NAG Library Routine Document

1Purpose

f06rcf 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 $n$ by $n$ symmetric matrix.

2Specification

Fortran Interface
 Function f06rcf ( norm, uplo, n, a, lda, work)
 Real (Kind=nag_wp) :: f06rcf Integer, Intent (In) :: n, lda Real (Kind=nag_wp), Intent (In) :: a(lda,*) Real (Kind=nag_wp), Intent (Inout) :: work(*) Character (1), Intent (In) :: norm, uplo
#include <nagmk26.h>
 double f06rcf_ (const char *norm, const char *uplo, const Integer *n, const double a[], const Integer *lda, double work[], const Charlen length_norm, const Charlen length_uplo)

None.

None.

5Arguments

1:     $\mathbf{norm}$ – 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 (= the $1$-norm for a symmetric matrix).
${\mathbf{norm}}=\text{'F'}$ or $\text{'E'}$
The Frobenius (or Euclidean) norm.
${\mathbf{norm}}=\text{'M'}$
The value ${\mathrm{max}}_{i,j}\left|{a}_{ij}\right|$ (not a norm).
Constraint: ${\mathbf{norm}}=\text{'1'}$, $\text{'O'}$, $\text{'I'}$, $\text{'F'}$, $\text{'E'}$ or $\text{'M'}$.
2:     $\mathbf{uplo}$ – Character(1)Input
On entry: specifies whether the upper or lower triangular part of $A$ is stored.
${\mathbf{uplo}}=\text{'U'}$
The upper triangular part of $A$ is stored.
${\mathbf{uplo}}=\text{'L'}$
The lower triangular part of $A$ is stored.
Constraint: ${\mathbf{uplo}}=\text{'U'}$ or $\text{'L'}$.
3:     $\mathbf{n}$ – IntegerInput
On entry: $n$, the order of the matrix $A$.
When ${\mathbf{n}}=0$, f06rcf returns zero.
Constraint: ${\mathbf{n}}\ge 0$.
4:     $\mathbf{a}\left({\mathbf{lda}},*\right)$ – Real (Kind=nag_wp) arrayInput
Note: the second dimension of the array a must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$.
On entry: the $n$ by $n$ symmetric matrix $A$.
• If ${\mathbf{uplo}}=\text{'U'}$, the upper triangular part of $A$ must be stored and the elements of the array below the diagonal are not referenced.
• If ${\mathbf{uplo}}=\text{'L'}$, the lower triangular part of $A$ must be stored and the elements of the array above the diagonal are not referenced.
5:     $\mathbf{lda}$ – IntegerInput
On entry: the first dimension of the array a as declared in the (sub)program from which f06rcf is called.
Constraint: ${\mathbf{lda}}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$.
6:     $\mathbf{work}\left(*\right)$ – Real (Kind=nag_wp) arrayWorkspace
Note: the dimension of the array work must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$ if ${\mathbf{norm}}=\text{'1'}$, $\text{'O'}$ or $\text{'I'}$, and at least $1$ otherwise.

None.

Not applicable.

8Parallelism and Performance

f06rcf is not threaded in any implementation.