nag_rand_leap_frog (g05khc) (PDF version)
g05 Chapter Contents
g05 Chapter Introduction
NAG C 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 actual argument supplied must be the array state supplied to the initialization functions 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

NE_BAD_PARAM
On entry, argument value had an illegal value.
NE_INT
On entry, n=value.
Constraint: n1.
NE_INT_2
On entry, k=value and n=value.
Constraint: 0<kn.
NE_INT_ARRAY
On entry, cannot use leap-frog with the base generator defined by state.
NE_INTERNAL_ERROR
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.
NE_INVALID_STATE
On entry, state vector has been corrupted or not initialized.

7  Accuracy

Not applicable.

8  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.

9  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).

9.1  Program Text

Program Text (g05khce.c)

9.2  Program Data

None.

9.3  Program Results

Program Results (g05khce.r)


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

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012