NAG CL Interface
f16rac (dge_​norm)

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1 Purpose

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×n matrix.

2 Specification

#include <nag.h>
void  f16rac (Nag_OrderType order, Nag_NormType norm, Integer m, Integer n, const double a[], Integer pda, double *r, NagError *fail)
The function may be called by the names: f16rac, nag_blast_dge_norm or nag_dge_norm.

3 Description

Given a real m×n matrix, A, 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  
maxi,j|aij| .  

4 References

Basic Linear Algebra Subprograms Technical (BLAST) Forum (2001) Basic Linear Algebra Subprograms Technical (BLAST) Forum Standard University of Tennessee, Knoxville, Tennessee

5 Arguments

1: order Nag_OrderType Input
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 3.1.3 in the Introduction to the NAG Library CL Interface for a more detailed explanation of the use of this argument.
Constraint: order=Nag_RowMajor or Nag_ColMajor.
2: norm Nag_NormType Input
On entry: specifies the value to be returned.
The 1-norm.
The -norm.
The Frobenius (or Euclidean) norm.
The value maxi,j|aij| (not a norm).
Constraint: norm=Nag_OneNorm, Nag_InfNorm, Nag_FrobeniusNorm or Nag_MaxNorm.
3: m Integer Input
On entry: m, the number of rows of the matrix A.
If m=0, r is set to zero.
Constraint: m0.
4: n Integer Input
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 double Input
Note: the dimension, dim, of the array a must be at least
  • max(1,pda×n) when order=Nag_ColMajor;
  • max(1,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×n matrix A.
6: pda Integer Input
On entry: the stride separating row or column elements (depending on the value of order) in the array a.
  • if order=Nag_ColMajor, pdamax(1,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 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
On entry, argument value had an illegal value.
On entry, m=value.
Constraint: m0.
On entry, n=value.
Constraint: n0.
On entry, pda=value, m=value.
Constraint: pdamax(1,m).
On entry, pda=value and n=value.
Constraint: pdan.
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.
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface 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

f16rac is not threaded in any implementation.

9 Further Comments


10 Example

See Section 10 in f07agc and f08qlc.