STAT/TKDInterpolatorBase.cxx

   1 #include "TKDInterpolatorBase.h"
   2 #include "TKDNodeInfo.h"
   3 #include "TKDTree.h"
   4
   5 #include "TClonesArray.h"
   6 #include "TLinearFitter.h"
   7 #include "TTree.h"
   8 #include "TH2.h"
   9 #include "TObjArray.h"
  10 #include "TObjString.h"
  11 #include "TBox.h"
  12 #include "TGraph.h"
  13 #include "TMarker.h"
  14 #include "TMath.h"
  15 #include "TVectorD.h"
  16 #include "TMatrixD.h"
  17
  18 ClassImp(TKDInterpolatorBase)
  19
  20 /////////////////////////////////////////////////////////////////////
  21 // Memory setup of protected data members
  22 // fRefPoints : evaluation point of PDF for each terminal node of underlying KD Tree.
  23 // | 1st terminal node (fNDim point coordinates) | 2nd terminal node (fNDim point coordinates) | ...
  24 //
  25 // fRefValues : evaluation value/error of PDF for each terminal node of underlying KD Tree.
  26 // | 1st terminal node (value) | 2nd terminal node (value) | ... | 1st terminal node (error) | 2nd terminal node (error) | ...
  27 //
  28 // status = |0|0|0|0|0|1(tri-cubic weights)|1(STORE)|1 INT(0 COG )|
  29 /////////////////////////////////////////////////////////////////////
  30
  31
  32 //_________________________________________________________________
  33 TKDInterpolatorBase::TKDInterpolatorBase(Int_t dim) :
  34         fNSize(dim)
  35         ,fNTNodes(0)
  36         ,fTNodes(0x0)
  37         ,fStatus(4)
  38         ,fLambda(1 + dim + (dim*(dim+1)>>1))
  39         ,fDepth(-1)
  40         ,fAlpha(.5)
  41         ,fRefPoints(0x0)
  42         ,fBuffer(0x0)
  43         ,fKDhelper(0x0)
  44         ,fFitter(0x0)
  45 {
  46 // Default constructor. To be used with care since in this case building
  47 // of data structure is completly left to the user responsability.
  48 }
  49
  50 //_________________________________________________________________
  51 void    TKDInterpolatorBase::Build(Int_t n)
  52 {
  53         // allocate memory for data
  54
  55         if(fTNodes) delete fTNodes;
  56         fNTNodes = n;
  57         fTNodes = new TClonesArray("TKDNodeInfo", fNTNodes);
  58         for(int in=0; in<fNTNodes; in++) new ((*fTNodes)[in]) TKDNodeInfo(fNSize);
  59 }
  60
  61 //_________________________________________________________________
  62 TKDInterpolatorBase::~TKDInterpolatorBase()
  63 {
  64         if(fFitter) delete fFitter;
  65         if(fKDhelper) delete fKDhelper;
  66         if(fBuffer) delete [] fBuffer;
  67
  68         if(fRefPoints){
  69                 for(int idim=0; idim<fNSize; idim++) delete [] fRefPoints[idim] ;
  70                 delete [] fRefPoints;
  71         }
  72         if(fTNodes) delete fTNodes;
  73 }
  74
  75
  76 //__________________________________________________________________
  77 Bool_t  TKDInterpolatorBase::GetCOGPoint(Int_t inode, Float_t *&coord, Float_t &val, Float_t &err) const
  78 {
  79         if(inode < 0 || inode > fNTNodes) return kFALSE;
  80
  81         TKDNodeInfo *node = (TKDNodeInfo*)(*fTNodes)[inode];
  82         coord = &(node->Data()[0]);
  83         val = node->Val()[0];
  84         err = node->Val()[1];
  85         return kTRUE;
  86 }
  87
  88 //_________________________________________________________________
  89 TKDNodeInfo* TKDInterpolatorBase::GetNodeInfo(Int_t inode) const
  90 {
  91         if(!fTNodes || inode >= fNTNodes) return 0x0;
  92         return (TKDNodeInfo*)(*fTNodes)[inode];
  93 }
  94
  95
  96 //__________________________________________________________________
  97 void TKDInterpolatorBase::GetStatus()
  98 {
  99 // Prints the status of the interpolator
 100
 101         printf("Interpolator Status :\n");
 102         printf("  Dim    : %d [%d]\n", fNSize, fLambda);
 103         printf("  Method : %s\n", fStatus&1 ? "INT" : "COG");
 104         printf("  Store  : %s\n", fStatus&2 ? "YES" : "NO");
 105         printf("  Weights: %s\n", fStatus&4 ? "YES" : "NO");
 106
 107         printf("fNTNodes %d\n", fNTNodes);        //Number of evaluation data points
 108         for(int i=0; i<fNTNodes; i++){
 109                 TKDNodeInfo *node = (TKDNodeInfo*)(*fTNodes)[i];
 110                 printf("%d ", i); node->Print();
 111         }
 112 }
 113
 114 //_________________________________________________________________
 115 Double_t TKDInterpolatorBase::Eval(const Double_t *point, Double_t &result, Double_t &error, Bool_t force)
 116 {
 117 // Evaluate PDF for "point". The result is returned in "result" and error in "error". The function returns the chi2 of the fit.
 118 //
 119 // Observations:
 120 //
 121 // 1. The default method used for interpolation is kCOG.
 122 // 2. The initial number of neighbors used for the estimation is set to Int(alpha*fLambda) (alpha = 1.5)
 123
 124         Float_t pointF[50]; // local Float_t conversion for "point"
 125         for(int idim=0; idim<fNSize; idim++) pointF[idim] = (Float_t)point[idim];
 126         Int_t nodeIndex = GetNodeIndex(pointF);
 127         if(nodeIndex<0){
 128                 result = 0.;
 129                 error = 1.E10;
 130                 return 0.;
 131         }
 132         TKDNodeInfo *node = (TKDNodeInfo*)(*fTNodes)[nodeIndex];
 133         if((fStatus&1) && node->Cov() && !force) return node->CookPDF(point, result, error);
 134
 135         // Allocate memory
 136         if(!fBuffer) fBuffer = new Double_t[2*fLambda];
 137         if(!fKDhelper){
 138                 fRefPoints = new Float_t*[fNSize];
 139                 for(int id=0; id<fNSize; id++){
 140                         fRefPoints[id] = new Float_t[fNTNodes];
 141                         for(int in=0; in<fNTNodes; in++) fRefPoints[id][in] = ((TKDNodeInfo*)(*fTNodes)[in])->Data()[id];
 142                 }
 143                 fKDhelper = new TKDTreeIF(fNTNodes, fNSize, 30, fRefPoints);
 144                 fKDhelper->MakeBoundaries();
 145         }
 146         if(!fFitter) fFitter = new TLinearFitter(fLambda, Form("hyp%d", fLambda-1));
 147
 148         // generate parabolic for nD
 149         //Float_t alpha = Float_t(2*lambda + 1) / fNTNodes; // the bandwidth or smoothing parameter
 150         //Int_t npoints = Int_t(alpha * fNTNodes);
 151         //printf("Params : %d NPoints %d\n", lambda, npoints);
 152         // prepare workers
 153
 154         Int_t *index,  // indexes of NN
 155               ipar,    // local looping variable
 156                                 npoints = Int_t((1.+fAlpha)*fLambda); // number of data points used for interpolation
 157         Float_t *dist, // distances of NN
 158                                         d,     // NN normalized distance
 159                                         w0,    // work
 160                                         w;     // tri-cubic weight function
 161
 162         do{
 163                 // find nearest neighbors
 164                 for(int idim=0; idim<fNSize; idim++) pointF[idim] = (Float_t)point[idim];
 165                 if(!fKDhelper->FindNearestNeighbors(pointF, npoints+1, index, dist)){
 166                         Error("Eval()", Form("Failed retriving %d neighbours for point:", npoints));
 167                         for(int idim=0; idim<fNSize; idim++) printf("%f ", point[idim]);
 168                         printf("\n");
 169                         return -1;
 170                 }
 171                 // add points to fitter
 172                 fFitter->ClearPoints();
 173                 TKDNodeInfo *tnode = 0x0;
 174                 for(int in=0; in<npoints; in++){
 175                         tnode = (TKDNodeInfo*)(*fTNodes)[index[in]];
 176                         //tnode->Print();
 177                         if(fStatus&1){ // INT
 178                                 Float_t *bounds = &(tnode->Data()[fNSize]);
 179                                 ipar = 0;
 180                                 for(int idim=0; idim<fNSize; idim++){
 181                                         fBuffer[ipar++] = .5*(bounds[2*idim] + bounds[2*idim+1]);
 182                                         fBuffer[ipar++] = (bounds[2*idim]*bounds[2*idim] + bounds[2*idim] * bounds[2*idim+1] + bounds[2*idim+1] * bounds[2*idim+1])/3.;
 183                                         for(int jdim=idim+1; jdim<fNSize; jdim++) fBuffer[ipar++] = (bounds[2*idim] + bounds[2*idim+1]) * (bounds[2*jdim] + bounds[2*jdim+1]) * .25;
 184                                 }
 185                         } else { // COG
 186                                 Float_t *p = &(tnode->Data()[0]);
 187                                 ipar = 0;
 188                                 for(int idim=0; idim<fNSize; idim++){
 189                                         fBuffer[ipar++] = p[idim];
 190                                         for(int jdim=idim; jdim<fNSize; jdim++) fBuffer[ipar++] = p[idim]*p[jdim];
 191                                 }
 192                         }
 193
 194                         // calculate tri-cubic weighting function
 195                         if(fStatus&4){
 196                                 d = dist[in]/ dist[npoints];
 197                                 w0 = (1. - d*d*d); w = w0*w0*w0;
 198                         } else w = 1.;
 199
 200 //                      printf("x[");
 201 //                      for(int idim=0; idim<fLambda-1; idim++) printf("%f ", fBuffer[idim]);
 202 //                      printf("]  v[%f +- %f] (%f, %f)\n", tnode->Val()[0], tnode->Val()[1]/w, tnode->Val()[1], w);
 203                         fFitter->AddPoint(fBuffer, tnode->Val()[0], tnode->Val()[1]/w);
 204                 }
 205                 npoints += 4;
 206         } while(fFitter->Eval());
 207
 208         // retrive fitter results
 209         TMatrixD cov(fLambda, fLambda);
 210         TVectorD par(fLambda);
 211         fFitter->GetCovarianceMatrix(cov);
 212         fFitter->GetParameters(par);
 213         Double_t chi2 = fFitter->GetChisquare()/(npoints - 4 - fLambda);
 214
 215         // store results
 216         if(fStatus&2 && fStatus&1) node->Store(par, cov);
 217
 218         // Build df/dpi|x values
 219         Double_t *fdfdp = &fBuffer[fLambda];
 220         ipar = 0;
 221         fdfdp[ipar++] = 1.;
 222         for(int idim=0; idim<fNSize; idim++){
 223                 fdfdp[ipar++] = point[idim];
 224                 for(int jdim=idim; jdim<fNSize; jdim++) fdfdp[ipar++] = point[idim]*point[jdim];
 225         }
 226
 227         // calculate estimation
 228         result =0.; error = 0.;
 229         for(int i=0; i<fLambda; i++){
 230                 result += fdfdp[i]*par(i);
 231                 for(int j=0; j<fLambda; j++) error += fdfdp[i]*fdfdp[j]*cov(i,j);
 232         }
 233         error = TMath::Sqrt(error);
 234
 235         return chi2;
 236 }
 237
 238 //_________________________________________________________________
 239 void TKDInterpolatorBase::DrawBins(UInt_t ax1, UInt_t ax2, Float_t ax1min, Float_t ax1max, Float_t ax2min, Float_t ax2max)
 240 {
 241 // Draw nodes structure projected on plane "ax1:ax2". The parameter
 242 // "depth" specifies the bucket size per node. If depth == -1 draw only
 243 // terminal nodes and evaluation points (default -1 i.e. bucket size per node equal bucket size specified by the user)
 244 //
 245 // Observation:
 246 // This function creates the nodes (TBox) array for the specified depth
 247 // but don't delete it. Abusing this function may cause memory leaks !
 248
 249
 250
 251         TH2 *h2 = new TH2S("hNodes", "", 100, ax1min, ax1max, 100, ax2min, ax2max);
 252         h2->GetXaxis()->SetTitle(Form("x_{%d}", ax1));
 253         h2->GetYaxis()->SetTitle(Form("x_{%d}", ax2));
 254         h2->Draw();
 255
 256         const Float_t kBorder = 0.;//1.E-4;
 257         TBox *boxArray = new TBox[fNTNodes], *box;
 258         Float_t *bounds = 0x0;
 259         for(int inode = 0; inode < fNTNodes; inode++){
 260                 box = &boxArray[inode];
 261                 box->SetFillStyle(3002);
 262                 box->SetFillColor(50+inode/*Int_t(gRandom->Uniform()*50.)*/);
 263
 264                 bounds = &(((TKDNodeInfo*)(*fTNodes)[inode])->Data()[fNSize]);
 265                 box->DrawBox(bounds[2*ax1]+kBorder, bounds[2*ax2]+kBorder, bounds[2*ax1+1]-kBorder, bounds[2*ax2+1]-kBorder);
 266         }
 267
 268         // Draw reference points
 269         TGraph *ref = new TGraph(fNTNodes);
 270         ref->SetMarkerStyle(3);
 271         ref->SetMarkerSize(.7);
 272         ref->SetMarkerColor(2);
 273         for(int inode = 0; inode < fNTNodes; inode++){
 274                 TKDNodeInfo *node = (TKDNodeInfo*)(*fTNodes)[inode];
 275                 ref->SetPoint(inode, node->Data()[ax1], node->Data()[ax2]);
 276         }
 277         ref->Draw("p");
 278         return;
 279 }
 280
 281 //__________________________________________________________________
 282 void TKDInterpolatorBase::SetInterpolationMethod(Bool_t on)
 283 {
 284 // Set interpolation bit to "on".
 285
 286         if(on) fStatus += fStatus&1 ? 0 : 1;
 287         else fStatus += fStatus&1 ? -1 : 0;
 288 }
 289
 290
 291 //_________________________________________________________________
 292 void TKDInterpolatorBase::SetStore(Bool_t on)
 293 {
 294 // Set store bit to "on"
 295
 296         if(on) fStatus += fStatus&2 ? 0 : 2;
 297         else fStatus += fStatus&2 ? -2 : 0;
 298 }
 299
 300 //_________________________________________________________________
 301 void TKDInterpolatorBase::SetWeights(Bool_t on)
 302 {
 303 // Set weights bit to "on"
 304
 305         if(on) fStatus += fStatus&4 ? 0 : 4;
 306         else fStatus += fStatus&4 ? -4 : 0;
 307 }