1 #include "TKDInterpolatorBase.h"
2 #include "TKDNodeInfo.h"
6 #include "TClonesArray.h"
7 #include "TLinearFitter.h"
10 #include "TObjArray.h"
11 #include "TObjString.h"
16 ClassImp(TKDInterpolatorBase)
18 /////////////////////////////////////////////////////////////////////
19 // Memory setup of protected data members
20 // fRefPoints : evaluation point of PDF for each terminal node of underlying KD Tree.
21 // | 1st terminal node (fNDim point coordinates) | 2nd terminal node (fNDim point coordinates) | ...
23 // fRefValues : evaluation value/error of PDF for each terminal node of underlying KD Tree.
24 // | 1st terminal node (value) | 2nd terminal node (value) | ... | 1st terminal node (error) | 2nd terminal node (error) | ...
26 // status = |0|0|0|0|0|1(tri-cubic weights)|1(STORE)|1 INT(0 COG )|
27 /////////////////////////////////////////////////////////////////////
30 //_________________________________________________________________
31 TKDInterpolatorBase::TKDInterpolatorBase(Int_t dim) :
36 ,fLambda(1 + dim + (dim*(dim+1)>>1))
44 // Default constructor. To be used with care since in this case building
45 // of data structure is completly left to the user responsability.
49 //_________________________________________________________________
50 Bool_t TKDInterpolatorBase::Build(Int_t n)
52 // allocate memory for data
53 if(Int_t((1.+fAlpha)*fLambda) > n){ // check granularity
54 Error("TKDInterpolatorBase::Build()", Form("Minimum number of points [%d] needed for interpolation exceeds number of evaluation points [%d]. Please increase granularity.", Int_t((1.+fAlpha)*fLambda), n));
59 Warning("TKDInterpolatorBase::Build()", "Data already allocated.");
62 fNodes = new TClonesArray("TKDNodeInfo", n);
66 for(int in=0; in<n; in++) new ((*fNodes)[in]) TKDNodeInfo(fNSize);
71 //_________________________________________________________________
72 Bool_t TKDInterpolatorBase::Bootstrap()
75 Error("TKDInterpolatorBase::Bootstrap()", "Nodes missing. Nothing to bootstrap from.");
78 Int_t in = GetNTNodes(); TKDNodeInfo *n(NULL);
80 if(!(n=(TKDNodeInfo*)(*fNodes)[in])){
81 Error("TKDInterpolatorBase::Bootstrap()", Form("Node @ %d missing.", in));
85 if(!fNSize) fNSize = n->GetDimension();
86 //n->SetNode(fNSize, ...);
88 fLambda = n->GetNpar();
92 //_________________________________________________________________
93 TKDInterpolatorBase::~TKDInterpolatorBase()
95 if(fFitter) delete fFitter;
96 if(fKDhelper) delete fKDhelper;
97 if(fBuffer) delete [] fBuffer;
100 for(int idim=0; idim<fNSize; idim++) delete [] fRefPoints[idim] ;
101 delete [] fRefPoints;
107 if(fNodesDraw) delete [] fNodesDraw;
110 if((h2 = (TH2S*)gROOT->FindObject("hKDnodes"))) delete h2;
114 //__________________________________________________________________
115 Bool_t TKDInterpolatorBase::GetCOGPoint(Int_t inode, Float_t *&coord, Float_t &val, Float_t &err) const
117 if(inode < 0 || inode > GetNTNodes()) return kFALSE;
119 TKDNodeInfo *node = (TKDNodeInfo*)(*fNodes)[inode];
120 coord = &(node->Data()[0]);
121 val = node->Val()[0];
122 err = node->Val()[1];
126 //_________________________________________________________________
127 TKDNodeInfo* TKDInterpolatorBase::GetNodeInfo(Int_t inode) const
129 if(!fNodes || inode >= GetNTNodes()) return NULL;
130 return (TKDNodeInfo*)(*fNodes)[inode];
133 //_________________________________________________________________
134 Int_t TKDInterpolatorBase::GetNTNodes() const
136 return fNodes?fNodes->GetEntriesFast():0;
139 //_________________________________________________________________
140 Bool_t TKDInterpolatorBase::GetRange(Int_t ax, Float_t &min, Float_t &max) const
142 if(!fNodes) return kFALSE;
143 Int_t ndim = ((TKDNodeInfo*)(*fNodes)[0])->GetDimension();
144 if(ax<0 || ax>=ndim){
148 min=1.e10; max=-1.e10;
149 Float_t axmin, axmax;
150 for(Int_t in=GetNTNodes(); in--; ){
151 TKDNodeInfo *node = (TKDNodeInfo*)((*fNodes)[in]);
152 node->GetBoundary(ax, axmin, axmax);
153 if(axmin<min) min = axmin;
154 if(axmax>max) max = axmax;
160 //__________________________________________________________________
161 void TKDInterpolatorBase::GetStatus(Option_t *opt)
163 // Prints the status of the interpolator
165 printf("Interpolator Status[%d] :\n", fStatus);
166 printf(" Dim : %d [%d]\n", fNSize, fLambda);
167 printf(" Method : %s\n", UseCOG() ? "COG" : "INT");
168 printf(" Store : %s\n", HasStore() ? "YES" : "NO");
169 printf(" Weights: %s\n", UseWeights() ? "YES" : "NO");
171 if(strcmp(opt, "all") != 0 ) return;
172 printf("GetNTNodes() %d\n", GetNTNodes()); //Number of evaluation data points
173 for(int i=0; i<GetNTNodes(); i++){
174 TKDNodeInfo *node = (TKDNodeInfo*)(*fNodes)[i];
175 printf("%d ", i); node->Print();
179 //_________________________________________________________________
180 Double_t TKDInterpolatorBase::Eval(const Double_t *point, Double_t &result, Double_t &error, Bool_t force)
182 // Evaluate PDF for "point". The result is returned in "result" and error in "error". The function returns the chi2 of the fit.
186 // 1. The default method used for interpolation is kCOG.
187 // 2. The initial number of neighbors used for the estimation is set to Int(alpha*fLambda) (alpha = 1.5)
189 Float_t pointF[50]; // local Float_t conversion for "point"
190 for(int idim=0; idim<fNSize; idim++) pointF[idim] = (Float_t)point[idim];
191 Int_t nodeIndex = GetNodeIndex(pointF);
193 Error("TKDInterpolatorBase::Eval()", "Can not retrive node for data point.");
198 TKDNodeInfo *node = (TKDNodeInfo*)(*fNodes)[nodeIndex];
199 if(node->Par() && !force){
200 //printf("Node @ %d\n", nodeIndex); node->Print("a");
201 return node->CookPDF(point, result, error);
205 if(!fBuffer) fBuffer = new Double_t[2*fLambda];
207 fRefPoints = new Float_t*[fNSize];
208 for(int id=0; id<fNSize; id++){
209 fRefPoints[id] = new Float_t[GetNTNodes()];
210 for(int in=0; in<GetNTNodes(); in++) fRefPoints[id][in] = ((TKDNodeInfo*)(*fNodes)[in])->Data()[id];
212 Info("TKDInterpolatorBase::Eval()", Form("Build TKDTree(%d, %d, %d)", GetNTNodes(), fNSize, kNhelper));
213 fKDhelper = new TKDTreeIF(GetNTNodes(), fNSize, kNhelper, fRefPoints);
215 fKDhelper->MakeBoundariesExact();
217 if(!fFitter) fFitter = new TLinearFitter(fLambda, Form("hyp%d", fLambda-1));
219 // generate parabolic for nD
220 //Float_t alpha = Float_t(2*lambda + 1) / GetNTNodes(); // the bandwidth or smoothing parameter
221 //Int_t npoints = Int_t(alpha * GetNTNodes());
222 //printf("Params : %d NPoints %d\n", lambda, npoints);
225 Int_t ipar, // local looping variable
226 npoints_new = Int_t((1.+fAlpha)*fLambda),
227 npoints(0); // number of data points used for interpolation
228 Int_t *index = new Int_t[2*npoints_new]; // indexes of NN
229 Float_t *dist = new Float_t[2*npoints_new], // distances of NN
230 d, // NN normalized distance
232 w; // tri-cubic weight function
234 Bool_t kDOWN = kFALSE;
237 Info("TKDInterpolatorBase::Eval()", Form("Interpolation failed. Trying to increase the number of interpolation points from %d to %d.", npoints, npoints_new));
239 if(npoints == npoints_new){
240 Error("TKDInterpolatorBase::Eval()", Form("Interpolation failed and number of interpolation points (%d) Can not be increased further.", npoints));
244 delete [] dist; delete [] index;
246 } else npoints = npoints_new;
247 if(npoints > GetNTNodes()){
248 Warning("TKDInterpolatorBase::Eval()", Form("The number of interpolation points requested (%d) exceeds number of PDF values (%d). Downscale.", npoints, GetNTNodes()));
249 npoints = GetNTNodes();
253 // find nearest neighbors
254 for(int idim=0; idim<fNSize; idim++) pointF[idim] = (Float_t)point[idim];
255 fKDhelper->FindNearestNeighbors(pointF, npoints+1, index, dist);
257 // add points to fitter
258 fFitter->ClearPoints();
259 TKDNodeInfo *tnode = NULL;
260 for(int in=0; in<npoints; in++){
261 tnode = (TKDNodeInfo*)(*fNodes)[index[in]];
264 Float_t *p = &(tnode->Data()[0]);
266 for(int idim=0; idim<fNSize; idim++){
267 fBuffer[ipar++] = p[idim];
268 for(int jdim=idim; jdim<fNSize; jdim++) fBuffer[ipar++] = p[idim]*p[jdim];
271 Float_t *bounds = &(tnode->Data()[fNSize]);
273 for(int idim=0; idim<fNSize; idim++){
274 fBuffer[ipar++] = .5*(bounds[2*idim] + bounds[2*idim+1]);
275 fBuffer[ipar++] = (bounds[2*idim]*bounds[2*idim] + bounds[2*idim] * bounds[2*idim+1] + bounds[2*idim+1] * bounds[2*idim+1])/3.;
276 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;
280 // calculate tri-cubic weighting function
282 d = dist[in]/dist[npoints];
283 w0 = (1. - d*d*d); w = w0*w0*w0;
284 if(w<1.e-30) continue;
287 // printf("%2d d[%f] w[%f] x[", index[in], d, w);
288 // for(int idim=0; idim<fLambda-1; idim++) printf("%f ", fBuffer[idim]);
289 // printf("]\n"); printf("v[%f +- %f] (%f, %f)\n", tnode->Val()[0], tnode->Val()[1]/w, tnode->Val()[1], w);
290 fFitter->AddPoint(fBuffer, tnode->Val()[0], tnode->Val()[1]/w);
292 npoints_new = npoints+ (kDOWN ? 0 : kdN);
293 } while(fFitter->Eval());
297 // retrive fitter results
298 TMatrixD cov(fLambda, fLambda);
299 TVectorD par(fLambda);
300 fFitter->GetCovarianceMatrix(cov);
301 fFitter->GetParameters(par);
302 Double_t chi2 = fFitter->GetChisquare()/(npoints - 4 - fLambda);
305 node->Store(&par, HasStore()?&cov:NULL);
307 // Build df/dpi|x values
308 Double_t *fdfdp = &fBuffer[fLambda];
311 for(int idim=0; idim<fNSize; idim++){
312 fdfdp[ipar++] = point[idim];
313 for(int jdim=idim; jdim<fNSize; jdim++) fdfdp[ipar++] = point[idim]*point[jdim];
316 // calculate estimation
317 result =0.; error = 0.;
318 for(int i=0; i<fLambda; i++){
319 result += fdfdp[i]*par(i);
320 for(int j=0; j<fLambda; j++) error += fdfdp[i]*fdfdp[j]*cov(i,j);
322 error = TMath::Sqrt(error);
326 //_________________________________________________________________
327 void TKDInterpolatorBase::DrawProjection(UInt_t ax1, UInt_t ax2)
329 // Draw nodes structure projected on plane "ax1:ax2". The parameter
330 // "depth" specifies the bucket size per node. If depth == -1 draw only
331 // terminal nodes and evaluation points (default -1 i.e. bucket size per node equal bucket size specified by the user)
334 Float_t ax1min, ax1max, ax2min, ax2max;
335 GetRange(ax1, ax1min, ax1max);
336 GetRange(ax2, ax2min, ax2max);
338 if(!(h2 = (TH2S*)gROOT->FindObject("hKDnodes"))){
339 h2 = new TH2S("hKDnodes", "", 100, ax1min, ax1max, 100, ax2min, ax2max);
341 h2->GetXaxis()->SetRangeUser(ax1min, ax1max);
342 h2->GetXaxis()->SetTitle(Form("x_{%d}", ax1));
343 h2->GetYaxis()->SetRangeUser(ax2min, ax2max);
344 h2->GetYaxis()->SetTitle(Form("x_{%d}", ax2));
348 if(!fNodesDraw) fNodesDraw = new TKDNodeInfo::TKDNodeDraw[GetNTNodes()];
349 TKDNodeInfo::TKDNodeDraw *box = NULL;
350 for(Int_t in=GetNTNodes(); in--; ){
351 box = &(fNodesDraw[in]);
352 box->SetNode((TKDNodeInfo*)((*fNodes)[in]), fNSize, ax1, ax2);
359 //_________________________________________________________________
360 void TKDInterpolatorBase::SetAlpha(Float_t a)
363 Warning("TKDInterpolatorBase::SetAlpha()", "The scale parameter has to be larger than 0.5");
368 if(Int_t((a+1.)*fLambda) > GetNTNodes()){
369 fAlpha = TMath::Max(0.5, Float_t(GetNTNodes())/fLambda-1.);
370 Warning("TKDInterpolatorBase::SetAlpha()", Form("Interpolation neighborhood exceeds number of evaluation points. Downscale alpha to %f", fAlpha));
371 printf("n[%d] nodes[%d]\n", Int_t((fAlpha+1.)*fLambda), GetNTNodes());