NAG Library Routine Document

G05KFF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     GENID – INTEGERInput

On entry: must contain the type of base generator to use.

$\mathbf{GENID}=1$

NAG basic generator.

$\mathbf{GENID}=2$

Wichmann Hill I generator.

$\mathbf{GENID}=3$

Mersenne Twister.

$\mathbf{GENID}=4$

Wichmann Hill II generator.

$\mathbf{GENID}=5$

ACORN generator.

$\mathbf{GENID}=6$

L'Ecuyer MRG32k3a generator.

See the G05 Chapter Introduction for details of each of the base generators.

Constraint: $\mathbf{GENID}=1$, $2$, $3$, $4$, $5$ or $6$.

2:     SUBID – INTEGERInput

On entry: if $\mathbf{GENID}=2$, SUBID indicates which of the $273$ sub-generators to use. In this case, the $\left(\left(\left|\mathbf{SUBID}\right|+272\right) mod 273\right)+1$ sub-generator is used.

If $\mathbf{GENID}=5$, SUBID indicates the values of $k$ and $p$ to use, where $k$ is the order of the generator, and $p$ controls the size of the modulus, $M$, with $M=2^{\left(p\times 30\right)}$. If $\mathbf{SUBID}<1$, the default values of $k=10$ and $p=2$ are used, otherwise values for $k$ and $p$ are calculated from the formula, $\mathbf{SUBID}=k+1000\left(p-1\right)$.

If $\mathbf{GENID}=6$ and $\mathbf{SUBID}\mathrm{ mod }2=0$ the range of the generator is set to $\left(0,1\right]$, otherwise the range is set to $\left(0,1\right)$; in this case the sequence is identical to the implementation of MRG32k3a in TestU01 (see L'Ecuyer and Simard (2002)) for identical seeds.

For all other values of GENID, SUBID is not referenced.

3:     SEED(LSEED) – INTEGER arrayInput

On entry: the initial (seed) values for the selected base generator. The number of initial values required varies with each of the base generators.

If $\mathbf{GENID}=1$, one seed is required.

If $\mathbf{GENID}=2$, four seeds are required.

If $\mathbf{GENID}=3$, $624$ seeds are required.

If $\mathbf{GENID}=4$, four seeds are required.

If $\mathbf{GENID}=5$, $\left(k+1\right)p$ seeds are required, where $k$ and $p$ are defined by SUBID. For the ACORN generator it is recommended that an odd value is used for $\mathbf{SEED}\left(1\right)$.

If $\mathbf{GENID}=6$, six seeds are required.

If insufficient seeds are provided then the first $\mathbf{LSEED}-1$ values supplied in SEED are used and the remaining values are randomly generated using the NAG basic generator. In such cases the NAG basic generator is initialized using the value supplied in $\mathbf{SEED}\left(\mathbf{LSEED}\right)$.

Constraint: $\mathbf{SEED}\left(\mathit{i}\right)\ge 1$, for $\mathit{i}=1,2,\dots ,\mathbf{LSEED}$.

4:     LSEED – INTEGERInput

On entry: the size of the SEED array.

Constraint: $\mathbf{LSEED}\ge 1$.

5:     STATE(LSTATE) – INTEGER arrayCommunication Array

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

6:     LSTATE – INTEGERInput/Output

On entry: the dimension of the STATE array, or a value $<1$. If the Mersenne Twister ($\mathbf{GENID}=3$) is being used and the skip ahead routine G05KJF or G05KKF will be called subsequently, then you must ensure that $\mathbf{LSTATE}\ge 1260$.

On exit: if $\mathbf{LSTATE}<1$ on entry, then the required length of the STATE array for the chosen base generator, otherwise LSTATE is unchanged. When $\mathbf{GENID}=3$ (Mersenne Twister) a value of $1260$ is returned, allowing for the skip ahead routine to be subsequently called. In all other cases the minimum length, as documented in the constraints below, is returned.

Constraints:

• if $\mathbf{GENID}=1$, $\mathbf{LSTATE}\ge 17$;
• if $\mathbf{GENID}=2$, $\mathbf{LSTATE}\ge 21$;
• if $\mathbf{GENID}=3$, $\mathbf{LSTATE}\ge 633$;
• if $\mathbf{GENID}=4$, $\mathbf{LSTATE}\ge 29$;
• if $\mathbf{GENID}=5$, $\mathbf{LSTATE}\ge \max \left(\left(k+1\right)\times p+9,14\right)+3$, where $k$ and $p$ are defined by SUBID;
• if $\mathbf{GENID}=6$, $\mathbf{LSTATE}\ge 58$;
• otherwise $\mathbf{LSTATE}<1$.

7:     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.

On exit: $\mathbf{IFAIL}=\mathbf{0}$ or $-1$ unless the routine detects an error or a warning has been flagged (see Section 6).

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.

6  Error Indicators and Warnings

$\mathbf{IFAIL}=-1$

Minimum length for STATE array returned in parameter LSTATE but STATE array not initialized.

$\mathbf{IFAIL}=1$

On entry, $\mathbf{GENID}\ne 1$, $2$, $3$, $4$, $5$ or $6$.

$\mathbf{IFAIL}=2$

On entry,

invalid SUBID.

$\mathbf{IFAIL}=3$

On entry, $\mathbf{SEED}\left(i\right)\le 0$ for at least one $i$.

$\mathbf{IFAIL}=4$

On entry, $\mathbf{LSEED}<1$.

$\mathbf{IFAIL}=6$

On entry, $\mathbf{LSTATE}>0$ and LSTATE is too small for specified base generator.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (g05kffe.f90)

9.2  Program Data

Program Data (g05kffe.d)

9.3  Program Results

Program Results (g05kffe.r)