NAG Toolbox: nag_rand_sample_wgt (g05ne)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

1:     $\mathrm{order}$ – string (length ≥ 1)

A flag indicating the sorted status of the wt vector.

$\mathbf{order}=\text{'A'}$

wt is sorted in ascending order,

$\mathbf{order}=\text{'D'}$

wt is sorted in descending order,

$\mathbf{order}=\text{'U'}$

wt is unsorted and nag_rand_sample_wgt (g05ne) will sort the weights prior to using them.

Irrespective of the value of order, no checks are made on the sorted status of wt, e.g., it is possible to supply $\mathbf{order}=\text{'A'}$, even when wt is not sorted. In such cases the wt array will not be sorted internally, but nag_rand_sample_wgt (g05ne) will still work correctly except, possibly, in cases of extreme weight values.

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

Constraint: $\mathbf{order}=\text{'A'}$, $\text{'D'}$ or $\text{'U'}$.

2:     $\mathrm{wt}\left(\mathbf{n}\right)$ – double array

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

Constraints:

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

3:     $\mathrm{pop}$ – string (length ≥ 1)

A flag indicating whether a population to be sampled has been supplied.

$\mathbf{pop}=\text{'D'}$

the population is assumed to be the integers $\left(1,2,\dots ,\mathbf{n}\right)$ and ipop is not referenced,

$\mathbf{pop}=\text{'S'}$

the population must be supplied in ipop.

Constraint: $\mathbf{pop}=\text{'D'}$ or $\text{'S'}$.

4:     $\mathrm{ipop}\left(:\right)$ – int64int32nag_int array

The dimension of the array ipop must be at least $\mathbf{n}$ if $\mathbf{pop}=\text{'S'}$

The population to be sampled. If $\mathbf{pop}=\text{'D'}$ 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 $\mathbf{wt}\left(i\right)\ne 0,\mathbf{wt}\left(j\right)\ne 0$ and $i\ne j$ then there is a nonzero probability that the sample will contain both $\mathbf{ipop}\left(i\right)$ and $\mathbf{ipop}\left(j\right)$. If $\mathbf{ipop}\left(i\right)=\mathbf{ipop}\left(j\right)$ then that value can appear in isampl more than once.

5:     $\mathrm{m}$ – int64int32nag_int scalar

$m$, the size of the sample required.

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

6:     $\mathrm{state}\left(:\right)$ – 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:     $\mathrm{n}$ – int64int32nag_int scalar

Default: the dimension of the array wt.

$n$, the size of the population.

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

Output Parameters

1:     $\mathrm{isampl}\left(\mathbf{m}\right)$ – int64int32nag_int array

The selected sample.

2:     $\mathrm{state}\left(:\right)$ – int64int32nag_int array

Contains updated information on the state of the generator.

3:     $\mathrm{ifail}$ – int64int32nag_int scalar

$\mathbf{ifail}=\mathbf{0}$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

   $\mathbf{ifail}=1$

On entry, $\mathbf{order}=\_$ was an illegal value.

On entry, order had an illegal value.

   $\mathbf{ifail}=2$

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

   $\mathbf{ifail}=3$

On entry, pop had an illegal value.

   $\mathbf{ifail}=5$

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

   $\mathbf{ifail}=7$

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

   $\mathbf{ifail}=8$

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

   $\mathbf{ifail}=21$

Constraint: must be at least m nonzero weights.

   $\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

   $\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

   $\mathbf{ifail}=-999$

Dynamic memory allocation failed.

Accuracy

Further Comments

Example

Open in the MATLAB editor: g05ne_example

function g05ne_example


fprintf('g05ne example results\n\n');

genid = int64(3);
subid = int64(0);
seed  = [int64(1762543)];
% Initialise the generator to a repeatable sequence
[state, ifail] = g05kf( ...
                        genid, subid, seed);

% Data to sample with weights
ipop = [int64(171); 52; 172; 139; 196;
                125;  36;  70;  25;  86;
                 76;  37; 185;  40;  90;
                 27;  79; 118; 142; 127;
                101;  22;  41; 199;  59];
wt = [ 85.54;  71.78; 118.13;  13.68; 153.60;
      165.35; 122.35;  35.87; 151.78; 128.33;
      178.27; 183.37; 165.81; 101.41; 145.16;
       42.01;  59.08;  17.53;  87.14;  69.20;
       31.13;  60.26;  21.00;  85.06; 119.73];

% Generate the sample sice m without replacement, unequal weights
m     = int64(10);
pop   = 's';
order = 'u';
[isampl, state, ifail] = g05ne( ...
                                order, wt, pop, ipop, m, state);

% Display the results
disp(isampl);

g05ne example results

                  125
                   41
                  185
                   40
                   37
                  196
                   22
                   25
                   76
                  172