NAG Library Routine Document

g05pxf (matrix_orthog)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{side}$ – Character(1)Input

On entry: indicates whether the matrix $A$ is multiplied on the left or right by the random orthogonal matrix $U$.

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

The matrix $A$ is multiplied on the left, i.e., premultiplied.

$\mathbf{side}=\text{'R'}$

The matrix $A$ is multiplied on the right, i.e., post-multiplied.

Constraint: $\mathbf{side}=\text{'L'}$ or $\text{'R'}$.

2:     $\mathbf{init}$ – Character(1)Input

On entry: indicates whether or not a should be initialized to the identity matrix.

$\mathbf{init}=\text{'I'}$

a is initialized to the identity matrix.

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

a is not initialized and the matrix $A$ must be supplied in a.

Constraint: $\mathbf{init}=\text{'I'}$ or $\text{'N'}$.

3:     $\mathbf{m}$ – IntegerInput

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

Constraints:

• if $\mathbf{side}=\text{'L'}$, $\mathbf{m}>1$;
• otherwise $\mathbf{m}\ge 1$.

4:     $\mathbf{n}$ – IntegerInput

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

Constraints:

• if $\mathbf{side}=\text{'R'}$, $\mathbf{n}>1$;
• otherwise $\mathbf{n}\ge 1$.

5:     $\mathbf{state}\left(*\right)$ – Integer arrayCommunication Array

Note: the actual argument supplied must be the array state supplied to the initialization routines g05kff or g05kgf.

On entry: contains information on the selected base generator and its current state.

On exit: contains updated information on the state of the generator.

6:     $\mathbf{a}\left(\mathbf{lda},\mathbf{n}\right)$ – Real (Kind=nag_wp) arrayInput/Output

On entry: if $\mathbf{init}=\text{'N'}$, a must contain the matrix $A$.

On exit: the matrix $UA$ when $\mathbf{side}=\text{'L'}$ or the matrix $AU$ when $\mathbf{side}=\text{'R'}$.

7:     $\mathbf{lda}$ – IntegerInput

On entry: the first dimension of the array a as declared in the (sub)program from which g05pxf is called.

Constraint: $\mathbf{lda}\ge \mathbf{m}$.

8:     $\mathbf{ifail}$ – IntegerInput/Output

On entry: ifail must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this argument, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of ifail on exit.

On exit: $\mathbf{ifail}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6

Error Indicators and Warnings

$\mathbf{ifail}=1$

On entry, side is not valid: $\mathbf{side}=〈\mathit{\text{value}}〉$.

$\mathbf{ifail}=2$

On entry, init is not valid: $\mathbf{init}=〈\mathit{\text{value}}〉$.

$\mathbf{ifail}=3$

On entry, $\mathbf{side}=〈\mathit{\text{value}}〉$, $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{side}=\text{'L'}$, $\mathbf{m}>1$; otherwise $\mathbf{m}\ge 1$.

$\mathbf{ifail}=4$

On entry, $\mathbf{side}=〈\mathit{\text{value}}〉$, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{side}=\text{'R'}$, $\mathbf{n}>1$; otherwise $\mathbf{n}\ge 1$.

$\mathbf{ifail}=5$

On entry, state vector has been corrupted or not initialized.

$\mathbf{ifail}=7$

On entry, $\mathbf{lda}=〈\mathit{\text{value}}〉$ and $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{lda}\ge \mathbf{m}$.

$\mathbf{ifail}=8$

On entry, $\mathbf{side}=〈\mathit{\text{value}}〉$, $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{side}=\text{'L'}$, $\mathbf{m}>1$; otherwise $\mathbf{m}\ge 1$.

On entry, $\mathbf{side}=〈\mathit{\text{value}}〉$, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{side}=\text{'R'}$, $\mathbf{n}>1$; otherwise $\mathbf{n}\ge 1$.

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 3.9 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 3.8 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (g05pxfe.f90)

10.2

Program Data

Program Data (g05pxfe.d)

10.3

Program Results

Program Results (g05pxfe.r)