# NAG Library Routine Document

## 1Purpose

f06ubf 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 $n$ band matrix.

## 2Specification

Fortran Interface
 Function f06ubf ( norm, n, kl, ku, ab, ldab, work)
 Real (Kind=nag_wp) :: f06ubf Integer, Intent (In) :: n, kl, ku, ldab Real (Kind=nag_wp), Intent (Inout) :: work(*) Complex (Kind=nag_wp), Intent (In) :: ab(ldab,*) Character (1), Intent (In) :: norm
#include <nagmk26.h>
 double f06ubf_ (const char *norm, const Integer *n, const Integer *kl, const Integer *ku, const Complex ab[], const Integer *ldab, 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 ${\mathbf{n}}=0$, f06ubf returns zero.
Constraint: ${\mathbf{n}}\ge 0$.
3:     $\mathbf{kl}$ – IntegerInput
On entry: ${k}_{l}$, the number of subdiagonals within the band of $A$.
Constraint: ${\mathbf{kl}}\ge 0$.
4:     $\mathbf{ku}$ – IntegerInput
On entry: ${k}_{u}$, the number of superdiagonals within the band of $A$.
Constraint: ${\mathbf{ku}}\ge 0$.
5:     $\mathbf{ab}\left({\mathbf{ldab}},*\right)$ – Complex (Kind=nag_wp) arrayInput
Note: the second dimension of the array ab must be at least ${\mathbf{n}}$.
On entry: the $n$ by $n$ band matrix $A$.
The matrix is stored in rows $1$ to ${k}_{l}+{k}_{u}+1$, more precisely, the element ${A}_{ij}$ must be stored in
 $abku+1+i-jj for ​max1,j-ku≤i≤minn,j+kl.$
6:     $\mathbf{ldab}$ – IntegerInput
On entry: the first dimension of the array ab as declared in the (sub)program from which f06ubf is called.
Constraint: ${\mathbf{ldab}}\ge {\mathbf{kl}}+{\mathbf{ku}}+1$.
7:     $\mathbf{work}\left(*\right)$ – 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

f06ubf is not threaded in any implementation.