python 高斯约当消元法求逆矩阵

judge函数判断该矩阵该矩阵是否有逆矩阵

calculate计算逆矩阵

import sys


class MatrixInverse:
    """"求逆矩阵"""

    def __init__(self, matrix):
        self.matrix = matrix
        self.a = len(self.matrix)
        self.b = len(self.matrix[0])
        if self.a != self.b:
            print("该矩阵不可求逆矩阵")

    def judge(self):
        c = 1
        e = 0
        m = self.matrix
        for i in range(self.a):
            for j in range(self.a):
                c = c * m[j % self.a][(i + j) % self.a]
                # print(f"{j % self.a},{(i + j) % self.a}")
            e = e + c
            c = 1
        for i in range(self.a):
            for j, k in zip(range(0, self.a*2, 2), range(self.a)):
                c = c * m[k % self.a][(i + j) % self.a]
                # print(f"{k % self.a},{(i + j) % self.a}")
            e = e - c
            c = 1
        print(f"该矩阵的值为：{e}", end=",")
        if e != 0:
            print("存在逆矩阵。")
        else:
            print("不存在逆矩阵。")
        return e

    def calculate(self):
        """使用高斯约当消元法计算所给矩阵的逆矩阵"""
        if MatrixInverse.judge(self) == 0:
            sys.exit()
        d = [[0 for i in range(self.a*2)] for j in range(self.a)]
        e = [[0 for i in range(self.a)] for j in range(self.a)]
        for i, j in zip(range(self.a), range(self.a)):
            e[i][j] = 1
        for i in range(self.a):
            for j in range(self.a):
                d[i][j] = self.matrix[i][j]
        for i in range(self.a):
            for j in range(self.a, self.a*2):
                d[i][j] = e[i][j-self.a]
        """重新选取主元"""
        m1 = []
        for i in range(self.a):
            m1.append(i)
        for i in range(self.a):
            m = 0
            while m < self.a:  # 这两个循环为选取主元
                if d[m][i] != 0 and i < self.a and m in m1:
                    c2 = d[m][i]  # c2 为选取的主元,m为行，i为列。
                    for x in range(self.a*2):  # 本循环改变主元所在行的元素，各元素除以主元
                        d[m][x] = d[m][x]/c2  # 防止 d[i][m] 的变化
                    for j in range(self.a):  # 本循环以主元所在行为标准，改变其他行
                        c3 = d[j][i]
                        for k in range(self.a*2):
                            if j != m:
                                d[j][k] = d[j][k]/c3 - d[m][k]
                    m1.remove(m)
                    m = self.a  # i 列产生主元后，本列不再产生主元，切换到下一列
                else:
                    m += 1
        for i in range(self.a):
            for j in range(self.a):
                if d[i][j] != 0:
                    c5 = d[i][j]
                    for k in range(self.a*2):
                        d[i][k] = d[i][k]/c5
        """将逆矩阵保存在d2中"""
        d2 = [[0 for i in range(self.a)] for j in range(self.a)]
        for i in range(self.a):
            for j in range(self.a, self.a*2):
                d2[i][j-self.a] = float('%.2f' % d[i][j])
        print("该矩阵的逆矩阵为：")
        print(d2)


n = [[1, 2, 3], [0, 0, 0], [3, 4, 3]]
s = MatrixInverse(n)
s.calculate()

结果: 

代码只支持二维矩阵