root/library/bdm/base/bdmbase.h @ 536

/*!
  \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
{

typedef std::map<string, int> RVmap;
//! Internal global variable storing sizes of RVs
extern ivec RV_SIZES;
//! Internal global variable storing names of RVs
extern Array<string> RV_NAMES;

//! 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) {
                        it_assert_debug (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 = "RV_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 = "RV_NAMES";
names [label="{<1> \"b\" | <2> \"c\" | <3>\"a\" }"];
color = "white"
}
subgraph cluster2{
node [shape=record];
label = "RV_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
{
        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:
                //! 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);
        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);

                int _dsize() const {
                        return dsize;
                }

                //! Recount size of the corresponding data vector
                int countsize() const;
                ivec cumsizes() const;
                int length() const {
                        return len;
                }
                int id (int at) const {
                        return ids (at);
                }
                int size (int at) const {
                        return RV_SIZES (ids (at));
                }
                int time (int at) const {
                        return times (at);
                }
                std::string name (int at) const {
                        return RV_NAMES (ids (at));
                }
                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;
                //! 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 (int delta);
                //!@}

                //!\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;
                //! 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 min (times);
                }
                //!@}

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

                \code
                rv = {
                  class = "RV"; // class name
                  // UNIQUE IDENTIFIER same names = same variable
                  names = ( "a", "b", "c", ...);   // which will be used e.g. in loggers

                  //optional arguments
                  sizes = [1, 2, 3, ...];         // (optional) default = ones()
                  times = [-1, -2, 0, ...];       // time shifts with respect to current time (optional) 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();
};
UIREGISTER (RV);
SHAREDPTR (RV);

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

//!Default empty RV that can be used as default argument
extern RV RV0;

//! 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;
        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;
                }
};

class mpdf;

//! Probability density function with numerical statistics, e.g. posterior density.

class epdf : public root
{
        protected:
                //! dimension of the random variable
                int dim;
                //! Description of the random variable
                RV rv;

        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() : dim (0), rv() {};
                epdf (const epdf &e) : dim (e.dim), rv (e.rv) {};
                epdf (const RV &rv0) : dim (rv0._dsize()) {
                        set_rv (rv0);
                };
                void set_parameters (int dim0) {
                        dim = dim0;
                }
                //!@}

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

                //! Returns a sample, \f$ x \f$ from density \f$ f_x()\f$
                virtual vec sample() const {
                        it_error ("not implemented");
                        return vec (0);
                }

                //! 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 {
                        it_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 {
                        it_error ("not implemneted");
                        return vec (0);
                };

                //! return expected variance (not covariance!)
                virtual vec variance() const {
                        it_error ("not implemneted");
                        return vec (0);
                };
                //! 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:
                //! @{

                //!Name its rv
                void set_rv (const RV &rv0) {
                        rv = rv0;
                }   //it_assert_debug(isnamed(),""); };
                //! True if rv is assigned
                bool isnamed() const {
                        bool b = (dim == rv._dsize());
                        return b;
                }
                //! Return name (fails when isnamed is false)
                const RV& _rv() const {
                        it_assert_debug (isnamed(), "");
                        return rv;
                }
                //!@}

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

                //! Size of the random variable
                int dimension() const {
                        return dim;
                }
                //! 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);
                        }
                }

};
SHAREDPTR(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;
        private:
                //! internal epdf, used only as cache to avoid virtual calls of \c _rv() and \c _dimension()
                epdf* ep;

        protected:
                //! set internal pointer \c ep to point to given \c iepdf
                void set_ep (epdf &iepdf) {
                        ep = &iepdf;
                }
                //! set internal pointer \c ep to point to given \c iepdf
                void set_ep (epdf *iepdfp) {
                        ep = iepdfp;
                }

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

                mpdf() : dimc (0), rvc(), ep (NULL) { }

                mpdf (const mpdf &m) : dimc (m.dimc), rvc (m.rvc), ep (m.ep) { }
                //!@}

                //! \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) {it_error ("Not implemented");return vec (0);};

                //! 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 &dt, const vec &cond) {it_error ("Not implemented");return 0.0;}

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

                //! Array<vec> version of evallogcond
                virtual vec evallogcond_m (const Array<vec> &Dt, const vec &cond) {it_error ("Not implemented");return vec (0);}

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

                RV _rv() const {
                        return ep->_rv();
                }
                RV _rvc() {
                        return rvc;
                }

                int dimension() const {
                        return ep->dimension();
                }
                int dimensionc() {
                        return dimc;
                }

                //! 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) {
                        ep->set_rv (rv0);
                }
                bool isnamed() {
                        return (ep->isnamed()) && (dimc == rvc._dsize());
                }
                //!@}
};
SHAREDPTR(mpdf);

//! 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);}
                //! 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) {
                        it_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);
};

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

                //! set connection, rv must be fully present in rv_up
                void set_connection (const RV &rv, const RV &rv_up) {
                        downsize = rv._dsize();
                        upsize = rv_up._dsize();
                        v2v_up = rv.dataind (rv_up);

                        it_assert_debug (v2v_up.length() == downsize, "rv is not fully in rv_up");
                }

                //! set connection using indices
                void set_connection (int ds, int us, const ivec &upind) {
                        downsize = ds;
                        upsize = us;
                        v2v_up = upind;

                        it_assert_debug (v2v_up.length() == downsize, "rv is not fully in rv_up");
                }

                //! Get val for myself from val of "Up"
                vec pushdown (const vec &val_up) {
                        it_assert_debug (upsize == val_up.length(), "Wrong val_up");
                        return get_vec (val_up, v2v_up);
                }

                //! Fill val of "Up" by my pieces
                void pushup (vec &val_up, const vec &val) {
                        it_assert_debug (downsize == val.length(), "Wrong val");
                        it_assert_debug (upsize == val_up.length(), "Wrong val_up");
                        set_subvector (val_up, v2v_up, val);
                }
};

//! 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) {
                        datalink::set_connection (rv, rv_up);
                        condsize = rvc._dsize();
                        //establish v2c connection
                        rvc.dataind (rv_up, v2c_lo, v2c_up);
                }

                //!Construct condition
                vec get_cond (const vec &val_up) {
                        vec tmp (condsize);
                        set_subvector (tmp, v2c_lo, val_up (v2c_up));
                        return tmp;
                }
                //! Copy corresponding values to Up.condition
                void pushup_cond (vec &val_up, const vec &val, const vec &cond) {
                        it_assert_debug (downsize == val.length(), "Wrong val");
                        it_assert_debug (upsize == val_up.length(), "Wrong val_up");
                        set_subvector (val_up, v2v_up, val);
                        set_subvector (val_up, v2c_up, 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);
                        it_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 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;
        public:
                //!Default constructor
                logger() : entries (0), names (0) {}

                //! 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) = 0;
                //! log this double
                virtual void logit (int id, const double &d) = 0;

                //! Shifts storage position for another time step.
                virtual void step() = 0;

                //! Finalize storing information
                virtual void finalize() {};

                //! Initialize the storage
                virtual void init() {};

};

/*! \brief Unconditional mpdf, allows using epdf in the role of mpdf.

*/
class mepdf : public mpdf
{
                //! Internal shared pointer to epdf
                shared_ptr<epdf> iepdf;
        public:
                //!Default constructor
                mepdf() { }
                //! Set internal shared pointer
                mepdf (shared_ptr<epdf> em) {
                        iepdf = em;
                        set_ep (*iepdf.get());
                        dimc = 0;
                }

                //! empty
                vec samplecond(const vec &cond){return iepdf->sample();}
                double evallogcond(const vec &val, const vec &cond){return iepdf->evallog(val);}

                //! Load from structure with elements:
                //!  \code
                //! { class = "mepdf",
                //!   epdf = {class="epdf_offspring",...}
                //! }
                //! \endcode
                //!@}
                void from_setting (const Setting &set);
};
UIREGISTER (mepdf);
SHAREDPTR (mepdf);

//! \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: (i) data aquisition, (ii) data-preprocessing, (iii) scaling of data, and (iv) 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).

*/

class DS : public root
{
        protected:
                int dtsize;
                int utsize;
                //!Description of data returned by \c getdata().
                RV Drv;
                //!Description of data witten by by \c write().
                RV Urv; //
                //! Remember its own index in Logger L
                int L_dt, L_ut;
        public:
                //! default constructors
                DS() : Drv(), Urv() {};
                //! Returns full vector of observed data=[output, input]
                virtual void getdata (vec &dt) {
                        it_error ("abstract class");
                };
                //! Returns data records at indeces.
                virtual void getdata (vec &dt, const ivec &indeces) {
                        it_error ("abstract class");
                };
                //! Accepts action variable and schedule it for application.
                virtual void write (vec &ut) {
                        it_error ("abstract class");
                };
                //! Accepts action variables at specific indeces
                virtual void write (vec &ut, const ivec &indeces) {
                        it_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() = 0;

                //! Register DS for logging into logger L
                virtual void log_add (logger &L) {
                        it_assert_debug (dtsize == Drv._dsize(), "");
                        it_assert_debug (utsize == Urv._dsize(), "");

                        L_dt = L.add (Drv, "");
                        L_ut = L.add (Urv, "");
                }
                //! Register DS for logging into logger L
                virtual void logit (logger &L) {
                        vec tmp (Drv._dsize() + Urv._dsize());
                        getdata (tmp);
                        // d is first in getdata
                        L.logit (L_dt, tmp.left (Drv._dsize()));
                        // u follows after d in getdata
                        L.logit (L_ut, tmp.mid (Drv._dsize(), Urv._dsize()));
                }
                //!access function
                virtual RV _drv() const {
                        return concat (Drv, Urv);
                }
                //!access function
                const RV& _urv() const {
                        return Urv;
                }
                //! set random rvariables
                virtual void set_drv (const  RV &drv, const RV &urv) {
                        Drv = drv;
                        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 | d_1,\ldots,d_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]

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 conditioned by a known constant, \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]

The value of \f$ c_t \f$ is set by function condition().

*/

class BM : public root
{
        protected:
                //! Random variable of the data (optional)
                RV drv;
                //!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() : ll (0), evalll (true), LIDs (4), LFlags (4) {
                        LIDs = -1;/*empty IDs*/
                        LFlags = 0;
                        LFlags (0) = 1;  /*log only mean*/
                };
                BM (const BM &B) :  drv (B.drv), ll (B.ll), evalll (B.evalll) {}
                //! 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 &dt) = 0;
                //! Batch Bayes rule (columns of Dt are observations)
                virtual void bayesB (const mat &Dt);
                //! Evaluates predictive log-likelihood of the given data record
                //! I.e. marginal likelihood of the data with the posterior integrated out.
                virtual double logpred (const vec &dt) const {
                        it_error ("Not implemented");
                        return 0.0;
                }
                //! Matrix version of logpred
                vec logpred_m (const mat &dt) const {
                        vec tmp (dt.cols());
                        for (int i = 0; i < dt.cols(); i++) {
                                tmp (i) = logpred (dt.get_col (i));
                        }
                        return tmp;
                }

                //!Constructs a predictive density \f$ f(d_{t+1} |d_{t}, \ldots d_{0}) \f$
                virtual epdf* epredictor() const {
                        it_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 {
                        it_error ("Not implemented");
                        return NULL;
                };
                //!@}

                //! \name Extension to conditional BM
                //! This extension is useful e.g. in Marginalized Particle Filter (\ref bdm::MPF).
                //! Alternatively, it can be used for automated connection to DS when the condition is observed
                //!@{

                //! Name of extension variable
                RV rvc;
                //! access function
                const RV& _rvc() const {
                        return rvc;
                }

                //! Substitute \c val for \c rvc.
                virtual void condition (const vec &val) {
                        it_error ("Not implemented!");
                };

                //!@}


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

                const RV& _drv() const {
                        return drv;
                }
                void set_drv (const RV &rv) {
                        drv = rv;
                }
                void set_rv (const RV &rv) {
                        const_cast<epdf&> (posterior()).set_rv (rv);
                }
                double _ll() const {
                        return ll;
                }
                void set_evalll (bool evl0) {
                        evalll = evl0;
                }
                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) {
                        LFlags (0) = 1;
                        if (opt.find ("logbounds") != string::npos) {
                                LFlags (1) = 1;
                                LFlags (2) = 1;
                        }
                        if (opt.find ("logll") != string::npos) {
                                LFlags (3) = 1;
                        }
                }
                //! IDs of storages in loggers 4:[1=mean,2=lb,3=ub,4=ll]
                ivec LIDs;

                //! Flags for logging - same size as LIDs, each entry correspond to the same in LIDs
                ivec LFlags;
                //! Add all logged variables to a logger
                virtual void log_add (logger &L, const string &name = "") {
                        // internal
                        RV r;
                        if (posterior().isnamed()) {
                                r = posterior()._rv();
                        } else {
                                r = RV ("est", posterior().dimension());
                        };

                        // Add mean value
                        if (LFlags (0)) LIDs (0) = L.add (r, name + "mean_");
                        if (LFlags (1)) LIDs (1) = L.add (r, name + "lb_");
                        if (LFlags (2)) LIDs (2) = L.add (r, name + "ub_");
                        if (LFlags (3)) LIDs (3) = L.add (RV ("ll", 1), name);              //TODO: "local" RV
                }
                virtual void logit (logger &L) {
                        L.logit (LIDs (0), posterior().mean());
                        if (LFlags (1) || LFlags (2)) {        //if one of them is off, its LID==-1 and will not be stored
                                vec ub, lb;
                                posterior().qbounds (lb, ub);
                                L.logit (LIDs (1), lb);
                                L.logit (LIDs (2), ub);
                        }
                        if (LFlags (3)) L.logit (LIDs (3), ll);
                }
                //!@}
};

typedef Array<shared_ptr<epdf> > epdf_array;

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 &dt, const vec &cond)
{
        double tmp;
        condition (cond);
        tmp = iepdf.evallog (dt);
        // it_assert_debug(std::isfinite(tmp), "Infinite value");
        return tmp;
}

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

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

}; //namespace
#endif // BDMBASE_H