/*--------------------------------------------------------------------*/
/*     Copyright (C) 2004-2016  Serge Iovleff, Université Lille 1, Inria

    This program is free software; you can redistribute it and/or modify
    it under the terms of the GNU Lesser General Public License as
    published by the Free Software Foundation; either version 2 of the
    License, or (at your option) any later version.

    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU Lesser General Public License for more details.

    You should have received a copy of the GNU Lesser General Public
    License along with this program; if not, write to the
    Free Software Foundation, Inc.,
    59 Temple Place,
    Suite 330,
    Boston, MA 02111-1307
    USA

    Contact : S..._DOT_I..._AT_stkpp.org (see copyright for ...)
*/

/*
 * Project: stkpp::Clustering
 * created on: 5 sept. 2013
 * Author:  iovleff, serge.iovleff@stkpp.org
 **/

/** @file STK_Gamma_a_bk.h
 *  @brief In this file we define the Gamma_pk_a_bk and Gamma_p_a_bk models.
 **/

#ifndef STK_GAMMA_A_BK_H
#define STK_GAMMA_A_BK_H

#include <STatistiK/include/STK_Law_Exponential.h>
#include "../GammaModels/STK_GammaBase.h"

namespace STK
{
template<class Array>class Gamma_a_bk;

namespace hidden
{
/** @ingroup Clustering
 * Traits class for the Gamma_a_bk traits policy
 **/
template<class Array_>
struct MixtureTraits< Gamma_a_bk<Array_> >
{
  typedef Array_ Array;
  /** Type of the structure storing the parameters of a Mixture Gamma_a_bk model*/
  typedef ModelParameters<Clust::Gamma_a_bk_> Parameters;
};

} // namespace Clust

/** @ingroup Clustering
 *  Gamma_a_bk is a mixture model of the following form
 * \f[
 *     f(\mathbf{x}_i|\theta) = \sum_{k=1}^K p_k
 *     \prod_{j=1}^p\left(\frac{x_i^j}{b_{k}}\right)^{a-1}
 *                   \frac{e^{-x_i^j/b_{k}}}{b_{k} \, \Gamma(a)},
 *      \quad x_i^j>0, \quad i=1,\ldots,n.
 * \f]
 **/
template<class Array>
class Gamma_a_bk: public GammaBase< Gamma_a_bk<Array> >
{
  public:
    typedef GammaBase< Gamma_a_bk<Array> > Base;
    using Base::param_;
    
    using Base::p_data;
    using Base::moments;
    using Base::meanjk;
    using Base::variancejk;
    using Base::meank;
    using Base::variancek;

    /** default constructor
     * @param nbCluster number of cluster in the model
     **/
    Gamma_a_bk( int nbCluster): Base(nbCluster) {}
    /** copy constructor
     *  @param model The model to copy
     **/
    Gamma_a_bk( Gamma_a_bk const& model): Base(model) {}
    /** destructor */
    ~Gamma_a_bk() {}
    /** Initialize randomly the parameters of the Gamma mixture. The shape
     *  will be selected randomly using an exponential of parameter mean^2/variance
     *  and the scale will be selected randomly using an exponential of parameter
     *  variance/mean.
     */
    void randomInit( CArrayXX const*  p_tik, CPointX const* p_tk) ;
    /** Compute the run( CArrayXX const*  p_tik, CPointX const* p_tk) . */
    bool run( CArrayXX const*  p_tik, CPointX const* p_tk) ;
    /** @return the number of free parameters of the model */
    inline int computeNbFreeParameters() const { return this->nbCluster()+1;}
};

template<class Array>
void Gamma_a_bk<Array>::randomInit( CArrayXX const*  p_tik, CPointX const* p_tk) 
{
  // compute moments
  this->moments(p_tik);
  Real value = 0.0;
  for (int k= p_tik->beginCols(); k < p_tik->endCols(); ++k)
  {
    Real mean = meank(k), variance = variancek(k);
    // generate scales
    param_.scale_[k] = Law::Exponential::rand(variance/mean);
    value += p_tk->elt(k) * (mean*mean/variance);
  }
  param_.shape_ = STK::Law::Exponential::rand(value/this->nbSample());
#ifdef STK_MIXTURE_VERY_VERBOSE
  stk_cout << _T(" Gamma_a_bk<Array>::randomInit( CArrayXX const*  p_tik, CPointX const* p_tk)  done\n");
#endif
}


/* Compute the weighted mean and the common variance. */
template<class Array>
bool Gamma_a_bk<Array>::run( CArrayXX const*  p_tik, CPointX const* p_tk) 
{
  if (!moments(p_tik)) { return false;}
  // estimate a
  Real y =0.0, x0 = 0.0, x1 = param_.shape_;
  for (int k= p_tik->beginCols(); k < p_tik->endCols(); ++k)
  {
    Real mean = meank(k);
    y  += p_tk->elt(k) * (param_.meanLog_[k] - std::log(mean)).sum();
    x0 += p_tk->elt(k) * (mean*mean/variancek(k));
  }
  y  /= (this->nbSample()*this->nbVariable());
  x0 /= this->nbSample();
  // moment estimate and oldest value
  if ((x0 <=0.) || (isNA(x0))) return false;

  // get shape
  hidden::invPsiMLog f(y);
  Real a = Algo::findZero(f, x0, x1, 1e-08);
  if (!Arithmetic<Real>::isFinite(a))
  {
#ifdef STK_MIXTURE_DEBUG
    stk_cout << "ML estimation failed in Gamma_a_bjk::run( CArrayXX const*  p_tik, CPointX const* p_tk) \n";
    stk_cout << "x0 =" << x0 << _T("\n";);
    stk_cout << "f(x0) =" << f(x0) << _T("\n";);
    stk_cout << "x1 =" << x1 << _T("\n";);
    stk_cout << "f(x1) =" << f(x1) << _T("\n";);
#endif
    a = x0; // use moment estimate
  }
  // set values
  param_.shape_ = a;
  // estimate b
  for (int k= p_tik->beginCols(); k < p_tik->endCols(); ++k)
  { param_.scale_[k] = meank(k)/a;}
  return true;
}

}  // namespace STK


#endif /* STK_Gamma_A_BK_H */
