matrix_norm

Computes various norms of a rectangular matrix.

#include <imsl.h>

float imsl_f_matrix_norm (int m, int n, float a[], ..., 0)

The type double function is imsl_d_matrix_norm.

int m (Input)
The number of rows in matrix A.

int n (Input)
The number of columns in matrix A.

float a[] (Input)
Matrix for which the norm will be computed.

The requested norm of the input matrix. If the norm cannot be computed, NaN is returned.

#include <imsl.h>

float imsl_f_matrix_norm (int m, int n, float a[],

IMSL_ONE_NORM,

IMSL_INF_NORM,

IMSL_ONE_NORM,
Compute the 1-norm of matrix A,

IMSL_INF_NORM,
Compute the infinity norm of matrix A,

By default, imsl_f_matrix_norm computes the Frobenius norm

If the option IMSL_ONE_NORM is selected, the 1-norm

is returned. If the option IMSL_INF_NORM is selected, the infinity norm

is returned.

Compute the Frobenius norm, infinity norm, and one norm of matrix A.

#include <imsl.h>

int main()

{

float a[] = {1.0, 2.0, -2.0, 3.0,

-2.0, 1.0, 3.0, 0.0,

0.0, 3.0, 1.0, -7.0,

5.0, -2.0, 7.0, 6.0,

4.0, 3.0, 4.0, 0.0};

int m = 5, n = 4;

float frobenius_norm, inf_norm, one_norm;

frobenius_norm = imsl_f_matrix_norm(m, n, a, 0);

inf_norm = imsl_f_matrix_norm(m, n, a, IMSL_INF_NORM, 0);

one_norm = imsl_f_matrix_norm(m, n, a, IMSL_ONE_NORM, 0);

printf("Frobenius norm = %f\n", frobenius_norm);

printf("Infinity norm = %f\n", inf_norm);

printf("One norm = %f\n", one_norm);

}

Output

Frobenius norm = 15.684387

Infinity norm = 20.000000

One norm = 17.000000