nag_zhb_norm (f16uec) (PDF version)
f16 Chapter Contents
f16 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_zhb_norm (f16uec)

+ Contents

    1  Purpose
    7  Accuracy
    9  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

The BLAS Technical Forum Standard (2001) http://www.netlib.org/blas/blast-forum

5  Arguments

1:     orderNag_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 3.2.1.3 in the Essential Introduction for a more detailed explanation of the use of this argument.
Constraint: order=Nag_RowMajor or Nag_ColMajor.
2:     normNag_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:     uploNag_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:     nIntegerInput
On entry: n, the order of the matrix A.
If n=0, then n is set to zero.
Constraint: n0.
5:     kIntegerInput
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:     pdabIntegerInput
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:     rdouble *Output
On exit: the value of the norm specified by norm.
9:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
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.

7  Accuracy

The BLAS standard requires accurate implementations which avoid unnecessary over/underflow (see Section 2.7 of The BLAS Technical Forum Standard (2001)).

8  Further Comments

None.

9  Example

See Section 9 in nag_zpbcon (f07huc).

nag_zhb_norm (f16uec) (PDF version)
f16 Chapter Contents
f16 Chapter Introduction
NAG C Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012