PiecewiseInterpolation.cxx

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/** \class PiecewiseInterpolation
 * \ingroup HistFactory
 * The PiecewiseInterpolation is a class that can morph distributions into each other, which
 * is useful to estimate systematic uncertainties. Given a nominal distribution and one or
 * more altered or distorted ones, it computes a new shape depending on the value of the nuisance
 * parameters \f$ \alpha_i \f$:
 * \f[
 *   A = \sum_i \mathrm{Interpolate}(\mathrm{low}_i, \mathrm{nominal}, \mathrm{high}_i, \alpha_i).
 * \f]
 * If an \f$ \alpha_i \f$ is zero, the distribution is identical to the nominal distribution, at
 * \f$ \pm 1 \f$ it is identical to the up/down distribution for that specific \f$ i \f$.
 *
 * The class supports several interpolation methods, which can be selected for each parameter separately
 * using setInterpCode(). The default interpolation code is 4. This performs
 * - \f$ |\alpha | > 1 \f$: Linear extrapolation.
 * - \f$ |\alpha | < 1 \f$: Polynomial interpolation. A sixth-order polynomial is used. Its coefficients
 * are chosen such that function, first, and second derivative at \f$ \alpha \pm 1 \f$ match the values
 * that the extrapolation procedure uses.
 */
 
#include "RooStats/HistFactory/PiecewiseInterpolation.h"
 
#include "RooFit.h"
 
#include "Riostream.h"
#include "TBuffer.h"
 
#include "RooAbsReal.h"
#include "RooAbsPdf.h"
#include "RooErrorHandler.h"
#include "RooArgSet.h"
#include "RooRealVar.h"
#include "RooMsgService.h"
#include "RooNumIntConfig.h"
#include "RooTrace.h"
#include "RunContext.h"
 
#include <exception>
#include <math.h>
#include <algorithm>
 
using namespace std;
 
ClassImp(PiecewiseInterpolation);
;
 
 
////////////////////////////////////////////////////////////////////////////////
 
PiecewiseInterpolation::PiecewiseInterpolation()
{
  _positiveDefinite=false;
  TRACE_CREATE
}
 
 
 
////////////////////////////////////////////////////////////////////////////////
/// Construct a new interpolation. The value of the function will be
/// \f[
///   A = \sum_i \mathrm{Interpolate}(\mathrm{low}_i, \mathrm{nominal}, \mathrm{high}_i).
/// \f]
/// \param name Name of the object.
/// \param title Title (for e.g. plotting)
/// \param nominal Nominal value of the function.
/// \param lowSet  Set of down variations.
/// \param highSet Set of up variations.
/// \param paramSet Parameters that control the interpolation.
/// \param takeOwnership If true, the PiecewiseInterpolation object will take ownership of the arguments in the low, high and parameter sets.
PiecewiseInterpolation::PiecewiseInterpolation(const char* name, const char* title, const RooAbsReal& nominal,
                      const RooArgList& lowSet, 
                      const RooArgList& highSet,
                      const RooArgList& paramSet,
                      Bool_t takeOwnership) :
  RooAbsReal(name, title),
  _nominal("!nominal","nominal value", this, (RooAbsReal&)nominal),
  _lowSet("!lowSet","low-side variation",this),
  _highSet("!highSet","high-side variation",this),
  _paramSet("!paramSet","high-side variation",this),
  _positiveDefinite(false)
 
{
  // KC: check both sizes
  if (lowSet.getSize() != highSet.getSize()) {
    coutE(InputArguments) << "PiecewiseInterpolation::ctor(" << GetName() << ") ERROR: input lists should be of equal length" << endl ;
    RooErrorHandler::softAbort() ;    
  }
 
  RooFIter inputIter1 = lowSet.fwdIterator() ;
  RooAbsArg* comp ;
  while((comp = inputIter1.next())) {
    if (!dynamic_cast<RooAbsReal*>(comp)) {
      coutE(InputArguments) << "PiecewiseInterpolation::ctor(" << GetName() << ") ERROR: component " << comp->GetName() 
             << " in first list is not of type RooAbsReal" << endl ;
      RooErrorHandler::softAbort() ;
    }
    _lowSet.add(*comp) ;
    if (takeOwnership) {
      _ownedList.addOwned(*comp) ;
    }
  }
 
 
  RooFIter inputIter2 = highSet.fwdIterator() ;
  while((comp = inputIter2.next())) {
    if (!dynamic_cast<RooAbsReal*>(comp)) {
      coutE(InputArguments) << "PiecewiseInterpolation::ctor(" << GetName() << ") ERROR: component " << comp->GetName() 
             << " in first list is not of type RooAbsReal" << endl ;
      RooErrorHandler::softAbort() ;
    }
    _highSet.add(*comp) ;
    if (takeOwnership) {
      _ownedList.addOwned(*comp) ;
    }
  }
 
 
  RooFIter inputIter3 = paramSet.fwdIterator() ;
  while((comp = inputIter3.next())) {
    if (!dynamic_cast<RooAbsReal*>(comp)) {
      coutE(InputArguments) << "PiecewiseInterpolation::ctor(" << GetName() << ") ERROR: component " << comp->GetName() 
             << " in first list is not of type RooAbsReal" << endl ;
      RooErrorHandler::softAbort() ;
    }
    _paramSet.add(*comp) ;
    if (takeOwnership) {
      _ownedList.addOwned(*comp) ;
    }
    _interpCode.push_back(0); // default code: linear interpolation
  }
 
  
  // Choose special integrator by default 
  specialIntegratorConfig(kTRUE)->method1D().setLabel("RooBinIntegrator") ;
  TRACE_CREATE
}
 
 
 
////////////////////////////////////////////////////////////////////////////////
/// Copy constructor
 
PiecewiseInterpolation::PiecewiseInterpolation(const PiecewiseInterpolation& other, const char* name) :
  RooAbsReal(other, name), 
  _nominal("!nominal",this,other._nominal),
  _lowSet("!lowSet",this,other._lowSet),
  _highSet("!highSet",this,other._highSet),
  _paramSet("!paramSet",this,other._paramSet),
  _positiveDefinite(other._positiveDefinite),
  _interpCode(other._interpCode)
{
  // Member _ownedList is intentionally not copy-constructed -- ownership is not transferred
  TRACE_CREATE
}
 
 
 
////////////////////////////////////////////////////////////////////////////////
/// Destructor
 
PiecewiseInterpolation::~PiecewiseInterpolation() 
{
  TRACE_DESTROY
}
 
 
 
 
////////////////////////////////////////////////////////////////////////////////
/// Calculate and return current value of self
 
Double_t PiecewiseInterpolation::evaluate() const 
{
  ///////////////////
  Double_t nominal = _nominal;
  Double_t sum(nominal) ;
 
  for (unsigned int i=0; i < _paramSet.size(); ++i) {
    auto param = static_cast<RooAbsReal*>(_paramSet.at(i));
    auto low   = static_cast<RooAbsReal*>(_lowSet.at(i));
    auto high  = static_cast<RooAbsReal*>(_highSet.at(i));
    Int_t icode = _interpCode[i] ;
 
    switch(icode) {
    case 0: {
      // piece-wise linear
      if(param->getVal()>0)
        sum +=  param->getVal()*(high->getVal() - nominal );
      else
        sum += param->getVal()*(nominal - low->getVal());
      break ;
    }
    case 1: {
      // pice-wise log
      if(param->getVal()>=0)
        sum *= pow(high->getVal()/nominal, +param->getVal());
      else
        sum *= pow(low->getVal()/nominal,  -param->getVal());
      break ;
    }
    case 2: {
      // parabolic with linear
      double a = 0.5*(high->getVal()+low->getVal())-nominal;
      double b = 0.5*(high->getVal()-low->getVal());
      double c = 0;
      if(param->getVal()>1 ){
        sum += (2*a+b)*(param->getVal()-1)+high->getVal()-nominal;
      } else if(param->getVal()<-1 ) {
        sum += -1*(2*a-b)*(param->getVal()+1)+low->getVal()-nominal;
      } else {
        sum +=  a*pow(param->getVal(),2) + b*param->getVal()+c;
      }
      break ;
    }
    case 3: {
      //parabolic version of log-normal
      double a = 0.5*(high->getVal()+low->getVal())-nominal;
      double b = 0.5*(high->getVal()-low->getVal());
      double c = 0;
      if(param->getVal()>1 ){
        sum += (2*a+b)*(param->getVal()-1)+high->getVal()-nominal;
      } else if(param->getVal()<-1 ) {
        sum += -1*(2*a-b)*(param->getVal()+1)+low->getVal()-nominal;
      } else {
        sum +=  a*pow(param->getVal(),2) + b*param->getVal()+c;
      }
      break ;
    }
    case 4: {
 
      // WVE ****************************************************************
      // WVE *** THIS CODE IS CRITICAL TO HISTFACTORY FIT CPU PERFORMANCE ***
      // WVE *** Do not modify unless you know what you are doing...      ***
      // WVE ****************************************************************
 
      double x  = param->getVal();      
      if (x>1) {
        sum += x*(high->getVal() - nominal );
      } else if (x<-1) {
        sum += x*(nominal - low->getVal());
      } else {
        double eps_plus = high->getVal() - nominal;
        double eps_minus = nominal - low->getVal();
        double S = 0.5 * (eps_plus + eps_minus);
        double A = 0.0625 * (eps_plus - eps_minus);
 
        //fcns+der+2nd_der are eq at bd
 
        double val = nominal + x * (S + x * A * ( 15 + x * x * (-10 + x * x * 3  ) ) ); 
 
 
        if (val < 0) val = 0;
        sum += val-nominal;
      }
      break ;
 
      // WVE ****************************************************************
    }
    case 5: {
 
      double x0 = 1.0;//boundary;
      double x  = param->getVal();
 
      if (x > x0 || x < -x0)
      {
        if(x>0)
          sum += x*(high->getVal() - nominal );
        else
          sum += x*(nominal - low->getVal());
      }
      else if (nominal != 0)
      {
        double eps_plus = high->getVal() - nominal;
        double eps_minus = nominal - low->getVal();
        double S = (eps_plus + eps_minus)/2;
        double A = (eps_plus - eps_minus)/2;
 
        //fcns+der are eq at bd
        double a = S;
        double b = 3*A/(2*x0);
        //double c = 0;
        double d = -A/(2*x0*x0*x0);
 
        double val = nominal + a*x + b*pow(x, 2) + 0/*c*pow(x, 3)*/ + d*pow(x, 4);
        if (val < 0) val = 0;
 
        //cout << "Using interp code 5, val = " << val << endl;
 
        sum += val-nominal;
      }
      break ;
    }
    default: {
      coutE(InputArguments) << "PiecewiseInterpolation::evaluate ERROR:  " << param->GetName() 
                 << " with unknown interpolation code" << icode << endl ;
      break ;
    }
    }
  }
 
  if(_positiveDefinite && (sum<0)){
    sum = 0;
    //     cout <<"sum < 0 forcing  positive definite"<<endl;
    //     int code = 1;
    //     RooArgSet* myset = new RooArgSet();
    //     cout << "integral = " << analyticalIntegralWN(code, myset) << endl;
  } else if(sum<0){
    cxcoutD(Tracing) <<"PiecewiseInterpolation::evaluate -  sum < 0, not forcing positive definite"<<endl;
  }
  return sum;
 
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// Interpolate between input distributions for all values of the observable in `evalData`.
/// \param[in/out] evalData Struct holding spans pointing to input data. The results of this function will be stored here.
/// \param[in] normSet Arguments to normalise over.
RooSpan<double> PiecewiseInterpolation::evaluateSpan(RooBatchCompute::RunContext& evalData, const RooArgSet* normSet) const {
  auto nominal = _nominal->getValues(evalData, normSet);
  auto sum = evalData.makeBatch(this, nominal.size());
  std::copy(nominal.begin(), nominal.end(), sum.begin());
 
  for (unsigned int i=0; i < _paramSet.size(); ++i) {
    const double param = static_cast<RooAbsReal*>(_paramSet.at(i))->getVal();
    auto low   = static_cast<RooAbsReal*>(_lowSet.at(i) )->getValues(evalData, normSet);
    auto high  = static_cast<RooAbsReal*>(_highSet.at(i))->getValues(evalData, normSet);
    const int icode = _interpCode[i];
 
    switch(icode) {
    case 0: {
      // piece-wise linear
      for (unsigned int j=0; j < nominal.size(); ++j) {
        if(param >0)
          sum[j] += param * (high[j]    - nominal[j]);
        else
          sum[j] += param * (nominal[j] - low[j]    );
      }
      break;
    }
    case 1: {
      // pice-wise log
      for (unsigned int j=0; j < nominal.size(); ++j) {
        if(param >=0)
          sum[j] *= pow(high[j]/ nominal[j], +param);
        else
          sum[j] *= pow(low[j] / nominal[j], -param);
      }
      break;
    }
    case 2:
      // parabolic with linear
      for (unsigned int j=0; j < nominal.size(); ++j) {
        const double a = 0.5*(high[j]+low[j])-nominal[j];
        const double b = 0.5*(high[j]-low[j]);
        const double c = 0;
        if (param > 1.) {
          sum[j] += (2*a+b)*(param -1)+high[j]-nominal[j];
        } else if (param < -1.) {
          sum[j] += -1*(2*a-b)*(param +1)+low[j]-nominal[j];
        } else {
          sum[j] +=  a*pow(param ,2) + b*param +c;
        }
      }
      break;
    case 3: {
      //parabolic version of log-normal
      for (unsigned int j=0; j < nominal.size(); ++j) {
        const double a = 0.5*(high[j]+low[j])-nominal[j];
        const double b = 0.5*(high[j]-low[j]);
        const double c = 0;
        if (param > 1.) {
          sum[j] += (2*a+b)*(param -1)+high[j]-nominal[j];
        } else if (param < -1.) {
          sum[j] += -1*(2*a-b)*(param +1)+low[j]-nominal[j];
        } else {
          sum[j] +=  a*pow(param ,2) + b*param +c;
        }
      }
      break;
    }
    case 4:
      for (unsigned int j=0; j < nominal.size(); ++j) {
        const double x  = param;
        if (x > 1.) {
          sum[j] += x * (high[j]    - nominal[j]);
        } else if (x < -1.) {
          sum[j] += x * (nominal[j] - low[j]);
        } else {
          const double eps_plus = high[j] - nominal[j];
          const double eps_minus = nominal[j] - low[j];
          const double S = 0.5 * (eps_plus + eps_minus);
          const double A = 0.0625 * (eps_plus - eps_minus);
 
          double val = nominal[j] + x * (S + x * A * ( 15. + x * x * (-10. + x * x * 3.  ) ) );
 
          if (val < 0.) val = 0.;
          sum[j] += val - nominal[j];
        }
      }
      break;
    case 5:
      for (unsigned int j=0; j < nominal.size(); ++j) {
        if (param > 1. || param < -1.) {
          if(param>0)
            sum[j] += param * (high[j]    - nominal[j]);
          else
            sum[j] += param * (nominal[j] - low[j]    );
        } else if (nominal[j] != 0) {
          const double eps_plus = high[j] - nominal[j];
          const double eps_minus = nominal[j] - low[j];
          const double S = (eps_plus + eps_minus)/2;
          const double A = (eps_plus - eps_minus)/2;
 
          //fcns+der are eq at bd
          const double a = S;
          const double b = 3*A/(2*1.);
          //double c = 0;
          const double d = -A/(2*1.*1.*1.);
 
          double val = nominal[j] + a * param + b * pow(param, 2) + d * pow(param, 4);
          if (val < 0.) val = 0.;
 
          sum[j] += val - nominal[j];
        }
      }
      break;
    default:
      coutE(InputArguments) << "PiecewiseInterpolation::evaluateSpan(): " << _paramSet[i].GetName()
                       << " with unknown interpolation code" << icode << std::endl;
      throw std::invalid_argument("PiecewiseInterpolation::evaluateSpan() got invalid interpolation code " + std::to_string(icode));
      break;
    }
  }
 
  if (_positiveDefinite) {
    for (double& val : sum) {
      if (val < 0.)
        val = 0.;
    }
  }
 
  return sum;
}
 
////////////////////////////////////////////////////////////////////////////////
 
Bool_t PiecewiseInterpolation::setBinIntegrator(RooArgSet& allVars) 
{
  if(allVars.getSize()==1){
    RooAbsReal* temp = const_cast<PiecewiseInterpolation*>(this);
    temp->specialIntegratorConfig(kTRUE)->method1D().setLabel("RooBinIntegrator")  ;
    int nbins = ((RooRealVar*) allVars.first())->numBins();
    temp->specialIntegratorConfig(kTRUE)->getConfigSection("RooBinIntegrator").setRealValue("numBins",nbins);
    return true;
  }else{
    cout << "Currently BinIntegrator only knows how to deal with 1-d "<<endl;
    return false;
  }
  return false;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Advertise that all integrals can be handled internally.
 
Int_t PiecewiseInterpolation::getAnalyticalIntegralWN(RooArgSet& allVars, RooArgSet& analVars, 
                        const RooArgSet* normSet, const char* /*rangeName*/) const 
{
  /*
  cout << "---------------------------\nin PiecewiseInterpolation get analytic integral " <<endl;
  cout << "all vars = "<<endl;
  allVars.Print("v");
  cout << "anal vars = "<<endl;
  analVars.Print("v");
  cout << "normset vars = "<<endl;
  if(normSet2)
    normSet2->Print("v");
  */
 
 
  // Handle trivial no-integration scenario
  if (allVars.getSize()==0) return 0 ;
  if (_forceNumInt) return 0 ;
 
 
  // Force using numeric integration
  // use special numeric integrator  
  return 0;
  
 
  // KC: check if interCode=0 for all 
  RooFIter paramIterExtra(_paramSet.fwdIterator()) ;
  int i=0;
  while( paramIterExtra.next() ) {
    if(!_interpCode.empty() && _interpCode[i]!=0){
      // can't factorize integral
      cout <<"can't factorize integral"<<endl;
      return 0;
    }
    ++i;
  }
 
  // Select subset of allVars that are actual dependents
  analVars.add(allVars) ;
  //  RooArgSet* normSet = normSet2 ? getObservables(normSet2) : 0 ;
  //  RooArgSet* normSet = getObservables();
  //  RooArgSet* normSet = 0;
 
 
  // Check if this configuration was created before
  Int_t sterileIdx(-1) ;
  CacheElem* cache = (CacheElem*) _normIntMgr.getObj(normSet,&analVars,&sterileIdx) ;
  if (cache) {
    return _normIntMgr.lastIndex()+1 ;
  }
  
  // Create new cache element
  cache = new CacheElem ;
 
  // Make list of function projection and normalization integrals 
  RooAbsReal *func ;
  //  const RooArgSet* nset = _paramList.nset() ;
 
  // do nominal
  func = (RooAbsReal*)(&_nominal.arg()) ;
  RooAbsReal* funcInt = func->createIntegral(analVars) ;
  cache->_funcIntList.addOwned(*funcInt) ;
 
  // do variations
  RooFIter lowIter(_lowSet.fwdIterator()) ;
  RooFIter highIter(_highSet.fwdIterator()) ;
  RooFIter paramIter(_paramSet.fwdIterator()) ;
 
  //  int i=0;
  i=0;
  while(paramIter.next() ) {
    func = (RooAbsReal*)lowIter.next() ;
    funcInt = func->createIntegral(analVars) ;
    cache->_lowIntList.addOwned(*funcInt) ;
 
    func = (RooAbsReal*)highIter.next() ;
    funcInt = func->createIntegral(analVars) ;
    cache->_highIntList.addOwned(*funcInt) ;
    ++i;
  }
 
  // Store cache element
  Int_t code = _normIntMgr.setObj(normSet,&analVars,(RooAbsCacheElement*)cache,0) ;
 
  return code+1 ; 
}
 
 
 
 
////////////////////////////////////////////////////////////////////////////////
/// Implement analytical integrations by doing appropriate weighting from  component integrals
/// functions to integrators of components
 
Double_t PiecewiseInterpolation::analyticalIntegralWN(Int_t code, const RooArgSet* /*normSet2*/,const char* /*rangeName*/) const 
{
  /*
  cout <<"Enter analytic Integral"<<endl;
  printDirty(true);
  //  _nominal.arg().setDirtyInhibit(kTRUE) ;
  _nominal.arg().setShapeDirty() ;
  RooAbsReal* temp ;
  RooFIter lowIter(_lowSet.fwdIterator()) ;
  while((temp=(RooAbsReal*)lowIter.next())) {
    //    temp->setDirtyInhibit(kTRUE) ;
    temp->setShapeDirty() ;
  }
  RooFIter highIter(_highSet.fwdIterator()) ;
  while((temp=(RooAbsReal*)highIter.next())) {
    //    temp->setDirtyInhibit(kTRUE) ;
    temp->setShapeDirty() ;
  }
  */
 
  /*
  RooAbsArg::setDirtyInhibit(kTRUE);
  printDirty(true);
  cout <<"done setting dirty inhibit = true"<<endl;
 
  // old integral, only works for linear and not positive definite
  CacheElem* cache = (CacheElem*) _normIntMgr.getObjByIndex(code-1) ;
 
  
 std::unique_ptr<RooArgSet> vars2( getParameters(RooArgSet()) );
 std::unique_ptr<RooArgSet> iset(  _normIntMgr.nameSet2ByIndex(code-1)->select(*vars2) );            
 cout <<"iset = "<<endl;
 iset->Print("v");
 
  double sum = 0;
  RooArgSet* vars = getVariables();
  vars->remove(_paramSet);
  _paramSet.Print("v");
  vars->Print("v");
  if(vars->getSize()==1){
    RooRealVar* obs = (RooRealVar*) vars->first();
    for(int i=0; i<obs->numBins(); ++i){
      obs->setVal( obs->getMin() + (.5+i)*(obs->getMax()-obs->getMin())/obs->numBins());
      sum+=evaluate()*(obs->getMax()-obs->getMin())/obs->numBins();
      cout << "obs = " << obs->getVal() << " sum = " << sum << endl;
    }
  } else{
    cout <<"only know how to deal with 1 observable right now"<<endl;
  }
  */
 
  /*
  _nominal.arg().setDirtyInhibit(kFALSE) ;
  RooFIter lowIter2(_lowSet.fwdIterator()) ;
  while((temp=(RooAbsReal*)lowIter2.next())) {
    temp->setDirtyInhibit(kFALSE) ;
  }
  RooFIter highIter2(_highSet.fwdIterator()) ;
  while((temp=(RooAbsReal*)highIter2.next())) {
    temp->setDirtyInhibit(kFALSE) ;
  }
  */
  
  /*
  RooAbsArg::setDirtyInhibit(kFALSE);
  printDirty(true);
  cout <<"done"<<endl;
  cout << "sum = " <<sum<<endl;
  //return sum;
  */  
 
  // old integral, only works for linear and not positive definite
  CacheElem* cache = (CacheElem*) _normIntMgr.getObjByIndex(code-1) ;
  if( cache==NULL ) {
    std::cout << "Error: Cache Element is NULL" << std::endl;
    throw std::exception();
  }
 
  // old integral, only works for linear and not positive definite
  RooFIter funcIntIter = cache->_funcIntList.fwdIterator() ;
  RooFIter lowIntIter = cache->_lowIntList.fwdIterator() ;
  RooFIter highIntIter = cache->_highIntList.fwdIterator() ;
  RooAbsReal *funcInt(0), *low(0), *high(0), *param(0) ;
  Double_t value(0) ;
  Double_t nominal(0);
 
  // get nominal 
  int i=0;
  while(( funcInt = (RooAbsReal*)funcIntIter.next())) {
    value += funcInt->getVal() ;
    nominal = value;
    i++;
  }
  if(i==0 || i>1) { cout << "problem, wrong number of nominal functions"<<endl; }
 
  // now get low/high variations
  i = 0;
  RooFIter paramIter(_paramSet.fwdIterator()) ;
 
  // KC: old interp code with new iterator
  while( (param=(RooAbsReal*)paramIter.next()) ) {
    low = (RooAbsReal*)lowIntIter.next() ;
    high = (RooAbsReal*)highIntIter.next() ;
    
    if(param->getVal()>0) {
      value += param->getVal()*(high->getVal() - nominal );
    } else {
      value += param->getVal()*(nominal - low->getVal());
    }
    ++i;
  }
 
  /* // MB : old bit of interpolation code
  while( (param=(RooAbsReal*)_paramIter->Next()) ) {
    low = (RooAbsReal*)lowIntIter->Next() ;
    high = (RooAbsReal*)highIntIter->Next() ;
    
    if(param->getVal()>0) {
      value += param->getVal()*(high->getVal() - nominal );
    } else {
      value += param->getVal()*(nominal - low->getVal());
    }
    ++i;
  }
  */
 
  /* KC: the code below is wrong.  Can't pull out a constant change to a non-linear shape deformation.
  while( (param=(RooAbsReal*)paramIter.next()) ) {
    low = (RooAbsReal*)lowIntIter.next() ;
    high = (RooAbsReal*)highIntIter.next() ;
 
    if(_interpCode.empty() || _interpCode.at(i)==0){
      // piece-wise linear
      if(param->getVal()>0)
   value +=  param->getVal()*(high->getVal() - nominal );
      else
   value += param->getVal()*(nominal - low->getVal());
    } else if(_interpCode.at(i)==1){
      // pice-wise log
      if(param->getVal()>=0)
   value *= pow(high->getVal()/nominal, +param->getVal());
      else
   value *= pow(low->getVal()/nominal,  -param->getVal());
    } else if(_interpCode.at(i)==2){
      // parabolic with linear
      double a = 0.5*(high->getVal()+low->getVal())-nominal;
      double b = 0.5*(high->getVal()-low->getVal());
      double c = 0;
      if(param->getVal()>1 ){
   value += (2*a+b)*(param->getVal()-1)+high->getVal()-nominal;
      } else if(param->getVal()<-1 ) {
   value += -1*(2*a-b)*(param->getVal()+1)+low->getVal()-nominal;
      } else {
   value +=  a*pow(param->getVal(),2) + b*param->getVal()+c;
      }
    } else if(_interpCode.at(i)==3){
      //parabolic version of log-normal
      double a = 0.5*(high->getVal()+low->getVal())-nominal;
      double b = 0.5*(high->getVal()-low->getVal());
      double c = 0;
      if(param->getVal()>1 ){
   value += (2*a+b)*(param->getVal()-1)+high->getVal()-nominal;
      } else if(param->getVal()<-1 ) {
   value += -1*(2*a-b)*(param->getVal()+1)+low->getVal()-nominal;
      } else {
   value +=  a*pow(param->getVal(),2) + b*param->getVal()+c;
      }
   
    } else {
      coutE(InputArguments) << "PiecewiseInterpolation::analyticalIntegralWN ERROR:  " << param->GetName() 
             << " with unknown interpolation code" << endl ;
    }
    ++i;
  }
  */
 
  //  cout << "value = " << value <<endl;
  return value;
}
 
 
////////////////////////////////////////////////////////////////////////////////
 
void PiecewiseInterpolation::setInterpCode(RooAbsReal& param, int code){
  int index = _paramSet.index(&param);
  if(index<0){
      coutE(InputArguments) << "PiecewiseInterpolation::setInterpCode ERROR:  " << param.GetName() 
             << " is not in list" << endl ;
  } else {
      coutW(InputArguments) << "PiecewiseInterpolation::setInterpCode :  " << param.GetName() 
             << " is now " << code << endl ;
    _interpCode.at(index) = code;
  }
}
 
 
////////////////////////////////////////////////////////////////////////////////
 
void PiecewiseInterpolation::setAllInterpCodes(int code){
  for(unsigned int i=0; i<_interpCode.size(); ++i){
    _interpCode.at(i) = code;
  }
}
 
 
////////////////////////////////////////////////////////////////////////////////
 
void PiecewiseInterpolation::printAllInterpCodes(){
  for(unsigned int i=0; i<_interpCode.size(); ++i){
    coutI(InputArguments) <<"interp code for " << _paramSet.at(i)->GetName() << " = " << _interpCode.at(i) <<endl;
  }
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// WVE note: assumes nominal and alternates have identical structure, must add explicit check
 
std::list<Double_t>* PiecewiseInterpolation::binBoundaries(RooAbsRealLValue& obs, Double_t xlo, Double_t xhi) const 
{
  return _nominal.arg().binBoundaries(obs,xlo,xhi) ;  
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// WVE note: assumes nominal and alternates have identical structure, must add explicit check
 
Bool_t PiecewiseInterpolation::isBinnedDistribution(const RooArgSet& obs) const 
{
  return _nominal.arg().isBinnedDistribution(obs) ;
}
 
 
 
////////////////////////////////////////////////////////////////////////////////
 
std::list<Double_t>* PiecewiseInterpolation::plotSamplingHint(RooAbsRealLValue& obs, Double_t xlo, Double_t xhi) const 
{
  return _nominal.arg().plotSamplingHint(obs,xlo,xhi) ;  
}
 
////////////////////////////////////////////////////////////////////////////////
/// Stream an object of class PiecewiseInterpolation.
 
void PiecewiseInterpolation::Streamer(TBuffer &R__b)
{
   if (R__b.IsReading()) {
      R__b.ReadClassBuffer(PiecewiseInterpolation::Class(),this);
      specialIntegratorConfig(kTRUE)->method1D().setLabel("RooBinIntegrator") ;      
      if (_interpCode.empty()) _interpCode.resize(_paramSet.getSize());
   } else {
      R__b.WriteClassBuffer(PiecewiseInterpolation::Class(),this);
   }
}
 
 
/*
////////////////////////////////////////////////////////////////////////////////
/// Customized printing of arguments of a PiecewiseInterpolation to more intuitively reflect the contents of the
/// product operator construction
 
void PiecewiseInterpolation::printMetaArgs(ostream& os) const 
{
  _lowIter->Reset() ;
  if (_highIter) {
    _highIter->Reset() ;
  }
 
  Bool_t first(kTRUE) ;
    
  RooAbsArg* arg1, *arg2 ;
  if (_highSet.getSize()!=0) { 
 
    while((arg1=(RooAbsArg*)_lowIter->Next())) {
      if (!first) {
   os << " + " ;
      } else {
   first = kFALSE ;
      }
      arg2=(RooAbsArg*)_highIter->Next() ;
      os << arg1->GetName() << " * " << arg2->GetName() ;
    }
 
  } else {
    
    while((arg1=(RooAbsArg*)_lowIter->Next())) {
      if (!first) {
   os << " + " ;
      } else {
   first = kFALSE ;
      }
      os << arg1->GetName() ; 
    }  
 
  }
 
  os << " " ;    
}
 
*/