tensorflow实现线性回归（矩阵解法）

import matplotlib.pyplot as plt

import numpy as np

import tensorflow as tf

sess = tf.Session()

x_vals = np.linspace(0,10,100) # [0,10]之间产生100个等差数值

y_vals = x_vals + np.random.normal(0,1,100) # 正态分布，产生100 个数值

x_vals_column = np.transpose(np.matrix(x_vals)) #将x的值转换为一列

ones_column = np.transpose(np.matrix(np.repeat(1,100))) #生成一列元素全为1的矩阵，共100个元素

A = np.column_stack((x_vals_column,ones_column)) #将x值和上面的组合成一个新的矩阵[100,2]

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

A_tensor = tf.constant(A) #将矩阵转化为tensorflow的张量

b_tensor = tf.constant(b)

tA_A = tf.matmul(tf.transpose(A_tensor),A_tensor) #将A 的转置和A做矩阵乘法

tA_A_inv = tf.matrix_inverse(tA_A) #求逆矩阵

product = tf.matmul(tA_A_inv,tf.transpose(A_tensor))

solution = tf.matmul(product,b_tensor)

solution_eval = sess.run(solution) #求解系数矩阵

slope = solution_eval[0][0]

y_intercept = solution_eval[1][0]

print(‘slope: ‘,str(slope))

print(‘y_intercept: ‘,str(y_intercept))

best_fit = []

for i in x_vals:

best_fit.append(slope*i + y_intercept)

plt.plot(x_vals,y_vals,’o’,color = ‘g’,label=’Data’)

plt.plot(x_vals,best_fit,’r-‘,label=’Best fit line’,linewidth = 4)

plt.legend(loc=’upper left’)

plt.show()