Line data Source code
1 : #include "TKDInterpolatorBase.h"
2 : #include "TKDNodeInfo.h"
3 : #include "TKDTree.h"
4 :
5 : #include "TROOT.h"
6 : #include "TClonesArray.h"
7 : #include "TLinearFitter.h"
8 : #include "TTree.h"
9 : #include "TH2.h"
10 : #include "TObjArray.h"
11 : #include "TObjString.h"
12 : #include "TMath.h"
13 : #include "TVectorD.h"
14 : #include "TMatrixD.h"
15 :
16 128 : ClassImp(TKDInterpolatorBase)
17 :
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) | ...
22 : //
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) | ...
25 : //
26 : // status = |0|0|0|0|0|1(tri-cubic weights)|1(STORE)|1 INT(0 COG )|
27 : /////////////////////////////////////////////////////////////////////
28 :
29 :
30 : //_________________________________________________________________
31 : TKDInterpolatorBase::TKDInterpolatorBase(Int_t dim) :
32 220 : fNSize(dim)
33 220 : ,fNodes(NULL)
34 220 : ,fNodesDraw(NULL)
35 220 : ,fStatus(0)
36 220 : ,fLambda(1 + dim + (dim*(dim+1)>>1))
37 220 : ,fDepth(-1)
38 220 : ,fAlpha(.5)
39 220 : ,fRefPoints(NULL)
40 220 : ,fBuffer(NULL)
41 220 : ,fKDhelper(NULL)
42 220 : ,fFitter(NULL)
43 440 : {
44 : // Default constructor. To be used with care since in this case building
45 : // of data structure is completly left to the user responsability.
46 220 : UseWeights();
47 220 : }
48 :
49 : //_________________________________________________________________
50 : Bool_t TKDInterpolatorBase::Build(Int_t n)
51 : {
52 : // allocate memory for data
53 0 : if(Int_t((1.+fAlpha)*fLambda) > n){ // check granularity
54 0 : Error("TKDInterpolatorBase::Build()", "Minimum number of points [%d] needed for interpolation exceeds number of evaluation points [%d]. Please increase granularity.", Int_t((1.+fAlpha)*fLambda), n);
55 0 : return kFALSE;
56 : }
57 :
58 0 : if(fNodes){
59 0 : Warning("TKDInterpolatorBase::Build()", "Data already allocated.");
60 0 : fNodes->Delete();
61 0 : } else {
62 0 : fNodes = new TClonesArray("TKDNodeInfo", n);
63 0 : fNodes->SetOwner();
64 : }
65 :
66 0 : for(int in=0; in<n; in++) new ((*fNodes)[in]) TKDNodeInfo(fNSize);
67 :
68 0 : return kTRUE;
69 0 : }
70 :
71 : //_________________________________________________________________
72 : Bool_t TKDInterpolatorBase::Bootstrap()
73 : {
74 0 : if(!fNodes){
75 0 : Error("TKDInterpolatorBase::Bootstrap()", "Nodes missing. Nothing to bootstrap from.");
76 0 : return kFALSE;
77 : }
78 0 : Int_t in = GetNTNodes(); TKDNodeInfo *n(NULL);
79 0 : while(in--){
80 0 : if(!(n=(TKDNodeInfo*)(*fNodes)[in])){
81 0 : Error("TKDInterpolatorBase::Bootstrap()", "Node @ %d missing.", in);
82 0 : return kFALSE;
83 : }
84 0 : n->Bootstrap();
85 0 : if(!fNSize) fNSize = n->GetDimension();
86 : //n->SetNode(fNSize, ...);
87 : }
88 0 : fLambda = n->GetNpar();
89 0 : return kTRUE;
90 0 : }
91 :
92 : //_________________________________________________________________
93 : TKDInterpolatorBase::~TKDInterpolatorBase()
94 0 : {
95 0 : if(fFitter) delete fFitter;
96 0 : if(fKDhelper) delete fKDhelper;
97 0 : if(fBuffer) delete [] fBuffer;
98 :
99 0 : if(fRefPoints){
100 0 : for(int idim=0; idim<fNSize; idim++) delete [] fRefPoints[idim] ;
101 0 : delete [] fRefPoints;
102 : }
103 0 : if(fNodes){
104 0 : fNodes->Delete();
105 0 : delete fNodes;
106 : }
107 0 : if(fNodesDraw) delete [] fNodesDraw;
108 :
109 : TH2 *h2=NULL;
110 0 : if((h2 = (TH2S*)gROOT->FindObject("hKDnodes"))) delete h2;
111 0 : }
112 :
113 :
114 : //__________________________________________________________________
115 : Bool_t TKDInterpolatorBase::GetCOGPoint(Int_t inode, Float_t *&coord, Float_t &val, Float_t &err) const
116 : {
117 0 : if(inode < 0 || inode > GetNTNodes()) return kFALSE;
118 :
119 0 : TKDNodeInfo *node = (TKDNodeInfo*)(*fNodes)[inode];
120 0 : coord = &(node->Data()[0]);
121 0 : val = node->Val()[0];
122 0 : err = node->Val()[1];
123 : return kTRUE;
124 0 : }
125 :
126 : //_________________________________________________________________
127 : TKDNodeInfo* TKDInterpolatorBase::GetNodeInfo(Int_t inode) const
128 : {
129 0 : if(!fNodes || inode >= GetNTNodes()) return NULL;
130 0 : return (TKDNodeInfo*)(*fNodes)[inode];
131 0 : }
132 :
133 : //_________________________________________________________________
134 : Int_t TKDInterpolatorBase::GetNTNodes() const
135 : {
136 0 : return fNodes?fNodes->GetEntriesFast():0;
137 : }
138 :
139 : //_________________________________________________________________
140 : Bool_t TKDInterpolatorBase::GetRange(Int_t ax, Float_t &min, Float_t &max) const
141 : {
142 0 : if(!fNodes) return kFALSE;
143 0 : Int_t ndim = ((TKDNodeInfo*)(*fNodes)[0])->GetDimension();
144 0 : if(ax<0 || ax>=ndim){
145 0 : min=0.; max=0.;
146 0 : return kFALSE;
147 : }
148 0 : min=1.e10; max=-1.e10;
149 0 : Float_t axmin, axmax;
150 0 : for(Int_t in=GetNTNodes(); in--; ){
151 0 : TKDNodeInfo *node = (TKDNodeInfo*)((*fNodes)[in]);
152 0 : node->GetBoundary(ax, axmin, axmax);
153 0 : if(axmin<min) min = axmin;
154 0 : if(axmax>max) max = axmax;
155 : }
156 :
157 : return kTRUE;
158 0 : }
159 :
160 : //__________________________________________________________________
161 : void TKDInterpolatorBase::GetStatus(Option_t *opt)
162 : {
163 : // Prints the status of the interpolator
164 :
165 0 : printf("Interpolator Status[%d] :\n", fStatus);
166 0 : printf(" Dim : %d [%d]\n", fNSize, fLambda);
167 0 : printf(" Method : %s\n", UseCOG() ? "COG" : "INT");
168 0 : printf(" Store : %s\n", HasStore() ? "YES" : "NO");
169 0 : printf(" Weights: %s\n", UseWeights() ? "YES" : "NO");
170 :
171 0 : if(strcmp(opt, "all") != 0 ) return;
172 0 : printf("GetNTNodes() %d\n", GetNTNodes()); //Number of evaluation data points
173 0 : for(int i=0; i<GetNTNodes(); i++){
174 0 : TKDNodeInfo *node = (TKDNodeInfo*)(*fNodes)[i];
175 0 : printf("%d ", i); node->Print();
176 : }
177 0 : }
178 :
179 : //_________________________________________________________________
180 : Double_t TKDInterpolatorBase::Eval(const Double_t *point, Double_t &result, Double_t &error, Bool_t force)
181 : {
182 : // Evaluate PDF for "point". The result is returned in "result" and error in "error". The function returns the chi2 of the fit.
183 : //
184 : // Observations:
185 : //
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)
188 :
189 0 : Float_t pointF[50]; // local Float_t conversion for "point"
190 0 : for(int idim=0; idim<fNSize; idim++) pointF[idim] = (Float_t)point[idim];
191 0 : Int_t nodeIndex = GetNodeIndex(pointF);
192 0 : if(nodeIndex<0){
193 0 : Error("TKDInterpolatorBase::Eval()", "Can not retrive node for data point.");
194 0 : result = 0.;
195 0 : error = 1.E10;
196 0 : return 0.;
197 : }
198 0 : TKDNodeInfo *node = (TKDNodeInfo*)(*fNodes)[nodeIndex];
199 0 : if(node->Par() && !force){
200 : //printf("Node @ %d\n", nodeIndex); node->Print("a");
201 0 : return node->CookPDF(point, result, error);
202 : }
203 :
204 : // Allocate memory
205 0 : if(!fBuffer) fBuffer = new Double_t[2*fLambda];
206 0 : if(!fKDhelper){
207 0 : fRefPoints = new Float_t*[fNSize];
208 0 : for(int id=0; id<fNSize; id++){
209 0 : fRefPoints[id] = new Float_t[GetNTNodes()];
210 0 : for(int in=0; in<GetNTNodes(); in++) fRefPoints[id][in] = ((TKDNodeInfo*)(*fNodes)[in])->Data()[id];
211 : }
212 0 : Info("TKDInterpolatorBase::Eval()", "Build TKDTree(%d, %d, %d)", GetNTNodes(), fNSize, kNhelper);
213 0 : fKDhelper = new TKDTreeIF(GetNTNodes(), fNSize, kNhelper, fRefPoints);
214 0 : fKDhelper->Build();
215 0 : fKDhelper->MakeBoundariesExact();
216 0 : }
217 0 : if(!fFitter) fFitter = new TLinearFitter(fLambda, Form("hyp%d", fLambda-1));
218 :
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);
223 : // prepare workers
224 :
225 : Int_t ipar, // local looping variable
226 0 : npoints_new = Int_t((1.+fAlpha)*fLambda),
227 : npoints(0); // number of data points used for interpolation
228 0 : Int_t *index = new Int_t[2*npoints_new]; // indexes of NN
229 0 : Float_t *dist = new Float_t[2*npoints_new], // distances of NN
230 : d, // NN normalized distance
231 : w0, // work
232 : w; // tri-cubic weight function
233 :
234 : Bool_t kDOWN = kFALSE;
235 0 : do{
236 0 : if(npoints){
237 0 : Info("TKDInterpolatorBase::Eval()", "Interpolation failed. Trying to increase the number of interpolation points from %d to %d.", npoints, npoints_new);
238 0 : }
239 0 : if(npoints == npoints_new){
240 0 : Error("TKDInterpolatorBase::Eval()", "Interpolation failed and number of interpolation points (%d) Can not be increased further.", npoints);
241 0 : result = 0.;
242 0 : error = 1.E10;
243 : // clean memory
244 0 : delete [] dist; delete [] index;
245 0 : return 0.;
246 : } else npoints = npoints_new;
247 0 : if(npoints > GetNTNodes()){
248 0 : Warning("TKDInterpolatorBase::Eval()", "The number of interpolation points requested (%d) exceeds number of PDF values (%d). Downscale.", npoints, GetNTNodes());
249 0 : npoints = GetNTNodes();
250 : kDOWN = kTRUE;
251 0 : }
252 :
253 : // find nearest neighbors
254 0 : for(int idim=0; idim<fNSize; idim++) pointF[idim] = (Float_t)point[idim];
255 0 : fKDhelper->FindNearestNeighbors(pointF, npoints+1, index, dist);
256 :
257 : // add points to fitter
258 0 : fFitter->ClearPoints();
259 : TKDNodeInfo *tnode = NULL;
260 0 : for(int in=0; in<npoints; in++){
261 0 : tnode = (TKDNodeInfo*)(*fNodes)[index[in]];
262 : //tnode->Print();
263 0 : if(UseCOG()){ // COG
264 0 : Float_t *p = &(tnode->Data()[0]);
265 : ipar = 0;
266 0 : for(int idim=0; idim<fNSize; idim++){
267 0 : fBuffer[ipar++] = p[idim];
268 0 : for(int jdim=idim; jdim<fNSize; jdim++) fBuffer[ipar++] = p[idim]*p[jdim];
269 : }
270 0 : } else { // INT
271 0 : Float_t *bounds = &(tnode->Data()[fNSize]);
272 : ipar = 0;
273 0 : for(int idim=0; idim<fNSize; idim++){
274 0 : fBuffer[ipar++] = .5*(bounds[2*idim] + bounds[2*idim+1]);
275 0 : 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 0 : 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;
277 : }
278 : }
279 :
280 : // calculate tri-cubic weighting function
281 0 : if(UseWeights()){
282 0 : d = dist[in]/dist[npoints];
283 0 : w0 = (1. - d*d*d); w = w0*w0*w0;
284 0 : if(w<1.e-30) continue;
285 : } else w = 1.;
286 :
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 0 : fFitter->AddPoint(fBuffer, tnode->Val()[0], tnode->Val()[1]/w);
291 0 : }
292 0 : npoints_new = npoints+ (kDOWN ? 0 : kdN);
293 0 : } while(fFitter->Eval());
294 0 : delete [] index;
295 0 : delete [] dist;
296 :
297 : // retrive fitter results
298 0 : TMatrixD cov(fLambda, fLambda);
299 0 : TVectorD par(fLambda);
300 0 : fFitter->GetCovarianceMatrix(cov);
301 0 : fFitter->GetParameters(par);
302 0 : Double_t chi2 = fFitter->GetChisquare()/(npoints - 4 - fLambda);
303 :
304 : // store results
305 0 : node->Store(&par, HasStore()?&cov:NULL);
306 :
307 : // Build df/dpi|x values
308 0 : Double_t *fdfdp = &fBuffer[fLambda];
309 : ipar = 0;
310 0 : fdfdp[ipar++] = 1.;
311 0 : for(int idim=0; idim<fNSize; idim++){
312 0 : fdfdp[ipar++] = point[idim];
313 0 : for(int jdim=idim; jdim<fNSize; jdim++) fdfdp[ipar++] = point[idim]*point[jdim];
314 : }
315 :
316 : // calculate estimation
317 0 : result =0.; error = 0.;
318 0 : for(int i=0; i<fLambda; i++){
319 0 : result += fdfdp[i]*par(i);
320 0 : for(int j=0; j<fLambda; j++) error += fdfdp[i]*fdfdp[j]*cov(i,j);
321 : }
322 0 : error = TMath::Sqrt(error);
323 : return chi2;
324 0 : }
325 :
326 : //_________________________________________________________________
327 : void TKDInterpolatorBase::DrawProjection(UInt_t ax1, UInt_t ax2)
328 : {
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)
332 : //
333 :
334 0 : Float_t ax1min, ax1max, ax2min, ax2max;
335 0 : GetRange(ax1, ax1min, ax1max);
336 0 : GetRange(ax2, ax2min, ax2max);
337 : TH2 *h2 = NULL;
338 0 : if(!(h2 = (TH2S*)gROOT->FindObject("hKDnodes"))){
339 0 : h2 = new TH2S("hKDnodes", "", 100, ax1min, ax1max, 100, ax2min, ax2max);
340 0 : }
341 0 : h2->GetXaxis()->SetRangeUser(ax1min, ax1max);
342 0 : h2->GetXaxis()->SetTitle(Form("x_{%d}", ax1));
343 0 : h2->GetYaxis()->SetRangeUser(ax2min, ax2max);
344 0 : h2->GetYaxis()->SetTitle(Form("x_{%d}", ax2));
345 0 : h2->Draw();
346 :
347 :
348 0 : if(!fNodesDraw) fNodesDraw = new TKDNodeInfo::TKDNodeDraw[GetNTNodes()];
349 : TKDNodeInfo::TKDNodeDraw *box = NULL;
350 0 : for(Int_t in=GetNTNodes(); in--; ){
351 0 : box = &(fNodesDraw[in]);
352 0 : box->SetNode((TKDNodeInfo*)((*fNodes)[in]), fNSize, ax1, ax2);
353 0 : box->Draw();
354 : }
355 :
356 : return;
357 0 : }
358 :
359 : //_________________________________________________________________
360 : void TKDInterpolatorBase::SetAlpha(Float_t a)
361 : {
362 0 : if(a<0.5){
363 0 : Warning("TKDInterpolatorBase::SetAlpha()", "The scale parameter has to be larger than 0.5");
364 0 : fAlpha = 0.5;
365 0 : return;
366 : }
367 : // check value
368 0 : if(Int_t((a+1.)*fLambda) > GetNTNodes()){
369 0 : fAlpha = TMath::Max(0.5, Float_t(GetNTNodes())/fLambda-1.);
370 0 : Warning("TKDInterpolatorBase::SetAlpha()", "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());
372 0 : return;
373 : }
374 0 : fAlpha = a;
375 0 : return;
376 0 : }
377 :
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