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Chapter Contents
Chapter Introduction
NAG Toolbox

## Purpose

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)

## 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:     $\mathrm{n}$int64int32nag_int scalar
$n$, where the number of places to skip-ahead is defined as ${2}^{n}$.
Constraint: ${\mathbf{n}}\ge 0$.
2:     $\mathrm{state}\left(:\right)$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.

None.

### Output Parameters

1:     $\mathrm{state}\left(:\right)$int64int32nag_int array
Contains updated information on the state of the generator.
2:     $\mathrm{ifail}$int64int32nag_int scalar
${\mathbf{ifail}}={\mathbf{0}}$ unless the function detects an error (see Error Indicators and Warnings).

## Error Indicators and Warnings

Errors or warnings detected by the function:
${\mathbf{ifail}}=1$
Constraint: ${\mathbf{n}}\ge 0$.
${\mathbf{ifail}}=2$
On entry, state vector has been corrupted or not initialized.
${\mathbf{ifail}}=3$
On entry, cannot use skip-ahead with the base generator defined by state.
${\mathbf{ifail}}=4$
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).
${\mathbf{ifail}}=-99$
${\mathbf{ifail}}=-399$
Your licence key may have expired or may not have been installed correctly.
${\mathbf{ifail}}=-999$
Dynamic memory allocation failed.

## Accuracy

Not applicable.

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).
```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

```