HistoToWorkspaceFactoryFast.cxx

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// @(#)root/roostats:$Id:  cranmer $
// Author: Kyle Cranmer, Akira Shibata
/*************************************************************************
 * Copyright (C) 1995-2008, Rene Brun and Fons Rademakers.               *
 * All rights reserved.                                                  *
 *                                                                       *
 * For the licensing terms see $ROOTSYS/LICENSE.                         *
 * For the list of contributors see $ROOTSYS/README/CREDITS.             *
 *************************************************************************/
 
////////////////////////////////////////////////////////////////////////////////
 
/** \class RooStats::HistFactory::HistoToWorkspaceFactoryFast
 * \ingroup HistFactory
 * This class provides helper functions for creating likelihood models from histograms.
 * It is used by RooStats::HistFactory::MakeModelAndMeasurementFast.
 *
 * A tutorial showing how to create a HistFactory model is hf001_example.C
 */
 
 
#ifndef __CINT__
#include "RooGlobalFunc.h"
#endif
 
#include "RooDataSet.h"
#include "RooRealVar.h"
#include "RooConstVar.h"
#include "RooAddition.h"
#include "RooProduct.h"
#include "RooProdPdf.h"
#include "RooAddPdf.h"
#include "RooGaussian.h"
#include "RooPoisson.h"
#include "RooExponential.h"
#include "RooRandom.h"
#include "RooCategory.h"
#include "RooSimultaneous.h"
#include "RooMultiVarGaussian.h"
#include "RooNumIntConfig.h"
#include "RooProfileLL.h"
#include "RooFitResult.h"
#include "RooDataHist.h"
#include "RooHistFunc.h"
#include "RooHistPdf.h"
#include "RooRealSumPdf.h"
#include "RooWorkspace.h"
#include "RooCustomizer.h"
#include "RooPlot.h"
#include "RooHelpers.h"
#include "RooBinning.h"
#include "RooBinWidthFunction.h"
#include "RooStats/RooStatsUtils.h"
#include "RooStats/ModelConfig.h"
#include "RooStats/HistFactory/PiecewiseInterpolation.h"
#include "RooStats/HistFactory/ParamHistFunc.h"
#include "RooStats/AsymptoticCalculator.h"
#include "HFMsgService.h"
 
#include "TH1.h"
#include "TStopwatch.h"
#include "TVectorD.h"
#include "TMatrixDSym.h"
 
// specific to this package
#include "RooStats/HistFactory/LinInterpVar.h"
#include "RooStats/HistFactory/FlexibleInterpVar.h"
#include "RooStats/HistFactory/HistoToWorkspaceFactoryFast.h"
#include "RooStats/HistFactory/Measurement.h"
#include "RooStats/HistFactory/HistFactoryException.h"
 
#include <algorithm>
#include <memory>
#include <utility>
 
#define VERBOSE
 
#define alpha_Low "-5"
#define alpha_High "5"
#define NoHistConst_Low "0"
#define NoHistConst_High "2000"
 
// use this order for safety on library loading
using namespace RooFit ;
using namespace RooStats ;
using namespace std ;
 
ClassImp(RooStats::HistFactory::HistoToWorkspaceFactoryFast);
 
namespace RooStats{
namespace HistFactory{
 
  HistoToWorkspaceFactoryFast::HistoToWorkspaceFactoryFast(RooStats::HistFactory::Measurement& measurement) :
    HistoToWorkspaceFactoryFast{measurement, Configuration{}} {}
 
  HistoToWorkspaceFactoryFast::HistoToWorkspaceFactoryFast(RooStats::HistFactory::Measurement& measurement,
                                                           Configuration const& cfg) :
    fSystToFix( measurement.GetConstantParams() ),
    fParamValues( measurement.GetParamValues() ),
    fNomLumi( measurement.GetLumi() ),
    fLumiError( measurement.GetLumi()*measurement.GetLumiRelErr() ),
    fLowBin( measurement.GetBinLow() ),
    fHighBin( measurement.GetBinHigh() ),
    fCfg{cfg} {
 
    // Set Preprocess functions
    SetFunctionsToPreprocess( measurement.GetPreprocessFunctions() );
 
  }
 
  void HistoToWorkspaceFactoryFast::ConfigureWorkspaceForMeasurement( const std::string& ModelName, RooWorkspace* ws_single, Measurement& measurement ) {
 
    // Configure a workspace by doing any
    // necessary post-processing and by
    // creating a ModelConfig
 
    // Make a ModelConfig and configure it
    ModelConfig * proto_config = (ModelConfig *) ws_single->obj("ModelConfig");
    if( proto_config == nullptr ) {
      std::cout << "Error: Did not find 'ModelConfig' object in file: " << ws_single->GetName()
      << std::endl;
      throw hf_exc();
    }
 
    std::vector<std::string> poi_list = measurement.GetPOIList();
    if( poi_list.empty() ) {
      cxcoutWHF << "No Parametetrs of interest are set" << std::endl;
    }
 
 
    std::stringstream sstream;
    sstream << "Setting Parameter(s) of Interest as: ";
    for(unsigned int i = 0; i < poi_list.size(); ++i) {
      sstream << poi_list.at(i) << " ";
    }
    cxcoutIHF << sstream.str() << endl;
 
    RooArgSet params;
    for( unsigned int i = 0; i < poi_list.size(); ++i ) {
      std::string poi_name = poi_list.at(i);
      RooRealVar* poi = (RooRealVar*) ws_single->var(poi_name);
      if(poi){
        params.add(*poi);
      }
      else {
   std::cout << "WARNING: Can't find parameter of interest: " << poi_name
        << " in Workspace. Not setting in ModelConfig." << std::endl;
   //throw hf_exc();
      }
    }
    proto_config->SetParametersOfInterest(params);
 
    // Name of an 'edited' model, if necessary
    std::string NewModelName = "newSimPdf"; // <- This name is hard-coded in HistoToWorkspaceFactoryFast::EditSyt.  Probably should be changed to : std::string("new") + ModelName;
 
    // Set the ModelConfig's Params of Interest
    RooAbsData* expData = ws_single->data("asimovData");
    if( !expData ) {
      std::cout << "Error: Failed to find dataset: " << expData
      << " in workspace" << std::endl;
      throw hf_exc();
    }
    if(poi_list.size()!=0){
      proto_config->GuessObsAndNuisance(*expData, RooMsgService::instance().isActive(static_cast<TObject*>(nullptr), RooFit::HistFactory, RooFit::INFO));
    }
 
    // Now, let's loop over any additional asimov datasets
    // that we need to make
 
    // Get the pdf
    // Notice that we get the "new" pdf, this is the one that is
    // used in the creation of these asimov datasets since they
    // are fitted (or may be, at least).
    RooAbsPdf* pdf = ws_single->pdf(NewModelName);
    if( !pdf ) pdf = ws_single->pdf( ModelName );
    const RooArgSet* observables = ws_single->set("observables");
 
    // Create a SnapShot of the nominal values
    std::string SnapShotName = "NominalParamValues";
    ws_single->saveSnapshot(SnapShotName.c_str(), ws_single->allVars());
 
    for( unsigned int i=0; i<measurement.GetAsimovDatasets().size(); ++i) {
 
      // Set the variable values and "const" ness with the workspace
      RooStats::HistFactory::Asimov& asimov = measurement.GetAsimovDatasets().at(i);
      std::string AsimovName = asimov.GetName();
 
      cxcoutPHF << "Generating additional Asimov Dataset: " << AsimovName << std::endl;
      asimov.ConfigureWorkspace(ws_single);
      std::unique_ptr<RooDataSet> asimov_dataset{static_cast<RooDataSet*>(AsymptoticCalculator::GenerateAsimovData(*pdf, *observables))};
 
      cxcoutPHF << "Importing Asimov dataset" << std::endl;
      bool failure = ws_single->import(*asimov_dataset, Rename(AsimovName.c_str()));
      if( failure ) {
        std::cout << "Error: Failed to import Asimov dataset: " << AsimovName
        << std::endl;
   throw hf_exc();
      }
 
      // Load the snapshot at the end of every loop iteration
      // so we start each loop with a "clean" snapshot
      ws_single->loadSnapshot(SnapShotName.c_str());
    }
 
    // Cool, we're done
    return; // ws_single;
  }
 
 
  // We want to eliminate this interface and use the measurment directly
  RooWorkspace* HistoToWorkspaceFactoryFast::MakeSingleChannelModel( Measurement& measurement, Channel& channel ) {
 
    // This is a pretty light-weight wrapper function
    //
    // Take a fully configured measurement as well as
    // one of its channels
    //
    // Return a workspace representing that channel
    // Do this by first creating a vector of EstimateSummary's
    // and this by configuring the workspace with any post-processing
 
    // Get the channel's name
    string ch_name = channel.GetName();
 
    // Create a workspace for a SingleChannel from the Measurement Object
    RooWorkspace* ws_single = this->MakeSingleChannelWorkspace(measurement, channel);
    if( ws_single == nullptr ) {
      cxcoutF(HistFactory) << "Error: Failed to make Single-Channel workspace for channel: " << ch_name
      << " and measurement: " << measurement.GetName() << std::endl;
      throw hf_exc();
    }
 
    // Finally, configure that workspace based on
    // properties of the measurement
    HistoToWorkspaceFactoryFast::ConfigureWorkspaceForMeasurement( "model_"+ch_name, ws_single, measurement );
 
    return ws_single;
 
  }
 
  RooWorkspace* HistoToWorkspaceFactoryFast::MakeCombinedModel( Measurement& measurement ) {
 
    // This function takes a fully configured measurement
    // which may contain several channels and returns
    // a workspace holding the combined model
    //
    // This can be used, for example, within a script to produce
    // a combined workspace on-the-fly
    //
    // This is a static function (for now) to make
    // it a one-liner
 
      RooHelpers::LocalChangeMsgLevel changeMsgLvl(RooFit::INFO, 0u, RooFit::ObjectHandling, false);
 
    // First, we create an instance of a HistFactory
    HistoToWorkspaceFactoryFast factory( measurement );
 
    // Loop over the channels and create the individual workspaces
    vector<std::unique_ptr<RooWorkspace>> channel_workspaces;
    vector<string>        channel_names;
 
    for( unsigned int chanItr = 0; chanItr < measurement.GetChannels().size(); ++chanItr ) {
 
      HistFactory::Channel& channel = measurement.GetChannels().at( chanItr );
 
      if( ! channel.CheckHistograms() ) {
        cxcoutFHF << "MakeModelAndMeasurementsFast: Channel: " << channel.GetName()
            << " has uninitialized histogram pointers" << std::endl;
        throw hf_exc();
      }
 
      string ch_name = channel.GetName();
      channel_names.push_back(ch_name);
 
      // GHL: Renaming to 'MakeSingleChannelWorkspace'
      RooWorkspace* ws_single = factory.MakeSingleChannelModel( measurement, channel );
 
      channel_workspaces.emplace_back(ws_single);
 
    }
 
 
    // Now, combine the individual channel workspaces to
    // form the combined workspace
    RooWorkspace* ws = factory.MakeCombinedModel( channel_names, channel_workspaces );
 
 
    // Configure the workspace
    HistoToWorkspaceFactoryFast::ConfigureWorkspaceForMeasurement( "simPdf", ws, measurement );
 
    // Done.  Return the pointer
    return ws;
 
  }
 
/// Create observables of type RooRealVar. Creates 1 to 3 observables, depending on the type of the histogram.
RooArgList HistoToWorkspaceFactoryFast::createObservables(const TH1 *hist, RooWorkspace *proto) const {
  RooArgList observables;
 
  for (unsigned int idx=0; idx < fObsNameVec.size(); ++idx) {
    if (!proto->var(fObsNameVec[idx])) {
      const TAxis *axis = (idx == 0) ? hist->GetXaxis() : (idx == 1 ? hist->GetYaxis() : hist->GetZaxis());
      Int_t nbins = axis->GetNbins();
      double xmin = axis->GetXmin();
      double xmax = axis->GetXmax();
      // create observable
      auto obs = static_cast<RooRealVar*>(proto->factory(
          Form("%s[%f,%f]", fObsNameVec[idx].c_str(), xmin, xmax)));
      if(strlen(axis->GetTitle())>0) obs->SetTitle(axis->GetTitle());
      obs->setBins(nbins);
      if (axis->IsVariableBinSize()) {
        RooBinning binning(nbins, axis->GetXbins()->GetArray());
        obs->setBinning(binning);
      }
    }
 
    observables.add(*proto->var(fObsNameVec[idx]));
  }
 
  return observables;
}
 
  /// Create the nominal hist function from `hist`, and register it in the workspace.
  RooHistFunc* HistoToWorkspaceFactoryFast::MakeExpectedHistFunc(const TH1* hist,RooWorkspace* proto, string prefix,
      const RooArgList& observables) const {
    if(hist) {
      cxcoutI(HistFactory) << "processing hist " << hist->GetName() << endl;
    } else {
      cxcoutF(HistFactory) << "hist is empty" << endl;
      R__ASSERT(hist != 0);
      return nullptr;
    }
 
    // determine histogram dimensionality
    unsigned int histndim(1);
    std::string classname = hist->ClassName();
    if      (classname.find("TH1")==0) { histndim=1; }
    else if (classname.find("TH2")==0) { histndim=2; }
    else if (classname.find("TH3")==0) { histndim=3; }
    R__ASSERT( histndim==fObsNameVec.size() );
 
    prefix += "_Hist_alphanominal";
 
    RooDataHist histDHist((prefix + "DHist").c_str(),"",observables,hist);
    RooHistFunc histFunc(prefix.c_str(),"",observables,histDHist,0);
 
    proto->import(histFunc, RecycleConflictNodes());
    auto histFuncInWS = static_cast<RooHistFunc*>(proto->arg(prefix.c_str()));
 
    return histFuncInWS;
  }
 
  namespace {
 
  void makeGaussianConstraint(RooAbsArg& param, RooWorkspace& proto, bool isUniform,
                              std::vector<std::string> & constraintTermNames) {
      std::string paramName = param.GetName();
      std::string constraintName = paramName + "Constraint";
 
      // do nothing if the constraint term already exists
      if(proto.pdf(constraintName)) return;
 
      // case systematic is uniform (asssume they are like a Gaussian but with
      // a large width (100 instead of 1)
      const double gaussSigma = isUniform ? 100. : 1.0;
      if (isUniform) {
         cxcoutIHF << "Added a uniform constraint for " << paramName << " as a Gaussian constraint with a very large sigma " << std::endl;
      }
 
      std::stringstream command;
      command << "Gaussian::" << constraintName << "(" << paramName << ",nom_" << paramName << "[0.,-10,10],"
              << gaussSigma << ")";
      constraintTermNames.emplace_back(proto.factory(command.str())->GetName());
      auto * normParam = proto.var(std::string("nom_") + paramName);
      normParam->setConstant();
      const_cast<RooArgSet*>(proto.set("globalObservables"))->add(*normParam);
  }
 
  /// Make list of abstract parameters that interpolate in space of variations.
  RooArgList makeInterpolationParameters(std::vector<HistoSys> const& histoSysList, RooWorkspace& proto) {
    RooArgList params( ("alpha_Hist") );
 
    // range is set using defined macro (see top of the page)
    string range=string("[")+alpha_Low+","+alpha_High+"]";
 
    for(auto const& histoSys : histoSysList) {
      const std::string histoSysName = histoSys.GetName();
      RooRealVar* temp = proto.var("alpha_" + histoSysName);
      if(!temp){
        temp = (RooRealVar*) proto.factory("alpha_" + histoSysName + range);
      }
      params.add(* temp );
    }
 
    return params;
  }
 
  /// Create a linear interpolation object that holds nominal and systematics, import it into the workspace,
  /// and return a pointer to it.
  RooAbsArg* makeLinInterp(RooArgList const& interpolationParams,
                           RooHistFunc* nominalFunc,
                           RooWorkspace* proto, const std::vector<HistoSys>& histoSysList,
                           const string& prefix,
                           const RooArgList& observables) {
 
    // now make function that linearly interpolates expectation between variations
    // get low/high variations to interpolate between
    vector<double> low, high;
    RooArgSet lowSet, highSet;
    //ES// for(unsigned int j=0; j<lowHist.size(); ++j){
    for(unsigned int j=0; j<histoSysList.size(); ++j){
      std::stringstream str;
      str<<"_"<<j;
 
      const HistoSys& histoSys = histoSysList.at(j);
      RooDataHist* lowDHist = new RooDataHist((prefix+str.str()+"lowDHist").c_str(),"",observables, histoSys.GetHistoLow());
      RooDataHist* highDHist = new RooDataHist((prefix+str.str()+"highDHist").c_str(),"",observables, histoSys.GetHistoHigh());
      RooHistFunc* lowFunc = new RooHistFunc((prefix+str.str()+"low").c_str(),"",observables,*lowDHist,0) ;
      RooHistFunc* highFunc = new RooHistFunc((prefix+str.str()+"high").c_str(),"",observables,*highDHist,0) ;
      lowSet.add(*lowFunc);
      highSet.add(*highFunc);
    }
 
    // this is sigma(params), a piece-wise linear interpolation
    PiecewiseInterpolation interp(prefix.c_str(),"",*nominalFunc,lowSet,highSet,interpolationParams);
    interp.setPositiveDefinite();
    interp.setAllInterpCodes(4); // LM: change to 4 (piece-wise linear to 6th order polynomial interpolation + linear extrapolation )
    // KC: interpo codes 1 etc. don't have proper analytic integral.
    RooArgSet observableSet(observables);
    interp.setBinIntegrator(observableSet);
    interp.forceNumInt();
 
    proto->import(interp, RecycleConflictNodes()); // individual params have already been imported in first loop of this function
 
    auto interpInWS = proto->arg(prefix.c_str());
    assert(interpInWS);
 
    return interpInWS;
  }
 
  }
 
  // GHL: Consider passing the NormFactor list instead of the entire sample
  std::unique_ptr<RooProduct> HistoToWorkspaceFactoryFast::CreateNormFactor(RooWorkspace* proto, string& channel, string& sigmaEpsilon, Sample& sample, bool doRatio){
 
    std::vector<string> prodNames;
 
    vector<NormFactor> normList = sample.GetNormFactorList();
    vector<string> normFactorNames, rangeNames;
 
 
    string overallNorm_times_sigmaEpsilon = sample.GetName() + "_" + channel + "_scaleFactors";
    auto sigEps = proto->arg(sigmaEpsilon.c_str());
    assert(sigEps);
    auto normFactor = std::make_unique<RooProduct>(overallNorm_times_sigmaEpsilon.c_str(), overallNorm_times_sigmaEpsilon.c_str(), RooArgList(*sigEps));
 
    if(normList.size() > 0){
 
      for(vector<NormFactor>::iterator itr = normList.begin(); itr != normList.end(); ++itr){
 
        NormFactor& norm = *itr;
 
        string varname;
        if(doRatio) {
          varname = norm.GetName() + "_" + channel;
        }
        else {
          varname=norm.GetName();
        }
 
        // GHL: Check that the NormFactor doesn't already exist
        //      (it may have been created as a function expression
        //       during preprocessing)
        std::stringstream range;
        range << "[" << norm.GetVal() << "," << norm.GetLow() << "," << norm.GetHigh() << "]";
 
        if( proto->obj(varname) == nullptr) {
          cxcoutI(HistFactory) << "making normFactor: " << norm.GetName() << endl;
          // remove "doRatio" and name can be changed when ws gets imported to the combined model.
          proto->factory(varname + range.str());
        }
 
        prodNames.push_back(varname);
        rangeNames.push_back(range.str());
        normFactorNames.push_back(varname);
      }
 
 
      for (const auto& name : prodNames) {
        auto arg = proto->arg(name.c_str());
        assert(arg);
        normFactor->addTerm(arg);
      }
 
    }
 
    unsigned int rangeIndex=0;
    for( vector<string>::iterator nit = normFactorNames.begin(); nit!=normFactorNames.end(); ++nit){
      if( count (normFactorNames.begin(), normFactorNames.end(), *nit) > 1 ){
        cxcoutI(HistFactory) <<"<NormFactor Name =\""<<*nit<<"\"> is duplicated for <Sample Name=\""
            << sample.GetName() << "\">, but only one factor will be included.  \n Instead, define something like"
            << "\n\t<Function Name=\""<<*nit<<"Squared\" Expression=\""<<*nit<<"*"<<*nit<<"\" Var=\""<<*nit<<rangeNames.at(rangeIndex)
            << "\"> \nin your top-level XML's <Measurment> entry and use <NormFactor Name=\""<<*nit<<"Squared\" in your channel XML file."<< endl;
      }
      ++rangeIndex;
    }
 
    return normFactor;
  }
 
   void HistoToWorkspaceFactoryFast::AddConstraintTerms(RooWorkspace* proto, Measurement & meas, string prefix,
                         string interpName,
                         std::vector<OverallSys>& systList,
                         vector<string>& constraintTermNames,
                         vector<string>& totSystTermNames) {
 
    // add variables for all the relative overall uncertainties we expect
    // range is set using defined macro (see top of the page)
 
    string range=string("[0,")+alpha_Low+","+alpha_High+"]";
    totSystTermNames.push_back(prefix);
 
    RooArgSet params(prefix.c_str());
    vector<double> lowVec, highVec;
 
    std::map<std::string, double>::iterator itconstr;
    for(unsigned int i = 0; i < systList.size(); ++i) {
 
      OverallSys& sys = systList.at(i);
      std::string strname = sys.GetName();
      const char * name = strname.c_str();
 
      // case of no systematic (is it possible)
      if (meas.GetNoSyst().count(sys.GetName()) > 0 ) {
        cxcoutI(HistFactory) << "HistoToWorkspaceFast::AddConstraintTerm - skip systematic " << sys.GetName() << std::endl;
        continue;
      }
      // case systematic is a  gamma constraint
      if (meas.GetGammaSyst().count(sys.GetName()) > 0 ) {
         double relerr = meas.GetGammaSyst().find(sys.GetName() )->second;
         if (relerr <= 0) {
           cxcoutI(HistFactory) << "HistoToWorkspaceFast::AddConstraintTerm - zero uncertainty assigned - skip systematic  " << sys.GetName() << std::endl;
           continue;
         }
         double tauVal = 1./(relerr*relerr);
         double sqtau = 1./relerr;
         RooAbsArg * beta = proto->factory(TString::Format("beta_%s[1,0,10]",name) );
         // the global observable (y_s)
         RooAbsArg * yvar = proto->factory(TString::Format("nom_%s[%f,0,10]",beta->GetName(),tauVal)) ;
         // the rate of the gamma distribution (theta)
         RooAbsArg * theta = proto->factory(TString::Format("theta_%s[%f]",name,1./tauVal));
         // find alpha as function of beta
         RooAbsArg* alphaOfBeta = proto->factory(TString::Format("PolyVar::alphaOfBeta_%s(beta_%s,{%f,%f})",name,name,-sqtau,sqtau));
 
         // add now the constraint itself  Gamma_beta_constraint(beta, y+1, tau, 0 )
         // build the gamma parameter k = as y_s + 1
         RooAbsArg * kappa = proto->factory(TString::Format("sum::k_%s(%s,1.)",name,yvar->GetName()) );
         RooAbsArg * gamma = proto->factory(TString::Format("Gamma::%sConstraint(%s, %s, %s, 0.0)",beta->GetName(),beta->GetName(), kappa->GetName(), theta->GetName() ) );
         if (RooMsgService::instance().isActive(static_cast<TObject*>(nullptr), RooFit::HistFactory, RooFit::DEBUG)) {
           alphaOfBeta->Print("t");
           gamma->Print("t");
         }
         constraintTermNames.push_back(gamma->GetName());
         // set global observables
         RooRealVar * gobs = dynamic_cast<RooRealVar*>(yvar); assert(gobs);
         gobs->setConstant(true);
         const_cast<RooArgSet*>(proto->set("globalObservables"))->add(*yvar);
 
         // add alphaOfBeta in the list of params to interpolate
         params.add(*alphaOfBeta);
         cxcoutI(HistFactory) << "Added a gamma constraint for " << name << std::endl;
 
      }
      else {
         RooRealVar* alpha = (RooRealVar*) proto->var(prefix + sys.GetName());
         if(!alpha) {
            alpha = (RooRealVar*) proto->factory(prefix + sys.GetName() + range);
         }
         // add the Gaussian constraint part
         const bool isUniform = meas.GetUniformSyst().count(sys.GetName()) > 0;
         makeGaussianConstraint(*alpha, *proto, isUniform, constraintTermNames);
 
         // check if exists a log-normal constraint
         if (meas.GetLogNormSyst().count(sys.GetName()) == 0 &&  meas.GetGammaSyst().count(sys.GetName()) == 0 ) {
            // just add the alpha for the parameters of the FlexibleInterpVar function
            params.add(*alpha);
         }
                  // case systematic is a  log-normal constraint
         if (meas.GetLogNormSyst().count(sys.GetName()) > 0 ) {
            // log normal constraint for parameter
            double relerr = meas.GetLogNormSyst().find(sys.GetName() )->second;
            double tauVal = 1./relerr;
            std::string tauName = "tau_" + sys.GetName();
            proto->factory(TString::Format("%s[%f]",tauName.c_str(),tauVal ) );
            double kappaVal = 1. + relerr;
            std::string kappaName = "kappa_" + sys.GetName();
            proto->factory(TString::Format("%s[%f]",kappaName.c_str(),kappaVal ) );
            const char * alphaName = alpha->GetName();
 
            std::string alphaOfBetaName = "alphaOfBeta_" + sys.GetName();
            RooAbsArg * alphaOfBeta = proto->factory(TString::Format("expr::%s('%s*(pow(%s,%s)-1.)',%s,%s,%s)",alphaOfBetaName.c_str(),
                                                                     tauName.c_str(),kappaName.c_str(),alphaName,
                                                                     tauName.c_str(),kappaName.c_str(),alphaName ) );
 
            cxcoutI(HistFactory) << "Added a log-normal constraint for " << name << std::endl;
            if (RooMsgService::instance().isActive(static_cast<TObject*>(nullptr), RooFit::HistFactory, RooFit::DEBUG))
              alphaOfBeta->Print("t");
            params.add(*alphaOfBeta);
         }
 
      }
      // add low/high vectors
      double low = sys.GetLow();
      double high = sys.GetHigh();
      lowVec.push_back(low);
      highVec.push_back(high);
 
    }  // end sys loop
 
    if(systList.size() > 0){
       // this is epsilon(alpha_j), a piece-wise linear interpolation
       //      LinInterpVar interp( (interpName).c_str(), "", params, 1., lowVec, highVec);
 
       assert(!params.empty());
       assert(int(lowVec.size()) == params.getSize() );
 
       FlexibleInterpVar interp( (interpName).c_str(), "", params, 1., lowVec, highVec);
       interp.setAllInterpCodes(4); // LM: change to 4 (piece-wise linear to 6th order polynomial interpolation + linear extrapolation )
       //interp.setAllInterpCodes(0); // simple linear interpolation
       proto->import(interp); // params have already been imported in first loop of this function
    } else{
       // some strange behavior if params,lowVec,highVec are empty.
       //cout << "WARNING: No OverallSyst terms" << endl;
       RooConstVar interp( (interpName).c_str(), "", 1.);
       proto->import(interp); // params have already been imported in first loop of this function
    }
 
    // std::cout << "after creating FlexibleInterpVar " << std::endl;
    // proto->Print();
 
  }
 
 
  void  HistoToWorkspaceFactoryFast::MakeTotalExpected(RooWorkspace* proto, const string& totName,
                         const vector<RooProduct*>& sampleScaleFactors, std::vector<vector<RooAbsArg*>>& sampleHistFuncs) const {
    assert(sampleScaleFactors.size() == sampleHistFuncs.size());
 
    // for ith bin calculate totN_i =  lumi * sum_j expected_j * syst_j
 
    if (fObsNameVec.empty() && !fObsName.empty())
      throw std::logic_error("HistFactory didn't process the observables correctly. Please file a bug report.");
 
    auto firstHistFunc = dynamic_cast<const RooHistFunc*>(sampleHistFuncs.front().front());
    if (!firstHistFunc) {
      auto piecewiseInt = dynamic_cast<const PiecewiseInterpolation*>(sampleHistFuncs.front().front());
      firstHistFunc = dynamic_cast<const RooHistFunc*>(piecewiseInt->nominalHist());
    }
    assert(firstHistFunc);
 
    // Prepare a function to divide all bin contents by bin width to get a density:
    const std::string binWidthFunctionName = totName + "_binWidth";
    RooBinWidthFunction binWidth(binWidthFunctionName.c_str(), "Divide by bin width to obtain probability density", *firstHistFunc, true);
    proto->import(binWidth);
    auto binWidthWS = proto->function(binWidthFunctionName.c_str());
    assert(binWidthWS);
 
    // Loop through samples and create products of their functions:
    RooArgSet coefList;
    RooArgSet shapeList;
    for (unsigned int i=0; i < sampleHistFuncs.size(); ++i) {
      assert(!sampleHistFuncs[i].empty());
      coefList.add(*sampleScaleFactors[i]);
 
      std::vector<RooAbsArg*>& thisSampleHistFuncs = sampleHistFuncs[i];
      thisSampleHistFuncs.push_back(binWidthWS);
 
      if (thisSampleHistFuncs.size() == 1) {
        // Just one function. Book it.
        shapeList.add(*thisSampleHistFuncs.front());
      } else {
        // Have multiple functions. We need to multiply them.
        std::string name = thisSampleHistFuncs.front()->GetName();
        auto pos = name.find("Hist_alpha");
        if (pos != std::string::npos) {
          name = name.substr(0, pos) + "shapes";
        } else if ( (pos = name.find("nominal")) != std::string::npos) {
          name = name.substr(0, pos) + "shapes";
        }
 
        RooProduct shapeProduct(name.c_str(), thisSampleHistFuncs.front()->GetTitle(), RooArgSet(thisSampleHistFuncs.begin(), thisSampleHistFuncs.end()));
        proto->import(shapeProduct, RecycleConflictNodes());
        shapeList.add(*proto->function(name.c_str()));
      }
    }
 
    // Sum all samples
    RooRealSumPdf tot(totName.c_str(), totName.c_str(), shapeList, coefList, true);
    tot.specialIntegratorConfig(true)->method1D().setLabel("RooBinIntegrator")  ;
    tot.specialIntegratorConfig(true)->method2D().setLabel("RooBinIntegrator")  ;
    tot.specialIntegratorConfig(true)->methodND().setLabel("RooBinIntegrator")  ;
    tot.forceNumInt();
 
    // for mixed generation in RooSimultaneous
    tot.setAttribute("GenerateBinned"); // for use with RooSimultaneous::generate in mixed mode
 
    // Enable the binned likelihood optimization
    if(fCfg.binnedFitOptimization) {
      tot.setAttribute("BinnedLikelihood");
    }
 
    proto->import(tot, RecycleConflictNodes());
  }
 
  //////////////////////////////////////////////////////////////////////////////
 
  void HistoToWorkspaceFactoryFast::PrintCovarianceMatrix(RooFitResult* result, RooArgSet* params, string filename){
 
    FILE* covFile = fopen ((filename).c_str(),"w");
    fprintf(covFile," ") ;
    for (auto const *myargi : static_range_cast<RooRealVar *>(*params)) {
      if(myargi->isConstant()) continue;
      fprintf(covFile," & %s",  myargi->GetName());
    }
    fprintf(covFile,"\\\\ \\hline \n" );
    for (auto const *myargi : static_range_cast<RooRealVar *>(*params)) {
      if(myargi->isConstant()) continue;
      fprintf(covFile,"%s", myargi->GetName());
      for (auto const *myargj : static_range_cast<RooRealVar *>(*params)) {
        if(myargj->isConstant()) continue;
        cout << myargi->GetName() << "," << myargj->GetName();
        fprintf(covFile, " & %.2f", result->correlation(*myargi, *myargj));
      }
      cout << endl;
      fprintf(covFile, " \\\\\n");
    }
    fclose(covFile);
 
  }
 
 
  ///////////////////////////////////////////////
  RooWorkspace* HistoToWorkspaceFactoryFast::MakeSingleChannelWorkspace(Measurement& measurement, Channel& channel) {
 
    // check inputs (see JIRA-6890 )
 
    if (channel.GetSamples().empty()) {
      Error("MakeSingleChannelWorkspace",
          "The input Channel does not contain any sample - return a nullptr");
      return 0;
    }
 
    const TH1* channel_hist_template = channel.GetSamples().front().GetHisto();
    if (channel_hist_template == nullptr) {
      channel.CollectHistograms();
      channel_hist_template = channel.GetSamples().front().GetHisto();
    }
    if (channel_hist_template == nullptr) {
      std::ostringstream stream;
      stream << "The sample " << channel.GetSamples().front().GetName()
                   << " in channel " << channel.GetName() << " does not contain a histogram. This is the channel:\n";
      channel.Print(stream);
      Error("MakeSingleChannelWorkspace", "%s", stream.str().c_str());
      return 0;
    }
 
    if( ! channel.CheckHistograms() ) {
      std::cout << "MakeSingleChannelWorkspace: Channel: " << channel.GetName()
                      << " has uninitialized histogram pointers" << std::endl;
      throw hf_exc();
    }
 
 
 
    // Set these by hand inside the function
    vector<string> systToFix = measurement.GetConstantParams();
    bool doRatio=false;
 
    // to time the macro
    TStopwatch t;
    t.Start();
    //ES// string channel_name=summary[0].channel;
    string channel_name = channel.GetName();
 
    /// MB: reset observable names for each new channel.
    fObsNameVec.clear();
 
    /// MB: label observables x,y,z, depending on histogram dimensionality
    /// GHL: Give it the first sample's nominal histogram as a template
    ///      since the data histogram may not be present
    if (fObsNameVec.empty()) { GuessObsNameVec(channel_hist_template); }
 
    for ( unsigned int idx=0; idx<fObsNameVec.size(); ++idx ) {
      fObsNameVec[idx] = "obs_" + fObsNameVec[idx] + "_" + channel_name ;
    }
 
    if (fObsNameVec.empty()) {
      fObsName= "obs_" + channel_name; // set name ov observable
      fObsNameVec.push_back( fObsName );
    }
 
    if (fObsNameVec.empty() || fObsNameVec.size() >= 3) {
      throw hf_exc("HistFactory is limited to 1- to 3-dimensional histograms.");
    }
 
    cxcoutP(HistFactory) << "\n-----------------------------------------\n"
        << "\tStarting to process '"
        << channel_name << "' channel with " << fObsNameVec.size() << " observables"
        << "\n-----------------------------------------\n" << endl;
 
    //
    // our main workspace that we are using to construct the model
    //
    RooWorkspace* proto = new RooWorkspace(channel_name.c_str(), (channel_name+" workspace").c_str());
    auto proto_config = make_unique<ModelConfig>("ModelConfig", proto);
    proto_config->SetWorkspace(*proto);
 
    // preprocess functions
    vector<string>::iterator funcIter = fPreprocessFunctions.begin();
    for(;funcIter!= fPreprocessFunctions.end(); ++funcIter){
      cxcoutI(HistFactory) << "will preprocess this line: " << *funcIter <<endl;
      proto->factory(*funcIter);
      proto->Print();
    }
 
    RooArgSet likelihoodTerms("likelihoodTerms"), constraintTerms("constraintTerms");
    vector<string> likelihoodTermNames, constraintTermNames, totSystTermNames;
    // All histogram functions to be multiplied in each sample
    std::vector<std::vector<RooAbsArg*>> allSampleHistFuncs;
    std::vector<RooProduct*> sampleScaleFactors;
 
    std::vector< pair<string,string> >   statNamePairs;
    std::vector< pair<const TH1*, std::unique_ptr<TH1>> > statHistPairs; // <nominal, error>
    const std::string statFuncName = "mc_stat_" + channel_name;
 
    string prefix, range;
 
    /////////////////////////////
    // shared parameters
    // this is ratio of lumi to nominal lumi.  We will include relative uncertainty in model
    std::stringstream lumiStr;
    // lumi range
    lumiStr << "Lumi[" << fNomLumi << ",0," << 10.*fNomLumi << "]";
    proto->factory(lumiStr.str());
    cxcoutI(HistFactory) << "lumi str = " << lumiStr.str() << endl;
 
    std::stringstream lumiErrorStr;
    lumiErrorStr << "nominalLumi["<<fNomLumi << ",0,"<<fNomLumi+10*fLumiError<<"]," << fLumiError ;
    proto->factory("Gaussian::lumiConstraint(Lumi,"+lumiErrorStr.str()+")");
    proto->var("nominalLumi")->setConstant();
    proto->defineSet("globalObservables","nominalLumi");
    //likelihoodTermNames.push_back("lumiConstraint");
    constraintTermNames.push_back("lumiConstraint");
    cxcoutI(HistFactory) << "lumi Error str = " << lumiErrorStr.str() << endl;
 
    //proto->factory("SigXsecOverSM[1.,0.5,1..8]");
    ///////////////////////////////////
    // loop through estimates, add expectation, floating bin predictions,
    // and terms that constrain floating to expectation via uncertainties
    // GHL: Loop over samples instead, which doesn't contain the data
    for (Sample& sample : channel.GetSamples()) {
      string overallSystName = sample.GetName() + "_" + channel_name + "_epsilon";
 
      string systSourcePrefix = "alpha_";
 
      // constraintTermNames and totSystTermNames are vectors that are passed
      // by reference and filled by this method
      AddConstraintTerms(proto,measurement, systSourcePrefix, overallSystName,
          sample.GetOverallSysList(), constraintTermNames , totSystTermNames);
 
      allSampleHistFuncs.emplace_back();
      std::vector<RooAbsArg*>& sampleHistFuncs = allSampleHistFuncs.back();
 
      // GHL: Consider passing the NormFactor list instead of the entire sample
      auto normFactors = CreateNormFactor(proto, channel_name, overallSystName, sample, doRatio);
      assert(normFactors);
 
      // Create the string for the object
      // that is added to the RooRealSumPdf
      // for this channel
//      string syst_x_expectedPrefix = "";
 
      // get histogram
      //ES// TH1* nominal = it->nominal;
      const TH1* nominal = sample.GetHisto();
 
      // MB : HACK no option to have both non-hist variations and hist variations ?
      // get histogram
      // GHL: Okay, this is going to be non-trivial.
      //      We will loop over histosys's, which contain both
      //      the low hist and the high hist together.
 
      // Logic:
      //        - If we have no HistoSys's, do part A
      //        - else, if the histo syst's don't match, return (we ignore this case)
      //        - finally, we take the syst's and apply the linear interpolation w/ constraint
      string expPrefix = sample.GetName() + "_" + channel_name;
      // create roorealvar observables
      RooArgList observables = createObservables(sample.GetHisto(), proto);
      RooHistFunc* nominalHistFunc = MakeExpectedHistFunc(sample.GetHisto(), proto, expPrefix, observables);
      assert(nominalHistFunc);
 
      if(sample.GetHistoSysList().empty()) {
        // If no HistoSys
        cxcoutI(HistFactory) << sample.GetName() + "_" + channel_name + " has no variation histograms " << endl;
 
        sampleHistFuncs.push_back(nominalHistFunc);
      } else {
        // If there ARE HistoSys(s)
        // name of source for variation
        string constraintPrefix = sample.GetName() + "_" + channel_name + "_Hist_alpha";
 
        // make list of abstract parameters that interpolate in space of variations
        RooArgList interpParams = makeInterpolationParameters(sample.GetHistoSysList(), *proto);
 
        // next, cerate the constraint terms
        for(std::size_t i = 0; i < interpParams.size(); ++i) {
          bool isUniform = measurement.GetUniformSyst().count(sample.GetHistoSysList()[i].GetName()) > 0;
          makeGaussianConstraint(interpParams[i], *proto, isUniform, constraintTermNames);
        }
 
        // finally, create the interpolated function
        sampleHistFuncs.push_back( makeLinInterp(interpParams, nominalHistFunc, proto,
            sample.GetHistoSysList(), constraintPrefix, observables) );
      }
 
      sampleHistFuncs.front()->SetTitle( (nominal && strlen(nominal->GetTitle())>0) ? nominal->GetTitle() : sample.GetName().c_str() );
 
      ////////////////////////////////////
      // Add StatErrors to this Channel //
      ////////////////////////////////////
 
      if( sample.GetStatError().GetActivate() ) {
 
        if( fObsNameVec.size() > 3 ) {
          cxcoutF(HistFactory) << "Cannot include Stat Error for histograms of more than 3 dimensions."
              << std::endl;
          throw hf_exc();
        } else {
 
          // If we are using StatUncertainties, we multiply this object
          // by the ParamHistFunc and then pass that to the
          // RooRealSumPdf by appending it's name to the list
 
          cxcoutI(HistFactory) << "Sample: "     << sample.GetName()  << " to be included in Stat Error "
              << "for channel " << channel_name
              << std::endl;
 
          string UncertName  = sample.GetName() + "_" + channel_name + "_StatAbsolUncert";
          std::unique_ptr<TH1> statErrorHist;
 
          if( sample.GetStatError().GetErrorHist() == nullptr ) {
            // Make the absolute stat error
            cxcoutI(HistFactory) << "Making Statistical Uncertainty Hist for "
                << " Channel: " << channel_name
                << " Sample: "  << sample.GetName()
                << std::endl;
            statErrorHist.reset(MakeAbsolUncertaintyHist( UncertName, nominal));
          } else {
            // clone the error histograms because in case the sample has not error hist
            // it is created in MakeAbsolUncertainty
            // we need later to clean statErrorHist
            statErrorHist.reset(static_cast<TH1*>(sample.GetStatError().GetErrorHist()->Clone()));
            // We assume the (relative) error is provided.
            // We must turn it into an absolute error
            // using the nominal histogram
            cxcoutI(HistFactory) << "Using external histogram for Stat Errors for "
                << "\tChannel: " << channel_name
                << "\tSample: "  << sample.GetName()
                << "\tError Histogram: " << statErrorHist->GetName() << std::endl;
            // Multiply the relative stat uncertainty by the
            // nominal to get the overall stat uncertainty
            statErrorHist->Multiply( nominal );
            statErrorHist->SetName( UncertName.c_str() );
          }
 
          // Save the nominal and error hists
          // for the building of constraint terms
          statHistPairs.emplace_back(nominal, std::move(statErrorHist));
 
          // To do the 'conservative' version, we would need to do some
          // intervention here.  We would probably need to create a different
          // ParamHistFunc for each sample in the channel.  The would nominally
          // use the same gamma's, so we haven't increased the number of parameters
          // However, if a bin in the 'nominal' histogram is 0, we simply need to
          // change the parameter in that bin in the ParamHistFunc for this sample.
          // We also need to add a constraint term.
          //  Actually, we'd probably not use the ParamHistFunc...?
          //  we could remove the dependence in this ParamHistFunc on the ith gamma
          //  and then create the poisson term: Pois(tau | n_exp)Pois(data | n_exp)
 
 
          // Next, try to get the common ParamHistFunc (it may have been
          // created by another sample in this channel)
          // or create it if it doesn't yet exist:
          ParamHistFunc* paramHist = dynamic_cast<ParamHistFunc*>( proto->function(statFuncName.c_str()) );
          if( paramHist == nullptr ) {
 
            // Get a RooArgSet of the observables:
            // Names in the list fObsNameVec:
            RooArgList theObservables;
            std::vector<std::string>::iterator itr = fObsNameVec.begin();
            for (int idx=0; itr!=fObsNameVec.end(); ++itr, ++idx ) {
              theObservables.add( *proto->var(*itr) );
            }
 
            // Create the list of terms to
            // control the bin heights:
            std::string ParamSetPrefix  = "gamma_stat_" + channel_name;
            double gammaMin = 0.0;
            double gammaMax = 10.0;
            RooArgList statFactorParams = ParamHistFunc::createParamSet(*proto,
                ParamSetPrefix.c_str(),
                theObservables,
                gammaMin, gammaMax);
 
            ParamHistFunc statUncertFunc(statFuncName.c_str(), statFuncName.c_str(),
                theObservables, statFactorParams );
 
            proto->import( statUncertFunc, RecycleConflictNodes() );
 
            paramHist = (ParamHistFunc*) proto->function( statFuncName.c_str() );
          }
 
          // apply stat function to sample
          sampleHistFuncs.push_back(paramHist);
        }
      } // END: if DoMcStat
 
 
      ///////////////////////////////////////////
      // Create a ShapeFactor for this channel //
      ///////////////////////////////////////////
 
      if( sample.GetShapeFactorList().size() > 0 ) {
 
        if( fObsNameVec.size() > 3 ) {
          cxcoutF(HistFactory) << "Cannot include Stat Error for histograms of more than 3 dimensions."
              << std::endl;
          throw hf_exc();
        } else {
 
          cxcoutI(HistFactory) << "Sample: "     << sample.GetName() << " in channel: " << channel_name
              << " to be include a ShapeFactor."
              << std::endl;
 
          for(unsigned int i=0; i < sample.GetShapeFactorList().size(); ++i) {
 
            ShapeFactor& shapeFactor = sample.GetShapeFactorList().at(i);
 
            std::string funcName = channel_name + "_" + shapeFactor.GetName() + "_shapeFactor";
            ParamHistFunc* paramHist = (ParamHistFunc*) proto->function( funcName.c_str() );
            if( paramHist == nullptr ) {
 
              RooArgList theObservables;
              std::vector<std::string>::iterator itr = fObsNameVec.begin();
              for (int idx=0; itr!=fObsNameVec.end(); ++itr, ++idx ) {
                theObservables.add( *proto->var(*itr) );
              }
 
              // Create the Parameters
              std::string funcParams = "gamma_" + shapeFactor.GetName();
 
              // GHL: Again, we are putting hard ranges on the gamma's
              //      We should change this to range from 0 to /inf
              RooArgList shapeFactorParams = ParamHistFunc::createParamSet(*proto,
                  funcParams.c_str(),
                  theObservables, 0, 1000);
 
              // Create the Function
              ParamHistFunc shapeFactorFunc( funcName.c_str(), funcName.c_str(),
                  theObservables, shapeFactorParams );
 
              // Set an initial shape, if requested
              if( shapeFactor.GetInitialShape() != nullptr ) {
                TH1* initialShape = static_cast<TH1*>(shapeFactor.GetInitialShape()->Clone());
                cxcoutI(HistFactory) << "Setting Shape Factor: " << shapeFactor.GetName()
                   << " to have initial shape from hist: "
                   << initialShape->GetName()
                   << std::endl;
                shapeFactorFunc.setShape( initialShape );
              }
 
              // Set the variables constant, if requested
              if( shapeFactor.IsConstant() ) {
                cxcoutI(HistFactory) << "Setting Shape Factor: " << shapeFactor.GetName()
                   << " to be constant" << std::endl;
                shapeFactorFunc.setConstant(true);
              }
 
              proto->import( shapeFactorFunc, RecycleConflictNodes() );
              paramHist = (ParamHistFunc*) proto->function( funcName.c_str() );
 
            } // End: Create ShapeFactor ParamHistFunc
 
            sampleHistFuncs.push_back(paramHist);
          } // End loop over ShapeFactor Systematics
        }
      } // End: if ShapeFactorName!=""
 
 
      ////////////////////////////////////////
      // Create a ShapeSys for this channel //
      ////////////////////////////////////////
 
      if( !sample.GetShapeSysList().empty() ) {
 
        if( fObsNameVec.size() > 3 ) {
          cxcoutF(HistFactory) << "Cannot include Stat Error for histograms of more than 3 dimensions."
              << std::endl;
          throw hf_exc();
        } else {
 
          // List of ShapeSys ParamHistFuncs
          std::vector<string> ShapeSysNames;
 
          for( unsigned int i = 0; i < sample.GetShapeSysList().size(); ++i) {
 
            // Create the ParamHistFunc's
            // Create their constraint terms and add them
            // to the list of constraint terms
 
            // Create a single RooProduct over all of these
            // paramHistFunc's
 
            // Send the name of that product to the RooRealSumPdf
 
            RooStats::HistFactory::ShapeSys& shapeSys = sample.GetShapeSysList().at(i);
 
            cxcoutI(HistFactory) << "Sample: " << sample.GetName() << " in channel: " << channel_name
                << " to include a ShapeSys." << std::endl;
 
            std::string funcName = channel_name + "_" + shapeSys.GetName() + "_ShapeSys";
            ShapeSysNames.push_back( funcName );
            ParamHistFunc* paramHist = (ParamHistFunc*) proto->function( funcName.c_str() );
            if( paramHist == nullptr ) {
 
              //std::string funcParams = "gamma_" + it->shapeFactorName;
              //paramHist = CreateParamHistFunc( proto, fObsNameVec, funcParams, funcName );
 
              RooArgList theObservables;
              std::vector<std::string>::iterator itr = fObsNameVec.begin();
              for(; itr!=fObsNameVec.end(); ++itr ) {
                theObservables.add( *proto->var(*itr) );
              }
 
              // Create the Parameters
              std::string funcParams = "gamma_" + shapeSys.GetName();
              RooArgList shapeFactorParams = ParamHistFunc::createParamSet(*proto,
                  funcParams.c_str(),
                  theObservables, 0, 10);
 
              // Create the Function
              ParamHistFunc shapeFactorFunc( funcName.c_str(), funcName.c_str(),
                  theObservables, shapeFactorParams );
 
              proto->import( shapeFactorFunc, RecycleConflictNodes() );
              paramHist = (ParamHistFunc*) proto->function( funcName.c_str() );
 
            } // End: Create ShapeFactor ParamHistFunc
 
            // Create the constraint terms and add
            // them to the workspace (proto)
            // as well as the list of constraint terms (constraintTermNames)
 
            // The syst should be a fractional error
            const TH1* shapeErrorHist = shapeSys.GetErrorHist();
 
            // Constraint::Type shapeConstraintType = Constraint::Gaussian;
            Constraint::Type systype = shapeSys.GetConstraintType();
            if( systype == Constraint::Gaussian) {
              systype = Constraint::Gaussian;
            }
            if( systype == Constraint::Poisson ) {
              systype = Constraint::Poisson;
            }
 
            double minShapeUncertainty = 0.0;
            RooArgList shapeConstraints = createStatConstraintTerms(proto, constraintTermNames,
                *paramHist, shapeErrorHist,
                systype,
                minShapeUncertainty);
 
          } // End: Loop over ShapeSys vector in this EstimateSummary
 
          // Now that we have the list of ShapeSys ParamHistFunc names,
          // we create the total RooProduct
          // we multiply the expected functio
 
 
          for( unsigned int i = 0; i < ShapeSysNames.size(); ++i ) {
            auto func = proto->function(ShapeSysNames.at(i).c_str());
            assert(func);
            sampleHistFuncs.push_back(func);
          }
 
        } // End: NumObsVar == 1
 
      } // End: !GetShapeSysList.empty()
 
 
      // GHL: This was pretty confusing before,
      //      hopefully using the measurement directly
      //      will improve it
      auto lumi = proto->arg("Lumi");
      if( !sample.GetNormalizeByTheory() ) {
        if (!lumi) {
          TString lumiParamString;
          lumiParamString += measurement.GetLumi();
          lumiParamString.ReplaceAll(' ', TString());
          lumi = proto->factory(("Lumi[" + lumiParamString + "]").Data());
        } else {
          static_cast<RooAbsRealLValue*>(lumi)->setVal(measurement.GetLumi());
        }
      }
      assert(lumi);
      normFactors->addTerm(lumi);
 
      // Append the name of the "node"
      // that is to be summed with the
      // RooRealSumPdf
      proto->import(*normFactors, RecycleConflictNodes());
      auto normFactorsInWS = dynamic_cast<RooProduct*>(proto->arg(normFactors->GetName()));
      assert(normFactorsInWS);
 
      sampleScaleFactors.push_back(normFactorsInWS);
    } // END: Loop over EstimateSummaries
 
    // If a non-zero number of samples call for
    // Stat Uncertainties, create the statFactor functions
    if(!statHistPairs.empty()) {
 
      // Create the histogram of (binwise)
      // stat uncertainties:
      unique_ptr<TH1> fracStatError( MakeScaledUncertaintyHist( channel_name + "_StatUncert" + "_RelErr", statHistPairs) );
      if( fracStatError == nullptr ) {
        cxcoutE(HistFactory) << "Error: Failed to make ScaledUncertaintyHist for: "
            << channel_name + "_StatUncert" + "_RelErr" << std::endl;
        throw hf_exc();
      }
 
      // Using this TH1* of fractinal stat errors,
      // create a set of constraint terms:
      ParamHistFunc* chanStatUncertFunc = (ParamHistFunc*) proto->function( statFuncName.c_str() );
      cxcoutI(HistFactory) << "About to create Constraint Terms from: "
          << chanStatUncertFunc->GetName()
          << " params: " << chanStatUncertFunc->paramList()
          << std::endl;
 
      // Get the constraint type and the
      // rel error threshold from the (last)
      // EstimateSummary looped over (but all
      // should be the same)
 
      // Get the type of StatError constraint from the channel
      Constraint::Type statConstraintType = channel.GetStatErrorConfig().GetConstraintType();
      if( statConstraintType == Constraint::Gaussian) {
        cxcoutI(HistFactory) << "Using Gaussian StatErrors in channel: " << channel.GetName() << std::endl;
      }
      if( statConstraintType == Constraint::Poisson ) {
        cxcoutI(HistFactory) << "Using Poisson StatErrors in channel: " << channel.GetName()  << std::endl;
      }
 
      double statRelErrorThreshold = channel.GetStatErrorConfig().GetRelErrorThreshold();
      RooArgList statConstraints = createStatConstraintTerms(proto, constraintTermNames,
          *chanStatUncertFunc, fracStatError.get(),
          statConstraintType,
          statRelErrorThreshold);
 
    } // END: Loop over stat Hist Pairs
 
 
    ///////////////////////////////////
    // for ith bin calculate totN_i =  lumi * sum_j expected_j * syst_j
    MakeTotalExpected(proto, channel_name+"_model",
        sampleScaleFactors, allSampleHistFuncs);
    likelihoodTermNames.push_back(channel_name+"_model");
 
    //////////////////////////////////////
    // fix specified parameters
    for(unsigned int i=0; i<systToFix.size(); ++i){
      RooRealVar* temp = proto->var(systToFix.at(i));
      if(temp) {
        // set the parameter constant
        temp->setConstant();
 
        // remove the corresponding auxiliary observable from the global observables
        RooRealVar* auxMeas = nullptr;
        if(systToFix.at(i)=="Lumi"){
          auxMeas = proto->var("nominalLumi");
        } else {
          auxMeas = proto->var(std::string("nom_") + temp->GetName());
        }
 
        if(auxMeas){
          const_cast<RooArgSet*>(proto->set("globalObservables"))->remove(*auxMeas);
        } else{
          cxcoutE(HistFactory) << "could not corresponding auxiliary measurement  "
              << TString::Format("nom_%s",temp->GetName()) << endl;
        }
      } else {
        cxcoutE(HistFactory) << "could not find variable " << systToFix.at(i)
            << " could not set it to constant" << endl;
      }
    }
 
    //////////////////////////////////////
    // final proto model
    for(unsigned int i=0; i<constraintTermNames.size(); ++i){
      RooAbsArg* proto_arg = (proto->arg(constraintTermNames[i].c_str()));
      if( proto_arg==nullptr ) {
        cxcoutF(HistFactory) << "Error: Cannot find arg set: " << constraintTermNames.at(i)
            << " in workspace: " << proto->GetName() << std::endl;
        throw hf_exc();
      }
      constraintTerms.add( *proto_arg );
      //  constraintTerms.add(* proto_arg(proto->arg(constraintTermNames[i].c_str())) );
    }
    for(unsigned int i=0; i<likelihoodTermNames.size(); ++i){
      RooAbsArg* proto_arg = (proto->arg(likelihoodTermNames[i].c_str()));
      if( proto_arg==nullptr ) {
        cxcoutF(HistFactory) << "Error: Cannot find arg set: " << likelihoodTermNames.at(i)
            << " in workspace: " << proto->GetName() << std::endl;
        throw hf_exc();
      }
      likelihoodTerms.add( *proto_arg );
    }
    proto->defineSet("constraintTerms",constraintTerms);
    proto->defineSet("likelihoodTerms",likelihoodTerms);
 
    // list of observables
    RooArgList observables;
    std::string observablesStr;
 
    std::vector<std::string>::iterator itr = fObsNameVec.begin();
    for(; itr!=fObsNameVec.end(); ++itr ) {
      observables.add( *proto->var(*itr) );
      if (!observablesStr.empty()) { observablesStr += ","; }
      observablesStr += *itr;
    }
 
    // We create two sets, one for backwards compatability
    // The other to make a consistent naming convention
    // between individual channels and the combined workspace
    proto->defineSet("observables", TString::Format("%s",observablesStr.c_str()));
    proto->defineSet("observablesSet", TString::Format("%s",observablesStr.c_str()));
 
    // Create the ParamHistFunc
    // after observables have been made
    cxcoutP(HistFactory) << "\n-----------------------------------------\n"
        << "\timport model into workspace"
        << "\n-----------------------------------------\n" << endl;
 
    auto model = make_unique<RooProdPdf>(
        ("model_"+channel_name).c_str(),    // MB : have changed this into conditional pdf. Much faster for toys!
        "product of Poissons accross bins for a single channel",
        constraintTerms, Conditional(likelihoodTerms,observables));
    // can give channel a title by setting title of corresponding data histogram
    if (channel.GetData().GetHisto() && strlen(channel.GetData().GetHisto()->GetTitle())>0) {
       model->SetTitle(channel.GetData().GetHisto()->GetTitle());
    }
    proto->import(*model,RecycleConflictNodes());
 
    proto_config->SetPdf(*model);
    proto_config->SetObservables(observables);
    proto_config->SetGlobalObservables(*proto->set("globalObservables"));
    //    proto->writeToFile(("results/model_"+channel+".root").c_str());
    // fill out nuisance parameters in model config
    //    proto_config->GuessObsAndNuisance(*proto->data("asimovData"));
    proto->import(*proto_config,proto_config->GetName());
    proto->importClassCode();
 
    ///////////////////////////
    // make data sets
    // THis works and is natural, but the memory size of the simultaneous dataset grows exponentially with channels
    // New Asimov Generation: Use the code in the Asymptotic calculator
    // Need to get the ModelConfig...
    int asymcalcPrintLevel = 0;
    if (RooMsgService::instance().isActive(static_cast<TObject*>(nullptr), RooFit::HistFactory, RooFit::INFO)) asymcalcPrintLevel = 1;
    if (RooMsgService::instance().isActive(static_cast<TObject*>(nullptr), RooFit::HistFactory, RooFit::DEBUG)) asymcalcPrintLevel = 2;
    AsymptoticCalculator::SetPrintLevel(asymcalcPrintLevel);
    unique_ptr<RooAbsData> asimov_dataset(AsymptoticCalculator::GenerateAsimovData(*model, observables));
    proto->import(dynamic_cast<RooDataSet&>(*asimov_dataset), Rename("asimovData"));
 
    // GHL: Determine to use data if the hist isn't 'nullptr'
    if(TH1 const* mnominal = channel.GetData().GetHisto()) {
      // This works and is natural, but the memory size of the simultaneous
      // dataset grows exponentially with channels.
      RooDataSet dataset{"obsData","",*proto->set("observables"), RooFit::WeightVar("weightVar")};
      ConfigureHistFactoryDataset( dataset, *mnominal, *proto, fObsNameVec );
      proto->import(dataset);
    } // End: Has non-null 'data' entry
 
 
    for(auto const& data : channel.GetAdditionalData()) {
      if(data.GetName().empty()) {
        cxcoutF(HistFactory) << "Error: Additional Data histogram for channel: " << channel.GetName()
                << " has no name! The name always needs to be set for additional datasets, "
                << "either via the \"Name\" tag in the XML or via RooStats::HistFactory::Data::SetName()." << std::endl;
        throw hf_exc();
      }
      std::string const& dataName = data.GetName();
      TH1 const* mnominal = data.GetHisto();
      if( !mnominal ) {
        cxcoutF(HistFactory) << "Error: Additional Data histogram for channel: " << channel.GetName()
                << " with name: " << dataName << " is nullptr" << std::endl;
        throw hf_exc();
      }
 
      // THis works and is natural, but the memory size of the simultaneous dataset grows exponentially with channels
      RooDataSet dataset{dataName.c_str(), "", *proto->set("observables"), RooFit::WeightVar("weightVar")};
      ConfigureHistFactoryDataset( dataset, *mnominal, *proto, fObsNameVec );
      proto->import(dataset);
 
    }
 
    if (RooMsgService::instance().isActive(static_cast<TObject*>(nullptr), RooFit::HistFactory, RooFit::INFO))
      proto->Print();
 
    return proto;
  }
 
 
  void HistoToWorkspaceFactoryFast::ConfigureHistFactoryDataset( RooDataSet& obsDataUnbinned,
                         TH1 const& mnominal,
                         RooWorkspace& proto,
                         std::vector<std::string> const& obsNameVec) {
 
    // Take a RooDataSet and fill it with the entries
    // from a TH1*, using the observable names to
    // determine the columns
 
     if (obsNameVec.empty() ) {
        Error("ConfigureHistFactoryDataset","Invalid input - return");
        return;
     }
 
    TAxis const* ax = mnominal.GetXaxis();
    TAxis const* ay = mnominal.GetYaxis();
    TAxis const* az = mnominal.GetZaxis();
 
    for (int i=1; i<=ax->GetNbins(); ++i) { // 1 or more dimension
 
      double xval = ax->GetBinCenter(i);
      proto.var( obsNameVec[0] )->setVal( xval );
 
      if(obsNameVec.size()==1) {
   double fval = mnominal.GetBinContent(i);
   obsDataUnbinned.add( *proto.set("observables"), fval );
      } else { // 2 or more dimensions
 
   for(int j=1; j<=ay->GetNbins(); ++j) {
     double yval = ay->GetBinCenter(j);
     proto.var( obsNameVec[1] )->setVal( yval );
 
     if(obsNameVec.size()==2) {
       double fval = mnominal.GetBinContent(i,j);
       obsDataUnbinned.add( *proto.set("observables"), fval );
     } else { // 3 dimensions
 
       for(int k=1; k<=az->GetNbins(); ++k) {
         double zval = az->GetBinCenter(k);
         proto.var( obsNameVec[2] )->setVal( zval );
         double fval = mnominal.GetBinContent(i,j,k);
         obsDataUnbinned.add( *proto.set("observables"), fval );
       }
     }
   }
      }
    }
  }
 
  void HistoToWorkspaceFactoryFast::GuessObsNameVec(const TH1* hist)
  {
    fObsNameVec.clear();
 
    // determine histogram dimensionality
    unsigned int histndim(1);
    std::string classname = hist->ClassName();
    if      (classname.find("TH1")==0) { histndim=1; }
    else if (classname.find("TH2")==0) { histndim=2; }
    else if (classname.find("TH3")==0) { histndim=3; }
 
    for ( unsigned int idx=0; idx<histndim; ++idx ) {
      if (idx==0) { fObsNameVec.push_back("x"); }
      if (idx==1) { fObsNameVec.push_back("y"); }
      if (idx==2) { fObsNameVec.push_back("z"); }
    }
  }
 
 
  RooWorkspace* HistoToWorkspaceFactoryFast::MakeCombinedModel(vector<string> ch_names, vector<std::unique_ptr<RooWorkspace>>& chs)
  {
    RooHelpers::LocalChangeMsgLevel changeMsgLvl(RooFit::INFO, 0, RooFit::ObjectHandling, false);
 
     // check first the inputs (see JIRA-6890)
     if (ch_names.empty() || chs.empty() ) {
        Error("MakeCombinedModel","Input vectors are empty - return a nullptr");
        return 0;
     }
     if (chs.size()  <  ch_names.size() ) {
        Error("MakeCombinedModel","Input vector of workspace has an invalid size - return a nullptr");
        return 0;
     }
 
    //
    /// These things were used for debugging. Maybe useful in the future
    //
 
    map<string, RooAbsPdf*> pdfMap;
    vector<RooAbsPdf*> models;
 
    RooArgList obsList;
    for(unsigned int i = 0; i< ch_names.size(); ++i){
      ModelConfig * config = (ModelConfig *) chs[i]->obj("ModelConfig");
      obsList.add(*config->GetObservables());
    }
    cxcoutI(HistFactory) <<"full list of observables:\n" << obsList << std::endl;
 
    RooArgSet globalObs;
    stringstream channelString;
    channelString << "channelCat[";
    for(unsigned int i = 0; i< ch_names.size(); ++i){
      string channel_name=ch_names[i];
      if (i == 0 && isdigit(channel_name[0])) {
        throw std::invalid_argument("The first channel name for HistFactory cannot start with a digit. Got " + channel_name);
      }
      if (channel_name.find(',') != std::string::npos) {
        throw std::invalid_argument("Channel names for HistFactory cannot contain ','. Got " + channel_name);
      }
 
      if (i == 0) channelString << channel_name ;
      else channelString << ',' << channel_name ;
      RooWorkspace * ch=chs[i].get();
 
      RooAbsPdf* model = ch->pdf("model_"+channel_name);
      if(!model) cout <<"failed to find model for channel"<<endl;
      //      cout << "int = " << model->createIntegral(*obsN)->getVal() << endl;;
      models.push_back(model);
      globalObs.add(*ch->set("globalObservables"), /*silent=*/true); // silent because observables might exist in other channel.
 
      //      constrainedParams->add( * ch->set("constrainedParams") );
      pdfMap[channel_name]=model;
    }
    channelString << "]";
 
    cxcoutP(HistFactory) << "\n-----------------------------------------\n"
        << "\tEntering combination"
        << "\n-----------------------------------------\n" << endl;
    RooWorkspace* combined = new RooWorkspace("combined");
    //    RooWorkspace* combined = chs[0];
 
 
    RooCategory* channelCat = dynamic_cast<RooCategory*>( combined->factory(channelString.str()) );
    if (!channelCat) throw std::runtime_error("Unable to construct a category from string " + channelString.str());
 
    auto simPdf= std::make_unique<RooSimultaneous>("simPdf","",pdfMap, *channelCat);
    auto combined_config = std::make_unique<ModelConfig>("ModelConfig", combined);
    combined_config->SetWorkspace(*combined);
    //    combined_config->SetNuisanceParameters(*constrainedParams);
 
    combined->import(globalObs);
    combined->defineSet("globalObservables",globalObs);
    combined_config->SetGlobalObservables(*combined->set("globalObservables"));
 
    combined->factory("weightVar[0,-1e10,1e10]");
    obsList.add(*combined->var("weightVar"));
    combined->defineSet("observables",{obsList, *channelCat}, /*importMissing=*/true);
    combined_config->SetObservables(*combined->set("observables"));
 
 
    // Now merge the observable datasets across the channels
    for(RooAbsData * data : chs[0]->allData()) {
      // We are excluding the Asimov data, because it needs to be regenerated
      // later after the parameter values are set.
      if(std::string("asimovData") != data->GetName()) {
        MergeDataSets(combined, chs, ch_names, data->GetName(), obsList, channelCat);
      }
    }
 
 
    if (RooMsgService::instance().isActive(static_cast<TObject*>(nullptr), RooFit::HistFactory, RooFit::INFO))
      combined->Print();
 
    cxcoutP(HistFactory) << "\n-----------------------------------------\n"
            << "\tImporting combined model"
            << "\n-----------------------------------------\n" << endl;
    combined->import(*simPdf,RecycleConflictNodes());
 
    std::map< std::string, double>::iterator param_itr = fParamValues.begin();
    for( ; param_itr != fParamValues.end(); ++param_itr ){
      // make sure they are fixed
      std::string paramName = param_itr->first;
      double paramVal = param_itr->second;
 
      if(RooRealVar* temp = combined->var( paramName )) {
        temp->setVal( paramVal );
        cxcoutI(HistFactory) <<"setting " << paramName << " to the value: " << paramVal <<  endl;
      } else
        cxcoutE(HistFactory) << "could not find variable " << paramName << " could not set its value" << endl;
    }
 
 
    for(unsigned int i=0; i<fSystToFix.size(); ++i){
      // make sure they are fixed
      if(RooRealVar* temp = combined->var(fSystToFix[i])) {
        temp->setConstant();
        cxcoutI(HistFactory) <<"setting " << fSystToFix.at(i) << " constant" << endl;
      } else
        cxcoutE(HistFactory) << "could not find variable " << fSystToFix.at(i) << " could not set it to constant" << endl;
    }
 
    ///
    /// writing out the model in graphViz
    ///
    //    RooAbsPdf* customized=combined->pdf("simPdf");
    //combined_config->SetPdf(*customized);
    combined_config->SetPdf(*simPdf);
    //    combined_config->GuessObsAndNuisance(*simData);
    //    customized->graphVizTree(("results/"+fResultsPrefixStr.str()+"_simul.dot").c_str());
    combined->import(*combined_config,combined_config->GetName());
    combined->importClassCode();
    //    combined->writeToFile("results/model_combined.root");
 
 
    ////////////////////////////////////////////
    // Make toy simultaneous dataset
    cxcoutP(HistFactory) << "\n-----------------------------------------\n"
        << "\tcreate toy data for " << channelString.str()
        << "\n-----------------------------------------\n" << endl;
 
 
    // now with weighted datasets
    // First Asimov
 
    // Create Asimov data for the combined dataset
    std::unique_ptr<RooDataSet> asimov_combined{static_cast<RooDataSet*>(AsymptoticCalculator::GenerateAsimovData(
                                  *combined->pdf("simPdf"),
                                  obsList))};
    if( asimov_combined ) {
      combined->import( *asimov_combined, Rename("asimovData"));
    }
    else {
      std::cout << "Error: Failed to create combined asimov dataset" << std::endl;
      throw hf_exc();
    }
 
    return combined;
  }
 
 
  RooDataSet* HistoToWorkspaceFactoryFast::MergeDataSets(RooWorkspace* combined,
                      std::vector<std::unique_ptr<RooWorkspace>>& wspace_vec,
                      std::vector<std::string> const& channel_names,
                      std::string const& dataSetName,
                      RooArgList const& obsList,
                      RooCategory* channelCat) {
 
    // Create the total dataset
    std::unique_ptr<RooDataSet> simData;
 
    // Loop through channels, get their individual datasets,
    // and add them to the combined dataset
    for(unsigned int i = 0; i< channel_names.size(); ++i){
 
      // Grab the dataset for the existing channel
      cxcoutPHF << "Merging data for channel " << channel_names[i].c_str() << std::endl;
      RooDataSet* obsDataInChannel = (RooDataSet*) wspace_vec[i]->data(dataSetName.c_str());
      if( !obsDataInChannel ) {
   std::cout << "Error: Can't find DataSet: " << dataSetName
        << " in channel: " << channel_names.at(i)
        << std::endl;
   throw hf_exc();
      }
 
      // Create the new Dataset
      auto tempData = std::make_unique<RooDataSet>(channel_names[i].c_str(),"",
                    obsList, Index(*channelCat),
                    WeightVar("weightVar"),
                    Import(channel_names[i].c_str(),*obsDataInChannel));
      if(simData) {
   simData->append(*tempData);
      }
      else {
   simData = std::move(tempData);
      }
    } // End Loop Over Channels
 
    // Check that we successfully created the dataset
    // and import it into the workspace
    if(simData) {
      combined->import(*simData, Rename(dataSetName.c_str()));
      return static_cast<RooDataSet*>(combined->data(dataSetName));
    }
    else {
      std::cout << "Error: Unable to merge observable datasets" << std::endl;
      throw hf_exc();
      return nullptr;
    }
  }
 
 
  TH1* HistoToWorkspaceFactoryFast::MakeAbsolUncertaintyHist( const std::string& Name, const TH1* Nominal ) {
 
    // Take a nominal TH1* and create
    // a TH1 representing the binwise
    // errors (taken from the nominal TH1)
 
    TH1* ErrorHist = (TH1*) Nominal->Clone( Name.c_str() );
    ErrorHist->Reset();
 
    Int_t numBins   = Nominal->GetNbinsX()*Nominal->GetNbinsY()*Nominal->GetNbinsZ();
    Int_t binNumber = 0;
 
    // Loop over bins
    for( Int_t i_bin = 0; i_bin < numBins; ++i_bin) {
 
      binNumber++;
      // Ignore underflow / overflow
      while( Nominal->IsBinUnderflow(binNumber) || Nominal->IsBinOverflow(binNumber) ){
   binNumber++;
      }
 
      double histError = Nominal->GetBinError( binNumber );
 
      // Check that histError != NAN
      if( histError != histError ) {
   std::cout << "Warning: In histogram " << Nominal->GetName()
        << " bin error for bin " << i_bin
        << " is NAN.  Not using Error!!!"
        << std::endl;
   throw hf_exc();
   //histError = sqrt( histContent );
   //histError = 0;
      }
 
      // Check that histError ! < 0
      if( histError < 0  ) {
   std::cout << "Warning: In histogram " << Nominal->GetName()
        << " bin error for bin " << binNumber
        << " is < 0.  Setting Error to 0"
        << std::endl;
   //histError = sqrt( histContent );
   histError = 0;
      }
 
      ErrorHist->SetBinContent( binNumber, histError );
 
    }
 
    return ErrorHist;
 
  }
 
  // Take a list of < nominal, absolError > TH1* pairs
  // and construct a single histogram representing the
  // total fractional error as:
 
  // UncertInQuad(bin i) = Sum: absolUncert*absolUncert
  // Total(bin i)        = Sum: Value
  //
  // TotalFracError(bin i) = Sqrt( UncertInQuad(i) ) / TotalBin(i)
  std::unique_ptr<TH1> HistoToWorkspaceFactoryFast::MakeScaledUncertaintyHist( const std::string& Name, std::vector< std::pair<const TH1*, std::unique_ptr<TH1>> > const& HistVec ) const {
 
 
    unsigned int numHists = HistVec.size();
 
    if( numHists == 0 ) {
      cxcoutE(HistFactory) << "Warning: Empty Hist Vector, cannot create total uncertainty" << std::endl;
      return nullptr;
    }
 
    const TH1* HistTemplate = HistVec.at(0).first;
    Int_t numBins = HistTemplate->GetNbinsX()*HistTemplate->GetNbinsY()*HistTemplate->GetNbinsZ();
 
  // Check that all histograms
  // have the same bins
  for( unsigned int i = 0; i < HistVec.size(); ++i ) {
 
    const TH1* nominal = HistVec.at(i).first;
    const TH1* error   = HistVec.at(i).second.get();
 
    if( nominal->GetNbinsX()*nominal->GetNbinsY()*nominal->GetNbinsZ() != numBins ) {
      cxcoutE(HistFactory) << "Error: Provided hists have unequal bins" << std::endl;
      return nullptr;
    }
    if( error->GetNbinsX()*error->GetNbinsY()*error->GetNbinsZ() != numBins ) {
      cxcoutE(HistFactory) << "Error: Provided hists have unequal bins" << std::endl;
      return nullptr;
    }
  }
 
  std::vector<double> TotalBinContent( numBins, 0.0);
  std::vector<double> HistErrorsSqr( numBins, 0.0);
 
  Int_t binNumber = 0;
 
  // Loop over bins
  for( Int_t i_bins = 0; i_bins < numBins; ++i_bins) {
 
    binNumber++;
    while( HistTemplate->IsBinUnderflow(binNumber) || HistTemplate->IsBinOverflow(binNumber) ){
      binNumber++;
    }
 
    for( unsigned int i_hist = 0; i_hist < numHists; ++i_hist ) {
 
      const TH1* nominal = HistVec.at(i_hist).first;
      const TH1* error   = HistVec.at(i_hist).second.get();
 
      //Int_t binNumber = i_bins + 1;
 
      double histValue  = nominal->GetBinContent( binNumber );
      double histError  = error->GetBinContent( binNumber );
      /*
      std::cout << " Getting Bin content for Stat Uncertainty"
      << " Nom name: " << nominal->GetName()
      << " Err name: " << error->GetName()
      << " HistNumber: " << i_hist << " bin: " << binNumber
      << " Value: " << histValue << " Error: " << histError
      << std::endl;
      */
 
      if( histError != histError ) {
        cxcoutE(HistFactory) << "In histogram " << error->GetName()
        << " bin error for bin " << binNumber
        << " is NAN.  Not using error!!";
        throw hf_exc();
      }
 
      TotalBinContent.at(i_bins) += histValue;
      HistErrorsSqr.at(i_bins)   += histError*histError; // Add in quadrature
 
    }
  }
 
  binNumber = 0;
 
  // Creat the output histogram
  TH1* ErrorHist = (TH1*) HistTemplate->Clone( Name.c_str() );
  ErrorHist->Reset();
 
  // Fill the output histogram
  for( Int_t i = 0; i < numBins; ++i) {
 
    //    Int_t binNumber = i + 1;
    binNumber++;
    while( ErrorHist->IsBinUnderflow(binNumber) || ErrorHist->IsBinOverflow(binNumber) ){
      binNumber++;
    }
 
    double ErrorsSqr = HistErrorsSqr.at(i);
    double TotalVal  = TotalBinContent.at(i);
 
    if( TotalVal <= 0 ) {
      cxcoutW(HistFactory) << "Warning: Sum of histograms for bin: " << binNumber
      << " is <= 0.  Setting error to 0"
      << std::endl;
 
      ErrorHist->SetBinContent( binNumber, 0.0 );
      continue;
    }
 
    double RelativeError = sqrt(ErrorsSqr) / TotalVal;
 
    // If we otherwise get a NAN
    // it's an error
    if( RelativeError != RelativeError ) {
      cxcoutE(HistFactory) << "Error: bin " << i << " error is NAN\n"
          << " HistErrorsSqr: " << ErrorsSqr
      << " TotalVal: " << TotalVal;
      throw hf_exc();
    }
 
    // 0th entry in vector is
    // the 1st bin in TH1
    // (we ignore underflow)
 
    // Error and bin content are interchanged because for some reason, the other functions
    // use the bin content to convey the error ...
    ErrorHist->SetBinError(binNumber, TotalVal);
    ErrorHist->SetBinContent(binNumber, RelativeError);
 
    cxcoutI(HistFactory) << "Making Total Uncertainty for bin " << binNumber
         << " Error = " << sqrt(ErrorsSqr)
         << " CentralVal = " << TotalVal
         << " RelativeError = " << RelativeError << "\n";
 
  }
 
  return std::unique_ptr<TH1>(ErrorHist);
}
 
 
 
  RooArgList HistoToWorkspaceFactoryFast::
  createStatConstraintTerms( RooWorkspace* proto, vector<string>& constraintTermNames,
              ParamHistFunc& paramHist, const TH1* uncertHist,
              Constraint::Type type, double minSigma ) {
 
 
  // Take a RooArgList of RooAbsReal's and
  // create N constraint terms (one for
  // each gamma) whose relative uncertainty
  // is the value of the ith RooAbsReal
  //
  // The integer "type" controls the type
  // of constraint term:
  //
  // type == 0 : NONE
  // type == 1 : Gaussian
  // type == 2 : Poisson
  // type == 3 : LogNormal
 
  RooArgList ConstraintTerms;
 
  RooArgList paramSet = paramHist.paramList();
 
  // Must get the full size of the TH1
  // (No direct method to do this...)
  Int_t numBins   = uncertHist->GetNbinsX()*uncertHist->GetNbinsY()*uncertHist->GetNbinsZ();
  Int_t numParams = paramSet.getSize();
  //  Int_t numBins   = uncertHist->GetNbinsX()*uncertHist->GetNbinsY()*uncertHist->GetNbinsZ();
 
  // Check that there are N elements
  // in the RooArgList
  if( numBins != numParams ) {
    std::cout << "Error: In createStatConstraintTerms, encountered bad number of bins" << std::endl;
    std::cout << "Given histogram with " << numBins << " bins,"
         << " but require exactly " << numParams << std::endl;
    throw hf_exc();
  }
 
  Int_t TH1BinNumber = 0;
  for( Int_t i = 0; i < paramSet.getSize(); ++i) {
 
    TH1BinNumber++;
 
    while( uncertHist->IsBinUnderflow(TH1BinNumber) || uncertHist->IsBinOverflow(TH1BinNumber) ){
      TH1BinNumber++;
    }
 
    RooRealVar& gamma = (RooRealVar&) (paramSet[i]);
 
    cxcoutI(HistFactory) << "Creating constraint for: " << gamma.GetName()
         << ". Type of constraint: " << type <<  std::endl;
 
    // Get the sigma from the hist
    // (the relative uncertainty)
    const double sigmaRel = uncertHist->GetBinContent(TH1BinNumber);
 
    // If the sigma is <= 0,
    // do cont create the term
    if( sigmaRel <= 0 ){
      cxcoutI(HistFactory) << "Not creating constraint term for "
      << gamma.GetName()
      << " because sigma = " << sigmaRel
      << " (sigma<=0)"
      << " (TH1 bin number = " << TH1BinNumber << ")"
      << std::endl;
      gamma.setConstant(true);
      continue;
    }
 
    // set reasonable ranges for gamma parameters
    gamma.setMax( 1 + 5*sigmaRel );
    gamma.setMin( 0. );
 
    // Make Constraint Term
    std::string constrName = string(gamma.GetName()) + "_constraint";
    std::string nomName = string("nom_") + gamma.GetName();
    std::string sigmaName = string(gamma.GetName()) + "_sigma";
    std::string poisMeanName = string(gamma.GetName()) + "_poisMean";
 
    if( type == Constraint::Gaussian ) {
 
      // Type 1 : RooGaussian
 
      // Make sigma
 
      RooConstVar constrSigma( sigmaName.c_str(), sigmaName.c_str(), sigmaRel );
 
      // Make "observed" value
      RooRealVar constrNom(nomName.c_str(), nomName.c_str(), 1.0,0,10);
      constrNom.setConstant( true );
 
      // Make the constraint:
      RooGaussian gauss( constrName.c_str(), constrName.c_str(),
          constrNom, gamma, constrSigma );
 
      proto->import( gauss, RecycleConflictNodes() );
 
      // Give reasonable starting point for pre-fit errors by setting it to the absolute sigma
      // Mostly useful for pre-fit plotting.
      gamma.setError(sigmaRel);
    } else if( type == Constraint::Poisson ) {
 
      double tau = 1/sigmaRel/sigmaRel; // this is correct Poisson equivalent to a Gaussian with mean 1 and stdev sigma
 
      // Make nominal "observed" value
      RooRealVar constrNom(nomName.c_str(), nomName.c_str(), tau);
      constrNom.setMin(0);
      constrNom.setConstant( true );
 
      // Make the scaling term
      std::string scalingName = string(gamma.GetName()) + "_tau";
      RooConstVar poissonScaling( scalingName.c_str(), scalingName.c_str(), tau);
 
      // Make mean for scaled Poisson
      RooProduct constrMean( poisMeanName.c_str(), poisMeanName.c_str(), RooArgSet(gamma, poissonScaling) );
      //proto->import( constrSigma, RecycleConflictNodes() );
      //proto->import( constrSigma );
 
      // Type 2 : RooPoisson
      RooPoisson pois(constrName.c_str(), constrName.c_str(), constrNom, constrMean);
      pois.setNoRounding(true);
      proto->import( pois, RecycleConflictNodes() );
 
      if (std::string(gamma.GetName()).find("gamma_stat") != std::string::npos) {
        // Give reasonable starting point for pre-fit errors.
        // Mostly useful for pre-fit plotting.
        gamma.setError(sigmaRel);
      }
 
    } else {
 
      std::cout << "Error: Did not recognize Stat Error constraint term type: "
      << type << " for : " << paramHist.GetName() << std::endl;
      throw hf_exc();
    }
 
    // If the sigma value is less
    // than a supplied threshold,
    // set the variable to constant
    if( sigmaRel < minSigma ) {
      cxcoutW(HistFactory) << "Warning:  Bin " << i << " = " << sigmaRel
      << " and is < " << minSigma
      << ". Setting: " << gamma.GetName() << " to constant"
      << std::endl;
      gamma.setConstant(true);
    }
 
    constraintTermNames.push_back( constrName );
    ConstraintTerms.add( *proto->pdf(constrName) );
 
    // Add the "observed" value to the
    // list of global observables:
    RooArgSet* globalSet = const_cast<RooArgSet*>(proto->set("globalObservables"));
 
    RooRealVar* nomVarInWorkspace = proto->var(nomName);
    if( ! globalSet->contains(*nomVarInWorkspace) ) {
      globalSet->add( *nomVarInWorkspace );
    }
 
  } // end loop over parameters
 
  return ConstraintTerms;
 
}
 
} // namespace RooStats
} // namespace HistFactory