/*  fwdmodel_dsc.cc - Implements a convolution based model for DSC analysis

    Michael Chappell, FMRIB Image Analysis Group

    Copyright (C) 2008 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 "fwdmodel_dsc.h"

#include <iostream>
#include <newmatio.h>
#include <stdexcept>
#include "newimage/newimageall.h"
using namespace NEWIMAGE;
#include "easylog.h"
#include "miscmaths/miscprob.h"

string DSCFwdModel::ModelVersion() const
{
  return "$Id: fwdmodel_dsc.cc,v 1.8 2011/08/04 13:40:11 chappell Exp $";
}

void DSCFwdModel::HardcodedInitialDists(MVNDist& prior, 
    MVNDist& posterior) const
{
    Tracer_Plus tr("DSCFwdModel::HardcodedInitialDists");
    assert(prior.means.Nrows() == NumParams());

     SymmetricMatrix precisions = IdentityMatrix(NumParams()) * 1e-12;

    // Set priors
    // CBF
     prior.means(cbf_index()) = 0;
     precisions(cbf_index(),cbf_index()) = 1e-12;
     if (imageprior) precisions(cbf_index(),cbf_index()) = 100;

     if (infermtt) {
       // Transit mean parameter
       prior.means(gmu_index()) = 1.5; //1; //10;
       precisions(gmu_index(),gmu_index()) = 10; //0.01;
       if (imageprior) precisions(gmu_index(),gmu_index()) = 100;
     }

     if (inferlambda) {
       // Transit labmda parameter (log)
       prior.means(lambda_index()) = 2; //10;
       precisions(lambda_index(),lambda_index()) = 1; //0.01;
     }

     if (inferdelay) {
       // delay parameter
       prior.means(delta_index()) = 0;
       precisions(delta_index(),delta_index()) = 1;
     }

     // signal magnitude parameter
     prior.means(sig0_index()) = 100;
     precisions(sig0_index(),sig0_index()) = 1e-6;

     if (inferart) {
       //arterial component parameters
       prior.means(art_index()) = 0;
	 precisions(art_index(),art_index()) = 1e-12;
       prior.means(art_index()+1) = 0;
       precisions(art_index()+1,art_index()+1) = 0.04;
     }

     if (inferret) {
       //some tracer is retained
       prior.means(ret_index()) = 0;
       precisions(ret_index(),ret_index()) = 1e4;
     }
    
   
    // Set precsions on priors
    prior.SetPrecisions(precisions);
    
    // Set initial posterior
    posterior = prior;

    // For parameters with uniformative prior chosoe more sensible inital posterior
    // Tissue perfusion
    posterior.means(cbf_index()) = 0.1;
    precisions(cbf_index(),cbf_index()) = 10;

 //     if (infermtt) {
//        // Transit mean parameter
//        posterior.means(gmu_index()) = 1; //10;
//        precisions(gmu_index(),gmu_index()) = 10; //0.01;
//      }

//      if (inferlambda) {
//        // Transit labmda parameter
//        posterior.means(lambda_index()) = 1; //10;
//        precisions(lambda_index(),lambda_index()) = 10; //0.01;
//      }

    if (inferart) {
      posterior.means(art_index()) = 0;
      precisions(art_index(),art_index()) = 10;
    }

    posterior.SetPrecisions(precisions);
    
}    
    
    

void DSCFwdModel::Evaluate(const ColumnVector& params, ColumnVector& result) const
{
  Tracer_Plus tr("DSCFwdModel::Evaluate");

    // ensure that values are reasonable
    // negative check
   ColumnVector paramcpy = params;
    for (int i=1;i<=NumParams();i++) {
      if (params(i)<0) { paramcpy(i) = 0; }
      }
  
   // parameters that are inferred - extract and give sensible names
   float cbf;
   float gmu; //mean of the transit time distribution
   float lambda; // log lambda (fromt ransit distirbution)
   float delta;
   float sig0; //'inital' value of the signal
   float artmag;
   float artdelay;
   float tracerret;

   // extract values from params
   //cbf = paramcpy(cbf_index());
   cbf = paramcpy(cbf_index());

   if (infermtt) {
     gmu = params(gmu_index()); //this is the log of the mtt so we can have -ve values
   }
   else {gmu = 0;}
   if (inferlambda) {
     lambda = params(lambda_index()); //this is the log of lambda so we can have -ve values
   }
   else {
     lambda = 0;
   }

   if (inferdelay) {
   delta = params(delta_index()); // NOTE: delta is allowed to be negative
   }
   else {
     delta = 0;
   }
   sig0 = paramcpy(sig0_index());

   if (inferart) {
     //artmag = paramcpy(art_index());
     artmag = paramcpy(art_index());
     artdelay = params(art_index()+1);
   }
     
   if (inferret) {
     tracerret = tanh(paramcpy(ret_index()));
   }
   else tracerret = 0.0;

   // sensible limits on delta (beyond which it gets silly trying to estimate it)
   if (delta > ntpts/2*delt) {delta = ntpts/2*delt;}
   if (delta < -ntpts/2*delt) {delta = -ntpts/2*delt;}   


   //cout << "aif: " << aif.t() << endl;

 

   // deal with delay parameter - this shifts the aif
   ColumnVector aifnew(aif);
   aifnew = aifshift(aif,delta,hdelt);

   ColumnVector C_art(aif);
   if (inferart) {
     //local arterial contribution is the aif, but with a local time shift
     C_art = artmag*aifshift(aif,artdelay,hdelt);
   }

   /*
   int nshift = floor(delta/hdelt); // number of time points of shift associated with delta
   float minorshift = delta - nshift*hdelt; // shift within the sampled time points (this is always a 'forward' shift)
      
   ColumnVector aifnew(nhtpts);
   int index;
   for (int i=1; i<=nhtpts; i++) {
     index = i-nshift;
     if (index==1) { aifnew(i) = aif(1)*minorshift/hdelt; } //linear interpolation with zero as 'previous' time point
     else if (index < 1) { aifnew(i) = 0; }
     else if (index>nhtpts) { aifnew(i) = aif(nhtpts); }
     else {
       //linear interpolation
       aifnew(i) = aif(index) + (aif(index-1)-aif(index))*minorshift/hdelt;
     }
   }
   */
   
     
   ColumnVector residue;
   residue.ReSize(nhtpts);
   
   // Evaluate the residue function
   //if (gmu > 10) gmu = 10;


   // gmu and lambda are actually the log versions
  
   //if (gmu<=0.1) gmu = 0.1;
   //if (lambda<=0.1) lambda = 0.1;
   //float alph = exp(lambda);
   //float bet = gmu/exp(lambda);
   //cout << "transitm: " << gmu << " transitv: " << exp(lambda) << "alph: " << alph << " bet: " << bet << endl
   //for (int i=1; i<=ntpts; i++) {
   //  residue(i) = gdtrc(1/bet,alph,htsamp(i)-htsamp(1));
   //  }

    gmu = exp(gmu);
    lambda = exp(lambda);
    if (lambda > 10) lambda=10;
    float gvar = gmu*gmu/lambda;   

   //float alpha = exp(lambda);
   //float beta = exp(gmu); //gmu temporarily is actually the beta parameter
   //gmu = alpha*beta;
   //float gvar = alpha*beta*beta;

   residue = 1 - gammacdf(htsamp.t()-htsamp(1),gmu,gvar).t();

   //tracer retention
   residue = (1-tracerret)*residue + tracerret;

   //cout << cbf << "  " << gmu << "  " << gvar << "  " << delta << "  " << sig0 << endl;
   /*float alpha = gmu*gmu/gvar;
   float beta = gmu/alpha;
   for (int i=1; i <=residue.Nrows(); i++) {
     residue(i) = evalresidue(tsamp(i),alpha,beta);
     }*/

   // Do the convolution
   // form the convolution matrix (there is probably a better way!)
   
   //aifnew = aif;
   
   //cout << "--------------------" << endl;
   //cout << "cbf: " << cbf << " gmu: " << gmu << " log(lambda): " << lambda << " delta: " << delta << " sig0: " << sig0 << endl;

   //cout << "residue: " << residue.t() << endl;
   //cout << "aifnew: " << aifnew.t() << endl;

   LowerTriangularMatrix A(nhtpts); A=0.0;

   if (convmtx=="simple")
     {
       // Simple convolution matrix
       for (int i=1; i<=nhtpts; i++) {
	 for (int j=1; j <= i; j++) {
	   A(i,j) = aifnew(i-j+1); //note we are using the local aifnew here! (i.e. it has been suitably time shifted)
	 }
       }
     }
   //cout << "new run" << endl;
   //cout << A << endl;

   else if (convmtx=="voltera")
     {
       ColumnVector aifextend(nhtpts+2);
       ColumnVector zero(1);
       zero=0;
       aifextend = zero & aifnew & zero;
       int x, y, z;
       //voltera convolution matrix (as defined by Sourbron 2007) - assume zeros outside aif range
       for (int i=1; i<=nhtpts; i++) {
	 for (int j=1; j <= i; j++) {
	   //cout << i << "  " << j << endl;
	   x = i+1;y=j+1; z = i-j+1;
	   if (j==1) { A(i,j) =(2*aifextend(x) + aifextend(x-1))/6; }
	   else if (j==i) { A(i,j) = (2*aifextend(2) + aifextend(3))/6; }
	   else { 
	     A(i,j) =  (4*aifextend(z) + aifextend(z-1) + aifextend(z+1))/6; 
	     //cout << x << "  " << y << "  " << z << "  " << ( 4*aifextend(z) + aifextend(z-1) + aifextend(z+1) )/6 << "  " << 1/6*(4*aifextend(z) + aifextend(z-1) + aifextend(z+1)) << endl;
	     // cout << aifextend(z) << "  " << aifextend(z-1) << "  " << aifextend(z+1) << endl;
	   }
	   //cout << i << "  " << j << "  " << aifextend(z) << "  " << A(i,j) << endl<<endl;
	 }
       }
     }

   //cout << A << endl;

   // do the multiplication
   ColumnVector C; 
   C = cbf*hdelt*A*residue;
   //convert to the DSC signal

   //cout  << "C: " << C.t() << endl;

   //cout << "sig0: " << sig0 << " r2: " << r2 << " te: " << te << endl;
   
   //cout<< htsamp.t() << endl;

   ColumnVector C_low(ntpts);
   for (int i=1; i<=ntpts; i++) {
     C_low(i) = C((i-1)*upsample+1);
     //C_low(i) = interp1(htsamp,C,tsamp(i));
     if (inferart) { //add in arterial contribution
       C_low(i) += C_art((i-1)*upsample+1);
     }
     } 

   result.ReSize(ntpts);
   for (int i=1; i<=ntpts; i++) {
     result(i) = sig0*exp(-C_low(i)*te);
   }

   for (int i=1; i<=ntpts; i++) {
     if (isnan(result(i)) || isinf(result(i))) {
       LOG << "Warning NaN of inf in result" << endl;
       LOG << "result: " << result.t() << endl;
       LOG << "params: " << params.t() << endl;
       result=0.0; 
       break;
	 }
   }


   // downsample back to normal time points
   //cout << estsig.t() << endl;
   //result.ReSize(ntpts);
   //result=estsig;
   /*for (int i=1; i<=ntpts; i++) {
     result(i) = interp1(htsamp,estsig,tsamp(i));
     }
   if ((result-estsig).SumAbsoluteValue()>0.1){
     cout << result.t() << endl;
     cout << estsig.t() << endl;
     }*/

   //cout << result.t()<< endl;
}

DSCFwdModel::DSCFwdModel(ArgsType& args)
{
  Tracer_Plus tr("DSCFwdModel::DSCFwdModel");
    string scanParams = args.ReadWithDefault("scan-params","cmdline");
    
    if (scanParams == "cmdline")
    {
      // specify command line parameters here
      te = convertTo<double>(args.Read("te"));
      
      delt = convertTo<double>(args.Read("delt"));

      // specify options of the model
      infermtt = args.ReadBool("infermtt");
      inferlambda = args.ReadBool("inferlambda");
      inferdelay = args.ReadBool("inferdelay");

      inferart = args.ReadBool("inferart"); //infer arterial component

      inferret = args.ReadBool("inferret");

      convmtx = args.ReadWithDefault("convmtx","simple");
      
      // Read in the arterial signal
      ColumnVector artsig;
      string artfile = args.Read("aif");
      artsig = read_ascii_matrix( artfile );

      // establish number of time points from the arterial signal
      ntpts = artsig.Nrows();

      // Create vector of sampled times
      tsamp.ReSize(ntpts);
      for (int i=1; i<=ntpts; i++) {
	tsamp(i) = (i-1)*delt;
      }

      imageprior = args.ReadBool("imageprior"); //temp way to indicate we have some image priors (very fixed meaning!)          

       // calculate the arterial input function (from upsampled artsig)
      ColumnVector aif_low(ntpts);
      aif_low = -1/te*log(artsig/artsig(1)); //using first value from aif input as time zero value
      
      // upsample the signal
      upsample=1;
      nhtpts=(ntpts-1)*upsample+1;
      htsamp.ReSize(nhtpts); 
      aif.ReSize(nhtpts);
      htsamp(1) = tsamp(1); aif(1) = aif_low(1);
      hdelt = delt/upsample;
      int j=0; int ii=0;
      for (int i=2; i<=nhtpts-1; i++) {
	htsamp(i) = htsamp(i-1)+hdelt;
	j = floor((i-1)/upsample)+1;
	ii= i - upsample*(j-1)-1;
	aif(i) = aif_low(j) + ii/upsample*(aif_low(j+1) - aif_low(j));
      }
      htsamp(nhtpts)=tsamp(ntpts);
      aif(nhtpts) = aif_low(ntpts);

      doard=false;
      if (inferart) doard=true;     

      // add information about the parameters to the log
      /* do logging here*/
   
    }

    else
        throw invalid_argument("Only --scan-params=cmdline is accepted at the moment");    
    
 
}

void DSCFwdModel::ModelUsage()
{ 
  cout << "Model usagae for DSC model...";
}

void DSCFwdModel::DumpParameters(const ColumnVector& vec,
                                    const string& indent) const
{
    
}

void DSCFwdModel::NameParams(vector<string>& names) const
{
  names.clear();
  
  names.push_back("cbf");
  if (infermtt) names.push_back("transitm");
  if (inferlambda) names.push_back("lambda");
  
  if (inferdelay)
  names.push_back("delay");

  names.push_back("sig0");
  
  if (inferart) {
    names.push_back("abv");
    names.push_back("artdelay");
  }
  if (inferret) {
    names.push_back("ret");
  }
}



ColumnVector DSCFwdModel::aifshift( const ColumnVector& aif, const float delta, const float hdelt ) const
{
  // Shift a vector in time by interpolation (linear)
  // NB Makes assumptions where extrapolation is called for.
   int nshift = floor(delta/hdelt); // number of time points of shift associated with delta
   float minorshift = delta - nshift*hdelt; // shift within the sampled time points (this is always a 'forward' shift)
      
   ColumnVector aifnew(aif);
   int index;
   for (int i=1; i<=nhtpts; i++) {
     index = i-nshift;
     if (index==1) { aifnew(i) = aif(1)*minorshift/hdelt; } //linear interpolation with zero as 'previous' time point
     else if (index < 1) { aifnew(i) = 0; } // extrapolation before the first time point - assume aif is zero
     else if (index>nhtpts) { aifnew(i) = aif(nhtpts); } // extrapolation beyond the final time point - assume aif takes the value of the final time point
     else {
       //linear interpolation
       aifnew(i) = aif(index) + (aif(index-1)-aif(index))*minorshift/hdelt;
     }
   }
   return aifnew;
}


void DSCFwdModel::SetupARD( const MVNDist& theta, MVNDist& thetaPrior, double& Fard)
{
  Tracer_Plus tr("ASL_PVC_FwdModel::SetupARD");

  if (doard)
    {
      //sort out ARD indices
      if (inferart)  ard_index.push_back(art_index());


      Fard = 0;

      int ardindex;
      for (unsigned int i=0; i<ard_index.size(); i++) {
	//iterate over all ARD parameters
	ardindex = ard_index[i];

	SymmetricMatrix PriorPrec;
	PriorPrec = thetaPrior.GetPrecisions();
	
	PriorPrec(ardindex,ardindex) = 1e-12; //set prior to be initally non-informative
	
	thetaPrior.SetPrecisions(PriorPrec);
	
	thetaPrior.means(ardindex)=0;
	
	//set the Free energy contribution from ARD term
	SymmetricMatrix PostCov = theta.GetCovariance();
	double b = 2/(theta.means(ardindex)*theta.means(ardindex) + PostCov(ardindex,ardindex));
	Fard += -1.5*(log(b) + digamma(0.5)) - 0.5 - gammaln(0.5) - 0.5*log(b); //taking c as 0.5 - which it will be!
      }
  }
  return;
}

void DSCFwdModel::UpdateARD(
				const MVNDist& theta,
				MVNDist& thetaPrior, double& Fard) const
{
  Tracer_Plus tr("ASL_PVC_FwdModel::UpdateARD");
  
  if (doard)
    Fard=0;
    {
      int ardindex;
      for (unsigned int i=0; i<ard_index.size(); i++) {
	//iterate over all ARD parameters
	ardindex = ard_index[i];

  
      SymmetricMatrix PriorCov;
      SymmetricMatrix PostCov;
      PriorCov = thetaPrior.GetCovariance();
      PostCov = theta.GetCovariance();

      PriorCov(ardindex,ardindex) = theta.means(ardindex)*theta.means(ardindex) + PostCov(ardindex,ardindex);

      
      thetaPrior.SetCovariance(PriorCov);

      //Calculate the extra terms for the free energy
      double b = 2/(theta.means(ardindex)*theta.means(ardindex) + PostCov(ardindex,ardindex));
      Fard += -1.5*(log(b) + digamma(0.5)) - 0.5 - gammaln(0.5) - 0.5*log(b); //taking c as 0.5 - which it will be!
    }
  }

  return;

  }