/* *
 * 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 an Ornstein-Uhlenbeck process
 * as in {@link OrnsteinUhlenbeckProcess}, but
 * the process is generated using the simple Euler scheme
 * 

 * 
 * 

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

 * where 
 * Zj∼N(0, 1).
 * This is a good approximation only for small time intervals 
 * tj - tj-1.
 * 
 */
public class OrnsteinUhlenbeckProcessEuler extends OrnsteinUhlenbeckProcess {



   /**
    * Constructor with 
    * parameters α = alpha, b, σ = sigma and initial
    * value 
    * X(t0) = x0. The normal variates Zj will be 
    * generated by inversion using the stream stream.
    * 
    */
   public OrnsteinUhlenbeckProcessEuler (double x0, double alpha, double b,
                                         double sigma, RandomStream stream)
    {
      this (x0, alpha, b, sigma, new NormalGen (stream));
   }


   /**
    * Here, the normal variate generator is specified directly
    * instead of specifying the stream.
    * The normal generator gen can use another method than inversion.
    * 
    */
   public OrnsteinUhlenbeckProcessEuler (double x0, double alpha, double b,
                                         double sigma, NormalGen gen)  {
      super (x0, alpha, b, sigma, gen);
   }


   /**
    * Generates and returns the next observation at time tj+1 =
    *  nextTime. Assumes the previous observation time is 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 xOld = path[observationIndex];
      double x = xOld + (beta - xOld) * alphadt[observationIndex]
                 + sigmasqrdt[observationIndex] * gen.nextDouble();
      observationIndex++;
      path[observationIndex] = x;
      return x;
   }

   public double nextObservation (double nextTime) {
      double previousTime = t[observationIndex];
      double xOld = path[observationIndex];
      observationIndex++;
      t[observationIndex] = nextTime;
      double dt = nextTime - previousTime;
      double x = xOld + alpha * (beta - xOld) * dt
           + sigma * Math.sqrt (dt) * gen.nextDouble();
      path[observationIndex] = x;
      return x;
   }


   /**
    * Generates and returns 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 = x + alpha * (beta - x) * dt
            + sigma * Math.sqrt (dt) * gen.nextDouble();
      return x;
    }


   /**
    * Generates a sample path of the process at all observation times,
    *  which are provided in array t.
    *  Note that t[0] should be the observation time of x0, 
    *  the initial value of the process, and t[] should have at least d + 1
    *  elements (see the setObservationTimes method).
    * 
    */
   public double[] generatePath() {
      double x;
      double xOld = x0;
      for (int j = 0; j < d; j++) {
          x = xOld + (beta - xOld)*alphadt[j] + sigmasqrdt[j]*gen.nextDouble();
          path[j + 1] = x;
          xOld = x;
      }
      observationIndex = d;
      return path;
   }


   protected void initArrays(int d) {
      double dt;
      for (int j = 0; j < d; j++) {
          dt = t[j+1] - t[j];
          alphadt[j]      = alpha * (dt);
          sigmasqrdt[j]   = sigma * Math.sqrt (dt);
      }
   }
}