root/library/bdm/stat/emix.cpp @ 773

#include "emix.h"

namespace bdm {

void emix::validate (){
        bdm_assert ( Coms.length() > 0, "There has to be at least one component." );

        bdm_assert ( Coms.length() == w.length(), "It is obligatory to define weights of all the components." );

        double sum_w = sum ( w );
        bdm_assert ( sum_w != 0, "There has to be a component with non-zero weight." );
        w = w / sum_w;

        int dim = Coms ( 0 )->dimension();
        for ( int i = 1; i < Coms.length(); i++ ) {
                bdm_assert ( dim == ( Coms ( i )->dimension() ), "Component sizes do not match!" );
                bdm_assert ( Coms(i)->isnamed() , "An unnamed component is forbidden here!" );
        }

        set_rv ( Coms ( 0 )->_rv() ); 
}

void emix::from_setting ( const Setting &set ) {
        UI::get ( Coms, set, "pdfs", UI::compulsory );

        if ( !UI::get ( w, set, "weights", UI::optional ) ) {
                int len = Coms.length();
                w.set_length ( len );
                w = 1.0 / len;
        }

        validate();
}


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();
}

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

vec emix::variance() const {
        //non-central moment
        vec mom2 = zeros ( dim );
        for ( int i = 0; i < w.length(); i++ ) {
                mom2 += w ( i ) * ( Coms ( i )->variance() + pow ( Coms ( i )->mean(), 2 ) );
        }
        //central moment
        return mom2 - pow ( mean(), 2 );
}

double emix::evallog ( const vec &val ) const {
        int i;
        double sum = 0.0;
        for ( i = 0; i < w.length(); i++ ) {
                sum += w ( i ) * exp ( Coms ( i )->evallog ( val ) );
        }
        if ( sum == 0.0 ) {
                sum = std::numeric_limits<double>::epsilon();
        }
        double tmp = log ( sum );
        bdm_assert_debug ( std::isfinite ( tmp ), "Infinite" );
        return tmp;
}

vec emix::evallog_mat ( const mat &Val ) const {
        vec x = zeros ( Val.cols() );
        for ( int i = 0; i < w.length(); i++ ) {
                x += w ( i ) * exp ( Coms ( i )->evallog_mat ( Val ) );
        }
        return log ( x );
};

mat emix::evallog_coms ( const mat &Val ) const {
        mat X ( w.length(), Val.cols() );
        for ( int i = 0; i < w.length(); i++ ) {
                X.set_row ( i, w ( i ) *exp ( Coms ( i )->evallog_mat ( Val ) ) );
        }
        return X;
}

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._w() = w;
        target._Coms() = Cn;
        target.validate();
}

shared_ptr<pdf> emix::condition ( const RV &rv ) const {
        bdm_assert ( isnamed(), "rvs are not assigned" );
        mratio *tmp = new mratio ( this, rv );
        return shared_ptr<pdf> ( 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._w() = w;
        target._Coms() = Cn;
        target.validate();
}

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;
};

double mprod::evallogcond ( const vec &val, const vec &cond ) {
        int i;
        double res = 0.0;
        for ( i = pdfs.length() - 1; i >= 0; i-- ) {
                /*                      if ( pdfs(i)->_rvc().count() >0) {
                                                pdfs ( i )->condition ( dls ( i )->get_cond ( val,cond ) );
                                        }
                                        // add logarithms
                                        res += epdfs ( i )->evallog ( dls ( i )->pushdown ( val ) );*/
                res += pdfs ( i )->evallogcond (
                           dls ( i )->pushdown ( val ),
                           dls ( i )->get_cond ( val, cond )
                       );
        }
        return res;
}

vec mprod::evallogcond_mat ( const mat &Dt, const vec &cond ) {
        vec tmp ( Dt.cols() );
        for ( int i = 0; i < Dt.cols(); i++ ) {
                tmp ( i ) = evallogcond ( Dt.get_col ( i ), cond );
        }
        return tmp;
}

vec mprod::evallogcond_mat ( const Array<vec> &Dt, const vec &cond ) {
        vec tmp ( Dt.length() );
        for ( int i = 0; i < Dt.length(); i++ ) {
                tmp ( i ) = evallogcond ( Dt ( i ), cond );
        }
        return tmp;
}

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

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

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

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

void mmix::validate()
{       
        bdm_assert ( Coms.length() > 0, "There has to be at least one component." );

        bdm_assert ( Coms.length() == w.length(), "It is obligatory to define weights of all the components." );

        double sum_w = sum ( w );
        bdm_assert ( sum_w != 0, "There has to be a component with non-zero weight." );
        w = w / sum_w;

        int dim = Coms ( 0 )->dimension();
        int dimc = Coms ( 0 )->dimensionc();
        for ( int i = 1; i < Coms.length(); i++ ) {
                bdm_assert ( dim == ( Coms ( i )->dimension() ), "Component sizes do not match!" );
                bdm_assert ( dimc == ( Coms ( i )->dimensionc() ), "Component sizes do not match!" );
                bdm_assert ( Coms(i)->isnamed() , "An unnamed component is forbidden here!" );
        }

        set_rv ( Coms ( 0 )->_rv() );
        set_rvc ( Coms ( 0 )->_rvc() );
}

void mmix::from_setting ( const Setting &set ) {
        UI::get ( Coms, set, "pdfs", UI::compulsory );

        if ( !UI::get ( w, set, "weights", UI::optional ) ) {
                int len = Coms.length();
                w.set_length ( len );
                w = 1.0 / len;
        }
}

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 );
}

vec eprod::mean() const {
        vec tmp ( dim );
        for ( int i = 0; i < epdfs.length(); i++ ) {
                vec pom = epdfs ( i )->mean();
                dls ( i )->pushup ( tmp, pom );
        }
        return tmp;
}

vec eprod::variance() const {
        vec tmp ( dim ); //second moment
        for ( int i = 0; i < epdfs.length(); i++ ) {
                vec pom = epdfs ( i )->mean();
                dls ( i )->pushup ( tmp, pow ( pom, 2 ) );
        }
        return tmp - pow ( mean(), 2 );
}
vec eprod::sample() const {
        vec tmp ( dim );
        for ( int i = 0; i < epdfs.length(); i++ ) {
                vec pom = epdfs ( i )->sample();
                dls ( i )->pushup ( tmp, pom );
        }
        return tmp;
}
double eprod::evallog ( const vec &val ) const {
        double tmp = 0;
        for ( int i = 0; i < epdfs.length(); i++ ) {
                tmp += epdfs ( i )->evallog ( dls ( i )->pushdown ( val ) );
        }
        bdm_assert_debug ( std::isfinite ( tmp ), "Infinite" );
        return tmp;
}

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