G05SPF (PDF version)
G05 Chapter Contents
G05 Chapter Introduction
NAG Library Manual

NAG Library Routine Document

G05SPF

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

G05SPF generates a vector of pseudorandom numbers from a triangular distribution with parameters xmin, xmed and xmax.

2  Specification

SUBROUTINE G05SPF ( N, XMIN, XMED, XMAX, STATE, X, IFAIL)
INTEGER  N, STATE(*), IFAIL
REAL (KIND=nag_wp)  XMIN, XMED, XMAX, X(N)

3  Description

The triangular distribution has a PDF (probability density function) that is triangular in profile. The base of the triangle ranges from x=xmin to x=xmax and the PDF has a maximum value of 2xmax-xmin  at x=xmed. If xmin=xmed=xmax then x=xmed with probability 1; otherwise the triangular distribution has PDF:
fx = x-xmin xmed-xmin × 2 xmax-xmin ​ if ​xminxxmed, fx= xmax-x xmax-xmed ×2xmax-xmin ​ if ​xmed<xxmax, fx=0 ​ otherwise.  
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 G05SPF.

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:     XMIN – REAL (KIND=nag_wp)Input
On entry: the end point xmin of the triangular distribution.
3:     XMED – REAL (KIND=nag_wp)Input
On entry: the median of the distribution xmed (also the location of the vertex of the triangular distribution at which the PDF reaches a maximum).
Constraint: XMEDXMIN.
4:     XMAX – REAL (KIND=nag_wp)Input
On entry: the end point xmax of the triangular distribution.
Constraint: XMAXXMED.
5:     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.
6:     XN – REAL (KIND=nag_wp) arrayOutput
On exit: the n pseudorandom numbers from the specified triangular distribution.
7:     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, XMED=value and XMIN=value.
Constraint: XMEDXMIN.
IFAIL=4
On entry, XMAX=value and XMED=value.
Constraint: XMAXXMED.
IFAIL=5
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

G05SPF 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

None.

10  Example

This example prints five pseudorandom numbers from a triangular distribution with parameters xmin=-1.0, xmed=0.5 and xmax=1.0, generated by a single call to G05SPF, after initialization by G05KFF.

10.1  Program Text

Program Text (g05spfe.f90)

10.2  Program Data

Program Data (g05spfe.d)

10.3  Program Results

Program Results (g05spfe.r)


G05SPF (PDF version)
G05 Chapter Contents
G05 Chapter Introduction
NAG Library Manual

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