NAG CL Interface
f16uec (zhb_​norm)

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1 Purpose

f16uec calculates the value of the 1-norm, the -norm, the Frobenius norm or the maximum absolute value of the elements of a complex n×n Hermitian band matrix.

2 Specification

#include <nag.h>
void  f16uec (Nag_OrderType order, Nag_NormType norm, Nag_UploType uplo, Integer n, Integer k, const Complex ab[], Integer pdab, double *r, NagError *fail)
The function may be called by the names: f16uec, nag_blast_zhb_norm or nag_zhb_norm.

3 Description

Given a complex n×n Hermitian band matrix, A, f16uec calculates one of the values given by
A1=maxji=1n|aij|,  
A=maxij= 1n|aij|,  
AF=(i=1nj=1n |aij|2)1/2  
or
maxi,j|aij|.  
Note that, since A is symmetric, A1=A.

4 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

5 Arguments

1: order Nag_OrderType Input
On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by order=Nag_RowMajor. See Section 3.1.3 in the Introduction to the NAG Library CL Interface for a more detailed explanation of the use of this argument.
Constraint: order=Nag_RowMajor or Nag_ColMajor.
2: norm Nag_NormType Input
On entry: specifies the value to be returned.
norm=Nag_OneNorm
The 1-norm.
norm=Nag_InfNorm
The -norm.
norm=Nag_FrobeniusNorm
The Frobenius (or Euclidean) norm.
norm=Nag_MaxNorm
The value maxi,j|aij| (not a norm).
Constraint: norm=Nag_OneNorm, Nag_InfNorm, Nag_FrobeniusNorm or Nag_MaxNorm.
3: uplo Nag_UploType Input
On entry: specifies whether the upper or lower triangular part of A is stored.
uplo=Nag_Upper
The upper triangular part of A is stored.
uplo=Nag_Lower
The lower triangular part of A is stored.
Constraint: uplo=Nag_Upper or Nag_Lower.
4: n Integer Input
On entry: n, the order of the matrix A.
If n=0, n is set to zero.
Constraint: n0.
5: k Integer Input
On entry: k, the number of subdiagonals or superdiagonals of the matrix A.
Constraint: k0.
6: ab[dim] const Complex Input
Note: the dimension, dim, of the array ab must be at least max(1,pdab×n).
On entry: the n×n Hermitian band matrix A.
This is stored as a notional two-dimensional array with row elements or column elements stored contiguously. The storage of elements of Aij, depends on the order and uplo arguments as follows:
if order=Nag_ColMajor and uplo=Nag_Upper,
Aij is stored in ab[k+i-j+(j-1)×pdab], for j=1,,n and i=max(1,j-k),,j;
if order=Nag_ColMajor and uplo=Nag_Lower,
Aij is stored in ab[i-j+(j-1)×pdab], for j=1,,n and i=j,,min(n,j+k);
if order=Nag_RowMajor and uplo=Nag_Upper,
Aij is stored in ab[j-i+(i-1)×pdab], for i=1,,n and j=i,,min(n,i+k);
if order=Nag_RowMajor and uplo=Nag_Lower,
Aij is stored in ab[k+j-i+(i-1)×pdab], for i=1,,n and j=max(1,i-k),,i.
7: pdab Integer Input
On entry: the stride separating row or column elements (depending on the value of order) of the matrix A in the array ab.
Constraint: pdabk+1.
8: r double * Output
On exit: the value of the norm specified by norm.
9: fail NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
NE_BAD_PARAM
On entry, argument value had an illegal value.
NE_INT
On entry, k=value.
Constraint: k0.
On entry, n=value.
Constraint: n0.
NE_INT_2
On entry, pdab=value, k=value.
Constraint: pdabk+1.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.

7 Accuracy

The BLAS standard requires accurate implementations which avoid unnecessary over/underflow (see Section 2.7 of Basic Linear Algebra Subprograms Technical (BLAST) Forum (2001)).

8 Parallelism and Performance

f16uec is not threaded in any implementation.

9 Further Comments

None.

10 Example

See f07huc.