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4c0d7bc7 1// ----------------------------------------------------------------------
fef6f2b3 2// AliPWGHistoTools
4c0d7bc7 3//
4// This class provides some tools which can be useful in the analsis
5// of spectra, to fit or transform histograms. See the comments of the
6// individual methods for details
7//
8// Author: M. Floris (CERN)
9// ----------------------------------------------------------------------
10
fef6f2b3 11#include "AliPWGHistoTools.h"
4c0d7bc7 12#include "TH1D.h"
13#include "TF1.h"
14#include "TH1.h"
15#include "TMath.h"
16#include "TGraphErrors.h"
17#include "TVirtualFitter.h"
18#include "TMinuit.h"
19#include "AliLog.h"
8681985a 20#include "TSpline.h"
4c0d7bc7 21#include <iostream>
8681985a 22#include "TGraphAsymmErrors.h"
4c0d7bc7 23
24using namespace std;
25
4c0d7bc7 26
fef6f2b3 27ClassImp(AliPWGHistoTools)
4c0d7bc7 28
fef6f2b3 29TF1 * AliPWGHistoTools::fdNdptForETCalc = 0;
90421222 30
fef6f2b3 31AliPWGHistoTools::AliPWGHistoTools() {
4c0d7bc7 32 // ctor
33}
34
fef6f2b3 35AliPWGHistoTools::~AliPWGHistoTools(){
4c0d7bc7 36 // dtor
37}
38
fef6f2b3 39TH1 * AliPWGHistoTools::GetdNdmtFromdNdpt(const TH1 * hpt, Double_t mass) {
4c0d7bc7 40 // convert the x axis from pt to mt. Assumes you have 1/pt dNdpt in the histo you start with
41
42 Int_t nbins = hpt->GetNbinsX();
43 Float_t * xbins = new Float_t[nbins+1];
44 for(Int_t ibins = 0; ibins <= nbins; ibins++){
45 xbins[ibins] = TMath::Sqrt(hpt->GetBinLowEdge(ibins+1)*hpt->GetBinLowEdge(ibins+1) +
0e019ec6 46 mass *mass) - mass;
77233d47 47 // // xbins[ibins] = TMath::Sqrt(hpt->GetBinLowEdge(ibins+1)*hpt->GetBinLowEdge(ibins+1) +
48 // // mass *mass);
4c0d7bc7 49 // cout << ibins << " "<< xbins[ibins] << endl;
50
51 }
52
53 TH1D * hmt = new TH1D(TString(hpt->GetName())+"_mt",
54 TString(hpt->GetName())+"_mt",
55 nbins, xbins);
56 for(Int_t ibins = 1; ibins <= nbins; ibins++){
57 hmt->SetBinContent(ibins, hpt->GetBinContent(ibins));
58 hmt->SetBinError(ibins, hpt->GetBinError(ibins));
59
60 }
61
62 hmt->SetXTitle("m_{t} - m_{0} (GeV/c^{2})");
63 hmt->SetYTitle("1/m_{t} dN/dm_{t} (a.u.)");
0e019ec6 64 hmt->SetMarkerStyle(hpt->GetMarkerStyle());
65 hmt->SetMarkerColor(hpt->GetMarkerColor());
66 hmt->SetLineColor(hpt->GetLineColor());
4fd89c20 67
4c0d7bc7 68 return hmt;
69
70}
71
fef6f2b3 72TH1 * AliPWGHistoTools::GetdNdptFromdNdmt(const TH1 * hmt, Double_t mass) {
9ca56c22 73 // convert the x axis from mt to pt. Assumes you have 1/mt dNdmt in the histo you start with
74
75 Int_t nbins = hmt->GetNbinsX();
76 Float_t * xbins = new Float_t[nbins+1];
77 for(Int_t ibins = 0; ibins <= nbins; ibins++){
78 xbins[ibins] = TMath::Sqrt((hmt->GetBinLowEdge(ibins+1)+mass)*(hmt->GetBinLowEdge(ibins+1)+mass) -
79 mass *mass);
80 xbins[ibins] = Float_t(TMath::Nint(xbins[ibins]*100))/100;
81 // // xbins[ibins] = TMath::Sqrt(hmt->GetBinLowEdge(ibins+1)*hmt->GetBinLowEdge(ibins+1) +
82 // // mass *mass);
83 cout << ibins << " "<< xbins[ibins] << endl;
84
85 }
86
87 TH1D * hptL = new TH1D(TString(hmt->GetName())+"_pt",
88 TString(hmt->GetName())+"_pt",
89 nbins, xbins);
90 for(Int_t ibins = 1; ibins <= nbins; ibins++){
91 hptL->SetBinContent(ibins, hmt->GetBinContent(ibins));
92 hptL->SetBinError(ibins, hmt->GetBinError(ibins));
93
94 }
95
96 hptL->SetXTitle("p_{t} (GeV/c)");
97 hptL->SetYTitle("1/p_{t} dN/dp_{t} (a.u.)");
98 hptL->SetMarkerStyle(hmt->GetMarkerStyle());
99 hptL->SetMarkerColor(hmt->GetMarkerColor());
100 hptL->SetLineColor(hmt->GetLineColor());
101
102 return hptL;
103
104}
105
106
fef6f2b3 107TH1 * AliPWGHistoTools::GetdNdPtFromOneOverPt(const TH1 * h1Pt) {
4c0d7bc7 108
109 // convert an histo from 1/pt dNdpt to dNdpt, using the pt at the center of the bin
110
111
112 TH1 * hPt = (TH1 *) h1Pt->Clone((TString(h1Pt->GetName()) + "_inv").Data());
113 hPt->Reset();
114
115 Int_t nbinx = hPt->GetNbinsX();
116
117 for(Int_t ibinx = 1; ibinx <= nbinx; ibinx++){
118
119 Double_t cont = h1Pt->GetBinContent(ibinx);
120 Double_t err = h1Pt->GetBinError(ibinx);
121
122 Double_t pt = h1Pt->GetBinCenter(ibinx);
123
c3c47c65 124 if(pt > 0) {
4c0d7bc7 125 cont *= pt;
126 err *= pt;
127 } else {
128 cont = 0;
129 err = 0;
130 }
131
132 hPt->SetBinContent(ibinx, cont);
133 hPt->SetBinError(ibinx, err);
134
135 }
136
137 hPt->SetXTitle("p_{t} (GeV)");
138 hPt->SetYTitle("dN/dp_{t} (GeV^{-2})");
139
140 return hPt;
141
142}
143
144
145
146
fef6f2b3 147TH1 * AliPWGHistoTools::GetOneOverPtdNdPt(const TH1 * hPt) {
4c0d7bc7 148
149 // convert an histo from dNdpt to 1/pt dNdpt, using the pt at the center of the bin
150
151 TH1 * h1Pt = (TH1 *) hPt->Clone((TString(hPt->GetName()) + "_inv").Data());
152 h1Pt->Reset();
153
154 Int_t nbinx = h1Pt->GetNbinsX();
155
156 for(Int_t ibinx = 1; ibinx <= nbinx; ibinx++){
157
158 Double_t cont = hPt->GetBinContent(ibinx);
159 Double_t err = hPt->GetBinError(ibinx);
160
161 Double_t pt = hPt->GetBinCenter(ibinx);
162
c3c47c65 163 if(pt > 0) {
4c0d7bc7 164 cont /= pt;
165 err /= pt;
166 } else {
167 cont = 0;
168 err = 0;
169 }
170
171 h1Pt->SetBinContent(ibinx, cont);
172 h1Pt->SetBinError(ibinx, err);
173
174 }
175
176 h1Pt->SetXTitle("p_{t} (GeV)");
177 h1Pt->SetYTitle("1/p_{t} dN/dp_{t} (GeV^{-2})");
178
179 return h1Pt;
180
181}
182
183
fef6f2b3 184TGraphErrors * AliPWGHistoTools::GetGraphFromHisto(const TH1F * h, Bool_t binWidth) {
4c0d7bc7 185 // Convert a histo to a graph
186 // if binWidth is true ex is set to the bin width of the histos, otherwise it is set to zero
187 Int_t nbin = h->GetNbinsX();
188
189 TGraphErrors * g = new TGraphErrors();
190 Int_t ipoint = 0;
191 for(Int_t ibin = 1; ibin <= nbin; ibin++){
192 Double_t xerr = binWidth ? h->GetBinWidth(ibin)/2 : 0;
3beb22a2 193 if (h->GetBinContent(ibin)) {
4c0d7bc7 194 g->SetPoint (ipoint, h->GetBinCenter(ibin), h->GetBinContent(ibin));
195 g->SetPointError(ipoint, xerr, h->GetBinError(ibin));
196 ipoint++;
197 }
198 }
199
200 g->SetMarkerStyle(h->GetMarkerStyle());
201 g->SetMarkerColor(h->GetMarkerColor());
202 g->SetLineColor(h->GetLineColor());
2210b002 203 g->SetLineStyle(h->GetLineStyle());
204 g->SetLineWidth(h->GetLineWidth());
4c0d7bc7 205
206 g->SetTitle(h->GetTitle());
207 g->SetName(TString("g_")+h->GetName());
208
209 return g;
210
211}
212
fef6f2b3 213TH1F * AliPWGHistoTools::GetHistoFromGraph(const TGraphErrors * g, const TH1F* hTemplate) {
4c0d7bc7 214
215 // convert a graph to histo with the binning of hTemplate.
216 // Warning: the template should be chosen
217 // properly: if you have two graph points in the same histo bin this
218 // won't work!
219
220 TH1F * h = (TH1F*) hTemplate->Clone(TString("h_")+g->GetName());
221 h->Reset();
222 Int_t npoint = g->GetN();
223 // g->Print();
224 for(Int_t ipoint = 0; ipoint < npoint; ipoint++){
225 Float_t x = g->GetX() [ipoint];
226 Float_t y = g->GetY() [ipoint];
fef6f2b3 227 Float_t ey = 0;
228 if(g->InheritsFrom("TGraphErrors"))
229 ey = g->GetEY()[ipoint];
4c0d7bc7 230 Int_t bin = h->FindBin(x);
231 // cout << "bin: "<< bin << " -> " << x << ", "<< y <<", " << ey << endl;
232
233 h->SetBinContent(bin,y);
234 h->SetBinError (bin,ey);
235 }
236
237 h->SetMarkerStyle(g->GetMarkerStyle());
238 h->SetMarkerColor(g->GetMarkerColor());
239 h->SetLineColor (g->GetLineColor());
240
241
242 return h;
243}
244
fef6f2b3 245TGraphErrors * AliPWGHistoTools::ConcatenateGraphs(const TGraphErrors * g1,const TGraphErrors * g2){
4c0d7bc7 246
247 // concatenates two graphs
248
249 Int_t npoint1=g1->GetN();
250 Int_t npoint2=g2->GetN();
251
252 TGraphErrors * gClone = (TGraphErrors*) g1->Clone();
253
254// for(Int_t ipoint = 0; ipoint < npoint1; ipoint++){
255// gClone->SetPointError(ipoint,0,g1->GetEY()[ipoint]);
256
257// }
258 for(Int_t ipoint = 0; ipoint < npoint2; ipoint++){
259 gClone->SetPoint(ipoint+npoint1,g2->GetX()[ipoint],g2->GetY()[ipoint]);
260 gClone->SetPointError(ipoint+npoint1,g2->GetEX()[ipoint],g2->GetEY()[ipoint]);
261 // gClone->SetPointError(ipoint+npoint1,0,g2->GetEY()[ipoint]);
262 }
263
264 gClone->GetHistogram()->GetXaxis()->SetTimeDisplay(1);
265 gClone->SetTitle(TString(gClone->GetTitle())+" + "+g2->GetTitle());
266 gClone->SetName(TString(gClone->GetName())+"_"+g2->GetName());
267
268 return gClone;
269}
270
271
fef6f2b3 272TH1F * AliPWGHistoTools::Combine3HistosWithErrors(const TH1 * h1, const TH1 * h2, const TH1* h3,
3725266c 273 TH1 * he1, TH1 * he2, TH1 * he3,
3beb22a2 274 const TH1* htemplate, Int_t statFrom,
3725266c 275 Float_t renorm1, Float_t renorm2, Float_t renorm3,
276 TH1 ** hSyst, Bool_t errorFromBinContent) {
ee08b77d 277
278 // Combines 3 histos (h1,h2,h3), weighting by the errors provided in
279 // he1,he2,he3, supposed to be the independent systematic errors.
280 // he1,he2,he3 are also assumed to have the same binning as h1,h2,h3
281 // The combined histo must fit the template provided (no check is performed on this)
282 // The histogram are supposed to come from the same (nearly) sample
283 // of tracks. statFrom tells the stat error of which of the 3 is
284 // going to be assigned to the combined
285 // Optionally, it is possible to rescale any of the histograms.
3725266c 286 // if hSyst is give, the histo is filled with combined syst error vs pt
287 // if errorFromBinContent is true, the weights are taken from the he* content rather than errors
ee08b77d 288 TH1F * hcomb = (TH1F*) htemplate->Clone(TString("hComb_")+h1->GetName()+"_"+h2->GetName()+h3->GetName());
289
290 // TODO: I should have used an array for h*local...
291
292 // Clone histos locally to rescale them
293 TH1F * h1local = (TH1F*) h1->Clone();
294 TH1F * h2local = (TH1F*) h2->Clone();
295 TH1F * h3local = (TH1F*) h3->Clone();
296 h1local->Scale(renorm1);
297 h2local->Scale(renorm2);
298 h3local->Scale(renorm3);
299
3beb22a2 300 const TH1 * hStatError = 0;
ee08b77d 301 if (statFrom == 0) hStatError = h1;
302 else if (statFrom == 1) hStatError = h2;
303 else if (statFrom == 2) hStatError = h3;
37e1d042 304 else {
fef6f2b3 305 Printf("AliPWGHistoTools::Combine3HistosWithErrors: wrong value of the statFrom parameter");
37e1d042 306 return NULL;
307 }
fef6f2b3 308 Printf("AliPWGHistoTools::Combine3HistosWithErrors: improve error on combined");
ee08b77d 309 // Loop over all bins and take weighted mean of all points
310 Int_t nBinComb = hcomb->GetNbinsX();
311 for(Int_t ibin = 1; ibin <= nBinComb; ibin++){
312 Int_t ibin1 = h1local->FindBin(hcomb->GetBinCenter(ibin));
313 Int_t ibin2 = h2local->FindBin(hcomb->GetBinCenter(ibin));
314 Int_t ibin3 = h3local->FindBin(hcomb->GetBinCenter(ibin));
315 Int_t ibinError = -1; // bin used to get stat error
316
317 if (statFrom == 0) ibinError = ibin1;
318 else if (statFrom == 1) ibinError = ibin2;
319 else if (statFrom == 2) ibinError = ibin3;
fef6f2b3 320 else Printf("AliPWGHistoTools::Combine3HistosWithErrors: wrong value of the statFrom parameter");
ee08b77d 321
322
323 Double_t y[3];
324 Double_t ye[3];
325 y[0] = h1local->GetBinContent(ibin1);
326 y[1] = h2local->GetBinContent(ibin2);
327 y[2] = h3local->GetBinContent(ibin3);
3725266c 328 if (errorFromBinContent) {
329 ye[0] = he1->GetBinContent(he1->FindBin(hcomb->GetBinCenter(ibin)));
330 ye[1] = he2->GetBinContent(he2->FindBin(hcomb->GetBinCenter(ibin)));
331 ye[2] = he3->GetBinContent(he3->FindBin(hcomb->GetBinCenter(ibin)));
332 } else {
333 ye[0] = he1->GetBinError(ibin1);
334 ye[1] = he2->GetBinError(ibin2);
335 ye[2] = he3->GetBinError(ibin3);
336 }
ee08b77d 337 // Set error to 0 if content is 0 (means it was not filled)
3beb22a2 338 if(!h1local->GetBinContent(ibin1)) ye[0] = 0;
339 if(!h2local->GetBinContent(ibin2)) ye[1] = 0;
340 if(!h3local->GetBinContent(ibin3)) ye[2] = 0;
ee08b77d 341
342 // Compute weighted mean
3725266c 343 // cout << "Bins: "<< ibin1 << " " << ibin2 << " " << ibin3 << endl;
ee08b77d 344 Double_t mean, err;
345 WeightedMean(3,y,ye,mean,err);
346
347
348 // Fill combined
ee08b77d 349 hcomb->SetBinContent(ibin,mean);
350 Double_t statError = 0;
3beb22a2 351 if (hStatError->GetBinContent(ibinError)) {
ee08b77d 352 // cout << "def" << endl;
353 statError = hStatError->GetBinError(ibinError)/hStatError->GetBinContent(ibinError)*hcomb->GetBinContent(ibin);
354 }
3beb22a2 355 else if (h1local->GetBinContent(ibin1)) {
ee08b77d 356 // cout << "1" << endl;
357 statError = h1local->GetBinError(ibin1)/h1local->GetBinContent(ibin1)*hcomb->GetBinContent(ibin);
358 }
3beb22a2 359 else if (h2local->GetBinContent(ibin2)) {
ee08b77d 360 // cout << "2" << endl;
361 statError = h2local->GetBinError(ibin2)/h2local->GetBinContent(ibin2)*hcomb->GetBinContent(ibin);
362 }
3beb22a2 363 else if (h3local->GetBinContent(ibin3)) {
ee08b77d 364 // cout << "3" << endl;
365 statError = h3local->GetBinError(ibin3)/h3local->GetBinContent(ibin3)*hcomb->GetBinContent(ibin);
366 }
367 hcomb->SetBinError (ibin,statError);
3725266c 368 if(hSyst) (*hSyst)->SetBinContent(ibin,err);
ee08b77d 369 // cout << "BIN " << ibin << " " << mean << " " << statError << endl;
370
371 }
372
373 hcomb->SetMarkerStyle(hStatError->GetMarkerStyle());
374 hcomb->SetMarkerColor(hStatError->GetMarkerColor());
375 hcomb->SetLineColor (hStatError->GetLineColor());
376
377 hcomb->SetXTitle(hStatError->GetXaxis()->GetTitle());
378 hcomb->SetYTitle(hStatError->GetYaxis()->GetTitle());
379
380 delete h1local;
381 delete h2local;
382 delete h3local;
383
384 return hcomb;
385}
386
387
fef6f2b3 388void AliPWGHistoTools::GetMeanDataAndExtrapolation(const TH1 * hData, TF1 * fExtrapolation, Double_t &mean, Double_t &error, Float_t min, Float_t max){
ddecf727 389 // Computes the mean of the combined data and extrapolation in a
390 // given range, use data where they are available and the function
391 // where data are not available
90421222 392 // ERROR from DATA ONLY is returned in this version!
ddecf727 393 //
fef6f2b3 394 Printf("AliPWGHistoTools::GetMeanDataAndExtrapolation: WARNING from data only");
ddecf727 395 Float_t minData = GetLowestNotEmptyBinEdge (hData);
58eeda84 396 Int_t minDataBin = GetLowestNotEmptyBin (hData);
ddecf727 397 Float_t maxData = GetHighestNotEmptyBinEdge(hData);
58eeda84 398 Int_t maxDataBin = GetHighestNotEmptyBin (hData);
ddecf727 399 Double_t integral = 0;
400 mean = 0;
401 error = 0;
402 if (min < minData) {
403 // Compute integral exploiting root function to calculate moments, "unnormalizing" them
404 mean += fExtrapolation->Mean(min,minData)*fExtrapolation->Integral(min,minData);
405 integral += fExtrapolation->Integral(min,minData);
406 cout << " Low "<< mean << " " << integral << endl;
407
408 }
409
410 if (max > maxData) {
411 // Compute integral exploiting root function to calculate moments, "unnormalizing" them
412 mean += fExtrapolation->Mean(maxData,max)*fExtrapolation->Integral(maxData,max);
413 integral += fExtrapolation->Integral(maxData,max);
414 cout << " Hi "<< mean << " " << integral << endl;
415 }
416 Float_t err2 = 0;
417
418 for(Int_t ibin = minDataBin; ibin <= maxDataBin; ibin++){
419 if(hData->GetBinCenter(ibin) < min) continue;
420 if(hData->GetBinCenter(ibin) > max) continue;
1fe08fa5 421 if(hData->GetBinContent(ibin)) {
422 mean = mean + (hData->GetBinCenter(ibin) * hData->GetBinWidth(ibin)* hData->GetBinContent(ibin));
423 err2 = err2 + TMath::Power(hData->GetBinError(ibin) * hData->GetBinCenter(ibin) * hData->GetBinWidth(ibin),2);
424 integral = integral + hData->GetBinContent(ibin) * hData->GetBinWidth(ibin);
425 }
426 else {
427 Double_t locMin = hData->GetBinLowEdge(ibin);
428 Double_t locMax = hData->GetBinLowEdge(ibin) + hData->GetBinWidth(ibin);
429 mean += fExtrapolation->Mean(locMin,locMax)*fExtrapolation->Integral(locMin,locMax);
430 Double_t deltaIntegral = fExtrapolation->Integral(locMin,locMax);
431 integral += deltaIntegral;
432 cout << "WARNING: bin " << ibin << " is empty, patching with function (+" << deltaIntegral<<")" << endl;
433 }
ddecf727 434 }
435 cout << " Data "<< mean << " " << integral << endl;
436
437 mean = mean/integral;
ffcaf7be 438 error = TMath::Sqrt(err2)/integral;
ddecf727 439
4c0d7bc7 440
ddecf727 441}
442
fef6f2b3 443TH1F * AliPWGHistoTools::CombineHistos(const TH1 * h1, TH1 * h2, const TH1* htemplate, Float_t renorm1){
4c0d7bc7 444 // Combine two histos. This assumes the histos have the same binning
445 // in the overlapping region. It computes the arithmetic mean in the
446 // overlapping region and assigns as an error the relative error
447 // h2. TO BE IMPROVED
448
449 TH1F * hcomb = (TH1F*) htemplate->Clone(TString(h1->GetName())+"_"+h2->GetName());
450
451 TH1F * h1local = (TH1F*) h1->Clone();
452 h1local->Scale(renorm1);
453
454 Int_t nBinComb = hcomb->GetNbinsX();
455 for(Int_t ibin = 1; ibin <= nBinComb; ibin++){
456 Int_t ibin1 = h1local->FindBin(hcomb->GetBinCenter(ibin));
457 Int_t ibin2 = h2->FindBin(hcomb->GetBinCenter(ibin));
458
3beb22a2 459 if (!h1local->GetBinContent(ibin1) && !h2->GetBinContent(ibin2) ) {
4c0d7bc7 460 // None has data: go to next bin
461 hcomb->SetBinContent(ibin,0);
462 hcomb->SetBinError (ibin,0);
3beb22a2 463 } else if(h1local->GetBinContent(ibin1) && !h2->GetBinContent(ibin2)) {
4c0d7bc7 464 // take data from h1local:
465 hcomb->SetBinContent(ibin,h1local->GetBinContent(ibin1));
466 hcomb->SetBinError (ibin,h1local->GetBinError(ibin1));
3beb22a2 467 } else if(!h1local->GetBinContent(ibin1) && h2->GetBinContent(ibin2)) {
4c0d7bc7 468 // take data from h2:
469 hcomb->SetBinContent(ibin,h2->GetBinContent(ibin2));
470 hcomb->SetBinError (ibin,h2->GetBinError(ibin2));
471 } else {
472 hcomb->SetBinContent(ibin,(h1local->GetBinContent(ibin1) +h2->GetBinContent(ibin2))/2);
473 // hcomb->SetBinError (ibin,h1local->GetBinError(ibin1)/h1local->GetBinContent(ibin1)*hcomb->GetBinContent(ibin));
474 hcomb->SetBinError (ibin,h2->GetBinError(ibin2)/h2->GetBinContent(ibin2)*hcomb->GetBinContent(ibin));
475 }
476
477
478 }
479
480
481 hcomb->SetMarkerStyle(h1local->GetMarkerStyle());
482 hcomb->SetMarkerColor(h1local->GetMarkerColor());
483 hcomb->SetLineColor (h1local->GetLineColor());
484
485 hcomb->SetXTitle(h1local->GetXaxis()->GetTitle());
486 hcomb->SetYTitle(h1local->GetYaxis()->GetTitle());
487 delete h1local;
488 return hcomb;
489
490}
491
492
fef6f2b3 493void AliPWGHistoTools::GetFromHistoGraphDifferentX(const TH1F * h, TF1 * f, TGraphErrors ** gBarycentre, TGraphErrors ** gXlw) {
4c0d7bc7 494
495 // Computes the baycentre in each bin and the xlw as defined in NIMA
496 // 355 - 541 using f. Returs 2 graphs with the same y content of h
497 // but with a different x (barycentre and xlw)
498
499 Int_t nbin = h->GetNbinsX();
500
501 (*gBarycentre) = new TGraphErrors();
502 (*gXlw) = new TGraphErrors();
503
504 Int_t ipoint = 0;
505 for(Int_t ibin = 1; ibin <= nbin; ibin++){
506 Float_t min = h->GetBinLowEdge(ibin);
507 Float_t max = h->GetBinLowEdge(ibin+1);
508 Double_t xerr = 0;
509 Double_t xbar = f->Mean(min,max);
c3c47c65 510 // compute xLW
4c0d7bc7 511 Double_t temp = 1./(max-min) * f->Integral(min,max);
512 Double_t epsilon = 0.000000001;
513 Double_t increment = 0.0000000001;
c3c47c65 514 Double_t xLW = min;
4c0d7bc7 515
c3c47c65 516 while ((f->Eval(xLW)- temp) > epsilon) {
517 xLW += increment;
518 if(xLW > max) {
519 Printf("Cannot find xLW");
4c0d7bc7 520 break;
521 }
522 }
523
524 if (h->GetBinContent(ibin)!=0) {
525 (*gBarycentre)->SetPoint (ipoint, xbar, h->GetBinContent(ibin));
526 (*gBarycentre)->SetPointError(ipoint, xerr, h->GetBinError(ibin));
c3c47c65 527 (*gXlw) ->SetPoint (ipoint, xLW, h->GetBinContent(ibin));
4c0d7bc7 528 (*gXlw) ->SetPointError(ipoint, xerr, h->GetBinError(ibin));
529 ipoint++;
530 }
531 }
532
533 (*gBarycentre)->SetMarkerStyle(h->GetMarkerStyle());
534 (*gBarycentre)->SetMarkerColor(h->GetMarkerColor());
535 (*gBarycentre)->SetLineColor(h->GetLineColor());
536
537 (*gBarycentre)->SetTitle(h->GetTitle());
538 (*gBarycentre)->SetName(TString("g_")+h->GetName());
539
540 (*gXlw)->SetMarkerStyle(h->GetMarkerStyle());
541 (*gXlw)->SetMarkerColor(h->GetMarkerColor());
542 (*gXlw)->SetLineColor(h->GetLineColor());
543 (*gXlw)->SetTitle(h->GetTitle());
544 (*gXlw)->SetName(TString("g_")+h->GetName());
545
546
547}
548
549
fef6f2b3 550Float_t AliPWGHistoTools::GetMean(TH1F * h, Float_t min, Float_t max, Float_t * error) {
4c0d7bc7 551
3472a634 552 // Get the mean of histo in a range; root is not reliable in sub
553 // ranges with variable binning.
4c0d7bc7 554 Int_t minBin = h->FindBin(min);
ddecf727 555 Int_t maxBin = h->FindBin(max-0.00001);
4c0d7bc7 556
557 Float_t mean = 0 ;
558 Float_t integral = 0;
ddecf727 559 Float_t err2 = 0;
560 for(Int_t ibin = minBin; ibin <= maxBin; ibin++){
4c0d7bc7 561 mean = mean + (h->GetBinCenter(ibin) * h->GetBinWidth(ibin)* h->GetBinContent(ibin));
ddecf727 562 err2 = err2 + TMath::Power(h->GetBinError(ibin) * h->GetBinCenter(ibin) * h->GetBinWidth(ibin),2);
4c0d7bc7 563 integral = integral + h->GetBinContent(ibin) * h->GetBinWidth(ibin);
564 }
565
ddecf727 566 Float_t value = mean/integral;
567 if (error) (*error) = TMath::Sqrt(err2);
568 return value;
4c0d7bc7 569
570
571}
572
fef6f2b3 573void AliPWGHistoTools::GetMean(TF1 * func, Float_t &mean, Float_t &error, Float_t min, Float_t max, Int_t normPar) {
4c0d7bc7 574
3472a634 575 // Get the mean of function in a range; If normPar is >= 0, it means
576 // that the function is defined such that par[normPar] is its
577 // integral. In this case the error on meanpt can be calculated
578 // correctly. Otherwise, the function is normalized in get moment,
579 // but the error is not computed correctly.
4c0d7bc7 580
3472a634 581 return GetMoment("fMean", TString("x*")+func->GetExpFormula(), func, mean, error, min, max, normPar);
4c0d7bc7 582
583}
584
fef6f2b3 585void AliPWGHistoTools::GetMeanSquare(TF1 * func, Float_t &mean, Float_t &error, Float_t min, Float_t max, Int_t normPar) {
4c0d7bc7 586
3472a634 587 // Get the mean2 of function in a range; If normPar is >= 0, it means
588 // that the function is defined such that par[normPar] is its
589 // integral. In this case the error on meanpt can be calculated
590 // correctly. Otherwise, the function is normalized in get moment,
591 // but the error is not computed correctly.
4c0d7bc7 592
3472a634 593 return GetMoment("fMean2", TString("x*x*")+func->GetExpFormula(), func, mean, error, min, max, normPar);
4c0d7bc7 594
595
596}
597
fef6f2b3 598void AliPWGHistoTools::GetMoment(TString name, TString var, TF1 * func, Float_t &mean, Float_t &error, Float_t min, Float_t max, Int_t normPar) {
4c0d7bc7 599
600 // returns the integral of a function derived from func by prefixing some operation.
3472a634 601 // the derived function MUST have the same parameter in the same order
4c0d7bc7 602 // Used as a base method for mean and mean2
3472a634 603 // If normPar is >= 0, it means that the function is defined such
604 // that par[normPar] is its integral. In this case the error on
605 // meanpt can be calculated correctly. Otherwise, the function is
606 // normalized using its numerical integral, but the error is not computed
607 // correctly.
608
609 // TODO:
610 // - improve to propagate error also in the case you need the
611 // numerical integrals (will be rather slow)
612 // - this version assumes that func is defined using a
613 // TFormula. Generalize to the case of a C++ function
614
fef6f2b3 615 if (normPar<0) Printf("AliPWGHistoTools::GetMoment: Warning: If normalization is required, the error may bot be correct");
616 if (!strcmp(func->GetExpFormula(),"")) Printf("AliPWGHistoTools::GetMoment: Warning: Empty formula in the base function");
4c0d7bc7 617 Int_t npar = func->GetNpar();
618
3472a634 619 // Definition changes according to the value of normPar
620 TF1 * f = normPar < 0 ?
621 new TF1(name, var) : // not normalized
622 new TF1(name, var+Form("/[%d]",normPar)); // normalized with par normPar
623
624 // integr is used to normalize if no parameter is provided
625 Double_t integr = normPar < 0 ? func->Integral(min,max) : 1;
4c0d7bc7 626
627 // The parameter of the function used to compute the mean should be
628 // the same as the parent function: fixed if needed and they should
629 // also have the same errors.
630
631 // cout << "npar :" << npar << endl;
632
633 for(Int_t ipar = 0; ipar < npar; ipar++){
634 Double_t parmin, parmax;
635 Double_t value = func->GetParameter(ipar);
3472a634 636 f->SetParameter(ipar,value);
4c0d7bc7 637 func->GetParLimits(ipar, parmin, parmax);
638 if ( parmin == parmax ) {
3beb22a2 639 // if ( parmin || (parmin == 1 && !value) ) { // not sure we I check parmin == 1 here.
640 if ( parmin || (TMath::Abs(parmin-1)<0.000001 && !value) ) { // not sure we I check parmin == 1 here. Changed like this because of coding conventions. Does it still work? FIXME
4c0d7bc7 641 f->FixParameter(ipar,func->GetParameter(ipar));
642 // cout << "Fixing " << ipar << "("<<value<<","<<parmin<<","<<parmax<<")"<<endl;
643 }
644 else {
645 f->SetParError (ipar,func->GetParError(ipar) );
646 // cout << "Setting Err" << ipar << "("<<func->GetParError(ipar)<<")"<<endl;
647 }
648 }
649 else {
650 f->SetParError (ipar,func->GetParError(ipar) );
651 // cout << "Setting Err" << ipar << "("<<func->GetParError(ipar)<<")"<<endl;
652 }
653 }
3472a634 654
655// f->Print();
656// cout << "----" << endl;
657// func->Print();
658
659 mean = normPar < 0 ? f->Integral (min,max)/integr : f->Integral (min,max);
660 error = normPar < 0 ? f->IntegralError(min,max)/integr : f->IntegralError(min,max);
4c0d7bc7 661// cout << "Mean " << mean <<"+-"<< error<< endl;
662// cout << "Integral Error " << error << endl;
663
664}
665
4c0d7bc7 666
667
fef6f2b3 668Bool_t AliPWGHistoTools::Fit (TH1 * h1, TF1* func, Float_t min, Float_t max) {
4c0d7bc7 669
670 // Fits h1 with func, preforms several checks on the quality of the
671 // fit and tries to improve it. If the fit is not good enough, it
672 // returs false.
673
674 Double_t amin; Double_t edm; Double_t errdef; Int_t nvpar; Int_t nparx;
675 TVirtualFitter *fitter;
676 cout << "--- Fitting : " << h1->GetName() << " ["<< h1->GetTitle() <<"] ---"<< endl;
677
678 h1-> Fit(func,"IME0","",min,max);
679 Int_t fitResult = h1-> Fit(func,"IME0","",min,max);
680// h1-> Fit(func,"0","",min,max);
681// Int_t fitResult = h1-> Fit(func,"0IE","",min,max);
682
683
684// From TH1:
685// The fitStatus is 0 if the fit is OK (i.e no error occurred). The
686// value of the fit status code is negative in case of an error not
687// connected with the minimization procedure, for example when a wrong
688// function is used. Otherwise the return value is the one returned
689// from the minimization procedure. When TMinuit (default case) or
690// Minuit2 are used as minimizer the status returned is : fitStatus =
691// migradResult + 10*minosResult + 100*hesseResult +
692// 1000*improveResult. TMinuit will return 0 (for migrad, minos,
693// hesse or improve) in case of success and 4 in case of error (see
694// the documentation of TMinuit::mnexcm). So for example, for an error
695// only in Minos but not in Migrad a fitStatus of 40 will be returned.
696// Minuit2 will return also 0 in case of success and different values
697// in migrad minos or hesse depending on the error. See in this case
698// the documentation of Minuit2Minimizer::Minimize for the
699// migradResult, Minuit2Minimizer::GetMinosError for the minosResult
700// and Minuit2Minimizer::Hesse for the hesseResult. If other
701// minimizers are used see their specific documentation for the status
702// code returned. For example in the case of Fumili, for the status
703// returned see TFumili::Minimize.
704
705
706 if( gMinuit->fLimset ) {
fef6f2b3 707 Printf("ERROR: AliPWGHistoTools: Parameters at limits");
4c0d7bc7 708 return kFALSE;
709 }
710
711
712 ///
713 fitter = TVirtualFitter::GetFitter();
714 Int_t fitStat = fitter->GetStats(amin, edm, errdef, nvpar, nparx);
715
716 if( ( (fitStat < 3 && gMinuit->fCstatu != "UNCHANGED ")|| (edm > 1e6) || (fitResult !=0 && fitResult < 4000) ) &&
717 TString(gMinuit->fCstatu) != "SUCCESSFUL" &&
718 TString(gMinuit->fCstatu) != "CONVERGED " ) {
719 if(fitStat < 3 && gMinuit->fCstatu != "UNCHANGED ") {
fef6f2b3 720 Printf("WARNING: AliPWGHistoTools: Cannot properly compute errors");
4c0d7bc7 721 if (fitStat == 0) Printf(" not calculated at all");
722 if (fitStat == 1) Printf(" approximation only, not accurate");
723 if (fitStat == 2) Printf(" full matrix, but forced positive-definite");
724 }
725
726 if (edm > 1e6) {
727
fef6f2b3 728 Printf("WARNING: AliPWGHistoTools: Huge EDM (%f): Fit probably failed!", edm);
4c0d7bc7 729 }
730 if (fitResult != 0) {
fef6f2b3 731 Printf("WARNING: AliPWGHistoTools: Fit Result (%d)", fitResult);
4c0d7bc7 732 }
733
fef6f2b3 734 Printf ("AliPWGHistoTools: Trying Again with Strategy = 2");
4c0d7bc7 735
736 gMinuit->Command("SET STRATEGY 2"); // more effort
737 fitResult = 0;
738 fitResult = h1-> Fit(func,"0","",min,max);
739 fitResult = h1-> Fit(func,"IME0","",min,max);
740 fitResult = h1-> Fit(func,"IME0","",min,max);
741
742 fitter = TVirtualFitter::GetFitter();
743
744 fitStat = fitter->GetStats(amin, edm, errdef, nvpar, nparx);
745
746 if(fitStat < 3 && gMinuit->fCstatu != "UNCHANGED ") {
fef6f2b3 747 Printf("ERROR: AliPWGHistoTools: Cannot properly compute errors");
4c0d7bc7 748 if (fitStat == 0) Printf(" not calculated at all");
749 if (fitStat == 1) Printf(" approximation only, not accurate");
750 if (fitStat == 2) Printf(" full matrix, but forced positive-definite");
751 cout << "[" <<gMinuit->fCstatu<<"]" << endl;
752 return kFALSE;
753 }
754
755 if (edm > 1e6) {
fef6f2b3 756 Printf("ERROR: AliPWGHistoTools: Huge EDM (%f): Fit probably failed!", edm);
4c0d7bc7 757
758 return kFALSE;
759 }
760 if (fitResult != 0) {
fef6f2b3 761 Printf("ERROR: AliPWGHistoTools: Fit Result (%d)", fitResult);
4c0d7bc7 762
763 return kFALSE;
764 }
765
766 gMinuit->Command("SET STRATEGY 1"); // back to normal value
767
768 }
769
770 cout << "---- FIT OK ----" << endl;
771
772 return kTRUE;
773
774}
775
fef6f2b3 776Int_t AliPWGHistoTools::GetLowestNotEmptyBin(const TH1*h) {
4c0d7bc7 777
778 // Return the index of the lowest non empty bin in the histo h
779
780 Int_t nbin = h->GetNbinsX();
781 for(Int_t ibin = 1; ibin <= nbin; ibin++){
782 if(h->GetBinContent(ibin)>0) return ibin;
783 }
784
785 return -1;
786
787}
788
fef6f2b3 789Int_t AliPWGHistoTools::GetHighestNotEmptyBin(const TH1*h) {
4c0d7bc7 790
791 // Return the index of the highest non empty bin in the histo h
792
793 Int_t nbin = h->GetNbinsX();
794 for(Int_t ibin = nbin; ibin > 0; ibin--){
795 if(h->GetBinContent(ibin)>0) return ibin;
796 }
797
798 return -1;
799
800}
801
fef6f2b3 802void AliPWGHistoTools::GetResiduals(const TGraphErrors * gdata, const TF1 * func, TH1F ** hres, TGraphErrors ** gres) {
4c0d7bc7 803
804 // Returns a graph of residuals vs point and the res/err distribution
805
806 Int_t npoint = gdata->GetN();
807
808 (*gres) =new TGraphErrors();
809 (*hres) = new TH1F(TString("hres_")+gdata->GetName()+"-"+func->GetName(),
810 TString("hres_")+gdata->GetName()+"-"+func->GetName(),
811 20,-5,5);
812
813
814 for(Int_t ipoint = 0; ipoint < npoint; ipoint++){
815 Float_t x = gdata->GetX()[ipoint];
816 Float_t res = (gdata->GetY()[ipoint] - func->Eval(x))/func->Eval(x);
817 Float_t err = gdata->GetEY()[ipoint]/func->Eval(x);
818 (*hres)->Fill(res/err);
819 (*gres)->SetPoint(ipoint, x, res/err);
820 // (*gres)->SetPointError(ipoint, 0, err);
821
822 }
823
824 (*gres)->SetMarkerStyle(gdata->GetMarkerStyle());
825 (*gres)->SetMarkerColor(gdata->GetMarkerColor());
826 (*gres)->SetLineColor (gdata->GetLineColor());
827 (*gres)->GetHistogram()->GetYaxis()->SetTitle("(data-function)/function");
828 (*hres)->SetMarkerStyle(gdata->GetMarkerStyle());
829 (*hres)->SetMarkerColor(gdata->GetMarkerColor());
830 (*hres)->SetLineColor (gdata->GetLineColor());
831
832
833
834}
835
fef6f2b3 836void AliPWGHistoTools::GetResiduals(const TH1F* hdata, const TF1 * func, TH1F ** hres, TH1F ** hresVsBin) {
4c0d7bc7 837
838 // Returns an histo of residuals bin by bin and the res/err distribution
839
840 if (!func) {
fef6f2b3 841 Printf("AliPWGHistoTools::GetResiduals: No function provided");
4c0d7bc7 842 return;
843 }
844 if (!hdata) {
fef6f2b3 845 Printf("AliPWGHistoTools::GetResiduals: No data provided");
4c0d7bc7 846 return;
847 }
848
849 (*hresVsBin) = (TH1F*) hdata->Clone(TString("hres_")+hdata->GetName());
850 (*hresVsBin)->Reset();
851 (*hres) = new TH1F(TString("hres_")+hdata->GetName()+"-"+func->GetName(),
852 TString("hres_")+hdata->GetName()+"-"+func->GetName(),
853 20,-5,5);
854
855 Int_t nbin = hdata->GetNbinsX();
856 for(Int_t ibin = 1; ibin <= nbin; ibin++){
3beb22a2 857 if(!hdata->GetBinContent(ibin)) continue;
4c0d7bc7 858 Float_t res = (hdata->GetBinContent(ibin) - func->Eval(hdata->GetBinCenter(ibin)) ) /
859 func->Eval(hdata->GetBinCenter(ibin));
860 Float_t err = hdata->GetBinError (ibin) / func->Eval(hdata->GetBinCenter(ibin));
861 (*hresVsBin)->SetBinContent(ibin,res);
862 (*hresVsBin)->SetBinError (ibin,err);
863 (*hres)->Fill(res/err);
864
865 }
866
867 (*hresVsBin)->SetMarkerStyle(hdata->GetMarkerStyle());
868 (*hresVsBin)->SetMarkerColor(hdata->GetMarkerColor());
869 (*hresVsBin)->SetLineColor (hdata->GetLineColor() );
870 (*hresVsBin)->GetYaxis()->SetTitle("(data-function)/function");
871 (*hres)->SetMarkerStyle(hdata->GetMarkerStyle());
872 (*hres)->SetMarkerColor(hdata->GetMarkerColor());
873 (*hres)->SetLineColor (hdata->GetLineColor() );
874
875}
876
fef6f2b3 877void AliPWGHistoTools::GetYield(TH1* h, TF1 * f, Double_t &yield, Double_t &yieldError, Float_t min, Float_t max,
4c0d7bc7 878 Double_t *partialYields, Double_t *partialYieldsErrors){
879
880 // Returns the yield extracted from the data in the histo where
881 // there are points and from the fit to extrapolate, in the given
882 // range.
883
884 // Partial yields are also returned if the corresponding pointers are non null
885
886 Int_t bin1 = h->FindBin(min);
887 Int_t bin2 = h->FindBin(max);
888 Float_t bin1Edge = GetLowestNotEmptyBinEdge (h);
889 Float_t bin2Edge = GetHighestNotEmptyBinEdge(h);
1fe08fa5 890 Int_t lowestNE = GetLowestNotEmptyBin (h);
891 Int_t highestNE = GetHighestNotEmptyBin(h);
892
893 Double_t integralFromHistoError = 0;
894 Double_t integralFromHisto = 0;
895 // Double_t integralFromHisto = DoIntegral(h,bin1,bin2,-1,-1,-1,-1,integralFromHistoError,"width",1);
4c0d7bc7 896
1fe08fa5 897 for(Int_t ibin = TMath::Max(bin1,lowestNE); ibin <= TMath::Min(bin2,highestNE); ibin++){
898 if(h->GetBinContent(ibin)) {
899 integralFromHisto = integralFromHisto + h->GetBinContent(ibin) * h->GetBinWidth(ibin);
900 integralFromHistoError = integralFromHistoError + h->GetBinError(ibin)*h->GetBinError(ibin) * h->GetBinWidth(ibin);
901 }
902 else {
903 Double_t locMin = h->GetBinLowEdge(ibin);
904 Double_t locMax = h->GetBinLowEdge(ibin) + h->GetBinWidth(ibin);
905 Double_t deltaIntegral = f->Integral(locMin,locMax);
906 integralFromHisto += deltaIntegral;
907 integralFromHistoError = integralFromHistoError + f->IntegralError(locMin,locMax)*f->IntegralError(locMin,locMax);
908 cout << "WARNING: bin " << ibin << " is empty, patching with function (+" << deltaIntegral<<")" << endl;
909 }
910 }
911
912 integralFromHistoError = TMath::Sqrt(integralFromHistoError);// ok, this is a bit dumb. Just in case the code above is changed again.
913
4c0d7bc7 914
915 Double_t integralBelow = min < bin1Edge ? f->Integral(min,bin1Edge) : 0;
916 Double_t integralBelowError = min < bin1Edge ? f->IntegralError(min,bin1Edge) : 0;
917 Double_t integralAbove = max > bin2Edge ? f->Integral(bin2Edge,max) : 0;
169d33f6 918 Double_t integralAboveError = max > bin2Edge ? f->IntegralError(bin2Edge,max) : 0;
4c0d7bc7 919
3beb22a2 920// cout << "GetYield INFO" << endl;
921// cout << " " << bin1Edge << " " << bin2Edge << endl;
922// cout << " " << integralFromHisto << " " << integralBelow << " " << integralAbove << endl;
923// cout << " " << integralFromHistoError << " " << integralBelowError << " " << integralAboveError << endl;
4c0d7bc7 924
925 if(partialYields) {
926 partialYields[0] = integralFromHisto;
927 partialYields[1] = integralBelow;
928 partialYields[2] = integralAbove;
929 }
930 if(partialYieldsErrors) {
931 partialYieldsErrors[0] = integralFromHistoError;
932 partialYieldsErrors[1] = integralBelowError;
933 partialYieldsErrors[2] = integralAboveError;
934 }
935 yield = integralFromHisto+integralBelow+integralAbove;
936 yieldError = TMath::Sqrt(integralFromHistoError*integralFromHistoError+
937 integralBelowError*integralBelowError+
938 integralAboveError*integralAboveError);
939
940}
941
fef6f2b3 942TGraphErrors * AliPWGHistoTools::DivideGraphByFunc(const TGraphErrors * g, const TF1 * f, Bool_t invert){
4c0d7bc7 943
944 // Divides g/f. If invert == true => f/g
945
946 TGraphErrors * gRatio = new TGraphErrors();
947 Int_t npoint = g->GetN();
948 for(Int_t ipoint = 0; ipoint < npoint; ipoint++){
949 Double_t x = g->GetX()[ipoint];
950 Double_t ratio = invert ? f->Eval(x)/g->GetY()[ipoint] :g->GetY()[ipoint]/f->Eval(x);
951 gRatio->SetPoint (ipoint, x, ratio);
90421222 952 if(f->Eval(x) && strcmp(g->ClassName(),"TGraphAsymmErrors")) gRatio->SetPointError(ipoint, 0, g->GetEY()[ipoint]/f->Eval(x));
4c0d7bc7 953 // cout << x << " " << g->GetY()[ipoint] << " " << f->Eval(x) << endl;
954
955 }
956 gRatio->SetMarkerStyle(20);
957 //gRatio->Print();
958 return gRatio;
959
960}
961
8681985a 962TGraphErrors * AliPWGHistoTools::Divide2Graphs(const TGraph * g1, const TGraph * g2, Int_t strategy){
963
964 // Divides g1/g2,
965 // 2 strategies are possible:
966 // - strategy = 0 looks for point with very close centers (also propagates error in this case)
967 // - strategy = 1 Loop over all points from g1 (xi,yi), interpolates the TGraphs with a spline and computes the ratio as yi / SplineG2(xi)
90421222 968
90421222 969 TGraphErrors * gRatio = new TGraphErrors();
8681985a 970
971 if(strategy == 0) {
972 Int_t ipoint=0;
973 Int_t npoint1 = g1->GetN();
974 Int_t npoint2 = g2->GetN();
975 for(Int_t ipoint1 = 0; ipoint1 < npoint1; ipoint1++){
976 Double_t x1 = g1->GetX()[ipoint1];
977 for(Int_t ipoint2 = 0; ipoint2 < npoint2; ipoint2++){
978 Double_t x2 = g2->GetX()[ipoint2];
979 if((TMath::Abs(x1-x2)/(x1+x2)*2)<0.01) {
980 Double_t ratio = g2->GetY()[ipoint2] ? g1->GetY()[ipoint1]/g2->GetY()[ipoint2] : 0;
981 Double_t eratio = 0;
982 if(g1->InheritsFrom("TGraphErrors") && g2->InheritsFrom("TGraphErrors")) {
983 eratio = g2->GetY()[ipoint2] ?
984 TMath::Sqrt(g1->GetEY()[ipoint1]*g1->GetEY()[ipoint1]/g1->GetY()[ipoint1]/g1->GetY()[ipoint1] +
985 g2->GetEY()[ipoint2]/g2->GetY()[ipoint2]/g2->GetY()[ipoint2] ) * ratio
986 : 0;
987 }
988 gRatio->SetPoint (ipoint, x1, ratio);
989 gRatio->SetPointError(ipoint, 0, eratio);
990 ipoint++;
991 cout << ipoint << " [" << x1 << "] " << g1->GetY()[ipoint1] << "/" << g2->GetY()[ipoint2] << " = " << ratio <<"+-"<<eratio<< endl;
992
993 // cout << x << " " << g->GetY()[ipoint] << " " << f->Eval(x) << endl;
fef6f2b3 994 }
90421222 995
90421222 996 }
90421222 997 }
998 }
8681985a 999 else if (strategy == 1) {
1000 TSpline3 * splG2 = new TSpline3("fGraphSplG2",g2);
1001 Int_t npoint1 = g1->GetN();
1002 for(Int_t ipoint1 = 0; ipoint1 < npoint1; ipoint1++){
1003 Double_t x1 = g1->GetX()[ipoint1];
1004 Double_t y1 = g1->GetY()[ipoint1];
1005 Double_t ratio = y1/splG2->Eval(x1);
1006 gRatio->SetPoint(ipoint1, x1, ratio);
1007
1008 }
1009 delete splG2;
1010 }
1011 else Printf("AliPWGHistoTools::Divide2Graphs(): Invalid strategy [%d]", strategy);
1012
1013 gRatio->SetMarkerStyle(20);
90421222 1014 //gRatio->Print();
1015 return gRatio;
1016
fef6f2b3 1017}
1018TGraphErrors * AliPWGHistoTools::Add2Graphs(const TGraphErrors * g1, const TGraphErrors * g2){
1019
1020 // Sums g1/g2, looks for point with very close centers
1021 Int_t ipoint=0;
1022 TGraphErrors * gSum = new TGraphErrors();
1023 Int_t npoint1 = g1->GetN();
1024 Int_t npoint2 = g2->GetN();
1025 for(Int_t ipoint1 = 0; ipoint1 < npoint1; ipoint1++){
1026 Double_t x1 = g1->GetX()[ipoint1];
1027 for(Int_t ipoint2 = 0; ipoint2 < npoint2; ipoint2++){
1028 Double_t x2 = g2->GetX()[ipoint2];
1029 if((TMath::Abs(x1-x2)/(x1+x2)*2)<0.01) {
1030 Double_t sum = g1->GetY()[ipoint1]+g2->GetY()[ipoint2];
1031 Double_t esum = 0;
1032 if(g1->InheritsFrom("TGraphErrors") && g2->InheritsFrom("TGraphErrors")) {
1033 esum =
1034 TMath::Sqrt(g1->GetEY()[ipoint1]*g1->GetEY()[ipoint1] +
1035 g2->GetEY()[ipoint2]*g2->GetEY()[ipoint2] ) ;
1036
1037 }
1038 gSum->SetPoint (ipoint, x1, sum);
1039 gSum->SetPointError(ipoint, 0, esum);
1040 ipoint++;
1041 cout << ipoint << " [" << x1 << "] " << g1->GetY()[ipoint1] << "+" << g2->GetY()[ipoint2] << " = " << sum <<"+-"<<esum<< endl;
1042
1043 // cout << x << " " << g->GetY()[ipoint] << " " << f->Eval(x) << endl;
1044 }
1045
1046 }
1047 }
1048 gSum->SetMarkerStyle(20);
1049 //gSum->Print();
1050 return gSum;
1051
90421222 1052}
1053
fef6f2b3 1054TGraphErrors * AliPWGHistoTools::DivideGraphByHisto(const TGraphErrors * g, TH1 * h, Bool_t invert){
4c0d7bc7 1055
1056 // Divides g/h. If invert == true => h/g
1057
169d33f6 1058 Bool_t skipError = kFALSE;
1059 if(!strcmp(g->ClassName(),"TGraph")) skipError = kTRUE;
1060 if(!strcmp(g->ClassName(),"TGraphAsymmErrors")) skipError = kTRUE;
1061 if(skipError) {
1062 Printf("WARNING: Skipping graph errors");
1063 }
4c0d7bc7 1064 TGraphErrors * gRatio = new TGraphErrors();
1065 Int_t npoint = g->GetN();
1066 for(Int_t ipoint = 0; ipoint < npoint; ipoint++){
1067 Double_t xj = g->GetX()[ipoint];
1068 Double_t yj = g->GetY()[ipoint];
169d33f6 1069 Double_t yje = skipError ? 0 : g->GetEY()[ipoint];
4c0d7bc7 1070
1071 Int_t binData = h->FindBin(xj);
1072 Double_t yd = h->GetBinContent(binData);
1073 Double_t yde = h->GetBinError(binData);
1074 Double_t xd = h->GetBinCenter(binData);
1075
4c0d7bc7 1076
1077
3beb22a2 1078 if (!yd) continue;
4c0d7bc7 1079
1080 if (TMath::Abs(xd-xj)/TMath::Abs(xd) > 0.01){
1081 Printf( "WARNING: bin center (%f) and x graph (%f) are more than 1 %% away, skipping",xd,xj );
1082 continue;
1083
1084 }
1085
1086 Double_t ratio = invert ? yd/yj : yj/yd;
1087
1088 gRatio->SetPoint(ipoint, xj, ratio);
1089 gRatio->SetPointError(ipoint, 0, TMath::Sqrt(yde*yde/yd/yd + yje*yje/yj/yj)*ratio);
1090 // gRatio->SetPointError(ipoint, 0, yje/yj * ratio);
1091 }
1092
1093 return gRatio;
1094
1095
1096}
1097
fef6f2b3 1098TH1F * AliPWGHistoTools::DivideHistoByFunc(TH1F * h, TF1 * f, Bool_t invert){
4c0d7bc7 1099
1100 // Divides h/f. If invert == true => f/g
1101 // Performs the integral of f on the bin range to perform the ratio
1102 // Returns a histo with the same binnig as h
1103
1104 // Prepare histo for ratio
1105 TH1F * hRatio = (TH1F*) h->Clone(TString("hRatio_")+h->GetName()+"_"+f->GetName());
1106 hRatio->Reset();
1107 // Set y title
1108 if(!invert) hRatio->SetYTitle(TString(h->GetName())+"/"+f->GetName());
1109 else hRatio->SetYTitle(TString(f->GetName())+"/"+h->GetName());
1110
1111 // Loop over all bins
1112 Int_t nbin = hRatio->GetNbinsX();
1113
1114 for(Int_t ibin = 1; ibin <= nbin; ibin++){
1115 Double_t yhisto = h->GetBinContent(ibin);
1116 Double_t yerror = h->GetBinError(ibin);
1117 Double_t xmin = h->GetBinLowEdge(ibin);
1118 Double_t xmax = h->GetBinLowEdge(ibin+1);
1119 Double_t yfunc = f->Integral(xmin,xmax)/(xmax-xmin);
097f6933 1120 Double_t ratio = yfunc&&yhisto ? (invert ? yfunc/yhisto : yhisto/yfunc) : 0 ;
1121 Double_t error = yfunc ? yerror/yfunc : 0 ;
4c0d7bc7 1122 hRatio->SetBinContent(ibin,ratio);
1123 hRatio->SetBinError (ibin,error);
1124 }
1125
1126 return hRatio;
1127
1128}
ee08b77d 1129
fef6f2b3 1130void AliPWGHistoTools::WeightedMean(Int_t npoints, const Double_t *x, const Double_t *xerr, Double_t &mean, Double_t &meanerr){
ee08b77d 1131
3beb22a2 1132 // Performs the weighted mean of npoints numbers in x with errors in xerr
ee08b77d 1133
1134 mean = 0;
1135 meanerr = 0;
1136
1137 Double_t sumweight = 0;
1138
1139 for (Int_t ipoint = 0; ipoint < npoints; ipoint++){
1140
1141 Double_t xerr2 = xerr[ipoint]*xerr[ipoint];
1142 if(xerr2>0){
1143 // cout << "xe2 " << xerr2 << endl;
1144 Double_t weight = 1. / xerr2;
1145 sumweight += weight;
1146 mean += weight * x[ipoint];
3725266c 1147 }// else cout << " Skipping " << ipoint << endl;
ee08b77d 1148
1149 }
1150
1151
1152 if(sumweight){
1153 mean /= sumweight;
1154 meanerr = TMath::Sqrt(1./ sumweight);
1155 }
1156 else {
3725266c 1157 // cout << " No sumweight" << endl;
ee08b77d 1158 mean = 0;
1159 meanerr = 0;
1160 }
1161
1162
1163}
3725266c 1164
fef6f2b3 1165TH1 * AliPWGHistoTools::GetRelativeError(TH1 * h){
57b5143c 1166 // Returns an histogram with the same binning as h, filled with the relative error bin by bin
1167 TH1 * hrel = (TH1*) h->Clone(TString(h->GetName())+"_rel");
1168 hrel->Reset();
1169 Int_t nbin = hrel->GetNbinsX();
1170 for(Int_t ibin = 1; ibin <= nbin; ibin++){
097f6933 1171 if(h->GetBinError(ibin)){
1172 hrel->SetBinContent(ibin,h->GetBinError(ibin)/h->GetBinContent(ibin));
1173 } else {
1174 hrel->SetBinContent(ibin,0);
1175 }
57b5143c 1176 hrel->SetBinError(ibin,0);
1177 }
1178
1179 return hrel;
1180}
1181
1182
fef6f2b3 1183void AliPWGHistoTools::GetValueAndError(TH1 * hdest, const TH1 * hvalue, const TH1 * herror, Bool_t isPercentError) {
3725266c 1184
1185 // Put into source, bin-by-bin, the values from hvalue and the
1186 // errors from content from herror.
1187 // Used mainly to combine histos of systemati errors with their spectra
1188 // Set isPercentError to kTRUE if the error is given in %
1189
1190 if(hdest == NULL){
fef6f2b3 1191 Printf("AliPWGHistoTools::GetValueAndError Errror: hdest is null");
3725266c 1192 return;
1193 }
1194
1195
1196 Int_t nbin = hdest->GetNbinsX();
1197 Int_t nBinSourceVal = hvalue->GetNbinsX();
1198 Int_t nBinSourceErr = herror->GetNbinsX();
1199
1200 for(Int_t iBinDest = 1; iBinDest <= nbin; iBinDest++){
1201 Float_t lowPtDest=hdest->GetBinLowEdge(iBinDest);
1202 Float_t binWidDest=hdest->GetBinWidth(iBinDest);
1203 // Loop over Source bins and find overlapping bins to Dest
1204 // First value then error
1205 // Value
1206 Bool_t foundValue = kFALSE;
1207 for(Int_t iBinSourceVal=1; iBinSourceVal<=nBinSourceVal; iBinSourceVal++){
1208 Float_t lowPtSource= hvalue->GetBinLowEdge(iBinSourceVal) ;
1209 Float_t binWidSource= hvalue->GetBinWidth(iBinSourceVal);
1210 if(TMath::Abs(lowPtDest-lowPtSource)<0.001 && TMath::Abs(binWidSource-binWidDest)<0.001){
1211 Double_t content = hvalue->GetBinContent(iBinSourceVal);
1212 hdest->SetBinContent(iBinDest, content);
1213 foundValue = kTRUE;
1214 break;
1215 }
1216 }
1217 // if (!foundValue){
fef6f2b3 1218 // Printf("AliPWGHistoTools::GetValueAndError: Error: cannot find matching value source bin for destination %d",iBinDest);
3725266c 1219 // }
1220
1221 // Error
1222 Bool_t foundError = kFALSE;
1223 for(Int_t iBinSourceErr=1; iBinSourceErr<=nBinSourceErr; iBinSourceErr++){
1224 Float_t lowPtSource= herror->GetBinLowEdge(iBinSourceErr) ;
1225 Float_t binWidSource= herror->GetBinWidth(iBinSourceErr);
1226 if(TMath::Abs(lowPtDest-lowPtSource)<0.001 && TMath::Abs(binWidSource-binWidDest)<0.001){
1227 Double_t error = herror->GetBinContent(iBinSourceErr);
1228 // cout << "-> " << iBinDest << " " << error << " " << hdest->GetBinContent(iBinDest) << endl;
1229
1230 hdest->SetBinError(iBinDest, isPercentError ? error * hdest->GetBinContent(iBinDest) : error);
1231 foundError=kTRUE;
1232 break;
1233 }
1234 }
1235 // if (!foundError ){
fef6f2b3 1236 // Printf("AliPWGHistoTools::GetValueAndError: Error: cannot find matching error source bin for destination %d",iBinDest);
3725266c 1237 // }
1238 }
1239
1240
1241}
1242
fef6f2b3 1243void AliPWGHistoTools::AddHisto(TH1 * hdest, const TH1* hsource, Bool_t getMirrorBins) {
3725266c 1244
1245 // Adds hsource to hdest bin by bin, even if they have a different
1246 // binning If getMirrorBins is true, it takes the negative bins
1247 // (Needed because sometimes the TPC uses the positive axis for
1248 // negative particles and the possitive axis for positive
1249 // particles).
1250
1251
1252 if (hdest == NULL) {
1253 Printf("Error: hdest is NULL\n");
37e1d042 1254 return;
3725266c 1255 }
1256 if (hsource == NULL) {
1257 Printf("Error: hsource is NULL\n");
37e1d042 1258 return;
3725266c 1259 }
1260
1261 Int_t nBinSource = hsource->GetNbinsX();
1262 Int_t nBinDest = hdest->GetNbinsX();
1263
1264 // Loop over destination bins,
1265 for(Int_t iBinDest=1; iBinDest<=nBinDest; iBinDest++){
1266 Float_t lowPtDest=hdest->GetBinLowEdge(iBinDest);
1267 Float_t binWidDest=hdest->GetBinWidth(iBinDest);
1268 // Loop over Source bins and find overlapping bins to Dest
1269 Bool_t found = kFALSE;
1270 for(Int_t iBinSource=1; iBinSource<=nBinSource; iBinSource++){
1271 Float_t lowPtSource= getMirrorBins ? -hsource->GetBinLowEdge(iBinSource)+hsource->GetBinWidth(iBinSource) : hsource->GetBinLowEdge(iBinSource) ;
1272 Float_t binWidSource= hsource->GetBinWidth(iBinSource) ;
1273 if(TMath::Abs(lowPtDest-lowPtSource)<0.001 && TMath::Abs(binWidSource-binWidDest)<0.001){
1274 Float_t dest=hdest->GetBinContent(iBinDest);
1275 Float_t source=hsource->GetBinContent(iBinSource);
1276 Float_t edest=hdest->GetBinError(iBinDest);
1277 Float_t esource=hsource->GetBinError(iBinSource);
1278 Double_t cont=dest+source;
1279 Double_t econt=TMath::Sqrt(edest*edest+esource*esource);
1280 hdest->SetBinContent(iBinDest,cont);
1281 hdest->SetBinError (iBinDest,econt);
1282 found = kTRUE;
1283
1284 break;
1285 }
1286 }
77233d47 1287 // if (!found){
1288 // Printf("Error: cannot find matching source bin for destination %d",iBinDest);
1289 // }
3725266c 1290 }
1291
1292
1293}
1294
fef6f2b3 1295void AliPWGHistoTools::GetHistoCombinedErrors(TH1 * hdest, const TH1 * h1) {
058137a6 1296
1297 // Combine the errors of hdest with the errors of h1, summing in
1298 // quadrature. Results are put in hdest. Histograms are assumed to
1299 // have the same binning
1300
1301 Int_t nbin = hdest->GetNbinsX();
90421222 1302 for(Int_t ibin = 1; ibin <= nbin; ibin++){
058137a6 1303 Double_t e1 = hdest->GetBinError(ibin);
1304 Double_t e2 = h1->GetBinError(ibin);
1305 hdest->SetBinError(ibin, TMath::Sqrt(e1*e1+e2*e2));
1306 }
1307
90421222 1308
058137a6 1309}
d8e6677d 1310
fef6f2b3 1311TH1F * AliPWGHistoTools::DivideHistosDifferentBins(const TH1F* h1, const TH1F* h2) {
d8e6677d 1312 // Divides 2 histos even if they have a different binning. Finds
1313 // overlapping bins and divides them
1314
1315 // 1. clone histo
1316 TH1F * hRatio = new TH1F(*h1);
1317 Int_t nBinsH1=h1->GetNbinsX();
1318 Int_t nBinsH2=h2->GetNbinsX();
1319 // Loop over H1 bins,
1320 for(Int_t iBin=1; iBin<=nBinsH1; iBin++){
1321 hRatio->SetBinContent(iBin,0.);
1322 hRatio->SetBinContent(iBin,0.);
1323 Float_t lowPtH1=h1->GetBinLowEdge(iBin);
1324 Float_t binWidH1=h1->GetBinWidth(iBin);
1325 // Loop over H2 bins and find overlapping bins to H1
1326 for(Int_t jBin=1; jBin<=nBinsH2; jBin++){
1327 Float_t lowPtH2=h2->GetBinLowEdge(jBin);
1328 Float_t binWidH2=h2->GetBinWidth(jBin);
1329 if(TMath::Abs(lowPtH1-lowPtH2)<0.001 && TMath::Abs(binWidH2-binWidH1)<0.001){
1330 Float_t numer=h1->GetBinContent(iBin);
1331 Float_t denom=h2->GetBinContent(jBin);
1332 Float_t enumer=h1->GetBinError(iBin);
1333 Float_t edenom=h2->GetBinError(jBin);
1334 Double_t ratio=0.;
1335 Double_t eratio=0.;
1336 if(numer>0. && denom>0.){
1337 ratio=numer/denom;
1338 eratio=ratio*TMath::Sqrt((enumer/numer)*(enumer/numer)+(edenom/denom)*(edenom/denom));
1339 }
1340 hRatio->SetBinContent(iBin,ratio);
1341 hRatio->SetBinError(iBin,eratio);
1342 break;
1343 }
1344 }
1345 }
1346 return hRatio;
1347}
57b5143c 1348
fef6f2b3 1349Double_t AliPWGHistoTools::DoIntegral(TH1* h, Int_t binx1, Int_t binx2, Int_t biny1, Int_t biny2, Int_t binz1, Int_t binz2, Double_t & error ,
57b5143c 1350 Option_t *option, Bool_t doError)
1351{
1352 // function to compute integral and optionally the error between the limits
1353 // specified by the bin number values working for all histograms (1D, 2D and 3D)
1354 // copied from TH! to fix a bug still present in 5-27-06b
1355 Int_t nbinsx = h->GetNbinsX();
1356 if (binx1 < 0) binx1 = 0;
1357 if (binx2 > nbinsx+1 || binx2 < binx1) binx2 = nbinsx+1;
1358 if (h->GetDimension() > 1) {
1359 Int_t nbinsy = h->GetNbinsY();
1360 if (biny1 < 0) biny1 = 0;
1361 if (biny2 > nbinsy+1 || biny2 < biny1) biny2 = nbinsy+1;
1362 } else {
1363 biny1 = 0; biny2 = 0;
1364 }
1365 if (h->GetDimension() > 2) {
1366 Int_t nbinsz = h->GetNbinsZ();
1367 if (binz1 < 0) binz1 = 0;
1368 if (binz2 > nbinsz+1 || binz2 < binz1) binz2 = nbinsz+1;
1369 } else {
1370 binz1 = 0; binz2 = 0;
1371 }
1372
1373 // - Loop on bins in specified range
1374 TString opt = option;
1375 opt.ToLower();
1376 Bool_t width = kFALSE;
1377 if (opt.Contains("width")) width = kTRUE;
1378
1379
1380 Double_t dx = 1.;
1381 Double_t dy = 1.;
1382 Double_t dz = 1.;
1383 Double_t integral = 0;
1384 Double_t igerr2 = 0;
1385 for (Int_t binx = binx1; binx <= binx2; ++binx) {
1386 if (width) dx = h->GetXaxis()->GetBinWidth(binx);
1387 for (Int_t biny = biny1; biny <= biny2; ++biny) {
1388 if (width) dy = h->GetYaxis()->GetBinWidth(biny);
1389 for (Int_t binz = binz1; binz <= binz2; ++binz) {
1390 if (width) dz = h->GetZaxis()->GetBinWidth(binz);
1391 Int_t bin = h->GetBin(binx, biny, binz);
1392 if (width) integral += h->GetBinContent(bin)*dx*dy*dz;
1393 else integral += h->GetBinContent(bin);
1394 if (doError) {
1395 if (width) igerr2 += h->GetBinError(bin)*h->GetBinError(bin)*dx*dy*dz*dx*dy*dz;
1396 else igerr2 += h->GetBinError(bin)*h->GetBinError(bin);
1397 }
1398 // cout << h->GetBinContent(bin) << " " << h->GetBinError(bin) << " " << dx*dy*dz << " " << integral << " +- " << igerr2 << endl;
1399
1400 }
1401 }
1402 }
1403
1404 if (doError) error = TMath::Sqrt(igerr2);
1405 return integral;
1406}
90421222 1407
fef6f2b3 1408Double_t AliPWGHistoTools::dMtdptFunction(Double_t *x, Double_t *p) {
90421222 1409
1410 // Computes the dmt/dptdeta function using the dN/dpt function
1411 // This is a protected function used internally by GetdMtdy to integrate dN/dpt function using mt as a weight
1412 // The mass of the particle is given as p[0]
1413 Double_t pt = x[0];
1414 Double_t mass = p[0];
1415 Double_t mt = TMath::Sqrt(pt*pt + mass*mass);
1416 Double_t jacobian = pt/mt;
1417 if(!fdNdptForETCalc){
fef6f2b3 1418 Printf("AliPWGHistoTools::dMtdptFunction: ERROR: fdNdptForETCalc not defined");
90421222 1419 return 0;
1420 }
1421 Double_t dNdpt = fdNdptForETCalc->Eval(pt);
1422 return dNdpt*mt*jacobian; // FIXME: do I have to normalize somehow?
1423
1424}
1425
fef6f2b3 1426Double_t AliPWGHistoTools::GetdMtdEta(TH1 *hData, TF1 * fExtrapolation, Double_t mass) {
90421222 1427 // Computes dMtdEta integrating dN/dptdy with the proper weights and jacobian.
5e1a7931 1428 Printf("WARNING ALIBWTOOLS::GetdMtdEta: ONLY USING FUNCTION FOR THE TIME BEING, hData");
1429 if(!hData) {
1430 Printf("hData not set");
1431 }
90421222 1432
1433 // Assign the fiunction used internally by dMtdptFunction
1434 fdNdptForETCalc = fExtrapolation;
1435 // Create the function to be integrated
1436 TF1 * funcdMtdPt = new TF1 ("funcdMtdPt", dMtdptFunction, 0.0, 20, 1);
1437 funcdMtdPt->SetParameter(0,mass);
1438 // Integrate it
1439 Double_t dMtdEta = funcdMtdPt->Integral(0,100);
1440 // Clean up
1441 fdNdptForETCalc=0;
1442 delete funcdMtdPt;
1443 //return
1444 return dMtdEta;
1445
1446}
1fe08fa5 1447
1448
1449
8681985a 1450
1451void AliPWGHistoTools::ScaleGraph(TGraph * g1, Double_t scale) {
1452
1453 // Scale a grh by the factor scale. If g1 is a TGraph(Asym)Error, errors are also scaled
1454
1455 if(!g1) return;
1456 Bool_t isErrors = TString(g1->ClassName()) == "TGraphErrors";
1457 Bool_t isAErrors = TString(g1->ClassName()) == "TGraphAsymmErrors";
1458
1459 Int_t npoint = g1->GetN();
1460 for (Int_t ipoint = 0; ipoint<npoint; ipoint++) {
1461 Double_t x = g1->GetX()[ipoint];
1462 Double_t y = g1->GetY()[ipoint];
1463 Double_t val = y*scale;
1464 g1->SetPoint(ipoint, x, val);
1465 // if it is aclass with errors, also scale those
1466 if (isAErrors) {
1467 Double_t errxlow = g1->GetEXlow() [ipoint];
1468 Double_t errxhigh = g1->GetEXhigh()[ipoint];
1469 Double_t errylow = g1->GetEYlow() [ipoint]*scale;
1470 Double_t erryhigh = g1->GetEYhigh()[ipoint]*scale;
1471 ((TGraphAsymmErrors*)g1)->SetPointError(ipoint, errxlow, errxhigh, errylow, erryhigh);
1472 }
1473 else if (isErrors) {
1474 Double_t erry = g1->GetEY()[ipoint]*scale;
1475 ((TGraphErrors*)g1)->SetPointError(ipoint, g1->GetEX()[ipoint], erry);
1476 }
1477 }
1478
1479
1480}