertainty, N, epsilon=0.05):
rho = 1 - Fibonacci(N)/Fibonacci(N+1)
ax3.plot3D(np.linspace(dom[1], dom[1], 5), np.linspace(0, f(dom[1]), 5), np.linspace(0,0,5), 'blue')
ax3.plot3D(np.linspace(dom[0], dom[0], 5), np.linspace(0, f(dom[0]), 5), np.linspace(0,0,5), 'purple')
#print(f'dom: {dom},\n f({dom[0]}) = {f(dom[0])}, f({dom[1]}) = {f(dom[1])}, rho: {rho}')
while (abs(dom[1] - dom[0]) > uncertainty):
if f(dom[0]) < f(dom[1]):
dom[1] = dom[1] - rho*(dom[1] - dom[0])
ax3.plot3D(np.linspace(dom[1], dom[1], 5), np.linspace(0, f(dom[1]), 5), np.linspace(0,0,5), 'blue')
else:
dom[0] = dom[0] + rho*(dom[1] - dom[0])
ax3.plot3D(np.linspace(dom[0], dom[0], 5), np.linspace(0, f(dom[0]), 5), np.linspace(0,0,5), 'purple')
rho = 1 - rho/(1- rho)
if (1/2 - epsilon) < rho <= (1/2 + epsilon):
rho = rho - epsilon
#print(f'dom: {dom},\n f({dom[0]}) = {f(dom[0])}, f({dom[1]}) = {f(dom[1])}, rho: {rho}')
#print(f'final range -> dom: {dom}')
return dom
def NewtonSearch(f, uncertainty, xi):
x = symbols('x')
h = f.subs(x,xi).evalf()/diff(f).subs(x,xi).evalf()
while (abs(h) > uncertainty):
h = f.subs(x,xi).evalf()/diff(f).subs(x,xi).evalf()
xi = xi - h
ax3.plot3D(np.linspace(0, float(xi), 5), np.linspace(0, float(func.subs(x,xi).evalf()), 5), np.linspace(0,0,5), 'purple')
return xi
def SecantSearch(f, uncertainty, x1, x0):
x = symbols('x')
while (f.subs(x,x1) != f.subs(x,x0)):
xprime = ((x1 - ((diff(f).subs(x,x1).evalf()*(x1-x0)))))/(diff(f).subs(x,x1).evalf() - diff(f).subs(x,x0).evalf())
x0 = x1
x1 = xprime
return x1
def SecantMethod(f, uncertainty, x1, x0):
it = 0
while (abs(f(x1)) > uncertainty):
it += 1
buffr = x1
x1 = x1 - (x1 - x0)*f(x1) / (f(x1) - f(x0))
x0 = buffr
return x1
print(10*'-' + "Golden Search with Uncertainty = 0.3" + 10*'-')
print(GoldenSearch(f, [1,2], 0.3))
print(10*'-' + "Fibonacci Search with Uncertainty = 0.3, N = 4" + 10*'-')
print(FibSearch(f, [1,2], 0.3, 4))
print(10*'-' + "Golden Search with Uncertainty = 0.2" + 10*'-')
print(GoldenSearch(f, [1,2], 0.2))
print(10*'-' + "Newton-Raphson Search with Uncertainty=0.002, x0=0.07" + 10*'-')
x = symbols('x')
func = 48*x*(1+x)**4 - (1+x)**4 - 7
evaluation = NewtonSearch(func, 0.002, 0.07)
print(f'x: {evaluation}, f(x): {func.subs(x,evaluation)}')
print(10*'-' + "Secant Search with Uncertainty=10e-5, x0=0, x1=1" + 10*'-')
func = (x**2)*exp(-x/2) - 1
evaluation = SecantSearch(func, 10e-5, 1, 0)
print(f'x: {evaluation}, f(x): {func.subs(x,evaluation).evalf()}')
print(10*'-' + "Secant Method with Uncertainty=10e-5, x0=0, x1=1" + 10*'-')
def f(x):
return (x**2)*math.exp(-x/2) - 1
evaluation = SecantMethod(f, 10e-5, 1, 0)
print(f'x: {evaluation}, f(x): {func.subs(x,evaluation).evalf()}')
plt.show()