#include <stdio.h>
#include <stdlib.h>
#include <malloc.h>
void MatrixOpp(double *A, int m, int n, double* invmat);
void MatrixInver(double *A, int m, int n, double* invmat);
double Surplus(double A[], int m, int n);
int matrix_inv(double* p, int num, double* invmat);
void MatrixOpp(double A[], int m, int n, double* invmat)
{
int i, j, x, y, k;
double *SP = NULL, *AB = NULL, *B = NULL, X;
SP = (double *) malloc(m * n * sizeof(double));
AB = (double *) malloc(m * n * sizeof(double));
B = (double *) malloc(m * n * sizeof(double));
X = Surplus(A, m, n);
X = 1 / X;
for (i = 0; i < m; i++)
for (j = 0; j < n; j++)
{
for (k = 0; k < m * n; k++)
B[k] = A[k];
{
for (x = 0; x < n; x++)
B[i * n + x] = 0;
for (y = 0; y < m; y++)
B[m * y + j] = 0;
B[i * n + j] = 1;
SP[i * n + j] = Surplus(B, m, n);
AB[i * n + j] = X * SP[i * n + j];
}
}
MatrixInver(AB, m, n, invmat);
free(SP);
free(AB);
free(B);
}
void MatrixInver(double A[], int m, int n, double* invmat)
{
int i, j;
double *B = invmat;
for (i = 0; i < n; i++)
for (j = 0; j < m; j++)
B[i * m + j] = A[j * n + i];
}
double Surplus(double A[], int m, int n)
{
int i, j, k, p, r;
double X, temp = 1, temp1 = 1, s = 0, s1 = 0;
if (n == 2)
{
for (i = 0; i < m; i++)
for (j = 0; j < n; j++)
if ((i + j) % 2)
temp1 *= A[i * n + j];
else
temp *= A[i * n + j];
X = temp - temp1;
}
else
{
for (k = 0; k < n; k++)
{
for (i = 0, j = k; i < m, j < n; i++, j++)
temp *= A[i * n + j];
if (m - i)
{
for (p = m - i, r = m - 1; p > 0; p--, r--)
temp *= A[r * n + p - 1];
}
s += temp;
temp = 1;
}
for (k = n - 1; k >= 0; k--)
{
for (i = 0, j = k; i < m, j >= 0; i++, j--)
temp1 *= A[i * n + j];
if (m - i)
{
for (p = m - 1, r = i; r < m; p--, r++)
temp1 *= A[r * n + p];
}
s1 += temp1;
temp1 = 1;
}
X = s - s1;
}
return X;
}
int matrix_inv(double* p, int num, double* invmat)
{
if (p == NULL || invmat == NULL)
{
return 1;
}
if (num > 10)
{
return 2;
}
MatrixOpp(p, num, num, invmat);
return 0;
}
int main()
{
int i, j;
int num;
double *arr=NULL;
double *result=NULL;
int flag;
printf("请输入矩阵维数:\n");
scanf("%d",&num);
arr=(double *)malloc(sizeof(double)*num*num);
result=(double *)malloc(sizeof(double)*num*num);
printf("请输入%d*%d矩阵:\n", num, num);
for (i = 0; i < num; i++)
{
for (j = 0; j < num; j++)
{
scanf("%lf", &arr[i * num + j]);
}
}
flag = matrix_inv(arr, num, result);
if(flag==0)
{
printf("逆矩阵为:\n");
for (i = 0; i < num * num; i++)
{
printf("%lf\t ", *(result + i));
if (i % num == (num - 1))
printf("\n");
}
}
else if(flag==1)
{
printf("p/q为空\n");
}
else
{
printf("超过最大维数\n");
}
system("PAUSE");
free(arr);
free(result);
return 0;
}
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