Added Analysis of forward, away and transverse zone as a function of pt of the jet...
[u/mrichter/AliRoot.git] / JETAN / AliKMeansClustering.cxx
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70f2ce9d 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. *
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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 *
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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// Implemenatation of the K-Means Clustering Algorithm
17// See http://en.wikipedia.org/wiki/K-means_clustering and references therein.
18//
19// This particular implementation is the so called Soft K-means algorithm.
20// It has been modified to work on the cylindrical topology in eta-phi space.
21//
22// Author: Andreas Morsch (CERN)
23// andreas.morsch@cern.ch
24
25#include "AliKMeansClustering.h"
26#include <TMath.h>
27#include <TRandom.h>
28
29ClassImp(AliKMeansClustering)
30
31Double_t AliKMeansClustering::fBeta = 10.;
32
33void AliKMeansClustering::SoftKMeans(Int_t k, Int_t n, Double_t* x, Double_t* y, Double_t* mx, Double_t* my , Double_t* rk )
34{
35 //
36 // The soft K-means algorithm
37 //
38 Int_t i,j;
39 //
40 // (1) Initialisation of the k means
41
42 for (i = 0; i < k; i++) {
43 mx[i] = 2. * TMath::Pi() * gRandom->Rndm();
44 my[i] = -1. + 2. * gRandom->Rndm();
45 }
46
47 //
48 // (2a) The responsibilities
49 Double_t** r = new Double_t*[n]; // responsibilities
50 for (j = 0; j < n; j++) {r[j] = new Double_t[k];}
51 //
52 // (2b) Normalisation
53 Double_t* nr = new Double_t[n];
54
55 // (3) Iterations
56 Int_t nit = 0;
57
58 while(1) {
59 nit++;
60 //
61 // Assignment step
62 //
63 for (j = 0; j < n; j++) {
64 nr[j] = 0.;
65 for (i = 0; i < k; i++) {
66 r[j][i] = TMath::Exp(- fBeta * d(mx[i], my[i], x[j], y[j]));
67 nr[j] += r[j][i];
68 } // mean i
69 } // data point j
70
71 for (j = 0; j < n; j++) {
72 for (i = 0; i < k; i++) {
73 r[j][i] /= nr[j];
74 } // mean i
75 } // data point j
76
77 //
78 // Update step
79 Double_t di = 0;
80
81 for (i = 0; i < k; i++) {
82 Double_t oldx = mx[i];
83 Double_t oldy = my[i];
84
85 mx[i] = x[0];
86 my[i] = y[0];
87 rk[i] = r[0][i];
88
89 for (j = 1; j < n; j++) {
90 Double_t xx = x[j];
91//
92// Here we have to take into acount the cylinder topology where phi is defined mod 2xpi
93// If two coordinates are separated by more than pi in phi one has to be shifted by +/- 2 pi
94
95 Double_t dx = mx[i] - x[j];
96 if (dx > TMath::Pi()) xx += 2. * TMath::Pi();
97 if (dx < -TMath::Pi()) xx -= 2. * TMath::Pi();
98 mx[i] = mx[i] * rk[i] + r[j][i] * xx;
99 my[i] = my[i] * rk[i] + r[j][i] * y[j];
100 rk[i] += r[j][i];
101 mx[i] /= rk[i];
102 my[i] /= rk[i];
103 if (mx[i] > 2. * TMath::Pi()) mx[i] -= 2. * TMath::Pi();
104 if (mx[i] < 0. ) mx[i] += 2. * TMath::Pi();
105 } // Data
106 di += d(mx[i], my[i], oldx, oldy);
107 } // means
108 //
109 // ending condition
110 if (di < 1.e-8 || nit > 1000) break;
111 } // while
112
113// Clean-up
114 delete[] nr;
115 for (j = 0; j < n; j++) delete[] r[j];
116 delete[] r;
117}
118
77f42a25 119void AliKMeansClustering::SoftKMeans2(Int_t k, Int_t n, Double_t* x, Double_t* y, Double_t* mx, Double_t* my , Double_t* sigma2, Double_t* rk )
120{
121 //
122 // The soft K-means algorithm
123 //
124 Int_t i,j;
125 //
126 // (1) Initialisation of the k means
127 //
128 // (there is an optimized version for initialisation called kmeans++)
129 for (i = 0; i < k; i++) {
130 mx[i] = 2. * TMath::Pi() * gRandom->Rndm();
131 my[i] = -1. + 2. * gRandom->Rndm();
132 }
133
134 //
135 // (2a) The responsibilities
136 Double_t** r = new Double_t*[n]; // responsibilities
137 for (j = 0; j < n; j++) {r[j] = new Double_t[k];}
138 //
139 // (2b) Normalisation
140 Double_t* nr = new Double_t[n];
141 //
142 // (2c) Weights
143 Double_t* pi = new Double_t[k];
144 //
145 // (2d) Initialise the responsibilties and weights
146 for (j = 0; j < n; j++) {
147 nr[j] = 0.;
148 for (i = 0; i < k; i++) {
149 r[j][i] = TMath::Exp(- fBeta * d(mx[i], my[i], x[j], y[j]));
150 nr[j] += r[j][i];
151 } // mean i
152 } // data point j
153
154 for (i = 0; i < k; i++) {
155 rk[i] = 0.;
156 sigma2[i] = 1./fBeta;
157
158 for (j = 0; j < n; j++) {
159 r[j][i] /= nr[j];
160 rk[i] += r[j][i];
161 } // mean i
162 pi[i] = rk[i] / Double_t(n);
163 } // data point j
164
165
166 // (3) Iterations
167 Int_t nit = 0;
168
169 while(1) {
170 nit++;
171 //
172 // Assignment step
173 //
174 for (j = 0; j < n; j++) {
175 nr[j] = 0.;
176 for (i = 0; i < k; i++) {
177 r[j][i] = pi[i] * TMath::Exp(- fBeta * d(mx[i], my[i], x[j], y[j]))
178 / (TMath::Sqrt(2. * sigma2[i]) * TMath::Pi());
179 nr[j] += r[j][i];
180 } // mean i
181 } // data point j
182
183 for (i = 0; i < k; i++) {
184 for (j = 0; j < n; j++) {
185 r[j][i] /= nr[j];
186 } // mean i
187 } // data point j
188
189 //
190 // Update step
191 Double_t di = 0;
192
193 for (i = 0; i < k; i++) {
194 Double_t oldx = mx[i];
195 Double_t oldy = my[i];
196
197 mx[i] = x[0];
198 my[i] = y[0];
199 rk[i] = r[0][i];
200
201 for (j = 1; j < n; j++) {
202 Double_t xx = x[j];
203//
204// Here we have to take into acount the cylinder topology where phi is defined mod 2xpi
205// If two coordinates are separated by more than pi in phi one has to be shifted by +/- 2 pi
206
207 Double_t dx = mx[i] - x[j];
208 if (dx > TMath::Pi()) xx += 2. * TMath::Pi();
209 if (dx < -TMath::Pi()) xx -= 2. * TMath::Pi();
210 mx[i] = mx[i] * rk[i] + r[j][i] * xx;
211 my[i] = my[i] * rk[i] + r[j][i] * y[j];
212 rk[i] += r[j][i];
213 mx[i] /= rk[i];
214 my[i] /= rk[i];
215 if (mx[i] > 2. * TMath::Pi()) mx[i] -= 2. * TMath::Pi();
216 if (mx[i] < 0. ) mx[i] += 2. * TMath::Pi();
217 } // Data
218 di += d(mx[i], my[i], oldx, oldy);
219 } // means
220 //
221 // Sigma
222 for (i = 0; i < k; i++) {
223 sigma2[i] = 0.;
224 for (j = 1; j < n; j++) {
225 sigma2[i] += 2. * r[j][i] * d(mx[i], my[i], x[j], y[j]);
226 } // Data
227 sigma2[i] /= rk[i];
228 } // Clusters
229 //
230 // Fractions
231 for (i = 0; i < k; i++) pi[i] = rk[i] / Double_t(n);
232 //
233// ending condition
234 if (di < 1.e-8 || nit > 1000) break;
235 } // while
236
237// Clean-up
238 delete[] nr;
239 delete[] pi;
240 for (j = 0; j < n; j++) delete[] r[j];
241 delete[] r;
242}
243
70f2ce9d 244Double_t AliKMeansClustering::d(Double_t mx, Double_t my, Double_t x, Double_t y)
245{
246 //
247 // Distance definition
248 // Quasi - Euclidian on the eta-phi cylinder
249
250 Double_t dx = TMath::Abs(mx-x);
251 if (dx > TMath::Pi()) dx = 2. * TMath::Pi() - dx;
252
8422e0a8 253 return (0.5*(dx * dx + (my - y) * (my - y)));
70f2ce9d 254}