F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentF06RJF

Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

## 1  Purpose

F06RJF returns, via the function name, 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 $n$ trapezoidal matrix (triangular if $m=n$).

## 2  Specification

 FUNCTION F06RJF ( NORM, UPLO, DIAG, M, N, A, LDA, WORK)
 REAL (KIND=nag_wp) F06RJF
 INTEGER M, N, LDA REAL (KIND=nag_wp) A(LDA,*), WORK(*) CHARACTER(1) NORM, UPLO, DIAG

None.

None.

## 5  Parameters

1:     NORM – CHARACTER(1)Input
On entry: specifies the value to be returned.
${\mathbf{NORM}}=\text{'1'}$ or $\text{'O'}$
The $1$-norm.
${\mathbf{NORM}}=\text{'I'}$
The $\infty$-norm.
${\mathbf{NORM}}=\text{'F'}$ or $\text{'E'}$
The Frobenius (or Euclidean) norm.
${\mathbf{NORM}}=\text{'M'}$
The value $\underset{i,j}{\mathrm{max}}\phantom{\rule{0.25em}{0ex}}\left|{a}_{ij}\right|$ (not a norm).
Constraint: ${\mathbf{NORM}}=\text{'1'}$, $\text{'O'}$, $\text{'I'}$, $\text{'F'}$, $\text{'E'}$ or $\text{'M'}$.
2:     UPLO – CHARACTER(1)Input
On entry: specifies whether $A$ is upper or lower trapezoidal.
${\mathbf{UPLO}}=\text{'U'}$
$A$ is upper trapezoidal.
${\mathbf{UPLO}}=\text{'L'}$
$A$ is lower trapezoidal.
Constraint: ${\mathbf{UPLO}}=\text{'U'}$ or $\text{'L'}$.
3:     DIAG – CHARACTER(1)Input
On entry: specifies whether $A$ has nonunit or unit diagonal elements.
${\mathbf{DIAG}}=\text{'N'}$
The diagonal elements are stored explicitly.
${\mathbf{DIAG}}=\text{'U'}$
The diagonal elements are assumed to be $1$, and are not referenced.
Constraint: ${\mathbf{DIAG}}=\text{'N'}$ or $\text{'U'}$.
4:     M – INTEGERInput
On entry: $m$, the number of rows of the matrix $A$.
When ${\mathbf{M}}=0$, F06RJF is set to zero.
Constraint: ${\mathbf{M}}\ge 0$.
5:     N – INTEGERInput
On entry: $n$, the number of columns of the matrix $A$.
When ${\mathbf{N}}=0$, F06RJF is set to zero.
Constraint: ${\mathbf{N}}\ge 0$.
6:     A(LDA,$*$) – REAL (KIND=nag_wp) arrayInput
Note: the second dimension of the array A must be at least ${\mathbf{N}}$.
On entry: the $m$ by $n$ trapezoidal matrix $A$.
• If ${\mathbf{UPLO}}=\text{'U'}$, $A$ is upper trapezoidal and the elements of the array below the diagonal are not referenced.
• If ${\mathbf{UPLO}}=\text{'L'}$, $A$ is lower trapezoidal and the elements of the array above the diagonal are not referenced.
• If ${\mathbf{DIAG}}=\text{'U'}$, the diagonal elements of $A$ are assumed to be $1$, and are not referenced.
7:     LDA – INTEGERInput
On entry: the first dimension of the array A as declared in the (sub)program from which F06RJF is called.
Constraint: ${\mathbf{LDA}}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{M}}\right)$.
8:     WORK($*$) – REAL (KIND=nag_wp) arrayWorkspace
Note: the dimension of the array WORK must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{M}}\right)$ if ${\mathbf{NORM}}=\text{'I'}$, and at least $1$ otherwise.

None.

Not applicable.

None.

None.