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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" | |
21f3a443 | 35 | |
36 | // | |
37 | // includes neccessary for test functions | |
38 | // | |
39 | #include "TSystem.h" | |
40 | #include "TRandom.h" | |
41 | #include "TStopwatch.h" | |
42 | #include "TTreeStream.h" | |
43 | ||
44 | #include "TStatToolkit.h" | |
45 | ||
46 | ||
47 | ClassImp(TStatToolkit) // Class implementation to enable ROOT I/O | |
48 | ||
49 | TStatToolkit::TStatToolkit() : TObject() | |
50 | { | |
51 | // | |
52 | // Default constructor | |
53 | // | |
54 | } | |
55 | /////////////////////////////////////////////////////////////////////////// | |
56 | TStatToolkit::~TStatToolkit() | |
57 | { | |
58 | // | |
59 | // Destructor | |
60 | // | |
61 | } | |
62 | ||
63 | ||
64 | //_____________________________________________________________________________ | |
65 | void TStatToolkit::EvaluateUni(Int_t nvectors, Double_t *data, Double_t &mean | |
66 | , Double_t &sigma, Int_t hh) | |
67 | { | |
68 | // | |
69 | // Robust estimator in 1D case MI version - (faster than ROOT version) | |
70 | // | |
71 | // For the univariate case | |
72 | // estimates of location and scatter are returned in mean and sigma parameters | |
73 | // the algorithm works on the same principle as in multivariate case - | |
74 | // it finds a subset of size hh with smallest sigma, and then returns mean and | |
75 | // sigma of this subset | |
76 | // | |
77 | ||
78 | if (hh==0) | |
79 | hh=(nvectors+2)/2; | |
80 | 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}; | |
81 | Int_t *index=new Int_t[nvectors]; | |
82 | TMath::Sort(nvectors, data, index, kFALSE); | |
83 | ||
84 | Int_t nquant = TMath::Min(Int_t(Double_t(((hh*1./nvectors)-0.5)*40))+1, 11); | |
85 | Double_t factor = faclts[TMath::Max(0,nquant-1)]; | |
86 | ||
87 | Double_t sumx =0; | |
88 | Double_t sumx2 =0; | |
89 | Int_t bestindex = -1; | |
90 | Double_t bestmean = 0; | |
91 | Double_t bestsigma = (data[index[nvectors-1]]-data[index[0]]+1.); // maximal possible sigma | |
92 | bestsigma *=bestsigma; | |
93 | ||
94 | for (Int_t i=0; i<hh; i++){ | |
95 | sumx += data[index[i]]; | |
96 | sumx2 += data[index[i]]*data[index[i]]; | |
97 | } | |
98 | ||
99 | Double_t norm = 1./Double_t(hh); | |
100 | Double_t norm2 = 1./Double_t(hh-1); | |
101 | for (Int_t i=hh; i<nvectors; i++){ | |
102 | Double_t cmean = sumx*norm; | |
103 | Double_t csigma = (sumx2 - hh*cmean*cmean)*norm2; | |
104 | if (csigma<bestsigma){ | |
105 | bestmean = cmean; | |
106 | bestsigma = csigma; | |
107 | bestindex = i-hh; | |
108 | } | |
109 | ||
110 | sumx += data[index[i]]-data[index[i-hh]]; | |
111 | sumx2 += data[index[i]]*data[index[i]]-data[index[i-hh]]*data[index[i-hh]]; | |
112 | } | |
113 | ||
114 | Double_t bstd=factor*TMath::Sqrt(TMath::Abs(bestsigma)); | |
115 | mean = bestmean; | |
116 | sigma = bstd; | |
117 | delete [] index; | |
118 | ||
119 | } | |
120 | ||
121 | ||
122 | ||
123 | void TStatToolkit::EvaluateUniExternal(Int_t nvectors, Double_t *data, Double_t &mean, Double_t &sigma, Int_t hh, Float_t externalfactor) | |
124 | { | |
125 | // Modified version of ROOT robust EvaluateUni | |
126 | // robust estimator in 1D case MI version | |
127 | // added external factor to include precision of external measurement | |
128 | // | |
129 | ||
130 | if (hh==0) | |
131 | hh=(nvectors+2)/2; | |
132 | 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}; | |
133 | Int_t *index=new Int_t[nvectors]; | |
134 | TMath::Sort(nvectors, data, index, kFALSE); | |
135 | // | |
136 | Int_t nquant = TMath::Min(Int_t(Double_t(((hh*1./nvectors)-0.5)*40))+1, 11); | |
137 | Double_t factor = faclts[0]; | |
138 | if (nquant>0){ | |
139 | // fix proper normalization - Anja | |
140 | factor = faclts[nquant-1]; | |
141 | } | |
142 | ||
143 | // | |
144 | // | |
145 | Double_t sumx =0; | |
146 | Double_t sumx2 =0; | |
147 | Int_t bestindex = -1; | |
148 | Double_t bestmean = 0; | |
149 | Double_t bestsigma = -1; | |
150 | for (Int_t i=0; i<hh; i++){ | |
151 | sumx += data[index[i]]; | |
152 | sumx2 += data[index[i]]*data[index[i]]; | |
153 | } | |
154 | // | |
155 | Double_t kfactor = 2.*externalfactor - externalfactor*externalfactor; | |
156 | Double_t norm = 1./Double_t(hh); | |
157 | for (Int_t i=hh; i<nvectors; i++){ | |
158 | Double_t cmean = sumx*norm; | |
159 | Double_t csigma = (sumx2*norm - cmean*cmean*kfactor); | |
160 | if (csigma<bestsigma || bestsigma<0){ | |
161 | bestmean = cmean; | |
162 | bestsigma = csigma; | |
163 | bestindex = i-hh; | |
164 | } | |
165 | // | |
166 | // | |
167 | sumx += data[index[i]]-data[index[i-hh]]; | |
168 | sumx2 += data[index[i]]*data[index[i]]-data[index[i-hh]]*data[index[i-hh]]; | |
169 | } | |
170 | ||
171 | Double_t bstd=factor*TMath::Sqrt(TMath::Abs(bestsigma)); | |
172 | mean = bestmean; | |
173 | sigma = bstd; | |
174 | delete [] index; | |
175 | } | |
176 | ||
177 | ||
178 | //_____________________________________________________________________________ | |
179 | Int_t TStatToolkit::Freq(Int_t n, const Int_t *inlist | |
180 | , Int_t *outlist, Bool_t down) | |
181 | { | |
182 | // | |
183 | // Sort eleements according occurancy | |
184 | // The size of output array has is 2*n | |
185 | // | |
186 | ||
187 | Int_t * sindexS = new Int_t[n]; // temp array for sorting | |
188 | Int_t * sindexF = new Int_t[2*n]; | |
b8072cce | 189 | for (Int_t i=0;i<n;i++) sindexS[i]=0; |
190 | for (Int_t i=0;i<2*n;i++) sindexF[i]=0; | |
21f3a443 | 191 | // |
192 | TMath::Sort(n,inlist, sindexS, down); | |
193 | Int_t last = inlist[sindexS[0]]; | |
194 | Int_t val = last; | |
195 | sindexF[0] = 1; | |
196 | sindexF[0+n] = last; | |
197 | Int_t countPos = 0; | |
198 | // | |
199 | // find frequency | |
200 | for(Int_t i=1;i<n; i++){ | |
201 | val = inlist[sindexS[i]]; | |
202 | if (last == val) sindexF[countPos]++; | |
203 | else{ | |
204 | countPos++; | |
205 | sindexF[countPos+n] = val; | |
206 | sindexF[countPos]++; | |
207 | last =val; | |
208 | } | |
209 | } | |
210 | if (last==val) countPos++; | |
211 | // sort according frequency | |
212 | TMath::Sort(countPos, sindexF, sindexS, kTRUE); | |
213 | for (Int_t i=0;i<countPos;i++){ | |
214 | outlist[2*i ] = sindexF[sindexS[i]+n]; | |
215 | outlist[2*i+1] = sindexF[sindexS[i]]; | |
216 | } | |
217 | delete [] sindexS; | |
218 | delete [] sindexF; | |
219 | ||
220 | return countPos; | |
221 | ||
222 | } | |
223 | ||
224 | //___TStatToolkit__________________________________________________________________________ | |
3d7cc0b4 | 225 | void TStatToolkit::TruncatedMean(const TH1 * his, TVectorD *param, Float_t down, Float_t up, Bool_t verbose){ |
21f3a443 | 226 | // |
227 | // | |
228 | // | |
229 | Int_t nbins = his->GetNbinsX(); | |
230 | Float_t nentries = his->GetEntries(); | |
231 | Float_t sum =0; | |
232 | Float_t mean = 0; | |
233 | Float_t sigma2 = 0; | |
234 | Float_t ncumul=0; | |
235 | for (Int_t ibin=1;ibin<nbins; ibin++){ | |
236 | ncumul+= his->GetBinContent(ibin); | |
237 | Float_t fraction = Float_t(ncumul)/Float_t(nentries); | |
238 | if (fraction>down && fraction<up){ | |
239 | sum+=his->GetBinContent(ibin); | |
240 | mean+=his->GetBinCenter(ibin)*his->GetBinContent(ibin); | |
241 | sigma2+=his->GetBinCenter(ibin)*his->GetBinCenter(ibin)*his->GetBinContent(ibin); | |
242 | } | |
243 | } | |
244 | mean/=sum; | |
245 | sigma2= TMath::Sqrt(TMath::Abs(sigma2/sum-mean*mean)); | |
246 | if (param){ | |
247 | (*param)[0] = his->GetMaximum(); | |
248 | (*param)[1] = mean; | |
249 | (*param)[2] = sigma2; | |
250 | ||
251 | } | |
252 | if (verbose) printf("Mean\t%f\t Sigma2\t%f\n", mean,sigma2); | |
253 | } | |
254 | ||
255 | void TStatToolkit::LTM(TH1F * his, TVectorD *param , Float_t fraction, Bool_t verbose){ | |
256 | // | |
257 | // LTM | |
258 | // | |
259 | Int_t nbins = his->GetNbinsX(); | |
260 | Int_t nentries = (Int_t)his->GetEntries(); | |
261 | Double_t *data = new Double_t[nentries]; | |
262 | Int_t npoints=0; | |
263 | for (Int_t ibin=1;ibin<nbins; ibin++){ | |
264 | Float_t entriesI = his->GetBinContent(ibin); | |
265 | Float_t xcenter= his->GetBinCenter(ibin); | |
266 | for (Int_t ic=0; ic<entriesI; ic++){ | |
267 | if (npoints<nentries){ | |
268 | data[npoints]= xcenter; | |
269 | npoints++; | |
270 | } | |
271 | } | |
272 | } | |
273 | Double_t mean, sigma; | |
274 | Int_t npoints2=TMath::Min(Int_t(fraction*Float_t(npoints)),npoints-1); | |
275 | npoints2=TMath::Max(Int_t(0.5*Float_t(npoints)),npoints2); | |
276 | TStatToolkit::EvaluateUni(npoints, data, mean,sigma,npoints2); | |
277 | delete [] data; | |
278 | if (verbose) printf("Mean\t%f\t Sigma2\t%f\n", mean,sigma);if (param){ | |
279 | (*param)[0] = his->GetMaximum(); | |
280 | (*param)[1] = mean; | |
281 | (*param)[2] = sigma; | |
282 | } | |
283 | } | |
284 | ||
94a43b22 | 285 | Double_t TStatToolkit::FitGaus(TH1* his, TVectorD *param, TMatrixD */*matrix*/, Float_t xmin, Float_t xmax, Bool_t verbose){ |
21f3a443 | 286 | // |
287 | // Fit histogram with gaussian function | |
288 | // | |
289 | // Prameters: | |
290 | // return value- chi2 - if negative ( not enough points) | |
291 | // his - input histogram | |
292 | // param - vector with parameters | |
293 | // xmin, xmax - range to fit - if xmin=xmax=0 - the full histogram range used | |
294 | // Fitting: | |
295 | // 1. Step - make logarithm | |
296 | // 2. Linear fit (parabola) - more robust - always converge | |
297 | // 3. In case of small statistic bins are averaged | |
298 | // | |
299 | static TLinearFitter fitter(3,"pol2"); | |
300 | TVectorD par(3); | |
301 | TVectorD sigma(3); | |
302 | TMatrixD mat(3,3); | |
303 | if (his->GetMaximum()<4) return -1; | |
304 | if (his->GetEntries()<12) return -1; | |
305 | if (his->GetRMS()<mat.GetTol()) return -1; | |
306 | Float_t maxEstimate = his->GetEntries()*his->GetBinWidth(1)/TMath::Sqrt((TMath::TwoPi()*his->GetRMS())); | |
307 | Int_t dsmooth = TMath::Nint(6./TMath::Sqrt(maxEstimate)); | |
308 | ||
309 | if (maxEstimate<1) return -1; | |
310 | Int_t nbins = his->GetNbinsX(); | |
311 | Int_t npoints=0; | |
312 | // | |
313 | ||
314 | ||
315 | if (xmin>=xmax){ | |
316 | xmin = his->GetXaxis()->GetXmin(); | |
317 | xmax = his->GetXaxis()->GetXmax(); | |
318 | } | |
319 | for (Int_t iter=0; iter<2; iter++){ | |
320 | fitter.ClearPoints(); | |
321 | npoints=0; | |
322 | for (Int_t ibin=1;ibin<nbins+1; ibin++){ | |
323 | Int_t countB=1; | |
324 | Float_t entriesI = his->GetBinContent(ibin); | |
325 | for (Int_t delta = -dsmooth; delta<=dsmooth; delta++){ | |
326 | if (ibin+delta>1 &&ibin+delta<nbins-1){ | |
327 | entriesI += his->GetBinContent(ibin+delta); | |
328 | countB++; | |
329 | } | |
330 | } | |
331 | entriesI/=countB; | |
332 | Double_t xcenter= his->GetBinCenter(ibin); | |
333 | if (xcenter<xmin || xcenter>xmax) continue; | |
334 | Double_t error=1./TMath::Sqrt(countB); | |
335 | Float_t cont=2; | |
336 | if (iter>0){ | |
337 | if (par[0]+par[1]*xcenter+par[2]*xcenter*xcenter>20) return 0; | |
338 | cont = TMath::Exp(par[0]+par[1]*xcenter+par[2]*xcenter*xcenter); | |
339 | if (cont>1.) error = 1./TMath::Sqrt(cont*Float_t(countB)); | |
340 | } | |
341 | if (entriesI>1&&cont>1){ | |
342 | fitter.AddPoint(&xcenter,TMath::Log(Float_t(entriesI)),error); | |
343 | npoints++; | |
344 | } | |
345 | } | |
346 | if (npoints>3){ | |
347 | fitter.Eval(); | |
348 | fitter.GetParameters(par); | |
349 | }else{ | |
350 | break; | |
351 | } | |
352 | } | |
353 | if (npoints<=3){ | |
354 | return -1; | |
355 | } | |
356 | fitter.GetParameters(par); | |
357 | fitter.GetCovarianceMatrix(mat); | |
358 | if (TMath::Abs(par[1])<mat.GetTol()) return -1; | |
359 | if (TMath::Abs(par[2])<mat.GetTol()) return -1; | |
360 | Double_t chi2 = fitter.GetChisquare()/Float_t(npoints); | |
361 | //fitter.GetParameters(); | |
362 | if (!param) param = new TVectorD(3); | |
cb1d20de | 363 | // if (!matrix) matrix = new TMatrixD(3,3); // Covariance matrix to be implemented |
21f3a443 | 364 | (*param)[1] = par[1]/(-2.*par[2]); |
365 | (*param)[2] = 1./TMath::Sqrt(TMath::Abs(-2.*par[2])); | |
366 | (*param)[0] = TMath::Exp(par[0]+ par[1]* (*param)[1] + par[2]*(*param)[1]*(*param)[1]); | |
367 | if (verbose){ | |
368 | par.Print(); | |
369 | mat.Print(); | |
370 | param->Print(); | |
371 | printf("Chi2=%f\n",chi2); | |
372 | TF1 * f1= new TF1("f1","[0]*exp(-(x-[1])^2/(2*[2]*[2]))",his->GetXaxis()->GetXmin(),his->GetXaxis()->GetXmax()); | |
373 | f1->SetParameter(0, (*param)[0]); | |
374 | f1->SetParameter(1, (*param)[1]); | |
375 | f1->SetParameter(2, (*param)[2]); | |
376 | f1->Draw("same"); | |
377 | } | |
378 | return chi2; | |
379 | } | |
380 | ||
cb1d20de | 381 | Double_t TStatToolkit::FitGaus(Float_t *arr, Int_t nBins, Float_t xMin, Float_t xMax, TVectorD *param, TMatrixD */*matrix*/, Bool_t verbose){ |
21f3a443 | 382 | // |
383 | // Fit histogram with gaussian function | |
384 | // | |
385 | // Prameters: | |
386 | // nbins: size of the array and number of histogram bins | |
387 | // xMin, xMax: histogram range | |
388 | // param: paramters of the fit (0-Constant, 1-Mean, 2-Sigma) | |
389 | // matrix: covariance matrix -- not implemented yet, pass dummy matrix!!! | |
390 | // | |
391 | // Return values: | |
392 | // >0: the chi2 returned by TLinearFitter | |
393 | // -3: only three points have been used for the calculation - no fitter was used | |
394 | // -2: only two points have been used for the calculation - center of gravity was uesed for calculation | |
395 | // -1: only one point has been used for the calculation - center of gravity was uesed for calculation | |
396 | // -4: invalid result!! | |
397 | // | |
398 | // Fitting: | |
399 | // 1. Step - make logarithm | |
400 | // 2. Linear fit (parabola) - more robust - always converge | |
401 | // | |
402 | static TLinearFitter fitter(3,"pol2"); | |
403 | static TMatrixD mat(3,3); | |
404 | static Double_t kTol = mat.GetTol(); | |
405 | fitter.StoreData(kFALSE); | |
406 | fitter.ClearPoints(); | |
407 | TVectorD par(3); | |
408 | TVectorD sigma(3); | |
3d7cc0b4 | 409 | TMatrixD matA(3,3); |
21f3a443 | 410 | TMatrixD b(3,1); |
411 | Float_t rms = TMath::RMS(nBins,arr); | |
412 | Float_t max = TMath::MaxElement(nBins,arr); | |
413 | Float_t binWidth = (xMax-xMin)/(Float_t)nBins; | |
414 | ||
415 | Float_t meanCOG = 0; | |
416 | Float_t rms2COG = 0; | |
417 | Float_t sumCOG = 0; | |
418 | ||
419 | Float_t entries = 0; | |
420 | Int_t nfilled=0; | |
421 | ||
422 | for (Int_t i=0; i<nBins; i++){ | |
423 | entries+=arr[i]; | |
424 | if (arr[i]>0) nfilled++; | |
425 | } | |
426 | ||
427 | if (max<4) return -4; | |
428 | if (entries<12) return -4; | |
429 | if (rms<kTol) return -4; | |
430 | ||
431 | Int_t npoints=0; | |
432 | // | |
433 | ||
434 | // | |
435 | for (Int_t ibin=0;ibin<nBins; ibin++){ | |
436 | Float_t entriesI = arr[ibin]; | |
437 | if (entriesI>1){ | |
438 | Double_t xcenter = xMin+(ibin+0.5)*binWidth; | |
439 | ||
440 | Float_t error = 1./TMath::Sqrt(entriesI); | |
441 | Float_t val = TMath::Log(Float_t(entriesI)); | |
442 | fitter.AddPoint(&xcenter,val,error); | |
443 | if (npoints<3){ | |
3d7cc0b4 | 444 | matA(npoints,0)=1; |
445 | matA(npoints,1)=xcenter; | |
446 | matA(npoints,2)=xcenter*xcenter; | |
21f3a443 | 447 | b(npoints,0)=val; |
448 | meanCOG+=xcenter*entriesI; | |
449 | rms2COG +=xcenter*entriesI*xcenter; | |
450 | sumCOG +=entriesI; | |
451 | } | |
452 | npoints++; | |
453 | } | |
454 | } | |
455 | ||
456 | ||
457 | Double_t chi2 = 0; | |
458 | if (npoints>=3){ | |
459 | if ( npoints == 3 ){ | |
460 | //analytic calculation of the parameters for three points | |
3d7cc0b4 | 461 | matA.Invert(); |
21f3a443 | 462 | TMatrixD res(1,3); |
3d7cc0b4 | 463 | res.Mult(matA,b); |
21f3a443 | 464 | par[0]=res(0,0); |
465 | par[1]=res(0,1); | |
466 | par[2]=res(0,2); | |
467 | chi2 = -3.; | |
468 | } else { | |
469 | // use fitter for more than three points | |
470 | fitter.Eval(); | |
471 | fitter.GetParameters(par); | |
472 | fitter.GetCovarianceMatrix(mat); | |
473 | chi2 = fitter.GetChisquare()/Float_t(npoints); | |
474 | } | |
475 | if (TMath::Abs(par[1])<kTol) return -4; | |
476 | if (TMath::Abs(par[2])<kTol) return -4; | |
477 | ||
478 | if (!param) param = new TVectorD(3); | |
cb1d20de | 479 | //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 | 480 | |
481 | (*param)[1] = par[1]/(-2.*par[2]); | |
482 | (*param)[2] = 1./TMath::Sqrt(TMath::Abs(-2.*par[2])); | |
483 | Double_t lnparam0 = par[0]+ par[1]* (*param)[1] + par[2]*(*param)[1]*(*param)[1]; | |
484 | if ( lnparam0>307 ) return -4; | |
485 | (*param)[0] = TMath::Exp(lnparam0); | |
486 | if (verbose){ | |
487 | par.Print(); | |
488 | mat.Print(); | |
489 | param->Print(); | |
490 | printf("Chi2=%f\n",chi2); | |
491 | TF1 * f1= new TF1("f1","[0]*exp(-(x-[1])^2/(2*[2]*[2]))",xMin,xMax); | |
492 | f1->SetParameter(0, (*param)[0]); | |
493 | f1->SetParameter(1, (*param)[1]); | |
494 | f1->SetParameter(2, (*param)[2]); | |
495 | f1->Draw("same"); | |
496 | } | |
497 | return chi2; | |
498 | } | |
499 | ||
500 | if (npoints == 2){ | |
501 | //use center of gravity for 2 points | |
502 | meanCOG/=sumCOG; | |
503 | rms2COG /=sumCOG; | |
504 | (*param)[0] = max; | |
505 | (*param)[1] = meanCOG; | |
506 | (*param)[2] = TMath::Sqrt(TMath::Abs(meanCOG*meanCOG-rms2COG)); | |
507 | chi2=-2.; | |
508 | } | |
509 | if ( npoints == 1 ){ | |
510 | meanCOG/=sumCOG; | |
511 | (*param)[0] = max; | |
512 | (*param)[1] = meanCOG; | |
513 | (*param)[2] = binWidth/TMath::Sqrt(12); | |
514 | chi2=-1.; | |
515 | } | |
516 | return chi2; | |
517 | ||
518 | } | |
519 | ||
520 | ||
3d7cc0b4 | 521 | Float_t TStatToolkit::GetCOG(const Short_t *arr, Int_t nBins, Float_t xMin, Float_t xMax, Float_t *rms, Float_t *sum) |
21f3a443 | 522 | { |
523 | // | |
524 | // calculate center of gravity rms and sum for array 'arr' with nBins an a x range xMin to xMax | |
525 | // return COG; in case of failure return xMin | |
526 | // | |
527 | Float_t meanCOG = 0; | |
528 | Float_t rms2COG = 0; | |
529 | Float_t sumCOG = 0; | |
530 | Int_t npoints = 0; | |
531 | ||
532 | Float_t binWidth = (xMax-xMin)/(Float_t)nBins; | |
533 | ||
534 | for (Int_t ibin=0; ibin<nBins; ibin++){ | |
535 | Float_t entriesI = (Float_t)arr[ibin]; | |
536 | Double_t xcenter = xMin+(ibin+0.5)*binWidth; | |
537 | if ( entriesI>0 ){ | |
538 | meanCOG += xcenter*entriesI; | |
539 | rms2COG += xcenter*entriesI*xcenter; | |
540 | sumCOG += entriesI; | |
541 | npoints++; | |
542 | } | |
543 | } | |
544 | if ( sumCOG == 0 ) return xMin; | |
545 | meanCOG/=sumCOG; | |
546 | ||
547 | if ( rms ){ | |
548 | rms2COG /=sumCOG; | |
549 | (*rms) = TMath::Sqrt(TMath::Abs(meanCOG*meanCOG-rms2COG)); | |
550 | if ( npoints == 1 ) (*rms) = binWidth/TMath::Sqrt(12); | |
551 | } | |
552 | ||
553 | if ( sum ) | |
554 | (*sum) = sumCOG; | |
555 | ||
556 | return meanCOG; | |
557 | } | |
558 | ||
559 | ||
560 | ||
561 | /////////////////////////////////////////////////////////////// | |
562 | ////////////// TEST functions ///////////////////////// | |
563 | /////////////////////////////////////////////////////////////// | |
564 | ||
565 | ||
566 | ||
567 | ||
568 | ||
569 | void TStatToolkit::TestGausFit(Int_t nhistos){ | |
570 | // | |
571 | // Test performance of the parabolic - gaussian fit - compare it with | |
572 | // ROOT gauss fit | |
573 | // nhistos - number of histograms to be used for test | |
574 | // | |
575 | TTreeSRedirector *pcstream = new TTreeSRedirector("fitdebug.root"); | |
576 | ||
577 | Float_t *xTrue = new Float_t[nhistos]; | |
578 | Float_t *sTrue = new Float_t[nhistos]; | |
579 | TVectorD **par1 = new TVectorD*[nhistos]; | |
580 | TVectorD **par2 = new TVectorD*[nhistos]; | |
581 | TMatrixD dummy(3,3); | |
582 | ||
583 | ||
584 | TH1F **h1f = new TH1F*[nhistos]; | |
585 | TF1 *myg = new TF1("myg","gaus"); | |
586 | TF1 *fit = new TF1("fit","gaus"); | |
587 | gRandom->SetSeed(0); | |
588 | ||
589 | //init | |
590 | for (Int_t i=0;i<nhistos; i++){ | |
591 | par1[i] = new TVectorD(3); | |
592 | par2[i] = new TVectorD(3); | |
593 | h1f[i] = new TH1F(Form("h1f%d",i),Form("h1f%d",i),20,-10,10); | |
594 | xTrue[i]= gRandom->Rndm(); | |
595 | gSystem->Sleep(2); | |
596 | sTrue[i]= .75+gRandom->Rndm()*.5; | |
597 | myg->SetParameters(1,xTrue[i],sTrue[i]); | |
598 | h1f[i]->FillRandom("myg"); | |
599 | } | |
600 | ||
601 | TStopwatch s; | |
602 | s.Start(); | |
603 | //standard gaus fit | |
604 | for (Int_t i=0; i<nhistos; i++){ | |
605 | h1f[i]->Fit(fit,"0q"); | |
606 | (*par1[i])(0) = fit->GetParameter(0); | |
607 | (*par1[i])(1) = fit->GetParameter(1); | |
608 | (*par1[i])(2) = fit->GetParameter(2); | |
609 | } | |
610 | s.Stop(); | |
611 | printf("Gaussian fit\t"); | |
612 | s.Print(); | |
613 | ||
614 | s.Start(); | |
615 | //TStatToolkit gaus fit | |
616 | for (Int_t i=0; i<nhistos; i++){ | |
617 | TStatToolkit::FitGaus(h1f[i]->GetArray()+1,h1f[i]->GetNbinsX(),h1f[i]->GetXaxis()->GetXmin(),h1f[i]->GetXaxis()->GetXmax(),par2[i],&dummy); | |
618 | } | |
619 | ||
620 | s.Stop(); | |
621 | printf("Parabolic fit\t"); | |
622 | s.Print(); | |
623 | //write stream | |
624 | for (Int_t i=0;i<nhistos; i++){ | |
625 | Float_t xt = xTrue[i]; | |
626 | Float_t st = sTrue[i]; | |
627 | (*pcstream)<<"data" | |
628 | <<"xTrue="<<xt | |
629 | <<"sTrue="<<st | |
630 | <<"pg.="<<(par1[i]) | |
631 | <<"pa.="<<(par2[i]) | |
632 | <<"\n"; | |
633 | } | |
634 | //delete pointers | |
635 | for (Int_t i=0;i<nhistos; i++){ | |
636 | delete par1[i]; | |
637 | delete par2[i]; | |
638 | delete h1f[i]; | |
639 | } | |
640 | delete pcstream; | |
641 | delete []h1f; | |
642 | delete []xTrue; | |
643 | delete []sTrue; | |
644 | // | |
645 | delete []par1; | |
646 | delete []par2; | |
647 | ||
648 | } | |
649 | ||
650 | ||
651 | ||
652 | TGraph2D * TStatToolkit::MakeStat2D(TH3 * his, Int_t delta0, Int_t delta1, Int_t type){ | |
653 | // | |
654 | // | |
655 | // | |
656 | // delta - number of bins to integrate | |
657 | // type - 0 - mean value | |
658 | ||
659 | TAxis * xaxis = his->GetXaxis(); | |
660 | TAxis * yaxis = his->GetYaxis(); | |
661 | // TAxis * zaxis = his->GetZaxis(); | |
662 | Int_t nbinx = xaxis->GetNbins(); | |
663 | Int_t nbiny = yaxis->GetNbins(); | |
664 | char name[1000]; | |
665 | Int_t icount=0; | |
666 | TGraph2D *graph = new TGraph2D(nbinx*nbiny); | |
667 | TF1 f1("f1","gaus"); | |
668 | for (Int_t ix=0; ix<nbinx;ix++) | |
669 | for (Int_t iy=0; iy<nbiny;iy++){ | |
670 | Float_t xcenter = xaxis->GetBinCenter(ix); | |
671 | Float_t ycenter = yaxis->GetBinCenter(iy); | |
cb1d20de | 672 | snprintf(name,1000,"%s_%d_%d",his->GetName(), ix,iy); |
21f3a443 | 673 | TH1 *projection = his->ProjectionZ(name,ix-delta0,ix+delta0,iy-delta1,iy+delta1); |
674 | Float_t stat= 0; | |
675 | if (type==0) stat = projection->GetMean(); | |
676 | if (type==1) stat = projection->GetRMS(); | |
677 | if (type==2 || type==3){ | |
678 | TVectorD vec(3); | |
679 | TStatToolkit::LTM((TH1F*)projection,&vec,0.7); | |
680 | if (type==2) stat= vec[1]; | |
681 | if (type==3) stat= vec[0]; | |
682 | } | |
683 | if (type==4|| type==5){ | |
684 | projection->Fit(&f1); | |
685 | if (type==4) stat= f1.GetParameter(1); | |
686 | if (type==5) stat= f1.GetParameter(2); | |
687 | } | |
688 | //printf("%d\t%f\t%f\t%f\n", icount,xcenter, ycenter, stat); | |
689 | graph->SetPoint(icount,xcenter, ycenter, stat); | |
690 | icount++; | |
691 | } | |
692 | return graph; | |
693 | } | |
694 | ||
695 | TGraph * TStatToolkit::MakeStat1D(TH3 * his, Int_t delta1, Int_t type){ | |
696 | // | |
697 | // | |
698 | // | |
699 | // delta - number of bins to integrate | |
700 | // type - 0 - mean value | |
701 | ||
702 | TAxis * xaxis = his->GetXaxis(); | |
703 | TAxis * yaxis = his->GetYaxis(); | |
704 | // TAxis * zaxis = his->GetZaxis(); | |
705 | Int_t nbinx = xaxis->GetNbins(); | |
706 | Int_t nbiny = yaxis->GetNbins(); | |
707 | char name[1000]; | |
708 | Int_t icount=0; | |
709 | TGraph *graph = new TGraph(nbinx); | |
710 | TF1 f1("f1","gaus"); | |
711 | for (Int_t ix=0; ix<nbinx;ix++){ | |
712 | Float_t xcenter = xaxis->GetBinCenter(ix); | |
713 | // Float_t ycenter = yaxis->GetBinCenter(iy); | |
cb1d20de | 714 | snprintf(name,1000,"%s_%d",his->GetName(), ix); |
21f3a443 | 715 | TH1 *projection = his->ProjectionZ(name,ix-delta1,ix+delta1,0,nbiny); |
716 | Float_t stat= 0; | |
717 | if (type==0) stat = projection->GetMean(); | |
718 | if (type==1) stat = projection->GetRMS(); | |
719 | if (type==2 || type==3){ | |
720 | TVectorD vec(3); | |
721 | TStatToolkit::LTM((TH1F*)projection,&vec,0.7); | |
722 | if (type==2) stat= vec[1]; | |
723 | if (type==3) stat= vec[0]; | |
724 | } | |
725 | if (type==4|| type==5){ | |
726 | projection->Fit(&f1); | |
727 | if (type==4) stat= f1.GetParameter(1); | |
728 | if (type==5) stat= f1.GetParameter(2); | |
729 | } | |
730 | //printf("%d\t%f\t%f\t%f\n", icount,xcenter, ycenter, stat); | |
731 | graph->SetPoint(icount,xcenter, stat); | |
732 | icount++; | |
733 | } | |
734 | return graph; | |
735 | } | |
736 | ||
737 | ||
738 | ||
739 | ||
740 | ||
88b1c775 | 741 | TString* 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 | 742 | // |
743 | // fit an arbitrary function, specified by formula into the data, specified by drawCommand and cuts | |
744 | // returns chi2, fitParam and covMatrix | |
745 | // returns TString with fitted formula | |
746 | // | |
dd46129c | 747 | |
21f3a443 | 748 | TString formulaStr(formula); |
749 | TString drawStr(drawCommand); | |
750 | TString cutStr(cuts); | |
dd46129c | 751 | TString ferr("1"); |
752 | ||
753 | TString strVal(drawCommand); | |
754 | if (strVal.Contains(":")){ | |
755 | TObjArray* valTokens = strVal.Tokenize(":"); | |
756 | drawStr = valTokens->At(0)->GetName(); | |
757 | ferr = valTokens->At(1)->GetName(); | |
758 | } | |
759 | ||
21f3a443 | 760 | |
761 | formulaStr.ReplaceAll("++", "~"); | |
762 | TObjArray* formulaTokens = formulaStr.Tokenize("~"); | |
763 | Int_t dim = formulaTokens->GetEntriesFast(); | |
764 | ||
765 | fitParam.ResizeTo(dim); | |
766 | covMatrix.ResizeTo(dim,dim); | |
767 | ||
768 | TLinearFitter* fitter = new TLinearFitter(dim+1, Form("hyp%d",dim)); | |
769 | fitter->StoreData(kTRUE); | |
770 | fitter->ClearPoints(); | |
771 | ||
772 | Int_t entries = tree->Draw(drawStr.Data(), cutStr.Data(), "goff", stop-start, start); | |
773 | if (entries == -1) return new TString("An ERROR has occured during fitting!"); | |
774 | Double_t **values = new Double_t*[dim+1] ; | |
dd46129c | 775 | // |
776 | entries = tree->Draw(ferr.Data(), cutStr.Data(), "goff", stop-start, start); | |
b8072cce | 777 | if (entries == -1) { |
778 | delete []values; | |
779 | return new TString("An ERROR has occured during fitting!"); | |
780 | } | |
dd46129c | 781 | Double_t *errors = new Double_t[entries]; |
782 | memcpy(errors, tree->GetV1(), entries*sizeof(Double_t)); | |
21f3a443 | 783 | |
784 | for (Int_t i = 0; i < dim + 1; i++){ | |
785 | Int_t centries = 0; | |
786 | if (i < dim) centries = tree->Draw(((TObjString*)formulaTokens->At(i))->GetName(), cutStr.Data(), "goff", stop-start,start); | |
787 | else centries = tree->Draw(drawStr.Data(), cutStr.Data(), "goff", stop-start,start); | |
788 | ||
b8072cce | 789 | if (entries != centries) { |
790 | delete []errors; | |
791 | delete []values; | |
792 | return new TString("An ERROR has occured during fitting!"); | |
793 | } | |
21f3a443 | 794 | values[i] = new Double_t[entries]; |
795 | memcpy(values[i], tree->GetV1(), entries*sizeof(Double_t)); | |
796 | } | |
797 | ||
798 | // add points to the fitter | |
799 | for (Int_t i = 0; i < entries; i++){ | |
800 | Double_t x[1000]; | |
801 | for (Int_t j=0; j<dim;j++) x[j]=values[j][i]; | |
dd46129c | 802 | fitter->AddPoint(x, values[dim][i], errors[i]); |
21f3a443 | 803 | } |
804 | ||
805 | fitter->Eval(); | |
2c629c56 | 806 | if (frac>0.5 && frac<1){ |
807 | fitter->EvalRobust(frac); | |
88b1c775 | 808 | }else{ |
809 | if (fix0) { | |
810 | fitter->FixParameter(0,0); | |
811 | fitter->Eval(); | |
812 | } | |
2c629c56 | 813 | } |
21f3a443 | 814 | fitter->GetParameters(fitParam); |
815 | fitter->GetCovarianceMatrix(covMatrix); | |
816 | chi2 = fitter->GetChisquare(); | |
b8072cce | 817 | npoints = entries; |
21f3a443 | 818 | TString *preturnFormula = new TString(Form("( %f+",fitParam[0])), &returnFormula = *preturnFormula; |
819 | ||
820 | for (Int_t iparam = 0; iparam < dim; iparam++) { | |
821 | returnFormula.Append(Form("%s*(%f)",((TObjString*)formulaTokens->At(iparam))->GetName(),fitParam[iparam+1])); | |
822 | if (iparam < dim-1) returnFormula.Append("+"); | |
823 | } | |
824 | returnFormula.Append(" )"); | |
4d61c301 | 825 | |
826 | ||
b8072cce | 827 | for (Int_t j=0; j<dim+1;j++) delete [] values[j]; |
4d61c301 | 828 | |
829 | ||
cb1d20de | 830 | delete formulaTokens; |
831 | delete fitter; | |
832 | delete[] values; | |
b8072cce | 833 | delete[] errors; |
cb1d20de | 834 | return preturnFormula; |
835 | } | |
836 | ||
837 | TString* 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){ | |
838 | // | |
839 | // fit an arbitrary function, specified by formula into the data, specified by drawCommand and cuts | |
840 | // returns chi2, fitParam and covMatrix | |
841 | // returns TString with fitted formula | |
842 | // | |
843 | ||
844 | TString formulaStr(formula); | |
845 | TString drawStr(drawCommand); | |
846 | TString cutStr(cuts); | |
847 | TString ferr("1"); | |
848 | ||
849 | TString strVal(drawCommand); | |
850 | if (strVal.Contains(":")){ | |
851 | TObjArray* valTokens = strVal.Tokenize(":"); | |
852 | drawStr = valTokens->At(0)->GetName(); | |
853 | ferr = valTokens->At(1)->GetName(); | |
854 | } | |
855 | ||
856 | ||
857 | formulaStr.ReplaceAll("++", "~"); | |
858 | TObjArray* formulaTokens = formulaStr.Tokenize("~"); | |
859 | Int_t dim = formulaTokens->GetEntriesFast(); | |
860 | ||
861 | fitParam.ResizeTo(dim); | |
862 | covMatrix.ResizeTo(dim,dim); | |
863 | ||
864 | TLinearFitter* fitter = new TLinearFitter(dim+1, Form("hyp%d",dim)); | |
865 | fitter->StoreData(kTRUE); | |
866 | fitter->ClearPoints(); | |
867 | ||
868 | Int_t entries = tree->Draw(drawStr.Data(), cutStr.Data(), "goff", stop-start, start); | |
869 | if (entries == -1) return new TString("An ERROR has occured during fitting!"); | |
870 | Double_t **values = new Double_t*[dim+1] ; | |
871 | // | |
872 | entries = tree->Draw(ferr.Data(), cutStr.Data(), "goff", stop-start, start); | |
b8072cce | 873 | if (entries == -1) { |
874 | delete [] values; | |
875 | return new TString("An ERROR has occured during fitting!"); | |
876 | } | |
cb1d20de | 877 | Double_t *errors = new Double_t[entries]; |
878 | memcpy(errors, tree->GetV1(), entries*sizeof(Double_t)); | |
879 | ||
880 | for (Int_t i = 0; i < dim + 1; i++){ | |
881 | Int_t centries = 0; | |
882 | if (i < dim) centries = tree->Draw(((TObjString*)formulaTokens->At(i))->GetName(), cutStr.Data(), "goff", stop-start,start); | |
883 | else centries = tree->Draw(drawStr.Data(), cutStr.Data(), "goff", stop-start,start); | |
884 | ||
b8072cce | 885 | if (entries != centries) { |
886 | delete []errors; | |
887 | delete []values; | |
888 | return new TString("An ERROR has occured during fitting!"); | |
889 | } | |
cb1d20de | 890 | values[i] = new Double_t[entries]; |
891 | memcpy(values[i], tree->GetV1(), entries*sizeof(Double_t)); | |
892 | } | |
893 | ||
894 | // add points to the fitter | |
895 | for (Int_t i = 0; i < entries; i++){ | |
896 | Double_t x[1000]; | |
897 | for (Int_t j=0; j<dim;j++) x[j]=values[j][i]; | |
898 | fitter->AddPoint(x, values[dim][i], errors[i]); | |
899 | } | |
900 | if (constrain>0){ | |
901 | for (Int_t i = 0; i < dim; i++){ | |
902 | Double_t x[1000]; | |
903 | for (Int_t j=0; j<dim;j++) if (i!=j) x[j]=0; | |
904 | x[i]=1.; | |
905 | fitter->AddPoint(x, 0, constrain); | |
906 | } | |
907 | } | |
908 | ||
909 | ||
910 | fitter->Eval(); | |
911 | if (frac>0.5 && frac<1){ | |
912 | fitter->EvalRobust(frac); | |
913 | } | |
914 | fitter->GetParameters(fitParam); | |
915 | fitter->GetCovarianceMatrix(covMatrix); | |
916 | chi2 = fitter->GetChisquare(); | |
917 | npoints = entries; | |
cb1d20de | 918 | |
919 | TString *preturnFormula = new TString(Form("( %f+",fitParam[0])), &returnFormula = *preturnFormula; | |
920 | ||
921 | for (Int_t iparam = 0; iparam < dim; iparam++) { | |
922 | returnFormula.Append(Form("%s*(%f)",((TObjString*)formulaTokens->At(iparam))->GetName(),fitParam[iparam+1])); | |
923 | if (iparam < dim-1) returnFormula.Append("+"); | |
924 | } | |
925 | returnFormula.Append(" )"); | |
926 | ||
b8072cce | 927 | for (Int_t j=0; j<dim+1;j++) delete [] values[j]; |
cb1d20de | 928 | |
929 | ||
930 | ||
931 | delete formulaTokens; | |
932 | delete fitter; | |
933 | delete[] values; | |
b8072cce | 934 | delete[] errors; |
cb1d20de | 935 | return preturnFormula; |
936 | } | |
937 | ||
938 | ||
939 | ||
940 | TString* 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){ | |
941 | // | |
942 | // fit an arbitrary function, specified by formula into the data, specified by drawCommand and cuts | |
943 | // returns chi2, fitParam and covMatrix | |
944 | // returns TString with fitted formula | |
945 | // | |
946 | ||
947 | TString formulaStr(formula); | |
948 | TString drawStr(drawCommand); | |
949 | TString cutStr(cuts); | |
950 | TString ferr("1"); | |
951 | ||
952 | TString strVal(drawCommand); | |
953 | if (strVal.Contains(":")){ | |
954 | TObjArray* valTokens = strVal.Tokenize(":"); | |
955 | drawStr = valTokens->At(0)->GetName(); | |
956 | ferr = valTokens->At(1)->GetName(); | |
957 | } | |
958 | ||
959 | ||
960 | formulaStr.ReplaceAll("++", "~"); | |
961 | TObjArray* formulaTokens = formulaStr.Tokenize("~"); | |
962 | Int_t dim = formulaTokens->GetEntriesFast(); | |
963 | ||
964 | fitParam.ResizeTo(dim); | |
965 | covMatrix.ResizeTo(dim,dim); | |
966 | TString fitString="x0"; | |
967 | for (Int_t i=1; i<dim; i++) fitString+=Form("++x%d",i); | |
968 | TLinearFitter* fitter = new TLinearFitter(dim, fitString.Data()); | |
969 | fitter->StoreData(kTRUE); | |
970 | fitter->ClearPoints(); | |
971 | ||
972 | Int_t entries = tree->Draw(drawStr.Data(), cutStr.Data(), "goff", stop-start, start); | |
973 | if (entries == -1) return new TString("An ERROR has occured during fitting!"); | |
974 | Double_t **values = new Double_t*[dim+1] ; | |
975 | // | |
976 | entries = tree->Draw(ferr.Data(), cutStr.Data(), "goff", stop-start, start); | |
b8072cce | 977 | if (entries == -1) { |
978 | delete []values; | |
979 | return new TString("An ERROR has occured during fitting!"); | |
980 | } | |
cb1d20de | 981 | Double_t *errors = new Double_t[entries]; |
982 | memcpy(errors, tree->GetV1(), entries*sizeof(Double_t)); | |
983 | ||
984 | for (Int_t i = 0; i < dim + 1; i++){ | |
985 | Int_t centries = 0; | |
986 | if (i < dim) centries = tree->Draw(((TObjString*)formulaTokens->At(i))->GetName(), cutStr.Data(), "goff", stop-start,start); | |
987 | else centries = tree->Draw(drawStr.Data(), cutStr.Data(), "goff", stop-start,start); | |
988 | ||
b8072cce | 989 | if (entries != centries) { |
990 | delete []errors; | |
991 | delete []values; | |
992 | return new TString("An ERROR has occured during fitting!"); | |
993 | } | |
cb1d20de | 994 | values[i] = new Double_t[entries]; |
995 | memcpy(values[i], tree->GetV1(), entries*sizeof(Double_t)); | |
996 | } | |
997 | ||
998 | // add points to the fitter | |
999 | for (Int_t i = 0; i < entries; i++){ | |
1000 | Double_t x[1000]; | |
1001 | for (Int_t j=0; j<dim;j++) x[j]=values[j][i]; | |
1002 | fitter->AddPoint(x, values[dim][i], errors[i]); | |
1003 | } | |
1004 | ||
1005 | fitter->Eval(); | |
1006 | if (frac>0.5 && frac<1){ | |
1007 | fitter->EvalRobust(frac); | |
1008 | } | |
1009 | fitter->GetParameters(fitParam); | |
1010 | fitter->GetCovarianceMatrix(covMatrix); | |
1011 | chi2 = fitter->GetChisquare(); | |
1012 | npoints = entries; | |
cb1d20de | 1013 | |
1014 | TString *preturnFormula = new TString("("), &returnFormula = *preturnFormula; | |
1015 | ||
1016 | for (Int_t iparam = 0; iparam < dim; iparam++) { | |
1017 | returnFormula.Append(Form("%s*(%f)",((TObjString*)formulaTokens->At(iparam))->GetName(),fitParam[iparam])); | |
1018 | if (iparam < dim-1) returnFormula.Append("+"); | |
1019 | } | |
1020 | returnFormula.Append(" )"); | |
1021 | ||
1022 | ||
b8072cce | 1023 | for (Int_t j=0; j<dim+1;j++) delete [] values[j]; |
cb1d20de | 1024 | |
21f3a443 | 1025 | delete formulaTokens; |
1026 | delete fitter; | |
1027 | delete[] values; | |
b8072cce | 1028 | delete[] errors; |
21f3a443 | 1029 | return preturnFormula; |
1030 | } | |
7c9cf6e4 | 1031 | |
1032 | ||
1033 | ||
1034 | ||
1035 | ||
3d7cc0b4 | 1036 | Int_t TStatToolkit::GetFitIndex(const TString fString, const TString subString){ |
7c9cf6e4 | 1037 | // |
1038 | // fitString - ++ separated list of fits | |
1039 | // substring - ++ separated list of the requiered substrings | |
1040 | // | |
1041 | // return the last occurance of substring in fit string | |
1042 | // | |
1043 | TObjArray *arrFit = fString.Tokenize("++"); | |
1044 | TObjArray *arrSub = subString.Tokenize("++"); | |
1045 | Int_t index=-1; | |
1046 | for (Int_t i=0; i<arrFit->GetEntries(); i++){ | |
1047 | Bool_t isOK=kTRUE; | |
1048 | TString str =arrFit->At(i)->GetName(); | |
1049 | for (Int_t isub=0; isub<arrSub->GetEntries(); isub++){ | |
1050 | if (str.Contains(arrSub->At(isub)->GetName())==0) isOK=kFALSE; | |
1051 | } | |
1052 | if (isOK) index=i; | |
1053 | } | |
1054 | return index; | |
1055 | } | |
1056 | ||
1057 | ||
3d7cc0b4 | 1058 | TString TStatToolkit::FilterFit(const TString &input, const TString filter, TVectorD ¶m, TMatrixD & covar){ |
7c9cf6e4 | 1059 | // |
1060 | // Filter fit expression make sub-fit | |
1061 | // | |
1062 | TObjArray *array0= input.Tokenize("++"); | |
1063 | TObjArray *array1= filter.Tokenize("++"); | |
1064 | //TString *presult=new TString("(0"); | |
1065 | TString result="(0.0"; | |
1066 | for (Int_t i=0; i<array0->GetEntries(); i++){ | |
1067 | Bool_t isOK=kTRUE; | |
1068 | TString str(array0->At(i)->GetName()); | |
1069 | for (Int_t j=0; j<array1->GetEntries(); j++){ | |
1070 | if (str.Contains(array1->At(j)->GetName())==0) isOK=kFALSE; | |
1071 | } | |
1072 | if (isOK) { | |
1073 | result+="+"+str; | |
1074 | result+=Form("*(%f)",param[i+1]); | |
1075 | printf("%f\t%f\t%s\n",param[i+1], TMath::Sqrt(covar(i+1,i+1)),str.Data()); | |
1076 | } | |
1077 | } | |
1078 | result+="-0.)"; | |
1079 | return result; | |
1080 | } | |
1081 | ||
1082 | void TStatToolkit::Update1D(Double_t delta, Double_t sigma, Int_t s1, TMatrixD &vecXk, TMatrixD &covXk){ | |
1083 | // | |
1084 | // Update parameters and covariance - with one measurement | |
1085 | // Input: | |
1086 | // vecXk - input vector - Updated in function | |
1087 | // covXk - covariance matrix - Updated in function | |
1088 | // delta, sigma, s1 - new measurement, rms of new measurement and the index of measurement | |
1089 | const Int_t knMeas=1; | |
1090 | Int_t knElem=vecXk.GetNrows(); | |
1091 | ||
1092 | TMatrixD mat1(knElem,knElem); // update covariance matrix | |
1093 | TMatrixD matHk(1,knElem); // vector to mesurement | |
1094 | TMatrixD vecYk(knMeas,1); // Innovation or measurement residual | |
1095 | TMatrixD matHkT(knElem,knMeas); // helper matrix Hk transpose | |
1096 | TMatrixD matSk(knMeas,knMeas); // Innovation (or residual) covariance | |
1097 | TMatrixD matKk(knElem,knMeas); // Optimal Kalman gain | |
1098 | TMatrixD covXk2(knElem,knElem); // helper matrix | |
1099 | TMatrixD covXk3(knElem,knElem); // helper matrix | |
1100 | TMatrixD vecZk(1,1); | |
1101 | TMatrixD measR(1,1); | |
1102 | vecZk(0,0)=delta; | |
1103 | measR(0,0)=sigma*sigma; | |
1104 | // | |
1105 | // reset matHk | |
1106 | for (Int_t iel=0;iel<knElem;iel++) | |
1107 | for (Int_t ip=0;ip<knMeas;ip++) matHk(ip,iel)=0; | |
1108 | //mat1 | |
1109 | for (Int_t iel=0;iel<knElem;iel++) { | |
1110 | for (Int_t jel=0;jel<knElem;jel++) mat1(iel,jel)=0; | |
1111 | mat1(iel,iel)=1; | |
1112 | } | |
1113 | // | |
1114 | matHk(0, s1)=1; | |
1115 | vecYk = vecZk-matHk*vecXk; // Innovation or measurement residual | |
1116 | matHkT=matHk.T(); matHk.T(); | |
1117 | matSk = (matHk*(covXk*matHkT))+measR; // Innovation (or residual) covariance | |
1118 | matSk.Invert(); | |
1119 | matKk = (covXk*matHkT)*matSk; // Optimal Kalman gain | |
1120 | vecXk += matKk*vecYk; // updated vector | |
1121 | covXk2= (mat1-(matKk*matHk)); | |
1122 | covXk3 = covXk2*covXk; | |
1123 | covXk = covXk3; | |
1124 | Int_t nrows=covXk3.GetNrows(); | |
1125 | ||
1126 | for (Int_t irow=0; irow<nrows; irow++) | |
1127 | for (Int_t icol=0; icol<nrows; icol++){ | |
1128 | // rounding problems - make matrix again symteric | |
1129 | covXk(irow,icol)=(covXk3(irow,icol)+covXk3(icol,irow))*0.5; | |
1130 | } | |
1131 | } | |
1132 | ||
1133 | ||
1134 | ||
3d7cc0b4 | 1135 | void TStatToolkit::Constrain1D(const TString &input, const TString filter, TVectorD ¶m, TMatrixD & covar, Double_t mean, Double_t sigma){ |
7c9cf6e4 | 1136 | // |
1137 | // constrain linear fit | |
1138 | // input - string description of fit function | |
1139 | // filter - string filter to select sub fits | |
1140 | // param,covar - parameters and covariance matrix of the fit | |
1141 | // mean,sigma - new measurement uning which the fit is updated | |
1142 | // | |
ae45c94d | 1143 | |
7c9cf6e4 | 1144 | TObjArray *array0= input.Tokenize("++"); |
1145 | TObjArray *array1= filter.Tokenize("++"); | |
1146 | TMatrixD paramM(param.GetNrows(),1); | |
1147 | for (Int_t i=0; i<=array0->GetEntries(); i++){paramM(i,0)=param(i);} | |
1148 | ||
ae45c94d | 1149 | if (filter.Length()==0){ |
1150 | TStatToolkit::Update1D(mean, sigma, 0, paramM, covar);// | |
1151 | }else{ | |
1152 | for (Int_t i=0; i<array0->GetEntries(); i++){ | |
1153 | Bool_t isOK=kTRUE; | |
1154 | TString str(array0->At(i)->GetName()); | |
1155 | for (Int_t j=0; j<array1->GetEntries(); j++){ | |
1156 | if (str.Contains(array1->At(j)->GetName())==0) isOK=kFALSE; | |
1157 | } | |
1158 | if (isOK) { | |
1159 | TStatToolkit::Update1D(mean, sigma, i+1, paramM, covar);// | |
1160 | } | |
7c9cf6e4 | 1161 | } |
1162 | } | |
1163 | for (Int_t i=0; i<=array0->GetEntries(); i++){ | |
1164 | param(i)=paramM(i,0); | |
1165 | } | |
1166 | } | |
1167 | ||
ae45c94d | 1168 | TString TStatToolkit::MakeFitString(const TString &input, const TVectorD ¶m, const TMatrixD & covar, Bool_t verbose){ |
7c9cf6e4 | 1169 | // |
1170 | // | |
1171 | // | |
1172 | TObjArray *array0= input.Tokenize("++"); | |
ae45c94d | 1173 | TString result=Form("(%f",param[0]); |
1174 | printf("%f\t%f\t\n", param[0], TMath::Sqrt(covar(0,0))); | |
7c9cf6e4 | 1175 | for (Int_t i=0; i<array0->GetEntries(); i++){ |
1176 | TString str(array0->At(i)->GetName()); | |
1177 | result+="+"+str; | |
1178 | result+=Form("*(%f)",param[i+1]); | |
ae45c94d | 1179 | if (verbose) printf("%f\t%f\t%s\n", param[i+1], TMath::Sqrt(covar(i+1,i+1)),str.Data()); |
7c9cf6e4 | 1180 | } |
1181 | result+="-0.)"; | |
1182 | return result; | |
1183 | } | |
df0a2a0a | 1184 | |
1185 | ||
1186 | TGraph * TStatToolkit::MakeGraphSparse(TTree * tree, const char * expr, const char * cut){ | |
1187 | // | |
1188 | // Make a sparse draw of the variables | |
1189 | // | |
1190 | const Int_t entries = tree->Draw(expr,cut,"goff"); | |
1191 | // TGraph * graph = (TGraph*)gPad->GetPrimitive("Graph"); // 2D | |
1192 | TGraph * graph = new TGraph (entries, tree->GetV2(),tree->GetV1()); | |
1193 | // | |
1194 | Int_t *index = new Int_t[entries]; | |
1195 | TMath::Sort(entries,graph->GetX(),index,kFALSE); | |
1196 | ||
3d7cc0b4 | 1197 | Double_t *tempArray = new Double_t[entries]; |
df0a2a0a | 1198 | |
1199 | Double_t count = 0.5; | |
baa0041d | 1200 | Double_t *vrun = new Double_t[entries]; |
1201 | Int_t icount=0; | |
1202 | // | |
3d7cc0b4 | 1203 | tempArray[index[0]] = count; |
baa0041d | 1204 | vrun[0] = graph->GetX()[index[0]]; |
df0a2a0a | 1205 | for(Int_t i=1;i<entries;i++){ |
1206 | if(graph->GetX()[index[i]]==graph->GetX()[index[i-1]]) | |
3d7cc0b4 | 1207 | tempArray[index[i]] = count; |
df0a2a0a | 1208 | else if(graph->GetX()[index[i]]!=graph->GetX()[index[i-1]]){ |
1209 | count++; | |
baa0041d | 1210 | icount++; |
3d7cc0b4 | 1211 | tempArray[index[i]] = count; |
baa0041d | 1212 | vrun[icount]=graph->GetX()[index[i]]; |
df0a2a0a | 1213 | } |
1214 | } | |
1215 | ||
1216 | const Int_t newNbins = int(count+0.5); | |
1217 | Double_t *newBins = new Double_t[newNbins+1]; | |
1218 | for(Int_t i=0; i<=count+1;i++){ | |
1219 | newBins[i] = i; | |
1220 | } | |
1221 | ||
3d7cc0b4 | 1222 | TGraph *graphNew = new TGraph(entries,tempArray,graph->GetY()); |
df0a2a0a | 1223 | graphNew->GetXaxis()->Set(newNbins,newBins); |
1224 | ||
1225 | Char_t xName[50]; | |
df0a2a0a | 1226 | for(Int_t i=0;i<count;i++){ |
baa0041d | 1227 | snprintf(xName,50,"%d",Int_t(vrun[i])); |
df0a2a0a | 1228 | graphNew->GetXaxis()->SetBinLabel(i+1,xName); |
1229 | } | |
1230 | graphNew->GetHistogram()->SetTitle(""); | |
1231 | ||
3d7cc0b4 | 1232 | delete [] tempArray; |
df0a2a0a | 1233 | delete [] index; |
1234 | delete [] newBins; | |
baa0041d | 1235 | delete [] vrun; |
df0a2a0a | 1236 | return graphNew; |
1237 | } | |
1238 |