BCIntegrate.cxx

/*
 * Copyright (C) 2007-2014, the BAT core developer team
 * All rights reserved.
 *
 * For the licensing terms see doc/COPYING.
 * For documentation see http://mpp.mpg.de/bat
 */

// ---------------------------------------------------------
#include <config.h>

#include "BCIntegrate.h"
#include "BCLog.h"
#include "BCMath.h"
#include "BCParameter.h"
#include "BCH2D.h"
#include "BCH1D.h"

#include <TH1D.h>
#include <TH2D.h>
#include <TH3D.h>
#include <TCanvas.h>
#include <TFile.h>
#include <TMinuit.h>
#include <TRandom3.h>
#include <TString.h>
#include <TTree.h>
#include <TKey.h>
#include <TStyle.h>

#ifdef HAVE_CUBA_H
#include <cuba.h>
#endif

#include <math.h>
#include <limits>

namespace
{
  class BCIntegrateHolder
  {
  private:
    BCIntegrate * global_this;

  public:

    BCIntegrateHolder() :
      global_this(NULL)
    {
    }

    static BCIntegrate * instance(BCIntegrate * obj = NULL)
    {
      static BCIntegrateHolder result;
      if (obj)
        result.global_this = obj;

      return result.global_this;
    }
  };
}

// ---------------------------------------------------------
BCIntegrate::BCIntegrate() : BCEngineMCMC(),
                             fID(BCLog::GetHIndex()),
                             fMinuit(0),
                             fMinuitErrorFlag(0),
                             fFlagIgnorePrevOptimization(false),
                             fSAT0(100),
                             fSATmin(0.1),
                             fTreeSA(0),
                             fFlagWriteSAToFile(false),
                             fSANIterations(0),
                             fSATemperature(0),
                             fSALogProb(0),
                             fMarginalized1D(0),
                             fMarginalized2D(0),
                             fFlagMarginalized(false),
                             fOptimizationMethodCurrent(BCIntegrate::kOptDefault),
                             fOptimizationMethodUsed(BCIntegrate::kOptEmpty),
                             fIntegrationMethodCurrent(BCIntegrate::kIntDefault),
                             fIntegrationMethodUsed(BCIntegrate::kIntEmpty),
                             fMarginalizationMethodCurrent(BCIntegrate::kMargDefault),
                             fMarginalizationMethodUsed(BCIntegrate::kMargEmpty),
                             fSASchedule(BCIntegrate::kSACauchy),
                             fNIterationsMin(0),
                             fNIterationsMax(1000000),
                             fNIterationsPrecisionCheck(1000),
                             fNIterationsOutput(0),
                             fNIterations(0),
                             fLogMaximum(-std::numeric_limits<double>::max()),
                             fIntegral(-1),
                             fRelativePrecision(1e-2),
                             fAbsolutePrecision(1e-6),
                             fError(-999.),
                             fCubaIntegrationMethod(BCIntegrate::kCubaVegas)
{
    fMinuitArglist[0] = 20000;
    fMinuitArglist[1] = 0.01;
}

// ---------------------------------------------------------
BCIntegrate::BCIntegrate(const BCIntegrate & other) : BCEngineMCMC(other)
{
    Copy(other);
}

// ---------------------------------------------------------
BCIntegrate & BCIntegrate::operator = (const BCIntegrate & other)
{
    Copy(other);
    return *this;
}

// ---------------------------------------------------------
void BCIntegrate::Copy(const BCIntegrate & other)
{
   BCEngineMCMC::Copy(other);

   fID                       = other.fID;
   fBestFitParameters        = other.fBestFitParameters;
   fBestFitParameterErrors   = other.fBestFitParameterErrors;
   fLogMaximum               = other.fLogMaximum;
   fMinuit                   = new TMinuit();
   fMinuitArglist[0]         = other.fMinuitArglist[0];
   fMinuitArglist[1]         = other.fMinuitArglist[1];
   fMinuitErrorFlag          = other.fMinuitErrorFlag;
   fFlagIgnorePrevOptimization = other.fFlagIgnorePrevOptimization;
   fSAT0                     = other.fSAT0;
   fSATmin                   = other.fSATmin;
   fTreeSA = 0;
   fFlagWriteSAToFile        = other.fFlagWriteSAToFile;
   fSANIterations            = other.fSANIterations;
   fSATemperature            = other.fSATemperature;
   fSALogProb                = other.fSALogProb;
   fSAx                      = other.fSAx;
   fMarginalized1D           = other.fMarginalized1D;
   fMarginalized2D           = other.fMarginalized2D;
   fOptimizationMethodCurrent= other.fOptimizationMethodCurrent;
   fOptimizationMethodUsed   = other.fOptimizationMethodUsed;
   fIntegrationMethodCurrent = other.fIntegrationMethodCurrent;
   fIntegrationMethodUsed    = other.fIntegrationMethodUsed;
   fMarginalizationMethodCurrent = other.fMarginalizationMethodCurrent;
   fMarginalizationMethodUsed= other.fMarginalizationMethodUsed;
   fSASchedule               = other.fSASchedule;
   fNIterationsMin           = other.fNIterationsMin;
   fNIterationsMax           = other.fNIterationsMax;
   fNIterationsPrecisionCheck= other.fNIterationsPrecisionCheck;
   fNIterationsOutput        = other.fNIterationsOutput;
   fNIterations              = other.fNIterations;
   fIntegral                 = other.fIntegral;
   fRelativePrecision        = other.fRelativePrecision;
   fAbsolutePrecision        = other.fAbsolutePrecision;
   fError                    = other.fError;
   fCubaIntegrationMethod    = other.fCubaIntegrationMethod;
   fCubaVegasOptions         = other.fCubaVegasOptions;
   fCubaSuaveOptions         = other.fCubaSuaveOptions;
   fCubaDivonneOptions       = other.fCubaDivonneOptions;
   fCubaCuhreOptions         = other.fCubaCuhreOptions;
   fFlagMarginalized         = other.fFlagMarginalized;
}

// ---------------------------------------------------------
BCIntegrate::~BCIntegrate()
{
   delete fMinuit;
}

// ---------------------------------------------------------
double BCIntegrate::GetBestFitParameter(unsigned index) const
{
   if( ! fParameters.ValidIndex(index))
      return -1e+111;

   if(fBestFitParameters.empty()) {
      BCLog::OutError("BCIntegrate::GetBestFitParameter : Mode finding not yet run, returning center of the range.");
      return (fParameters[index]->GetUpperLimit() + fParameters[index]->GetLowerLimit() ) / 2.;
   }

   return fBestFitParameters[index];
}

// ---------------------------------------------------------
double BCIntegrate::GetBestFitParameterError(unsigned index) const
{
   if( ! fParameters.ValidIndex(index)) {
      BCLog::OutError("BCIntegrate::GetBestFitParameterError : Parameter index out of range, returning -1.");
      return -1;
   }

   /*
   if(fBestFitParameterErrors.size()==0) {
      BCLog::OutError("BCIntegrate::GetBestFitParameterError : Mode finding not yet run, returning -1.");
      return -1.;
   }

   if(fBestFitParameterErrors[index]<0.)
      BCLog::OutWarning("BCIntegrate::GetBestFitParameterError : Parameter error not available, returning -1.");
   */

   return fBestFitParameterErrors[index];
}

// ---------------------------------------------------------
double BCIntegrate::Eval(const std::vector<double> & /*x*/)
{
   BCLog::OutWarning( "BCIntegrate::Eval. No function. Function needs to be overloaded.");
   return 0;
}

// ---------------------------------------------------------
double BCIntegrate::LogEval(const std::vector<double> &x)
{
   // this method should better also be overloaded
   return log(Eval(x));
}

// ---------------------------------------------------------
void BCIntegrate::ResetResults()
{
   BCEngineMCMC::ResetResults();

   fBestFitParameterErrors.clear();
   fBestFitParameters.clear();
   fLogMaximum = -std::numeric_limits<double>::max();

   // remove marginalized histograms
   // set marginalization flag
   fFlagMarginalized = false;
}

// ---------------------------------------------------------
unsigned BCIntegrate::GetNIntegrationVariables() {
    unsigned n = 0;
    for(unsigned i = 0; i < fParameters.Size(); ++i)
        if ( ! fParameters[i]->Fixed())
            ++n;
    return n;
}

// ---------------------------------------------------------
double BCIntegrate::CalculateIntegrationVolume() {
   double integrationVolume = -1.;

   for(unsigned i = 0; i < fParameters.Size(); i++)
      if ( ! fParameters[i]->Fixed()) {
         if (integrationVolume<0)
            integrationVolume = 1;
         integrationVolume *= fParameters[i]->GetRangeWidth();
      }

   if (integrationVolume<0)
      integrationVolume = 0;

   return integrationVolume;
}

// ---------------------------------------------------------
double BCIntegrate::Integrate()
{
  // check if parameters are defined
  if (fParameters.Size() < 1) {
    BCLog::OutError("BCIntegrate::Integrate : No parameters defined. Aborting.");
    return -1.;
  }

  // output
  if (!(fIntegrationMethodCurrent == BCIntegrate::kIntDefault) && !(fIntegrationMethodCurrent == BCIntegrate::kIntEmpty))
    BCLog::OutSummary(Form("Integrate using %s", DumpCurrentIntegrationMethod().c_str()));

  switch(fIntegrationMethodCurrent)
    {

      // Empty
    case BCIntegrate::kIntEmpty:
      {
        BCLog::OutWarning("BCIntegrate::Integrate : No integration method chosen.");
        return 0;
      }


      // Monte Carlo Integration
    case BCIntegrate::kIntMonteCarlo:
      {
        std::vector<double> sums (2,0.0);
        sums.push_back(CalculateIntegrationVolume());
        fIntegral = Integrate(kIntMonteCarlo,
                              &BCIntegrate::GetRandomVectorInParameterSpace,
                              &BCIntegrate::EvaluatorMC,
                              &IntegralUpdaterMC,
                              sums);

        // set used integration method
        fIntegrationMethodUsed = BCIntegrate::kIntMonteCarlo;

        // return integral
        return fIntegral;
      }

      // CUBA library
    case BCIntegrate::kIntCuba:
      {
        fIntegral = IntegrateCuba();

        // set used integration method
        fIntegrationMethodUsed = BCIntegrate::kIntCuba;

        // return integral
        return fIntegral;
      }

      // CUBA library
    case BCIntegrate::kIntGrid:
      {
        fIntegral = IntegrateSlice();

        // set used integration method
        fIntegrationMethodUsed = BCIntegrate::kIntGrid;

        // return integral
        return fIntegral;
      }

      // default
    case BCIntegrate::kIntDefault:
      {
        if (GetNFreeParameters() <= 2)
          SetIntegrationMethod(BCIntegrate::kIntGrid);
        else
#ifdef HAVE_CUBA_H
          SetIntegrationMethod(BCIntegrate::kIntCuba);
#else
        SetIntegrationMethod(BCIntegrate::kIntMonteCarlo);
#endif
        return Integrate();
      }

    default:
      BCLog::OutError(TString::Format("BCIntegrate::Integrate : Invalid integration method: %d", fIntegrationMethodCurrent));
      break;
    }

  return 0;
}

// ---------------------------------------------------------
double BCIntegrate::Integrate(BCIntegrationMethod intmethod)
{
    // remember original method
  BCIntegrationMethod method_temp = fIntegrationMethodCurrent;

  // set method
  SetIntegrationMethod(intmethod);

  // run algorithm
  double integral = Integrate();

  // re-set original method
  SetIntegrationMethod(method_temp);

  // return integral
  return integral;

}

// ---------------------------------------------------------
void BCIntegrate::SetBestFitParameters(const std::vector<double> &x, const double &new_value, double &old_value) {
    if (new_value < old_value)
        return;
    old_value = new_value;
    SetBestFitParameters(x);
}

// ---------------------------------------------------------
unsigned BCIntegrate::IntegrationOutputFrequency() const
{
    if (fNIterationsOutput > 0)
        return fNIterationsOutput;
    const unsigned nwrite = fNIterationsMax / 10;
    if(nwrite < 10000)
        return 1000;
    if(nwrite < 100000)
        return 10000;
    if(nwrite < 1000000)
        return 100000;
    return 1000000;
}

// ---------------------------------------------------------
void BCIntegrate::LogOutputAtStartOfIntegration(BCIntegrationMethod type, BCCubaMethod cubatype)
{
   const unsigned NVarNow = GetNIntegrationVariables();

   BCLog::LogLevel level = BCLog::summary;

   if(fParameters.Size() != NVarNow) {

      level = BCLog::detail;
      bool printed = false;

      if (type==kIntCuba)
      {
         BCLog::OutDetail(TString::Format("Running %s (%s) integration over %i dimensions out of %i.",
               DumpIntegrationMethod(type).c_str(),
               DumpCubaIntegrationMethod(cubatype).c_str(),
               NVarNow, fParameters.Size()));
         printed = true;
      }

      if (not printed)
         BCLog::OutDetail(TString::Format("Running %s integration over %i dimensions out of %i.",
               DumpIntegrationMethod(type).c_str(),
               NVarNow, fParameters.Size()));

      BCLog::OutDetail(" --> Fixed parameters:");
      for(unsigned i = 0; i < fParameters.Size(); i++)
         if(fParameters[i]->Fixed())
            BCLog::OutDetail(TString::Format("      %3i :  %g", i, fParameters[i]->GetFixedValue()));
   }
   else {
      bool printed = false;

      if (type==kIntCuba) {
         BCLog::OutDetail(TString::Format("Running %s (%s) integration over %i dimensions.",
               DumpIntegrationMethod(type).c_str(),
               DumpCubaIntegrationMethod(cubatype).c_str(),
               NVarNow));
         printed = true;
      }

      if (not printed)
         BCLog::OutDetail(TString::Format("Running %s integration over %i dimensions.",
               DumpIntegrationMethod(type).c_str(),
               NVarNow));
   }

   if (GetNIterationsMin() > 0 && GetNIterationsMax() > 0 ) {
     BCLog::Out(level, TString::Format(" --> Minimum number of iterations: %i", GetNIterationsMin()));
     BCLog::Out(level, TString::Format(" --> Maximum number of iterations: %i", GetNIterationsMax()));
   }
   BCLog::Out(level, TString::Format(" --> Target relative precision:    %e", GetRelativePrecision()));
   BCLog::Out(level, TString::Format(" --> Target absolute precision:    %e", GetAbsolutePrecision()));
}

// ---------------------------------------------------------
void BCIntegrate::LogOutputAtEndOfIntegration(double integral, double absprecision, double relprecision, int nIterations)
{
   BCLog::OutSummary(TString::Format(" --> Result of integration:        %e +- %e", integral, absprecision));
   BCLog::OutSummary(TString::Format(" --> Obtained relative precision:  %e. ", relprecision));
   if (nIterations >= 0)
     BCLog::OutSummary(TString::Format(" --> Number of iterations:         %i", nIterations));
}

// ---------------------------------------------------------
void BCIntegrate::LogOutputAtIntegrationStatusUpdate(BCIntegrationMethod type, double integral, double absprecision, int nIterations)
{
    BCLog::OutDetail(TString::Format("%s. Iteration %i, integral: %e +- %e.", DumpIntegrationMethod(type).c_str(), nIterations, integral, absprecision));
}

// ---------------------------------------------------------
double BCIntegrate::Integrate(BCIntegrationMethod type, tRandomizer randomizer, tEvaluator evaluator, tIntegralUpdater updater,
      std::vector<double> &sums)
{
    LogOutputAtStartOfIntegration(type, NCubaMethods);

    // reset variables
    double pmax = 0.;
    double integral = 0.;
    double absprecision = 2.*fAbsolutePrecision;
    double relprecision = 2.*fRelativePrecision;

    std::vector<double> randx (fParameters.Size(), 0.);

    // how often to print out the info line to screen
    int nwrite = IntegrationOutputFrequency();

    // reset number of iterations
    fNIterations = 0;
    bool accepted;

    // iterate while number of iterations is lower than minimum number of iterations
    // or precision is not reached and the number of iterations is lower than maximum number of iterations
    while ((GetRelativePrecision() < relprecision and GetAbsolutePrecision() < absprecision and GetNIterations() < GetNIterationsMax())
          or GetNIterations() < GetNIterationsMin())
        {

            // get random numbers
            (this->*randomizer)(randx);

            // evaluate function at sampled point
            // updating sums & checking for maximum probability

            SetBestFitParameters(randx, (this->*evaluator)(sums,randx,accepted), pmax);

            // increase number of iterations
            if (accepted)
               fNIterations++;

            // update precisions
            if (fNIterations % fNIterationsPrecisionCheck == 0) {
                (*updater)(sums, fNIterations, integral, absprecision);
                relprecision = absprecision / integral;
            }

            // write status
            if (fNIterations % nwrite == 0) {
                double temp_integral;
                double temp_absprecision;
                (*updater)(sums, fNIterations, temp_integral, temp_absprecision);
                LogOutputAtIntegrationStatusUpdate(type, temp_integral, temp_absprecision, fNIterations);
            }
        }

    // calculate integral
    (*updater)(sums, fNIterations, integral, absprecision);
    relprecision = absprecision / integral;

    if (unsigned(fNIterations) >= fMCMCNIterationsMax)
       BCLog::OutWarning("BCIntegrate::Integrate: Did not converge within maximum number of iterations");

    // print to log
    LogOutputAtEndOfIntegration(integral, absprecision, relprecision, fNIterations);

    fError = absprecision;
    return integral;
}

// ---------------------------------------------------------
double BCIntegrate::EvaluatorMC(std::vector<double> &sums, const std::vector<double> &point, bool &accepted) {
    const double value = Eval(point);

    // all samples accepted in sample-mean integration
    accepted = true;

    // add value to sum and sum of squares
    sums[0] += value;
    sums[1] += value * value;

    return value;
}

// ---------------------------------------------------------
void BCIntegrate::IntegralUpdaterMC(const std::vector<double> &sums, const int &nIterations, double &integral, double &absprecision) {
    // sample mean including the volume of the parameter space
    integral = sums[2] * sums[0] / nIterations;

    // unbiased estimate
    absprecision = sqrt((1.0 / (nIterations - 1)) * (sums[2] * sums[2] * sums[1] / double(nIterations) - integral * integral));
}

// ---------------------------------------------------------
bool BCIntegrate::CheckMarginalizationAvailability(BCMarginalizationMethod type) {
  switch(type)
    {
    case BCIntegrate::kMargMonteCarlo:
      return false;
    case BCIntegrate::kMargMetropolis:
      return true;
    case BCIntegrate::kMargGrid:
      return true;
    case BCIntegrate::kMargDefault:
      return true;
    default:
      BCLog::OutError(TString::Format("BCIntegrate::CheckMarginalizationAvailability. Invalid marginalization method: %d.", type));
      break;
    }
  return false;
}

// ---------------------------------------------------------
bool BCIntegrate::CheckMarginalizationIndices(TH1* hist, const std::vector<unsigned> &index) {
    if (index.size()==0) {
        BCLog::OutError("BCIntegrate::Marginalize : No marginalization parameters chosen.");
        return false;
    }

    if (index.size() >= 4 or index.size() > fParameters.Size()) {
        BCLog::OutError("BCIntegrate::Marginalize : Too many marginalization parameters.");
        return false;
    }

    if ((int)index.size()<hist->GetDimension()) {
        BCLog::OutError(TString::Format("BCIntegrate::Marginalize : Too few (%d) indices supplied for histogram dimension (%d)",(int)index.size(),hist->GetDimension()));
        return false;
    }

    for (unsigned i=0; i<index.size(); i++) {
        // check if indices are in bounds
        if ( ! fParameters.ValidIndex(index[i])) {
            BCLog::OutError(TString::Format("BCIntegrate::Marginalize : Parameter index (%d) out of bound.",index[i]));
            return false;
        }
        // check for duplicate indices
        for (unsigned j=0; j<index.size(); j++)
            if (i!=j and index[i]==index[j]) {
                BCLog::OutError(TString::Format("BCIntegrate::Marginalize : Parameter index (%d) appears more than once",index[i]));
                return false;
            }
    }
    return true;
}
#if 0
// ---------------------------------------------------------
TH1D* BCIntegrate::Marginalize(BCIntegrationMethod type, unsigned index)
{
    BCParameter * par = fParameters.Get(index);
    if ( ! par)
        return NULL;

    // create histogram
    TH1D * hist = new TH1D(TString::Format("h1_%s", par->GetName().data()),
                           TString::Format(";%s;(unit %s)^{-1};", par->GetName().data(), par->GetName().data()),
                           par->GetNbins(), par->GetLowerLimit(), par->GetUpperLimit());

    // fill histogram
    std::vector<unsigned> indices(1, index);
    Marginalize(hist, type, indices);

    return hist;
}

// ---------------------------------------------------------
TH2D* BCIntegrate::Marginalize(BCIntegrationMethod type, unsigned index1, unsigned index2)
{
   BCParameter * par1 = fParameters.Get(index1);
   BCParameter * par2 = fParameters.Get(index2);
   if ( ! par1 || par2)
      return NULL;

    // create histogram
    TH2D * hist = new TH2D(TString::Format("h2_%s_%s", par1->GetName().data(), par2->GetName().data()),
                                                 TString::Format(";%s;%s;(unit %s)^{-1}(unit %s)^{-1}",
                                                            par1->GetName().data(), par2->GetName().data(),
                                                            par1->GetName().data(), par2->GetName().data()),
                                                            par1->GetNbins(), par1->GetLowerLimit(), par1->GetUpperLimit(),
                                                            par2->GetNbins(), par2->GetLowerLimit(), par2->GetUpperLimit());

    // fill histogram
    std::vector<unsigned> indices;
    indices.push_back(index1);
    indices.push_back(index2);
    Marginalize(hist,type,indices);

    return hist;
}

// ---------------------------------------------------------
bool BCIntegrate::Marginalize(TH1* hist, BCIntegrationMethod type, const std::vector<unsigned> &index)
{
  // debugKK: does this method really marginalize?

  //    if (!CheckMarginalizationAvailability(type))
  //        return false;

    if (!CheckMarginalizationIndices(hist,index))
        return false;

    // todo is this true?
    // Currently this does not seem to work for Cuba integration beyond 1 dimension
    if (type==kIntCuba and hist->GetDimension()>1) {
        BCLog::OutError("BCIntegrate::Marginalize : Cuba integration currently only functions for 1D marginalization.");
        return false;
    }

    // generate string output
    char * parnames = new char;
    for (unsigned i=0; i<index.size(); i++) {
        parnames = Form("%s %d (%s),",parnames,index[i],fParameters[i]->GetName().data());
    }
    if (index.size()==1)
        BCLog::OutDebug(TString::Format(" --> Marginalizing model w/r/t parameter%s using %s.",parnames, DumpCurrentMarginalizationMethod().c_str()));
    else
        BCLog::OutDebug(TString::Format(" --> Marginalizing model w/r/t parameters%s using %s.",parnames, DumpCurrentMarginalizationMethod().c_str()));

    // Store original integration limits and fixed flags
    // and unfix marginalization parameters;
    std::vector<double> origMins, origMaxs;
    std::vector<bool> origFix;
    for (unsigned i=0; i<index.size(); i++) {
       BCParameter * par = fParameters[index[i]];
        origMins.push_back(par->GetLowerLimit());
        origMaxs.push_back(par->GetUpperLimit());
        origFix.push_back(par->Fixed());
        par->Fix(false);
    }

    // Set histogram title to indicate fixed variables
   std::string title;
   for (unsigned i=0; i < fParameters.Size(); ++i)
      if (fParameters[i]->Fixed()) {
         title += TString::Format(" (%s=%e)", fParameters[i]->GetName().data(), fParameters[i]->GetFixedValue());
      }
   if ( ! title.empty())
   {
      hist -> SetTitle(("Fixed: "+title).data());
   }

    // get bin count
    int N = hist->GetNbinsX() * hist->GetNbinsY() * hist->GetNbinsZ();

    // Store fNIterationsMax and change
    int nIterationsMax = fNIterationsMax;
    fNIterationsMax = fNIterationsMax / N;
    if (fNIterationsMax<fNIterationsMin)
        fNIterationsMax = fNIterationsMin;

    // todo not thread safe!
    // integrate each bin
    for (int i=1; i<=hist->GetNbinsX(); i++) {
        fParameters[index[0]]->SetLowerLimit(hist->GetXaxis()->GetBinLowEdge(i));
        fParameters[index[0]]->SetUpperLimit(hist->GetXaxis()->GetBinLowEdge(i+1));
        double binwidth1d = hist -> GetXaxis() -> GetBinWidth(i);
        if (hist->GetDimension()>1)
            for (int j=1; j<=hist->GetNbinsY(); j++) {
                fParameters[index[1]]->SetLowerLimit(hist -> GetYaxis() -> GetBinLowEdge(j));
                fParameters[index[1]]->SetUpperLimit(hist -> GetYaxis() -> GetBinLowEdge(j+1));
                double binwidth2d = binwidth1d * hist->GetYaxis()->GetBinWidth(j);
                if (hist->GetDimension()>2)
                    for (int k=1; k<=hist->GetNbinsZ(); k++) {
                        fParameters[index[2]]->SetLowerLimit(hist -> GetZaxis() -> GetBinLowEdge(k));
                        fParameters[index[2]]->SetUpperLimit(hist -> GetZaxis() -> GetBinLowEdge(k+1));
                        double binwidth3d = binwidth2d * hist->GetZaxis()->GetBinWidth(k);
                        hist -> SetBinContent(i, j, k, Integrate(type)/binwidth3d);
                        hist -> SetBinError  (i, j, k, GetError()/binwidth3d);
                    }
                else {
                    hist -> SetBinContent(i, j, Integrate(type)/binwidth2d);
                    hist -> SetBinError  (i, j, GetError()/binwidth2d);
                }
            }
        else {
            hist -> SetBinContent(i, Integrate(type)/binwidth1d);
            hist -> SetBinError  (i, GetError()/binwidth1d);
        }
    }

    // restore original integration limits and fixed flags
    for (unsigned i=0; i<index.size(); i++) {
        fParameters[index[i]]->SetLowerLimit(origMins[i]);
        fParameters[index[i]]->SetUpperLimit(origMaxs[i]);
        fParameters[index[i]]->Fix(origFix[i]);
    }

    // restore original fNIterationsMax
    fNIterationsMax = nIterationsMax;

    return true;
}
#endif

// ---------------------------------------------------------
int BCIntegrate::MarginalizeAll()
{
  // check if parameters are defined
  if (fParameters.Size() < 1) {
    BCLog::OutError("BCIntegrate::MarginalizeAll : No parameters defined. Aborting.");
    return 0;
  }

  // check if marginalization method is defined
  if (!CheckMarginalizationAvailability(GetMarginalizationMethod())) {
    BCLog::OutError(Form("BCIntegrate::MarginalizeAll : Marginalization method not implemented \'%s\'. Aborting.", DumpCurrentMarginalizationMethod().c_str()));
    return 0;
  }

  // output
  if (!(fMarginalizationMethodCurrent == BCIntegrate::kMargDefault) && !(fMarginalizationMethodCurrent == BCIntegrate::kMargEmpty))
    BCLog::OutSummary(Form("Marginalize using %s", DumpCurrentMarginalizationMethod().c_str()));

  switch (GetMarginalizationMethod())
    {

      // Empty
    case BCIntegrate::kMargEmpty:
      {
        BCLog::OutWarning("BCIntegrate::MarginalizeAll : No marginalization method chosen.");
        return 0;
      }

      // Markov Chain Monte Carlo
    case BCIntegrate::kMargMetropolis:
      {
        // start preprocess
        MarginalizePreprocess();

        // run the Markov chains
        MCMCMetropolis();

        // start postprocess
        MarginalizePostprocess();

        // set pointers to marginalized distributions
        unsigned int npar = GetNParameters();

        fMarginalized1D.clear();
        for (unsigned int i = 0; i < npar; ++i) {
          fMarginalized1D.push_back(MCMCGetH1Marginalized(i));
        }

        fMarginalized2D.clear();
        if (npar > 1) {
          for (unsigned int i = 0; i < npar; ++i) {
            for (unsigned int j = 0; j < npar; ++j) {
              if (i < j)
                fMarginalized2D.push_back(MCMCGetH2Marginalized(i, j));
            }
          }
        }

        // set used marginalization method
        fMarginalizationMethodUsed = BCIntegrate::kMargMetropolis;

        // check if mode is better than previous one
        if ( (!fFlagIgnorePrevOptimization) && (fLogMaximum < fMCMCLogMaximum) ) {
          fBestFitParameters      = fMCMCBestFitParameters;
          fBestFitParameterErrors.assign(fParameters.Size(),-1.);
          fLogMaximum             = fMCMCLogMaximum;
          fOptimizationMethodUsed = BCIntegrate::kOptMetropolis;
        }

      break;
      }

      // Sample Mean
    case BCIntegrate::kMargMonteCarlo:
      {
        return 0;
      }

      // Slice
    case BCIntegrate::kMargGrid:
      {
        std::vector<double> fixpoint(GetNParameters());
        for (unsigned int i = 0; i < GetNParameters(); ++i) {
          if (fParameters[i]->Fixed())
            fixpoint[i] = fParameters[i]->GetFixedValue();
          else
            fixpoint[i] = 0;
        }

        // start preprocess
        MarginalizePreprocess();

        // store highest probability
        double probmax = -std::numeric_limits<double>::infinity();
        std::vector<double> bestfit_parameters(fParameters.Size(), -std::numeric_limits<double>::infinity());
        // correct fixed parameter values
        // the other should have been determined above
        for (unsigned i = 0; i < fParameters.Size(); ++i)
           if (fParameters[i]->Fixed())
              bestfit_parameters[i] = fParameters[i]->GetFixedValue();

        fMarginalized1D.clear();
        if (GetNFreeParameters() == 1) {
          for (unsigned int i = 0; i < GetNParameters(); ++i) {
            if (!fParameters[i]->Fixed()) {
              // calculate slice
              BCH1D* hist_temp = GetSlice(fParameters[i], fixpoint, 0);
              fMarginalized1D.push_back(hist_temp);

              // remember best fit before it is normalized and the value is wrong
              const int index = hist_temp->GetHistogram()->GetMaximumBin();
              probmax = hist_temp->GetHistogram()->GetBinContent(index);
              bestfit_parameters.at(i) = hist_temp->GetHistogram()->GetBinCenter(index);

              // normalize to unity
              hist_temp->GetHistogram()->Scale(1./hist_temp->GetHistogram()->Integral());
            }
            else
              fMarginalized1D.push_back(0);
          }

          fMarginalized2D.clear();
          for (unsigned int i = 0; i < GetNParameters(); ++i) {
            for (unsigned int j = 0; j < GetNParameters(); ++j) {
              if (i >= j)
                continue;
              else
                fMarginalized2D.push_back(0);
            }
          }
        }
        else if (GetNFreeParameters() == 2) {
          // create a 2D histogram

          BCH2D* hist2d_temp = 0;

          fMarginalized2D.clear();
          for (unsigned int i = 0; i < GetNParameters(); ++i) {
            for (unsigned int j = 0; j < GetNParameters(); ++j) {
              if (i >= j)
                continue;
              if (!fParameters[i]->Fixed() && !fParameters[j]->Fixed()) {
                // calculate slice
                hist2d_temp = GetSlice(GetParameter(i), GetParameter(j), fixpoint, 0);
                fMarginalized2D.push_back(hist2d_temp);

                // remember best fit before it is normalized and the value is wrong
                int index1, index2, useless_index;
                hist2d_temp->GetHistogram()->GetMaximumBin(index1, index2, useless_index);
                probmax = hist2d_temp->GetHistogram()->GetBinContent(index1, index2, useless_index);
                bestfit_parameters.at(i) = hist2d_temp->GetHistogram()->GetXaxis()->GetBinCenter(index1);
                bestfit_parameters.at(j) = hist2d_temp->GetHistogram()->GetYaxis()->GetBinCenter(index2);

                // normalize to unity
                hist2d_temp->GetHistogram()->Scale(1./hist2d_temp->GetHistogram()->Integral());
              }
              else
                fMarginalized2D.push_back(0);
            }
          }

          // marginalize by projecting
          fMarginalized1D.clear();
          for (unsigned int i = 0; i < GetNParameters(); ++i)
            fMarginalized1D.push_back(0);
          for (unsigned int i = 0; i < GetNParameters(); ++i) {
            for (unsigned int j = 0; j < GetNParameters(); ++j) {
              if (i >= j)
                continue;
              if (!fParameters[i]->Fixed() && !fParameters[j]->Fixed()) {
                BCH1D* hist_x = new BCH1D( hist2d_temp->GetHistogram()->ProjectionX() );
                hist_x->GetHistogram()->UseCurrentStyle(); // reset style because histogram is created by a projection
                hist_x->GetHistogram()->SetStats(kFALSE);
                fMarginalized1D[i] = hist_x;
                BCH1D* hist_y = new BCH1D( hist2d_temp->GetHistogram()->ProjectionY() );
                hist_y->GetHistogram()->UseCurrentStyle(); // reset style because histogram is created by a projection
                hist_y->GetHistogram()->SetStats(kFALSE);
                fMarginalized1D[j] = hist_y;
              }
            }
          }
        }
        else {
          BCLog::OutWarning("BCIntegrate::MarginalizeAll : Option works for 1D and 2D problems.");
          return 0;
        }

        // save if improved the log posterior

        if (fBestFitParameters.empty() || probmax > fMCMCLogMaximum) {
           fLogMaximum = probmax;
           fBestFitParameters = bestfit_parameters;
           fBestFitParameterErrors.assign(fBestFitParameters.size(), std::numeric_limits<double>::infinity());
           // todo can't set this one yet
           //           fOptimizationMethodUsed =
        }

        BCLog::OutDetail(" --> Global mode from Grid:");
        BCLog::OutDebug(Form(" --> Posterior value: %g", probmax));
        int ndigits = (int) log10(fParameters.Size());
        for (unsigned i = 0; i < fParameters.Size(); ++i)
            BCLog::OutDetail(TString::Format(" -->      parameter %*i:   %.4g", ndigits+1, i, bestfit_parameters[i]));

        // start postprocess
        MarginalizePostprocess();

        // set used marginalization method
        fMarginalizationMethodUsed = BCIntegrate::kMargGrid;

      break;
      }

      // default
    case BCIntegrate::kMargDefault:
      {
        if ( GetNFreeParameters() <= 2 ) {
          SetMarginalizationMethod(BCIntegrate::kMargGrid);
        }
        else {
          SetMarginalizationMethod(BCIntegrate::kMargMetropolis);
        }

        // call again
        return MarginalizeAll();

      break;
      }

    default:
      BCLog::OutError(TString::Format("BCIntegrate::MarginalizeAll : Invalid marginalization method: %d", GetMarginalizationMethod()));
      return 0;
      break;
    }

  // set flag
  fFlagMarginalized = true;

  return 1;
}

// ---------------------------------------------------------
int BCIntegrate::MarginalizeAll(BCIntegrate::BCMarginalizationMethod margmethod)
{
  // remember original method
  BCMarginalizationMethod method_temp = fMarginalizationMethodCurrent;

  // set method
  SetMarginalizationMethod(margmethod);

  // run algorithm
  int result = MarginalizeAll();

  // re-set original method
  SetMarginalizationMethod(method_temp);

  // return result
  return result;
}

// ---------------------------------------------------------
BCH1D * BCIntegrate::GetSlice(const BCParameter* parameter, const std::vector<double> parameters, int nbins, bool flag_norm)
{
    // check if parameter exists
    if (!parameter) {
        BCLog::OutError("BCIntegrate::GetSlice : Parameter does not exist.");
        return 0;
    }

  // check if parameter is fixed
  if (parameter->Fixed())
    return 0;

    // create local copy of parameter set
    std::vector<double> parameters_temp;
    parameters_temp = parameters;

    // check if parameter set if defined
    if (parameters_temp.empty() && GetNParameters() == 1) {
        parameters_temp.push_back(0);
    }
    else if (parameters_temp.empty() && GetNParameters() != 1) {
        BCLog::OutError("BCIntegrate::GetSlice : No parameters defined.");
        return 0;
    }

    // calculate number of bins
    if (nbins <= 0)
        nbins = parameter->GetNbins();

    // create histogram
    TH1D * hist = new TH1D("", "", nbins, parameter->GetLowerLimit(), parameter->GetUpperLimit());
  hist->UseCurrentStyle();

    // set axis labels
    hist->SetXTitle(parameter->GetLatexName().data());
    if (GetNParameters() == 1)
        hist->SetYTitle(Form("p(%s|data)", parameter->GetLatexName().data()));
    else
        hist->SetYTitle(Form("p(%s|data, all other parameters fixed)", parameter->GetLatexName().data()));
    hist->SetStats(kFALSE);

    // fill histogram
    for (int i = 1; i <= nbins; ++i) {
        double par_temp = hist->GetBinCenter(i);
        parameters_temp[fParameters.Index(parameter->GetName())] = par_temp;
        double prob = Eval(parameters_temp);
        hist->SetBinContent(i, prob);
    }

    // normalize
    if (flag_norm)
        hist->Scale(1.0/hist->Integral());

    // set histogram
    BCH1D * hprob = new BCH1D();
    hprob->SetHistogram(hist);

    return hprob;
}

// ---------------------------------------------------------
BCH2D* BCIntegrate::GetSlice(const BCParameter* parameter1, const BCParameter* parameter2, const std::vector<double> parameters, int nbins, bool flag_norm)
{
  return GetSlice(parameter1->GetName().c_str(), parameter2->GetName().c_str(), parameters, nbins, flag_norm);
}

// ---------------------------------------------------------
BCH2D* BCIntegrate::GetSlice(const char* name1, const char* name2, const std::vector<double> parameters, int nbins, bool flag_norm)
{
  return GetSlice(fParameters.Index(name1), fParameters.Index(name2), parameters, nbins, flag_norm);
}

// ---------------------------------------------------------
BCH2D* BCIntegrate::GetSlice(unsigned index1, unsigned index2, const std::vector<double> parameters, int nbins, bool flag_norm)
{
   // check if parameters exists
   if (!fParameters.ValidIndex(index1) || !fParameters.ValidIndex(index2)) {
      BCLog::OutError("BCIntegrate::GetSlice : Parameter does not exist.");
      return 0;
   }

   // check if parameters are fixed
   if (fParameters[index1]->Fixed() || fParameters[index2]->Fixed())
     return 0;

   // create local copy of parameter set
   std::vector<double> parameters_temp;
   parameters_temp = parameters;

   // check number of dimensions
   if (GetNParameters() < 2) {
      BCLog::OutError("BCIntegrate::GetSlice : Number of parameters need to be at least 2.");
   }

   // check if parameter set if defined
   if (parameters_temp.size()==0 && GetNParameters()==2) {
      parameters_temp.push_back(0);
      parameters_temp.push_back(0);
   }
   else if (parameters_temp.size()==0 && GetNParameters()>2) {
      BCLog::OutError("BCIntegrate::GetSlice : No parameters defined.");
      return 0;
   }

   // calculate number of bins
   const BCParameter * p1 = fParameters.Get(index1);
   const BCParameter * p2 = fParameters.Get(index2);
   unsigned nbins1, nbins2;
   if (nbins <= 0) {
      nbins1 = p1->GetNbins();
      nbins2 = p2->GetNbins();
   } else {
      nbins1 = nbins2 = nbins;
   }

   // create histogram
   TH2D * hist = new TH2D("", "", nbins1, p1->GetLowerLimit(), p1->GetUpperLimit(),
                          nbins2, p2->GetLowerLimit(), p2->GetUpperLimit());
   hist->UseCurrentStyle();

   // set axis labels
   hist->SetXTitle(Form("%s", p1->GetLatexName().data()));
   hist->SetYTitle(Form("%s", p2->GetLatexName().data()));
   hist->SetStats(kFALSE);

   // fill histogram
   for (unsigned int ix = 1; ix <= nbins1; ++ix) {
      for (unsigned int iy = 1; iy <= nbins2; ++iy) {
         double par_temp1 = hist->GetXaxis()->GetBinCenter(ix);
         double par_temp2 = hist->GetYaxis()->GetBinCenter(iy);

         parameters_temp[index1] = par_temp1;
         parameters_temp[index2] = par_temp2;

         double prob = Eval(parameters_temp);
         hist->SetBinContent(ix, iy, prob);
      }
   }

   // calculate normalization
   double norm = hist->Integral("width");

   // normalize
   if (flag_norm)
      hist->Scale(1.0/norm);

   // set histogram
   BCH2D * hprob = new BCH2D();
   hprob->SetHistogram(hist);

   // renormalize
   hist->Scale(norm / hist->Integral("width"));

   return hprob;
}
// ---------------------------------------------------------
double BCIntegrate::GetRandomPoint(std::vector<double> &x)
{
   GetRandomVectorInParameterSpace(x);
   return Eval(x);
}

// ---------------------------------------------------------
void BCIntegrate::GetRandomVectorUnitHypercube(std::vector<double> &x) const
{
   fRandom->RndmArray(x.size(), &x.front());
}

// ---------------------------------------------------------
void BCIntegrate::GetRandomVectorInParameterSpace(std::vector<double> &x) const
{
     GetRandomVectorUnitHypercube(x);

     for (unsigned i = 0; i < fParameters.Size(); i++){
         if (fParameters[i]->Fixed())
             x[i] = fParameters[i]->GetFixedValue();
         else
             x[i] = fParameters[i]->GetLowerLimit() + x[i] * fParameters[i]->GetRangeWidth();
     }
}

// ---------------------------------------------------------
BCH1D * BCIntegrate::GetMarginalized(const BCParameter * parameter)
{
   if ( !parameter)
      return 0;
   return GetMarginalized(fParameters.Index(parameter->GetName()));
}

// ---------------------------------------------------------
BCH1D * BCIntegrate::GetMarginalized(unsigned index)
{
  // check if marginalized histogram exists
  if (fMarginalized1D.size() <= index)
    return 0;

  // get histogram
  BCH1D * htemp = fMarginalized1D.at(index);

  // check if histogram exists
  if (!htemp)
    return 0;

  // set global mode
  if (fBestFitParameters.size() == GetNParameters())
    htemp->SetGlobalMode(fBestFitParameters.at(index));

  // set axis labels
   htemp->GetHistogram()->SetName(Form("hist_%i_%s", fID, fParameters[index]->GetName().data()));
   htemp->GetHistogram()->SetYTitle(Form("p(%s|data)", fParameters[index]->GetLatexName().data()));

   // return histogram
   return htemp;
}

 // ---------------------------------------------------------
int BCIntegrate::ReadMarginalizedFromFile(const char * file)
{
   TFile * froot = TFile::Open(file);
   if (!froot->IsOpen()) {
      BCLog::OutError(Form("BCIntegrate::ReadMarginalizedFromFile : Couldn't open file %s.", file));
      return 0;
   }

   // We reset the MCMCEngine here for the moment.
   // In the future maybe we only want to do this if the engine
   // wans't initialized at all or when there were some changes
   // in the model.
   // But maybe we want reset everything since we're overwriting
   // the marginalized distributions anyway.
   MCMCInitialize();

   int k = 0;
   int n = GetNParameters();
   for (int i = 0; i < n; i++) {
      const BCParameter * a = GetParameter(i);
      TKey * key = froot->GetKey(TString::Format("hist_%i_%s", fID, a->GetName().data()));
      if (key) {
         TH1D * h1 = (TH1D*) key->ReadObjectAny(TH1D::Class());
         h1->SetDirectory(0);
         if (SetMarginalized(i, h1))
            k++;
      }
      else
         BCLog::OutWarning(
               Form("BCIntegrate::ReadMarginalizedFromFile : Couldn't read histogram \"hist_%i_%s\" from file %s.",
                     fID, a->GetName().data(), file));
   }

   for (int i = 0; i < n - 1; i++) {
      for (int j = i + 1; j < n; j++) {
         const BCParameter * a = GetParameter(i);
         const BCParameter * b = GetParameter(j);
         TKey * key = froot->GetKey(
               TString::Format("hist_%i_%s_%s",fID, a->GetName().data(),b->GetName().data()));
         if (key) {
            TH2D * h2 = (TH2D*) key->ReadObjectAny(TH2D::Class());
            h2->SetDirectory(0);
            if (SetMarginalized(i, j, h2))
               k++;
         }
         else
            BCLog::OutWarning(
                  Form("BCIntegrate::ReadMarginalizedFromFile : Couldn't read histogram \"hist_%i_%s_%s\" from file %s.",
                        fID, a->GetName().data(), b->GetName().data(), file));
      }
   }

   froot->Close();

   return k;
}


// ---------------------------------------------------------
int BCIntegrate::PrintAllMarginalized1D(const char * filebase)
{
   if (fMCMCH1Marginalized.size() == 0) {
      BCLog::OutError("BCIntegrate::PrintAllMarginalized : Marginalized distributions not available.");
      return 0;
   }

   int n = GetNParameters();
   for (int i = 0; i < n; i++) {
      const BCParameter * a = GetParameter(i);
      if (GetMarginalized(a))
         GetMarginalized(a)->Print(Form("%s_1D_%s.pdf", filebase, a->GetName().data()));
   }

   return n;
}

// ---------------------------------------------------------
int BCIntegrate::PrintAllMarginalized2D(const char * filebase)
{
   if (fMCMCH2Marginalized.size() == 0) {
      BCLog::OutError("BCIntegrate::PrintAllMarginalized : Marginalized distributions not available.");
      return 0;
   }

   int k = 0;
   int n = GetNParameters();
   for (int i = 0; i < n - 1; i++) {
      for (int j = i + 1; j < n; j++) {
         const BCParameter * a = GetParameter(i);
         const BCParameter * b = GetParameter(j);

         double meana = (a->GetLowerLimit() + a->GetUpperLimit()) / 2.;
         double deltaa = (a->GetUpperLimit() - a->GetLowerLimit());
         if (deltaa <= 1e-7 * meana)
            continue;

         double meanb = (b->GetLowerLimit() + b->GetUpperLimit()) / 2.;
         double deltab = (b->GetUpperLimit() - b->GetLowerLimit());
         if (deltab <= 1e-7 * meanb)
            continue;

         if (GetMarginalized(a, b))
            GetMarginalized(a, b)->Print(
                  Form("%s_2D_%s_%s.pdf",filebase, a->GetName().data(), b->GetName().data()));
         k++;
      }
   }

   return k;
}

// ---------------------------------------------------------
int BCIntegrate::PrintAllMarginalized(const char * file, std::string options1d, std::string options2d, unsigned int hdiv, unsigned int vdiv)
{
   if (fMarginalized1D.size() == 0 and fMarginalized2D.size() == 0) {
      BCLog::OutError("BCIntegrate::PrintAllMarginalized : Marginalized distributions not available.");
      return 0;
   }

   // count all valid (non NULL) histograms
   int nvalid1D = 0;
   int nvalid2D = 0;

   for (unsigned i = 0 ; i < fMarginalized1D.size() ; ++i) {
     if (BCH1D * h = fMarginalized1D[i])
       if (h->GetHistogram())
         nvalid1D++;
   }

   for (unsigned i = 0 ; i < fMarginalized2D.size() ; ++i) {
     if (BCH2D * h = fMarginalized2D[i])
       if (h->GetHistogram())
         nvalid2D++;
   }

   std::string filename(file);

   // check if file extension does not exist or is not pdf or ps
   if ( (filename.find_last_of(".") == std::string::npos) or
         ((filename.substr(filename.find_last_of(".")+1) != "pdf") and
               (filename.substr(filename.find_last_of(".")+1) != "ps"))) {
      // make it a PDF file
      filename += ".pdf";
   }

   int c_width  = gStyle->GetCanvasDefW(); // default canvas width
   int c_height = gStyle->GetCanvasDefH(); // default canvas height

   if (hdiv > vdiv) {
      if (hdiv > 3) {
         c_width = 1000;
         c_height = 700;
      }
      else {
         c_width = 800;
         c_height = 600;
      }
   }
   else if (hdiv < vdiv) {
      if (hdiv > 3) {
         c_height = 1000;
         c_width = 700;
      }
      else {
         c_height = 800;
         c_width = 600;
      }
   }

   const unsigned nplots = nvalid1D + nvalid2D;

   // give out warning if too many plots
   BCLog::OutSummary(Form("Printing all marginalized distributions (%d x 1D + %d x 2D = %d) into file %s",
                          nvalid1D, nvalid2D, nplots, filename.c_str()));
   if (nplots > 100)
      BCLog::OutDetail("This can take a while...");

   // setup the canvas and file
   TCanvas c("c", "canvas", c_width, c_height);
   c.Divide(hdiv, vdiv);

   // for clean up later
   std::vector<BCH1D *> h1;

   // count plots
   unsigned n = 0;

   // open file for printing
   c.Print(std::string( filename + "[").c_str());

   for (unsigned i = 0; i < fParameters.Size(); ++i) {
      BCH1D * h = GetMarginalized(i);
      h1.push_back(h);

      // check if histogram exists
      if ( !h)
         continue;

      // if current page is full, switch to new page
      if (n != 0 && n % (hdiv * vdiv) == 0) {
         c.Print(filename.c_str());
         c.Clear("D");
      }

      // go to next pad
      c.cd(n % (hdiv * vdiv) + 1);

      h->Draw(options1d);

      if (++n % 100 == 0)
         BCLog::OutDetail(Form(" --> %d plots done", n));
   }

   // print page if any were plots were drawn
   if (n>0) {
      c.Print(filename.c_str());
      c.Clear("D");
   }

   // for clean up later
   std::vector<BCH2D *> h2;

   // check how many 2D plots are actually drawn, despite no histogram filling or delta prior
   unsigned k = 0;
   for (unsigned i = 0; i < fParameters.Size() - 1; ++i) {
      for (unsigned j = i + 1; j < fParameters.Size(); ++j) {
         // check if histogram exists, or skip if one par has a delta prior
         h2.push_back(GetMarginalized(i, j));
         if ( !h2.back())
            continue;

         // get corresponding parameters
         BCParameter * a = GetParameter(i);
         BCParameter * b = GetParameter(j);

         // if current page is full, switch to new page, but only if there is data to plot
         if ((k != 0 && k % (hdiv * vdiv) == 0)) {
            c.Print(filename.c_str());
            c.Clear("D");
         }

         // go to next pad
         c.cd(k % (hdiv * vdiv) + 1);

         const double meana = (a->GetLowerLimit() + a->GetUpperLimit()) / 2.;
         if (a->GetRangeWidth() <= 1e-7 * meana)
            continue;

         const double meanb = (b->GetLowerLimit() + b->GetUpperLimit()) / 2.;
         if (b->GetRangeWidth() <= 1e-7 * meanb)
            continue;

         h2.back()->Draw(options2d);
         ++k;

         if ((n + k) % 100 == 0)
            BCLog::OutDetail(Form(" --> %d plots done", n + k));
      }
   }

   if (k>0) {
      c.Print(filename.c_str());
   }

   if ((n + k) > 100 && (n + k) % 100 != 0)
      BCLog::OutDetail(Form(" --> %d plots done", n + k));

   c.Print(std::string( filename + "]").c_str());

   // return total number of drawn histograms
   return n + k;
}

// ---------------------------------------------------------
BCH2D * BCIntegrate::GetMarginalized(const BCParameter * par1, const BCParameter * par2)
{
   if ( !par1 or !par2 or (par1 == par2) )
      return 0;

  return GetMarginalized(fParameters.Index(par1->GetName()), fParameters.Index(par2->GetName()));
}

// ---------------------------------------------------------
BCH2D * BCIntegrate::GetMarginalized(unsigned index1, unsigned index2)
{
  // swap indices if necessary
  if (index1 > index2) {
    unsigned indexTemp = index1;
    index1 = index2;
    index2 = indexTemp;
  }

  // check if marginalized histogram exists
  if (fMarginalized2D.size() <= GetNParameters() * index1 - (index1 * index1 + 3 * index1) / 2 + index2 - 1)
    return 0;

  // get histogram
  BCH2D * htemp =  fMarginalized2D.at(GetNParameters() * index1 - (index1 * index1 + 3 * index1) / 2 + index2 - 1);

  // check if histogram exists
  if ( !htemp)
    return 0;

  // set global mode
  if (fBestFitParameters.size() == GetNParameters()) {
    double gmode[] = { fBestFitParameters.at(index1), fBestFitParameters.at(index2) };
    htemp->SetGlobalMode(gmode);
  }

  // set name
  htemp->GetHistogram()->SetName(Form("hist_%i_%s_%s", fID,
                                      fParameters[index1]->GetName().data(),
                                      fParameters[index2]->GetName().data()));

  // return histogram
  return htemp;
}

// ---------------------------------------------------------
std::vector<double> BCIntegrate::FindMode(std::vector<double> start)
{
  if (fParameters.Size() < 1) {
    BCLog::OutError("FindMode : No parameters defined. Aborting.");
    return std::vector<double>();
  }

  if (start.empty() && fBestFitParameters.size() == fParameters.Size())
     start = fBestFitParameters;

  std::vector<double> mode_temp(GetNParameters());
  std::vector<double> errors_temp(GetNParameters());
  BCIntegrate::BCOptimizationMethod method_temp = fOptimizationMethodCurrent;

  // output
  if (!(fOptimizationMethodCurrent == BCIntegrate::kOptDefault) && !(fOptimizationMethodCurrent == BCIntegrate::kOptEmpty))
    BCLog::OutSummary(Form("Finding mode using %s", DumpCurrentOptimizationMethod().c_str()));

  switch (fOptimizationMethodCurrent)
    {
    case BCIntegrate::kOptEmpty:
      {
        BCLog::OutWarning("BCIntegrate::FindMode : No optimization method chosen.");
        return std::vector<double>();
      }
    case BCIntegrate::kOptSimAnn:
      {
        FindModeSA(mode_temp, errors_temp, start);

        break;
      }

    case BCIntegrate::kOptMinuit:
      {
        int printlevel = -1;
        if (BCLog::GetLogLevelScreen() <= BCLog::detail)
          printlevel = 0;
        if (BCLog::GetLogLevelScreen() <= BCLog::debug)
          printlevel = 1;

        BCIntegrate::FindModeMinuit(mode_temp, errors_temp, start, printlevel);

        break;
      }

    case BCIntegrate::kOptMetropolis:
      {
        FindModeMCMC(mode_temp, errors_temp);

        break;
      }
    case BCIntegrate::kOptDefault:
      {
        SetOptimizationMethod(BCIntegrate::kOptMinuit);

        return FindMode(start);
      }

    default:
      BCLog::OutError(Form("BCIntegrate::FindMode : Invalid mode finding method: %d", GetOptimizationMethod()));
      return std::vector<double>();
    }

  // calculate function at new mode
  double fcnatmode_temp = Eval(mode_temp);

  // check if the mode found mode is better than the previous estimate
  if ( (!fFlagIgnorePrevOptimization) && (fcnatmode_temp < fLogMaximum) ) {
    // set best fit parameters
    if (mode_temp.size() == fBestFitParameters.size())
      mode_temp      = fBestFitParameters;
    else
      BCLog::OutError("BCIntegrate::FindMode : previous mode has a different number of parameters than current.");

    if (errors_temp.size() == fBestFitParameterErrors.size())
      errors_temp    = fBestFitParameterErrors;
    else
      BCLog::OutError("BCIntegrate::FindMode : previous error estimate has a different number of parameters than current.");

    fcnatmode_temp = fLogMaximum;
    method_temp    = fOptimizationMethodUsed;
  }

  // set the best-fit parameters
  fBestFitParameters      = mode_temp;
  fBestFitParameterErrors = errors_temp;
  fLogMaximum             = fcnatmode_temp;

  // set used optimization method
  fOptimizationMethodUsed = method_temp;

  // return the new mode
  return mode_temp;

}

// ---------------------------------------------------------
std::vector<double> BCIntegrate::FindMode(BCIntegrate::BCOptimizationMethod optmethod, std::vector<double> start)
{
  // remember original method
  BCOptimizationMethod method_temp = fOptimizationMethodCurrent;

  // set method
  SetOptimizationMethod(optmethod);

  // run algorithm
  std::vector<double> mode = FindMode(start);

  // re-set original method
  SetOptimizationMethod(method_temp);

  // return mode
  return mode;
}

// ---------------------------------------------------------
TMinuit * BCIntegrate::GetMinuit()
{
   if (!fMinuit)
      fMinuit = new TMinuit();

   return fMinuit;
}

// ---------------------------------------------------------
std::vector<double> BCIntegrate::FindModeMinuit(std::vector<double> &mode, std::vector<double> &errors, std::vector<double> start, int printlevel)
{
   if (fParameters.Size() < 1) {
      BCLog::OutError("BCIntegrate::FindModeMinuit : No parameters defined. Aborting.");
      return std::vector<double>();
   }

   bool have_start = true;

   // check start values
   if (start.size() == 0)
     have_start = false;
   else if (start.size() != fParameters.Size()) {
     have_start = false;
     BCLog::OutWarning("BCIntegrate::FindModeMinuit : Start point not valid (mismatch of dimensions), set to center.");
   }

   // check if point is allowed
   if (have_start) {
     for (unsigned int i = 0; i <fParameters.Size(); ++i) {
       if (!fParameters[i]->IsValid(start[i]))
         have_start = false;
       if (fParameters[i]->Fixed() && start[i] != fParameters[i]->GetFixedValue())
         have_start = false;
     }
     if (!have_start)
       BCLog::OutWarning("BCIntegrate::FindModeMinuit : Start point not valid (parameter not inside valid range), set to center.");
   }

   // set global this
   ::BCIntegrateHolder::instance(this);

   // define minuit
   if (fMinuit)
      delete fMinuit;
   fMinuit = new TMinuit(fParameters.Size());

   // set print level
   fMinuit->SetPrintLevel(printlevel);

   // set function
   fMinuit->SetFCN(&BCIntegrate::FCNLikelihood);

   // set UP for likelihood
   fMinuit->SetErrorDef(0.5);

   // set parameters
   int flag;
   for (unsigned i = 0; i < fParameters.Size(); i++) {
      double starting_point = (fParameters[i]->GetUpperLimit() + fParameters[i]->GetLowerLimit()) / 2.;
      if(have_start)
         starting_point = start[i];
      if (fParameters[i]->Fixed())
         starting_point = fParameters[i]->GetFixedValue();
      fMinuit->mnparm(i,
                      fParameters[i]->GetName().data(),
                      starting_point,
                      fParameters[i]->GetRangeWidth() / 100.,
                      fParameters[i]->GetLowerLimit(),
                      fParameters[i]->GetUpperLimit(),
                      flag);
   }

   for (unsigned i = 0; i < fParameters.Size(); i++)
      if (fParameters[i]->Fixed())
         fMinuit->FixParameter(i);

   // do mcmc minimization
   //   fMinuit->mnseek();

   // do minimization
   fMinuit->mnexcm("MIGRAD", fMinuitArglist, 2, flag);

   // improve search for local minimum
   //   fMinuit->mnimpr();

   // copy flag and result
   fMinuitErrorFlag = flag;
   //   std::vector<double> localMode(fParameters.Size(), 0);
   //   std::vector<double> errors(fParameters.Size(), 0);
   for (unsigned i = 0; i < fParameters.Size(); i++) {
      fMinuit->GetParameter(i, mode[i], errors[i]);
   }

   // delete minuit
   delete fMinuit;
   fMinuit = 0;

   return mode;
}

// ---------------------------------------------------------
void BCIntegrate::InitializeSATree()
{
  if (fTreeSA)
    delete fTreeSA;
  fTreeSA = new TTree("SATree", "SATree");

   fTreeSA->Branch("Iteration",      &fSANIterations,   "iteration/I");
   // todo make consistent with examples and test
   // remove because would require fixed number of parameters, and just superfluous info
//   fTreeSA->Branch("NParameters",    &fNvar,            "parameters/I");
   fTreeSA->Branch("Temperature",    &fSATemperature,   "temperature/D");
   fTreeSA->Branch("LogProbability", &fSALogProb,       "log(probability)/D");

   for (unsigned i = 0; i < fParameters.Size(); ++i)
      fTreeSA->Branch(TString::Format("Parameter%i", i), &fSAx[i], TString::Format("parameter %i/D", i));
}

// ---------------------------------------------------------
std::vector<double> BCIntegrate::FindModeSA(std::vector<double> &mode, std::vector<double> &errors, std::vector<double> start)
{
   // note: if f(x) is the function to be minimized, then
   // f(x) := - LogEval(parameters)

   bool have_start = true;
   std::vector<double> x, y; // vectors for current state, new proposed state and best fit up to now
   double fval_x, fval_y, fval_mode; // function values at points x, y and mode (we save them rather than to re-calculate them every time)
   int t = 1; // time iterator

   // check start values
   if (start.size() == 0)
     have_start = false;
   else if (start.size() != fParameters.Size()) {
     have_start = false;
     BCLog::OutWarning("BCIntegrate::FindModeSA : Start point not valid (mismatch of dimensions), set to center.");
   }

   // check if point is allowed
   if (have_start) {
     for (unsigned int i = 0; i <fParameters.Size(); ++i) {
       if (!fParameters[i]->IsValid(start[i]))
         have_start = false;
       if (fParameters[i]->Fixed() && start[i] != fParameters[i]->GetFixedValue())
         have_start = false;
     }
     if (!have_start)
       BCLog::OutWarning("BCIntegrate::FindModeSA : Start point not valid (parameter not inside valid range), set to center.");
   }

   // if no starting point is given, set to center of parameter space
   if ( !have_start ) {
      start.clear();
      for (unsigned i=0; i<fParameters.Size(); i++)
         if (fParameters[i]->Fixed())
            start.push_back(fParameters[i]->GetFixedValue());
         else
            start.push_back((fParameters[i]->GetLowerLimit() + fParameters[i]->GetUpperLimit()) / 2.);
   }

   // set current state and best fit to starting point
   x = start;
   mode = start;

   // calculate function value at starting point
   fval_x = fval_mode = LogEval(x);

   // run while still "hot enough"
   while ( SATemperature(t) > fSATmin ) {
      // generate new state
      y = GetProposalPointSA(x, t);

      // check if the proposed point is inside the phase space
      // if not, reject it
      bool in_range = true;

      for (unsigned i = 0; i < fParameters.Size(); i++)
         if ( !fParameters[i]->IsValid(y[i]))
            in_range = false;

      if ( in_range ){
         // calculate function value at new point
         fval_y = LogEval(y);

         // is it better than the last one?
         // if so, update state and chef if it is the new best fit...
         if (fval_y >= fval_x) {
            x = y;

            fval_x = fval_y;

            if (fval_y > fval_mode) {
               mode = y;
               fval_mode = fval_y;
            }
         }
         // ...else, only accept new state w/ certain probability
         else {
            if (fRandom->Rndm() <= exp( (fval_y - fval_x) / SATemperature(t) )) {
               x = y;
               fval_x = fval_y;
            }
         }
      }

      // update tree variables
      fSANIterations = t;
      fSATemperature = SATemperature(t);
      fSALogProb = fval_x;
      fSAx = x;

      // fill tree
      if (fFlagWriteSAToFile && fTreeSA)
         fTreeSA->Fill();

      // increate t
      t++;
   }

   // calculate uncertainty
   errors.assign(fParameters.Size(),-1);

   return mode;
}

// ---------------------------------------------------------
double BCIntegrate::SATemperature(double t)
{
   // do we have Cauchy (default), Boltzmann or custom annealing schedule?
   if (fSASchedule == BCIntegrate::kSABoltzmann)
      return SATemperatureBoltzmann(t);
   else if (fSASchedule == BCIntegrate::kSACauchy)
      return SATemperatureCauchy(t);
   else
      return SATemperatureCustom(t);
}

// ---------------------------------------------------------
double BCIntegrate::SATemperatureBoltzmann(double t)
{
   return fSAT0 / log((double)(t + 1));
}

// ---------------------------------------------------------
double BCIntegrate::SATemperatureCauchy(double t)
{
   return fSAT0 / (double)t;
}

// ---------------------------------------------------------
double BCIntegrate::SATemperatureCustom(double /*t*/)
{
   BCLog::OutError("BCIntegrate::SATemperatureCustom : No custom temperature schedule defined");
   return 0.;
}

// ---------------------------------------------------------
std::vector<double> BCIntegrate::GetProposalPointSA(const std::vector<double> &x, int t)
{
   // do we have Cauchy (default), Boltzmann or custom annealing schedule?
   if (fSASchedule == BCIntegrate::kSABoltzmann)
      return GetProposalPointSABoltzmann(x, t);
   else if (fSASchedule == BCIntegrate::kSACauchy)
      return GetProposalPointSACauchy(x, t);
   else
      return GetProposalPointSACustom(x, t);
}

// ---------------------------------------------------------
std::vector<double> BCIntegrate::GetProposalPointSABoltzmann(const std::vector<double> &x, int t)
{
   std::vector<double> y;
   y.clear();
   double new_val, norm;

   for (unsigned i = 0; i < fParameters.Size(); i++) {
      if (fParameters[i]->Fixed()) {
         y.push_back(fParameters[i]->GetFixedValue());
      }
      else {
         norm = fParameters[i]->GetRangeWidth() * SATemperature(t) / 2.;
         new_val = x[i] + norm * fRandom->Gaus();
         y.push_back(new_val);
      }
   }

   return y;
}

// ---------------------------------------------------------
std::vector<double> BCIntegrate::GetProposalPointSACauchy(const std::vector<double> &x, int t)
{
   std::vector<double> y;
   y.clear();

   if (fParameters.Size() == 1) {
      double cauchy, new_val, norm;

      if (fParameters[0]->Fixed()) {
         y.push_back(fParameters[0]->GetFixedValue());
      }
      else {
         norm = fParameters[0]->GetRangeWidth() * SATemperature(t) / 2.;
         cauchy = tan(3.14159 * (fRandom->Rndm() - 0.5));
         new_val = x[0] + norm * cauchy;
         y.push_back(new_val);
      }
   }
   else {
      // use sampling to get radial n-dim Cauchy distribution

      // first generate a random point uniformly distributed on a
      // fNvar-dimensional hypersphere
      y = SAHelperGetRandomPointOnHypersphere();

      // scale the vector by a random factor determined by the radial
      // part of the fNvar-dimensional Cauchy distribution
      double radial = SATemperature(t) * SAHelperGetRadialCauchy();

      // scale y by radial part and the size of dimension i in phase space
      // afterwards, move by x
      for (unsigned i = 0; i < fParameters.Size(); i++) {
         if (fParameters[i]->Fixed()) {
            y[i] = fParameters[i]->GetFixedValue(); }
         else {
            y[i] = fParameters[i]->GetRangeWidth() * y[i] * radial / 2. + x[i];
         }
      }
   }

   return y;
}

// ---------------------------------------------------------
std::vector<double> BCIntegrate::GetProposalPointSACustom(const std::vector<double> & /*x*/, int /*t*/)
{
   BCLog::OutError("BCIntegrate::GetProposalPointSACustom : No custom proposal function defined");
   return std::vector<double>(fParameters.Size());
}

// ---------------------------------------------------------
std::vector<double> BCIntegrate::SAHelperGetRandomPointOnHypersphere()
{
   std::vector<double> rand_point(fParameters.Size());

   // This method can only be called with fNvar >= 2 since the 1-dim case
   // is already hard wired into the Cauchy annealing proposal function.
   // To speed things up, hard-code fast method for 2 and dimensions.
   // The algorithm for 2D can be found at
   // http://mathworld.wolfram.com/CirclePointPicking.html
   // For 3D just using ROOT's algorithm.
   if (fParameters.Size() == 2) {
      double x1, x2, s;
      do {
         x1 = fRandom->Rndm() * 2. - 1.;
         x2 = fRandom->Rndm() * 2. - 1.;
         s = x1*x1 + x2*x2;
      }
      while (s >= 1);

      rand_point[0] = (x1*x1 - x2*x2) / s;
      rand_point[1] = (2.*x1*x2) / s;
   }
   else if (fParameters.Size() == 3) {
      fRandom->Sphere(rand_point[0], rand_point[1], rand_point[2], 1.0);
   }
   else {
      double s = 0.,
         gauss_num;

      for (unsigned i = 0; i < fParameters.Size(); i++) {
         gauss_num = fRandom->Gaus();
         rand_point[i] = gauss_num;
         s += gauss_num * gauss_num;
      }
      s = sqrt(s);

      for (unsigned i = 0; i < fParameters.Size(); i++)
         rand_point[i] = rand_point[i] / s;
   }

   return rand_point;
}

// ---------------------------------------------------------
double BCIntegrate::SAHelperGetRadialCauchy()
{
   // theta is sampled from a rather complicated distribution,
   // so first we create a lookup table with 10000 random numbers
   // once and then, each time we need a new random number,
   // we just look it up in the table.
   double theta;

   // static vectors for theta-sampling-map
   static double map_u[10001];
   static double map_theta[10001];
   static bool initialized = false;
   static unsigned map_dimension = 0;

   // is the lookup-table already initialized? if not, do it!
   if (!initialized or map_dimension != fParameters.Size()) {
      double init_theta;
      double beta = SAHelperSinusToNIntegral(fParameters.Size() - 1, 1.57079632679);

      for (int i = 0; i <= 10000; i++) {
         init_theta = 3.14159265 * (double)i / 5000.;
         map_theta[i] = init_theta;

         map_u[i] = SAHelperSinusToNIntegral(fParameters.Size() - 1, init_theta) / beta;
      }

      map_dimension = fParameters.Size();
      initialized = true;
   } // initializing is done.

   // generate uniform random number for sampling
   double u = fRandom->Rndm();

   // Find the two elements just greater than and less than u
   // using a binary search (O(log(N))).
   int lo = 0;
   int up = 10000;
   int mid;

   while (up != lo) {
      mid = ((up - lo + 1) / 2) + lo;

      if (u >= map_u[mid])
         lo = mid;
      else
         up = mid - 1;
   }
   up++;

   // perform linear interpolation:
   theta = map_theta[lo] + (u - map_u[lo]) / (map_u[up] - map_u[lo]) * (map_theta[up] - map_theta[lo]);

   return tan(theta);
}

// ---------------------------------------------------------
double BCIntegrate::SAHelperSinusToNIntegral(int dim, double theta)
{
   if (dim < 1)
      return theta;
   else if (dim == 1)
      return (1. - cos(theta));
   else if (dim == 2)
      return 0.5 * (theta - sin(theta) * cos(theta));
   else if (dim == 3)
      return (2. - sin(theta) * sin(theta) * cos(theta) - 2. * cos(theta)) / 3.;
   else
      return - pow(sin(theta), (double)(dim - 1)) * cos(theta) / (double)dim
         + (double)(dim - 1) / (double)dim
         * SAHelperSinusToNIntegral(dim - 2, theta);
}

// ---------------------------------------------------------
void BCIntegrate::FCNLikelihood(int & /*npar*/, double * /*grad*/, double &fval, double * par, int /*flag*/)
{
   // copy parameters
   static std::vector<double> parameters;

   // calculate number of active + fixed parameters
   // remember: npar is just the number of _active_ parameters while
   // par is a vector of _all_ parameters
   int nparameters = ::BCIntegrateHolder::instance()->GetNParameters();

   // adjust size if needed
   parameters.resize(nparameters, 0.0);

   // copy values
   std::copy(par, par + nparameters, parameters.begin());

   // evaluate, for efficiency don't check if npar matches
   fval = - ::BCIntegrateHolder::instance()->LogEval(parameters);
}

// ---------------------------------------------------------
std::vector<double> BCIntegrate::FindModeMCMC(std::vector<double> &mode, std::vector<double> &errors)
{
   // call PreRun
   MCMCMetropolisPreRun();

   // loop over all chains and find the maximum point
   double logProb = -std::numeric_limits<double>::max();
   unsigned index = 0;
   for (unsigned i = 0; i < fMCMCNChains; ++i) {
      if (MCMCGetMaximumLogProb().at(i) > logProb){
         index = i;
         logProb = MCMCGetMaximumLogProb().at(i);
      }
   }

   mode = MCMCGetMaximumPoint(index);
   errors.assign(fParameters.Size(),-1.);

   return mode;
}

// ---------------------------------------------------------
void BCIntegrate::SetIntegrationMethod(BCIntegrate::BCIntegrationMethod method)
{
   if (method >= BCIntegrate::NIntMethods) {
      BCLog::OutError(Form("BCIntegrate::SetIntegrationMethod: Invalid method '%d' ", method));
      return;
   }
   if (method == BCIntegrate::kIntCuba) {
#ifndef HAVE_CUBA_H
      BCLog::OutError("BCIntegrate::SetIntegrationMethod: Cuba not enabled during configure");
#endif
   }
   fIntegrationMethodCurrent = method;
}

// ---------------------------------------------------------
void BCIntegrate::SetCubaIntegrationMethod(BCIntegrate::BCCubaMethod type)
{
#ifdef HAVE_CUBA_H
   switch(type) {
      case BCIntegrate::kCubaVegas:
      case BCIntegrate::kCubaSuave:
      case BCIntegrate::kCubaDivonne:
      case BCIntegrate::kCubaCuhre:
         fCubaIntegrationMethod = type;
         return;
      default:
         BCLog::OutError(TString::Format("Integration method of type %d is not defined for Cuba",type));
         return;
   }
#else
   (void) type; // suppress compiler warning about unused parameters
   BCLog::OutError("SetCubaIntegrationMethod: Cuba not enabled during configure");
#endif
}

// ---------------------------------------------------------
int BCIntegrate::CubaIntegrand(const int * ndim, const double xx[],
      const int * /*ncomp*/, double ff[], void * userdata)
{
   BCIntegrate * local_this = static_cast<BCIntegrate *>(userdata);

   // scale variables
   double jacobian = 1.0;

   // create local parameter vector
   // important for thread safety, though not super efficient
   std::vector<double> scaled_parameters(local_this->fParameters.Size());

   // stay in sync with the possible lower number of parameters
   // that cuba sees due to fixing in BAT
   unsigned cubaIndex = 0;
   unsigned batIndex = 0;
   for (batIndex = 0; batIndex < local_this->fParameters.Size(); ++batIndex) {
     const BCParameter * p = local_this->fParameters[batIndex];

         // get the scaled parameter value
         if (p->Fixed())
             scaled_parameters[batIndex] = p->GetFixedValue();
         else {
             // convert from unit hypercube to actual parameter hyperrectangle
             scaled_parameters[batIndex] = p->GetLowerLimit() + xx[cubaIndex] * p->GetRangeWidth();

             // multiply range to jacobian
             jacobian *= p->GetRangeWidth();

             // one more parameter that cuba varies
             ++cubaIndex;
         }
   }

   if (cubaIndex != unsigned(*ndim))
     BCLog::OutError(Form("BCIntegrate::CubaIntegrand: mismatch between variable parameters"
                                              "in BAT (%d) and Cuba(%d)", batIndex, cubaIndex));

   // call function to integrate
   ff[0] = local_this->Eval(scaled_parameters);

   // multiply jacobian
   ff[0] *= jacobian;

   return 0;
}

// ---------------------------------------------------------
double BCIntegrate::IntegrateCuba(BCCubaMethod cubatype) {
#if HAVE_CUBA_H
   LogOutputAtStartOfIntegration(kIntCuba, cubatype);

   // integrand has only one component
   static const int ncomp = 1;

   // don't store integration in a slot for reuse
   static const int gridno = -1;

   // we don't want dumps of internal state
   static const char * statefile = "";

   // only evaluate at one position in parameter space at a time
   static const int nvec = 1;

#ifdef CUBAVERSION_40
   // we have no spinning cores
   int * spin = 0;
#endif

   // cuba returns info in these variables
   int fail = 0;
   int nregions = 0;
   std::vector<double> integral(ncomp, -1);
   std::vector<double> error(ncomp, -1);
   std::vector<double> prob(ncomp, -1);

   // reset number of iterations
   fNIterations = 0;

   // Cuba needs int variable
   int nIntegrationVariables = GetNIntegrationVariables();

   switch (cubatype) {

   case BCIntegrate::kCubaVegas:
      Vegas(nIntegrationVariables, ncomp,
            &BCIntegrate::CubaIntegrand, static_cast<void *>(this),
            nvec,
            fRelativePrecision, fAbsolutePrecision,
            fCubaVegasOptions.flags, fRandom->GetSeed(),
            fNIterationsMin, fNIterationsMax,
            fCubaVegasOptions.nstart, fCubaVegasOptions.nincrease, fCubaVegasOptions.nbatch,
            gridno, statefile,
#ifdef CUBAVERSION_40
            spin,
#endif
            &fNIterations, &fail,
            &integral[0], &error[0], &prob[0]);
      break;

   case BCIntegrate::kCubaSuave:
      Suave(nIntegrationVariables, ncomp,
            &BCIntegrate::CubaIntegrand, static_cast<void *>(this),
            nvec,
            fRelativePrecision, fAbsolutePrecision,
            fCubaSuaveOptions.flags, fRandom->GetSeed(),
            fNIterationsMin, fNIterationsMax,
            fCubaSuaveOptions.nnew, fCubaSuaveOptions.flatness,
            statefile,
#ifdef CUBAVERSION_40
            spin,
#endif
            &nregions, &fNIterations, &fail,
            &integral[0], &error[0], &prob[0]);
      break;

   case BCIntegrate::kCubaDivonne:
      if (nIntegrationVariables < 2 or nIntegrationVariables > 33)
         BCLog::OutError("BCIntegrate::IntegrateCuba(Divonne): Divonne only works in 1 < d < 34");
      else {
         // no extra info supported
         static const int ngiven = 0;
         static const int nextra = ngiven;
         Divonne(nIntegrationVariables, ncomp,
               &BCIntegrate::CubaIntegrand, static_cast<void *>(this),
               nvec,
               fRelativePrecision, fAbsolutePrecision,
               fCubaDivonneOptions.flags, fRandom->GetSeed(),
               fNIterationsMin, fNIterationsMax,
               fCubaDivonneOptions.key1, fCubaDivonneOptions.key2, fCubaDivonneOptions.key3,
               fCubaDivonneOptions.maxpass, fCubaDivonneOptions.border,
               fCubaDivonneOptions.maxchisq, fCubaDivonneOptions.mindeviation,
               ngiven, nIntegrationVariables /*ldxgiven*/, NULL, nextra, NULL,
               statefile,
#ifdef CUBAVERSION_40
            spin,
#endif
               &nregions, &fNIterations, &fail,
               &integral[0], &error[0], &prob[0]);
      }
      break;

   case BCIntegrate::kCubaCuhre:
      if (nIntegrationVariables < 2)
         BCLog::OutError("BCIntegrate::IntegrateCuba(Cuhre): Cuhre(cubature) only works in d > 1");

      Cuhre(nIntegrationVariables, ncomp,
            &BCIntegrate::CubaIntegrand, static_cast<void *>(this),
            nvec,
            fRelativePrecision, fAbsolutePrecision,
            fCubaCuhreOptions.flags, fNIterationsMin, fNIterationsMax,
            fCubaCuhreOptions.key,
            statefile,
#ifdef CUBAVERSION_40
            spin,
#endif
            &nregions, &fNIterations, &fail,
            &integral[0], &error[0], &prob[0]);
      break;

   case BCIntegrate::NCubaMethods:
   default:
      BCLog::OutError("Cuba integration method not set.");
      error[0] = -1;
      integral[0] = -1;
      break;
   }

   fError = error[0];
   double result = integral[0];

   if (fail != 0) {
      BCLog::OutWarning(" Warning, integral did not converge with the given set of parameters. ");
      BCLog::OutWarning(TString::Format(" neval    = %d", fNIterations));
      BCLog::OutWarning(TString::Format(" fail     = %d", fail));
      BCLog::OutWarning(TString::Format(" integral = %e", result));
      BCLog::OutWarning(TString::Format(" error    = %e", fError));
      BCLog::OutWarning(TString::Format(" prob     = %e", prob[0]));

      // handle cases in which cuba does not alter integral
      if (fNIterations == 0)
      {
         fError = -1;
         result = -1;
      }

   } else
      LogOutputAtEndOfIntegration(result,fError,fError/result,fNIterations);

   return result;
#else
   (void) cubatype; // suppress compiler warning about unused parameters
   BCLog::OutError("IntegrateCuba: Cuba not enabled during configure");
   return -1;
#endif
}

// ---------------------------------------------------------
double BCIntegrate::IntegrateSlice()
{
  // print to log
  LogOutputAtStartOfIntegration(fIntegrationMethodCurrent, NCubaMethods);

  double integral = -1;
  double absprecision  = -1;
  double relprecision  = -1;
  fError = -1;

  // calculate values are which the function should be evaluated
  std::vector<double> fixpoint(GetNParameters());
  for (unsigned int i = 0; i < GetNParameters(); ++i) {
    if (fParameters[i]->Fixed())
      fixpoint[i] = fParameters[i]->GetFixedValue();
    else
      fixpoint[i] = 0;
  }

  if (GetNFreeParameters() == 1) {
    for (unsigned int i = 0; i < GetNParameters(); ++i) {
      if (!fParameters[i]->Fixed()) {
        // calculate slice
        BCH1D* hist_temp = GetSlice(fParameters[i], fixpoint, 0, false);

        // calculate integral
        integral = hist_temp->GetHistogram()->Integral("width");

        // free memory
        delete hist_temp;
      }
    }
  }
  else if (GetNFreeParameters() == 2) {
    for (unsigned int i = 0; i < GetNParameters(); ++i) {
      for (unsigned int j = 0; j < GetNParameters(); ++j) {
        if (i >= j)
          continue;
        if (!fParameters[i]->Fixed() && !fParameters[j]->Fixed()) {
          // calculate slice
          BCH2D* hist_temp = GetSlice(GetParameter(i), GetParameter(j), fixpoint, 0, false);

          // calculate integral
          integral = hist_temp->GetHistogram()->Integral("width");

        // free memory
        delete hist_temp;
        }
      }
    }
  }
  else {
    BCLog::OutWarning("BCIntegrate::IntegrateSlice: Method only implemented for 1D and 2D problems. Return -1.");

    integral = -1;
  }

    // print to log
    LogOutputAtEndOfIntegration(integral, absprecision, relprecision, -1);

  return integral;
}

// ---------------------------------------------------------
void BCIntegrate::SAInitialize()
{
   fSAx.clear();
   fSAx.assign(fParameters.Size(), 0.0);
}

// ---------------------------------------------------------
std::string BCIntegrate::DumpIntegrationMethod(BCIntegrate::BCIntegrationMethod type)
{
   switch(type) {
      case BCIntegrate::kIntEmpty:
         return "Empty";
      case BCIntegrate::kIntMonteCarlo:
         return "Sample Mean Monte Carlo";
      case BCIntegrate::kIntCuba:
         return "Cuba";
      case BCIntegrate::kIntGrid:
         return "Grid";
      default:
         return "Undefined";
   }
}

// ---------------------------------------------------------
std::string BCIntegrate::DumpMarginalizationMethod(BCIntegrate::BCMarginalizationMethod type)
{
   switch(type) {
      case BCIntegrate::kMargEmpty:
         return "Empty";
      case BCIntegrate::kMargMonteCarlo:
         return "Sample Mean Monte Carlo";
      case BCIntegrate::kMargMetropolis:
         return "Metropolis";
      case BCIntegrate::kMargGrid:
         return "Grid";
      case BCIntegrate::kMargDefault:
         return "Default";
      default:
         return "Undefined";
   }
}

// ---------------------------------------------------------
std::string BCIntegrate::DumpOptimizationMethod(BCIntegrate::BCOptimizationMethod type)
{
   switch(type) {
      case BCIntegrate::kOptEmpty:
         return "Empty";
      case BCIntegrate::kOptSimAnn:
         return "Simulated Annealing";
      case BCIntegrate::kOptMetropolis:
         return "Metropolis MCMC";
      case BCIntegrate::kOptMinuit:
         return "Minuit";
      case BCIntegrate::kOptDefault:
         return "Default";
      default:
         return "Undefined";
   }
}

// ---------------------------------------------------------
std::string BCIntegrate::DumpCubaIntegrationMethod(BCIntegrate::BCCubaMethod type)
{
   switch(type) {
      case BCIntegrate::kCubaVegas:
         return "Vegas";
      case BCIntegrate::kCubaSuave:
         return "Suave";
      case BCIntegrate::kCubaDivonne:
         return "Divonne";
      case BCIntegrate::kCubaCuhre:
         return "Cuhre";
      default:
         return "Undefined";
   }
}

namespace BCCubaOptions
{
General::General() :
      ncomp(1),
      flags(0),
      nregions(0),
      neval(0),
      fail(0),
      error(0),
      prob(0)
{}

General::~General()
{}

/*
 * copy values from demo-c.c shipping with cuba 3.2
 * for three-dimensional examples.
 */

Vegas::Vegas() :
      General(),
      nstart(1000),
      nincrease(500),
      nbatch(1000),
      gridno(0)
{}

Suave::Suave() :
      General(),
      nnew(1000),
      flatness(25)
{}

Divonne::Divonne() :
      General(),
      key1(47),
      key2(1),
      key3(1),
      maxpass(5),
      border(0),
      maxchisq(10),
      mindeviation(0.25)
{}

Cuhre::Cuhre() :
      General(),
      key(0) // let cuba choose default cubature rule
{}
}