Computes various norms of a matrix stored in band storage mode.

Synopsis

#include <imsl.h>

float imsl_f_matrix_norm_band (int n, float a[], int nlc, int nuc, ..., 0)

The type double function is imsl_d_matrix_norm_band.

Required Arguments

int n   (Input)
The order of matrix A.

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

int nlc   (Input)
Number of lower codiagonals of A.

int nuc   (Input)
Number of upper codiagonals of A.

Return Value

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

Synopsis with Optional Arguments

#include <imsl.h>

float imsl_f_matrix_norm_band (int n, float a[], int nlc, int nuc,
IMSL_ONE_NORM,
IMSL_INF_NORM,
IMSL_SYMMETRIC,
0)

Optional Arguments

IMSL_ONE_NORM,
Compute the 1-norm of matrix A,

IMSL_INF_NORM,
Compute the infinity norm of matrix A,

IMSL_SYMMETRIC,
Matrix A is stored in band symmetric storage mode.

Description

By default, imsl_f_matrix_norm_band 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.

Examples

Example 1

Compute the Frobenius norm, infinity norm, and one norm of matrix A. Matrix A is stored in band storage mode.

#include <imsl.h>

void main()

{

        float a[] = {0.0, 2.0, 3.0, -1.0,

                     1.0, 1.0, 1.0, 1.0,

                     0.0, 3.0, 4.0, 0.0};

        int          nlc = 1, nuc = 1;

        int          n = 4;

        float        frobenius_norm, inf_norm, one_norm;

        frobenius_norm = imsl_f_matrix_norm_band(n, a, nlc, nuc, 0);

        inf_norm = imsl_f_matrix_norm_band(n, a, nlc, nuc,

                                      IMSL_INF_NORM, 0);

        one_norm = imsl_f_matrix_norm_band(n, a, nlc, nuc,

                                      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 = 6.557438

Infinity norm  = 5.000000

One norm       = 8.000000

Example 2

Compute the Frobenius norm, infinity norm, and one norm of matrix A. Matrix A is stored in sym­metric band storage mode.

#include <imsl.h>

 

void main()

{

        float a[] = {0.0, 0.0, 7.0, 3.0, 1.0, 4.0,

                     0.0, 5.0, 1.0, 2.0, 1.0, 2.0,

                     1.0, 2.0, 4.0, 6.0, 3.0, 1.0};

        int          nlc = 2, nuc = 2;

        int          n = 6;

        float        frobenius_norm, inf_norm, one_norm;

 

        frobenius_norm = imsl_f_matrix_norm_band(n, a, nlc, nuc,

                                      IMSL_SYMMETRIC, 0);

 

        inf_norm = imsl_f_matrix_norm_band(n, a, nlc, nuc,

                                      IMSL_INF_NORM,

                                      IMSL_SYMMETRIC, 0);

 

        one_norm = imsl_f_matrix_norm_band(n, a, nlc, nuc,

                                      IMSL_ONE_NORM,

                                      IMSL_SYMMETRIC, 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 = 16.941074

Infinity norm  = 16.000000

One norm       = 16.000000

Visual Numerics, Inc. Visual Numerics - Developers of IMSL and PV-WAVE http://www.vni.com/ PHONE: 713.784.3131 FAX:713.781.9260