NAG Library Function Document

nag_rand_sample_unequal (g05nec)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{sortorder}$ – Nag_SortOrderInput

On entry: a flag indicating the sorted status of the wt vector.

$\mathbf{sortorder}=\mathrm{Nag\_Ascending}$

wt is sorted in ascending order,

$\mathbf{sortorder}=\mathrm{Nag\_Descending}$

wt is sorted in descending order,

$\mathbf{sortorder}=\mathrm{Nag\_Unsorted}$

wt is unsorted and nag_rand_sample_unequal (g05nec) will sort the weights prior to using them.

Irrespective of the value of sortorder, no checks are made on the sorted status of wt, e.g., it is possible to supply $\mathbf{sortorder}=\mathrm{Nag\_Ascending}$, even when wt is not sorted. In such cases the wt array will not be sorted internally, but nag_rand_sample_unequal (g05nec) will still work correctly except, possibly, in cases of extreme weight values.

It is usually more efficient to specify a value of sortorder that is consistent with the status of wt.

Constraint: $\mathbf{sortorder}=\mathrm{Nag\_Ascending}$, $\mathrm{Nag\_Descending}$ or $\mathrm{Nag\_Unsorted}$.

2:    $\mathbf{wt}\left[\mathbf{n}\right]$ – const doubleInput

On entry: $w_i$, the relative probability weights. These weights need not sum to $1.0$.

Constraints:

• $\mathbf{wt}\left[\mathit{i}-1\right]\ge 0.0$, for $\mathit{i}=1,2,\dots ,\mathbf{n}$;
• at least m values must be nonzero.

3:    $\mathbf{ipop}\left[\mathit{dim}\right]$ – const IntegerInput

Note: the dimension, dim, of the array ipop must be at least

• $\mathbf{n}$ when ipop is not NULL.

On entry: the population to be sampled. If $\mathbf{ipop}\text{is}\mathbf{NULL}$ then the population is assumed to be the set of values $\left(1,2,\dots ,\mathbf{n}\right)$ and the array ipop is not referenced. Elements of ipop with the same value are not combined, therefore if $\mathbf{wt}\left[i-1\right]\ne 0,\mathbf{wt}\left[j-1\right]\ne 0$ and $i\ne j$ then there is a nonzero probability that the sample will contain both $\mathbf{ipop}\left[i-1\right]$ and $\mathbf{ipop}\left[j-1\right]$. If $\mathbf{ipop}\left[i-1\right]=\mathbf{ipop}\left[j-1\right]$ then that value can appear in isampl more than once.

4:    $\mathbf{n}$ – IntegerInput

On entry: $n$, the size of the population.

Constraint: $\mathbf{n}\ge 1$.

5:    $\mathbf{isampl}\left[\mathbf{m}\right]$ – IntegerOutput

On exit: the selected sample.

6:    $\mathbf{m}$ – IntegerInput

On entry: $m$, the size of the sample required.

Constraint: $0\le \mathbf{m}\le \mathbf{n}$.

7:    $\mathbf{state}\left[\mathit{dim}\right]$ – IntegerCommunication 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.

8:    $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.

NE_BAD_PARAM

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: $0\le \mathbf{m}\le \mathbf{n}$.

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.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_INVALID_STATE

On entry, state vector has been corrupted or not initialized.

NE_NEG_WEIGHT

On entry, at least one weight was less than zero.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

NE_NON_ZERO_WEIGHTS

On entry, $\mathbf{m}=〈\mathit{\text{value}}〉$, number of nonzero weights $=〈\mathit{\text{value}}〉$.
Constraint: must be at least m nonzero weights.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (g05nece.c)

10.2

Program Data

Program Data (g05nece.d)

10.3

Program Results

Program Results (g05nece.r)