用TensorFlow内建的Cholesky矩阵分解法实现矩阵分解的线性回归

# 线性回归：矩阵分解法
# 通过分解矩阵的方法求解有时更高效并且数值稳定
#----------------------------------
#
# This function shows how to use TensorFlow to
# solve linear regression via the matrix inverse.
#
# Given Ax=b, and a Cholesky decomposition such that
#  A = L*L' then we can get solve for x via
# 1) L*y=t(A)*b
# 2) L'*x=y

import matplotlib.pyplot as plt
import numpy as np
import tensorflow as tf
from tensorflow.python.framework import ops
ops.reset_default_graph()

# Create graph
sess = tf.Session()

# Create the data
x_vals = np.linspace(0, 10, 100)
y_vals = x_vals + np.random.normal(0, 1, 100)

# Create design matrix
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))

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

# Create tensors
A_tensor = tf.constant(A)
b_tensor = tf.constant(b)

# 找到方阵的Cholesky矩阵分解
tA_A = tf.matmul(tf.transpose(A_tensor), A_tensor)
# TensorFlow的cholesky（）函数仅仅返回矩阵分解的下三角矩阵，
# 因为上三角矩阵是下三角矩阵的转置矩阵。
L = tf.cholesky(tA_A)

# Solve L*y=t(A)*b
tA_b = tf.matmul(tf.transpose(A_tensor), b)
sol1 = tf.matrix_solve(L, tA_b)

# Solve L' * y = sol1
sol2 = tf.matrix_solve(tf.transpose(L), sol1)

solution_eval = sess.run(sol2)

# 抽取系数
slope = solution_eval[0][0]
y_intercept = solution_eval[1][0]

print('slope: ' + str(slope))
print('y_intercept: ' + str(y_intercept))

# Get best fit line
best_fit = []
for i in x_vals:
best_fit.append(slope*i+y_intercept)

# Plot the results
plt.plot(x_vals, y_vals, 'o', label='Data')
plt.plot(x_vals, best_fit, 'r-', label='Best fit line', linewidth=3)
plt.legend(loc='upper left')
plt.show()

slope: 0.998921420857
y_intercept: 0.0799919541665