Python最小二乘法矩阵


						最小二乘法矩阵





#! /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)



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