矩阵求逆c++实现

矩阵求逆c++实现

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2014-05-02[我来说两句](http://www.2cto.com/kf/201405/297388.html#comment_iframe)来源：矩阵求逆c++实现

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高斯消元法可以用来找出一个可逆矩阵的逆矩阵。设A 为一个N * N的矩阵，其逆矩阵可被两个分块矩阵表示出来。将一个N * N单位矩阵 放在A 的右手边，形成一个N * 2N的分块矩阵B = [A,I] 。经过高斯消元法的计算程序后，矩阵B 的左手边会变成一个单位矩阵I ，而逆矩阵A ^(-1) 会出现在B 的右手边。假如高斯消元法不能将A 化为三角形的格式，那就代表A 是一个不可逆的矩阵。应用上，高斯消元法极少被用来求出逆矩阵。高斯消元法通常只为线性方程组求解。

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`//********************************``//*** 求任何一个实矩阵的逆***``//********************************``#include` `"stdafx.h"``#include ``#include ``#include ``#include ``using namespace std;``#define N` `10` `//定义方阵的最大阶数为10``//函数的声明部分``float` `MatDet(``float` `*p,` `int` `n);` `//求矩阵的行列式``float` `Creat_M(``float` `*p,` `int` `m,` `int` `n,` `int` `k);` `//求矩阵元素A(m, n)的代数余之式``void` `print(``float` `*p,` `int` `n);` `//输出矩阵n*n``bool Gauss(``float` `A[][N],` `float` `B[][N],` `int` `n);` `//采用部分主元的高斯消去法求方阵A的逆矩阵B``int` `main()``{``float` `*buffer, *p;` `//定义数组首地址指针变量``int` `row, num;` `//定义矩阵的行数和矩阵元素个数``int` `i, j;``float` `determ;` `//定义矩阵的行列式``float` `a[N][N], b[N][N];``int` `n;``cout <<` `"采用逆矩阵的定义法求矩阵的逆矩阵!n"``;``cout <<` `"请输入矩阵的行数: "``;``cin >> row;``num =` `2` `* row * row;``buffer = (``float` `*)calloc(num, sizeof(``float``));` `//分配内存单元``p = buffer;``if` `(NULL != p)``{``for` `(i =` `0``; i < row; i++)``{``cout <<` `"Please input the number of "` `<< i+``1` `<<` `" row: "``;``for` `(j =` `0``; j < row; j++)``{``cin >> *p++;``}``}``}``else``{``cout <<` `"Can't distribute memoryn"``;``}``cout <<` `"The original matrix : n"``;``print(buffer, row);` `//打印该矩阵``determ = MatDet(buffer, row);` `//求整个矩阵的行列式``p = buffer + row * row;``if` `(determ !=` `0``)``{``cout <<` `"The determinant of the matrix is "` `<< determ << endl;``for` `(i =` `0``; i < row; i++)` `//求逆矩阵``{``for` `(j =` `0``; j < row; j++)``{``*(p+j*row+i) = Creat_M(buffer, i, j, row)/determ;``}``}``cout <<` `"The inverse matrix is: "` `<< endl;``print(p, row);` `//打印该矩阵``}``else``{``cout <<` `"The determinant is 0, and there is no inverse matrix!n"``;``}``free(buffer);` `//释放内存空间``cout <<` `"采用部分主元的高斯消去法求方阵的逆矩阵!n"``;``cout <<` `"请输入方阵的阶数: "``;``cin >> n;``cout <<` `"请输入"` `<< n <<` `"阶方阵: n"``;``//输入一个n阶方阵``for` `(i =` `0``; i < n; i++)``{``for` `(j =` `0``; j < n; j++)``{``cin >> a[i][j];``}``}``//运用高斯消去法求该矩阵的逆矩阵并输出``if` `(Gauss(a, b, n))``{``cout <<` `"该方阵的逆矩阵为: n"``;``for` `(i =` `0``; i < n; i++)``{``cout << setw(``4``);``for` `(j =` `0``; j < n; j++)``{``cout << b[i][j] << setw(``10``);``}``cout << endl;``}``}``getchar();``return` `0``;``}``//-----------------------------------------------``//功能: 求矩阵(n*n)的行列式``//入口参数: 矩阵的首地址，矩阵的行数``//返回值: 矩阵的行列式值``//----------------------------------------------``float` `MatDet(``float` `*p,` `int` `n)``{``int` `r, c, m;``int` `lop =` `0``;``float` `result =` `0``;``float` `mid =` `1``;``if` `(n !=` `1``)``{``lop = (n ==` `2``) ?` `1` `: n;` `//控制求和循环次数,若为2阶，则循环1次，否则为n次``for` `(m =` `0``; m < lop; m++)``{``mid =` `1``;` `//顺序求和, 主对角线元素相乘之和``for` `(r =` `0``, c = m; r < n; r++, c++)``{``mid = mid * (*(p+r*n+c%n));``}``result += mid;``}``for` `(m =` `0``; m < lop; m++)``{``mid =` `1``;` `//逆序相减, 减去次对角线元素乘积``for` `(r =` `0``, c = n-``1``-m+n; r < n; r++, c--)``{``mid = mid * (*(p+r*n+c%n));``}``result -= mid;``}``}``else``result = *p;``return` `result;``}``//----------------------------------------------------------------------------``//功能: 求k*k矩阵中元素A(m, n)的代数余之式``//入口参数: k*k矩阵的首地址，矩阵元素A的下标m,n,矩阵行数k``//返回值: k*k矩阵中元素A(m, n)的代数余之式``//----------------------------------------------------------------------------``float` `Creat_M(``float` `*p,` `int` `m,` `int` `n,` `int` `k)``{``int` `len;``int` `i, j;``float` `mid_result =` `0``;``int` `sign =` `1``;``float` `*p_creat, *p_mid;``len = (k-``1``)*(k-``1``);` `//k阶矩阵的代数余之式为k-1阶矩阵``p_creat = (``float``*)calloc(len, sizeof(``float``));` `//分配内存单元``p_mid = p_creat;``for` `(i =` `0``; i < k; i++)``{``for` `(j =` `0``; j < k; j++)``{``if` `(i != m && j != n)` `//将除第i行和第j列外的所有元素存储到以p_mid为首地址的内存单元``{``*p_mid++ = *(p+i*k+j);``}``}``}``sign = (m+n)%``2` `==` `0` `?` `1` `: -``1``;` `//代数余之式前面的正、负号``mid_result = (``float``)sign*MatDet(p_creat, k-``1``);``free(p_creat);``return` `mid_result;``}``//-----------------------------------------------------``//功能: 打印n*n矩阵``//入口参数: n*n矩阵的首地址,矩阵的行数n``//返回值: 无返回值``//-----------------------------------------------------``void` `print(``float` `*p,` `int` `n)``{``int` `i, j;``for` `(i =` `0``; i < n; i++)``{``cout << setw(``4``);``for` `(j =` `0``; j < n; j++)``{``cout << setiosflags(ios::right) << *p++ << setw(``10``);``}``cout << endl;``}``}``//------------------------------------------------------------------``//功能: 采用部分主元的高斯消去法求方阵A的逆矩阵B``//入口参数: 输入方阵，输出方阵，方阵阶数``//返回值: true or false``//-------------------------------------------------------------------``bool Gauss(``float` `A[][N],` `float` `B[][N],` `int` `n)``{``int` `i, j, k;``float` `max, temp;``float` `t[N][N];` `//临时矩阵``//将A矩阵存放在临时矩阵t[n][n]中``for` `(i =` `0``; i < n; i++)``{``for` `(j =` `0``; j < n; j++)``{``t[i][j] = A[i][j];``}``}``//初始化B矩阵为单位阵``for` `(i =` `0``; i < n; i++)``{``for` `(j =` `0``; j < n; j++)``{``B[i][j] = (i == j) ? (``float``)``1` `:` `0``;``}``}``for` `(i =` `0``; i < n; i++)``{``//寻找主元``max = t[i][i];``k = i;``for` `(j = i+``1``; j < n; j++)``{``if` `(fabs(t[j][i]) > fabs(max))``{``max = t[j][i];``k = j;``}``}``//如果主元所在行不是第i行，进行行交换``if` `(k != i)``{``for` `(j =` `0``; j < n; j++)``{``temp = t[i][j];``t[i][j] = t[k][j];``t[k][j] = temp;``//B伴随交换``temp = B[i][j];``B[i][j] = B[k][j];``B[k][j] = temp;``}``}``//判断主元是否为0, 若是, 则矩阵A不是满秩矩阵,不存在逆矩阵``if` `(t[i][i] ==` `0``)``{``cout <<` `"There is no inverse matrix!"``;``return` `false``;``}``//消去A的第i列除去i行以外的各行元素``temp = t[i][i];``for` `(j =` `0``; j < n; j++)``{``t[i][j] = t[i][j] / temp;` `//主对角线上的元素变为1``B[i][j] = B[i][j] / temp;` `//伴随计算``}``for` `(j =` `0``; j < n; j++)` `//第0行->第n行``{``if` `(j != i)` `//不是第i行``{``temp = t[j][i];``for` `(k =` `0``; k < n; k++)` `//第j行元素 - i行元素*j列i行元素``{``t[j][k] = t[j][k] - t[i][k]*temp;``B[j][k] = B[j][k] - B[i][k]*temp;``}``}``}``}``getchar();``return` `true``;``}`

实验结果：


原文链接: https://www.cnblogs.com/zhxshseu/p/5292287.html

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