nag_zge_norm (f16uac) (PDF version)
f16 Chapter Contents
f16 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_zge_norm (f16uac)

+ Contents

    1  Purpose
    7  Accuracy
    9  Example

1  Purpose

nag_zge_norm (f16uac) calculates the value of the 1-norm, the -norm, the Frobenius norm or the maximum absolute value of the elements of a complex m by n matrix.

2  Specification

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

3  Description

Given a complex m by n matrix, A, nag_zge_norm (f16uac) calculates one of the values given by
A1=maxji=1maij,
A=maxij= 1naij,
AF=i=1mj=1n aij21/2
or
maxi,jaij.

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:     mIntegerInput
On entry: m, the number of rows of the matrix A.
If m=0, then m is set to zero.
Constraint: m0.
4:     nIntegerInput
On entry: n, the number of columns of the matrix A.
If n=0, then n is set to zero.
Constraint: n0.
5:     a[dim]const ComplexInput
Note: the dimension, dim, of the array a must be at least
  • max1,pda×n when order=Nag_ColMajor;
  • max1,m×pda when order=Nag_RowMajor.
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].
On entry: the m by n matrix A.
6:     pdaIntegerInput
On entry: the stride separating row or column elements (depending on the value of order) in the array a.
Constraints:
  • if order=Nag_ColMajor, pdamax1,m;
  • if order=Nag_RowMajor, pdan.
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, m=value.
Constraint: m0.
On entry, n=value.
Constraint: n0.
NE_INT_2
On entry, pda=value, m=value.
Constraint: pdamax1,m.
On entry, pda=value and n=value.
Constraint: pdan.
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.

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_zgecon (f07auc) and nag_ztrsna (f08qyc).

nag_zge_norm (f16uac) (PDF version)
f16 Chapter Contents
f16 Chapter Introduction
NAG C Library Manual

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