用Tensorflow求逆矩阵

线性回归算法能表示为矩阵计算，Ax=b。这里要解决的是用矩阵x来求解系数。

1.导入必要的编程库，初始化计算图，并生成数据。

>>> import matplotlib.pyplot as plt
>>> import numpy as np
>>> import tensorflow as tf

>>> sess=tf.Session()

>>> x_vals=np.linspace(0,10,100)

>>> y_vals=x_vals+np.random.normal(0,1,100)

2.创建后续求逆方法所需的矩阵。创建A矩阵，其为矩阵x_vals_column和ones_column的合并。然后以矩阵y_vals创建b矩阵。

>>> x_vals_column=np.transpose(np.matrix(x_vals))
>>> ones_column=np.transpose(np.matrix(np.repeat(1,100)))

>>> A=np.column_stack((x_vals_column,ones_column))

>>> b=np.transpose(np.matrix(y_vals))

3.将A和b矩阵转换成张量

>>> A_tensor=tf.constant(A)

>>> b_tensor=tf.constant(b)

4.使用tf.matrix_inverse（）方法求逆

>>> tA_A=tf.matmul(tf.transpose(A_tensor),A_tensor)
>>> tA_A_inv=tf.matrix_inverse(tA_A)
>>> product=tf.matmul(tA_A_inv,tf.transpose(A_tensor))
>>> solution=tf.matmul(product,b_tensor)

>>> solution_eval=sess.run(solution)

5.从解中抽取系数、斜率和y截距

>>> slope=solution_eval[0][0]
>>> y_intercept=solution_eval[1][0]
>>> print('slope:'+str(slope))
slope:0.9469285572619588
>>> print('y_intercept:'+str(y_intercept))
y_intercept:0.2053153160416511
>>> best_fit=[]
>>> for i in x_vals:
...   best_fit.append(slope*i+y_intercept)
...
>>> plt.plot(x_vals,y_vals,'o',label='Data')
[<matplotlib.lines.Line2D object at 0x000001ED8EA34390>]
>>> plt.plot(x_vals,best_fit,'r-',label='Best fit line',linewidth=3)
[<matplotlib.lines.Line2D object at 0x000001ED8BF32FD0>]
>>> plt.legend(loc='upper left')
<matplotlib.legend.Legend object at 0x000001ED8EA34D68>

>>> plt.show()