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21f3a443 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 TStatToolkit
19//
20// Subset of matheamtical functions not included in the TMath
21//
22
23///////////////////////////////////////////////////////////////////////////
24#include "TMath.h"
25#include "Riostream.h"
26#include "TH1F.h"
27#include "TH3.h"
28#include "TF1.h"
29#include "TTree.h"
30#include "TChain.h"
31#include "TObjString.h"
32#include "TLinearFitter.h"
33
34//
35// includes neccessary for test functions
36//
37#include "TSystem.h"
38#include "TRandom.h"
39#include "TStopwatch.h"
40#include "TTreeStream.h"
41
42#include "TStatToolkit.h"
43
44
45ClassImp(TStatToolkit) // Class implementation to enable ROOT I/O
46
47TStatToolkit::TStatToolkit() : TObject()
48{
49 //
50 // Default constructor
51 //
52}
53///////////////////////////////////////////////////////////////////////////
54TStatToolkit::~TStatToolkit()
55{
56 //
57 // Destructor
58 //
59}
60
61
62//_____________________________________________________________________________
63void TStatToolkit::EvaluateUni(Int_t nvectors, Double_t *data, Double_t &mean
64 , Double_t &sigma, Int_t hh)
65{
66 //
67 // Robust estimator in 1D case MI version - (faster than ROOT version)
68 //
69 // For the univariate case
70 // estimates of location and scatter are returned in mean and sigma parameters
71 // the algorithm works on the same principle as in multivariate case -
72 // it finds a subset of size hh with smallest sigma, and then returns mean and
73 // sigma of this subset
74 //
75
76 if (hh==0)
77 hh=(nvectors+2)/2;
78 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};
79 Int_t *index=new Int_t[nvectors];
80 TMath::Sort(nvectors, data, index, kFALSE);
81
82 Int_t nquant = TMath::Min(Int_t(Double_t(((hh*1./nvectors)-0.5)*40))+1, 11);
83 Double_t factor = faclts[TMath::Max(0,nquant-1)];
84
85 Double_t sumx =0;
86 Double_t sumx2 =0;
87 Int_t bestindex = -1;
88 Double_t bestmean = 0;
89 Double_t bestsigma = (data[index[nvectors-1]]-data[index[0]]+1.); // maximal possible sigma
90 bestsigma *=bestsigma;
91
92 for (Int_t i=0; i<hh; i++){
93 sumx += data[index[i]];
94 sumx2 += data[index[i]]*data[index[i]];
95 }
96
97 Double_t norm = 1./Double_t(hh);
98 Double_t norm2 = 1./Double_t(hh-1);
99 for (Int_t i=hh; i<nvectors; i++){
100 Double_t cmean = sumx*norm;
101 Double_t csigma = (sumx2 - hh*cmean*cmean)*norm2;
102 if (csigma<bestsigma){
103 bestmean = cmean;
104 bestsigma = csigma;
105 bestindex = i-hh;
106 }
107
108 sumx += data[index[i]]-data[index[i-hh]];
109 sumx2 += data[index[i]]*data[index[i]]-data[index[i-hh]]*data[index[i-hh]];
110 }
111
112 Double_t bstd=factor*TMath::Sqrt(TMath::Abs(bestsigma));
113 mean = bestmean;
114 sigma = bstd;
115 delete [] index;
116
117}
118
119
120
121void TStatToolkit::EvaluateUniExternal(Int_t nvectors, Double_t *data, Double_t &mean, Double_t &sigma, Int_t hh, Float_t externalfactor)
122{
123 // Modified version of ROOT robust EvaluateUni
124 // robust estimator in 1D case MI version
125 // added external factor to include precision of external measurement
126 //
127
128 if (hh==0)
129 hh=(nvectors+2)/2;
130 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};
131 Int_t *index=new Int_t[nvectors];
132 TMath::Sort(nvectors, data, index, kFALSE);
133 //
134 Int_t nquant = TMath::Min(Int_t(Double_t(((hh*1./nvectors)-0.5)*40))+1, 11);
135 Double_t factor = faclts[0];
136 if (nquant>0){
137 // fix proper normalization - Anja
138 factor = faclts[nquant-1];
139 }
140
141 //
142 //
143 Double_t sumx =0;
144 Double_t sumx2 =0;
145 Int_t bestindex = -1;
146 Double_t bestmean = 0;
147 Double_t bestsigma = -1;
148 for (Int_t i=0; i<hh; i++){
149 sumx += data[index[i]];
150 sumx2 += data[index[i]]*data[index[i]];
151 }
152 //
153 Double_t kfactor = 2.*externalfactor - externalfactor*externalfactor;
154 Double_t norm = 1./Double_t(hh);
155 for (Int_t i=hh; i<nvectors; i++){
156 Double_t cmean = sumx*norm;
157 Double_t csigma = (sumx2*norm - cmean*cmean*kfactor);
158 if (csigma<bestsigma || bestsigma<0){
159 bestmean = cmean;
160 bestsigma = csigma;
161 bestindex = i-hh;
162 }
163 //
164 //
165 sumx += data[index[i]]-data[index[i-hh]];
166 sumx2 += data[index[i]]*data[index[i]]-data[index[i-hh]]*data[index[i-hh]];
167 }
168
169 Double_t bstd=factor*TMath::Sqrt(TMath::Abs(bestsigma));
170 mean = bestmean;
171 sigma = bstd;
172 delete [] index;
173}
174
175
176//_____________________________________________________________________________
177Int_t TStatToolkit::Freq(Int_t n, const Int_t *inlist
178 , Int_t *outlist, Bool_t down)
179{
180 //
181 // Sort eleements according occurancy
182 // The size of output array has is 2*n
183 //
184
185 Int_t * sindexS = new Int_t[n]; // temp array for sorting
186 Int_t * sindexF = new Int_t[2*n];
b8072cce 187 for (Int_t i=0;i<n;i++) sindexS[i]=0;
188 for (Int_t i=0;i<2*n;i++) sindexF[i]=0;
21f3a443 189 //
190 TMath::Sort(n,inlist, sindexS, down);
191 Int_t last = inlist[sindexS[0]];
192 Int_t val = last;
193 sindexF[0] = 1;
194 sindexF[0+n] = last;
195 Int_t countPos = 0;
196 //
197 // find frequency
198 for(Int_t i=1;i<n; i++){
199 val = inlist[sindexS[i]];
200 if (last == val) sindexF[countPos]++;
201 else{
202 countPos++;
203 sindexF[countPos+n] = val;
204 sindexF[countPos]++;
205 last =val;
206 }
207 }
208 if (last==val) countPos++;
209 // sort according frequency
210 TMath::Sort(countPos, sindexF, sindexS, kTRUE);
211 for (Int_t i=0;i<countPos;i++){
212 outlist[2*i ] = sindexF[sindexS[i]+n];
213 outlist[2*i+1] = sindexF[sindexS[i]];
214 }
215 delete [] sindexS;
216 delete [] sindexF;
217
218 return countPos;
219
220}
221
222//___TStatToolkit__________________________________________________________________________
223void TStatToolkit::TruncatedMean(TH1F * his, TVectorD *param, Float_t down, Float_t up, Bool_t verbose){
224 //
225 //
226 //
227 Int_t nbins = his->GetNbinsX();
228 Float_t nentries = his->GetEntries();
229 Float_t sum =0;
230 Float_t mean = 0;
231 Float_t sigma2 = 0;
232 Float_t ncumul=0;
233 for (Int_t ibin=1;ibin<nbins; ibin++){
234 ncumul+= his->GetBinContent(ibin);
235 Float_t fraction = Float_t(ncumul)/Float_t(nentries);
236 if (fraction>down && fraction<up){
237 sum+=his->GetBinContent(ibin);
238 mean+=his->GetBinCenter(ibin)*his->GetBinContent(ibin);
239 sigma2+=his->GetBinCenter(ibin)*his->GetBinCenter(ibin)*his->GetBinContent(ibin);
240 }
241 }
242 mean/=sum;
243 sigma2= TMath::Sqrt(TMath::Abs(sigma2/sum-mean*mean));
244 if (param){
245 (*param)[0] = his->GetMaximum();
246 (*param)[1] = mean;
247 (*param)[2] = sigma2;
248
249 }
250 if (verbose) printf("Mean\t%f\t Sigma2\t%f\n", mean,sigma2);
251}
252
253void TStatToolkit::LTM(TH1F * his, TVectorD *param , Float_t fraction, Bool_t verbose){
254 //
255 // LTM
256 //
257 Int_t nbins = his->GetNbinsX();
258 Int_t nentries = (Int_t)his->GetEntries();
259 Double_t *data = new Double_t[nentries];
260 Int_t npoints=0;
261 for (Int_t ibin=1;ibin<nbins; ibin++){
262 Float_t entriesI = his->GetBinContent(ibin);
263 Float_t xcenter= his->GetBinCenter(ibin);
264 for (Int_t ic=0; ic<entriesI; ic++){
265 if (npoints<nentries){
266 data[npoints]= xcenter;
267 npoints++;
268 }
269 }
270 }
271 Double_t mean, sigma;
272 Int_t npoints2=TMath::Min(Int_t(fraction*Float_t(npoints)),npoints-1);
273 npoints2=TMath::Max(Int_t(0.5*Float_t(npoints)),npoints2);
274 TStatToolkit::EvaluateUni(npoints, data, mean,sigma,npoints2);
275 delete [] data;
276 if (verbose) printf("Mean\t%f\t Sigma2\t%f\n", mean,sigma);if (param){
277 (*param)[0] = his->GetMaximum();
278 (*param)[1] = mean;
279 (*param)[2] = sigma;
280 }
281}
282
cb1d20de 283Double_t TStatToolkit::FitGaus(TH1F* his, TVectorD *param, TMatrixD */*matrix*/, Float_t xmin, Float_t xmax, Bool_t verbose){
21f3a443 284 //
285 // Fit histogram with gaussian function
286 //
287 // Prameters:
288 // return value- chi2 - if negative ( not enough points)
289 // his - input histogram
290 // param - vector with parameters
291 // xmin, xmax - range to fit - if xmin=xmax=0 - the full histogram range used
292 // Fitting:
293 // 1. Step - make logarithm
294 // 2. Linear fit (parabola) - more robust - always converge
295 // 3. In case of small statistic bins are averaged
296 //
297 static TLinearFitter fitter(3,"pol2");
298 TVectorD par(3);
299 TVectorD sigma(3);
300 TMatrixD mat(3,3);
301 if (his->GetMaximum()<4) return -1;
302 if (his->GetEntries()<12) return -1;
303 if (his->GetRMS()<mat.GetTol()) return -1;
304 Float_t maxEstimate = his->GetEntries()*his->GetBinWidth(1)/TMath::Sqrt((TMath::TwoPi()*his->GetRMS()));
305 Int_t dsmooth = TMath::Nint(6./TMath::Sqrt(maxEstimate));
306
307 if (maxEstimate<1) return -1;
308 Int_t nbins = his->GetNbinsX();
309 Int_t npoints=0;
310 //
311
312
313 if (xmin>=xmax){
314 xmin = his->GetXaxis()->GetXmin();
315 xmax = his->GetXaxis()->GetXmax();
316 }
317 for (Int_t iter=0; iter<2; iter++){
318 fitter.ClearPoints();
319 npoints=0;
320 for (Int_t ibin=1;ibin<nbins+1; ibin++){
321 Int_t countB=1;
322 Float_t entriesI = his->GetBinContent(ibin);
323 for (Int_t delta = -dsmooth; delta<=dsmooth; delta++){
324 if (ibin+delta>1 &&ibin+delta<nbins-1){
325 entriesI += his->GetBinContent(ibin+delta);
326 countB++;
327 }
328 }
329 entriesI/=countB;
330 Double_t xcenter= his->GetBinCenter(ibin);
331 if (xcenter<xmin || xcenter>xmax) continue;
332 Double_t error=1./TMath::Sqrt(countB);
333 Float_t cont=2;
334 if (iter>0){
335 if (par[0]+par[1]*xcenter+par[2]*xcenter*xcenter>20) return 0;
336 cont = TMath::Exp(par[0]+par[1]*xcenter+par[2]*xcenter*xcenter);
337 if (cont>1.) error = 1./TMath::Sqrt(cont*Float_t(countB));
338 }
339 if (entriesI>1&&cont>1){
340 fitter.AddPoint(&xcenter,TMath::Log(Float_t(entriesI)),error);
341 npoints++;
342 }
343 }
344 if (npoints>3){
345 fitter.Eval();
346 fitter.GetParameters(par);
347 }else{
348 break;
349 }
350 }
351 if (npoints<=3){
352 return -1;
353 }
354 fitter.GetParameters(par);
355 fitter.GetCovarianceMatrix(mat);
356 if (TMath::Abs(par[1])<mat.GetTol()) return -1;
357 if (TMath::Abs(par[2])<mat.GetTol()) return -1;
358 Double_t chi2 = fitter.GetChisquare()/Float_t(npoints);
359 //fitter.GetParameters();
360 if (!param) param = new TVectorD(3);
cb1d20de 361 // if (!matrix) matrix = new TMatrixD(3,3); // Covariance matrix to be implemented
21f3a443 362 (*param)[1] = par[1]/(-2.*par[2]);
363 (*param)[2] = 1./TMath::Sqrt(TMath::Abs(-2.*par[2]));
364 (*param)[0] = TMath::Exp(par[0]+ par[1]* (*param)[1] + par[2]*(*param)[1]*(*param)[1]);
365 if (verbose){
366 par.Print();
367 mat.Print();
368 param->Print();
369 printf("Chi2=%f\n",chi2);
370 TF1 * f1= new TF1("f1","[0]*exp(-(x-[1])^2/(2*[2]*[2]))",his->GetXaxis()->GetXmin(),his->GetXaxis()->GetXmax());
371 f1->SetParameter(0, (*param)[0]);
372 f1->SetParameter(1, (*param)[1]);
373 f1->SetParameter(2, (*param)[2]);
374 f1->Draw("same");
375 }
376 return chi2;
377}
378
cb1d20de 379Double_t TStatToolkit::FitGaus(Float_t *arr, Int_t nBins, Float_t xMin, Float_t xMax, TVectorD *param, TMatrixD */*matrix*/, Bool_t verbose){
21f3a443 380 //
381 // Fit histogram with gaussian function
382 //
383 // Prameters:
384 // nbins: size of the array and number of histogram bins
385 // xMin, xMax: histogram range
386 // param: paramters of the fit (0-Constant, 1-Mean, 2-Sigma)
387 // matrix: covariance matrix -- not implemented yet, pass dummy matrix!!!
388 //
389 // Return values:
390 // >0: the chi2 returned by TLinearFitter
391 // -3: only three points have been used for the calculation - no fitter was used
392 // -2: only two points have been used for the calculation - center of gravity was uesed for calculation
393 // -1: only one point has been used for the calculation - center of gravity was uesed for calculation
394 // -4: invalid result!!
395 //
396 // Fitting:
397 // 1. Step - make logarithm
398 // 2. Linear fit (parabola) - more robust - always converge
399 //
400 static TLinearFitter fitter(3,"pol2");
401 static TMatrixD mat(3,3);
402 static Double_t kTol = mat.GetTol();
403 fitter.StoreData(kFALSE);
404 fitter.ClearPoints();
405 TVectorD par(3);
406 TVectorD sigma(3);
407 TMatrixD A(3,3);
408 TMatrixD b(3,1);
409 Float_t rms = TMath::RMS(nBins,arr);
410 Float_t max = TMath::MaxElement(nBins,arr);
411 Float_t binWidth = (xMax-xMin)/(Float_t)nBins;
412
413 Float_t meanCOG = 0;
414 Float_t rms2COG = 0;
415 Float_t sumCOG = 0;
416
417 Float_t entries = 0;
418 Int_t nfilled=0;
419
420 for (Int_t i=0; i<nBins; i++){
421 entries+=arr[i];
422 if (arr[i]>0) nfilled++;
423 }
424
425 if (max<4) return -4;
426 if (entries<12) return -4;
427 if (rms<kTol) return -4;
428
429 Int_t npoints=0;
430 //
431
432 //
433 for (Int_t ibin=0;ibin<nBins; ibin++){
434 Float_t entriesI = arr[ibin];
435 if (entriesI>1){
436 Double_t xcenter = xMin+(ibin+0.5)*binWidth;
437
438 Float_t error = 1./TMath::Sqrt(entriesI);
439 Float_t val = TMath::Log(Float_t(entriesI));
440 fitter.AddPoint(&xcenter,val,error);
441 if (npoints<3){
442 A(npoints,0)=1;
443 A(npoints,1)=xcenter;
444 A(npoints,2)=xcenter*xcenter;
445 b(npoints,0)=val;
446 meanCOG+=xcenter*entriesI;
447 rms2COG +=xcenter*entriesI*xcenter;
448 sumCOG +=entriesI;
449 }
450 npoints++;
451 }
452 }
453
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 }
473 if (TMath::Abs(par[1])<kTol) return -4;
474 if (TMath::Abs(par[2])<kTol) return -4;
475
476 if (!param) param = new TVectorD(3);
cb1d20de 477 //if (!matrix) matrix = new TMatrixD(3,3); // !!!!might be a memory leek. use dummy matrix pointer to call this function! // Covariance matrix to be implemented
21f3a443 478
479 (*param)[1] = par[1]/(-2.*par[2]);
480 (*param)[2] = 1./TMath::Sqrt(TMath::Abs(-2.*par[2]));
481 Double_t lnparam0 = par[0]+ par[1]* (*param)[1] + par[2]*(*param)[1]*(*param)[1];
482 if ( lnparam0>307 ) return -4;
483 (*param)[0] = TMath::Exp(lnparam0);
484 if (verbose){
485 par.Print();
486 mat.Print();
487 param->Print();
488 printf("Chi2=%f\n",chi2);
489 TF1 * f1= new TF1("f1","[0]*exp(-(x-[1])^2/(2*[2]*[2]))",xMin,xMax);
490 f1->SetParameter(0, (*param)[0]);
491 f1->SetParameter(1, (*param)[1]);
492 f1->SetParameter(2, (*param)[2]);
493 f1->Draw("same");
494 }
495 return chi2;
496 }
497
498 if (npoints == 2){
499 //use center of gravity for 2 points
500 meanCOG/=sumCOG;
501 rms2COG /=sumCOG;
502 (*param)[0] = max;
503 (*param)[1] = meanCOG;
504 (*param)[2] = TMath::Sqrt(TMath::Abs(meanCOG*meanCOG-rms2COG));
505 chi2=-2.;
506 }
507 if ( npoints == 1 ){
508 meanCOG/=sumCOG;
509 (*param)[0] = max;
510 (*param)[1] = meanCOG;
511 (*param)[2] = binWidth/TMath::Sqrt(12);
512 chi2=-1.;
513 }
514 return chi2;
515
516}
517
518
519Float_t TStatToolkit::GetCOG(Short_t *arr, Int_t nBins, Float_t xMin, Float_t xMax, Float_t *rms, Float_t *sum)
520{
521 //
522 // calculate center of gravity rms and sum for array 'arr' with nBins an a x range xMin to xMax
523 // return COG; in case of failure return xMin
524 //
525 Float_t meanCOG = 0;
526 Float_t rms2COG = 0;
527 Float_t sumCOG = 0;
528 Int_t npoints = 0;
529
530 Float_t binWidth = (xMax-xMin)/(Float_t)nBins;
531
532 for (Int_t ibin=0; ibin<nBins; ibin++){
533 Float_t entriesI = (Float_t)arr[ibin];
534 Double_t xcenter = xMin+(ibin+0.5)*binWidth;
535 if ( entriesI>0 ){
536 meanCOG += xcenter*entriesI;
537 rms2COG += xcenter*entriesI*xcenter;
538 sumCOG += entriesI;
539 npoints++;
540 }
541 }
542 if ( sumCOG == 0 ) return xMin;
543 meanCOG/=sumCOG;
544
545 if ( rms ){
546 rms2COG /=sumCOG;
547 (*rms) = TMath::Sqrt(TMath::Abs(meanCOG*meanCOG-rms2COG));
548 if ( npoints == 1 ) (*rms) = binWidth/TMath::Sqrt(12);
549 }
550
551 if ( sum )
552 (*sum) = sumCOG;
553
554 return meanCOG;
555}
556
557
558
559///////////////////////////////////////////////////////////////
560////////////// TEST functions /////////////////////////
561///////////////////////////////////////////////////////////////
562
563
564
565
566
567void TStatToolkit::TestGausFit(Int_t nhistos){
568 //
569 // Test performance of the parabolic - gaussian fit - compare it with
570 // ROOT gauss fit
571 // nhistos - number of histograms to be used for test
572 //
573 TTreeSRedirector *pcstream = new TTreeSRedirector("fitdebug.root");
574
575 Float_t *xTrue = new Float_t[nhistos];
576 Float_t *sTrue = new Float_t[nhistos];
577 TVectorD **par1 = new TVectorD*[nhistos];
578 TVectorD **par2 = new TVectorD*[nhistos];
579 TMatrixD dummy(3,3);
580
581
582 TH1F **h1f = new TH1F*[nhistos];
583 TF1 *myg = new TF1("myg","gaus");
584 TF1 *fit = new TF1("fit","gaus");
585 gRandom->SetSeed(0);
586
587 //init
588 for (Int_t i=0;i<nhistos; i++){
589 par1[i] = new TVectorD(3);
590 par2[i] = new TVectorD(3);
591 h1f[i] = new TH1F(Form("h1f%d",i),Form("h1f%d",i),20,-10,10);
592 xTrue[i]= gRandom->Rndm();
593 gSystem->Sleep(2);
594 sTrue[i]= .75+gRandom->Rndm()*.5;
595 myg->SetParameters(1,xTrue[i],sTrue[i]);
596 h1f[i]->FillRandom("myg");
597 }
598
599 TStopwatch s;
600 s.Start();
601 //standard gaus fit
602 for (Int_t i=0; i<nhistos; i++){
603 h1f[i]->Fit(fit,"0q");
604 (*par1[i])(0) = fit->GetParameter(0);
605 (*par1[i])(1) = fit->GetParameter(1);
606 (*par1[i])(2) = fit->GetParameter(2);
607 }
608 s.Stop();
609 printf("Gaussian fit\t");
610 s.Print();
611
612 s.Start();
613 //TStatToolkit gaus fit
614 for (Int_t i=0; i<nhistos; i++){
615 TStatToolkit::FitGaus(h1f[i]->GetArray()+1,h1f[i]->GetNbinsX(),h1f[i]->GetXaxis()->GetXmin(),h1f[i]->GetXaxis()->GetXmax(),par2[i],&dummy);
616 }
617
618 s.Stop();
619 printf("Parabolic fit\t");
620 s.Print();
621 //write stream
622 for (Int_t i=0;i<nhistos; i++){
623 Float_t xt = xTrue[i];
624 Float_t st = sTrue[i];
625 (*pcstream)<<"data"
626 <<"xTrue="<<xt
627 <<"sTrue="<<st
628 <<"pg.="<<(par1[i])
629 <<"pa.="<<(par2[i])
630 <<"\n";
631 }
632 //delete pointers
633 for (Int_t i=0;i<nhistos; i++){
634 delete par1[i];
635 delete par2[i];
636 delete h1f[i];
637 }
638 delete pcstream;
639 delete []h1f;
640 delete []xTrue;
641 delete []sTrue;
642 //
643 delete []par1;
644 delete []par2;
645
646}
647
648
649
650TGraph2D * TStatToolkit::MakeStat2D(TH3 * his, Int_t delta0, Int_t delta1, Int_t type){
651 //
652 //
653 //
654 // delta - number of bins to integrate
655 // type - 0 - mean value
656
657 TAxis * xaxis = his->GetXaxis();
658 TAxis * yaxis = his->GetYaxis();
659 // TAxis * zaxis = his->GetZaxis();
660 Int_t nbinx = xaxis->GetNbins();
661 Int_t nbiny = yaxis->GetNbins();
662 char name[1000];
663 Int_t icount=0;
664 TGraph2D *graph = new TGraph2D(nbinx*nbiny);
665 TF1 f1("f1","gaus");
666 for (Int_t ix=0; ix<nbinx;ix++)
667 for (Int_t iy=0; iy<nbiny;iy++){
668 Float_t xcenter = xaxis->GetBinCenter(ix);
669 Float_t ycenter = yaxis->GetBinCenter(iy);
cb1d20de 670 snprintf(name,1000,"%s_%d_%d",his->GetName(), ix,iy);
21f3a443 671 TH1 *projection = his->ProjectionZ(name,ix-delta0,ix+delta0,iy-delta1,iy+delta1);
672 Float_t stat= 0;
673 if (type==0) stat = projection->GetMean();
674 if (type==1) stat = projection->GetRMS();
675 if (type==2 || type==3){
676 TVectorD vec(3);
677 TStatToolkit::LTM((TH1F*)projection,&vec,0.7);
678 if (type==2) stat= vec[1];
679 if (type==3) stat= vec[0];
680 }
681 if (type==4|| type==5){
682 projection->Fit(&f1);
683 if (type==4) stat= f1.GetParameter(1);
684 if (type==5) stat= f1.GetParameter(2);
685 }
686 //printf("%d\t%f\t%f\t%f\n", icount,xcenter, ycenter, stat);
687 graph->SetPoint(icount,xcenter, ycenter, stat);
688 icount++;
689 }
690 return graph;
691}
692
693TGraph * TStatToolkit::MakeStat1D(TH3 * his, Int_t delta1, Int_t type){
694 //
695 //
696 //
697 // delta - number of bins to integrate
698 // type - 0 - mean value
699
700 TAxis * xaxis = his->GetXaxis();
701 TAxis * yaxis = his->GetYaxis();
702 // TAxis * zaxis = his->GetZaxis();
703 Int_t nbinx = xaxis->GetNbins();
704 Int_t nbiny = yaxis->GetNbins();
705 char name[1000];
706 Int_t icount=0;
707 TGraph *graph = new TGraph(nbinx);
708 TF1 f1("f1","gaus");
709 for (Int_t ix=0; ix<nbinx;ix++){
710 Float_t xcenter = xaxis->GetBinCenter(ix);
711 // Float_t ycenter = yaxis->GetBinCenter(iy);
cb1d20de 712 snprintf(name,1000,"%s_%d",his->GetName(), ix);
21f3a443 713 TH1 *projection = his->ProjectionZ(name,ix-delta1,ix+delta1,0,nbiny);
714 Float_t stat= 0;
715 if (type==0) stat = projection->GetMean();
716 if (type==1) stat = projection->GetRMS();
717 if (type==2 || type==3){
718 TVectorD vec(3);
719 TStatToolkit::LTM((TH1F*)projection,&vec,0.7);
720 if (type==2) stat= vec[1];
721 if (type==3) stat= vec[0];
722 }
723 if (type==4|| type==5){
724 projection->Fit(&f1);
725 if (type==4) stat= f1.GetParameter(1);
726 if (type==5) stat= f1.GetParameter(2);
727 }
728 //printf("%d\t%f\t%f\t%f\n", icount,xcenter, ycenter, stat);
729 graph->SetPoint(icount,xcenter, stat);
730 icount++;
731 }
732 return graph;
733}
734
735
736
737
738
88b1c775 739TString* TStatToolkit::FitPlane(TTree *tree, const char* drawCommand, const char* formula, const char* cuts, Double_t & chi2, Int_t &npoints, TVectorD &fitParam, TMatrixD &covMatrix, Float_t frac, Int_t start, Int_t stop,Bool_t fix0){
21f3a443 740 //
741 // fit an arbitrary function, specified by formula into the data, specified by drawCommand and cuts
742 // returns chi2, fitParam and covMatrix
743 // returns TString with fitted formula
744 //
dd46129c 745
21f3a443 746 TString formulaStr(formula);
747 TString drawStr(drawCommand);
748 TString cutStr(cuts);
dd46129c 749 TString ferr("1");
750
751 TString strVal(drawCommand);
752 if (strVal.Contains(":")){
753 TObjArray* valTokens = strVal.Tokenize(":");
754 drawStr = valTokens->At(0)->GetName();
755 ferr = valTokens->At(1)->GetName();
756 }
757
21f3a443 758
759 formulaStr.ReplaceAll("++", "~");
760 TObjArray* formulaTokens = formulaStr.Tokenize("~");
761 Int_t dim = formulaTokens->GetEntriesFast();
762
763 fitParam.ResizeTo(dim);
764 covMatrix.ResizeTo(dim,dim);
765
766 TLinearFitter* fitter = new TLinearFitter(dim+1, Form("hyp%d",dim));
767 fitter->StoreData(kTRUE);
768 fitter->ClearPoints();
769
770 Int_t entries = tree->Draw(drawStr.Data(), cutStr.Data(), "goff", stop-start, start);
771 if (entries == -1) return new TString("An ERROR has occured during fitting!");
772 Double_t **values = new Double_t*[dim+1] ;
dd46129c 773 //
774 entries = tree->Draw(ferr.Data(), cutStr.Data(), "goff", stop-start, start);
b8072cce 775 if (entries == -1) {
776 delete []values;
777 return new TString("An ERROR has occured during fitting!");
778 }
dd46129c 779 Double_t *errors = new Double_t[entries];
780 memcpy(errors, tree->GetV1(), entries*sizeof(Double_t));
21f3a443 781
782 for (Int_t i = 0; i < dim + 1; i++){
783 Int_t centries = 0;
784 if (i < dim) centries = tree->Draw(((TObjString*)formulaTokens->At(i))->GetName(), cutStr.Data(), "goff", stop-start,start);
785 else centries = tree->Draw(drawStr.Data(), cutStr.Data(), "goff", stop-start,start);
786
b8072cce 787 if (entries != centries) {
788 delete []errors;
789 delete []values;
790 return new TString("An ERROR has occured during fitting!");
791 }
21f3a443 792 values[i] = new Double_t[entries];
793 memcpy(values[i], tree->GetV1(), entries*sizeof(Double_t));
794 }
795
796 // add points to the fitter
797 for (Int_t i = 0; i < entries; i++){
798 Double_t x[1000];
799 for (Int_t j=0; j<dim;j++) x[j]=values[j][i];
dd46129c 800 fitter->AddPoint(x, values[dim][i], errors[i]);
21f3a443 801 }
802
803 fitter->Eval();
2c629c56 804 if (frac>0.5 && frac<1){
805 fitter->EvalRobust(frac);
88b1c775 806 }else{
807 if (fix0) {
808 fitter->FixParameter(0,0);
809 fitter->Eval();
810 }
2c629c56 811 }
21f3a443 812 fitter->GetParameters(fitParam);
813 fitter->GetCovarianceMatrix(covMatrix);
814 chi2 = fitter->GetChisquare();
b8072cce 815 npoints = entries;
21f3a443 816 TString *preturnFormula = new TString(Form("( %f+",fitParam[0])), &returnFormula = *preturnFormula;
817
818 for (Int_t iparam = 0; iparam < dim; iparam++) {
819 returnFormula.Append(Form("%s*(%f)",((TObjString*)formulaTokens->At(iparam))->GetName(),fitParam[iparam+1]));
820 if (iparam < dim-1) returnFormula.Append("+");
821 }
822 returnFormula.Append(" )");
4d61c301 823
824
b8072cce 825 for (Int_t j=0; j<dim+1;j++) delete [] values[j];
4d61c301 826
827
cb1d20de 828 delete formulaTokens;
829 delete fitter;
830 delete[] values;
b8072cce 831 delete[] errors;
cb1d20de 832 return preturnFormula;
833}
834
835TString* TStatToolkit::FitPlaneConstrain(TTree *tree, const char* drawCommand, const char* formula, const char* cuts, Double_t & chi2, Int_t &npoints, TVectorD &fitParam, TMatrixD &covMatrix, Float_t frac, Int_t start, Int_t stop,Double_t constrain){
836 //
837 // fit an arbitrary function, specified by formula into the data, specified by drawCommand and cuts
838 // returns chi2, fitParam and covMatrix
839 // returns TString with fitted formula
840 //
841
842 TString formulaStr(formula);
843 TString drawStr(drawCommand);
844 TString cutStr(cuts);
845 TString ferr("1");
846
847 TString strVal(drawCommand);
848 if (strVal.Contains(":")){
849 TObjArray* valTokens = strVal.Tokenize(":");
850 drawStr = valTokens->At(0)->GetName();
851 ferr = valTokens->At(1)->GetName();
852 }
853
854
855 formulaStr.ReplaceAll("++", "~");
856 TObjArray* formulaTokens = formulaStr.Tokenize("~");
857 Int_t dim = formulaTokens->GetEntriesFast();
858
859 fitParam.ResizeTo(dim);
860 covMatrix.ResizeTo(dim,dim);
861
862 TLinearFitter* fitter = new TLinearFitter(dim+1, Form("hyp%d",dim));
863 fitter->StoreData(kTRUE);
864 fitter->ClearPoints();
865
866 Int_t entries = tree->Draw(drawStr.Data(), cutStr.Data(), "goff", stop-start, start);
867 if (entries == -1) return new TString("An ERROR has occured during fitting!");
868 Double_t **values = new Double_t*[dim+1] ;
869 //
870 entries = tree->Draw(ferr.Data(), cutStr.Data(), "goff", stop-start, start);
b8072cce 871 if (entries == -1) {
872 delete [] values;
873 return new TString("An ERROR has occured during fitting!");
874 }
cb1d20de 875 Double_t *errors = new Double_t[entries];
876 memcpy(errors, tree->GetV1(), entries*sizeof(Double_t));
877
878 for (Int_t i = 0; i < dim + 1; i++){
879 Int_t centries = 0;
880 if (i < dim) centries = tree->Draw(((TObjString*)formulaTokens->At(i))->GetName(), cutStr.Data(), "goff", stop-start,start);
881 else centries = tree->Draw(drawStr.Data(), cutStr.Data(), "goff", stop-start,start);
882
b8072cce 883 if (entries != centries) {
884 delete []errors;
885 delete []values;
886 return new TString("An ERROR has occured during fitting!");
887 }
cb1d20de 888 values[i] = new Double_t[entries];
889 memcpy(values[i], tree->GetV1(), entries*sizeof(Double_t));
890 }
891
892 // add points to the fitter
893 for (Int_t i = 0; i < entries; i++){
894 Double_t x[1000];
895 for (Int_t j=0; j<dim;j++) x[j]=values[j][i];
896 fitter->AddPoint(x, values[dim][i], errors[i]);
897 }
898 if (constrain>0){
899 for (Int_t i = 0; i < dim; i++){
900 Double_t x[1000];
901 for (Int_t j=0; j<dim;j++) if (i!=j) x[j]=0;
902 x[i]=1.;
903 fitter->AddPoint(x, 0, constrain);
904 }
905 }
906
907
908 fitter->Eval();
909 if (frac>0.5 && frac<1){
910 fitter->EvalRobust(frac);
911 }
912 fitter->GetParameters(fitParam);
913 fitter->GetCovarianceMatrix(covMatrix);
914 chi2 = fitter->GetChisquare();
915 npoints = entries;
cb1d20de 916
917 TString *preturnFormula = new TString(Form("( %f+",fitParam[0])), &returnFormula = *preturnFormula;
918
919 for (Int_t iparam = 0; iparam < dim; iparam++) {
920 returnFormula.Append(Form("%s*(%f)",((TObjString*)formulaTokens->At(iparam))->GetName(),fitParam[iparam+1]));
921 if (iparam < dim-1) returnFormula.Append("+");
922 }
923 returnFormula.Append(" )");
924
b8072cce 925 for (Int_t j=0; j<dim+1;j++) delete [] values[j];
cb1d20de 926
927
928
929 delete formulaTokens;
930 delete fitter;
931 delete[] values;
b8072cce 932 delete[] errors;
cb1d20de 933 return preturnFormula;
934}
935
936
937
938TString* TStatToolkit::FitPlaneFixed(TTree *tree, const char* drawCommand, const char* formula, const char* cuts, Double_t & chi2, Int_t &npoints, TVectorD &fitParam, TMatrixD &covMatrix, Float_t frac, Int_t start, Int_t stop){
939 //
940 // fit an arbitrary function, specified by formula into the data, specified by drawCommand and cuts
941 // returns chi2, fitParam and covMatrix
942 // returns TString with fitted formula
943 //
944
945 TString formulaStr(formula);
946 TString drawStr(drawCommand);
947 TString cutStr(cuts);
948 TString ferr("1");
949
950 TString strVal(drawCommand);
951 if (strVal.Contains(":")){
952 TObjArray* valTokens = strVal.Tokenize(":");
953 drawStr = valTokens->At(0)->GetName();
954 ferr = valTokens->At(1)->GetName();
955 }
956
957
958 formulaStr.ReplaceAll("++", "~");
959 TObjArray* formulaTokens = formulaStr.Tokenize("~");
960 Int_t dim = formulaTokens->GetEntriesFast();
961
962 fitParam.ResizeTo(dim);
963 covMatrix.ResizeTo(dim,dim);
964 TString fitString="x0";
965 for (Int_t i=1; i<dim; i++) fitString+=Form("++x%d",i);
966 TLinearFitter* fitter = new TLinearFitter(dim, fitString.Data());
967 fitter->StoreData(kTRUE);
968 fitter->ClearPoints();
969
970 Int_t entries = tree->Draw(drawStr.Data(), cutStr.Data(), "goff", stop-start, start);
971 if (entries == -1) return new TString("An ERROR has occured during fitting!");
972 Double_t **values = new Double_t*[dim+1] ;
973 //
974 entries = tree->Draw(ferr.Data(), cutStr.Data(), "goff", stop-start, start);
b8072cce 975 if (entries == -1) {
976 delete []values;
977 return new TString("An ERROR has occured during fitting!");
978 }
cb1d20de 979 Double_t *errors = new Double_t[entries];
980 memcpy(errors, tree->GetV1(), entries*sizeof(Double_t));
981
982 for (Int_t i = 0; i < dim + 1; i++){
983 Int_t centries = 0;
984 if (i < dim) centries = tree->Draw(((TObjString*)formulaTokens->At(i))->GetName(), cutStr.Data(), "goff", stop-start,start);
985 else centries = tree->Draw(drawStr.Data(), cutStr.Data(), "goff", stop-start,start);
986
b8072cce 987 if (entries != centries) {
988 delete []errors;
989 delete []values;
990 return new TString("An ERROR has occured during fitting!");
991 }
cb1d20de 992 values[i] = new Double_t[entries];
993 memcpy(values[i], tree->GetV1(), entries*sizeof(Double_t));
994 }
995
996 // add points to the fitter
997 for (Int_t i = 0; i < entries; i++){
998 Double_t x[1000];
999 for (Int_t j=0; j<dim;j++) x[j]=values[j][i];
1000 fitter->AddPoint(x, values[dim][i], errors[i]);
1001 }
1002
1003 fitter->Eval();
1004 if (frac>0.5 && frac<1){
1005 fitter->EvalRobust(frac);
1006 }
1007 fitter->GetParameters(fitParam);
1008 fitter->GetCovarianceMatrix(covMatrix);
1009 chi2 = fitter->GetChisquare();
1010 npoints = entries;
cb1d20de 1011
1012 TString *preturnFormula = new TString("("), &returnFormula = *preturnFormula;
1013
1014 for (Int_t iparam = 0; iparam < dim; iparam++) {
1015 returnFormula.Append(Form("%s*(%f)",((TObjString*)formulaTokens->At(iparam))->GetName(),fitParam[iparam]));
1016 if (iparam < dim-1) returnFormula.Append("+");
1017 }
1018 returnFormula.Append(" )");
1019
1020
b8072cce 1021 for (Int_t j=0; j<dim+1;j++) delete [] values[j];
cb1d20de 1022
21f3a443 1023 delete formulaTokens;
1024 delete fitter;
1025 delete[] values;
b8072cce 1026 delete[] errors;
21f3a443 1027 return preturnFormula;
1028}
7c9cf6e4 1029
1030
1031
1032
1033
1034Int_t TStatToolkit::GetFitIndex(TString fString, TString subString){
1035 //
1036 // fitString - ++ separated list of fits
1037 // substring - ++ separated list of the requiered substrings
1038 //
1039 // return the last occurance of substring in fit string
1040 //
1041 TObjArray *arrFit = fString.Tokenize("++");
1042 TObjArray *arrSub = subString.Tokenize("++");
1043 Int_t index=-1;
1044 for (Int_t i=0; i<arrFit->GetEntries(); i++){
1045 Bool_t isOK=kTRUE;
1046 TString str =arrFit->At(i)->GetName();
1047 for (Int_t isub=0; isub<arrSub->GetEntries(); isub++){
1048 if (str.Contains(arrSub->At(isub)->GetName())==0) isOK=kFALSE;
1049 }
1050 if (isOK) index=i;
1051 }
1052 return index;
1053}
1054
1055
1056TString TStatToolkit::FilterFit(TString &input, TString filter, TVectorD &param, TMatrixD & covar){
1057 //
1058 // Filter fit expression make sub-fit
1059 //
1060 TObjArray *array0= input.Tokenize("++");
1061 TObjArray *array1= filter.Tokenize("++");
1062 //TString *presult=new TString("(0");
1063 TString result="(0.0";
1064 for (Int_t i=0; i<array0->GetEntries(); i++){
1065 Bool_t isOK=kTRUE;
1066 TString str(array0->At(i)->GetName());
1067 for (Int_t j=0; j<array1->GetEntries(); j++){
1068 if (str.Contains(array1->At(j)->GetName())==0) isOK=kFALSE;
1069 }
1070 if (isOK) {
1071 result+="+"+str;
1072 result+=Form("*(%f)",param[i+1]);
1073 printf("%f\t%f\t%s\n",param[i+1], TMath::Sqrt(covar(i+1,i+1)),str.Data());
1074 }
1075 }
1076 result+="-0.)";
1077 return result;
1078}
1079
1080void TStatToolkit::Update1D(Double_t delta, Double_t sigma, Int_t s1, TMatrixD &vecXk, TMatrixD &covXk){
1081 //
1082 // Update parameters and covariance - with one measurement
1083 // Input:
1084 // vecXk - input vector - Updated in function
1085 // covXk - covariance matrix - Updated in function
1086 // delta, sigma, s1 - new measurement, rms of new measurement and the index of measurement
1087 const Int_t knMeas=1;
1088 Int_t knElem=vecXk.GetNrows();
1089
1090 TMatrixD mat1(knElem,knElem); // update covariance matrix
1091 TMatrixD matHk(1,knElem); // vector to mesurement
1092 TMatrixD vecYk(knMeas,1); // Innovation or measurement residual
1093 TMatrixD matHkT(knElem,knMeas); // helper matrix Hk transpose
1094 TMatrixD matSk(knMeas,knMeas); // Innovation (or residual) covariance
1095 TMatrixD matKk(knElem,knMeas); // Optimal Kalman gain
1096 TMatrixD covXk2(knElem,knElem); // helper matrix
1097 TMatrixD covXk3(knElem,knElem); // helper matrix
1098 TMatrixD vecZk(1,1);
1099 TMatrixD measR(1,1);
1100 vecZk(0,0)=delta;
1101 measR(0,0)=sigma*sigma;
1102 //
1103 // reset matHk
1104 for (Int_t iel=0;iel<knElem;iel++)
1105 for (Int_t ip=0;ip<knMeas;ip++) matHk(ip,iel)=0;
1106 //mat1
1107 for (Int_t iel=0;iel<knElem;iel++) {
1108 for (Int_t jel=0;jel<knElem;jel++) mat1(iel,jel)=0;
1109 mat1(iel,iel)=1;
1110 }
1111 //
1112 matHk(0, s1)=1;
1113 vecYk = vecZk-matHk*vecXk; // Innovation or measurement residual
1114 matHkT=matHk.T(); matHk.T();
1115 matSk = (matHk*(covXk*matHkT))+measR; // Innovation (or residual) covariance
1116 matSk.Invert();
1117 matKk = (covXk*matHkT)*matSk; // Optimal Kalman gain
1118 vecXk += matKk*vecYk; // updated vector
1119 covXk2= (mat1-(matKk*matHk));
1120 covXk3 = covXk2*covXk;
1121 covXk = covXk3;
1122 Int_t nrows=covXk3.GetNrows();
1123
1124 for (Int_t irow=0; irow<nrows; irow++)
1125 for (Int_t icol=0; icol<nrows; icol++){
1126 // rounding problems - make matrix again symteric
1127 covXk(irow,icol)=(covXk3(irow,icol)+covXk3(icol,irow))*0.5;
1128 }
1129}
1130
1131
1132
1133void TStatToolkit::Constrain1D(TString &input, TString filter, TVectorD &param, TMatrixD & covar, Double_t mean, Double_t sigma){
1134 //
1135 // constrain linear fit
1136 // input - string description of fit function
1137 // filter - string filter to select sub fits
1138 // param,covar - parameters and covariance matrix of the fit
1139 // mean,sigma - new measurement uning which the fit is updated
1140 //
1141 TObjArray *array0= input.Tokenize("++");
1142 TObjArray *array1= filter.Tokenize("++");
1143 TMatrixD paramM(param.GetNrows(),1);
1144 for (Int_t i=0; i<=array0->GetEntries(); i++){paramM(i,0)=param(i);}
1145
1146 for (Int_t i=0; i<array0->GetEntries(); i++){
1147 Bool_t isOK=kTRUE;
1148 TString str(array0->At(i)->GetName());
1149 for (Int_t j=0; j<array1->GetEntries(); j++){
1150 if (str.Contains(array1->At(j)->GetName())==0) isOK=kFALSE;
1151 }
1152 if (isOK) {
1153 TStatToolkit::Update1D(mean, sigma, i+1, paramM, covar);//
1154 }
1155 }
1156 for (Int_t i=0; i<=array0->GetEntries(); i++){
1157 param(i)=paramM(i,0);
1158 }
1159}
1160
1161TString TStatToolkit::MakeFitString(TString &input, TVectorD &param, TMatrixD & covar){
1162 //
1163 //
1164 //
1165 TObjArray *array0= input.Tokenize("++");
1166 TString result="(0.0";
1167 for (Int_t i=0; i<array0->GetEntries(); i++){
1168 TString str(array0->At(i)->GetName());
1169 result+="+"+str;
1170 result+=Form("*(%f)",param[i+1]);
1171 printf("%f\t%f\t%s\n", param[i+1], TMath::Sqrt(covar(i+1,i+1)),str.Data());
1172 }
1173 result+="-0.)";
1174 return result;
1175}