nag_rand_leap_frog (g05khc) (PDF version)
g05 Chapter Contents
g05 Chapter Introduction
NAG Library Manual

NAG Library Function Document

nag_rand_leap_frog (g05khc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_rand_leap_frog (g05khc) allows for the generation of multiple, independent, sequences of pseudorandom numbers using the leap-frog method.

2  Specification

#include <nag.h>
#include <nagg05.h>
void  nag_rand_leap_frog (Integer n, Integer k, Integer state[], NagError *fail)

3  Description

nag_rand_leap_frog (g05khc) adjusts a base generator to allow multiple, independent, sequences of pseudorandom numbers to be generated via the leap-frog method (see the g05 Chapter Introduction for details).
If, prior to calling nag_rand_leap_frog (g05khc) the base generator defined by state would produce random numbers x1 , x2 , x3 , , then after calling nag_rand_leap_frog (g05khc) the generator will produce random numbers xk , xk+n , xk+2n , xk+3n , .
One of the initialization functions nag_rand_init_repeatable (g05kfc) (for a repeatable sequence if computed sequentially) or nag_rand_init_nonrepeatable (g05kgc) (for a non-repeatable sequence) must be called prior to the first call to nag_rand_leap_frog (g05khc).
The leap-frog algorithm can be used in conjunction with the NAG basic generator, both the Wichmann–Hill I and Wichmann–Hill II generators, the Mersenne Twister and L'Ecuyer.

4  References

Knuth D E (1981) The Art of Computer Programming (Volume 2) (2nd Edition) Addison–Wesley

5  Arguments

1:     nIntegerInput
On entry: n, the total number of sequences required.
Constraint: n>0.
2:     kIntegerInput
On entry: k, the number of the current sequence.
Constraint: 0<kn.
3:     state[dim]IntegerCommunication Array
Note: the dimension, dim, of this array is dictated by the requirements of associated functions that must have been previously called. This array MUST be the same array passed as argument state in the previous call to nag_rand_init_repeatable (g05kfc) or nag_rand_init_nonrepeatable (g05kgc).
On entry: contains information on the selected base generator and its current state.
On exit: contains updated information on the state of the generator.
4:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

On entry, argument value had an illegal value.
On entry, n=value.
Constraint: n1.
On entry, k=value and n=value.
Constraint: 0<kn.
On entry, cannot use leap-frog with the base generator defined by state.
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
On entry, state vector has been corrupted or not initialized.

7  Accuracy

Not applicable.

8  Parallelism and Performance

Not applicable.

9  Further Comments

The leap-frog method tends to be less efficient than other methods of producing multiple, independent sequences. See the g05 Chapter Introduction for alternative choices.

10  Example

This example creates three independent sequences using nag_rand_leap_frog (g05khc), after initialization by nag_rand_init_repeatable (g05kfc). Five variates from a uniform distribution are then generated from each sequence using nag_rand_basic (g05sac).

10.1  Program Text

Program Text (g05khce.c)

10.2  Program Data


10.3  Program Results

Program Results (g05khce.r)

nag_rand_leap_frog (g05khc) (PDF version)
g05 Chapter Contents
g05 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2014