nag_dsy_norm (f16rcc) (PDF version)
f16 Chapter Contents
f16 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_dsy_norm (f16rcc)

+ Contents

    1  Purpose
    7  Accuracy
    9  Example

1  Purpose

nag_dsy_norm (f16rcc) calculates the value of the 1-norm, the -norm, the Frobenius norm or the maximum absolute value of the elements of a real n by n symmetric matrix.

2  Specification

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

3  Description

Given a real n by n symmetric matrix, A, nag_dsy_norm (f16rcc) calculates one of the values given by
A1=maxji=1naij, (the 1norm of A)
A=maxij= 1naij, (the -norm of A)
AF=i=1nj=1n aij21/2 (the Frobenius norm of A), or
maxi,jaij (the maximum absolute element value of A).
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:     a[dim]const doubleInput
Note: the dimension, dim, of the array a must be at least max1,pda×n.
On entry: the n by n symmetric matrix A.
If order=Nag_ColMajor, Aij is stored in a[j-1×pda+i-1].
If order=Nag_RowMajor, Aij is stored in a[i-1×pda+j-1].
If uplo=Nag_Upper, the upper triangular part of A must be stored and the elements of the array below the diagonal are not referenced.
If uplo=Nag_Lower, the lower triangular part of A must be stored and the elements of the array above the diagonal are not referenced.
6:     pdaIntegerInput
On entry: the stride separating row or column elements (depending on the value of order) of the matrix A in the array a.
Constraint: pdamax1,n.
7:     rdouble *Output
On exit: the value of the norm specified by norm.
8:     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, n=value.
Constraint: n0.
NE_INT_2
On entry, pda=value, n=value.
Constraint: pdamax1,n.

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_dpocon (f07fgc) and nag_dsycon (f07mgc).

nag_dsy_norm (f16rcc) (PDF version)
f16 Chapter Contents
f16 Chapter Introduction
NAG C Library Manual

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