root/library/bdm/stat/emix.cpp @ 675

#include "emix.h"

namespace bdm {

void emix::set_parameters ( const vec &w0, const Array<shared_ptr<epdf> > &Coms0 ) {
        w = w0 / sum ( w0 );
        dim = Coms0 ( 0 )->dimension();
        bool isnamed = Coms0 ( 0 )->isnamed();
        int i;
        RV tmp_rv;
        if ( isnamed ) tmp_rv = Coms0 ( 0 )->_rv();

        for ( i = 0; i < w.length(); i++ ) {
                bdm_assert ( dim == ( Coms0 ( i )->dimension() ), "Component sizes do not match!" );
                bdm_assert ( !isnamed || tmp_rv.equal ( Coms0 ( i )->_rv() ), "Component RVs do not match!" );
        }

        Coms = Coms0;

        if ( isnamed ) epdf::set_rv ( tmp_rv ); //coms aer already OK, no need for set_rv
}

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();
}

shared_ptr<epdf> emix::marginal ( const RV &rv ) const {
        emix *tmp = new emix();
        shared_ptr<epdf> narrow(tmp);
        marginal ( rv, *tmp );
        return narrow;
}

void emix::marginal ( const RV &rv, emix &target ) const {
        bdm_assert ( isnamed(), "rvs are not assigned" );

        Array<shared_ptr<epdf> > Cn ( Coms.length() );
        for ( int i = 0; i < Coms.length(); i++ ) {
                Cn ( i ) = Coms ( i )->marginal ( rv );
        }

        target.set_parameters ( w, Cn );
}

shared_ptr<mpdf> emix::condition ( const RV &rv ) const {
        bdm_assert ( isnamed(), "rvs are not assigned" );
        mratio *tmp = new mratio ( this, rv );
        return shared_ptr<mpdf>(tmp);
}

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++ ) {
                bdm_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++ ) {
                        bdm_error ( "Not implemented" );
                        // *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() );
}

shared_ptr<epdf> egiwmix::marginal ( const RV &rv ) const {
        emix *tmp = new emix();
        shared_ptr<epdf> narrow(tmp);
        marginal ( rv, *tmp );
        return narrow;
}

void egiwmix::marginal ( const RV &rv, emix &target ) const {
        bdm_assert_debug ( isnamed(), "rvs are not assigned" );

        Array<shared_ptr<epdf> > Cn ( Coms.length() );
        for ( int i = 0; i < Coms.length(); i++ ) {
                Cn ( i ) = Coms ( i )->marginal ( rv );
        }

        target.set_parameters ( w, Cn );
}

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;
};

void mprod::set_elements (const Array<shared_ptr<mpdf> > &mFacs ) {
        mpdfs = mFacs;
        dls.set_size ( mFacs.length() );

        rv = get_composite_rv ( mpdfs, true );
        dim = rv._dsize();

        for ( int i = 0; i < mpdfs.length(); i++ ) {
                RV rvx = mpdfs ( i )->_rvc().subt ( rv );
                rvc.add ( rvx ); // add rv to common rvc
        }
        dimc=rvc._dsize();

        // rv and rvc established = > we can link them with mpdfs
        for ( int i = 0; i < mpdfs.length(); i++ ) {
                dls ( i ) = new datalink_m2m;
                dls ( i )->set_connection ( mpdfs ( i )->_rv(), mpdfs ( i )->_rvc(), _rv(), _rvc() );
        }
}

vec mmix::samplecond(const vec &cond) {
        //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 )->samplecond(cond);
}

}
// 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.
//                      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;}*/
//              }
//      };