NAG FL Interface
g05kff (init_​repeat)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{genid}$ – Integer Input

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: $\mathbf{subid}$ – Integer Input

On entry: if $\mathbf{genid}=2$, subid indicates which of the $273$ sub-generators to use. In this case, the $((\left|\mathbf{subid}\right|+272) mod 273)+1$ 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 $M=2^{(p\times 30)}$. 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, $\mathbf{subid}=k+1000(p-1)$.

If $\mathbf{genid}=6$ and $\mathbf{subid}\mathrm{ mod }2=0$ the range of the generator is set to $(0,1]$, otherwise the range is set to $(0,1)$; 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: $\mathbf{seed}\left(\mathbf{lseed}\right)$ – Integer array Input

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 $\mathbf{genid}=5$, $(k+1)p$ 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: $\mathbf{lseed}$ – Integer Input

On entry: the size of the seed array.

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

5: $\mathbf{state}\left(\mathbf{lstate}\right)$ – Integer array Communication Array

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

6: $\mathbf{lstate}$ – Integer Input/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 $\mathbf{genid}=5$, $\mathbf{lstate}\ge \max ((k+1)\times p+9,14)+3$, where $k$ and $p$ are defined by subid;
• if $\mathbf{genid}=6$, $\mathbf{lstate}\ge 61$;
• otherwise $\mathbf{lstate}<1$.

7: $\mathbf{ifail}$ – Integer Input/Output

On entry: ifail must be set to $0$, $-1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.

A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $-1$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $-1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $-\mathbf{1}$ 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, $\mathbf{genid}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{genid}=1$, $2$, $3$, $4$, $5$ or $6$.

$\mathbf{ifail}=3$

On entry, invalid seed.

$\mathbf{ifail}=4$

On entry, $\mathbf{lseed}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{lseed}\ge 1$.

$\mathbf{ifail}=6$

On entry, $\mathbf{lstate}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{lstate}\le 0$ or $\mathbf{lstate}\ge ⟨\mathit{\text{value}}⟩$.

$\mathbf{ifail}=-1$

Required length of state array returned in lstate but state array not initialized.

$\mathbf{ifail}=-99$

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

See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-399$

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

See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results