G05 Chapter Contents
G05 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentG05SQF

Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

## 1  Purpose

G05SQF generates a vector of pseudorandom numbers uniformly distributed over the interval $\left[a,b\right]$.

## 2  Specification

 SUBROUTINE G05SQF ( N, A, B, STATE, X, IFAIL)
 INTEGER N, STATE(*), IFAIL REAL (KIND=nag_wp) A, B, X(N)

## 3  Description

If $a=0$ and $b=1$, G05SQF returns the next $n$ values ${y}_{i}$ from a uniform $\left(0,1\right]$ generator (see G05SAF for details).
For other values of $a$ and $b$, G05SQF applies the transformation
 $xi=a+b-ayi.$
The routine ensures that the values ${x}_{i}$ lie in the closed interval $\left[a,b\right]$.
One of the initialization routines G05KFF (for a repeatable sequence if computed sequentially) or G05KGF (for a non-repeatable sequence) must be called prior to the first call to G05SQF.

## 4  References

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

## 5  Parameters

1:     N – INTEGERInput
On entry: $n$, the number of pseudorandom numbers to be generated.
Constraint: ${\mathbf{N}}\ge 0$.
2:     A – REAL (KIND=nag_wp)Input
3:     B – REAL (KIND=nag_wp)Input
On entry: the end points $a$ and $b$ of the uniform distribution.
Constraint: ${\mathbf{A}}\le {\mathbf{B}}$.
4:     STATE($*$) – INTEGER arrayCommunication Array
Note: the actual argument supplied must be the array STATE supplied to the initialization routines G05KFF or G05KGF.
On entry: contains information on the selected base generator and its current state.
On exit: contains updated information on the state of the generator.
5:     X(N) – REAL (KIND=nag_wp) arrayOutput
On exit: the $n$ pseudorandom numbers from the specified uniform distribution.
6:     IFAIL – INTEGERInput/Output
On entry: IFAIL must be set to $0$, $-1\text{​ or ​}1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{​ or ​}1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is $0$. When the value $-\mathbf{1}\text{​ or ​}\mathbf{1}$ is used it is essential to test the value of IFAIL on exit.
On exit: ${\mathbf{IFAIL}}={\mathbf{0}}$ unless the routine detects an error or a warning has been flagged (see Section 6).

## 6  Error Indicators and Warnings

If on entry ${\mathbf{IFAIL}}={\mathbf{0}}$ or $-{\mathbf{1}}$, explanatory error messages are output on the current error message unit (as defined by X04AAF).
Errors or warnings detected by the routine:
${\mathbf{IFAIL}}=1$
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.

Not applicable.

## 8  Further Comments

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 $b$, G05SQF may return a value of $a$ due to numerical rounding.

## 9  Example

This example prints five pseudorandom numbers from a uniform distribution between $-1.0$ and $1.0$, generated by a single call to G05SQF, after initialization by G05KFF.

### 9.1  Program Text

Program Text (g05sqfe.f90)

### 9.2  Program Data

Program Data (g05sqfe.d)

### 9.3  Program Results

Program Results (g05sqfe.r)