root/library/bdm/estim/kalman.h @ 681

/*!
  \file
  \brief Bayesian Filtering for linear Gaussian models (Kalman Filter) and extensions
  \author Vaclav Smidl.

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

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

#ifndef KF_H
#define KF_H


#include "../math/functions.h"
#include "../stat/exp_family.h"
#include "../math/chmat.h"
#include "../base/user_info.h"

namespace bdm
{

/*!
 * \brief Basic elements of linear state-space model

Parameter evolution model:\f[ x_t = A x_{t-1} + B u_t + Q^{1/2} e_t \f]
Observation model: \f[ y_t = C x_{t-1} + C u_t + Q^{1/2} w_t. \f]
Where $e_t$ and $w_t$ are independent vectors Normal(0,1)-distributed disturbances.
 */
template<class sq_T>
class StateSpace
{
        protected:
                //! Matrix A
                mat A;
                //! Matrix B
                mat B;
                //! Matrix C
                mat C;
                //! Matrix D
                mat D;
                //! Matrix Q in square-root form
                sq_T Q;
                //! Matrix R in square-root form
                sq_T R;
        public:
                StateSpace() :  A(), B(), C(), D(), Q(), R() {}
                //!copy constructor
                StateSpace(const StateSpace<sq_T> &S0) :  A(S0.A), B(S0.B), C(S0.C), D(S0.D), Q(S0.Q), R(S0.R) {}
                //! set all matrix parameters
                void set_parameters (const mat &A0, const  mat &B0, const  mat &C0, const  mat &D0, const  sq_T &Q0, const sq_T &R0);
                //! validation
                void validate();
                //! not virtual in this case
                void from_setting (const Setting &set) {
                        UI::get (A, set, "A", UI::compulsory);
                        UI::get (B, set, "B", UI::compulsory);
                        UI::get (C, set, "C", UI::compulsory);
                        UI::get (D, set, "D", UI::compulsory);
                        mat Qtm, Rtm;
                        if(!UI::get(Qtm, set, "Q", UI::optional)){
                                vec dq;
                                UI::get(dq, set, "dQ", UI::compulsory);
                                Qtm=diag(dq);
                        }
                        if(!UI::get(Rtm, set, "R", UI::optional)){
                                vec dr;
                                UI::get(dr, set, "dQ", UI::compulsory);
                                Rtm=diag(dr);
                        }
                        R=Rtm; // automatic conversion
                        Q=Qtm; 
                        
                        validate();
                }               
                //! access function
                const mat& _A() const {return A;}
                //! access function
                const mat& _B()const {return B;}
                //! access function
                const mat& _C()const {return C;}
                //! access function
                const mat& _D()const {return D;}
                //! access function
                const sq_T& _Q()const {return Q;}
                //! access function
                const sq_T& _R()const {return R;}
};

//! Common abstract base for Kalman filters 
template<class sq_T>
class Kalman: public BM, public StateSpace<sq_T>
{
        protected:
                //! id of output
                RV yrv;
                //! Kalman gain
                mat  _K;
                //!posterior
                enorm<sq_T> est;
                //!marginal on data f(y|y)
                enorm<sq_T>  fy;
        public:
                Kalman<sq_T>() : BM(), StateSpace<sq_T>(), yrv(), _K(),  est(){}
                //! Copy constructor
                Kalman<sq_T>(const Kalman<sq_T> &K0) : BM(K0), StateSpace<sq_T>(K0), yrv(K0.yrv), _K(K0._K),  est(K0.est), fy(K0.fy){}
                //!set statistics of the posterior
                void set_statistics (const vec &mu0, const mat &P0) {est.set_parameters (mu0, P0); };
                //!set statistics of the posterior
                void set_statistics (const vec &mu0, const sq_T &P0) {est.set_parameters (mu0, P0); };
                //! return correctly typed posterior (covariant return)
                const enorm<sq_T>& posterior() const {return est;}
                //! load basic elements of Kalman from structure
                void from_setting (const Setting &set) {
                        StateSpace<sq_T>::from_setting(set);
                                                
                        mat P0; vec mu0;
                        UI::get(mu0, set, "mu0", UI::optional);
                        UI::get(P0, set,  "P0", UI::optional);
                        set_statistics(mu0,P0);
                        // Initial values
                        UI::get (yrv, set, "yrv", UI::optional);
                        UI::get (rvc, set, "urv", UI::optional);
                        set_yrv(concat(yrv,rvc));
                        
                        validate();
                }
                //! validate object
                void validate() {
                        StateSpace<sq_T>::validate();
                        dimy = this->C.rows();
                        dimc = this->B.cols();
                        set_dim(this->A.rows());
                        
                        bdm_assert(est.dimension(), "Statistics and model parameters mismatch");
                }
};
/*!
* \brief Basic Kalman filter with full matrices
*/

class KalmanFull : public Kalman<fsqmat>
{
        public:
                //! For EKFfull;
                KalmanFull() :Kalman<fsqmat>(){};
                //! Here dt = [yt;ut] of appropriate dimensions
                void bayes (const vec &yt, const vec &cond=empty_vec);
                BM* _copy_() const {
                        KalmanFull* K = new KalmanFull;
                        K->set_parameters (A, B, C, D, Q, R);
                        K->set_statistics (est._mu(), est._R());
                        return K;
                }
};
UIREGISTER(KalmanFull);


/*! \brief Kalman filter in square root form

Trivial example:
\include kalman_simple.cpp

Complete constructor:
*/
class KalmanCh : public Kalman<chmat>
{
        protected:
                //! @{ \name Internal storage - needs initialize()
                //! pre array (triangular matrix)
                mat preA;
                //! post array (triangular matrix)
                mat postA;
                //!@}
        public:
                //! copy constructor
                BM* _copy_() const {
                        KalmanCh* K = new KalmanCh;
                        K->set_parameters (A, B, C, D, Q, R);
                        K->set_statistics (est._mu(), est._R());
                        K->validate();
                        return K;
                }
                //! set parameters for adapt from Kalman
                void set_parameters (const mat &A0, const mat &B0, const mat &C0, const mat &D0, const chmat &Q0, const chmat &R0);
                //! initialize internal parametetrs
                void initialize();

                /*!\brief  Here dt = [yt;ut] of appropriate dimensions

                The following equality hold::\f[
                \left[\begin{array}{cc}
                R^{0.5}\\
                P_{t|t-1}^{0.5}C' & P_{t|t-1}^{0.5}CA'\\
                & Q^{0.5}\end{array}\right]<\mathrm{orth.oper.}>=\left[\begin{array}{cc}
                R_{y}^{0.5} & KA'\\
                & P_{t+1|t}^{0.5}\\
                \\\end{array}\right]\f]

                Thus this object evaluates only predictors! Not filtering densities.
                */
                void bayes (const vec &yt, const vec &cond=empty_vec);

                void from_setting(const Setting &set){
                        Kalman<chmat>::from_setting(set);
                        validate();
                }
                void validate() {
                        Kalman<chmat>::validate();
                        initialize();
                }
};
UIREGISTER(KalmanCh);

/*!
\brief Extended Kalman Filter in full matrices

An approximation of the exact Bayesian filter with Gaussian noices and non-linear evolutions of their mean.
*/
class EKFfull : public KalmanFull
{
        protected:
                //! Internal Model f(x,u)
                shared_ptr<diffbifn> pfxu;

                //! Observation Model h(x,u)
                shared_ptr<diffbifn> phxu;

        public:
                //! Default constructor
                EKFfull ();

                //! Set nonlinear functions for mean values and covariance matrices.
                void set_parameters (const shared_ptr<diffbifn> &pfxu, const shared_ptr<diffbifn> &phxu, const mat Q0, const mat R0);

                //! Here dt = [yt;ut] of appropriate dimensions
                void bayes (const vec &yt, const vec &cond=empty_vec);
                //! set estimates
                void set_statistics (const vec &mu0, const mat &P0) {
                        est.set_parameters (mu0, P0);
                };
                //! access function
                const mat _R() {
                        return est._R().to_mat();
                }
                void from_setting (const Setting &set) {
                        shared_ptr<diffbifn> IM = UI::build<diffbifn> ( set, "IM", UI::compulsory );
                        shared_ptr<diffbifn> OM = UI::build<diffbifn> ( set, "OM", UI::compulsory );
                        
                        //statistics
                        int dim = IM->dimension();
                        vec mu0;
                        if ( !UI::get ( mu0, set, "mu0" ) )
                                mu0 = zeros ( dim );
                        
                        mat P0;
                        vec dP0;
                        if ( UI::get ( dP0, set, "dP0" ) )
                                P0 = diag ( dP0 );
                        else if ( !UI::get ( P0, set, "P0" ) )
                                P0 = eye ( dim );
                        
                        set_statistics ( mu0, P0 );
                        
                        //parameters
                        vec dQ, dR;
                        UI::get ( dQ, set, "dQ", UI::compulsory );
                        UI::get ( dR, set, "dR", UI::compulsory );
                        set_parameters ( IM, OM, diag ( dQ ), diag ( dR ) );
                        
                        //connect
                        shared_ptr<RV> drv = UI::build<RV> ( set, "drv", UI::compulsory );
                        set_yrv ( *drv );
                        shared_ptr<RV> rv = UI::build<RV> ( set, "rv", UI::compulsory );
                        set_rv ( *rv );
                        
                        string options;
                        if ( UI::get ( options, set, "options" ) )
                                set_options ( options );
//                      pfxu = UI::build<diffbifn>(set, "IM", UI::compulsory);
//                      phxu = UI::build<diffbifn>(set, "OM", UI::compulsory);
//                      
//                      mat R0;
//                      UI::get(R0, set, "R",UI::compulsory);
//                      mat Q0;
//                      UI::get(Q0, set, "Q",UI::compulsory);
//                      
//                      
//                      mat P0; vec mu0;
//                      UI::get(mu0, set, "mu0", UI::optional);
//                      UI::get(P0, set,  "P0", UI::optional);
//                      set_statistics(mu0,P0);
//                      // Initial values
//                      UI::get (yrv, set, "yrv", UI::optional);
//                      UI::get (urv, set, "urv", UI::optional);
//                      set_drv(concat(yrv,urv));
// 
//                      // setup StateSpace
//                      pfxu->dfdu_cond(mu0, zeros(pfxu->_dimu()), A,true);
//                      phxu->dfdu_cond(mu0, zeros(pfxu->_dimu()), C,true);
//                      
                        validate();
                }
                void validate() {
                        // check stats and IM and OM
                }
};
UIREGISTER(EKFfull);


/*!
\brief Extended Kalman Filter in Square root

An approximation of the exact Bayesian filter with Gaussian noices and non-linear evolutions of their mean.
*/

class EKFCh : public KalmanCh
{
        protected:
                //! Internal Model f(x,u)
                shared_ptr<diffbifn> pfxu;

                //! Observation Model h(x,u)
                shared_ptr<diffbifn> phxu;
        public:
                //! copy constructor duplicated - calls different set_parameters
                BM* _copy_() const {
                        EKFCh* E = new EKFCh;
                        E->set_parameters (pfxu, phxu, Q, R);
                        E->set_statistics (est._mu(), est._R());
                        return E;
                }
                //! Set nonlinear functions for mean values and covariance matrices.
                void set_parameters (const shared_ptr<diffbifn> &pfxu, const shared_ptr<diffbifn> &phxu, const chmat Q0, const chmat R0);

                //! Here dt = [yt;ut] of appropriate dimensions
                void bayes (const vec &yt, const vec &cond=empty_vec);

                void from_setting (const Setting &set);

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

};

UIREGISTER (EKFCh);
SHAREDPTR (EKFCh);


//////// INstance

/*! \brief (Switching) Multiple Model
The model runs several models in parallel and evaluates thier weights (fittness).

The statistics of the resulting density are merged using (geometric?) combination.

The next step is performed with the new statistics for all models.
*/
class MultiModel: public BM
{
        protected:
                //! List of models between which we switch
                Array<EKFCh*> Models;
                //! vector of model weights
                vec w;
                //! cache of model lls
                vec _lls;
                //! type of switching policy [1=maximum,2=...]
                int policy;
                //! internal statistics
                enorm<chmat> est;
        public:
                //! set internal parameters
                void set_parameters (Array<EKFCh*> A, int pol0 = 1) {
                        Models = A;//TODO: test if evalll is set
                        w.set_length (A.length());
                        _lls.set_length (A.length());
                        policy = pol0;

                        est.set_rv (RV ("MM", A (0)->posterior().dimension(), 0));
                        est.set_parameters (A (0)->posterior().mean(), A (0)->posterior()._R());
                }
                void bayes (const vec &yt, const vec &cond=empty_vec) {
                        int n = Models.length();
                        int i;
                        for (i = 0; i < n; i++) {
                                Models (i)->bayes (yt);
                                _lls (i) = Models (i)->_ll();
                        }
                        double mlls = max (_lls);
                        w = exp (_lls - mlls);
                        w /= sum (w);   //normalization
                        //set statistics
                        switch (policy) {
                                case 1: {
                                        int mi = max_index (w);
                                        const enorm<chmat> &st = Models (mi)->posterior() ;
                                        est.set_parameters (st.mean(), st._R());
                                }
                                break;
                                default:
                                        bdm_error ("unknown policy");
                        }
                        // copy result to all models
                        for (i = 0; i < n; i++) {
                                Models (i)->set_statistics (est.mean(), est._R());
                        }
                }
                //! return correctly typed posterior (covariant return)
                const enorm<chmat>& posterior() const {
                        return est;
                }

                void from_setting (const Setting &set);

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

};

UIREGISTER (MultiModel);
SHAREDPTR (MultiModel);

//! conversion of outer ARX model (mlnorm) to state space model 
/*!
The model is constructed as:
\f[ x_{t+1} = Ax_t + B u_t + R^{1/2} e_t, y_t=Cx_t+Du_t + R^{1/2}w_t, \f]
For example, for:
Using Frobenius form, see [].

For easier use in the future, indeces theta_in_A and theta_in_C are set. TODO - explain
*/
//template<class sq_T>
class StateCanonical: public StateSpace<fsqmat>{
        protected:
                //! remember connection from theta ->A
                datalink_part th2A;
                //! remember connection from theta ->C
                datalink_part th2C;
                //! remember connection from theta ->D
                datalink_part th2D;
                //!cached first row of A
                vec A1row;
                //!cached first row of C
                vec C1row;
                //!cached first row of D
                vec D1row;
                
        public:
                //! set up this object to match given mlnorm
                void connect_mlnorm(const mlnorm<fsqmat> &ml){
                        //get ids of yrv                                
                        const RV &yrv = ml._rv();
                        //need to determine u_t - it is all in _rvc that is not in ml._rv()
                        RV rgr0 = ml._rvc().remove_time();
                        RV urv = rgr0.subt(yrv); 
                        
                        //We can do only 1d now... :(
                        bdm_assert(yrv._dsize()==1, "Only for SISO so far..." );

                        // create names for 
                        RV xrv; //empty
                        RV Crv; //empty
                        int td=ml._rvc().mint();
                        // assuming strictly proper function!!!
                        for (int t=-1;t>=td;t--){
                                xrv.add(yrv.copy_t(t));
                                Crv.add(urv.copy_t(t));
                        }
                                                
                        // get mapp
                        th2A.set_connection(xrv, ml._rvc());
                        th2C.set_connection(Crv, ml._rvc());
                        th2D.set_connection(urv, ml._rvc());

                        //set matrix sizes
                        this->A=zeros(xrv._dsize(),xrv._dsize());
                        for (int j=1; j<xrv._dsize(); j++){A(j,j-1)=1.0;} // off diagonal
                                this->B=zeros(xrv._dsize(),1);
                                this->B(0) = 1.0;
                                this->C=zeros(1,xrv._dsize());
                                this->D=zeros(1,urv._dsize());
                                this->Q = zeros(xrv._dsize(),xrv._dsize());
                        // R is set by update
                        
                        //set cache
                        this->A1row = zeros(xrv._dsize());
                        this->C1row = zeros(xrv._dsize());
                        this->D1row = zeros(urv._dsize());
                        
                        update_from(ml);
                        validate();
                };
                //! fast function to update parameters from ml - not checked for compatibility!!
                void update_from(const mlnorm<fsqmat> &ml){
                        
                        vec theta = ml._A().get_row(0); // this 
                        
                        th2A.filldown(theta,A1row);
                        th2C.filldown(theta,C1row);
                        th2D.filldown(theta,D1row);

                        R = ml._R();

                        A.set_row(0,A1row);
                        C.set_row(0,C1row+D1row*A1row);
                        D.set_row(0,D1row);
                        
                }
};

/////////// INSTANTIATION

template<class sq_T>
void StateSpace<sq_T>::set_parameters (const mat &A0, const  mat &B0, const  mat &C0, const  mat &D0, const  sq_T &Q0, const sq_T &R0)
{

        A = A0;
        B = B0;
        C = C0;
        D = D0;
        R = R0;
        Q = Q0;
        validate();
}

template<class sq_T>
void StateSpace<sq_T>::validate(){
        bdm_assert (A.cols() == A.rows(), "KalmanFull: A is not square");
        bdm_assert (B.rows() == A.rows(), "KalmanFull: B is not compatible");
        bdm_assert (C.cols() == A.rows(), "KalmanFull: C is not compatible");
        bdm_assert ( (D.rows() == C.rows()) && (D.cols() == B.cols()), "KalmanFull: D is not compatible");
        bdm_assert ( (Q.cols() == A.rows()) && (Q.rows() == A.rows()), "KalmanFull: Q is not compatible");
        bdm_assert ( (R.cols() == C.rows()) && (R.rows() == C.rows()), "KalmanFull: R is not compatible");
}

}
#endif // KF_H