C语言用指针完成矩阵求逆
时间: 2023-07-20 20:09:51 浏览: 56
矩阵求逆是一个比较复杂的计算问题,需要用到高级的数学算法和数据结构。在C语言中,可以使用指针完成矩阵求逆的计算,但是需要编写复杂的程序来实现。
以下是一个使用指针完成矩阵求逆的C语言示例程序:
```c
#include <stdio.h>
// 计算矩阵行列式的值
float determinant(float **mat, int n){
float det = 0;
float **submat;
if (n == 2) {
return ((mat[0][0] * mat[1][1]) - (mat[1][0] * mat[0][1]));
}
else {
submat = (float **)malloc((n-1)*sizeof(float *));
for (int i = 0; i < n-1; i++){
submat[i] = (float *)malloc((n-1)*sizeof(float));
}
for (int x = 0; x < n; x++){
int subi = 0;
for (int i = 1; i < n; i++){
int subj = 0;
for (int j = 0; j < n; j++){
if (j == x)
continue;
submat[subi][subj] = mat[i][j];
subj++;
}
subi++;
}
det = det + (mat[0][x] * pow(-1,x) * determinant(submat,n-1));
}
for (int i = 0; i < n-1; i++){
free(submat[i]);
}
free(submat);
}
return det;
}
// 计算伴随矩阵
void adjoint(float **mat, float **adj, int n){
if (n == 1){
adj[0][0] = 1;
return;
}
int sign = 1;
float **submat;
submat = (float **)malloc((n-1)*sizeof(float *));
for (int i = 0; i < n-1; i++){
submat[i] = (float *)malloc((n-1)*sizeof(float));
}
for (int i = 0; i < n; i++){
for (int j = 0; j < n; j++){
int subi = 0;
for (int x = 0; x < n; x++){
if (x == i)
continue;
int subj = 0;
for (int y = 0; y < n; y++){
if (y == j)
continue;
submat[subi][subj] = mat[x][y];
subj++;
}
subi++;
}
float det = determinant(submat, n-1);
adj[j][i] = sign * det;
sign = -sign;
}
}
for (int i = 0; i < n-1; i++){
free(submat[i]);
}
free(submat);
}
// 计算矩阵的逆
void inverse(float **mat, float **inv, int n){
float det = determinant(mat, n);
if (det == 0){
printf("Inverse of Entered Matrix is not possible\n");
return;
}
float **adj;
adj = (float **)malloc(n*sizeof(float *));
for (int i = 0; i < n; i++){
adj[i] = (float *)malloc(n*sizeof(float));
}
adjoint(mat, adj, n);
for (int i = 0; i < n; i++){
for (int j = 0; j < n; j++){
inv[i][j] = adj[i][j] / det;
}
}
for (int i = 0; i < n; i++){
free(adj[i]);
}
free(adj);
}
int main(){
float **mat, **inv;
int n;
printf("Enter the order of matrix: ");
scanf("%d", &n);
mat = (float **)malloc(n*sizeof(float *));
inv = (float **)malloc(n*sizeof(float *));
for (int i = 0; i < n; i++){
mat[i] = (float *)malloc(n*sizeof(float));
inv[i] = (float *)malloc(n*sizeof(float));
}
printf("Enter the elements of matrix:\n");
for (int i = 0; i < n; i++){
for (int j = 0; j < n; j++){
scanf("%f", &mat[i][j]);
}
}
inverse(mat, inv, n);
printf("Inverse of the matrix:\n");
for (int i = 0; i < n; i++){
for (int j = 0; j < n; j++){
printf("%f ", inv[i][j]);
}
printf("\n");
}
for (int i = 0; i < n; i++){
free(mat[i]);
free(inv[i]);
}
free(mat);
free(inv);
return 0;
}
```
这个程序使用了指针来动态分配矩阵和伴随矩阵的内存空间,并使用递归算法来计算矩阵行列式和伴随矩阵。然后,它使用伴随矩阵和行列式的值来计算矩阵的逆。