g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

# NAG Library Function Documentnag_rngs_permute (g05nac)

## 1  Purpose

nag_rngs_permute (g05nac) performs a pseudorandom permutation of a vector of integers.

## 2  Specification

 #include #include
 void nag_rngs_permute (Integer index[], Integer n, Integer igen, Integer iseed[], NagError *fail)

## 3  Description

nag_rngs_permute (g05nac) 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 $n$ (greater than $25$ say), it is theoretically impossible that all $n!$ permutations may occur, as $n!$ exceeds the cycle length of nag_rngs_basic (g05kac) for any valid value of igen. For practical purposes this is irrelevant, as the time necessary to generate all possible permutations is many millenia.
One of the initialization functions nag_rngs_init_repeatable (g05kbc) (for a repeatable sequence if computed sequentially) or nag_rngs_init_nonrepeatable (g05kcc) (for a non-repeatable sequence) must be called prior to the first call to nag_rngs_permute (g05nac).

## 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:     index[n]IntegerInput/Output
On entry: the $n$ integer values to be permuted.
On exit: the $n$ permuted integer values.
2:     nIntegerInput
On entry: the number of values to be permuted.
Constraint: ${\mathbf{n}}\ge 1$.
3:     igenIntegerInput
On entry: must contain the identification number for the generator to be used to return a pseudorandom number and should remain unchanged following initialization by a prior call to nag_rngs_init_repeatable (g05kbc) or nag_rngs_init_nonrepeatable (g05kcc).
4:     iseed[$4$]IntegerCommunication Array
On entry: contains values which define the current state of the selected generator.
On exit: contains updated values defining the new state of the selected generator.
5:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

## 6  Error Indicators and Warnings

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.

Not applicable.

None.

## 9  Example

In the example program a vector containing the first eight positive integers in ascending order is permuted by a call to nag_rngs_permute (g05nac) and the permutation is printed. This is repeated a total of ten times, after initialization by nag_rngs_init_repeatable (g05kbc).

### 9.1  Program Text

Program Text (g05nace.c)

None.

### 9.3  Program Results

Program Results (g05nace.r)