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40df175f | 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 | /* $Id:$ */ | |
17 | ||
18 | /* History of cvs commits: | |
19 | * $Log$ | |
20 | */ | |
21 | ||
22 | //______________________________________________________ | |
23 | // Author : Aleksei Pavlinov; IHEP, Protvino, Russia | |
24 | // Feb 17, 2009 | |
25 | // Implementation of fit procedure from ALICE-INT-2008-026: | |
26 | // "Time and amplitude reconstruction from sampling | |
27 | // measurements of the PHOS signal profile" | |
28 | // M.Yu.Bogolyubsky and .. | |
29 | // | |
30 | // Fit by function en*x*x*exp(-2.*x): x = (t-t0)/tau. | |
31 | // The main goal is fast estimation of amplitude and t0. | |
32 | // | |
33 | ||
34 | // --- AliRoot header files --- | |
35 | #include "AliCaloFastAltroFitv0.h" | |
36 | ||
37 | #include <TH1.h> | |
38 | #include <TF1.h> | |
39 | #include <TCanvas.h> | |
40 | #include <TGraphErrors.h> | |
41 | #include <TMath.h> | |
42 | ||
43 | #include <math.h> | |
44 | ||
45 | ClassImp(AliCaloFastAltroFitv0) | |
46 | ||
47 | //____________________________________________________________________________ | |
48 | AliCaloFastAltroFitv0::AliCaloFastAltroFitv0() | |
49 | : TNamed(), | |
50 | fSig(0),fTau(0),fN(0),fPed(0), fAmp(0),fAmpErr(0),fT0(0),fT0Err(0),fChi2(0.),fNDF(0) | |
51 | ,fNfit(0),fTfit(0),fAmpfit(0), fStdFun(0) | |
52 | { | |
53 | } | |
54 | ||
55 | //____________________________________________________________________________ | |
56 | AliCaloFastAltroFitv0::AliCaloFastAltroFitv0(const char* name, const char* title, | |
57 | const Double_t sig, const Double_t tau, const Double_t n) | |
58 | : TNamed(name, title), | |
59 | fSig(sig),fTau(tau),fN(n),fPed(0), fAmp(0),fAmpErr(0),fT0(0),fT0Err(0),fChi2(0.),fNDF(0) | |
60 | ,fNfit(0),fTfit(0),fAmpfit(0), fStdFun(0) | |
61 | { | |
62 | if(strlen(name)==0) SetName("CaloFastAltroFitv0"); | |
63 | } | |
64 | ||
65 | //____________________________________________________________________________ | |
66 | AliCaloFastAltroFitv0::AliCaloFastAltroFitv0(const AliCaloFastAltroFitv0 &obj) | |
67 | : TNamed(obj), | |
68 | fSig(0),fTau(0),fN(2.),fPed(0), fAmp(0),fAmpErr(0),fT0(0),fT0Err(0),fChi2(0.),fNDF(0) | |
69 | ,fNfit(0),fTfit(0),fAmpfit(0), fStdFun(0) | |
70 | { | |
71 | } | |
72 | ||
73 | //____________________________________________________________________________ | |
74 | AliCaloFastAltroFitv0::~AliCaloFastAltroFitv0() | |
75 | { | |
76 | if(fTfit) delete [] fTfit; | |
77 | if(fAmpfit) delete [] fAmpfit; | |
78 | } | |
79 | ||
80 | //____________________________________________________________________________ | |
81 | AliCaloFastAltroFitv0& AliCaloFastAltroFitv0::operator= (const AliCaloFastAltroFitv0 &/*obj*/) | |
82 | { | |
83 | // Not implemented yet | |
84 | return (*this); | |
85 | } | |
86 | ||
87 | void AliCaloFastAltroFitv0::FastFit(Int_t* t, Int_t* y, Int_t nPoints, Double_t sig, Double_t tau, | |
88 | Double_t n, Double_t ped, Double_t tMax) | |
89 | { | |
90 | // n 2 here and unused | |
91 | n = 2.; | |
92 | Reset(); | |
93 | ||
94 | fSig = sig; | |
95 | fTau = tau; | |
96 | fPed = ped; | |
97 | ||
40df175f | 98 | Int_t ii=0; |
99 | CutRightPart(t,y,nPoints,tMax, ii); | |
100 | nPoints = ii; | |
101 | ||
102 | fNfit = 0; | |
103 | fTfit = new Double_t[nPoints]; | |
104 | fAmpfit = new Double_t[nPoints]; | |
105 | ||
106 | ||
107 | DeductPedestal(t,y,nPoints, tau,ped, fTfit,fAmpfit,fNfit); | |
108 | // printf(" n %i : fNfit %i : ped %f \n", n, fNfit, ped); | |
109 | // for(int i=0; i<fNfit; i++) | |
110 | // printf(" i %i : fAmpfit %7.2f : fTfit %7.2f \n", i, fAmpfit[i], fTfit[i]); | |
111 | ||
112 | if(fNfit>=2) { | |
113 | FastFit(fTfit,fAmpfit,fNfit,sig,tau, fAmp,fAmpErr, fT0,fT0Err,fChi2); | |
114 | ||
115 | if(fChi2> 0.0) fNDF = fNfit - 2; | |
116 | else fNDF = 0; | |
117 | } else if(fNfit==1){ | |
118 | Reset(); // What to do here => fT0 = fTfit[0]; fAmp = fAmpFit[0] ?? | |
119 | } else { | |
120 | Reset(); | |
121 | } | |
122 | } | |
123 | ||
124 | //____________________________________________________________________________ | |
125 | void AliCaloFastAltroFitv0::FastFit(TH1F* h, Double_t sig, Double_t tau, Double_t n, | |
126 | Double_t ped, Double_t tMax) | |
127 | { | |
128 | // Service method for convinience only | |
129 | Reset(); | |
130 | ||
131 | if(h==0) return; | |
132 | Int_t nPoints = h->GetNbinsX(); | |
61f3c0f2 | 133 | if(nPoints<2) return; // Sep 07, 09 |
40df175f | 134 | |
135 | Int_t* t = new Int_t[nPoints]; | |
136 | Int_t* y = new Int_t[nPoints]; | |
137 | ||
138 | for(Int_t i=0; i<nPoints; i++) { | |
139 | t[i] = i+1; | |
140 | y[i] = Int_t(h->GetBinContent(i+1)); | |
141 | } | |
142 | ||
143 | if(nPoints>=2) { | |
144 | FastFit(t,y,nPoints, sig,tau,n,ped, tMax); | |
145 | } | |
146 | ||
147 | delete [] t; | |
148 | delete [] y; | |
149 | } | |
150 | ||
151 | void AliCaloFastAltroFitv0::Reset() | |
152 | { | |
153 | // Reset variables | |
154 | fSig = fTau = 0.0; | |
155 | fAmp = fAmpErr = fT0 = fT0Err = 0.0; | |
156 | fChi2 = -1.; | |
157 | fNDF = fNfit = 0; | |
61f3c0f2 | 158 | |
159 | if(fTfit) delete [] fTfit; | |
160 | if(fAmpfit) delete [] fAmpfit; | |
40df175f | 161 | fTfit = fAmpfit = 0; |
162 | } | |
163 | ||
164 | ||
165 | void AliCaloFastAltroFitv0::GetFitResult(Double_t &,Double_t &eamp,Double_t &t0,Double_t &et0, | |
166 | Double_t &chi2, Int_t &ndf) const | |
167 | { | |
168 | // Return results of fitting procedure | |
169 | amp = fAmp; | |
170 | eamp = fAmpErr; | |
171 | t0 = fT0; | |
172 | et0 = fT0Err; | |
173 | chi2 = fChi2; | |
174 | ndf = fNDF; | |
175 | } | |
176 | ||
177 | void AliCaloFastAltroFitv0::GetFittedPoints(Int_t &nfit, Double_t* ar[2]) const | |
178 | { | |
179 | nfit = fNfit; | |
180 | ar[0] = fTfit; | |
181 | ar[1] = fAmpfit; | |
182 | } | |
183 | // | |
184 | // static functions | |
185 | // | |
186 | void AliCaloFastAltroFitv0::CutRightPart(Int_t *t,Int_t *y,Int_t nPoints,Double_t tMax, Int_t &ii) | |
187 | { | |
61f3c0f2 | 188 | // Cut right part of altro sample : static function |
40df175f | 189 | Int_t tt=0; |
190 | for(Int_t i=0; i<nPoints; i++) { | |
191 | tt = t[i]; | |
192 | if(tMax && tt <= Int_t(tMax)) { | |
193 | t[ii] = tt; | |
194 | y[ii] = y[i]; | |
195 | ii++; | |
196 | } | |
197 | } | |
198 | if(0) printf(" ii %i -> ii %i : tMax %7.2f \n", nPoints, ii, tMax); | |
199 | } | |
200 | ||
201 | void AliCaloFastAltroFitv0::DeductPedestal(Int_t* t, Int_t* y, Int_t n, Double_t tau, Double_t ped, | |
202 | Double_t* tn, Double_t* yn, Int_t &nn) | |
203 | { | |
61f3c0f2 | 204 | // Pedestal deduction if ped is positive : static function |
40df175f | 205 | // Discard part od samle if it is not compact. |
206 | static Double_t yMinUnderPed=2.; // should be tune | |
207 | Int_t ymax=0, nmax=0; | |
208 | for(Int_t i=0; i<n; i++){ | |
209 | if(y[i]>ymax) { | |
210 | ymax = y[i]; | |
211 | nmax = i; | |
212 | } | |
213 | } | |
214 | Int_t i1 = nmax - Int_t(tau); | |
215 | //i1 = 0; | |
216 | i1 = i1<0?0:i1; | |
217 | Int_t i2 = n; | |
218 | ||
219 | nn = 0; | |
220 | Double_t yd=0.0, tdiff=0.0;; | |
221 | for(Int_t i=i1; i<i2; i++) { | |
222 | if(ped>0.0) { | |
223 | yd = Double_t(y[i]) - ped; | |
224 | } else { | |
225 | yd = Double_t(y[i]); | |
226 | } | |
227 | if(yd < yMinUnderPed) continue; | |
228 | ||
229 | if(i>i1 && nn>0){ | |
230 | tdiff = t[i] - tn[nn-1]; | |
231 | // printf(" i %i : nn %i : tdiff %6.2f : tn[nn] %6.2f \n", i,nn, tdiff, tn[nn-1]); | |
232 | if(tdiff>1.) { | |
233 | // discard previous points if its are before maximum point and with gap>1 | |
234 | if(i<nmax ) { | |
235 | nn = 0; // nn--; | |
236 | // if point with gap after maximum - finish selection | |
237 | } else if(i>=nmax ) { | |
238 | break; | |
239 | } | |
240 | } | |
241 | // Far away from maximum | |
242 | //if(i-nmax > Int_t(5*tau)) break; | |
243 | } | |
244 | tn[nn] = Double_t(t[i]); | |
245 | yn[nn] = yd; | |
246 | //printf("i %i : nn %i : tn %6.2f : yn %6.2f \n", i, nn, tn[nn], yn[nn]); | |
247 | nn++; | |
248 | } | |
249 | //printf(" nmax %i : n %i : nn %i i1 %i \n", nmax, n, nn, i1); | |
250 | } | |
251 | ||
252 | void AliCaloFastAltroFitv0::FastFit(const Double_t* t, const Double_t* y, const Int_t n, | |
253 | const Double_t sig, const Double_t tau, | |
254 | Double_t &, Double_t &eamp, Double_t &t0, Double_t &et0, Double_t &chi2) | |
255 | { | |
61f3c0f2 | 256 | // static function |
40df175f | 257 | // It is case of n=k=2 : fnn = x*x*exp(2 - 2*x) |
258 | // Input: | |
259 | // n - number of points | |
260 | // t[n] - array of time bins | |
261 | // y[n] - array of amplitudes after pedestal subtractions; | |
262 | // sig - error of amplitude measurement (one value for all channels) | |
263 | // tau - filter time response (in timebin units) | |
264 | // Output: | |
265 | // amp - amplitude at t0; | |
266 | // t0 - time of max amplitude; | |
267 | static Double_t xx; // t/tau | |
268 | static Double_t a, b, c; | |
269 | static Double_t f02, f12, f22; // functions | |
270 | static Double_t f02d, f12d, f22d; // functions derivations | |
271 | ||
272 | chi2 = -1.; | |
273 | ||
274 | if(n<2) { | |
275 | printf(" AliCaloFastAltroFitv0::FastFit : n<=%i \n", n); | |
276 | return; | |
277 | } | |
278 | ||
279 | a = b = c = 0.0; | |
280 | for(Int_t i=0; i<n; i++){ | |
281 | xx = t[i]/tau; | |
282 | f02 = exp(-2.*xx); | |
283 | f12 = xx*f02; | |
284 | f22 = xx*f12; | |
285 | // Derivations | |
286 | f02d = -2.*f02; | |
287 | f12d = f02 - 2.*f12; | |
288 | f22d = 2.*(f12 - f22); | |
289 | // | |
290 | a += f02d * y[i]; | |
291 | b -= 2.*f12d * y[i]; | |
292 | c += f22d * y[i]; | |
293 | } | |
294 | Double_t t01=0.0, t02=0.0; | |
295 | Double_t amp1=0.0, amp2=0.0, chi21=0.0, chi22=0.0; | |
296 | if(QuadraticRoots(a,b,c, t01,t02)) { | |
297 | t01 *= tau; | |
298 | t02 *= tau; | |
299 | Amplitude(t,y,n, sig, tau, t01, amp1, chi21); | |
300 | Amplitude(t,y,n, sig, tau, t02, amp2, chi22); | |
301 | if(0) { | |
302 | printf(" t01 %f : t02 %f \n", t01, t02); | |
303 | printf(" amp1 %f : amp2 %f \n", amp1, amp2); | |
304 | printf(" chi21 %f : chi22 %f \n", chi21, chi22); | |
305 | } | |
306 | // t0 less on one tau with comparing with value from "canonical equation" | |
307 | amp = amp1; | |
308 | t0 = t01; | |
309 | chi2 = chi21; | |
310 | if(chi21 > chi22) { | |
311 | amp = amp2; | |
312 | t0 = t02; | |
313 | chi2 = chi22; | |
314 | } | |
315 | if(tau<3.) { // EMCAL case : small tau | |
316 | t0 += -0.03; | |
317 | Amplitude(t,y,n, sig, tau, t0, amp, chi2); | |
318 | } | |
319 | CalculateParsErrors(t, y, n, sig, tau, amp, t0, eamp, et0); | |
320 | ||
321 | // Fill1(); | |
322 | ||
323 | // DrawFastFunction(amp, t0, fUtils->GetPedestalValue(), "1"); | |
324 | // DrawFastFunction(amp1, t01, fUtils->GetPedestalValue(), "1"); | |
325 | // DrawFastFunction(amp2, t02, fUtils->GetPedestalValue(), "2"); | |
326 | } else { | |
327 | chi2 = t01; // no roots, bad fit - negative chi2 | |
328 | } | |
329 | } | |
330 | ||
331 | Bool_t AliCaloFastAltroFitv0::QuadraticRoots(const Double_t a, const Double_t b, const Double_t c, | |
332 | Double_t &x1, Double_t &x2) | |
333 | { | |
334 | // Resolve quadratic equations a*x**2 + b*x + c | |
335 | //printf(" a %12.5e b %12.5e c %12.5e \n", a, b, c); | |
336 | static Double_t dtmp = 0.0, dtmpCut = -1.e-6; | |
337 | static Int_t ierr=0; | |
338 | dtmp = b*b - 4.*a*c; | |
339 | ||
340 | if(dtmp>=dtmpCut && dtmp<0.0) { | |
341 | if(ierr<5 || ierr%1000==0) | |
61f3c0f2 | 342 | printf("%i small neg. sq. : dtmp %12.5e \n", ierr, dtmp); |
343 | ierr++; | |
40df175f | 344 | dtmp = 0.0; |
345 | } | |
346 | if(dtmp>=0.0) { | |
347 | dtmp = sqrt(dtmp); | |
348 | x1 = (-b + dtmp) / (2.*a); | |
349 | x2 = (-b - dtmp) / (2.*a); | |
350 | ||
351 | // printf(" x1 %f : x2 %f \n", x1, x2); | |
352 | return kTRUE; | |
353 | } else { | |
354 | x1 = dtmp; | |
61f3c0f2 | 355 | if(ierr<5 || ierr%1000==0) |
356 | printf(" %i neg. sq. : dtmp %12.5e \n", ierr, dtmp); | |
357 | ierr++; | |
40df175f | 358 | return kFALSE; |
359 | } | |
360 | } | |
361 | ||
362 | void AliCaloFastAltroFitv0::Amplitude(const Double_t* t,const Double_t* y,const Int_t n, | |
363 | const Double_t sig, const Double_t tau, const Double_t t0, | |
364 | Double_t &, Double_t &chi2) | |
365 | { | |
366 | // Calculate parameters error too - Mar 24,09 | |
367 | // sig is independent from points | |
368 | amp = 0.; | |
369 | Double_t x=0.0, f=0.0, den=0.0, f02; | |
370 | for(Int_t i=0; i<n; i++){ | |
371 | x = (t[i] - t0)/tau; | |
372 | f02 = exp(-2.*x); | |
373 | f = x*x*f02; | |
374 | amp += f*y[i]; | |
375 | den += f*f; | |
376 | } | |
377 | if(den>0.0) amp /= den; | |
378 | // | |
379 | // chi2 calculation | |
380 | // | |
381 | Double_t dy=0.0; | |
382 | chi2=0.; | |
383 | for(Int_t i=0; i<n; i++){ | |
384 | x = (t[i] - t0)/tau; | |
385 | f02 = exp(-2.*x); | |
386 | f = amp*x*x*f02; | |
387 | dy = y[i]-f; | |
388 | chi2 += dy*dy; | |
389 | // printf(" %i : y %f -> f %f : dy %f \n", i, y[i], f, dy); | |
390 | } | |
391 | chi2 /= (sig*sig); | |
392 | } | |
393 | ||
394 | void AliCaloFastAltroFitv0::CalculateParsErrors(const Double_t* t, const Double_t* /*y*/, const Int_t n, | |
395 | const Double_t sig, const Double_t tau, | |
396 | Double_t &, Double_t &t0, Double_t &eamp, Double_t &et0) | |
397 | { | |
398 | // Remember that fmax = exp(-n); | |
399 | // fmax_nk = (n/k)**n*exp(-n) => n=k=2 => exp(-n) = exp(-2.) | |
400 | static Double_t cc = exp(-2.); | |
401 | // static Double_t cc = exp(-fN); // mean(N)~1.5 ?? | |
402 | ||
403 | Double_t sumf2=0.0, sumfd2=0.0, x, f02, f12, f22, f22d; | |
404 | ||
405 | for(Int_t i=0; i<n; i++){ | |
406 | x = (t[i] - t0)/tau; | |
407 | f02 = exp(-2.*x); | |
408 | f12 = x*f02; | |
409 | f22 = x*f12; | |
410 | sumf2 += f22 * f22; | |
411 | // | |
412 | f22d = 2.*(f12 - f22); | |
413 | sumfd2 += f22d * f22d; | |
414 | } | |
415 | et0 = (sig/amp)/sqrt(sumfd2); | |
416 | eamp = sig/sqrt(sumf2); | |
417 | ||
418 | amp *= cc; | |
419 | eamp *= cc; | |
420 | } | |
421 | ||
422 | // | |
423 | // Drawing | |
424 | // | |
425 | TCanvas* AliCaloFastAltroFitv0::DrawFastFunction() | |
426 | { | |
427 | // QA of fitting | |
428 | if(fNfit<=0) return 0; // no points | |
429 | ||
430 | static TCanvas *c = 0; | |
431 | if(c==0) { | |
432 | c = new TCanvas("fastFun","fastFun",800,600); | |
433 | } | |
434 | ||
435 | c->cd(); | |
436 | ||
437 | Double_t* eamp = new Double_t[fNfit]; | |
438 | Double_t* et = new Double_t[fNfit]; | |
439 | ||
440 | for(Int_t i=0; i<fNfit; i++) { | |
441 | eamp[i] = fSig; | |
442 | et[i] = 0.0; | |
443 | } | |
444 | ||
445 | TGraphErrors *gr = new TGraphErrors(fNfit, fTfit,fAmpfit, et,eamp); | |
446 | gr->Draw("Ap"); | |
447 | gr->SetTitle(Form("Fast Fit : #chi^{2}/ndf = %8.2f / %i", GetChi2(), GetNDF())); | |
448 | gr->GetHistogram()->SetXTitle(" time bin "); | |
449 | gr->GetHistogram()->SetYTitle(" amplitude "); | |
450 | ||
451 | if(fStdFun==0) { | |
452 | fStdFun = new TF1("stdFun", StdResponseFunction, 0., fTfit[fNfit-1]+2., 5); | |
453 | fStdFun->SetParNames("amp","t0","tau","N","ped"); | |
454 | } | |
455 | fStdFun->SetParameter(0, GetEnergy()); | |
456 | fStdFun->SetParameter(1, GetTime() + GetTau()); | |
457 | fStdFun->SetParameter(2, GetTau()); // | |
458 | fStdFun->SetParameter(3, GetN()); // 2 | |
459 | fStdFun->SetParameter(4, 0.); // | |
460 | ||
461 | fStdFun->SetLineColor(kBlue); | |
462 | fStdFun->SetLineWidth(1); | |
463 | ||
464 | fStdFun->Draw("same"); | |
465 | ||
466 | delete [] eamp; | |
467 | delete [] et; | |
468 | ||
469 | c->Update(); | |
470 | ||
471 | return c; | |
472 | } | |
473 | ||
474 | Double_t AliCaloFastAltroFitv0::StdResponseFunction(const Double_t *x, const Double_t *par) | |
475 | { | |
61f3c0f2 | 476 | // Static Standard Response Function : |
40df175f | 477 | // look to Double_t AliEMCALRawUtils::RawResponseFunction(Double_t *x, Double_t *par) |
478 | // Using for drawing only. | |
479 | // | |
480 | // Shape of the electronics raw reponse: | |
481 | // It is a semi-gaussian, 2nd order Gamma function (n=2) of the general form | |
482 | // | |
483 | // t' = (t - t0 + tau) / tau | |
484 | // F = A * t**N * exp( N * ( 1 - t) ) for t >= 0 | |
485 | // F = 0 for t < 0 | |
486 | // | |
487 | // parameters: | |
488 | // A: par[0] // Amplitude = peak value | |
489 | // t0: par[1] | |
490 | // tau: par[2] | |
491 | // N: par[3] | |
492 | // ped: par[4] | |
493 | // | |
494 | static Double_t signal , tau, n, ped, xx; | |
495 | ||
496 | tau = par[2]; | |
497 | n = par[3]; | |
498 | ped = par[4]; | |
499 | xx = ( x[0] - par[1] + tau ) / tau ; | |
500 | ||
501 | if (xx <= 0) | |
502 | signal = ped ; | |
503 | else { | |
504 | signal = ped + par[0] * TMath::Power(xx , n) * TMath::Exp(n * (1 - xx )) ; | |
505 | } | |
506 | return signal ; | |
507 | } |