NAG FL Interfaceg05khf (init_​leapfrog)

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1Purpose

g05khf allows for the generation of multiple, independent, sequences of pseudorandom numbers using the leap-frog method.

2Specification

Fortran Interface
 Subroutine g05khf ( n, k,
 Integer, Intent (In) :: n, k Integer, Intent (Inout) :: state(*), ifail
#include <nag.h>
 void g05khf_ (const Integer *n, const Integer *k, Integer state[], Integer *ifail)
The routine may be called by the names g05khf or nagf_rand_init_leapfrog.

3Description

g05khf adjusts a base generator to allow multiple, independent, sequences of pseudorandom numbers to be generated via the leap-frog method (see the G05 Chapter Introduction for details).
If, prior to calling g05khf the base generator defined by state would produce random numbers ${x}_{1},{x}_{2},{x}_{3},\dots$, then after calling g05khf the generator will produce random numbers ${x}_{k},{x}_{k+n},{x}_{k+2n},{x}_{k+3n},\dots$.
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 g05khf.
The leap-frog algorithm can be used in conjunction with the NAG basic generator, both the Wichmann–Hill I and Wichmann–Hill II generators, the Mersenne Twister and L'Ecuyer.

4References

Knuth D E (1981) The Art of Computer Programming (Volume 2) (2nd Edition) Addison–Wesley

5Arguments

1: $\mathbf{n}$Integer Input
On entry: $n$, the total number of sequences required.
Constraint: ${\mathbf{n}}>0$.
2: $\mathbf{k}$Integer Input
On entry: $k$, the number of the current sequence.
Constraint: $0<{\mathbf{k}}\le {\mathbf{n}}$.
3: $\mathbf{state}\left(*\right)$Integer array Communication Array
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.
4: $\mathbf{ifail}$Integer Input/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, ${\mathbf{n}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{n}}\ge 1$.
${\mathbf{ifail}}=2$
On entry, ${\mathbf{k}}=⟨\mathit{\text{value}}⟩$ and ${\mathbf{n}}=⟨\mathit{\text{value}}⟩$.
Constraint: $0<{\mathbf{k}}\le {\mathbf{n}}$.
${\mathbf{ifail}}=3$
On entry, state vector has been corrupted or not initialized.
${\mathbf{ifail}}=4$
On entry, cannot use leap-frog with the base generator defined by state.
${\mathbf{ifail}}=-99$
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.

Not applicable.

8Parallelism and Performance

g05khf is not threaded in any implementation.

The leap-frog method tends to be less efficient than other methods of producing multiple, independent sequences. See the G05 Chapter Introduction for alternative choices.

10Example

This example creates three independent sequences using g05khf, after initialization by g05kff. Five variates from a uniform distribution are then generated from each sequence using g05saf.

10.1Program Text

Program Text (g05khfe.f90)

10.2Program Data

Program Data (g05khfe.d)

10.3Program Results

Program Results (g05khfe.r)