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# NAG Toolbox: nag_rand_dist_uniform (g05sq)

## Purpose

nag_rand_dist_uniform (g05sq) generates a vector of pseudorandom numbers uniformly distributed over the interval $\left[a,b\right]$.

## Syntax

[state, x, ifail] = g05sq(n, a, b, state)
[state, x, ifail] = nag_rand_dist_uniform(n, a, b, state)

## Description

If $a=0$ and $b=1$, nag_rand_dist_uniform (g05sq) returns the next $n$ values ${y}_{i}$ from a uniform $\left(0,1\right]$ generator (see nag_rand_dist_uniform01 (g05sa) for details).
For other values of $a$ and $b$, nag_rand_dist_uniform (g05sq) applies the transformation
 $xi=a+b-ayi.$
The function ensures that the values ${x}_{i}$ lie in the closed interval $\left[a,b\right]$.
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_dist_uniform (g05sq).

## 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 numbers to be generated.
Constraint: ${\mathbf{n}}\ge 0$.
2:     $\mathrm{a}$ – double scalar
3:     $\mathrm{b}$ – double scalar
The end points $a$ and $b$ of the uniform distribution.
Constraint: ${\mathbf{a}}\le {\mathbf{b}}$.
4:     $\mathrm{state}\left(:\right)$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:     $\mathrm{x}\left({\mathbf{n}}\right)$ – double array
The $n$ pseudorandom numbers from the specified uniform distribution.
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: ${\mathbf{n}}\ge 0$.
${\mathbf{ifail}}=3$
Constraint: ${\mathbf{b}}\ge {\mathbf{a}}$.
${\mathbf{ifail}}=4$
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.

## Accuracy

Not applicable.

Although ${y}_{i}$ takes a value from the half closed interval $\left(0,1\right]$ and ${x}_{i}=a+\left(b-a\right){y}_{i}$, ${x}_{i}$ is documented as taking values from the closed interval $\left[a,b\right]$. This is because for some values of $a$ and $b$, nag_rand_dist_uniform (g05sq) may return a value of $a$ due to numerical rounding.

## Example

This example prints five pseudorandom numbers from a uniform distribution between $-1.0$ and $1.0$, generated by a single call to nag_rand_dist_uniform (g05sq), after initialization by nag_rand_init_repeat (g05kf).
```function g05sq_example

fprintf('g05sq 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(5);

% Parameters
a = -1;
b = 1;

% Generate variates from a Uniform (a,b) distribution
[state, x, ifail] = g05sq( ...
n, a, b, state);

disp('Variates');
disp(x);

```
```g05sq example results

Variates
0.2727
-0.7870
0.4921
0.5965
-0.7908

```

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Chapter Introduction
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