IMSL_MATRIX_NORM

The IMSL_MATRIX_NORM function computes various norms of a rectangular matrix, a matrix stored in band format, and a matrix stored in coordinate format.

Note: This routine requires an IDL Analyst license. For more information, contact your Exelis VIS sales or technical support representative.

By default, IMSL_MATRIX_NORM computes the Frobenius norm:

If the keyword One_Norm is used, the one norm

is returned. If the keyword Inf_Norm is used, the infinity norm

is returned.

Examples

For additional information on using IMSL_MATRIX_NORM, see Additional Examples.

Example 1

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

a = TRANSPOSE([[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]])

frobenius_norm = IMSL_MATRIX_NORM(a)

inf_norm = IMSL_MATRIX_NORM(a, /INF_NORM)

one_norm = IMSL_MATRIX_NORM(a, /ONE_NORM)

PRINT, 'Frobenius norm = ', frobenius_norm

PRINT, 'Infinity norm = ', inf_norm

PRINT, 'One norm = ', one_norm

 

Frobenius norm = 15.6844

Infinity norm = 20.0000

One norm = 17.0000

Syntax

To compute various norms of a rectangular matrix:

Result = IMSL_MATRIX_NORM(a [, /DOUBLE] [, INF_NORM=value] [, ONE_NORM=value] [, SYMMETRIC=value])

To compute various norms of a matrix stored in band format:

Result = IMSL_MATRIX_NORM(n, nlca, nuca, a [, /DOUBLE] [, INF_NORM=value] [, ONE_NORM=value] [, SYMMETRIC=value])

To compute various norms of a matrix stored in coordinate format:

Result = IMSL_MATRIX_NORM(nrows, ncols, a [, /DOUBLE] [, INF_NORM=value] [, ONE_NORM=value] [, SYMMETRIC=value])

Return Value

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

Arguments

a

Matrix for which the norm will be computed.

n

The order of matrix a.

ncols

The number of columns in matrix a.

nlca

Number of lower codiagonals of a.

nrows

The number of rows in matrix a.

nuca

Number of upper co-diagonals of a.

Keywords

DOUBLE

If present and nonzero, double precision is used.

INF_NORM

If present and nonzero, IMSL_MATRIX_NORM computes the infinity norm of matrix a.

ONE_NORM

If present and nonzero, IMSL_MATRIX_NORM computes the one norm of matrix a.

SYMMETIC

If present and nonzero, matrix a is stored in symmetric storage mode. Keyword SYMMETRIC can not be used with a rectangular matrix.

Additional Examples

Example 2

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

nlca = 1

nuca = 1

n = 4

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]

frobenius_norm = IMSL_MATRIX_NORM(n, nlca, nuca, a)

inf_norm = IMSL_MATRIX_NORM(n, nlca, nuca, a, /INF_NORM)

one_norm = IMSL_MATRIX_NORM(n, nlca, nuca, a, /ONE_NORM)

PRINT, 'Frobenius norm = ', frobenius_norm

PRINT, 'Infinity norm = ', inf_norm

PRINT, 'One norm = ', one_norm

 

Frobenius norm = 6.55744

Infinity norm = 5.00000

One norm = 8.00000

Example 3

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

nlca = 2

nuca = 2

n = 6

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]

frobenius_norm = IMSL_MATRIX_NORM(n, nlca, nuca, a, /SYMMETRIC)

inf_norm = IMSL_MATRIX_NORM(n, nlca, nuca, a, /INF_NORM, $

/SYMMETRIC)

one_norm = IMSL_MATRIX_NORM(n, nlca, nuca, a, /ONE_NORM, $

/SYMMETRIC)

PRINT, 'Frobenius norm = ', frobenius_norm

PRINT, 'Infinity norm = ', inf_norm

PRINT, 'One norm = ', one_norm

 

Frobenius norm = 16.9411

Infinity norm = 16.0000

One norm = 16.0000

Example 4

Compute the Frobenius norm, infinity norm, and one norm of matrix a. Matrix a is stored in coordinate format.

nrows = 6

ncols = 6

a = REPLICATE(imsl_f_sp_elem, 15)

a(*).row = [0, 1, 1, 1, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5]

a(*).col = [0, 1, 2, 3, 2, 0, 3, 4, 0, 3, 4, 5, 0, 1, 5]

a(*).val = [10.0, 10.0, -3.0, -1.0, 15.0, $

-2.0, 10.0, -1.0, -1.0, -5.0, 1.0, -3.0, -1.0, -2.0, 6.0]

frobenius_norm = IMSL_MATRIX_NORM(nrows, ncols, a)

inf_norm = IMSL_MATRIX_NORM(nrows, ncols, a, /INF_NORM)

one_norm = IMSL_MATRIX_NORM(nrows, ncols, a, /ONE_NORM)

PRINT, 'Frobenius norm = ', frobenius_norm

PRINT, 'Infinity norm = ', inf_norm

PRINT, 'One norm = ', one_norm

 

Frobenius norm = 24.8395

Infinity norm = 15.0000

One norm = 18.0000

Example 5

Compute the Frobenius norm, infinity norm and one norm of matrix a. Matrix a is stored in symmetric coordinate format.

nrows = 6

ncols = 6

a = REPLICATE(imsl_f_sp_elem, 9)

a(*).row = [0, 0, 0, 1, 1, 2, 2, 4, 4]

a(*).col = [0, 2, 5, 3, 4, 2, 5, 4, 5]

a(*).val = [10.0, -1.0, 5.0, 2.0, 3.0, 3.0, 4.0, -1.0, 4.0]

frobenius_norm = IMSL_MATRIX_NORM(nrows, ncols, a, /SYMMETRIC)

inf_norm = IMSL_MATRIX_NORM(nrows, ncols, a, /INF_NORM, $

/SYMMETRIC)

one_norm = IMSL_MATRIX_NORM(nrows, ncols, a, /ONE_NORM, $

/SYMMETRIC)

PRINT, 'Frobenius norm = ', frobenius_norm

PRINT, 'Infinity norm = ', inf_norm

PRINT, 'One norm = ', one_norm

 

Frobenius norm = 15.8745

Infinity norm = 16.0000

One norm = 16.0000

Version History

6.4

Introduced
   

See Also

 

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