G05SQF (PDF version)
G05 Chapter Contents
G05 Chapter Introduction
NAG Library Manual

NAG Library Routine Document

G05SQF

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.

 Contents

    1  Purpose
    7  Accuracy

1  Purpose

G05SQF generates a vector of pseudorandom numbers uniformly distributed over the interval a,b.

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 yi from a uniform 0,1 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 xi lie in the closed interval a,b.
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  Arguments

1:     N – INTEGERInput
On entry: n, the number of pseudorandom numbers to be generated.
Constraint: N0.
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: AB.
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:     XN – 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​ or ​1. If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value -1​ 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 argument, the recommended value is 0. When the value -1​ or ​1 is used it is essential to test the value of IFAIL on exit.
On exit: IFAIL=0 unless the routine detects an error or a warning has been flagged (see Section 6).

6  Error Indicators and Warnings

If on entry IFAIL=0 or -1, explanatory error messages are output on the current error message unit (as defined by X04AAF).
Errors or warnings detected by the routine:
IFAIL=1
On entry, N=value.
Constraint: N0.
IFAIL=3
On entry, A=value and B=value.
Constraint: BA.
IFAIL=4
On entry, STATE vector has been corrupted or not initialized.
IFAIL=-99
An unexpected error has been triggered by this routine. Please contact NAG.
See Section 3.9 in How to Use the NAG Library and its Documentation for further information.
IFAIL=-399
Your licence key may have expired or may not have been installed correctly.
See Section 3.8 in How to Use the NAG Library and its Documentation for further information.
IFAIL=-999
Dynamic memory allocation failed.
See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

7  Accuracy

Not applicable.

8  Parallelism and Performance

G05SQF is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the Users' Note for your implementation for any additional implementation-specific information.

9  Further Comments

Although yi takes a value from the half closed interval 0,1 and xi=a+b-ayi, xi is documented as taking values from the closed interval a,b. This is because for some values of a and b, G05SQF may return a value of a due to numerical rounding.

10  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.

10.1  Program Text

Program Text (g05sqfe.f90)

10.2  Program Data

Program Data (g05sqfe.d)

10.3  Program Results

Program Results (g05sqfe.r)


G05SQF (PDF version)
G05 Chapter Contents
G05 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2016