NAG FL Interfacef06rkf (dlantp)

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1Purpose

f06rkf 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 $n×n$ triangular matrix, stored in packed form.

2Specification

Fortran Interface
 Function f06rkf ( norm, uplo, diag, n, ap, work)
 Real (Kind=nag_wp) :: f06rkf Integer, Intent (In) :: n Real (Kind=nag_wp), Intent (In) :: ap(*) Real (Kind=nag_wp), Intent (Inout) :: work(*) Character (1), Intent (In) :: norm, uplo, diag
#include <nag.h>
 double f06rkf_ (const char *norm, const char *uplo, const char *diag, const Integer *n, const double ap[], double work[], const Charlen length_norm, const Charlen length_uplo, const Charlen length_diag)
The routine may be called by the names f06rkf or nagf_blas_dlantp.

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.
${\mathbf{norm}}=\text{'F'}$ or $\text{'E'}$
The Frobenius (or Euclidean) norm.
${\mathbf{norm}}=\text{'M'}$
The value $\underset{i,j}{\mathrm{max}}\phantom{\rule{0.25em}{0ex}}|{a}_{ij}|$ (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 $A$ is upper or lower triangular.
${\mathbf{uplo}}=\text{'U'}$
$A$ is upper triangular.
${\mathbf{uplo}}=\text{'L'}$
$A$ is lower triangular.
Constraint: ${\mathbf{uplo}}=\text{'U'}$ or $\text{'L'}$.
3: $\mathbf{diag}$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: $\mathbf{n}$Integer Input
On entry: $n$, the order of the matrix $A$.
When ${\mathbf{n}}=0$, f06rkf returns zero.
Constraint: ${\mathbf{n}}\ge 0$.
5: $\mathbf{ap}\left(*\right)$Real (Kind=nag_wp) array Input
Note: the dimension of the array ap must be at least ${\mathbf{n}}×\left({\mathbf{n}}+1\right)/2$.
On entry: the $n×n$ triangular matrix $A$, packed by columns.
More precisely,
• if ${\mathbf{uplo}}=\text{'U'}$, the upper triangle of $A$ must be stored with element ${A}_{ij}$ in ${\mathbf{ap}}\left(i+j\left(j-1\right)/2\right)$ for $i\le j$;
• if ${\mathbf{uplo}}=\text{'L'}$, the lower triangle of $A$ must be stored with element ${A}_{ij}$ in ${\mathbf{ap}}\left(i+\left(2n-j\right)\left(j-1\right)/2\right)$ for $i\ge j$.
If ${\mathbf{diag}}=\text{'U'}$, the diagonal elements of $A$ are assumed to be $1$, and are not referenced; the same storage scheme is used whether ${\mathbf{diag}}=\text{'N'}$ or ‘U’.
6: $\mathbf{work}\left(*\right)$Real (Kind=nag_wp) array Workspace
Note: the dimension of the array work must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$ if ${\mathbf{norm}}=\text{'I'}$, and at least $1$ otherwise.

None.

Not applicable.

8Parallelism and Performance

f06rkf is not threaded in any implementation.