NAG Library Function Document

1Purpose

nag_rand_permute (g05ncc) performs a pseudorandom permutation of a vector of integers.

2Specification

 #include #include
 void nag_rand_permute (Integer indx[], Integer n, Integer state[], NagError *fail)

3Description

nag_rand_permute (g05ncc) permutes the elements of an integer array without inspecting their values. Each of the $n!$ possible permutations of the $n$ values may be regarded as being equally probable.
Even for modest values of $n$ it is theoretically impossible that all $n!$ permutations may occur, as $n!$ 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 functions nag_rand_init_repeatable (g05kfc) (for a repeatable sequence if computed sequentially) or nag_rand_init_nonrepeatable (g05kgc) (for a non-repeatable sequence) must be called prior to the first call to nag_rand_permute (g05ncc).

4References

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

5Arguments

1:    $\mathbf{indx}\left[{\mathbf{n}}\right]$IntegerInput/Output
On entry: the $n$ integer values to be permuted.
On exit: the $n$ permuted integer values.
2:    $\mathbf{n}$IntegerInput
On entry: the number of values to be permuted.
Constraint: ${\mathbf{n}}\ge 1$.
3:    $\mathbf{state}\left[\mathit{dim}\right]$IntegerCommunication Array
Note: the dimension, $\mathit{dim}$, 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.
4:    $\mathbf{fail}$NagError *Input/Output
The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.
On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.
NE_INT
On entry, ${\mathbf{n}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{n}}\ge 1$.
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 2.7.6 in How to Use the NAG Library and its Documentation 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 2.7.5 in How to Use the NAG Library and its Documentation for further information.

Not applicable.

8Parallelism and Performance

nag_rand_permute (g05ncc) 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 function. Please also consult the Users' Note for your implementation for any additional implementation-specific information.

None.

10Example

In the example program a vector containing the first eight positive integers in ascending order is permuted by a call to nag_rand_permute (g05ncc) and the permutation is printed. This is repeated a total of ten times, after initialization by nag_rand_init_repeatable (g05kfc).

10.1Program Text

Program Text (g05ncce.c)

None.

10.3Program Results

Program Results (g05ncce.r)

© The Numerical Algorithms Group Ltd, Oxford, UK. 2017