NAG Library Routine Document

f06ucf (zlanhe)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

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 ${\max }_{i,j}\left|a_{ij}\right|$ (not a norm).

Constraint: $\mathbf{norm}=\text{'1'}$, $\text{'O'}$, $\text{'I'}$, $\text{'F'}$, $\text{'E'}$ or $\text{'M'}$.

2:     $\mathbf{uplo}$ – 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:     $\mathbf{n}$ – IntegerInput

On entry: $n$, the order of the matrix $A$.

When $\mathbf{n}=0$, f06ucf returns zero.

Constraint: $\mathbf{n}\ge 0$.

4:     $\mathbf{a}\left(\mathbf{lda},*\right)$ – Complex (Kind=nag_wp) arrayInput

Note: the second dimension of the array a must be at least $\max \left(1,\mathbf{n}\right)$.

On entry: the $n$ by $n$ Hermitian matrix $A$.

• If $\mathbf{uplo}=\text{'U'}$, the upper triangular part of $A$ must be stored and the elements of the array below the diagonal are not referenced.
• If $\mathbf{uplo}=\text{'L'}$, the lower triangular part of $A$ must be stored and the elements of the array above the diagonal are not referenced.

5:     $\mathbf{lda}$ – IntegerInput

On entry: the first dimension of the array a as declared in the (sub)program from which f06ucf is called.

Constraint: $\mathbf{lda}\ge \max \left(1,\mathbf{n}\right)$.

6:     $\mathbf{work}\left(*\right)$ – Real (Kind=nag_wp) arrayWorkspace

Note: the dimension of the array work must be at least $\max \left(1,\mathbf{n}\right)$ if $\mathbf{norm}=\text{'1'}$, $\text{'O'}$ or $\text{'I'}$, and at least $1$ otherwise.

6

Error Indicators and Warnings

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example