# NAG Library Routine Document

## 1Purpose

f06rpf 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 tridiagonal matrix $A$.

## 2Specification

Fortran Interface
 Function f06rpf ( norm, n, d, e)
 Real (Kind=nag_wp) :: f06rpf Integer, Intent (In) :: n Real (Kind=nag_wp), Intent (In) :: d(*), e(*) Character (1), Intent (In) :: norm
#include nagmk26.h
 double f06rpf_ (const char *norm, const Integer *n, const double d[], const double e[], const Charlen length_norm)

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:     $\mathbf{n}$ – IntegerInput
On entry: $n$, the order of the matrix $A$.
When ${\mathbf{n}}=0$, f06rpf returns zero.
Constraint: ${\mathbf{n}}\ge 0$.
3:     $\mathbf{d}\left(*\right)$ – Real (Kind=nag_wp) arrayInput
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 the tridiagonal matrix $A$.
4:     $\mathbf{e}\left(*\right)$ – Real (Kind=nag_wp) arrayInput
Note: the dimension of the array e must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}-1\right)$.
On entry: the ($n-1$) subdiagonal or superdiagonal elements of the tridiagonal matrix $A$.

None.

Not applicable.

## 8Parallelism and Performance

f06rpf is not threaded in any implementation.