NAG Library Routine Document

F06UJF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     $\mathrm{NORM}$ – 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:     $\mathrm{UPLO}$ – CHARACTER(1)Input

On entry: specifies whether $A$ is upper or lower trapezoidal.

$\mathbf{UPLO}=\text{'U'}$

$A$ is upper trapezoidal.

$\mathbf{UPLO}=\text{'L'}$

$A$ is lower trapezoidal.

Constraint: $\mathbf{UPLO}=\text{'U'}$ or $\text{'L'}$.

3:     $\mathrm{DIAG}$ – CHARACTER(1)Input

On entry: specifies whether $A$ has nonunit or unit diagonal elements.

$\mathbf{DIAG}=\text{'N'}$

The diagonal elements are stored explicitly.

$\mathbf{DIAG}=\text{'U'}$

The diagonal elements are assumed to be $1$, and are not referenced.

Constraint: $\mathbf{DIAG}=\text{'N'}$ or $\text{'U'}$.

4:     $\mathrm{M}$ – INTEGERInput

On entry: $m$, the number of rows of the matrix $A$.

When $\mathbf{M}=0$, F06UJF is set to zero.

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

5:     $\mathrm{N}$ – INTEGERInput

On entry: $n$, the number of columns of the matrix $A$.

When $\mathbf{N}=0$, F06UJF is set to zero.

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

6:     $\mathrm{A}\left(\mathbf{LDA},*\right)$ – COMPLEX (KIND=nag_wp) arrayInput

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

On entry: the $m$ by $n$ trapezoidal matrix $A$.

• If $\mathbf{UPLO}=\text{'U'}$, $A$ is upper trapezoidal and the elements of the array below the diagonal are not referenced.
• If $\mathbf{UPLO}=\text{'L'}$, $A$ is lower trapezoidal and the elements of the array above the diagonal are not referenced.
• If $\mathbf{DIAG}=\text{'U'}$, the diagonal elements of $A$ are assumed to be $1$, and are not referenced.

7:     $\mathrm{LDA}$ – INTEGERInput

On entry: the first dimension of the array A as declared in the (sub)program from which F06UJF is called.

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

8:     $\mathrm{WORK}\left(*\right)$ – REAL (KIND=nag_wp) arrayWorkspace

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

6  Error Indicators and Warnings

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example