/*!
  \file
  \brief Probability distributions for Mixtures of pdfs
  \author Vaclav Smidl.

  -----------------------------------
  BDM++ - C++ library for Bayesian Decision Making under Uncertainty

  Using IT++ for numerical operations
  -----------------------------------
*/

#ifndef MX_H
#define MX_H

#include "libBM.h"
#include "libEF.h"
//#include <std>

using namespace itpp;

//this comes first because it is used inside emix!

/*! \brief Class representing ratio of two densities
which arise e.g. by applying the Bayes rule.
It represents density in the form:
\f[
f(rv|rvc) = \frac{f(rv,rvc)}{f(rvc)}
\f]
where \f$ f(rvc) = \int f(rv,rvc) d\ rv \f$.

In particular this type of arise by conditioning of a mixture model.

At present the only supported operation is evallogcond().
 */
class mratio: public mpdf {
protected:
	//! Nominator in the form of mpdf
	const epdf* nom;
	//!Denominator in the form of epdf
	epdf* den;
	//!flag for destructor
	bool destroynom;
	//!datalink between conditional and nom
	datalink_m2e dl;
public:
	//!Default constructor. By default, the given epdf is not copied!
	//! It is assumed that this function will be used only temporarily.
	mratio ( const epdf* nom0, const RV &rv, bool copy=false ) :mpdf ( rv,nom0->_rv().subt ( rv ) ), dl ( rv,rvc,nom0->_rv() ) {
		if ( copy ) {
//			nom = nom0->_copy_();
			it_error ( "todo" );
			destroynom=true;
		}
		else {
			nom = nom0;
			destroynom = false;
		}
		it_assert_debug ( rvc.length() >0,"Makes no sense to use this object!" );
		den = nom->marginal ( rvc );
	};
	double evallogcond ( const vec &val, const vec &cond ) {
		double tmp;
		vec nom_val ( rv.count() +rvc.count() );
		dl.fill_val_cond ( nom_val,val,cond );
		tmp = exp ( nom->evallog ( nom_val ) - den->evallog ( cond ) );
		it_assert_debug(std::isfinite(tmp),"Infinite value");
		return tmp;
	}
	//! Object takes ownership of nom and will destroy it
	void ownnom() {destroynom=true;}
	//! Default destructor
	~mratio() {delete den; if ( destroynom ) {delete nom;}}
};

/*!
* \brief Mixture of epdfs

Density function:
\f[
f(x) = \sum_{i=1}^{n} w_{i} f_i(x), \quad \sum_{i=1}^n w_i = 1.
\f]
where \f$f_i(x)\f$ is any density on random variable \f$x\f$, called \a component,

*/
class emix : public epdf {
protected:
	//! weights of the components
	vec w;
	//! Component (epdfs)
	Array<epdf*> Coms;
	//!Flag if owning Coms
	bool destroyComs;
public:
	//!Default constructor
	emix ( const RV &rv ) : epdf ( rv ) {};
	//! Set weights \c w and components \c Coms
	//!By default Coms are copied inside. Parameter \c copy can be set to false if Coms live externally. Use method ownComs() if Coms should be destroyed by the destructor.
	void set_parameters ( const vec &w, const Array<epdf*> &Coms, bool copy=true );

	vec sample() const;
	vec mean() const {
		int i; vec mu = zeros ( rv.count() );
		for ( i = 0;i < w.length();i++ ) {mu += w ( i ) * Coms ( i )->mean(); }
		return mu;
	}
	vec variance() const {
		//non-central moment
		vec mom2 = zeros(rv.count());
		for ( int i = 0;i < w.length();i++ ) {mom2 += w ( i ) * pow(Coms ( i )->mean(),2); }
		//central moment
		return mom2-pow(mean(),2);
	}
	double 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 );
		it_assert_debug(std::isfinite(tmp),"Infinite");
		return tmp;
	};
	vec evallog_m ( const mat &Val ) const {
		vec x=zeros ( Val.cols() );
		for ( int i = 0; i < w.length(); i++ ) {
			x+= w ( i ) *exp ( Coms ( i )->evallog_m ( Val ) );
		}
		return log ( x );
	};
	//! Auxiliary function that returns pdflog for each component
	mat evallog_M ( 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_m ( Val ) ) );
		}
		return X;
	};

	emix* marginal ( const RV &rv ) const;
	mratio* condition ( const RV &rv ) const; //why not mratio!!

//Access methods
	//! returns a pointer to the internal mean value. Use with Care!
	vec& _w() {return w;}
	virtual ~emix() {if ( destroyComs ) {for ( int i=0;i<Coms.length();i++ ) {delete Coms ( i );}}}
	//! Auxiliary function for taking ownership of the Coms()
	void ownComs() {destroyComs=true;}

	//!access function
	epdf* _Coms ( int i ) {return Coms ( i );}
};

/*! \brief Chain rule decomposition of epdf

Probability density in the form of Chain-rule decomposition:
\[
f(x_1,x_2,x_3) = f(x_1|x_2,x_3)f(x_2,x_3)f(x_3)
\]
Note that
*/
class mprod: public compositepdf, public mpdf {
protected:
	//! pointers to epdfs - shortcut to mpdfs()._epdf()
	Array<epdf*> epdfs;
	//! Data link for each mpdfs
	Array<datalink_m2m*> dls;
public:
	/*!\brief Constructor from list of mFacs,
	*/
	mprod ( Array<mpdf*> mFacs ) : compositepdf ( mFacs ), mpdf ( getrv ( true ),RV() ), epdfs ( n ), dls ( n ) {
		setrvc ( rv,rvc );
		// rv and rvc established = > we can link them with mpdfs
		for ( int i = 0;i < n;i++ ) {
			dls ( i ) = new datalink_m2m ( mpdfs ( i )->_rv(), mpdfs ( i )->_rvc(), rv, rvc );
		}

		for ( int i=0;i<n;i++ ) {
			epdfs ( i ) =& ( mpdfs ( i )->_epdf() );
		}
	};

	double evallogcond ( const vec &val, const vec &cond ) {
		int i;
		double res = 1.0;
		for ( i = n - 1;i >= 0;i-- ) {
			/*			if ( mpdfs(i)->_rvc().count() >0) {
							mpdfs ( i )->condition ( dls ( i )->get_cond ( val,cond ) );
						}
						// add logarithms
						res += epdfs ( i )->evallog ( dls ( i )->get_val ( val ) );*/
			res *= mpdfs ( i )->evallogcond (
			           dls ( i )->get_val ( val ),
			           dls ( i )->get_cond ( val, cond )
			       );
		}
		return res;
	}
	vec samplecond ( const vec &cond, double &ll ) {
		//! Ugly hack to help to discover if mpfs are not in proper order. Correct solution = check that explicitely.
		vec smp= std::numeric_limits<double>::infinity() * ones ( rv.count() );
		vec smpi;
		ll = 0;
		// Hard assumption here!!! We are going backwards, to assure that samples that are needed from smp are already generated!
		for ( int i = ( n - 1 );i >= 0;i-- ) {
			if ( mpdfs ( i )->_rvc().count() ) {
				mpdfs ( i )->condition ( dls ( i )->get_cond ( smp ,cond ) ); // smp is val here!!
			}
			smpi = epdfs ( i )->sample();
			// copy contribution of this pdf into smp
			dls ( i )->fill_val ( smp, smpi );
			// add ith likelihood contribution
			ll+=epdfs ( i )->evallog ( smpi );
		}
		return smp;
	}
	mat samplecond ( const vec &cond, vec &ll, int N ) {
		mat Smp ( rv.count(),N );
		for ( int i=0;i<N;i++ ) {Smp.set_col ( i,samplecond ( cond,ll ( i ) ) );}
		return Smp;
	}

	~mprod() {};
};

//! Product of independent epdfs. For dependent pdfs, use mprod.
class eprod: public epdf {
protected:
	//! Components (epdfs)
	Array<const epdf*> epdfs;
	//! Array of indeces
	Array<datalink_e2e*> dls;
public:
	eprod ( const Array<const epdf*> epdfs0 ) : epdf ( RV() ),epdfs ( epdfs0 ),dls ( epdfs.length() ) {
		bool independent=true;
		for ( int i=0;i<epdfs.length();i++ ) {
			independent=rv.add ( epdfs ( i )->_rv() );
			it_assert_debug ( independent==true, "eprod:: given components are not independent ." );
		}
		for ( int i=0;i<epdfs.length();i++ ) {
			dls ( i ) = new datalink_e2e ( epdfs ( i )->_rv() , rv );
		}
	}

	vec mean() const {
		vec tmp ( rv.count() );
		for ( int i=0;i<epdfs.length();i++ ) {
			vec pom = epdfs ( i )->mean();
			dls ( i )->fill_val ( tmp, pom );
		}
		return tmp;
	}
	vec variance() const {
		vec tmp ( rv.count() ); //second moment
		for ( int i=0;i<epdfs.length();i++ ) {
			vec pom = epdfs ( i )->mean();
			dls ( i )->fill_val ( tmp, pow(pom,2) );
		}
		return tmp-pow(mean(),2);
	}
	vec sample() const {
		vec tmp ( rv.count() );
		for ( int i=0;i<epdfs.length();i++ ) {
			vec pom = epdfs ( i )->sample();
			dls ( i )->fill_val ( tmp, pom );
		}
		return tmp;
	}
	double evallog ( const vec &val ) const {
		double tmp=0;
		for ( int i=0;i<epdfs.length();i++ ) {
			tmp+=epdfs ( i )->evallog ( dls ( i )->get_val ( val ) );
		}
		it_assert_debug(std::isfinite(tmp),"Infinite");
		return tmp;
	}
	//!access function
	const epdf* operator () ( int i ) const {it_assert_debug ( i<epdfs.length(),"wrong index" );return epdfs ( i );}

	//!Destructor
	~eprod() {for ( int i=0;i<epdfs.length();i++ ) {delete dls ( i );}}
};


/*! \brief Mixture of mpdfs with constant weights, all mpdfs are of equal type

*/
class mmix : public mpdf {
protected:
	//! Component (epdfs)
	Array<mpdf*> Coms;
	//!Internal epdf
	emix Epdf;
public:
	//!Default constructor
	mmix ( RV &rv, RV &rvc ) : mpdf ( rv, rvc ), Epdf ( rv ) {ep = &Epdf;};
	//! Set weights \c w and components \c R
	void set_parameters ( const vec &w, const Array<mpdf*> &Coms ) {
		Array<epdf*> Eps ( Coms.length() );

		for ( int i = 0;i < Coms.length();i++ ) {
			Eps ( i ) = & ( Coms ( i )->_epdf() );
		}
		Epdf.set_parameters ( w, Eps );
	};

	void condition ( const vec &cond ) {
		for ( int i = 0;i < Coms.length();i++ ) {Coms ( i )->condition ( cond );}
	};
};

#endif //MX_H