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finmath lib is a Mathematical Finance Library in Java. It provides algorithms and methodologies related to mathematical finance.
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/*
 * (c) Copyright Christian P. Fries, Germany. Contact: [email protected].
 *
 * Created on 09.02.2004
 */
package net.finmath.montecarlo;

import java.io.Serializable;

import net.finmath.randomnumbers.MersenneTwister;
import net.finmath.stochastic.RandomVariableInterface;
import net.finmath.time.TimeDiscretizationInterface;

/**
 * Implementation of a time-discrete n-dimensional Brownian motion
 * W = (W₁,...,W_n) where W_i is
 * a Brownian motion and W_i, W_j are
 * independent for i not equal j.
 * 
 * For a correlated Brownian motion with see
 * {@link net.finmath.montecarlo.CorrelatedBrownianMotion}.
 * 
 * Here the dimension n is called factors since this Brownian motion is used to
 * generate multi-dimensional multi-factor Ito processes and there one might
 * use a different number of factors to generate Ito processes of different
 * dimension. 
 *
 * The quadruppel (time discretization, number of factors, number of paths, seed)
 * defines the state of an object of this class, i.e., BrownianMotion for which
 * there parameters agree, generate the same random numbers.
 *
 * The class is immutable and thread safe. It uses lazy initialization.
 * 
 * @author Christian Fries
 * @version 1.6
 */
public class BrownianMotion implements BrownianMotionInterface, Serializable {

	private static final long serialVersionUID = -5430067621669213475L;

	private final TimeDiscretizationInterface						timeDiscretization;

	private final int			numberOfFactors;
	private final int			numberOfPaths;
	private final int			seed;

	private final AbstractRandomVariableFactory randomVariableFactory;

	private transient	RandomVariableInterface[][]	brownianIncrements;
	private final		Object						brownianIncrementsLazyInitLock = new Object();

	/**
	 * Construct a Brownian motion.
	 * 
	 * The constructor allows to set the factory to be used for the construction of
	 * random variables. This allows to generate Brownian increments represented
	 * by different implementations of the RandomVariableInterface (e.g. the RandomVariableLowMemory internally
	 * using float representations).
	 * 
	 * @param timeDiscretization The time discretization used for the Brownian increments.
	 * @param numberOfFactors Number of factors.
	 * @param numberOfPaths Number of paths to simulate.
	 * @param seed The seed of the random number generator.
	 * @param randomVariableFactory Factory to be used to create random variable.
	 */
	public BrownianMotion(
			TimeDiscretizationInterface timeDiscretization,
			int numberOfFactors,
			int numberOfPaths,
			int seed,
			AbstractRandomVariableFactory randomVariableFactory) {
		super();
		this.timeDiscretization = timeDiscretization;
		this.numberOfFactors	= numberOfFactors;
		this.numberOfPaths		= numberOfPaths;
		this.seed				= seed;

		this.randomVariableFactory = randomVariableFactory;

		this.brownianIncrements	= null; 	// Lazy initialization
	}

	/**
	 * Construct a Brownian motion.
	 * 
	 * @param timeDiscretization The time discretization used for the Brownian increments.
	 * @param numberOfFactors Number of factors.
	 * @param numberOfPaths Number of paths to simulate.
	 * @param seed The seed of the random number generator.
	 */
	public BrownianMotion(
			TimeDiscretizationInterface timeDiscretization,
			int numberOfFactors,
			int numberOfPaths,
			int seed) {
		this(timeDiscretization, numberOfFactors, numberOfPaths, seed, new RandomVariableFactory());
	}

	@Override
	public BrownianMotionInterface getCloneWithModifiedSeed(int seed) {
		return new BrownianMotion(getTimeDiscretization(), getNumberOfFactors(), getNumberOfPaths(), seed);
	}

	@Override
	public BrownianMotionInterface getCloneWithModifiedTimeDiscretization(TimeDiscretizationInterface newTimeDiscretization) {
		/// @TODO This can be improved: a complete recreation of the Brownian motion wouldn't be necessary!
		return new BrownianMotion(newTimeDiscretization, getNumberOfFactors(), getNumberOfPaths(), getSeed());
	}

	@Override
	public RandomVariableInterface getBrownianIncrement(int timeIndex, int factor) {

		// Thread safe lazy initialization
		synchronized(brownianIncrementsLazyInitLock) {
			if(brownianIncrements == null) doGenerateBrownianMotion();
		}

		/*
		 *  We return an immutable object which ensures that the receiver does not alter the data.
		 */
		return brownianIncrements[timeIndex][factor];
	}

	/**
	 * Lazy initialization of brownianIncrement. Synchronized to ensure thread safety of lazy init.
	 */
	private void doGenerateBrownianMotion() {
		if(brownianIncrements != null) return;	// Nothing to do

		// Create random number sequence generator
		MersenneTwister mersenneTwister = new MersenneTwister(seed);

		// Allocate memory
		double[][][] brownianIncrementsArray = new double[timeDiscretization.getNumberOfTimeSteps()][numberOfFactors][numberOfPaths];

		// Pre-calculate square roots of deltaT
		double[] sqrtOfTimeStep = new double[timeDiscretization.getNumberOfTimeSteps()];
		for(int timeIndex=0; timeIndex