#include "RooFit.h"
#include "RooMsgService.h"
#include "TIterator.h"
#include "TIterator.h"
#include "TList.h"
#include "RooAddModel.h"
#include "RooDataSet.h"
#include "RooRealProxy.h"
#include "RooPlot.h"
#include "RooRealVar.h"
#include "RooAddGenContext.h"
#include "RooRealConstant.h"
#include "RooNameReg.h"
#include "RooMsgService.h"
#include "Riostream.h"
ClassImp(RooAddModel)
;
RooAddModel::RooAddModel() :
_refCoefNorm("!refCoefNorm","Reference coefficient normalization set",this,kFALSE,kFALSE),
_refCoefRangeName(0),
_codeReg(10),
_snormList(0)
{
_pdfIter = _pdfList.createIterator() ;
_coefIter = _coefList.createIterator() ;
_coefCache = new Double_t[10] ;
_coefErrCount = _errorCount ;
}
RooAddModel::RooAddModel(const char *name, const char *title, const RooArgList& inPdfList, const RooArgList& inCoefList, Bool_t ownPdfList) :
RooResolutionModel(name,title,((RooResolutionModel*)inPdfList.at(0))->convVar()),
_refCoefNorm("!refCoefNorm","Reference coefficient normalization set",this,kFALSE,kFALSE),
_refCoefRangeName(0),
_projectCoefs(kFALSE),
_projCacheMgr(this,10),
_intCacheMgr(this,10),
_codeReg(10),
_pdfList("!pdfs","List of PDFs",this),
_coefList("!coefficients","List of coefficients",this),
_haveLastCoef(kFALSE),
_allExtendable(kFALSE)
{
if (inPdfList.getSize()>inCoefList.getSize()+1) {
coutE(InputArguments) << "RooAddModel::RooAddModel(" << GetName()
<< ") number of pdfs and coefficients inconsistent, must have Npdf=Ncoef or Npdf=Ncoef+1" << endl ;
assert(0) ;
}
_pdfIter = _pdfList.createIterator() ;
_coefIter = _coefList.createIterator() ;
TIterator* pdfIter = inPdfList.createIterator() ;
TIterator* coefIter = inCoefList.createIterator() ;
RooAbsPdf* pdf ;
RooAbsReal* coef ;
while((coef = (RooAbsPdf*)coefIter->Next())) {
pdf = (RooAbsPdf*) pdfIter->Next() ;
if (!pdf) {
coutE(InputArguments) << "RooAddModel::RooAddModel(" << GetName()
<< ") number of pdfs and coefficients inconsistent, must have Npdf=Ncoef or Npdf=Ncoef+1" << endl ;
assert(0) ;
}
if (!dynamic_cast<RooAbsReal*>(coef)) {
coutE(InputArguments) << "RooAddModel::RooAddModel(" << GetName() << ") coefficient " << coef->GetName() << " is not of type RooAbsReal, ignored" << endl ;
continue ;
}
if (!dynamic_cast<RooAbsReal*>(pdf)) {
coutE(InputArguments) << "RooAddModel::RooAddModel(" << GetName() << ") pdf " << pdf->GetName() << " is not of type RooAbsPdf, ignored" << endl ;
continue ;
}
_pdfList.add(*pdf) ;
_coefList.add(*coef) ;
}
pdf = (RooAbsPdf*) pdfIter->Next() ;
if (pdf) {
if (!dynamic_cast<RooAbsReal*>(pdf)) {
coutE(InputArguments) << "RooAddModel::RooAddModel(" << GetName() << ") last pdf " << coef->GetName() << " is not of type RooAbsPdf, fatal error" << endl ;
assert(0) ;
}
_pdfList.add(*pdf) ;
} else {
_haveLastCoef=kTRUE ;
}
delete pdfIter ;
delete coefIter ;
_coefCache = new Double_t[_pdfList.getSize()] ;
_coefErrCount = _errorCount ;
if (ownPdfList) {
_ownedComps.addOwned(_pdfList) ;
}
}
RooAddModel::RooAddModel(const RooAddModel& other, const char* name) :
RooResolutionModel(other,name),
_refCoefNorm("!refCoefNorm",this,other._refCoefNorm),
_refCoefRangeName((TNamed*)other._refCoefRangeName),
_projectCoefs(other._projectCoefs),
_projCacheMgr(other._projCacheMgr,this),
_intCacheMgr(other._intCacheMgr,this),
_codeReg(other._codeReg),
_pdfList("!pdfs",this,other._pdfList),
_coefList("!coefficients",this,other._coefList),
_haveLastCoef(other._haveLastCoef),
_allExtendable(other._allExtendable)
{
_pdfIter = _pdfList.createIterator() ;
_coefIter = _coefList.createIterator() ;
_coefCache = new Double_t[_pdfList.getSize()] ;
_coefErrCount = _errorCount ;
}
RooAddModel::~RooAddModel()
{
delete _pdfIter ;
delete _coefIter ;
if (_coefCache) delete[] _coefCache ;
}
void RooAddModel::fixCoefNormalization(const RooArgSet& refCoefNorm)
{
if (refCoefNorm.getSize()==0) {
_projectCoefs = kFALSE ;
return ;
}
_projectCoefs = kTRUE ;
_refCoefNorm.removeAll() ;
_refCoefNorm.add(refCoefNorm) ;
_projCacheMgr.reset() ;
}
void RooAddModel::fixCoefRange(const char* rangeName)
{
_refCoefRangeName = (TNamed*)RooNameReg::ptr(rangeName) ;
if (_refCoefRangeName) _projectCoefs = kTRUE ;
}
RooResolutionModel* RooAddModel::convolution(RooFormulaVar* inBasis, RooAbsArg* owner) const
{
if (inBasis->findServer(0) != x.absArg()) {
coutE(InputArguments) << "RooAddModel::convolution(" << GetName()
<< ") convolution parameter of basis function and PDF don't match" << endl ;
ccoutE(InputArguments) << "basis->findServer(0) = " << inBasis->findServer(0) << " " << inBasis->findServer(0)->GetName() << endl ;
ccoutE(InputArguments) << "x.absArg() = " << x.absArg() << " " << x.absArg()->GetName() << endl ;
inBasis->Print("v") ;
return 0 ;
}
TString newName(GetName()) ;
newName.Append("_conv_") ;
newName.Append(inBasis->GetName()) ;
newName.Append("_[") ;
newName.Append(owner->GetName()) ;
newName.Append("]") ;
TString newTitle(GetTitle()) ;
newTitle.Append(" convoluted with basis function ") ;
newTitle.Append(inBasis->GetName()) ;
_pdfIter->Reset() ;
RooResolutionModel* model ;
RooArgList modelList ;
while((model = (RooResolutionModel*)_pdfIter->Next())) {
RooResolutionModel* conv = model->convolution(inBasis,owner) ;
modelList.add(*conv) ;
}
_coefIter->Reset() ;
RooAbsReal* coef ;
RooArgList theCoefList ;
while((coef = (RooAbsReal*)_coefIter->Next())) {
theCoefList.add(*coef) ;
}
RooAddModel* convSum = new RooAddModel(newName,newTitle,modelList,theCoefList,kTRUE) ;
convSum->changeBasis(inBasis) ;
return convSum ;
}
Int_t RooAddModel::basisCode(const char* name) const
{
TIterator* mIter = _pdfList.createIterator() ;
RooResolutionModel* model ;
Bool_t first(kTRUE), code(0) ;
while((model = (RooResolutionModel*)mIter->Next())) {
Int_t subCode = model->basisCode(name) ;
if (first) {
code = subCode ;
} else if (subCode==0) {
code = 0 ;
}
}
delete mIter ;
return code ;
}
RooAddModel::CacheElem* RooAddModel::getProjCache(const RooArgSet* nset, const RooArgSet* iset, const char* rangeName) const
{
CacheElem* cache = (CacheElem*) _projCacheMgr.getObj(nset,iset,0,RooNameReg::ptr(rangeName)) ;
if (cache) {
return cache ;
}
cache = new CacheElem ;
RooArgSet *fullDepList = getObservables(nset) ;
if (iset) {
fullDepList->remove(*iset,kTRUE,kTRUE) ;
}
_pdfIter->Reset() ;
_coefIter->Reset() ;
RooAbsPdf* pdf ;
RooAbsReal* coef ;
while((pdf=(RooAbsPdf*)_pdfIter->Next())) {
coef=(RooAbsPdf*)_coefIter->Next() ;
RooArgSet supNSet(*fullDepList) ;
RooArgSet* pdfDeps = pdf->getObservables(nset) ;
if (pdfDeps) {
supNSet.remove(*pdfDeps,kTRUE,kTRUE) ;
delete pdfDeps ;
}
RooArgSet* coefDeps = coef ? coef->getObservables(nset) : 0 ;
if (coefDeps) {
supNSet.remove(*coefDeps,kTRUE,kTRUE) ;
delete coefDeps ;
}
RooAbsReal* snorm ;
TString name(GetName()) ;
name.Append("_") ;
name.Append(pdf->GetName()) ;
name.Append("_SupNorm") ;
if (supNSet.getSize()>0) {
snorm = new RooRealIntegral(name,"Supplemental normalization integral",RooRealConstant::value(1.0),supNSet) ;
} else {
snorm = new RooRealVar(name,"Unit Supplemental normalization integral",1.0) ;
}
cache->_suppNormList.addOwned(*snorm) ;
}
delete fullDepList ;
if (_verboseEval>1) {
cxcoutD(Caching) << "RooAddModel::syncSuppNormList(" << GetName() << ") synching supplemental normalization list for norm" << (nset?*nset:RooArgSet()) << endl ;
if (dologD(Caching)) {
cache->_suppNormList.Print("v") ;
}
}
if (!_projectCoefs || _basis!=0 ) {
_projCacheMgr.setObj(nset,iset,cache,RooNameReg::ptr(rangeName)) ;
return cache ;
}
RooArgSet* nset2 = nset ? getObservables(nset) : new RooArgSet() ;
if (!nset2->equals(_refCoefNorm) || _refCoefRangeName !=0 || rangeName !=0 ) {
coutI(Caching) << "RooAddModel::syncCoefProjList(" << GetName() << ") creating coefficient projection integrals" << endl ;
ccoutI(Caching) << " from current normalization: " ; nset2->Print("1") ;
ccoutI(Caching) << " with current range: " << (rangeName?rangeName:"<none>") << endl ;
ccoutI(Caching) << " to reference normalization: " ; _refCoefNorm.Print("1") ;
ccoutI(Caching) << " with reference range: " << (_refCoefRangeName?RooNameReg::str(_refCoefRangeName):"<none>") << endl ;
_pdfIter->Reset() ;
RooAbsPdf* thePdf ;
while((thePdf=(RooAbsPdf*)_pdfIter->Next())) {
RooAbsReal* pdfProj ;
if (!nset2->equals(_refCoefNorm)) {
pdfProj = thePdf->createIntegral(*nset2,_refCoefNorm) ;
pdfProj->setOperMode(operMode()) ;
} else {
TString name(GetName()) ;
name.Append("_") ;
name.Append(thePdf->GetName()) ;
name.Append("_ProjectNorm") ;
pdfProj = new RooRealVar(name,"Unit Projection normalization integral",1.0) ;
}
cache->_projList.addOwned(*pdfProj) ;
RooArgSet supNormSet(_refCoefNorm) ;
RooArgSet* deps = thePdf->getParameters(RooArgSet()) ;
supNormSet.remove(*deps,kTRUE,kTRUE) ;
delete deps ;
RooAbsReal* snorm ;
TString name(GetName()) ;
name.Append("_") ;
name.Append(thePdf->GetName()) ;
name.Append("_ProjSupNorm") ;
if (supNormSet.getSize()>0) {
snorm = new RooRealIntegral(name,"Projection Supplemental normalization integral",
RooRealConstant::value(1.0),supNormSet) ;
} else {
snorm = new RooRealVar(name,"Unit Projection Supplemental normalization integral",1.0) ;
}
cache->_suppProjList.addOwned(*snorm) ;
RooAbsReal* rangeProj1 ;
if (_refCoefRangeName && _refCoefNorm.getSize()>0) {
rangeProj1 = thePdf->createIntegral(_refCoefNorm,_refCoefNorm,RooNameReg::str(_refCoefRangeName)) ;
rangeProj1->setOperMode(operMode()) ;
} else {
TString theName(GetName()) ;
theName.Append("_") ;
theName.Append(thePdf->GetName()) ;
theName.Append("_RangeNorm1") ;
rangeProj1 = new RooRealVar(theName,"Unit range normalization integral",1.0) ;
}
cache->_refRangeProjList.addOwned(*rangeProj1) ;
RooAbsReal* rangeProj2 ;
if (rangeName && _refCoefNorm.getSize()>0) {
rangeProj2 = thePdf->createIntegral(_refCoefNorm,_refCoefNorm,rangeName) ;
rangeProj2->setOperMode(operMode()) ;
} else {
TString theName(GetName()) ;
theName.Append("_") ;
theName.Append(thePdf->GetName()) ;
theName.Append("_RangeNorm2") ;
rangeProj2 = new RooRealVar(theName,"Unit range normalization integral",1.0) ;
}
cache->_rangeProjList.addOwned(*rangeProj2) ;
}
}
delete nset2 ;
_projCacheMgr.setObj(nset,iset,cache,RooNameReg::ptr(rangeName)) ;
return cache ;
}
void RooAddModel::updateCoefficients(CacheElem& cache, const RooArgSet* nset) const
{
Int_t i ;
if (_allExtendable) {
Double_t coefSum(0) ;
for (i=0 ; i<_pdfList.getSize() ; i++) {
_coefCache[i] = ((RooAbsPdf*)_pdfList.at(i))->expectedEvents(_refCoefNorm.getSize()>0?&_refCoefNorm:nset) ;
coefSum += _coefCache[i] ;
}
if (coefSum==0.) {
coutW(Eval) << "RooAddModel::updateCoefCache(" << GetName() << ") WARNING: total number of expected events is 0" << endl ;
} else {
for (i=0 ; i<_pdfList.getSize() ; i++) {
_coefCache[i] /= coefSum ;
}
}
} else {
if (_haveLastCoef) {
Double_t coefSum(0) ;
for (i=0 ; i<_coefList.getSize() ; i++) {
_coefCache[i] = ((RooAbsPdf*)_coefList.at(i))->getVal(nset) ;
coefSum += _coefCache[i] ;
}
for (i=0 ; i<_coefList.getSize() ; i++) {
_coefCache[i] /= coefSum ;
}
} else {
Double_t lastCoef(1) ;
for (i=0 ; i<_coefList.getSize() ; i++) {
_coefCache[i] = ((RooAbsPdf*)_coefList.at(i))->getVal(nset) ;
cxcoutD(Caching) << "SYNC: orig coef[" << i << "] = " << _coefCache[i] << endl ;
lastCoef -= _coefCache[i] ;
}
_coefCache[_coefList.getSize()] = lastCoef ;
cxcoutD(Caching) << "SYNC: orig coef[" << _coefList.getSize() << "] = " << _coefCache[_coefList.getSize()] << endl ;
if ((lastCoef<-1e-05 || (lastCoef-1)>1e-5) && _coefErrCount-->0) {
coutW(Eval) << "RooAddModel::updateCoefCache(" << GetName()
<< " WARNING: sum of PDF coefficients not in range [0-1], value="
<< 1-lastCoef << endl ;
if (_coefErrCount==0) {
coutW(Eval) << " (no more will be printed)" << endl ;
}
}
}
}
if ((!_projectCoefs) || cache._projList.getSize()==0) {
return ;
}
Double_t coefSum(0) ;
for (i=0 ; i<_pdfList.getSize() ; i++) {
RooAbsPdf::globalSelectComp(kTRUE) ;
RooAbsReal* pp = ((RooAbsReal*)cache._projList.at(i)) ;
RooAbsReal* sn = ((RooAbsReal*)cache._suppProjList.at(i)) ;
RooAbsReal* r1 = ((RooAbsReal*)cache._refRangeProjList.at(i)) ;
RooAbsReal* r2 = ((RooAbsReal*)cache._rangeProjList.at(i)) ;
if (dologD(Eval)) {
cxcoutD(Eval) << "pp = " << pp->GetName() << endl
<< "sn = " << sn->GetName() << endl
<< "r1 = " << r1->GetName() << endl
<< "r2 = " << r2->GetName() << endl ;
r1->printStream(ccoutD(Eval),kName|kArgs|kValue,kSingleLine) ;
r1->printCompactTree(ccoutD(Eval)) ;
}
Double_t proj = pp->getVal()/sn->getVal()*(r2->getVal()/r1->getVal()) ;
RooAbsPdf::globalSelectComp(kFALSE) ;
_coefCache[i] *= proj ;
coefSum += _coefCache[i] ;
}
for (i=0 ; i<_pdfList.getSize() ; i++) {
_coefCache[i] /= coefSum ;
}
}
Double_t RooAddModel::evaluate() const
{
const RooArgSet* nset = _normSet ;
CacheElem* cache = getProjCache(nset) ;
updateCoefficients(*cache,nset) ;
_pdfIter->Reset() ;
_coefIter->Reset() ;
RooAbsPdf* pdf ;
Double_t snormVal ;
Double_t value(0) ;
Int_t i(0) ;
while((pdf = (RooAbsPdf*)_pdfIter->Next())) {
if (_coefCache[i]!=0.) {
snormVal = nset ? ((RooAbsReal*)cache->_suppNormList.at(i))->getVal() : 1.0 ;
Double_t pdfVal = pdf->getVal(nset) ;
if (pdf->isSelectedComp()) {
value += pdfVal*_coefCache[i]/snormVal ;
cxcoutD(Eval) << "RooAddModel::evaluate(" << GetName() << ") value += ["
<< pdf->GetName() << "] " << pdfVal << " * " << _coefCache[i] << " / " << snormVal << endl ;
}
}
i++ ;
}
return value ;
}
void RooAddModel::resetErrorCounters(Int_t resetValue)
{
RooAbsPdf::resetErrorCounters(resetValue) ;
_coefErrCount = resetValue ;
}
Bool_t RooAddModel::checkObservables(const RooArgSet* nset) const
{
Bool_t ret(kFALSE) ;
_pdfIter->Reset() ;
_coefIter->Reset() ;
RooAbsReal* coef ;
RooAbsReal* pdf ;
while((coef=(RooAbsReal*)_coefIter->Next())) {
pdf = (RooAbsReal*)_pdfIter->Next() ;
if (pdf->observableOverlaps(nset,*coef)) {
coutE(InputArguments) << "RooAddModel::checkObservables(" << GetName() << "): ERROR: coefficient " << coef->GetName()
<< " and PDF " << pdf->GetName() << " have one or more dependents in common" << endl ;
ret = kTRUE ;
}
}
return ret ;
}
Int_t RooAddModel::getAnalyticalIntegralWN(RooArgSet& allVars, RooArgSet& analVars,
const RooArgSet* normSet, const char* rangeName) const
{
if (_forceNumInt) return 0 ;
analVars.add(allVars) ;
Int_t code ;
RooArgList *cilist ;
getCompIntList(normSet,&allVars,cilist,code,rangeName) ;
return code+1 ;
}
void RooAddModel::getCompIntList(const RooArgSet* nset, const RooArgSet* iset, pRooArgList& compIntList, Int_t& code, const char* isetRangeName) const
{
Int_t sterileIdx(-1) ;
IntCacheElem* cache = (IntCacheElem*) _intCacheMgr.getObj(nset,iset,&sterileIdx,RooNameReg::ptr(isetRangeName)) ;
if (cache) {
code = _intCacheMgr.lastIndex() ;
compIntList = &cache->_intList ;
return ;
}
cache = new IntCacheElem ;
_pdfIter->Reset() ;
RooResolutionModel* model ;
while ((model=(RooResolutionModel*)_pdfIter->Next())) {
RooAbsReal* intPdf = model->createIntegral(*iset,nset,0,isetRangeName) ;
cache->_intList.addOwned(*intPdf) ;
}
code = _intCacheMgr.setObj(nset,iset,(RooAbsCacheElement*)cache,RooNameReg::ptr(isetRangeName)) ;
compIntList = &cache->_intList ;
}
Double_t RooAddModel::analyticalIntegralWN(Int_t code, const RooArgSet* normSet, const char* rangeName) const
{
if (code==0) {
return getVal(normSet) ;
}
IntCacheElem* cache = (IntCacheElem*) _intCacheMgr.getObjByIndex(code-1) ;
RooArgList* compIntList ;
if (cache==0) {
RooArgSet* vars = getParameters(RooArgSet()) ;
RooArgSet* nset = _intCacheMgr.nameSet1ByIndex(code-1)->select(*vars) ;
RooArgSet* iset = _intCacheMgr.nameSet2ByIndex(code-1)->select(*vars) ;
Int_t code2(-1) ;
getCompIntList(nset,iset,compIntList,code2,rangeName) ;
delete vars ;
delete nset ;
delete iset ;
} else {
compIntList = &cache->_intList ;
}
const RooArgSet* nset = _normSet ;
CacheElem* pcache = getProjCache(nset) ;
updateCoefficients(*pcache,nset) ;
TIterator* compIntIter = compIntList->createIterator() ;
_coefIter->Reset() ;
RooAbsReal* pdfInt ;
Double_t snormVal ;
Double_t value(0) ;
Int_t i(0) ;
while((pdfInt = (RooAbsReal*)compIntIter->Next())) {
if (_coefCache[i]!=0.) {
snormVal = nset ? ((RooAbsReal*)pcache->_suppNormList.at(i))->getVal() : 1.0 ;
Double_t intVal = pdfInt->getVal(nset) ;
value += intVal*_coefCache[i]/snormVal ;
cxcoutD(Eval) << "RooAddModel::evaluate(" << GetName() << ") value += ["
<< pdfInt->GetName() << "] " << intVal << " * " << _coefCache[i] << " / " << snormVal << endl ;
}
i++ ;
}
delete compIntIter ;
return value ;
}
Double_t RooAddModel::expectedEvents(const RooArgSet* nset) const
{
Double_t expectedTotal(0.0);
RooAbsPdf* pdf ;
if (_allExtendable) {
_pdfIter->Reset() ;
while((pdf = (RooAbsPdf*)_pdfIter->Next())) {
expectedTotal += pdf->expectedEvents(nset) ;
}
} else {
_coefIter->Reset() ;
RooAbsReal* coef ;
while((coef=(RooAbsReal*)_coefIter->Next())) {
expectedTotal += coef->getVal() ;
}
}
return expectedTotal;
}
void RooAddModel::selectNormalization(const RooArgSet* depSet, Bool_t force)
{
if (!force && _refCoefNorm.getSize()!=0) {
return ;
}
if (!depSet) {
fixCoefNormalization(RooArgSet()) ;
return ;
}
RooArgSet* myDepSet = getObservables(depSet) ;
fixCoefNormalization(*myDepSet) ;
delete myDepSet ;
}
void RooAddModel::selectNormalizationRange(const char* rangeName, Bool_t force)
{
if (!force && _refCoefRangeName) {
return ;
}
fixCoefRange(rangeName) ;
}
RooAbsGenContext* RooAddModel::genContext(const RooArgSet &vars, const RooDataSet *prototype,
const RooArgSet* auxProto, Bool_t verbose) const
{
return new RooAddGenContext(*this,vars,prototype,auxProto,verbose) ;
}
Bool_t RooAddModel::isDirectGenSafe(const RooAbsArg& arg) const
{
_pdfIter->Reset() ;
RooAbsPdf* pdf ;
while((pdf=(RooAbsPdf*)_pdfIter->Next())) {
if (!pdf->isDirectGenSafe(arg)) {
return kFALSE ;
}
}
return kTRUE ;
}
Int_t RooAddModel::getGenerator(const RooArgSet& directVars, RooArgSet &, Bool_t ) const
{
_pdfIter->Reset() ;
RooAbsPdf* pdf ;
while((pdf=(RooAbsPdf*)_pdfIter->Next())) {
RooArgSet tmp ;
if (pdf->getGenerator(directVars,tmp)==0) {
return 0 ;
}
}
return 1 ;
}
void RooAddModel::generateEvent(Int_t )
{
assert(0) ;
}
RooArgList RooAddModel::CacheElem::containedArgs(Action)
{
RooArgList allNodes;
allNodes.add(_projList) ;
allNodes.add(_suppProjList) ;
allNodes.add(_refRangeProjList) ;
allNodes.add(_rangeProjList) ;
return allNodes ;
}
RooArgList RooAddModel::IntCacheElem::containedArgs(Action)
{
RooArgList allNodes(_intList) ;
return allNodes ;
}
void RooAddModel::printMetaArgs(ostream& os) const
{
_pdfIter->Reset() ;
_coefIter->Reset() ;
Bool_t first(kTRUE) ;
os << "(" ;
RooAbsArg* coef, *pdf ;
while((coef=(RooAbsArg*)_coefIter->Next())) {
if (!first) {
os << " + " ;
} else {
first = kFALSE ;
}
pdf=(RooAbsArg*)_pdfIter->Next() ;
os << coef->GetName() << " * " << pdf->GetName() ;
}
pdf = (RooAbsArg*) _pdfIter->Next() ;
if (pdf) {
os << " + [%] * " << pdf->GetName() ;
}
os << ") " ;
}