NAG FL Interface
g05kkf (init_​skipahead_​power2)

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1 Purpose

g05kkf allows for the generation of multiple, independent, sequences of pseudorandom numbers using the skip-ahead method. The base pseudorandom number sequence defined by state is advanced 2n places.

2 Specification

Fortran Interface
Subroutine g05kkf ( n, state, ifail)
Integer, Intent (In) :: n
Integer, Intent (Inout) :: state(*), ifail
C Header Interface
#include <nag.h>
void  g05kkf_ (const Integer *n, Integer state[], Integer *ifail)
The routine may be called by the names g05kkf or nagf_rand_init_skipahead_power2.

3 Description

g05kkf adjusts a base generator to allow multiple, independent, sequences of pseudorandom numbers to be generated via the skip-ahead method (see the G05 Chapter Introduction for details).
If, prior to calling g05kkf the base generator defined by state would produce random numbers x1 , x2 , x3 , , then after calling g05kkf the generator will produce random numbers x2n+1 , x2n+2 , x2n+3 , .
One of the initialization routines g05kff (for a repeatable sequence if computed sequentially) or g05kgf (for a non-repeatable sequence) must be called prior to the first call to g05kkf.
The skip-ahead algorithm can be used in conjunction with any of the six base generators discussed in the G05 Chapter Introduction.

4 References

Haramoto H, Matsumoto M, Nishimura T, Panneton F and L'Ecuyer P (2008) Efficient jump ahead for F2-linear random number generators INFORMS J. on Computing 20(3) 385–390
Knuth D E (1981) The Art of Computer Programming (Volume 2) (2nd Edition) Addison–Wesley

5 Arguments

1: n Integer Input
On entry: n, where the number of places to skip-ahead is defined as 2n.
Constraint: n0.
2: state(*) Integer array Communication 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.
3: 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 -1 or 1 is used it is essential to test the value of ifail on exit.
On exit: ifail=0 unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry ifail=0 or −1, explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
On entry, n=value.
Constraint: n0.
On entry, state vector has been corrupted or not initialized.
On entry, cannot use skip-ahead with the base generator defined by state.
On entry, the state vector defined on initialization is not large enough to perform a skip-ahead (applies to Mersenne Twister base generator). See the initialization routine g05kff or g05kgf.
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.
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.
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
g05kkf is not threaded in any implementation.

9 Further Comments

Calling g05kkf and then generating a series of uniform values using g05saf is equivalent to, but more efficient than, calling g05saf and discarding the first 2n values. This may not be the case for distributions other than the uniform, as some distributional generators require more than one uniform variate to generate a single draw from the required distribution.

10 Example

This example initializes a base generator using g05kff and then uses g05kkf to advance the sequence 217 places before generating five variates from a uniform distribution using g05saf.

10.1 Program Text

Program Text (g05kkfe.f90)

10.2 Program Data

Program Data (g05kkfe.d)

10.3 Program Results

Program Results (g05kkfe.r)