F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentF06RBF

Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

## 1  Purpose

F06RBF 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 $n$ band matrix.

## 2  Specification

 FUNCTION F06RBF ( NORM, N, KL, KU, AB, LDAB, WORK)
 REAL (KIND=nag_wp) F06RBF
 INTEGER N, KL, KU, LDAB REAL (KIND=nag_wp) AB(LDAB,*), WORK(*) CHARACTER(1) NORM

None.

None.

## 5  Parameters

1:     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:     N – INTEGERInput
On entry: $n$, the order of the matrix $A$.
When ${\mathbf{N}}=0$, F06RBF returns zero.
Constraint: ${\mathbf{N}}\ge 0$.
3:     KL – INTEGERInput
On entry: ${k}_{l}$, the number of subdiagonals within the band of $A$.
Constraint: ${\mathbf{KL}}\ge 0$.
4:     KU – INTEGERInput
On entry: ${k}_{u}$, the number of superdiagonals within the band of $A$.
Constraint: ${\mathbf{KU}}\ge 0$.
5:     AB(LDAB,$*$) – REAL (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:     LDAB – INTEGERInput
On entry: the first dimension of the array AB as declared in the (sub)program from which F06RBF is called.
Constraint: ${\mathbf{LDAB}}\ge {\mathbf{KL}}+{\mathbf{KU}}+1$.
7:     WORK($*$) – 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.