NAG Library Function Document

nag_dge_norm (f16rac)

 Contents

    1  Purpose
    7  Accuracy
    10  Example

1
Purpose

nag_dge_norm (f16rac) calculates the value of the 1-norm, the -norm, the Frobenius norm, or the maximum absolute value of the elements of a real m by n matrix.

2
Specification

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

3
Description

Given a real m by n matrix, A, nag_dge_norm (f16rac) calculates one of the values given by
A1= maxj i=1 m aij ,  
A = maxi j=1 n aij ,  
AF= i=1 m j=1 n aij 2 1/2  
or
maxi,jaij .  

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

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:     m IntegerInput
On entry: m, the number of rows of the matrix A.
If m=0, r is set to zero.
Constraint: m0.
4:     n IntegerInput
On entry: n, the number of columns of the matrix A.
If n=0, r 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 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:     pda IntegerInput
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:     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, 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.
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_dge_norm (f16rac) is not threaded in any implementation.

9
Further Comments

None.

10
Example

See Section 10 in nag_dgecon (f07agc) and nag_dtrsna (f08qlc).
© The Numerical Algorithms Group Ltd, Oxford, UK. 2017