NAG Library Routine Document

G05YLF

1 Purpose

2 Specification

3 Description

4 References

5 Parameters

1:   GENID – INTEGERInput

On entry: must identify the quasi-random generator to use.

$\mathbf{GENID}=1$

Sobol generator.

$\mathbf{GENID}=2$

Sobol (A659) generator.

$\mathbf{GENID}=3$

Niederreiter generator.

$\mathbf{GENID}=4$

Faure generator.

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

2:   IDIM – INTEGERInput

On entry: the number of dimensions required.

Constraints:

• if $\mathbf{GENID}=1$, $1\le \mathbf{IDIM}\le 10000$;
• if $\mathbf{GENID}=2$, $1\le \mathbf{IDIM}\le 1111$;
• if $\mathbf{GENID}=3$, $1\le \mathbf{IDIM}\le 318$;
• if $\mathbf{GENID}=4$, $1\le \mathbf{IDIM}\le 40$.

3:   IREF(LIREF) – INTEGER arrayCommunication Array

On exit: contains initialization information for use by the generator routines G05YJF, G05YKF and G05YMF. IREF must not be altered in any way between initialization and calls of the generator routines.

4:   LIREF – INTEGERInput

On entry: the dimension of the array IREF as declared in the (sub)program from which G05YLF is called.

Constraints:

• if $\mathbf{GENID}=1$, $2$ or $3$, $\mathbf{LIREF}\ge 32\times \mathbf{IDIM}+7$;
• if $\mathbf{GENID}=4$, $\mathbf{LIREF}\ge 407$.

5:   ISKIP – INTEGERInput

On entry: the number of terms of the sequence to skip on initialization for the Sobol and Niederreiter generators. If $\mathbf{GENID}=4$, ISKIP is ignored.

Constraint: if $\mathbf{GENID}=1$, $2$ or $3$, $0\le \mathbf{ISKIP}\le 2^{30}$.

6:   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, $\mathbf{GENID}<1$,

or $\mathbf{GENID}>4$.

$\mathbf{IFAIL}=2$

On entry, $\mathbf{IDIM}<1$,

or IDIM is too large.

$\mathbf{IFAIL}=4$

On entry, LIREF is too small.

$\mathbf{IFAIL}=5$

The value of $\mathbf{ISKIP}<0$ or ISKIP is too large.

7 Accuracy

8 Further Comments

9 Example