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

# Syntax

C#
```public static void g05sq(
int n,
double a,
double b,
G05..::..G05State g05state,
double[] x,
out int ifail
)```
Visual Basic
```Public Shared Sub g05sq ( _
n As Integer, _
a As Double, _
b As Double, _
g05state As G05..::..G05State, _
x As Double(), _
<OutAttribute> ByRef ifail As Integer _
)```
Visual C++
```public:
static void g05sq(
int n,
double a,
double b,
G05..::..G05State^ g05state,
array<double>^ x,
[OutAttribute] int% ifail
)```
F#
```static member g05sq :
n : int *
a : float *
b : float *
g05state : G05..::..G05State *
x : float[] *
ifail : int byref -> unit
```

#### Parameters

n
Type: System..::..Int32
On entry: $n$, the number of pseudorandom numbers to be generated.
Constraint: ${\mathbf{n}}\ge 0$.
a
Type: System..::..Double
On entry: the end points $a$ and $b$ of the uniform distribution.
Constraint: ${\mathbf{a}}\le {\mathbf{b}}$.
b
Type: System..::..Double
On entry: the end points $a$ and $b$ of the uniform distribution.
Constraint: ${\mathbf{a}}\le {\mathbf{b}}$.
g05state
Type: NagLibrary..::..G05..::..G05State
An Object of type G05.G05State.
x
Type: array<System..::..Double>[]()[][]
An array of size [n]
On exit: the $n$ pseudorandom numbers from the specified uniform distribution.
ifail
Type: System..::..Int32%
On exit: ${\mathbf{ifail}}={0}$ unless the method detects an error or a warning has been flagged (see [Error Indicators and Warnings]).

# Description

If $a=0$ and $b=1$, g05sq returns the next $n$ values ${y}_{i}$ from a uniform $\left(0,1\right]$ generator (see g05sa for details).
For other values of $a$ and $b$, g05sq applies the transformation
 $xi=a+b-ayi.$
The method ensures that the values ${x}_{i}$ lie in the closed interval $\left[a,b\right]$.
One of the initialization methods (G05KFF not in this release) (for a repeatable sequence if computed sequentially) or (G05KGF not in this release) (for a non-repeatable sequence) must be called prior to the first call to g05sq.

# References

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

# Error Indicators and Warnings

Errors or warnings detected by the method:
${\mathbf{ifail}}=1$
On entry, ${\mathbf{n}}<0$.
${\mathbf{ifail}}=3$
On entry, ${\mathbf{b}}<{\mathbf{a}}$.
${\mathbf{ifail}}=4$
 On entry, state vector was not initialized or has been corrupted.
${\mathbf{ifail}}=-9000$
An error occured, see message report.
${\mathbf{ifail}}=-8000$
Negative dimension for array $〈\mathit{\text{value}}〉$
${\mathbf{ifail}}=-6000$
Invalid Parameters $〈\mathit{\text{value}}〉$

Not applicable.

# Parallelism and Performance

None.

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 $b$, g05sq may return a value of $a$ due to numerical rounding.