求逆矩阵的C++程序

/*/* 求任何一个矩阵的逆*/*#include #include #include #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*nbool Gauss(float AN, float BN, int n); /采用部分主元的高斯消去法求方阵A的逆矩阵Bint 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 aNN, bNN; int n; cout 采用逆矩阵的定义法求矩阵的逆矩阵!n; cout 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 *p+; else cout Cant 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 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 aij; /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 bij setw(10); cout endl; 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 AN, float BN, int n) int i, j, k; float max, temp; float tNN; /临时矩阵 /将A矩阵存放在临时矩阵tnn中 for (i = 0; i n; i+) for (j = 0; j n; j+) tij = Aij; /初始化B矩阵为单位阵 for (i = 0; i n; i+) for (j = 0; j n; j+) Bij = (i = j) ? (float)1 : 0; for (i = 0; i n; i+) /寻找主元 max = tii; k = i; for (j = i+1; j fabs(max) max = tji; 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 = tij; tij = tkj; tkj = temp; /B伴随交换 temp = Bij; Bij = Bkj; Bkj = 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 (tii = 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 = tii; for (j = 0; j n; j+) tij = tij / temp; /主对角线上的元素变