forked from dad-119/python-project
-
Notifications
You must be signed in to change notification settings - Fork 0
/
cost function code
322 lines (266 loc) · 10.3 KB
/
cost function code
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
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
# importing
import csv
import math
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.patches as mpatches
from mpl_toolkits.mplot3d import Axes3D
from matplotlib.animation import FuncAnimation
from matplotlib import cm
#cost function
def compute_cost(X, y, theta):
J = 0
k=1
A = np.subtract(np.dot(X, theta), y)
J = (0.5) * (np.dot(A.T, A))
if k==0:
return
return J[0, 0]
#gradient descent
def gradient_descent(X, y, theta, alpha, epsilon, flag):
J_hist = []
all_thetas0 = []
all_thetas1 = []
bt_val = 0
while (1):
gradient = alpha * np.dot(X.T, np.subtract(np.dot(X, theta), y))
cost_curr = compute_cost(X, y, theta)
# print(cost_curr)
J_hist.append(cost_curr)
all_thetas0.append(theta[0])
all_thetas1.append(theta[1])
if (len(J_hist) >= 2):
if (math.fabs(J_hist[len(J_hist) - 1] - J_hist[len(J_hist) - 2]) <
epsilon):
break
if (len(J_hist) >= 2):
if (math.fabs(J_hist[len(J_hist) - 1] - J_hist[len(J_hist) - 2]) >
9999):
bt_val = 1
break
theta = theta - gradient
if (flag == 1):
plt.figure(2)
plt.plot(J_hist)
plt.xlabel('Number of Iterations -->')
plt.ylabel('Value of the Cost function(J) -->')
plt.title('Checking convergence with alpha : ' + str(float(alpha)))
plt.show(block=False)
raw_input("Hit Enter To Close")
plt.close()
return theta, np.array(all_thetas0), np.array(all_thetas1), np.array(
J_hist), bt_val
#main function
def main(x_training, y_training):
x_training = x_training.T
y_training = y_training.T
#plot the initial training data
print('\n\nPlotting the data...\n')
plt.figure(1)
plt.plot(x_training, y_training, 'ro')
plt.xlabel('Acidity -->')
plt.ylabel('Density -->')
plt.title('Training Set')
plt.show(block=False)
raw_input('\nPress Enter to close\n')
plt.close()
#Design matrix X
x_training = (x_training - np.mean(x_training)) / (
np.std(x_training)) #feature scaling using mean normalization
# x_training = (x_training - np.mean(x_training)) / (np.max(x_training) - np.mean(x_training))
m = y_training.shape[0] #number of training examples
X = np.hstack((np.reshape(np.ones(m), (m, 1)), x_training))
theta = np.reshape(np.zeros(2), (2, 1)) #0-initialization of theta
#some gradient descent settings
epsilon = math.pow(10, -10)
alpha = 0.0007
print('\nTesting the cost function ...\n')
#compute and display the initial cost
J = compute_cost(X, y_training, theta)
print('With theta = [0 ; 0]\nCost computed = ' + str(J) + '\n')
#run gradient descent
print('\n Running Gradient Descent Algorithm... \n')
# print(theta)
theta, thetas0, thetas1, all_cost, _ = gradient_descent(
X, y_training, theta, alpha, epsilon, 1)
opti0 = theta[0, 0]
opti1 = theta[1, 0]
print("Optimal Value of Theta-0" + str(opti0))
print("Optimal Value of Theta-0" + str(opti1))
#plotting the predicted line learnt from linear regression
plt.figure(3)
plt.plot(x_training, y_training, 'ro', label='Input Example', markersize=5)
plt.xlabel('Acidity -->')
plt.ylabel('Density -->')
plt.title('Prediction Model using Linear Regression')
plt.plot(x_training, np.dot(X, theta), label='Prediction Line')
plt.legend()
plt.show(block=False)
raw_input('\nPress Enter to close\n')
plt.close()
#Visualizing J(theta_0, theta_1) as a 3D-mesh followed from one of the quesions on stackoverflow
print('Visualizing J(theta_0, theta_1) ...\n')
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ms = np.linspace(-0.2, 2.0, 100)
bs = np.linspace(-1, 1, 100)
M, B = np.meshgrid(ms, bs)
zs = np.array([
compute_cost(X, y_training, np.array([[mp], [bp]]))
for mp, bp in zip(np.ravel(M), np.ravel(B))
])
Z = zs.reshape(M.shape)
surf = ax.plot_surface(M, B, Z, rstride=1, cstride=1, color='b', alpha=0.5, cmap=cm.coolwarm, linewidth=0, antialiased=False)
blue_patch = mpatches.Patch(color='blue', label='Cost Function')
red_patch = mpatches.Patch(color='red', label='Path taken by GD')
ax.plot(thetas0, thetas1, all_cost, color='r', alpha=0.5)
ax.set_xlabel('theta(0)')
ax.set_ylabel('theta(1)')
ax.set_zlabel('J(theta)')
plt.legend(loc='upper left', handles=[blue_patch, red_patch])
fig.colorbar(surf, shrink=0.5, aspect=5)
ax.set_title('J(theta) vs theta')
plt.show(block=False)
raw_input('\nPress Enter to close\n')
plt.close()
#Plotting the contour
print('\nPlotting the contour ... \n')
fig = plt.figure()
CS = plt.contour(M, B, Z, 25)
plt.clabel(CS, inline=1, fontsize=10)
plt.plot([opti0], [opti1], color='r', marker='x', label='Optimal Value')
plt.legend()
plt.xlabel('Theta0 -->')
plt.ylabel('Theta1 -->')
plt.title('Contour plot')
plt.show(block=False)
raw_input('\nPress Enter to close\n')
plt.close()
#plotting the GD animation using animation
print('\n3D Animation of GD Convergence ...\n')
plot_3D(X, y_training, thetas0, thetas1, all_cost, opti0, opti1)
#plotting the contour animation using looping
print('\nContour Animation of GD Convergence ...\n')
plot_contour(X, y_training, alpha, epsilon)
plt.close()
#plotting for other values of eta
eta = [0.001, 0.005, 0.009, 0.013, 0.017, 0.021, 0.025]
check = 0
for some_alpha in eta:
if (check == 0):
print('\nContour Animation of GD Convergence with eta = ' +
str(some_alpha) + '\n')
bt_val = plot_contour(X, y_training, some_alpha, epsilon)
if (bt_val == 1):
check = 1
print('Gradient Descent doesn\'t converge for eta : ' +
str(some_alpha) + '\n')
else:
print('Gradient Descent doesn\'t converge for eta : ' +
str(some_alpha) + '\n')
return
def plot_contour(X, y_training, alpha, epsilon):
theta = np.reshape(np.zeros(2), (2, 1)) #0-initialization of theta
theta, thetas0, thetas1, all_cost, bt_val = gradient_descent(
X, y_training, theta, alpha, epsilon, 0)
if (bt_val == 1):
return bt_val
opti0 = theta[0, 0]
opti1 = theta[1, 0]
ms = np.linspace(-0.2, 2.0, 100)
bs = np.linspace(-1, 1, 100)
M, B = np.meshgrid(ms, bs)
zs = np.array([
compute_cost(X, y_training, np.array([[mp], [bp]]))
for mp, bp in zip(np.ravel(M), np.ravel(B))
])
Z = zs.reshape(M.shape)
fig = plt.figure()
CS = plt.contour(M, B, Z, 25)
plt.clabel(CS, inline=1, fontsize=10)
plt.plot([opti0], [opti1], color='r', marker='x', label='Optimal Value')
plt.legend()
plt.xlabel('Theta0 -->')
plt.ylabel('Theta1 -->')
plt.title('Contour plot with Learning Rate : ' + str(alpha))
for i in range(0, len(all_cost), 2):
plt.plot(thetas0[:i], thetas1[:i], color='r')
plt.draw()
plt.pause(0.05)
print('Iteration : ' + str(i))
print('It converges in ' + str(len(all_cost)) + ' iterations\n')
plt.show(block=False)
raw_input('\nPress Enter to close\n')
return 0
def plot_3D(X, y_training, thetas0, thetas1, all_cost, opti0, opti1):
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ms = np.linspace(-0.2, 2.0, 100)
bs = np.linspace(-1, 1, 100)
M, B = np.meshgrid(ms, bs)
zs = np.array([
compute_cost(X, y_training, np.array([[mp], [bp]]))
for mp, bp in zip(np.ravel(M), np.ravel(B))
])
Z = zs.reshape(M.shape)
ax.plot_surface(M, B, Z, rstride=1, cstride=1, color='b', alpha=0.5)
blue_patch = mpatches.Patch(color='blue', label='Cost Function')
red_patch = mpatches.Patch(color='red', label='Path taken by GD')
ax.set_xlabel('theta(0)')
ax.set_ylabel('theta(1)')
ax.set_zlabel('J(theta)')
plt.legend(loc='upper left', handles=[blue_patch, red_patch])
ax.set_title('J(theta) vs theta')
theta0_new = []
theta1_new = []
cost_new = []
j = 0
num_iterations = len(all_cost)
#one way by using animation, issues setting the interval time
def init():
ax.plot_surface(M, B, Z, rstride=1, cstride=1, color='b', alpha=0.5)
plt.plot(
[opti0], [opti1], color='r', marker='x', label='Optimal Value')
return
def update(i, step_size):
j = (step_size * i)
theta0_new.append(thetas0[j])
theta1_new.append(thetas1[j])
cost_new.append(all_cost[j])
ax.plot(theta0_new, theta1_new, cost_new, color='r')
plt.draw()
print('Iteration : ' + str(j) + ', Error Value : ' + str(all_cost[j]))
if (i == ((num_iterations - 1) / step_size - 1)):
print('\nConverged Successfully\n')
return
step_size = 2
ani = FuncAnimation(
fig,
update,
frames=(num_iterations - 1) / step_size,
fargs=(step_size, ),
init_func=init,
interval=1,
repeat=False)
# for i in range(0, num_iterations, step_size):
# ax.plot(thetas0[:i], thetas0[:i], all_cost[:i], color='r')
# plt.draw()
# plt.pause(0.0005)
# print('Iteration : ' + str(i))
plt.show(block=False)
raw_input('\nPress Enter to close\n')
plt.close()
if __name__ == '__main__':
x_training = [] #denotes the input training set
y_training = [] #denotes the outpur training set
with open('./Assignment_1_datasets/linearX.csv') as csvfile:
read_csv = csv.reader(csvfile, delimiter=',')
for row in read_csv:
x_training.append(row[0])
with open('./Assignment_1_datasets/linearY.csv') as csvfile:
read_csv = csv.reader(csvfile, delimiter=',')
for row in read_csv:
y_training.append(row[0])
main(
np.array([x_training]).astype(np.float),
np.array([y_training]).astype(np.float))