# NAG FL Interfacef06uef (zlanhb)

## ▸▿ Contents

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## 1Purpose

f06uef 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 $n×n$ Hermitian band matrix.

## 2Specification

Fortran Interface
 Function f06uef ( norm, uplo, n, k, ab, ldab, work)
 Real (Kind=nag_wp) :: f06uef Integer, Intent (In) :: n, k, ldab Real (Kind=nag_wp), Intent (Inout) :: work(*) Complex (Kind=nag_wp), Intent (In) :: ab(ldab,*) Character (1), Intent (In) :: norm, uplo
#include <nag.h>
 double f06uef_ (const char *norm, const char *uplo, const Integer *n, const Integer *k, const Complex ab[], const Integer *ldab, double work[], const Charlen length_norm, const Charlen length_uplo)
The routine may be called by the names f06uef or nagf_blas_zlanhb.

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 (= the $1$-norm for a Hermitian matrix).
${\mathbf{norm}}=\text{'F'}$ or $\text{'E'}$
The Frobenius (or Euclidean) norm.
${\mathbf{norm}}=\text{'M'}$
The value ${\mathrm{max}}_{i,j}|{a}_{ij}|$ (not a norm).
Constraint: ${\mathbf{norm}}=\text{'1'}$, $\text{'O'}$, $\text{'I'}$, $\text{'F'}$, $\text{'E'}$ or $\text{'M'}$.
2: $\mathbf{uplo}$Character(1) Input
On entry: specifies whether the upper or lower triangular part of $A$ is stored.
${\mathbf{uplo}}=\text{'U'}$
The upper triangular part of $A$ is stored.
${\mathbf{uplo}}=\text{'L'}$
The lower triangular part of $A$ is stored.
Constraint: ${\mathbf{uplo}}=\text{'U'}$ or $\text{'L'}$.
3: $\mathbf{n}$Integer Input
On entry: $n$, the order of the matrix $A$.
When ${\mathbf{n}}=0$, f06uef returns zero.
Constraint: ${\mathbf{n}}\ge 0$.
4: $\mathbf{k}$Integer Input
On entry: $k$, the number of subdiagonals or superdiagonals of the matrix $A$.
Constraint: ${\mathbf{k}}\ge 0$.
5: $\mathbf{ab}\left({\mathbf{ldab}},*\right)$Complex (Kind=nag_wp) array Input
Note: the second dimension of the array ab must be at least ${\mathbf{n}}$.
On entry: the $n×n$ Hermitian band matrix $A$.
The matrix is stored in rows $1$ to $k+1$, more precisely,
• if ${\mathbf{uplo}}=\text{'U'}$, the elements of the upper triangle of $A$ within the band must be stored with element ${A}_{ij}$ in ${\mathbf{ab}}\left(k+1+i-j,j\right)\text{​ for ​}\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,j-k\right)\le i\le j$;
• if ${\mathbf{uplo}}=\text{'L'}$, the elements of the lower triangle of $A$ within the band must be stored with element ${A}_{ij}$ in ${\mathbf{ab}}\left(1+i-j,j\right)\text{​ for ​}j\le i\le \mathrm{min}\phantom{\rule{0.125em}{0ex}}\left(n,j+k\right)\text{.}$
6: $\mathbf{ldab}$Integer Input
On entry: the first dimension of the array ab as declared in the (sub)program from which f06uef is called.
Constraint: ${\mathbf{ldab}}\ge {\mathbf{k}}+1$.
7: $\mathbf{work}\left(*\right)$Real (Kind=nag_wp) array Workspace
Note: the dimension of the array work must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$ if ${\mathbf{norm}}=\text{'1'}$, $\text{'O'}$ or $\text{'I'}$, and at least $1$ otherwise.

None.

Not applicable.

## 8Parallelism and Performance

f06uef is not threaded in any implementation.