/*  mcmc_mh.cc

    Mark Woolrich, Tim Behrens, FMRIB Image Analysis Group

    Copyright (C) 2002 University of Oxford  */

/*  Part of FSL - FMRIB's Software Library
    http://www.fmrib.ox.ac.uk/fsl
    fsl@fmrib.ox.ac.uk
    
    Developed at FMRIB (Oxford Centre for Functional Magnetic Resonance
    Imaging of the Brain), Department of Clinical Neurology, Oxford
    University, Oxford, UK
    
    
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#include "mcmc_mh.h"
#include "utils/log.h"
#include "miscmaths/miscmaths.h"
#include "miscmaths/miscprob.h"
#include "newimage/newimageall.h"
#include "utils/tracer_plus.h"
#include <set>

using namespace Utilities;
using namespace MISCMATHS;
using namespace NEWIMAGE;

namespace Gs {


  void Mcmc_Mh::setup()
  {
    Tracer_Plus trace("Mcmc_Mh::setup");
    
    beta_naccepted = 0;
    phi_naccepted = 0;
    gamma_naccepted = 0;
    beta_nrejected = 0;
    phi_nrejected = 0;
    gamma_nrejected = 0;

    gamma_latest.ReSize(nevs);
    gamma_samples.ReSize(nevs,nsamples);
    beta_latest.ReSize(ngs);
    beta_samples.ReSize(ngs,nsamples);
    phi_latest.ReSize(ntpts);
    phi_samples.ReSize(ntpts,nsamples);
    likelihood_samples.ReSize(nsamples);
    likelihood_samples = 0;

    Matrix gamC;
    reshape(gamC, gamma_S, nevs, nevs); // gamC is Covariance
    
    gamma_latest = gamma_mean;
    gamma_proposal_std = sqrt(diag(gamC))*8;
    gamma_samples = 0;

    for(int g = 1; g <= ngs; g++)
      {
//      // use when sampling from precision
// 	  beta_latest(g) = 1.0/(beta_b(g)/beta_c(g));

// 	beta_proposal_std(g) = 4.0/(sqrt(beta_b(g)/Sqr(beta_c(g))));

// 	// use when sampling from variance
	beta_latest(g) = beta_b(g)/beta_c(g);

	beta_proposal_std(g) = 4.0*(sqrt(beta_b(g)/Sqr(beta_c(g))));

	// use when sampling from log(variance)
// 	  beta_latest(g) = log((beta_b(g)/beta_c(g)));

// 	beta_proposal_std(g) = fabs(log(4.0*(sqrt(beta_b(g)/Sqr(beta_c(g))))));

      }

    for(int t = 1; t <= ntpts; t++)
      {
	phi_latest(t) = varcopedata(t);

	if(opts.dofvarcopefile.value() != string(""))
	  phi_proposal_std(t) = sqrt(2*Sqr(varcopedata(t))/dofvarcopedata(t))/2;
      }

    beta_samples = 0;
    phi_samples = 0;
 
    for(int g = 1; g <= ngs; g++)
      {
	beta_prior_energy_old(g) = beta_prior_energy(g);
      }
    
    if(uncertainty_in_varcopes)
      {
	for(int t = 1; t <= ntpts; t++)
	{
	  phi_prior_energy_old(t) = phi_prior_energy(t);
	}
      }
    sumovere = 0;

    for(int t = 1; t <= ntpts; t++)
      {
	prec_ontwo(t) = 0.5/(phi_latest(t)+beta_latest(design.getgroup(t)));
	logprec_ontwo(t) = log(2*prec_ontwo(t))/2.0;

	for(int e = 1; e <= nevs; e++)
	  {
	    sumovere(t) += design_matrix(t,e)*gamma_latest(e);
	    // 	OUT(gamma_latest(e));
	    // 	OUT(design_matrix(t,e));
	  }	
      }

    likelihood_energy_old = likelihood_energy(0,0,false);

    // if all_jump
//     likelihood_energy_old = 0;
//     for(int g = 1; g <= ngs; g++)
//       {
// 	likelihood_energy_old += beta_prior_energy(g);
//       }
    
//     likelihood_energy_old += likelihood_energy();

  }

  void Mcmc_Mh::jump()
  {
    Tracer_Plus trace("Mcmc_Mh::jump");
        
    //    all_jump();

    beta_jump();

    if(uncertainty_in_varcopes)
      phi_jump();

    gamma_jump();

    if(subsampcount>40)
      {
	  for(int g = 1; g <= ngs; g++)
	    beta_proposal_std(g) *= 0.65/((1+beta_nrejected(g))/float(1+beta_naccepted(g)+beta_nrejected(g)));
	
	if(uncertainty_in_varcopes)
	  for(int t = 1; t <= ntpts; t++)
	    phi_proposal_std(t) *= 0.65/((1+phi_nrejected(t))/float(1+phi_naccepted(t)+phi_nrejected(t)));
	
	for(int e = 1; e <= nevs; e++)
	  gamma_proposal_std(e) *= 0.65/((1+gamma_nrejected(e))/float(1+gamma_naccepted(e)+gamma_nrejected(e)));
	
	beta_naccepted = 0;
	phi_naccepted = 0;
	gamma_naccepted = 0;
	beta_nrejected = 0;
	phi_nrejected = 0;
	gamma_nrejected = 0;

	subsampcount = 0;
      }
    else
      {	
	subsampcount++;
      }

  } 

  void Mcmc_Mh::beta_jump()
  {
    Tracer_Plus trace("Mcmc_Mh::beta_jump");

//     if(sampcount>9844)
//        GsOptions::getInstance().debuglevel.set_value("2");

    for(int g = 1; g <= ngs; g++)
      {
	// store old values
	float beta_old = beta_latest(g);
	ColumnVector prec_ontwo_old = prec_ontwo;
	ColumnVector logprec_ontwo_old = logprec_ontwo;

	// propose new value	
	beta_latest(g) += normrnd().AsScalar()*beta_proposal_std(g);	  

	// use when sampling from log(variance)
	//	if(abs(beta_latest(g)) > 50) {beta_latest(g) = beta_old; beta_nrejected(g)++; return;}

	// use when sampling from variance
	if(beta_latest(g) <= 0) {beta_latest(g) = beta_old; beta_nrejected(g)++; return;}
	
	float likelihood_energy_new = likelihood_energy(0,0,true);	
	float beta_prior_energy_new = beta_prior_energy(g);

	// calculate acceptance threshold
	float tmp = unifrnd().AsScalar();
	float energy_new = likelihood_energy_new + beta_prior_energy_new;
	float energy_old = likelihood_energy_old + beta_prior_energy_old(g);

	if(GsOptions::getInstance().debuglevel.value()==2)
	  {
	    cout << "--------------" << endl;	
	    OUT(varcopedata.t());
	    OUT(copedata.t());
	    OUT(sampcount);
	    OUT(gamma_latest.t());	    
	    OUT(beta_latest(g));
	    OUT(beta_proposal_std(g));
	    OUT(beta_old);
	    OUT(beta_prior_energy_new);
	    OUT(beta_prior_energy_old(g));
	    OUT(likelihood_energy_new);
	    OUT(likelihood_energy_old);
	    OUT(energy_new);
	    OUT(energy_old);
	    OUT(tmp);
	    OUT(exp(energy_old - energy_new));
	  }

	bool accept = exp(energy_old - energy_new) > tmp;
	
	if(accept)
	  {
	    if(GsOptions::getInstance().debuglevel.value()==2)
	      {
		cout << "accepted" << endl;
	      }
	    beta_prior_energy_old(g) = beta_prior_energy_new;
	    likelihood_energy_old = likelihood_energy_new;
	    beta_naccepted(g)++;
	  }
	else
	  {
	    if(GsOptions::getInstance().debuglevel.value()==2)
	      {
		cout << "rejected" << endl;
	      }
	    // restore old values
	    beta_latest(g) = beta_old;

	    prec_ontwo = prec_ontwo_old;
	    logprec_ontwo = logprec_ontwo_old;

	    beta_nrejected(g)++;
	  }
      }
  }

  void Mcmc_Mh::phi_jump()
  {
    Tracer_Plus trace("Mcmc_Mh::phi_jump");

//     if(sampcount>9844)
//        GsOptions::getInstance().debuglevel.set_value("2");

    for(int t = 1; t <= ntpts; t++)
      {
	// store old values
	float phi_old = phi_latest(t);
	ColumnVector prec_ontwo_old = prec_ontwo;
	ColumnVector logprec_ontwo_old = logprec_ontwo;

	// propose new value	
	phi_latest(t) += normrnd().AsScalar()*phi_proposal_std(t);	  

	if(phi_latest(t) <= 0) {phi_latest(t) = phi_old; phi_nrejected(t)++; return;}
	
	float likelihood_energy_new = likelihood_energy_phichanged(t);	
	float phi_prior_energy_new = phi_prior_energy(t);
	float beta_prior_energy_new = beta_prior_energy(design.getgroup(t));

	// calculate acceptance threshold
	float tmp = unifrnd().AsScalar();
	float energy_new = likelihood_energy_new + phi_prior_energy_new + beta_prior_energy_new;
	float energy_old = likelihood_energy_old + phi_prior_energy_old(t) + beta_prior_energy_old(design.getgroup(t));

	if(GsOptions::getInstance().debuglevel.value()==2)
	  {
	    cout << "--------------" << endl;	
	    OUT(varcopedata.t());
	    OUT(copedata.t());
	    OUT(sampcount);
	    OUT(gamma_latest.t());	    
	    OUT(phi_latest(t));
	    OUT(phi_proposal_std(t));
	    OUT(phi_old);
	    OUT(phi_prior_energy_new);
	    OUT(phi_prior_energy_old(t));
	    OUT(likelihood_energy_new);
	    OUT(likelihood_energy_old);
	    OUT(energy_new);
	    OUT(energy_old);
	    OUT(tmp);
	    OUT(exp(energy_old - energy_new));
	  }

	bool accept = exp(energy_old - energy_new) > tmp;
	
	if(accept)
	  {
	    if(GsOptions::getInstance().debuglevel.value()==2)
	      {
		cout << "accepted" << endl;
	      }
	    phi_prior_energy_old(t) = phi_prior_energy_new;
	    beta_prior_energy_old(design.getgroup(t)) = beta_prior_energy_new;
	    likelihood_energy_old = likelihood_energy_new;
	    phi_naccepted(t)++;
	  }
	else
	  {
	    if(GsOptions::getInstance().debuglevel.value()==2)
	      {
		cout << "rejected" << endl;
	      }
	    // restore old values
	    phi_latest(t) = phi_old;
	    prec_ontwo = prec_ontwo_old;
	    logprec_ontwo = logprec_ontwo_old;

	    phi_nrejected(t)++;
	  }
      }
  }

//   void Mcmc_Mh::gamma_jump()
//   {
//     Tracer_Plus trace("Mcmc_Mh::gamma_jump");

//     // store old values
//     // propose new values
//     ColumnVector gamma_old(nevs);
//     for(int e = 1; e <= nevs; e++)
//       {
// 	gamma_old(e) = gamma_latest(e);       
// 	gamma_latest(e) += normal.Next()*gamma_proposal_std(e);
//       }
    
//     float likelihood_energy_new = likelihood_energy();	

//     // calculate acceptance threshold
//     float tmp = uniform.Next();
//     bool accept = exp(likelihood_energy_old - likelihood_energy_new) > tmp;
    
//     if(accept)
//       {
// 	likelihood_energy_old = likelihood_energy_new;
// 	gamma_naccepted(1)++;
//       }
//     else
//       {
// 	// restore old values
// 	for(int e = 1; e <= nevs; e++)
// 	  {
// 	    gamma_latest(e) = gamma_old(e);
// 	  }
	
// 	gamma_nrejected(1)++;
//       }
//   }

  void Mcmc_Mh::gamma_jump()
  {
    Tracer_Plus trace("Mcmc_Mh::gamma_jump");
    
    for(int e = 1; e <= nevs; e++)
      {
	// store old values
	float gamma_old = gamma_latest(e);       
	ColumnVector sumovere_old = sumovere;

	// propose new values	
	gamma_latest(e) += normrnd().AsScalar()*gamma_proposal_std(e);      

	float likelihood_energy_new = likelihood_energy(e,gamma_old,false);	

	// calculate acceptance threshold

	float tmp = unifrnd().AsScalar();

	bool accept = exp(likelihood_energy_old - likelihood_energy_new) > tmp;

	if(accept)
	  {
	    likelihood_energy_old = likelihood_energy_new;
	    gamma_naccepted(e)++;
	  }
	else
	  {
	    // restore old values	    
	    gamma_latest(e) = gamma_old;
	     sumovere = sumovere_old;
	    gamma_nrejected(e)++;
	  }
      } 
  }

//   void Mcmc_Mh::all_jump()
//   {
//     Tracer_Plus trace("Mcmc_Mh::all_jump");

//     // store old values
//     // propose new values
//     ColumnVector gamma_old(nevs);
//     for(int e = 1; e <= nevs; e++)
//       {
// 	gamma_old(e) = gamma_latest(e);       
// 	gamma_latest(e) += normrnd().AsScalar()*gamma_proposal_std(e);
//       }

//     ColumnVector beta_old(ngs);
//     float energy_new = 0.0;

//     for(int g = 1; g <= ngs; g++)
//       {
// 	beta_old(g) = beta_latest(g);
// 	beta_latest(g) += normrnd().AsScalar()*beta_proposal_std(g);	  
// 	if(beta_latest(g) <= 0) {beta_latest(g) = beta_old(g);}
// 	energy_new += beta_prior_energy(g);
//       }
    
//     energy_new += likelihood_energy();	

//     // calculate acceptance threshold
//     float tmp = unifrnd().AsScalar();
//     bool accept = exp(likelihood_energy_old - energy_new) > tmp;
    
//     if(accept)
//       {
// 	likelihood_energy_old = energy_new;
// 	gamma_naccepted(1)++;
//       }
//     else
//       {
// 	// restore old values
// 	for(int e = 1; e <= nevs; e++)
// 	  {
// 	    gamma_latest(e) = gamma_old(e);
// 	  }

// 	for(int g = 1; g <= ngs; g++)
// 	  {
// 	    beta_latest(g) = beta_old(g);
// 	  }
	
// 	gamma_nrejected(1)++;
//       }
//   }

  float Mcmc_Mh::likelihood_energy(const int echanged, const float gamma_old, const bool betachanged)
  {
    Tracer_Plus trace("Mcmc_Mh::likelihood_energy");

    float en = 0.0;

//     OUT(copedata);
//     OUT(varcopedata);
//     OUT(design_matrix);
    float gamlatest = 0;

    if(echanged>0) gamlatest= gamma_latest(echanged);

    // matlab:   n = 4;y = ones(n)*o+eye(n)*k;inv(y),det(y)    
    for(int t = 1; t <= ntpts; t++)
      {
	//float sumovere = 0.0;

// 	OUT(t);

	if(echanged>0)
	  {
	    sumovere(t) += (gamlatest-gamma_old)*design_matrix(t,echanged);
	  }

	// use when sampling from variance
	if(betachanged)
	  {
	    if(!infer_outliers)
	      {
		prec_ontwo(t) = 0.5/(phi_latest(t)+beta_latest(design.getgroup(t)));				
	      }
	    else
	      {
		float vr=Sqr(1-prob_outlier(t))*(phi_latest(t)+beta_latest(design.getgroup(t)))+Sqr(prob_outlier(t))*(phi_latest(t)+beta_latest(design.getgroup(t))+beta_outlier[design.getgroup(t)-1]);
		prec_ontwo(t) = 0.5/vr;
	      }
	    logprec_ontwo(t) = log(2*prec_ontwo(t))/2.0;
	  }

	// for inferring outliers we do not need the log(l_kf + (1-l_k)(1-f)) term as it is a constant wrt mcmc params
	en += -logprec_ontwo(t) + prec_ontwo(t)*Sqr(copedata(t) - sumovere(t));

	//float prec = 1.0/(phi_latest(t)+beta_latest(design.getgroup(t)));
	//en += -0.5*log(prec)+0.5*prec*Sqr(copedata(t) - sumovere(t));

	// use when sampling from log(variance)
// 	if(betachanged)
// 	  {
// 	    prec_ontwo(t) = 0.5/(phi_latest(t)+exp(beta_latest(design.getgroup(t))));
// 	    logprec_ontwo(t) = log(2*prec_ontwo(t))/2.0;
// 	  }
// 	en += -logprec_ontwo(t) + prec_ontwo(t)*Sqr(copedata(t) - sumovere(t));

// 	OUT(varcopedata(t));
// 	OUT(beta_latest(design.getgroup(t)));
// 	OUT(prec);
// 	OUT(design.getgroup(t));	
	  
      }

    //    OUT(energy);
    return en;
  }
  
  float Mcmc_Mh::likelihood_energy_phichanged(const int t)
  {    
    // logprec_ontwo(t) and prec_ontwo(t) will be calculated using phi_old
    float old_energy = (-logprec_ontwo(t) + prec_ontwo(t)*Sqr(copedata(t) - sumovere(t)));

    // recalculate logprec_ontwo(t) and prec_ontwo(t) using phi_latest
    prec_ontwo(t) = 0.5/(phi_latest(t)+beta_latest(design.getgroup(t)));
    logprec_ontwo(t) = log(2*prec_ontwo(t))/2.0;
    float new_energy = (-logprec_ontwo(t) + prec_ontwo(t)*Sqr(copedata(t) - sumovere(t)));

    float en = likelihood_energy_old - old_energy + new_energy;

    return en;
  }

  float Mcmc_Mh::beta_prior_energy(int g)
  {
    Tracer_Plus trace("Mcmc_Mh::beta_prior_energy");
    
    float en = 0.0;
    
    // prior is 1/beta (beta is variance)
    en = log(beta_latest(g));

    return en;
  }

  float Mcmc_Mh::phi_prior_energy(int t)
  {
    Tracer_Plus trace("Mcmc_Mh::phi_prior_energy");
    
    // p276 Lee
    float S = dofvarcopedata(t)/varcopedata(t);
    float en = -(dofvarcopedata(t)/2-1)*log(phi_latest(t)) + 0.5*S*phi_latest(t);

    return en;
  }

  void Mcmc_Mh::sample(int samp)
  {
    Tracer_Plus trace("Mcmc_Mh::sample");

    sampcount++;    

    for(int g = 1; g <= ngs; g++)
      beta_samples(g,samp) = beta_latest(g);

    for(int t = 1; t <= ntpts; t++)
      phi_samples(t,samp) = phi_latest(t);

    for(int e = 1; e <= nevs; e++)
      gamma_samples(e,samp) = gamma_latest(e);	

    likelihood_samples(samp) = likelihood_energy_old;

    //    sample_sumsquares(samp);
  }

//   void Mcmc_Mh::sample_sumsquares(int samp)
//   {
//     Tracer_Plus trace("Mcmc_Mh::sample_sumsquares");
    
//     ss_samples[0](samp) = sumsquare_residuals(design_matrix,copedata,gamma_latest);
    
//     for(int f = 1; f < design.getnumfcontrasts()+1; f++)
//       {	
// 	const Matrix& reduceddm = design.getfreduceddm(f);
	
// // 	OUT(copedata.t());
// // 	OUT(gamma_latest.t());
// // 	OUT(reduceddm);

// 		ss_samples[f](samp) = sumsquare_residuals(reduceddm,copedata,gamma_latest);
//       }
//   }
  
//   float Mcmc_Mh::sumsquare_residuals(const Matrix& pdm, const ColumnVector& pdata, const ColumnVector& ppes)
//   {
//     Tracer_Plus trace("Mcmc_Mh::sumsquare_residuals");

//     float ss = 0.0;

//     for(int t = 1; t <= ntpts; t++)
//       {
// 	float sumovere = 0.0;
	
// 	for(int e = 1; e <= nevs; e++)
// 	  {
// 	    sumovere += pdm(t,e)*ppes(e);
// 	  }
// 	float prec = 1.0/(varcopedata(t)+exp(beta_latest(design.getgroup(t))));

// 	ss += prec*Sqr(pdata(t) - sumovere);
// 	//ss += Sqr(pdata(t) - sumovere);
	
//       }

//     ss = ss/ntpts;

//     return ss;
//   }
  
//   void Mcmc_Mh::dic(float& DIC, float& pd)
//   {       
//     Tracer_Plus trace("Mcmc_Mh::dic");

    // calc Dthetabar
    // set latest params to posterior means
//     gamma_latest = mean(gamma_samples,2);
//     beta_latest = mean(beta_samples,2); 

//     float Dthetabar = 2*likelihood_energy();

//     // calc Dbar
//     float Dbar = mean(2*likelihood_samples).AsScalar();
    
//     // pd = Dbar - Dthetabar
//     pd = Dbar - Dthetabar;

//     // DIC = Dbar + pd
//     DIC = Dbar + pd;
//   }

  void Mcmc_Mh::run()
  {
    Tracer_Plus trace("Mcmc_Mh::run");
    
    int samples = 1;
    int jumps = 0;
    int subsamplejumps = 0;

    while(true)
      {
	jumps++;
	subsamplejumps++;
	    
  	jump();

	if(subsamplejumps >= opts.sampleevery.value())
	  {
	    subsamplejumps = 0;
	    
	    // sample components after burnin
	    if(jumps > opts.burnin.value())
	      {	   		
		sample(samples);
		samples++;
		
		if(samples>nsamples)
		  break;
	      }
	  }
      }    
  }

}