root/library/bdm/base/bdmbase.h @ 685

/*!
  \file
  \brief Basic structures of probability calculus: random variables, probability densities, Bayes rule
  \author Vaclav Smidl.

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

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

#ifndef BDMBASE_H
#define BDMBASE_H

#include <map>

#include "../itpp_ext.h"
#include "../bdmroot.h"
#include "../shared_ptr.h"
#include "user_info.h"

using namespace libconfig;
using namespace itpp;
using namespace std;

namespace bdm {
//! Structure of RV, i.e. RVs expanded into a flat list of IDs, used for debugging.
class str {
public:
        //! vector id ids (non-unique!)
        ivec ids;
        //! vector of times
        ivec times;
        //!Default constructor
        str ( ivec ids0, ivec times0 ) : ids ( ids0 ), times ( times0 ) {
                bdm_assert ( times0.length() == ids0.length(), "Incompatible input" );
        };
};

/*!
* \brief Class representing variables, most often random variables

The purpose of this class is to decribe a vector of data. Such description is used for connecting various vectors between each other, see class datalink.

The class is implemented using global variables to assure uniqueness of description:

 In is a vector
\dot
digraph datalink {
rankdir=LR;
subgraph cluster0 {
node [shape=record];
label = "MAP \n std::map<string,int>";
map [label="{{\"a\"| \"b\" | \"c\"} | {<3> 3 |<1> 1|<2> 2}}"];
color = "white"
}
subgraph cluster1{
node [shape=record];
label = "NAMES";
names [label="{<1> \"b\" | <2> \"c\" | <3>\"a\" }"];
color = "white"
}
subgraph cluster2{
node [shape=record];
label = "SIZES";
labelloc = b;
sizes [label="{<1>1 |<2> 4 |<3> 1}"];
color = "white"
}
map:1 -> names:1;
map:1 -> sizes:1;
map:3 -> names:3;
map:3 -> sizes:3;
}
\enddot
*/

class RV : public root {
private:
        typedef std::map<string, int> str2int_map;

        //! Internal global variable storing sizes of RVs
        static ivec SIZES;
        //! Internal global variable storing names of RVs
        static Array<string> NAMES;

        //! TODO
        const static int BUFFER_STEP;

        //! TODO
        static str2int_map MAP;

public:

protected:
        //! size of the data vector
        int dsize;
        //! number of individual rvs
        int len;
        //! Vector of unique IDs
        ivec ids;
        //! Vector of shifts from current time
        ivec times;

private:
        enum enum_dummy {dummy};

        //! auxiliary function used in constructor
        void init ( const Array<std::string> &in_names, const ivec &in_sizes, const ivec &in_times );
        int init ( const string &name, int size );
        //! Private constructor from IDs, potentially dangerous since all ids must be valid!
        //! dummy is there to prevent confusion with RV(" string");
        explicit RV ( const ivec &ids0, enum_dummy dum ) : dsize ( 0 ), len ( ids0.length() ), ids ( ids0 ), times ( zeros_i ( ids0.length() ) ) {
                dsize = countsize();
        }
public:
        //! \name Constructors
        //!@{

        //! Full constructor
        RV ( const Array<std::string> &in_names, const ivec &in_sizes, const ivec &in_times ) {
                init ( in_names, in_sizes, in_times );
        }

        //! Constructor with times=0
        RV ( const Array<std::string> &in_names, const ivec &in_sizes ) {
                init ( in_names, in_sizes, zeros_i ( in_names.length() ) );
        }

        //! Constructor with sizes=1, times=0
        RV ( const Array<std::string> &in_names ) {
                init ( in_names, ones_i ( in_names.length() ), zeros_i ( in_names.length() ) );
        }

        //! Constructor of empty RV
        RV() : dsize ( 0 ), len ( 0 ), ids ( 0 ), times ( 0 ) {}

        //! Constructor of a single RV with given id
        RV ( string name, int sz, int tm = 0 );

        // compiler-generated copy constructor is used
        //!@}

        //! \name Access functions
        //!@{

        //! State output, e.g. for debugging.
        friend std::ostream &operator<< ( std::ostream &os, const RV &rv );

        string to_string() const {ostringstream o; o << *this; return o.str();}
        
        //! total size of a random variable
        int _dsize() const {
                return dsize;
        }

        //! access function
        const ivec& _ids() const {
                return ids;
        }

        //! Recount size of the corresponding data vector
        int countsize() const;
        //! Vector of cumulative sizes of RV
        ivec cumsizes() const;
        //! Number of named parts
        int length() const {
                return len;
        }
        int id ( int at ) const {
                return ids ( at );
        }
        int size ( int at ) const {
                return SIZES ( ids ( at ) );
        }
        int time ( int at ) const {
                return times ( at );
        }
        std::string name ( int at ) const {
                return NAMES ( ids ( at ) );
        }
        //! returns name of a scalar at position scalat, i.e. it can be in the middle of vector name, in that case it adds "_%d" to it
        std::string scalarname ( int scalat ) const {
                bdm_assert(scalat<dsize,"Wrong input index");
                int id=0;
                int scalid=0;
                while (scalid+SIZES(ids(id))<=scalat)  { scalid+=SIZES(ids(id)); id++;};
                //now id is the id of variable of interest
                if (size(id)==1)
                        return  NAMES ( ids ( id ) );
                else
                        return  NAMES ( ids ( id ) )+ "_" + num2str(scalat-scalid);

        }
        void set_time ( int at, int time0 ) {
                times ( at ) = time0;
        }
        //!@}

        //! \name Algebra on Random Variables
        //!@{

        //! Find indices of self in another rv, \return ivec of the same size as self.
        ivec findself ( const RV &rv2 ) const;
        //! Find indices of self in another rv, ignore time, \return ivec of the same size as self.
        ivec findself_ids ( const RV &rv2 ) const;
        //! Compare if \c rv2 is identical to this \c RV
        bool equal ( const RV &rv2 ) const;
        //! Add (concat) another variable to the current one, \return true if all rv2 were added, false if rv2 is in conflict
        bool add ( const RV &rv2 );
        //! Subtract  another variable from the current one
        RV subt ( const RV &rv2 ) const;
        //! Select only variables at indices ind
        RV subselect ( const ivec &ind ) const;

        //! Select only variables at indices ind
        RV operator() ( const ivec &ind ) const {
                return subselect ( ind );
        }

        //! Select from data vector starting at di1 to di2
        RV operator() ( int di1, int di2 ) const;

        //! Shift \c time by delta.
        void t_plus ( int delta );
        //!@}

        //! @{ \name Time manipulation functions
        //! returns rvs with time set to 0 and removed duplicates
        RV remove_time() const {
                return RV ( unique ( ids ), dummy );
        }
        //! create new RV from the current one with time shifted by given value
        RV copy_t(int dt) const {
                RV tmp=*this;
                tmp.t_plus(dt);
                return tmp;
        }
        //! return rvs with expanded delayes and sorted in the order of: \f$ [ rv_{0}, rv_{-1},\ldots  rv_{max_delay}]\f$
        RV expand_delayes() const {
                RV rvt = this->remove_time(); //rv at t=0
                RV tmp = rvt;
                int td = mint();
                for ( int i = -1; i >= td; i-- ) {
                        rvt.t_plus ( -1 );
                        tmp.add ( rvt ); //shift u1
                }
                return tmp;
        }
        //!@}

        //!\name Relation to vectors
        //!@{

        //! generate \c str from rv, by expanding sizes
        str tostr() const;
        //! when this rv is a part of bigger rv, this function returns indices of self in the data vector of the bigger crv.
        //! Then, data can be copied via: data_of_this = cdata(ind);
        ivec dataind ( const RV &crv ) const;
        //! same as dataind but this time crv should not be complete supperset of rv.
        ivec dataind_part ( const RV &crv ) const;
        //! generate mutual indices when copying data between self and crv.
        //! Data are copied via: data_of_this(selfi) = data_of_rv2(rv2i)
        void dataind ( const RV &rv2, ivec &selfi, ivec &rv2i ) const;
        //! Minimum time-offset
        int mint() const {
                        return times.length()>0 ? min (times) : 0;
        }
        //!@}

        /*! \brief UI for class RV (description of data vectors)

        \code
        class = 'RV';                   
        names = {'a', 'b', 'c', ...};   // UNIQUE IDENTIFIER same names = same variable
                                                                        // names are also used when storing results 
        --- optional ---
        sizes = [1, 2, 3, ...];         // size of each name. default = ones()
                                                                        // if size = -1, it is found out from previous instances of the same name
        times = [-1, -2, 0, ...];       // time shifts with respect to current time, default = zeros()
        \endcode
        */
        void from_setting ( const Setting &set );

        // TODO dodelat void to_setting( Setting &set ) const;

        //! Invalidate all named RVs. Use before initializing any RV instances, with care...
        static void clear_all();
        //! function for debugging RV related stuff
        string show_all();

};
UIREGISTER ( RV );
SHAREDPTR ( RV );

//! Concat two random variables
RV concat ( const RV &rv1, const RV &rv2 );

/*!
@brief Class for storing results (and semi-results) of an experiment

This class abstracts logging of results from implementation. This class replaces direct logging of results (e.g. to files or to global variables) by calling methods of a logger. Specializations of this abstract class for specific storage method are designed.
*/
class logger : public root {
        protected:
                //! RVs of all logged variables.
                Array<RV> entries;
                //! Names of logged quantities, e.g. names of algorithm variants
                Array<string> names;
                //!separator of prefixes of entries
                const string separator;
        public:
                //!Default constructor
                logger(const string separator0) : entries ( 0 ), names ( 0 ), separator(separator0) {}
                
                //! returns an identifier which will be later needed for calling the \c logit() function
                //! For empty RV it returns -1, this entry will be ignored by \c logit().
                virtual int add ( const RV &rv, string prefix = "" ) {
                        int id;
                        if ( rv._dsize() > 0 ) {
                                id = entries.length();
                                names = concat ( names, prefix ); // diff
                                entries.set_length ( id + 1, true );
                                entries ( id ) = rv;
                        } else {
                                id = -1;
                        }
                        return id; // identifier of the last entry
                }
                
                //! log this vector
                virtual void logit ( int id, const vec &v ) {
                        bdm_error ( "Not implemented" );
                };
                //! log this double
                virtual void logit ( int id, const double &d ) {
                        bdm_error ( "Not implemented" );
                };
                
                //! Shifts storage position for another time step.
                virtual void step() {
                        bdm_error ( "Not implemneted" );
                };
                
                //! Finalize storing information
                virtual void finalize() {};
                
                //! Initialize the storage
                virtual void init() {};
                
                //!separator of prefixes for this logger
                const string& prefix_sep() {return separator;}
};


//! Class representing function \f$f(x)\f$ of variable \f$x\f$ represented by \c rv
class fnc : public root {
protected:
        //! Length of the output vector
        int dimy;
        //! Length of the input vector
        int dimc;
public:
        //!default constructor
        fnc() {};
        //! function evaluates numerical value of \f$f(x)\f$ at \f$x=\f$ \c cond
        virtual vec eval ( const vec &cond ) {
                return vec ( 0 );
        };

        //! function substitutes given value into an appropriate position
        virtual void condition ( const vec &val ) {};

        //! access function
        int dimension() const {
                return dimy;
        }
        //! access function
        int dimensionc() const {
                return dimc;
        }
};

class epdf;

//! Conditional probability density, e.g. modeling \f$ f( x | y) \f$, where \f$ x \f$ is random variable, \c rv, and \f$ y \f$ is conditioning variable, \c rvc.
class mpdf : public root {
protected:
        //!dimension of the condition
        int dimc;
        //! random variable in condition
        RV rvc;

        //! dimension of random variable
        int dim;

        //! random variable
        RV rv;

public:
        //! \name Constructors
        //! @{

        mpdf() : dimc ( 0 ), rvc(), dim(0), rv() { }

        mpdf ( const mpdf &m ) : dimc ( m.dimc ), rvc ( m.rvc ), dim( m.dim), rv( m.rv ) { }
        
        //! copy of the current object - make sure to implement
        virtual mpdf* _copy_() const {return new mpdf(*this);}
        //!@}

        //! \name Matematical operations
        //!@{

        //! Returns a sample from the density conditioned on \c cond, \f$x \sim epdf(rv|cond)\f$. \param cond is numeric value of \c rv
        virtual vec samplecond ( const vec &cond ) {
                bdm_error ( "Not implemented" );
                return vec();
        }

        //! Returns \param N samples from the density conditioned on \c cond, \f$x \sim epdf(rv|cond)\f$. \param cond is numeric value of \c rv
        virtual mat samplecond_m ( const vec &cond, int N );

        //! Shortcut for conditioning and evaluation of the internal epdf. In some cases,  this operation can be implemented efficiently.
        virtual double evallogcond ( const vec &yt, const vec &cond ) {
                bdm_error ( "Not implemented" );
                return 0.0;
        }

        //! Matrix version of evallogcond
        virtual vec evallogcond_m ( const mat &Yt, const vec &cond ) {
                vec v ( Yt.cols() );
                for ( int i = 0; i < Yt.cols(); i++ ) {
                        v ( i ) = evallogcond ( Yt.get_col ( i ), cond );
                }
                return v;
        }

        //! Array<vec> version of evallogcond
        virtual vec evallogcond_m ( const Array<vec> &Yt, const vec &cond ) {
                bdm_error ( "Not implemented" );
                return vec();
        }

        //! \name Access to attributes
        //! @{

        const RV& _rv() const {
                return rv;
        }
        const RV& _rvc() const {
                return rvc;
        }

        int dimension() const {
                return dim;
        }
        int dimensionc() {
                return dimc;
        }

        //! access function
        void set_dim(int d) {dim=d;}
        //! access function
        void set_dimc(int d) {dimc=d;}
        //! Load from structure with elements:
        //!  \code
        //! { class = "mpdf_offspring",
        //!   rv = {class="RV", names=(...),}; // RV describing meaning of random variable
        //!   rvc= {class="RV", names=(...),}; // RV describing meaning of random variable in condition
        //!   // elements of offsprings
        //! }
        //! \endcode
        //!@}
        void from_setting ( const Setting &set );
        //!@}

        //! \name Connection to other objects
        //!@{
        void set_rvc ( const RV &rvc0 ) {
                rvc = rvc0;
        }
        void set_rv ( const RV &rv0 ) {
                rv = rv0;
        }

        bool isnamed() const {
                return ( dim == rv._dsize() ) && ( dimc == rvc._dsize() );
        }
        //!@}
};
SHAREDPTR ( mpdf );

//! Probability density function with numerical statistics, e.g. posterior density.
class epdf : public mpdf {

public:
        /*! \name Constructors
         Construction of each epdf should support two types of constructors:
        \li empty constructor,
        \li copy constructor,

        The following constructors should be supported for convenience:
        \li constructor followed by calling \c set_parameters()
        \li constructor accepting random variables calling \c set_rv()

         All internal data structures are constructed as empty. Their values (including sizes) will be set by method \c set_parameters(). This way references can be initialized in constructors.
        @{*/
        epdf() {};
        epdf ( const epdf &e ) : mpdf(e) {};
        void set_parameters ( int dim0 ) {
                dim = dim0;
        }
        epdf* _copy_() const {return new epdf(*this);}
        //!@}

        //! \name Matematical Operations
        //!@{

        //! Returns a sample, \f$ x \f$ from density \f$ f_x()\f$
        virtual vec sample() const {
                bdm_error ( "not implemented" );
                return vec();
        }

        //! Returns N samples, \f$ [x_1 , x_2 , \ldots \ \f$  from density \f$ f_x(rv)\f$
        virtual mat sample_m ( int N ) const;

        //! Compute log-probability of argument \c val
        //! In case the argument is out of suport return -Infinity
        virtual double evallog ( const vec &val ) const {
                bdm_error ( "not implemented" );
                return 0.0;
        }

        //! Compute log-probability of multiple values argument \c val
        virtual vec evallog_m ( const mat &Val ) const;

        //! Compute log-probability of multiple values argument \c val
        virtual vec evallog_m ( const Array<vec> &Avec ) const;

        //! Return conditional density on the given RV, the remaining rvs will be in conditioning
        virtual shared_ptr<mpdf> condition ( const RV &rv ) const;

        //! Return marginal density on the given RV, the remainig rvs are intergrated out
        virtual shared_ptr<epdf> marginal ( const RV &rv ) const;

        //! return expected value
        virtual vec mean() const {
                bdm_error ( "not implemneted" );
                return vec();
        }

        //! return expected variance (not covariance!)
        virtual vec variance() const {
                bdm_error ( "not implemneted" );
                return vec();
        }

        //! Lower and upper bounds of \c percentage % quantile, returns mean-2*sigma as default
        virtual void qbounds ( vec &lb, vec &ub, double percentage = 0.95 ) const {
                vec mea = mean();
                vec std = sqrt ( variance() );
                lb = mea - 2 * std;
                ub = mea + 2 * std;
        };
        //!@}

        //! \name Connection to other classes
        //! Description of the random quantity via attribute \c rv is optional.
        //! For operations such as sampling \c rv does not need to be set. However, for \c marginalization
        //! and \c conditioning \c rv has to be set. NB:
        //! @{

        //! store values of the epdf on the following levels:
        //!  #1 mean
        //!  #2 mean + lower & upper bound
        void log_register(logger &L, const string &prefix){
                RV r;
                if ( isnamed() ) {
                        r = _rv();
                } else {
                        r = RV ( "", dimension() );
                };
                root::log_register(L,prefix);
                logrec->ids.set_size(3);
                if (log_level >0){
                        logrec->ids(0) = logrec->L.add ( r, prefix + logrec->L.prefix_sep()+ "mean" );
                }
                if (log_level >1){
                        logrec->ids(1) = logrec->L.add ( r, prefix + logrec->L.prefix_sep()+ "lb" );
                        logrec->ids(2) = logrec->L.add ( r, prefix + logrec->L.prefix_sep()+ "ub" );
                }
        }
        void log_write() const {
                if (log_level>0) {
                        logrec->L.logit( logrec->ids(0), mean() );
                }
                if (log_level>2) {
                        vec lb; vec ub;
                        qbounds(lb,ub);
                        logrec->L.logit( logrec->ids(1), lb );
                        logrec->L.logit( logrec->ids(2), ub );
                }
        }
        //!@}

        //! \name Access to attributes
        //! @{

        //! Load from structure with elements:
        //!  \code
        //! { rv = {class="RV", names=(...),}; // RV describing meaning of random variable
        //!   // elements of offsprings
        //! }
        //! \endcode
        //!@}
        void from_setting ( const Setting &set ) {
                shared_ptr<RV> r = UI::build<RV> ( set, "rv", UI::optional );
                if ( r ) {
                        set_rv ( *r );
                }
        }

        vec samplecond ( const vec &cond ) {
                return sample();
        }
        double evallogcond ( const vec &val, const vec &cond ) {
                return evallog ( val );
        }
};
SHAREDPTR ( epdf );

//! Mpdf with internal epdf that is modified by function \c condition
template <class EPDF>
class mpdf_internal: public mpdf {
protected :
        //! Internal epdf used for sampling
        EPDF iepdf;
public:
        //! constructor
        mpdf_internal() : mpdf(), iepdf() {
//              set_ep ( iepdf ); TODO!
        }

        //! Update \c iepdf so that it represents this mpdf conditioned on \c rvc = cond
        //! This function provides convenient reimplementation in offsprings
        virtual void condition ( const vec &cond ) {
                bdm_error ( "Not implemented" );
        }

        //!access function to iepdf
        EPDF& e() {
                return iepdf;
        }

        //! Reimplements samplecond using \c condition()
        vec samplecond ( const vec &cond );
        //! Reimplements evallogcond using \c condition()
        double evallogcond ( const vec &val, const vec &cond );
        //! Efficient version of evallogcond for matrices
        virtual vec evallogcond_m ( const mat &Dt, const vec &cond );
        //! Efficient version of evallogcond for Array<vec>
        virtual vec evallogcond_m ( const Array<vec> &Dt, const vec &cond );
        //! Efficient version of samplecond
        virtual mat samplecond_m ( const vec &cond, int N );
        
        void validate() {
                iepdf.validate();
                if (rv._dsize()< iepdf._rv()._dsize()) {rv=iepdf._rv();};
                dim = iepdf.dimension();
        }
};

/*! \brief DataLink is a connection between two data vectors Up and Down

Up can be longer than Down. Down must be fully present in Up (TODO optional)
See chart:
\dot
digraph datalink {
  node [shape=record];
  subgraph cluster0 {
    label = "Up";
      up [label="<1>|<2>|<3>|<4>|<5>"];
    color = "white"
}
  subgraph cluster1{
    label = "Down";
    labelloc = b;
      down [label="<1>|<2>|<3>"];
    color = "white"
}
    up:1 -> down:1;
    up:3 -> down:2;
    up:5 -> down:3;
}
\enddot

*/
class datalink {
protected:
        //! Remember how long val should be
        int downsize;

        //! Remember how long val of "Up" should be
        int upsize;

        //! val-to-val link, indices of the upper val
        ivec v2v_up;

public:
        //! Constructor
        datalink() : downsize ( 0 ), upsize ( 0 ) { }

        //! Convenience constructor
        datalink ( const RV &rv, const RV &rv_up ) {
                set_connection ( rv, rv_up );
        }

        //! set connection, rv must be fully present in rv_up
        virtual void set_connection ( const RV &rv, const RV &rv_up );

        //! set connection using indices
        virtual void set_connection ( int ds, int us, const ivec &upind );

        //! Get val for myself from val of "Up"
        vec pushdown ( const vec &val_up ) {
                vec tmp ( downsize );
                filldown ( val_up, tmp );
                return tmp;
        }
        //! Get val for vector val_down from val of "Up"
        virtual void filldown ( const vec &val_up, vec &val_down ) {
                bdm_assert_debug ( upsize == val_up.length(), "Wrong val_up" );
                val_down = val_up ( v2v_up );
        }
        //! Fill val of "Up" by my pieces
        virtual void pushup ( vec &val_up, const vec &val ) {
                bdm_assert_debug ( downsize == val.length(), "Wrong val" );
                bdm_assert_debug ( upsize == val_up.length(), "Wrong val_up" );
                set_subvector ( val_up, v2v_up, val );
        }
        //! access functions
        int _upsize() {
                return upsize;
        }
        //! access functions
        int _downsize() {
                return downsize;
        }
        //! for future use
        virtual ~datalink(){}
};

/*! Extension of datalink to fill only part of Down
*/
class datalink_part : public datalink {
protected:
        //! indeces of values in vector downsize
        ivec v2v_down;
public:
        void set_connection ( const RV &rv, const RV &rv_up );
        //! Get val for vector val_down from val of "Up"
        void filldown ( const vec &val_up, vec &val_down ) {
                set_subvector ( val_down, v2v_down, val_up ( v2v_up ) );
        }
};

/*! \brief Datalink that buffers delayed values - do not forget to call step()

Up is current data, Down is their subset with possibly delayed values
*/
class datalink_buffered: public datalink_part {
protected:
        //! History, ordered as \f$[Up_{t-1},Up_{t-2}, \ldots]\f$
        vec history;
        //! rv of the history
        RV Hrv;
        //! h2v : indeces in down
        ivec h2v_down;
        //! h2v : indeces in history
        ivec h2v_hist;
        //! v2h: indeces of up too be pushed to h
        ivec v2h_up;
public:

        datalink_buffered() : datalink_part(), history ( 0 ), h2v_down ( 0 ), h2v_hist ( 0 ) {};
        //! push current data to history
        void step ( const vec &val_up ) {
                if ( v2h_up.length() > 0 ) {
                        history.shift_right ( 0, v2h_up.length() );
                  history.set_subvector ( 0, val_up(v2h_up) ); 
                }
        }
        //! Get val for myself from val of "Up"
        vec pushdown ( const vec &val_up ) {
                vec tmp ( downsize );
                filldown ( val_up, tmp );
                return tmp;
        }

        void filldown ( const vec &val_up, vec &val_down ) {
                bdm_assert_debug ( val_down.length() >= downsize, "short val_down" );

                set_subvector ( val_down, v2v_down, val_up ( v2v_up ) ); // copy direct values
                set_subvector ( val_down, h2v_down, history ( h2v_hist ) ); // copy delayed values
        }

        void set_connection ( const RV &rv, const RV &rv_up ) {
                // create link between up and down
                datalink_part::set_connection ( rv, rv_up );

                // create rvs of history
                // we can store only what we get in rv_up - everything else is removed
                ivec valid_ids = rv.findself_ids ( rv_up );
                RV rv_hist = rv.subselect ( find ( valid_ids >= 0 ) ); // select only rvs that are in rv_up
                RV rv_hist0 =rv_hist.remove_time();  // these RVs will form history at time =0
                // now we need to know what is needed from Up
                rv_hist = rv_hist.expand_delayes(); // full regressor - including time 0
                Hrv=rv_hist.subt(rv_hist0);   // remove time 0
                history = zeros ( Hrv._dsize() );

                // decide if we need to copy val to history
                if (Hrv._dsize() >0) {
                        v2h_up = rv_hist0.dataind(rv_up); // indeces of elements of rv_up to be copied
                } // else v2h_up is empty
                
                Hrv.dataind ( rv, h2v_hist, h2v_down );

                downsize = v2v_down.length() + h2v_down.length();
                upsize = v2v_up.length();
        }
        //! set history of variable given by \c rv1 to values of \c hist.
        void set_history(const RV& rv1, const vec &hist0){
                bdm_assert(rv1._dsize()==hist0.length(),"hist is not compatible with given rv1");
                ivec ind_H;
                ivec ind_h0;
                Hrv.dataind(rv1, ind_H, ind_h0); // find indeces of rv in 
                set_subvector(history, ind_H, hist0(ind_h0)); // copy given hist to appropriate places
        }
};

//! buffered datalink from 2 vectors to 1
class datalink_2to1_buffered {
protected:
        //! link 1st vector to down
        datalink_buffered dl1;
        //! link 2nd vector to down
        datalink_buffered dl2;
public:
        //! set connection between RVs
        void set_connection ( const RV &rv, const RV &rv_up1, const RV &rv_up2 ) {
                dl1.set_connection ( rv, rv_up1 );
                dl2.set_connection ( rv, rv_up2 );
        }
        //! fill values of down from the values of the two up vectors
        void filldown ( const vec &val1, const vec &val2, vec &val_down ) {
                bdm_assert_debug ( val_down.length() >= dl1._downsize() + dl2._downsize(), "short val_down" );
                dl1.filldown ( val1, val_down );
                dl2.filldown ( val2, val_down );
        }
        //! update buffer
        void step ( const vec &dt, const vec &ut ) {
                dl1.step ( dt );
                dl2.step ( ut );
        }
};



//! Data link with a condition.
class datalink_m2e: public datalink {
protected:
        //! Remember how long cond should be
        int condsize;

        //!upper_val-to-local_cond link, indices of the upper val
        ivec v2c_up;

        //!upper_val-to-local_cond link, indices of the local cond
        ivec v2c_lo;

public:
        //! Constructor
        datalink_m2e() : condsize ( 0 ) { }

        //! Set connection between vectors
        void set_connection ( const RV &rv, const RV &rvc, const RV &rv_up );

        //!Construct condition
        vec get_cond ( const vec &val_up );

        //! Copy corresponding values to Up.condition
        void pushup_cond ( vec &val_up, const vec &val, const vec &cond );
};

//!DataLink is a connection between mpdf and its superordinate (Up)
//! This class links
class datalink_m2m: public datalink_m2e {
protected:
        //!cond-to-cond link, indices of the upper cond
        ivec c2c_up;
        //!cond-to-cond link, indices of the local cond
        ivec c2c_lo;

public:
        //! Constructor
        datalink_m2m() {};
        //! Set connection between the vectors
        void set_connection ( const RV &rv, const RV &rvc, const RV &rv_up, const RV &rvc_up ) {
                datalink_m2e::set_connection ( rv, rvc, rv_up );
                //establish c2c connection
                rvc.dataind ( rvc_up, c2c_lo, c2c_up );
                bdm_assert_debug ( c2c_lo.length() + v2c_lo.length() == condsize, "cond is not fully given" );
        }

        //! Get cond for myself from val and cond of "Up"
        vec get_cond ( const vec &val_up, const vec &cond_up ) {
                vec tmp ( condsize );
                set_subvector ( tmp, v2c_lo, val_up ( v2c_up ) );
                set_subvector ( tmp, c2c_lo, cond_up ( c2c_up ) );
                return tmp;
        }
        //! Fill

};


//! \brief Combines RVs from a list of mpdfs to a single one.
RV get_composite_rv ( const Array<shared_ptr<mpdf> > &mpdfs, bool checkoverlap = false );

/*! \brief Abstract class for discrete-time sources of data.

The class abstracts operations of: 
\li  data aquisition, 
\li  data-preprocessing, such as  scaling of data, 
\li  data resampling from the task of estimation and control.
Moreover, for controlled systems, it is able to receive the desired control action and perform it in the next step. (Or as soon as possible).

The DataSource has three main data interaction structures:
\li input, \f$ u_t \f$, 
\li output \f$ y_t \f$,
\li data, \f$ d_t=[y_t,u_t, \ldots ]\f$ a collection of all inputs and outputs and possibly some internal variables too.

*/

class DS : public root {
protected:
                //! size of data returned by \c getdata()
        int dtsize;
                //! size of data
        int utsize;
                //!size of output
                int ytsize;
        //!Description of data returned by \c getdata().
        RV Drv;
        //!Description of data witten by by \c write().
        RV Urv; //
                //!Description of output data
                RV Yrv; //
public:
        //! default constructors
        DS() : dtsize(0),utsize(0),ytsize(0),Drv(), Urv(),Yrv() {log_level=1;};

        //! Returns maximum number of provided data, by default it is set to maximum allowed length, shorter DS should overload this method! See, MemDS.max_length().
        virtual int max_length() {return std::numeric_limits< int >::max();}
        //! Returns full vector of observed data=[output, input]
        virtual void getdata ( vec &dt ) const {
                bdm_error ( "abstract class" );
        }
        //! Returns data records at indeces.
        virtual void getdata ( vec &dt, const ivec &indeces ) {
                bdm_error ( "abstract class" );
        }

        //! Accepts action variable and schedule it for application.
        virtual void write (const vec &ut ) {
                bdm_error ( "abstract class" );
        }

        //! Accepts action variables at specific indeces
        virtual void write (const vec &ut, const ivec &indeces ) {
                bdm_error ( "abstract class" );
        }

        //! Moves from \f$ t \f$ to \f$ t+1 \f$, i.e. perfroms the actions and reads response of the system.
        virtual void step() 
        {
                bdm_error ( "abstract class" );
        }

        //! Register DS for logging into logger L
        virtual void log_register (logger &L,  const string &prefix ) {
                bdm_assert ( ytsize == Yrv._dsize(), "invalid DS: ytsize (" + num2str ( ytsize ) + ") different from Drv " + num2str ( Yrv._dsize() ) );
                bdm_assert ( utsize == Urv._dsize(), "invalid DS: utsize (" + num2str ( utsize ) + ") different from Urv " + num2str ( Urv._dsize() ) );

                root::log_register(L,prefix);
                //we know that 
                if (log_level >0){
                        logrec->ids.set_size(2);
                        logrec->ids(0) = logrec->L.add ( Yrv, prefix );
                        logrec->ids(1) = logrec->L.add ( Urv, prefix );
                }
        }
        //! Register DS for logging into logger L
        virtual void log_write ( ) const {
                if (log_level >0) {
                        vec tmp ( Yrv._dsize() + Urv._dsize());
                        getdata ( tmp );
                        // d is first in getdata
                        logrec->L.logit ( logrec->ids(0), tmp.left ( Yrv._dsize() ) );
                        // u follows after d in getdata
                        logrec->L.logit ( logrec->ids(1), tmp.mid ( Yrv._dsize(), Urv._dsize() ) );
                }
        }
        //!access function
        virtual const RV& _drv() const {
                return Drv;
        }
        //!access function
        const RV& _urv() const {
                return Urv;
        }
        //!access function
        const RV& _yrv() const {
                return Yrv;
        }
        //! set random variables
        virtual void set_drv (const  RV &yrv, const RV &urv) {
                Yrv = yrv;
                Drv = concat(yrv,urv);
                Urv = urv;
        }
};

/*! \brief Bayesian Model of a system, i.e. all uncertainty is modeled by probabilities.

This object represents exact or approximate evaluation of the Bayes rule:
\f[
f(\theta_t | y_1,\ldots,y_t, u_1,\ldots,u_t) = \frac{f(y_t|\theta_t,\cdot) f(\theta_t|d_1,\ldots,d_{t-1})}{f(y_t|d_1,\ldots,d_{t-1})}
\f]
where:
 * \f$ y_t \f$ is the variable 
Access to the resulting posterior density is via function \c posterior().

As a "side-effect" it also evaluates log-likelihood of the data, which can be accessed via function _ll().
It can also evaluate predictors of future values of \f$y_t\f$, see functions epredictor() and predictor().

Alternatively, it can evaluate posterior density with rvc replaced by the given values, \f$ c_t \f$:
\f[
f(\theta_t | c_t, d_1,\ldots,d_t) \propto  f(y_t,\theta_t|c_t,\cdot, d_1,\ldots,d_{t-1})
\f]


*/

class BM : public root {
protected:
        //! Random variable of the data (optional)
        RV yrv;
        //! size of the data record
        int dimy;
        //! Name of extension variable
        RV rvc;
        //! size of the conditioning vector
        int dimc;
        
        //!Logarithm of marginalized data likelihood.
        double ll;
        //!  If true, the filter will compute likelihood of the data record and store it in \c ll . Set to false if you want to save computational time.
        bool evalll;

public:
        //! \name Constructors
        //! @{

        BM() : yrv(),dimy(0),rvc(),dimc(0), ll ( 0 ), evalll ( true ) { };
        BM ( const BM &B ) :  yrv ( B.yrv ), dimy(B.dimy), rvc ( B.rvc ), ll ( B.ll ), evalll ( B.evalll ) {}
        //! \brief Copy function required in vectors, Arrays of BM etc. Have to be DELETED manually!
        //! Prototype: \code BM* _copy_() const {return new BM(*this);} \endcode
        virtual BM* _copy_() const { return NULL; };
        //!@}

        //! \name Mathematical operations
        //!@{

        /*! \brief Incremental Bayes rule
        @param dt vector of input data
        */
        virtual void bayes ( const vec &yt, const vec &cond=empty_vec ) = 0;
        //! Batch Bayes rule (columns of Dt are observations)
        virtual void bayes_batch ( const mat &Dt );
        //! Evaluates predictive log-likelihood of the given data record
        //! I.e. marginal likelihood of the data with the posterior integrated out. 
        //! This function evaluates only \f$ y_t \f$, condition is assumed to be the last used in bayes(). 
        //! See bdm::BM::predictor for conditional version.
        virtual double logpred ( const vec &yt ) const {
                bdm_error ( "Not implemented" );
                return 0.0;
        }

        //! Matrix version of logpred
        vec logpred_m ( const mat &Yt ) const {
                vec tmp ( Yt.cols() );
                for ( int i = 0; i < Yt.cols(); i++ ) {
                        tmp ( i ) = logpred ( Yt.get_col ( i ) );
                }
                return tmp;
        }

        //!Constructs a predictive density \f$ f(d_{t+1} |d_{t}, \ldots d_{0}) \f$
        virtual epdf* epredictor() const {
                bdm_error ( "Not implemented" );
                return NULL;
        };
        //!Constructs conditional density of 1-step ahead predictor \f$ f(d_{t+1} |d_{t+h-1}, \ldots d_{t}) \f$
        virtual mpdf* predictor() const {
                bdm_error ( "Not implemented" );
                return NULL;
        };
        //!@}


        //! \name Access to attributes
        //!@{
                //! access function
                const RV& _rvc() const {
                        return rvc;
                }
                //! access function
                int dimensionc() const {
                        return dimc;
                }
                //! access function
                int dimensiony() const {
                        return dimy;
                }
                //! access function
                int dimension() const {
                        return posterior().dimension();
                }
                //! access function
        const RV& _yrv() const {
                return yrv;
        }
        //! access function
        void set_yrv ( const RV &rv ) {
                yrv = rv;
        }
        //! access to rv of the posterior
        void set_rv ( const RV &rv ) {
                const_cast<epdf&>(posterior()).set_rv ( rv );
        }
        //! access function
        void set_dim ( int dim ) {
                const_cast<epdf&>(posterior()).set_dim ( dim );
        }
        //! return internal log-likelihood of the last data vector
        double _ll() const {
                return ll;
        }
        //! switch evaluation of log-likelihood on/off
        void set_evalll ( bool evl0 ) {
                evalll = evl0;
        }
        //! return posterior density
        virtual const epdf& posterior() const = 0;
        //!@}

        //! \name Logging of results
        //!@{

        //! Set boolean options from a string, recognized are: "logbounds,logll"
        virtual void set_options ( const string &opt ) {
                if ( opt.find ( "logbounds" ) != string::npos ) {
                        const_cast<epdf&>(posterior()).set_log_level(2) ;
                } else {
                        const_cast<epdf&>(posterior()).set_log_level(1) ;
                }
                if ( opt.find ( "logll" ) != string::npos ) {
                        log_level = 1;
                }
        }

        //! Add all logged variables to a logger
        //! Log levels two digits: xy where
        //!  * y = 0/1 log-likelihood is to be logged
        //!  * x = level of the posterior (typically 0/1/2 for nothing/mean/bounds)
        virtual void log_register ( logger &L, const string &prefix = "" ) {
                root::log_register(L,prefix);           

                const_cast<epdf&>(posterior()).log_register(L, prefix+L.prefix_sep()+"apost"); 
                
                if ((log_level) > 0){
                        logrec->ids.set_size(1);
                        logrec->ids(0) = L.add(RV("ll",1), prefix+L.prefix_sep()+"ll");
                }
        }
        //! Save results to the given logger, details of what is stored is configured by \c LIDs and \c options
        virtual void log_write ( ) const {
                posterior().log_write();
                if (log_level >0) { logrec->L.logit ( logrec->ids ( 0 ), ll );}
        }
        //!@}
        void from_setting ( const Setting &set ) {
                shared_ptr<RV> r = UI::build<RV> ( set, "yrv", UI::optional );
                if ( r ) {
                        set_yrv ( *r );
                }
                shared_ptr<RV> r2 = UI::build<RV> ( set, "rvc", UI::optional );
                if ( r2 ) {
                        rvc =   *r2;
                }
                shared_ptr<RV> r3 = UI::build<RV> ( set, "rv", UI::optional );
                if ( r3 ) {
                        set_rv(*r3);
                }
                
                string opt;
                if ( UI::get ( opt, set, "options", UI::optional ) ) {
                        set_options ( opt );
                }
        }

};
//! array of pointers to epdf
typedef Array<shared_ptr<epdf> > epdf_array;
//! array of pointers to mpdf
typedef Array<shared_ptr<mpdf> > mpdf_array;

template<class EPDF>
vec mpdf_internal<EPDF>::samplecond ( const vec &cond ) {
        condition ( cond );
        vec temp = iepdf.sample();
        return temp;
}

template<class EPDF>
mat mpdf_internal<EPDF>::samplecond_m ( const vec &cond, int N ) {
        condition ( cond );
        mat temp ( dimension(), N );
        vec smp ( dimension() );
        for ( int i = 0; i < N; i++ ) {
                smp = iepdf.sample();
                temp.set_col ( i, smp );
        }

        return temp;
}

template<class EPDF>
double mpdf_internal<EPDF>::evallogcond ( const vec &yt, const vec &cond ) {
        double tmp;
        condition ( cond );
        tmp = iepdf.evallog ( yt );
        return tmp;
}

template<class EPDF>
vec mpdf_internal<EPDF>::evallogcond_m ( const mat &Yt, const vec &cond ) {
        condition ( cond );
        return iepdf.evallog_m ( Yt );
}

template<class EPDF>
vec mpdf_internal<EPDF>::evallogcond_m ( const Array<vec> &Yt, const vec &cond ) {
        condition ( cond );
        return iepdf.evallog_m ( Yt );
}

}; //namespace
#endif // BDMBASE_H