libEF.h

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#ifndef EF_H
#define EF_H


#include "libBM.h"
#include "../math/chmat.h"
//#include <std>

namespace bdm {


extern Uniform_RNG UniRNG;
extern Normal_RNG NorRNG;
extern Gamma_RNG GamRNG;

class eEF : public epdf {
public:
//      eEF() :epdf() {};
        eEF ( ) :epdf ( ) {};
        virtual double lognc() const =0;
        virtual void dupdate ( mat &v ) {it_error ( "Not implemented" );};
        virtual double evallog_nn ( const vec &val ) const{it_error ( "Not implemented" );return 0.0;};
        virtual double evallog ( const vec &val ) const {double tmp;tmp= evallog_nn ( val )-lognc();it_assert_debug ( std::isfinite ( tmp ),"Infinite value" ); return tmp;}
        virtual vec evallog ( const mat &Val ) const {
                vec x ( Val.cols() );
                for ( int i=0;i<Val.cols();i++ ) {x ( i ) =evallog_nn ( Val.get_col ( i ) ) ;}
                return x-lognc();
        }
        virtual void pow ( double p ) {it_error ( "Not implemented" );};
};

class mEF : public mpdf {

public:
        mEF ( ) :mpdf ( ) {};
};

class BMEF : public BM {
protected:
        double frg;
        double last_lognc;
public:
        BMEF ( double frg0=1.0 ) :BM ( ), frg ( frg0 ) {}
        BMEF ( const BMEF &B ) :BM ( B ), frg ( B.frg ), last_lognc ( B.last_lognc ) {}
        virtual void set_statistics ( const BMEF* BM0 ) {it_error ( "Not implemented" );};
        virtual void bayes ( const vec &data, const double w ) {};
        //original Bayes
        void bayes ( const vec &dt );
        virtual void flatten ( const BMEF * B ) {it_error ( "Not implemented" );}
//      virtual void flatten ( double nu0 ) {it_error ( "Not implemented" );}

        BMEF* _copy_ () const {it_error ( "function _copy_ not implemented for this BM" ); return NULL;};
};

template<class sq_T>
class mlnorm;

template<class sq_T>
class enorm : public eEF {
protected:
        vec mu;
        sq_T R;
public:

        enorm ( ) :eEF ( ), mu ( ),R ( ) {};
        enorm ( const vec &mu,const sq_T &R ) {set_parameters ( mu,R );}
        void set_parameters ( const vec &mu,const sq_T &R );


        void dupdate ( mat &v,double nu=1.0 );

        vec sample() const;
        mat sample ( int N ) const;
        double evallog_nn ( const vec &val ) const;
        double lognc () const;
        vec mean() const {return mu;}
        vec variance() const {return diag ( R.to_mat() );}
//      mlnorm<sq_T>* condition ( const RV &rvn ) const ;
        mpdf* condition ( const RV &rvn ) const ;
//      enorm<sq_T>* marginal ( const RV &rv ) const;
        epdf* marginal ( const RV &rv ) const;


        vec& _mu() {return mu;}
        void set_mu ( const vec mu0 ) { mu=mu0;}
        sq_T& _R() {return R;}
        const sq_T& _R() const {return R;}

};

class egiw : public eEF {
protected:
        ldmat V;
        double nu;
        int dimx;
        int nPsi;
public:
        egiw() :eEF() {};
        egiw ( int dimx0, ldmat V0, double nu0=-1.0 ) :eEF() {set_parameters ( dimx0,V0, nu0 );};

        void set_parameters ( int dimx0, ldmat V0, double nu0=-1.0 ) {
                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 sample() const;
        vec mean() const;
        vec variance() const;
        void mean_mat ( mat &M, mat&R ) const;
        double evallog_nn ( const vec &val ) const;
        double lognc () const;
        void pow ( double p ) {V*=p;nu*=p;};


        ldmat& _V() {return V;}
        const ldmat& _V() const {return V;}
        double& _nu()  {return nu;}
        const double& _nu() const {return nu;}
};

class eDirich: public eEF {
protected:
        vec beta;
        double gamma;
public:

        eDirich () : eEF ( ) {};
        eDirich ( const eDirich &D0 ) : eEF () {set_parameters ( D0.beta );};
        eDirich ( const vec &beta0 ) {set_parameters ( beta0 );};
        void set_parameters ( const vec &beta0 ) {
                beta= beta0;
                dim = beta.length();
                gamma = sum ( beta );
        }

        vec sample() const {it_error ( "Not implemented" );return vec_1 ( 0.0 );};
        vec mean() const {return beta/gamma;};
        vec variance() const {return elem_mult ( beta, ( beta+1 ) ) / ( gamma* ( gamma+1 ) );}
        double evallog_nn ( const vec &val ) const {
                double tmp; tmp= ( beta-1 ) *log ( val );               it_assert_debug ( std::isfinite ( tmp ),"Infinite value" );
                return tmp;
        };
        double lognc () const {
                double tmp;
                double gam=sum ( beta );
                double lgb=0.0;
                for ( int i=0;i<beta.length();i++ ) {lgb+=lgamma ( beta ( i ) );}
                tmp= lgb-lgamma ( gam );
                it_assert_debug ( std::isfinite ( tmp ),"Infinite value" );
                return tmp;
        };
        vec& _beta()  {return beta;}
};

class multiBM : public BMEF {
protected:
        eDirich est;
        vec &beta;
public:
        multiBM ( ) : BMEF ( ),est ( ),beta ( est._beta() ) {if ( beta.length() >0 ) {last_lognc=est.lognc();}else{last_lognc=0.0;}}
        multiBM ( const multiBM &B ) : BMEF ( B ),est ( B.est ),beta ( est._beta() ) {}
        void set_statistics ( const BM* mB0 ) {const multiBM* mB=dynamic_cast<const multiBM*> ( mB0 ); beta=mB->beta;}
        void bayes ( const vec &dt ) {
                if ( frg<1.0 ) {beta*=frg;last_lognc=est.lognc();}
                beta+=dt;
                if ( evalll ) {ll=est.lognc()-last_lognc;}
        }
        double logpred ( const vec &dt ) const {
                eDirich pred ( est );
                vec &beta = pred._beta();

                double lll;
                if ( frg<1.0 )
                        {beta*=frg;lll=pred.lognc();}
                else
                        if ( evalll ) {lll=last_lognc;}
                        else{lll=pred.lognc();}

                beta+=dt;
                return pred.lognc()-lll;
        }
        void flatten ( const BMEF* B ) {
                const multiBM* E=dynamic_cast<const multiBM*> ( B );
                // sum(beta) should be equal to sum(B.beta)
                const vec &Eb=E->beta;//const_cast<multiBM*> ( E )->_beta();
                beta*= ( sum ( Eb ) /sum ( beta ) );
                if ( evalll ) {last_lognc=est.lognc();}
        }
        const epdf& posterior() const {return est;};
        const eDirich* _e() const {return &est;};
        void set_parameters ( const vec &beta0 ) {
                est.set_parameters ( beta0 );
                if ( evalll ) {last_lognc=est.lognc();}
        }
};

class egamma : public eEF {
protected:
        vec alpha;
        vec beta;
public :
        egamma ( ) :eEF ( ), alpha(0), beta(0) {};
        egamma ( const vec &a, const vec &b ) {set_parameters ( a, b );};
        void set_parameters ( const vec &a, const vec &b ) {alpha=a,beta=b;dim = alpha.length();};

        vec sample() const;
//      mat sample ( int N ) const;
        double evallog ( const vec &val ) const;
        double lognc () const;
        vec& _alpha() {return alpha;}
        vec& _beta() {return beta;}
        vec mean() const {return elem_div ( alpha,beta );}
        vec variance() const {return elem_div ( alpha,elem_mult ( beta,beta ) ); }
};

class eigamma : public egamma {
protected:
public :

        vec sample() const {return 1.0/egamma::sample();};
        vec mean() const {return elem_div ( beta,alpha-1 );}
        vec variance() const {vec mea=mean(); return elem_div ( elem_mult ( mea,mea ),alpha-2 );}
};
/*
class emix : public epdf {
protected:
        int n;
        vec &w;
        Array<epdf*> Coms;
public:
        emix ( const RV &rv, vec &w0): epdf(rv), n(w0.length()), w(w0), Coms(n) {};
        void set_parameters( int &i, double wi, epdf* ep){w(i)=wi;Coms(i)=ep;}
        vec mean(){vec pom; for(int i=0;i<n;i++){pom+=Coms(i)->mean()*w(i);} return pom;};
        vec sample() {it_error ( "Not implemented" );return 0;}
};
*/


class euni: public epdf {
protected:
        vec low;
        vec high;
        vec distance;
        double nk;
        double lnk;
public:
        euni ( ) :epdf ( ) {}
        euni ( const vec &low0, const vec &high0 ) {set_parameters ( low0,high0 );}
        void set_parameters ( const vec &low0, const vec &high0 ) {
                distance = high0-low0;
                it_assert_debug ( min ( distance ) >0.0,"bad support" );
                low = low0;
                high = high0;
                nk = prod ( 1.0/distance );
                lnk = log ( nk );
                dim = low.length();
        }

        double eval ( const vec &val ) const  {return nk;}
        double evallog ( const vec &val ) const  {return lnk;}
        vec sample() const {
                vec smp ( dim );
#pragma omp critical
                UniRNG.sample_vector ( dim ,smp );
                return low+elem_mult ( distance,smp );
        }
        vec mean() const {return ( high-low ) /2.0;}
        vec variance() const {return ( pow ( high,2 ) +pow ( low,2 ) +elem_mult ( high,low ) ) /3.0;}
};


template<class sq_T>
class mlnorm : public mEF {
protected:
        enorm<sq_T> epdf;
        mat A;
        vec mu_const;
        vec& _mu; //cached epdf.mu;
public:
        mlnorm ( ) :mEF (),epdf ( ),A ( ),_mu ( epdf._mu() ) {ep =&epdf; };
        mlnorm ( const  mat &A, const vec &mu0, const sq_T &R ) :epdf ( ),_mu ( epdf._mu() ) {
                ep =&epdf; set_parameters ( A,mu0,R );
        };
        void set_parameters ( const  mat &A, const vec &mu0, const sq_T &R );
        void condition ( const vec &cond );

        vec& _mu_const() {return mu_const;}
        mat& _A() {return A;}
        mat _R() {return epdf._R().to_mat();}

        template<class sq_M>
        friend std::ostream &operator<< ( std::ostream &os,  mlnorm<sq_M> &ml );
};

template<class sq_T>
class mgnorm : public mEF {
protected:
        enorm<sq_T> epdf;
        vec &mu;
        fnc* g;
public:
        mgnorm() :mu ( epdf._mu() ) {ep=&epdf;}
        void set_parameters ( fnc* g0, const sq_T &R0 ) {g=g0; epdf.set_parameters ( zeros ( g->dimension() ), R0 );}
        void condition ( const vec &cond ) {mu=g->eval ( cond );};
};

class mlstudent : public mlnorm<ldmat> {
protected:
        ldmat Lambda;
        ldmat &_R;
        ldmat Re;
public:
        mlstudent ( ) :mlnorm<ldmat> (),
                        Lambda (),      _R ( epdf._R() ) {}
        void set_parameters ( const mat &A0, const vec &mu0, const ldmat &R0, const ldmat& Lambda0 ) {
                it_assert_debug ( A0.rows() ==mu0.length(),"" );
                it_assert_debug ( R0.rows() ==A0.rows(),"" );

                epdf.set_parameters ( mu0,Lambda ); //
                A = A0;
                mu_const = mu0;
                Re=R0;
                Lambda = Lambda0;
        }
        void condition ( const vec &cond ) {
                _mu = A*cond + mu_const;
                double zeta;
                //ugly hack!
                if ( ( cond.length() +1 ) ==Lambda.rows() ) {
                        zeta = Lambda.invqform ( concat ( cond, vec_1 ( 1.0 ) ) );
                }
                else {
                        zeta = Lambda.invqform ( cond );
                }
                _R = Re;
                _R*= ( 1+zeta );// / ( nu ); << nu is in Re!!!!!!
        };

};
class mgamma : public mEF {
protected:
        egamma epdf;
        double k;
        vec &_beta;

public:
        mgamma ( ) : mEF ( ), epdf (), _beta ( epdf._beta() ) {ep=&epdf;};
        void set_parameters ( double k, const vec &beta0 );
        void condition ( const vec &val ) {_beta=k/val;};
};

class migamma : public mEF {
protected:
        eigamma epdf;
        double k;
        vec &_alpha;
        vec &_beta;

public:
        migamma ( ) : mEF (), epdf ( ), _alpha ( epdf._alpha() ), _beta ( epdf._beta() ) {ep=&epdf;};
        migamma ( const migamma &m ) : mEF (), epdf ( m.epdf ), _alpha ( epdf._alpha() ), _beta ( epdf._beta() ) {ep=&epdf;};

        void set_parameters ( int len, double k0 ) {
                k=k0;
                epdf.set_parameters ( ( 1.0/ ( k*k ) +2.0 ) *ones ( len ) /*alpha*/, ones ( len ) /*beta*/ );
                dimc = dimension();
        };
        void condition ( const vec &val ) {
                _beta=elem_mult ( val, ( _alpha-1.0 ) );
        };
};

class mgamma_fix : public mgamma {
protected:
        double l;
        vec refl;
public:
        mgamma_fix ( ) : mgamma ( ),refl () {};
        void set_parameters ( double k0 , vec ref0, double l0 ) {
                mgamma::set_parameters ( k0, ref0 );
                refl=pow ( ref0,1.0-l0 );l=l0;
                dimc=dimension();
        };

        void condition ( const vec &val ) {vec mean=elem_mult ( refl,pow ( val,l ) ); _beta=k/mean;};
};


class migamma_ref : public migamma {
protected:
        double l;
        vec refl;
public:
        migamma_ref ( ) : migamma (),refl ( ) {};
        void set_parameters ( double k0 , vec ref0, double l0 ) {
                migamma::set_parameters ( ref0.length(), k0 );
                refl=pow ( ref0,1.0-l0 );
                l=l0;
                dimc = dimension();
        };

        void condition ( const vec &val ) {
                vec mean=elem_mult ( refl,pow ( val,l ) );
                migamma::condition ( mean );
        };
};

class elognorm: public enorm<ldmat>{
        public:
                vec sample() const {return exp(enorm<ldmat>::sample());};
                vec mean() const {vec var=enorm<ldmat>::variance();return exp(mu - 0.5*var);};
                
};

class mlognorm : public mpdf {
        protected:
                elognorm eno;
                double sig2;
                vec &mu;
        public:
                mlognorm ( ) : eno (), mu(eno._mu()) {ep=&eno;};
                void set_parameters ( int size, double k) {
                        sig2 = 0.5*log(k*k+1);
                        eno.set_parameters(zeros(size),2*sig2*eye(size));
                        
                        dimc = size;
                };

                void condition ( const vec &val ) {
                        mu=log(val)-sig2;//elem_mult ( refl,pow ( val,l ) );
                };
};

class iW : public epdf{
        public:
                vec sample(){return vec();}
};

enum RESAMPLING_METHOD { MULTINOMIAL = 0, STRATIFIED = 1, SYSTEMATIC = 3 };
class eEmp: public epdf {
protected :
        int n;
        vec w;
        Array<vec> samples;
public:
        eEmp ( ) :epdf ( ),w ( ),samples ( ) {};
        eEmp ( const eEmp &e ) : epdf ( e ), w ( e.w ), samples ( e.samples ) {};

        void set_statistics ( const vec &w0, const epdf* pdf0 );
        void set_statistics ( const epdf* pdf0 , int n ) {set_statistics ( ones ( n ) /n,pdf0 );};
        void set_samples ( const epdf* pdf0 );
        void set_parameters ( int n0, bool copy=true ) {n=n0; w.set_size ( n0,copy );samples.set_size ( n0,copy );};
        vec& _w()  {return w;};
        const vec& _w() const {return w;};
        Array<vec>& _samples() {return samples;};
        const Array<vec>& _samples() const {return samples;};
        ivec resample ( RESAMPLING_METHOD method=SYSTEMATIC );
        vec sample() const {it_error ( "Not implemented" );return 0;}
        double evallog ( const vec &val ) const {it_error ( "Not implemented" );return 0.0;}
        vec mean() const {
                vec pom=zeros ( dim );
                for ( int i=0;i<n;i++ ) {pom+=samples ( i ) *w ( i );}
                return pom;
        }
        vec variance() const {
                vec pom=zeros ( dim );
                for ( int i=0;i<n;i++ ) {pom+=pow ( samples ( i ),2 ) *w ( i );}
                return pom-pow ( mean(),2 );
        }
        void qbounds ( vec &lb, vec &ub, double perc=0.95 ) const {
                // lb in inf so than it will be pushed below;
                lb.set_size(dim);
                ub.set_size(dim);
                lb = std::numeric_limits<double>::infinity();
                ub = -std::numeric_limits<double>::infinity();
                int j;
                for ( int i=0;i<n;i++ ) {
                        for ( j=0;j<dim; j++ ) {
                                if ( samples ( i ) ( j ) <lb ( j ) ) {lb ( j ) =samples ( i ) ( j );}
                                if ( samples ( i ) ( j ) >ub ( j ) ) {ub ( j ) =samples ( i ) ( j );}
                        }
                }
        }
};



template<class sq_T>
void enorm<sq_T>::set_parameters ( const vec &mu0, const sq_T &R0 ) {
//Fixme test dimensions of mu0 and R0;
        mu = mu0;
        R = R0;
        dim = mu0.length();
};

template<class sq_T>
void enorm<sq_T>::dupdate ( mat &v, double nu ) {
        //
};

// template<class sq_T>
// void enorm<sq_T>::tupdate ( double phi, mat &vbar, double nubar ) {
//      //
// };

template<class sq_T>
vec enorm<sq_T>::sample() const {
        vec x ( dim );
#pragma omp critical
        NorRNG.sample_vector ( dim,x );
        vec smp = R.sqrt_mult ( x );

        smp += mu;
        return smp;
};

template<class sq_T>
mat enorm<sq_T>::sample ( int N ) const {
        mat X ( dim,N );
        vec x ( dim );
        vec pom;
        int i;

        for ( i=0;i<N;i++ ) {
#pragma omp critical
                NorRNG.sample_vector ( dim,x );
                pom = R.sqrt_mult ( x );
                pom +=mu;
                X.set_col ( i, pom );
        }

        return X;
};

// template<class sq_T>
// double enorm<sq_T>::eval ( const vec &val ) const {
//      double pdfl,e;
//      pdfl = evallog ( val );
//      e = exp ( pdfl );
//      return e;
// };

template<class sq_T>
double enorm<sq_T>::evallog_nn ( const vec &val ) const {
        // 1.83787706640935 = log(2pi)
        double tmp=-0.5* ( R.invqform ( mu-val ) );// - lognc();
        return  tmp;
};

template<class sq_T>
inline double enorm<sq_T>::lognc () const {
        // 1.83787706640935 = log(2pi)
        double tmp=0.5* ( R.cols() * 1.83787706640935 +R.logdet() );
        return tmp;
};

template<class sq_T>
void mlnorm<sq_T>::set_parameters ( const mat &A0, const vec &mu0, const sq_T &R0 ) {
        it_assert_debug ( A0.rows() ==mu0.length(),"" );
        it_assert_debug ( A0.rows() ==R0.rows(),"" );

        epdf.set_parameters ( zeros ( A0.rows() ),R0 );
        A = A0;
        mu_const = mu0;
        dimc=A0.cols();
}

// template<class sq_T>
// vec mlnorm<sq_T>::samplecond (const  vec &cond, double &lik ) {
//      this->condition ( cond );
//      vec smp = epdf.sample();
//      lik = epdf.eval ( smp );
//      return smp;
// }

// template<class sq_T>
// mat mlnorm<sq_T>::samplecond (const vec &cond, vec &lik, int n ) {
//      int i;
//      int dim = rv.count();
//      mat Smp ( dim,n );
//      vec smp ( dim );
//      this->condition ( cond );
//
//      for ( i=0; i<n; i++ ) {
//              smp = epdf.sample();
//              lik ( i ) = epdf.eval ( smp );
//              Smp.set_col ( i ,smp );
//      }
//
//      return Smp;
// }

template<class sq_T>
void mlnorm<sq_T>::condition ( const vec &cond ) {
        _mu = A*cond + mu_const;
//R is already assigned;
}

template<class sq_T>
epdf* enorm<sq_T>::marginal ( const RV &rvn ) const {
        it_assert_debug ( isnamed(), "rv description is not assigned" );
        ivec irvn = rvn.dataind ( rv );

        sq_T Rn ( R,irvn ); //select rows and columns of R

        enorm<sq_T>* tmp = new enorm<sq_T>;
        tmp->set_rv ( rvn );
        tmp->set_parameters ( mu ( irvn ), Rn );
        return tmp;
}

template<class sq_T>
mpdf* enorm<sq_T>::condition ( const RV &rvn ) const {

        it_assert_debug ( isnamed(),"rvs are not assigned" );

        RV rvc = rv.subt ( rvn );
        it_assert_debug ( ( rvc._dsize() +rvn._dsize() ==rv._dsize() ),"wrong rvn" );
        //Permutation vector of the new R
        ivec irvn = rvn.dataind ( rv );
        ivec irvc = rvc.dataind ( rv );
        ivec perm=concat ( irvn , irvc );
        sq_T Rn ( R,perm );

        //fixme - could this be done in general for all sq_T?
        mat S=Rn.to_mat();
        //fixme
        int n=rvn._dsize()-1;
        int end=R.rows()-1;
        mat S11 = S.get ( 0,n, 0, n );
        mat S12 = S.get ( 0, n , rvn._dsize(), end );
        mat S22 = S.get ( rvn._dsize(), end, rvn._dsize(), end );

        vec mu1 = mu ( irvn );
        vec mu2 = mu ( irvc );
        mat A=S12*inv ( S22 );
        sq_T R_n ( S11 - A *S12.T() );

        mlnorm<sq_T>* tmp=new mlnorm<sq_T> ( );
        tmp->set_rv ( rvn ); tmp->set_rvc ( rvc );
        tmp->set_parameters ( A,mu1-A*mu2,R_n );
        return tmp;
}


template<class sq_T>
std::ostream &operator<< ( std::ostream &os,  mlnorm<sq_T> &ml ) {
        os << "A:"<< ml.A<<endl;
        os << "mu:"<< ml.mu_const<<endl;
        os << "R:" << ml.epdf._R().to_mat() <<endl;
        return os;
};

}
#endif //EF_H

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