1 // Author: Daniel.Lohner@cern.ch
3 #include "AliTRDNDFast.h"
6 extern Double_t langaufunc(Double_t *x, Double_t *par) {
8 // needs protection, parameter [3]>0!!!!!
9 // needs protection, parameter [4]>0!!!!!
12 //par[0]=Width (scale) parameter of Landau density
13 //par[1]=Most Probable (MP, location) parameter of Landau density
14 //par[2]=Total area (integral -inf to inf, normalization constant)
15 //par[3]=Width (sigma) of convoluted Gaussian function
16 //par[4]=Exponential Slope Parameter
18 //In the Landau distribution (represented by the CERNLIB approximation),
19 //the maximum is located at x=-0.22278298 with the location parameter=0.
20 //This shift is corrected within this function, so that the actual
21 //maximum is identical to the MP parameter.
24 Double_t invsq2pi = 0.3989422804014; // (2 pi)^(-1/2)
25 Double_t mpshift = -0.22278298; // Landau maximum location
28 Double_t np = 100.0; // number of convolution stpdf
29 Double_t sc = 5.0; // convolution extends to +-sc Gaussian sigmas
40 // MP shift correction
41 mpc = par[1] - mpshift * par[0];
43 // Range of convolution integral
44 xlow = x[0] - sc * par[3];
45 xupp = x[0] + sc * par[3];
48 if(xupp<xlow)cout<<"ERROR: Convolution around Negative MPV"<<endl;
50 step = (xupp-xlow) / np;
52 // Convolution integral of Landau and Gaussian by sum
53 for(i=1.0; i<=np/2; i++) {
54 xx = xlow + (i-.5) * step;
55 fland = TMath::Landau(xx,mpc,par[0])*TMath::Exp(-par[4]*xx) / par[0]; // mpc taken out
56 sum += fland * TMath::Gaus(x[0],xx,par[3]);
58 xx = xupp - (i-.5) * step;
59 fland = TMath::Landau(xx,mpc,par[0])*TMath::Exp(-par[4]*xx) / par[0]; // mpc taken out
60 sum += fland * TMath::Gaus(x[0],xx,par[3]);
63 return (par[2] * step * sum * invsq2pi / par[3]);
68 ClassImp(AliTRDNDFast);
70 AliTRDNDFast::AliTRDNDFast(): TObject(),
77 // default constructor
80 AliTRDNDFast::AliTRDNDFast(const char *name,Int_t ndim,Int_t nbins,Double_t xlow,Double_t xup): TObject(),
88 for(Int_t idim=0;idim<fNDim;idim++){
89 fHistos[idim]=new TH1F(Form("%s_axis_%d",fTitle.Data(),idim),Form("%s_axis_%d",fTitle.Data(),idim),nbins,xlow,xup);
90 fHistos[idim]->SetDirectory(0);
94 AliTRDNDFast::AliTRDNDFast(const AliTRDNDFast &ref) : TObject(ref),
103 for(Int_t idim=0;idim<fNDim;idim++){
104 fHistos[idim]=(TH1F*)ref.fHistos[idim]->Clone(Form("%s_axis_%d",GetName(),idim));
105 fHistos[idim]->SetDirectory(0);
106 for(Int_t ipar=0;ipar<kNpar;ipar++)fPars[idim][ipar]=ref.fPars[idim][ipar];
110 AliTRDNDFast &AliTRDNDFast::operator=(const AliTRDNDFast &ref){
112 // Assignment operator
115 TObject::operator=(ref);
120 for(Int_t idim=0;idim<fNDim;idim++){
121 for(Int_t ipar=0;ipar<kNpar;ipar++)fPars[idim][ipar]=ref.fPars[idim][ipar];
127 AliTRDNDFast::~AliTRDNDFast(){
132 void AliTRDNDFast::Init(){
134 for(Int_t ipar=0;ipar<kNpar;ipar++)fPars[ipar].Set(fNDim);
135 fFunc=new TF1*[fNDim];
136 fHistos=new TH1F*[fNDim];
137 for(Int_t idim=0;idim<fNDim;idim++){
139 for(Int_t ipar=0;ipar<kNpar;ipar++)fPars[ipar].SetAt(0,idim);
144 void AliTRDNDFast::Cleanup(){
146 for(Int_t idim=0;idim<fNDim;idim++){
148 delete fHistos[idim];
156 for(Int_t ipar=0;ipar<kNpar;ipar++){
161 for(Int_t idim=0;idim<fNDim;idim++){
172 void AliTRDNDFast::PrintPars(){
173 for(Int_t idim=0;idim<fNDim;idim++){
174 for(Int_t ipar=0;ipar<kNpar;ipar++)cout<<idim<<" "<<ipar<<" "<<GetParam(idim,ipar)<<endl;
178 void AliTRDNDFast::ScaleLangauFun(TF1 *func,Double_t mpv){
180 Double_t start[kNpar],low[kNpar],high[kNpar];
181 for(Int_t ii=0;ii<kNpar;ii++){
182 start[ii]=func->GetParameter(ii);
183 func->GetParLimits(ii,low[ii],high[ii]);
186 Double_t scalefactor=mpv/start[1];
188 for(Int_t ii=0;ii<kNpar;ii++){
190 if(ii==0||ii==1||ii==3)scale=scalefactor;
191 if(ii==4)scale=1./scalefactor;
195 func->SetParLimits(ii, low[ii], high[ii]);
197 func->SetParameters(start);
200 //---------------------------------------------------------------
201 //---------------------------------------------------------------
202 TF1 *AliTRDNDFast::GetLangauFun(TString funcname,Double_t range[2],Double_t scalefactor){
204 Double_t start[kNpar] = {120, 1000, 1, 100, 1e-5};
205 Double_t low[kNpar] = {10, 300, 0.01, 1, 0.};
206 Double_t high[kNpar] = {1000, 3000, 100, 1000, 1.};
208 TF1 *hlandauE=new TF1(funcname.Data(),langaufunc,0,range[1],kNpar);
209 hlandauE->SetParameters(start);
210 hlandauE->SetParNames("Width","MP","Area","GSigma","delta");
211 for (int i=0; i<kNpar; i++) {
212 hlandauE->SetParLimits(i, low[i], high[i]);
215 if(scalefactor!=1){ScaleLangauFun(hlandauE,scalefactor*start[1]);}
220 TF1 *AliTRDNDFast::FitLandau(TString name,TH1F *htemp,Double_t range[2],TString option){
222 TF1 *fitlandau1D=GetLangauFun(name,range);
223 TF1 fit("land","landau");
224 Double_t max=htemp->GetXaxis()->GetBinCenter(htemp->GetMaximumBin());
225 fit.SetParameter(1,max);
226 fit.SetParLimits(1,0,htemp->GetXaxis()->GetXmax());
227 fit.SetParameter(2,0.3*max); // MPV may never become negative!!!!!
228 htemp->Fit("land",option.Data(),"",range[0],range[1]);
229 ScaleLangauFun(fitlandau1D,fit.GetParameter(1));
230 htemp->Fit(fitlandau1D,option.Data(),"",range[0],range[1]); // range for references
234 void AliTRDNDFast::BuildHistos(){
236 for(Int_t idim=0;idim<fNDim;idim++){
237 fHistos[idim]->Reset();
239 Double_t pars[kNpar];
240 for(Int_t ipar=0;ipar<kNpar;ipar++)pars[ipar]=GetParam(idim,ipar);
241 // Also Fill overflow bins!!!
242 for(Int_t ii=1;ii<=fHistos[idim]->GetNbinsX()+1;ii++){
243 Double_t xval=fHistos[idim]->GetXaxis()->GetBinCenter(ii);
244 Double_t val=langaufunc(&xval,&pars[0]);
245 //Double_t val=fFunc[idim]->Eval(xval);
246 fHistos[idim]->SetBinContent(ii,val);
249 fHistos[idim]->Scale(1./fHistos[idim]->Integral(1,fHistos[idim]->GetNbinsX(),"width"));
253 void AliTRDNDFast::Build(Double_t **pars){
255 for(Int_t idim=0;idim<fNDim;idim++){
256 for(Int_t ipar=0;ipar<kNpar;ipar++){
257 fPars[ipar].SetAt(pars[idim][ipar],idim);
264 void AliTRDNDFast::Build(TH1F **hdEdx,TString path){
268 TCanvas *CANV=new TCanvas("a","a");
269 if(fNDim==2)CANV->Divide(2,1);
270 if(fNDim==3)CANV->Divide(2,2);
271 if(fNDim>6)CANV->Divide(3,3);
272 // Fit and Extract Parameters
273 for(Int_t idim=0;idim<fNDim;idim++){
276 range[0]=hdEdx[idim]->GetXaxis()->GetXmin();
277 range[1]=hdEdx[idim]->GetXaxis()->GetXmax();
279 hdEdx[idim]->Scale(1./hdEdx[idim]->Integral(1,hdEdx[idim]->GetNbinsX(),"width"));
281 fFunc[idim]=FitLandau(Form("fit%d",idim),hdEdx[idim],range,"RMB0");
283 fFunc[idim]->SetParameter(2,fFunc[idim]->GetParameter(2)/fFunc[idim]->Integral(range[0],range[1]));
284 hdEdx[idim]->DrawCopy();
285 fFunc[idim]->DrawCopy("same");
287 for(Int_t ipar=0;ipar<kNpar;ipar++)fPars[ipar].SetAt(fFunc[idim]->GetParameter(ipar),idim);
289 if(path!="")CANV->Print(Form("%s/%s_Build.pdf",path.Data(),fTitle.Data()));
295 Double_t AliTRDNDFast::Eval(Double_t *point) const{
297 for(Int_t idim=0;idim<fNDim;idim++){
298 Int_t bin=fHistos[idim]->GetXaxis()->FindBin(point[idim]);
299 val*=fHistos[idim]->GetBinContent(bin);
304 void AliTRDNDFast::Random(Double_t *point) const{
305 for(Int_t idim=0;idim<fNDim;idim++){
306 point[idim]=fHistos[idim]->GetRandom();
310 void AliTRDNDFast::Random(Double_t *point,AliTRDNDFast *nd0,AliTRDNDFast *nd1,Double_t w0,Double_t w1){
311 for(Int_t idim=0;idim<nd0->fNDim;idim++){
312 point[idim]=GetRandomInterpolation(nd0->fHistos[idim],nd1->fHistos[idim],w0,w1);
316 Int_t AliTRDNDFast::BinarySearchInterpolation(Int_t start,Int_t end,Double_t *a0,Double_t *a1,Double_t w0,Double_t w1,Double_t val){
318 if((end-start)==1)return start;
319 Int_t mid=Int_t((end+start)/2);
320 Double_t valmid=(w0*a0[mid]+w1*a1[mid])/(w0+w1);
321 if(val>=valmid)return BinarySearchInterpolation(mid,end,a0,a1,w0,w1,val);
322 return BinarySearchInterpolation(start,mid,a0,a1,w0,w1,val);
325 Double_t AliTRDNDFast::GetRandomInterpolation(TH1F *hist0,TH1F *hist1,Double_t w0,Double_t w1){
327 // Draw Random Variable
328 Double_t rand=gRandom->Rndm();
330 // Get Integral Arrays
331 Double_t *integral0=hist0->GetIntegral();
332 Double_t *integral1=hist1->GetIntegral();
334 Int_t nbinsX=hist0->GetNbinsX();
336 Int_t ibin=BinarySearchInterpolation(1,nbinsX+1,integral0,integral1,w0,w1,rand);
337 return hist0->GetXaxis()->GetBinCenter(ibin);