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_repeat (g05kf) (for a repeatable sequence if computed sequentially) or nag_rand_init_nonrepeat (g05kg) (for a non-repeatable sequence) must be called prior to the first call to nag_rand_permute (g05nc).

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

Parameters

Compulsory Input Parameters

1: $indx (n)$ – int64int32nag_int array: The $n$ integer values to be permuted.
2: $state (:)$ – int64int32nag_int array: Note: the actual argument supplied must be the array state supplied to the initialization routines nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg).

Contains information on the selected base generator and its current state.

Optional Input Parameters

1: $n$ – int64int32nag_int scalar: Default: the dimension of the array indx.
The number of values to be permuted.

Constraint: $n \geq 1$ .

Output Parameters

1: $indx (n)$ – int64int32nag_int array: The $n$ permuted integer values.
2: $state (:)$ – int64int32nag_int array: Contains updated information on the state of the generator.
3: $ifail$ – int64int32nag_int scalar: $ifail = 0$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Errors or warnings detected by the function:

$ifail = 2$: Constraint: $n \geq 1$ .

$ifail = 3$: On entry, state vector has been corrupted or not initialized.

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.

$ifail = - 999$: Dynamic memory allocation failed.

Accuracy

Not applicable.

Further Comments

None.

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 (g05nc) and the permutation is printed. This is repeated a total of ten times, after initialization by nag_rand_init_repeat (g05kf).

Open in the MATLAB editor: g05nc_example

function g05nc_example


fprintf('g05nc example results\n\n');

% Initialize the seed and identify the base generator
seed  = [int64(1762543)];
genid = int64(1);
subid =  int64(1);

% Initialize the generator to a repeatable sequence
[state, ifail] = g05kf( ...
                        genid, subid, seed);

index = zeros(10, 8, 'int64');

% Set up the index vector
index1 = int64([1:8]);

fprintf(' 10 Permutations of first 8 integers\n');
% Permutate 10 times
for j = 1:10
  % Call the permutation routine
  [index(j,:), state, ifail] = g05nc( ...
                                      index1, state);
end

% Display variates
disp(double(index));

g05nc example results

 10 Permutations of first 8 integers
     6     2     4     8     1     3     5     7
     8     6     4     2     7     3     1     5
     4     2     8     7     5     6     3     1
     1     6     4     5     2     3     7     8
     1     7     3     8     4     2     5     6
     6     3     4     7     1     2     8     5
     6     4     1     8     2     5     3     7
     3     2     1     7     5     8     6     4
     4     2     1     5     3     6     8     7
     1     5     6     4     2     7     8     3

PDF version (NAG web site, 64-bit version, 64-bit version)

Chapter Contents

Chapter Introduction

NAG Toolbox