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import numpy as np
from matplotlib import pyplot as plt
x_data = [1,2,3,4]
y_data = [6.8,9.8,13.2,16.2]
loss_list = list()
def forward(a,x,b):
return a*x+b
def lossFunction(a,x,y,b):
y_pred = forward(a,x,b)
loss = (y_pred - y)**2
return loss
a_list = list()
b_list = list()
if __name__ == '__main__':
for a in np.arange(0,6,0.1):
for b in np.arange(0,6,0.1):
sum_loss = 0
for i in range(4):
sum_loss += lossFunction(a, x_data[i], y_data[i],b)
loss_list.append(sum_loss/4)
a_list.append(a)
b_list.append(b)
plt.plot(a_list,loss_list)
plt.xlabel('a')
plt.ylabel('loss')
print(min(loss_list))
loss_min_index = loss_list.index(min(loss_list))
print(loss_min_index)
a_wanted = a_list[loss_min_index]
b_wanted = b_list[loss_min_index]
print(f'a_wanted = {a_wanted}, b_wanted ={b_wanted}')
# plt.show()
# a_wanted = a_list[loss_list.index(min(loss_list))]
# print(forward(a_wanted, 4))
print(forward(a_wanted, 5, b_wanted))
采用梯度方法
import numpy as np
from matplotlib import pyplot as plt
data_x = [1, 2, 3]
data_y = [2, 4, 6]
loss_list = list()
a_list = list()
alpha = 0.01
def forward(x):
return a * x
def lossFunction(x, y):
y_pred = forward(x)
loss = (y_pred - y) ** 2
return loss
def predict(x, a_):
return a_ * x
def gradient(a, x, y):
a = a - alpha * 2 * (a * x - y) * x
return a
if __name__ == '__main__':
a = 0
for epoch in range(1000):
# for a in np.arange(0, 4, 0.1):
sum_loss = 0
for i in range(3):
sum_loss += lossFunction(data_x[i], data_y[i])
a = gradient(a, data_x[i], data_y[i])
loss_list.append(sum_loss / 3)
a_list.append(a)
plt.subplot(211)
plt.plot(a_list)
plt.subplot(212)
plt.plot(loss_list)
plt.show()
plt.figure()
plt.plot(a_list, loss_list)
plt.xlabel('a')
plt.ylabel('loss')
plt.show()
min_value = min(loss_list)
index_lossMin = loss_list.index(min_value)
print(index_lossMin)
proper_a = a_list[index_lossMin]
print(proper_a)
print("Please input the desired x:")
desired_x = input()
print(f"The predict output for the linear model is {predict(float(desired_x), proper_a)}")
loss最小
import numpy as np
from matplotlib import pyplot as plt
data_x = [1, 2, 3]
data_y = [2, 4, 6]
loss_list = list()
a_list = list()
def forward(x):
return a * x
def lossFunction(x, y):
y_pred = forward(x)
loss = (y_pred - y) ** 2
return loss
def predict(x,a_):
return a_*x
if __name__ == '__main__':
for a in np.arange(0, 4, 0.1):
sum_loss = 0
for i in range(3):
sum_loss += lossFunction(data_x[i], data_y[i])
loss_list.append(sum_loss / 3)
a_list.append(a)
plt.figure()
plt.plot(a_list, loss_list)
# plt.title("")
plt.xlabel('a')
plt.ylabel('loss')
# plt.show()
min_value = min(loss_list)
index_lossMin = loss_list.index(min_value)
print(index_lossMin)
proper_a = a_list[index_lossMin]
print(proper_a)
print("Please input the desired x:")
desired_x = input()
print(f"The predict output for the linear model is {predict(float(desired_x),proper_a)}")
import time
import numpy as np
from matplotlib import pyplot as plt
import random
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