g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

NAG Library Function Documentnag_rngs_sample (g05nbc)

1  Purpose

nag_rngs_sample (g05nbc) selects a pseudorandom sample without replacement from an integer vector.

2  Specification

 #include #include
 void nag_rngs_sample (const Integer ipop[], Integer n, Integer isampl[], Integer m, Integer igen, Integer iseed[], NagError *fail)

3  Description

nag_rngs_sample (g05nbc) selects $m$ elements from a population vector ipop of length $n$ and places them in a sample vector isampl. Their order in ipop will be preserved in isampl. Each of the $\left(\begin{array}{c}n\\ m\end{array}\right)$ possible combinations of elements of isampl may be regarded as being equally probable.
For moderate or large values of $n$ (greater than $75$ say), it is theoretically impossible that all combinations of size $m$ may occur, unless $m$ is near 1 or near $n$. This is because $\left(\begin{array}{c}n\\ m\end{array}\right)$ exceeds the cycle length of nag_rngs_basic (g05kac) for all valid values of igen. For practical purposes this is irrelevant, as the time taken to generate all possible combinations is many millenia.
One of the initialization functions nag_rngs_init_repeatable (g05kbc) (for a repeatable sequence if computed sequentially) or nag_rngs_init_nonrepeatable (g05kcc) (for a non-repeatable sequence) must be called prior to the first call to nag_rngs_sample (g05nbc).

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:     ipop[n]const IntegerInput
On entry: the population to be sampled.
2:     nIntegerInput
On entry: the number of elements in the population vector to be sampled.
Constraint: ${\mathbf{n}}\ge 1$.
3:     isampl[m]IntegerOutput
On exit: the selected sample.
4:     mIntegerInput
On entry: the sample size.
Constraint: $1\le {\mathbf{m}}\le {\mathbf{n}}$.
5:     igenIntegerInput
On entry: must contain the identification number for the generator to be used to return a pseudorandom number and should remain unchanged following initialization by a prior call to nag_rngs_init_repeatable (g05kbc) or nag_rngs_init_nonrepeatable (g05kcc).
6:     iseed[$4$]IntegerCommunication Array
On entry: contains values which define the current state of the selected generator.
On exit: contains updated values defining the new state of the selected generator.
7:     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_INT_2
On entry, ${\mathbf{m}}=〈\mathit{\text{value}}〉$ and ${\mathbf{n}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{m}}\ge 1$ and ${\mathbf{m}}\le {\mathbf{n}}$.
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.

7  Accuracy

Not applicable.

The time taken by nag_rngs_sample (g05nbc) 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 ${\mathbf{ipop}}\left[\mathit{i}-1\right]=\mathit{i}$, for $\mathit{i}=1,2,\dots ,n$; (b) use nag_rngs_sample (g05nbc) 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_rngs_permute (g05nac) is more efficient.

9  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_rngs_sample (g05nbc) after initialization by nag_rngs_init_repeatable (g05kbc).

9.1  Program Text

Program Text (g05nbce.c)

None.

9.3  Program Results

Program Results (g05nbce.r)