110 lines
2.8 KiB
Python
110 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:
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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:
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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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