1. 刘二大人《PyTorch深度学习实践》线性模型 作业
- 导入库函数
import numpy as np
import matplotlib.pyplot as plt
from matplotlib import cm
from mpl_toolkits.mplot3d import Axes3D
- 设置数据集
x_data = [1.0, 2.0, 3.0]
y_data = [2.0, 4.0, 6.0]
- 定义前向传播函数
def forward(w, b, x):
return w * x + b
- 定义损失函数
def loss(y_hat, y):
return (y_hat - y) ** 2
- 选取 w 和 b
w_list = np.arange(0.0, 4.0, 0.1)
b_list = np.arange(-2.0, 2.1, 0.1)
- 将 w 和 b 转化为二维矩阵，并初始化mse
w, b = numpy.meshgrid(w_list, b_list)
mse = numpy.zeros(w.shape) # 一定要注意 mse 维度要与 w 维度一致，否则画三维图时会报错
print(f'w.shape=' + str(w.shape))
print(w)
print(f'b.shape=' + str(b.shape))
print(b)
print(f'mse.shape=' + str(mse.shape))
输出结果为：
w.shape=(41, 40)
[[0. 0.1 0.2 ... 3.7 3.8 3.9]
[0. 0.1 0.2 ... 3.7 3.8 3.9]
[0. 0.1 0.2 ... 3.7 3.8 3.9]
...
[0. 0.1 0.2 ... 3.7 3.8 3.9]
[0. 0.1 0.2 ... 3.7 3.8 3.9]
[0. 0.1 0.2 ... 3.7 3.8 3.9]]
b.shape=(41, 40)
[[-2. -2. -2. ... -2. -2. -2. ]
[-1.9 -1.9 -1.9 ... -1.9 -1.9 -1.9]
[-1.8 -1.8 -1.8 ... -1.8 -1.8 -1.8]
...
[ 1.8 1.8 1.8 ... 1.8 1.8 1.8]
[ 1.9 1.9 1.9 ... 1.9 1.9 1.9]
[ 2. 2. 2. ... 2. 2. 2. ]]
mse.shape=(41, 40)
- 计算 mse
for x, y in zip(x_data, y_data):
_y = forward(w, b, x)
print(_y)
mse += loss(_y, y)
mse /= len(x_data)
输出结果为：
[[-2. -1.9 -1.8 ... 1.7 1.8 1.9]
[-1.9 -1.8 -1.7 ... 1.8 1.9 2. ]
[-1.8 -1.7 -1.6 ... 1.9 2. 2.1]
...
[ 1.8 1.9 2. ... 5.5 5.6 5.7]
[ 1.9 2. 2.1 ... 5.6 5.7 5.8]
[ 2. 2.1 2.2 ... 5.7 5.8 5.9]]
[[-2. -1.8 -1.6 ... 5.4 5.6 5.8]
[-1.9 -1.7 -1.5 ... 5.5 5.7 5.9]
[-1.8 -1.6 -1.4 ... 5.6 5.8 6. ]
...
[ 1.8 2. 2.2 ... 9.2 9.4 9.6]
[ 1.9 2.1 2.3 ... 9.3 9.5 9.7]
[ 2. 2.2 2.4 ... 9.4 9.6 9.8]]
[[-2. -1.7 -1.4 ... 9.1 9.4 9.7]
[-1.9 -1.6 -1.3 ... 9.2 9.5 9.8]
[-1.8 -1.5 -1.2 ... 9.3 9.6 9.9]
...
[ 1.8 2.1 2.4 ... 12.9 13.2 13.5]
[ 1.9 2.2 2.5 ... 13. 13.3 13.6]
[ 2. 2.3 2.6 ... 13.1 13.4 13.7]]
- 绘制三维曲面
h = plt.contourf(w, b, mse)
fig = plt.figure()
ax = Axes3D(fig)
plt.xlabel(r'w', fontsize=20, color='cyan')
plt.ylabel(r'b', fontsize=20, color='cyan')
ax.plot_surface(w, b, mse, rstride=1, cstride=1, cmap=plt.get_cmap('rainbow'))
plt.show()
