# NAG Library Routine Document

## 1Purpose

f06umf 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 complex $n$ by $n$ upper Hessenberg matrix.

## 2Specification

Fortran Interface
 Function f06umf ( norm, n, a, lda, work)
 Real (Kind=nag_wp) :: f06umf Integer, Intent (In) :: n, lda Real (Kind=nag_wp), Intent (Inout) :: work(*) Complex (Kind=nag_wp), Intent (In) :: a(lda,*) Character (1), Intent (In) :: norm
#include nagmk26.h
 double f06umf_ ( const char *norm, const Integer *n, const Complex a[], const Integer *lda, double work[], 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 ${\mathbf{n}}=0$, f06umf returns zero.
Constraint: ${\mathbf{n}}\ge 0$.
3:     $\mathbf{a}\left({\mathbf{lda}},*\right)$ – Complex (Kind=nag_wp) arrayInput
Note: the second dimension of the array a must be at least ${\mathbf{n}}$.
On entry: the $n$ by $n$ upper Hessenberg matrix $A$; elements of the array below the first subdiagonal are not referenced.
4:     $\mathbf{lda}$ – IntegerInput
On entry: the first dimension of the array a as declared in the (sub)program from which f06umf is called.
Constraint: ${\mathbf{lda}}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$.
5:     $\mathbf{work}\left(*\right)$ – 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 ${\mathbf{norm}}=\text{'I'}$, and at least $1$ otherwise.

None.

Not applicable.

## 8Parallelism and Performance

f06umf is not threaded in any implementation.