STK_Law_Categorical.h

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/*     Copyright (C) 2004-2016  Serge Iovleff, Université Lille 1, Inria
 
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 Free Software Foundation, Inc.,
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 */
 
/*
 * Project:  stkpp::STatistiK::Law
 * created on: 23 janv. 2013
 * Author:   iovleff, S..._Dot_I..._At_stkpp_Dot_org (see copyright for ...)
 **/
 
#ifndef STK_LAW_CATEGORICAL_H
#define STK_LAW_CATEGORICAL_H
 
#include <Arrays/include/STK_Array2DVector.h>
#include "STK_Law_IUnivLaw.h"
 
namespace STK
{
 
namespace Law
{
 
class Categorical: public IUnivLaw<int>
{
  public:
    typedef IUnivLaw<int> Base;
    inline Categorical(): Base(_T("Categorical")), prob_(1,1) { computeCumProb();}
    Categorical(Array2DVector<Real> const& prob): Base(_T("Categorical")), prob_(prob)
    { computeCumProb();}
    template <class OtherArray>
    Categorical(OtherArray const& prob): Base(_T("Categorical"))
    { prob_ = prob; computeCumProb();}
    inline virtual ~Categorical() {}
 
    inline Array2DVector<Real> const& prob() const { return prob_;}
    inline Array2DVector<Real> const& cumProb() const { return cumProb_;}
 
    template<class OtherArray>
    inline void setProb(OtherArray const& prob )
    { prob_ = prob; computeCumProb();}
 
    virtual int rand() const;
    virtual Real cdf(Real const& t) const;
    virtual Real pdf(int const& x) const;
    virtual Real lpdf(int const& x) const;
    virtual int icdf(Real const& prob) const;
 
    template<class OtherArray>
    static int rand(OtherArray const& prob)
    {
      Real u = Law::generator.randUnif(), cum = 0.;
      for(int k = prob.begin(); k< prob.lastIdx(); k++)
      {
        cum += prob[k];
        if (u<=cum) return k;
      }
      return prob.lastIdx();
    }
    template<class OtherArray>
    static Real lpdf(int const& x, OtherArray const& prob)
    { return (prob[x] == 0) ? -Arithmetic<Real>::infinity() : std::log(prob[x]);}
 
  protected:
    Array2DVector<Real> prob_;
    Array2DVector<Real> cumProb_;
 
  private:
    void computeCumProb();
};
 
/* @return a @c Type random variate . */
inline int Categorical::rand() const
{
  Real u = Law::generator.randUnif();
  int k;
  for(k = cumProb_.begin(); k< cumProb_.end(); k++)
  { if (u<=cumProb_[k]) return k;}
  return k;
}
 
/* @brief compute the probability distribution function (density)
 *  Give the value of the pdf at the point x.
 *  @param x the value to compute the pdf.
 *  @return the value of the pdf
 **/
inline Real Categorical::pdf(int const& x) const
{ return prob_[x];}
/* @brief compute the log probability distribution function
 *  Give the value of the log-pdf at the point x.
 *  @param x the value to compute the lpdf.
 *  @return the value of the log-pdf
 **/
inline Real Categorical::lpdf(int const& x) const
{ return (prob_[x] == 0) ? -Arithmetic<Real>::infinity() : std::log(prob_[x]);}
/* @brief compute the cumulative distribution function
 *  Give the probability that a Categorical random variate is less or equal
 *  to t.
 *  @param t the value to compute the cdf.
 *  @return the value of the cdf
 **/
inline Real Categorical::cdf(Real const& t) const
{ return (t<prob_.begin()) ? 0. : (t>=prob_.lastIdx()) ? 1. : cumProb_[std::floor(t)];}
 
/* @brief inverse cumulative distribution function
 *  Compute the Real quantile t such that the probability of a random
 *  variate less to t is less or equal to p.
 *  @param p value of the probability giving the quantile
 **/
inline int Categorical::icdf(Real const& prob) const
{
  if (prob<0) STKDOMAIN_ERROR_1ARG(Categorical::icdf,prob,prob must be >= 0);
  if (prob>1) STKDOMAIN_ERROR_1ARG(Categorical::icdf,prob,prob must be <= 1);
  int k;
  for (k = cumProb_.begin(); k< cumProb_.lastIdx(); ++k)
  { if (cumProb_[k] >= prob) return k;}
  return k;
}
 
inline void Categorical::computeCumProb()
{
  cumProb_.resize(prob_.range());
  Real sum=0.;
  for (int k=prob_.begin(); k< prob_.end(); ++k)
  { cumProb_[k] = (sum+=prob_[k]);}
  // normalize
  if (sum) {cumProb_/=sum; prob_ /=sum;}
  else {STKINVALIDARGUMENT_ERROR_NO_ARG(Categorical::computeCumProb,sum of the probabilities is zero);}
}
 
} // namespace Law
 
} // namespace STK
 
#endif /* STK_LAW_CATEGORICAL_H */