package umontreal.iro.lecuyer.probdistmulti;

/**
 * Classes implementing multi-dimensional discrete distributions over the integers
 * should inherit from this class.
 * It specifies the signature of methods for computing the mass function
 * (or probability) 
 * p(x1, x2,…, xd) = P[X1 = x1, X2 = x2,…, Xd = xd] and the cumulative probabilities 
 * for a random vector X with a discrete distribution over the integers.
 * 
 */
public abstract class DiscreteDistributionIntMulti {
   protected int dimension;
  

   /**
    * Returns the probability mass function 
    * p(x1, x2,…, xd),
    *    which should be a real number in [0, 1].
    *  
    * @param x value at which the mass function must be evaluated
    * 
    *    @return the mass function evaluated at x
    * 
    */
   public abstract double prob (int[] x);


   /**
    * Computes the cumulative probability function F of the distribution evaluated
    *    at x, assuming the lowest values start at 0, i.e. computes
    * 
    * 

    * 

    * F(x1, x2,…, xd) = ∑s1=0x1∑s2=0x2 ... ∑sd=0xdp(s1, s2,…, sd).
    * 

    * Uses the naive implementation, is very inefficient and may underflows.
    * 
    */
   public double cdf (int x[]) {
      int is[] = new int[x.length];
      for (int i = 0; i < is.length; i++)
         is[i] = 0;

      boolean end = false;
      double sum = 0.0;
      int j;
      while (!end) {
         sum += prob (is);
         is[0]++;

         if (is[0] > x[0]) {
            is[0] = 0;
            j = 1;
            while (j < x.length && is[j] == x[j])
               is[j++] = 0;

            if (j == x.length)
               end = true;
            else
               is[j]++;
         }
      }

      return sum;
   }


   /**
    * Returns the dimension d of the distribution.
    * 
    */
   public int getDimension() {
      return dimension;
   }


   /**
    * Returns the mean vector of the distribution, defined as 
    * μi = E[Xi].
    * 
    */
   public abstract double[] getMean();


   /**
    * Returns the variance-covariance matrix of the distribution, defined as
    * 
   
    * σij = E[(Xi - μi)(Xj - μj)].
    * 
    */
   public abstract double[][] getCovariance();


   /**
    * Returns the correlation matrix of the distribution, defined as
    *       
    * ρij = σij/(σ_iiσ_jj)1/2.
    * 
    */
   public abstract double[][] getCorrelation();

}