g05 Chapter Contents
g05 Chapter Introduction
NAG Library Manual

# NAG Library Function Documentnag_rand_permute (g05ncc)

## 1  Purpose

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

## 2  Specification

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

## 3  Description

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).

## 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]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:     state[$\mathit{dim}$]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:     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.
NE_INVALID_STATE
On entry, state vector has been corrupted or not initialized.

Not applicable.

Not applicable.

None.

## 10  Example

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).

### 10.1  Program Text

Program Text (g05ncce.c)

None.

### 10.3  Program Results

Program Results (g05ncce.r)