root/library/bdm/estim/kalman.cpp @ 679

#include "kalman.h"

namespace bdm {

using std::endl;



void KalmanFull::bayes ( const vec &yt, const vec &cond ) {
        bdm_assert_debug ( yt.length() == ( dimy ), "KalmanFull::bayes wrong size of dt" );

        const vec &u = cond; // in this case cond=ut
        const vec &y = yt;
        
        vec& mu = est._mu();
        mat &P = est._R();
        mat& _Ry = fy._R();
        vec& yp = fy._mu();
        //Time update
        mu = A * mu + B * u;
        P  = A * P * A.transpose() + (mat)Q;

        //Data update
        _Ry = C * P * C.transpose() + (mat)R;
        _K = P * C.transpose() * inv ( _Ry );
        P -= _K * C * P; // P = P -KCP;
        yp = C * mu + D * u;
        mu += _K * ( y - yp );

        if ( evalll ) {
                ll=fy.evallog(y);
        }
};



/////////////////////////////// EKFS
EKFfull::EKFfull ( ) : KalmanFull () {};

void EKFfull::set_parameters ( const shared_ptr<diffbifn> &pfxu0, const shared_ptr<diffbifn> &phxu0, const mat Q0, const mat R0 ) {
        pfxu = pfxu0;
        phxu = phxu0;

        set_dim( pfxu0->_dimx());
        dimy = phxu0->dimension();
        dimc = pfxu0->_dimu();
        est.set_parameters( zeros(dimension()), eye(dimension()) );

        A.set_size ( dimension(), dimension() );
        C.set_size ( dimy, dimension() );
        //initialize matrices A C, later, these will be only updated!
        pfxu->dfdx_cond ( est._mu(), zeros ( dimc ), A, true );
        B.clear();
        phxu->dfdx_cond ( est._mu(), zeros ( dimc ), C, true );
        D.clear();

        R = R0;
        Q = Q0;
}

void EKFfull::bayes ( const vec &yt, const vec &cond) {
        bdm_assert_debug ( yt.length() == ( dimy ), "EKFull::bayes wrong size of dt" );
        bdm_assert_debug ( cond.length() == ( dimc ), "EKFull::bayes wrong size of dt" );
        
        const vec &u = cond;
        const vec &y = yt; //lazy to change it
        vec &mu = est._mu();
        mat &P = est._R();
        mat& _Ry = fy._R();
        vec& yp = fy._mu();
        
        pfxu->dfdx_cond ( mu, zeros ( dimc ), A, true );
        phxu->dfdx_cond ( mu, zeros ( dimc ), C, true );

        //Time update
        mu = pfxu->eval ( mu, u );// A*mu + B*u;
        P  = A * P * A.transpose() + (mat)Q;

        //Data update
        _Ry = C * P * C.transpose() + (mat)R;
        _K = P * C.transpose() * inv ( _Ry );
        P -= _K * C * P; // P = P -KCP;
        yp = phxu->eval ( mu, u );
        mu += _K * ( y - yp );

        if ( BM::evalll ) {
                ll=fy.evallog(y);
        }
};



void KalmanCh::set_parameters ( const mat &A0, const mat &B0, const mat &C0, const mat &D0, const chmat &Q0, const chmat &R0 ) {

        ( ( StateSpace<chmat>* ) this )->set_parameters ( A0, B0, C0, D0, Q0, R0 );
        
        _K=zeros(dimension(),dimy);
}

void KalmanCh::initialize(){
        preA = zeros ( dimy + dimension() + dimension(), dimy + dimension() );
//      preA.clear();
        preA.set_submatrix ( 0, 0, R._Ch() );
        preA.set_submatrix ( dimy + dimension(), dimy, Q._Ch() );
}

void KalmanCh::bayes ( const vec &yt, const vec &cond ) {
        bdm_assert_debug(yt.length()==dimy, "yt mismatch");
        bdm_assert_debug(cond.length()==dimc, "yt mismatch");
        
        const vec &u = cond;
        const vec &y = yt;
        vec pom ( dimy );

        chmat &_P=est._R();
        vec &_mu = est._mu();
        mat _K(dimension(),dimy);
        chmat &_Ry=fy._R();
        vec &_yp = fy._mu();
        //TODO get rid of Q in qr()!
//      mat Q;

        //R and Q are already set in set_parameters()
        preA.set_submatrix ( dimy, 0, ( _P._Ch() ) *C.T() );
        //Fixme can be more efficient if .T() is not used
        preA.set_submatrix ( dimy, dimy, ( _P._Ch() ) *A.T() );

        if ( !qr ( preA, postA ) ) {
                bdm_warning ( "QR in KalmanCh unstable!" );
        }

        ( _Ry._Ch() ) = postA ( 0, dimy - 1, 0, dimy - 1 );
        _K = inv ( A ) * ( postA ( 0, dimy - 1 , dimy, dimy + dimension() - 1 ) ).T();
        ( _P._Ch() ) = postA ( dimy, dimy + dimension() - 1, dimy, dimy + dimension() - 1 );

        _mu = A * ( _mu ) + B * u;
        _yp = C * _mu - D * u;

        backward_substitution ( _Ry._Ch(), ( y - _yp ), pom );
        _mu += ( _K ) * pom;

        /*              cout << "P:" <<_P.to_mat() <<endl;
                        cout << "Ry:" <<_Ry.to_mat() <<endl;
                        cout << "_K:" <<_K <<endl;*/

        if ( evalll == true ) { //likelihood of observation y
                ll = fy.evallog ( y );
        }
}



void EKFCh::set_parameters ( const shared_ptr<diffbifn> &pfxu0, const shared_ptr<diffbifn> &phxu0, const chmat Q0, const chmat R0 ) {
        pfxu = pfxu0;
        phxu = phxu0;

        set_dim( pfxu0->_dimx());
        dimy = phxu0->dimension();
        dimc = pfxu0->_dimu();
        
        vec &_mu = est._mu();
        // if mu is not set, set it to zeros, just for constant terms of A and C
        if ( _mu.length() != dimension() ) _mu = zeros ( dimension() ); 
        A = zeros ( dimension(), dimension() );
        C = zeros ( dimy, dimension() );
        preA = zeros ( dimy + dimension() + dimension(), dimy + dimension() );

        //initialize matrices A C, later, these will be only updated!
        pfxu->dfdx_cond ( _mu, zeros ( dimc ), A, true );
//      pfxu->dfdu_cond ( *_mu,zeros ( dimu ),B,true );
        B.clear();
        phxu->dfdx_cond ( _mu, zeros ( dimc ), C, true );
//      phxu->dfdu_cond ( *_mu,zeros ( dimu ),D,true );
        D.clear();

        R = R0;
        Q = Q0;

        // Cholesky special!
        preA.clear();
        preA.set_submatrix ( 0, 0, R._Ch() );
        preA.set_submatrix ( dimy + dimension(), dimy, Q._Ch() );
}


void EKFCh::bayes ( const vec &yt, const vec &cond ) {

        vec pom ( dimy );
        const vec &u = cond;
        const vec &y = yt;
        vec &_mu = est._mu();
        chmat &_P = est._R();
        chmat &_Ry = fy._R();
        vec &_yp = fy._mu();
        
        pfxu->dfdx_cond ( _mu, u, A, false ); //update A by a derivative of fx
        phxu->dfdx_cond ( _mu, u, C, false ); //update A by a derivative of fx

        //R and Q are already set in set_parameters()
        preA.set_submatrix ( dimy, 0, ( _P._Ch() ) *C.T() );
        //Fixme can be more efficient if .T() is not used
        preA.set_submatrix ( dimy, dimy, ( _P._Ch() ) *A.T() );

//      mat Sttm = _P->to_mat();
//      cout << preA <<endl;
//      cout << "_mu:" << _mu <<endl;

        if ( !qr ( preA, postA ) ) {
                bdm_warning ( "QR in EKFCh unstable!" );
        }


        ( _Ry._Ch() ) = postA ( 0, dimy - 1, 0, dimy - 1 );
        _K = inv ( A ) * ( postA ( 0, dimy - 1 , dimy, dimy + dimension() - 1 ) ).T();
        ( _P._Ch() ) = postA ( dimy, dimy + dimension() - 1, dimy, dimy + dimension() - 1 );

//      mat iRY = inv(_Ry->to_mat());
//      mat Stt = Sttm - Sttm * C.T() * iRY * C * Sttm;
//      mat _K2 = Stt*C.T()*inv(R.to_mat());

        // prediction
        _mu = pfxu->eval ( _mu , u );
        _yp = phxu->eval ( _mu, u );

        /*      vec mu2 = *_mu + ( _K2 ) * ( y-*_yp );*/

        //correction //= initial value is already prediction!
        backward_substitution ( _Ry._Ch(), ( y - _yp ), pom );
        _mu += ( _K ) * pom ;

        /*      _K = (_P->to_mat())*C.transpose() * ( _iRy->to_mat() );
                *_mu = pfxu->eval ( *_mu ,u ) + ( _K )* ( y-*_yp );*/

//              cout << "P:" <<_P.to_mat() <<endl;
//              cout << "Ry:" <<_Ry.to_mat() <<endl;
//      cout << "_mu:" <<_mu <<endl;
//      cout << "dt:" <<dt <<endl;

        if ( evalll == true ) { //likelihood of observation y
                ll = fy.evallog ( y );
        }
}

void EKFCh::from_setting ( const Setting &set ) {
        shared_ptr<diffbifn> IM = UI::build<diffbifn> ( set, "IM", UI::compulsory );
        shared_ptr<diffbifn> OM = UI::build<diffbifn> ( set, "OM", UI::compulsory );

        //statistics
        int dim = IM->dimension();
        vec mu0;
        if ( !UI::get ( mu0, set, "mu0" ) )
                mu0 = zeros ( dim );

        mat P0;
        vec dP0;
        if ( UI::get ( dP0, set, "dP0" ) )
                P0 = diag ( dP0 );
        else if ( !UI::get ( P0, set, "P0" ) )
                P0 = eye ( dim );

        set_statistics ( mu0, P0 );

        //parameters
        vec dQ, dR;
        UI::get ( dQ, set, "dQ", UI::compulsory );
        UI::get ( dR, set, "dR", UI::compulsory );
        set_parameters ( IM, OM, diag ( dQ ), diag ( dR ) );

        //connect
        shared_ptr<RV> drv = UI::build<RV> ( set, "drv", UI::compulsory );
        set_yrv ( *drv );
        shared_ptr<RV> rv = UI::build<RV> ( set, "rv", UI::compulsory );
        set_rv ( *rv );

        string options;
        if ( UI::get ( options, set, "options" ) )
                set_options ( options );
}

void MultiModel::from_setting ( const Setting &set ) {
        Array<EKFCh*> A;
        UI::get ( A, set, "models", UI::compulsory );

        set_parameters ( A );
        set_yrv ( A ( 0 )->_yrv() );
        //set_rv(A(0)->_rv());

        string options;
        if ( set.lookupValue ( "options", options ) )
                set_options ( options );
}

}