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284050f7 1/**************************************************************************
2 * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
3 * *
4 * Author: The ALICE Off-line Project. *
5 * Contributors are mentioned in the code where appropriate. *
6 * *
7 * Permission to use, copy, modify and distribute this software and its *
8 * documentation strictly for non-commercial purposes is hereby granted *
9 * without fee, provided that the above copyright notice appears in all *
10 * copies and that both the copyright notice and this permission notice *
11 * appear in the supporting documentation. The authors make no claims *
12 * about the suitability of this software for any purpose. It is *
13 * provided "as is" without express or implied warranty. *
14 **************************************************************************/
15
16
17///////////////////////////////////////////////////////////////////////////
18// Class AliMathBase
19//
20// Subset of matheamtical functions not included in the TMath
21//
22
23///////////////////////////////////////////////////////////////////////////
24#include "TMath.h"
25#include "AliMathBase.h"
26#include "Riostream.h"
f6659a9d 27#include "TH1F.h"
3392b4c9 28#include "TH3.h"
f6659a9d 29#include "TF1.h"
30#include "TLinearFitter.h"
5608e15a 31
9c56b409 32#include "AliExternalTrackParam.h"
33
5608e15a 34//
35// includes neccessary for test functions
36//
37
38#include "TSystem.h"
39#include "TRandom.h"
40#include "TStopwatch.h"
41#include "TTreeStream.h"
284050f7 42
43ClassImp(AliMathBase) // Class implementation to enable ROOT I/O
44
45AliMathBase::AliMathBase() : TObject()
46{
5608e15a 47 //
48 // Default constructor
49 //
284050f7 50}
51///////////////////////////////////////////////////////////////////////////
52AliMathBase::~AliMathBase()
53{
5608e15a 54 //
55 // Destructor
56 //
284050f7 57}
58
59
60//_____________________________________________________________________________
61void AliMathBase::EvaluateUni(Int_t nvectors, Double_t *data, Double_t &mean
62 , Double_t &sigma, Int_t hh)
63{
64 //
65 // Robust estimator in 1D case MI version - (faster than ROOT version)
66 //
67 // For the univariate case
68 // estimates of location and scatter are returned in mean and sigma parameters
69 // the algorithm works on the same principle as in multivariate case -
70 // it finds a subset of size hh with smallest sigma, and then returns mean and
71 // sigma of this subset
72 //
73
74 if (hh==0)
75 hh=(nvectors+2)/2;
76 Double_t faclts[]={2.6477,2.5092,2.3826,2.2662,2.1587,2.0589,1.9660,1.879,1.7973,1.7203,1.6473};
77 Int_t *index=new Int_t[nvectors];
78 TMath::Sort(nvectors, data, index, kFALSE);
79
80 Int_t nquant = TMath::Min(Int_t(Double_t(((hh*1./nvectors)-0.5)*40))+1, 11);
d9e9045c 81 Double_t factor = faclts[TMath::Max(0,nquant-1)];
284050f7 82
83 Double_t sumx =0;
84 Double_t sumx2 =0;
85 Int_t bestindex = -1;
86 Double_t bestmean = 0;
07d955de 87 Double_t bestsigma = (data[index[nvectors-1]]-data[index[0]]+1.); // maximal possible sigma
88 bestsigma *=bestsigma;
89
284050f7 90 for (Int_t i=0; i<hh; i++){
91 sumx += data[index[i]];
92 sumx2 += data[index[i]]*data[index[i]];
93 }
94
95 Double_t norm = 1./Double_t(hh);
96 Double_t norm2 = 1./Double_t(hh-1);
97 for (Int_t i=hh; i<nvectors; i++){
98 Double_t cmean = sumx*norm;
99 Double_t csigma = (sumx2 - hh*cmean*cmean)*norm2;
100 if (csigma<bestsigma){
101 bestmean = cmean;
102 bestsigma = csigma;
103 bestindex = i-hh;
104 }
105
106 sumx += data[index[i]]-data[index[i-hh]];
107 sumx2 += data[index[i]]*data[index[i]]-data[index[i-hh]]*data[index[i-hh]];
108 }
109
110 Double_t bstd=factor*TMath::Sqrt(TMath::Abs(bestsigma));
111 mean = bestmean;
112 sigma = bstd;
113 delete [] index;
114
115}
116
117
118
119void AliMathBase::EvaluateUniExternal(Int_t nvectors, Double_t *data, Double_t &mean, Double_t &sigma, Int_t hh, Float_t externalfactor)
120{
121 // Modified version of ROOT robust EvaluateUni
122 // robust estimator in 1D case MI version
123 // added external factor to include precision of external measurement
124 //
125
126 if (hh==0)
127 hh=(nvectors+2)/2;
128 Double_t faclts[]={2.6477,2.5092,2.3826,2.2662,2.1587,2.0589,1.9660,1.879,1.7973,1.7203,1.6473};
129 Int_t *index=new Int_t[nvectors];
130 TMath::Sort(nvectors, data, index, kFALSE);
131 //
132 Int_t nquant = TMath::Min(Int_t(Double_t(((hh*1./nvectors)-0.5)*40))+1, 11);
133 Double_t factor = faclts[0];
134 if (nquant>0){
135 // fix proper normalization - Anja
136 factor = faclts[nquant-1];
137 }
138
139 //
140 //
141 Double_t sumx =0;
142 Double_t sumx2 =0;
143 Int_t bestindex = -1;
144 Double_t bestmean = 0;
145 Double_t bestsigma = -1;
146 for (Int_t i=0; i<hh; i++){
147 sumx += data[index[i]];
148 sumx2 += data[index[i]]*data[index[i]];
149 }
150 //
151 Double_t kfactor = 2.*externalfactor - externalfactor*externalfactor;
152 Double_t norm = 1./Double_t(hh);
153 for (Int_t i=hh; i<nvectors; i++){
154 Double_t cmean = sumx*norm;
155 Double_t csigma = (sumx2*norm - cmean*cmean*kfactor);
156 if (csigma<bestsigma || bestsigma<0){
157 bestmean = cmean;
158 bestsigma = csigma;
159 bestindex = i-hh;
160 }
161 //
162 //
163 sumx += data[index[i]]-data[index[i-hh]];
164 sumx2 += data[index[i]]*data[index[i]]-data[index[i-hh]]*data[index[i-hh]];
165 }
166
167 Double_t bstd=factor*TMath::Sqrt(TMath::Abs(bestsigma));
168 mean = bestmean;
169 sigma = bstd;
170 delete [] index;
171}
172
173
174//_____________________________________________________________________________
175Int_t AliMathBase::Freq(Int_t n, const Int_t *inlist
176 , Int_t *outlist, Bool_t down)
177{
178 //
179 // Sort eleements according occurancy
180 // The size of output array has is 2*n
181 //
182
183 Int_t * sindexS = new Int_t[n]; // temp array for sorting
184 Int_t * sindexF = new Int_t[2*n];
185 for (Int_t i=0;i<n;i++) sindexF[i]=0;
186 //
187 TMath::Sort(n,inlist, sindexS, down);
188 Int_t last = inlist[sindexS[0]];
189 Int_t val = last;
190 sindexF[0] = 1;
191 sindexF[0+n] = last;
192 Int_t countPos = 0;
193 //
194 // find frequency
195 for(Int_t i=1;i<n; i++){
196 val = inlist[sindexS[i]];
197 if (last == val) sindexF[countPos]++;
198 else{
199 countPos++;
200 sindexF[countPos+n] = val;
201 sindexF[countPos]++;
202 last =val;
203 }
204 }
205 if (last==val) countPos++;
206 // sort according frequency
207 TMath::Sort(countPos, sindexF, sindexS, kTRUE);
208 for (Int_t i=0;i<countPos;i++){
209 outlist[2*i ] = sindexF[sindexS[i]+n];
210 outlist[2*i+1] = sindexF[sindexS[i]];
211 }
212 delete [] sindexS;
213 delete [] sindexF;
214
215 return countPos;
216
217}
f6659a9d 218
219//___AliMathBase__________________________________________________________________________
220void AliMathBase::TruncatedMean(TH1F * his, TVectorD *param, Float_t down, Float_t up, Bool_t verbose){
221 //
222 //
223 //
224 Int_t nbins = his->GetNbinsX();
225 Float_t nentries = his->GetEntries();
226 Float_t sum =0;
227 Float_t mean = 0;
228 Float_t sigma2 = 0;
229 Float_t ncumul=0;
230 for (Int_t ibin=1;ibin<nbins; ibin++){
231 ncumul+= his->GetBinContent(ibin);
232 Float_t fraction = Float_t(ncumul)/Float_t(nentries);
233 if (fraction>down && fraction<up){
234 sum+=his->GetBinContent(ibin);
235 mean+=his->GetBinCenter(ibin)*his->GetBinContent(ibin);
236 sigma2+=his->GetBinCenter(ibin)*his->GetBinCenter(ibin)*his->GetBinContent(ibin);
237 }
238 }
239 mean/=sum;
240 sigma2= TMath::Sqrt(TMath::Abs(sigma2/sum-mean*mean));
241 if (param){
242 (*param)[0] = his->GetMaximum();
243 (*param)[1] = mean;
244 (*param)[2] = sigma2;
245
246 }
247 if (verbose) printf("Mean\t%f\t Sigma2\t%f\n", mean,sigma2);
248}
249
250void AliMathBase::LTM(TH1F * his, TVectorD *param , Float_t fraction, Bool_t verbose){
251 //
252 // LTM
253 //
254 Int_t nbins = his->GetNbinsX();
255 Int_t nentries = (Int_t)his->GetEntries();
256 Double_t *data = new Double_t[nentries];
257 Int_t npoints=0;
258 for (Int_t ibin=1;ibin<nbins; ibin++){
259 Float_t entriesI = his->GetBinContent(ibin);
260 Float_t xcenter= his->GetBinCenter(ibin);
261 for (Int_t ic=0; ic<entriesI; ic++){
262 if (npoints<nentries){
263 data[npoints]= xcenter;
264 npoints++;
265 }
266 }
267 }
268 Double_t mean, sigma;
269 Int_t npoints2=TMath::Min(Int_t(fraction*Float_t(npoints)),npoints-1);
270 npoints2=TMath::Max(Int_t(0.5*Float_t(npoints)),npoints2);
271 AliMathBase::EvaluateUni(npoints, data, mean,sigma,npoints2);
272 delete [] data;
273 if (verbose) printf("Mean\t%f\t Sigma2\t%f\n", mean,sigma);if (param){
274 (*param)[0] = his->GetMaximum();
275 (*param)[1] = mean;
276 (*param)[2] = sigma;
277 }
278}
279
d9a129b4 280Double_t AliMathBase::FitGaus(TH1F* his, TVectorD *param, TMatrixD */*matrix*/, Float_t xmin, Float_t xmax, Bool_t verbose){
f6659a9d 281 //
282 // Fit histogram with gaussian function
283 //
284 // Prameters:
285 // return value- chi2 - if negative ( not enough points)
286 // his - input histogram
287 // param - vector with parameters
288 // xmin, xmax - range to fit - if xmin=xmax=0 - the full histogram range used
289 // Fitting:
290 // 1. Step - make logarithm
291 // 2. Linear fit (parabola) - more robust - always converge
292 // 3. In case of small statistic bins are averaged
293 //
294 static TLinearFitter fitter(3,"pol2");
295 TVectorD par(3);
296 TVectorD sigma(3);
297 TMatrixD mat(3,3);
298 if (his->GetMaximum()<4) return -1;
299 if (his->GetEntries()<12) return -1;
300 if (his->GetRMS()<mat.GetTol()) return -1;
5608e15a 301 Float_t maxEstimate = his->GetEntries()*his->GetBinWidth(1)/TMath::Sqrt((TMath::TwoPi()*his->GetRMS()));
f6659a9d 302 Int_t dsmooth = TMath::Nint(6./TMath::Sqrt(maxEstimate));
303
304 if (maxEstimate<1) return -1;
305 Int_t nbins = his->GetNbinsX();
306 Int_t npoints=0;
307 //
308
309
310 if (xmin>=xmax){
311 xmin = his->GetXaxis()->GetXmin();
312 xmax = his->GetXaxis()->GetXmax();
313 }
314 for (Int_t iter=0; iter<2; iter++){
315 fitter.ClearPoints();
316 npoints=0;
5608e15a 317 for (Int_t ibin=1;ibin<nbins+1; ibin++){
f6659a9d 318 Int_t countB=1;
319 Float_t entriesI = his->GetBinContent(ibin);
320 for (Int_t delta = -dsmooth; delta<=dsmooth; delta++){
321 if (ibin+delta>1 &&ibin+delta<nbins-1){
322 entriesI += his->GetBinContent(ibin+delta);
323 countB++;
324 }
325 }
326 entriesI/=countB;
327 Double_t xcenter= his->GetBinCenter(ibin);
328 if (xcenter<xmin || xcenter>xmax) continue;
329 Double_t error=1./TMath::Sqrt(countB);
330 Float_t cont=2;
331 if (iter>0){
332 if (par[0]+par[1]*xcenter+par[2]*xcenter*xcenter>20) return 0;
333 cont = TMath::Exp(par[0]+par[1]*xcenter+par[2]*xcenter*xcenter);
334 if (cont>1.) error = 1./TMath::Sqrt(cont*Float_t(countB));
335 }
336 if (entriesI>1&&cont>1){
337 fitter.AddPoint(&xcenter,TMath::Log(Float_t(entriesI)),error);
338 npoints++;
339 }
340 }
341 if (npoints>3){
342 fitter.Eval();
343 fitter.GetParameters(par);
344 }else{
345 break;
346 }
347 }
348 if (npoints<=3){
349 return -1;
350 }
351 fitter.GetParameters(par);
352 fitter.GetCovarianceMatrix(mat);
353 if (TMath::Abs(par[1])<mat.GetTol()) return -1;
354 if (TMath::Abs(par[2])<mat.GetTol()) return -1;
355 Double_t chi2 = fitter.GetChisquare()/Float_t(npoints);
356 //fitter.GetParameters();
357 if (!param) param = new TVectorD(3);
d9a129b4 358 //if (!matrix) matrix = new TMatrixD(3,3);
f6659a9d 359 (*param)[1] = par[1]/(-2.*par[2]);
360 (*param)[2] = 1./TMath::Sqrt(TMath::Abs(-2.*par[2]));
361 (*param)[0] = TMath::Exp(par[0]+ par[1]* (*param)[1] + par[2]*(*param)[1]*(*param)[1]);
362 if (verbose){
363 par.Print();
364 mat.Print();
365 param->Print();
366 printf("Chi2=%f\n",chi2);
367 TF1 * f1= new TF1("f1","[0]*exp(-(x-[1])^2/(2*[2]*[2]))",his->GetXaxis()->GetXmin(),his->GetXaxis()->GetXmax());
368 f1->SetParameter(0, (*param)[0]);
369 f1->SetParameter(1, (*param)[1]);
370 f1->SetParameter(2, (*param)[2]);
371 f1->Draw("same");
372 }
373 return chi2;
374}
375
d9a129b4 376Double_t AliMathBase::FitGaus(Float_t *arr, Int_t nBins, Float_t xMin, Float_t xMax, TVectorD *param, TMatrixD */*matrix*/, Bool_t verbose){
5608e15a 377 //
378 // Fit histogram with gaussian function
379 //
380 // Prameters:
5f645a6e 381 // nbins: size of the array and number of histogram bins
382 // xMin, xMax: histogram range
00bb7de0 383 // param: paramters of the fit (0-Constant, 1-Mean, 2-Sigma, 3-Sum)
5f645a6e 384 // matrix: covariance matrix -- not implemented yet, pass dummy matrix!!!
385 //
386 // Return values:
387 // >0: the chi2 returned by TLinearFitter
388 // -3: only three points have been used for the calculation - no fitter was used
389 // -2: only two points have been used for the calculation - center of gravity was uesed for calculation
390 // -1: only one point has been used for the calculation - center of gravity was uesed for calculation
391 // -4: invalid result!!
392 //
5608e15a 393 // Fitting:
394 // 1. Step - make logarithm
395 // 2. Linear fit (parabola) - more robust - always converge
5608e15a 396 //
397 static TLinearFitter fitter(3,"pol2");
398 static TMatrixD mat(3,3);
399 static Double_t kTol = mat.GetTol();
400 fitter.StoreData(kFALSE);
401 fitter.ClearPoints();
402 TVectorD par(3);
403 TVectorD sigma(3);
404 TMatrixD A(3,3);
405 TMatrixD b(3,1);
5f645a6e 406 Float_t rms = TMath::RMS(nBins,arr);
407 Float_t max = TMath::MaxElement(nBins,arr);
408 Float_t binWidth = (xMax-xMin)/(Float_t)nBins;
5608e15a 409
410 Float_t meanCOG = 0;
411 Float_t rms2COG = 0;
412 Float_t sumCOG = 0;
413
414 Float_t entries = 0;
415 Int_t nfilled=0;
416
d9a129b4 417 if (!param) param = new TVectorD(4);
61d38705 418
5f645a6e 419 for (Int_t i=0; i<nBins; i++){
5608e15a 420 entries+=arr[i];
421 if (arr[i]>0) nfilled++;
422 }
00bb7de0 423 (*param)[0] = 0;
424 (*param)[1] = 0;
425 (*param)[2] = 0;
426 (*param)[3] = 0;
5608e15a 427
5f645a6e 428 if (max<4) return -4;
429 if (entries<12) return -4;
430 if (rms<kTol) return -4;
5608e15a 431
00bb7de0 432 (*param)[3] = entries;
5608e15a 433
00bb7de0 434 Int_t npoints=0;
5f645a6e 435 for (Int_t ibin=0;ibin<nBins; ibin++){
436 Float_t entriesI = arr[ibin];
5608e15a 437 if (entriesI>1){
5f645a6e 438 Double_t xcenter = xMin+(ibin+0.5)*binWidth;
5608e15a 439 Float_t error = 1./TMath::Sqrt(entriesI);
440 Float_t val = TMath::Log(Float_t(entriesI));
441 fitter.AddPoint(&xcenter,val,error);
5f645a6e 442 if (npoints<3){
443 A(npoints,0)=1;
444 A(npoints,1)=xcenter;
445 A(npoints,2)=xcenter*xcenter;
446 b(npoints,0)=val;
447 meanCOG+=xcenter*entriesI;
448 rms2COG +=xcenter*entriesI*xcenter;
449 sumCOG +=entriesI;
450 }
5608e15a 451 npoints++;
452 }
453 }
5608e15a 454
455 Double_t chi2 = 0;
456 if (npoints>=3){
457 if ( npoints == 3 ){
458 //analytic calculation of the parameters for three points
459 A.Invert();
460 TMatrixD res(1,3);
461 res.Mult(A,b);
462 par[0]=res(0,0);
463 par[1]=res(0,1);
464 par[2]=res(0,2);
465 chi2 = -3.;
466 } else {
467 // use fitter for more than three points
468 fitter.Eval();
469 fitter.GetParameters(par);
470 fitter.GetCovarianceMatrix(mat);
471 chi2 = fitter.GetChisquare()/Float_t(npoints);
472 }
5f645a6e 473 if (TMath::Abs(par[1])<kTol) return -4;
474 if (TMath::Abs(par[2])<kTol) return -4;
5608e15a 475
d9a129b4 476 //if (!param) param = new TVectorD(4);
00bb7de0 477 if ( param->GetNrows()<4 ) param->ResizeTo(4);
d9a129b4 478 //if (!matrix) matrix = new TMatrixD(3,3); // !!!!might be a memory leek. use dummy matrix pointer to call this function!
5608e15a 479
480 (*param)[1] = par[1]/(-2.*par[2]);
481 (*param)[2] = 1./TMath::Sqrt(TMath::Abs(-2.*par[2]));
5f645a6e 482 Double_t lnparam0 = par[0]+ par[1]* (*param)[1] + par[2]*(*param)[1]*(*param)[1];
483 if ( lnparam0>307 ) return -4;
484 (*param)[0] = TMath::Exp(lnparam0);
5608e15a 485 if (verbose){
486 par.Print();
487 mat.Print();
488 param->Print();
489 printf("Chi2=%f\n",chi2);
5f645a6e 490 TF1 * f1= new TF1("f1","[0]*exp(-(x-[1])^2/(2*[2]*[2]))",xMin,xMax);
5608e15a 491 f1->SetParameter(0, (*param)[0]);
492 f1->SetParameter(1, (*param)[1]);
493 f1->SetParameter(2, (*param)[2]);
494 f1->Draw("same");
495 }
496 return chi2;
497 }
498
499 if (npoints == 2){
500 //use center of gravity for 2 points
501 meanCOG/=sumCOG;
502 rms2COG /=sumCOG;
503 (*param)[0] = max;
504 (*param)[1] = meanCOG;
505 (*param)[2] = TMath::Sqrt(TMath::Abs(meanCOG*meanCOG-rms2COG));
506 chi2=-2.;
507 }
508 if ( npoints == 1 ){
5f645a6e 509 meanCOG/=sumCOG;
5608e15a 510 (*param)[0] = max;
511 (*param)[1] = meanCOG;
512 (*param)[2] = binWidth/TMath::Sqrt(12);
513 chi2=-1.;
514 }
515 return chi2;
516
517}
518
519
5f645a6e 520Float_t AliMathBase::GetCOG(Short_t *arr, Int_t nBins, Float_t xMin, Float_t xMax, Float_t *rms, Float_t *sum)
521{
522 //
523 // calculate center of gravity rms and sum for array 'arr' with nBins an a x range xMin to xMax
524 // return COG; in case of failure return xMin
525 //
526 Float_t meanCOG = 0;
527 Float_t rms2COG = 0;
528 Float_t sumCOG = 0;
529 Int_t npoints = 0;
530
531 Float_t binWidth = (xMax-xMin)/(Float_t)nBins;
532
533 for (Int_t ibin=0; ibin<nBins; ibin++){
534 Float_t entriesI = (Float_t)arr[ibin];
535 Double_t xcenter = xMin+(ibin+0.5)*binWidth;
536 if ( entriesI>0 ){
537 meanCOG += xcenter*entriesI;
538 rms2COG += xcenter*entriesI*xcenter;
539 sumCOG += entriesI;
540 npoints++;
541 }
542 }
543 if ( sumCOG == 0 ) return xMin;
544 meanCOG/=sumCOG;
545
546 if ( rms ){
547 rms2COG /=sumCOG;
548 (*rms) = TMath::Sqrt(TMath::Abs(meanCOG*meanCOG-rms2COG));
549 if ( npoints == 1 ) (*rms) = binWidth/TMath::Sqrt(12);
550 }
551
552 if ( sum )
553 (*sum) = sumCOG;
554
555 return meanCOG;
556}
557
558
bb7e41dd 559Double_t AliMathBase::ErfcFast(Double_t x){
560 // Fast implementation of the complementary error function
561 // The error of the approximation is |eps(x)| < 5E-4
562 // See Abramowitz and Stegun, p.299, 7.1.27
563
564 Double_t z = TMath::Abs(x);
565 Double_t ans = 1+z*(0.278393+z*(0.230389+z*(0.000972+z*0.078108)));
566 ans = 1.0/ans;
567 ans *= ans;
568 ans *= ans;
569
570 return (x>=0.0 ? ans : 2.0 - ans);
571}
5608e15a 572
573///////////////////////////////////////////////////////////////
574////////////// TEST functions /////////////////////////
575///////////////////////////////////////////////////////////////
576
577
578
579
580
581void AliMathBase::TestGausFit(Int_t nhistos){
582 //
583 // Test performance of the parabolic - gaussian fit - compare it with
584 // ROOT gauss fit
585 // nhistos - number of histograms to be used for test
586 //
587 TTreeSRedirector *pcstream = new TTreeSRedirector("fitdebug.root");
588
589 Float_t *xTrue = new Float_t[nhistos];
590 Float_t *sTrue = new Float_t[nhistos];
591 TVectorD **par1 = new TVectorD*[nhistos];
592 TVectorD **par2 = new TVectorD*[nhistos];
593 TMatrixD dummy(3,3);
594
595
596 TH1F **h1f = new TH1F*[nhistos];
597 TF1 *myg = new TF1("myg","gaus");
598 TF1 *fit = new TF1("fit","gaus");
599 gRandom->SetSeed(0);
600
601 //init
602 for (Int_t i=0;i<nhistos; i++){
603 par1[i] = new TVectorD(3);
604 par2[i] = new TVectorD(3);
605 h1f[i] = new TH1F(Form("h1f%d",i),Form("h1f%d",i),20,-10,10);
606 xTrue[i]= gRandom->Rndm();
607 gSystem->Sleep(2);
608 sTrue[i]= .75+gRandom->Rndm()*.5;
609 myg->SetParameters(1,xTrue[i],sTrue[i]);
610 h1f[i]->FillRandom("myg");
611 }
612
613 TStopwatch s;
614 s.Start();
615 //standard gaus fit
616 for (Int_t i=0; i<nhistos; i++){
617 h1f[i]->Fit(fit,"0q");
618 (*par1[i])(0) = fit->GetParameter(0);
619 (*par1[i])(1) = fit->GetParameter(1);
620 (*par1[i])(2) = fit->GetParameter(2);
621 }
622 s.Stop();
623 printf("Gaussian fit\t");
624 s.Print();
625
626 s.Start();
627 //AliMathBase gaus fit
628 for (Int_t i=0; i<nhistos; i++){
5f645a6e 629 AliMathBase::FitGaus(h1f[i]->GetArray()+1,h1f[i]->GetNbinsX(),h1f[i]->GetXaxis()->GetXmin(),h1f[i]->GetXaxis()->GetXmax(),par2[i],&dummy);
5608e15a 630 }
631
632 s.Stop();
633 printf("Parabolic fit\t");
634 s.Print();
635 //write stream
636 for (Int_t i=0;i<nhistos; i++){
637 Float_t xt = xTrue[i];
638 Float_t st = sTrue[i];
639 (*pcstream)<<"data"
640 <<"xTrue="<<xt
641 <<"sTrue="<<st
642 <<"pg.="<<(par1[i])
643 <<"pa.="<<(par2[i])
644 <<"\n";
645 }
646 //delete pointers
647 for (Int_t i=0;i<nhistos; i++){
648 delete par1[i];
649 delete par2[i];
650 delete h1f[i];
651 }
652 delete pcstream;
653 delete []h1f;
654 delete []xTrue;
655 delete []sTrue;
656 //
657 delete []par1;
658 delete []par2;
659
660}
661
662
663
3392b4c9 664TGraph2D * AliMathBase::MakeStat2D(TH3 * his, Int_t delta0, Int_t delta1, Int_t type){
665 //
666 //
667 //
668 // delta - number of bins to integrate
669 // type - 0 - mean value
670
671 TAxis * xaxis = his->GetXaxis();
672 TAxis * yaxis = his->GetYaxis();
673 // TAxis * zaxis = his->GetZaxis();
674 Int_t nbinx = xaxis->GetNbins();
675 Int_t nbiny = yaxis->GetNbins();
61d38705 676 const Int_t nc=1000;
677 char name[nc];
3392b4c9 678 Int_t icount=0;
679 TGraph2D *graph = new TGraph2D(nbinx*nbiny);
680 TF1 f1("f1","gaus");
681 for (Int_t ix=0; ix<nbinx;ix++)
682 for (Int_t iy=0; iy<nbiny;iy++){
683 Float_t xcenter = xaxis->GetBinCenter(ix);
684 Float_t ycenter = yaxis->GetBinCenter(iy);
61d38705 685 snprintf(name,nc,"%s_%d_%d",his->GetName(), ix,iy);
3392b4c9 686 TH1 *projection = his->ProjectionZ(name,ix-delta0,ix+delta0,iy-delta1,iy+delta1);
687 Float_t stat= 0;
688 if (type==0) stat = projection->GetMean();
689 if (type==1) stat = projection->GetRMS();
690 if (type==2 || type==3){
691 TVectorD vec(3);
692 AliMathBase::LTM((TH1F*)projection,&vec,0.7);
693 if (type==2) stat= vec[1];
694 if (type==3) stat= vec[0];
695 }
696 if (type==4|| type==5){
697 projection->Fit(&f1);
698 if (type==4) stat= f1.GetParameter(1);
699 if (type==5) stat= f1.GetParameter(2);
700 }
701 //printf("%d\t%f\t%f\t%f\n", icount,xcenter, ycenter, stat);
702 graph->SetPoint(icount,xcenter, ycenter, stat);
703 icount++;
704 }
705 return graph;
706}
5608e15a 707
3392b4c9 708TGraph * AliMathBase::MakeStat1D(TH3 * his, Int_t delta1, Int_t type){
709 //
710 //
711 //
712 // delta - number of bins to integrate
713 // type - 0 - mean value
714
715 TAxis * xaxis = his->GetXaxis();
716 TAxis * yaxis = his->GetYaxis();
717 // TAxis * zaxis = his->GetZaxis();
718 Int_t nbinx = xaxis->GetNbins();
719 Int_t nbiny = yaxis->GetNbins();
61d38705 720 const Int_t nc=1000;
721 char name[nc];
3392b4c9 722 Int_t icount=0;
723 TGraph *graph = new TGraph(nbinx);
724 TF1 f1("f1","gaus");
725 for (Int_t ix=0; ix<nbinx;ix++){
726 Float_t xcenter = xaxis->GetBinCenter(ix);
727 // Float_t ycenter = yaxis->GetBinCenter(iy);
61d38705 728 snprintf(name,nc,"%s_%d",his->GetName(), ix);
3392b4c9 729 TH1 *projection = his->ProjectionZ(name,ix-delta1,ix+delta1,0,nbiny);
730 Float_t stat= 0;
731 if (type==0) stat = projection->GetMean();
732 if (type==1) stat = projection->GetRMS();
733 if (type==2 || type==3){
734 TVectorD vec(3);
735 AliMathBase::LTM((TH1F*)projection,&vec,0.7);
736 if (type==2) stat= vec[1];
737 if (type==3) stat= vec[0];
738 }
739 if (type==4|| type==5){
740 projection->Fit(&f1);
741 if (type==4) stat= f1.GetParameter(1);
742 if (type==5) stat= f1.GetParameter(2);
743 }
744 //printf("%d\t%f\t%f\t%f\n", icount,xcenter, ycenter, stat);
745 graph->SetPoint(icount,xcenter, stat);
746 icount++;
747 }
748 return graph;
749}
09a29b67 750
751Double_t AliMathBase::TruncatedGaus(Double_t mean, Double_t sigma, Double_t cutat)
752{
753 // return number generated according to a gaussian distribution N(mean,sigma) truncated at cutat
754 //
755 Double_t value;
756 do{
757 value=gRandom->Gaus(mean,sigma);
758 }while(TMath::Abs(value-mean)>cutat);
759 return value;
760}
4c5881a0 761
762Double_t AliMathBase::TruncatedGaus(Double_t mean, Double_t sigma, Double_t leftCut, Double_t rightCut)
763{
764 // return number generated according to a gaussian distribution N(mean,sigma)
765 // truncated at leftCut and rightCut
766 //
767 Double_t value;
768 do{
769 value=gRandom->Gaus(mean,sigma);
770 }while((value-mean)<-leftCut || (value-mean)>rightCut);
771 return value;
772}
f6d87824 773
774Double_t AliMathBase::BetheBlochAleph(Double_t bg,
775 Double_t kp1,
776 Double_t kp2,
777 Double_t kp3,
778 Double_t kp4,
779 Double_t kp5) {
780 //
d46683db 781 // This is the empirical ALEPH parameterization of the Bethe-Bloch formula.
782 // It is normalized to 1 at the minimum.
783 //
784 // bg - beta*gamma
785 //
786 // The default values for the kp* parameters are for ALICE TPC.
787 // The returned value is in MIP units
f6d87824 788 //
789
9c56b409 790 return AliExternalTrackParam::BetheBlochAleph(bg,kp1,kp2,kp3,kp4,kp5);
d46683db 791}