1 | // Nsubjettiness Package
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2 | // Questions/Comments? jthaler@jthaler.net
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3 | //
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4 | // Copyright (c) 2011-14
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5 | // Jesse Thaler, Ken Van Tilburg, Christopher K. Vermilion, and TJ Wilkason
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6 | //
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7 | // $Id: AxesFinder.cc 670 2014-06-06 01:24:42Z jthaler $
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8 | //----------------------------------------------------------------------
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9 | // This file is part of FastJet contrib.
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10 | //
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11 | // It is free software; you can redistribute it and/or modify it under
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12 | // the terms of the GNU General Public License as published by the
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13 | // Free Software Foundation; either version 2 of the License, or (at
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14 | // your option) any later version.
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15 | //
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16 | // It is distributed in the hope that it will be useful, but WITHOUT
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17 | // ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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18 | // or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
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19 | // License for more details.
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20 | //
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21 | // You should have received a copy of the GNU General Public License
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22 | // along with this code. If not, see <http://www.gnu.org/licenses/>.
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23 | //----------------------------------------------------------------------
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24 |
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25 | #include "AxesFinder.hh"
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26 |
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27 | FASTJET_BEGIN_NAMESPACE // defined in fastjet/internal/base.hh
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28 |
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29 | namespace contrib{
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30 |
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31 | ///////
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32 | //
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33 | // Functions for minimization.
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34 | //
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35 | ///////
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36 |
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37 | // Given starting axes, update to find better axes by using Kmeans clustering around the old axes
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38 | template <int N>
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39 | std::vector<LightLikeAxis> AxesFinderFromOnePassMinimization::UpdateAxesFast(const std::vector <LightLikeAxis> & old_axes,
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40 | const std::vector <fastjet::PseudoJet> & inputJets) const {
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41 | assert(old_axes.size() == N);
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42 |
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43 | // some storage, declared static to save allocation/re-allocation costs
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44 | static LightLikeAxis new_axes[N];
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45 | static fastjet::PseudoJet new_jets[N];
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46 | for (int n = 0; n < N; ++n) {
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47 | new_axes[n].reset(0.0,0.0,0.0,0.0);
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48 | new_jets[n].reset_momentum(0.0,0.0,0.0,0.0);
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49 | }
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50 |
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51 | double precision = _precision;
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52 |
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53 | /////////////// Assignment Step //////////////////////////////////////////////////////////
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54 | std::vector<int> assignment_index(inputJets.size());
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55 | int k_assign = -1;
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56 |
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57 | for (unsigned i = 0; i < inputJets.size(); i++){
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58 | double smallestDist = std::numeric_limits<double>::max(); //large number
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59 | for (int k = 0; k < N; k++) {
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60 | double thisDist = old_axes[k].DistanceSq(inputJets[i]);
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61 | if (thisDist < smallestDist) {
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62 | smallestDist = thisDist;
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63 | k_assign = k;
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64 | }
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65 | }
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66 | if (smallestDist > sq(_Rcutoff)) {k_assign = -1;}
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67 | assignment_index[i] = k_assign;
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68 | }
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69 |
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70 | //////////////// Update Step /////////////////////////////////////////////////////////////
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71 | double distPhi, old_dist;
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72 | for (unsigned i = 0; i < inputJets.size(); i++) {
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73 | int old_jet_i = assignment_index[i];
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74 | if (old_jet_i == -1) {continue;}
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75 |
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76 | const fastjet::PseudoJet& inputJet_i = inputJets[i];
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77 | LightLikeAxis& new_axis_i = new_axes[old_jet_i];
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78 | double inputPhi_i = inputJet_i.phi();
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79 | double inputRap_i = inputJet_i.rap();
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80 |
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81 | // optimize pow() call
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82 | // add noise (the precision term) to make sure we don't divide by zero
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83 | if (_beta == 1.0) {
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84 | double DR = std::sqrt(sq(precision) + old_axes[old_jet_i].DistanceSq(inputJet_i));
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85 | old_dist = 1.0/DR;
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86 | } else if (_beta == 2.0) {
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87 | old_dist = 1.0;
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88 | } else if (_beta == 0.0) {
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89 | double DRSq = sq(precision) + old_axes[old_jet_i].DistanceSq(inputJet_i);
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90 | old_dist = 1.0/DRSq;
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91 | } else {
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92 | old_dist = sq(precision) + old_axes[old_jet_i].DistanceSq(inputJet_i);
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93 | old_dist = std::pow(old_dist, (0.5*_beta-1.0));
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94 | }
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95 |
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96 | // TODO: Put some of these addition functions into light-like axes
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97 | // rapidity sum
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98 | new_axis_i.set_rap(new_axis_i.rap() + inputJet_i.perp() * inputRap_i * old_dist);
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99 | // phi sum
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100 | distPhi = inputPhi_i - old_axes[old_jet_i].phi();
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101 | if (fabs(distPhi) <= M_PI){
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102 | new_axis_i.set_phi( new_axis_i.phi() + inputJet_i.perp() * inputPhi_i * old_dist );
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103 | } else if (distPhi > M_PI) {
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104 | new_axis_i.set_phi( new_axis_i.phi() + inputJet_i.perp() * (-2*M_PI + inputPhi_i) * old_dist );
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105 | } else if (distPhi < -M_PI) {
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106 | new_axis_i.set_phi( new_axis_i.phi() + inputJet_i.perp() * (+2*M_PI + inputPhi_i) * old_dist );
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107 | }
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108 | // weights sum
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109 | new_axis_i.set_weight( new_axis_i.weight() + inputJet_i.perp() * old_dist );
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110 | // momentum magnitude sum
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111 | new_jets[old_jet_i] += inputJet_i;
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112 | }
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113 | // normalize sums
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114 | for (int k = 0; k < N; k++) {
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115 | if (new_axes[k].weight() == 0) {
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116 | // no particles were closest to this axis! Return to old axis instead of (0,0,0,0)
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117 | new_axes[k] = old_axes[k];
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118 | } else {
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119 | new_axes[k].set_rap( new_axes[k].rap() / new_axes[k].weight() );
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120 | new_axes[k].set_phi( new_axes[k].phi() / new_axes[k].weight() );
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121 | new_axes[k].set_phi( std::fmod(new_axes[k].phi() + 2*M_PI, 2*M_PI) );
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122 | new_axes[k].set_mom( std::sqrt(new_jets[k].modp2()) );
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123 | }
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124 | }
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125 | std::vector<LightLikeAxis> new_axes_vec(N);
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126 | for (unsigned k = 0; k < N; ++k) new_axes_vec[k] = new_axes[k];
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127 | return new_axes_vec;
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128 | }
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129 |
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130 | // Given N starting axes, this function updates all axes to find N better axes.
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131 | // (This is just a wrapper for the templated version above.)
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132 | std::vector<LightLikeAxis> AxesFinderFromOnePassMinimization::UpdateAxes(const std::vector <LightLikeAxis> & old_axes,
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133 | const std::vector <fastjet::PseudoJet> & inputJets) const {
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134 | int N = old_axes.size();
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135 | switch (N) {
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136 | case 1: return UpdateAxesFast<1>(old_axes, inputJets);
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137 | case 2: return UpdateAxesFast<2>(old_axes, inputJets);
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138 | case 3: return UpdateAxesFast<3>(old_axes, inputJets);
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139 | case 4: return UpdateAxesFast<4>(old_axes, inputJets);
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140 | case 5: return UpdateAxesFast<5>(old_axes, inputJets);
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141 | case 6: return UpdateAxesFast<6>(old_axes, inputJets);
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142 | case 7: return UpdateAxesFast<7>(old_axes, inputJets);
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143 | case 8: return UpdateAxesFast<8>(old_axes, inputJets);
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144 | case 9: return UpdateAxesFast<9>(old_axes, inputJets);
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145 | case 10: return UpdateAxesFast<10>(old_axes, inputJets);
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146 | case 11: return UpdateAxesFast<11>(old_axes, inputJets);
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147 | case 12: return UpdateAxesFast<12>(old_axes, inputJets);
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148 | case 13: return UpdateAxesFast<13>(old_axes, inputJets);
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149 | case 14: return UpdateAxesFast<14>(old_axes, inputJets);
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150 | case 15: return UpdateAxesFast<15>(old_axes, inputJets);
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151 | case 16: return UpdateAxesFast<16>(old_axes, inputJets);
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152 | case 17: return UpdateAxesFast<17>(old_axes, inputJets);
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153 | case 18: return UpdateAxesFast<18>(old_axes, inputJets);
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154 | case 19: return UpdateAxesFast<19>(old_axes, inputJets);
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155 | case 20: return UpdateAxesFast<20>(old_axes, inputJets);
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156 | default: std::cout << "N-jettiness is hard-coded to only allow up to 20 jets!" << std::endl;
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157 | return std::vector<LightLikeAxis>();
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158 | }
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159 |
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160 | }
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161 |
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162 | // uses minimization of N-jettiness to continually update axes until convergence.
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163 | // The function returns the axes found at the (local) minimum
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164 | std::vector<fastjet::PseudoJet> AxesFinderFromOnePassMinimization::getAxes(int n_jets, const std::vector <fastjet::PseudoJet> & inputJets, const std::vector<fastjet::PseudoJet>& seedAxes) const {
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165 |
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166 | // convert from PseudoJets to LightLikeAxes
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167 | std::vector< LightLikeAxis > old_axes(n_jets, LightLikeAxis(0,0,0,0));
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168 | for (int k = 0; k < n_jets; k++) {
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169 | old_axes[k].set_rap( seedAxes[k].rap() );
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170 | old_axes[k].set_phi( seedAxes[k].phi() );
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171 | }
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172 |
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173 | // Find new axes by iterating (only one pass here)
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174 | std::vector< LightLikeAxis > new_axes(n_jets, LightLikeAxis(0,0,0,0));
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175 | double cmp = std::numeric_limits<double>::max(); //large number
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176 | int h = 0;
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177 | while (cmp > _precision && h < _halt) { // Keep updating axes until near-convergence or too many update steps
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178 | cmp = 0.0;
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179 | h++;
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180 | new_axes = UpdateAxes(old_axes, inputJets); // Update axes
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181 | for (int k = 0; k < n_jets; k++) {
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182 | cmp += old_axes[k].Distance(new_axes[k]);
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183 | }
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184 | cmp = cmp / ((double) n_jets);
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185 | old_axes = new_axes;
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186 | }
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187 |
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188 | // Convert from internal LightLikeAxes to PseudoJet
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189 | std::vector<fastjet::PseudoJet> outputAxes;
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190 | for (int k = 0; k < n_jets; k++) {
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191 | fastjet::PseudoJet temp = old_axes[k].ConvertToPseudoJet();
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192 | outputAxes.push_back(temp);
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193 | }
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194 |
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195 | // this is used to debug the minimization routine to make sure that it works.
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196 | bool do_debug = false;
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197 | if (do_debug) {
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198 | // get this information to make sure that minimization is working properly
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199 | TauComponents seed_tau_components = _measureFunction.result(inputJets, seedAxes);
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200 | double seed_tau = seed_tau_components.tau();
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201 | TauComponents tau_components = _measureFunction.result(inputJets, outputAxes);
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202 | double outputTau = tau_components.tau();
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203 | assert(outputTau <= seed_tau);
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204 | }
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205 |
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206 | return outputAxes;
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207 | }
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208 |
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209 | PseudoJet AxesFinderFromKmeansMinimization::jiggle(const PseudoJet& axis) const {
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210 | double phi_noise = ((double)rand()/(double)RAND_MAX) * _noise_range * 2.0 - _noise_range;
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211 | double rap_noise = ((double)rand()/(double)RAND_MAX) * _noise_range * 2.0 - _noise_range;
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212 |
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213 | double new_phi = axis.phi() + phi_noise;
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214 | if (new_phi >= 2.0*M_PI) new_phi -= 2.0*M_PI;
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215 | if (new_phi <= -2.0*M_PI) new_phi += 2.0*M_PI;
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216 |
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217 | PseudoJet newAxis(0,0,0,0);
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218 | newAxis.reset_PtYPhiM(axis.perp(),axis.rap() + rap_noise,new_phi);
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219 | return newAxis;
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220 | }
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221 |
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222 |
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223 | // Repeatedly calls the one pass finder to try to find global minimum
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224 | std::vector<fastjet::PseudoJet> AxesFinderFromKmeansMinimization::getAxes(int n_jets, const std::vector <fastjet::PseudoJet> & inputJets, const std::vector<fastjet::PseudoJet>& seedAxes) const {
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225 |
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226 | // first iteration
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227 | std::vector<fastjet::PseudoJet> bestAxes = _onePassFinder.getAxes(n_jets, inputJets, seedAxes);
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228 |
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229 | double bestTau = (_measureFunction.result(inputJets,bestAxes)).tau();
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230 |
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231 | for (int l = 1; l < _n_iterations; l++) { // Do minimization procedure multiple times (l = 1 to start since first iteration is done already)
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232 |
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233 | // Add noise to current best axes
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234 | std::vector< PseudoJet > noiseAxes(n_jets, PseudoJet(0,0,0,0));
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235 | for (int k = 0; k < n_jets; k++) {
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236 | noiseAxes[k] = jiggle(bestAxes[k]);
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237 | }
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238 |
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239 | std::vector<fastjet::PseudoJet> testAxes = _onePassFinder.getAxes(n_jets, inputJets, noiseAxes);
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240 | double testTau = (_measureFunction.result(inputJets,testAxes)).tau();
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241 |
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242 | if (testTau < bestTau) {
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243 | bestTau = testTau;
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244 | bestAxes = testAxes;
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245 | }
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246 | }
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247 |
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248 | return bestAxes;
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249 | }
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250 |
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251 | // Uses minimization of the geometric distance in order to find the minimum axes.
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252 | // It continually updates until it reaches convergence or it reaches the maximum number of attempts.
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253 | // This is essentially the same as a stable cone finder.
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254 | std::vector<fastjet::PseudoJet> AxesFinderFromGeometricMinimization::getAxes(int /*n_jets*/, const std::vector <fastjet::PseudoJet> & particles, const std::vector<fastjet::PseudoJet>& currentAxes) const {
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255 |
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256 | std::vector<fastjet::PseudoJet> seedAxes = currentAxes;
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257 | double seedTau = _function.tau(particles, seedAxes);
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258 |
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259 | for (int i = 0; i < _nAttempts; i++) {
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260 |
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261 | std::vector<fastjet::PseudoJet> newAxes(seedAxes.size(),fastjet::PseudoJet(0,0,0,0));
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262 |
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263 | // find closest axis and assign to that
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264 | for (unsigned int i = 0; i < particles.size(); i++) {
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265 |
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266 | // start from unclustered beam measure
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267 | int minJ = -1;
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268 | double minDist = _function.beam_distance_squared(particles[i]);
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269 |
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270 | // which axis am I closest to?
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271 | for (unsigned int j = 0; j < seedAxes.size(); j++) {
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272 | double tempDist = _function.jet_distance_squared(particles[i],seedAxes[j]);
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273 | if (tempDist < minDist) {
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274 | minDist = tempDist;
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275 | minJ = j;
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276 | }
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277 | }
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278 |
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279 | // if not unclustered, then cluster
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280 | if (minJ != -1) newAxes[minJ] += particles[i];
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281 | }
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282 |
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283 | // calculate tau on new axes
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284 | seedAxes = newAxes;
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285 | double tempTau = _function.tau(particles, newAxes);
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286 |
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287 | // close enough to stop?
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288 | if (fabs(tempTau - seedTau) < _accuracy) break;
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289 | seedTau = tempTau;
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290 | }
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291 |
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292 | return seedAxes;
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293 | }
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294 |
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295 | // Go from internal LightLikeAxis to PseudoJet
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296 | fastjet::PseudoJet LightLikeAxis::ConvertToPseudoJet() {
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297 | double px, py, pz, E;
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298 | E = _mom;
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299 | pz = (std::exp(2.0*_rap) - 1.0) / (std::exp(2.0*_rap) + 1.0) * E;
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300 | px = std::cos(_phi) * std::sqrt( std::pow(E,2) - std::pow(pz,2) );
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301 | py = std::sin(_phi) * std::sqrt( std::pow(E,2) - std::pow(pz,2) );
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302 | return fastjet::PseudoJet(px,py,pz,E);
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303 | }
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304 |
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305 | } //namespace contrib
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306 |
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307 | FASTJET_END_NAMESPACE
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