/* *
 * Title:        

 * Description:  

 * Copyright:    Copyright (c) 

 * Company:      

 * @author
 * @version 1.0
 */


package umontreal.iro.lecuyer.stochprocess;
import umontreal.iro.lecuyer.rng.*;
import umontreal.iro.lecuyer.probdist.*;
import umontreal.iro.lecuyer.randvar.*;



/**
 * This class represents a Brownian motion process 
 * {X(t) : t >= 0},
 * sampled at times 
 * 0 = t0 < t1 <  ...  < td.
 * This process obeys the stochastic differential equation
 * 

 * 
 * 

 * dX(t) = μdt + σdB(t),
 * 

 * with initial condition X(0) = x0,
 * where μ and σ are the drift and volatility parameters,
 * and 
 * {B(t), t >= 0} is a standard Brownian motion
 * (with drift 0 and volatility 1).
 * This process has stationary and independent increments over disjoint
 * time intervals (it is a Lévy process) and the increment over an interval
 * of length t is normally distributed with mean μt and variance 
 * σ2t.
 * 
 * 

 * In this class, this process is generated using the sequential (or random walk)
 * technique:  X(0) = x0 and
 * 

 * 
 * 

 * X(tj) - X(tj-1) = μ(tj - tj-1) + σ(t_j - t_j-1)1/2Zj
 * 

 * where 
 * Zj∼N(0, 1).
 * 
 */
public class BrownianMotion extends StochasticProcess  {
    protected NormalGen    gen;
    protected double       mu,
                           sigma;
    // Precomputed values for standard BM
    protected double[]     mudt,
                           sigmasqrdt;



   /**
    * Constructs a new BrownianMotion with
    * parameters μ = mu, σ = sigma and initial value
    * 
    * X(t0) = x0.
    * The normal variates Zj in will be
    * generated by inversion using stream.
    * 
    */
   public BrownianMotion (double x0, double mu, double sigma,
                          RandomStream stream) {
        this (x0, mu, sigma, new NormalGen (stream));
    }


   /**
    * Constructs a new BrownianMotion with parameters μ =
    * mu, σ = sigma and initial value 
    * X(t0) = x0.
    * Here, the normal variate generator
    * {@link umontreal.iro.lecuyer.randvar.NormalGen NormalGen} is specified
    * directly instead of specifying the stream and using inversion.
    * The normal generator gen can use another method than inversion.
    * 
    */
   public BrownianMotion (double x0, double mu, double sigma, NormalGen gen) {
        this.mu    = mu;
        this.sigma = sigma;
        this.x0    = x0;
        this.gen   = gen;
    }
 

   public double nextObservation() {
        double x = path[observationIndex];
        x += mudt[observationIndex]
             + sigmasqrdt[observationIndex] * gen.nextDouble();
        observationIndex++;
        path[observationIndex] = x;
        return x;
    }


   /**
    * Generates and returns the next observation at time tj+1 =
    *  nextTime. It uses the previous observation time tj defined earlier
    * (either by this method or by setObservationTimes),
    * as well as the value of the previous observation X(tj).
    * Warning: This method will reset the observations time tj+1
    * for this process to nextTime. The user must make sure that
    * the tj+1 supplied is 
    *  >= tj.
    * 
    */
   public double nextObservation (double nextTime)  {
        // This method is useful for generating variance gamma processes
        double x = path[observationIndex];
        double previousTime = t[observationIndex];
        observationIndex++;
        t[observationIndex] = nextTime;
        double dt = nextTime - previousTime;
        x += mu * dt + sigma * Math.sqrt (dt) * gen.nextDouble();
        path[observationIndex] = x;
        return x;
    }


   /**
    * Generates an observation of the process in dt time units,
    * assuming that the process has value x at the current time.
    * Uses the process parameters specified in the constructor.
    * Note that this method does not affect the sample path of the process
    * stored internally (if any).
    * 
    */
   public double nextObservation (double x, double dt)  {
        x += mu * dt + sigma * Math.sqrt (dt) * gen.nextDouble();
        return x;
    }


   public double[] generatePath() {
        double x = x0;
        for (int j = 0; j < d; j++) {
            x += mudt[j] + sigmasqrdt[j] * gen.nextDouble();
            path[j + 1] = x;
        }
        observationIndex   = d;
        observationCounter = d;
        return path;
    }

   /**
    * Same as generatePath(), but a vector of uniform random numbers
    * must be provided to the method.  These uniform random numbers are used
    * to generate the path.
    * 
    */
   public double[] generatePath (double[] uniform01)  {
        double x = x0;
        for (int j = 0; j < d; j++) {
            x += mudt[j] + sigmasqrdt[j] * NormalDist.inverseF01(uniform01[j]);
            path[j + 1] = x;
        }
        observationIndex   = d;
        observationCounter = d;
        return path;
    }


   public double[] generatePath (RandomStream stream) {
        gen.setStream (stream);
        return generatePath();
    }

   /**
    * Resets the parameters 
    * X(t0) = x0, 
    * μ = mu and
    * 
    * σ = sigma of the process.
    * Warning: This method will recompute some quantities stored internally,
    * which may be slow if called too frequently.
    * 
    */
   public void setParams (double x0, double mu, double sigma)  {
        this.x0    = x0;
        this.mu    = mu;
        if (sigma <= 0)
           throw new IllegalArgumentException ("sigma <= 0");
        this.sigma = sigma;
        if (observationTimesSet) init(); // Otherwise not needed.
    }


   /**
    * Resets the random stream of the normal generator to stream.
    * 
    */
   public void setStream (RandomStream stream)  { gen.setStream (stream); }


   /**
    * Returns the random stream of the normal generator.
    * 
    */
   public RandomStream getStream()  { return gen.getStream (); }


   /**
    * Returns the value of μ.
    * 
    */
   public double getMu()  { return mu; }


   /**
    * Returns the value of σ.
    * 
    */
   public double getSigma()  { return sigma; }


   /**
    * Returns the normal random variate generator used.
    * The {@link umontreal.iro.lecuyer.rng.RandomStream RandomStream}
    * used by that generator can be changed via
    * getGen().setStream(stream), for example.
    * 
    */
   public NormalGen getGen()  { return gen; }
 

    // This is called by setObservationTimes to precompute constants
    // in order to speed up the path generation.
   protected void init() {
        super.init();
        mudt       = new double[d];
        sigmasqrdt = new double[d];
        for (int j = 0; j < d; j++) {
            double dt     = t[j+1] - t[j];
            mudt[j]       = mu * dt;
            sigmasqrdt[j] = sigma * Math.sqrt (dt);
        }
     }

}