RooWorkspace* makeInvertedANFit(TTree* tree, float forceSigma=-1, bool constrainMu=false, float forceMu=-1) {
RooWorkspace *ws = new RooWorkspace("ws","");
std::vector< TString (*)(TString, RooRealVar&, RooWorkspace&) > bkgPdfList;
bkgPdfList.push_back(makeSingleExp);
bkgPdfList.push_back(makeDoubleExp);
#if DEBUG==0
//bkgPdfList.push_back(makeTripleExp);
bkgPdfList.push_back(makeModExp);
bkgPdfList.push_back(makeSinglePow);
bkgPdfList.push_back(makeDoublePow);
bkgPdfList.push_back(makePoly2);
bkgPdfList.push_back(makePoly3);
#endif
RooRealVar mgg("mgg","m_{#gamma#gamma}",103,160,"GeV");
mgg.setBins(38);
mgg.setRange("sideband_low", 103,120);
mgg.setRange("sideband_high",131,160);
mgg.setRange("signal",120,131);
RooRealVar MR("MR","",0,3000,"GeV");
MR.setBins(60);
RooRealVar Rsq("t1Rsq","",0,1,"GeV");
Rsq.setBins(20);
RooRealVar hem1_M("hem1_M","",-1,2000,"GeV");
hem1_M.setBins(40);
RooRealVar hem2_M("hem2_M","",-1,2000,"GeV");
hem2_M.setBins(40);
RooRealVar ptgg("ptgg","p_{T}^{#gamma#gamma}",0,500,"GeV");
ptgg.setBins(50);
RooDataSet data("data","",tree,RooArgSet(mgg,MR,Rsq,hem1_M,hem2_M,ptgg));
RooDataSet* blind_data = (RooDataSet*)data.reduce("mgg<121 || mgg>130");
std::vector<TString> tags;
//fit many different background models
for(auto func = bkgPdfList.begin(); func != bkgPdfList.end(); func++) {
TString tag = (*func)("bonly",mgg,*ws);
tags.push_back(tag);
ws->pdf("bonly_"+tag+"_ext")->fitTo(data,RooFit::Strategy(0),RooFit::Extended(kTRUE),RooFit::Range("sideband_low,sideband_high"));
RooFitResult* bres = ws->pdf("bonly_"+tag+"_ext")->fitTo(data,RooFit::Strategy(2),RooFit::Save(kTRUE),RooFit::Extended(kTRUE),RooFit::Range("sideband_low,sideband_high"));
bres->SetName(tag+"_bonly_fitres");
ws->import(*bres);
//make blinded fit
RooPlot *fmgg_b = mgg.frame();
blind_data->plotOn(fmgg_b,RooFit::Range("sideband_low,sideband_high"));
TBox blindBox(121,fmgg_b->GetMinimum()-(fmgg_b->GetMaximum()-fmgg_b->GetMinimum())*0.015,130,fmgg_b->GetMaximum());
blindBox.SetFillColor(kGray);
fmgg_b->addObject(&blindBox);
ws->pdf("bonly_"+tag+"_ext")->plotOn(fmgg_b,RooFit::LineColor(kRed),RooFit::Range("Full"),RooFit::NormRange("sideband_low,sideband_high"));
fmgg_b->SetName(tag+"_blinded_frame");
ws->import(*fmgg_b);
delete fmgg_b;
//set all the parameters constant
RooArgSet* vars = ws->pdf("bonly_"+tag)->getVariables();
RooFIter iter = vars->fwdIterator();
RooAbsArg* a;
while( (a = iter.next()) ){
if(string(a->GetName()).compare("mgg")==0) continue;
static_cast<RooRealVar*>(a)->setConstant(kTRUE);
}
//make the background portion of the s+b fit
(*func)("b",mgg,*ws);
RooRealVar sigma(tag+"_s_sigma","",5,0,100);
if(forceSigma!=-1) {
sigma.setVal(forceSigma);
sigma.setConstant(true);
}
RooRealVar mu(tag+"_s_mu","",126,120,132);
if(forceMu!=-1) {
mu.setVal(forceMu);
mu.setConstant(true);
}
RooGaussian sig(tag+"_sig_model","",mgg,mu,sigma);
RooRealVar Nsig(tag+"_sb_Ns","",5,0,100);
RooRealVar Nbkg(tag+"_sb_Nb","",100,0,100000);
RooRealVar HiggsMass("HiggsMass","",125.1);
RooRealVar HiggsMassError("HiggsMassError","",0.24);
RooGaussian HiggsMassConstraint("HiggsMassConstraint","",mu,HiggsMass,HiggsMassError);
RooAddPdf fitModel(tag+"_sb_model","",RooArgList( *ws->pdf("b_"+tag), sig ),RooArgList(Nbkg,Nsig));
RooFitResult* sbres;
RooAbsReal* nll;
if(constrainMu) {
fitModel.fitTo(data,RooFit::Strategy(0),RooFit::Extended(kTRUE),RooFit::ExternalConstraints(RooArgSet(HiggsMassConstraint)));
sbres = fitModel.fitTo(data,RooFit::Strategy(2),RooFit::Save(kTRUE),RooFit::Extended(kTRUE),RooFit::ExternalConstraints(RooArgSet(HiggsMassConstraint)));
nll = fitModel.createNLL(data,RooFit::NumCPU(4),RooFit::Extended(kTRUE),RooFit::ExternalConstraints(RooArgSet(HiggsMassConstraint)));
} else {
fitModel.fitTo(data,RooFit::Strategy(0),RooFit::Extended(kTRUE));
sbres = fitModel.fitTo(data,RooFit::Strategy(2),RooFit::Save(kTRUE),RooFit::Extended(kTRUE));
nll = fitModel.createNLL(data,RooFit::NumCPU(4),RooFit::Extended(kTRUE));
}
sbres->SetName(tag+"_sb_fitres");
ws->import(*sbres);
ws->import(fitModel);
RooPlot *fmgg = mgg.frame();
data.plotOn(fmgg);
fitModel.plotOn(fmgg);
ws->pdf("b_"+tag+"_ext")->plotOn(fmgg,RooFit::LineColor(kRed),RooFit::Range("Full"),RooFit::NormRange("Full"));
fmgg->SetName(tag+"_frame");
ws->import(*fmgg);
delete fmgg;
RooMinuit(*nll).migrad();
RooPlot *fNs = Nsig.frame(0,25);
fNs->SetName(tag+"_Nsig_pll");
RooAbsReal *pll = nll->createProfile(Nsig);
//nll->plotOn(fNs,RooFit::ShiftToZero(),RooFit::LineColor(kRed));
pll->plotOn(fNs);
ws->import(*fNs);
delete fNs;
RooPlot *fmu = mu.frame(125,132);
fmu->SetName(tag+"_mu_pll");
RooAbsReal *pll_mu = nll->createProfile(mu);
pll_mu->plotOn(fmu);
ws->import(*fmu);
delete fmu;
}
RooArgSet weights("weights");
RooArgSet pdfs_bonly("pdfs_bonly");
RooArgSet pdfs_b("pdfs_b");
RooRealVar minAIC("minAIC","",1E10);
//compute AIC stuff
for(auto t = tags.begin(); t!=tags.end(); t++) {
RooAbsPdf *p_bonly = ws->pdf("bonly_"+*t);
RooAbsPdf *p_b = ws->pdf("b_"+*t);
RooFitResult *sb = (RooFitResult*)ws->obj(*t+"_bonly_fitres");
RooRealVar k(*t+"_b_k","",p_bonly->getParameters(RooArgSet(mgg))->getSize());
RooRealVar nll(*t+"_b_minNll","",sb->minNll());
RooRealVar Npts(*t+"_b_N","",blind_data->sumEntries());
RooFormulaVar AIC(*t+"_b_AIC","2*@0+2*@1+2*@1*(@1+1)/(@2-@1-1)",RooArgSet(nll,k,Npts));
ws->import(AIC);
if(AIC.getVal() < minAIC.getVal()) {
minAIC.setVal(AIC.getVal());
}
//aicExpSum+=TMath::Exp(-0.5*AIC.getVal()); //we will need this precomputed for the next step
pdfs_bonly.add(*p_bonly);
pdfs_b.add(*p_b);
}
ws->import(minAIC);
//compute the AIC weight
float aicExpSum=0;
for(auto t = tags.begin(); t!=tags.end(); t++) {
RooFormulaVar *AIC = (RooFormulaVar*)ws->obj(*t+"_b_AIC");
aicExpSum+=TMath::Exp(-0.5*(AIC->getVal()-minAIC.getVal())); //we will need this precomputed for the next step
}
std::cout << "aicExpSum: " << aicExpSum << std::endl;
for(auto t = tags.begin(); t!=tags.end(); t++) {
RooFormulaVar *AIC = (RooFormulaVar*)ws->obj(*t+"_b_AIC");
RooRealVar *AICw = new RooRealVar(*t+"_b_AICWeight","",TMath::Exp(-0.5*(AIC->getVal()-minAIC.getVal()))/aicExpSum);
if( TMath::IsNaN(AICw->getVal()) ) {AICw->setVal(0);}
ws->import(*AICw);
std::cout << *t << ": " << AIC->getVal()-minAIC.getVal() << " " << AICw->getVal() << std::endl;
weights.add(*AICw);
}
RooAddPdf bonly_AIC("bonly_AIC","",pdfs_bonly,weights);
RooAddPdf b_AIC("b_AIC","",pdfs_b,weights);
//b_AIC.fitTo(data,RooFit::Strategy(0),RooFit::Extended(kTRUE),RooFit::Range("sideband_low,sideband_high"));
//RooFitResult* bres = b_AIC.fitTo(data,RooFit::Strategy(2),RooFit::Save(kTRUE),RooFit::Extended(kTRUE),RooFit::Range("sideband_low,sideband_high"));
//bres->SetName("AIC_b_fitres");
//ws->import(*bres);
//make blinded fit
RooPlot *fmgg_b = mgg.frame(RooFit::Range("sideband_low,sideband_high"));
blind_data->plotOn(fmgg_b,RooFit::Range("sideband_low,sideband_high"));
TBox blindBox(121,fmgg_b->GetMinimum()-(fmgg_b->GetMaximum()-fmgg_b->GetMinimum())*0.015,130,fmgg_b->GetMaximum());
blindBox.SetFillColor(kGray);
fmgg_b->addObject(&blindBox);
bonly_AIC.plotOn(fmgg_b,RooFit::LineColor(kRed),RooFit::Range("Full"),RooFit::NormRange("sideband_low,sideband_high"));
fmgg_b->SetName("AIC_blinded_frame");
ws->import(*fmgg_b);
delete fmgg_b;
#if 1
RooRealVar sigma("AIC_s_sigma","",5,0,100);
if(forceSigma!=-1) {
sigma.setVal(forceSigma);
sigma.setConstant(true);
}
RooRealVar mu("AIC_s_mu","",126,120,132);
if(forceMu!=-1) {
mu.setVal(forceMu);
mu.setConstant(true);
}
RooGaussian sig("AIC_sig_model","",mgg,mu,sigma);
RooRealVar Nsig("AIC_sb_Ns","",5,0,100);
RooRealVar Nbkg("AIC_sb_Nb","",100,0,100000);
RooRealVar HiggsMass("HiggsMass","",125.1);
RooRealVar HiggsMassError("HiggsMassError","",0.24);
RooGaussian HiggsMassConstraint("HiggsMassConstraint","",mu,HiggsMass,HiggsMassError);
RooAddPdf fitModel("AIC_sb_model","",RooArgList( b_AIC, sig ),RooArgList(Nbkg,Nsig));
RooFitResult* sbres;
RooAbsReal *nll;
if(constrainMu) {
fitModel.fitTo(data,RooFit::Strategy(0),RooFit::Extended(kTRUE),RooFit::ExternalConstraints(RooArgSet(HiggsMassConstraint)));
sbres = fitModel.fitTo(data,RooFit::Strategy(2),RooFit::Save(kTRUE),RooFit::Extended(kTRUE),RooFit::ExternalConstraints(RooArgSet(HiggsMassConstraint)));
nll = fitModel.createNLL(data,RooFit::NumCPU(4),RooFit::Extended(kTRUE),RooFit::ExternalConstraints(RooArgSet(HiggsMassConstraint)));
} else {
fitModel.fitTo(data,RooFit::Strategy(0),RooFit::Extended(kTRUE));
sbres = fitModel.fitTo(data,RooFit::Strategy(2),RooFit::Save(kTRUE),RooFit::Extended(kTRUE));
nll = fitModel.createNLL(data,RooFit::NumCPU(4),RooFit::Extended(kTRUE));
}
assert(nll!=0);
sbres->SetName("AIC_sb_fitres");
ws->import(*sbres);
ws->import(fitModel);
RooPlot *fmgg = mgg.frame();
data.plotOn(fmgg);
fitModel.plotOn(fmgg);
ws->pdf("b_AIC")->plotOn(fmgg,RooFit::LineColor(kRed),RooFit::Range("Full"),RooFit::NormRange("Full"));
fmgg->SetName("AIC_frame");
ws->import(*fmgg);
delete fmgg;
RooMinuit(*nll).migrad();
RooPlot *fNs = Nsig.frame(0,25);
fNs->SetName("AIC_Nsig_pll");
RooAbsReal *pll = nll->createProfile(Nsig);
//nll->plotOn(fNs,RooFit::ShiftToZero(),RooFit::LineColor(kRed));
pll->plotOn(fNs);
ws->import(*fNs);
delete fNs;
RooPlot *fmu = mu.frame(125,132);
fmu->SetName("AIC_mu_pll");
RooAbsReal *pll_mu = nll->createProfile(mu);
pll_mu->plotOn(fmu);
ws->import(*fmu);
delete fmu;
std::cout << "min AIC: " << minAIC.getVal() << std::endl;
for(auto t = tags.begin(); t!=tags.end(); t++) {
RooFormulaVar *AIC = (RooFormulaVar*)ws->obj(*t+"_b_AIC");
RooRealVar *AICw = ws->var(*t+"_b_AICWeight");
RooRealVar* k = ws->var(*t+"_b_k");
printf("%s & %0.0f & %0.2f & %0.2f \\\\\n",t->Data(),k->getVal(),AIC->getVal()-minAIC.getVal(),AICw->getVal());
//std::cout << k->getVal() << " " << AIC->getVal()-minAIC.getVal() << " " << AICw->getVal() << std::endl;
}
#endif
return ws;
}
void LVector::mBasis(
const tmv::ConstVectorView<double>& x, const tmv::ConstVectorView<double>& y,
const tmv::ConstVectorView<double>* invsig,
tmv::MatrixView<T> psi, int order, double sigma)
{
assert (y.size()==x.size());
assert (psi.nrows()==x.size() && psi.ncols()==PQIndex::size(order));
const int N=order;
const int npts_full = x.size();
// It's faster to build the psi matrix in blocks so that more of the matrix stays in
// L1 cache. For a (typical) 256 KB L2 cache size, this corresponds to 8 columns in the
// cache, which is pretty good, since we are usually working on 4 columns at a time,
// plus either X and Y or 3 Lq vectors.
const int BLOCKING_FACTOR=4096;
const int max_npts = std::max(BLOCKING_FACTOR,npts_full);
tmv::DiagMatrix<double> Rsq_full(max_npts);
tmv::Matrix<double> A_full(max_npts,2);
tmv::Matrix<double> tmp_full(max_npts,2);
tmv::DiagMatrix<double> Lmq_full(max_npts);
tmv::DiagMatrix<double> Lmqm1_full(max_npts);
tmv::DiagMatrix<double> Lmqm2_full(max_npts);
for (int ilo=0; ilo<npts_full; ilo+=BLOCKING_FACTOR) {
const int ihi = std::min(npts_full, ilo + BLOCKING_FACTOR);
const int npts = ihi-ilo;
// Cast arguments as diagonal matrices so we can access
// vectorized element-by-element multiplication
tmv::ConstDiagMatrixView<double> X = DiagMatrixViewOf(x.subVector(ilo,ihi));
tmv::ConstDiagMatrixView<double> Y = DiagMatrixViewOf(y.subVector(ilo,ihi));
// Get the appropriate portion of our temporary matrices.
tmv::DiagMatrixView<double> Rsq = Rsq_full.subDiagMatrix(0,npts);
tmv::MatrixView<double> A = A_full.rowRange(0,npts);
tmv::MatrixView<double> tmp = tmp_full.rowRange(0,npts);
// We need rsq values twice, so store them here.
Rsq = X*X;
Rsq += Y*Y;
// This matrix will keep track of real & imag parts
// of prefactor * exp(-r^2/2) (x+iy)^m / sqrt(m!)
// Build the Gaussian factor
for (int i=0; i<npts; i++) A.ref(i,0) = std::exp(-0.5*Rsq(i));
mBasisHelper<T>::applyPrefactor(A.col(0),sigma);
A.col(1).setZero();
// Put 1/sigma factor into every point if doing a design matrix:
if (invsig) A.col(0) *= tmv::DiagMatrixViewOf(invsig->subVector(ilo,ihi));
// Assign the m=0 column first:
psi.col( PQIndex(0,0).rIndex(), ilo,ihi ) = A.col(0);
// Then ascend m's at q=0:
for (int m=1; m<=N; m++) {
int rIndex = PQIndex(m,0).rIndex();
// Multiply by (X+iY)/sqrt(m), including a factor 2 first time through
tmp = Y * A;
A = X * A;
A.col(0) += tmp.col(1);
A.col(1) -= tmp.col(0);
A *= m==1 ? 2. : 1./sqrtn(m);
psi.subMatrix(ilo,ihi,rIndex,rIndex+2) = mBasisHelper<T>::Asign(m%4) * A;
}
// Make three DiagMatrix to hold Lmq's during recurrence calculations
boost::shared_ptr<tmv::DiagMatrixView<double> > Lmq(
new tmv::DiagMatrixView<double>(Lmq_full.subDiagMatrix(0,npts)));
boost::shared_ptr<tmv::DiagMatrixView<double> > Lmqm1(
new tmv::DiagMatrixView<double>(Lmqm1_full.subDiagMatrix(0,npts)));
boost::shared_ptr<tmv::DiagMatrixView<double> > Lmqm2(
new tmv::DiagMatrixView<double>(Lmqm2_full.subDiagMatrix(0,npts)));
for (int m=0; m<=N; m++) {
PQIndex pq(m,0);
int iQ0 = pq.rIndex();
// Go to q=1:
pq.incN();
if (pq.pastOrder(N)) continue;
{ // q == 1
const int p = pq.getP();
const int q = pq.getQ();
const int iQ = pq.rIndex();
Lmqm1->setAllTo(1.); // This is Lm0.
*Lmq = Rsq - (p+q-1.);
*Lmq *= mBasisHelper<T>::Lsign(1.) / (sqrtn(p)*sqrtn(q));
if (m==0) {
psi.col(iQ,ilo,ihi) = (*Lmq) * psi.col(iQ0,ilo,ihi);
} else {
psi.subMatrix(ilo,ihi,iQ,iQ+2) = (*Lmq) * psi.subMatrix(ilo,ihi,iQ0,iQ0+2);
}
}
// do q=2,...
for (pq.incN(); !pq.pastOrder(N); pq.incN()) {
const int p = pq.getP();
const int q = pq.getQ();
const int iQ = pq.rIndex();
// cycle the Lmq vectors
// Lmqm2 <- Lmqm1
// Lmqm1 <- Lmq
// Lmq <- Lmqm2
Lmqm2.swap(Lmqm1);
Lmqm1.swap(Lmq);
double invsqrtpq = 1./sqrtn(p)/sqrtn(q);
*Lmq = Rsq - (p+q-1.);
*Lmq *= mBasisHelper<T>::Lsign(invsqrtpq) * *Lmqm1;
*Lmq -= (sqrtn(p-1)*sqrtn(q-1)*invsqrtpq) * (*Lmqm2);
if (m==0) {
psi.col(iQ,ilo,ihi) = (*Lmq) * psi.col(iQ0,ilo,ihi);
} else {
psi.subMatrix(ilo,ihi,iQ,iQ+2) = (*Lmq) * psi.subMatrix(ilo,ihi,iQ0,iQ0+2);
}
}
}
}
}