NAG C Library Function Document

nag_rand_orthog_matrix (g05pxc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{side}$ – Nag_SideTypeInput

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

$\mathbf{side}=\mathrm{Nag\_LeftSide}$

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

$\mathbf{side}=\mathrm{Nag\_RightSide}$

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

Constraint: $\mathbf{side}=\mathrm{Nag\_LeftSide}$ or $\mathrm{Nag\_RightSide}$.

2:    $\mathbf{init}$ – Nag_InitializeAInput

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

$\mathbf{init}=\mathrm{Nag\_InitializeI}$

a is initialized to the identity matrix.

$\mathbf{init}=\mathrm{Nag\_InputA}$

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

Constraint: $\mathbf{init}=\mathrm{Nag\_InitializeI}$ or $\mathrm{Nag\_InputA}$.

3:    $\mathbf{m}$ – IntegerInput

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

Constraints:

• if $\mathbf{side}=\mathrm{Nag\_LeftSide}$, $\mathbf{m}>1$;
• otherwise $\mathbf{m}\ge 1$.

4:    $\mathbf{n}$ – IntegerInput

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

Constraints:

• if $\mathbf{side}=\mathrm{Nag\_RightSide}$, $\mathbf{n}>1$;
• otherwise $\mathbf{n}\ge 1$.

5:    $\mathbf{state}\left[\mathit{dim}\right]$ – IntegerCommunication Array

Note: the dimension, $\mathit{dim}$, of this array is dictated by the requirements of associated functions that must have been previously called. This array MUST be the same array passed as argument state in the previous call to nag_rand_init_repeatable (g05kfc) or nag_rand_init_nonrepeatable (g05kgc).

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:    $\mathbf{a}\left[\mathbf{m}\times \mathbf{pda}\right]$ – doubleInput/Output

On entry: if $\mathbf{init}=\mathrm{Nag\_InputA}$, a must contain the matrix $A$, with the $\left(i,j\right)$th element of $A$ stored in $\mathbf{a}\left[\left(i-1\right)\times \mathbf{pda}+j-1\right]$.

On exit: the matrix $UA$ when $\mathbf{side}=\mathrm{Nag\_LeftSide}$ or the matrix $AU$ when $\mathbf{side}=\mathrm{Nag\_RightSide}$.

7:    $\mathbf{pda}$ – IntegerInput

On entry: the stride separating matrix column elements in the array a.

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

8:    $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_ENUM_INT

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

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

NE_INT

On entry, $\mathbf{pda}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pda}>0$.

NE_INT_2

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

NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_INVALID_STATE

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

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 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 (g05pxce.c)

10.2

Program Data

10.3

Program Results

Program Results (g05pxce.r)