Added V0A23 (V0 rings 2-3), V0C01 (V0 rings 0-1) and V0S = V0A23+V0C01
[u/mrichter/AliRoot.git] / STEER / STEERBase / AliMathBase.cxx
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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"
a8752eef 31#include "AliLog.h"
5608e15a 32
9c56b409 33#include "AliExternalTrackParam.h"
34
5608e15a 35//
36// includes neccessary for test functions
37//
38
39#include "TSystem.h"
40#include "TRandom.h"
41#include "TStopwatch.h"
42#include "TTreeStream.h"
284050f7 43
44ClassImp(AliMathBase) // Class implementation to enable ROOT I/O
45
46AliMathBase::AliMathBase() : TObject()
47{
5608e15a 48 //
49 // Default constructor
50 //
284050f7 51}
52///////////////////////////////////////////////////////////////////////////
53AliMathBase::~AliMathBase()
54{
5608e15a 55 //
56 // Destructor
57 //
284050f7 58}
59
60
61//_____________________________________________________________________________
62void AliMathBase::EvaluateUni(Int_t nvectors, Double_t *data, Double_t &mean
63 , Double_t &sigma, Int_t hh)
64{
65 //
66 // Robust estimator in 1D case MI version - (faster than ROOT version)
67 //
68 // For the univariate case
69 // estimates of location and scatter are returned in mean and sigma parameters
70 // the algorithm works on the same principle as in multivariate case -
71 // it finds a subset of size hh with smallest sigma, and then returns mean and
72 // sigma of this subset
73 //
74
a8752eef 75 if (nvectors<2) {
76 AliErrorClass(Form("nvectors = %d, should be > 1",nvectors));
77 return;
78 }
79 if (hh<2)
284050f7 80 hh=(nvectors+2)/2;
81 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};
82 Int_t *index=new Int_t[nvectors];
83 TMath::Sort(nvectors, data, index, kFALSE);
84
85 Int_t nquant = TMath::Min(Int_t(Double_t(((hh*1./nvectors)-0.5)*40))+1, 11);
d9e9045c 86 Double_t factor = faclts[TMath::Max(0,nquant-1)];
284050f7 87
88 Double_t sumx =0;
89 Double_t sumx2 =0;
90 Int_t bestindex = -1;
91 Double_t bestmean = 0;
07d955de 92 Double_t bestsigma = (data[index[nvectors-1]]-data[index[0]]+1.); // maximal possible sigma
93 bestsigma *=bestsigma;
94
284050f7 95 for (Int_t i=0; i<hh; i++){
96 sumx += data[index[i]];
97 sumx2 += data[index[i]]*data[index[i]];
98 }
99
100 Double_t norm = 1./Double_t(hh);
101 Double_t norm2 = 1./Double_t(hh-1);
102 for (Int_t i=hh; i<nvectors; i++){
103 Double_t cmean = sumx*norm;
104 Double_t csigma = (sumx2 - hh*cmean*cmean)*norm2;
105 if (csigma<bestsigma){
106 bestmean = cmean;
107 bestsigma = csigma;
108 bestindex = i-hh;
109 }
110
111 sumx += data[index[i]]-data[index[i-hh]];
112 sumx2 += data[index[i]]*data[index[i]]-data[index[i-hh]]*data[index[i-hh]];
113 }
114
115 Double_t bstd=factor*TMath::Sqrt(TMath::Abs(bestsigma));
116 mean = bestmean;
117 sigma = bstd;
118 delete [] index;
119
120}
121
122
123
124void AliMathBase::EvaluateUniExternal(Int_t nvectors, Double_t *data, Double_t &mean, Double_t &sigma, Int_t hh, Float_t externalfactor)
125{
126 // Modified version of ROOT robust EvaluateUni
127 // robust estimator in 1D case MI version
128 // added external factor to include precision of external measurement
129 //
130
131 if (hh==0)
132 hh=(nvectors+2)/2;
133 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};
134 Int_t *index=new Int_t[nvectors];
135 TMath::Sort(nvectors, data, index, kFALSE);
136 //
137 Int_t nquant = TMath::Min(Int_t(Double_t(((hh*1./nvectors)-0.5)*40))+1, 11);
138 Double_t factor = faclts[0];
139 if (nquant>0){
140 // fix proper normalization - Anja
141 factor = faclts[nquant-1];
142 }
143
144 //
145 //
146 Double_t sumx =0;
147 Double_t sumx2 =0;
148 Int_t bestindex = -1;
149 Double_t bestmean = 0;
150 Double_t bestsigma = -1;
151 for (Int_t i=0; i<hh; i++){
152 sumx += data[index[i]];
153 sumx2 += data[index[i]]*data[index[i]];
154 }
155 //
156 Double_t kfactor = 2.*externalfactor - externalfactor*externalfactor;
157 Double_t norm = 1./Double_t(hh);
158 for (Int_t i=hh; i<nvectors; i++){
159 Double_t cmean = sumx*norm;
160 Double_t csigma = (sumx2*norm - cmean*cmean*kfactor);
161 if (csigma<bestsigma || bestsigma<0){
162 bestmean = cmean;
163 bestsigma = csigma;
164 bestindex = i-hh;
165 }
166 //
167 //
168 sumx += data[index[i]]-data[index[i-hh]];
169 sumx2 += data[index[i]]*data[index[i]]-data[index[i-hh]]*data[index[i-hh]];
170 }
171
172 Double_t bstd=factor*TMath::Sqrt(TMath::Abs(bestsigma));
173 mean = bestmean;
174 sigma = bstd;
175 delete [] index;
176}
177
178
179//_____________________________________________________________________________
180Int_t AliMathBase::Freq(Int_t n, const Int_t *inlist
181 , Int_t *outlist, Bool_t down)
182{
183 //
184 // Sort eleements according occurancy
185 // The size of output array has is 2*n
186 //
187
188 Int_t * sindexS = new Int_t[n]; // temp array for sorting
189 Int_t * sindexF = new Int_t[2*n];
190 for (Int_t i=0;i<n;i++) sindexF[i]=0;
191 //
192 TMath::Sort(n,inlist, sindexS, down);
193 Int_t last = inlist[sindexS[0]];
194 Int_t val = last;
195 sindexF[0] = 1;
196 sindexF[0+n] = last;
197 Int_t countPos = 0;
198 //
199 // find frequency
200 for(Int_t i=1;i<n; i++){
201 val = inlist[sindexS[i]];
202 if (last == val) sindexF[countPos]++;
203 else{
204 countPos++;
205 sindexF[countPos+n] = val;
206 sindexF[countPos]++;
207 last =val;
208 }
209 }
210 if (last==val) countPos++;
211 // sort according frequency
212 TMath::Sort(countPos, sindexF, sindexS, kTRUE);
213 for (Int_t i=0;i<countPos;i++){
214 outlist[2*i ] = sindexF[sindexS[i]+n];
215 outlist[2*i+1] = sindexF[sindexS[i]];
216 }
217 delete [] sindexS;
218 delete [] sindexF;
219
220 return countPos;
221
222}
f6659a9d 223
224//___AliMathBase__________________________________________________________________________
225void AliMathBase::TruncatedMean(TH1F * his, TVectorD *param, Float_t down, Float_t up, Bool_t verbose){
226 //
227 //
228 //
229 Int_t nbins = his->GetNbinsX();
230 Float_t nentries = his->GetEntries();
231 Float_t sum =0;
232 Float_t mean = 0;
233 Float_t sigma2 = 0;
234 Float_t ncumul=0;
235 for (Int_t ibin=1;ibin<nbins; ibin++){
236 ncumul+= his->GetBinContent(ibin);
237 Float_t fraction = Float_t(ncumul)/Float_t(nentries);
238 if (fraction>down && fraction<up){
239 sum+=his->GetBinContent(ibin);
240 mean+=his->GetBinCenter(ibin)*his->GetBinContent(ibin);
241 sigma2+=his->GetBinCenter(ibin)*his->GetBinCenter(ibin)*his->GetBinContent(ibin);
242 }
243 }
244 mean/=sum;
245 sigma2= TMath::Sqrt(TMath::Abs(sigma2/sum-mean*mean));
246 if (param){
247 (*param)[0] = his->GetMaximum();
248 (*param)[1] = mean;
249 (*param)[2] = sigma2;
250
251 }
252 if (verbose) printf("Mean\t%f\t Sigma2\t%f\n", mean,sigma2);
253}
254
255void AliMathBase::LTM(TH1F * his, TVectorD *param , Float_t fraction, Bool_t verbose){
256 //
257 // LTM
258 //
259 Int_t nbins = his->GetNbinsX();
260 Int_t nentries = (Int_t)his->GetEntries();
261 Double_t *data = new Double_t[nentries];
262 Int_t npoints=0;
263 for (Int_t ibin=1;ibin<nbins; ibin++){
264 Float_t entriesI = his->GetBinContent(ibin);
265 Float_t xcenter= his->GetBinCenter(ibin);
266 for (Int_t ic=0; ic<entriesI; ic++){
267 if (npoints<nentries){
268 data[npoints]= xcenter;
269 npoints++;
270 }
271 }
272 }
273 Double_t mean, sigma;
274 Int_t npoints2=TMath::Min(Int_t(fraction*Float_t(npoints)),npoints-1);
275 npoints2=TMath::Max(Int_t(0.5*Float_t(npoints)),npoints2);
276 AliMathBase::EvaluateUni(npoints, data, mean,sigma,npoints2);
277 delete [] data;
278 if (verbose) printf("Mean\t%f\t Sigma2\t%f\n", mean,sigma);if (param){
279 (*param)[0] = his->GetMaximum();
280 (*param)[1] = mean;
281 (*param)[2] = sigma;
282 }
283}
284
d9a129b4 285Double_t AliMathBase::FitGaus(TH1F* his, TVectorD *param, TMatrixD */*matrix*/, Float_t xmin, Float_t xmax, Bool_t verbose){
f6659a9d 286 //
287 // Fit histogram with gaussian function
288 //
289 // Prameters:
290 // return value- chi2 - if negative ( not enough points)
291 // his - input histogram
292 // param - vector with parameters
293 // xmin, xmax - range to fit - if xmin=xmax=0 - the full histogram range used
294 // Fitting:
295 // 1. Step - make logarithm
296 // 2. Linear fit (parabola) - more robust - always converge
297 // 3. In case of small statistic bins are averaged
298 //
299 static TLinearFitter fitter(3,"pol2");
300 TVectorD par(3);
301 TVectorD sigma(3);
302 TMatrixD mat(3,3);
303 if (his->GetMaximum()<4) return -1;
304 if (his->GetEntries()<12) return -1;
305 if (his->GetRMS()<mat.GetTol()) return -1;
5608e15a 306 Float_t maxEstimate = his->GetEntries()*his->GetBinWidth(1)/TMath::Sqrt((TMath::TwoPi()*his->GetRMS()));
f6659a9d 307 Int_t dsmooth = TMath::Nint(6./TMath::Sqrt(maxEstimate));
308
309 if (maxEstimate<1) return -1;
310 Int_t nbins = his->GetNbinsX();
311 Int_t npoints=0;
312 //
313
314
315 if (xmin>=xmax){
316 xmin = his->GetXaxis()->GetXmin();
317 xmax = his->GetXaxis()->GetXmax();
318 }
319 for (Int_t iter=0; iter<2; iter++){
320 fitter.ClearPoints();
321 npoints=0;
5608e15a 322 for (Int_t ibin=1;ibin<nbins+1; ibin++){
f6659a9d 323 Int_t countB=1;
324 Float_t entriesI = his->GetBinContent(ibin);
325 for (Int_t delta = -dsmooth; delta<=dsmooth; delta++){
326 if (ibin+delta>1 &&ibin+delta<nbins-1){
327 entriesI += his->GetBinContent(ibin+delta);
328 countB++;
329 }
330 }
331 entriesI/=countB;
332 Double_t xcenter= his->GetBinCenter(ibin);
333 if (xcenter<xmin || xcenter>xmax) continue;
334 Double_t error=1./TMath::Sqrt(countB);
335 Float_t cont=2;
336 if (iter>0){
337 if (par[0]+par[1]*xcenter+par[2]*xcenter*xcenter>20) return 0;
338 cont = TMath::Exp(par[0]+par[1]*xcenter+par[2]*xcenter*xcenter);
339 if (cont>1.) error = 1./TMath::Sqrt(cont*Float_t(countB));
340 }
341 if (entriesI>1&&cont>1){
342 fitter.AddPoint(&xcenter,TMath::Log(Float_t(entriesI)),error);
343 npoints++;
344 }
345 }
346 if (npoints>3){
347 fitter.Eval();
348 fitter.GetParameters(par);
349 }else{
350 break;
351 }
352 }
353 if (npoints<=3){
354 return -1;
355 }
356 fitter.GetParameters(par);
357 fitter.GetCovarianceMatrix(mat);
358 if (TMath::Abs(par[1])<mat.GetTol()) return -1;
359 if (TMath::Abs(par[2])<mat.GetTol()) return -1;
360 Double_t chi2 = fitter.GetChisquare()/Float_t(npoints);
361 //fitter.GetParameters();
362 if (!param) param = new TVectorD(3);
d9a129b4 363 //if (!matrix) matrix = new TMatrixD(3,3);
f6659a9d 364 (*param)[1] = par[1]/(-2.*par[2]);
365 (*param)[2] = 1./TMath::Sqrt(TMath::Abs(-2.*par[2]));
366 (*param)[0] = TMath::Exp(par[0]+ par[1]* (*param)[1] + par[2]*(*param)[1]*(*param)[1]);
367 if (verbose){
368 par.Print();
369 mat.Print();
370 param->Print();
371 printf("Chi2=%f\n",chi2);
372 TF1 * f1= new TF1("f1","[0]*exp(-(x-[1])^2/(2*[2]*[2]))",his->GetXaxis()->GetXmin(),his->GetXaxis()->GetXmax());
373 f1->SetParameter(0, (*param)[0]);
374 f1->SetParameter(1, (*param)[1]);
375 f1->SetParameter(2, (*param)[2]);
376 f1->Draw("same");
377 }
378 return chi2;
379}
380
d9a129b4 381Double_t AliMathBase::FitGaus(Float_t *arr, Int_t nBins, Float_t xMin, Float_t xMax, TVectorD *param, TMatrixD */*matrix*/, Bool_t verbose){
5608e15a 382 //
383 // Fit histogram with gaussian function
384 //
385 // Prameters:
5f645a6e 386 // nbins: size of the array and number of histogram bins
387 // xMin, xMax: histogram range
00bb7de0 388 // param: paramters of the fit (0-Constant, 1-Mean, 2-Sigma, 3-Sum)
5f645a6e 389 // matrix: covariance matrix -- not implemented yet, pass dummy matrix!!!
390 //
391 // Return values:
392 // >0: the chi2 returned by TLinearFitter
393 // -3: only three points have been used for the calculation - no fitter was used
394 // -2: only two points have been used for the calculation - center of gravity was uesed for calculation
395 // -1: only one point has been used for the calculation - center of gravity was uesed for calculation
396 // -4: invalid result!!
397 //
5608e15a 398 // Fitting:
399 // 1. Step - make logarithm
400 // 2. Linear fit (parabola) - more robust - always converge
5608e15a 401 //
402 static TLinearFitter fitter(3,"pol2");
403 static TMatrixD mat(3,3);
404 static Double_t kTol = mat.GetTol();
405 fitter.StoreData(kFALSE);
406 fitter.ClearPoints();
407 TVectorD par(3);
408 TVectorD sigma(3);
409 TMatrixD A(3,3);
410 TMatrixD b(3,1);
5f645a6e 411 Float_t rms = TMath::RMS(nBins,arr);
412 Float_t max = TMath::MaxElement(nBins,arr);
413 Float_t binWidth = (xMax-xMin)/(Float_t)nBins;
5608e15a 414
415 Float_t meanCOG = 0;
416 Float_t rms2COG = 0;
417 Float_t sumCOG = 0;
418
419 Float_t entries = 0;
420 Int_t nfilled=0;
421
d9a129b4 422 if (!param) param = new TVectorD(4);
61d38705 423
5f645a6e 424 for (Int_t i=0; i<nBins; i++){
5608e15a 425 entries+=arr[i];
426 if (arr[i]>0) nfilled++;
427 }
00bb7de0 428 (*param)[0] = 0;
429 (*param)[1] = 0;
430 (*param)[2] = 0;
431 (*param)[3] = 0;
5608e15a 432
5f645a6e 433 if (max<4) return -4;
434 if (entries<12) return -4;
435 if (rms<kTol) return -4;
5608e15a 436
00bb7de0 437 (*param)[3] = entries;
5608e15a 438
00bb7de0 439 Int_t npoints=0;
5f645a6e 440 for (Int_t ibin=0;ibin<nBins; ibin++){
441 Float_t entriesI = arr[ibin];
5608e15a 442 if (entriesI>1){
5f645a6e 443 Double_t xcenter = xMin+(ibin+0.5)*binWidth;
5608e15a 444 Float_t error = 1./TMath::Sqrt(entriesI);
445 Float_t val = TMath::Log(Float_t(entriesI));
446 fitter.AddPoint(&xcenter,val,error);
5f645a6e 447 if (npoints<3){
448 A(npoints,0)=1;
449 A(npoints,1)=xcenter;
450 A(npoints,2)=xcenter*xcenter;
451 b(npoints,0)=val;
452 meanCOG+=xcenter*entriesI;
453 rms2COG +=xcenter*entriesI*xcenter;
454 sumCOG +=entriesI;
455 }
5608e15a 456 npoints++;
457 }
458 }
5608e15a 459
460 Double_t chi2 = 0;
461 if (npoints>=3){
462 if ( npoints == 3 ){
463 //analytic calculation of the parameters for three points
464 A.Invert();
465 TMatrixD res(1,3);
466 res.Mult(A,b);
467 par[0]=res(0,0);
468 par[1]=res(0,1);
469 par[2]=res(0,2);
470 chi2 = -3.;
471 } else {
472 // use fitter for more than three points
473 fitter.Eval();
474 fitter.GetParameters(par);
475 fitter.GetCovarianceMatrix(mat);
476 chi2 = fitter.GetChisquare()/Float_t(npoints);
477 }
5f645a6e 478 if (TMath::Abs(par[1])<kTol) return -4;
479 if (TMath::Abs(par[2])<kTol) return -4;
5608e15a 480
d9a129b4 481 //if (!param) param = new TVectorD(4);
00bb7de0 482 if ( param->GetNrows()<4 ) param->ResizeTo(4);
d9a129b4 483 //if (!matrix) matrix = new TMatrixD(3,3); // !!!!might be a memory leek. use dummy matrix pointer to call this function!
5608e15a 484
485 (*param)[1] = par[1]/(-2.*par[2]);
486 (*param)[2] = 1./TMath::Sqrt(TMath::Abs(-2.*par[2]));
5f645a6e 487 Double_t lnparam0 = par[0]+ par[1]* (*param)[1] + par[2]*(*param)[1]*(*param)[1];
488 if ( lnparam0>307 ) return -4;
489 (*param)[0] = TMath::Exp(lnparam0);
5608e15a 490 if (verbose){
491 par.Print();
492 mat.Print();
493 param->Print();
494 printf("Chi2=%f\n",chi2);
5f645a6e 495 TF1 * f1= new TF1("f1","[0]*exp(-(x-[1])^2/(2*[2]*[2]))",xMin,xMax);
5608e15a 496 f1->SetParameter(0, (*param)[0]);
497 f1->SetParameter(1, (*param)[1]);
498 f1->SetParameter(2, (*param)[2]);
499 f1->Draw("same");
500 }
501 return chi2;
502 }
503
504 if (npoints == 2){
505 //use center of gravity for 2 points
506 meanCOG/=sumCOG;
507 rms2COG /=sumCOG;
508 (*param)[0] = max;
509 (*param)[1] = meanCOG;
510 (*param)[2] = TMath::Sqrt(TMath::Abs(meanCOG*meanCOG-rms2COG));
511 chi2=-2.;
512 }
513 if ( npoints == 1 ){
5f645a6e 514 meanCOG/=sumCOG;
5608e15a 515 (*param)[0] = max;
516 (*param)[1] = meanCOG;
517 (*param)[2] = binWidth/TMath::Sqrt(12);
518 chi2=-1.;
519 }
520 return chi2;
521
522}
523
524
5f645a6e 525Float_t AliMathBase::GetCOG(Short_t *arr, Int_t nBins, Float_t xMin, Float_t xMax, Float_t *rms, Float_t *sum)
526{
527 //
528 // calculate center of gravity rms and sum for array 'arr' with nBins an a x range xMin to xMax
529 // return COG; in case of failure return xMin
530 //
531 Float_t meanCOG = 0;
532 Float_t rms2COG = 0;
533 Float_t sumCOG = 0;
534 Int_t npoints = 0;
535
536 Float_t binWidth = (xMax-xMin)/(Float_t)nBins;
537
538 for (Int_t ibin=0; ibin<nBins; ibin++){
539 Float_t entriesI = (Float_t)arr[ibin];
540 Double_t xcenter = xMin+(ibin+0.5)*binWidth;
541 if ( entriesI>0 ){
542 meanCOG += xcenter*entriesI;
543 rms2COG += xcenter*entriesI*xcenter;
544 sumCOG += entriesI;
545 npoints++;
546 }
547 }
548 if ( sumCOG == 0 ) return xMin;
549 meanCOG/=sumCOG;
550
551 if ( rms ){
552 rms2COG /=sumCOG;
553 (*rms) = TMath::Sqrt(TMath::Abs(meanCOG*meanCOG-rms2COG));
554 if ( npoints == 1 ) (*rms) = binWidth/TMath::Sqrt(12);
555 }
556
557 if ( sum )
558 (*sum) = sumCOG;
559
560 return meanCOG;
561}
562
563
bb7e41dd 564Double_t AliMathBase::ErfcFast(Double_t x){
565 // Fast implementation of the complementary error function
566 // The error of the approximation is |eps(x)| < 5E-4
567 // See Abramowitz and Stegun, p.299, 7.1.27
568
569 Double_t z = TMath::Abs(x);
570 Double_t ans = 1+z*(0.278393+z*(0.230389+z*(0.000972+z*0.078108)));
571 ans = 1.0/ans;
572 ans *= ans;
573 ans *= ans;
574
575 return (x>=0.0 ? ans : 2.0 - ans);
576}
5608e15a 577
578///////////////////////////////////////////////////////////////
579////////////// TEST functions /////////////////////////
580///////////////////////////////////////////////////////////////
581
582
583
584
585
586void AliMathBase::TestGausFit(Int_t nhistos){
587 //
588 // Test performance of the parabolic - gaussian fit - compare it with
589 // ROOT gauss fit
590 // nhistos - number of histograms to be used for test
591 //
592 TTreeSRedirector *pcstream = new TTreeSRedirector("fitdebug.root");
593
594 Float_t *xTrue = new Float_t[nhistos];
595 Float_t *sTrue = new Float_t[nhistos];
596 TVectorD **par1 = new TVectorD*[nhistos];
597 TVectorD **par2 = new TVectorD*[nhistos];
598 TMatrixD dummy(3,3);
599
600
601 TH1F **h1f = new TH1F*[nhistos];
602 TF1 *myg = new TF1("myg","gaus");
603 TF1 *fit = new TF1("fit","gaus");
604 gRandom->SetSeed(0);
605
606 //init
607 for (Int_t i=0;i<nhistos; i++){
608 par1[i] = new TVectorD(3);
609 par2[i] = new TVectorD(3);
610 h1f[i] = new TH1F(Form("h1f%d",i),Form("h1f%d",i),20,-10,10);
611 xTrue[i]= gRandom->Rndm();
612 gSystem->Sleep(2);
613 sTrue[i]= .75+gRandom->Rndm()*.5;
614 myg->SetParameters(1,xTrue[i],sTrue[i]);
615 h1f[i]->FillRandom("myg");
616 }
617
618 TStopwatch s;
619 s.Start();
620 //standard gaus fit
621 for (Int_t i=0; i<nhistos; i++){
622 h1f[i]->Fit(fit,"0q");
623 (*par1[i])(0) = fit->GetParameter(0);
624 (*par1[i])(1) = fit->GetParameter(1);
625 (*par1[i])(2) = fit->GetParameter(2);
626 }
627 s.Stop();
628 printf("Gaussian fit\t");
629 s.Print();
630
631 s.Start();
632 //AliMathBase gaus fit
633 for (Int_t i=0; i<nhistos; i++){
5f645a6e 634 AliMathBase::FitGaus(h1f[i]->GetArray()+1,h1f[i]->GetNbinsX(),h1f[i]->GetXaxis()->GetXmin(),h1f[i]->GetXaxis()->GetXmax(),par2[i],&dummy);
5608e15a 635 }
636
637 s.Stop();
638 printf("Parabolic fit\t");
639 s.Print();
640 //write stream
641 for (Int_t i=0;i<nhistos; i++){
642 Float_t xt = xTrue[i];
643 Float_t st = sTrue[i];
644 (*pcstream)<<"data"
645 <<"xTrue="<<xt
646 <<"sTrue="<<st
647 <<"pg.="<<(par1[i])
648 <<"pa.="<<(par2[i])
649 <<"\n";
650 }
651 //delete pointers
652 for (Int_t i=0;i<nhistos; i++){
653 delete par1[i];
654 delete par2[i];
655 delete h1f[i];
656 }
657 delete pcstream;
658 delete []h1f;
659 delete []xTrue;
660 delete []sTrue;
661 //
662 delete []par1;
663 delete []par2;
664
665}
666
667
668
3392b4c9 669TGraph2D * AliMathBase::MakeStat2D(TH3 * his, Int_t delta0, Int_t delta1, Int_t type){
670 //
671 //
672 //
673 // delta - number of bins to integrate
674 // type - 0 - mean value
675
676 TAxis * xaxis = his->GetXaxis();
677 TAxis * yaxis = his->GetYaxis();
678 // TAxis * zaxis = his->GetZaxis();
679 Int_t nbinx = xaxis->GetNbins();
680 Int_t nbiny = yaxis->GetNbins();
61d38705 681 const Int_t nc=1000;
682 char name[nc];
3392b4c9 683 Int_t icount=0;
684 TGraph2D *graph = new TGraph2D(nbinx*nbiny);
685 TF1 f1("f1","gaus");
686 for (Int_t ix=0; ix<nbinx;ix++)
687 for (Int_t iy=0; iy<nbiny;iy++){
688 Float_t xcenter = xaxis->GetBinCenter(ix);
689 Float_t ycenter = yaxis->GetBinCenter(iy);
61d38705 690 snprintf(name,nc,"%s_%d_%d",his->GetName(), ix,iy);
3392b4c9 691 TH1 *projection = his->ProjectionZ(name,ix-delta0,ix+delta0,iy-delta1,iy+delta1);
692 Float_t stat= 0;
693 if (type==0) stat = projection->GetMean();
694 if (type==1) stat = projection->GetRMS();
695 if (type==2 || type==3){
696 TVectorD vec(3);
697 AliMathBase::LTM((TH1F*)projection,&vec,0.7);
698 if (type==2) stat= vec[1];
699 if (type==3) stat= vec[0];
700 }
701 if (type==4|| type==5){
702 projection->Fit(&f1);
703 if (type==4) stat= f1.GetParameter(1);
704 if (type==5) stat= f1.GetParameter(2);
705 }
706 //printf("%d\t%f\t%f\t%f\n", icount,xcenter, ycenter, stat);
707 graph->SetPoint(icount,xcenter, ycenter, stat);
708 icount++;
709 }
710 return graph;
711}
5608e15a 712
3392b4c9 713TGraph * AliMathBase::MakeStat1D(TH3 * his, Int_t delta1, Int_t type){
714 //
715 //
716 //
717 // delta - number of bins to integrate
718 // type - 0 - mean value
719
720 TAxis * xaxis = his->GetXaxis();
721 TAxis * yaxis = his->GetYaxis();
722 // TAxis * zaxis = his->GetZaxis();
723 Int_t nbinx = xaxis->GetNbins();
724 Int_t nbiny = yaxis->GetNbins();
61d38705 725 const Int_t nc=1000;
726 char name[nc];
3392b4c9 727 Int_t icount=0;
728 TGraph *graph = new TGraph(nbinx);
729 TF1 f1("f1","gaus");
730 for (Int_t ix=0; ix<nbinx;ix++){
731 Float_t xcenter = xaxis->GetBinCenter(ix);
732 // Float_t ycenter = yaxis->GetBinCenter(iy);
61d38705 733 snprintf(name,nc,"%s_%d",his->GetName(), ix);
3392b4c9 734 TH1 *projection = his->ProjectionZ(name,ix-delta1,ix+delta1,0,nbiny);
735 Float_t stat= 0;
736 if (type==0) stat = projection->GetMean();
737 if (type==1) stat = projection->GetRMS();
738 if (type==2 || type==3){
739 TVectorD vec(3);
740 AliMathBase::LTM((TH1F*)projection,&vec,0.7);
741 if (type==2) stat= vec[1];
742 if (type==3) stat= vec[0];
743 }
744 if (type==4|| type==5){
745 projection->Fit(&f1);
746 if (type==4) stat= f1.GetParameter(1);
747 if (type==5) stat= f1.GetParameter(2);
748 }
749 //printf("%d\t%f\t%f\t%f\n", icount,xcenter, ycenter, stat);
750 graph->SetPoint(icount,xcenter, stat);
751 icount++;
752 }
753 return graph;
754}
09a29b67 755
756Double_t AliMathBase::TruncatedGaus(Double_t mean, Double_t sigma, Double_t cutat)
757{
758 // return number generated according to a gaussian distribution N(mean,sigma) truncated at cutat
759 //
760 Double_t value;
761 do{
762 value=gRandom->Gaus(mean,sigma);
763 }while(TMath::Abs(value-mean)>cutat);
764 return value;
765}
4c5881a0 766
767Double_t AliMathBase::TruncatedGaus(Double_t mean, Double_t sigma, Double_t leftCut, Double_t rightCut)
768{
769 // return number generated according to a gaussian distribution N(mean,sigma)
770 // truncated at leftCut and rightCut
771 //
772 Double_t value;
773 do{
774 value=gRandom->Gaus(mean,sigma);
775 }while((value-mean)<-leftCut || (value-mean)>rightCut);
776 return value;
777}
f6d87824 778
779Double_t AliMathBase::BetheBlochAleph(Double_t bg,
780 Double_t kp1,
781 Double_t kp2,
782 Double_t kp3,
783 Double_t kp4,
784 Double_t kp5) {
785 //
d46683db 786 // This is the empirical ALEPH parameterization of the Bethe-Bloch formula.
787 // It is normalized to 1 at the minimum.
788 //
789 // bg - beta*gamma
790 //
791 // The default values for the kp* parameters are for ALICE TPC.
792 // The returned value is in MIP units
f6d87824 793 //
794
9c56b409 795 return AliExternalTrackParam::BetheBlochAleph(bg,kp1,kp2,kp3,kp4,kp5);
d46683db 796}
6d93083f 797
798Double_t AliMathBase::Gamma(Double_t k)
799{
800 // from
801 // Hisashi Tanizaki
802 // http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.158.3866&rep=rep1&type=pdf
803 // A. Morsch 14/01/2014
804 static Double_t n=0;
805 static Double_t c1=0;
806 static Double_t c2=0;
807 static Double_t b1=0;
808 static Double_t b2=0;
809 if (k > 0) {
810 if (k < 0.4)
811 n = 1./k;
812 else if (k >= 0.4 && k < 4)
813 n = 1./k + (k - 0.4)/k/3.6;
814 else if (k >= 4.)
815 n = 1./TMath::Sqrt(k);
816 b1 = k - 1./n;
817 b2 = k + 1./n;
818 c1 = (k < 0.4)? 0 : b1 * (TMath::Log(b1) - 1.)/2.;
819 c2 = b2 * (TMath::Log(b2) - 1.)/2.;
820 }
821 Double_t x;
822 Double_t y = -1.;
823 while (1) {
824 Double_t nu1 = gRandom->Rndm();
825 Double_t nu2 = gRandom->Rndm();
826 Double_t w1 = c1 + TMath::Log(nu1);
827 Double_t w2 = c2 + TMath::Log(nu2);
828 y = n * (b1 * w2 - b2 * w1);
829 if (y < 0) continue;
830 x = n * (w2 - w1);
831 if (TMath::Log(y) >= x) break;
832 }
833 return TMath::Exp(x);
834}