NAG Library Routine Document

G05REF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     N – INTEGERInput

On entry: $n$, the number of bivariates to generate.

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

2:     THETA – REAL (KIND=nag_wp)Input

On entry: $\theta$, the copula parameter.

Constraint: $\mathbf{THETA}\ge -1.0$.

3:     SORDER – INTEGERInput

On entry: determines the storage order of variates; the $\left(\mathit{i},\mathit{j}\right)$th variate is stored in $\mathbf{X}\left(\mathit{i},\mathit{j}\right)$ if $\mathbf{SORDER}=1$, and $\mathbf{X}\left(\mathit{j},\mathit{i}\right)$ if $\mathbf{SORDER}=2$, for $\mathit{i}=1,2,\dots ,n$ and $\mathit{j}=1,2$.

Constraint: $\mathbf{SORDER}=1$ or $2$.

4:     STATE($*$) – 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.

5:     X(LDX,SDX) – REAL (KIND=nag_wp) arrayOutput

On exit: the $n$ bivariate uniforms with joint distribution described by $C_{\theta }$, with $\mathbf{X}\left(i,j\right)$ holding the $i$th value for the $j$th dimension if $\mathbf{SORDER}=1$ and the $j$th value for the $i$th dimension of $\mathbf{SORDER}=2$.

6:     LDX – INTEGERInput

On entry: the first dimension of the array X as declared in the (sub)program from which G05REF is called.

Constraints:

• if $\mathbf{SORDER}=1$, $\mathbf{LDX}\ge \mathbf{N}$;
• if $\mathbf{SORDER}=2$, $\mathbf{LDX}\ge 2$.

7:     SDX – INTEGERInput

On entry: the second dimension of the array X as declared in the (sub)program from which G05REF is called.

Constraints:

• if $\mathbf{SORDER}=1$, $\mathbf{SDX}\ge 2$;
• if $\mathbf{SORDER}=2$, $\mathbf{SDX}\ge \mathbf{N}$.

8:     IFAIL – INTEGERInput/Output

On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction 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 parameter, 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,

STATE vector was not initialized or has been corrupted.

$\mathbf{IFAIL}=2$

On entry,

$\mathbf{THETA}<-1.0$.

$\mathbf{IFAIL}=3$

On entry,

$\mathbf{N}<0$.

$\mathbf{IFAIL}=4$

On entry,

$\mathbf{SORDER}\ne 1$ and $\mathbf{SORDER}\ne 2$.

$\mathbf{IFAIL}=6$

On entry,	$\mathbf{SORDER}=1$ and $\mathbf{LDX}<\mathbf{N}$,
or	$\mathbf{SORDER}=2$ and $\mathbf{LDX}<2$.

$\mathbf{IFAIL}=7$

On entry,	$\mathbf{SORDER}=1$ and $\mathbf{SDX}<2$,
or	$\mathbf{SORDER}=2$ and $\mathbf{SDX}<\mathbf{N}$.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (g05refe.f90)

9.2  Program Data

Program Data (g05refe.d)

9.3  Program Results

Program Results (g05refe.r)