Python实现最小二乘法：原理、视角与代码解析

#! /usr/bin/env python
# -*- coding: utf-8 -*-
import numpy as np
def calc_left_k_mat(k):
 """
 获得左侧k矩阵
 :param k:
 :return:
 """
 k_mat = []
 for i in range(k + 1):
  now_line = []
  for j in range(k + 1):
   now_line.append(j + i)
  k_mat.append(now_line)
 return k_mat
def calc_right_k_mat(k):
 """
 计算右侧矩阵
 :param k:
 :return:
 """
 k_mat = []
 for i in range(k + 1):
  k_mat.append([i, i + 1])
 return k_mat
def pow_k(x, k):
 """
 计算x列表中的k次方和
 :param x: 点集合的x坐标
 :param k: k值
 :return:
 """
 sum = 0
 for i in x:
  sum += i ** k
 return sum
def get_left_mat_with_x(k_mat, k):
 """
 将 左侧k矩阵运算得到左侧新的矩阵
 :param k_mat:
 :param k:
 :return:
 """
 left_mat = []
 for kl in k_mat:
  now_data = []
  for k in kl:
   now_data.append(pow_k(x, k))
  left_mat.append(now_data)
 return left_mat
def get_right_mat_with(right_k_mat):
 """
 将 右侧k矩阵运算得到右侧新的矩阵
 :param right_k_mat:
 :return:
 """
 right_mat = []
 for i in range(len(right_k_mat)):
  sum = 0
  for xL, yL in zip(x, y):
   a = (xL ** right_k_mat[i][0]) * (yL ** right_k_mat[i][1])
   sum += a
  right_mat.append(sum)
 return right_mat
def fuse_mat(left, right):
 """
 融合两个矩阵
 :param left:
 :param right:
 :return:
 """
 new_mat = []
 for i in range(len(left)):
  asd = np.append(left[i], right[i])
  new_mat.append(list(asd))
 return new_mat
if __name__ == '__main__':
 k = 3
 x = [1, 2, 3]
 y = [1, 2, 3]
 # 计算原始左侧K矩阵
 left_k_mat = calc_left_k_mat(k)
 print("原始左侧K矩阵")
 print(left_k_mat)
 # 计算原始右侧K矩阵
 right_k_mat = calc_right_k_mat(k)
 print("原始右侧k矩阵")
 print(right_k_mat)
 # 计算左侧 k 矩阵
 new_left_mat = get_left_mat_with_x(k_mat=left_k_mat, k=k)
 # 计算右侧 k 矩阵
 new_right_mat = get_right_mat_with(right_k_mat=right_k_mat)
 print("计算后左侧K矩阵")
 print(new_left_mat)
 print("计算后右侧侧K矩阵")
 print(new_right_mat)
 print("-----" * 10)
 # 融合两个矩阵 左侧 矩阵每一行增加 右侧矩阵的对应行
 new_all = fuse_mat(new_left_mat, new_right_mat)
 print("完整矩阵")
 print(new_all)