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//******************************************************************************
//
// File: NormalPrng.java
// Package: edu.rit.numeric
// Unit: Class edu.rit.numeric.NormalPrng
//
// This Java source file is copyright (C) 2008 by Alan Kaminsky. All rights
// reserved. For further information, contact the author, Alan Kaminsky, at
// ark@cs.rit.edu.
//
// This Java source file is part of the Parallel Java Library ("PJ"). PJ is free
// software; you can redistribute it and/or modify it under the terms of the GNU
// General Public License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// PJ is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
// A PARTICULAR PURPOSE. See the GNU General Public License for more details.
//
// Linking this library statically or dynamically with other modules is making a
// combined work based on this library. Thus, the terms and conditions of the
// GNU General Public License cover the whole combination.
//
// As a special exception, the copyright holders of this library give you
// permission to link this library with independent modules to produce an
// executable, regardless of the license terms of these independent modules, and
// to copy and distribute the resulting executable under terms of your choice,
// provided that you also meet, for each linked independent module, the terms
// and conditions of the license of that module. An independent module is a
// module which is not derived from or based on this library. If you modify this
// library, you may extend this exception to your version of the library, but
// you are not obligated to do so. If you do not wish to do so, delete this
// exception statement from your version.
//
// A copy of the GNU General Public License is provided in the file gpl.txt. You
// may also obtain a copy of the GNU General Public License on the World Wide
// Web at http://www.gnu.org/licenses/gpl.html.
//
//******************************************************************************
package edu.rit.numeric;
import edu.rit.util.Random;
/**
* Class NormalPrng provides a pseudorandom number generator (PRNG) that
* generates random numbers with a normal distribution.
* <P>
* Every two calls of the <TT>next()</TT> method result in two calls of the
* underlying uniform PRNG's <TT>nextDouble()</TT> method. More precisely, the
* first of a pair of <TT>next()</TT> calls does two <TT>nextDouble()</TT>
* calls, the second of a pair of <TT>next()</TT> calls does not call
* <TT>nextDouble()</TT>.
* <P>
* Class NormalPrng uses the Box-Muller method to generate a standard normal
* distribution. Let <I>x</I><SUB>1</SUB> and <I>x</I><SUB>2</SUB> be drawn from
* a uniform distribution between 0 and 1. Then <I>y</I><SUB>1</SUB> and
* <I>y</I><SUB>2</SUB>, defined as follows, are drawn from a standard normal
* distribution.
* <CENTER>
* <I>y</I><SUB>1</SUB> = sqrt(−2 ln <I>x</I><SUB>1</SUB>) cos 2π<I>x</I><SUB>2</SUB>
* <BR><I>y</I><SUB>2</SUB> = sqrt(−2 ln <I>x</I><SUB>1</SUB>) sin 2π<I>x</I><SUB>2</SUB>
* </CENTER>
* And (μ + σ<I>y</I><SUB>1</SUB>) and
* (μ + σ<I>y</I><SUB>2</SUB>) are drawn from a normal
* distribution with mean μ and standard deviation σ.
* <P>
* <I>Note:</I> While slower than other techniques, this technique does a fixed
* number of <TT>nextDouble()</TT> calls to generate each normally distributed
* random number. This behavior is important when parallel programs generate
* random numbers.
*
* @author Alan Kaminsky
* @version 10-Jun-2008
*/
public class NormalPrng
extends DoublePrng
{
// Hidden data members.
private double myMean;
private double myStdev;
private double u1 = -1.0;
private double u2;
private static final double TWO_PI = 2.0*Math.PI;
// Exported constructors.
/**
* Construct a new standard normal PRNG. The mean is 0 and the standard
* deviation is 1.
*
* @param theUniformPrng The underlying uniform PRNG.
*
* @exception NullPointerException
* (unchecked exception) Thrown if <TT>theUniformPrng</TT> is null.
*/
public NormalPrng
(Random theUniformPrng)
{
this (theUniformPrng, 0.0, 1.0);
}
/**
* Construct a new normal PRNG with the given mean and standard deviation.
*
* @param theUniformPrng The underlying uniform PRNG.
* @param theMean Mean of the normal distribution.
* @param theStdev Standard deviation of the normal distribution.
*
* @exception NullPointerException
* (unchecked exception) Thrown if <TT>theUniformPrng</TT> is null.
*/
public NormalPrng
(Random theUniformPrng,
double theMean,
double theStdev)
{
super (theUniformPrng);
myMean = theMean;
myStdev = theStdev;
}
// Exported operations.
/**
* Returns the next random number.
*
* @return Random number.
*/
public double next()
{
double y;
if (u1 == -1.0)
{
double x1 = myUniformPrng.nextDouble();
double x2 = myUniformPrng.nextDouble();
u1 = Math.sqrt(-2.0*Math.log(x1));
u2 = TWO_PI*x2;
y = u1*Math.cos(u2);
}
else
{
y = u1*Math.sin(u2);
u1 = -1.0;
}
return myMean + myStdev*y;
}
}
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