NAG Library Routine Document

G05RKF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     $\mathrm{N}$ – INTEGERInput

On entry: $n$, the number of pseudorandom uniform variates to generate.

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

2:     $\mathrm{M}$ – INTEGERInput

On entry: $m$, the number of dimensions.

Constraint: $\mathbf{M}\ge 2$.

3:     $\mathrm{THETA}$ – REAL (KIND=nag_wp)Input

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

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

4:     $\mathrm{SORDER}$ – 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 $\mathit{j}=1,2,\dots ,m$.

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

5:     $\mathrm{STATE}\left(*\right)$ – 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:     $\mathrm{X}\left(\mathbf{LDX},\mathbf{SDX}\right)$ – REAL (KIND=nag_wp) arrayOutput

On exit: the pseudorandom uniform variates 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 $\mathbf{SORDER}=2$.

7:     $\mathrm{LDX}$ – INTEGERInput

On entry: the first dimension of the array X as declared in the (sub)program from which G05RKF is called.

Constraints:

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

8:     $\mathrm{SDX}$ – INTEGERInput

On entry: the second dimension of the array X as declared in the (sub)program from which G05RKF is called.

Constraints:

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

9:     $\mathrm{IFAIL}$ – 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, corrupt STATE parameter.

$\mathbf{IFAIL}=2$

On entry, invalid THETA: $\mathbf{THETA}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{THETA}\ge 1.0$.

$\mathbf{IFAIL}=3$

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

$\mathbf{IFAIL}=4$

On entry, $\mathbf{M}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{M}\ge 2$.

$\mathbf{IFAIL}=5$

On entry, invalid SORDER.
Constraint: $\mathbf{SORDER}=1$ or $2$.

$\mathbf{IFAIL}=7$

On entry, LDX must be at least $〈\mathit{\text{value}}〉$: $\mathbf{LDX}=〈\mathit{\text{value}}〉$.

$\mathbf{IFAIL}=8$

On entry, SDX must be at least $〈\mathit{\text{value}}〉$: $\mathbf{SDX}=〈\mathit{\text{value}}〉$.

$\mathbf{IFAIL}=-99$

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

See Section 3.8 in the Essential Introduction for further information.

$\mathbf{IFAIL}=-399$

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

See Section 3.7 in the Essential Introduction for further information.

$\mathbf{IFAIL}=-999$

Dynamic memory allocation failed.

See Section 3.6 in the Essential Introduction for further information.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (g05rkfe.f90)

10.2  Program Data

Program Data (g05rkfe.d)

10.3  Program Results

Program Results (g05rkfe.r)