# NAG FL Interfacef06rnf (dlangt)

## 1Purpose

f06rnf 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 $n$ tridiagonal matrix $A$.

## 2Specification

Fortran Interface
 Function f06rnf ( norm, n, dl, d, du)
 Real (Kind=nag_wp) :: f06rnf Integer, Intent (In) :: n Real (Kind=nag_wp), Intent (In) :: dl(*), d(*), du(*) Character (1), Intent (In) :: norm
#include <nag.h>
 double f06rnf_ (const char *norm, const Integer *n, const double dl[], const double d[], const double du[], const Charlen length_norm)
The routine may be called by the names f06rnf or nagf_blas_dlangt.

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 $\underset{i,j}{\mathrm{max}}\phantom{\rule{0.25em}{0ex}}\left|{a}_{ij}\right|$ (not a norm).
Constraint: ${\mathbf{norm}}=\text{'1'}$, $\text{'O'}$, $\text{'I'}$, $\text{'F'}$, $\text{'E'}$ or $\text{'M'}$.
2: $\mathbf{n}$Integer Input
On entry: $n$, the order of the matrix $A$.
When ${\mathbf{n}}=0$, f06rnf returns zero.
Constraint: ${\mathbf{n}}\ge 0$.
3: $\mathbf{dl}\left(*\right)$Real (Kind=nag_wp) array Input
Note: the dimension of the array dl must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}-1\right)$.
On entry: the ($n-1$) subdiagonal elements of $A$.
4: $\mathbf{d}\left(*\right)$Real (Kind=nag_wp) array Input
Note: the dimension of the array d must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$.
On entry: the $n$ diagonal elements of $A$.
5: $\mathbf{du}\left(*\right)$Real (Kind=nag_wp) array Input
Note: the dimension of the array du must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}-1\right)$.
On entry: the ($n-1$) superdiagonal elements of $A$.

None.

Not applicable.

## 8Parallelism and Performance

f06rnf is not threaded in any implementation.