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Chapter Contents
Chapter Introduction
NAG Toolbox

# NAG Toolbox: nag_rand_dist_uniform (g05sq)

## Purpose

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

## Syntax

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

## Description

If a = 0$a=0$ and b = 1$b=1$, nag_rand_dist_uniform (g05sq) returns the next n$n$ values yi${y}_{i}$ from a uniform (0,1]$\left(0,1\right]$ generator (see nag_rand_dist_uniform01 (g05sa) for details).
For other values of a$a$ and b$b$, nag_rand_dist_uniform (g05sq) applies the transformation
 xi = a + (b − a)yi. $xi=a+(b-a)yi.$
The function ensures that the values xi${x}_{i}$ lie in the closed interval [a,b]$\left[a,b\right]$.
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:     n – int64int32nag_int scalar
n$n$, the number of pseudorandom numbers to be generated.
Constraint: n0${\mathbf{n}}\ge 0$.
2:     a – double scalar
3:     b – double scalar
The end points a$a$ and b$b$ of the uniform distribution.
Constraint: ab${\mathbf{a}}\le {\mathbf{b}}$.
4:     state( : $:$) – 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.

None.

### Output Parameters

1:     state( : $:$) – 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 updated information on the state of the generator.
2:     x(n) – double array
The n$n$ pseudorandom numbers from the specified uniform distribution.
3:     ifail – int64int32nag_int scalar
${\mathrm{ifail}}={\mathbf{0}}$ unless the function detects an error (see [Error Indicators and Warnings]).

## Error Indicators and Warnings

Errors or warnings detected by the function:
ifail = 1${\mathbf{ifail}}=1$
On entry, n < 0${\mathbf{n}}<0$.
ifail = 3${\mathbf{ifail}}=3$
On entry, b < a${\mathbf{b}}<{\mathbf{a}}$.
ifail = 4${\mathbf{ifail}}=4$
 On entry, state vector was not initialized or has been corrupted.

## Accuracy

Not applicable.

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

## Example

```function nag_rand_dist_uniform_example
% Initialize the seed
seed = [int64(1762543)];
% genid and subid identify the base generator
genid = int64(1);
subid =  int64(1);
n = int64(5);
a = -1;
b = 1;
% Initialize the generator to a repeatable sequence
[state, ifail] = nag_rand_init_repeat(genid, subid, seed);
[state, x, ifail] = nag_rand_dist_uniform(n, a, b, state)
```
```

state =

17
1234
1
0
4110
11820
23399
29340
17917
13895
19930
8
0
1234
1
1
1234

x =

0.2727
-0.7870
0.4921
0.5965
-0.7908

ifail =

0

```
```function g05sq_example
% Initialize the seed
seed = [int64(1762543)];
% genid and subid identify the base generator
genid = int64(1);
subid =  int64(1);
n = int64(5);
a = -1;
b = 1;
% Initialize the generator to a repeatable sequence
[state, ifail] = g05kf(genid, subid, seed);
[state, x, ifail] = g05sq(n, a, b, state)
```
```

state =

17
1234
1
0
4110
11820
23399
29340
17917
13895
19930
8
0
1234
1
1
1234

x =

0.2727
-0.7870
0.4921
0.5965
-0.7908

ifail =

0

```