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[u/mrichter/AliRoot.git] / PWGCF / Correlations / DPhi / DiHadronPID / AliFunctionsDiHadronPID.cxx
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07d62e30 1/*************************************************************************
2* Copyright(c) 1998-2008, ALICE Experiment at CERN, All rights reserved. *
3* *
4* Author: The ALICE Off-line Project. *
5* Contributors are mentioned in the code where appropriate. *
6* *
7* Permission to use, copy, modify and distribute this software and its *
8* documentation strictly for non-commercial purposes is hereby granted *
9* without fee, provided that the above copyright notice appears in all *
10* copies and that both the copyright notice and this permission notice *
11* appear in the supporting documentation. The authors make no claims *
12* about the suitability of this software for any purpose. It is *
13* provided "as is" without express or implied warranty. *
14**************************************************************************/
15
16// -----------------------------------------------------------------------
17// Definitions the mathematical functions used in the DiHadronPID
18// analysis.
19// -----------------------------------------------------------------------
20// Author: Misha Veldhoen (misha.veldhoen@cern.ch)
21
a5422983 22#include "AliFunctionsDiHadronPID.h"
23
07d62e30 24#include <iostream>
a5422983 25using namespace std;
07d62e30 26
27#include "AliExternalTrackParam.h"
07d62e30 28#include "TF1.h"
29
07d62e30 30// -----------------------------------------------------------------------
31AliFunctionsDiHadronPID::AliFunctionsDiHadronPID()
32
33{
34
35 // Constructor.
36
37}
38
39// -----------------------------------------------------------------------
40AliFunctionsDiHadronPID::~AliFunctionsDiHadronPID()
41
42{
43
44 // Destructor.
45
46}
07d62e30 47
01f5c9f4
LM		 48// -----------------------------------------------------------------------
49Int_t AliFunctionsDiHadronPID::Power(Int_t base, Int_t power) {
07d62e30 50
01f5c9f4 51 // Power function for integers (not available in TMath).
07d62e30 52
01f5c9f4
LM		 53 if (power > 0) {
54 Int_t result = 1;
55 for (Int_t ii = 0; ii < power; ++ii) {result *= base;}
56 return result;
57 } else {
58 if (power == 0) {return 1;}
59 else {
60 cout << Form("%s::%s -> WARNING: Method doesn't work for negative powers.",__FILE__,__func__) << endl;
61 return -999;
62 }
63 }
07d62e30 64
65}
01f5c9f4 66
07d62e30 67// -----------------------------------------------------------------------
fe463f34 68Double_t AliFunctionsDiHadronPID::Gaussian1D(Double_t xx, Double_t integral, Double_t mu, Double_t sigma, Double_t binwidth) {
07d62e30 69
70 // The other implementation should make use of this one.
71 Double_t norm = (binwidth*integral)/(TMath::Sqrt(2.*TMath::Pi())*sigma);
72 Double_t gaussian = TMath::Exp(-(xx-mu)*(xx-mu)/(2.*sigma*sigma));
73
74 return (norm*gaussian);
75
76}
07d62e30 77
07d62e30 78// -----------------------------------------------------------------------
fe463f34 79Double_t AliFunctionsDiHadronPID::Gaussian1DTail(Double_t xx, Double_t integral, Double_t mu, Double_t sigma, Double_t tail, Double_t binwidth) {
07d62e30 80
81 // Gaussian with exponential tail on the right, I is the integral.
82 // For function definition see: FitFunctions.nb
83
84 Double_t kappa = mu + tail;
85
86 if (mu >= kappa) return 0.; // Function becomes ill-defined.
87
88 Double_t beta = sigma*sigma/(kappa-mu);
89 Double_t BB = TMath::Exp( (kappa*kappa-mu*mu)/(2.*sigma*sigma) );
90 Double_t norm1 = beta*TMath::Exp( -(mu-kappa)*(mu-kappa)/(2.*sigma*sigma) );
91 Double_t norm2 = TMath::Sqrt(TMath::Pi()/2.)*sigma*TMath::Erfc( (mu-kappa)/(TMath::Sqrt2()*sigma) );
92 Double_t norm = norm1 + norm2;
93
94 Double_t funcleft = binwidth * (integral/norm)*TMath::Exp(-(xx-mu)*(xx-mu)/(2.*sigma*sigma));
95 Double_t funcright = binwidth * (integral/norm)*BB*TMath::Exp(-xx/beta);
96
97 if (xx <= kappa) return funcleft;
98 else return funcright;
99
100}
101
102// -----------------------------------------------------------------------
fe463f34 103Double_t AliFunctionsDiHadronPID::Gaussian2D(Double_t xx, Double_t yy, Double_t integral,
104 Double_t mux, Double_t muy, Double_t sigmax, Double_t sigmay,
105 Double_t binwidthx, Double_t binwidthy) {
07d62e30 106
107 // 2D Gaussian.
108 Double_t GaussianX = Gaussian1D(xx, 1., mux, sigmax, binwidthx);
109 Double_t GaussianY = Gaussian1D(yy, 1., muy, sigmay, binwidthy);
110
111 return integral * GaussianX * GaussianY;
112
113}
114
115// -----------------------------------------------------------------------
fe463f34 116Double_t AliFunctionsDiHadronPID::Gaussian2DTailX(Double_t xx, Double_t yy, Double_t integral,
117 Double_t mux, Double_t muy, Double_t sigmax, Double_t sigmay,
118 Double_t tailx, Double_t binwidthx, Double_t binwidthy) {
07d62e30 119
120 // 2D Gaussian with exponential tail in X direction.
121 Double_t GaussianTailX = Gaussian1DTail(xx, 1., mux, sigmax, tailx, binwidthx);
122 Double_t GaussianY = Gaussian1D(yy, 1., muy, sigmay, binwidthy);
123
124 return integral * GaussianTailX * GaussianY;
125
126}
127
128// -----------------------------------------------------------------------
fe463f34 129Double_t AliFunctionsDiHadronPID::Gaussian2DTailY(Double_t xx, Double_t yy, Double_t integral,
130 Double_t mux, Double_t muy, Double_t sigmax, Double_t sigmay,
131 Double_t taily, Double_t binwidthx, Double_t binwidthy) {
07d62e30 132
133 // 2D Gaussian with exponential tail in Y direction.
134 Double_t GaussianX = Gaussian1D(xx, 1., mux, sigmax, binwidthx);
135 Double_t GaussianTailY = Gaussian1DTail(yy, 1., muy, sigmay, taily, binwidthy);
136
137 return integral * GaussianX * GaussianTailY;
138
139}
140
141// -----------------------------------------------------------------------
fe463f34 142Double_t AliFunctionsDiHadronPID::Gaussian2DTailXY(Double_t xx, Double_t yy, Double_t integral,
143 Double_t mux, Double_t muy, Double_t sigmax, Double_t sigmay,
144 Double_t tailx, Double_t taily, Double_t binwidthx, Double_t binwidthy) {
07d62e30 145
146 // 2D Gaussian with exponential tail in X- and Y direction.
147 Double_t GaussianTailX = Gaussian1DTail(xx, 1., mux, sigmax, tailx, binwidthx);
148 Double_t GaussianTailY = Gaussian1DTail(yy, 1., muy, sigmay, taily, binwidthy);
149
150 return integral * GaussianTailX * GaussianTailY;
151
07d62e30 152}
153
07d62e30 154// -----------------------------------------------------------------------
fe463f34 155Double_t AliFunctionsDiHadronPID::PolyPenalty(Double_t xx, Double_t center, Double_t flatwidth, const Int_t polyorder) {
07d62e30 156
157 // Penalty function for a chi^2 fit. The function is defined as:
158 // 1 for |xx - center| < flatwidth,
159 // (|xx - center| - flatwidth) ^ polyorder for |xx - center| > flatwidth.
160
161 Double_t fx = 1.;
162 if (TMath::Abs(xx - center) > flatwidth) {
163 fx = TMath::Power( (TMath::Abs(xx - center) - flatwidth), polyorder ) + 1.;
164 }
165
166 return fx;
167
168}
169
170// -----------------------------------------------------------------------
fe463f34 171TCanvas* AliFunctionsDiHadronPID::TestPolyPenalty(Double_t range, Double_t center, Double_t flatwidth, const Int_t polyorder) {
07d62e30 172
173 // Creates an example of the TestPolyPenalty function.
174 TF1* tf = new TF1("tf",Form("AliFunctionsDiHadronPID::PolyPenalty(x,[0],[1],%i)",polyorder),-range,range);
175 tf->SetParameters(center,flatwidth);
176 TCanvas* cvs = TCanvas::MakeDefCanvas();
177 tf->Draw();
178
179 return cvs;
180
181}
182
07d62e30 183// -----------------------------------------------------------------------
fe463f34 184Double_t AliFunctionsDiHadronPID::TOFExpTime(Double_t pT, Double_t eta, Double_t mass) {
07d62e30 185
186 // For description see ../Documents/TOFtime.tex
187
188 Double_t AA = (2. * pT) / ( Charge() * BTPC() * GeVperkg() );
189 Double_t BB = TMath::ASin( (Charge() * BTPC() * 0.01 * RTOF() * GeVperkg() ) / (2. * pT * C()) );
190 Double_t CC = TMath::Sqrt( mass*mass/(pT*pT) + TMath::CosH(eta)*TMath::CosH(eta) );
191
192 return (1.e12*AA*BB*CC); // Time returned in ps.
193
194}
195
196// -----------------------------------------------------------------------
fe463f34 197Double_t AliFunctionsDiHadronPID::TPCExpdEdX(Double_t pT, Double_t eta, Double_t mass) {
07d62e30 198
199 // Not so neat solution, however the easiest for now.
200
201 // Prameters taken from the constructor of AliTPCPIDResponse:
202 Double_t MIP = 50.;
203 Double_t Kp[5] = {0.0283086, 2.63394e+01, 5.04114e-11, 2.12543, 4.88663};
204
205 Double_t betaGamma = TMath::Abs( (pT * TMath::CosH(eta)) / mass );
206
207 // Implementation as in AliTPCPIDResponse.
208 return MIP * AliExternalTrackParam::BetheBlochAleph(betaGamma,Kp[0],Kp[1],Kp[2],Kp[3],Kp[4]);
209
210}