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Chapter Contents
Chapter Introduction
NAG Toolbox

NAG Toolbox: nag_rand_logical (g05tb)

Purpose

nag_rand_logical (g05tb) generates a vector of pseudorandom logical values – true with probability $p$ and false with probability $\left(1-p\right)$.

Syntax

[state, x, ifail] = g05tb(n, p, state)
[state, x, ifail] = nag_rand_logical(n, p, state)

Description

nag_rand_logical (g05tb) generates $n$ logical values ${x}_{i}$ from the relation
 $yi
where ${y}_{i}$ is a pseudorandom number from a uniform distribution over $\left(0,1\right]$, generated by nag_rand_dist_uniform01 (g05sa) using the values of state as input to this function.
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_logical (g05tb).

References

Knuth D E (1981) The Art of Computer Programming (Volume 2) (2nd Edition) Addison–Wesley

Parameters

Compulsory Input Parameters

1:     $\mathrm{n}$int64int32nag_int scalar
$n$, the number of pseudorandom logical values to be generated.
Constraint: ${\mathbf{n}}\ge 0$.
2:     $\mathrm{p}$ – double scalar
Must contain the probability of nag_rand_logical (g05tb) returning true.
Constraint: $0.0\le {\mathbf{p}}\le 1.0$.
3:     $\mathrm{state}\left(:\right)$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.

None.

Output Parameters

1:     $\mathrm{state}\left(:\right)$int64int32nag_int array
Contains updated information on the state of the generator.
2:     $\mathrm{x}\left({\mathbf{n}}\right)$ – logical array
The $n$ logical values.
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

Errors or warnings detected by the function:
${\mathbf{ifail}}=1$
Constraint: ${\mathbf{n}}\ge 0$.
${\mathbf{ifail}}=2$
Constraint: $0.0\le {\mathbf{p}}\le 1.0$.
${\mathbf{ifail}}=3$
On entry, state vector has been corrupted or not initialized.
${\mathbf{ifail}}=-99$
${\mathbf{ifail}}=-399$
Your licence key may have expired or may not have been installed correctly.
${\mathbf{ifail}}=-999$
Dynamic memory allocation failed.

Not applicable.

None.

Example

This example prints the first $20$ pseudorandom logical values generated by nag_rand_logical (g05tb) after initialization by nag_rand_init_repeat (g05kf), when the probability of a true value is $0.5$.
```function g05tb_example

fprintf('g05tb example results\n\n');

% Initialize the base generator to a repeatable sequence
seed  = [int64(1762543)];
genid = int64(1);
subid = int64(1);
[state, ifail] = g05kf( ...
genid, subid, seed);

% Number of variates
n = int64(20);

% Parameters
p = 0.5;

% Generate variates from a logical distribution
[state, x, ifail] = g05tb( ...
n, p, state);

disp('Variates');
for i = 1:n
if x(i)
fprintf('    true\n');
else
fprintf('    false\n');
end
end

```
```g05tb example results

Variates
false
true
false
false
true
true
true
false
true
false
true
true
false
true
false
true
true
false
false
false
```