NAG Library Function Document

nag_zhf_norm (f16ukc)

 Contents

    1  Purpose
    7  Accuracy

1
Purpose

nag_zhf_norm (f16ukc) returns the value of the 1-norm, the -norm, the Frobenius norm, or the maximum absolute value of the elements of a complex Hermitian matrix A stored in Rectangular Full Packed (RFP) format.

2
Specification

#include <nag.h>
#include <nagf16.h>
void  nag_zhf_norm (Nag_OrderType order, Nag_NormType norm, Nag_RFP_Store transr, Nag_UploType uplo, Integer n, const Complex ar[], double *r, NagError *fail)

3
Description

Given a complex n by n symmetric matrix, A, nag_zhf_norm (f16ukc) calculates one of the values given by
A1=maxji=1naij (the 1-norm of A),
A=maxij= 1naij (the -norm of A),
AF=i=1nj=1naij21/2 (the Frobenius norm of A),   or
maxi,jaij (the maximum absolute element value of A).
A is stored in compact form using the RFP format. The RFP storage format is described in Section 3.3.3 in the f07 Chapter Introduction.

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
Gustavson F G, Waśniewski J, Dongarra J J and Langou J (2010) Rectangular full packed format for Cholesky's algorithm: factorization, solution, and inversion ACM Trans. Math. Software 37, 2

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:     transr Nag_RFP_StoreInput
On entry: specifies whether the normal RFP representation of A or its conjugate transpose is stored.
transr=Nag_RFP_Normal
The matrix A is stored in normal RFP format.
transr=Nag_RFP_ConjTrans
The conjugate transpose of the RFP representation of the matrix A is stored.
Constraint: transr=Nag_RFP_Normal or Nag_RFP_ConjTrans.
4:     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.
5:     n IntegerInput
On entry: n, the order of the matrix A.
If n=0, nag_zhf_norm (f16ukc) returns immediately.
Constraint: n0.
6:     ar[n×n+1/2] const ComplexInput
On entry: the upper or lower triangular part (as specified by uplo) of the n by n Hermitian matrix A, in either normal or transposed RFP format (as specified by transr). The storage format is described in detail in Section 3.3.3 in the f07 Chapter Introduction.
7:     r double *Output
On exit: the value of the norm specified by norm.
8:     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, n=value.
Constraint: n0.
NE_INTERNAL_ERROR
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.
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_zhf_norm (f16ukc) is not threaded in any implementation.

9
Further Comments

None.

10
Example

This example reads in the lower triangular part of a symmetric matrix, converts this to RFP format, then calculates the norm of the matrix for each of the available norm types.

10.1
Program Text

Program Text (f16ukce.c)

10.2
Program Data

Program Data (f16ukce.d)

10.3
Program Results

Program Results (f16ukce.r)

© The Numerical Algorithms Group Ltd, Oxford, UK. 2017