# 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)