NAG Library Routine Document

F06UMF

1  Purpose

2  Specification

3  Description

4  References

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 ${\displaystyle \underset{i,j}{\max }}\left|a_{ij}\right|$ (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 $\mathbf{N}=0$, F06UMF returns zero.

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

3:     A(LDA,$*$) – COMPLEX (KIND=nag_wp) arrayInput

Note: the second dimension of the array A must be at least $\mathbf{N}$.

On entry: the $n$ by $n$ upper Hessenberg matrix $A$; elements of the array below the first subdiagonal are not referenced.

4:     LDA – INTEGERInput

On entry: the first dimension of the array A as declared in the (sub)program from which F06UMF is called.

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

5:     WORK($*$) – REAL (KIND=nag_wp) arrayWorkspace

Note: the dimension of the array WORK must be at least $\max \left(1,\mathbf{N}\right)$ if $\mathbf{NORM}=\text{'I'}$, and at least $1$ otherwise.

6  Error Indicators and Warnings

7  Accuracy

8  Further Comments

9  Example