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Chapter Introduction
NAG Toolbox

NAG Toolbox: nag_rand_init_skipahead_power2 (g05kk)

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 2n2n 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 x1 , x2 , x3 , x1 , x2 , x3 , , then after calling nag_rand_init_skipahead_power2 (g05kk) the generator will produce random numbers x2n + 1 , x2n + 2 , x2n + 3 , x2n+1 , x2n+2 , x2n+3 , .
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
nn, where the number of places to skip-ahead is defined as 2n2n.
Constraint: n0n0.
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.

Input Parameters Omitted from the MATLAB Interface

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
ifail = 0ifail=0 unless the function detects an error (see [Error Indicators and Warnings]).

Error Indicators and Warnings

Errors or warnings detected by the function:
  ifail = 1ifail=1
Constraint: n0n0.
  ifail = 2ifail=2
On entry, state vector has been corrupted or not initialized. On entry, state vector has been corrupted or not initialized.
  ifail = 3ifail=3
On entry, cannot use skip-ahead with the base generator defined by state.
  ifail = 4ifail=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 = 999ifail=-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 2n2n 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
[state, ifail] = nag_rand_init_skipahead_power2(n, state);

% 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



PDF version (NAG web site, 64-bit version, 64-bit version)
Chapter Contents
Chapter Introduction
NAG Toolbox

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