g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

# NAG Library Function Documentnag_rand_leap_frog (g05khc)

## 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 #include
 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 ${x}_{1},{x}_{2},{x}_{3},\dots$, then after calling nag_rand_leap_frog (g05khc) the generator will produce random numbers ${x}_{k},{x}_{k+n},{x}_{k+2n},{x}_{k+3n},\dots$.
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: ${\mathbf{n}}>0$.
2:     kIntegerInput
On entry: $k$, the number of the current sequence.
Constraint: $0<{\mathbf{k}}\le {\mathbf{n}}$.
3:     state[$\mathit{dim}$]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

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.
NE_INT
On entry, ${\mathbf{n}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{n}}\ge 1$.
NE_INT_2
On entry, ${\mathbf{k}}=〈\mathit{\text{value}}〉$ and ${\mathbf{n}}=〈\mathit{\text{value}}〉$.
Constraint: $0<{\mathbf{k}}\le {\mathbf{n}}$.
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.

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)

None.

### 9.3  Program Results

Program Results (g05khce.r)