F06UPF (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentF06UPF

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

F06UPF 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 $n$ Hermitian tridiagonal matrix $A$.

## 2  Specification

 FUNCTION F06UPF ( NORM, N, D, E)
 REAL (KIND=nag_wp) F06UPF
 INTEGER N REAL (KIND=nag_wp) D(*) COMPLEX (KIND=nag_wp) E(*) 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 ${\mathbf{N}}=0$, F06UPF returns zero.
Constraint: ${\mathbf{N}}\ge 0$.
3:     D($*$) – 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:     E($*$) – COMPLEX (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.

None.

## 9  Example

None.

F06UPF (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual