c 语言求矩阵的二范数
时间: 2024-01-25 16:05:19 浏览: 29
矩阵的二范数定义为矩阵的所有特征值的平方和再开平方,可以使用以下 C 语言代码实现:
```c
#include <stdio.h>
#include <math.h>
#define ROWS 3
#define COLS 3
void matrix_transpose(double mat[][COLS], double transposed[][ROWS]) {
for (int i = 0; i < ROWS; ++i) {
for (int j = 0; j < COLS; ++j) {
transposed[j][i] = mat[i][j];
}
}
}
double matrix_norm(double mat[][COLS]) {
double transposed[COLS][ROWS];
matrix_transpose(mat, transposed);
double product[ROWS][ROWS];
for (int i = 0; i < ROWS; ++i) {
for (int j = 0; j < ROWS; ++j) {
double sum = 0.0;
for (int k = 0; k < COLS; ++k) {
sum += mat[i][k] * transposed[k][j];
}
product[i][j] = sum;
}
}
double eigenvalues[ROWS];
double eigenvectors[ROWS][ROWS];
int info;
char jobz = 'N';
char uplo = 'U';
int n = ROWS;
double work[3 * ROWS - 1];
int lwork = 3 * ROWS - 1;
double rwork[3 * ROWS - 2];
dsyev_(&jobz, &uplo, &n, &product[0][0], &n, &eigenvalues[0], &work[0], &lwork, &rwork[0], &info);
double eigenvalue_sum = 0.0;
for (int i = 0; i < ROWS; ++i) {
eigenvalue_sum += eigenvalues[i];
}
return sqrt(eigenvalue_sum);
}
int main() {
double mat[ROWS][COLS] = {
{1.0, 2.0, 3.0},
{4.0, 5.0, 6.0},
{7.0, 8.0, 9.0}
};
printf("The matrix norm is %f\n", matrix_norm(mat));
return 0;
}
```
这里使用了 BLAS 和 LAPACK 库中的 `dsyev` 函数来计算矩阵的特征值和特征向量。需要在编译时链接这两个库,例如:
```bash
gcc -o matrix_norm matrix_norm.c -lblas -llapack
```