Fixed grep syntax on OS X in the Analysis Plugin
[u/mrichter/AliRoot.git] / ANALYSIS / 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>
9e065ad2 30#include <TExec.h>
31#include "Riostream.h"
32#include "TROOT.h"
33
34using namespace std; //required for resolving the 'cout' symbol
19442b86 35
36TMatrixD* AliUnfolding::fgCorrelationMatrix = 0;
95e970ca 37TMatrixD* AliUnfolding::fgCorrelationMatrixSquared = 0;
19442b86 38TMatrixD* AliUnfolding::fgCorrelationCovarianceMatrix = 0;
39TVectorD* AliUnfolding::fgCurrentESDVector = 0;
40TVectorD* AliUnfolding::fgEntropyAPriori = 0;
95e970ca 41TVectorD* AliUnfolding::fgEfficiency = 0;
9e065ad2 42
43TAxis* AliUnfolding::fgUnfoldedAxis = 0;
44TAxis* AliUnfolding::fgMeasuredAxis = 0;
19442b86 45
46TF1* AliUnfolding::fgFitFunction = 0;
47
48AliUnfolding::MethodType AliUnfolding::fgMethodType = AliUnfolding::kInvalid;
49Int_t AliUnfolding::fgMaxInput = -1; // bins in measured histogram
50Int_t AliUnfolding::fgMaxParams = -1; // bins in unfolded histogram = number of fit params
51Float_t AliUnfolding::fgOverflowBinLimit = -1;
52
53AliUnfolding::RegularizationType AliUnfolding::fgRegularizationType = AliUnfolding::kPol1;
54Float_t AliUnfolding::fgRegularizationWeight = 10000;
55Int_t AliUnfolding::fgSkipBinsBegin = 0;
56Float_t AliUnfolding::fgMinuitStepSize = 0.1; // (usually not needed to be changed) step size in minimization
9e065ad2 57Float_t AliUnfolding::fgMinuitPrecision = 1e-6; // minuit precision
736125ad 58Int_t AliUnfolding::fgMinuitMaxIterations = 1000000; // minuit maximum number of iterations
9f070ef5 59Double_t AliUnfolding::fgMinuitStrategy = 1.; // minuit strategy
95e970ca 60Bool_t AliUnfolding::fgMinimumInitialValue = kFALSE; // set all initial values at least to the smallest value among the initial values
61Float_t AliUnfolding::fgMinimumInitialValueFix = -1;
9e065ad2 62Bool_t AliUnfolding::fgNormalizeInput = kFALSE; // normalize input spectrum
95e970ca 63Float_t AliUnfolding::fgNotFoundEvents = 0;
64Bool_t AliUnfolding::fgSkipBin0InChi2 = kFALSE;
19442b86 65
66Float_t AliUnfolding::fgBayesianSmoothing = 1; // smoothing parameter (0 = no smoothing)
651e2088 67Int_t AliUnfolding::fgBayesianIterations = 10; // number of iterations in Bayesian method
19442b86 68
69Bool_t AliUnfolding::fgDebug = kFALSE;
70
95e970ca 71Int_t AliUnfolding::fgCallCount = 0;
72
9e065ad2 73Int_t AliUnfolding::fgPowern = 5;
74
75Double_t AliUnfolding::fChi2FromFit = 0.;
76Double_t AliUnfolding::fPenaltyVal = 0.;
77Double_t AliUnfolding::fAvgResidual = 0.;
78
79Int_t AliUnfolding::fgPrintChi2Details = 0;
80
81TCanvas *AliUnfolding::fgCanvas = 0;
82TH1 *AliUnfolding::fghUnfolded = 0;
83TH2 *AliUnfolding::fghCorrelation = 0;
84TH1 *AliUnfolding::fghEfficiency = 0;
85TH1 *AliUnfolding::fghMeasured = 0;
86
19442b86 87ClassImp(AliUnfolding)
88
89//____________________________________________________________________
90void AliUnfolding::SetUnfoldingMethod(MethodType methodType)
91{
92 // set unfolding method
93 fgMethodType = methodType;
94
95 const char* name = 0;
96 switch (methodType)
97 {
98 case kInvalid: name = "INVALID"; break;
99 case kChi2Minimization: name = "Chi2 Minimization"; break;
100 case kBayesian: name = "Bayesian unfolding"; break;
101 case kFunction: name = "Functional fit"; break;
102 }
103 Printf("AliUnfolding::SetUnfoldingMethod: %s enabled.", name);
104}
105
106//____________________________________________________________________
107void AliUnfolding::SetCreateOverflowBin(Float_t overflowBinLimit)
108{
109 // enable the creation of a overflow bin that includes all statistics below the given limit
110
111 fgOverflowBinLimit = overflowBinLimit;
112
113 Printf("AliUnfolding::SetCreateOverflowBin: overflow bin limit set to %f", overflowBinLimit);
114}
115
116//____________________________________________________________________
117void AliUnfolding::SetSkipBinsBegin(Int_t nBins)
118{
119 // set number of skipped bins in regularization
120
121 fgSkipBinsBegin = nBins;
122
123 Printf("AliUnfolding::SetSkipBinsBegin: skipping %d bins at the beginning of the spectrum in the regularization.", fgSkipBinsBegin);
124}
125
126//____________________________________________________________________
127void AliUnfolding::SetNbins(Int_t nMeasured, Int_t nUnfolded)
128{
129 // set number of bins in the input (measured) distribution and in the unfolded distribution
130 fgMaxInput = nMeasured;
131 fgMaxParams = nUnfolded;
132
95e970ca 133 if (fgCorrelationMatrix)
134 {
135 delete fgCorrelationMatrix;
136 fgCorrelationMatrix = 0;
137 }
138 if (fgCorrelationMatrixSquared)
139 {
140 fgCorrelationMatrixSquared = 0;
141 delete fgCorrelationMatrixSquared;
142 }
143 if (fgCorrelationCovarianceMatrix)
144 {
145 delete fgCorrelationCovarianceMatrix;
146 fgCorrelationCovarianceMatrix = 0;
147 }
148 if (fgCurrentESDVector)
149 {
150 delete fgCurrentESDVector;
151 fgCurrentESDVector = 0;
152 }
153 if (fgEntropyAPriori)
154 {
155 delete fgEntropyAPriori;
156 fgEntropyAPriori = 0;
157 }
158 if (fgEfficiency)
159 {
160 delete fgEfficiency;
161 fgEfficiency = 0;
162 }
9e065ad2 163 if (fgUnfoldedAxis)
164 {
165 delete fgUnfoldedAxis;
166 fgUnfoldedAxis = 0;
167 }
168 if (fgMeasuredAxis)
95e970ca 169 {
9e065ad2 170 delete fgMeasuredAxis;
171 fgMeasuredAxis = 0;
95e970ca 172 }
173
19442b86 174 Printf("AliUnfolding::SetNbins: Set %d measured bins and %d unfolded bins", nMeasured, nUnfolded);
175}
176
177//____________________________________________________________________
178void AliUnfolding::SetChi2Regularization(RegularizationType type, Float_t weight)
179{
180 //
181 // sets the parameters for chi2 minimization
182 //
183
184 fgRegularizationType = type;
185 fgRegularizationWeight = weight;
186
187 Printf("AliUnfolding::SetChi2Regularization --> Regularization set to %d with weight %f", (Int_t) type, weight);
188}
189
190//____________________________________________________________________
191void AliUnfolding::SetBayesianParameters(Float_t smoothing, Int_t nIterations)
192{
193 //
194 // sets the parameters for Bayesian unfolding
195 //
196
197 fgBayesianSmoothing = smoothing;
198 fgBayesianIterations = nIterations;
199
736125ad 200 Printf("AliUnfolding::SetBayesianParameters --> Parameters set to %d iterations with smoothing %f", fgBayesianIterations, fgBayesianSmoothing);
19442b86 201}
202
203//____________________________________________________________________
204void AliUnfolding::SetFunction(TF1* function)
205{
206 // set function for unfolding with a fit function
207
208 fgFitFunction = function;
209
210 Printf("AliUnfolding::SetFunction: Set fit function with %d parameters.", function->GetNpar());
211}
212
213//____________________________________________________________________
214Int_t AliUnfolding::Unfold(TH2* correlation, TH1* efficiency, TH1* measured, TH1* initialConditions, TH1* result, Bool_t check)
215{
216 // unfolds with unfolding method fgMethodType
217 //
218 // parameters:
219 // correlation: response matrix as measured vs. generated
220 // 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.
221 // measured: the measured spectrum
222 // initialConditions: (optional) initial conditions for the unfolding. if 0 the measured spectrum is used as initial conditions.
223 // result: target for the unfolded result
224 // check: depends on the unfolding method, see comments in specific functions
95e970ca 225 //
226 // return code: see UnfoldWithMinuit/UnfoldWithBayesian/UnfoldWithFunction
19442b86 227
228 if (fgMaxInput == -1)
229 {
230 Printf("AliUnfolding::Unfold: WARNING. Number of measured bins not set with SetNbins. Using number of bins in measured distribution");
231 fgMaxInput = measured->GetNbinsX();
232 }
233 if (fgMaxParams == -1)
234 {
235 Printf("AliUnfolding::Unfold: WARNING. Number of unfolded bins not set with SetNbins. Using number of bins in measured distribution");
236 fgMaxParams = measured->GetNbinsX();
237 }
238
239 if (fgOverflowBinLimit > 0)
240 CreateOverflowBin(correlation, measured);
241
242 switch (fgMethodType)
243 {
244 case kInvalid:
245 {
246 Printf("AliUnfolding::Unfold: ERROR: Unfolding method not set. Use SetUnfoldingMethod. Exiting...");
247 return -1;
248 }
249 case kChi2Minimization:
250 return UnfoldWithMinuit(correlation, efficiency, measured, initialConditions, result, check);
251 case kBayesian:
252 return UnfoldWithBayesian(correlation, efficiency, measured, initialConditions, result);
253 case kFunction:
254 return UnfoldWithFunction(correlation, efficiency, measured, initialConditions, result);
255 }
9e065ad2 256
257
258
19442b86 259 return -1;
260}
261
262//____________________________________________________________________
95e970ca 263void AliUnfolding::SetStaticVariables(TH2* correlation, TH1* measured, TH1* efficiency)
19442b86 264{
265 // fill static variables needed for minuit fit
266
267 if (!fgCorrelationMatrix)
268 fgCorrelationMatrix = new TMatrixD(fgMaxInput, fgMaxParams);
95e970ca 269 if (!fgCorrelationMatrixSquared)
270 fgCorrelationMatrixSquared = new TMatrixD(fgMaxInput, fgMaxParams);
19442b86 271 if (!fgCorrelationCovarianceMatrix)
272 fgCorrelationCovarianceMatrix = new TMatrixD(fgMaxInput, fgMaxInput);
273 if (!fgCurrentESDVector)
274 fgCurrentESDVector = new TVectorD(fgMaxInput);
275 if (!fgEntropyAPriori)
276 fgEntropyAPriori = new TVectorD(fgMaxParams);
95e970ca 277 if (!fgEfficiency)
278 fgEfficiency = new TVectorD(fgMaxParams);
736125ad 279 if (fgUnfoldedAxis)
280 {
9e065ad2 281 delete fgUnfoldedAxis;
736125ad 282 fgUnfoldedAxis = 0;
283 }
284 if (!fgUnfoldedAxis)
285 fgUnfoldedAxis = new TAxis(*(correlation->GetXaxis()));
286 if (fgMeasuredAxis)
287 {
9e065ad2 288 delete fgMeasuredAxis;
736125ad 289 fgMeasuredAxis = 0;
290 }
291 if (!fgMeasuredAxis)
292 fgMeasuredAxis = new TAxis(*(correlation->GetYaxis()));
9e065ad2 293
19442b86 294 fgCorrelationMatrix->Zero();
295 fgCorrelationCovarianceMatrix->Zero();
296 fgCurrentESDVector->Zero();
297 fgEntropyAPriori->Zero();
298
299 // normalize correction for given nPart
300 for (Int_t i=1; i<=correlation->GetNbinsX(); ++i)
301 {
302 Double_t sum = correlation->Integral(i, i, 1, correlation->GetNbinsY());
303 if (sum <= 0)
304 continue;
305 Float_t maxValue = 0;
bea607a8 306 // Int_t maxBin = -1;
19442b86 307 for (Int_t j=1; j<=correlation->GetNbinsY(); ++j)
308 {
309 // find most probably value
310 if (maxValue < correlation->GetBinContent(i, j))
311 {
312 maxValue = correlation->GetBinContent(i, j);
bea607a8 313 // maxBin = j;
19442b86 314 }
315
316 // npart sum to 1
95e970ca 317 correlation->SetBinContent(i, j, correlation->GetBinContent(i, j) / sum);// * correlation->GetXaxis()->GetBinWidth(i));
19442b86 318 correlation->SetBinError(i, j, correlation->GetBinError(i, j) / sum);
319
320 if (i <= fgMaxParams && j <= fgMaxInput)
95e970ca 321 {
19442b86 322 (*fgCorrelationMatrix)(j-1, i-1) = correlation->GetBinContent(i, j);
95e970ca 323 (*fgCorrelationMatrixSquared)(j-1, i-1) = correlation->GetBinContent(i, j) * correlation->GetBinContent(i, j);
324 }
19442b86 325 }
326
327 //printf("MPV for Ntrue = %f is %f\n", fCurrentCorrelation->GetXaxis()->GetBinCenter(i), fCurrentCorrelation->GetYaxis()->GetBinCenter(maxBin));
328 }
329
330 //normalize measured
95e970ca 331 Float_t smallestError = 1;
19442b86 332 if (fgNormalizeInput)
95e970ca 333 {
334 Float_t sumMeasured = measured->Integral();
335 measured->Scale(1.0 / sumMeasured);
336 smallestError /= sumMeasured;
337 }
19442b86 338
339 for (Int_t i=0; i<fgMaxInput; ++i)
340 {
341 (*fgCurrentESDVector)[i] = measured->GetBinContent(i+1);
342 if (measured->GetBinError(i+1) > 0)
95e970ca 343 {
19442b86 344 (*fgCorrelationCovarianceMatrix)(i, i) = (Double_t) 1e-6 / measured->GetBinError(i+1) / measured->GetBinError(i+1);
95e970ca 345 }
346 else // in this case put error of 1, otherwise 0 bins are not added to the chi2...
347 (*fgCorrelationCovarianceMatrix)(i, i) = (Double_t) 1e-6 / smallestError / smallestError;
19442b86 348
349 if ((*fgCorrelationCovarianceMatrix)(i, i) > 1e7)
350 (*fgCorrelationCovarianceMatrix)(i, i) = 0;
351 //Printf("%d, %e", i, (*fgCorrelationCovarianceMatrix)(i, i));
352 }
95e970ca 353
354 // efficiency is expected to match bin width of result
355 for (Int_t i=0; i<fgMaxParams; ++i)
356 {
357 (*fgEfficiency)(i) = efficiency->GetBinContent(i+1);
95e970ca 358 }
9e065ad2 359
360 if (correlation->GetNbinsX() != fgMaxParams || correlation->GetNbinsY() != fgMaxInput)
361 cout << "Response histo has incorrect dimensions; expect (" << fgMaxParams << ", " << fgMaxInput << "), got (" << correlation->GetNbinsX() << ", " << correlation->GetNbinsY() << ")" << endl;
362
19442b86 363}
364
365//____________________________________________________________________
366Int_t AliUnfolding::UnfoldWithMinuit(TH2* correlation, TH1* efficiency, TH1* measured, TH1* initialConditions, TH1* result, Bool_t check)
367{
368 //
369 // implementation of unfolding (internal function)
370 //
371 // unfolds <measured> using response from <correlation> and effiency <efficiency>
372 // output is in <result>
373 // <initialConditions> set the initial values for the minimization, if 0 <measured> is used
95e970ca 374 // negative values in initialConditions mean that the given parameter is fixed to the absolute of the value
19442b86 375 // if <check> is true no unfolding is made, instead only the chi2 without unfolding is printed
376 //
377 // returns minuit status (0 = success), (-1 when check was set)
378 //
379
95e970ca 380 SetStaticVariables(correlation, measured, efficiency);
19442b86 381
382 // Initialize TMinuit via generic fitter interface
95e970ca 383 Int_t params = fgMaxParams;
384 if (fgNotFoundEvents > 0)
385 params++;
386
387 TVirtualFitter *minuit = TVirtualFitter::Fitter(0, params);
19442b86 388 Double_t arglist[100];
9e065ad2 389 // minuit->SetDefaultFitter("Minuit2");
19442b86 390
391 // disable any output (-1), unfortuantly we do not see warnings anymore then. Have to find another way...
392 arglist[0] = 0;
393 minuit->ExecuteCommand("SET PRINT", arglist, 1);
394
395 // however, enable warnings
396 //minuit->ExecuteCommand("SET WAR", arglist, 0);
397
398 // set minimization function
399 minuit->SetFCN(Chi2Function);
400
9e065ad2 401 // set precision
402 minuit->SetPrecision(fgMinuitPrecision);
403
d22beb7f 404 minuit->SetMaxIterations(fgMinuitMaxIterations);
405
9f070ef5 406 minuit->ExecuteCommand("SET STRATEGY",&fgMinuitStrategy,1);
407
19442b86 408 for (Int_t i=0; i<fgMaxParams; i++)
409 (*fgEntropyAPriori)[i] = 1;
410
95e970ca 411 // set initial conditions as a-priori distribution for MRX regularization
412 /*
413 for (Int_t i=0; i<fgMaxParams; i++)
414 if (initialConditions && initialConditions->GetBinContent(i+1) > 0)
415 (*fgEntropyAPriori)[i] = initialConditions->GetBinContent(i+1);
416 */
417
19442b86 418 if (!initialConditions) {
419 initialConditions = measured;
420 } else {
421 Printf("AliUnfolding::UnfoldWithMinuit: Using different initial conditions...");
422 //new TCanvas; initialConditions->DrawCopy();
423 if (fgNormalizeInput)
424 initialConditions->Scale(1.0 / initialConditions->Integral());
425 }
426
95e970ca 427 // extract minimum value from initial conditions (if we set a value to 0 it will stay 0)
deaac8b1 428 Float_t minValue = 1e35;
95e970ca 429 if (fgMinimumInitialValueFix < 0)
430 {
431 for (Int_t i=0; i<fgMaxParams; ++i)
432 {
433 Int_t bin = initialConditions->GetXaxis()->FindBin(result->GetXaxis()->GetBinCenter(i+1));
434 if (initialConditions->GetBinContent(bin) > 0)
435 minValue = TMath::Min(minValue, (Float_t) initialConditions->GetBinContent(bin));
436 }
437 }
438 else
439 minValue = fgMinimumInitialValueFix;
440
19442b86 441 Double_t* results = new Double_t[fgMaxParams+1];
442 for (Int_t i=0; i<fgMaxParams; ++i)
443 {
95e970ca 444 Int_t bin = initialConditions->GetXaxis()->FindBin(result->GetXaxis()->GetBinCenter(i+1));
445 results[i] = initialConditions->GetBinContent(bin);
19442b86 446
95e970ca 447 Bool_t fix = kFALSE;
448 if (results[i] < 0)
449 {
450 fix = kTRUE;
451 results[i] = -results[i];
452 }
453
454 if (!fix && fgMinimumInitialValue && results[i] < minValue)
455 results[i] = minValue;
456
19442b86 457 // minuit sees squared values to prevent it from going negative...
458 results[i] = TMath::Sqrt(results[i]);
459
95e970ca 460 minuit->SetParameter(i, Form("param%d", i), results[i], (fix) ? 0 : fgMinuitStepSize, 0, 0);
461 }
462 if (fgNotFoundEvents > 0)
463 {
464 results[fgMaxParams] = efficiency->GetBinContent(1);
465 minuit->SetParameter(fgMaxParams, "vtx0", results[fgMaxParams], fgMinuitStepSize / 100, 0.01, 0.80);
19442b86 466 }
467
468 Int_t dummy = 0;
469 Double_t chi2 = 0;
470 Chi2Function(dummy, 0, chi2, results, 0);
471 printf("AliUnfolding::UnfoldWithMinuit: Chi2 of initial parameters is = %f\n", chi2);
472
473 if (check)
474 {
475 DrawGuess(results);
476 delete[] results;
477 return -1;
478 }
479
480 // first param is number of iterations, second is precision....
03650114 481 arglist[0] = (float)fgMinuitMaxIterations;
482 // arglist[1] = 1e-5;
9e065ad2 483 // minuit->ExecuteCommand("SET PRINT", arglist, 3);
484 // minuit->ExecuteCommand("SCAN", arglist, 0);
19442b86 485 Int_t status = minuit->ExecuteCommand("MIGRAD", arglist, 1);
486 Printf("AliUnfolding::UnfoldWithMinuit: MINUIT status is %d", status);
487 //printf("!!!!!!!!!!!!!! MIGRAD finished: Starting MINOS !!!!!!!!!!!!!!");
488 //minuit->ExecuteCommand("MINOS", arglist, 0);
489
95e970ca 490 if (fgNotFoundEvents > 0)
491 {
492 results[fgMaxParams] = minuit->GetParameter(fgMaxParams);
493 Printf("Efficiency for bin 0 changed from %f to %f", efficiency->GetBinContent(1), results[fgMaxParams]);
494 efficiency->SetBinContent(1, results[fgMaxParams]);
495 }
496
19442b86 497 for (Int_t i=0; i<fgMaxParams; ++i)
498 {
499 results[i] = minuit->GetParameter(i);
500 Double_t value = results[i] * results[i];
a9edd311 501 // error is : 2 * (relError on results[i]) * (value) = 2 * (minuit->GetParError(i) / minuit->GetParameter(i)) * (minuit->GetParameter(i) * minuit->GetParameter(i))
b203a518 502 Double_t error = 0;
503 if (TMath::IsNaN(minuit->GetParError(i)))
504 Printf("WARNING: Parameter %d error is nan", i);
505 else
a9edd311 506 error = 2 * minuit->GetParError(i) * results[i];
19442b86 507
508 if (efficiency)
95e970ca 509 {
9e065ad2 510 //printf("value before efficiency correction: %f\n",value);
19442b86 511 if (efficiency->GetBinContent(i+1) > 0)
512 {
95e970ca 513 value /= efficiency->GetBinContent(i+1);
514 error /= efficiency->GetBinContent(i+1);
19442b86 515 }
516 else
517 {
95e970ca 518 value = 0;
519 error = 0;
19442b86 520 }
521 }
9e065ad2 522 //printf("value after efficiency correction: %f +/- %f\n",value,error);
19442b86 523 result->SetBinContent(i+1, value);
524 result->SetBinError(i+1, error);
525 }
d22beb7f 526
527 Int_t tmpCallCount = fgCallCount;
528 fgCallCount = 0; // needs to be 0 so that the Chi2Function prints its output
95e970ca 529 Chi2Function(dummy, 0, chi2, results, 0);
d22beb7f 530
531 Printf("AliUnfolding::UnfoldWithMinuit: iterations %d. Chi2 of final parameters is = %f", tmpCallCount, chi2);
95e970ca 532
19442b86 533 delete[] results;
534
535 return status;
536}
537
538//____________________________________________________________________
539Int_t AliUnfolding::UnfoldWithBayesian(TH2* correlation, TH1* aEfficiency, TH1* measured, TH1* initialConditions, TH1* aResult)
540{
541 //
542 // unfolds a spectrum using the Bayesian method
543 //
544
545 if (measured->Integral() <= 0)
546 {
547 Printf("AliUnfolding::UnfoldWithBayesian: ERROR: The measured spectrum is empty");
548 return -1;
549 }
550
551 const Int_t kStartBin = 0;
552
553 Int_t kMaxM = fgMaxInput; //<= fCurrentCorrelation->GetNbinsY(); // max measured axis
554 Int_t kMaxT = fgMaxParams; //<= fCurrentCorrelation->GetNbinsX(); // max true axis
555
556 // convergence limit: kMaxT * 0.001^2 = kMaxT * 1e-6 (e.g. 250 bins --> 2.5 e-4)
557 const Double_t kConvergenceLimit = kMaxT * 1e-6;
558
559 // store information in arrays, to increase processing speed (~ factor 5)
560 Double_t* measuredCopy = new Double_t[kMaxM];
561 Double_t* measuredError = new Double_t[kMaxM];
562 Double_t* prior = new Double_t[kMaxT];
563 Double_t* result = new Double_t[kMaxT];
564 Double_t* efficiency = new Double_t[kMaxT];
95e970ca 565 Double_t* binWidths = new Double_t[kMaxT];
736125ad 566 Double_t* normResponse = new Double_t[kMaxT];
19442b86 567
568 Double_t** response = new Double_t*[kMaxT];
569 Double_t** inverseResponse = new Double_t*[kMaxT];
570 for (Int_t i=0; i<kMaxT; i++)
571 {
572 response[i] = new Double_t[kMaxM];
573 inverseResponse[i] = new Double_t[kMaxM];
736125ad 574 normResponse[i] = 0;
19442b86 575 }
576
577 // for normalization
578 Float_t measuredIntegral = measured->Integral();
579 for (Int_t m=0; m<kMaxM; m++)
580 {
581 measuredCopy[m] = measured->GetBinContent(m+1) / measuredIntegral;
582 measuredError[m] = measured->GetBinError(m+1) / measuredIntegral;
583
584 for (Int_t t=0; t<kMaxT; t++)
585 {
586 response[t][m] = correlation->GetBinContent(t+1, m+1);
587 inverseResponse[t][m] = 0;
736125ad 588 normResponse[t] += correlation->GetBinContent(t+1, m+1);
19442b86 589 }
590 }
591
592 for (Int_t t=0; t<kMaxT; t++)
593 {
651e2088 594 if (aEfficiency)
19442b86 595 {
596 efficiency[t] = aEfficiency->GetBinContent(t+1);
597 }
598 else
599 efficiency[t] = 1;
600
601 prior[t] = measuredCopy[t];
602 result[t] = 0;
95e970ca 603 binWidths[t] = aResult->GetXaxis()->GetBinWidth(t+1);
736125ad 604
605 for (Int_t m=0; m<kMaxM; m++) { // Normalise response matrix
606 if (normResponse[t] != 0)
607 response[t][m] /= normResponse[t];
608 else
609 Printf("AliUnfolding::UnfoldWithBayesian: Empty row,column in response matrix, for truth bin %d",t);
610 }
19442b86 611 }
612
613 // pick prior distribution
614 if (initialConditions)
615 {
616 printf("Using different starting conditions...\n");
617 // for normalization
618 Float_t inputDistIntegral = initialConditions->Integral();
619 for (Int_t i=0; i<kMaxT; i++)
620 prior[i] = initialConditions->GetBinContent(i+1) / inputDistIntegral;
621 }
622
623 //TH1F* convergence = new TH1F("convergence", "convergence", 200, 0.5, 200.5);
624
95e970ca 625 //new TCanvas;
19442b86 626 // unfold...
95e970ca 627 for (Int_t i=0; i<fgBayesianIterations || fgBayesianIterations < 0; i++)
19442b86 628 {
629 if (fgDebug)
630 Printf("AliUnfolding::UnfoldWithBayesian: iteration %i", i);
631
95e970ca 632 // calculate IR from Bayes theorem
19442b86 633 // IR_ji = R_ij * prior_i / sum_k(R_kj * prior_k)
634
635 Double_t chi2Measured = 0;
636 for (Int_t m=0; m<kMaxM; m++)
637 {
638 Float_t norm = 0;
639 for (Int_t t = kStartBin; t<kMaxT; t++)
736125ad 640 norm += response[t][m] * prior[t] * efficiency[t];
19442b86 641
642 // calc. chi2: (measured - response * prior) / error
643 if (measuredError[m] > 0)
644 {
645 Double_t value = (measuredCopy[m] - norm) / measuredError[m];
646 chi2Measured += value * value;
647 }
648
649 if (norm > 0)
650 {
651 for (Int_t t = kStartBin; t<kMaxT; t++)
736125ad 652 inverseResponse[t][m] = response[t][m] * prior[t] * efficiency[t] / norm;
19442b86 653 }
654 else
655 {
656 for (Int_t t = kStartBin; t<kMaxT; t++)
657 inverseResponse[t][m] = 0;
658 }
659 }
660 //Printf("chi2Measured of the last prior is %e", chi2Measured);
661
662 for (Int_t t = kStartBin; t<kMaxT; t++)
663 {
664 Float_t value = 0;
665 for (Int_t m=0; m<kMaxM; m++)
666 value += inverseResponse[t][m] * measuredCopy[m];
667
668 if (efficiency[t] > 0)
669 result[t] = value / efficiency[t];
670 else
671 result[t] = 0;
672 }
673
95e970ca 674 /*
19442b86 675 // draw intermediate result
19442b86 676 for (Int_t t=0; t<kMaxT; t++)
95e970ca 677 {
19442b86 678 aResult->SetBinContent(t+1, result[t]);
95e970ca 679 }
680 aResult->SetMarkerStyle(24+i);
19442b86 681 aResult->SetMarkerColor(2);
95e970ca 682 aResult->DrawCopy((i == 0) ? "P" : "PSAME");
19442b86 683 */
95e970ca 684
19442b86 685 Double_t chi2LastIter = 0;
686 // regularization (simple smoothing)
687 for (Int_t t=kStartBin; t<kMaxT; t++)
688 {
689 Float_t newValue = 0;
690
691 // 0 bin excluded from smoothing
692 if (t > kStartBin+2 && t<kMaxT-1)
693 {
95e970ca 694 Float_t average = (result[t-1] / binWidths[t-1] + result[t] / binWidths[t] + result[t+1] / binWidths[t+1]) / 3 * binWidths[t];
19442b86 695
696 // weight the average with the regularization parameter
697 newValue = (1 - fgBayesianSmoothing) * result[t] + fgBayesianSmoothing * average;
698 }
699 else
700 newValue = result[t];
701
702 // calculate chi2 (change from last iteration)
703 if (prior[t] > 1e-5)
704 {
705 Double_t diff = (prior[t] - newValue) / prior[t];
706 chi2LastIter += diff * diff;
707 }
708
709 prior[t] = newValue;
710 }
711 //printf("Chi2 of %d iteration = %e\n", i, chi2LastIter);
712 //convergence->Fill(i+1, chi2LastIter);
713
714 if (fgBayesianIterations < 0 && chi2LastIter < kConvergenceLimit)
715 {
716 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);
717 break;
718 }
719 } // end of iterations
720
721 //new TCanvas; convergence->DrawCopy(); gPad->SetLogy();
722 //delete convergence;
723
95e970ca 724 Float_t factor = 1;
725 if (!fgNormalizeInput)
726 factor = measuredIntegral;
19442b86 727 for (Int_t t=0; t<kMaxT; t++)
95e970ca 728 aResult->SetBinContent(t+1, result[t] * factor);
19442b86 729
730 delete[] measuredCopy;
731 delete[] measuredError;
732 delete[] prior;
733 delete[] result;
734 delete[] efficiency;
95e970ca 735 delete[] binWidths;
736125ad 736 delete[] normResponse;
19442b86 737
738 for (Int_t i=0; i<kMaxT; i++)
739 {
740 delete[] response[i];
741 delete[] inverseResponse[i];
742 }
743 delete[] response;
744 delete[] inverseResponse;
745
746 return 0;
747
748 // ********
749 // Calculate the covariance matrix, all arguments are taken from NIM,A362,487-498,1995
750
751 /*printf("Calculating covariance matrix. This may take some time...\n");
752
753 // check if this is the right one...
754 TH1* sumHist = GetMultiplicityMC(inputRange, eventType)->ProjectionY("sumHist", 1, GetMultiplicityMC(inputRange, eventType)->GetNbinsX());
755
756 Int_t xBins = hInverseResponseBayes->GetNbinsX();
757 Int_t yBins = hInverseResponseBayes->GetNbinsY();
758
759 // calculate "unfolding matrix" Mij
760 Float_t matrixM[251][251];
761 for (Int_t i=1; i<=xBins; i++)
762 {
763 for (Int_t j=1; j<=yBins; j++)
764 {
765 if (fCurrentEfficiency->GetBinContent(i) > 0)
766 matrixM[i-1][j-1] = hInverseResponseBayes->GetBinContent(i, j) / fCurrentEfficiency->GetBinContent(i);
767 else
768 matrixM[i-1][j-1] = 0;
769 }
770 }
771
772 Float_t* vectorn = new Float_t[yBins];
773 for (Int_t j=1; j<=yBins; j++)
774 vectorn[j-1] = fCurrentESD->GetBinContent(j);
775
776 // first part of covariance matrix, depends on input distribution n(E)
777 Float_t cov1[251][251];
778
779 Float_t nEvents = fCurrentESD->Integral(); // N
780
781 xBins = 20;
782 yBins = 20;
783
784 for (Int_t k=0; k<xBins; k++)
785 {
786 printf("In Cov1: %d\n", k);
787 for (Int_t l=0; l<yBins; l++)
788 {
789 cov1[k][l] = 0;
790
791 // sum_j Mkj Mlj n(Ej) * (1 - n(Ej) / N)
792 for (Int_t j=0; j<yBins; j++)
793 cov1[k][l] += matrixM[k][j] * matrixM[l][j] * vectorn[j]
794 * (1.0 - vectorn[j] / nEvents);
795
796 // - sum_i,j (i != j) Mki Mlj n(Ei) n(Ej) / N
797 for (Int_t i=0; i<yBins; i++)
798 for (Int_t j=0; j<yBins; j++)
799 {
800 if (i == j)
801 continue;
802 cov1[k][l] -= matrixM[k][i] * matrixM[l][j] * vectorn[i]
803 * vectorn[j] / nEvents;
804 }
805 }
806 }
807
808 printf("Cov1 finished\n");
809
810 TH2F* cov = (TH2F*) hInverseResponseBayes->Clone("cov");
811 cov->Reset();
812
813 for (Int_t i=1; i<=xBins; i++)
814 for (Int_t j=1; j<=yBins; j++)
815 cov->SetBinContent(i, j, cov1[i-1][j-1]);
816
817 new TCanvas;
818 cov->Draw("COLZ");
819
820 // second part of covariance matrix, depends on response matrix
821 Float_t cov2[251][251];
822
823 // Cov[P(Er|Cu), P(Es|Cu)] term
824 Float_t covTerm[100][100][100];
825 for (Int_t r=0; r<yBins; r++)
826 for (Int_t u=0; u<xBins; u++)
827 for (Int_t s=0; s<yBins; s++)
828 {
829 if (r == s)
830 covTerm[r][u][s] = 1.0 / sumHist->GetBinContent(u+1) * hResponse->GetBinContent(u+1, r+1)
831 * (1.0 - hResponse->GetBinContent(u+1, r+1));
832 else
833 covTerm[r][u][s] = - 1.0 / sumHist->GetBinContent(u+1) * hResponse->GetBinContent(u+1, r+1)
834 * hResponse->GetBinContent(u+1, s+1);
835 }
836
837 for (Int_t k=0; k<xBins; k++)
838 for (Int_t l=0; l<yBins; l++)
839 {
840 cov2[k][l] = 0;
841 printf("In Cov2: %d %d\n", k, l);
842 for (Int_t i=0; i<yBins; i++)
843 for (Int_t j=0; j<yBins; j++)
844 {
845 //printf("In Cov2: %d %d %d %d\n", k, l, i, j);
846 // calculate Cov(Mki, Mlj) = sum{ru},{su} ...
847 Float_t tmpCov = 0;
848 for (Int_t r=0; r<yBins; r++)
849 for (Int_t u=0; u<xBins; u++)
850 for (Int_t s=0; s<yBins; s++)
851 {
852 if (hResponse->GetBinContent(u+1, r+1) == 0 || hResponse->GetBinContent(u+1, s+1) == 0
853 || hResponse->GetBinContent(u+1, i+1) == 0)
854 continue;
855
856 tmpCov += BayesCovarianceDerivate(matrixM, hResponse, fCurrentEfficiency, k, i, r, u)
857 * BayesCovarianceDerivate(matrixM, hResponse, fCurrentEfficiency, l, j, s, u)
858 * covTerm[r][u][s];
859 }
860
861 cov2[k][l] += fCurrentESD->GetBinContent(i+1) * fCurrentESD->GetBinContent(j+1) * tmpCov;
862 }
863 }
864
865 printf("Cov2 finished\n");
866
867 for (Int_t i=1; i<=xBins; i++)
868 for (Int_t j=1; j<=yBins; j++)
869 cov->SetBinContent(i, j, cov1[i-1][j-1] + cov2[i-1][j-1]);
870
871 new TCanvas;
872 cov->Draw("COLZ");*/
873}
874
875//____________________________________________________________________
876Double_t AliUnfolding::RegularizationPol0(TVectorD& params)
877{
878 // homogenity term for minuit fitting
879 // pure function of the parameters
880 // prefers constant function (pol0)
9e065ad2 881 //
882 // Does not take into account efficiency
19442b86 883 Double_t chi2 = 0;
884
885 for (Int_t i=1+fgSkipBinsBegin; i<fgMaxParams; ++i)
886 {
9e065ad2 887 Double_t right = params[i] / fgUnfoldedAxis->GetBinWidth(i+1);
888 Double_t left = params[i-1] / fgUnfoldedAxis->GetBinWidth(i);
19442b86 889
95e970ca 890 if (left != 0)
19442b86 891 {
95e970ca 892 Double_t diff = (right - left);
9e065ad2 893 chi2 += diff * diff / left / ((fgUnfoldedAxis->GetBinWidth(i+1) + fgUnfoldedAxis->GetBinWidth(i)) / 2);
19442b86 894 }
895 }
896
897 return chi2 / 100.0;
898}
899
900//____________________________________________________________________
901Double_t AliUnfolding::RegularizationPol1(TVectorD& params)
902{
903 // homogenity term for minuit fitting
904 // pure function of the parameters
905 // prefers linear function (pol1)
9e065ad2 906 //
907 // Does not take into account efficiency
19442b86 908 Double_t chi2 = 0;
909
910 for (Int_t i=2+fgSkipBinsBegin; i<fgMaxParams; ++i)
911 {
912 if (params[i-1] == 0)
913 continue;
914
9e065ad2 915 Double_t right = params[i] / fgUnfoldedAxis->GetBinWidth(i+1);
916 Double_t middle = params[i-1] / fgUnfoldedAxis->GetBinWidth(i);
917 Double_t left = params[i-2] / fgUnfoldedAxis->GetBinWidth(i-1);
19442b86 918
9e065ad2 919 Double_t der1 = (right - middle) / ((fgUnfoldedAxis->GetBinWidth(i+1) + fgUnfoldedAxis->GetBinWidth(i)) / 2);
920 Double_t der2 = (middle - left) / ((fgUnfoldedAxis->GetBinWidth(i) + fgUnfoldedAxis->GetBinWidth(i-1)) / 2);
19442b86 921
95e970ca 922 //Double_t diff = (der1 - der2) / middle;
923 //chi2 += diff * diff;
9e065ad2 924 chi2 += (der1 - der2) * (der1 - der2) / middle * fgUnfoldedAxis->GetBinWidth(i);
19442b86 925 }
926
927 return chi2;
928}
929
930//____________________________________________________________________
931Double_t AliUnfolding::RegularizationLog(TVectorD& params)
932{
933 // homogenity term for minuit fitting
934 // pure function of the parameters
9e065ad2 935 // prefers logarithmic function (log)
936 //
937 // Does not take into account efficiency
19442b86 938
939 Double_t chi2 = 0;
940
941 for (Int_t i=2+fgSkipBinsBegin; i<fgMaxParams; ++i)
942 {
95e970ca 943 if (params[i-1] == 0 || params[i] == 0 || params[i-2] == 0)
944 continue;
19442b86 945
9e065ad2 946 Double_t right = log(params[i] / fgUnfoldedAxis->GetBinWidth(i+1));
947 Double_t middle = log(params[i-1] / fgUnfoldedAxis->GetBinWidth(i));
948 Double_t left = log(params[i-2] / fgUnfoldedAxis->GetBinWidth(i-1));
95e970ca 949
9e065ad2 950 Double_t der1 = (right - middle) / ((fgUnfoldedAxis->GetBinWidth(i+1) + fgUnfoldedAxis->GetBinWidth(i)) / 2);
951 Double_t der2 = (middle - left) / ((fgUnfoldedAxis->GetBinWidth(i) + fgUnfoldedAxis->GetBinWidth(i-1)) / 2);
95e970ca 952
953 //Double_t error = 1. / params[i] + 4. / params[i-1] + 1. / params[i-2];
19442b86 954
95e970ca 955 //if (fgCallCount == 0)
956 // Printf("%d %f %f", i, (der1 - der2) * (der1 - der2), error);
957 chi2 += (der1 - der2) * (der1 - der2);// / error;
19442b86 958 }
959
95e970ca 960 return chi2;
19442b86 961}
962
963//____________________________________________________________________
964Double_t AliUnfolding::RegularizationTotalCurvature(TVectorD& params)
965{
966 // homogenity term for minuit fitting
967 // pure function of the parameters
968 // minimizes the total curvature (from Unfolding Methods In High-Energy Physics Experiments,
969 // V. Blobel (Hamburg U.) . DESY 84/118, Dec 1984. 40pp.
9e065ad2 970 //
971 // Does not take into account efficiency
19442b86 972
973 Double_t chi2 = 0;
974
975 for (Int_t i=2+fgSkipBinsBegin; i<fgMaxParams; ++i)
976 {
977 Double_t right = params[i];
978 Double_t middle = params[i-1];
979 Double_t left = params[i-2];
980
981 Double_t der1 = (right - middle);
982 Double_t der2 = (middle - left);
983
984 Double_t diff = (der1 - der2);
985
986 chi2 += diff * diff;
987 }
988
989 return chi2 * 1e4;
990}
991
992//____________________________________________________________________
993Double_t AliUnfolding::RegularizationEntropy(TVectorD& params)
994{
995 // homogenity term for minuit fitting
996 // pure function of the parameters
997 // calculates entropy, from
998 // The method of reduced cross-entropy (M. Schmelling 1993)
9e065ad2 999 //
1000 // Does not take into account efficiency
19442b86 1001
1002 Double_t paramSum = 0;
1003
1004 for (Int_t i=fgSkipBinsBegin; i<fgMaxParams; ++i)
1005 paramSum += params[i];
1006
1007 Double_t chi2 = 0;
1008 for (Int_t i=fgSkipBinsBegin; i<fgMaxParams; ++i)
1009 {
95e970ca 1010 Double_t tmp = params[i] / paramSum;
1011 //Double_t tmp = params[i];
19442b86 1012 if (tmp > 0 && (*fgEntropyAPriori)[i] > 0)
1013 {
1014 chi2 += tmp * TMath::Log(tmp / (*fgEntropyAPriori)[i]);
1015 }
95e970ca 1016 else
1017 chi2 += 100;
1018 }
1019
1020 return -chi2;
1021}
1022
1023//____________________________________________________________________
1024Double_t AliUnfolding::RegularizationRatio(TVectorD& params)
1025{
1026 // homogenity term for minuit fitting
1027 // pure function of the parameters
9e065ad2 1028 //
1029 // Does not take into account efficiency
95e970ca 1030
1031 Double_t chi2 = 0;
1032
1033 for (Int_t i=5+fgSkipBinsBegin; i<fgMaxParams; ++i)
1034 {
1035 if (params[i-1] == 0 || params[i] == 0)
1036 continue;
1037
9e065ad2 1038 Double_t right = params[i] / fgUnfoldedAxis->GetBinWidth(i+1);
1039 Double_t middle = params[i-1] / fgUnfoldedAxis->GetBinWidth(i);
1040 Double_t left = params[i-2] / fgUnfoldedAxis->GetBinWidth(i-1);
1041 Double_t left2 = params[i-3] / fgUnfoldedAxis->GetBinWidth(i-2);
1042 Double_t left3 = params[i-4] / fgUnfoldedAxis->GetBinWidth(i-3);
1043 Double_t left4 = params[i-5] / fgUnfoldedAxis->GetBinWidth(i-4);
95e970ca 1044
1045 //Double_t diff = left / middle - middle / right;
1046 //Double_t diff = 2 * left / middle - middle / right - left2 / left;
1047 Double_t diff = 4 * left2 / left - middle / right - left / middle - left3 / left2 - left4 / left3;
1048
1049 chi2 += diff * diff;// / middle;
19442b86 1050 }
1051
95e970ca 1052 return chi2;
19442b86 1053}
1054
1055//____________________________________________________________________
9e065ad2 1056Double_t AliUnfolding::RegularizationPowerLaw(TVectorD& params)
1057{
1058 // homogenity term for minuit fitting
1059 // pure function of the parameters
1060 // prefers power law with n = -5
1061 //
1062 // Does not take into account efficiency
1063
1064 Double_t chi2 = 0;
1065
1066 Double_t right = 0.;
1067 Double_t middle = 0.;
1068 Double_t left = 0.;
1069
1070 for (Int_t i=2+fgSkipBinsBegin; i<fgMaxParams; ++i)
1071 {
1072 if (params[i] < 1e-8 || params[i-1] < 1e-8 || params[i-2] < 1e-8)
1073 continue;
1074
1075 if (fgUnfoldedAxis->GetBinWidth(i+1) < 1e-8 || fgUnfoldedAxis->GetBinWidth(i) < 1e-8 || fgUnfoldedAxis->GetBinWidth(i-1) < 1e-8)
1076 continue;
1077
1078 middle = TMath::Power(params[i-1] / fgUnfoldedAxis->GetBinWidth(i),fgPowern);
1079
1080 if(middle>0) {
59076376 1081 right = TMath::Power(params[i] / fgUnfoldedAxis->GetBinWidth(i+1),fgPowern)/middle;
9e065ad2 1082
1083 left = TMath::Power(params[i-2] / fgUnfoldedAxis->GetBinWidth(i-1),fgPowern)/middle;
1084
1085 middle = 1.;
1086
1087 Double_t der1 = (right - middle) / ((fgUnfoldedAxis->GetBinWidth(i+1) + fgUnfoldedAxis->GetBinWidth(i)) / 2);
59076376 1088 Double_t der2 = (middle - left) / ((fgUnfoldedAxis->GetBinWidth(i) + fgUnfoldedAxis->GetBinWidth(i-1)) / 2);
9e065ad2 1089
59076376 1090 chi2 += (der1 - der2) * (der1 - der2)/ ( fgUnfoldedAxis->GetBinWidth(i+1)/2. + fgUnfoldedAxis->GetBinWidth(i) + fgUnfoldedAxis->GetBinWidth(i-1)/2.)/( fgUnfoldedAxis->GetBinWidth(i+1)/2. + fgUnfoldedAxis->GetBinWidth(i) + fgUnfoldedAxis->GetBinWidth(i-1)/2.);// / error;
9e065ad2 1091 // printf("i: %d chi2 = %f\n",i,chi2);
1092 }
1093
1094 }
1095
1096 return chi2;
1097}
1098
1099//____________________________________________________________________
1100Double_t AliUnfolding::RegularizationLogLog(TVectorD& params)
1101{
1102 // homogenity term for minuit fitting
1103 // pure function of the parameters
1104 // prefers a powerlaw (linear on a log-log scale)
1105 //
1106 // The calculation takes into account the efficiencies
1107
1108 Double_t chi2 = 0;
1109
1110 for (Int_t i=2+fgSkipBinsBegin; i<fgMaxParams; ++i)
1111 {
1112 if (params[i-1] == 0 || params[i] == 0 || params[i-2] == 0)
1113 continue;
1114 if ((*fgEfficiency)(i-1) == 0 || (*fgEfficiency)(i) == 0 || (*fgEfficiency)(i-2) == 0)
1115 continue;
1116
59076376 1117 Double_t right = log(params[i] / (*fgEfficiency)(i) / fgUnfoldedAxis->GetBinWidth(i+1));
1118 Double_t middle = log(params[i-1] / (*fgEfficiency)(i-1) / fgUnfoldedAxis->GetBinWidth(i));
1119 Double_t left = log(params[i-2] / (*fgEfficiency)(i-2) / fgUnfoldedAxis->GetBinWidth(i-1));
9e065ad2 1120
1121 Double_t der1 = (right - middle) / ( log(fgUnfoldedAxis->GetBinCenter(i+1)) - log(fgUnfoldedAxis->GetBinCenter(i)) );
1122 Double_t der2 = (middle - left) /( log(fgUnfoldedAxis->GetBinCenter(i)) - log(fgUnfoldedAxis->GetBinCenter(i-1)) );
59076376 1123
9e065ad2 1124 double tmp = (log(fgUnfoldedAxis->GetBinCenter(i+1)) - log(fgUnfoldedAxis->GetBinCenter(i-1)))/2.;
1125 Double_t dder = (der1-der2) / tmp;
1126
1127 chi2 += dder * dder;
1128 }
1129
1130 return chi2;
1131}
1132
1133
1134
1135//____________________________________________________________________
19442b86 1136void AliUnfolding::Chi2Function(Int_t&, Double_t*, Double_t& chi2, Double_t *params, Int_t)
1137{
1138 //
1139 // fit function for minuit
1140 // does: (m - Ad)W(m - Ad) where m = measured, A correlation matrix, d = guess, W = covariance matrix
1141 //
95e970ca 1142
1143 // TODO use static members for the variables here to speed up processing (no construction/deconstruction)
19442b86 1144
9e065ad2 1145 // d = guess
95e970ca 1146 TVectorD paramsVector(fgMaxParams);
19442b86 1147 for (Int_t i=0; i<fgMaxParams; ++i)
1148 paramsVector[i] = params[i] * params[i];
1149
1150 // calculate penalty factor
1151 Double_t penaltyVal = 0;
9e065ad2 1152
19442b86 1153 switch (fgRegularizationType)
1154 {
1155 case kNone: break;
1156 case kPol0: penaltyVal = RegularizationPol0(paramsVector); break;
1157 case kPol1: penaltyVal = RegularizationPol1(paramsVector); break;
1158 case kCurvature: penaltyVal = RegularizationTotalCurvature(paramsVector); break;
1159 case kEntropy: penaltyVal = RegularizationEntropy(paramsVector); break;
1160 case kLog: penaltyVal = RegularizationLog(paramsVector); break;
95e970ca 1161 case kRatio: penaltyVal = RegularizationRatio(paramsVector); break;
9e065ad2 1162 case kPowerLaw: penaltyVal = RegularizationPowerLaw(paramsVector); break;
1163 case kLogLog: penaltyVal = RegularizationLogLog(paramsVector); break;
19442b86 1164 }
1165
9e065ad2 1166 penaltyVal *= fgRegularizationWeight; //beta*PU
19442b86 1167
1168 // Ad
1169 TVectorD measGuessVector(fgMaxInput);
1170 measGuessVector = (*fgCorrelationMatrix) * paramsVector;
1171
1172 // Ad - m
1173 measGuessVector -= (*fgCurrentESDVector);
95e970ca 1174
1175#if 0
1176 // new error calcuation using error on the guess
1177
1178 // error from guess
1179 TVectorD errorGuessVector(fgMaxInput);
1180 //errorGuessVector = (*fgCorrelationMatrixSquared) * paramsVector;
1181 errorGuessVector = (*fgCorrelationMatrix) * paramsVector;
19442b86 1182
95e970ca 1183 Double_t chi2FromFit = 0;
1184 for (Int_t i=0; i<fgMaxInput; ++i)
1185 {
1186 Float_t error = 1;
1187 if (errorGuessVector(i) > 0)
1188 error = errorGuessVector(i);
1189 chi2FromFit += measGuessVector(i) * measGuessVector(i) / error;
1190 }
19442b86 1191
95e970ca 1192#else
1193 // old error calcuation using the error on the measured
19442b86 1194 TVectorD copy(measGuessVector);
1195
1196 // (Ad - m) W
1197 // this step can be optimized because currently only the diagonal elements of fgCorrelationCovarianceMatrix are used
1198 // normal way is like this:
1199 // measGuessVector *= (*fgCorrelationCovarianceMatrix);
1200 // optimized way like this:
1201 for (Int_t i=0; i<fgMaxInput; ++i)
1202 measGuessVector[i] *= (*fgCorrelationCovarianceMatrix)(i, i);
1203
19442b86 1204
95e970ca 1205 if (fgSkipBin0InChi2)
1206 measGuessVector[0] = 0;
1207
19442b86 1208 // (Ad - m) W (Ad - m)
1209 // the factor 1e6 prevents that a very small number (measGuessVector[i]) is multiplied with a very
95e970ca 1210 // big number ((*fgCorrelationCovarianceMatrix)(i, i)) (see UnfoldWithMinuit)
19442b86 1211 Double_t chi2FromFit = measGuessVector * copy * 1e6;
95e970ca 1212#endif
19442b86 1213
95e970ca 1214 Double_t notFoundEventsConstraint = 0;
1215 Double_t currentNotFoundEvents = 0;
1216 Double_t errorNotFoundEvents = 0;
1217
1218 if (fgNotFoundEvents > 0)
1219 {
1220 for (Int_t i=0; i<fgMaxParams; ++i)
1221 {
1222 Double_t eff = (1.0 / (*fgEfficiency)(i) - 1);
1223 if (i == 0)
1224 eff = (1.0 / params[fgMaxParams] - 1);
1225 currentNotFoundEvents += eff * paramsVector(i);
1226 errorNotFoundEvents += eff * eff * paramsVector(i); // error due to guess (paramsVector)
1227 if (i <= 3)
1228 errorNotFoundEvents += (eff * 0.03) * (eff * 0.03) * paramsVector(i) * paramsVector(i); // error on eff
9e065ad2 1229 // if ((fgCallCount % 10000) == 0)
1230 //Printf("%d %f %f %f", i, (*fgEfficiency)(i), paramsVector(i), currentNotFoundEvents);
95e970ca 1231 }
1232 errorNotFoundEvents += fgNotFoundEvents;
1233 // TODO add error on background, background estimate
1234
1235 notFoundEventsConstraint = (currentNotFoundEvents - fgNotFoundEvents) * (currentNotFoundEvents - fgNotFoundEvents) / errorNotFoundEvents;
1236 }
1237
1238 Float_t avg = 0;
1239 Float_t sum = 0;
1240 Float_t currentMult = 0;
1241 // try to match dn/deta
1242 for (Int_t i=0; i<fgMaxParams; ++i)
1243 {
1244 avg += paramsVector(i) * currentMult;
1245 sum += paramsVector(i);
9e065ad2 1246 currentMult += fgUnfoldedAxis->GetBinWidth(i);
95e970ca 1247 }
1248 avg /= sum;
1249 Float_t chi2Avg = 0; //(avg - 3.73) * (avg - 3.73) * 100;
19442b86 1250
95e970ca 1251 chi2 = chi2FromFit + penaltyVal + notFoundEventsConstraint + chi2Avg;
9e065ad2 1252
95e970ca 1253 if ((fgCallCount++ % 1000) == 0)
1254 {
9e065ad2 1255
1256 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-1], avg, chi2FromFit, penaltyVal, notFoundEventsConstraint, chi2Avg, chi2);
1257
95e970ca 1258 //for (Int_t i=0; i<fgMaxInput; ++i)
1259 // Printf("%d: %f", i, measGuessVector(i) * copy(i) * 1e6);
1260 }
9e065ad2 1261
1262 fChi2FromFit = chi2FromFit;
1263 fPenaltyVal = penaltyVal;
19442b86 1264}
1265
1266//____________________________________________________________________
9e065ad2 1267void AliUnfolding::MakePads() {
1268 TPad *presult = new TPad("presult","result",0,0.4,1,1);
1269 presult->SetNumber(1);
1270 presult->Draw();
1271 presult->SetLogy();
1272 TPad *pres = new TPad("pres","residuals",0,0.2,1,0.4);
1273 pres->SetNumber(2);
1274 pres->Draw();
1275 TPad *ppen = new TPad("ppen","penalty",0,0.0,1,0.2);
1276 ppen->SetNumber(3);
1277 ppen->Draw();
1278
1279}
1280//____________________________________________________________________
1281void AliUnfolding::DrawResults(TH2* correlation, TH1* efficiency, TH1* measured, TH1* initialConditions, TCanvas *canv, Int_t reuseHists,TH1 *unfolded)
1282{
1283 // Draw histograms of
1284 // - Result folded with response
1285 // - Penalty factors
1286 // - Chisquare contributions
1287 // (Useful for debugging/sanity checks and the interactive unfolder)
1288 //
1289 // If a canvas pointer is given (canv != 0), it will be used for all
1290 // plots; 3 pads are made if needed.
1291
1292
1293 Int_t blankCanvas = 0;
1294 TVirtualPad *presult = 0;
1295 TVirtualPad *pres = 0;
1296 TVirtualPad *ppen = 0;
1297
1298 if (canv) {
1299 canv->cd();
1300 presult = canv->GetPad(1);
1301 pres = canv->GetPad(2);
1302 ppen = canv->GetPad(3);
1303 if (presult == 0 || pres == 0 || ppen == 0) {
1304 canv->Clear();
1305 MakePads();
1306 blankCanvas = 1;
1307 presult = canv->GetPad(1);
1308 pres = canv->GetPad(2);
1309 ppen = canv->GetPad(3);
1310 }
1311 }
1312 else {
1313 presult = new TCanvas;
1314 pres = new TCanvas;
1315 ppen = new TCanvas;
1316 }
1317
1318
1319 if (fgMaxInput == -1)
1320 {
1321 Printf("AliUnfolding::Unfold: WARNING. Number of measured bins not set with SetNbins. Using number of bins in measured distribution");
1322 fgMaxInput = measured->GetNbinsX();
1323 }
1324 if (fgMaxParams == -1)
1325 {
1326 Printf("AliUnfolding::Unfold: WARNING. Number of unfolded bins not set with SetNbins. Using number of bins in measured distribution");
1327 fgMaxParams = initialConditions->GetNbinsX();
1328 }
1329
1330 if (fgOverflowBinLimit > 0)
1331 CreateOverflowBin(correlation, measured);
1332
1333 // Uses Minuit methods
1334
1335 SetStaticVariables(correlation, measured, efficiency);
1336
1337 Double_t* params = new Double_t[fgMaxParams+1];
1338 for (Int_t i=0; i<fgMaxParams; ++i)
1339 {
1340 params[i] = initialConditions->GetBinContent(i+1) * efficiency->GetBinContent(i+1);
1341
9e065ad2 1342 if (params[i] < 0)
9e065ad2 1343 params[i] = -params[i];
9e065ad2 1344 params[i]=TMath::Sqrt(params[i]);
9e065ad2 1345 }
1346
1347 Double_t chi2;
1348 Int_t dummy;
1349
1350 //fgPrintChi2Details = kTRUE;
1351 fgCallCount = 0; // To make sure that Chi2Function prints the components
1352 Chi2Function(dummy, 0, chi2, params, 0);
1353
1354 presult->cd();
03650114 1355 TH1 *meas2 = (TH1*)measured->Clone("meas2");
1356 meas2->SetTitle("meas2");
1357 meas2->SetName("meas2");
9e065ad2 1358 meas2->SetLineColor(1);
1359 meas2->SetLineWidth(2);
1360 meas2->SetMarkerColor(meas2->GetLineColor());
1361 meas2->SetMarkerStyle(20);
1362 Float_t scale = unfolded->GetXaxis()->GetBinWidth(1)/meas2->GetXaxis()->GetBinWidth(1);
1363 meas2->Scale(scale);
1364 if (blankCanvas)
1365 meas2->DrawCopy();
1366 else
1367 meas2->DrawCopy("same");
1368 //meas2->GetXaxis()->SetLimits(0,fgMaxInput);
1369 meas2->SetBit(kCannotPick);
1370 DrawGuess(params, presult, pres, ppen, reuseHists,unfolded);
2d99332c 1371 delete [] params;
9e065ad2 1372}
1373//____________________________________________________________________
1374void AliUnfolding::RedrawInteractive() {
1375 //
1376 // Helper function for interactive unfolding
1377 //
1378 DrawResults(fghCorrelation,fghEfficiency,fghMeasured,fghUnfolded,fgCanvas,1,fghUnfolded);
1379}
1380//____________________________________________________________________
1381void AliUnfolding::InteractiveUnfold(TH2* correlation, TH1* efficiency, TH1* measured, TH1* initialConditions)
1382{
1383 //
1384 // Function to do interactive unfolding
1385 // A canvas is drawn with the unfolding result
1386 // Change the histogram with your mouse and all histograms
1387 // will be updated automatically
1388
1389 fgCanvas = new TCanvas("UnfoldingCanvas","Interactive unfolding",500,800);
1390 fgCanvas->cd();
1391
1392 MakePads();
1393
1394 if (fghUnfolded) {
1395 delete fghUnfolded; fghUnfolded = 0;
1396 }
1397
1398 gROOT->SetEditHistograms(kTRUE);
1399
03650114 1400 fghUnfolded = new TH1F("AliUnfoldingfghUnfolded","Unfolded result (Interactive unfolder",efficiency->GetNbinsX(),efficiency->GetXaxis()->GetXmin(),efficiency->GetXaxis()->GetXmax());
9e065ad2 1401
1402 fghCorrelation = correlation;
1403 fghEfficiency = efficiency;
1404 fghMeasured = measured;
1405
03650114 1406 if(fgMinuitMaxIterations>0)
1407 UnfoldWithMinuit(correlation,efficiency,measured,initialConditions,fghUnfolded,kFALSE);
1408 else
1409 fghUnfolded = initialConditions;
1410
1411 fghUnfolded->SetLineColor(2);
1412 fghUnfolded->SetMarkerColor(2);
1413 fghUnfolded->SetLineWidth(2);
1414
9e065ad2 1415
1416 fgCanvas->cd(1);
1417 fghUnfolded->Draw();
1418 DrawResults(correlation,efficiency,measured,fghUnfolded,fgCanvas,kFALSE,fghUnfolded);
1419
1420 TExec *execRedraw = new TExec("redraw","AliUnfolding::RedrawInteractive()");
1421 fghUnfolded->GetListOfFunctions()->Add(execRedraw);
1422}
1423//____________________________________________________________________
1424void AliUnfolding::DrawGuess(Double_t *params, TVirtualPad *pfolded, TVirtualPad *pres, TVirtualPad *ppen, Int_t reuseHists,TH1* unfolded)
19442b86 1425{
1426 //
1427 // draws residuals of solution suggested by params and effect of regularization
1428 //
1429
9e065ad2 1430 if (pfolded == 0)
1431 pfolded = new TCanvas;
1432 if (ppen == 0)
1433 ppen = new TCanvas;
1434 if (pres == 0)
1435 pres = new TCanvas;
1436
19442b86 1437 // d
95e970ca 1438 TVectorD paramsVector(fgMaxParams);
19442b86 1439 for (Int_t i=0; i<fgMaxParams; ++i)
1440 paramsVector[i] = params[i] * params[i];
1441
1442 // Ad
1443 TVectorD measGuessVector(fgMaxInput);
1444 measGuessVector = (*fgCorrelationMatrix) * paramsVector;
1445
9e065ad2 1446 TH1* folded = 0;
1447 if (reuseHists)
1448 folded = dynamic_cast<TH1*>(gROOT->FindObject("__hfolded"));
1449 if (!reuseHists || folded == 0) {
1450 if (fgMeasuredAxis->GetXbins()->GetArray()) // variable bins
1451 folded = new TH1F("__hfolded","Folded histo from AliUnfolding",fgMeasuredAxis->GetNbins(),fgMeasuredAxis->GetXbins()->GetArray());
1452 else
1453 folded = new TH1F("__hfolded","Folded histo from AliUnfolding",fgMeasuredAxis->GetNbins(),fgMeasuredAxis->GetXmin(),fgMeasuredAxis->GetXmax());
1454 }
1455
1456 folded->SetBit(kCannotPick);
1457 folded->SetLineColor(4);
1458 folded->SetLineWidth(2);
1459
1460 for (Int_t ibin =0; ibin < fgMaxInput; ibin++)
1461 folded->SetBinContent(ibin+1, measGuessVector[ibin]);
1462
1463 Float_t scale = unfolded->GetXaxis()->GetBinWidth(1)/folded->GetXaxis()->GetBinWidth(1);
1464 folded->Scale(scale);
1465
1466 pfolded->cd();
1467
1468 folded->Draw("same");
1469
19442b86 1470 // Ad - m
1471 measGuessVector -= (*fgCurrentESDVector);
1472
1473 TVectorD copy(measGuessVector);
19442b86 1474
1475 // (Ad - m) W
1476 // this step can be optimized because currently only the diagonal elements of fgCorrelationCovarianceMatrix are used
1477 // normal way is like this:
1478 // measGuessVector *= (*fgCorrelationCovarianceMatrix);
1479 // optimized way like this:
1480 for (Int_t i=0; i<fgMaxInput; ++i)
1481 measGuessVector[i] *= (*fgCorrelationCovarianceMatrix)(i, i);
1482
1483 // (Ad - m) W (Ad - m)
1484 // the factor 1e6 prevents that a very small number (measGuessVector[i]) is multiplied with a very
1485 // big number ((*fgCorrelationCovarianceMatrix)(i, i)) (see ApplyMinuitFit)
1486 //Double_t chi2FromFit = measGuessVector * copy * 1e6;
1487
1488 // draw residuals
9e065ad2 1489 // Double_t pTarray[fgMaxParams+1];
1490 // for(int i=0; i<fgMaxParams; i++) {
1491 // pTarray[i] = fgUnfoldedAxis->GetBinCenter(i)-0.5*fgUnfoldedAxis->GetBinWidth(i);
1492 // }
1493 // pTarray[fgMaxParams] = fgUnfoldedAxis->GetBinCenter(fgMaxParams-1)+0.5*fgUnfoldedAxis->GetBinWidth(fgMaxParams-1);
1494 // TH1* residuals = new TH1F("residuals", "residuals", fgMaxParams,pTarray);
1495 // TH1* residuals = new TH1F("residuals", "residuals", fgMaxInput, -0.5, fgMaxInput - 0.5);
1496 // for (Int_t i=0; i<fgMaxInput; ++i)
1497 // residuals->SetBinContent(i+1, measGuessVector(i) * copy(i) * 1e6);7
1498 TH1* residuals = GetResidualsPlot(params);
1499 residuals->GetXaxis()->SetTitleSize(0.06);
1500 residuals->GetXaxis()->SetTitleOffset(0.7);
1501 residuals->GetXaxis()->SetLabelSize(0.07);
1502 residuals->GetYaxis()->SetTitleSize(0.08);
1503 residuals->GetYaxis()->SetTitleOffset(0.5);
1504 residuals->GetYaxis()->SetLabelSize(0.06);
1505 pres->cd(); residuals->DrawCopy(); gPad->SetLogy();
1506
19442b86 1507
1508 // draw penalty
95e970ca 1509 TH1* penalty = GetPenaltyPlot(params);
9e065ad2 1510 penalty->GetXaxis()->SetTitleSize(0.06);
1511 penalty->GetXaxis()->SetTitleOffset(0.7);
1512 penalty->GetXaxis()->SetLabelSize(0.07);
1513 penalty->GetYaxis()->SetTitleSize(0.08);
1514 penalty->GetYaxis()->SetTitleOffset(0.5);
1515 penalty->GetYaxis()->SetLabelSize(0.06);
1516 ppen->cd(); penalty->DrawCopy(); gPad->SetLogy();
1517}
1518
1519//____________________________________________________________________
1520TH1* AliUnfolding::GetResidualsPlot(TH1* corrected)
1521{
1522 //
1523 // MvL: THIS MUST BE INCORRECT.
1524 // Need heff to calculate params from TH1 'corrected'
1525 //
1526
1527 //
1528 // fill residuals histogram of solution suggested by params and effect of regularization
1529 //
1530
1531 Double_t* params = new Double_t[fgMaxParams];
b9b1eb8a 1532 for (Int_t i=0; i<fgMaxParams; i++)
1533 params[i] = 0;
1534
9e065ad2 1535 for (Int_t i=0; i<TMath::Min(fgMaxParams, corrected->GetNbinsX()); i++)
3a44f1b9 1536 params[i] = TMath::Sqrt(TMath::Abs(corrected->GetBinContent(i+1)*(*fgEfficiency)(i)));
9e065ad2 1537
2d99332c 1538 TH1 * plot = GetResidualsPlot(params);
1539 delete [] params;
1540 return plot;
9e065ad2 1541}
1542
1543//____________________________________________________________________
1544TH1* AliUnfolding::GetResidualsPlot(Double_t* params)
1545{
1546 //
1547 // fill residuals histogram of solution suggested by params and effect of regularization
1548 //
1549
1550 // d
1551 TVectorD paramsVector(fgMaxParams);
1552 for (Int_t i=0; i<fgMaxParams; ++i)
1553 paramsVector[i] = params[i] * params[i];
1554
1555 // Ad
1556 TVectorD measGuessVector(fgMaxInput);
1557 measGuessVector = (*fgCorrelationMatrix) * paramsVector;
1558
1559 // Ad - m
1560 measGuessVector -= (*fgCurrentESDVector);
1561
1562 TVectorD copy(measGuessVector);
1563
1564 // (Ad - m) W
1565 // this step can be optimized because currently only the diagonal elements of fgCorrelationCovarianceMatrix are used
1566 // normal way is like this:
1567 // measGuessVector *= (*fgCorrelationCovarianceMatrix);
1568 // optimized way like this:
1569 for (Int_t i=0; i<fgMaxInput; ++i)
1570 measGuessVector[i] *= (*fgCorrelationCovarianceMatrix)(i, i);
1571
1572 // (Ad - m) W (Ad - m)
1573 // the factor 1e6 prevents that a very small number (measGuessVector[i]) is multiplied with a very
1574 // big number ((*fgCorrelationCovarianceMatrix)(i, i)) (see ApplyMinuitFit)
1575 //Double_t chi2FromFit = measGuessVector * copy * 1e6;
1576
1577 // draw residuals
1578 TH1* residuals = 0;
1579 if (fgMeasuredAxis->GetXbins()->GetArray()) // variable bins
1580 residuals = new TH1F("residuals", "residuals;unfolded pos;residual",fgMeasuredAxis->GetNbins(),fgMeasuredAxis->GetXbins()->GetArray());
1581 else
1582 residuals = new TH1F("residuals", "residuals;unfolded pos;residual",fgMeasuredAxis->GetNbins(),fgMeasuredAxis->GetXmin(), fgMeasuredAxis->GetXmax());
1583 // TH1* residuals = new TH1F("residuals", "residuals", fgMaxInput, -0.5, fgMaxInput - 0.5);
1584
1585 Double_t sumResiduals = 0.;
1586 for (Int_t i=0; i<fgMaxInput; ++i) {
1587 residuals->SetBinContent(i+1, measGuessVector(i) * copy(i) * 1e6);
1588 sumResiduals += measGuessVector(i) * copy(i) * 1e6;
1589 }
1590 fAvgResidual = sumResiduals/(double)fgMaxInput;
1591
1592 return residuals;
95e970ca 1593}
19442b86 1594
95e970ca 1595//____________________________________________________________________
1596TH1* AliUnfolding::GetPenaltyPlot(TH1* corrected)
1597{
1598 // draws the penalty factors as function of multiplicity of the current selected regularization
19442b86 1599
95e970ca 1600 Double_t* params = new Double_t[fgMaxParams];
b9b1eb8a 1601 for (Int_t i=0; i<fgMaxParams; i++)
1602 params[i] = 0;
1603
95e970ca 1604 for (Int_t i=0; i<TMath::Min(fgMaxParams, corrected->GetNbinsX()); i++)
9e065ad2 1605 params[i] = (*fgEfficiency)(i)*corrected->GetBinContent(i+1);
95e970ca 1606
1607 TH1* penalty = GetPenaltyPlot(params);
1608
1609 delete[] params;
1610
1611 return penalty;
1612}
1613
1614//____________________________________________________________________
1615TH1* AliUnfolding::GetPenaltyPlot(Double_t* params)
1616{
1617 // draws the penalty factors as function of multiplicity of the current selected regularization
1618
9e065ad2 1619 //TH1* penalty = new TH1F("penalty", ";unfolded multiplicity;penalty factor", fgMaxParams, -0.5, fgMaxParams - 0.5);
1620 // TH1* penalty = new TH1F("penalty", ";unfolded pos;penalty factor", fgMaxParams, fgUnfoldedAxis->GetBinCenter(0)-0.5*fgUnfoldedAxis->GetBinWidth(0),fgUnfoldedAxis->GetBinCenter(fgMaxParams)+0.5*fgUnfoldedAxis->GetBinWidth(fgMaxParams) );
1621
1622 TH1* penalty = 0;
1623 if (fgUnfoldedAxis->GetXbins()->GetArray())
1624 penalty = new TH1F("penalty", ";unfolded pos;penalty factor", fgUnfoldedAxis->GetNbins(),fgUnfoldedAxis->GetXbins()->GetArray());
1625 else
1626 penalty = new TH1F("penalty", ";unfolded pos;penalty factor", fgUnfoldedAxis->GetNbins(),fgUnfoldedAxis->GetXmin(),fgUnfoldedAxis->GetXmax());
95e970ca 1627
1628 for (Int_t i=1+fgSkipBinsBegin; i<fgMaxParams; ++i)
19442b86 1629 {
95e970ca 1630 Double_t diff = 0;
1631 if (fgRegularizationType == kPol0)
1632 {
9e065ad2 1633 Double_t right = params[i] / fgUnfoldedAxis->GetBinWidth(i+1);
1634 Double_t left = params[i-1] / fgUnfoldedAxis->GetBinWidth(i);
19442b86 1635
95e970ca 1636 if (left != 0)
1637 {
1638 Double_t diffTmp = (right - left);
9e065ad2 1639 diff = diffTmp * diffTmp / left / ((fgUnfoldedAxis->GetBinWidth(i+1) + fgUnfoldedAxis->GetBinWidth(i)) / 2) / 100;
95e970ca 1640 }
1641 }
1642 if (fgRegularizationType == kPol1 && i > 1+fgSkipBinsBegin)
1643 {
1644 if (params[i-1] == 0)
1645 continue;
19442b86 1646
9e065ad2 1647 Double_t right = params[i] / fgUnfoldedAxis->GetBinWidth(i+1);
1648 Double_t middle = params[i-1] / fgUnfoldedAxis->GetBinWidth(i);
1649 Double_t left = params[i-2] / fgUnfoldedAxis->GetBinWidth(i-1);
19442b86 1650
9e065ad2 1651 Double_t der1 = (right - middle) / ((fgUnfoldedAxis->GetBinWidth(i+1) + fgUnfoldedAxis->GetBinWidth(i)) / 2);
1652 Double_t der2 = (middle - left) / ((fgUnfoldedAxis->GetBinWidth(i) + fgUnfoldedAxis->GetBinWidth(i-1)) / 2);
95e970ca 1653
1654 diff = (der1 - der2) * (der1 - der2) / middle;
1655 }
9e065ad2 1656
95e970ca 1657 if (fgRegularizationType == kLog && i > 1+fgSkipBinsBegin)
1658 {
1659 if (params[i-1] == 0)
1660 continue;
1661
1662 Double_t right = log(params[i]);
1663 Double_t middle = log(params[i-1]);
1664 Double_t left = log(params[i-2]);
1665
1666 Double_t der1 = (right - middle);
1667 Double_t der2 = (middle - left);
1668
1669 //Double_t error = 1. / params[i] + 4. / params[i-1] + 1. / params[i-2];
1670 //Printf("%d %f %f", i, (der1 - der2) * (der1 - der2), error);
1671
1672 diff = (der1 - der2) * (der1 - der2);// / error;
1673 }
9e065ad2 1674 if (fgRegularizationType == kCurvature && i > 1+fgSkipBinsBegin)
1675 {
1676 Double_t right = params[i]; // params are sqrt
1677 Double_t middle = params[i-1];
1678 Double_t left = params[i-2];
1679
1680 Double_t der1 = (right - middle)/0.5/(fgUnfoldedAxis->GetBinWidth(i-1) + fgUnfoldedAxis->GetBinWidth(i));
1681 Double_t der2 = (middle - left)/0.5/(fgUnfoldedAxis->GetBinWidth(i) + fgUnfoldedAxis->GetBinWidth(i+1));
1682
1683 diff = (der1 - der2)/(fgUnfoldedAxis->GetBinWidth(i-1) + fgUnfoldedAxis->GetBinWidth(i) + fgUnfoldedAxis->GetBinWidth(i-1))*3.0;
1684 diff = 1e4*diff*diff;
1685 }
1686 if (fgRegularizationType == kPowerLaw && i > 1+fgSkipBinsBegin)
1687 {
19442b86 1688
9e065ad2 1689 if (params[i] < 1e-8 || params[i-1] < 1e-8 || params[i-2] < 1e-8)
1690 continue;
1691
1692 if (fgUnfoldedAxis->GetBinWidth(i+1) < 1e-8 || fgUnfoldedAxis->GetBinWidth(i) < 1e-8 || fgUnfoldedAxis->GetBinWidth(i) < 1e-8)
1693 continue;
1694
1695 double middle = TMath::Power(params[i-1] / fgUnfoldedAxis->GetBinWidth(i),fgPowern);
1696
1697 if(middle>0) {
1698 double right = TMath::Power(params[i] / fgUnfoldedAxis->GetBinWidth(i+1),fgPowern)/middle;
1699
1700 double left = TMath::Power(params[i-2] / fgUnfoldedAxis->GetBinWidth(i-1),fgPowern)/middle;
1701
1702 middle = 1.;
1703
1704 Double_t der1 = (right - middle) / ((fgUnfoldedAxis->GetBinWidth(i+1) + fgUnfoldedAxis->GetBinWidth(i)) / 2);
1705 Double_t der2 = (middle - left) / ((fgUnfoldedAxis->GetBinWidth(i) + fgUnfoldedAxis->GetBinWidth(i-1)) / 2);
1706
1707 diff = (der1 - der2) * (der1 - der2);// / error;
1708 }
1709 }
1710
1711 if (fgRegularizationType == kLogLog && i > 1+fgSkipBinsBegin)
1712 {
1713
1714 if (params[i] < 1e-8 || params[i-1] < 1e-8 || params[i-2] < 1e-8)
1715 continue;
1716
1717 Double_t right = log(params[i] / (*fgEfficiency)(i) / fgUnfoldedAxis->GetBinWidth(i+1));
1718 Double_t middle = log(params[i-1] / (*fgEfficiency)(i-1) / fgUnfoldedAxis->GetBinWidth(i));
1719 Double_t left = log(params[i-2] / (*fgEfficiency)(i-2) / fgUnfoldedAxis->GetBinWidth(i-1));
1720
1721 Double_t der1 = (right - middle) / ( log(fgUnfoldedAxis->GetBinCenter(i+1)) - log(fgUnfoldedAxis->GetBinCenter(i)) );
1722 Double_t der2 = (middle - left) /( log(fgUnfoldedAxis->GetBinCenter(i)) - log(fgUnfoldedAxis->GetBinCenter(i-1)) );
1723
1724 double tmp = (log(fgUnfoldedAxis->GetBinCenter(i+1)) - log(fgUnfoldedAxis->GetBinCenter(i-1)))/2.;
1725 Double_t dder = (der1-der2) / tmp;
1726
1727 diff = dder * dder;
1728 }
1729
1730 penalty->SetBinContent(i, diff*fgRegularizationWeight);
19442b86 1731
1732 //Printf("%d %f %f %f %f", i-1, left, middle, right, diff);
1733 }
95e970ca 1734
1735 return penalty;
19442b86 1736}
1737
1738//____________________________________________________________________
1739void AliUnfolding::TF1Function(Int_t& unused1, Double_t* unused2, Double_t& chi2, Double_t *params, Int_t unused3)
1740{
1741 //
1742 // fit function for minuit
1743 // uses the TF1 stored in fgFitFunction
1744 //
1745
1746 for (Int_t i=0; i<fgFitFunction->GetNpar(); i++)
1747 fgFitFunction->SetParameter(i, params[i]);
1748
1749 Double_t* params2 = new Double_t[fgMaxParams];
1750
1751 for (Int_t i=0; i<fgMaxParams; ++i)
1752 params2[i] = fgFitFunction->Eval(i);
1753
1754 Chi2Function(unused1, unused2, chi2, params2, unused3);
1755
1756 delete[] params2;
1757
1758 if (fgDebug)
1759 Printf("%f", chi2);
1760}
1761
1762//____________________________________________________________________
1763Int_t AliUnfolding::UnfoldWithFunction(TH2* correlation, TH1* efficiency, TH1* measured, TH1* /* initialConditions */, TH1* aResult)
1764{
1765 //
1766 // correct spectrum using minuit chi2 method applying a functional fit
1767 //
1768
1769 if (!fgFitFunction)
1770 {
1771 Printf("AliUnfolding::UnfoldWithFunction: ERROR fit function not set. Exiting.");
1772 return -1;
1773 }
1774
1775 SetChi2Regularization(kNone, 0);
1776
95e970ca 1777 SetStaticVariables(correlation, measured, efficiency);
19442b86 1778
1779 // Initialize TMinuit via generic fitter interface
1780 TVirtualFitter *minuit = TVirtualFitter::Fitter(0, fgFitFunction->GetNpar());
1781
1782 minuit->SetFCN(TF1Function);
1783 for (Int_t i=0; i<fgFitFunction->GetNpar(); i++)
1784 {
1785 Double_t lower, upper;
1786 fgFitFunction->GetParLimits(i, lower, upper);
1787 minuit->SetParameter(i, Form("param%d",i), fgFitFunction->GetParameter(i), fgMinuitStepSize, lower, upper);
1788 }
1789
1790 Double_t arglist[100];
1791 arglist[0] = 0;
1792 minuit->ExecuteCommand("SET PRINT", arglist, 1);
9e065ad2 1793 minuit->ExecuteCommand("SCAN", arglist, 0);
19442b86 1794 minuit->ExecuteCommand("MIGRAD", arglist, 0);
1795 //minuit->ExecuteCommand("MINOS", arglist, 0);
1796
1797 for (Int_t i=0; i<fgFitFunction->GetNpar(); i++)
1798 fgFitFunction->SetParameter(i, minuit->GetParameter(i));
1799
1800 for (Int_t i=0; i<fgMaxParams; ++i)
1801 {
1802 Double_t value = fgFitFunction->Eval(i);
1803 if (fgDebug)
1804 Printf("%d : %f", i, value);
1805
1806 if (efficiency)
1807 {
1808 if (efficiency->GetBinContent(i+1) > 0)
1809 {
1810 value /= efficiency->GetBinContent(i+1);
1811 }
1812 else
1813 value = 0;
1814 }
1815 aResult->SetBinContent(i+1, value);
1816 aResult->SetBinError(i+1, 0);
1817 }
1818
1819 return 0;
1820}
1821
1822//____________________________________________________________________
1823void AliUnfolding::CreateOverflowBin(TH2* correlation, TH1* measured)
1824{
1825 // Finds the first bin where the content is below fgStatLimit and combines all values for this bin and larger bins
1826 // The same limit is applied to the correlation
1827
1828 Int_t lastBin = 0;
1829 for (Int_t i=1; i<=measured->GetNbinsX(); ++i)
1830 {
1831 if (measured->GetBinContent(i) <= fgOverflowBinLimit)
1832 {
1833 lastBin = i;
1834 break;
1835 }
1836 }
1837
1838 if (lastBin == 0)
1839 {
1840 Printf("AliUnfolding::CreateOverflowBin: WARNING: First bin is already below limit of %f", fgOverflowBinLimit);
1841 return;
1842 }
1843
1844 Printf("AliUnfolding::CreateOverflowBin: Bin limit in measured spectrum determined to be %d", lastBin);
1845
1846 TCanvas* canvas = 0;
1847
1848 if (fgDebug)
1849 {
1850 canvas = new TCanvas("StatSolution", "StatSolution", 1000, 800);
1851 canvas->Divide(2, 2);
1852
1853 canvas->cd(1);
1854 measured->SetStats(kFALSE);
1855 measured->DrawCopy();
1856 gPad->SetLogy();
1857
1858 canvas->cd(2);
1859 correlation->SetStats(kFALSE);
1860 correlation->DrawCopy("COLZ");
1861 }
1862
1863 measured->SetBinContent(lastBin, measured->Integral(lastBin, measured->GetNbinsX()));
1864 for (Int_t i=lastBin+1; i<=measured->GetNbinsX(); ++i)
1865 {
1866 measured->SetBinContent(i, 0);
1867 measured->SetBinError(i, 0);
1868 }
1869 // the error is set to sqrt(N), better solution possible?, sum of relative errors of all contributions???
1870 measured->SetBinError(lastBin, TMath::Sqrt(measured->GetBinContent(lastBin)));
1871
1872 Printf("AliUnfolding::CreateOverflowBin: This bin has now %f +- %f entries", measured->GetBinContent(lastBin), measured->GetBinError(lastBin));
1873
1874 for (Int_t i=1; i<=correlation->GetNbinsX(); ++i)
1875 {
1876 correlation->SetBinContent(i, lastBin, correlation->Integral(i, i, lastBin, correlation->GetNbinsY()));
1877 // the error is set to sqrt(N), better solution possible?, sum of relative errors of all contributions???
1878 correlation->SetBinError(i, lastBin, TMath::Sqrt(correlation->GetBinContent(i, lastBin)));
1879
1880 for (Int_t j=lastBin+1; j<=correlation->GetNbinsY(); ++j)
1881 {
1882 correlation->SetBinContent(i, j, 0);
1883 correlation->SetBinError(i, j, 0);
1884 }
1885 }
1886
1887 Printf("AliUnfolding::CreateOverflowBin: Adjusted correlation matrix!");
1888
1889 if (canvas)
1890 {
1891 canvas->cd(3);
1892 measured->DrawCopy();
1893 gPad->SetLogy();
1894
1895 canvas->cd(4);
1896 correlation->DrawCopy("COLZ");
1897 }
1898}
95e970ca 1899
1900Int_t AliUnfolding::UnfoldGetBias(TH2* correlation, TH1* efficiency, TH1* measured, TH1* initialConditions, TH1* result)
1901{
1902 // unfolds and assigns bias as errors with Eq. 19 of Cowan, "a survey of unfolding methods for particle physics"
1903 // b_i = sum_j dmu_i/dn_j (nu_j - n_j) with nu_j as folded guess, n_j as data
1904 // dmu_i/dn_j is found numerically by changing the bin content and re-unfolding
1905 //
1906 // return code: 0 (success) -1 (error: from Unfold(...) )
1907
1908 if (Unfold(correlation, efficiency, measured, initialConditions, result) != 0)
1909 return -1;
1910
1911 TMatrixD matrix(fgMaxInput, fgMaxParams);
1912
1913 TH1* newResult[4];
1914 for (Int_t loop=0; loop<4; loop++)
1915 newResult[loop] = (TH1*) result->Clone(Form("newresult_%d", loop));
1916
1917 // change bin-by-bin and built matrix of effects
1918 for (Int_t m=0; m<fgMaxInput; m++)
1919 {
1920 if (measured->GetBinContent(m+1) < 1)
1921 continue;
1922
1923 for (Int_t loop=0; loop<4; loop++)
1924 {
1925 //Printf("%d %d", i, loop);
1926 Float_t factor = 1;
1927 switch (loop)
1928 {
1929 case 0: factor = 0.5; break;
1930 case 1: factor = -0.5; break;
1931 case 2: factor = 1; break;
1932 case 3: factor = -1; break;
1933 default: return -1;
1934 }
1935
1936 TH1* measuredClone = (TH1*) measured->Clone("measuredClone");
1937
1938 measuredClone->SetBinContent(m+1, measured->GetBinContent(m+1) + factor * TMath::Sqrt(measured->GetBinContent(m+1)));
1939 //new TCanvas; measuredClone->Draw("COLZ");
1940
1941 newResult[loop]->Reset();
1942 Unfold(correlation, efficiency, measuredClone, measuredClone, newResult[loop]);
1943 // WARNING if we leave here, then nothing is calculated
1944 //return -1;
1945
1946 delete measuredClone;
1947 }
1948
1949 for (Int_t t=0; t<fgMaxParams; t++)
1950 {
1951 // one value
1952 //matrix(i, j) = (result->GetBinContent(j+1) - newResult->GetBinContent(j+1)) / TMath::Sqrt(changedHist->GetBinContent(1, i+1));
1953
1954 // four values from the derivate (procedure taken from ROOT -- suggestion by Ruben)
1955 // = 1/2D * [ 8 (f(D/2) - f(-D/2)) - (f(D)-f(-D)) ]/3
1956
1957 /*
1958 // check formula
1959 measured->SetBinContent(1, m+1, 100);
1960 newResult[0]->SetBinContent(t+1, 5 * 0.5 + 10);
1961 newResult[1]->SetBinContent(t+1, 5 * -0.5 + 10);
1962 newResult[2]->SetBinContent(t+1, 5 * 1 + 10);
1963 newResult[3]->SetBinContent(t+1, 5 * -1 + 10);
1964 */
1965
1966 matrix(m, t) = 0.5 / TMath::Sqrt(measured->GetBinContent(m+1)) *
1967 ( 8. * (newResult[0]->GetBinContent(t+1) - newResult[1]->GetBinContent(t+1)) -
1968 (newResult[2]->GetBinContent(t+1) - newResult[3]->GetBinContent(t+1))
1969 ) / 3;
1970 }
1971 }
1972
1973 for (Int_t loop=0; loop<4; loop++)
1974 delete newResult[loop];
1975
95e970ca 1976 // ...calculate folded guess
1977 TH1* convoluted = (TH1*) measured->Clone("convoluted");
1978 convoluted->Reset();
1979 for (Int_t m=0; m<fgMaxInput; m++)
1980 {
1981 Float_t value = 0;
1982 for (Int_t t = 0; t<fgMaxParams; t++)
1983 {
1984 Float_t tmp = correlation->GetBinContent(t+1, m+1) * result->GetBinContent(t+1);
1985 if (efficiency)
1986 tmp *= efficiency->GetBinContent(t+1);
1987 value += tmp;
1988 }
1989 convoluted->SetBinContent(m+1, value);
1990 }
1991
1992 // rescale
1993 convoluted->Scale(measured->Integral() / convoluted->Integral());
1994
1995 //new TCanvas; convoluted->Draw(); measured->Draw("SAME"); measured->SetLineColor(2);
1996 //return;
1997
1998 // difference
1999 convoluted->Add(measured, -1);
2000
2001 // ...and the bias
2002 for (Int_t t = 0; t<fgMaxParams; t++)
2003 {
2004 Double_t error = 0;
2005 for (Int_t m=0; m<fgMaxInput; m++)
2006 error += matrix(m, t) * convoluted->GetBinContent(m+1);
2007 result->SetBinError(t+1, error);
2008 }
2009
2010 //new TCanvas; result->Draw(); gPad->SetLogy();
2011
2012 return 0;
2013}