1 | /* ======================================================================== *\
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2 | !
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3 | ! *
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4 | ! * This file is part of MARS, the MAGIC Analysis and Reconstruction
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5 | ! * Software. It is distributed to you in the hope that it can be a useful
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6 | ! * and timesaving tool in analysing Data of imaging Cerenkov telescopes.
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7 | ! * It is distributed WITHOUT ANY WARRANTY.
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8 | ! *
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9 | ! * Permission to use, copy, modify and distribute this software and its
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10 | ! * documentation for any purpose is hereby granted without fee,
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11 | ! * provided that the above copyright notice appear in all copies and
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12 | ! * that both that copyright notice and this permission notice appear
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13 | ! * in supporting documentation. It is provided "as is" without express
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14 | ! * or implied warranty.
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15 | ! *
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16 | !
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17 | !
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18 | ! Author(s): Thomas Hengstebeck 3/2003 <mailto:hengsteb@alwa02.physik.uni-siegen.de>
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19 | !
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20 | ! Copyright: MAGIC Software Development, 2000-2003
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21 | !
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22 | !
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23 | \* ======================================================================== */
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24 |
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25 | /////////////////////////////////////////////////////////////////////////////
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26 | // //
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27 | // MRanTree //
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28 | // //
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29 | // ParameterContainer for Tree structure //
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30 | // //
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31 | // //
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32 | /////////////////////////////////////////////////////////////////////////////
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33 | #include "MRanTree.h"
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34 |
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35 | #include <iostream>
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36 |
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37 | #include <TVector.h>
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38 | #include <TMatrix.h>
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39 | #include <TRandom.h>
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40 |
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41 | #include "MDataArray.h"
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42 |
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43 | #include "MLog.h"
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44 | #include "MLogManip.h"
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45 |
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46 | ClassImp(MRanTree);
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47 |
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48 | using namespace std;
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49 |
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50 | // --------------------------------------------------------------------------
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51 | //
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52 | // Default constructor.
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53 | //
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54 | MRanTree::MRanTree(const char *name, const char *title):fNdSize(0), fNumTry(3), fData(NULL)
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55 | {
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56 |
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57 | fName = name ? name : "MRanTree";
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58 | fTitle = title ? title : "Storage container for structure of a single tree";
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59 | }
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60 |
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61 | void MRanTree::SetNdSize(Int_t n)
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62 | {
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63 | // threshold nodesize of terminal nodes, i.e. the training data is splitted
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64 | // until there is only pure date in the subsets(=terminal nodes) or the
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65 | // subset size is LE n
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66 |
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67 | fNdSize=TMath::Max(1,n);//at least 1 event per node
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68 | }
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69 |
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70 | void MRanTree::SetNumTry(Int_t n)
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71 | {
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72 | // number of trials in random split selection:
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73 | // choose at least 1 variable to split in
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74 |
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75 | fNumTry=TMath::Max(1,n);
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76 | }
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77 |
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78 | void MRanTree::GrowTree(const TMatrix &mhad, const TMatrix &mgam,Int_t numdata, Int_t numdim,TArrayI &hadtrue,
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79 | TArrayI &datasort,TArrayI &datarang,TArrayF &tclasspop,TArrayI &jinbag,
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80 | TArrayF &winbag,TArrayF &weight)
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81 | {
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82 | // arrays have to be initialized with generous size, so number of total nodes (nrnodes)
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83 | // is estimated for worst case
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84 | Int_t nrnodes=2*numdata+1;
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85 |
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86 | // number of events in bootstrap sample
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87 | Int_t ninbag=0;
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88 | for (Int_t n=0;n<numdata;n++)
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89 | if(jinbag[n]==1) ninbag++;
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90 |
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91 | TArrayI bestsplit(nrnodes);
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92 | TArrayI bestsplitnext(nrnodes);
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93 | TArrayI nodepop(nrnodes);
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94 | TArrayI parent(nrnodes);
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95 | TArrayI nodex(numdata);
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96 | TArrayI nodestart(nrnodes);
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97 |
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98 | TArrayI ncase(numdata);
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99 | TArrayI iv(numdim);
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100 | TArrayI idmove(numdata);
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101 |
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102 | fBestVar.Set(nrnodes);
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103 | fTreeMap1.Set(nrnodes);
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104 | fTreeMap2.Set(nrnodes);
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105 | fBestSplit.Set(nrnodes);
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106 |
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107 | fTreeMap1.Reset();
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108 | fTreeMap2.Reset();
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109 | fBestSplit.Reset();
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110 |
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111 | fGiniDec.Set(numdim);
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112 | fGiniDec.Reset();
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113 |
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114 | // tree growing
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115 | BuildTree(datasort,datarang,hadtrue,numdim,numdata,bestsplit,
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116 | bestsplitnext,nodepop,nodestart,tclasspop,nrnodes,
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117 | idmove,ncase,parent,jinbag,iv,winbag,ninbag);
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118 |
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119 | // post processing, determine cut (or split) values fBestSplit
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120 | Int_t nhad=mhad.GetNrows();
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121 |
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122 | for(Int_t k=0; k<nrnodes; k++)
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123 | {
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124 | if (GetNodeStatus(k)==-1)
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125 | continue;
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126 |
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127 | const Int_t &bsp =bestsplit[k];
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128 | const Int_t &bspn=bestsplitnext[k];
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129 | const Int_t &msp =fBestVar[k];
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130 |
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131 | fBestSplit[k] = bsp<nhad ? mhad(bsp, msp):mgam(bsp-nhad, msp);
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132 | fBestSplit[k] += bspn<nhad ? mhad(bspn,msp):mgam(bspn-nhad,msp);
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133 | fBestSplit[k] /= 2;
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134 | }
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135 |
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136 | // resizing arrays to save memory
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137 | fBestVar.Set(fNumNodes);
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138 | fTreeMap1.Set(fNumNodes);
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139 | fTreeMap2.Set(fNumNodes);
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140 | fBestSplit.Set(fNumNodes);
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141 | }
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142 |
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143 | Int_t MRanTree::FindBestSplit(TArrayI &datasort,TArrayI &datarang,TArrayI &hadtrue,Int_t mdim,
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144 | Int_t numdata,Int_t ndstart,Int_t ndend,TArrayF &tclasspop,
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145 | Int_t &msplit,Float_t &decsplit,Int_t &nbest,TArrayI &ncase,
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146 | TArrayI &jinbag,TArrayI &iv,TArrayF &winbag,Int_t kbuild)
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147 | {
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148 | if(!gRandom)
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149 | {
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150 | *fLog << err << dbginf << "gRandom not initialized... aborting." << endl;
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151 | return kFALSE;
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152 | }
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153 |
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154 | // weighted class populations after split
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155 | TArrayF wc(2);
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156 | TArrayF wr(2); // right node
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157 |
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158 | // For the best split, msplit is the index of the variable (e.g Hillas par., zenith angle ,...)
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159 | // split on. decsplit is the decreae in impurity measured by Gini-index.
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160 | // nsplit is the case number of value of msplit split on,
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161 | // and nsplitnext is the case number of the next larger value of msplit.
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162 |
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163 | Int_t nc,nbestvar=0,k;
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164 | Float_t crit;
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165 | Float_t rrn, rrd, rln, rld, u;
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166 |
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167 | // compute initial values of numerator and denominator of Gini-index,
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168 | // Gini index= pno/dno
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169 | Float_t pno=0;
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170 | Float_t pdo=0;
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171 |
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172 | for (Int_t j=0;j<2;j++)
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173 | {
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174 | pno+=tclasspop[j]*tclasspop[j];
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175 | pdo+=tclasspop[j];
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176 | }
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177 |
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178 | const Double_t crit0=pno/pdo;
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179 | Int_t jstat=0;
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180 |
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181 | // start main loop through variables to find best split,
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182 | // (Gini-index as criterium crit)
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183 |
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184 | Double_t critmax=-1.0e20; // FIXME: Replace by a constant from limits.h
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185 |
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186 | // random split selection, number of trials = fNumTry
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187 | for(Int_t mt=0;mt<fNumTry;mt++)
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188 | {
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189 | Int_t mvar=Int_t(gRandom->Rndm()*mdim);
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190 |
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191 | // Gini index = rrn/rrd+rln/rld
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192 | rrn=pno;
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193 | rrd=pdo;
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194 | rln=0;
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195 | rld=0;
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196 |
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197 | TArrayF wl(2); // left node
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198 | wr = tclasspop;
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199 |
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200 | Double_t critvar=-1.0e20;
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201 |
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202 | for(Int_t nsp=ndstart;nsp<=ndend-1;nsp++)
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203 | {
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204 | nc=datasort[mvar*numdata+nsp];
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205 |
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206 | u=winbag[nc];
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207 | k=hadtrue[nc];
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208 |
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209 | rln=rln+u*(2*wl[k]+u);
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210 | rrn=rrn+u*(-2*wr[k]+u);
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211 | rld=rld+u;
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212 | rrd=rrd-u;
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213 |
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214 | wl[k]=wl[k]+u;
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215 | wr[k]=wr[k]-u;
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216 |
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217 | if (datarang[mvar*numdata+nc]<datarang[mvar*numdata+datasort[mvar*numdata+nsp+1]])
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218 | {
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219 | if (TMath::Min(rrd,rld)>1.0e-5)
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220 | {
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221 | crit=(rln/rld)+(rrn/rrd);
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222 | if (crit>critvar)
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223 | {
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224 | nbestvar=nsp;
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225 | critvar=crit;
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226 | }
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227 | }
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228 | }
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229 | }
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230 |
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231 | if (critvar>critmax) {
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232 | msplit=mvar;
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233 | nbest=nbestvar;
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234 | critmax=critvar;
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235 | }
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236 | }
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237 |
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238 | decsplit=critmax-crit0;
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239 | if (critmax<-1.0e10) jstat=1;
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240 |
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241 | return jstat;
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242 | }
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243 |
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244 | void MRanTree::MoveData(TArrayI &datasort,Int_t mdim,Int_t numdata,Int_t ndstart,
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245 | Int_t ndend,TArrayI &idmove,TArrayI &ncase,Int_t msplit,
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246 | Int_t nbest,Int_t &ndendl)
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247 | {
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248 | // This is the heart of the BuildTree construction. Based on the best split
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249 | // the data in the part of datasort corresponding to the current node is moved to the
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250 | // left if it belongs to the left child and right if it belongs to the right child-node.
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251 |
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252 | Int_t nc,k,ih;
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253 | TArrayI tdatasort(numdata);
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254 |
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255 | // compute idmove = indicator of case nos. going left
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256 |
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257 | for (Int_t nsp=ndstart;nsp<=nbest;nsp++)
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258 | {
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259 | nc=datasort[msplit*numdata+nsp];
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260 | idmove[nc]=1;
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261 | }
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262 | for (Int_t nsp=nbest+1;nsp<=ndend;nsp++)
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263 | {
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264 | nc=datasort[msplit*numdata+nsp];
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265 | idmove[nc]=0;
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266 | }
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267 | ndendl=nbest;
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268 |
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269 | // shift case. nos. right and left for numerical variables.
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270 |
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271 | for(Int_t msh=0;msh<mdim;msh++)
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272 | {
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273 | k=ndstart-1;
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274 | for (Int_t n=ndstart;n<=ndend;n++)
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275 | {
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276 | ih=datasort[msh*numdata+n];
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277 | if (idmove[ih]==1) {
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278 | k++;
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279 | tdatasort[k]=datasort[msh*numdata+n];
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280 | }
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281 | }
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282 |
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283 | for (Int_t n=ndstart;n<=ndend;n++)
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284 | {
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285 | ih=datasort[msh*numdata+n];
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286 | if (idmove[ih]==0){
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287 | k++;
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288 | tdatasort[k]=datasort[msh*numdata+n];
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289 | }
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290 | }
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291 | for(Int_t k=ndstart;k<=ndend;k++)
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292 | datasort[msh*numdata+k]=tdatasort[k];
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293 | }
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294 |
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295 | // compute case nos. for right and left nodes.
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296 |
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297 | for(Int_t n=ndstart;n<=ndend;n++)
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298 | ncase[n]=datasort[msplit*numdata+n];
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299 | }
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300 |
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301 | void MRanTree::BuildTree(TArrayI &datasort,TArrayI &datarang,TArrayI &hadtrue,Int_t mdim,
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302 | Int_t numdata,TArrayI &bestsplit,TArrayI &bestsplitnext,
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303 | TArrayI &nodepop,TArrayI &nodestart,TArrayF &tclasspop,
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304 | Int_t nrnodes,TArrayI &idmove,TArrayI &ncase,TArrayI &parent,
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305 | TArrayI &jinbag,TArrayI &iv,TArrayF &winbag,Int_t ninbag)
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306 | {
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307 | // Buildtree consists of repeated calls to two void functions, FindBestSplit and MoveData.
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308 | // Findbestsplit does just that--it finds the best split of the current node.
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309 | // MoveData moves the data in the split node right and left so that the data
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310 | // corresponding to each child node is contiguous.
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311 | //
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312 | // buildtree bookkeeping:
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313 | // ncur is the total number of nodes to date. nodestatus(k)=1 if the kth node has been split.
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314 | // nodestatus(k)=2 if the node exists but has not yet been split, and =-1 if the node is
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315 | // terminal. A node is terminal if its size is below a threshold value, or if it is all
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316 | // one class, or if all the data-values are equal. If the current node k is split, then its
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317 | // children are numbered ncur+1 (left), and ncur+2(right), ncur increases to ncur+2 and
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318 | // the next node to be split is numbered k+1. When no more nodes can be split, buildtree
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319 | // returns.
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320 |
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321 | Int_t msplit, nbest, ndendl;
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322 | Float_t decsplit=0;
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323 | TArrayF classpop(2*nrnodes);
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324 | TArrayI nodestatus(nrnodes);
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325 |
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326 | nodestart.Reset();
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327 | nodepop.Reset();
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328 |
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329 | for (Int_t j=0;j<2;j++)
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330 | classpop[j*nrnodes+0]=tclasspop[j];
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331 |
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332 | Int_t ncur=0;
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333 | nodestart[0]=0;
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334 | nodepop[0]=ninbag;
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335 | nodestatus[0]=2;
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336 |
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337 | // start main loop
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338 | for (Int_t kbuild=0;kbuild<nrnodes;kbuild++)
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339 | {
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340 | if (kbuild>ncur) break;
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341 | if (nodestatus[kbuild]!=2) continue;
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342 |
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343 | // initialize for next call to FindBestSplit
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344 |
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345 | const Int_t ndstart=nodestart[kbuild];
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346 | const Int_t ndend=ndstart+nodepop[kbuild]-1;
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347 | for (Int_t j=0;j<2;j++)
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348 | tclasspop[j]=classpop[j*nrnodes+kbuild];
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349 |
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350 | const Int_t jstat=FindBestSplit(datasort,datarang,hadtrue,mdim,numdata,
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351 | ndstart,ndend,tclasspop,msplit,decsplit,
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352 | nbest,ncase,jinbag,iv,winbag,kbuild);
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353 |
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354 | if(jstat==1) {
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355 | nodestatus[kbuild]=-1;
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356 | continue;
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357 | }else{
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358 | fBestVar[kbuild]=msplit;
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359 | fGiniDec[msplit]+=decsplit;
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360 |
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361 | bestsplit[kbuild]=datasort[msplit*numdata+nbest];
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362 | bestsplitnext[kbuild]=datasort[msplit*numdata+nbest+1];
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363 | }
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364 |
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365 | MoveData(datasort,mdim,numdata,ndstart,ndend,idmove,ncase,
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366 | msplit,nbest,ndendl);
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367 |
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368 | // leftnode no.= ncur+1, rightnode no. = ncur+2.
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369 |
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370 | nodepop[ncur+1]=ndendl-ndstart+1;
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371 | nodepop[ncur+2]=ndend-ndendl;
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372 | nodestart[ncur+1]=ndstart;
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373 | nodestart[ncur+2]=ndendl+1;
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374 |
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375 | // find class populations in both nodes
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376 |
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377 | for (Int_t n=ndstart;n<=ndendl;n++)
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378 | {
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379 | const Int_t nc=ncase[n];
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380 | const Int_t j=hadtrue[nc];
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381 | classpop[j*nrnodes+ncur+1]+=winbag[nc];
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382 | }
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383 |
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384 | for (Int_t n=ndendl+1;n<=ndend;n++)
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385 | {
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386 | const Int_t nc=ncase[n];
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387 | const Int_t j=hadtrue[nc];
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388 | classpop[j*nrnodes+ncur+2]+=winbag[nc];
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389 | }
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390 |
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391 | // check on nodestatus
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392 |
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393 | nodestatus[ncur+1]=2;
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394 | nodestatus[ncur+2]=2;
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395 | if (nodepop[ncur+1]<=fNdSize) nodestatus[ncur+1]=-1;
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396 | if (nodepop[ncur+2]<=fNdSize) nodestatus[ncur+2]=-1;
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397 |
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398 | Double_t popt1=0;
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399 | Double_t popt2=0;
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400 | for (Int_t j=0;j<2;j++)
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401 | {
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402 | popt1+=classpop[j*nrnodes+ncur+1];
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403 | popt2+=classpop[j*nrnodes+ncur+2];
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404 | }
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405 |
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406 | for (Int_t j=0;j<2;j++)
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407 | {
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408 | if (classpop[j*nrnodes+ncur+1]==popt1) nodestatus[ncur+1]=-1;
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409 | if (classpop[j*nrnodes+ncur+2]==popt2) nodestatus[ncur+2]=-1;
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410 | }
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411 |
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412 | fTreeMap1[kbuild]=ncur+1;
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413 | fTreeMap2[kbuild]=ncur+2;
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414 | parent[ncur+1]=kbuild;
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415 | parent[ncur+2]=kbuild;
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416 | nodestatus[kbuild]=1;
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417 | ncur+=2;
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418 | if (ncur>=nrnodes) break;
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419 | }
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420 |
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421 | // determine number of nodes
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422 | fNumNodes=nrnodes;
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423 | for (Int_t k=nrnodes-1;k>=0;k--)
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424 | {
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425 | if (nodestatus[k]==0) fNumNodes-=1;
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426 | if (nodestatus[k]==2) nodestatus[k]=-1;
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427 | }
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428 |
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429 | fNumEndNodes=0;
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430 | for (Int_t kn=0;kn<fNumNodes;kn++)
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431 | if(nodestatus[kn]==-1)
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432 | {
|
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433 | fNumEndNodes++;
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434 | Double_t pp=0;
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435 | for (Int_t j=0;j<2;j++)
|
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436 | {
|
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437 | if(classpop[j*nrnodes+kn]>pp)
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438 | {
|
---|
439 | // class + status of node kn coded into fBestVar[kn]
|
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440 | fBestVar[kn]=j-2;
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441 | pp=classpop[j*nrnodes+kn];
|
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442 | }
|
---|
443 | }
|
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444 | fBestSplit[kn] =classpop[1*nrnodes+kn];
|
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445 | fBestSplit[kn]/=(classpop[0*nrnodes+kn]+classpop[1*nrnodes+kn]);
|
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446 | }
|
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447 | }
|
---|
448 |
|
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449 | void MRanTree::SetRules(MDataArray *rules)
|
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450 | {
|
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451 | fData=rules;
|
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452 | }
|
---|
453 |
|
---|
454 | Double_t MRanTree::TreeHad(const TVector &event)
|
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455 | {
|
---|
456 | Int_t kt=0;
|
---|
457 | // to optimize on storage space node status and node class
|
---|
458 | // are coded into fBestVar:
|
---|
459 | // status of node kt = TMath::Sign(1,fBestVar[kt])
|
---|
460 | // class of node kt = fBestVar[kt]+2 (class defined by larger
|
---|
461 | // node population, actually not used)
|
---|
462 | // hadronness assigned to node kt = fBestSplit[kt]
|
---|
463 |
|
---|
464 | for (Int_t k=0;k<fNumNodes;k++)
|
---|
465 | {
|
---|
466 | if (fBestVar[kt]<0)
|
---|
467 | break;
|
---|
468 |
|
---|
469 | const Int_t m=fBestVar[kt];
|
---|
470 | kt = event(m)<=fBestSplit[kt] ? fTreeMap1[kt] : fTreeMap2[kt];
|
---|
471 | }
|
---|
472 |
|
---|
473 | return fBestSplit[kt];
|
---|
474 | }
|
---|
475 |
|
---|
476 | Double_t MRanTree::TreeHad(const TMatrixRow &event)
|
---|
477 | {
|
---|
478 | Int_t kt=0;
|
---|
479 | // to optimize on storage space node status and node class
|
---|
480 | // are coded into fBestVar:
|
---|
481 | // status of node kt = TMath::Sign(1,fBestVar[kt])
|
---|
482 | // class of node kt = fBestVar[kt]+2 (class defined by larger
|
---|
483 | // node population, actually not used)
|
---|
484 | // hadronness assigned to node kt = fBestSplit[kt]
|
---|
485 |
|
---|
486 | for (Int_t k=0;k<fNumNodes;k++)
|
---|
487 | {
|
---|
488 | if (fBestVar[kt]<0)
|
---|
489 | break;
|
---|
490 |
|
---|
491 | const Int_t m=fBestVar[kt];
|
---|
492 | kt = event(m)<=fBestSplit[kt] ? fTreeMap1[kt] : fTreeMap2[kt];
|
---|
493 | }
|
---|
494 |
|
---|
495 | return fBestSplit[kt];
|
---|
496 | }
|
---|
497 |
|
---|
498 | Double_t MRanTree::TreeHad(const TMatrix &m, Int_t ievt)
|
---|
499 | {
|
---|
500 | return TreeHad(TMatrixRow(m, ievt));
|
---|
501 | }
|
---|
502 |
|
---|
503 | Double_t MRanTree::TreeHad()
|
---|
504 | {
|
---|
505 | TVector event;
|
---|
506 | *fData >> event;
|
---|
507 |
|
---|
508 | return TreeHad(event);
|
---|
509 | }
|
---|
510 |
|
---|
511 | Bool_t MRanTree::AsciiWrite(ostream &out) const
|
---|
512 | {
|
---|
513 | TString str;
|
---|
514 | Int_t k;
|
---|
515 |
|
---|
516 | out.width(5);out<<fNumNodes<<endl;
|
---|
517 |
|
---|
518 | for (k=0;k<fNumNodes;k++)
|
---|
519 | {
|
---|
520 | str=Form("%f",GetBestSplit(k));
|
---|
521 |
|
---|
522 | out.width(5); out << k;
|
---|
523 | out.width(5); out << GetNodeStatus(k);
|
---|
524 | out.width(5); out << GetTreeMap1(k);
|
---|
525 | out.width(5); out << GetTreeMap2(k);
|
---|
526 | out.width(5); out << GetBestVar(k);
|
---|
527 | out.width(15); out << str<<endl;
|
---|
528 | out.width(5); out << GetNodeClass(k);
|
---|
529 | }
|
---|
530 | out<<endl;
|
---|
531 |
|
---|
532 | return k==fNumNodes;
|
---|
533 | }
|
---|