RooLagrangianMorphFunc.cxx

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/*****************************************************************************
 * Project: RooFit                                                           *
 * Package: RooLagrangianMorphing                                            *
 * @(#)root/roofit:$Id$
 * Authors:                                                                  *
 *  Lydia Brenner (lbrenner@cern.ch), Carsten Burgard (cburgard@cern.ch)     *
 *  Katharina Ecker (kecker@cern.ch), Adam Kaluza      (akaluza@cern.ch)     *
 *                                                                           *
 * Copyright (c) 2000-2005, Regents of the University of California          *
 *                          and Stanford University. All rights reserved.    *
 *                                                                           *
 * Redistribution and use in source and binary forms,                        *
 * with or without modification, are permitted according to the terms        *
 * listed in LICENSE (http://roofit.sourceforge.net/license.txt)             *
 *****************************************************************************/
 
/** \class RooLagrangianMorphFunc
    \ingroup Roofit
Class RooLagrangianMorphing is a implementation of the method of Effective
Lagrangian Morphing, described in ATL-PHYS-PUB-2015-047.
Effective Lagrangian Morphing is a method to construct a continuous signal
model in the coupling parameter space. Basic assumption is that shape and
cross section of a physical distribution is proportional to it's
squared matrix element.
The signal model is constructed by a weighted sum over N input distributions.
The calculation of the weights is based on Matrix Elements evaluated for the
different input scenarios.
The number of input files depends on the number of couplings in production
and decay vertices, and also whether the decay and production vertices
describe the same process or not.
**/
 
// uncomment to force UBLAS multiprecision matrices
// #define USE_UBLAS 1
// #undef USE_UBLAS
 
#include "Riostream.h"
 
#include "RooAbsCollection.h"
#include "RooArgList.h"
#include "RooArgProxy.h"
#include "RooArgSet.h"
#include "RooBinning.h"
#include "RooDataHist.h"
#include "RooFormulaVar.h"
#include "RooHistFunc.h"
#include "RooLagrangianMorphFunc.h"
#include "RooLinearCombination.h"
#include "RooParamHistFunc.h"
#include "RooProduct.h"
#include "RooRealVar.h"
#include "RooWorkspace.h"
#include "RooFactoryWSTool.h"
 
#include "ROOT/StringUtils.hxx"
#include "TFile.h"
#include "TFolder.h"
#include "TH1.h"
#include "TMap.h"
#include "TParameter.h"
#include "TRandom3.h"
 
#include <algorithm>
#include <cmath>
#include <cstddef>
#include <iostream>
#include <limits>
#include <map>
#include <memory>
#include <sstream>
#include <stdexcept>
#include <type_traits>
#include <typeinfo>
 
using namespace std;
ClassImp(RooLagrangianMorphFunc);
 
//#define _DEBUG_
 
///////////////////////////////////////////////////////////////////////////////
// PREPROCESSOR MAGIC /////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////
 
// various preprocessor helpers
#define NaN std::numeric_limits<double>::quiet_NaN()
 
constexpr static double morphLargestWeight = 10e7;
constexpr static double morphUnityDeviation = 10e-6;
 
///////////////////////////////////////////////////////////////////////////////
// TEMPLATE MAGIC /////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////
 
template <typename Test, template <typename...> class Ref>
struct is_specialization : std::false_type {
};
 
template <template <typename...> class Ref, typename... Args>
struct is_specialization<Ref<Args...>, Ref> : std::true_type {
};
 
///////////////////////////////////////////////////////////////////////////////
// LINEAR ALGEBRA HELPERS /////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////
 
////////////////////////////////////////////////////////////////////////////////
/// retrieve the size of a square matrix
 
template <class MatrixT>
inline size_t size(const MatrixT &matrix);
template <>
inline size_t size<TMatrixD>(const TMatrixD &mat)
{
   return mat.GetNrows();
}
 
////////////////////////////////////////////////////////////////////////////////
/// write a matrix to a stream
 
template <class MatrixT>
void writeMatrixToStreamT(const MatrixT &matrix, std::ostream &stream)
{
   if (!stream.good()) {
      return;
   }
   for (size_t i = 0; i < size(matrix); ++i) {
      for (size_t j = 0; j < size(matrix); ++j) {
#ifdef USE_UBLAS
         stream << std::setprecision(RooFit::SuperFloatPrecision::digits10) << matrix(i, j) << "\t";
#else
         stream << matrix(i, j) << "\t";
#endif
      }
      stream << std::endl;
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// write a matrix to a text file
 
template <class MatrixT>
inline void writeMatrixToFileT(const MatrixT &matrix, const char *fname)
{
   std::ofstream of(fname);
   if (!of.good()) {
      cerr << "unable to read file '" << fname << "'!" << std::endl;
   }
   writeMatrixToStreamT(matrix, of);
   of.close();
}
 
#ifdef USE_UBLAS
 
// boost includes
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wshadow"
#pragma GCC diagnostic ignored "-Wunused-local-typedefs"
#include <boost/numeric/ublas/io.hpp>
#include <boost/numeric/ublas/lu.hpp>
#include <boost/numeric/ublas/matrix.hpp>
#include <boost/numeric/ublas/matrix_expression.hpp>
#include <boost/numeric/ublas/symmetric.hpp> //inc diag
#include <boost/numeric/ublas/triangular.hpp>
#include <boost/operators.hpp>
 
#pragma GCC diagnostic pop
 
typedef boost::numeric::ublas::matrix<RooFit::SuperFloat> Matrix;
 
////////////////////////////////////////////////////////////////////////////////
/// write a matrix
 
inline void printMatrix(const Matrix &mat)
{
   for (size_t i = 0; i < mat.size1(); ++i) {
      for (size_t j = 0; j < mat.size2(); ++j) {
         std::cout << std::setprecision(RooFit::SuperFloatPrecision::digits10) << mat(i, j) << " ,\t";
      }
      std::cout << std::endl;
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// retrieve the size of a square matrix
 
template <>
inline size_t size<Matrix>(const Matrix &matrix)
{
   return matrix.size1();
}
 
////////////////////////////////////////////////////////////////////////////////
/// create a new diagonal matrix of size n
 
inline Matrix diagMatrix(size_t n)
{
   return boost::numeric::ublas::identity_matrix<RooFit::SuperFloat>(n);
}
 
////////////////////////////////////////////////////////////////////////////////
/// convert a matrix into a TMatrixD
 
inline TMatrixD makeRootMatrix(const Matrix &in)
{
   size_t n = size(in);
   TMatrixD mat(n, n);
   for (size_t i = 0; i < n; ++i) {
      for (size_t j = 0; j < n; ++j) {
         mat(i, j) = double(in(i, j));
      }
   }
   return mat;
}
 
////////////////////////////////////////////////////////////////////////////////
/// convert a TMatrixD into a matrix
 
inline Matrix makeSuperMatrix(const TMatrixD &in)
{
   size_t n = in.GetNrows();
   Matrix mat(n, n);
   for (size_t i = 0; i < n; ++i) {
      for (size_t j = 0; j < n; ++j) {
         mat(i, j) = double(in(i, j));
      }
   }
   return mat;
}
 
inline Matrix operator+=(const Matrix &rhs)
{
   return add(rhs);
}
inline Matrix operator*(const Matrix &m, const Matrix &otherM)
{
   return prod(m, otherM);
}
 
////////////////////////////////////////////////////////////////////////////////
/// calculate the inverse of a matrix, returning the condition
 
inline RooFit::SuperFloat invertMatrix(const Matrix &matrix, Matrix &inverse)
{
   boost::numeric::ublas::permutation_matrix<size_t> pm(size(matrix));
   RooFit::SuperFloat mnorm = norm_inf(matrix);
   Matrix lu(matrix);
   try {
      int res = lu_factorize(lu, pm);
      if (res != 0) {
         std::stringstream ss;
         ::writeMatrixToStreamT(matrix, ss);
         cxcoutP(Eval) << ss.str << std::endl;
      }
      // back-substitute to get the inverse
      lu_substitute(lu, pm, inverse);
   } catch (boost::numeric::ublas::internal_logic &error) {
      // coutE(Eval) << "boost::numberic::ublas error: matrix is not invertible!"
      // << std::endl;
   }
   RooFit::SuperFloat inorm = norm_inf(inverse);
   RooFit::SuperFloat condition = mnorm * inorm;
   return condition;
}
 
#else
 
#include "TDecompLU.h"
typedef TMatrixD Matrix;
 
////////////////////////////////////////////////////////////////////////////////
/// convert a matrix into a TMatrixD
 
inline TMatrixD makeRootMatrix(const Matrix &in)
{
   return TMatrixD(in);
}
 
////////////////////////////////////////////////////////////////////////////////
/// convert a TMatrixD into a Matrix
 
inline Matrix makeSuperMatrix(const TMatrixD &in)
{
   return in;
}
 
////////////////////////////////////////////////////////////////////////////////
/// create a new diagonal matrix of size n
 
inline Matrix diagMatrix(size_t n)
{
   TMatrixD mat(n, n);
   mat.UnitMatrix();
   return mat;
}
 
////////////////////////////////////////////////////////////////////////////////
/// write a matrix
 
inline void printMatrix(const TMatrixD &mat)
{
   writeMatrixToStreamT(mat, std::cout);
}
 
////////////////////////////////////////////////////////////////////////////////
// calculate the inverse of a matrix, returning the condition
 
inline double invertMatrix(const Matrix &matrix, Matrix &inverse)
{
   TDecompLU lu(matrix);
   bool status = lu.Invert(inverse);
   // check if the matrix is invertible
   if (!status) {
      std::cerr << " matrix is not invertible!" << std::endl;
   }
   double condition = lu.GetCondition();
   const size_t n = size(inverse);
   // sanitize numeric problems
   for (size_t i = 0; i < n; ++i)
      for (size_t j = 0; j < n; ++j)
         if (std::abs(inverse(i, j)) < 1e-9)
            inverse(i, j) = 0;
   return condition;
}
#endif
 
/////////////////////////////////////////////////////////////////////////////////
// LOCAL FUNCTIONS AND DEFINITIONS
// //////////////////////////////////////////////
/////////////////////////////////////////////////////////////////////////////////
/// anonymous namespace to prohibit use of these functions outside the class
/// itself
namespace {
///////////////////////////////////////////////////////////////////////////////
// HELPERS ////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////
 
typedef std::vector<std::vector<bool>> FeynmanDiagram;
typedef std::vector<std::vector<int>> MorphFuncPattern;
typedef std::map<int, std::unique_ptr<RooAbsReal>> FormulaList;
 
///////////////////////////////////////////////////////////////////////////////
/// (-?-)
 
inline TString makeValidName(const char *input)
{
   TString retval(input);
   retval.ReplaceAll("/", "_");
   retval.ReplaceAll("^", "");
   retval.ReplaceAll("*", "X");
   retval.ReplaceAll("[", "");
   retval.ReplaceAll("]", "");
   return retval;
}
 
//////////////////////////////////////////////////////////////////////////////
/// concatenate the names of objects in a collection to a single string
 
template <class List>
std::string concatNames(const List &c, const char *sep)
{
   std::stringstream ss;
   bool first = true;
   for (auto itr : c) {
      if (!first)
         ss << sep;
      ss << itr->GetName();
      first = false;
   }
   return ss.str();
}
 
///////////////////////////////////////////////////////////////////////////////
/// this is a workaround for the missing implicit conversion from
/// SuperFloat<>double
 
template <class A, class B>
inline void assignElement(A &a, const B &b)
{
   a = static_cast<A>(b);
}
///////////////////////////////////////////////////////////////////////////////
// read a matrix from a stream
 
template <class MatrixT>
inline MatrixT readMatrixFromStreamT(std::istream &stream)
{
   std::vector<std::vector<RooFit::SuperFloat>> matrix;
   std::vector<RooFit::SuperFloat> line;
   while (!stream.eof()) {
      if (stream.peek() == '\n') {
         stream.get();
         stream.peek();
         continue;
      }
      RooFit::SuperFloat val;
      stream >> val;
      line.push_back(val);
      while (stream.peek() == ' ' || stream.peek() == '\t') {
         stream.get();
      }
      if (stream.peek() == '\n') {
         matrix.push_back(line);
         line.clear();
      }
   }
   MatrixT retval(matrix.size(), matrix.size());
   for (size_t i = 0; i < matrix.size(); ++i) {
      if (matrix[i].size() != matrix.size()) {
         std::cerr << "matrix read from stream doesn't seem to be square!" << std::endl;
      }
      for (size_t j = 0; j < matrix[i].size(); ++j) {
         assignElement(retval(i, j), matrix[i][j]);
      }
   }
   return retval;
}
 
///////////////////////////////////////////////////////////////////////////////
/// read a matrix from a text file
 
template <class MatrixT>
inline MatrixT readMatrixFromFileT(const char *fname)
{
   std::ifstream in(fname);
   if (!in.good()) {
      std::cerr << "unable to read file '" << fname << "'!" << std::endl;
   }
   MatrixT mat = readMatrixFromStreamT<MatrixT>(in);
   in.close();
   return mat;
}
 
///////////////////////////////////////////////////////////////////////////////
/// convert a TH1* param hist into the corresponding ParamSet object
 
template <class T>
void readValues(std::map<const std::string, T> &myMap, TH1 *h_pc)
{
   if (h_pc) {
      // loop over all bins of the param_card histogram
      for (int ibx = 1; ibx <= h_pc->GetNbinsX(); ++ibx) {
         // read the value of one parameter
         const std::string s_coup(h_pc->GetXaxis()->GetBinLabel(ibx));
         double coup_val = h_pc->GetBinContent(ibx);
         // add it to the map
         if (!s_coup.empty()) {
            myMap[s_coup] = T(coup_val);
         }
      }
   }
}
 
///////////////////////////////////////////////////////////////////////////////
/// Set up folder ownership over its children, and treat likewise any subfolders.
/// @param theFolder: folder to update. Assumed to be a valid pointer
void setOwnerRecursive(TFolder *theFolder)
{
   theFolder->SetOwner();
   // And also need to set up ownership for nested folders
   auto subdirs = theFolder->GetListOfFolders();
   for (auto *subdir : *subdirs) {
      auto thisfolder = dynamic_cast<TFolder *>(subdir);
      if (thisfolder) {
         // no explicit deletion here, will be handled by parent
         setOwnerRecursive(thisfolder);
      }
   }
}
 
///////////////////////////////////////////////////////////////////////////////
/// Load a TFolder from a file while ensuring it owns its content.
/// This avoids memory leaks. Note that when fetching objects
/// from this folder, you need to clone them to prevent deletion.
/// Also recursively updates nested subfolders accordingly
/// @param inFile: Input file to read - assumed to be a valid pointer
/// @param folderName: Name of the folder to read from the file
/// @return a unique_ptr to the folder. Nullptr if not found.
std::unique_ptr<TFolder> readOwningFolderFromFile(TDirectory *inFile, const std::string &folderName)
{
   std::unique_ptr<TFolder> theFolder(inFile->Get<TFolder>(folderName.c_str()));
   if (!theFolder) {
      std::cerr << "Error: unable to access data from folder '" << folderName << "' from file '" << inFile->GetName()
                << "'!" << std::endl;
      return nullptr;
   }
   setOwnerRecursive(theFolder.get());
   return theFolder;
}
 
///////////////////////////////////////////////////////////////////////////////
/// Helper to load a single object from a file-resident TFolder, while
/// avoiding memory leaks.
/// @tparam AObjType Type of object to load.
/// @param inFile input file to load from. Expected to be a valid pointer
/// @param folderName Name of the TFolder to load from the file
/// @param objName Name of the object to load
/// @param notFoundError If set, print a detailed error if we didn't find something
/// @return Returns a pointer to a clone of the loaded object. Ownership assigned to the caller.
template <class AObjType>
std::unique_ptr<AObjType> loadFromFileResidentFolder(TDirectory *inFile, const std::string &folderName,
                                                     const std::string &objName, bool notFoundError = true)
{
   auto folder = readOwningFolderFromFile(inFile, folderName);
   if (!folder) {
      return nullptr;
   }
   AObjType *loadedObject = dynamic_cast<AObjType *>(folder->FindObject(objName.c_str()));
   if (!loadedObject) {
      if (notFoundError) {
         std::stringstream errstr;
         errstr << "Error: unable to retrieve object '" << objName << "' from folder '" << folderName
                << "'. contents are:";
         TIter next(folder->GetListOfFolders()->begin());
         TFolder *f;
         while ((f = (TFolder *)next())) {
            errstr << " " << f->GetName();
         }
         std::cerr << errstr.str() << std::endl;
      }
      return nullptr;
   }
   // replace the loaded object by a clone, as the loaded folder will delete the original
   // can use a static_cast - confirmed validity by initial cast above.
   return std::unique_ptr<AObjType>{static_cast<AObjType *>(loadedObject->Clone())};
}
 
///////////////////////////////////////////////////////////////////////////////
/// retrieve a ParamSet from a certain subfolder 'name' of the file
 
template <class T>
void readValues(std::map<const std::string, T> &myMap, TDirectory *file, const std::string &name,
                const std::string &key = "param_card", bool notFoundError = true)
{
   auto h_pc = loadFromFileResidentFolder<TH1F>(file, name, key, notFoundError);
   readValues(myMap, h_pc.get());
}
 
///////////////////////////////////////////////////////////////////////////////
/// retrieve the param_hists file and return a map of the parameter values
/// by providing a list of names, only the param_hists of those subfolders are
/// read leaving the list empty is interpreted as meaning 'read everything'
 
template <class T>
void readValues(std::map<const std::string, std::map<const std::string, T>> &inputParameters, TDirectory *f,
                const std::vector<std::string> &names, const std::string &key = "param_card", bool notFoundError = true)
{
   inputParameters.clear();
   // if the list of names is empty, we assume that this means 'all'
   // loop over all folders in the file
   for (size_t i = 0; i < names.size(); i++) {
      const std::string name(names[i]);
      // actually read an individual param_hist
      readValues(inputParameters[name], f, name, key, notFoundError);
   }
 
   // now the map is filled with all parameter values found for all samples
}
 
///////////////////////////////////////////////////////////////////////////////
/// open the file and return a file pointer
 
inline TDirectory *openFile(const std::string &filename)
{
   if (filename.empty()) {
      return gDirectory;
   } else {
      TFile *file = TFile::Open(filename.c_str(), "READ");
      if (!file || !file->IsOpen()) {
         if (file)
            delete file;
         std::cerr << "could not open file '" << filename << "'!" << std::endl;
      }
      return file;
   }
}
 
///////////////////////////////////////////////////////////////////////////////
/// open the file and return a file pointer
 
inline void closeFile(TDirectory *d)
{
   TFile *f = dynamic_cast<TFile *>(d);
   if (f) {
      f->Close();
      delete f;
      d = nullptr;
   }
}
 
///////////////////////////////////////////////////////////////////////////////
/// extract the operators from a single coupling
template <class T2>
inline void extractServers(const RooAbsArg &coupling, T2 &operators)
{
   int nservers = 0;
   for (const auto server : coupling.servers()) {
      extractServers(*server, operators);
      nservers++;
   }
   if (nservers == 0) {
      operators.add(coupling);
   }
}
 
///////////////////////////////////////////////////////////////////////////////
/// extract the operators from a list of couplings
 
template <class T1, class T2, typename std::enable_if<!is_specialization<T1, std::vector>::value, T1>::type * = nullptr>
inline void extractOperators(const T1 &couplings, T2 &operators)
{
   // coutD(InputArguments) << "extracting operators from
   // "<<couplings.getSize()<<" couplings" << std::endl;
   for (auto itr : couplings) {
      extractServers(*itr, operators);
   }
}
 
///////////////////////////////////////////////////////////////////////////////
/// extract the operators from a list of vertices
 
template <class T1, class T2, typename std::enable_if<is_specialization<T1, std::vector>::value, T1>::type * = nullptr>
inline void extractOperators(const T1 &vec, T2 &operators)
{
   for (const auto &v : vec) {
      extractOperators(v, operators);
   }
}
 
///////////////////////////////////////////////////////////////////////////////
/// extract the couplings from a given set and copy them to a new one
 
template <class T1, class T2>
inline void extractCouplings(const T1 &inCouplings, T2 &outCouplings)
{
   for (auto itr : inCouplings) {
      if (!outCouplings.find(itr->GetName())) {
         // coutD(InputArguments) << "adding parameter "<< obj->GetName() <<
         // std::endl;
         outCouplings.add(*itr);
      }
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// set parameter values first set all values to defaultVal (if value not
/// present in param_card then it should be 0)
 
inline bool setParam(RooRealVar *p, double val, bool force)
{
   bool ok = true;
   if (val > p->getMax()) {
      if (force) {
         p->setMax(val);
      } else {
         std::cerr << ": parameter " << p->GetName() << " out of bounds: " << val << " > " << p->getMax() << std::endl;
         ok = false;
      }
   } else if (val < p->getMin()) {
      if (force) {
         p->setMin(val);
      } else {
         std::cerr << ": parameter " << p->GetName() << " out of bounds: " << val << " < " << p->getMin() << std::endl;
         ok = false;
      }
   }
   if (ok)
      p->setVal(val);
   return ok;
}
 
////////////////////////////////////////////////////////////////////////////////
/// set parameter values first set all values to defaultVal (if value not
/// present in param_card then it should be 0)
 
template <class T1, class T2>
inline bool setParams(const T2 &args, T1 val)
{
   for (auto itr : args) {
      RooRealVar *param = dynamic_cast<RooRealVar *>(itr);
      if (!param)
         continue;
      setParam(param, val, true);
   }
   return true;
}
 
////////////////////////////////////////////////////////////////////////////////
/// set parameter values first set all values to defaultVal (if value not
/// present in param_card then it should be 0)
 
template <class T1, class T2>
inline bool
setParams(const std::map<const std::string, T1> &point, const T2 &args, bool force = false, T1 defaultVal = 0)
{
   bool ok = true;
   for (auto itr : args) {
      RooRealVar *param = dynamic_cast<RooRealVar *>(itr);
      if (!param || param->isConstant())
         continue;
      ok = setParam(param, defaultVal, force) && ok;
   }
   // set all parameters to the values in the param_card histogram
   for (auto paramit : point) {
      // loop over all the parameters
      const std::string param(paramit.first);
      // retrieve them from the map
      RooRealVar *p = dynamic_cast<RooRealVar *>(args.find(param.c_str()));
      if (!p)
         continue;
      // set them to their nominal value
      ok = setParam(p, paramit.second, force) && ok;
   }
   return ok;
}
 
////////////////////////////////////////////////////////////////////////////////
/// set parameter values first set all values to defaultVal (if value not
/// present in param_card then it should be 0)
 
template <class T>
inline bool setParams(TH1 *hist, const T &args, bool force = false)
{
   bool ok = true;
 
   for (auto itr : args) {
      RooRealVar *param = dynamic_cast<RooRealVar *>(itr);
      if (!param)
         continue;
      ok = setParam(param, 0., force) && ok;
   }
 
   // set all parameters to the values in the param_card histogram
   TAxis *ax = hist->GetXaxis();
   for (int i = 1; i <= ax->GetNbins(); ++i) {
      // loop over all the parameters
      RooRealVar *p = dynamic_cast<RooRealVar *>(args.find(ax->GetBinLabel(i)));
      if (!p)
         continue;
      // set them to their nominal value
      ok = setParam(p, hist->GetBinContent(i), force) && ok;
   }
   return ok;
}
 
////////////////////////////////////////////////////////////////////////////////
/// create a set of parameters
 
template <class T>
inline RooLagrangianMorphFunc::ParamSet getParams(const T &parameters)
{
   RooLagrangianMorphFunc::ParamSet retval;
   for (auto itr : parameters) {
      RooRealVar *param = dynamic_cast<RooRealVar *>(itr);
      if (!param)
         continue;
      retval[param->GetName()] = param->getVal();
   }
   return retval;
}
 
////////////////////////////////////////////////////////////////////////////////
/// collect the histograms from the input file and convert them to RooFit
/// objects
 
void collectHistograms(const char *name, TDirectory *file, std::map<std::string, int> &list_hf, RooArgList &physics,
                       RooRealVar &var, const std::string &varname,
                       const RooLagrangianMorphFunc::ParamMap &inputParameters, bool normalize)
{
   bool binningOK = false;
   for (auto sampleit : inputParameters) {
      const std::string sample(sampleit.first);
      auto hist = loadFromFileResidentFolder<TH1>(file, sample, varname, true);
      if (!hist)
         return;
 
      if (normalize) {
         hist.get()->Scale(1. / hist.get()->Integral());
      }
 
      auto it = list_hf.find(sample);
      if (it != list_hf.end()) {
         RooHistFunc *hf = (RooHistFunc *)(physics.at(it->second));
         hf->setValueDirty();
         // commenting out To-be-resolved
         // RooDataHist* dh = &(hf->dataHist());
         // RooLagrangianMorphFunc::setDataHistogram(hist,&var,dh);
         // RooArgSet vars;
         // vars.add(var);
         // dh->importTH1(vars,*hist,1.,false);
      } else {
         if (!binningOK) {
            int n = hist->GetNbinsX();
            std::vector<double> bins;
            for (int i = 1; i < n + 1; ++i) {
               bins.push_back(hist->GetBinLowEdge(i));
            }
            bins.push_back(hist->GetBinLowEdge(n) + hist->GetBinWidth(n));
            var.setBinning(RooBinning(n, &(bins[0])));
         }
 
         // generate the mean value
         TString histname = makeValidName(Form("dh_%s_%s", sample.c_str(), name));
         TString funcname = makeValidName(Form("phys_%s_%s", sample.c_str(), name));
         RooArgSet vars;
         vars.add(var);
 
         auto dh = std::make_unique<RooDataHist>(histname, histname, vars, hist.get());
         // add it to the list
         auto hf = std::make_unique<RooHistFunc>(funcname, funcname, var, std::move(dh));
         int idx = physics.getSize();
         list_hf[sample] = idx;
         physics.addOwned(std::move(hf));
      }
      // std::cout << "found histogram " << hist->GetName() << " with integral "
      // << hist->Integral() << std::endl;
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// collect the RooAbsReal objects from the input directory
 
void collectRooAbsReal(const char * /*name*/, TDirectory *file, std::map<std::string, int> &list_hf,
                       RooArgList &physics, const std::string &varname,
                       const RooLagrangianMorphFunc::ParamMap &inputParameters)
{
   for (auto sampleit : inputParameters) {
      const std::string sample(sampleit.first);
      auto obj = loadFromFileResidentFolder<RooAbsReal>(file, sample, varname, true);
      if (!obj)
         return;
      auto it = list_hf.find(sample);
      if (it == list_hf.end()) {
         int idx = physics.getSize();
         list_hf[sample] = idx;
         physics.addOwned(std::move(obj));
      }
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// collect the TParameter objects from the input file and convert them to
/// RooFit objects
 
template <class T>
void collectCrosssections(const char *name, TDirectory *file, std::map<std::string, int> &list_xs, RooArgList &physics,
                          const std::string &varname, const RooLagrangianMorphFunc::ParamMap &inputParameters)
{
   for (auto sampleit : inputParameters) {
      const std::string sample(sampleit.first);
      auto obj = loadFromFileResidentFolder<TObject>(file, sample, varname, false);
      TParameter<T> *xsection = nullptr;
      TParameter<T> *error = nullptr;
      TParameter<T> *p = dynamic_cast<TParameter<T> *>(obj.get());
      if (p) {
         xsection = p;
      }
      TPair *pair = dynamic_cast<TPair *>(obj.get());
      if (pair) {
         xsection = dynamic_cast<TParameter<T> *>(pair->Key());
         error = dynamic_cast<TParameter<T> *>(pair->Value());
      }
      if (!xsection) {
         std::stringstream errstr;
         errstr << "Error: unable to retrieve cross section '" << varname << "' from folder '" << sample;
         return;
      }
 
      auto it = list_xs.find(sample.c_str());
      RooRealVar *xs;
      if (it != list_xs.end()) {
         xs = (RooRealVar *)(physics.at(it->second));
         xs->setVal(xsection->GetVal());
      } else {
         std::string objname = Form("phys_%s_%s", name, sample.c_str());
         auto xsOwner = std::make_unique<RooRealVar>(objname.c_str(), objname.c_str(), xsection->GetVal());
         xs = xsOwner.get();
         xs->setConstant(true);
         int idx = physics.getSize();
         list_xs[sample] = idx;
         physics.addOwned(std::move(xsOwner));
         assert(physics.at(idx) == xs);
      }
      if (error) {
         xs->setError(error->GetVal());
      }
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// collect the TPair<TParameter,TParameter> objects from the input file and
/// convert them to RooFit objects
 
void collectCrosssectionsTPair(const char *name, TDirectory *file, std::map<std::string, int> &list_xs,
                               RooArgList &physics, const std::string &varname, const std::string &basefolder,
                               const RooLagrangianMorphFunc::ParamMap &inputParameters)
{
   auto pair = loadFromFileResidentFolder<TPair>(file, basefolder, varname, false);
   if (!pair)
      return;
   if (dynamic_cast<TParameter<double> *>(pair->Key())) {
      collectCrosssections<double>(name, file, list_xs, physics, varname, inputParameters);
   } else if (dynamic_cast<TParameter<float> *>(pair->Key())) {
      collectCrosssections<float>(name, file, list_xs, physics, varname, inputParameters);
   } else {
      std::cerr << "cannot morph objects of class 'TPair' if parameter is not "
                   "double or float!"
                << std::endl;
   }
}
 
///////////////////////////////////////////////////////////////////////////////
// FORMULA CALCULATION ////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////
 
////////////////////////////////////////////////////////////////////////////////
/// recursive function to determine polynomials
 
void collectPolynomialsHelper(const FeynmanDiagram &diagram, MorphFuncPattern &morphfunc, std::vector<int> &term,
                              int vertexid, bool first)
{
   if (vertexid > 0) {
      for (size_t i = 0; i < diagram[vertexid - 1].size(); ++i) {
         if (!diagram[vertexid - 1][i])
            continue;
         std::vector<int> newterm(term);
         newterm[i]++;
         if (first) {
            ::collectPolynomialsHelper(diagram, morphfunc, newterm, vertexid, false);
         } else {
            ::collectPolynomialsHelper(diagram, morphfunc, newterm, vertexid - 1, true);
         }
      }
   } else {
      bool found = false;
      for (size_t i = 0; i < morphfunc.size(); ++i) {
         bool thisfound = true;
         for (size_t j = 0; j < morphfunc[i].size(); ++j) {
            if (morphfunc[i][j] != term[j]) {
               thisfound = false;
               break;
            }
         }
         if (thisfound) {
            found = true;
            break;
         }
      }
      if (!found) {
         morphfunc.push_back(term);
      }
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// calculate the morphing function pattern based on a vertex map
 
void collectPolynomials(MorphFuncPattern &morphfunc, const FeynmanDiagram &diagram)
{
   int nvtx(diagram.size());
   std::vector<int> term(diagram[0].size(), 0);
 
   ::collectPolynomialsHelper(diagram, morphfunc, term, nvtx, true);
}
 
////////////////////////////////////////////////////////////////////////////////
/// build a vertex map based on vertices and couplings appearing
 
template <class List>
inline void fillFeynmanDiagram(FeynmanDiagram &diagram, const std::vector<List *> &vertices, RooArgList &couplings)
{
   const int ncouplings = couplings.getSize();
   // std::cout << "Number of couplings " << ncouplings << std::endl;
   for (auto const &vertex : vertices) {
      std::vector<bool> vertexCouplings(ncouplings, false);
      int idx = -1;
      RooAbsReal *coupling;
      for (auto citr : couplings) {
         coupling = dynamic_cast<RooAbsReal *>(citr);
         idx++;
         if (!coupling) {
            std::cerr << "encountered invalid list of couplings in vertex!" << std::endl;
            return;
         }
         if (vertex->find(coupling->GetName())) {
            vertexCouplings[idx] = true;
         }
      }
      diagram.push_back(vertexCouplings);
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// fill the matrix of coefficients
 
template <class MatrixT, class T1, class T2>
inline MatrixT buildMatrixT(const RooLagrangianMorphFunc::ParamMap &inputParameters, const FormulaList &formulas,
                            const T1 &args, const RooLagrangianMorphFunc::FlagMap &flagValues, const T2 &flags)
{
   const size_t dim = inputParameters.size();
   MatrixT matrix(dim, dim);
   int row = 0;
   for (auto sampleit : inputParameters) {
      const std::string sample(sampleit.first);
      // set all vars to value stored in input file
      if (!setParams<double>(sampleit.second, args, true, 0)) {
         std::cout << "unable to set parameters for sample " << sample << "!" << std::endl;
      }
      auto flagit = flagValues.find(sample);
      if (flagit != flagValues.end() && !setParams<int>(flagit->second, flags, true, 1)) {
         std::cout << "unable to set parameters for sample " << sample << "!" << std::endl;
      }
      // loop over all the formulas
      int col = 0;
      for (auto const &formula : formulas) {
         if (!formula.second) {
            std::cerr << "Error: invalid formula encountered!" << std::endl;
         }
         matrix(row, col) = formula.second->getVal();
         col++;
      }
      row++;
   }
   return matrix;
}
 
////////////////////////////////////////////////////////////////////////////////
/// check if the matrix is square
 
inline void checkMatrix(const RooLagrangianMorphFunc::ParamMap &inputParameters, const FormulaList &formulas)
{
   if (inputParameters.size() != formulas.size()) {
      std::stringstream ss;
      ss << "matrix is not square, consistency check failed: " << inputParameters.size() << " samples, "
         << formulas.size() << " expressions:" << std::endl;
      ss << "formulas: " << std::endl;
      for (auto const &formula : formulas) {
         ss << formula.second->GetTitle() << std::endl;
      }
      ss << "samples: " << std::endl;
      for (auto sample : inputParameters) {
         ss << sample.first << std::endl;
      }
      std::cerr << ss.str() << std::endl;
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// check if the entries in the inverted matrix are sensible
 
inline void inverseSanity(const Matrix &matrix, const Matrix &inverse, double &unityDeviation, double &largestWeight)
{
   Matrix unity(inverse * matrix);
 
   unityDeviation = 0.;
   largestWeight = 0.;
   const size_t dim = size(unity);
   for (size_t i = 0; i < dim; ++i) {
      for (size_t j = 0; j < dim; ++j) {
         if (inverse(i, j) > largestWeight) {
            largestWeight = (double)inverse(i, j);
         }
         if (std::abs(unity(i, j) - static_cast<int>(i == j)) > unityDeviation) {
            unityDeviation = std::abs((double)unity(i, j)) - static_cast<int>(i == j);
         }
      }
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// check for name conflicts between the input samples and an argument set
template <class List>
inline void checkNameConflict(const RooLagrangianMorphFunc::ParamMap &inputParameters, List &args)
{
   for (auto sampleit : inputParameters) {
      const std::string sample(sampleit.first);
      RooAbsArg *arg = args.find(sample.c_str());
      if (arg) {
         std::cerr << "detected name conflict: cannot use sample '" << sample
                   << "' - a parameter with the same name of type '" << arg->ClassName() << "' is present in set '"
                   << args.GetName() << "'!" << std::endl;
      }
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// build the formulas corresponding to the given set of input files and
///  the physics process
 
FormulaList buildFormulas(const char *mfname, const RooLagrangianMorphFunc::ParamMap &inputParameters,
                          const RooLagrangianMorphFunc::FlagMap &inputFlags, const MorphFuncPattern &morphfunc,
                          const RooArgList &couplings, const RooArgList &flags,
                          const std::vector<std::vector<std::string>> &nonInterfering)
{
   // example vbf hww:
   //                        Operators kSM,  kHww, kAww, kHdwR,kHzz, kAzz
   // std::vector<bool> vertexProd  = {true, true, true, true, true, true };
   // std::vector<bool> vertexDecay = {true, true, true, true, false,false};
   // diagram.push_back(vertexProd);
   // diagram.push_back(vertexDecay);
 
   const int ncouplings = couplings.getSize();
   std::vector<bool> couplingsZero(ncouplings, true);
   std::map<TString, bool> flagsZero;
 
   RooArgList operators;
   extractOperators(couplings, operators);
   size_t nOps = operators.getSize();
 
   for (auto sampleit : inputParameters) {
      const std::string sample(sampleit.first);
      if (!setParams(sampleit.second, operators, true)) {
         std::cerr << "unable to set parameters for sample '" << sample << "'!" << std::endl;
      }
 
      if ((int)nOps != (operators.getSize())) {
         std::cerr << "internal error, number of operators inconsistent!" << std::endl;
      }
 
      RooAbsReal *obj0;
      int idx = 0;
 
      for (auto itr1 : couplings) {
         obj0 = dynamic_cast<RooAbsReal *>(itr1);
         if (obj0->getVal() != 0) {
            couplingsZero[idx] = false;
         }
         idx++;
      }
   }
 
   for (auto itr2 : flags) {
      auto obj1 = dynamic_cast<RooAbsReal *>(itr2);
      int nZero = 0;
      int nNonZero = 0;
      for (auto sampleit : inputFlags) {
         const auto &flag = sampleit.second.find(obj1->GetName());
         if (flag != sampleit.second.end()) {
            if (flag->second == 0.)
               nZero++;
            else
               nNonZero++;
         }
      }
      if (nZero > 0 && nNonZero == 0)
         flagsZero[obj1->GetName()] = true;
      else
         flagsZero[obj1->GetName()] = false;
   }
 
   FormulaList formulas;
   for (size_t i = 0; i < morphfunc.size(); ++i) {
      RooArgList ss;
      bool isZero = false;
      std::string reason;
      // check if this is a blacklisted interference term
      for (const auto &group : nonInterfering) {
         int nInterferingOperators = 0;
         for (size_t j = 0; j < morphfunc[i].size(); ++j) {
            if (morphfunc[i][j] % 2 == 0)
               continue; // even exponents are not interference terms
            // if the coupling is part of a "pairwise non-interfering group"
            if (std::find(group.begin(), group.end(), couplings.at(j)->GetName()) != group.end()) {
               nInterferingOperators++;
            }
         }
         if (nInterferingOperators > 1) {
            isZero = true;
            reason = "blacklisted interference term!";
         }
      }
      int nNP = 0;
      if (!isZero) {
         // prepare the term
         for (size_t j = 0; j < morphfunc[i].size(); ++j) {
            const int exponent = morphfunc[i][j];
            if (exponent == 0)
               continue;
            RooAbsReal *coupling = dynamic_cast<RooAbsReal *>(couplings.at(j));
            for (int k = 0; k < exponent; ++k) {
               ss.add(*coupling);
               if (coupling->getAttribute("NewPhysics")) {
                  nNP++;
               }
            }
            std::string cname(coupling->GetName());
            if (coupling->getAttribute("LO") && exponent > 1) {
               isZero = true;
               reason = "coupling " + cname + " was listed as leading-order-only";
            }
            // mark the term as zero if any of the couplings are zero
            if (!isZero && couplingsZero[j]) {
               isZero = true;
               reason = "coupling " + cname + " is zero!";
            }
         }
      }
      // check and apply flags
      bool removedByFlag = false;
 
      for (auto itr : flags) {
         auto obj = dynamic_cast<RooAbsReal *>(itr);
         if (!obj)
            continue;
         TString sval(obj->getStringAttribute("NewPhysics"));
         int val = atoi(sval);
         if (val == nNP) {
            if (flagsZero.find(obj->GetName()) != flagsZero.end() && flagsZero.at(obj->GetName())) {
               removedByFlag = true;
               reason = Form("flag %s is zero", obj->GetName());
            }
            ss.add(*obj);
         }
      }
 
      // create and add the formula
      if (!isZero && !removedByFlag) {
         // build the name
         const auto name = std::string(mfname) + "_pol" + std::to_string(i);
         formulas[i] = std::make_unique<RooProduct>(name.c_str(), ::concatNames(ss, " * ").c_str(), ss);
      }
   }
   return formulas;
}
 
////////////////////////////////////////////////////////////////////////////////
/// create the weight formulas required for the morphing
 
FormulaList createFormulas(const char *name, const RooLagrangianMorphFunc::ParamMap &inputs,
                           const RooLagrangianMorphFunc::FlagMap &inputFlags,
                           const std::vector<std::vector<RooArgList *>> &diagrams, RooArgList &couplings,
                           const RooArgList &flags, const std::vector<std::vector<std::string>> &nonInterfering)
{
   MorphFuncPattern morphfuncpattern;
 
   for (const auto &vertices : diagrams) {
      FeynmanDiagram d;
      ::fillFeynmanDiagram(d, vertices, couplings);
      ::collectPolynomials(morphfuncpattern, d);
   }
   FormulaList retval = buildFormulas(name, inputs, inputFlags, morphfuncpattern, couplings, flags, nonInterfering);
   if (retval.empty()) {
      std::stringstream errorMsgStream;
      errorMsgStream
         << "no formulas are non-zero, check if any if your couplings is floating and missing from your param_cards!"
         << std::endl;
      const auto errorMsg = errorMsgStream.str();
      throw std::runtime_error(errorMsg);
   }
   checkMatrix(inputs, retval);
   return retval;
}
 
////////////////////////////////////////////////////////////////////////////////
/// build the sample weights required for the input templates
//
template <class T1>
inline void buildSampleWeights(T1 &weights, const char *fname, const RooLagrangianMorphFunc::ParamMap &inputParameters,
                               FormulaList &formulas, const Matrix &inverse)
{
   int sampleidx = 0;
 
   for (auto sampleit : inputParameters) {
      const std::string sample(sampleit.first);
      std::stringstream title;
      TString name_full(makeValidName(sample.c_str()));
      if (fname) {
         name_full.Append("_");
         name_full.Append(fname);
         name_full.Prepend("w_");
      }
 
      int formulaidx = 0;
      // build the formula with the correct normalization
      auto sampleformula = std::make_unique<RooLinearCombination>(name_full.Data());
      for (auto const &formulait : formulas) {
         const RooFit::SuperFloat val(inverse(formulaidx, sampleidx));
         sampleformula->add(val, formulait.second.get());
         formulaidx++;
      }
      weights.addOwned(std::move(sampleformula));
      sampleidx++;
   }
}
 
inline std::map<std::string, std::string>
buildSampleWeightStrings(const RooLagrangianMorphFunc::ParamMap &inputParameters, const FormulaList &formulas,
                         const Matrix &inverse)
{
   int sampleidx = 0;
   std::map<std::string, std::string> weights;
   for (auto sampleit : inputParameters) {
      const std::string sample(sampleit.first);
      std::stringstream str;
      int formulaidx = 0;
      // build the formula with the correct normalization
      for (auto const &formulait : formulas) {
         double val(inverse(formulaidx, sampleidx));
         if (val != 0.) {
            if (formulaidx > 0 && val > 0)
               str << " + ";
            str << val << "*(" << formulait.second->GetTitle() << ")";
         }
         formulaidx++;
      }
      weights[sample] = str.str();
      sampleidx++;
   }
   return weights;
}
} // namespace
 
///////////////////////////////////////////////////////////////////////////////
// CacheElem magic ////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////
 
class RooLagrangianMorphFunc::CacheElem : public RooAbsCacheElement {
public:
   std::unique_ptr<RooRealSumFunc> _sumFunc = nullptr;
   RooArgList _couplings;
 
   FormulaList _formulas;
   RooArgList _weights;
 
   Matrix _matrix;
   Matrix _inverse;
   double _condition;
 
   CacheElem(){};
   void operModeHook(RooAbsArg::OperMode) override{};
 
   //////////////////////////////////////////////////////////////////////////////
   /// retrieve the list of contained args
 
   RooArgList containedArgs(Action) override
   {
      RooArgList args(*_sumFunc);
      args.add(_weights);
      args.add(_couplings);
      for (auto const &it : _formulas) {
         args.add(*(it.second));
      }
      return args;
   }
 
   //////////////////////////////////////////////////////////////////////////////
   // default destructor
 
   ~CacheElem() override {}
 
   //////////////////////////////////////////////////////////////////////////////
   /// create the basic objects required for the morphing
 
   inline void createComponents(const RooLagrangianMorphFunc::ParamMap &inputParameters,
                                const RooLagrangianMorphFunc::FlagMap &inputFlags, const char *funcname,
                                const std::vector<std::vector<RooListProxy *>> &diagramProxyList,
                                const std::vector<std::vector<std::string>> &nonInterfering, const RooArgList &flags)
   {
      RooArgList operators;
      std::vector<std::vector<RooArgList *>> diagrams;
      for (const auto &diagram : diagramProxyList) {
         diagrams.emplace_back();
         for (RooArgList *vertex : diagram) {
            extractCouplings(*vertex, _couplings);
            diagrams.back().emplace_back(vertex);
         }
      }
      extractOperators(_couplings, operators);
      _formulas = ::createFormulas(funcname, inputParameters, inputFlags, diagrams, _couplings, flags, nonInterfering);
   }
 
   //////////////////////////////////////////////////////////////////////////////
   /// build and invert the morphing matrix
   template <class List>
   inline void buildMatrix(const RooLagrangianMorphFunc::ParamMap &inputParameters,
                           const RooLagrangianMorphFunc::FlagMap &inputFlags, const List &flags)
   {
      RooArgList operators;
      extractOperators(_couplings, operators);
      Matrix matrix(buildMatrixT<Matrix>(inputParameters, _formulas, operators, inputFlags, flags));
      if (size(matrix) < 1) {
         std::cerr << "input matrix is empty, please provide suitable input samples!" << std::endl;
      }
      Matrix inverse(diagMatrix(size(matrix)));
 
      double condition = (double)(invertMatrix(matrix, inverse));
      double unityDeviation, largestWeight;
      inverseSanity(matrix, inverse, unityDeviation, largestWeight);
      bool weightwarning(largestWeight > morphLargestWeight ? true : false);
      bool unitywarning(unityDeviation > morphUnityDeviation ? true : false);
 
      if (false) {
         if (unitywarning) {
            oocxcoutW((TObject *)0, Eval) << "Warning: The matrix inversion seems to be unstable. This can "
                                             "be a result to input samples that are not sufficiently "
                                             "different to provide any morphing power."
                                          << std::endl;
         } else if (weightwarning) {
            oocxcoutW((TObject *)0, Eval) << "Warning: Some weights are excessively large. This can be a "
                                             "result to input samples that are not sufficiently different to "
                                             "provide any morphing power."
                                          << std::endl;
         }
         oocxcoutW((TObject *)0, Eval) << "         Please consider the couplings "
                                          "encoded in your samples to cross-check:"
                                       << std::endl;
         for (auto sampleit : inputParameters) {
            const std::string sample(sampleit.first);
            oocxcoutW((TObject *)0, Eval) << "         " << sample << ": ";
            // set all vars to value stored in input file
            setParams(sampleit.second, operators, true);
            bool first = true;
            RooAbsReal *obj;
 
            for (auto itr : _couplings) {
               obj = dynamic_cast<RooAbsReal *>(itr);
               if (!first)
                  std::cerr << ", ";
               oocxcoutW((TObject *)0, Eval) << obj->GetName() << "=" << obj->getVal();
               first = false;
            }
            oocxcoutW((TObject *)0, Eval) << std::endl;
         }
      }
#ifndef USE_UBLAS
      _matrix.ResizeTo(matrix.GetNrows(), matrix.GetNrows());
      _inverse.ResizeTo(matrix.GetNrows(), matrix.GetNrows());
#endif
      _matrix = matrix;
      _inverse = inverse;
      _condition = condition;
   }
 
   ////////////////////////////////////////////////////////////////////////////////
   /// build the final morphing function
 
   inline void buildMorphingFunction(const char *name, const RooLagrangianMorphFunc::ParamMap &inputParameters,
                                     const std::map<std::string, int> &storage, const RooArgList &physics,
                                     bool allowNegativeYields, RooRealVar *observable, RooRealVar *binWidth)
   {
      if (!binWidth) {
         std::cerr << "invalid bin width given!" << std::endl;
         return;
      }
      if (!observable) {
         std::cerr << "invalid observable given!" << std::endl;
         return;
      }
 
      RooArgList operators;
      extractOperators(_couplings, operators);
 
      // retrieve the weights
      ::buildSampleWeights(_weights, name, inputParameters, _formulas, _inverse);
 
      // build the products of element and weight for each sample
      size_t i = 0;
      RooArgList sumElements;
      RooArgList scaleElements;
      for (auto sampleit : inputParameters) {
         // for now, we assume all the lists are nicely ordered
         TString prodname(makeValidName(sampleit.first.c_str()));
 
         RooAbsReal *obj = static_cast<RooAbsReal *>(physics.at(storage.at(prodname.Data())));
 
         if (!obj) {
            std::cerr << "unable to access physics object for " << prodname << std::endl;
            return;
         }
 
         RooAbsReal *weight = static_cast<RooAbsReal *>(_weights.at(i));
 
         if (!weight) {
            std::cerr << "unable to access weight object for " << prodname << std::endl;
            return;
         }
         prodname.Append("_");
         prodname.Append(name);
         RooArgList prodElems(*weight, *obj);
 
         allowNegativeYields = true;
         auto prod = std::make_unique<RooProduct>(prodname, prodname, prodElems);
         if (!allowNegativeYields) {
            auto maxname = std::string(prodname) + "_max0";
            RooArgSet prodset(*prod);
 
            auto max = std::make_unique<RooFormulaVar>(maxname.c_str(), "max(0," + prodname + ")", prodset);
            max->addOwnedComponents(std::move(prod));
            sumElements.addOwned(std::move(max));
         } else {
            sumElements.addOwned(std::move(prod));
         }
         scaleElements.add(*(binWidth));
         i++;
      }
 
      // put everything together
      _sumFunc = make_unique<RooRealSumFunc>(Form("%s_morphfunc", name), name, sumElements, scaleElements);
 
      if (!observable)
         std::cerr << "unable to access observable" << std::endl;
      _sumFunc.get()->addServer(*observable);
      if (!binWidth)
         std::cerr << "unable to access bin width" << std::endl;
      _sumFunc.get()->addServer(*binWidth);
      if (operators.getSize() < 1)
         std::cerr << "no operators listed" << std::endl;
      _sumFunc.get()->addServerList(operators);
      if (_weights.getSize() < 1)
         std::cerr << "unable to access weight objects" << std::endl;
      _sumFunc.get()->addOwnedComponents(std::move(sumElements));
      _sumFunc.get()->addServerList(sumElements);
      _sumFunc.get()->addServerList(scaleElements);
 
#ifdef USE_UBLAS
      std::cout.precision(std::numeric_limits<double>::digits);
#endif
   }
   //////////////////////////////////////////////////////////////////////////////
   /// create all the temporary objects required by the class
 
   static RooLagrangianMorphFunc::CacheElem *createCache(const RooLagrangianMorphFunc *func)
   {
      std::string obsName = func->getObservable()->GetName();
      RooLagrangianMorphFunc::ParamSet values = getParams(func->_operators);
 
      RooLagrangianMorphFunc::CacheElem *cache = new RooLagrangianMorphFunc::CacheElem();
 
      cache->createComponents(func->_config.paramCards, func->_config.flagValues, func->GetName(), func->_diagrams,
                              func->_nonInterfering, func->_flags);
 
      cache->buildMatrix(func->_config.paramCards, func->_config.flagValues, func->_flags);
      if (obsName.empty()) {
         std::cerr << "Matrix inversion succeeded, but no observable was "
                      "supplied. quitting..."
                   << std::endl;
         return cache;
      }
 
      oocxcoutP((TObject *)0, ObjectHandling) << "observable: " << func->getObservable()->GetName() << std::endl;
      oocxcoutP((TObject *)0, ObjectHandling) << "binWidth: " << func->getBinWidth()->GetName() << std::endl;
 
      setParams(func->_flags, 1);
      cache->buildMorphingFunction(func->GetName(), func->_config.paramCards, func->_sampleMap, func->_physics,
                                   func->_config.allowNegativeYields, func->getObservable(), func->getBinWidth());
      setParams(values, func->_operators, true);
      setParams(func->_flags, 1);
      return cache;
   }
 
   //////////////////////////////////////////////////////////////////////////////
   /// create all the temporary objects required by the class
   /// function variant with precomputed inverse matrix
 
   static RooLagrangianMorphFunc::CacheElem *createCache(const RooLagrangianMorphFunc *func, const Matrix &inverse)
   {
      RooLagrangianMorphFunc::ParamSet values = getParams(func->_operators);
 
      RooLagrangianMorphFunc::CacheElem *cache = new RooLagrangianMorphFunc::CacheElem();
 
      cache->createComponents(func->_config.paramCards, func->_config.flagValues, func->GetName(), func->_diagrams,
                              func->_nonInterfering, func->_flags);
 
#ifndef USE_UBLAS
      cache->_inverse.ResizeTo(inverse.GetNrows(), inverse.GetNrows());
#endif
      cache->_inverse = inverse;
      cache->_condition = NaN;
 
      setParams(func->_flags, 1);
      cache->buildMorphingFunction(func->GetName(), func->_config.paramCards, func->_sampleMap, func->_physics,
                                   func->_config.allowNegativeYields, func->getObservable(), func->getBinWidth());
      setParams(values, func->_operators, true);
      setParams(func->_flags, 1);
      return cache;
   }
};
 
///////////////////////////////////////////////////////////////////////////////
// Class Implementation ///////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////
 
////////////////////////////////////////////////////////////////////////////////
/// write a matrix to a file
 
void RooLagrangianMorphFunc::writeMatrixToFile(const TMatrixD &matrix, const char *fname)
{
   writeMatrixToFileT(matrix, fname);
}
 
////////////////////////////////////////////////////////////////////////////////
/// write a matrix to a stream
 
void RooLagrangianMorphFunc::writeMatrixToStream(const TMatrixD &matrix, std::ostream &stream)
{
   writeMatrixToStreamT(matrix, stream);
}
 
////////////////////////////////////////////////////////////////////////////////
/// read a matrix from a text file
 
TMatrixD RooLagrangianMorphFunc::readMatrixFromFile(const char *fname)
{
   return readMatrixFromFileT<TMatrixD>(fname);
}
 
////////////////////////////////////////////////////////////////////////////////
/// read a matrix from a stream
 
TMatrixD RooLagrangianMorphFunc::readMatrixFromStream(std::istream &stream)
{
   return readMatrixFromStreamT<TMatrixD>(stream);
}
 
////////////////////////////////////////////////////////////////////////////////
/// setup observable, recycle existing observable if defined
 
RooRealVar *RooLagrangianMorphFunc::setupObservable(const char *obsname, TClass *mode, TObject *inputExample)
{
   // cxcoutP(ObjectHandling) << "setting up observable" << std::endl;
   RooRealVar *obs = nullptr;
   bool obsExists(false);
   if (_observables.at(0) != 0) {
      obs = (RooRealVar *)_observables.at(0);
      obsExists = true;
   }
 
   if (mode && mode->InheritsFrom(RooHistFunc::Class())) {
      obs = (RooRealVar *)(dynamic_cast<RooHistFunc *>(inputExample)->getHistObsList().first());
      obsExists = true;
      _observables.add(*obs);
   } else if (mode && mode->InheritsFrom(RooParamHistFunc::Class())) {
      obs = (RooRealVar *)(dynamic_cast<RooParamHistFunc *>(inputExample)->paramList().first());
      obsExists = true;
      _observables.add(*obs);
   }
 
   //   Note: "found!" will be printed if s2 is a substring of s1, both s1 and s2
   //   are of type std::string. s1.find(s2)
   // obtain the observable
   if (!obsExists) {
      if (mode && mode->InheritsFrom(TH1::Class())) {
         TH1 *hist = (TH1 *)(inputExample);
         auto obsOwner =
            std::make_unique<RooRealVar>(obsname, obsname, hist->GetXaxis()->GetXmin(), hist->GetXaxis()->GetXmax());
         obs = obsOwner.get();
         addOwnedComponents(std::move(obsOwner));
         obs->setBins(hist->GetNbinsX());
      } else {
         auto obsOwner = std::make_unique<RooRealVar>(obsname, obsname, 0, 1);
         obs = obsOwner.get();
         addOwnedComponents(std::move(obsOwner));
         obs->setBins(1);
      }
      _observables.add(*obs);
   } else {
      if (strcmp(obsname, obs->GetName()) != 0) {
         coutW(ObjectHandling) << " name of existing observable " << _observables.at(0)->GetName()
                               << " does not match expected name " << obsname << std::endl;
      }
   }
 
   TString sbw = Form("binWidth_%s", makeValidName(obs->GetName()).Data());
   auto binWidth = std::make_unique<RooRealVar>(sbw.Data(), sbw.Data(), 1.);
   double bw = obs->numBins() / (obs->getMax() - obs->getMin());
   binWidth->setVal(bw);
   binWidth->setConstant(true);
   _binWidths.addOwned(std::move(binWidth));
 
   return obs;
}
 
//#ifndef USE_MULTIPRECISION_LC
//#pragma GCC diagnostic push
//#pragma GCC diagnostic ignored "-Wunused-parameter"
//#endif
 
////////////////////////////////////////////////////////////////////////////////
/// update sample weight (-?-)
 
inline void RooLagrangianMorphFunc::updateSampleWeights()
{
   //#ifdef USE_MULTIPRECISION_LC
   int sampleidx = 0;
   auto cache = this->getCache();
   const size_t n(size(cache->_inverse));
   for (auto sampleit : _config.paramCards) {
      const std::string sample(sampleit.first);
      // build the formula with the correct normalization
      RooLinearCombination *sampleformula = dynamic_cast<RooLinearCombination *>(this->getSampleWeight(sample.c_str()));
      if (!sampleformula) {
         coutE(ObjectHandling) << Form("unable to access formula for sample '%s'!", sample.c_str()) << std::endl;
         return;
      }
      cxcoutP(ObjectHandling) << "updating formula for sample '" << sample << "'" << std::endl;
      for (size_t formulaidx = 0; formulaidx < n; ++formulaidx) {
         const RooFit::SuperFloat val(cache->_inverse(formulaidx, sampleidx));
#ifdef USE_UBLAS
         if (val != val) {
#else
         if (std::isnan(val)) {
#endif
            coutE(ObjectHandling) << "refusing to propagate NaN!" << std::endl;
         }
         cxcoutP(ObjectHandling) << "   " << formulaidx << ":" << sampleformula->getCoefficient(formulaidx) << " -> "
                                 << val << std::endl;
         sampleformula->setCoefficient(formulaidx, val);
         assert(sampleformula->getCoefficient(formulaidx) == val);
      }
      sampleformula->setValueDirty();
      ++sampleidx;
   }
   //#else
   //  ERROR("updating sample weights currently not possible without boost!");
   //#endif
}
//#ifndef USE_MULTIPRECISION_LC
//#pragma GCC diagnostic pop
//#endif
 
////////////////////////////////////////////////////////////////////////////////
/// read the parameters from the input file
 
void RooLagrangianMorphFunc::readParameters(TDirectory *f)
{
   readValues<double>(_config.paramCards, f, _config.folderNames, "param_card", true);
   readValues<int>(_config.flagValues, f, _config.folderNames, "flags", false);
}
 
////////////////////////////////////////////////////////////////////////////////
/// retrieve the physics inputs
 
void RooLagrangianMorphFunc::collectInputs(TDirectory *file)
{
   std::string obsName;
   if (_config.observable) {
      _observables.add(*_config.observable);
      if (_config.observableName.empty()) {
         obsName = _observables.at(0)->GetName();
      } else {
         obsName = _config.observableName;
      }
   } else {
      obsName = _config.observableName;
   }
 
   cxcoutP(InputArguments) << "initializing physics inputs from file " << file->GetName() << " with object name(s) '"
                           << obsName << "'" << std::endl;
   auto folderNames = _config.folderNames;
   auto obj = loadFromFileResidentFolder<TObject>(file, folderNames.front(), obsName, true);
   if (!obj) {
      std::cerr << "unable to locate object '" << obsName << "' in folder '" << folderNames.front() << "'!"
                << std::endl;
      return;
   }
   std::string classname = obj->ClassName();
   TClass *mode = TClass::GetClass(obj->ClassName());
   this->setupObservable(obsName.c_str(), mode, obj.get());
 
   if (classname.find("TH1") != std::string::npos) {
      collectHistograms(this->GetName(), file, _sampleMap, _physics, *static_cast<RooRealVar *>(_observables.at(0)),
                        obsName, _config.paramCards, _config.normalize);
   } else if (classname.find("RooHistFunc") != std::string::npos ||
              classname.find("RooParamHistFunc") != std::string::npos ||
              classname.find("PiecewiseInterpolation") != std::string::npos) {
      collectRooAbsReal(this->GetName(), file, _sampleMap, _physics, obsName, _config.paramCards);
   } else if (classname.find("TParameter<double>") != std::string::npos) {
      collectCrosssections<double>(this->GetName(), file, _sampleMap, _physics, obsName, _config.paramCards);
   } else if (classname.find("TParameter<float>") != std::string::npos) {
      collectCrosssections<float>(this->GetName(), file, _sampleMap, _physics, obsName, _config.paramCards);
   } else if (classname.find("TPair") != std::string::npos) {
      collectCrosssectionsTPair(this->GetName(), file, _sampleMap, _physics, obsName, folderNames[0],
                                _config.paramCards);
   } else {
      std::cerr << "cannot morph objects of class '" << mode->GetName() << "'!" << std::endl;
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// print all the parameters and their values in the given sample to the console
 
void RooLagrangianMorphFunc::printParameters(const char *samplename) const
{
   for (const auto &param : _config.paramCards.at(samplename)) {
      if (this->hasParameter(param.first.c_str())) {
         std::cout << param.first << " = " << param.second;
         if (this->isParameterConstant(param.first.c_str()))
            std::cout << " (const)";
         std::cout << std::endl;
      }
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// print all the known samples to the console
 
void RooLagrangianMorphFunc::printSamples() const
{
   // print all the known samples to the console
   for (auto folder : _config.folderNames) {
      std::cout << folder << std::endl;
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// print the current physics values
 
void RooLagrangianMorphFunc::printPhysics() const
{
   for (const auto &sample : _sampleMap) {
      RooAbsArg *phys = _physics.at(sample.second);
      if (!phys)
         continue;
      phys->Print();
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// constructor with proper arguments
 
RooLagrangianMorphFunc::RooLagrangianMorphFunc(const char *name, const char *title, const Config &config)
   : RooAbsReal(name, title), _cacheMgr(this, 10, true, true), _physics("physics", "physics", this),
     _operators("operators", "set of operators", this), _observables("observables", "morphing observables", this),
     _binWidths("binWidths", "set of binWidth objects", this), _flags("flags", "flags", this), _config(config)
{
   this->init();
   this->disableInterferences(_config.nonInterfering);
   this->setup(false);
 
   TRACE_CREATE
}
 
////////////////////////////////////////////////////////////////////////////////
/// setup this instance with the given set of operators and vertices
/// if own=true, the class will own the operators template `<class Base>`
 
void RooLagrangianMorphFunc::setup(bool own)
{
   if (_config.couplings.size() > 0) {
      RooArgList operators;
      std::vector<RooListProxy *> vertices;
      extractOperators(_config.couplings, operators);
      vertices.push_back(new RooListProxy("!couplings", "set of couplings in the vertex", this, true, false));
      if (own) {
         _operators.addOwned(std::move(operators));
         vertices[0]->addOwned(_config.couplings);
      } else {
         _operators.add(operators);
         vertices[0]->add(_config.couplings);
      }
      _diagrams.push_back(vertices);
   }
 
   else if (_config.prodCouplings.size() > 0 && _config.decCouplings.size() > 0) {
      std::vector<RooListProxy *> vertices;
      RooArgList operators;
      cxcoutP(InputArguments) << "prod/dec couplings provided" << std::endl;
      extractOperators(_config.prodCouplings, operators);
      extractOperators(_config.decCouplings, operators);
      vertices.push_back(
         new RooListProxy("!production", "set of couplings in the production vertex", this, true, false));
      vertices.push_back(new RooListProxy("!decay", "set of couplings in the decay vertex", this, true, false));
      if (own) {
         _operators.addOwned(std::move(operators));
         vertices[0]->addOwned(_config.prodCouplings);
         vertices[1]->addOwned(_config.decCouplings);
      } else {
         cxcoutP(InputArguments) << "adding non-own operators" << std::endl;
         _operators.add(operators);
         vertices[0]->add(_config.prodCouplings);
         vertices[1]->add(_config.decCouplings);
      }
      _diagrams.push_back(vertices);
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// disable interference between terms
 
void RooLagrangianMorphFunc::disableInterference(const std::vector<const char *> &nonInterfering)
{
   // disable interference between the listed operators
   std::stringstream name;
   name << "noInteference";
   for (auto c : nonInterfering) {
      name << c;
   }
   _nonInterfering.emplace_back();
   for (auto c : nonInterfering) {
      _nonInterfering.back().emplace_back(c);
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// disable interference between terms
 
void RooLagrangianMorphFunc::disableInterferences(const std::vector<std::vector<const char *>> &nonInterfering)
{
   // disable interferences between the listed groups of operators
   for (size_t i = 0; i < nonInterfering.size(); ++i) {
      this->disableInterference(nonInterfering[i]);
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// initialise inputs required for the morphing function
 
void RooLagrangianMorphFunc::init()
{
   std::string filename = _config.fileName;
   TDirectory *file = openFile(filename.c_str());
   if (!file) {
      coutE(InputArguments) << "unable to open file '" << filename << "'!" << std::endl;
      return;
   }
   this->readParameters(file);
   checkNameConflict(_config.paramCards, _operators);
   this->collectInputs(file);
   closeFile(file);
   RooRealVar *nNP0 = new RooRealVar("nNP0", "nNP0", 1., 0, 1.);
   nNP0->setStringAttribute("NewPhysics", "0");
   nNP0->setConstant(true);
   _flags.add(*nNP0);
   RooRealVar *nNP1 = new RooRealVar("nNP1", "nNP1", 1., 0, 1.);
   nNP1->setStringAttribute("NewPhysics", "1");
   nNP1->setConstant(true);
   _flags.add(*nNP1);
   RooRealVar *nNP2 = new RooRealVar("nNP2", "nNP2", 1., 0, 1.);
   nNP2->setStringAttribute("NewPhysics", "2");
   nNP2->setConstant(true);
   _flags.add(*nNP2);
   RooRealVar *nNP3 = new RooRealVar("nNP3", "nNP3", 1., 0, 1.);
   nNP3->setStringAttribute("NewPhysics", "3");
   nNP3->setConstant(true);
   _flags.add(*nNP3);
   RooRealVar *nNP4 = new RooRealVar("nNP4", "nNP4", 1., 0, 1.);
   nNP4->setStringAttribute("NewPhysics", "4");
   nNP4->setConstant(true);
   _flags.add(*nNP4);
   // we can't use `addOwned` before, because the RooListProxy doesn't overload
   // `addOwned` correctly (it might in the future, then this can be changed).
   _flags.takeOwnership();
}
 
////////////////////////////////////////////////////////////////////////////////
/// copy constructor
 
RooLagrangianMorphFunc::RooLagrangianMorphFunc(const RooLagrangianMorphFunc &other, const char *name)
   : RooAbsReal(other, name), _cacheMgr(other._cacheMgr, this), _scale(other._scale), _sampleMap(other._sampleMap),
     _physics(other._physics.GetName(), this, other._physics),
     _operators(other._operators.GetName(), this, other._operators),
     _observables(other._observables.GetName(), this, other._observables),
     _binWidths(other._binWidths.GetName(), this, other._binWidths), _flags{other._flags.GetName(), this, other._flags},
     _config(other._config)
{
   for (size_t j = 0; j < other._diagrams.size(); ++j) {
      std::vector<RooListProxy *> diagram;
      for (size_t i = 0; i < other._diagrams[j].size(); ++i) {
         RooListProxy *list = new RooListProxy(other._diagrams[j][i]->GetName(), this, *(other._diagrams[j][i]));
         diagram.push_back(list);
      }
      _diagrams.push_back(diagram);
   }
   TRACE_CREATE
}
 
////////////////////////////////////////////////////////////////////////////////
/// set energy scale of the EFT expansion
 
void RooLagrangianMorphFunc::setScale(double val)
{
   _scale = val;
}
 
////////////////////////////////////////////////////////////////////////////////
/// get energy scale of the EFT expansion
 
double RooLagrangianMorphFunc::getScale()
{
   return _scale;
}
 
////////////////////////////////////////////////////////////////////////////////
// default constructor
 
RooLagrangianMorphFunc::RooLagrangianMorphFunc()
   : _cacheMgr(this, 10, true, true), _operators("operators", "set of operators", this, true, false),
     _observables("observable", "morphing observable", this, true, false),
     _binWidths("binWidths", "set of bin width objects", this, true, false)
{
   TRACE_CREATE
}
 
////////////////////////////////////////////////////////////////////////////////
/// default destructor
 
RooLagrangianMorphFunc::~RooLagrangianMorphFunc()
{
   for (auto const &diagram : _diagrams) {
      for (RooListProxy *vertex : diagram) {
         delete vertex;
      }
   }
   TRACE_DESTROY
}
 
////////////////////////////////////////////////////////////////////////////////
/// calculate the number of samples needed to morph a bivertex, 2-2 physics
/// process
 
int RooLagrangianMorphFunc::countSamples(int nprod, int ndec, int nboth)
{
   FeynmanDiagram diagram;
   std::vector<bool> prod;
   std::vector<bool> dec;
   for (int i = 0; i < nboth; ++i) {
      prod.push_back(true);
      dec.push_back(true);
   }
   for (int i = 0; i < nprod; ++i) {
      prod.push_back(true);
      dec.push_back(false);
   }
   for (int i = 0; i < ndec; ++i) {
      prod.push_back(false);
      dec.push_back(true);
   }
   diagram.push_back(prod);
   diagram.push_back(dec);
   MorphFuncPattern morphfuncpattern;
   ::collectPolynomials(morphfuncpattern, diagram);
   return morphfuncpattern.size();
}
 
////////////////////////////////////////////////////////////////////////////////
/// calculate the number of samples needed to morph a certain physics process
 
int RooLagrangianMorphFunc::countSamples(std::vector<RooArgList *> &vertices)
{
   RooArgList operators, couplings;
   for (auto vertex : vertices) {
      extractOperators(*vertex, operators);
      extractCouplings(*vertex, couplings);
   }
   FeynmanDiagram diagram;
   ::fillFeynmanDiagram(diagram, vertices, couplings);
   MorphFuncPattern morphfuncpattern;
   ::collectPolynomials(morphfuncpattern, diagram);
   return morphfuncpattern.size();
}
 
////////////////////////////////////////////////////////////////////////////////
/// create only the weight formulas. static function for external usage.
 
std::map<std::string, std::string>
RooLagrangianMorphFunc::createWeightStrings(const RooLagrangianMorphFunc::ParamMap &inputs,
                                            const std::vector<std::vector<std::string>> &vertices_str)
{
   std::stack<RooArgList> ownedVertices;
   std::vector<RooArgList *> vertices;
   RooArgList couplings;
   for (const auto &vtx : vertices_str) {
      ownedVertices.emplace();
      auto &vertex = ownedVertices.top();
      for (const auto &c : vtx) {
         auto coupling = static_cast<RooRealVar *>(couplings.find(c.c_str()));
         if (!coupling) {
            auto couplingOwner = std::make_unique<RooRealVar>(c.c_str(), c.c_str(), 1., 0., 10.);
            coupling = couplingOwner.get();
            couplings.addOwned(std::move(couplingOwner));
         }
         vertex.add(*coupling);
      }
      vertices.push_back(&vertex);
   }
   auto retval = RooLagrangianMorphFunc::createWeightStrings(inputs, vertices, couplings);
   return retval;
}
 
////////////////////////////////////////////////////////////////////////////////
/// create only the weight formulas. static function for external usage.
 
std::map<std::string, std::string>
RooLagrangianMorphFunc::createWeightStrings(const RooLagrangianMorphFunc::ParamMap &inputs,
                                            const std::vector<RooArgList *> &vertices, RooArgList &couplings)
{
   return createWeightStrings(inputs, vertices, couplings, {}, {}, {});
}
 
////////////////////////////////////////////////////////////////////////////////
/// create only the weight formulas. static function for external usage.
 
std::map<std::string, std::string>
RooLagrangianMorphFunc::createWeightStrings(const RooLagrangianMorphFunc::ParamMap &inputs,
                                            const std::vector<RooArgList *> &vertices, RooArgList &couplings,
                                            const RooLagrangianMorphFunc::FlagMap &flagValues, const RooArgList &flags,
                                            const std::vector<std::vector<std::string>> &nonInterfering)
{
   FormulaList formulas = ::createFormulas("", inputs, flagValues, {vertices}, couplings, flags, nonInterfering);
   RooArgSet operators;
   extractOperators(couplings, operators);
   Matrix matrix(::buildMatrixT<Matrix>(inputs, formulas, operators, flagValues, flags));
   if (size(matrix) < 1) {
      std::cerr << "input matrix is empty, please provide suitable input samples!" << std::endl;
   }
   Matrix inverse(::diagMatrix(size(matrix)));
   double condition __attribute__((unused)) = (double)(invertMatrix(matrix, inverse));
   auto retval = buildSampleWeightStrings(inputs, formulas, inverse);
   return retval;
}
 
////////////////////////////////////////////////////////////////////////////////
/// create only the weight formulas. static function for external usage.
 
RooArgSet RooLagrangianMorphFunc::createWeights(const RooLagrangianMorphFunc::ParamMap &inputs,
                                                const std::vector<RooArgList *> &vertices, RooArgList &couplings,
                                                const RooLagrangianMorphFunc::FlagMap &flagValues,
                                                const RooArgList &flags,
                                                const std::vector<std::vector<std::string>> &nonInterfering)
{
   FormulaList formulas = ::createFormulas("", inputs, flagValues, {vertices}, couplings, flags, nonInterfering);
   RooArgSet operators;
   extractOperators(couplings, operators);
   Matrix matrix(::buildMatrixT<Matrix>(inputs, formulas, operators, flagValues, flags));
   if (size(matrix) < 1) {
      std::cerr << "input matrix is empty, please provide suitable input samples!" << std::endl;
   }
   Matrix inverse(::diagMatrix(size(matrix)));
   double condition __attribute__((unused)) = (double)(invertMatrix(matrix, inverse));
   RooArgSet retval;
   ::buildSampleWeights(retval, (const char *)nullptr /* name */, inputs, formulas, inverse);
   return retval;
}
 
////////////////////////////////////////////////////////////////////////////////
/// create only the weight formulas. static function for external usage.
 
RooArgSet RooLagrangianMorphFunc::createWeights(const RooLagrangianMorphFunc::ParamMap &inputs,
                                                const std::vector<RooArgList *> &vertices, RooArgList &couplings)
{
   RooArgList flags;
   FlagMap flagValues;
   return RooLagrangianMorphFunc::createWeights(inputs, vertices, couplings, flagValues, flags, {});
}
 
////////////////////////////////////////////////////////////////////////////////
/// return the RooProduct that is the element of the RooRealSumPdfi
///  corresponding to the given sample name
 
RooProduct *RooLagrangianMorphFunc::getSumElement(const char *name) const
{
   auto mf = this->getFunc();
   if (!mf) {
      coutE(Eval) << "unable to retrieve morphing function" << std::endl;
      return nullptr;
   }
   RooArgSet *args = mf->getComponents();
   TString prodname(name);
   prodname.Append("_");
   prodname.Append(this->GetName());
 
   for (auto itr : *args) {
      RooProduct *prod = dynamic_cast<RooProduct *>(itr);
      if (!prod)
         continue;
      TString sname(prod->GetName());
      if (sname.CompareTo(prodname) == 0) {
         return prod;
      }
   }
   return nullptr;
}
////////////////////////////////////////////////////////////////////////////////
/// return the vector of sample names, used to build the morph func
 
std::vector<std::string> RooLagrangianMorphFunc::getSamples() const
{
   return _config.folderNames;
}
 
////////////////////////////////////////////////////////////////////////////////
/// retrieve the weight (prefactor) of a sample with the given name
 
RooAbsReal *RooLagrangianMorphFunc::getSampleWeight(const char *name)
{
   auto cache = this->getCache();
   auto wname = std::string("w_") + name + "_" + this->GetName();
   return dynamic_cast<RooAbsReal *>(cache->_weights.find(wname.c_str()));
}
 
////////////////////////////////////////////////////////////////////////////////
/// print the current sample weights
 
void RooLagrangianMorphFunc::printWeights() const
{
   this->printSampleWeights();
}
 
////////////////////////////////////////////////////////////////////////////////
/// print the current sample weights
 
void RooLagrangianMorphFunc::printSampleWeights() const
{
   auto *cache = this->getCache();
   for (const auto &sample : _sampleMap) {
      auto weightName = std::string("w_") + sample.first + "_" + this->GetName();
      auto weight = static_cast<RooAbsReal *>(cache->_weights.find(weightName.c_str()));
      if (!weight)
         continue;
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// randomize the parameters a bit
/// useful to test and debug fitting
 
void RooLagrangianMorphFunc::randomizeParameters(double z)
{
   RooRealVar *obj;
   TRandom3 r;
 
   for (auto itr : _operators) {
      obj = dynamic_cast<RooRealVar *>(itr);
      double val = obj->getVal();
      if (obj->isConstant())
         continue;
      double variation = r.Gaus(1, z);
      obj->setVal(val * variation);
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// retrive the new physics objects and update the weights in the morphing
/// function
 
bool RooLagrangianMorphFunc::updateCoefficients()
{
   auto cache = this->getCache();
 
   std::string filename = _config.fileName;
   TDirectory *file = openFile(filename.c_str());
   if (!file) {
      coutE(InputArguments) << "unable to open file '" << filename << "'!" << std::endl;
      return false;
   }
 
   this->readParameters(file);
 
   checkNameConflict(_config.paramCards, _operators);
   this->collectInputs(file);
 
   cache->buildMatrix(_config.paramCards, _config.flagValues, _flags);
   this->updateSampleWeights();
 
   closeFile(file);
   return true;
}
 
////////////////////////////////////////////////////////////////////////////////
/// setup the morphing function with a predefined inverse matrix
/// call this function *before* any other after creating the object
 
bool RooLagrangianMorphFunc::useCoefficients(const TMatrixD &inverse)
{
   auto cache = static_cast<RooLagrangianMorphFunc::CacheElem *>(_cacheMgr.getObj(0, (RooArgSet *)0));
   Matrix m = makeSuperMatrix(inverse);
   if (cache) {
      std::string filename = _config.fileName;
      cache->_inverse = m;
      TDirectory *file = openFile(filename.c_str());
      if (!file) {
         coutE(InputArguments) << "unable to open file '" << filename << "'!" << std::endl;
         return false;
      }
 
      this->readParameters(file);
      checkNameConflict(_config.paramCards, _operators);
      this->collectInputs(file);
 
      // then, update the weights in the morphing function
      this->updateSampleWeights();
 
      closeFile(file);
   } else {
      cache = RooLagrangianMorphFunc::CacheElem::createCache(this, m);
      if (!cache)
         coutE(Caching) << "unable to create cache!" << std::endl;
      _cacheMgr.setObj(0, 0, cache, 0);
   }
   return true;
}
 
////////////////////////////////////////////////////////////////////////////////
// setup the morphing function with a predefined inverse matrix
// call this function *before* any other after creating the object
 
bool RooLagrangianMorphFunc::useCoefficients(const char *filename)
{
   auto cache = static_cast<RooLagrangianMorphFunc::CacheElem *>(_cacheMgr.getObj(0, (RooArgSet *)0));
   if (cache) {
      return false;
   }
   cache = RooLagrangianMorphFunc::CacheElem::createCache(this, readMatrixFromFileT<Matrix>(filename));
   if (!cache)
      coutE(Caching) << "unable to create cache!" << std::endl;
   _cacheMgr.setObj(nullptr, nullptr, cache, nullptr);
   return true;
}
 
////////////////////////////////////////////////////////////////////////////////
/// write the inverse matrix to a file
 
bool RooLagrangianMorphFunc::writeCoefficients(const char *filename)
{
   auto cache = this->getCache();
   if (!cache)
      return false;
   writeMatrixToFileT(cache->_inverse, filename);
   return true;
}
 
////////////////////////////////////////////////////////////////////////////////
/// retrieve the cache object
 
typename RooLagrangianMorphFunc::CacheElem *RooLagrangianMorphFunc::getCache() const
{
   auto cache = static_cast<RooLagrangianMorphFunc::CacheElem *>(_cacheMgr.getObj(0, (RooArgSet *)0));
   if (!cache) {
      cxcoutP(Caching) << "creating cache from getCache function for " << this << std::endl;
      cxcoutP(Caching) << "current storage has size " << _sampleMap.size() << std::endl;
      cache = RooLagrangianMorphFunc::CacheElem::createCache(this);
      if (cache)
         _cacheMgr.setObj(nullptr, nullptr, cache, nullptr);
      else
         coutE(Caching) << "unable to create cache!" << std::endl;
   }
   return cache;
}
 
////////////////////////////////////////////////////////////////////////////////
/// return true if a cache object is present, false otherwise
 
bool RooLagrangianMorphFunc::hasCache() const
{
   return (bool)(_cacheMgr.getObj(nullptr, static_cast<RooArgSet *>(nullptr)));
}
 
////////////////////////////////////////////////////////////////////////////////
/// set one parameter to a specific value
 
void RooLagrangianMorphFunc::setParameter(const char *name, double value)
{
   RooRealVar *param = this->getParameter(name);
   if (!param) {
      return;
   }
   if (value > param->getMax())
      param->setMax(value);
   if (value < param->getMin())
      param->setMin(value);
   param->setVal(value);
}
 
////////////////////////////////////////////////////////////////////////////////
/// set one flag to a specific value
 
void RooLagrangianMorphFunc::setFlag(const char *name, double value)
{
   RooRealVar *param = this->getFlag(name);
   if (!param) {
      return;
   }
   param->setVal(value);
}
 
////////////////////////////////////////////////////////////////////////////////
/// set one parameter to a specific value and range
 
void RooLagrangianMorphFunc::setParameter(const char *name, double value, double min, double max)
{
   RooRealVar *param = this->getParameter(name);
   if (!param) {
      return;
   }
   param->setMin(min);
   param->setMax(max);
   param->setVal(value);
}
 
////////////////////////////////////////////////////////////////////////////////
/// set one parameter to a specific value and range
void RooLagrangianMorphFunc::setParameter(const char *name, double value, double min, double max, double error)
{
   RooRealVar *param = this->getParameter(name);
   if (!param) {
      return;
   }
   param->setMin(min);
   param->setMax(max);
   param->setVal(value);
   param->setError(error);
}
 
////////////////////////////////////////////////////////////////////////////////
/// return true if the parameter with the given name is set constant, false
/// otherwise
 
bool RooLagrangianMorphFunc::isParameterConstant(const char *name) const
{
   RooRealVar *param = this->getParameter(name);
   if (param) {
      return param->isConstant();
   }
   return true;
}
 
////////////////////////////////////////////////////////////////////////////////
/// retrieve the RooRealVar object incorporating the parameter with the given
/// name
RooRealVar *RooLagrangianMorphFunc::getParameter(const char *name) const
{
 
   return dynamic_cast<RooRealVar *>(_operators.find(name));
}
 
////////////////////////////////////////////////////////////////////////////////
/// retrieve the RooRealVar object incorporating the flag with the given name
 
RooRealVar *RooLagrangianMorphFunc::getFlag(const char *name) const
{
   return dynamic_cast<RooRealVar *>(_flags.find(name));
}
 
////////////////////////////////////////////////////////////////////////////////
/// check if a parameter of the given name is contained in the list of known
/// parameters
 
bool RooLagrangianMorphFunc::hasParameter(const char *name) const
{
   return this->getParameter(name);
}
 
////////////////////////////////////////////////////////////////////////////////
/// call setConstant with the boolean argument provided on the parameter with
/// the given name
 
void RooLagrangianMorphFunc::setParameterConstant(const char *name, bool constant) const
{
   RooRealVar *param = this->getParameter(name);
   if (param) {
      return param->setConstant(constant);
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// set one parameter to a specific value
 
double RooLagrangianMorphFunc::getParameterValue(const char *name) const
{
   RooRealVar *param = this->getParameter(name);
   if (param) {
      return param->getVal();
   }
   return 0.0;
}
 
////////////////////////////////////////////////////////////////////////////////
/// set the morphing parameters to those supplied in the given param hist
 
void RooLagrangianMorphFunc::setParameters(TH1 *paramhist)
{
   setParams(paramhist, _operators, false);
}
 
////////////////////////////////////////////////////////////////////////////////
/// set the morphing parameters to those supplied in the sample with the given
/// name
 
void RooLagrangianMorphFunc::setParameters(const char *foldername)
{
   std::string filename = _config.fileName;
   TDirectory *file = openFile(filename.c_str());
   auto paramhist = loadFromFileResidentFolder<TH1>(file, foldername, "param_card");
   setParams(paramhist.get(), _operators, false);
   closeFile(file);
}
 
/////////////////////////////////////////////////////////////////////////////////
/// retrieve the morphing parameters associated to the sample with the given
/// name
 
RooLagrangianMorphFunc::ParamSet RooLagrangianMorphFunc::getMorphParameters(const char *foldername) const
{
   const std::string name(foldername);
   return _config.paramCards.at(name);
}
 
////////////////////////////////////////////////////////////////////////////////
/// set the morphing parameters to those supplied in the list with the given
/// name
 
void RooLagrangianMorphFunc::setParameters(const RooArgList *list)
{
   for (auto itr : *list) {
      RooRealVar *param = dynamic_cast<RooRealVar *>(itr);
      if (!param)
         continue;
      this->setParameter(param->GetName(), param->getVal());
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// retrieve the histogram observable
 
RooRealVar *RooLagrangianMorphFunc::getObservable() const
{
   if (_observables.getSize() < 1) {
      coutE(InputArguments) << "observable not available!" << std::endl;
      return nullptr;
   }
   return static_cast<RooRealVar *>(_observables.at(0));
}
 
////////////////////////////////////////////////////////////////////////////////
/// retrieve the histogram observable
 
RooRealVar *RooLagrangianMorphFunc::getBinWidth() const
{
   if (_binWidths.getSize() < 1) {
      coutE(InputArguments) << "bin width not available!" << std::endl;
      return nullptr;
   }
   return static_cast<RooRealVar *>(_binWidths.at(0));
}
 
////////////////////////////////////////////////////////////////////////////////
/// retrieve a histogram output of the current morphing settings
 
TH1 *RooLagrangianMorphFunc::createTH1(const std::string &name)
{
   return this->createTH1(name, false);
}
 
////////////////////////////////////////////////////////////////////////////////
/// retrieve a histogram output of the current morphing settings
 
TH1 *RooLagrangianMorphFunc::createTH1(const std::string &name, bool correlateErrors)
{
   auto mf = std::make_unique<RooRealSumFunc>(*(this->getFunc()));
   RooRealVar *observable = this->getObservable();
 
   const int nbins = observable->getBins();
 
   auto hist = std::make_unique<TH1F>(name.c_str(), name.c_str(), nbins, observable->getBinning().array());
 
   RooArgSet *args = mf->getComponents();
   for (int i = 0; i < nbins; ++i) {
      observable->setBin(i);
      double val = 0;
      double unc2 = 0;
      double unc = 0;
      for (auto itr : *args) {
         RooProduct *prod = dynamic_cast<RooProduct *>(itr);
         if (!prod)
            continue;
         RooAbsArg *phys = prod->components().find(Form("phys_%s", prod->GetName()));
         RooHistFunc *hf = dynamic_cast<RooHistFunc *>(phys);
         if (!hf) {
            continue;
         }
         const RooDataHist &dhist = hf->dataHist();
         dhist.get(i);
         RooAbsReal *formula = dynamic_cast<RooAbsReal *>(prod->components().find(Form("w_%s", prod->GetName())));
         double weight = formula->getVal();
         unc2 += dhist.weightSquared() * weight * weight;
         unc += sqrt(dhist.weightSquared()) * weight;
         val += dhist.weight() * weight;
      }
      hist->SetBinContent(i + 1, val);
      hist->SetBinError(i + 1, correlateErrors ? unc : sqrt(unc2));
   }
   return hist.release();
}
 
////////////////////////////////////////////////////////////////////////////////
/// count the number of formulas that correspond to the current parameter set
 
int RooLagrangianMorphFunc::countContributingFormulas() const
{
   int nFormulas = 0;
   auto mf = std::make_unique<RooRealSumFunc>(*(this->getFunc()));
   if (!mf)
      coutE(InputArguments) << "unable to retrieve morphing function" << std::endl;
   RooArgSet *args = mf->getComponents();
   for (auto itr : *args) {
      RooProduct *prod = dynamic_cast<RooProduct *>(itr);
      if (prod->getVal() != 0) {
         nFormulas++;
      }
   }
   return nFormulas;
}
 
////////////////////////////////////////////////////////////////////////////////
/// check if there is any morphing power provided for the given parameter
/// morphing power is provided as soon as any two samples provide different,
/// non-zero values for this parameter
 
bool RooLagrangianMorphFunc::isParameterUsed(const char *paramname) const
{
   std::string pname(paramname);
   double val = 0;
   bool isUsed = false;
   for (const auto &sample : _config.paramCards) {
      double thisval = sample.second.at(pname);
      if (thisval != val) {
         if (val != 0)
            isUsed = true;
         val = thisval;
      }
   }
   return isUsed;
}
 
////////////////////////////////////////////////////////////////////////////////
/// check if there is any morphing power provided for the given coupling
/// morphing power is provided as soon as any two samples provide
/// different, non-zero values for this coupling
 
bool RooLagrangianMorphFunc::isCouplingUsed(const char *couplname)
{
   std::string cname(couplname);
   const RooArgList *args = this->getCouplingSet();
   RooAbsReal *coupling = dynamic_cast<RooAbsReal *>(args->find(couplname));
   if (!coupling)
      return false;
   RooLagrangianMorphFunc::ParamSet params = this->getMorphParameters();
   double val = 0;
   bool isUsed = false;
   for (const auto &sample : _config.paramCards) {
      this->setParameters(sample.second);
      double thisval = coupling->getVal();
      if (thisval != val) {
         if (val != 0)
            isUsed = true;
         val = thisval;
      }
   }
   this->setParameters(params);
   return isUsed;
}
 
////////////////////////////////////////////////////////////////////////////////
/// return the number of parameters in this morphing function
 
int RooLagrangianMorphFunc::nParameters() const
{
   return this->getParameterSet()->getSize();
}
 
////////////////////////////////////////////////////////////////////////////////
/// return the number of samples in this morphing function
 
int RooLagrangianMorphFunc::nPolynomials() const
{
   // return the number of samples in this morphing function
   auto cache = getCache();
   return cache->_formulas.size();
}
 
////////////////////////////////////////////////////////////////////////////////
/// print the contributing samples and their respective weights
 
void RooLagrangianMorphFunc::printEvaluation() const
{
   auto mf = std::make_unique<RooRealSumFunc>(*(this->getFunc()));
   if (!mf) {
      std::cerr << "Error: unable to retrieve morphing function" << std::endl;
      return;
   }
   RooArgSet *args = mf->getComponents();
   for (auto itr : *args) {
      RooAbsReal *formula = dynamic_cast<RooAbsReal *>(itr);
      if (formula) {
         TString name(formula->GetName());
         name.Remove(0, 2);
         name.Prepend("phys_");
         if (!args->find(name.Data())) {
            continue;
         }
         double val = formula->getVal();
         if (val != 0) {
            std::cout << formula->GetName() << ": " << val << " = " << formula->GetTitle() << std::endl;
         }
      }
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// get the set of parameters
 
const RooArgSet *RooLagrangianMorphFunc::getParameterSet() const
{
   return &(_operators);
}
 
////////////////////////////////////////////////////////////////////////////////
/// get the set of couplings
 
const RooArgList *RooLagrangianMorphFunc::getCouplingSet() const
{
   auto cache = getCache();
   return &(cache->_couplings);
}
 
////////////////////////////////////////////////////////////////////////////////
/// retrieve a set of couplings (-?-)
 
RooLagrangianMorphFunc::ParamSet RooLagrangianMorphFunc::getCouplings() const
{
   RooLagrangianMorphFunc::ParamSet couplings;
   for (auto obj : *(this->getCouplingSet())) {
      RooAbsReal *var = dynamic_cast<RooAbsReal *>(obj);
      if (!var)
         continue;
      const std::string name(var->GetName());
      double val = var->getVal();
      couplings[name] = val;
   }
   return couplings;
}
 
////////////////////////////////////////////////////////////////////////////////
/// retrieve the parameter set
 
RooLagrangianMorphFunc::ParamSet RooLagrangianMorphFunc::getMorphParameters() const
{
   return getParams(_operators);
}
 
////////////////////////////////////////////////////////////////////////////////
/// retrieve a set of couplings (-?-)
 
void RooLagrangianMorphFunc::setParameters(const ParamSet &params)
{
   setParams(params, _operators, false);
}
 
////////////////////////////////////////////////////////////////////////////////
/// (currently similar to cloning the Pdf
 
std::unique_ptr<RooWrapperPdf> RooLagrangianMorphFunc::createPdf() const
{
   auto cache = getCache();
   auto func = std::make_unique<RooRealSumFunc>(*(cache->_sumFunc));
 
   // create a wrapper on the roorealsumfunc
   return std::make_unique<RooWrapperPdf>(Form("pdf_%s", func->GetName()), Form("pdf of %s", func->GetTitle()), *func);
}
 
////////////////////////////////////////////////////////////////////////////////
/// get the func
 
RooRealSumFunc *RooLagrangianMorphFunc::getFunc() const
{
   auto cache = getCache();
   return cache->_sumFunc.get();
}
 
////////////////////////////////////////////////////////////////////////////////
/// return extended mored capabilities
 
RooAbsPdf::ExtendMode RooLagrangianMorphFunc::extendMode() const
{
   return this->createPdf()->extendMode();
}
 
////////////////////////////////////////////////////////////////////////////////
/// return expected number of events for extended likelihood calculation,
/// this is the sum of all coefficients
 
double RooLagrangianMorphFunc::expectedEvents(const RooArgSet *nset) const
{
   return this->createPdf()->expectedEvents(nset);
}
 
////////////////////////////////////////////////////////////////////////////////
/// return the number of expected events for the current parameter set
 
double RooLagrangianMorphFunc::expectedEvents() const
{
   RooArgSet set;
   set.add(*this->getObservable());
   return this->createPdf()->expectedEvents(set);
}
 
////////////////////////////////////////////////////////////////////////////////
/// return expected number of events for extended likelihood calculation,
/// this is the sum of all coefficients
 
double RooLagrangianMorphFunc::expectedEvents(const RooArgSet &nset) const
{
   return createPdf()->expectedEvents(&nset);
}
 
////////////////////////////////////////////////////////////////////////////////
/// return the expected uncertainty for the current parameter set
 
double RooLagrangianMorphFunc::expectedUncertainty() const
{
   RooRealVar *observable = this->getObservable();
   auto cache = this->getCache();
   double unc2 = 0;
   for (const auto &sample : _sampleMap) {
      RooAbsArg *phys = _physics.at(sample.second);
      auto weightName = std::string("w_") + sample.first + "_" + this->GetName();
      auto weight = static_cast<RooAbsReal *>(cache->_weights.find(weightName.c_str()));
      if (!weight) {
         coutE(InputArguments) << "unable to find object " + weightName << std::endl;
         return 0.0;
      }
      double newunc2 = 0;
      RooHistFunc *hf = dynamic_cast<RooHistFunc *>(phys);
      RooRealVar *rv = dynamic_cast<RooRealVar *>(phys);
      if (hf) {
         const RooDataHist &hist = hf->dataHist();
         for (Int_t j = 0; j < observable->getBins(); ++j) {
            hist.get(j);
            newunc2 += hist.weightSquared();
         }
      } else if (rv) {
         newunc2 = pow(rv->getError(), 2);
      }
      double w = weight->getVal();
      unc2 += newunc2 * w * w;
      // std::cout << phys->GetName() << " : " << weight->GetName() << "
      // thisweight: " <<  w << " thisxsec2: " << newunc2 << " weight " << weight
      // << std::endl;
   }
   return sqrt(unc2);
}
 
////////////////////////////////////////////////////////////////////////////////
/// print the parameters and their current values
 
void RooLagrangianMorphFunc::printParameters() const
{
   // print the parameters and their current values
   for (auto obj : _operators) {
      RooRealVar *param = static_cast<RooRealVar *>(obj);
      if (!param)
         continue;
      param->Print();
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// print the flags and their current values
 
void RooLagrangianMorphFunc::printFlags() const
{
   for (auto flag : _flags) {
      RooRealVar *param = static_cast<RooRealVar *>(flag);
      if (!param)
         continue;
      param->Print();
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// print a set of couplings
 
void RooLagrangianMorphFunc::printCouplings() const
{
   RooLagrangianMorphFunc::ParamSet couplings = this->getCouplings();
   for (auto c : couplings) {
      std::cout << c.first << ": " << c.second << std::endl;
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// retrieve the list of bin boundaries
 
std::list<double> *RooLagrangianMorphFunc::binBoundaries(RooAbsRealLValue &obs, double xlo, double xhi) const
{
   return this->getFunc()->binBoundaries(obs, xlo, xhi);
}
 
////////////////////////////////////////////////////////////////////////////////
/// retrieve the sample Hint
 
std::list<double> *RooLagrangianMorphFunc::plotSamplingHint(RooAbsRealLValue &obs, double xlo, double xhi) const
{
   return this->getFunc()->plotSamplingHint(obs, xlo, xhi);
}
 
////////////////////////////////////////////////////////////////////////////////
/// call getVal on the internal function
 
double RooLagrangianMorphFunc::evaluate() const
{
   // call getVal on the internal function
   const RooRealSumFunc *pdf = this->getFunc();
   RooArgSet nSet;
   for (auto &obs : _observables) {
      nSet.add(*obs);
   }
   if (pdf)
      return _scale * pdf->getVal(&nSet);
   else
      std::cerr << "unable to acquire in-built function!" << std::endl;
   return 0.;
}
 
////////////////////////////////////////////////////////////////////////////////
/// check if this PDF is a binned distribution in the given observable
 
bool RooLagrangianMorphFunc::isBinnedDistribution(const RooArgSet &obs) const
{
   return this->getFunc()->isBinnedDistribution(obs);
}
 
////////////////////////////////////////////////////////////////////////////////
/// check if observable exists in the RooArgSet (-?-)
 
bool RooLagrangianMorphFunc::checkObservables(const RooArgSet *nset) const
{
   return this->getFunc()->checkObservables(nset);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Force analytical integration for the given observable
 
bool RooLagrangianMorphFunc::forceAnalyticalInt(const RooAbsArg &arg) const
{
   return this->getFunc()->forceAnalyticalInt(arg);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Retrieve the mat
 
Int_t RooLagrangianMorphFunc::getAnalyticalIntegralWN(RooArgSet &allVars, RooArgSet &numVars, const RooArgSet *normSet,
                                                      const char *rangeName) const
{
   return this->getFunc()->getAnalyticalIntegralWN(allVars, numVars, normSet, rangeName);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Retrieve the matrix of coefficients
 
double RooLagrangianMorphFunc::analyticalIntegralWN(Int_t code, const RooArgSet *normSet, const char *rangeName) const
{
   return this->getFunc()->analyticalIntegralWN(code, normSet, rangeName);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Retrieve the matrix of coefficients
 
void RooLagrangianMorphFunc::printMetaArgs(std::ostream &os) const
{
   return this->getFunc()->printMetaArgs(os);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Retrieve the matrix of coefficients
 
RooAbsArg::CacheMode RooLagrangianMorphFunc::canNodeBeCached() const
{
   return this->getFunc()->canNodeBeCached();
}
 
////////////////////////////////////////////////////////////////////////////////
/// Retrieve the matrix of coefficients
 
void RooLagrangianMorphFunc::setCacheAndTrackHints(RooArgSet &arg)
{
   this->getFunc()->setCacheAndTrackHints(arg);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Retrieve the matrix of coefficients
 
TMatrixD RooLagrangianMorphFunc::getMatrix() const
{
   auto cache = getCache();
   if (!cache)
      coutE(Caching) << "unable to retrieve cache!" << std::endl;
   return makeRootMatrix(cache->_matrix);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Retrieve the matrix of coefficients after inversion
 
TMatrixD RooLagrangianMorphFunc::getInvertedMatrix() const
{
   auto cache = getCache();
   if (!cache)
      coutE(Caching) << "unable to retrieve cache!" << std::endl;
   return makeRootMatrix(cache->_inverse);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Retrieve the condition of the coefficient matrix. If the condition number
/// is very large, then the matrix is ill-conditioned and is almost singular.
/// The computation of the inverse is prone to large numerical errors
 
double RooLagrangianMorphFunc::getCondition() const
{
   auto cache = getCache();
   if (!cache)
      coutE(Caching) << "unable to retrieve cache!" << std::endl;
   return cache->_condition;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Return the RooRatio form of products and denominators of morphing functions
 
std::unique_ptr<RooRatio>
RooLagrangianMorphFunc::makeRatio(const char *name, const char *title, RooArgList &nr, RooArgList &dr)
{
   RooArgList num, denom;
   for (auto it : nr) {
      num.add(*it);
   }
   for (auto it : dr) {
      denom.add(*it);
   }
   // same for denom
   return make_unique<RooRatio>(name, title, num, denom);
}
 
// Register the factory interface
 
namespace {
 
// Helper function for factory interface
std::vector<std::string> asStringV(std::string const &arg)
{
   std::vector<std::string> out;
 
   for (std::string &tok : ROOT::Split(arg, ",{}", true)) {
      if (tok[0] == '\'') {
         out.emplace_back(tok.substr(1, tok.size() - 2));
      } else {
         throw std::runtime_error("Strings in factory expressions need to be in single quotes!");
      }
   }
 
   return out;
}
 
class LMIFace : public RooFactoryWSTool::IFace {
public:
   std::string
   create(RooFactoryWSTool &, const char *typeName, const char *instName, std::vector<std::string> args) override;
};
 
std::string LMIFace::create(RooFactoryWSTool &ft, const char * /*typeName*/, const char *instanceName,
                            std::vector<std::string> args)
{
   // Perform syntax check. Warn about any meta parameters other than the ones needed
   const std::array<std::string, 4> funcArgs{{"fileName", "observableName", "couplings", "folders"}};
   std::map<string, string> mappedInputs;
 
   for (unsigned int i = 1; i < args.size(); i++) {
      if (args[i].find("$fileName(") != 0 && args[i].find("$observableName(") != 0 &&
          args[i].find("$couplings(") != 0 && args[i].find("$folders(") != 0 && args[i].find("$NewPhysics(") != 0) {
         throw std::string(Form("%s::create() ERROR: unknown token %s encountered", instanceName, args[i].c_str()));
      }
   }
 
   for (unsigned int i = 0; i < args.size(); i++) {
      if (args[i].find("$NewPhysics(") == 0) {
         vector<string> subargs = ft.splitFunctionArgs(args[i].c_str());
         for (const auto &subarg : subargs) {
            std::vector<std::string> parts = ROOT::Split(subarg, "=");
            if (parts.size() == 2) {
               ft.ws().arg(parts[0].c_str())->setAttribute("NewPhysics", atoi(parts[1].c_str()));
            } else
               throw std::string(Form("%s::create() ERROR: unknown token %s encountered, check input provided for %s",
                                      instanceName, subarg.c_str(), args[i].c_str()));
         }
      } else {
         std::vector<string> subargs = ft.splitFunctionArgs(args[i].c_str());
         if (subargs.size() == 1) {
            string expr = ft.processExpression(subargs[0].c_str());
            for (auto const &param : funcArgs) {
               if (args[i].find(param) != string::npos)
                  mappedInputs[param] = subargs[0];
            }
         } else
            throw std::string(
               Form("Incorrect number of arguments in %s, have %d, expect 1", args[i].c_str(), (Int_t)subargs.size()));
      }
   }
 
   RooLagrangianMorphFunc::Config config;
   config.fileName = asStringV(mappedInputs["fileName"])[0];
   config.observableName = asStringV(mappedInputs["observableName"])[0];
   config.folderNames = asStringV(mappedInputs["folders"]);
   config.couplings.add(ft.asLIST(mappedInputs["couplings"].c_str()));
 
   ft.ws().import(RooLagrangianMorphFunc{instanceName, instanceName, config}, RooFit::Silence());
 
   return instanceName;
}
 
static Int_t init();
 
int dummy = init();
 
static Int_t init()
{
   RooFactoryWSTool::IFace *iface = new LMIFace;
   RooFactoryWSTool::registerSpecial("lagrangianmorph", iface);
   (void)dummy;
   return 0;
}
 
} // namespace