一.求線性方程的斜率

①最小二乘法

import numpy as np
from numpy.linalg import inv #逆矩陣
from numpy import dot #矩陣乘
from numpy import mat #矩陣

#y=2x 求線性方程的斜率
X = mat([1, 2, 3]).reshape(3, 1)  #reshape 的作用就是修改矩陣的維度
print(X)
Y = 2*X
# theta = (X'X)-1X'Y
theta = dot(dot(inv(dot(X.T, X)), X.T), Y)
print(theta)

②梯度下降演算法

import numpy as np
from numpy.linalg import inv #逆矩陣
from numpy import dot #矩陣乘
from numpy import mat #矩陣

#y=2x 求線性方程的斜率
X = mat([1, 2, 3]).reshape(3, 1)  #reshape 的作用就是修改矩陣的維度
Y = 2*X
# theta = (X'X)-1X'Y
#theta = dot(dot(inv(dot(X.T, X)), X.T), Y)
#theta = theta - alpha*(theta*X-Y)*X 梯度下降演算法
theta = 1.0
alpha = 0.1
for i in range(100):
    theta = theta + np.sum(alpha * (Y - dot(X, theta))*X.reshape(1, 3))/3.
print(theta)