不带行交换的Guass消去法，python实现

import numpy as np


# 合并A、b，增广矩阵AB


class gauss:

    def __init__(self, A: list, b_T: list):
        '''
        :param A: 矩阵A,n*n
        :param b_T: 常数项b的转置,n
        '''
        self.A = np.array(A)
        self.b_T = np.array(b_T)

        self.__n = len(self.b_T)

        # 用于保存返回值
        self.x = np.zeros(self.__n)

    def xiao_yuan(self):
        '''
        消去过程

        :return:
        '''
        b = self.b_T.reshape(-1, 1)
        # reshape(-1, 1) 转换成一列
        AB = np.column_stack((self.A, b))
        # 将A、b合并成增广矩阵AB
        for k in range(1, self.__n + 1):
            for i in range(k, self.__n):
                '''
                 这个循环内操作的矩阵，实际上被限制为原始矩阵截去前k行
                 外层循环：k=1 
                '''
                m = -AB[i][k - 1] / AB[k - 1][k - 1]
                AB[i] += AB[k - 1] * m
                # m乘方程式两边第一行加到第i行
            else:
                # print(f'第{k}次\n', AB)
                pass
        else:
            # 循环结束，重新对A、b_T进行赋值
            AB_T = AB.transpose()
            # 将AB 进行转置，用于重新拆分出A 和 b_T
            self.A = (AB_T[:len(AB_T) - 1]).transpose()
            self.b_T = AB_T[-1]

    def hui_dai(self):
        '''
        回代过程

        :return:
        '''

        def sum_ax(k: int):
            sum2 = 0.0
            for q in range(k + 1, self.__n):
                sum2 += (self.A[k][q] * self.x[q])
            return float(sum2)

        for j in range(self.__n - 1, -1, -1):
            if j == self.__n - 1:
                self.x[j] = self.b_T[j] / self.A[j][j]
            else:
                self.x[j] = (self.b_T[j] - sum_ax(k=j)) / self.A[j][j]

    def get_result(self):

        return self.x


A = [[0.2641, 0.1735, 0.8642],
     [0.9411, -0.0175, 0.1463],
     [-0.8641, -0.4243, 0.0711]]

b_T = [-0.7521, 0.6310, 0.2501]

G = gauss(A=A, b_T=b_T)

G.xiao_yuan()
G.hui_dai()

y = G.get_result()

因为起始坐标原因，函数传参部分细节需要注意