# NAG CL Interfaceg05ncc (permute)

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## 1Purpose

g05ncc performs a pseudorandom permutation of a vector of integers.

## 2Specification

 #include
 void g05ncc (Integer indx[], Integer n, Integer state[], NagError *fail)
The function may be called by the names: g05ncc or nag_rand_permute.

## 3Description

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 g05kfc (for a repeatable sequence if computed sequentially) or g05kgc (for a non-repeatable sequence) must be called prior to the first call to 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: $\mathbf{indx}\left[{\mathbf{n}}\right]$Integer Input/Output
On entry: the $n$ integer values to be permuted.
On exit: the $n$ permuted integer values.
2: $\mathbf{n}$Integer Input
On entry: the number of values to be permuted.
Constraint: ${\mathbf{n}}\ge 1$.
3: $\mathbf{state}\left[\mathit{dim}\right]$Integer Communication 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 7 in the Introduction to the NAG Library CL Interface).

## 6Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface 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 7.5 in the Introduction to the NAG Library CL Interface 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 8 in the Introduction to the NAG Library CL Interface for further information.

Not applicable.

## 8Parallelism and Performance

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 g05ncc and the permutation is printed. This is repeated a total of ten times, after initialization by g05kfc.

### 10.1Program Text

Program Text (g05ncce.c)

None.

### 10.3Program Results

Program Results (g05ncce.r)