root/library/bdm/stat/exp_family.cpp @ 730

#include <math.h>

#include <itpp/base/bessel.h>
#include "exp_family.h"

namespace bdm {

Uniform_RNG UniRNG;
Normal_RNG NorRNG;
Gamma_RNG GamRNG;

using std::cout;

        ///////////

void BMEF::bayes( const vec &yt, const vec &cond ) {
        this->bayes_weighted ( yt, cond, 1.0 );
};

void egiw::set_parameters (int dimx0, ldmat V0, double nu0) {
        dimx = dimx0;
        nPsi = V0.rows() - dimx;
        dim = dimx * (dimx + nPsi); // size(R) + size(Theta)
        
        V = V0;
        if (nu0 < 0) {
                nu = 0.1 + nPsi + 2 * dimx + 2; // +2 assures finite expected value of R
                // terms before that are sufficient for finite normalization
        } else {
                nu = nu0;
        }
}

vec egiw::sample() const {
        mat M;
        chmat R;
        sample_mat(M,R);
        
        return concat (cvectorize(M),cvectorize(R.to_mat()));
}

mat egiw::sample_mat(int n) const {
        // TODO - correct approach - convert to product of norm * Wishart
        mat M;
        ldmat Vz;
        ldmat Lam;
        factorize(M,Vz,Lam);
        
        chmat ChLam(Lam.to_mat());
        chmat iChLam;
        ChLam.inv(iChLam);
        
        eWishartCh Omega; //inverse Wishart, result is R, 
        Omega.set_parameters(iChLam,nu-2*nPsi-dimx); // 2*nPsi is there to match numercial simulations - check if analytically correct
        
        mat OmChi;
        mat Z(M.rows(),M.cols());

        mat Mi;
        mat RChiT;
        mat tmp(dimension(), n);
        for (int i=0; i<n;i++){
                OmChi=Omega.sample_mat();
                RChiT=inv(OmChi);
                Z=randn(M.rows(), M.cols());
                Mi = M + RChiT * Z * inv(Vz._L().T() *diag(sqrt(Vz._D())));
        
                tmp.set_col(i,concat (cvectorize(Mi),cvectorize(RChiT*RChiT.T())));
        }
        return tmp;
}

void egiw::sample_mat(mat &Mi, chmat &Ri)const{
        
        // TODO - correct approach - convert to product of norm * Wishart
        mat M;
        ldmat Vz;
        ldmat Lam;
        factorize(M,Vz,Lam);
        
        chmat Ch;
        Ch.setCh(Lam._L()*diag(sqrt(Lam._D())));
        chmat iCh;
        Ch.inv(iCh);
        
        eWishartCh Omega; //inverse Wishart, result is R, 
        Omega.set_parameters(iCh,nu-2*nPsi-dimx); // 2*nPsi is there to match numercial simulations - check if analytically correct
        
        chmat Omi;
        Omi.setCh(Omega.sample_mat());
        
        mat Z=randn(M.rows(), M.cols());
        Mi = M+ Omi._Ch() * Z * inv(Vz._L()*diag(sqrt(Vz._D())));
        Omi.inv(Ri);
}

double egiw::evallog_nn ( const vec &val ) const {
        int vend = val.length() - 1;

        if ( dimx == 1 ) { //same as the following, just quicker.
                double r = val ( vend ); //last entry!
                if ( r < 0 ) return -inf;
                vec Psi ( nPsi + dimx );
                Psi ( 0 ) = -1.0;
                Psi.set_subvector ( 1, val ( 0, vend - 1 ) ); // fill the rest

                double Vq = V.qform ( Psi );
                return -0.5* ( nu*log ( r ) + Vq / r );
        } else {
                mat Th = reshape ( val ( 0, nPsi * dimx - 1 ), nPsi, dimx );
                fsqmat R ( reshape ( val ( nPsi*dimx, vend ), dimx, dimx ) );
                double ldetR = R.logdet();
                if ( ldetR ) return -inf;
                mat Tmp = concat_vertical ( -eye ( dimx ), Th );
                fsqmat iR ( dimx );
                R.inv ( iR );

                return -0.5* ( nu*ldetR + trace ( iR.to_mat() *Tmp.T() *V.to_mat() *Tmp ) );
        }
}

double egiw::lognc() const {
        const vec& D = V._D();

        double m = nu - nPsi - dimx - 1;
#define log2  0.693147180559945286226763983
#define logpi 1.144729885849400163877476189
#define log2pi 1.83787706640935
#define Inf std::numeric_limits<double>::infinity()

        double nkG = 0.5 * dimx * ( -nPsi * log2pi + sum ( log ( D ( dimx, D.length() - 1 ) ) ) );
        // temporary for lgamma in Wishart
        double lg = 0;
        for ( int i = 0; i < dimx; i++ ) {
                lg += lgamma ( 0.5 * ( m - i ) );
        }

        double nkW = 0.5 * ( m * sum ( log ( D ( 0, dimx - 1 ) ) ) ) \
                     - 0.5 * dimx * ( m * log2 + 0.5 * ( dimx - 1 ) * log2pi )  - lg;

//      bdm_assert_debug ( ( ( -nkG - nkW ) > -Inf ) && ( ( -nkG - nkW ) < Inf ), "ARX improper" );
        if (-nkG - nkW==Inf){
                cout << "??" <<endl;
        }
        return -nkG - nkW;
}

vec egiw::est_theta() const {
        if ( dimx == 1 ) {
                const mat &L = V._L();
                int end = L.rows() - 1;

                mat iLsub = ltuinv ( L ( dimx, end, dimx, end ) );

                vec L0 = L.get_col ( 0 );

                return iLsub * L0 ( 1, end );
        } else {
                bdm_error ( "ERROR: est_theta() not implemented for dimx>1" );
                return vec();
        }
}

void egiw::factorize(mat &M, ldmat &Vz, ldmat &Lam) const{      
        const mat &L = V._L();
        const vec &D = V._D();
        int end = L.rows() - 1;
        
        Vz=ldmat(L ( dimx, end, dimx, end ), D(dimx,end));
        mat iLsub = ltuinv ( Vz._L());
        // set mean value
        mat Lpsi = L ( dimx, end, 0, dimx - 1 );
        M = iLsub * Lpsi;
        
        Lam =ldmat ( L (0, dimx-1, 0, dimx-1 ), D (0, dimx-1 ) );  //exp val of R
         if (1){ // test with Peterka
                 mat VF=V.to_mat();
                 mat Vf=VF(0,dimx-1,0, dimx-1);
                 mat Vzf = VF(dimx,end,0,dimx-1);
                 mat VZ = VF(dimx,end,dimx,end);
                 
                 mat Lam2 = Vf-Vzf.T()*inv(VZ)*Vzf;
         }
}

ldmat egiw::est_theta_cov() const {
        if ( dimx == 1 ) {
                const mat &L = V._L();
                const vec &D = V._D();
                int end = D.length() - 1;

                mat Lsub = L ( 1, end, 1, end );
//              mat Dsub = diag ( D ( 1, end ) );

                ldmat LD(inv(Lsub).T(), 1.0/D(1,end));
                return LD;

        } else {
                bdm_error ( "ERROR: est_theta_cov() not implemented for dimx>1" );
                return ldmat();
        }

}

vec egiw::mean() const {

        if ( dimx == 1 ) {
                const vec &D = V._D();
                int end = D.length() - 1;

                vec m ( dim );
                m.set_subvector ( 0, est_theta() );
                m ( end ) = D ( 0 ) / ( nu - nPsi - 2 * dimx - 2 );
                return m;
        } else {
                mat M;
                mat R;
                mean_mat ( M, R );
                return concat( cvectorize (  M),cvectorize( R ) );
        }

}

vec egiw::variance() const {
        int l = V.rows();
        // cut out rest of lower-right part of V
        const ldmat tmp ( V, linspace ( dimx, l - 1 ) );
        // invert it
        ldmat itmp ( l );
        tmp.inv ( itmp );
        
        // following Wikipedia notation
        // m=nu-nPsi-dimx-1, p=dimx 
        double mp1p=nu-nPsi-2*dimx; // m-p+1
        double mp1m=mp1p-2;         // m-p-1
        
        if ( dimx == 1 ) {
                double cove = V._D() ( 0 ) / mp1m ;

                vec var ( l );
                var.set_subvector ( 0, diag ( itmp.to_mat() ) *cove );
                var ( l - 1 ) = cove * cove / (mp1m-2);
                return var;
        } else {
                ldmat Vll( V, linspace(0,dimx-1)); // top-left part of V
                mat Y=Vll.to_mat();
                mat varY(Y.rows(), Y.cols()); 
                
                double denom = (mp1p-1)*mp1m*mp1m*(mp1m-2);         // (m-p)(m-p-1)^2(m-p-3)
                
                int i,j;
                for ( i=0; i<Y.rows(); i++){
                        for ( j=0; j<Y.cols(); j++){
                                varY(i,j) = (mp1p*Y(i,j)*Y(i,j) + mp1m * Y(i,i)* Y(j,j)) /denom;
                        }
                }
                vec mean_dR = diag(Y)/mp1m; // corresponds to cove
                vec var_th=diag ( itmp.to_mat() );
                vec var_Th ( mean_dR.length()*var_th.length() );
                // diagonal of diag(mean_dR) \kron diag(var_th)
                for (int i=0; i<mean_dR.length(); i++){
                        var_Th.set_subvector(i*var_th.length(), var_th*mean_dR(i));  
                }
                
                return concat(var_Th, cvectorize(varY));
        }
}

void egiw::mean_mat ( mat &M, mat&R ) const {
        const mat &L = V._L();
        const vec &D = V._D();
        int end = L.rows() - 1;

        ldmat ldR ( L ( 0, dimx - 1, 0, dimx - 1 ), D ( 0, dimx - 1 ) / ( nu - nPsi - 2*dimx - 2 ) ); //exp val of R
        mat iLsub = ltuinv ( L ( dimx, end, dimx, end ) );

        // set mean value
        mat Lpsi = L ( dimx, end, 0, dimx - 1 );
        M = iLsub * Lpsi;
        R = ldR.to_mat()  ;
}

vec egamma::sample() const {
        vec smp ( dim );
        int i;

        for ( i = 0; i < dim; i++ ) {
                if ( beta ( i ) > std::numeric_limits<double>::epsilon() ) {
                        GamRNG.setup ( alpha ( i ), beta ( i ) );
                } else {
                        GamRNG.setup ( alpha ( i ), std::numeric_limits<double>::epsilon() );
                }
#pragma omp critical
                smp ( i ) = GamRNG();
        }

        return smp;
}

// mat egamma::sample ( int N ) const {
//      mat Smp ( rv.count(),N );
//      int i,j;
//
//      for ( i=0; i<rv.count(); i++ ) {
//              GamRNG.setup ( alpha ( i ),beta ( i ) );
//
//              for ( j=0; j<N; j++ ) {
//                      Smp ( i,j ) = GamRNG();
//              }
//      }
//
//      return Smp;
// }

double egamma::evallog ( const vec &val ) const {
        double res = 0.0; //the rest will be added
        int i;

        if ( any ( val <= 0. ) ) return -inf;
        if ( any ( beta <= 0. ) ) return -inf;
        for ( i = 0; i < dim; i++ ) {
                res += ( alpha ( i ) - 1 ) * std::log ( val ( i ) ) - beta ( i ) * val ( i );
        }
        double tmp = res - lognc();;
        bdm_assert_debug ( std::isfinite ( tmp ), "Infinite value" );
        return tmp;
}

double egamma::lognc() const {
        double res = 0.0; //will be added
        int i;

        for ( i = 0; i < dim; i++ ) {
                res += lgamma ( alpha ( i ) ) - alpha ( i ) * std::log ( beta ( i ) ) ;
        }

        return res;
}

void mgamma::set_parameters ( double k0, const vec &beta0 ) {
        k = k0;
        iepdf.set_parameters ( k * ones ( beta0.length() ), beta0 );
        dimc = iepdf.dimension();
        dim = iepdf.dimension();
}

void eEmp::resample ( ivec &ind, RESAMPLING_METHOD method ) {
        ind = zeros_i ( n );
        ivec N_babies = zeros_i ( n );
        vec cumDist = cumsum ( w );
        vec u ( n );
        int i, j, parent;
        double u0;

        switch ( method ) {
        case MULTINOMIAL:
                u ( n - 1 ) = pow ( UniRNG.sample(), 1.0 / n );

                for ( i = n - 2; i >= 0; i-- ) {
                        u ( i ) = u ( i + 1 ) * pow ( UniRNG.sample(), 1.0 / ( i + 1 ) );
                }

                break;

        case STRATIFIED:

                for ( i = 0; i < n; i++ ) {
                        u ( i ) = ( i + UniRNG.sample() ) / n;
                }

                break;

        case SYSTEMATIC:
                u0 = UniRNG.sample();

                for ( i = 0; i < n; i++ ) {
                        u ( i ) = ( i + u0 ) / n;
                }

                break;

        default:
                bdm_error ( "PF::resample(): Unknown resampling method" );
        }

        // U is now full
        j = 0;

        for ( i = 0; i < n; i++ ) {
                while ( u ( i ) > cumDist ( j ) ) j++;

                N_babies ( j ) ++;
        }
        // We have assigned new babies for each Particle
        // Now, we fill the resulting index such that:
        // * particles with at least one baby should not move *
        // This assures that reassignment can be done inplace;

        // find the first parent;
        parent = 0;
        while ( N_babies ( parent ) == 0 ) parent++;

        // Build index
        for ( i = 0; i < n; i++ ) {
                if ( N_babies ( i ) > 0 ) {
                        ind ( i ) = i;
                        N_babies ( i ) --; //this index was now replicated;
                } else {
                        // test if the parent has been fully replicated
                        // if yes, find the next one
                        while ( ( N_babies ( parent ) == 0 ) || ( N_babies ( parent ) == 1 && parent > i ) ) parent++;

                        // Replicate parent
                        ind ( i ) = parent;

                        N_babies ( parent ) --; //this index was now replicated;
                }

        }

// copy the internals according to ind
        for ( i = 0; i < n; i++ ) {
                if ( ind ( i ) != i ) {
                        samples ( i ) = samples ( ind ( i ) );
                }
                w ( i ) = 1.0 / n;
        }
}

void eEmp::set_statistics ( const vec &w0, const epdf &epdf0 ) {
        dim = epdf0.dimension();
        w = w0;
        w /= sum ( w0 );//renormalize
        n = w.length();
        samples.set_size ( n );

        for ( int i = 0; i < n; i++ ) {
                samples ( i ) = epdf0.sample();
        }
}

void eEmp::set_samples ( const epdf* epdf0 ) {
        w = 1;
        w /= sum ( w );//renormalize

        for ( int i = 0; i < n; i++ ) {
                samples ( i ) = epdf0->sample();
        }
}

void migamma_ref::from_setting ( const Setting &set ) {
        vec ref;
        UI::get ( ref, set, "ref" , UI::compulsory );
        set_parameters ( set["k"], ref, set["l"] );
}

void mlognorm::from_setting ( const Setting &set ) {
        vec mu0;
        UI::get ( mu0, set, "mu0", UI::compulsory );
        set_parameters ( mu0.length(), set["k"] );
        condition ( mu0 );
}

};