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)总结
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