nag_rand_init_skipahead_power2 (g05kk) 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

2^{n}

places.

Syntax

[state, ifail] = g05kk(n, state)

[state, ifail] = nag_rand_init_skipahead_power2(n, state)

Description

nag_rand_init_skipahead_power2 (g05kk) 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 nag_rand_init_skipahead_power2 (g05kk) the base generator defined by state would produce random numbers

x_{1}, x_{2}, x_{3}, \dots

, then after calling nag_rand_init_skipahead_power2 (g05kk) the generator will produce random numbers

x_{2^{n} + 1}, x_{2^{n} + 2}, x_{2^{n} + 3}, \dots

One of the initialization functions nag_rand_init_repeat (g05kf) (for a repeatable sequence if computed sequentially) or nag_rand_init_nonrepeat (g05kg) (for a non-repeatable sequence) must be called prior to the first call to nag_rand_init_skipahead_power2 (g05kk).

The skip-ahead algorithm can be used in conjunction with any of the six base generators discussed in the G05 Chapter Introduction.

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

Parameters

Compulsory Input Parameters

1: $n$ – int64int32nag_int scalar: $n$ , where the number of places to skip-ahead is defined as $2^{n}$ .

Constraint: $n \geq 0$ .
2: $state (:)$ – int64int32nag_int array: Note: the actual argument supplied must be the array state supplied to the initialization routines nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg).

Contains information on the selected base generator and its current state.

Optional Input Parameters

None.

Output Parameters

1: $state (:)$ – int64int32nag_int array: Contains updated information on the state of the generator.
2: $ifail$ – int64int32nag_int scalar: $ifail = 0$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Errors or warnings detected by the function:

$ifail = 1$: Constraint: $n \geq 0$ .

$ifail = 2$: On entry, state vector has been corrupted or not initialized.

$ifail = 3$: On entry, cannot use skip-ahead with the base generator defined by state.

$ifail = 4$: 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 function nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg).

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.

$ifail = - 999$: Dynamic memory allocation failed.

Accuracy

Not applicable.

Further Comments

Calling nag_rand_init_skipahead_power2 (g05kk) and then generating a series of uniform values using nag_rand_dist_uniform01 (g05sa) is equivalent to, but more efficient than, calling nag_rand_dist_uniform01 (g05sa) and discarding the first

2^{n}

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.

Example

This example initializes a base generator using nag_rand_init_repeat (g05kf) and then uses nag_rand_init_skipahead_power2 (g05kk) to advance the sequence

2^{17}

places before generating five variates from a uniform distribution using nag_rand_dist_uniform01 (g05sa).

Open in the MATLAB editor: g05kk_example

function g05kk_example


fprintf('g05kk example results\n\n');

genid = int64(1);
subid = int64(1);
seed  = [int64(1762543)];

% Initialise the generator to a repeatable sequence
[state, ifail] = g05kf( ...
                        genid, subid, seed);

% Advance the sequence 2**n places
n = int64(17);
[state, ifail] = g05kk( ...
                        n, state);

% Generate nv variates from a uniform distribution
nv = int64(5);
[state, x, ifail] = g05sa( ...
                           nv, state);

% Display the variates
disp(x);

g05kk example results

    0.7357
    0.3521
    0.4188
    0.0046
    0.0365

PDF version (NAG web site, 64-bit version, 64-bit version)

Chapter Contents

Chapter Introduction

NAG Toolbox