The routine may be called by the names g05kjf or nagf_rand_init_skipahead.
3Description
g05kjf 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 g05kjf the base generator defined by state would produce random numbers ${x}_{1},{x}_{2},{x}_{3},\dots $, then after calling g05kjf the generator will produce random numbers ${x}_{n+1},{x}_{n+2},{x}_{n+3},\dots $.
One of the initialization routines g05kff (for a repeatable sequence if computed sequentially) or g05kgf (for a non-repeatable sequence) must be called prior to the first call to g05kjf.
The skip-ahead algorithm can be used in conjunction with any of the six base generators discussed in Chapter G05.
4References
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 Computing20(3) 385–390
Knuth D E (1981) The Art of Computer Programming (Volume 2) (2nd Edition) Addison–Wesley
5Arguments
1: $\mathbf{n}$ – IntegerInput
On entry: $n$, the number of places to skip ahead.
Note: the actual argument supplied must be the array state supplied to the initialization routines g05kff or g05kgf.
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: $\mathbf{ifail}$ – IntegerInput/Output
On entry: ifail must be set to $0$, $-1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $-1$ means that an error message is printed while a value of $1$ means that it is not.
If halting is not appropriate, the value $-1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $-\mathbf{1}$ or $\mathbf{1}$ is used it is essential to test the value of ifail on exit.
On exit: ${\mathbf{ifail}}={\mathbf{0}}$ unless the routine detects an error or a warning has been flagged (see Section 6).
6Error Indicators and Warnings
If on entry ${\mathbf{ifail}}=0$ or $-1$, explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
${\mathbf{ifail}}=1$
On entry, ${\mathbf{n}}=\u27e8\mathit{\text{value}}\u27e9$.
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 base generator is Mersenne Twister, but the state vector defined on initialization is not large enough to perform a skip ahead. See the initialization routine g05kfforg05kgf.
${\mathbf{ifail}}=-99$
An unexpected error has been triggered by this routine. Please
contact NAG.
See Section 7 in the Introduction to the NAG Library FL Interface for further information.
${\mathbf{ifail}}=-399$
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.
${\mathbf{ifail}}=-999$
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.
7Accuracy
Not applicable.
8Parallelism and Performance
g05kjf is not threaded in any implementation.
9Further Comments
Calling g05kjf and then generating a series of uniform values using g05saf is more efficient than, but equivalent to, calling g05saf 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 g05kjf once with ${\mathbf{n}}=k\times m$, or
(b)call g05kjf$k$ times with ${\mathbf{n}}=m$, 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 g05kjf once on each thread with ${\mathbf{n}}=(k-1)\times m$, where $k$ is a thread ID, taking a value between $1$ and $K$, or
(b)calling g05kjf on a single thread with ${\mathbf{n}}=m$, spawning the $K$ threads and then calling g05kjf 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.
10Example
This example initializes a base generator using g05kff and then uses g05kjf to advance the sequence 50 places before generating five variates from a uniform distribution using g05saf.