exceeds the cycle length of any of the base generators. For practical purposes this is irrelevant, as the time taken to generate all possible combinations 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_sample (g05nd).

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: $ipop (n)$ – int64int32nag_int array: The population to be sampled.
2: $m$ – int64int32nag_int scalar: The sample size.

Constraint: $1 \leq m \leq n$ .
3: $state (:)$ – 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 ipop.
The number of elements in the population vector to be sampled.

Constraint: $n \geq 1$ .

Output Parameters

1: $isampl (m)$ – int64int32nag_int array: The selected sample.
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: $n \geq 1$ .

$ifail = 4$: Constraint: $1 \leq m \leq n$ .

$ifail = 5$: 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

The time taken by nag_rand_sample (g05nd) is of order

n

In order to sample other kinds of vectors, or matrices of higher dimension, the following technique may be used:

(a)	set $ipop (i) = i$ , for $i = 1, 2, \dots, n$ ;
(b)	use nag_rand_sample (g05nd) to take a sample from ipop and put it into isampl;
(c)	use the contents of isampl as a set of indices to access the relevant vector or matrix.

In order to divide a population into several groups, nag_rand_permute (g05nc) is more efficient.

Example

In the example program random samples of size

1, 2, \dots, 8

are selected from a vector containing the first eight positive integers in ascending order. The samples are generated and printed for each sample size by a call to nag_rand_sample (g05nd) after initialization by nag_rand_init_repeat (g05kf).

Open in the MATLAB editor: g05nd_example

function g05nd_example


fprintf('g05nd example results\n\n');

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

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

in     = int64(8);
ipop   = int64([1:in]);
isampl = zeros(in, in, 'int64');

fprintf('\n Samples from the first 8 integers\n\n');
fprintf(' Sample size     Values\n');
for m=1:in
  [isampl(m, 1:m), state, ifail] = ...
     g05nd( ...
            ipop, m, state);

  fprintf('     %d           ', m);
  fprintf('%d ', isampl(m, 1:m));
  fprintf('\n');
end

g05nd example results


 Samples from the first 8 integers

 Sample size     Values
     1           2 
     2           3 6 
     3           1 5 7 
     4           2 6 7 8 
     5           1 2 3 4 8 
     6           1 3 4 5 6 7 
     7           1 3 4 5 6 7 8 
     8           1 2 3 4 5 6 7 8

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

Chapter Contents

Chapter Introduction

NAG Toolbox