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4b23a517 | 1 | |
2 | #include "AliTMinuitToolkit.h" | |
3 | #include <TNamed.h> | |
4 | #include <TVirtualFitter.h> | |
5 | #include <TH1F.h> | |
6 | #include <TH2F.h> | |
7 | #include <TF1.h> | |
8 | #include <TFormula.h> | |
9 | #include <TVectorD.h> | |
10 | #include <TMatrixD.h> | |
11 | #include <TMath.h> | |
12 | #include <TString.h> | |
13 | #include <TROOT.h> | |
14 | #include <TCanvas.h> | |
15 | #include <TRandom.h> | |
16 | ||
17 | ||
18 | //-------------------------------------------------------------------------- | |
19 | // | |
20 | // The AliTMinuitToolkit serves as an easy to use interface for the TMinuit | |
21 | // package: | |
22 | // | |
23 | // - It allows to fit a curve to one and two dimensional histograms | |
24 | // (TH2F::Fit() only allows to fit a hyperplane). | |
25 | // - Or n points can be specified directly via a n x 2 matrix. | |
26 | // - An option for robust fitting of non-linear functions is implemented. | |
27 | // | |
28 | // | |
29 | // 1. Setting the formula: | |
30 | // | |
31 | // The formula is simply set via "void SetFitFunction(TFormula * formula)". | |
32 | // | |
33 | // | |
34 | // 2. Adding the data points | |
35 | // | |
36 | // - In order to fit a histogram, use "void FitHistogram(TH1F * his)" or | |
37 | // "void FitHistogram(TH2F * his)". The fitter is started automatically | |
38 | // - Alternatively, the direct specification of the points is possible via | |
39 | // "void SetPoints(TMatrixD * points)". Note, that the each point | |
40 | // corresponds to one row in the matrix. The fitter is then started with | |
41 | // the command "void Fit()". | |
42 | // | |
43 | // | |
44 | // 3. Accessing the fit results | |
45 | // | |
46 | // The N parameters of the formula are stored in a N-dimensional vector which | |
47 | // is returned by "TVectorD * GetParameters()". In a similar the covariance | |
48 | // matrix of the fit is returned via "TMatrixD * GetCovarianceMatrix()" which | |
49 | // is of the type N x N. | |
50 | // | |
51 | // | |
52 | // 4. Non-linear robust fitting: | |
53 | // | |
54 | // Even a few outliers can lead to wrong results of a least-squares fitting | |
55 | // procedure. In this case the use of robust(resistant) methods can be | |
56 | // helpful, but a stronger dependence on starting values or convergence to | |
57 | // local minima can occur. | |
58 | // | |
59 | // The robust option becomes active if a weighting function is specified. | |
60 | // All points are sorted according to their distance to the curve and | |
61 | // weighted. The weighting function must be defined on the interval [0,1]. | |
62 | // | |
63 | // Some standard weighting functions are predefined in | |
64 | // "SetWeightFunction(Char_t * name, Float_t param1, Float_t param2 = 0)": | |
65 | // - "BOX" equals to 1 if x < param1 and to 0 if x > param1. | |
66 | // - "EXPONENTIAL" corresponds to "Math::Exp(-TMath::Log(param1)*x)" | |
67 | // - "ERRORFUNCTION" corresponds to "TMath::Erfc((x-param1)/param2)" | |
68 | // | |
69 | //------------------------------------------------------------------------- | |
70 | ||
71 | ||
72 | ClassImp(AliTMinuitToolkit) | |
73 | ||
74 | AliTMinuitToolkit::AliTMinuitToolkit() : | |
75 | TNamed(), | |
76 | fFormula(0), | |
77 | fWeightFunction(0), | |
78 | fFitAlgorithm(0), | |
79 | fPoints(0), | |
80 | fParam(0), | |
81 | fParamLimits(0), | |
82 | fCovar(0), | |
da7c9ae3 | 83 | fChi2(0), |
84 | fMaxCalls(0), | |
85 | fPrecision(0) | |
4b23a517 | 86 | { |
87 | // | |
88 | // standard constructor | |
89 | // | |
90 | fMaxCalls = 500; | |
91 | fPrecision = 1; | |
92 | } | |
93 | ||
94 | ||
da7c9ae3 | 95 | AliTMinuitToolkit::AliTMinuitToolkit(const AliTMinuitToolkit&) : |
96 | TNamed(), | |
97 | fFormula(0), | |
98 | fWeightFunction(0), | |
99 | fFitAlgorithm(0), | |
100 | fPoints(0), | |
101 | fParam(0), | |
102 | fParamLimits(0), | |
103 | fCovar(0), | |
104 | fChi2(0), | |
105 | fMaxCalls(0), | |
106 | fPrecision(0) | |
107 | { | |
108 | ||
109 | ||
110 | } | |
111 | ||
112 | ||
113 | AliTMinuitToolkit& AliTMinuitToolkit::operator=(const AliTMinuitToolkit&) { | |
114 | ||
115 | return *this; | |
116 | } | |
117 | ||
118 | ||
4b23a517 | 119 | |
120 | AliTMinuitToolkit::~AliTMinuitToolkit(){ | |
121 | // | |
122 | // destructor | |
123 | // | |
124 | delete fPoints; | |
125 | delete fWeightFunction; | |
126 | delete fParamLimits; | |
127 | delete fFormula; | |
128 | delete fParam; | |
129 | delete fCovar; | |
130 | delete fChi2; | |
131 | } | |
132 | ||
133 | void AliTMinuitToolkit::FitHistogram(TH1F * his) { | |
134 | // | |
135 | // Fit a one dimensional histogram | |
136 | // | |
137 | fPoints = new TMatrixD(his->GetNbinsX(), 2); | |
138 | ||
139 | for(Int_t ibin=0; ibin < his->GetNbinsX(); ibin++) { | |
140 | Double_t x = his->GetXaxis()->GetBinCenter(ibin+1); | |
141 | Double_t y = his->GetBinContent(ibin+1); | |
142 | ||
143 | (*fPoints)(ibin, 0) = x; | |
144 | (*fPoints)(ibin, 1) = y; | |
145 | } | |
146 | ||
147 | Fit(); | |
148 | } | |
149 | ||
150 | ||
151 | void AliTMinuitToolkit::FitHistogram(TH2F * his) { | |
152 | // | |
153 | // Fit a two dimensional histogram | |
154 | // | |
155 | fPoints = new TMatrixD((Long64_t)his->GetEntries(), 2); | |
156 | Long64_t entry = 0; | |
157 | ||
158 | for(Int_t ibin=0; ibin < his->GetNbinsX(); ibin++) { | |
159 | Double_t x = his->GetXaxis()->GetBinCenter(ibin); | |
160 | for(Int_t jbin=0; jbin < his->GetNbinsY(); jbin++) { | |
161 | Long64_t n = his->GetBin(ibin, jbin); | |
162 | Double_t y = his->GetYaxis()->GetBinCenter(jbin); | |
163 | for(Int_t ientries=0; ientries < his->GetBinContent(n); ientries++) { | |
164 | (*fPoints)(entry,0) = x; | |
165 | (*fPoints)(entry,1) = y; | |
166 | entry++; | |
167 | } | |
168 | ||
169 | } | |
170 | } | |
171 | ||
172 | Fit(); | |
173 | } | |
174 | ||
175 | ||
176 | void AliTMinuitToolkit::SetWeightFunction(Char_t * name, Float_t param1, Float_t param2) { | |
177 | // | |
178 | // Set the weight function which must be defined on the interval [0,1]. | |
179 | // | |
180 | TString FuncType(name); | |
181 | FuncType.ToUpper(); | |
182 | ||
183 | if (FuncType == "EXPONENTIAL") fWeightFunction = new TFormula("exp", Form("TMath::Exp(-TMath::Log(%f)*x)", param1)); | |
184 | if (FuncType == "BOX") fWeightFunction = new TFormula("box", Form("TMath::Erfc((x-%f)/0.0001)", param1)); | |
185 | if (FuncType == "ERRORFUNCTION") fWeightFunction = new TFormula("err", Form("TMath::Erfc((x-%f)/%f)", param1, param2));// !!!!!!!!!!!!!!!!! | |
186 | ||
187 | } | |
188 | ||
189 | ||
190 | void AliTMinuitToolkit::FitterFCN(int &npar, double *dummy, double &fchisq, double *gin, int iflag){ | |
191 | // | |
192 | // internal function which gives the specified function to the TMinuit function | |
193 | // | |
194 | ||
195 | // suppress warnings for unused variables: | |
196 | dummy = dummy; | |
197 | iflag = iflag; | |
198 | npar = npar; | |
199 | // | |
200 | AliTMinuitToolkit * fitter = (AliTMinuitToolkit*)TVirtualFitter::GetFitter()->GetObjectFit(); | |
201 | fchisq = 0; | |
202 | Int_t nvar = fitter->GetPoints()->GetNcols()-1; | |
203 | Int_t npoints = fitter->GetPoints()->GetNrows(); | |
204 | ||
205 | // sort points for weighting | |
d99c0447 | 206 | Double_t *sortList = new Double_t[npoints]; |
da7c9ae3 | 207 | Int_t *indexList = new Int_t[npoints]; |
4b23a517 | 208 | |
da7c9ae3 | 209 | TVectorD *Weight = new TVectorD(npoints); |
4b23a517 | 210 | |
211 | for (Int_t ipoint=0; ipoint<npoints; ipoint++){ | |
212 | Double_t x[100]; | |
213 | for (Int_t ivar=0; ivar<nvar; ivar++){ | |
214 | x[ivar] = (*fitter->GetPoints())(ipoint, ivar); | |
215 | } | |
216 | Float_t funx = fitter->GetFormula()->EvalPar(x,gin); | |
217 | sortList[ipoint] = TMath::Abs((*fitter->GetPoints())(ipoint, nvar) - funx); | |
218 | } | |
219 | ||
220 | TMath::Sort(npoints, sortList, indexList, false); | |
221 | ||
222 | Double_t t; | |
223 | for (Int_t ipoint=0; ipoint<npoints; ipoint++){ | |
224 | t = indexList[ipoint]/(Double_t)npoints; | |
da7c9ae3 | 225 | (*Weight)(ipoint) = fitter->GetWeightFunction()->Eval(t); |
4b23a517 | 226 | } |
227 | // | |
228 | // calculate chisquare | |
229 | for (Int_t ipoint=0; ipoint<npoints; ipoint++){ | |
230 | Double_t x[100]; | |
231 | for (Int_t ivar=0; ivar<nvar; ivar++){ | |
232 | x[ivar] = (*fitter->GetPoints())(ipoint, ivar); | |
233 | } | |
234 | Float_t funx = fitter->GetFormula()->EvalPar(x,gin); | |
235 | ||
236 | Double_t delta = (*fitter->GetPoints())(ipoint, nvar) - funx; | |
da7c9ae3 | 237 | fchisq+= delta*delta*(*Weight)(ipoint); |
4b23a517 | 238 | |
239 | } | |
da7c9ae3 | 240 | delete Weight; |
241 | delete sortList; | |
242 | delete indexList; | |
4b23a517 | 243 | } |
244 | ||
245 | ||
246 | void AliTMinuitToolkit::Fit() { | |
247 | // | |
248 | // internal function that calls the fitter | |
249 | // | |
250 | Int_t nparam = fParam->GetNrows(); | |
251 | ||
252 | // set all paramter limits to infinity as default | |
253 | if (fParamLimits == 0) { | |
254 | fParamLimits = new TMatrixD(nparam ,2); | |
255 | for (Int_t iparam=0; iparam<nparam; iparam++){ | |
256 | (*fParamLimits)(iparam, 0) = 0; | |
257 | (*fParamLimits)(iparam, 1) = 0; | |
258 | } | |
259 | } | |
260 | ||
261 | // set all weights to 1 as default | |
262 | if (fWeightFunction == 0) { | |
263 | fWeightFunction = new TFormula("constant", "1"); | |
264 | } | |
265 | ||
266 | // migrad fit algorithm as default | |
267 | if (fFitAlgorithm == 0) { | |
268 | fFitAlgorithm = "migrad"; | |
269 | } | |
270 | ||
271 | // set up the fitter | |
272 | TVirtualFitter *minuit = TVirtualFitter::Fitter(0, nparam); | |
273 | minuit->SetObjectFit(this); | |
274 | minuit->SetFCN((void*)(AliTMinuitToolkit::FitterFCN)); | |
275 | ||
276 | // initialize paramters (step size???) | |
277 | for (Int_t iparam=0; iparam<nparam; iparam++){ | |
278 | minuit->SetParameter(iparam, Form("p[%d]",iparam), (*fParam)(iparam), (*fParam)(iparam)/10, (*fParamLimits)(iparam, 0), (*fParamLimits)(iparam, 1)); | |
279 | } | |
280 | ||
281 | Double_t argList[2]; | |
282 | argList[0] = fMaxCalls; //maximal number of calls | |
283 | argList[1] = fPrecision; //tolerance normalized to 0.001 | |
284 | if (fMaxCalls == 500 && fPrecision == 1) minuit->ExecuteCommand(fFitAlgorithm, 0, 0); | |
285 | if (fMaxCalls != 500 || fPrecision != 1) minuit->ExecuteCommand(fFitAlgorithm, argList, 2); | |
286 | // two additional arguments can be specified ExecuteCommand("migrad", argList, 2) - use 0,0 for default | |
287 | ||
288 | // fill parameter vector | |
289 | for (Int_t ivar=0; ivar<nparam; ivar++){ | |
290 | (*fParam)(ivar) = minuit->GetParameter(ivar); | |
291 | } | |
292 | ||
293 | // fill covariance matrix | |
294 | fCovar = new TMatrixD(nparam, nparam); | |
295 | //TVirtualFitter *fitCov = TVirtualFitter::GetFitter(); | |
296 | for(Int_t i=0; i < nparam; i++) { | |
297 | for(Int_t j=0; j < nparam; j++) { | |
298 | (*fCovar)(i,j) = minuit->GetCovarianceMatrixElement(i,j); | |
299 | } | |
300 | } | |
301 | ||
302 | } | |
303 | ||
304 | ||
305 | ||
306 | void AliTMinuitToolkit::Test() { | |
307 | // | |
308 | // This test function shows the basic working principles of this class | |
309 | // and illustrates how a robust fit can improve the results | |
310 | // | |
311 | TFormula *FormExp = new TFormula("formExp", "[0]*TMath::Exp(-[1]*x)"); | |
312 | SetFitFunction(FormExp); | |
313 | SetFitAlgorithm("simplex"); | |
314 | // Set initial values | |
315 | TVectorD *vec1 = new TVectorD(2); | |
316 | (*vec1)(0) = 1800; | |
317 | (*vec1)(1) = 1; | |
318 | SetInitialParam(vec1); | |
319 | //provide some example histogram | |
320 | TH1F * hist = new TH1F("bla", "with (red) and without (black) robust option", 20,0,4); | |
321 | TRandom * rand = new TRandom(); | |
322 | for (Int_t i = 0; i < 10000; i++) { | |
323 | hist->Fill(rand->Exp(1)); | |
324 | if (i < 1000) hist->Fill(3); //"outliers" | |
325 | if (i < 1070) hist->Fill(3.5); | |
326 | if (i < 670) hist->Fill(2); | |
327 | if (i < 770) hist->Fill(1.5);//"outliers" | |
328 | if (i < 740) hist->Fill(1); | |
329 | } | |
330 | TCanvas * canv = new TCanvas(); | |
331 | canv->cd(1); | |
332 | hist->Draw(); | |
333 | // fit it with the exponential decay | |
334 | FitHistogram(hist); | |
335 | // draw fit function | |
336 | TF1 *func = new TF1("test", "[0]*TMath::Exp(-[1]*x)", 0, 6); | |
337 | func->SetParameter(0, (*GetParameters())(0)); | |
338 | func->SetParameter(1, (*GetParameters())(1)); | |
339 | func->Draw("same"); | |
340 | // robust fit | |
341 | TVectorD *vec2 = new TVectorD(2); | |
342 | (*vec2)(0) = 1800; | |
343 | (*vec2)(1) = 1; | |
344 | SetInitialParam(vec2); | |
345 | SetWeightFunction("Box", 0.7); | |
346 | FitHistogram(hist); | |
347 | TF1 *func2 = new TF1("test2", "[0]*TMath::Exp(-[1]*x)", 0, 6); | |
348 | func2->SetParameter(0, (*GetParameters())(0)); | |
349 | func2->SetParameter(1, (*GetParameters())(1)); | |
350 | func2->SetLineColor(kRed); | |
351 | func2->Draw("same"); | |
352 | ||
353 | } | |
354 |