factor.h

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/*  This file is part of libDAI - http://www.libdai.org/
 *
 *  Copyright (c) 2006-2011, The libDAI authors. All rights reserved.
 *
 *  Use of this source code is governed by a BSD-style license that can be found in the LICENSE file.
 */




#ifndef __defined_libdai_factor_h
#define __defined_libdai_factor_h


#include <iostream>
#include <functional>
#include <cmath>
#include <dai/prob.h>
#include <dai/varset.h>
#include <dai/index.h>
#include <dai/util.h>


namespace dai {



template <typename T>
class TFactor {
    private:
        VarSet _vs;
        TProb<T> _p;

    public:

        TFactor ( T p = 1 ) : _vs(), _p(1,p) {}

        TFactor( const Var &v ) : _vs(v), _p(v.states()) {}

        TFactor( const VarSet& vars ) : _vs(vars), _p() {
            _p = TProb<T>( BigInt_size_t( _vs.nrStates() ) );
        }

        TFactor( const VarSet& vars, T p ) : _vs(vars), _p() {
            _p = TProb<T>( BigInt_size_t( _vs.nrStates() ), p );
        }


        template<typename S>
        TFactor( const VarSet& vars, const std::vector<S> &x ) : _vs(vars), _p() {
            DAI_ASSERT( (BigInt)x.size() == vars.nrStates() );
            _p = TProb<T>( x.begin(), x.end(), x.size() );
        }


        TFactor( const VarSet& vars, const T* p ) : _vs(vars), _p() {
            size_t N = BigInt_size_t( _vs.nrStates() );
            _p = TProb<T>( p, p + N, N );
        }

        TFactor( const VarSet& vars, const TProb<T> &p ) : _vs(vars), _p(p) {
            DAI_ASSERT( _vs.nrStates() == (BigInt)_p.size() );
        }

        TFactor( const std::vector<Var> &vars, const std::vector<T> &p ) : _vs(vars.begin(), vars.end(), vars.size()), _p(p.size()) {
            BigInt nrStates = 1;
            for( size_t i = 0; i < vars.size(); i++ )
                nrStates *= vars[i].states();
            DAI_ASSERT( nrStates == p.size() );
            Permute permindex(vars);
            for( size_t li = 0; li < p.size(); ++li )
                _p.set( permindex.convertLinearIndex(li), p[li] );
        }


        void set( size_t i, T val ) { _p.set( i, val ); }

        T get( size_t i ) const { return _p[i]; }


        const TProb<T>& p() const { return _p; }

        TProb<T>& p() { return _p; }

        T operator[] (size_t i) const { return _p[i]; }

        const VarSet& vars() const { return _vs; }

        VarSet& vars() { return _vs; }


        size_t nrStates() const { return _p.size(); }

        T entropy() const { return _p.entropy(); }

        T max() const { return _p.max(); }

        T min() const { return _p.min(); }

        T sum() const { return _p.sum(); }
        
        T sumAbs() const { return _p.sumAbs(); }

        T maxAbs() const { return _p.maxAbs(); }

        bool hasNaNs() const { return _p.hasNaNs(); }

        bool hasNegatives() const { return _p.hasNegatives(); }

        T strength( const Var &i, const Var &j ) const;

        bool operator==( const TFactor<T>& y ) const {
            return (_vs == y._vs) && (_p == y._p);
        }

        std::string toString() const {
            std::stringstream ss;
            ss << *this;
            return ss.str();
        }


        TFactor<T> operator- () const { 
            // Note: the alternative (shorter) way of implementing this,
            //   return TFactor<T>( _vs, _p.abs() );
            // is slower because it invokes the copy constructor of TProb<T>
            TFactor<T> x;
            x._vs = _vs;
            x._p = -_p;
            return x;
        }

        TFactor<T> abs() const {
            TFactor<T> x;
            x._vs = _vs;
            x._p = _p.abs();
            return x;
        }

        TFactor<T> exp() const {
            TFactor<T> x;
            x._vs = _vs;
            x._p = _p.exp();
            return x;
        }


        TFactor<T> log(bool zero=false) const {
            TFactor<T> x;
            x._vs = _vs;
            x._p = _p.log(zero);
            return x;
        }


        TFactor<T> inverse(bool zero=true) const {
            TFactor<T> x;
            x._vs = _vs;
            x._p = _p.inverse(zero);
            return x;
        }


        TFactor<T> normalized( ProbNormType norm=NORMPROB ) const {
            TFactor<T> x;
            x._vs = _vs;
            x._p = _p.normalized( norm );
            return x;
        }


        TFactor<T>& randomize() { _p.randomize(); return *this; }

        TFactor<T>& setUniform() { _p.setUniform(); return *this; }

        TFactor<T>& takeAbs() { _p.takeAbs(); return *this; }

        TFactor<T>& takeExp() { _p.takeExp(); return *this; }


        TFactor<T>& takeLog( bool zero = false ) { _p.takeLog(zero); return *this; }


        T normalize( ProbNormType norm=NORMPROB ) { return _p.normalize( norm ); }


        TFactor<T>& fill (T x) { _p.fill( x ); return *this; }

        TFactor<T>& operator+= (T x) { _p += x; return *this; }

        TFactor<T>& operator-= (T x) { _p -= x; return *this; }

        TFactor<T>& operator*= (T x) { _p *= x; return *this; }

        TFactor<T>& operator/= (T x) { _p /= x; return *this; }

        TFactor<T>& operator^= (T x) { _p ^= x; return *this; }


        TFactor<T> operator+ (T x) const {
            // Note: the alternative (shorter) way of implementing this,
            //   TFactor<T> result(*this);
            //   result._p += x;
            // is slower because it invokes the copy constructor of TFactor<T>
            TFactor<T> result;
            result._vs = _vs;
            result._p = p() + x;
            return result;
        }

        TFactor<T> operator- (T x) const {
            TFactor<T> result;
            result._vs = _vs;
            result._p = p() - x;
            return result;
        }

        TFactor<T> operator* (T x) const {
            TFactor<T> result;
            result._vs = _vs;
            result._p = p() * x;
            return result;
        }

        TFactor<T> operator/ (T x) const {
            TFactor<T> result;
            result._vs = _vs;
            result._p = p() / x;
            return result;
        }

        TFactor<T> operator^ (T x) const {
            TFactor<T> result;
            result._vs = _vs;
            result._p = p() ^ x;
            return result;
        }



        template<typename binOp> TFactor<T>& binaryOp( const TFactor<T> &g, binOp op ) {
            if( _vs == g._vs ) // optimize special case
                _p.pwBinaryOp( g._p, op );
            else {
                TFactor<T> f(*this); // make a copy
                _vs |= g._vs;
                size_t N = BigInt_size_t( _vs.nrStates() );

                IndexFor i_f( f._vs, _vs );
                IndexFor i_g( g._vs, _vs );

                _p.p().clear();
                _p.p().reserve( N );
                for( size_t i = 0; i < N; i++, ++i_f, ++i_g )
                    _p.p().push_back( op( f._p[i_f], g._p[i_g] ) );
            }
            return *this;
        }


        TFactor<T>& operator+= (const TFactor<T>& g) { return binaryOp( g, std::plus<T>() ); }


        TFactor<T>& operator-= (const TFactor<T>& g) { return binaryOp( g, std::minus<T>() ); }


        TFactor<T>& operator*= (const TFactor<T>& g) { return binaryOp( g, std::multiplies<T>() ); }


        TFactor<T>& operator/= (const TFactor<T>& g) { return binaryOp( g, fo_divides0<T>() ); }



        template<typename binOp> TFactor<T> binaryTr( const TFactor<T> &g, binOp op ) const {
            // Note that to prevent a copy to be made, it is crucial 
            // that the result is declared outside the if-else construct.
            TFactor<T> result;
            if( _vs == g._vs ) { // optimize special case
                result._vs = _vs;
                result._p = _p.pwBinaryTr( g._p, op );
            } else {
                result._vs = _vs | g._vs;
                size_t N = BigInt_size_t( result._vs.nrStates() );

                IndexFor i_f( _vs, result.vars() );
                IndexFor i_g( g._vs, result.vars() );

                result._p.p().clear();
                result._p.p().reserve( N );
                for( size_t i = 0; i < N; i++, ++i_f, ++i_g )
                    result._p.p().push_back( op( _p[i_f], g[i_g] ) );
            }
            return result;
        }


        TFactor<T> operator+ (const TFactor<T>& g) const {
            return binaryTr(g,std::plus<T>());
        }


        TFactor<T> operator- (const TFactor<T>& g) const {
            return binaryTr(g,std::minus<T>());
        }


        TFactor<T> operator* (const TFactor<T>& g) const {
            return binaryTr(g,std::multiplies<T>());
        }


        TFactor<T> operator/ (const TFactor<T>& g) const {
            return binaryTr(g,fo_divides0<T>());
        }



        TFactor<T> slice( const VarSet& vars, size_t varsState ) const; 


        TFactor<T> embed(const VarSet & vars) const {
            DAI_ASSERT( vars >> _vs );
            if( _vs == vars )
                return *this;
            else
                return (*this) * TFactor<T>(vars / _vs, (T)1);
        }

        TFactor<T> marginal(const VarSet &vars, bool normed=true) const;

        TFactor<T> maxMarginal(const VarSet &vars, bool normed=true) const;
};


template<typename T> TFactor<T> TFactor<T>::slice( const VarSet& vars, size_t varsState ) const {
    DAI_ASSERT( vars << _vs );
    VarSet varsrem = _vs / vars;
    TFactor<T> result( varsrem, T(0) );

    // OPTIMIZE ME
    IndexFor i_vars (vars, _vs);
    IndexFor i_varsrem (varsrem, _vs);
    for( size_t i = 0; i < nrStates(); i++, ++i_vars, ++i_varsrem )
        if( (size_t)i_vars == varsState )
            result.set( i_varsrem, _p[i] );

    return result;
}


template<typename T> TFactor<T> TFactor<T>::marginal(const VarSet &vars, bool normed) const {
    VarSet res_vars = vars & _vs;

    TFactor<T> res( res_vars, 0.0 );

    IndexFor i_res( res_vars, _vs );
    for( size_t i = 0; i < _p.size(); i++, ++i_res )
        res.set( i_res, res[i_res] + _p[i] );

    if( normed )
        res.normalize( NORMPROB );

    return res;
}


template<typename T> TFactor<T> TFactor<T>::maxMarginal(const VarSet &vars, bool normed) const {
    VarSet res_vars = vars & _vs;

    TFactor<T> res( res_vars, 0.0 );

    IndexFor i_res( res_vars, _vs );
    for( size_t i = 0; i < _p.size(); i++, ++i_res )
        if( _p[i] > res._p[i_res] )
            res.set( i_res, _p[i] );

    if( normed )
        res.normalize( NORMPROB );

    return res;
}


template<typename T> T TFactor<T>::strength( const Var &i, const Var &j ) const {
    DAI_DEBASSERT( _vs.contains( i ) );
    DAI_DEBASSERT( _vs.contains( j ) );
    DAI_DEBASSERT( i != j );
    VarSet ij(i, j);

    T max = 0.0;
    for( size_t alpha1 = 0; alpha1 < i.states(); alpha1++ )
        for( size_t alpha2 = 0; alpha2 < i.states(); alpha2++ )
            if( alpha2 != alpha1 )
                for( size_t beta1 = 0; beta1 < j.states(); beta1++ )
                    for( size_t beta2 = 0; beta2 < j.states(); beta2++ )
                        if( beta2 != beta1 ) {
                            size_t as = 1, bs = 1;
                            if( i < j )
                                bs = i.states();
                            else
                                as = j.states();
                            T f1 = slice( ij, alpha1 * as + beta1 * bs ).p().divide( slice( ij, alpha2 * as + beta1 * bs ).p() ).max();
                            T f2 = slice( ij, alpha2 * as + beta2 * bs ).p().divide( slice( ij, alpha1 * as + beta2 * bs ).p() ).max();
                            T f = f1 * f2;
                            if( f > max )
                                max = f;
                        }

    return std::tanh( 0.25 * std::log( max ) );
}



template<typename T> std::ostream& operator<< (std::ostream& os, const TFactor<T>& f) {
    os << "(" << f.vars() << ", (";
    for( size_t i = 0; i < f.nrStates(); i++ )
        os << (i == 0 ? "" : ", ") << f[i];
    os << "))";
    return os;
}



template<typename T> T dist( const TFactor<T> &f, const TFactor<T> &g, ProbDistType dt ) {
    if( f.vars().empty() || g.vars().empty() )
        return -1;
    else {
        DAI_DEBASSERT( f.vars() == g.vars() );
        return dist( f.p(), g.p(), dt );
    }
}



template<typename T> TFactor<T> max( const TFactor<T> &f, const TFactor<T> &g ) {
    DAI_ASSERT( f.vars() == g.vars() );
    return TFactor<T>( f.vars(), max( f.p(), g.p() ) );
}



template<typename T> TFactor<T> min( const TFactor<T> &f, const TFactor<T> &g ) {
    DAI_ASSERT( f.vars() == g.vars() );
    return TFactor<T>( f.vars(), min( f.p(), g.p() ) );
}



template<typename T> T MutualInfo(const TFactor<T> &f) {
    DAI_ASSERT( f.vars().size() == 2 );
    VarSet::const_iterator it = f.vars().begin();
    Var i = *it; it++; Var j = *it;
    TFactor<T> projection = f.marginal(i) * f.marginal(j);
    return dist( f.normalized(), projection, DISTKL );
}


typedef TFactor<Real> Factor;



Factor createFactorIsing( const Var &x, Real h );



Factor createFactorIsing( const Var &x1, const Var &x2, Real J );



Factor createFactorExpGauss( const VarSet &vs, Real beta );



Factor createFactorPotts( const Var &x1, const Var &x2, Real J );



Factor createFactorDelta( const Var &v, size_t state );



Factor createFactorDelta( const VarSet& vs, size_t state );


} // end of namespace dai


#endif