g05kjc 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 g05kjc the base generator defined by state would produce random numbers

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

, then after calling g05kjc the generator will produce random numbers

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

One of the initialization functions g05kfc (for a repeatable sequence if computed sequentially) or g05kgc (for a non-repeatable sequence) must be called prior to the first call to g05kjc.

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

4 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

5 Arguments

1: $n$ – Integer Input: On entry: $n$ , the number of places to skip ahead.

Constraint: $n \geq 0$ .
2: $state [\dim]$ – Integer Communication Array: Note: the dimension, $\dim$ , of this array is dictated by the requirements of associated functions that must have been previously called. This array MUST be the same array passed as argument state in the previous call to 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.
3: $fail$ – NagError * Input/Output: The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL: Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
NE_ARRAY_SIZE: On entry, the base generator is Mersenne Twister, but the state vector defined on initialization is not large enough to perform a skip ahead. See the initialization function g05kfc or g05kgc.
NE_BAD_PARAM: On entry, argument $⟨ value ⟩$ had an illegal value.
NE_INT: On entry, $n = ⟨ value ⟩$ .
Constraint: $n \geq 0$ .
NE_INT_ARRAY: On entry, cannot use skip-ahead 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.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_INVALID_STATE: On entry, state vector has been corrupted or not initialized.
NE_NO_LICENCE: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.

g05kjc is not threaded in any implementation.

9 Further Comments

Calling g05kjc and then generating a series of uniform values using g05sac is more efficient than, but equivalent to, calling g05sac and discarding the first

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.

To skip ahead

k \times m

places you can either

(a)call g05kjc once with $n = k \times m$ , or
(b)call g05kjc $k$ times with $n = m$ , using the state vector output by the previous call as input to the next call

both approaches would result in the same sequence of values. When working in a multithreaded environment, where you want to generate (at most)

m

values on each of

K

threads, this would translate into either

(a)spawning the $K$ threads and calling g05kjc once on each thread with $n = (k - 1) \times m$ , where $k$ is a thread ID, taking a value between $1$ and $K$ , or
(b)calling g05kjc on a single thread with $n = m$ , spawning the $K$ threads and then calling g05kjc a further $k - 1$ times on each of the thread.

Due to the way skip ahead is implemented for the Mersenne Twister, approach (a) will tend to be more efficient if more than 30 threads are being used (i.e.,

K > 30

), otherwise approach (b) should probably be used. For all other base generators, approach (a) should be used. See the G05 Chapter Introduction for more details.

10 Example

This example initializes a base generator using g05kfc and then uses g05kjc to advance the sequence 50 places before generating five variates from a uniform distribution using g05sac.