- fixed coding violations (Gaute)
[u/mrichter/AliRoot.git] / PWG0 / AliUnfolding.cxx
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19442b86 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: AliUnfolding.cxx 31168 2009-02-23 15:18:45Z jgrosseo $ */
17
18// This class allows 1-dimensional unfolding.
19// Methods that are implemented are chi2 minimization and bayesian unfolding.
20//
21// Author: Jan.Fiete.Grosse-Oetringhaus@cern.ch
22
23#include "AliUnfolding.h"
24#include <TH1F.h>
25#include <TH2F.h>
26#include <TVirtualFitter.h>
27#include <TMath.h>
28#include <TCanvas.h>
29#include <TF1.h>
30
31TMatrixD* AliUnfolding::fgCorrelationMatrix = 0;
95e970ca 32TMatrixD* AliUnfolding::fgCorrelationMatrixSquared = 0;
19442b86 33TMatrixD* AliUnfolding::fgCorrelationCovarianceMatrix = 0;
34TVectorD* AliUnfolding::fgCurrentESDVector = 0;
35TVectorD* AliUnfolding::fgEntropyAPriori = 0;
95e970ca 36TVectorD* AliUnfolding::fgEfficiency = 0;
37TVectorD* AliUnfolding::fgBinWidths = 0;
19442b86 38
39TF1* AliUnfolding::fgFitFunction = 0;
40
41AliUnfolding::MethodType AliUnfolding::fgMethodType = AliUnfolding::kInvalid;
42Int_t AliUnfolding::fgMaxInput = -1; // bins in measured histogram
43Int_t AliUnfolding::fgMaxParams = -1; // bins in unfolded histogram = number of fit params
44Float_t AliUnfolding::fgOverflowBinLimit = -1;
45
46AliUnfolding::RegularizationType AliUnfolding::fgRegularizationType = AliUnfolding::kPol1;
47Float_t AliUnfolding::fgRegularizationWeight = 10000;
48Int_t AliUnfolding::fgSkipBinsBegin = 0;
49Float_t AliUnfolding::fgMinuitStepSize = 0.1; // (usually not needed to be changed) step size in minimization
95e970ca 50Bool_t AliUnfolding::fgMinimumInitialValue = kFALSE; // set all initial values at least to the smallest value among the initial values
51Float_t AliUnfolding::fgMinimumInitialValueFix = -1;
19442b86 52Bool_t AliUnfolding::fgNormalizeInput = kFALSE; // normalize input spectrum
95e970ca 53Float_t AliUnfolding::fgNotFoundEvents = 0;
54Bool_t AliUnfolding::fgSkipBin0InChi2 = kFALSE;
19442b86 55
56Float_t AliUnfolding::fgBayesianSmoothing = 1; // smoothing parameter (0 = no smoothing)
651e2088 57Int_t AliUnfolding::fgBayesianIterations = 10; // number of iterations in Bayesian method
19442b86 58
59Bool_t AliUnfolding::fgDebug = kFALSE;
60
95e970ca 61Int_t AliUnfolding::fgCallCount = 0;
62
19442b86 63ClassImp(AliUnfolding)
64
65//____________________________________________________________________
66void AliUnfolding::SetUnfoldingMethod(MethodType methodType)
67{
68 // set unfolding method
69 fgMethodType = methodType;
70
71 const char* name = 0;
72 switch (methodType)
73 {
74 case kInvalid: name = "INVALID"; break;
75 case kChi2Minimization: name = "Chi2 Minimization"; break;
76 case kBayesian: name = "Bayesian unfolding"; break;
77 case kFunction: name = "Functional fit"; break;
78 }
79 Printf("AliUnfolding::SetUnfoldingMethod: %s enabled.", name);
80}
81
82//____________________________________________________________________
83void AliUnfolding::SetCreateOverflowBin(Float_t overflowBinLimit)
84{
85 // enable the creation of a overflow bin that includes all statistics below the given limit
86
87 fgOverflowBinLimit = overflowBinLimit;
88
89 Printf("AliUnfolding::SetCreateOverflowBin: overflow bin limit set to %f", overflowBinLimit);
90}
91
92//____________________________________________________________________
93void AliUnfolding::SetSkipBinsBegin(Int_t nBins)
94{
95 // set number of skipped bins in regularization
96
97 fgSkipBinsBegin = nBins;
98
99 Printf("AliUnfolding::SetSkipBinsBegin: skipping %d bins at the beginning of the spectrum in the regularization.", fgSkipBinsBegin);
100}
101
102//____________________________________________________________________
103void AliUnfolding::SetNbins(Int_t nMeasured, Int_t nUnfolded)
104{
105 // set number of bins in the input (measured) distribution and in the unfolded distribution
106 fgMaxInput = nMeasured;
107 fgMaxParams = nUnfolded;
108
95e970ca 109 if (fgCorrelationMatrix)
110 {
111 delete fgCorrelationMatrix;
112 fgCorrelationMatrix = 0;
113 }
114 if (fgCorrelationMatrixSquared)
115 {
116 fgCorrelationMatrixSquared = 0;
117 delete fgCorrelationMatrixSquared;
118 }
119 if (fgCorrelationCovarianceMatrix)
120 {
121 delete fgCorrelationCovarianceMatrix;
122 fgCorrelationCovarianceMatrix = 0;
123 }
124 if (fgCurrentESDVector)
125 {
126 delete fgCurrentESDVector;
127 fgCurrentESDVector = 0;
128 }
129 if (fgEntropyAPriori)
130 {
131 delete fgEntropyAPriori;
132 fgEntropyAPriori = 0;
133 }
134 if (fgEfficiency)
135 {
136 delete fgEfficiency;
137 fgEfficiency = 0;
138 }
139 if (fgBinWidths)
140 {
141 delete fgBinWidths;
142 fgBinWidths = 0;
143 }
144
19442b86 145 Printf("AliUnfolding::SetNbins: Set %d measured bins and %d unfolded bins", nMeasured, nUnfolded);
146}
147
148//____________________________________________________________________
149void AliUnfolding::SetChi2Regularization(RegularizationType type, Float_t weight)
150{
151 //
152 // sets the parameters for chi2 minimization
153 //
154
155 fgRegularizationType = type;
156 fgRegularizationWeight = weight;
157
158 Printf("AliUnfolding::SetChi2Regularization --> Regularization set to %d with weight %f", (Int_t) type, weight);
159}
160
161//____________________________________________________________________
162void AliUnfolding::SetBayesianParameters(Float_t smoothing, Int_t nIterations)
163{
164 //
165 // sets the parameters for Bayesian unfolding
166 //
167
168 fgBayesianSmoothing = smoothing;
169 fgBayesianIterations = nIterations;
170
171 Printf("AliUnfolding::SetBayesianParameters --> Paramaters set to %d iterations with smoothing %f", fgBayesianIterations, fgBayesianSmoothing);
172}
173
174//____________________________________________________________________
175void AliUnfolding::SetFunction(TF1* function)
176{
177 // set function for unfolding with a fit function
178
179 fgFitFunction = function;
180
181 Printf("AliUnfolding::SetFunction: Set fit function with %d parameters.", function->GetNpar());
182}
183
184//____________________________________________________________________
185Int_t AliUnfolding::Unfold(TH2* correlation, TH1* efficiency, TH1* measured, TH1* initialConditions, TH1* result, Bool_t check)
186{
187 // unfolds with unfolding method fgMethodType
188 //
189 // parameters:
190 // correlation: response matrix as measured vs. generated
191 // efficiency: (optional) efficiency that is applied on the unfolded spectrum, i.e. it has to be in unfolded variables. If 0 no efficiency is applied.
192 // measured: the measured spectrum
193 // initialConditions: (optional) initial conditions for the unfolding. if 0 the measured spectrum is used as initial conditions.
194 // result: target for the unfolded result
195 // check: depends on the unfolding method, see comments in specific functions
95e970ca 196 //
197 // return code: see UnfoldWithMinuit/UnfoldWithBayesian/UnfoldWithFunction
19442b86 198
199 if (fgMaxInput == -1)
200 {
201 Printf("AliUnfolding::Unfold: WARNING. Number of measured bins not set with SetNbins. Using number of bins in measured distribution");
202 fgMaxInput = measured->GetNbinsX();
203 }
204 if (fgMaxParams == -1)
205 {
206 Printf("AliUnfolding::Unfold: WARNING. Number of unfolded bins not set with SetNbins. Using number of bins in measured distribution");
207 fgMaxParams = measured->GetNbinsX();
208 }
209
210 if (fgOverflowBinLimit > 0)
211 CreateOverflowBin(correlation, measured);
212
213 switch (fgMethodType)
214 {
215 case kInvalid:
216 {
217 Printf("AliUnfolding::Unfold: ERROR: Unfolding method not set. Use SetUnfoldingMethod. Exiting...");
218 return -1;
219 }
220 case kChi2Minimization:
221 return UnfoldWithMinuit(correlation, efficiency, measured, initialConditions, result, check);
222 case kBayesian:
223 return UnfoldWithBayesian(correlation, efficiency, measured, initialConditions, result);
224 case kFunction:
225 return UnfoldWithFunction(correlation, efficiency, measured, initialConditions, result);
226 }
227 return -1;
228}
229
230//____________________________________________________________________
95e970ca 231void AliUnfolding::SetStaticVariables(TH2* correlation, TH1* measured, TH1* efficiency)
19442b86 232{
233 // fill static variables needed for minuit fit
234
235 if (!fgCorrelationMatrix)
236 fgCorrelationMatrix = new TMatrixD(fgMaxInput, fgMaxParams);
95e970ca 237 if (!fgCorrelationMatrixSquared)
238 fgCorrelationMatrixSquared = new TMatrixD(fgMaxInput, fgMaxParams);
19442b86 239 if (!fgCorrelationCovarianceMatrix)
240 fgCorrelationCovarianceMatrix = new TMatrixD(fgMaxInput, fgMaxInput);
241 if (!fgCurrentESDVector)
242 fgCurrentESDVector = new TVectorD(fgMaxInput);
243 if (!fgEntropyAPriori)
244 fgEntropyAPriori = new TVectorD(fgMaxParams);
95e970ca 245 if (!fgEfficiency)
246 fgEfficiency = new TVectorD(fgMaxParams);
247 if (!fgBinWidths)
248 fgBinWidths = new TVectorD(fgMaxParams);
249
19442b86 250 fgCorrelationMatrix->Zero();
251 fgCorrelationCovarianceMatrix->Zero();
252 fgCurrentESDVector->Zero();
253 fgEntropyAPriori->Zero();
254
255 // normalize correction for given nPart
256 for (Int_t i=1; i<=correlation->GetNbinsX(); ++i)
257 {
258 Double_t sum = correlation->Integral(i, i, 1, correlation->GetNbinsY());
259 if (sum <= 0)
260 continue;
261 Float_t maxValue = 0;
262 Int_t maxBin = -1;
263 for (Int_t j=1; j<=correlation->GetNbinsY(); ++j)
264 {
265 // find most probably value
266 if (maxValue < correlation->GetBinContent(i, j))
267 {
268 maxValue = correlation->GetBinContent(i, j);
269 maxBin = j;
270 }
271
272 // npart sum to 1
95e970ca 273 correlation->SetBinContent(i, j, correlation->GetBinContent(i, j) / sum);// * correlation->GetXaxis()->GetBinWidth(i));
19442b86 274 correlation->SetBinError(i, j, correlation->GetBinError(i, j) / sum);
275
276 if (i <= fgMaxParams && j <= fgMaxInput)
95e970ca 277 {
19442b86 278 (*fgCorrelationMatrix)(j-1, i-1) = correlation->GetBinContent(i, j);
95e970ca 279 (*fgCorrelationMatrixSquared)(j-1, i-1) = correlation->GetBinContent(i, j) * correlation->GetBinContent(i, j);
280 }
19442b86 281 }
282
283 //printf("MPV for Ntrue = %f is %f\n", fCurrentCorrelation->GetXaxis()->GetBinCenter(i), fCurrentCorrelation->GetYaxis()->GetBinCenter(maxBin));
284 }
285
286 //normalize measured
95e970ca 287 Float_t smallestError = 1;
19442b86 288 if (fgNormalizeInput)
95e970ca 289 {
290 Float_t sumMeasured = measured->Integral();
291 measured->Scale(1.0 / sumMeasured);
292 smallestError /= sumMeasured;
293 }
19442b86 294
295 for (Int_t i=0; i<fgMaxInput; ++i)
296 {
297 (*fgCurrentESDVector)[i] = measured->GetBinContent(i+1);
298 if (measured->GetBinError(i+1) > 0)
95e970ca 299 {
19442b86 300 (*fgCorrelationCovarianceMatrix)(i, i) = (Double_t) 1e-6 / measured->GetBinError(i+1) / measured->GetBinError(i+1);
95e970ca 301 }
302 else // in this case put error of 1, otherwise 0 bins are not added to the chi2...
303 (*fgCorrelationCovarianceMatrix)(i, i) = (Double_t) 1e-6 / smallestError / smallestError;
19442b86 304
305 if ((*fgCorrelationCovarianceMatrix)(i, i) > 1e7)
306 (*fgCorrelationCovarianceMatrix)(i, i) = 0;
307 //Printf("%d, %e", i, (*fgCorrelationCovarianceMatrix)(i, i));
308 }
95e970ca 309
310 // efficiency is expected to match bin width of result
311 for (Int_t i=0; i<fgMaxParams; ++i)
312 {
313 (*fgEfficiency)(i) = efficiency->GetBinContent(i+1);
314 (*fgBinWidths)(i) = efficiency->GetXaxis()->GetBinWidth(i+1);
315 }
19442b86 316}
317
318//____________________________________________________________________
319Int_t AliUnfolding::UnfoldWithMinuit(TH2* correlation, TH1* efficiency, TH1* measured, TH1* initialConditions, TH1* result, Bool_t check)
320{
321 //
322 // implementation of unfolding (internal function)
323 //
324 // unfolds <measured> using response from <correlation> and effiency <efficiency>
325 // output is in <result>
326 // <initialConditions> set the initial values for the minimization, if 0 <measured> is used
95e970ca 327 // negative values in initialConditions mean that the given parameter is fixed to the absolute of the value
19442b86 328 // if <check> is true no unfolding is made, instead only the chi2 without unfolding is printed
329 //
330 // returns minuit status (0 = success), (-1 when check was set)
331 //
332
95e970ca 333 SetStaticVariables(correlation, measured, efficiency);
19442b86 334
335 // Initialize TMinuit via generic fitter interface
95e970ca 336 Int_t params = fgMaxParams;
337 if (fgNotFoundEvents > 0)
338 params++;
339
340 TVirtualFitter *minuit = TVirtualFitter::Fitter(0, params);
19442b86 341 Double_t arglist[100];
342
343 // disable any output (-1), unfortuantly we do not see warnings anymore then. Have to find another way...
344 arglist[0] = 0;
345 minuit->ExecuteCommand("SET PRINT", arglist, 1);
346
347 // however, enable warnings
348 //minuit->ExecuteCommand("SET WAR", arglist, 0);
349
350 // set minimization function
351 minuit->SetFCN(Chi2Function);
352
353 for (Int_t i=0; i<fgMaxParams; i++)
354 (*fgEntropyAPriori)[i] = 1;
355
95e970ca 356 // set initial conditions as a-priori distribution for MRX regularization
357 /*
358 for (Int_t i=0; i<fgMaxParams; i++)
359 if (initialConditions && initialConditions->GetBinContent(i+1) > 0)
360 (*fgEntropyAPriori)[i] = initialConditions->GetBinContent(i+1);
361 */
362
19442b86 363 if (!initialConditions) {
364 initialConditions = measured;
365 } else {
366 Printf("AliUnfolding::UnfoldWithMinuit: Using different initial conditions...");
367 //new TCanvas; initialConditions->DrawCopy();
368 if (fgNormalizeInput)
369 initialConditions->Scale(1.0 / initialConditions->Integral());
370 }
371
95e970ca 372 // extract minimum value from initial conditions (if we set a value to 0 it will stay 0)
373 Float_t minValue = 1e100;
374 if (fgMinimumInitialValueFix < 0)
375 {
376 for (Int_t i=0; i<fgMaxParams; ++i)
377 {
378 Int_t bin = initialConditions->GetXaxis()->FindBin(result->GetXaxis()->GetBinCenter(i+1));
379 if (initialConditions->GetBinContent(bin) > 0)
380 minValue = TMath::Min(minValue, (Float_t) initialConditions->GetBinContent(bin));
381 }
382 }
383 else
384 minValue = fgMinimumInitialValueFix;
385
19442b86 386 Double_t* results = new Double_t[fgMaxParams+1];
387 for (Int_t i=0; i<fgMaxParams; ++i)
388 {
95e970ca 389 Int_t bin = initialConditions->GetXaxis()->FindBin(result->GetXaxis()->GetBinCenter(i+1));
390 results[i] = initialConditions->GetBinContent(bin);
19442b86 391
95e970ca 392 Bool_t fix = kFALSE;
393 if (results[i] < 0)
394 {
395 fix = kTRUE;
396 results[i] = -results[i];
397 }
398
399 if (!fix && fgMinimumInitialValue && results[i] < minValue)
400 results[i] = minValue;
401
19442b86 402 // minuit sees squared values to prevent it from going negative...
403 results[i] = TMath::Sqrt(results[i]);
404
95e970ca 405 minuit->SetParameter(i, Form("param%d", i), results[i], (fix) ? 0 : fgMinuitStepSize, 0, 0);
406 }
407 if (fgNotFoundEvents > 0)
408 {
409 results[fgMaxParams] = efficiency->GetBinContent(1);
410 minuit->SetParameter(fgMaxParams, "vtx0", results[fgMaxParams], fgMinuitStepSize / 100, 0.01, 0.80);
19442b86 411 }
412
413 Int_t dummy = 0;
414 Double_t chi2 = 0;
415 Chi2Function(dummy, 0, chi2, results, 0);
416 printf("AliUnfolding::UnfoldWithMinuit: Chi2 of initial parameters is = %f\n", chi2);
417
418 if (check)
419 {
420 DrawGuess(results);
421 delete[] results;
422 return -1;
423 }
424
425 // first param is number of iterations, second is precision....
426 arglist[0] = 1e6;
427 //arglist[1] = 1e-5;
428 //minuit->ExecuteCommand("SCAN", arglist, 0);
429 Int_t status = minuit->ExecuteCommand("MIGRAD", arglist, 1);
430 Printf("AliUnfolding::UnfoldWithMinuit: MINUIT status is %d", status);
431 //printf("!!!!!!!!!!!!!! MIGRAD finished: Starting MINOS !!!!!!!!!!!!!!");
432 //minuit->ExecuteCommand("MINOS", arglist, 0);
433
95e970ca 434 if (fgNotFoundEvents > 0)
435 {
436 results[fgMaxParams] = minuit->GetParameter(fgMaxParams);
437 Printf("Efficiency for bin 0 changed from %f to %f", efficiency->GetBinContent(1), results[fgMaxParams]);
438 efficiency->SetBinContent(1, results[fgMaxParams]);
439 }
440
19442b86 441 for (Int_t i=0; i<fgMaxParams; ++i)
442 {
443 results[i] = minuit->GetParameter(i);
444 Double_t value = results[i] * results[i];
445 // error is : (relError) * (value) = (minuit->GetParError(i) / minuit->GetParameter(i)) * (minuit->GetParameter(i) * minuit->GetParameter(i))
446 Double_t error = minuit->GetParError(i) * results[i];
447
448 if (efficiency)
95e970ca 449 {
19442b86 450 if (efficiency->GetBinContent(i+1) > 0)
451 {
95e970ca 452 value /= efficiency->GetBinContent(i+1);
453 error /= efficiency->GetBinContent(i+1);
19442b86 454 }
455 else
456 {
95e970ca 457 value = 0;
458 error = 0;
19442b86 459 }
460 }
461
462 result->SetBinContent(i+1, value);
463 result->SetBinError(i+1, error);
464 }
465
95e970ca 466 fgCallCount = 0;
467 Chi2Function(dummy, 0, chi2, results, 0);
468 printf("AliUnfolding::UnfoldWithMinuit: Chi2 of final parameters is = %f\n", chi2);
469
19442b86 470 if (fgDebug)
471 DrawGuess(results);
472
473 delete[] results;
474
475 return status;
476}
477
478//____________________________________________________________________
479Int_t AliUnfolding::UnfoldWithBayesian(TH2* correlation, TH1* aEfficiency, TH1* measured, TH1* initialConditions, TH1* aResult)
480{
481 //
482 // unfolds a spectrum using the Bayesian method
483 //
484
485 if (measured->Integral() <= 0)
486 {
487 Printf("AliUnfolding::UnfoldWithBayesian: ERROR: The measured spectrum is empty");
488 return -1;
489 }
490
491 const Int_t kStartBin = 0;
492
493 Int_t kMaxM = fgMaxInput; //<= fCurrentCorrelation->GetNbinsY(); // max measured axis
494 Int_t kMaxT = fgMaxParams; //<= fCurrentCorrelation->GetNbinsX(); // max true axis
495
496 // convergence limit: kMaxT * 0.001^2 = kMaxT * 1e-6 (e.g. 250 bins --> 2.5 e-4)
497 const Double_t kConvergenceLimit = kMaxT * 1e-6;
498
499 // store information in arrays, to increase processing speed (~ factor 5)
500 Double_t* measuredCopy = new Double_t[kMaxM];
501 Double_t* measuredError = new Double_t[kMaxM];
502 Double_t* prior = new Double_t[kMaxT];
503 Double_t* result = new Double_t[kMaxT];
504 Double_t* efficiency = new Double_t[kMaxT];
95e970ca 505 Double_t* binWidths = new Double_t[kMaxT];
19442b86 506
507 Double_t** response = new Double_t*[kMaxT];
508 Double_t** inverseResponse = new Double_t*[kMaxT];
509 for (Int_t i=0; i<kMaxT; i++)
510 {
511 response[i] = new Double_t[kMaxM];
512 inverseResponse[i] = new Double_t[kMaxM];
513 }
514
515 // for normalization
516 Float_t measuredIntegral = measured->Integral();
517 for (Int_t m=0; m<kMaxM; m++)
518 {
519 measuredCopy[m] = measured->GetBinContent(m+1) / measuredIntegral;
520 measuredError[m] = measured->GetBinError(m+1) / measuredIntegral;
521
522 for (Int_t t=0; t<kMaxT; t++)
523 {
524 response[t][m] = correlation->GetBinContent(t+1, m+1);
525 inverseResponse[t][m] = 0;
526 }
527 }
528
529 for (Int_t t=0; t<kMaxT; t++)
530 {
651e2088 531 if (aEfficiency)
19442b86 532 {
533 efficiency[t] = aEfficiency->GetBinContent(t+1);
534 }
535 else
536 efficiency[t] = 1;
537
538 prior[t] = measuredCopy[t];
539 result[t] = 0;
95e970ca 540 binWidths[t] = aResult->GetXaxis()->GetBinWidth(t+1);
19442b86 541 }
542
543 // pick prior distribution
544 if (initialConditions)
545 {
546 printf("Using different starting conditions...\n");
547 // for normalization
548 Float_t inputDistIntegral = initialConditions->Integral();
549 for (Int_t i=0; i<kMaxT; i++)
550 prior[i] = initialConditions->GetBinContent(i+1) / inputDistIntegral;
551 }
552
553 //TH1F* convergence = new TH1F("convergence", "convergence", 200, 0.5, 200.5);
554
95e970ca 555 //new TCanvas;
19442b86 556 // unfold...
95e970ca 557 for (Int_t i=0; i<fgBayesianIterations || fgBayesianIterations < 0; i++)
19442b86 558 {
559 if (fgDebug)
560 Printf("AliUnfolding::UnfoldWithBayesian: iteration %i", i);
561
95e970ca 562 // calculate IR from Bayes theorem
19442b86 563 // IR_ji = R_ij * prior_i / sum_k(R_kj * prior_k)
564
565 Double_t chi2Measured = 0;
566 for (Int_t m=0; m<kMaxM; m++)
567 {
568 Float_t norm = 0;
569 for (Int_t t = kStartBin; t<kMaxT; t++)
570 norm += response[t][m] * prior[t];
571
572 // calc. chi2: (measured - response * prior) / error
573 if (measuredError[m] > 0)
574 {
575 Double_t value = (measuredCopy[m] - norm) / measuredError[m];
576 chi2Measured += value * value;
577 }
578
579 if (norm > 0)
580 {
581 for (Int_t t = kStartBin; t<kMaxT; t++)
582 inverseResponse[t][m] = response[t][m] * prior[t] / norm;
583 }
584 else
585 {
586 for (Int_t t = kStartBin; t<kMaxT; t++)
587 inverseResponse[t][m] = 0;
588 }
589 }
590 //Printf("chi2Measured of the last prior is %e", chi2Measured);
591
592 for (Int_t t = kStartBin; t<kMaxT; t++)
593 {
594 Float_t value = 0;
595 for (Int_t m=0; m<kMaxM; m++)
596 value += inverseResponse[t][m] * measuredCopy[m];
597
598 if (efficiency[t] > 0)
599 result[t] = value / efficiency[t];
600 else
601 result[t] = 0;
602 }
603
95e970ca 604 /*
19442b86 605 // draw intermediate result
19442b86 606 for (Int_t t=0; t<kMaxT; t++)
95e970ca 607 {
19442b86 608 aResult->SetBinContent(t+1, result[t]);
95e970ca 609 }
610 aResult->SetMarkerStyle(24+i);
19442b86 611 aResult->SetMarkerColor(2);
95e970ca 612 aResult->DrawCopy((i == 0) ? "P" : "PSAME");
19442b86 613 */
95e970ca 614
19442b86 615 Double_t chi2LastIter = 0;
616 // regularization (simple smoothing)
617 for (Int_t t=kStartBin; t<kMaxT; t++)
618 {
619 Float_t newValue = 0;
620
621 // 0 bin excluded from smoothing
622 if (t > kStartBin+2 && t<kMaxT-1)
623 {
95e970ca 624 Float_t average = (result[t-1] / binWidths[t-1] + result[t] / binWidths[t] + result[t+1] / binWidths[t+1]) / 3 * binWidths[t];
19442b86 625
626 // weight the average with the regularization parameter
627 newValue = (1 - fgBayesianSmoothing) * result[t] + fgBayesianSmoothing * average;
628 }
629 else
630 newValue = result[t];
631
632 // calculate chi2 (change from last iteration)
633 if (prior[t] > 1e-5)
634 {
635 Double_t diff = (prior[t] - newValue) / prior[t];
636 chi2LastIter += diff * diff;
637 }
638
639 prior[t] = newValue;
640 }
641 //printf("Chi2 of %d iteration = %e\n", i, chi2LastIter);
642 //convergence->Fill(i+1, chi2LastIter);
643
644 if (fgBayesianIterations < 0 && chi2LastIter < kConvergenceLimit)
645 {
646 Printf("AliUnfolding::UnfoldWithBayesian: Stopped Bayesian unfolding after %d iterations at chi2(change since last iteration) of %e; chi2Measured of the last prior is %e", i, chi2LastIter, chi2Measured);
647 break;
648 }
649 } // end of iterations
650
651 //new TCanvas; convergence->DrawCopy(); gPad->SetLogy();
652 //delete convergence;
653
95e970ca 654 Float_t factor = 1;
655 if (!fgNormalizeInput)
656 factor = measuredIntegral;
19442b86 657 for (Int_t t=0; t<kMaxT; t++)
95e970ca 658 aResult->SetBinContent(t+1, result[t] * factor);
19442b86 659
660 delete[] measuredCopy;
661 delete[] measuredError;
662 delete[] prior;
663 delete[] result;
664 delete[] efficiency;
95e970ca 665 delete[] binWidths;
19442b86 666
667 for (Int_t i=0; i<kMaxT; i++)
668 {
669 delete[] response[i];
670 delete[] inverseResponse[i];
671 }
672 delete[] response;
673 delete[] inverseResponse;
674
675 return 0;
676
677 // ********
678 // Calculate the covariance matrix, all arguments are taken from NIM,A362,487-498,1995
679
680 /*printf("Calculating covariance matrix. This may take some time...\n");
681
682 // check if this is the right one...
683 TH1* sumHist = GetMultiplicityMC(inputRange, eventType)->ProjectionY("sumHist", 1, GetMultiplicityMC(inputRange, eventType)->GetNbinsX());
684
685 Int_t xBins = hInverseResponseBayes->GetNbinsX();
686 Int_t yBins = hInverseResponseBayes->GetNbinsY();
687
688 // calculate "unfolding matrix" Mij
689 Float_t matrixM[251][251];
690 for (Int_t i=1; i<=xBins; i++)
691 {
692 for (Int_t j=1; j<=yBins; j++)
693 {
694 if (fCurrentEfficiency->GetBinContent(i) > 0)
695 matrixM[i-1][j-1] = hInverseResponseBayes->GetBinContent(i, j) / fCurrentEfficiency->GetBinContent(i);
696 else
697 matrixM[i-1][j-1] = 0;
698 }
699 }
700
701 Float_t* vectorn = new Float_t[yBins];
702 for (Int_t j=1; j<=yBins; j++)
703 vectorn[j-1] = fCurrentESD->GetBinContent(j);
704
705 // first part of covariance matrix, depends on input distribution n(E)
706 Float_t cov1[251][251];
707
708 Float_t nEvents = fCurrentESD->Integral(); // N
709
710 xBins = 20;
711 yBins = 20;
712
713 for (Int_t k=0; k<xBins; k++)
714 {
715 printf("In Cov1: %d\n", k);
716 for (Int_t l=0; l<yBins; l++)
717 {
718 cov1[k][l] = 0;
719
720 // sum_j Mkj Mlj n(Ej) * (1 - n(Ej) / N)
721 for (Int_t j=0; j<yBins; j++)
722 cov1[k][l] += matrixM[k][j] * matrixM[l][j] * vectorn[j]
723 * (1.0 - vectorn[j] / nEvents);
724
725 // - sum_i,j (i != j) Mki Mlj n(Ei) n(Ej) / N
726 for (Int_t i=0; i<yBins; i++)
727 for (Int_t j=0; j<yBins; j++)
728 {
729 if (i == j)
730 continue;
731 cov1[k][l] -= matrixM[k][i] * matrixM[l][j] * vectorn[i]
732 * vectorn[j] / nEvents;
733 }
734 }
735 }
736
737 printf("Cov1 finished\n");
738
739 TH2F* cov = (TH2F*) hInverseResponseBayes->Clone("cov");
740 cov->Reset();
741
742 for (Int_t i=1; i<=xBins; i++)
743 for (Int_t j=1; j<=yBins; j++)
744 cov->SetBinContent(i, j, cov1[i-1][j-1]);
745
746 new TCanvas;
747 cov->Draw("COLZ");
748
749 // second part of covariance matrix, depends on response matrix
750 Float_t cov2[251][251];
751
752 // Cov[P(Er|Cu), P(Es|Cu)] term
753 Float_t covTerm[100][100][100];
754 for (Int_t r=0; r<yBins; r++)
755 for (Int_t u=0; u<xBins; u++)
756 for (Int_t s=0; s<yBins; s++)
757 {
758 if (r == s)
759 covTerm[r][u][s] = 1.0 / sumHist->GetBinContent(u+1) * hResponse->GetBinContent(u+1, r+1)
760 * (1.0 - hResponse->GetBinContent(u+1, r+1));
761 else
762 covTerm[r][u][s] = - 1.0 / sumHist->GetBinContent(u+1) * hResponse->GetBinContent(u+1, r+1)
763 * hResponse->GetBinContent(u+1, s+1);
764 }
765
766 for (Int_t k=0; k<xBins; k++)
767 for (Int_t l=0; l<yBins; l++)
768 {
769 cov2[k][l] = 0;
770 printf("In Cov2: %d %d\n", k, l);
771 for (Int_t i=0; i<yBins; i++)
772 for (Int_t j=0; j<yBins; j++)
773 {
774 //printf("In Cov2: %d %d %d %d\n", k, l, i, j);
775 // calculate Cov(Mki, Mlj) = sum{ru},{su} ...
776 Float_t tmpCov = 0;
777 for (Int_t r=0; r<yBins; r++)
778 for (Int_t u=0; u<xBins; u++)
779 for (Int_t s=0; s<yBins; s++)
780 {
781 if (hResponse->GetBinContent(u+1, r+1) == 0 || hResponse->GetBinContent(u+1, s+1) == 0
782 || hResponse->GetBinContent(u+1, i+1) == 0)
783 continue;
784
785 tmpCov += BayesCovarianceDerivate(matrixM, hResponse, fCurrentEfficiency, k, i, r, u)
786 * BayesCovarianceDerivate(matrixM, hResponse, fCurrentEfficiency, l, j, s, u)
787 * covTerm[r][u][s];
788 }
789
790 cov2[k][l] += fCurrentESD->GetBinContent(i+1) * fCurrentESD->GetBinContent(j+1) * tmpCov;
791 }
792 }
793
794 printf("Cov2 finished\n");
795
796 for (Int_t i=1; i<=xBins; i++)
797 for (Int_t j=1; j<=yBins; j++)
798 cov->SetBinContent(i, j, cov1[i-1][j-1] + cov2[i-1][j-1]);
799
800 new TCanvas;
801 cov->Draw("COLZ");*/
802}
803
804//____________________________________________________________________
805Double_t AliUnfolding::RegularizationPol0(TVectorD& params)
806{
807 // homogenity term for minuit fitting
808 // pure function of the parameters
809 // prefers constant function (pol0)
810
811 Double_t chi2 = 0;
812
813 for (Int_t i=1+fgSkipBinsBegin; i<fgMaxParams; ++i)
814 {
95e970ca 815 Double_t right = params[i] / (*fgBinWidths)(i);
816 Double_t left = params[i-1] / (*fgBinWidths)(i-1);
19442b86 817
95e970ca 818 if (left != 0)
19442b86 819 {
95e970ca 820 Double_t diff = (right - left);
821 chi2 += diff * diff / left / (((*fgBinWidths)(i) + (*fgBinWidths)(i-1)) / 2);
19442b86 822 }
823 }
824
825 return chi2 / 100.0;
826}
827
828//____________________________________________________________________
829Double_t AliUnfolding::RegularizationPol1(TVectorD& params)
830{
831 // homogenity term for minuit fitting
832 // pure function of the parameters
833 // prefers linear function (pol1)
834
835 Double_t chi2 = 0;
836
837 for (Int_t i=2+fgSkipBinsBegin; i<fgMaxParams; ++i)
838 {
839 if (params[i-1] == 0)
840 continue;
841
95e970ca 842 Double_t right = params[i] / (*fgBinWidths)(i);
843 Double_t middle = params[i-1] / (*fgBinWidths)(i-1);
844 Double_t left = params[i-2] / (*fgBinWidths)(i-2);
19442b86 845
95e970ca 846 Double_t der1 = (right - middle) / (((*fgBinWidths)(i) + (*fgBinWidths)(i-1)) / 2);
847 Double_t der2 = (middle - left) / (((*fgBinWidths)(i-1) + (*fgBinWidths)(i-2)) / 2);
19442b86 848
95e970ca 849 //Double_t diff = (der1 - der2) / middle;
850 //chi2 += diff * diff;
851 chi2 += (der1 - der2) * (der1 - der2) / middle * (*fgBinWidths)(i-1);
19442b86 852 }
853
854 return chi2;
855}
856
857//____________________________________________________________________
858Double_t AliUnfolding::RegularizationLog(TVectorD& params)
859{
860 // homogenity term for minuit fitting
861 // pure function of the parameters
862 // prefers linear function (pol1)
863
864 Double_t chi2 = 0;
865
866 for (Int_t i=2+fgSkipBinsBegin; i<fgMaxParams; ++i)
867 {
95e970ca 868 if (params[i-1] == 0 || params[i] == 0 || params[i-2] == 0)
869 continue;
19442b86 870
95e970ca 871 Double_t right = log(params[i] / (*fgBinWidths)(i));
872 Double_t middle = log(params[i-1] / (*fgBinWidths)(i-1));
873 Double_t left = log(params[i-2] / (*fgBinWidths)(i-2));
874
875 Double_t der1 = (right - middle) / (((*fgBinWidths)(i) + (*fgBinWidths)(i-1)) / 2);
876 Double_t der2 = (middle - left) / (((*fgBinWidths)(i-1) + (*fgBinWidths)(i-2)) / 2);
877
878 //Double_t error = 1. / params[i] + 4. / params[i-1] + 1. / params[i-2];
19442b86 879
95e970ca 880 //if (fgCallCount == 0)
881 // Printf("%d %f %f", i, (der1 - der2) * (der1 - der2), error);
882 chi2 += (der1 - der2) * (der1 - der2);// / error;
19442b86 883 }
884
95e970ca 885 return chi2;
19442b86 886}
887
888//____________________________________________________________________
889Double_t AliUnfolding::RegularizationTotalCurvature(TVectorD& params)
890{
891 // homogenity term for minuit fitting
892 // pure function of the parameters
893 // minimizes the total curvature (from Unfolding Methods In High-Energy Physics Experiments,
894 // V. Blobel (Hamburg U.) . DESY 84/118, Dec 1984. 40pp.
895
896 Double_t chi2 = 0;
897
898 for (Int_t i=2+fgSkipBinsBegin; i<fgMaxParams; ++i)
899 {
900 Double_t right = params[i];
901 Double_t middle = params[i-1];
902 Double_t left = params[i-2];
903
904 Double_t der1 = (right - middle);
905 Double_t der2 = (middle - left);
906
907 Double_t diff = (der1 - der2);
908
909 chi2 += diff * diff;
910 }
911
912 return chi2 * 1e4;
913}
914
915//____________________________________________________________________
916Double_t AliUnfolding::RegularizationEntropy(TVectorD& params)
917{
918 // homogenity term for minuit fitting
919 // pure function of the parameters
920 // calculates entropy, from
921 // The method of reduced cross-entropy (M. Schmelling 1993)
922
923 Double_t paramSum = 0;
924
925 for (Int_t i=fgSkipBinsBegin; i<fgMaxParams; ++i)
926 paramSum += params[i];
927
928 Double_t chi2 = 0;
929 for (Int_t i=fgSkipBinsBegin; i<fgMaxParams; ++i)
930 {
95e970ca 931 Double_t tmp = params[i] / paramSum;
932 //Double_t tmp = params[i];
19442b86 933 if (tmp > 0 && (*fgEntropyAPriori)[i] > 0)
934 {
935 chi2 += tmp * TMath::Log(tmp / (*fgEntropyAPriori)[i]);
936 }
95e970ca 937 else
938 chi2 += 100;
939 }
940
941 return -chi2;
942}
943
944//____________________________________________________________________
945Double_t AliUnfolding::RegularizationRatio(TVectorD& params)
946{
947 // homogenity term for minuit fitting
948 // pure function of the parameters
949
950 Double_t chi2 = 0;
951
952 for (Int_t i=5+fgSkipBinsBegin; i<fgMaxParams; ++i)
953 {
954 if (params[i-1] == 0 || params[i] == 0)
955 continue;
956
957 Double_t right = params[i] / (*fgBinWidths)(i);
958 Double_t middle = params[i-1] / (*fgBinWidths)(i-1);
959 Double_t left = params[i-2] / (*fgBinWidths)(i-2);
960 Double_t left2 = params[i-3] / (*fgBinWidths)(i-3);
961 Double_t left3 = params[i-4] / (*fgBinWidths)(i-4);
962 Double_t left4 = params[i-5] / (*fgBinWidths)(i-5);
963
964 //Double_t diff = left / middle - middle / right;
965 //Double_t diff = 2 * left / middle - middle / right - left2 / left;
966 Double_t diff = 4 * left2 / left - middle / right - left / middle - left3 / left2 - left4 / left3;
967
968 chi2 += diff * diff;// / middle;
19442b86 969 }
970
95e970ca 971 return chi2;
19442b86 972}
973
974//____________________________________________________________________
975void AliUnfolding::Chi2Function(Int_t&, Double_t*, Double_t& chi2, Double_t *params, Int_t)
976{
977 //
978 // fit function for minuit
979 // does: (m - Ad)W(m - Ad) where m = measured, A correlation matrix, d = guess, W = covariance matrix
980 //
95e970ca 981
982 // TODO use static members for the variables here to speed up processing (no construction/deconstruction)
19442b86 983
984 // d
95e970ca 985 TVectorD paramsVector(fgMaxParams);
19442b86 986 for (Int_t i=0; i<fgMaxParams; ++i)
987 paramsVector[i] = params[i] * params[i];
988
989 // calculate penalty factor
990 Double_t penaltyVal = 0;
991 switch (fgRegularizationType)
992 {
993 case kNone: break;
994 case kPol0: penaltyVal = RegularizationPol0(paramsVector); break;
995 case kPol1: penaltyVal = RegularizationPol1(paramsVector); break;
996 case kCurvature: penaltyVal = RegularizationTotalCurvature(paramsVector); break;
997 case kEntropy: penaltyVal = RegularizationEntropy(paramsVector); break;
998 case kLog: penaltyVal = RegularizationLog(paramsVector); break;
95e970ca 999 case kRatio: penaltyVal = RegularizationRatio(paramsVector); break;
19442b86 1000 }
1001
1002 //if (penaltyVal > 1e10)
1003 // paramsVector2.Print();
1004
1005 penaltyVal *= fgRegularizationWeight;
1006
1007 // Ad
1008 TVectorD measGuessVector(fgMaxInput);
1009 measGuessVector = (*fgCorrelationMatrix) * paramsVector;
1010
1011 // Ad - m
1012 measGuessVector -= (*fgCurrentESDVector);
95e970ca 1013
1014#if 0
1015 // new error calcuation using error on the guess
1016
1017 // error from guess
1018 TVectorD errorGuessVector(fgMaxInput);
1019 //errorGuessVector = (*fgCorrelationMatrixSquared) * paramsVector;
1020 errorGuessVector = (*fgCorrelationMatrix) * paramsVector;
19442b86 1021
95e970ca 1022 Double_t chi2FromFit = 0;
1023 for (Int_t i=0; i<fgMaxInput; ++i)
1024 {
1025 Float_t error = 1;
1026 if (errorGuessVector(i) > 0)
1027 error = errorGuessVector(i);
1028 chi2FromFit += measGuessVector(i) * measGuessVector(i) / error;
1029 }
19442b86 1030 //measGuessVector.Print();
1031
95e970ca 1032#else
1033 // old error calcuation using the error on the measured
19442b86 1034 TVectorD copy(measGuessVector);
1035
1036 // (Ad - m) W
1037 // this step can be optimized because currently only the diagonal elements of fgCorrelationCovarianceMatrix are used
1038 // normal way is like this:
1039 // measGuessVector *= (*fgCorrelationCovarianceMatrix);
1040 // optimized way like this:
1041 for (Int_t i=0; i<fgMaxInput; ++i)
1042 measGuessVector[i] *= (*fgCorrelationCovarianceMatrix)(i, i);
1043
1044 //measGuessVector.Print();
1045
95e970ca 1046 if (fgSkipBin0InChi2)
1047 measGuessVector[0] = 0;
1048
19442b86 1049 // (Ad - m) W (Ad - m)
1050 // the factor 1e6 prevents that a very small number (measGuessVector[i]) is multiplied with a very
95e970ca 1051 // big number ((*fgCorrelationCovarianceMatrix)(i, i)) (see UnfoldWithMinuit)
19442b86 1052 Double_t chi2FromFit = measGuessVector * copy * 1e6;
95e970ca 1053#endif
19442b86 1054
95e970ca 1055 Double_t notFoundEventsConstraint = 0;
1056 Double_t currentNotFoundEvents = 0;
1057 Double_t errorNotFoundEvents = 0;
1058
1059 if (fgNotFoundEvents > 0)
1060 {
1061 for (Int_t i=0; i<fgMaxParams; ++i)
1062 {
1063 Double_t eff = (1.0 / (*fgEfficiency)(i) - 1);
1064 if (i == 0)
1065 eff = (1.0 / params[fgMaxParams] - 1);
1066 currentNotFoundEvents += eff * paramsVector(i);
1067 errorNotFoundEvents += eff * eff * paramsVector(i); // error due to guess (paramsVector)
1068 if (i <= 3)
1069 errorNotFoundEvents += (eff * 0.03) * (eff * 0.03) * paramsVector(i) * paramsVector(i); // error on eff
1070 //if ((fgCallCount % 10000) == 0)
1071 // Printf("%d %f %f %f", i, (*fgEfficiency)(i), paramsVector(i), currentNotFoundEvents);
1072 }
1073 errorNotFoundEvents += fgNotFoundEvents;
1074 // TODO add error on background, background estimate
1075
1076 notFoundEventsConstraint = (currentNotFoundEvents - fgNotFoundEvents) * (currentNotFoundEvents - fgNotFoundEvents) / errorNotFoundEvents;
1077 }
1078
1079 Float_t avg = 0;
1080 Float_t sum = 0;
1081 Float_t currentMult = 0;
1082 // try to match dn/deta
1083 for (Int_t i=0; i<fgMaxParams; ++i)
1084 {
1085 avg += paramsVector(i) * currentMult;
1086 sum += paramsVector(i);
1087 currentMult += (*fgBinWidths)(i);
1088 }
1089 avg /= sum;
1090 Float_t chi2Avg = 0; //(avg - 3.73) * (avg - 3.73) * 100;
19442b86 1091
95e970ca 1092 chi2 = chi2FromFit + penaltyVal + notFoundEventsConstraint + chi2Avg;
1093
1094 if ((fgCallCount++ % 1000) == 0)
1095 {
1096 Printf("AliUnfolding::Chi2Function: Iteration %d (ev %d %d +- %f) (%f) (%f): %f %f %f %f --> %f", fgCallCount-1, (Int_t) fgNotFoundEvents, (Int_t) currentNotFoundEvents, TMath::Sqrt(errorNotFoundEvents), params[fgMaxParams], avg, chi2FromFit, penaltyVal, notFoundEventsConstraint, chi2Avg, chi2);
1097 //for (Int_t i=0; i<fgMaxInput; ++i)
1098 // Printf("%d: %f", i, measGuessVector(i) * copy(i) * 1e6);
1099 }
19442b86 1100}
1101
1102//____________________________________________________________________
1103void AliUnfolding::DrawGuess(Double_t *params)
1104{
1105 //
1106 // draws residuals of solution suggested by params and effect of regularization
1107 //
1108
1109 // d
95e970ca 1110 TVectorD paramsVector(fgMaxParams);
19442b86 1111 for (Int_t i=0; i<fgMaxParams; ++i)
1112 paramsVector[i] = params[i] * params[i];
1113
1114 // Ad
1115 TVectorD measGuessVector(fgMaxInput);
1116 measGuessVector = (*fgCorrelationMatrix) * paramsVector;
1117
1118 // Ad - m
1119 measGuessVector -= (*fgCurrentESDVector);
1120
1121 TVectorD copy(measGuessVector);
1122 //copy.Print();
1123
1124 // (Ad - m) W
1125 // this step can be optimized because currently only the diagonal elements of fgCorrelationCovarianceMatrix are used
1126 // normal way is like this:
1127 // measGuessVector *= (*fgCorrelationCovarianceMatrix);
1128 // optimized way like this:
1129 for (Int_t i=0; i<fgMaxInput; ++i)
1130 measGuessVector[i] *= (*fgCorrelationCovarianceMatrix)(i, i);
1131
1132 // (Ad - m) W (Ad - m)
1133 // the factor 1e6 prevents that a very small number (measGuessVector[i]) is multiplied with a very
1134 // big number ((*fgCorrelationCovarianceMatrix)(i, i)) (see ApplyMinuitFit)
1135 //Double_t chi2FromFit = measGuessVector * copy * 1e6;
1136
1137 // draw residuals
1138 TH1* residuals = new TH1F("residuals", "residuals", fgMaxInput, -0.5, fgMaxInput - 0.5);
1139 for (Int_t i=0; i<fgMaxInput; ++i)
1140 residuals->SetBinContent(i+1, measGuessVector(i) * copy(i) * 1e6);
1141 new TCanvas; residuals->DrawCopy(); gPad->SetLogy();
1142
1143 // draw penalty
95e970ca 1144 TH1* penalty = GetPenaltyPlot(params);
1145
1146 new TCanvas; penalty->DrawCopy(); gPad->SetLogy();
1147}
19442b86 1148
95e970ca 1149//____________________________________________________________________
1150TH1* AliUnfolding::GetPenaltyPlot(TH1* corrected)
1151{
1152 // draws the penalty factors as function of multiplicity of the current selected regularization
19442b86 1153
95e970ca 1154 Double_t* params = new Double_t[fgMaxParams];
1155 for (Int_t i=0; i<TMath::Min(fgMaxParams, corrected->GetNbinsX()); i++)
1156 params[i] = corrected->GetBinContent(i+1);
1157
1158 TH1* penalty = GetPenaltyPlot(params);
1159
1160 delete[] params;
1161
1162 return penalty;
1163}
1164
1165//____________________________________________________________________
1166TH1* AliUnfolding::GetPenaltyPlot(Double_t* params)
1167{
1168 // draws the penalty factors as function of multiplicity of the current selected regularization
1169
1170 TH1* penalty = new TH1F("penalty", ";unfolded multiplicity;penalty factor", fgMaxParams, -0.5, fgMaxParams - 0.5);
1171
1172 for (Int_t i=1+fgSkipBinsBegin; i<fgMaxParams; ++i)
19442b86 1173 {
95e970ca 1174 Double_t diff = 0;
1175 if (fgRegularizationType == kPol0)
1176 {
1177 Double_t right = params[i] / (*fgBinWidths)(i);
1178 Double_t left = params[i-1] / (*fgBinWidths)(i-1);
19442b86 1179
95e970ca 1180 if (left != 0)
1181 {
1182 Double_t diffTmp = (right - left);
1183 diff = diffTmp * diffTmp / left / (((*fgBinWidths)(i) + (*fgBinWidths)(i-1)) / 2) / 100;
1184 }
1185 }
1186 if (fgRegularizationType == kPol1 && i > 1+fgSkipBinsBegin)
1187 {
1188 if (params[i-1] == 0)
1189 continue;
19442b86 1190
95e970ca 1191 Double_t right = params[i] / (*fgBinWidths)(i);
1192 Double_t middle = params[i-1] / (*fgBinWidths)(i-1);
1193 Double_t left = params[i-2] / (*fgBinWidths)(i-2);
19442b86 1194
95e970ca 1195 Double_t der1 = (right - middle) / (((*fgBinWidths)(i) + (*fgBinWidths)(i-1)) / 2);
1196 Double_t der2 = (middle - left) / (((*fgBinWidths)(i-1) + (*fgBinWidths)(i-2)) / 2);
1197
1198 diff = (der1 - der2) * (der1 - der2) / middle;
1199 }
1200 if (fgRegularizationType == kLog && i > 1+fgSkipBinsBegin)
1201 {
1202 if (params[i-1] == 0)
1203 continue;
1204
1205 Double_t right = log(params[i]);
1206 Double_t middle = log(params[i-1]);
1207 Double_t left = log(params[i-2]);
1208
1209 Double_t der1 = (right - middle);
1210 Double_t der2 = (middle - left);
1211
1212 //Double_t error = 1. / params[i] + 4. / params[i-1] + 1. / params[i-2];
1213 //Printf("%d %f %f", i, (der1 - der2) * (der1 - der2), error);
1214
1215 diff = (der1 - der2) * (der1 - der2);// / error;
1216 }
19442b86 1217
95e970ca 1218 penalty->SetBinContent(i, diff);
19442b86 1219
1220 //Printf("%d %f %f %f %f", i-1, left, middle, right, diff);
1221 }
95e970ca 1222
1223 return penalty;
19442b86 1224}
1225
1226//____________________________________________________________________
1227void AliUnfolding::TF1Function(Int_t& unused1, Double_t* unused2, Double_t& chi2, Double_t *params, Int_t unused3)
1228{
1229 //
1230 // fit function for minuit
1231 // uses the TF1 stored in fgFitFunction
1232 //
1233
1234 for (Int_t i=0; i<fgFitFunction->GetNpar(); i++)
1235 fgFitFunction->SetParameter(i, params[i]);
1236
1237 Double_t* params2 = new Double_t[fgMaxParams];
1238
1239 for (Int_t i=0; i<fgMaxParams; ++i)
1240 params2[i] = fgFitFunction->Eval(i);
1241
1242 Chi2Function(unused1, unused2, chi2, params2, unused3);
1243
1244 delete[] params2;
1245
1246 if (fgDebug)
1247 Printf("%f", chi2);
1248}
1249
1250//____________________________________________________________________
1251Int_t AliUnfolding::UnfoldWithFunction(TH2* correlation, TH1* efficiency, TH1* measured, TH1* /* initialConditions */, TH1* aResult)
1252{
1253 //
1254 // correct spectrum using minuit chi2 method applying a functional fit
1255 //
1256
1257 if (!fgFitFunction)
1258 {
1259 Printf("AliUnfolding::UnfoldWithFunction: ERROR fit function not set. Exiting.");
1260 return -1;
1261 }
1262
1263 SetChi2Regularization(kNone, 0);
1264
95e970ca 1265 SetStaticVariables(correlation, measured, efficiency);
19442b86 1266
1267 // Initialize TMinuit via generic fitter interface
1268 TVirtualFitter *minuit = TVirtualFitter::Fitter(0, fgFitFunction->GetNpar());
1269
1270 minuit->SetFCN(TF1Function);
1271 for (Int_t i=0; i<fgFitFunction->GetNpar(); i++)
1272 {
1273 Double_t lower, upper;
1274 fgFitFunction->GetParLimits(i, lower, upper);
1275 minuit->SetParameter(i, Form("param%d",i), fgFitFunction->GetParameter(i), fgMinuitStepSize, lower, upper);
1276 }
1277
1278 Double_t arglist[100];
1279 arglist[0] = 0;
1280 minuit->ExecuteCommand("SET PRINT", arglist, 1);
1281 minuit->ExecuteCommand("MIGRAD", arglist, 0);
1282 //minuit->ExecuteCommand("MINOS", arglist, 0);
1283
1284 for (Int_t i=0; i<fgFitFunction->GetNpar(); i++)
1285 fgFitFunction->SetParameter(i, minuit->GetParameter(i));
1286
1287 for (Int_t i=0; i<fgMaxParams; ++i)
1288 {
1289 Double_t value = fgFitFunction->Eval(i);
1290 if (fgDebug)
1291 Printf("%d : %f", i, value);
1292
1293 if (efficiency)
1294 {
1295 if (efficiency->GetBinContent(i+1) > 0)
1296 {
1297 value /= efficiency->GetBinContent(i+1);
1298 }
1299 else
1300 value = 0;
1301 }
1302 aResult->SetBinContent(i+1, value);
1303 aResult->SetBinError(i+1, 0);
1304 }
1305
1306 return 0;
1307}
1308
1309//____________________________________________________________________
1310void AliUnfolding::CreateOverflowBin(TH2* correlation, TH1* measured)
1311{
1312 // Finds the first bin where the content is below fgStatLimit and combines all values for this bin and larger bins
1313 // The same limit is applied to the correlation
1314
1315 Int_t lastBin = 0;
1316 for (Int_t i=1; i<=measured->GetNbinsX(); ++i)
1317 {
1318 if (measured->GetBinContent(i) <= fgOverflowBinLimit)
1319 {
1320 lastBin = i;
1321 break;
1322 }
1323 }
1324
1325 if (lastBin == 0)
1326 {
1327 Printf("AliUnfolding::CreateOverflowBin: WARNING: First bin is already below limit of %f", fgOverflowBinLimit);
1328 return;
1329 }
1330
1331 Printf("AliUnfolding::CreateOverflowBin: Bin limit in measured spectrum determined to be %d", lastBin);
1332
1333 TCanvas* canvas = 0;
1334
1335 if (fgDebug)
1336 {
1337 canvas = new TCanvas("StatSolution", "StatSolution", 1000, 800);
1338 canvas->Divide(2, 2);
1339
1340 canvas->cd(1);
1341 measured->SetStats(kFALSE);
1342 measured->DrawCopy();
1343 gPad->SetLogy();
1344
1345 canvas->cd(2);
1346 correlation->SetStats(kFALSE);
1347 correlation->DrawCopy("COLZ");
1348 }
1349
1350 measured->SetBinContent(lastBin, measured->Integral(lastBin, measured->GetNbinsX()));
1351 for (Int_t i=lastBin+1; i<=measured->GetNbinsX(); ++i)
1352 {
1353 measured->SetBinContent(i, 0);
1354 measured->SetBinError(i, 0);
1355 }
1356 // the error is set to sqrt(N), better solution possible?, sum of relative errors of all contributions???
1357 measured->SetBinError(lastBin, TMath::Sqrt(measured->GetBinContent(lastBin)));
1358
1359 Printf("AliUnfolding::CreateOverflowBin: This bin has now %f +- %f entries", measured->GetBinContent(lastBin), measured->GetBinError(lastBin));
1360
1361 for (Int_t i=1; i<=correlation->GetNbinsX(); ++i)
1362 {
1363 correlation->SetBinContent(i, lastBin, correlation->Integral(i, i, lastBin, correlation->GetNbinsY()));
1364 // the error is set to sqrt(N), better solution possible?, sum of relative errors of all contributions???
1365 correlation->SetBinError(i, lastBin, TMath::Sqrt(correlation->GetBinContent(i, lastBin)));
1366
1367 for (Int_t j=lastBin+1; j<=correlation->GetNbinsY(); ++j)
1368 {
1369 correlation->SetBinContent(i, j, 0);
1370 correlation->SetBinError(i, j, 0);
1371 }
1372 }
1373
1374 Printf("AliUnfolding::CreateOverflowBin: Adjusted correlation matrix!");
1375
1376 if (canvas)
1377 {
1378 canvas->cd(3);
1379 measured->DrawCopy();
1380 gPad->SetLogy();
1381
1382 canvas->cd(4);
1383 correlation->DrawCopy("COLZ");
1384 }
1385}
95e970ca 1386
1387Int_t AliUnfolding::UnfoldGetBias(TH2* correlation, TH1* efficiency, TH1* measured, TH1* initialConditions, TH1* result)
1388{
1389 // unfolds and assigns bias as errors with Eq. 19 of Cowan, "a survey of unfolding methods for particle physics"
1390 // b_i = sum_j dmu_i/dn_j (nu_j - n_j) with nu_j as folded guess, n_j as data
1391 // dmu_i/dn_j is found numerically by changing the bin content and re-unfolding
1392 //
1393 // return code: 0 (success) -1 (error: from Unfold(...) )
1394
1395 if (Unfold(correlation, efficiency, measured, initialConditions, result) != 0)
1396 return -1;
1397
1398 TMatrixD matrix(fgMaxInput, fgMaxParams);
1399
1400 TH1* newResult[4];
1401 for (Int_t loop=0; loop<4; loop++)
1402 newResult[loop] = (TH1*) result->Clone(Form("newresult_%d", loop));
1403
1404 // change bin-by-bin and built matrix of effects
1405 for (Int_t m=0; m<fgMaxInput; m++)
1406 {
1407 if (measured->GetBinContent(m+1) < 1)
1408 continue;
1409
1410 for (Int_t loop=0; loop<4; loop++)
1411 {
1412 //Printf("%d %d", i, loop);
1413 Float_t factor = 1;
1414 switch (loop)
1415 {
1416 case 0: factor = 0.5; break;
1417 case 1: factor = -0.5; break;
1418 case 2: factor = 1; break;
1419 case 3: factor = -1; break;
1420 default: return -1;
1421 }
1422
1423 TH1* measuredClone = (TH1*) measured->Clone("measuredClone");
1424
1425 measuredClone->SetBinContent(m+1, measured->GetBinContent(m+1) + factor * TMath::Sqrt(measured->GetBinContent(m+1)));
1426 //new TCanvas; measuredClone->Draw("COLZ");
1427
1428 newResult[loop]->Reset();
1429 Unfold(correlation, efficiency, measuredClone, measuredClone, newResult[loop]);
1430 // WARNING if we leave here, then nothing is calculated
1431 //return -1;
1432
1433 delete measuredClone;
1434 }
1435
1436 for (Int_t t=0; t<fgMaxParams; t++)
1437 {
1438 // one value
1439 //matrix(i, j) = (result->GetBinContent(j+1) - newResult->GetBinContent(j+1)) / TMath::Sqrt(changedHist->GetBinContent(1, i+1));
1440
1441 // four values from the derivate (procedure taken from ROOT -- suggestion by Ruben)
1442 // = 1/2D * [ 8 (f(D/2) - f(-D/2)) - (f(D)-f(-D)) ]/3
1443
1444 /*
1445 // check formula
1446 measured->SetBinContent(1, m+1, 100);
1447 newResult[0]->SetBinContent(t+1, 5 * 0.5 + 10);
1448 newResult[1]->SetBinContent(t+1, 5 * -0.5 + 10);
1449 newResult[2]->SetBinContent(t+1, 5 * 1 + 10);
1450 newResult[3]->SetBinContent(t+1, 5 * -1 + 10);
1451 */
1452
1453 matrix(m, t) = 0.5 / TMath::Sqrt(measured->GetBinContent(m+1)) *
1454 ( 8. * (newResult[0]->GetBinContent(t+1) - newResult[1]->GetBinContent(t+1)) -
1455 (newResult[2]->GetBinContent(t+1) - newResult[3]->GetBinContent(t+1))
1456 ) / 3;
1457 }
1458 }
1459
1460 for (Int_t loop=0; loop<4; loop++)
1461 delete newResult[loop];
1462
1463 //matrix.Print();
1464 //TH2* matrixHist = new TH2D(matrix); new TCanvas; matrixHist->Draw("BOX");
1465
1466 // ...calculate folded guess
1467 TH1* convoluted = (TH1*) measured->Clone("convoluted");
1468 convoluted->Reset();
1469 for (Int_t m=0; m<fgMaxInput; m++)
1470 {
1471 Float_t value = 0;
1472 for (Int_t t = 0; t<fgMaxParams; t++)
1473 {
1474 Float_t tmp = correlation->GetBinContent(t+1, m+1) * result->GetBinContent(t+1);
1475 if (efficiency)
1476 tmp *= efficiency->GetBinContent(t+1);
1477 value += tmp;
1478 }
1479 convoluted->SetBinContent(m+1, value);
1480 }
1481
1482 // rescale
1483 convoluted->Scale(measured->Integral() / convoluted->Integral());
1484
1485 //new TCanvas; convoluted->Draw(); measured->Draw("SAME"); measured->SetLineColor(2);
1486 //return;
1487
1488 // difference
1489 convoluted->Add(measured, -1);
1490
1491 // ...and the bias
1492 for (Int_t t = 0; t<fgMaxParams; t++)
1493 {
1494 Double_t error = 0;
1495 for (Int_t m=0; m<fgMaxInput; m++)
1496 error += matrix(m, t) * convoluted->GetBinContent(m+1);
1497 result->SetBinError(t+1, error);
1498 }
1499
1500 //new TCanvas; result->Draw(); gPad->SetLogy();
1501
1502 return 0;
1503}