-
Notifications
You must be signed in to change notification settings - Fork 1
/
Copy pathgif_rmsprop_ackley.py
136 lines (109 loc) · 5.46 KB
/
gif_rmsprop_ackley.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
import numpy as np
import matplotlib.mlab as mlab
import matplotlib.pyplot as plt
from matplotlib.animation import FuncAnimation
import math
# https://stackoverflow.com/questions/20228546/how-do-i-apply-some-function-to-a-python-meshgrid
@np.vectorize
# https://github.com/adhishagc/Ackley-Function
def ackley_function(x,y):
#returns the point value of the given coordinate
part_1 = -0.2*math.sqrt(0.5*(x*x + y*y))
part_2 = 0.5*(math.cos(2*math.pi*x) + math.cos(2*math.pi*y))
value = math.exp(1) + 20 - 20 * math.exp(part_1) - math.exp(part_2)
#returning the value
return value
def derivative_x(x,y):
part_1 = 2.82842712474619 * x * math.exp(-0.14142135623731 * math.sqrt(x*x + y*y))/(math.sqrt(x*x + y*y))
part_2 = math.pi * math.exp(0.5*(math.cos(2*math.pi*x) + math.cos(2*math.pi*y))) * math.sin(2*math.pi*x)
return part_1 + part_2
def derivative_y(x,y):
part_1 = 2.82842712474619 * y * math.exp(-0.14142135623731 * math.sqrt(x*x + y*y))/(math.sqrt(x*x + y*y))
part_2 = math.pi * math.exp(0.5*(math.cos(2*math.pi*x) + math.cos(2*math.pi*y))) * math.sin(2*math.pi*y)
return part_1 + part_2
delta = 0.01
x = np.arange(-5.0, 5.0, delta)
y = np.arange(-5.0, 5.0, delta)
# https://numpy.org/doc/stable/reference/generated/numpy.meshgrid.html
X, Y = np.meshgrid(x, y)
Z = ackley_function(X,Y)
# https://stackoverflow.com/questions/332289/how-do-you-change-the-size-of-figures-drawn-with-matplotlib
fig, ax = plt.subplots(figsize=[10, 10])
levels = np.arange(0.0, 15.0, 1)
CS = plt.contour(X, Y, Z, levels=levels)
plt.clabel(CS, inline=1, fontsize=10)
A = [-1, -0.5]
B = [0.2, -1.7]
C = [4.2, 0.4]
D = [-3.5, -0.6]
E = [-2.6, 2.3]
ax.plot(A[0], A[1], 'bo')
ax.plot(B[0], B[1], 'ro')
ax.plot(C[0], C[1], 'co')
ax.plot(D[0], D[1], 'mo')
ax.plot(E[0], E[1], 'ko')
# https://www.kite.com/python/answers/how-to-label-a-single-point-in-a-matplotlib-graph-in-python
ax.annotate("Point A", (A[0], A[1]))
ax.annotate("Point B", (B[0], B[1]))
ax.annotate("Point C", (C[0], C[1]))
ax.annotate("Point D", (D[0], D[1]))
ax.annotate("Point E", (E[0], E[1]))
a_history = [[],[]]
b_history = [[],[]]
c_history = [[],[]]
d_history = [[],[]]
e_history = [[],[]]
#learning_rate = 0.05
#epochs = 300
learning_rate = 0.2
epochs = 50
gamma = 0.90
# a running average of the magnitudes of recent gradients
grad_ra_A = [0,0]
grad_ra_B = [0,0]
grad_ra_C = [0,0]
grad_ra_D = [0,0]
grad_ra_E = [0,0]
for iter in range(epochs):
#ax.plot(A[0], A[1], 'bo')
#ax.plot(B[0], B[1], 'ro')
#ax.plot(C[0], C[1], 'co')
#ax.plot(D[0], D[1], 'mo')
#ax.plot(E[0], E[1], 'ko')
a_history[0].append(A[0]); a_history[1].append(A[1])
b_history[0].append(B[0]); b_history[1].append(B[1])
c_history[0].append(C[0]); c_history[1].append(C[1])
d_history[0].append(D[0]); d_history[1].append(D[1])
e_history[0].append(E[0]); e_history[1].append(E[1])
grad_ra_A[0] = gamma * grad_ra_A[0] + (1 - gamma) * (derivative_x(A[0], A[1]))**2
grad_ra_A[1] = gamma * grad_ra_A[1] + (1 - gamma) * (derivative_y(A[0], A[1]))**2
A[0] = A[0] - learning_rate * (1/math.sqrt(grad_ra_A[0])) * derivative_x(A[0], A[1])
A[1] = A[1] - learning_rate * (1/math.sqrt(grad_ra_A[1])) * derivative_y(A[0], A[1])
grad_ra_B[0] = gamma * grad_ra_B[0] + (1 - gamma) * (derivative_x(B[0], B[1]))**2
grad_ra_B[1] = gamma * grad_ra_B[1] + (1 - gamma) * (derivative_y(B[0], B[1]))**2
B[0] = B[0] - learning_rate * (1/math.sqrt(grad_ra_B[0])) * derivative_x(B[0], B[1])
B[1] = B[1] - learning_rate * (1/math.sqrt(grad_ra_B[1])) * derivative_y(B[0], B[1])
grad_ra_C[0] = gamma * grad_ra_C[0] + (1 - gamma) * (derivative_x(C[0], C[1]))**2
grad_ra_C[1] = gamma * grad_ra_C[1] + (1 - gamma) * (derivative_y(C[0], C[1]))**2
C[0] = C[0] - learning_rate * (1/math.sqrt(grad_ra_C[0])) * derivative_x(C[0], C[1])
C[1] = C[1] - learning_rate * (1/math.sqrt(grad_ra_C[1])) * derivative_y(C[0], C[1])
grad_ra_D[0] = gamma * grad_ra_D[0] + (1 - gamma) * (derivative_x(D[0], D[1]))**2
grad_ra_D[1] = gamma * grad_ra_D[1] + (1 - gamma) * (derivative_y(D[0], D[1]))**2
D[0] = D[0] - learning_rate * (1/math.sqrt(grad_ra_D[0])) * derivative_x(D[0], D[1])
D[1] = D[1] - learning_rate * (1/math.sqrt(grad_ra_D[1])) * derivative_y(D[0], D[1])
grad_ra_E[0] = gamma * grad_ra_E[0] + (1 - gamma) * (derivative_x(E[0], E[1]))**2
grad_ra_E[1] = gamma * grad_ra_E[1] + (1 - gamma) * (derivative_y(E[0], E[1]))**2
E[0] = E[0] - learning_rate * (1/math.sqrt(grad_ra_E[0])) * derivative_x(E[0], E[1])
E[1] = E[1] - learning_rate * (1/math.sqrt(grad_ra_E[1])) * derivative_y(E[0], E[1])
div = 1
#for i in range(0, epochs//10):
def animate(i):
# https://stackoverflow.com/questions/509211/understanding-slice-notation
ax.plot(a_history[0][i*div:(i+1)*div + 1], a_history[1][i*div:(i+1)*div + 1], color='blue', linewidth=4)
ax.plot(b_history[0][i*div:(i+1)*div + 1], b_history[1][i*div:(i+1)*div + 1], color='red', linewidth=4)
ax.plot(c_history[0][i*div:(i+1)*div + 1], c_history[1][i*div:(i+1)*div + 1], color='cyan', linewidth=4)
ax.plot(d_history[0][i*div:(i+1)*div + 1], d_history[1][i*div:(i+1)*div + 1], color='magenta', linewidth=4)
ax.plot(e_history[0][i*div:(i+1)*div + 1], e_history[1][i*div:(i+1)*div + 1], color='black', linewidth=4)
# https://eli.thegreenplace.net/2016/drawing-animated-gifs-with-matplotlib/
anim = FuncAnimation(fig, animate, frames=np.arange(0, epochs//div), interval=200)
anim.save('images/rmsprop-ackley-gamma-090.gif', dpi=80)