/*!
  \file
  \brief Bayesian Filtering for generalized autoregressive (ARX) model
  \author Vaclav Smidl.

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

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

#ifndef AR_H
#define AR_H

#include "../math/functions.h"
#include "../stat/exp_family.h"
#include "../base/user_info.h"
//#include "../estim/kalman.h"
#include "arx_straux.h"

namespace bdm {

/*!
* \brief Linear Autoregressive model with Gaussian noise

Regression of the following kind:
\f[
y_t = \theta_1 \psi_1 + \theta_2 + \psi_2 +\ldots + \theta_n \psi_n + r e_t
\f]
where unknown parameters \c rv are \f$[\theta r]\f$, regression vector \f$\psi=\psi(y_{1:t},u_{1:t})\f$ is a known function of past outputs and exogeneous variables \f$u_t\f$. Distrubances \f$e_t\f$ are supposed to be normally distributed:
\f[
e_t \sim \mathcal{N}(0,1).
\f]

See \ref tut_arx for mathematical treatment.

The easiest way how to use the class is:
\include arx_simple.cpp

	\todo sort out constant terms - bayes should accept vec without additional 1s
*/
class ARX: public BMEF {
protected:
	//!size of output variable (needed in regressors)
	int dimx;
	//!description of modelled data \f$ y_t \f$ in the likelihood function
	//! Do NOT access directly, only via \c get_yrv().
	RV _yrv;
	//! rv of regressor
	RV rgrrv;
	//! Posterior estimate of \f$\theta,r\f$ in the form of Normal-inverse Wishart density
	egiw est;
	//! cached value of est.V
	ldmat &V;
	//! cached value of est.nu
	double ν
	//! switch if constant is modelled or not
	bool have_constant;
	//! cached value of data vector for have_constant =true
	vec _dt;
	//! Alternative estimate of parameters, used in stabilized forgetting, see [Kulhavy]
	egiw alter_est;
public:
	//! \name Constructors
	//!@{
	ARX ( const double frg0 = 1.0 ) : BMEF ( frg0 ), est (), V ( est._V() ), nu ( est._nu() ), have_constant(true), _dt() {};
	ARX ( const ARX &A0 ) : BMEF (A0.frg), est (A0.est), V ( est._V() ), nu ( est._nu() ), have_constant(A0.have_constant), _dt(A0._dt) {
		dimx = A0.dimx;
		_yrv = A0._yrv;
		rgrrv = A0.rgrrv;
		set_drv(A0._drv());
	};
	ARX* _copy_() const;
	void set_parameters ( double frg0 ) {
		frg = frg0;
	}
	void set_constant ( bool const0 ) {
		have_constant=const0;
	}
	void set_statistics ( int dimx0, const ldmat V0, double nu0 = -1.0 ) {
		est.set_parameters ( dimx0, V0, nu0 );
		last_lognc = est.lognc();
		dimx = dimx0;
	}
	//!@}

	//! Set sufficient statistics
	void set_statistics ( const BMEF* BM0 );

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

	//! Weighted Bayes \f$ dt = [y_t psi_t] \f$.
	void bayes ( const vec &dt, const double w );
	void bayes ( const vec &dt ) {
		bayes ( dt, 1.0 );
	};
	double logpred ( const vec &dt ) const;
	void flatten ( const BMEF* B ) {
		const ARX* A = dynamic_cast<const ARX*> ( B );
		// nu should be equal to B.nu
		est.pow ( A->nu / nu );
		if ( evalll ) {
			last_lognc = est.lognc();
		}
	}
	//! Conditioned version of the predictor
	enorm<ldmat>* epredictor ( const vec &rgr ) const;
	//! Predictor for empty regressor
	enorm<ldmat>* epredictor() const {
		bdm_assert_debug ( dimx == V.rows() - 1, "Regressor is not only 1" );
		return epredictor ( vec_1 ( 1.0 ) );
	}
	//! conditional version of the predictor
	mlnorm<ldmat>* predictor() const;
	mlstudent* predictor_student() const;
	//! Brute force structure estimation.\return indeces of accepted regressors.
	ivec structure_est ( egiw Eg0 );
	//! Smarter structure estimation by Ludvik Tesar.\return indeces of accepted regressors.
	ivec structure_est_LT ( egiw Eg0 );
	//!@}

	//!\name Access attributes
	//!@{
		//! return correctly typed posterior (covariant return)
		const egiw& posterior() const {
		return est;
	}
	//!@}

	//!\name Connection
	//!@{
	void set_rv ( const RV &yrv0 , const RV &rgrrv0 ) {
		_yrv = yrv0;
		rgrrv=rgrrv0;
		set_drv(concat(yrv0, rgrrv));
	}

	RV& get_yrv() {
		//if yrv is not ready create it
		if ( _yrv._dsize() != dimx ) {
			int i = 0;
			while ( _yrv._dsize() < dimx ) {
				_yrv.add ( drv ( vec_1 ( i ) ) );
				i++;
			}
		}
		//yrv should be ready by now
		bdm_assert_debug ( _yrv._dsize() == dimx, "incompatible drv" );
		return _yrv;
	}
	//!@}

	/*! UI for ARX estimator

	\code
	class = 'ARX';
	rv    = RV({names_of_dt} )                 // description of output variables
	rgr   = RV({names_of_regressors}, [-1,-2]} // description of regressor variables
	constant = 1;                              // 0/1 switch if the constant term is modelled or not

	--- optional ---
	prior = {class='egiw',...};                // Prior density, when given default is used instead
	alternative = {class='egiw',...};          // Alternative density in stabilized estimation, when not given prior is used
	
	frg = 1.0;                                 // forgetting, default frg=1.0

	rv_param   = RV({names_of_parameters}}     // description of parametetr names 
											   // default: ["theta_i" and "r_i"]
	\endcode
	*/
	void from_setting ( const Setting &set );

	void validate() {
		bdm_assert(dimx == _yrv._dsize(), "RVs of parameters and regressor do not match");
		
	}
	//! function sets prior and alternative density 
	void set_prior(const RV &drv, egiw &prior){
		//TODO check ranges in RV and build prior
	};
	//! build default prior and alternative when all values are set
	void set_prior_default(egiw &prior){
		//assume 
		vec dV0(prior._V().rows());
		dV0.set_subvector(0,prior._dimx()-1, 1.0);
		dV0.set_subvector(prior._dimx(),dV0.length()-1, 1e-5);
		
		prior.set_parameters(prior._dimx(),ldmat(dV0));
	}
};

UIREGISTER ( ARX );
SHAREDPTR ( ARX );

/*! ARX model conditined by knowledge of the forgetting factor
\f[ f(\theta| d_1 \ldots d_t , \phi_t) \f]
*/
class ARXfrg : public ARX{
	public:
		ARXfrg():ARX(){};
		//! copy constructor
		ARXfrg(const ARXfrg &A0):ARX(A0){};
		ARXfrg* _copy_() const {ARXfrg *A = new ARXfrg(*this); return A;}
	void condition(const vec &val){
		frg = val(0);
	}
};
UIREGISTER(ARXfrg);
};
#endif // AR_H