f16 Chapter Contents
f16 Chapter Introduction
NAG C Library Manual

# NAG Library Function Documentnag_dge_norm (f16rac)

## 1  Purpose

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

## 2  Specification

 #include #include
 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

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 ${\mathbf{order}}=\mathrm{Nag_RowMajor}$. See Section 3.2.1.3 in the Essential Introduction for a more detailed explanation of the use of this argument.
Constraint: ${\mathbf{order}}=\mathrm{Nag_RowMajor}$ or Nag_ColMajor.
2:     normNag_NormTypeInput
On entry: specifies the value to be returned.
${\mathbf{norm}}=\mathrm{Nag_OneNorm}$
The $1$-norm.
${\mathbf{norm}}=\mathrm{Nag_InfNorm}$
The $\infty$-norm.
${\mathbf{norm}}=\mathrm{Nag_FrobeniusNorm}$
The Frobenius (or Euclidean) norm.
${\mathbf{norm}}=\mathrm{Nag_MaxNorm}$
The value $\underset{i,j}{\mathrm{max}}\phantom{\rule{0.25em}{0ex}}\left|{a}_{ij}\right|$ (not a norm).
Constraint: ${\mathbf{norm}}=\mathrm{Nag_OneNorm}$, $\mathrm{Nag_InfNorm}$, $\mathrm{Nag_FrobeniusNorm}$ or $\mathrm{Nag_MaxNorm}$.
3:     mIntegerInput
On entry: $m$, the number of rows of the matrix $A$.
If $m=0$, then m is set to zero.
Constraint: ${\mathbf{m}}\ge 0$.
4:     nIntegerInput
On entry: $n$, the number of columns of the matrix $A$.
If $n=0$, then n is set to zero.
Constraint: ${\mathbf{n}}\ge 0$.
5:     a[$\mathit{dim}$]const doubleInput
Note: the dimension, dim, of the array a must be at least
• $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{pda}}×{\mathbf{n}}\right)$ when ${\mathbf{order}}=\mathrm{Nag_ColMajor}$;
• $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{m}}×{\mathbf{pda}}\right)$ when ${\mathbf{order}}=\mathrm{Nag_RowMajor}$.
If ${\mathbf{order}}=\mathrm{Nag_ColMajor}$, ${A}_{ij}$ is stored in ${\mathbf{a}}\left[\left(j-1\right)×{\mathbf{pda}}+i-1\right]$.
If ${\mathbf{order}}=\mathrm{Nag_RowMajor}$, ${A}_{ij}$ is stored in ${\mathbf{a}}\left[\left(i-1\right)×{\mathbf{pda}}+j-1\right]$.
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 ${\mathbf{order}}=\mathrm{Nag_ColMajor}$, ${\mathbf{pda}}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{m}}\right)$;
• if ${\mathbf{order}}=\mathrm{Nag_RowMajor}$, ${\mathbf{pda}}\ge {\mathbf{n}}$.
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.
On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.
NE_INT
On entry, ${\mathbf{m}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{m}}\ge 0$.
On entry, ${\mathbf{n}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{n}}\ge 0$.
NE_INT_2
On entry, ${\mathbf{pda}}=〈\mathit{\text{value}}〉$, ${\mathbf{m}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{pda}}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{m}}\right)$.
On entry, ${\mathbf{pda}}=〈\mathit{\text{value}}〉$ and ${\mathbf{n}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{pda}}\ge {\mathbf{n}}$.
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)).