algorithm-in-python/math/numericalAnalysis/least_square.py

''' mbinary
#########################################################################
# File : least_square.py
# Author: mbinary
# Mail: zhuheqin1@gmail.com
# Blog: https://mbinary.xyz
# Github: https://github.com/mbinary
# Created Time: 2018-10-02  21:14
# Description:
#########################################################################
'''

'''*************************************************************************
    > File Name: least-square.py
    > Author: mbinary
    > Mail: zhuheqin1@gmail.com 
    > Created Time: Sat 07 Apr 2018 09:55:25 PM DST
    > Blog: https://mbinary.xyz
    > Description: 最小二乘法解线性方程组, 解矛盾方程组
 ************************************************************************'''




import re
import numpy as np
def solveConflitEqualtion(A, y):
    '''solve equation like this: Av = y,  
        A:m*n  v:n*1  y:m*1 
        return vector v
    '''
    A = np.matrix(A)
    y = np.array(y)
    ata = A.T*A
    print('AtA')
    print(ata)
    return np.linalg.solve(ata, A.T*y)  # note that is numpy.linalg.solve


def solveLinear(point, index):
    y = [[i[1]] for i in point]
    x = [[i[0]] for i in point]
    A = []
    for i in x:
        A.append([i[0]**j for j in index])
    res = solveConflitEqualtion(A, y)
    print('the solution is : \n', res)
    print('namely: ')
    items = ['{:.4f}x^{}'.format(res[i, 0], j) for i, j in enumerate(index)]
    print('phi(x) = ', ' + '.join(items))


def handleInput(s=None, y=None):
    # numPt = re.compile (r'\d*\.{0,1}\d+')
    if not s:
        s = input('input matrix A:m*n  //m>=n\n')
    s = s.replace(' ', '')
    li = re.findall(r'(\[(\d+)(,(\d+))+\])', s)
    li = [parseLst(i[0]) for i in li]
    if not y:
        y = input('input a vector y:n*1\n')
    y = parseLst(y)
    print('Equation: Av = y:')

    print('y is as follows: ')
    print(y)
    print('A is as follows: ')
    for i in li:
        for j in i:
            print('{}'.format(j).rjust(5), end='')
        print('')

    print('result v is as follows: ')
    res = solveConflitEqualtion(li, y)
    print(res)


def parseLst(s):
    s = s.strip('[]')
    li = s.split(',')
    li = [float(j) for j in li]
    return li


if __name__ == '__main__':
    '''
    li = '[[23,2],[2,5],[2,6]]'
    y = '[1,3]'
    while True:
        handleInput(li,y)
        s = input('input y to continue, n for exit')
        if s!='y':break
    '''
    point = [(-3, 14.3), (-2, 8.3), (-1, 4.7), (2, -8.3), (4, -22.7)]
    lst = [0, 3]
    solveLinear(point, lst)

    point = [(-3, 14.3), (-2, 8.3), (-1, 4.7), (2, 8.3), (4, 22.7)]
    lst = [0, 2]
    solveLinear(point, lst)

    A = [[1, 2], [2, 1], [1, 1]]
    y = [[5], [6], [4]]
    res = solveConflitEqualtion(A, y)

    print(res)
    A = [[1, -2], [1, 5], [2, 1], [1, 1]]
    y = [[1], [13.1], [7.9], [5.1]]
    print(solveConflitEqualtion(A, y))