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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 2n${2}^{n}$ 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 x1 , x2 , x3 , ${x}_{1},{x}_{2},{x}_{3},\dots$, then after calling nag_rand_init_skipahead_power2 (g05kk) the generator will produce random numbers x2n + 1 , x2n + 2 , x2n + 3 , ${x}_{{2}^{n}+1},{x}_{{2}^{n}+2},{x}_{{2}^{n}+3},\dots$.
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$n$, where the number of places to skip-ahead is defined as 2n${2}^{n}$.
Constraint: n0${\mathbf{n}}\ge 0$.
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.

None.

None.

Output Parameters

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

Error Indicators and Warnings

Errors or warnings detected by the function:
ifail = 1${\mathbf{ifail}}=1$
Constraint: n0${\mathbf{n}}\ge 0$.
ifail = 2${\mathbf{ifail}}=2$
On entry, state vector has been corrupted or not initialized. On entry, state vector has been corrupted or not initialized.
ifail = 3${\mathbf{ifail}}=3$
On entry, cannot use skip-ahead with the base generator defined by state.
ifail = 4${\mathbf{ifail}}=4$
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).
ifail = 999${\mathbf{ifail}}=-999$
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 2n${2}^{n}$ 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

```function nag_rand_init_skipahead_power2_example
genid = int64(1);
subid = int64(1);
seed  = [int64(1762543)];
n = int64(17);
nv = int64(5);

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

% Advance the sequence 2**n places

% Generate nv variates from a uniform distribution
[state, x, ifail] = nag_rand_dist_uniform01(nv, state);

% Display the variates
if ifail == 0
disp(x);
end
```
```
0.7357
0.3521
0.4188
0.0046
0.0365

```
```function g05kk_example
genid = int64(1);
subid = int64(1);
seed  = [int64(1762543)];
n = int64(17);
nv = int64(5);

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

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

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

% Display the variates
if ifail == 0
disp(x);
end
```
```
0.7357
0.3521
0.4188
0.0046
0.0365

```