NAG Library Routine Document
G05KJF allows for the generation of multiple, independent, sequences of pseudorandom numbers using the skip-ahead method.
The base pseudorandom number sequence defined by STATE
||N, STATE(*), IFAIL
G05KJF 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
If, prior to calling G05KJF the base generator defined by STATE
would produce random numbers
, then after calling G05KJF the generator will produce random numbers
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 G05KJF.
The skip-ahead algorithm can be used in conjunction with any of the six base generators discussed in Chapter G05
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
- 1: N – INTEGERInput
On entry: , the number of places to skip ahead.
- 2: STATE() – INTEGER arrayCommunication Array
the actual argument supplied must be the array STATE
supplied to the initialization routines G05KFF
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 – INTEGERInput/Output
must be set to
. 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
is recommended. If the output of error messages is undesirable, then the value
is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is
. When the value is used it is essential to test the value of IFAIL on exit.
unless the routine detects an error or a warning has been flagged (see Section 6
6 Error Indicators and Warnings
If on entry
, explanatory error messages are output on the current error message unit (as defined by X04AAF
Errors or warnings detected by the routine:
|On entry,||STATE vector was not initialized or has been corrupted.|
On entry, cannot use the skip-ahead method with the base generator defined by STATE
On entry, the base generator is Mersenne Twister, but the STATE
vector defined on initialization is not large enough to perform a skip-ahead. See the initialization routine G05KFF
Calling G05KJF and then generating a series of uniform values using G05SAF
is more efficient than, but equivalent to, calling G05SAF
and discarding the first
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.
To skip ahead
places you can either
||call G05KJF once with , or
||call G05KJF times with , using the STATE vector output by the previous call as input to the next call
both approaches would result in the same sequence of values. When working in a multithreaded environment, where you want to generate (at most)
values on each of
threads, this would translate into either
||spawning the threads and calling G05KJF once on each thread with , where is a thread ID, taking a value between and , or
||calling G05KJF on a single thread with , spawning the threads and then calling G05KJF a further times on each of the thread.
Due to the way skip ahead is implemented for the Mersenne Twister, approach (a)
will tend to be more efficient if more than 30 threads are being used (i.e.,
), otherwise approach (b)
should probably be used. For all other base generators, approach (a)
should be used. See the G05 Chapter Introduction
for more details.
This example initializes a base generator using G05KFF
and then uses G05KJF to advance the sequence 50 places before generating five variates from a uniform distribution using G05SAF
9.1 Program Text
Program Text (g05kjfe.f90)
9.2 Program Data
Program Data (g05kjfe.d)
9.3 Program Results
Program Results (g05kjfe.r)