f16ucc (pdf version)

Chapter Contents

Chapter Introduction

NAG C Library Contents

NAG C Library Function Document

nag_zhe_norm (f16ucc)

+− Contents

1 Purpose

2 Specification

3 Description

4 References

5 Parameters

6 Error Indicators and Warnings

7 Accuracy

8 Further Comments

9 Example

1 Purpose

nag_zhe_norm (f16ucc) calculates the value of the 1-norm, the infinity-norm the Frobenius norm, or the maximum absolute value of the elements, of a complex

n

n

Hermitian matrix.

2 Specification

#include <nag.h> #include <nagf16.h>
void nag_zhe_norm	(Nag_OrderType order, Nag_NormType norm, Nag_UploType uplo, Integer n, const Complex a[], Integer pda, double r, NagError fail)

3 Description

Given a complex

n

n

Hermitian matrix,

A

, nag_zhe_norm (f16ucc) calculates one of the values given by

{‖A‖}_{1} = \max_{j} \sum_{i = 1}^{n} |a_{i j}|,

{‖A‖}_{\infty} = \max_{i} \sum_{j = 1}^{n} |a_{i j}|,

{‖A‖}_{F} = {(\sum_{i = 1}^{n} \sum_{j = 1}^{n} {|a_{i j}|}^{2})}^{1 / 2},

\max_{i, j} |a_{i j}| .

Note that, since

A

{‖A‖}_{1} = {‖A‖}_{\infty}

4 References

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

5 Parameters

1: order – Nag_OrderTypeInput

On entry: the order parameter 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 2.2.1.4 of the Essential Introduction for a more detailed explanation of the use of this parameter.

Constraint: order

=

Nag_RowMajor or Nag_ColMajor.

2: norm – Nag_NormType Input

On entry: specifies the value to be returned:

if $norm$ $=$ Nag_OneNorm, the 1-norm;
if $norm$ $=$ Nag_InfNorm, the infinity-norm;
if $norm$ $=$ Nag_FrobeniusNorm, the Frobenius (or Euclidean) norm;
if $norm$ $=$ Nag_MaxNorm, the value $\max_{i, j} |a_{i j}|$ (not a norm).

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 as follows:

if $uplo$ $=$ Nag_Upper, the upper triangular part of $A$ is stored;
if $uplo$ $=$ Nag_Lower, the lower triangular part of $A$ is stored.

uplo

=

Nag_Upper or Nag_Lower.

4: n – Integer Input

n

, the order of the matrix

A

n \geq 0

5: a[ $\dim$ ] – const Complex Input

Note: the dimension, dim, of the array a must be at least

\max (1, pda \times \max (1, n))

.

If order

=

Nag_ColMajor, the

(i, j)

th element of the matrix

A

is stored in

a [(j - 1) \times pda + i - 1]

and if order

=

Nag_RowMajor, the

(i, j)

th element of the matrix

A

is stored in

a [(i - 1) \times pda + j - 1]

.

On entry: the

n

by

n

Hermitian matrix

A

. If

uplo

=

Nag_Upper, the upper triangle of

A

must be stored and the elements of the array below the diagonal are not referenced; if

uplo

=

Nag_Lower, the lower triangle of

A

must be stored and the elements of the array above the diagonal are not referenced.

6: pda – Integer Input

On entry: the stride separating matrix row or column elements (depending on the value of order) in the array a.

Constraint:

pda \geq \max (1, n)

.

7: r – double *Output

On exit: the value of the norm specified by norm.

8: fail – NagError *Input/Output

The NAG error parameter (see the Essential Introduction).

6 Error Indicators and Warnings

NE_INT: On entry, $n = 〈value〉$ .
Constraint: $n \geq 0$ .; On entry, $pda = 〈value〉$ .
Constraint: $pda \geq \max (1, n)$ .
NE_BAD_PARAM: On entry, parameter $〈value〉$ had an illegal value.

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

9 Example

See Section 9 of the documents for nag_zpocon (f07fuc) and nag_zhecon (f07muc).

f16ucc (pdf version)

Chapter Contents

Chapter Introduction

NAG C Library Contents

© The Numerical Algorithms Group Ltd, Oxford, UK. 2004