105 lines
2.8 KiB
Python
105 lines
2.8 KiB
Python
''' mbinary
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#########################################################################
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# File : least_square.py
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# Author: mbinary
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# Mail: zhuheqin1@gmail.com
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# Blog: https://mbinary.xyz
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# Github: https://github.com/mbinary
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# Created Time: 2018-10-02 21:14
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# Description:
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#########################################################################
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'''
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'''*************************************************************************
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> File Name: least-square.py
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> Author: mbinary
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> Mail: zhuheqin1@gmail.com
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> Created Time: Sat 07 Apr 2018 09:55:25 PM DST
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> Blog: https://mbinary.xyz
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> Description: 最小二乘法解线性方程组, 解矛盾方程组
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************************************************************************'''
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import re
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import numpy as np
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def solveConflitEqualtion(A,y):
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'''solve equation like this: Av = y,
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A:m*n v:n*1 y:m*1
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return vector v
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'''
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A = np.matrix(A)
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y = np.array(y)
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ata = A.T*A
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print('AtA')
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print(ata)
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return np.linalg.solve(ata,A.T*y) # note that is numpy.linalg.solve
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def solveLinear(point,index):
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y = [[i[1]] for i in point]
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x = [[i[0]] for i in point]
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A = []
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for i in x:
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A.append([i[0]**j for j in index])
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res = solveConflitEqualtion(A,y)
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print('the solution is : \n',res)
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print('namely: ')
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items = ['{:.4f}x^{}'.format(res[i,0],j) for i, j in enumerate(index)]
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print('phi(x) = ',' + '.join(items))
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def handleInput(s=None,y=None):
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# numPt = re.compile (r'\d*\.{0,1}\d+')
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if not s: s = input('input matrix A:m*n //m>=n\n')
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s = s.replace(' ','')
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li = re.findall(r'(\[(\d+)(,(\d+))+\])',s)
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li = [parseLst(i[0]) for i in li]
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if not y:y = input('input a vector y:n*1\n')
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y = parseLst(y)
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print('Equation: Av = y:')
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print('y is as follows: ')
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print(y)
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print('A is as follows: ')
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for i in li:
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for j in i:
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print('{}'.format(j).rjust(5),end='')
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print('')
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print('result v is as follows: ')
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res = solveConflitEqualtion(li,y)
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print(res)
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def parseLst(s):
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s = s.strip('[]')
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li = s.split(',')
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li = [float(j) for j in li]
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return li
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if __name__ == '__main__':
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'''
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li = '[[23,2],[2,5],[2,6]]'
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y = '[1,3]'
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while True:
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handleInput(li,y)
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s = input('input y to continue, n for exit')
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if s!='y':break
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'''
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point = [(-3,14.3),(-2,8.3),(-1,4.7),(2,-8.3),(4,-22.7)]
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lst = [0,3]
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solveLinear(point,lst)
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point= [(-3,14.3),(-2,8.3),(-1,4.7),(2,8.3),(4,22.7)]
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lst = [0,2]
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solveLinear(point,lst)
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A = [[1,2],[2,1],[1,1]]
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y = [[5],[6],[4]]
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res = solveConflitEqualtion(A,y)
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print(res)
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A = [[1,-2],[1,5],[2,1],[1,1]]
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y = [[1],[13.1],[7.9],[5.1]]
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print(solveConflitEqualtion(A,y))
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