is likely to exceed the cycle length of any of the base generators. For practical purposes this is irrelevant, as the time necessary to generate all possible permutations is many millenia.

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 g05ncf.

4 References

Kendall M G and Stuart A (1969) The Advanced Theory of Statistics (Volume 1) (3rd Edition) Griffin

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

5 Arguments

1: $indx (n)$ – Integer array Input/Output: On entry: the $n$ integer values to be permuted.

On exit: the $n$ permuted integer values.
2: $n$ – Integer Input: On entry: the number of values to be permuted.

Constraint: $n \geq 1$ .
3: $state (*)$ – 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: $ifail$ – 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 $- 1$ or $1$ is used it is essential to test the value of ifail on exit.

On exit: $ifail = 0$ unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry

ifail = 0

−1

, explanatory error messages are output on the current error message unit (as defined by x04aaf).

Errors or warnings detected by the routine:

$ifail = 2$: On entry, $n = ⟨ value ⟩$ .
Constraint: $n \geq 1$ .

$ifail = 3$: On entry, state vector has been corrupted or not initialized.

$ifail = - 99$: 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.

$ifail = - 399$: 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.

$ifail = - 999$: Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

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

g05ncf is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.

Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the Users' Note for your implementation for any additional implementation-specific information.

9 Further Comments

None.

10 Example

In the example program a vector containing the first eight positive integers in ascending order is permuted by a call to g05ncf and the permutation is printed. This is repeated a total of ten times, after initialization by g05kff.

g05nc: FL CL CPP AD PY MB

NAG FL Interfaceg05ncf (permute)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

NAG FL Interface
g05ncf (permute)