NAG Library Routine Document

F06UCF

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 (= 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:     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:     N – INTEGERInput

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

When $\mathbf{N}=0$, F06UCF returns zero.

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

4:     A(LDA,$*$) – 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:     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:     WORK($*$) – REAL (KIND=nag_wp) arrayWorkspace

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

6  Error Indicators and Warnings

7  Accuracy

8  Further Comments

9  Example