root/library/bdm/stat/emix.cpp @ 394

#include "emix.h"

namespace bdm{

void emix::set_parameters ( const vec &w0, const Array<epdf*> &Coms0, bool copy ) {
        w = w0/sum ( w0 );
        dim = Coms0(0)->dimension();
        int i;
        for ( i=0;i<w.length();i++ ) {
                it_assert_debug ( dim== ( Coms0 ( i )->dimension() ),"Component sizes do not match!" );
        }
        if ( copy ) {
                Coms.set_length(Coms0.length());
                for ( i=0;i<w.length();i++ ) {it_error("Not imp...");
                        *Coms ( i ) =*Coms0 ( i );}
                destroyComs=true;
        }
        else {
                Coms = Coms0;
                destroyComs=false;
        }
}

vec emix::sample() const {
        //Sample which component
        vec cumDist = cumsum ( w );
        double u0;
        #pragma omp critical
        u0 = UniRNG.sample();

        int i=0;
        while ( ( cumDist ( i ) <u0 ) && ( i< ( w.length()-1 ) ) ) {i++;}

        return Coms ( i )->sample();
}

emix* emix::marginal(const RV &rv) const{
        it_assert_debug(isnamed(), "rvs are not assigned");
                        
        Array<epdf*> Cn(Coms.length());
        for(int i=0;i<Coms.length();i++){Cn(i)=Coms(i)->marginal(rv);}
        emix* tmp = new emix();
        tmp->set_parameters(w,Cn,false);
        tmp->ownComs();
        return tmp;
}

mratio* emix::condition(const RV &rv) const{
        it_assert_debug(isnamed(), "rvs are not assigned");
        return new mratio(this,rv);
};

void egiwmix::set_parameters ( const vec &w0, const Array<egiw*> &Coms0, bool copy ) {
        w = w0/sum ( w0 );
        dim = Coms0(0)->dimension();
        int i;
        for ( i=0;i<w.length();i++ ) {
                it_assert_debug ( dim== ( Coms0 ( i )->dimension() ),"Component sizes do not match!" );
        }
        if ( copy ) {
                Coms.set_length(Coms0.length());
                for ( i=0;i<w.length();i++ ) {it_error("Not imp...");
                        *Coms ( i ) =*Coms0 ( i );}
                destroyComs=true;
        }
        else {
                Coms = Coms0;
                destroyComs=false;
        }
}

vec egiwmix::sample() const {
        //Sample which component
        vec cumDist = cumsum ( w );
        double u0;
        #pragma omp critical
        u0 = UniRNG.sample();

        int i=0;
        while ( ( cumDist ( i ) <u0 ) && ( i< ( w.length()-1 ) ) ) {i++;}

        return Coms ( i )->sample();
}

vec egiwmix::mean() const {
        int i; vec mu = zeros ( dim );
        for ( i = 0;i < w.length();i++ ) {mu += w ( i ) * Coms ( i )->mean(); }
        return mu;
}

vec egiwmix::variance() const {
        // non-central moment
        vec mom2 = zeros ( dim );
        for ( int i = 0;i < w.length();i++ ) {
                // pow is overloaded, we have to use another approach
                mom2 += w ( i ) * (Coms(i)->variance() + elem_mult ( Coms(i)->mean(), Coms(i)->mean() )); 
        }
        // central moment
        // pow is overloaded, we have to use another approach
        return mom2 - elem_mult( mean(), mean() );
}

emix* egiwmix::marginal(const RV &rv) const{
        it_assert_debug(isnamed(), "rvs are not assigned");
                        
        Array<epdf*> Cn(Coms.length());
        for(int i=0;i<Coms.length();i++){Cn(i)=Coms(i)->marginal(rv);}
        emix* tmp = new emix();
        tmp->set_parameters(w,Cn,false);
        tmp->ownComs();
        return tmp;
}

egiw*   egiwmix::approx() {
        // NB: dimx == 1 !!!
        // The following code might look a bit spaghetti-like,
        // consult Dedecius, K. et al.: Partial forgetting in AR models.

        double sumVecCommon;                            // common part for many terms in eq.
        int len = w.length();                           // no. of mix components        
        int dimLS = Coms(1)->_V()._D().length() - 1;    // dim of LS
        vec vecNu(len);                                 // vector of dfms of components
        vec vecD(len);                                  // vector of LS reminders of comps.
        vec vecCommon(len);                             // vector of common parts
        mat matVecsTheta;                               // matrix which rows are theta vects.

        // fill in the vectors vecNu, vecD and matVecsTheta
        for ( int i=0; i<len; i++ ) {
                vecNu.shift_left( Coms(i)->_nu() );
                vecD.shift_left( Coms(i)->_V()._D()(0) );
                matVecsTheta.append_row( Coms(i)->est_theta()  );
        }

        // calculate the common parts and their sum
        vecCommon = elem_mult ( w, elem_div(vecNu, vecD) );
        sumVecCommon = sum(vecCommon);

        // LS estimator of theta
        vec aprEstTheta(dimLS);  aprEstTheta.zeros();
        for ( int i=0; i<len; i++ ) {
                aprEstTheta +=  matVecsTheta.get_row( i ) * vecCommon ( i );
        }
        aprEstTheta /= sumVecCommon;
        
        
        // LS estimator of dfm
        double aprNu;
        double A = log( sumVecCommon );         // Term 'A' in equation

        for ( int i=0; i<len; i++ ) {
                A += w(i) * ( log( vecD(i) ) - psi( 0.5 * vecNu(i) ) );
        }

        aprNu = ( 1 + sqrt(1 + 2 * (A - LOG2)/3 ) ) / ( 2 * (A - LOG2) );


        // LS reminder (term D(0,0) in C-syntax)
        double aprD = aprNu / sumVecCommon;

        // Aproximation of cov
        // the following code is very numerically sensitive, thus
        // we have to eliminate decompositions etc. as much as possible
        mat aprC = zeros(dimLS, dimLS);
        for ( int i=0; i<len; i++ ) {
                aprC += Coms(i)->est_theta_cov().to_mat() * w(i); 
                vec tmp = ( matVecsTheta.get_row(i) - aprEstTheta );
                aprC += vecCommon(i) * outer_product( tmp, tmp);
        }

        // Construct GiW pdf :: BEGIN
        ldmat aprCinv ( inv(aprC) );
        vec D = concat( aprD, aprCinv._D() );
        mat L = eye(dimLS+1);
        L.set_submatrix(1,0, aprCinv._L() * aprEstTheta);
        L.set_submatrix(1,1, aprCinv._L());
        ldmat aprLD (L, D);

        egiw* aprgiw = new egiw(1, aprLD, aprNu);
        return aprgiw;
};

}
// mprod::mprod ( Array<mpdf*> mFacs, bool overlap) : mpdf ( RV(), RV() ), n ( mFacs.length() ), epdfs ( n ), mpdfs ( mFacs ), rvinds ( n ), rvcinrv ( n ), irvcs_rvc ( n ) {
//              int i;
//              bool rvaddok;
//              // Create rv
//              for ( i = 0;i < n;i++ ) {
//                      rvaddok=rv.add ( mpdfs ( i )->_rv() ); //add rv to common rvs.
//                      // If rvaddok==false, mpdfs overlap => assert error.
//                      it_assert_debug(rvaddok||overlap,"mprod::mprod() input mpdfs overlap in rv!");
//                      epdfs ( i ) = & ( mpdfs ( i )->posterior() ); // add pointer to epdf
//              };
//              // Create rvc
//              for ( i = 0;i < n;i++ ) {
//                      rvc.add ( mpdfs ( i )->_rvc().subt ( rv ) ); //add rv to common rvs.
//              };
//
// //           independent = true;
//              //test rvc of mpdfs and fill rvinds
//              for ( i = 0;i < n;i++ ) {
//                      // find ith rv in common rv
//                      rvsinrv ( i ) = mpdfs ( i )->_rv().dataind ( rv );
//                      // find ith rvc in common rv
//                      rvcinrv ( i ) = mpdfs ( i )->_rvc().dataind ( rv );
//                      // find ith rvc in common rv
//                      irvcs_rvc ( i ) = mpdfs ( i )->_rvc().dataind ( rvc );
//                      //
// /*                   if ( rvcinrv ( i ).length() >0 ) {independent = false;}
//                      if ( irvcs_rvc ( i ).length() >0 ) {independent = false;}*/
//              }
//      };