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[u/mrichter/AliRoot.git] / STAT / TStatToolkit.cxx
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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"
3d7cc0b4 33#include "TGraph2D.h"
34#include "TGraph.h"
b3453fe7 35#include "TGraphErrors.h"
377a7d60 36#include "TMultiGraph.h"
37#include "TCanvas.h"
38#include "TLatex.h"
39#include "TCut.h"
21f3a443 40
41//
42// includes neccessary for test functions
43//
44#include "TSystem.h"
45#include "TRandom.h"
46#include "TStopwatch.h"
47#include "TTreeStream.h"
48
49#include "TStatToolkit.h"
50
51
52ClassImp(TStatToolkit) // Class implementation to enable ROOT I/O
53
54TStatToolkit::TStatToolkit() : TObject()
55{
56 //
57 // Default constructor
58 //
59}
60///////////////////////////////////////////////////////////////////////////
61TStatToolkit::~TStatToolkit()
62{
63 //
64 // Destructor
65 //
66}
67
68
69//_____________________________________________________________________________
70void TStatToolkit::EvaluateUni(Int_t nvectors, Double_t *data, Double_t &mean
71 , Double_t &sigma, Int_t hh)
72{
73 //
74 // Robust estimator in 1D case MI version - (faster than ROOT version)
75 //
76 // For the univariate case
77 // estimates of location and scatter are returned in mean and sigma parameters
78 // the algorithm works on the same principle as in multivariate case -
79 // it finds a subset of size hh with smallest sigma, and then returns mean and
80 // sigma of this subset
81 //
82
83 if (hh==0)
84 hh=(nvectors+2)/2;
85 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};
86 Int_t *index=new Int_t[nvectors];
87 TMath::Sort(nvectors, data, index, kFALSE);
88
89 Int_t nquant = TMath::Min(Int_t(Double_t(((hh*1./nvectors)-0.5)*40))+1, 11);
90 Double_t factor = faclts[TMath::Max(0,nquant-1)];
91
92 Double_t sumx =0;
93 Double_t sumx2 =0;
94 Int_t bestindex = -1;
95 Double_t bestmean = 0;
96 Double_t bestsigma = (data[index[nvectors-1]]-data[index[0]]+1.); // maximal possible sigma
97 bestsigma *=bestsigma;
98
99 for (Int_t i=0; i<hh; i++){
100 sumx += data[index[i]];
101 sumx2 += data[index[i]]*data[index[i]];
102 }
103
104 Double_t norm = 1./Double_t(hh);
bd7b4d18 105 Double_t norm2 = (hh-1)>0 ? 1./Double_t(hh-1):1;
21f3a443 106 for (Int_t i=hh; i<nvectors; i++){
107 Double_t cmean = sumx*norm;
108 Double_t csigma = (sumx2 - hh*cmean*cmean)*norm2;
109 if (csigma<bestsigma){
110 bestmean = cmean;
111 bestsigma = csigma;
112 bestindex = i-hh;
113 }
114
115 sumx += data[index[i]]-data[index[i-hh]];
116 sumx2 += data[index[i]]*data[index[i]]-data[index[i-hh]]*data[index[i-hh]];
117 }
118
119 Double_t bstd=factor*TMath::Sqrt(TMath::Abs(bestsigma));
120 mean = bestmean;
121 sigma = bstd;
122 delete [] index;
123
124}
125
126
127
128void TStatToolkit::EvaluateUniExternal(Int_t nvectors, Double_t *data, Double_t &mean, Double_t &sigma, Int_t hh, Float_t externalfactor)
129{
130 // Modified version of ROOT robust EvaluateUni
131 // robust estimator in 1D case MI version
132 // added external factor to include precision of external measurement
133 //
134
135 if (hh==0)
136 hh=(nvectors+2)/2;
137 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};
138 Int_t *index=new Int_t[nvectors];
139 TMath::Sort(nvectors, data, index, kFALSE);
140 //
141 Int_t nquant = TMath::Min(Int_t(Double_t(((hh*1./nvectors)-0.5)*40))+1, 11);
142 Double_t factor = faclts[0];
143 if (nquant>0){
144 // fix proper normalization - Anja
145 factor = faclts[nquant-1];
146 }
147
148 //
149 //
150 Double_t sumx =0;
151 Double_t sumx2 =0;
152 Int_t bestindex = -1;
153 Double_t bestmean = 0;
154 Double_t bestsigma = -1;
155 for (Int_t i=0; i<hh; i++){
156 sumx += data[index[i]];
157 sumx2 += data[index[i]]*data[index[i]];
158 }
159 //
160 Double_t kfactor = 2.*externalfactor - externalfactor*externalfactor;
161 Double_t norm = 1./Double_t(hh);
162 for (Int_t i=hh; i<nvectors; i++){
163 Double_t cmean = sumx*norm;
164 Double_t csigma = (sumx2*norm - cmean*cmean*kfactor);
165 if (csigma<bestsigma || bestsigma<0){
166 bestmean = cmean;
167 bestsigma = csigma;
168 bestindex = i-hh;
169 }
170 //
171 //
172 sumx += data[index[i]]-data[index[i-hh]];
173 sumx2 += data[index[i]]*data[index[i]]-data[index[i-hh]]*data[index[i-hh]];
174 }
175
176 Double_t bstd=factor*TMath::Sqrt(TMath::Abs(bestsigma));
177 mean = bestmean;
178 sigma = bstd;
179 delete [] index;
180}
181
182
183//_____________________________________________________________________________
184Int_t TStatToolkit::Freq(Int_t n, const Int_t *inlist
185 , Int_t *outlist, Bool_t down)
186{
187 //
188 // Sort eleements according occurancy
189 // The size of output array has is 2*n
190 //
191
192 Int_t * sindexS = new Int_t[n]; // temp array for sorting
193 Int_t * sindexF = new Int_t[2*n];
b8072cce 194 for (Int_t i=0;i<n;i++) sindexS[i]=0;
195 for (Int_t i=0;i<2*n;i++) sindexF[i]=0;
21f3a443 196 //
197 TMath::Sort(n,inlist, sindexS, down);
198 Int_t last = inlist[sindexS[0]];
199 Int_t val = last;
200 sindexF[0] = 1;
201 sindexF[0+n] = last;
202 Int_t countPos = 0;
203 //
204 // find frequency
205 for(Int_t i=1;i<n; i++){
206 val = inlist[sindexS[i]];
207 if (last == val) sindexF[countPos]++;
208 else{
209 countPos++;
210 sindexF[countPos+n] = val;
211 sindexF[countPos]++;
212 last =val;
213 }
214 }
215 if (last==val) countPos++;
216 // sort according frequency
217 TMath::Sort(countPos, sindexF, sindexS, kTRUE);
218 for (Int_t i=0;i<countPos;i++){
219 outlist[2*i ] = sindexF[sindexS[i]+n];
220 outlist[2*i+1] = sindexF[sindexS[i]];
221 }
222 delete [] sindexS;
223 delete [] sindexF;
224
225 return countPos;
226
227}
228
229//___TStatToolkit__________________________________________________________________________
3d7cc0b4 230void TStatToolkit::TruncatedMean(const TH1 * his, TVectorD *param, Float_t down, Float_t up, Bool_t verbose){
21f3a443 231 //
232 //
233 //
234 Int_t nbins = his->GetNbinsX();
235 Float_t nentries = his->GetEntries();
236 Float_t sum =0;
237 Float_t mean = 0;
238 Float_t sigma2 = 0;
239 Float_t ncumul=0;
240 for (Int_t ibin=1;ibin<nbins; ibin++){
241 ncumul+= his->GetBinContent(ibin);
242 Float_t fraction = Float_t(ncumul)/Float_t(nentries);
243 if (fraction>down && fraction<up){
244 sum+=his->GetBinContent(ibin);
245 mean+=his->GetBinCenter(ibin)*his->GetBinContent(ibin);
246 sigma2+=his->GetBinCenter(ibin)*his->GetBinCenter(ibin)*his->GetBinContent(ibin);
247 }
248 }
249 mean/=sum;
250 sigma2= TMath::Sqrt(TMath::Abs(sigma2/sum-mean*mean));
251 if (param){
252 (*param)[0] = his->GetMaximum();
253 (*param)[1] = mean;
254 (*param)[2] = sigma2;
255
256 }
257 if (verbose) printf("Mean\t%f\t Sigma2\t%f\n", mean,sigma2);
258}
259
260void TStatToolkit::LTM(TH1F * his, TVectorD *param , Float_t fraction, Bool_t verbose){
261 //
262 // LTM
263 //
264 Int_t nbins = his->GetNbinsX();
265 Int_t nentries = (Int_t)his->GetEntries();
266 Double_t *data = new Double_t[nentries];
267 Int_t npoints=0;
268 for (Int_t ibin=1;ibin<nbins; ibin++){
269 Float_t entriesI = his->GetBinContent(ibin);
270 Float_t xcenter= his->GetBinCenter(ibin);
271 for (Int_t ic=0; ic<entriesI; ic++){
272 if (npoints<nentries){
273 data[npoints]= xcenter;
274 npoints++;
275 }
276 }
277 }
278 Double_t mean, sigma;
279 Int_t npoints2=TMath::Min(Int_t(fraction*Float_t(npoints)),npoints-1);
280 npoints2=TMath::Max(Int_t(0.5*Float_t(npoints)),npoints2);
281 TStatToolkit::EvaluateUni(npoints, data, mean,sigma,npoints2);
282 delete [] data;
283 if (verbose) printf("Mean\t%f\t Sigma2\t%f\n", mean,sigma);if (param){
284 (*param)[0] = his->GetMaximum();
285 (*param)[1] = mean;
286 (*param)[2] = sigma;
287 }
288}
289
94a43b22 290Double_t TStatToolkit::FitGaus(TH1* his, TVectorD *param, TMatrixD */*matrix*/, Float_t xmin, Float_t xmax, Bool_t verbose){
21f3a443 291 //
292 // Fit histogram with gaussian function
293 //
294 // Prameters:
295 // return value- chi2 - if negative ( not enough points)
296 // his - input histogram
297 // param - vector with parameters
298 // xmin, xmax - range to fit - if xmin=xmax=0 - the full histogram range used
299 // Fitting:
300 // 1. Step - make logarithm
301 // 2. Linear fit (parabola) - more robust - always converge
302 // 3. In case of small statistic bins are averaged
303 //
304 static TLinearFitter fitter(3,"pol2");
305 TVectorD par(3);
306 TVectorD sigma(3);
307 TMatrixD mat(3,3);
308 if (his->GetMaximum()<4) return -1;
309 if (his->GetEntries()<12) return -1;
310 if (his->GetRMS()<mat.GetTol()) return -1;
311 Float_t maxEstimate = his->GetEntries()*his->GetBinWidth(1)/TMath::Sqrt((TMath::TwoPi()*his->GetRMS()));
312 Int_t dsmooth = TMath::Nint(6./TMath::Sqrt(maxEstimate));
313
314 if (maxEstimate<1) return -1;
315 Int_t nbins = his->GetNbinsX();
316 Int_t npoints=0;
317 //
318
319
320 if (xmin>=xmax){
321 xmin = his->GetXaxis()->GetXmin();
322 xmax = his->GetXaxis()->GetXmax();
323 }
324 for (Int_t iter=0; iter<2; iter++){
325 fitter.ClearPoints();
326 npoints=0;
327 for (Int_t ibin=1;ibin<nbins+1; ibin++){
328 Int_t countB=1;
329 Float_t entriesI = his->GetBinContent(ibin);
330 for (Int_t delta = -dsmooth; delta<=dsmooth; delta++){
331 if (ibin+delta>1 &&ibin+delta<nbins-1){
332 entriesI += his->GetBinContent(ibin+delta);
333 countB++;
334 }
335 }
336 entriesI/=countB;
337 Double_t xcenter= his->GetBinCenter(ibin);
338 if (xcenter<xmin || xcenter>xmax) continue;
339 Double_t error=1./TMath::Sqrt(countB);
340 Float_t cont=2;
341 if (iter>0){
342 if (par[0]+par[1]*xcenter+par[2]*xcenter*xcenter>20) return 0;
343 cont = TMath::Exp(par[0]+par[1]*xcenter+par[2]*xcenter*xcenter);
344 if (cont>1.) error = 1./TMath::Sqrt(cont*Float_t(countB));
345 }
346 if (entriesI>1&&cont>1){
347 fitter.AddPoint(&xcenter,TMath::Log(Float_t(entriesI)),error);
348 npoints++;
349 }
350 }
351 if (npoints>3){
352 fitter.Eval();
353 fitter.GetParameters(par);
354 }else{
355 break;
356 }
357 }
358 if (npoints<=3){
359 return -1;
360 }
361 fitter.GetParameters(par);
362 fitter.GetCovarianceMatrix(mat);
363 if (TMath::Abs(par[1])<mat.GetTol()) return -1;
364 if (TMath::Abs(par[2])<mat.GetTol()) return -1;
365 Double_t chi2 = fitter.GetChisquare()/Float_t(npoints);
366 //fitter.GetParameters();
367 if (!param) param = new TVectorD(3);
cb1d20de 368 // if (!matrix) matrix = new TMatrixD(3,3); // Covariance matrix to be implemented
21f3a443 369 (*param)[1] = par[1]/(-2.*par[2]);
370 (*param)[2] = 1./TMath::Sqrt(TMath::Abs(-2.*par[2]));
371 (*param)[0] = TMath::Exp(par[0]+ par[1]* (*param)[1] + par[2]*(*param)[1]*(*param)[1]);
372 if (verbose){
373 par.Print();
374 mat.Print();
375 param->Print();
376 printf("Chi2=%f\n",chi2);
377 TF1 * f1= new TF1("f1","[0]*exp(-(x-[1])^2/(2*[2]*[2]))",his->GetXaxis()->GetXmin(),his->GetXaxis()->GetXmax());
378 f1->SetParameter(0, (*param)[0]);
379 f1->SetParameter(1, (*param)[1]);
380 f1->SetParameter(2, (*param)[2]);
381 f1->Draw("same");
382 }
383 return chi2;
384}
385
cb1d20de 386Double_t TStatToolkit::FitGaus(Float_t *arr, Int_t nBins, Float_t xMin, Float_t xMax, TVectorD *param, TMatrixD */*matrix*/, Bool_t verbose){
21f3a443 387 //
388 // Fit histogram with gaussian function
389 //
390 // Prameters:
391 // nbins: size of the array and number of histogram bins
392 // xMin, xMax: histogram range
393 // param: paramters of the fit (0-Constant, 1-Mean, 2-Sigma)
394 // matrix: covariance matrix -- not implemented yet, pass dummy matrix!!!
395 //
396 // Return values:
397 // >0: the chi2 returned by TLinearFitter
398 // -3: only three points have been used for the calculation - no fitter was used
399 // -2: only two points have been used for the calculation - center of gravity was uesed for calculation
400 // -1: only one point has been used for the calculation - center of gravity was uesed for calculation
401 // -4: invalid result!!
402 //
403 // Fitting:
404 // 1. Step - make logarithm
405 // 2. Linear fit (parabola) - more robust - always converge
406 //
407 static TLinearFitter fitter(3,"pol2");
408 static TMatrixD mat(3,3);
409 static Double_t kTol = mat.GetTol();
410 fitter.StoreData(kFALSE);
411 fitter.ClearPoints();
412 TVectorD par(3);
413 TVectorD sigma(3);
3d7cc0b4 414 TMatrixD matA(3,3);
21f3a443 415 TMatrixD b(3,1);
416 Float_t rms = TMath::RMS(nBins,arr);
417 Float_t max = TMath::MaxElement(nBins,arr);
418 Float_t binWidth = (xMax-xMin)/(Float_t)nBins;
419
420 Float_t meanCOG = 0;
421 Float_t rms2COG = 0;
422 Float_t sumCOG = 0;
423
424 Float_t entries = 0;
425 Int_t nfilled=0;
426
427 for (Int_t i=0; i<nBins; i++){
428 entries+=arr[i];
429 if (arr[i]>0) nfilled++;
430 }
431
432 if (max<4) return -4;
433 if (entries<12) return -4;
434 if (rms<kTol) return -4;
435
436 Int_t npoints=0;
437 //
438
439 //
440 for (Int_t ibin=0;ibin<nBins; ibin++){
441 Float_t entriesI = arr[ibin];
442 if (entriesI>1){
443 Double_t xcenter = xMin+(ibin+0.5)*binWidth;
444
445 Float_t error = 1./TMath::Sqrt(entriesI);
446 Float_t val = TMath::Log(Float_t(entriesI));
447 fitter.AddPoint(&xcenter,val,error);
448 if (npoints<3){
3d7cc0b4 449 matA(npoints,0)=1;
450 matA(npoints,1)=xcenter;
451 matA(npoints,2)=xcenter*xcenter;
21f3a443 452 b(npoints,0)=val;
453 meanCOG+=xcenter*entriesI;
454 rms2COG +=xcenter*entriesI*xcenter;
455 sumCOG +=entriesI;
456 }
457 npoints++;
458 }
459 }
460
461
462 Double_t chi2 = 0;
463 if (npoints>=3){
464 if ( npoints == 3 ){
465 //analytic calculation of the parameters for three points
3d7cc0b4 466 matA.Invert();
21f3a443 467 TMatrixD res(1,3);
3d7cc0b4 468 res.Mult(matA,b);
21f3a443 469 par[0]=res(0,0);
470 par[1]=res(0,1);
471 par[2]=res(0,2);
472 chi2 = -3.;
473 } else {
474 // use fitter for more than three points
475 fitter.Eval();
476 fitter.GetParameters(par);
477 fitter.GetCovarianceMatrix(mat);
478 chi2 = fitter.GetChisquare()/Float_t(npoints);
479 }
480 if (TMath::Abs(par[1])<kTol) return -4;
481 if (TMath::Abs(par[2])<kTol) return -4;
482
483 if (!param) param = new TVectorD(3);
cb1d20de 484 //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 485
486 (*param)[1] = par[1]/(-2.*par[2]);
487 (*param)[2] = 1./TMath::Sqrt(TMath::Abs(-2.*par[2]));
488 Double_t lnparam0 = par[0]+ par[1]* (*param)[1] + par[2]*(*param)[1]*(*param)[1];
489 if ( lnparam0>307 ) return -4;
490 (*param)[0] = TMath::Exp(lnparam0);
491 if (verbose){
492 par.Print();
493 mat.Print();
494 param->Print();
495 printf("Chi2=%f\n",chi2);
496 TF1 * f1= new TF1("f1","[0]*exp(-(x-[1])^2/(2*[2]*[2]))",xMin,xMax);
497 f1->SetParameter(0, (*param)[0]);
498 f1->SetParameter(1, (*param)[1]);
499 f1->SetParameter(2, (*param)[2]);
500 f1->Draw("same");
501 }
502 return chi2;
503 }
504
505 if (npoints == 2){
506 //use center of gravity for 2 points
507 meanCOG/=sumCOG;
508 rms2COG /=sumCOG;
509 (*param)[0] = max;
510 (*param)[1] = meanCOG;
511 (*param)[2] = TMath::Sqrt(TMath::Abs(meanCOG*meanCOG-rms2COG));
512 chi2=-2.;
513 }
514 if ( npoints == 1 ){
515 meanCOG/=sumCOG;
516 (*param)[0] = max;
517 (*param)[1] = meanCOG;
518 (*param)[2] = binWidth/TMath::Sqrt(12);
519 chi2=-1.;
520 }
521 return chi2;
522
523}
524
525
3d7cc0b4 526Float_t TStatToolkit::GetCOG(const Short_t *arr, Int_t nBins, Float_t xMin, Float_t xMax, Float_t *rms, Float_t *sum)
21f3a443 527{
528 //
529 // calculate center of gravity rms and sum for array 'arr' with nBins an a x range xMin to xMax
530 // return COG; in case of failure return xMin
531 //
532 Float_t meanCOG = 0;
533 Float_t rms2COG = 0;
534 Float_t sumCOG = 0;
535 Int_t npoints = 0;
536
537 Float_t binWidth = (xMax-xMin)/(Float_t)nBins;
538
539 for (Int_t ibin=0; ibin<nBins; ibin++){
540 Float_t entriesI = (Float_t)arr[ibin];
541 Double_t xcenter = xMin+(ibin+0.5)*binWidth;
542 if ( entriesI>0 ){
543 meanCOG += xcenter*entriesI;
544 rms2COG += xcenter*entriesI*xcenter;
545 sumCOG += entriesI;
546 npoints++;
547 }
548 }
549 if ( sumCOG == 0 ) return xMin;
550 meanCOG/=sumCOG;
551
552 if ( rms ){
553 rms2COG /=sumCOG;
554 (*rms) = TMath::Sqrt(TMath::Abs(meanCOG*meanCOG-rms2COG));
555 if ( npoints == 1 ) (*rms) = binWidth/TMath::Sqrt(12);
556 }
557
558 if ( sum )
559 (*sum) = sumCOG;
560
561 return meanCOG;
562}
563
564
565
566///////////////////////////////////////////////////////////////
567////////////// TEST functions /////////////////////////
568///////////////////////////////////////////////////////////////
569
570
571
572
573
574void TStatToolkit::TestGausFit(Int_t nhistos){
575 //
576 // Test performance of the parabolic - gaussian fit - compare it with
577 // ROOT gauss fit
578 // nhistos - number of histograms to be used for test
579 //
580 TTreeSRedirector *pcstream = new TTreeSRedirector("fitdebug.root");
581
582 Float_t *xTrue = new Float_t[nhistos];
583 Float_t *sTrue = new Float_t[nhistos];
584 TVectorD **par1 = new TVectorD*[nhistos];
585 TVectorD **par2 = new TVectorD*[nhistos];
586 TMatrixD dummy(3,3);
587
588
589 TH1F **h1f = new TH1F*[nhistos];
590 TF1 *myg = new TF1("myg","gaus");
591 TF1 *fit = new TF1("fit","gaus");
592 gRandom->SetSeed(0);
593
594 //init
595 for (Int_t i=0;i<nhistos; i++){
596 par1[i] = new TVectorD(3);
597 par2[i] = new TVectorD(3);
598 h1f[i] = new TH1F(Form("h1f%d",i),Form("h1f%d",i),20,-10,10);
599 xTrue[i]= gRandom->Rndm();
600 gSystem->Sleep(2);
601 sTrue[i]= .75+gRandom->Rndm()*.5;
602 myg->SetParameters(1,xTrue[i],sTrue[i]);
603 h1f[i]->FillRandom("myg");
604 }
605
606 TStopwatch s;
607 s.Start();
608 //standard gaus fit
609 for (Int_t i=0; i<nhistos; i++){
610 h1f[i]->Fit(fit,"0q");
611 (*par1[i])(0) = fit->GetParameter(0);
612 (*par1[i])(1) = fit->GetParameter(1);
613 (*par1[i])(2) = fit->GetParameter(2);
614 }
615 s.Stop();
616 printf("Gaussian fit\t");
617 s.Print();
618
619 s.Start();
620 //TStatToolkit gaus fit
621 for (Int_t i=0; i<nhistos; i++){
622 TStatToolkit::FitGaus(h1f[i]->GetArray()+1,h1f[i]->GetNbinsX(),h1f[i]->GetXaxis()->GetXmin(),h1f[i]->GetXaxis()->GetXmax(),par2[i],&dummy);
623 }
624
625 s.Stop();
626 printf("Parabolic fit\t");
627 s.Print();
628 //write stream
629 for (Int_t i=0;i<nhistos; i++){
630 Float_t xt = xTrue[i];
631 Float_t st = sTrue[i];
632 (*pcstream)<<"data"
633 <<"xTrue="<<xt
634 <<"sTrue="<<st
635 <<"pg.="<<(par1[i])
636 <<"pa.="<<(par2[i])
637 <<"\n";
638 }
639 //delete pointers
640 for (Int_t i=0;i<nhistos; i++){
641 delete par1[i];
642 delete par2[i];
643 delete h1f[i];
644 }
645 delete pcstream;
646 delete []h1f;
647 delete []xTrue;
648 delete []sTrue;
649 //
650 delete []par1;
651 delete []par2;
652
653}
654
655
656
657TGraph2D * TStatToolkit::MakeStat2D(TH3 * his, Int_t delta0, Int_t delta1, Int_t type){
658 //
659 //
660 //
661 // delta - number of bins to integrate
662 // type - 0 - mean value
663
664 TAxis * xaxis = his->GetXaxis();
665 TAxis * yaxis = his->GetYaxis();
666 // TAxis * zaxis = his->GetZaxis();
667 Int_t nbinx = xaxis->GetNbins();
668 Int_t nbiny = yaxis->GetNbins();
669 char name[1000];
670 Int_t icount=0;
671 TGraph2D *graph = new TGraph2D(nbinx*nbiny);
672 TF1 f1("f1","gaus");
673 for (Int_t ix=0; ix<nbinx;ix++)
674 for (Int_t iy=0; iy<nbiny;iy++){
675 Float_t xcenter = xaxis->GetBinCenter(ix);
676 Float_t ycenter = yaxis->GetBinCenter(iy);
cb1d20de 677 snprintf(name,1000,"%s_%d_%d",his->GetName(), ix,iy);
21f3a443 678 TH1 *projection = his->ProjectionZ(name,ix-delta0,ix+delta0,iy-delta1,iy+delta1);
679 Float_t stat= 0;
680 if (type==0) stat = projection->GetMean();
681 if (type==1) stat = projection->GetRMS();
682 if (type==2 || type==3){
683 TVectorD vec(3);
684 TStatToolkit::LTM((TH1F*)projection,&vec,0.7);
685 if (type==2) stat= vec[1];
686 if (type==3) stat= vec[0];
687 }
688 if (type==4|| type==5){
689 projection->Fit(&f1);
690 if (type==4) stat= f1.GetParameter(1);
691 if (type==5) stat= f1.GetParameter(2);
692 }
693 //printf("%d\t%f\t%f\t%f\n", icount,xcenter, ycenter, stat);
694 graph->SetPoint(icount,xcenter, ycenter, stat);
695 icount++;
696 }
697 return graph;
698}
699
700TGraph * TStatToolkit::MakeStat1D(TH3 * his, Int_t delta1, Int_t type){
701 //
702 //
703 //
704 // delta - number of bins to integrate
705 // type - 0 - mean value
706
707 TAxis * xaxis = his->GetXaxis();
708 TAxis * yaxis = his->GetYaxis();
709 // TAxis * zaxis = his->GetZaxis();
710 Int_t nbinx = xaxis->GetNbins();
711 Int_t nbiny = yaxis->GetNbins();
712 char name[1000];
713 Int_t icount=0;
714 TGraph *graph = new TGraph(nbinx);
715 TF1 f1("f1","gaus");
716 for (Int_t ix=0; ix<nbinx;ix++){
717 Float_t xcenter = xaxis->GetBinCenter(ix);
718 // Float_t ycenter = yaxis->GetBinCenter(iy);
cb1d20de 719 snprintf(name,1000,"%s_%d",his->GetName(), ix);
21f3a443 720 TH1 *projection = his->ProjectionZ(name,ix-delta1,ix+delta1,0,nbiny);
721 Float_t stat= 0;
722 if (type==0) stat = projection->GetMean();
723 if (type==1) stat = projection->GetRMS();
724 if (type==2 || type==3){
725 TVectorD vec(3);
726 TStatToolkit::LTM((TH1F*)projection,&vec,0.7);
727 if (type==2) stat= vec[1];
728 if (type==3) stat= vec[0];
729 }
730 if (type==4|| type==5){
731 projection->Fit(&f1);
732 if (type==4) stat= f1.GetParameter(1);
733 if (type==5) stat= f1.GetParameter(2);
734 }
735 //printf("%d\t%f\t%f\t%f\n", icount,xcenter, ycenter, stat);
736 graph->SetPoint(icount,xcenter, stat);
737 icount++;
738 }
739 return graph;
740}
741
742
743
744
745
88b1c775 746TString* 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 747 //
748 // fit an arbitrary function, specified by formula into the data, specified by drawCommand and cuts
749 // returns chi2, fitParam and covMatrix
750 // returns TString with fitted formula
751 //
dd46129c 752
21f3a443 753 TString formulaStr(formula);
754 TString drawStr(drawCommand);
755 TString cutStr(cuts);
dd46129c 756 TString ferr("1");
757
758 TString strVal(drawCommand);
759 if (strVal.Contains(":")){
760 TObjArray* valTokens = strVal.Tokenize(":");
761 drawStr = valTokens->At(0)->GetName();
762 ferr = valTokens->At(1)->GetName();
09d5920f 763 delete valTokens;
dd46129c 764 }
765
21f3a443 766
767 formulaStr.ReplaceAll("++", "~");
768 TObjArray* formulaTokens = formulaStr.Tokenize("~");
769 Int_t dim = formulaTokens->GetEntriesFast();
770
771 fitParam.ResizeTo(dim);
772 covMatrix.ResizeTo(dim,dim);
773
774 TLinearFitter* fitter = new TLinearFitter(dim+1, Form("hyp%d",dim));
775 fitter->StoreData(kTRUE);
776 fitter->ClearPoints();
777
778 Int_t entries = tree->Draw(drawStr.Data(), cutStr.Data(), "goff", stop-start, start);
09d5920f 779 if (entries == -1) {
780 delete formulaTokens;
781 return new TString("An ERROR has occured during fitting!");
782 }
bd7b4d18 783 Double_t **values = new Double_t*[dim+1] ;
784 for (Int_t i=0; i<dim+1; i++) values[i]=NULL;
dd46129c 785 //
786 entries = tree->Draw(ferr.Data(), cutStr.Data(), "goff", stop-start, start);
b8072cce 787 if (entries == -1) {
09d5920f 788 delete formulaTokens;
b8072cce 789 delete []values;
790 return new TString("An ERROR has occured during fitting!");
791 }
dd46129c 792 Double_t *errors = new Double_t[entries];
793 memcpy(errors, tree->GetV1(), entries*sizeof(Double_t));
21f3a443 794
795 for (Int_t i = 0; i < dim + 1; i++){
796 Int_t centries = 0;
797 if (i < dim) centries = tree->Draw(((TObjString*)formulaTokens->At(i))->GetName(), cutStr.Data(), "goff", stop-start,start);
798 else centries = tree->Draw(drawStr.Data(), cutStr.Data(), "goff", stop-start,start);
799
b8072cce 800 if (entries != centries) {
801 delete []errors;
802 delete []values;
803 return new TString("An ERROR has occured during fitting!");
804 }
21f3a443 805 values[i] = new Double_t[entries];
806 memcpy(values[i], tree->GetV1(), entries*sizeof(Double_t));
807 }
808
809 // add points to the fitter
810 for (Int_t i = 0; i < entries; i++){
811 Double_t x[1000];
812 for (Int_t j=0; j<dim;j++) x[j]=values[j][i];
dd46129c 813 fitter->AddPoint(x, values[dim][i], errors[i]);
21f3a443 814 }
815
816 fitter->Eval();
2c629c56 817 if (frac>0.5 && frac<1){
818 fitter->EvalRobust(frac);
88b1c775 819 }else{
820 if (fix0) {
821 fitter->FixParameter(0,0);
822 fitter->Eval();
823 }
2c629c56 824 }
21f3a443 825 fitter->GetParameters(fitParam);
826 fitter->GetCovarianceMatrix(covMatrix);
827 chi2 = fitter->GetChisquare();
b8072cce 828 npoints = entries;
21f3a443 829 TString *preturnFormula = new TString(Form("( %f+",fitParam[0])), &returnFormula = *preturnFormula;
830
831 for (Int_t iparam = 0; iparam < dim; iparam++) {
832 returnFormula.Append(Form("%s*(%f)",((TObjString*)formulaTokens->At(iparam))->GetName(),fitParam[iparam+1]));
833 if (iparam < dim-1) returnFormula.Append("+");
834 }
835 returnFormula.Append(" )");
4d61c301 836
837
b8072cce 838 for (Int_t j=0; j<dim+1;j++) delete [] values[j];
4d61c301 839
840
21f3a443 841 delete formulaTokens;
842 delete fitter;
843 delete[] values;
b8072cce 844 delete[] errors;
21f3a443 845 return preturnFormula;
846}
cb1d20de 847
848TString* 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){
849 //
850 // fit an arbitrary function, specified by formula into the data, specified by drawCommand and cuts
851 // returns chi2, fitParam and covMatrix
852 // returns TString with fitted formula
853 //
854
855 TString formulaStr(formula);
856 TString drawStr(drawCommand);
857 TString cutStr(cuts);
858 TString ferr("1");
859
860 TString strVal(drawCommand);
861 if (strVal.Contains(":")){
862 TObjArray* valTokens = strVal.Tokenize(":");
863 drawStr = valTokens->At(0)->GetName();
864 ferr = valTokens->At(1)->GetName();
09d5920f 865 delete valTokens;
cb1d20de 866 }
867
868
869 formulaStr.ReplaceAll("++", "~");
870 TObjArray* formulaTokens = formulaStr.Tokenize("~");
871 Int_t dim = formulaTokens->GetEntriesFast();
872
873 fitParam.ResizeTo(dim);
874 covMatrix.ResizeTo(dim,dim);
875
876 TLinearFitter* fitter = new TLinearFitter(dim+1, Form("hyp%d",dim));
877 fitter->StoreData(kTRUE);
878 fitter->ClearPoints();
879
880 Int_t entries = tree->Draw(drawStr.Data(), cutStr.Data(), "goff", stop-start, start);
09d5920f 881 if (entries == -1) {
882 delete formulaTokens;
883 return new TString("An ERROR has occured during fitting!");
884 }
cb1d20de 885 Double_t **values = new Double_t*[dim+1] ;
bd7b4d18 886 for (Int_t i=0; i<dim+1; i++) values[i]=NULL;
cb1d20de 887 //
888 entries = tree->Draw(ferr.Data(), cutStr.Data(), "goff", stop-start, start);
b8072cce 889 if (entries == -1) {
09d5920f 890 delete formulaTokens;
b8072cce 891 delete [] values;
892 return new TString("An ERROR has occured during fitting!");
893 }
cb1d20de 894 Double_t *errors = new Double_t[entries];
895 memcpy(errors, tree->GetV1(), entries*sizeof(Double_t));
896
897 for (Int_t i = 0; i < dim + 1; i++){
898 Int_t centries = 0;
899 if (i < dim) centries = tree->Draw(((TObjString*)formulaTokens->At(i))->GetName(), cutStr.Data(), "goff", stop-start,start);
900 else centries = tree->Draw(drawStr.Data(), cutStr.Data(), "goff", stop-start,start);
901
b8072cce 902 if (entries != centries) {
903 delete []errors;
904 delete []values;
09d5920f 905 delete formulaTokens;
b8072cce 906 return new TString("An ERROR has occured during fitting!");
907 }
cb1d20de 908 values[i] = new Double_t[entries];
909 memcpy(values[i], tree->GetV1(), entries*sizeof(Double_t));
910 }
911
912 // add points to the fitter
913 for (Int_t i = 0; i < entries; i++){
914 Double_t x[1000];
915 for (Int_t j=0; j<dim;j++) x[j]=values[j][i];
916 fitter->AddPoint(x, values[dim][i], errors[i]);
917 }
918 if (constrain>0){
919 for (Int_t i = 0; i < dim; i++){
920 Double_t x[1000];
921 for (Int_t j=0; j<dim;j++) if (i!=j) x[j]=0;
922 x[i]=1.;
923 fitter->AddPoint(x, 0, constrain);
924 }
925 }
926
927
928 fitter->Eval();
929 if (frac>0.5 && frac<1){
930 fitter->EvalRobust(frac);
931 }
932 fitter->GetParameters(fitParam);
933 fitter->GetCovarianceMatrix(covMatrix);
934 chi2 = fitter->GetChisquare();
935 npoints = entries;
cb1d20de 936
937 TString *preturnFormula = new TString(Form("( %f+",fitParam[0])), &returnFormula = *preturnFormula;
938
939 for (Int_t iparam = 0; iparam < dim; iparam++) {
940 returnFormula.Append(Form("%s*(%f)",((TObjString*)formulaTokens->At(iparam))->GetName(),fitParam[iparam+1]));
941 if (iparam < dim-1) returnFormula.Append("+");
942 }
943 returnFormula.Append(" )");
944
b8072cce 945 for (Int_t j=0; j<dim+1;j++) delete [] values[j];
cb1d20de 946
947
948
949 delete formulaTokens;
950 delete fitter;
951 delete[] values;
b8072cce 952 delete[] errors;
cb1d20de 953 return preturnFormula;
954}
955
956
957
958TString* 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){
959 //
960 // fit an arbitrary function, specified by formula into the data, specified by drawCommand and cuts
961 // returns chi2, fitParam and covMatrix
962 // returns TString with fitted formula
963 //
964
965 TString formulaStr(formula);
966 TString drawStr(drawCommand);
967 TString cutStr(cuts);
968 TString ferr("1");
969
970 TString strVal(drawCommand);
971 if (strVal.Contains(":")){
972 TObjArray* valTokens = strVal.Tokenize(":");
973 drawStr = valTokens->At(0)->GetName();
09d5920f 974 ferr = valTokens->At(1)->GetName();
975 delete valTokens;
cb1d20de 976 }
977
978
979 formulaStr.ReplaceAll("++", "~");
980 TObjArray* formulaTokens = formulaStr.Tokenize("~");
981 Int_t dim = formulaTokens->GetEntriesFast();
982
983 fitParam.ResizeTo(dim);
984 covMatrix.ResizeTo(dim,dim);
985 TString fitString="x0";
986 for (Int_t i=1; i<dim; i++) fitString+=Form("++x%d",i);
987 TLinearFitter* fitter = new TLinearFitter(dim, fitString.Data());
988 fitter->StoreData(kTRUE);
989 fitter->ClearPoints();
990
991 Int_t entries = tree->Draw(drawStr.Data(), cutStr.Data(), "goff", stop-start, start);
09d5920f 992 if (entries == -1) {
993 delete formulaTokens;
994 return new TString("An ERROR has occured during fitting!");
995 }
cb1d20de 996 Double_t **values = new Double_t*[dim+1] ;
bd7b4d18 997 for (Int_t i=0; i<dim+1; i++) values[i]=NULL;
cb1d20de 998 //
999 entries = tree->Draw(ferr.Data(), cutStr.Data(), "goff", stop-start, start);
b8072cce 1000 if (entries == -1) {
1001 delete []values;
09d5920f 1002 delete formulaTokens;
b8072cce 1003 return new TString("An ERROR has occured during fitting!");
1004 }
cb1d20de 1005 Double_t *errors = new Double_t[entries];
1006 memcpy(errors, tree->GetV1(), entries*sizeof(Double_t));
1007
1008 for (Int_t i = 0; i < dim + 1; i++){
1009 Int_t centries = 0;
1010 if (i < dim) centries = tree->Draw(((TObjString*)formulaTokens->At(i))->GetName(), cutStr.Data(), "goff", stop-start,start);
1011 else centries = tree->Draw(drawStr.Data(), cutStr.Data(), "goff", stop-start,start);
1012
b8072cce 1013 if (entries != centries) {
1014 delete []errors;
1015 delete []values;
09d5920f 1016 delete formulaTokens;
b8072cce 1017 return new TString("An ERROR has occured during fitting!");
1018 }
cb1d20de 1019 values[i] = new Double_t[entries];
1020 memcpy(values[i], tree->GetV1(), entries*sizeof(Double_t));
1021 }
1022
1023 // add points to the fitter
1024 for (Int_t i = 0; i < entries; i++){
1025 Double_t x[1000];
1026 for (Int_t j=0; j<dim;j++) x[j]=values[j][i];
1027 fitter->AddPoint(x, values[dim][i], errors[i]);
1028 }
1029
1030 fitter->Eval();
1031 if (frac>0.5 && frac<1){
1032 fitter->EvalRobust(frac);
1033 }
1034 fitter->GetParameters(fitParam);
1035 fitter->GetCovarianceMatrix(covMatrix);
1036 chi2 = fitter->GetChisquare();
1037 npoints = entries;
cb1d20de 1038
1039 TString *preturnFormula = new TString("("), &returnFormula = *preturnFormula;
1040
1041 for (Int_t iparam = 0; iparam < dim; iparam++) {
1042 returnFormula.Append(Form("%s*(%f)",((TObjString*)formulaTokens->At(iparam))->GetName(),fitParam[iparam]));
1043 if (iparam < dim-1) returnFormula.Append("+");
1044 }
1045 returnFormula.Append(" )");
1046
1047
b8072cce 1048 for (Int_t j=0; j<dim+1;j++) delete [] values[j];
cb1d20de 1049
1050 delete formulaTokens;
1051 delete fitter;
1052 delete[] values;
b8072cce 1053 delete[] errors;
cb1d20de 1054 return preturnFormula;
1055}
7c9cf6e4 1056
1057
1058
1059
1060
3d7cc0b4 1061Int_t TStatToolkit::GetFitIndex(const TString fString, const TString subString){
7c9cf6e4 1062 //
1063 // fitString - ++ separated list of fits
1064 // substring - ++ separated list of the requiered substrings
1065 //
1066 // return the last occurance of substring in fit string
1067 //
1068 TObjArray *arrFit = fString.Tokenize("++");
1069 TObjArray *arrSub = subString.Tokenize("++");
1070 Int_t index=-1;
1071 for (Int_t i=0; i<arrFit->GetEntries(); i++){
1072 Bool_t isOK=kTRUE;
1073 TString str =arrFit->At(i)->GetName();
1074 for (Int_t isub=0; isub<arrSub->GetEntries(); isub++){
1075 if (str.Contains(arrSub->At(isub)->GetName())==0) isOK=kFALSE;
1076 }
1077 if (isOK) index=i;
1078 }
09d5920f 1079 delete arrFit;
1080 delete arrSub;
7c9cf6e4 1081 return index;
1082}
1083
1084
3d7cc0b4 1085TString TStatToolkit::FilterFit(const TString &input, const TString filter, TVectorD &param, TMatrixD & covar){
7c9cf6e4 1086 //
1087 // Filter fit expression make sub-fit
1088 //
1089 TObjArray *array0= input.Tokenize("++");
1090 TObjArray *array1= filter.Tokenize("++");
1091 //TString *presult=new TString("(0");
1092 TString result="(0.0";
1093 for (Int_t i=0; i<array0->GetEntries(); i++){
1094 Bool_t isOK=kTRUE;
1095 TString str(array0->At(i)->GetName());
1096 for (Int_t j=0; j<array1->GetEntries(); j++){
1097 if (str.Contains(array1->At(j)->GetName())==0) isOK=kFALSE;
1098 }
1099 if (isOK) {
1100 result+="+"+str;
1101 result+=Form("*(%f)",param[i+1]);
1102 printf("%f\t%f\t%s\n",param[i+1], TMath::Sqrt(covar(i+1,i+1)),str.Data());
1103 }
1104 }
1105 result+="-0.)";
09d5920f 1106 delete array0;
1107 delete array1;
7c9cf6e4 1108 return result;
1109}
1110
1111void TStatToolkit::Update1D(Double_t delta, Double_t sigma, Int_t s1, TMatrixD &vecXk, TMatrixD &covXk){
1112 //
1113 // Update parameters and covariance - with one measurement
1114 // Input:
1115 // vecXk - input vector - Updated in function
1116 // covXk - covariance matrix - Updated in function
1117 // delta, sigma, s1 - new measurement, rms of new measurement and the index of measurement
1118 const Int_t knMeas=1;
1119 Int_t knElem=vecXk.GetNrows();
1120
1121 TMatrixD mat1(knElem,knElem); // update covariance matrix
1122 TMatrixD matHk(1,knElem); // vector to mesurement
1123 TMatrixD vecYk(knMeas,1); // Innovation or measurement residual
1124 TMatrixD matHkT(knElem,knMeas); // helper matrix Hk transpose
1125 TMatrixD matSk(knMeas,knMeas); // Innovation (or residual) covariance
1126 TMatrixD matKk(knElem,knMeas); // Optimal Kalman gain
1127 TMatrixD covXk2(knElem,knElem); // helper matrix
1128 TMatrixD covXk3(knElem,knElem); // helper matrix
1129 TMatrixD vecZk(1,1);
1130 TMatrixD measR(1,1);
1131 vecZk(0,0)=delta;
1132 measR(0,0)=sigma*sigma;
1133 //
1134 // reset matHk
1135 for (Int_t iel=0;iel<knElem;iel++)
1136 for (Int_t ip=0;ip<knMeas;ip++) matHk(ip,iel)=0;
1137 //mat1
1138 for (Int_t iel=0;iel<knElem;iel++) {
1139 for (Int_t jel=0;jel<knElem;jel++) mat1(iel,jel)=0;
1140 mat1(iel,iel)=1;
1141 }
1142 //
1143 matHk(0, s1)=1;
1144 vecYk = vecZk-matHk*vecXk; // Innovation or measurement residual
1145 matHkT=matHk.T(); matHk.T();
1146 matSk = (matHk*(covXk*matHkT))+measR; // Innovation (or residual) covariance
1147 matSk.Invert();
1148 matKk = (covXk*matHkT)*matSk; // Optimal Kalman gain
1149 vecXk += matKk*vecYk; // updated vector
1150 covXk2= (mat1-(matKk*matHk));
1151 covXk3 = covXk2*covXk;
1152 covXk = covXk3;
1153 Int_t nrows=covXk3.GetNrows();
1154
1155 for (Int_t irow=0; irow<nrows; irow++)
1156 for (Int_t icol=0; icol<nrows; icol++){
1157 // rounding problems - make matrix again symteric
1158 covXk(irow,icol)=(covXk3(irow,icol)+covXk3(icol,irow))*0.5;
1159 }
1160}
1161
1162
1163
3d7cc0b4 1164void TStatToolkit::Constrain1D(const TString &input, const TString filter, TVectorD &param, TMatrixD & covar, Double_t mean, Double_t sigma){
7c9cf6e4 1165 //
1166 // constrain linear fit
1167 // input - string description of fit function
1168 // filter - string filter to select sub fits
1169 // param,covar - parameters and covariance matrix of the fit
1170 // mean,sigma - new measurement uning which the fit is updated
1171 //
ae45c94d 1172
7c9cf6e4 1173 TObjArray *array0= input.Tokenize("++");
1174 TObjArray *array1= filter.Tokenize("++");
1175 TMatrixD paramM(param.GetNrows(),1);
1176 for (Int_t i=0; i<=array0->GetEntries(); i++){paramM(i,0)=param(i);}
1177
ae45c94d 1178 if (filter.Length()==0){
1179 TStatToolkit::Update1D(mean, sigma, 0, paramM, covar);//
1180 }else{
1181 for (Int_t i=0; i<array0->GetEntries(); i++){
1182 Bool_t isOK=kTRUE;
1183 TString str(array0->At(i)->GetName());
1184 for (Int_t j=0; j<array1->GetEntries(); j++){
1185 if (str.Contains(array1->At(j)->GetName())==0) isOK=kFALSE;
1186 }
1187 if (isOK) {
1188 TStatToolkit::Update1D(mean, sigma, i+1, paramM, covar);//
1189 }
7c9cf6e4 1190 }
1191 }
1192 for (Int_t i=0; i<=array0->GetEntries(); i++){
1193 param(i)=paramM(i,0);
1194 }
09d5920f 1195 delete array0;
1196 delete array1;
7c9cf6e4 1197}
1198
ae45c94d 1199TString TStatToolkit::MakeFitString(const TString &input, const TVectorD &param, const TMatrixD & covar, Bool_t verbose){
7c9cf6e4 1200 //
1201 //
1202 //
1203 TObjArray *array0= input.Tokenize("++");
ae45c94d 1204 TString result=Form("(%f",param[0]);
1205 printf("%f\t%f\t\n", param[0], TMath::Sqrt(covar(0,0)));
7c9cf6e4 1206 for (Int_t i=0; i<array0->GetEntries(); i++){
1207 TString str(array0->At(i)->GetName());
1208 result+="+"+str;
1209 result+=Form("*(%f)",param[i+1]);
ae45c94d 1210 if (verbose) printf("%f\t%f\t%s\n", param[i+1], TMath::Sqrt(covar(i+1,i+1)),str.Data());
7c9cf6e4 1211 }
1212 result+="-0.)";
09d5920f 1213 delete array0;
7c9cf6e4 1214 return result;
1215}
df0a2a0a 1216
1a8f4649 1217TGraphErrors * TStatToolkit::MakeGraphErrors(TTree * tree, const char * expr, const char * cut, Int_t mstyle, Int_t mcolor, Float_t msize, Float_t offset){
1218 //
1219 // Query a graph errors
1220 // return TGraphErrors specified by expr and cut
1221 // Example usage TStatToolkit::MakeGraphError(tree,"Y:X:ErrY","X>0", 25,2,0.4)
1222 // tree - tree with variable
1223 // expr - examp
1224 const Int_t entries = tree->Draw(expr,cut,"goff");
1225 if (entries<=0) {
1226 TStatToolkit t;
1227 t.Error("TStatToolkit::MakeGraphError",Form("Empty or Not valid expression (%s) or cut *%s)", expr,cut));
1228 return 0;
1229 }
1230 if ( tree->GetV2()==0){
1231 TStatToolkit t;
1232 t.Error("TStatToolkit::MakeGraphError",Form("Not valid expression (%s) ", expr));
1233 return 0;
1234 }
1235 TGraphErrors * graph=0;
1236 if ( tree->GetV3()!=0){
1237 graph = new TGraphErrors (entries, tree->GetV2(),tree->GetV1(),0,tree->GetV3());
1238 }else{
1239 graph = new TGraphErrors (entries, tree->GetV2(),tree->GetV1(),0,0);
1240 }
1241 graph->SetMarkerStyle(mstyle);
1242 graph->SetMarkerColor(mcolor);
1243 graph->SetLineColor(mcolor);
1244 if (msize>0) graph->SetMarkerSize(msize);
1245 for(Int_t i=0;i<graph->GetN();i++) graph->GetX()[i]+=offset;
1246 return graph;
1247
1248}
1249
df0a2a0a 1250
377a7d60 1251TGraph * TStatToolkit::MakeGraphSparse(TTree * tree, const char * expr, const char * cut, Int_t mstyle, Int_t mcolor, Float_t msize, Float_t offset){
df0a2a0a 1252 //
1253 // Make a sparse draw of the variables
d02b8756 1254 // Format of expr : Var:Run or Var:Run:ErrorY or Var:Run:ErrorY:ErrorX
1255 // offset : points can slightly be shifted in x for better visibility with more graphs
1256 //
1257 // Written by Weilin.Yu
1258 // updated & merged with QA-code by Patrick Reichelt
1259 //
1260 const Int_t entries = tree->Draw(expr,cut,"goff");
8fb3bea1 1261 if (entries<=0) {
1262 TStatToolkit t;
d02b8756 1263 t.Error("TStatToolkit::MakeGraphSparse",Form("Empty or Not valid expression (%s) or cut (%s)", expr, cut));
8fb3bea1 1264 return 0;
1265 }
df0a2a0a 1266 // TGraph * graph = (TGraph*)gPad->GetPrimitive("Graph"); // 2D
d02b8756 1267
1268 Double_t *graphY, *graphX;
1269 graphY = tree->GetV1();
1270 graphX = tree->GetV2();
1271
1272 // sort according to run number
eda18694 1273 Int_t *index = new Int_t[entries*4];
d02b8756 1274 TMath::Sort(entries,graphX,index,kFALSE);
df0a2a0a 1275
d02b8756 1276 // define arrays for the new graph
1277 Double_t *unsortedX = new Double_t[entries];
1278 Int_t *runNumber = new Int_t[entries];
df0a2a0a 1279 Double_t count = 0.5;
d02b8756 1280
1281 // evaluate arrays for the new graph according to the run-number
baa0041d 1282 Int_t icount=0;
d02b8756 1283 //first entry
1284 unsortedX[index[0]] = count;
1285 runNumber[0] = graphX[index[0]];
1286 // loop the rest of entries
1287 for(Int_t i=1;i<entries;i++)
1288 {
1289 if(graphX[index[i]]==graphX[index[i-1]])
1290 unsortedX[index[i]] = count;
1291 else if(graphX[index[i]]!=graphX[index[i-1]]){
df0a2a0a 1292 count++;
baa0041d 1293 icount++;
d02b8756 1294 unsortedX[index[i]] = count;
1295 runNumber[icount]=graphX[index[i]];
df0a2a0a 1296 }
1297 }
d02b8756 1298
1299 // count the number of xbins (run-wise) for the new graph
df0a2a0a 1300 const Int_t newNbins = int(count+0.5);
1301 Double_t *newBins = new Double_t[newNbins+1];
1302 for(Int_t i=0; i<=count+1;i++){
1303 newBins[i] = i;
1304 }
d02b8756 1305
1306 // define and fill the new graph
b3453fe7 1307 TGraph *graphNew = 0;
d02b8756 1308 if (tree->GetV3()) {
1309 if (tree->GetV4()) {
1310 graphNew = new TGraphErrors(entries,unsortedX,graphY,tree->GetV4(),tree->GetV3());
1311 }
1312 else { graphNew = new TGraphErrors(entries,unsortedX,graphY,0,tree->GetV3()); }
1313 }
1314 else { graphNew = new TGraphErrors(entries,unsortedX,graphY,0,0); }
1315 // with "Set(...)", the x-axis is being sorted
df0a2a0a 1316 graphNew->GetXaxis()->Set(newNbins,newBins);
d02b8756 1317
1318 // set the bins for the x-axis, apply shifting of points
df0a2a0a 1319 Char_t xName[50];
df0a2a0a 1320 for(Int_t i=0;i<count;i++){
d02b8756 1321 snprintf(xName,50,"%d",runNumber[i]);
df0a2a0a 1322 graphNew->GetXaxis()->SetBinLabel(i+1,xName);
d02b8756 1323 graphNew->GetX()[i]+=offset;
df0a2a0a 1324 }
d02b8756 1325
df0a2a0a 1326 graphNew->GetHistogram()->SetTitle("");
d02b8756 1327 graphNew->SetMarkerStyle(mstyle);
b3453fe7 1328 graphNew->SetMarkerColor(mcolor);
70989f8d 1329 if (msize>0) graphNew->SetMarkerSize(msize);
d02b8756 1330 delete [] unsortedX;
1331 delete [] runNumber;
df0a2a0a 1332 delete [] index;
1333 delete [] newBins;
d02b8756 1334 //
df0a2a0a 1335 return graphNew;
1336}
1337
377a7d60 1338
1339
1340//
d02b8756 1341// functions used for the trending
377a7d60 1342//
1343
1344Int_t TStatToolkit::MakeStatAlias(TTree * tree, const char * expr, const char * cut, const char * alias)
1345{
1346 //
1347 // Add alias using statistical values of a given variable.
1348 // (by MI, Patrick Reichelt)
1349 //
1350 // tree - input tree
1351 // expr - variable expression
1352 // cut - selection criteria
1353 // Output - return number of entries used to define variable
1354 // In addition mean, rms, median, and robust mean and rms (choosing fraction of data with smallest RMS)
1355 //
d02b8756 1356 /* Example usage:
1357 1.) create the robust estimators for variable expr="QA.TPC.CPass1.meanTPCncl" and create a corresponding
1358 aliases with the prefix alias[0]="ncl", calculated using fraction alias[1]="0.90"
1359
1360 TStatToolkit::MakeStatAlias(tree,"QA.TPC.CPass1.meanTPCncl","QA.TPC.CPass1.status>0","ncl:0.9");
1361 root [4] tree->GetListOfAliases().Print()
1362 OBJ: TNamed ncl_Median (130.964333+0)
1363 OBJ: TNamed ncl_Mean (122.120387+0)
1364 OBJ: TNamed ncl_RMS (33.509623+0)
1365 OBJ: TNamed ncl_Mean90 (131.503862+0)
1366 OBJ: TNamed ncl_RMS90 (3.738260+0)
1367 */
377a7d60 1368 //
d02b8756 1369 Int_t entries = tree->Draw(expr,cut,"goff");
377a7d60 1370 if (entries<=1){
1371 printf("Expression or cut not valid:\t%s\t%s\n", expr, cut);
1372 return 0;
1373 }
1374 //
1375 TObjArray* oaAlias = TString(alias).Tokenize(":");
1376 if (oaAlias->GetEntries()<2) return 0;
1377 Float_t entryFraction = atof( oaAlias->At(1)->GetName() );
1378 //
1379 Double_t median = TMath::Median(entries,tree->GetV1());
d02b8756 1380 Double_t mean = TMath::Mean(entries,tree->GetV1());
377a7d60 1381 Double_t rms = TMath::RMS(entries,tree->GetV1());
1382 Double_t meanEF=0, rmsEF=0;
1383 TStatToolkit::EvaluateUni(entries, tree->GetV1(), meanEF, rmsEF, entries*entryFraction);
1384 //
d02b8756 1385 tree->SetAlias(Form("%s_Median",oaAlias->At(0)->GetName()), Form("(%f+0)",median));
377a7d60 1386 tree->SetAlias(Form("%s_Mean",oaAlias->At(0)->GetName()), Form("(%f+0)",mean));
1387 tree->SetAlias(Form("%s_RMS",oaAlias->At(0)->GetName()), Form("(%f+0)",rms));
377a7d60 1388 tree->SetAlias(Form("%s_Mean%d",oaAlias->At(0)->GetName(),Int_t(entryFraction*100)), Form("(%f+0)",meanEF));
1389 tree->SetAlias(Form("%s_RMS%d",oaAlias->At(0)->GetName(),Int_t(entryFraction*100)), Form("(%f+0)",rmsEF));
1390 delete oaAlias;
1391 return entries;
1392}
1393
1394Int_t TStatToolkit::SetStatusAlias(TTree * tree, const char * expr, const char * cut, const char * alias)
1395{
1396 //
1397 // Add alias to trending tree using statistical values of a given variable.
1398 // (by MI, Patrick Reichelt)
1399 //
1400 // format of expr : varname (e.g. meanTPCncl)
1401 // format of cut : char like in TCut
1402 // format of alias: alias:query:entryFraction(EF) (fraction of entries used for uniformity evaluation)
1403 // e.g.: varname_Out:(abs(varname-meanEF)>6.*rmsEF):0.8
d02b8756 1404 // available internal variables are: 'varname, Median, Mean, MeanEF, RMS, RMSEF'
1405 // in the alias, 'varname' will be replaced by its content, and 'EF' by the percentage (e.g. MeanEF -> Mean80)
377a7d60 1406 //
1407 /* Example usage:
d02b8756 1408 1.) Define robust mean (possible, but easier done with TStatToolkit::MakeStatAlias(...))
1409 TStatToolkit::SetStatusAlias(tree, "meanTPCnclF", "meanTPCnclF>0", "meanTPCnclF_MeanEF:MeanEF:0.80") ;
377a7d60 1410 root [10] tree->GetListOfAliases()->Print()
1411 Collection name='TList', class='TList', size=1
d02b8756 1412 OBJ: TNamed meanTPCnclF_Mean80 0.899308
377a7d60 1413 2.) create alias outlyers - 6 sigma cut
d02b8756 1414 TStatToolkit::SetStatusAlias(tree, "meanTPCnclF", "meanTPCnclF>0", "meanTPCnclF_Out:(abs(meanTPCnclF-MeanEF)>6.*RMSEF):0.8")
1415 meanTPCnclF_Out ==> (abs(meanTPCnclF-0.899308)>6.*0.016590)
377a7d60 1416 3.) the same functionality as in 2.)
d02b8756 1417 TStatToolkit::SetStatusAlias(tree, "meanTPCnclF", "meanTPCnclF>0", "varname_Out2:(abs(varname-MeanEF)>6.*RMSEF):0.8")
1418 meanTPCnclF_Out2 ==> (abs(meanTPCnclF-0.899308)>6.*0.016590)
377a7d60 1419 */
1420 //
d02b8756 1421 Int_t entries = tree->Draw(expr,cut,"goff");
1422 if (entries<=1){
1423 printf("Expression or cut not valid:\t%s\t%s\n", expr, cut);
1424 return 0;
1425 }
1426 //
377a7d60 1427 TObjArray* oaVar = TString(expr).Tokenize(":");
1428 char varname[50];
377a7d60 1429 snprintf(varname,50,"%s", oaVar->At(0)->GetName());
d02b8756 1430 //
377a7d60 1431 TObjArray* oaAlias = TString(alias).Tokenize(":");
d02b8756 1432 if (oaAlias->GetEntries()<3) return 0;
377a7d60 1433 Float_t entryFraction = atof( oaAlias->At(2)->GetName() );
1434 //
377a7d60 1435 Double_t median = TMath::Median(entries,tree->GetV1());
d02b8756 1436 Double_t mean = TMath::Mean(entries,tree->GetV1());
377a7d60 1437 Double_t rms = TMath::RMS(entries,tree->GetV1());
1438 Double_t meanEF=0, rmsEF=0;
1439 TStatToolkit::EvaluateUni(entries, tree->GetV1(), meanEF, rmsEF, entries*entryFraction);
377a7d60 1440 //
1441 TString sAlias( oaAlias->At(0)->GetName() );
1442 sAlias.ReplaceAll("varname",varname);
d02b8756 1443 sAlias.ReplaceAll("MeanEF", Form("Mean%1.0f",entryFraction*100) );
1444 sAlias.ReplaceAll("RMSEF", Form("RMS%1.0f",entryFraction*100) );
377a7d60 1445 TString sQuery( oaAlias->At(1)->GetName() );
1446 sQuery.ReplaceAll("varname",varname);
1447 sQuery.ReplaceAll("MeanEF", Form("%f",meanEF) );
d02b8756 1448 sQuery.ReplaceAll("RMSEF", Form("%f",rmsEF) ); //make sure to replace 'RMSEF' before 'RMS'...
377a7d60 1449 sQuery.ReplaceAll("Median", Form("%f",median) );
d02b8756 1450 sQuery.ReplaceAll("Mean", Form("%f",mean) );
377a7d60 1451 sQuery.ReplaceAll("RMS", Form("%f",rms) );
d02b8756 1452 printf("define alias:\t%s = %s\n", sAlias.Data(), sQuery.Data());
377a7d60 1453 //
1454 char query[200];
1455 char aname[200];
1456 snprintf(query,200,"%s", sQuery.Data());
1457 snprintf(aname,200,"%s", sAlias.Data());
1458 tree->SetAlias(aname, query);
d02b8756 1459 delete oaVar;
1460 delete oaAlias;
377a7d60 1461 return entries;
1462}
1463
1464TMultiGraph* TStatToolkit::MakeStatusMultGr(TTree * tree, const char * expr, const char * cut, const char * alias, Int_t igr)
1465{
1466 //
1467 // Compute a trending multigraph that shows for which runs a variable has outliers.
1468 // (by MI, Patrick Reichelt)
1469 //
1470 // format of expr : varname:xaxis (e.g. meanTPCncl:run)
1471 // format of cut : char like in TCut
1472 // format of alias: (1):(varname_Out==0):(varname_Out)[:(varname_Warning):...]
1473 // in the alias, 'varname' will be replaced by its content (e.g. varname_Out -> meanTPCncl_Out)
d02b8756 1474 // note: the aliases 'varname_Out' etc have to be defined by function TStatToolkit::SetStatusAlias(...)
377a7d60 1475 // counter igr is used to shift the multigraph in y when filling a TObjArray.
1476 //
1477 TObjArray* oaVar = TString(expr).Tokenize(":");
d02b8756 1478 if (oaVar->GetEntries()<2) return 0;
377a7d60 1479 char varname[50];
1480 char var_x[50];
1481 snprintf(varname,50,"%s", oaVar->At(0)->GetName());
1482 snprintf(var_x ,50,"%s", oaVar->At(1)->GetName());
d02b8756 1483 //
377a7d60 1484 TString sAlias(alias);
1485 sAlias.ReplaceAll("varname",varname);
1486 TObjArray* oaAlias = TString(sAlias.Data()).Tokenize(":");
d02b8756 1487 if (oaAlias->GetEntries()<3) return 0;
377a7d60 1488 //
1489 char query[200];
1490 TMultiGraph* multGr = new TMultiGraph();
1491 Int_t marArr[6] = {24+igr%2, 20+igr%2, 20+igr%2, 20+igr%2, 22, 23};
1492 Int_t colArr[6] = {kBlack, kBlack, kRed, kOrange, kMagenta, kViolet};
1493 Double_t sizArr[6] = {1.2, 1.1, 1.0, 1.0, 1, 1};
1494 const Int_t ngr = oaAlias->GetEntriesFast();
1495 for (Int_t i=0; i<ngr; i++){
1496 if (i==2) continue; // the Fatal(Out) graph will be added in the end to be plotted on top!
1497 snprintf(query,200, "%f*(%s-0.5):%s", 1.+igr, oaAlias->At(i)->GetName(), var_x);
d02b8756 1498 multGr->Add( (TGraphErrors*) TStatToolkit::MakeGraphSparse(tree,query,cut,marArr[i],colArr[i],sizArr[i]) );
377a7d60 1499 }
1500 snprintf(query,200, "%f*(%s-0.5):%s", 1.+igr, oaAlias->At(2)->GetName(), var_x);
d02b8756 1501 multGr->Add( (TGraphErrors*) TStatToolkit::MakeGraphSparse(tree,query,cut,marArr[2],colArr[2],sizArr[2]) );
377a7d60 1502 //
1503 multGr->SetName(varname);
1504 multGr->SetTitle(varname); // used for y-axis labels. // details to be included!
d02b8756 1505 delete oaVar;
1506 delete oaAlias;
377a7d60 1507 return multGr;
1508}
1509
1510
1511void TStatToolkit::AddStatusPad(TCanvas* c1, Float_t padratio, Float_t bottommargin)
1512{
1513 //
1514 // add pad to bottom of canvas for Status graphs (by Patrick Reichelt)
1515 // call function "DrawStatusGraphs(...)" afterwards
1516 //
1517 TCanvas* c1_clone = (TCanvas*) c1->Clone("c1_clone");
1518 c1->Clear();
1519 // produce new pads
1520 c1->cd();
1521 TPad* pad1 = new TPad("pad1", "pad1", 0., padratio, 1., 1.);
1522 pad1->Draw();
1523 pad1->SetNumber(1); // so it can be called via "c1->cd(1);"
1524 c1->cd();
1525 TPad* pad2 = new TPad("pad2", "pad2", 0., 0., 1., padratio);
1526 pad2->Draw();
1527 pad2->SetNumber(2);
1528 // draw original canvas into first pad
1529 c1->cd(1);
1530 c1_clone->DrawClonePad();
1531 pad1->SetBottomMargin(0.001);
1532 pad1->SetRightMargin(0.01);
1533 // set up second pad
1534 c1->cd(2);
1535 pad2->SetGrid(3);
1536 pad2->SetTopMargin(0);
1537 pad2->SetBottomMargin(bottommargin); // for the long x-axis labels (runnumbers)
1538 pad2->SetRightMargin(0.01);
1539}
1540
1541
1542void TStatToolkit::DrawStatusGraphs(TObjArray* oaMultGr)
1543{
1544 //
1545 // draw Status graphs into active pad of canvas (by MI, Patrick Reichelt)
1546 // ...into bottom pad, if called after "AddStatusPad(...)"
1547 //
1548 const Int_t nvars = oaMultGr->GetEntriesFast();
1549 TGraph* grAxis = (TGraph*) ((TMultiGraph*) oaMultGr->At(0))->GetListOfGraphs()->At(0);
1550 grAxis->SetMaximum(0.5*nvars+0.5);
1551 grAxis->SetMinimum(0);
1552 grAxis->GetYaxis()->SetLabelSize(0);
1553 Int_t entries = grAxis->GetN();
1554 printf("entries (via GetN()) = %d\n",entries);
1555 grAxis->GetXaxis()->SetLabelSize(5.7*TMath::Min(TMath::Max(5./entries,0.01),0.03));
1556 grAxis->GetXaxis()->LabelsOption("v");
1557 grAxis->Draw("ap");
1558 //
1559 // draw multigraphs & names of status variables on the y axis
1560 for (Int_t i=0; i<nvars; i++){
1561 ((TMultiGraph*) oaMultGr->At(i))->Draw("p");
1562 TLatex* ylabel = new TLatex(-0.1, 0.5*i+0.5, ((TMultiGraph*) oaMultGr->At(i))->GetTitle());
1563 ylabel->SetTextAlign(32); //hor:right & vert:centered
1564 ylabel->SetTextSize(0.025/gPad->GetHNDC());
1565 ylabel->Draw();
1566 }
1567}