高斯消去法python（源码）

import numpy as np


def gauss(a, b):
    m, n = a.shape  # 获取矩阵的行数和列数
    c = np.zeros(n)  # 根据矩阵的行数构建一个一维0数组
    for i in range(n):
        # 限制条件
        if (a[i][i] == 0):  # 用高斯消去法解线性方程组时对角线元素不能为0
            print("no answer")

    # k表示第一层循环，(0，n-1)行
    # i表示第二层循环,(k+1,n)行,计算该行消元的系数
    # j表示列

    for k in range(n - 1):
        for i in range(k + 1, n):
            c[i] = a[i][k] / a[k][k]  # 计算出系数

            for j in range(k,m):  # 从K开始，减少不必要的计算
                a[i][j] = a[i][j] - c[i] * a[k][j]  # 对矩阵进行高斯消去
            b[i] = b[i] - c[i] * b[k]

        print(a)
        #print(b)
    x = np.zeros(n)

    x[n - 1] = b[n - 1] / a[n - 1][n - 1]  # 解出x[n-1],为回代作准备

    # 回代求出方程解
    for i in range(n-2, -1, -1):
        sum= 0.0
        for j in range(n-1, -1, -1):
            sum= sum + a[i][j] * x[j]
        x[i] = (b[i]-sum) / a[i][i]
        #print(sum)

    for i in range(n):
        print("x" + str(i + 1) + " = ","%.2f" % x[i])  # 输出结果


if __name__ == '__main__':
    a = np.array([[2.0, -1.0, 3.0, 2.0], [3.0, -3.0, 3.0, 2.0], [3.0, -1.0, -1.0, 2.0], [3.0, -1.0, 3.0, -1.0]])
    b = np.array([6.0, 5.0, 3.0, 4.0])
    gauss(a, b)