# naginterfaces.library.blast.zgb_​norm¶

naginterfaces.library.blast.zgb_norm(inorm, m, kl, ku, ab)[source]

zgb_norm calculates the value of the -norm, the -norm, the Frobenius norm or the maximum absolute value of the elements of a complex band matrix stored in banded packed form.

For full information please refer to the NAG Library document for f16ub

https://www.nag.com/numeric/nl/nagdoc_27.3/flhtml/f16/f16ubf.html

Parameters
inormint

Specifies the value to be returned.

The -norm.

The -norm of a row or column vector.

The Frobenius (or Euclidean) norm.

The -norm.

The value (not a norm).

mint

, the number of rows of the matrix . If on input, zgb_norm returns .

klint

, the number of subdiagonals within the band of . If on input, zgb_norm returns .

kuint

, the number of superdiagonals within the band of . If on input, zgb_norm returns .

abcomplex, array-like, shape

The band matrix .

Returns
nrmfloat

The value of the required norm of the matrix supplied in .

Notes

Given a complex band matrix, , zgb_norm calculates one of the values given by

 ∥A∥1=maxj(∑mi=1∣∣aij∣∣) (the 1-norm of A), ∥A∥∞=maxi(∑nj=1∣∣aij∣∣) (the ∞-norm of A), ∥A∥F=(∑mi=1∑nj=1∣∣aij∣∣2)1/2 (the Frobenius norm of A), or maxi,j(∣∣aij∣∣) (the maximum absolute element value of A).

If or is then additionally zgb_norm can calculate the value (the -norm of ).

References

Basic Linear Algebra Subprograms Technical (BLAST) Forum, 2001, Basic Linear Algebra Subprograms Technical (BLAST) Forum Standard, University of Tennessee, Knoxville, Tennessee, https://www.netlib.org/blas/blast-forum/blas-report.pdf