G05 Chapter Contents
G05 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentG05NCF

Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

## 1  Purpose

G05NCF performs a pseudorandom permutation of a vector of integers.

## 2  Specification

 SUBROUTINE G05NCF ( INDX, N, STATE, IFAIL)
 INTEGER INDX(N), N, STATE(*), IFAIL

## 3  Description

G05NCF 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 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  Parameters

1:     INDX(N) – INTEGER arrayInput/Output
On entry: the $n$ integer values to be permuted.
On exit: the $n$ permuted integer values.
2:     N – INTEGERInput
On entry: the number of values to be permuted.
Constraint: ${\mathbf{N}}\ge 1$.
3:     STATE($*$) – INTEGER arrayCommunication 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 – INTEGERInput/Output
On entry: IFAIL must be set to $0$, $-1\text{​ or ​}1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{​ or ​}1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is $0$. When the value $-\mathbf{1}\text{​ or ​}\mathbf{1}$ 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).

## 6  Error Indicators and Warnings

If on entry ${\mathbf{IFAIL}}={\mathbf{0}}$ or $-{\mathbf{1}}$, explanatory error messages are output on the current error message unit (as defined by X04AAF).
Errors or warnings detected by the routine:
${\mathbf{IFAIL}}=2$
On entry, ${\mathbf{N}}<1$.
${\mathbf{IFAIL}}=3$
 On entry, STATE vector was not initialized or has been corrupted.

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 G05NCF and the permutation is printed. This is repeated a total of ten times, after initialization by G05KFF.

### 9.1  Program Text

Program Text (g05ncfe.f90)

### 9.2  Program Data

Program Data (g05ncfe.d)

### 9.3  Program Results

Program Results (g05ncfe.r)