NAG Library Function Document

nag_zhb_norm (f16uec)

 Contents

    1  Purpose
    7  Accuracy
    10  Example

1
Purpose

nag_zhb_norm (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 by n Hermitian band matrix.

2
Specification

#include <nag.h>
#include <nagf16.h>
void  nag_zhb_norm (Nag_OrderType order, Nag_NormType norm, Nag_UploType uplo, Integer n, Integer k, const Complex ab[], Integer pdab, double *r, NagError *fail)

3
Description

Given a complex n by n Hermitian band matrix, A, nag_zhb_norm (f16uec) calculates one of the values given by
A1=maxji=1naij,  
A=maxij= 1naij,  
AF=i=1nj=1n aij21/2  
or
maxi,jaij.  
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 http://www.netlib.org/blas/blast-forum/blas-report.pdf

5
Arguments

1:     order Nag_OrderTypeInput
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 3.3.1.3 in How to Use the NAG Library and its Documentation for a more detailed explanation of the use of this argument.
Constraint: order=Nag_RowMajor or Nag_ColMajor.
2:     norm Nag_NormTypeInput
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,jaij (not a norm).
Constraint: norm=Nag_OneNorm, Nag_InfNorm, Nag_FrobeniusNorm or Nag_MaxNorm.
3:     uplo Nag_UploTypeInput
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 IntegerInput
On entry: n, the order of the matrix A.
If n=0, n is set to zero.
Constraint: n0.
5:     k IntegerInput
On entry: k, the number of subdiagonals or superdiagonals of the matrix A.
Constraint: k0.
6:     ab[dim] const ComplexInput
Note: the dimension, dim, of the array ab must be at least max1,pdab×n.
On entry: the n by 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=max1,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,,minn,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,,minn,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=max1,i-k,,i.
7:     pdab IntegerInput
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 3.7 in How to Use the NAG Library and its Documentation).

6
Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation 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 2.7.5 in How to Use the NAG Library and its Documentation 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

nag_zhb_norm (f16uec) is not threaded in any implementation.

9
Further Comments

None.

10
Example

See Section 10 in nag_zpbcon (f07huc).
© The Numerical Algorithms Group Ltd, Oxford, UK. 2017