#include <math.h>

#include <itpp/base/bessel.h>
#include "exp_family.h"

namespace bdm {

Uniform_RNG UniRNG;
Normal_RNG NorRNG;
Gamma_RNG GamRNG;

using std::cout;

///////////

void BMEF::bayes ( const vec &yt, const vec &cond ) {
	this->bayes_weighted ( yt, cond, 1.0 );
};

void egiw::set_parameters ( int dimx0, ldmat V0, double nu0 ) {
	dimx = dimx0;
	nPsi = V0.rows() - dimx;
	dim = dimx * ( dimx + nPsi ); // size(R) + size(Theta)

	V = V0;
	if ( nu0 < 0 ) {
		nu = 0.1 + nPsi + 2 * dimx + 2; // +2 assures finite expected value of R
		// terms before that are sufficient for finite normalization
	} else {
		nu = nu0;
	}
}

vec egiw::sample() const {
	mat M;
	chmat R;
	sample_mat ( M, R );

	return concat ( cvectorize ( M ), cvectorize ( R.to_mat() ) );
}

mat egiw::sample_mat ( int n ) const {
	// TODO - correct approach - convert to product of norm * Wishart
	mat M;
	ldmat Vz;
	ldmat Lam;
	factorize ( M, Vz, Lam );

	chmat ChLam ( Lam.to_mat() );
	chmat iChLam;
	ChLam.inv ( iChLam );

	eWishartCh Omega; //inverse Wishart, result is R,
	Omega.set_parameters ( iChLam, nu - 2*nPsi - dimx ); // 2*nPsi is there to match numercial simulations - check if analytically correct

	mat OmChi;
	mat Z ( M.rows(), M.cols() );

	mat Mi;
	mat RChiT;
	mat tmp ( dimension(), n );
	for ( int i = 0; i < n; i++ ) {
		OmChi = Omega.sample_mat();
		RChiT = inv ( OmChi );
		Z = randn ( M.rows(), M.cols() );
		Mi = M + RChiT * Z * inv ( Vz._L().T() * diag ( sqrt ( Vz._D() ) ) );

		tmp.set_col ( i, concat ( cvectorize ( Mi ), cvectorize ( RChiT*RChiT.T() ) ) );
	}
	return tmp;
}

void egiw::sample_mat ( mat &Mi, chmat &Ri ) const {

	// TODO - correct approach - convert to product of norm * Wishart
	mat M;
	ldmat Vz;
	ldmat Lam;
	factorize ( M, Vz, Lam );

	chmat Ch;
	Ch.setCh ( Lam._L() *diag ( sqrt ( Lam._D() ) ) );
	chmat iCh;
	Ch.inv ( iCh );

	eWishartCh Omega; //inverse Wishart, result is R,
	Omega.set_parameters ( iCh, nu - 2*nPsi - dimx ); // 2*nPsi is there to match numercial simulations - check if analytically correct

	chmat Omi;
	Omi.setCh ( Omega.sample_mat() );

	if (M._datasize()>0){
		mat Z = randn ( M.rows(), M.cols() );
		Mi = M + Omi._Ch() * Z * inv ( Vz._L() * diag ( sqrt ( Vz._D() ) ) );
	}
	Omi.inv ( Ri );
}

double egiw::evallog_nn ( const vec &val ) const {
	bdm_assert_debug(val.length()==dimx*(nPsi+dimx),"Incorrect cond in egiw::evallog_nn" );
	
	int vend = val.length() - 1;

	if ( dimx == 1 ) { //same as the following, just quicker.
		double r = val ( vend ); //last entry!
		if ( r < 0 ) return -inf;
		vec Psi ( nPsi + dimx );
		Psi ( 0 ) = -1.0;
		Psi.set_subvector ( 1, val ( 0, vend - 1 ) ); // fill the rest

		double Vq = V.qform ( Psi );
		return -0.5* ( nu*log ( r ) + Vq / r );
	} else {
		mat Tmp;
		if (nPsi>0){
			mat Th = reshape ( val ( 0, nPsi * dimx - 1 ), nPsi, dimx );
			Tmp = concat_vertical ( -eye ( dimx ), Th );
		} else {
			Tmp = -eye(dimx);
		}
		fsqmat R ( reshape ( val ( nPsi*dimx, vend ), dimx, dimx ) );
		double ldetR = R.logdet();
		if ( !isfinite(ldetR) ) return -inf;
		fsqmat iR ( dimx );
		R.inv ( iR );

		return -0.5* ( nu*ldetR + trace ( iR.to_mat() *Tmp.T() *V.to_mat() *Tmp ) );
	}
}

double egiw::lognc() const {
	const vec& D = V._D();

	double m = nu - nPsi - dimx - 1;
#define	log2  0.693147180559945286226763983
#define	logpi 1.144729885849400163877476189
#define log2pi 1.83787706640935
#define Inf std::numeric_limits<double>::infinity()

	double nkG = 0.5 * dimx * ( -nPsi * log2pi + sum ( log ( D.mid ( dimx, nPsi ) ) ) );
	// temporary for lgamma in Wishart
	double lg = 0;
	for ( int i = 0; i < dimx; i++ ) {
		lg += lgamma ( 0.5 * ( m - i ) );
	}

	double nkW = 0.5 * ( m * sum ( log ( D ( 0, dimx - 1 ) ) ) ) \
	             - 0.5 * dimx * ( m * log2 + 0.5 * ( dimx - 1 ) * log2pi )  - lg;

//	bdm_assert_debug ( ( ( -nkG - nkW ) > -Inf ) && ( ( -nkG - nkW ) < Inf ), "ARX improper" );
	if ( -nkG - nkW == Inf ) {
		cout << "??" << endl;
	}
	return -nkG - nkW;
}

vec egiw::est_theta() const {
	if ( dimx == 1 ) {
		const mat &L = V._L();
		int end = L.rows() - 1;

		mat iLsub = ltuinv ( L ( dimx, end, dimx, end ) );

		vec L0 = L.get_col ( 0 );

		return iLsub * L0 ( 1, end );
	} else {
		bdm_error ( "ERROR: est_theta() not implemented for dimx>1" );
		return vec();
	}
}

void egiw::factorize ( mat &M, ldmat &Vz, ldmat &Lam ) const {
	const mat &L = V._L();
	const vec &D = V._D();
	int end = L.rows() - 1;

	Lam = ldmat ( L ( 0, dimx - 1, 0, dimx - 1 ), D ( 0, dimx - 1 ) );  //exp val of R

	if (dimx<=end){
		Vz = ldmat ( L ( dimx, end, dimx, end ), D ( dimx, end ) );
		mat iLsub = ltuinv ( Vz._L() );
		// set mean value
		mat Lpsi = L ( dimx, end, 0, dimx - 1 );
		M = iLsub * Lpsi;
	}
/*	if ( 0 ) { // test with Peterka
		mat VF = V.to_mat();
		mat Vf = VF ( 0, dimx - 1, 0, dimx - 1 );
		mat Vzf = VF ( dimx, end, 0, dimx - 1 );
		mat VZ = VF ( dimx, end, dimx, end );

		mat Lam2 = Vf - Vzf.T() * inv ( VZ ) * Vzf;
	}*/
}

ldmat egiw::est_theta_cov() const {
	if ( dimx == 1 ) {
		const mat &L = V._L();
		const vec &D = V._D();
		int end = D.length() - 1;

		mat Lsub = L ( 1, end, 1, end );
//		mat Dsub = diag ( D ( 1, end ) );

		ldmat LD ( inv ( Lsub ).T(), 1.0 / D ( 1, end ) );
		return LD;

	} else {
		bdm_error ( "ERROR: est_theta_cov() not implemented for dimx>1" );
		return ldmat();
	}

}

vec egiw::mean() const {

	if ( dimx == 1 ) {
		const vec &D = V._D();
		int end = D.length() - 1;

		vec m ( dim );
		m.set_subvector ( 0, est_theta() );
		m ( end ) = D ( 0 ) / ( nu - nPsi - 2 * dimx - 2 );
		return m;
	} else {
		mat M;
		mat R;
		mean_mat ( M, R );
		return concat ( cvectorize ( M ), cvectorize ( R ) );
	}

}

vec egiw::variance() const {
	int l = V.rows();
	// cut out rest of lower-right part of V
	// invert it
	ldmat itmp ( l );
	if (dimx<l){
		const ldmat tmp ( V, linspace ( dimx, l - 1 ) );
		tmp.inv ( itmp );
	}
	// following Wikipedia notation
	// m=nu-nPsi-dimx-1, p=dimx
	double mp1p = nu - nPsi - 2 * dimx; // m-p+1
	double mp1m = mp1p - 2;     // m-p-1

	if ( dimx == 1 ) {
		double cove = V._D() ( 0 ) / mp1m ;

		vec var ( l );
		var.set_subvector ( 0, diag ( itmp.to_mat() ) *cove );
		var ( l - 1 ) = cove * cove / ( mp1m - 2 );
		return var;
	} else {
		ldmat Vll ( V, linspace ( 0, dimx - 1 ) ); // top-left part of V
		mat Y = Vll.to_mat();
		mat varY ( Y.rows(), Y.cols() );

		double denom = ( mp1p - 1 ) * mp1m * mp1m * ( mp1m - 2 );         // (m-p)(m-p-1)^2(m-p-3)

		int i, j;
		for ( i = 0; i < Y.rows(); i++ ) {
			for ( j = 0; j < Y.cols(); j++ ) {
				varY ( i, j ) = ( mp1p * Y ( i, j ) * Y ( i, j ) + mp1m * Y ( i, i ) * Y ( j, j ) ) / denom;
			}
		}
		vec mean_dR = diag ( Y ) / mp1m; // corresponds to cove
		vec var_th = diag ( itmp.to_mat() );
		vec var_Th ( mean_dR.length() *var_th.length() );
		// diagonal of diag(mean_dR) \kron diag(var_th)
		for ( int i = 0; i < mean_dR.length(); i++ ) {
			var_Th.set_subvector ( i*var_th.length(), var_th*mean_dR ( i ) );
		}

		return concat ( var_Th, cvectorize ( varY ) );
	}
}

void egiw::mean_mat ( mat &M, mat&R ) const {
	const mat &L = V._L();
	const vec &D = V._D();
	int end = L.rows() - 1;

	ldmat ldR ( L ( 0, dimx - 1, 0, dimx - 1 ), D ( 0, dimx - 1 ) / ( nu - nPsi - 2*dimx - 2 ) ); //exp val of R

	// set mean value
	if (dimx<=end){
		mat iLsub = ltuinv ( L ( dimx, end, dimx, end ) );
		mat Lpsi = L ( dimx, end, 0, dimx - 1 );
		M = iLsub * Lpsi;
	}
	R = ldR.to_mat()  ;
}

void egiw::log_register ( bdm::logger& L, const string& prefix ) {
	if ( log_level == 3 ) {
		root::log_register ( L, prefix );
		logrec->ids.set_length ( 2 );
		int th_dim = dimension() - dimx * ( dimx + 1 ) / 2;
		logrec->ids ( 0 ) = L.add_vector ( RV ( "", th_dim ), prefix + logrec->L.prefix_sep() + "mean" );
		logrec->ids ( 1 ) = L.add_vector ( RV ( "", th_dim * th_dim ), prefix + logrec->L.prefix_sep() + "variance" );
	} else {
		epdf::log_register ( L, prefix );
	}
}

void egiw::log_write() const {
	if ( log_level == 3 ) {
		mat M;
		ldmat Lam;
		ldmat Vz;
		factorize ( M, Vz, Lam );
		logrec->L.log_vector ( logrec->ids ( 0 ), est_theta() );
		logrec->L.log_vector ( logrec->ids ( 1 ), cvectorize ( est_theta_cov().to_mat() ) );
	} else {
		epdf::log_write();
	}

}

void multiBM::bayes ( const vec &yt, const vec &cond ) {
	if ( frg < 1.0 ) {
		beta *= frg;
		last_lognc = est.lognc();
	}
	beta += yt;
	if ( evalll ) {
		ll = est.lognc() - last_lognc;
	}
}

double multiBM::logpred ( const vec &yt ) const {
	eDirich pred ( est );
	vec &beta = pred._beta();

	double lll;
	if ( frg < 1.0 ) {
		beta *= frg;
		lll = pred.lognc();
	} else if ( evalll ) {
		lll = last_lognc;
	} else {
		lll = pred.lognc();
	}

	beta += yt;
	return pred.lognc() - lll;
}
void multiBM::flatten ( const BMEF* B ) {
	const multiBM* E = dynamic_cast<const multiBM*> ( B );
	// sum(beta) should be equal to sum(B.beta)
	const vec &Eb = E->beta;//const_cast<multiBM*> ( E )->_beta();
	beta *= ( sum ( Eb ) / sum ( beta ) );
	if ( evalll ) {
		last_lognc = est.lognc();
	}
}

vec egamma::sample() const {
	vec smp ( dim );
	int i;

	for ( i = 0; i < dim; i++ ) {
		if ( beta ( i ) > std::numeric_limits<double>::epsilon() ) {
			GamRNG.setup ( alpha ( i ), beta ( i ) );
		} else {
			GamRNG.setup ( alpha ( i ), std::numeric_limits<double>::epsilon() );
		}
#pragma omp critical
		smp ( i ) = GamRNG();
	}

	return smp;
}

// mat egamma::sample ( int N ) const {
// 	mat Smp ( rv.count(),N );
// 	int i,j;
//
// 	for ( i=0; i<rv.count(); i++ ) {
// 		GamRNG.setup ( alpha ( i ),beta ( i ) );
//
// 		for ( j=0; j<N; j++ ) {
// 			Smp ( i,j ) = GamRNG();
// 		}
// 	}
//
// 	return Smp;
// }

double egamma::evallog ( const vec &val ) const {
	double res = 0.0; //the rest will be added
	int i;

	if ( any ( val <= 0. ) ) return -inf;
	if ( any ( beta <= 0. ) ) return -inf;
	for ( i = 0; i < dim; i++ ) {
		res += ( alpha ( i ) - 1 ) * std::log ( val ( i ) ) - beta ( i ) * val ( i );
	}
	double tmp = res - lognc();;
	bdm_assert_debug ( std::isfinite ( tmp ), "Infinite value" );
	return tmp;
}

double egamma::lognc() const {
	double res = 0.0; //will be added
	int i;

	for ( i = 0; i < dim; i++ ) {
		res += lgamma ( alpha ( i ) ) - alpha ( i ) * std::log ( beta ( i ) ) ;
	}

	return res;
}

void mgamma::set_parameters ( double k0, const vec &beta0 ) {
	k = k0;
	iepdf.set_parameters ( k * ones ( beta0.length() ), beta0 );
	dimc = iepdf.dimension();
	dim = iepdf.dimension();
}

void eEmp::resample ( ivec &ind, RESAMPLING_METHOD method ) {
	ind = zeros_i ( n );
	ivec N_babies = zeros_i ( n );
	vec cumDist = cumsum ( w );
	vec u ( n );
	int i, j, parent;
	double u0;

	switch ( method ) {
	case MULTINOMIAL:
		u ( n - 1 ) = pow ( UniRNG.sample(), 1.0 / n );

		for ( i = n - 2; i >= 0; i-- ) {
			u ( i ) = u ( i + 1 ) * pow ( UniRNG.sample(), 1.0 / ( i + 1 ) );
		}

		break;

	case STRATIFIED:

		for ( i = 0; i < n; i++ ) {
			u ( i ) = ( i + UniRNG.sample() ) / n;
		}

		break;

	case SYSTEMATIC:
		u0 = UniRNG.sample();

		for ( i = 0; i < n; i++ ) {
			u ( i ) = ( i + u0 ) / n;
		}

		break;

	default:
		bdm_error ( "PF::resample(): Unknown resampling method" );
	}

	// U is now full
	j = 0;

	for ( i = 0; i < n; i++ ) {
		while ( u ( i ) > cumDist ( j ) ) j++;

		N_babies ( j ) ++;
	}
	// We have assigned new babies for each Particle
	// Now, we fill the resulting index such that:
	// * particles with at least one baby should not move *
	// This assures that reassignment can be done inplace;

	// find the first parent;
	parent = 0;
	while ( N_babies ( parent ) == 0 ) parent++;

	// Build index
	for ( i = 0; i < n; i++ ) {
		if ( N_babies ( i ) > 0 ) {
			ind ( i ) = i;
			N_babies ( i ) --; //this index was now replicated;
		} else {
			// test if the parent has been fully replicated
			// if yes, find the next one
			while ( ( N_babies ( parent ) == 0 ) || ( N_babies ( parent ) == 1 && parent > i ) ) parent++;

			// Replicate parent
			ind ( i ) = parent;

			N_babies ( parent ) --; //this index was now replicated;
		}

	}

// copy the internals according to ind
	for ( i = 0; i < n; i++ ) {
		if ( ind ( i ) != i ) {
			samples ( i ) = samples ( ind ( i ) );
		}
		w ( i ) = 1.0 / n;
	}
}

void eEmp::set_statistics ( const vec &w0, const epdf &epdf0 ) {
	dim = epdf0.dimension();
	w = w0;
	w /= sum ( w0 );//renormalize
	n = w.length();
	samples.set_size ( n );

	for ( int i = 0; i < n; i++ ) {
		samples ( i ) = epdf0.sample();
	}
}

void eEmp::set_samples ( const epdf* epdf0 ) {
	w = 1;
	w /= sum ( w );//renormalize

	for ( int i = 0; i < n; i++ ) {
		samples ( i ) = epdf0->sample();
	}
}

void migamma_ref::from_setting ( const Setting &set ) {
	vec ref;
	UI::get ( ref, set, "ref" , UI::compulsory );
	set_parameters ( set["k"], ref, set["l"] );
}

void mlognorm::from_setting ( const Setting &set ) {
	vec mu0;
	UI::get ( mu0, set, "mu0", UI::compulsory );
	set_parameters ( mu0.length(), set["k"] );
	condition ( mu0 );
}

void mlstudent::condition ( const vec &cond ) {
	if ( cond.length() > 0 ) {
		iepdf._mu() = A * cond + mu_const;
	} else {
		iepdf._mu() =  mu_const;
	}
	double zeta;
	//ugly hack!
	if ( ( cond.length() + 1 ) == Lambda.rows() ) {
		zeta = Lambda.invqform ( concat ( cond, vec_1 ( 1.0 ) ) );
	} else {
		zeta = Lambda.invqform ( cond );
	}
	_R = Re;
	_R *= ( 1 + zeta );// / ( nu ); << nu is in Re!!!!!!
}

void eEmp::qbounds ( vec &lb, vec &ub, double perc ) const {
	// lb in inf so than it will be pushed below;
	lb.set_size ( dim );
	ub.set_size ( dim );
	lb = std::numeric_limits<double>::infinity();
	ub = -std::numeric_limits<double>::infinity();
	int j;
	for ( int i = 0; i < n; i++ ) {
		for ( j = 0; j < dim; j++ ) {
			if ( samples ( i ) ( j ) < lb ( j ) ) {
				lb ( j ) = samples ( i ) ( j );
			}
			if ( samples ( i ) ( j ) > ub ( j ) ) {
				ub ( j ) = samples ( i ) ( j );
			}
		}
	}
}


};
