#pragma link C++ typedef TKDTreeIF;
+#pragma link C++ class TKDInterpolatorBase+;
+#pragma link C++ class TKDNodeInfo+;
+#pragma link C++ class TKDPDF+;
#pragma link C++ class TKDInterpolator+;
-#pragma link C++ class TKDInterpolator::TKDNodeInfo+;
#pragma link C++ class TKDSpline+;
#pragma link C++ class AliTMinuitToolkit+;
#include "TKDInterpolator.h"
+#include "TKDNodeInfo.h"
-#include "TLinearFitter.h"
-#include "TTree.h"
-#include "TH2.h"
-#include "TObjArray.h"
-#include "TObjString.h"
-#include "TBox.h"
-#include "TGraph.h"
-#include "TMarker.h"
-#include "TVectorD.h"
-#include "TMatrixD.h"
+#include "TClonesArray.h"
ClassImp(TKDInterpolator)
-ClassImp(TKDInterpolator::TKDNodeInfo)
-/////////////////////////////////////////////////////////////////////
-// Memory setup of protected data members
-// fRefPoints : evaluation point of PDF for each terminal node of underlying KD Tree.
-// | 1st terminal node (fNDim point coordinates) | 2nd terminal node (fNDim point coordinates) | ...
-//
-// fRefValues : evaluation value/error of PDF for each terminal node of underlying KD Tree.
-// | 1st terminal node (value) | 2nd terminal node (value) | ... | 1st terminal node (error) | 2nd terminal node (error) | ...
-//
-// status = |0|0|0|0|0|1(tri-cubic weights)|1(STORE)|1 INT(0 COG )|
-/////////////////////////////////////////////////////////////////////
-//_________________________________________________________________
-TKDInterpolator::TKDNodeInfo::TKDNodeInfo(const Int_t dim):
- fNDim(dim)
- ,fRefPoint(0x0)
- ,fRefValue(0.)
- ,fCov(0x0)
- ,fPar(0x0)
-{
- if(fNDim) Build(dim);
-}
-
-//_________________________________________________________________
-TKDInterpolator::TKDNodeInfo::~TKDNodeInfo()
-{
- if(fRefPoint) delete [] fRefPoint;
- if(fCov){
- delete fPar;
- delete fCov;
- }
-}
-
-//_________________________________________________________________
-void TKDInterpolator::TKDNodeInfo::Build(const Int_t dim)
-{
-// Allocate/Reallocate space for this node.
-
- if(!dim) return;
-
- fNDim = dim;
- Int_t lambda = Int_t(1 + fNDim + .5*fNDim*(fNDim+1));
- if(fRefPoint) delete [] fRefPoint;
- fRefPoint = new Float_t[fNDim];
- if(fCov){
- fCov->ResizeTo(lambda, lambda);
- fPar->ResizeTo(lambda);
- }
- return;
-}
//_________________________________________________________________
-void TKDInterpolator::TKDNodeInfo::Store(const TVectorD &par, const TMatrixD &cov)
-{
- if(!fCov){
- fCov = new TMatrixD(cov.GetNrows(), cov.GetNrows());
- fPar = new TVectorD(par.GetNrows());
- }
- (*fPar) = par;
- (*fCov) = cov;
-}
-
-//_________________________________________________________________
-Double_t TKDInterpolator::TKDNodeInfo::CookPDF(const Double_t *point, Double_t &result, Double_t &error)
-{
-// Recalculate the PDF for one node from the results of interpolation (parameters and covariance matrix)
-
- if(fNDim>10) return 0.; // support only up to 10 dimensions
-
- Int_t lambda = 1 + fNDim + (fNDim*(fNDim+1)>>1);
- Double_t fdfdp[66];
- Int_t ipar = 0;
- fdfdp[ipar++] = 1.;
- for(int idim=0; idim<fNDim; idim++){
- fdfdp[ipar++] = point[idim];
- for(int jdim=idim; jdim<fNDim; jdim++) fdfdp[ipar++] = point[idim]*point[jdim];
- }
-
- // calculate estimation
- result =0.; error = 0.;
- for(int i=0; i<lambda; i++){
- result += fdfdp[i]*(*fPar)(i);
- for(int j=0; j<lambda; j++) error += fdfdp[i]*fdfdp[j]*(*fCov)(i,j);
- }
- error = TMath::Sqrt(error);
-
- //printf("TKDNodeInfo::CookPDF() : %6.3f +- %6.3f\n", result, error);
-
- return 0.;
-}
-
-
-//_________________________________________________________________
-TKDInterpolator::TKDInterpolator() : TKDTreeIF()
- ,fNTNodes(0)
- ,fTNodes(0x0)
- ,fStatus(4)
- ,fLambda(0)
- ,fDepth(-1)
- ,fAlpha(.5)
- ,fRefPoints(0x0)
- ,fBuffer(0x0)
- ,fKDhelper(0x0)
- ,fFitter(0x0)
+TKDInterpolator::TKDInterpolator() :
+ TKDInterpolatorBase()
{
// Default constructor. To be used with care since in this case building
// of data structure is completly left to the user responsability.
}
//_________________________________________________________________
-TKDInterpolator::TKDInterpolator(Int_t npoints, Int_t ndim, UInt_t bsize, Float_t **data) : TKDTreeIF(npoints, ndim, bsize, data)
- ,fNTNodes(GetNTNodes())
- ,fTNodes(0x0)
- ,fStatus(4)
- ,fLambda(0)
- ,fDepth(-1)
- ,fAlpha(.5)
- ,fRefPoints(0x0)
- ,fBuffer(0x0)
- ,fKDhelper(0x0)
- ,fFitter(0x0)
+TKDInterpolator::TKDInterpolator(Int_t ndim, Int_t npoints) :
+ TKDInterpolatorBase(ndim)
{
// Wrapper constructor for the TKDTree.
- Build();
+ if(npoints) TKDInterpolatorBase::Build(npoints);
}
-//_________________________________________________________________
-TKDInterpolator::TKDInterpolator(TTree *t, const Char_t *var, const Char_t *cut, UInt_t bsize, Long64_t nentries, Long64_t firstentry) : TKDTreeIF()
- ,fNTNodes(0)
- ,fTNodes(0x0)
- ,fStatus(4)
- ,fLambda(0)
- ,fDepth(-1)
- ,fAlpha(.5)
- ,fRefPoints(0x0)
- ,fBuffer(0x0)
- ,fKDhelper(0x0)
- ,fFitter(0x0)
-{
-// Alocate data from a tree. The variables which have to be analysed are
-// defined in the "var" parameter as a colon separated list. The format should
-// be identical to that used by TTree::Draw().
-//
-//
-
- TObjArray *vars = TString(var).Tokenize(":");
- fNDim = vars->GetEntriesFast(); fNDimm = 2*fNDim;
- if(fNDim > 6/*kDimMax*/) Warning("TKDInterpolator(TTree*, const Char_t, const Char_t, UInt_t)", Form("Variable number exceed maximum dimension %d. Results are unpredictable.", 6/*kDimMax*/));
- fBucketSize = bsize;
-
- Int_t np;
- Double_t *v;
- for(int idim=0; idim<fNDim; idim++){
- if(!(np = t->Draw(((TObjString*)(*vars)[idim])->GetName(), cut, "goff", nentries, firstentry))){
- Warning("TKDInterpolator(TTree*, const Char_t, const Char_t, UInt_t)", Form("Can not access data for keys %s. Key defined on tree :", ((TObjString*)(*vars)[idim])->GetName() ));
- TIterator *it = (t->GetListOfLeaves())->MakeIterator();
- TObject *o;
- while((o = (*it)())) printf("\t%s\n", o->GetName());
- continue;
- }
- if(!fNpoints){
- fNpoints = np;
- //Info("TKDInterpolator(TTree*, const Char_t, const Char_t, UInt_t)", Form("Allocating %d data points in %d dimensions.", fNpoints, fNDim));
- fData = new Float_t*[fNDim];
- for(int idim=0; idim<fNDim; idim++) fData[idim] = new Float_t[fNpoints];
- kDataOwner = kTRUE;
- }
- v = t->GetV1();
- for(int ip=0; ip<fNpoints; ip++) fData[idim][ip] = (Float_t)v[ip];
- }
- TKDTreeIF::Build();
- Build();
-}
-
//_________________________________________________________________
TKDInterpolator::~TKDInterpolator()
{
- if(fFitter) delete fFitter;
- if(fKDhelper) delete fKDhelper;
- if(fBuffer) delete [] fBuffer;
-
- if(fRefPoints){
- for(int idim=0; idim<fNDim; idim++) delete [] fRefPoints[idim] ;
- delete [] fRefPoints;
- }
- if(fTNodes) delete [] fTNodes;
}
//_________________________________________________________________
-void TKDInterpolator::Build()
+void TKDInterpolator::AddNode(const TKDNodeInfo &node)
{
-// Fill interpolator's data array i.e.
-// - estimation points
-// - corresponding PDF values
-
- fNTNodes = TKDTreeIF::GetNTNodes();
- if(!fBoundaries) MakeBoundaries();
- fLambda = 1 + fNDim + (fNDim*(fNDim+1)>>1);
- //printf("after MakeBoundaries() %d\n", memory());
-
- // allocate memory for data
- fTNodes = new TKDNodeInfo[fNTNodes];
- for(int in=0; in<fNTNodes; in++) fTNodes[in].Build(fNDim);
- //printf("after BuildNodes() %d\n", memory());
-
- Float_t *bounds = 0x0;
- Int_t *indexPoints;
- for(int inode=0, tnode = fNnodes; inode<fNTNodes-1; inode++, tnode++){
- fTNodes[inode].fRefValue = Float_t(fBucketSize)/fNpoints;
- bounds = GetBoundary(tnode);
- for(int idim=0; idim<fNDim; idim++) fTNodes[inode].fRefValue /= (bounds[2*idim+1] - bounds[2*idim]);
-
- indexPoints = GetPointsIndexes(tnode);
- // loop points in this terminal node
- for(int idim=0; idim<fNDim; idim++){
- fTNodes[inode].fRefPoint[idim] = 0.;
- for(int ip = 0; ip<fBucketSize; ip++){
-/* printf("\t\tindex[%d] = %d %f\n", ip, indexPoints[ip], fData[idim][indexPoints[ip]]);*/
- fTNodes[inode].fRefPoint[idim] += fData[idim][indexPoints[ip]];
- }
- fTNodes[inode].fRefPoint[idim] /= fBucketSize;
- }
- }
-
- // analyze last (incomplete) terminal node
- Int_t counts = fNpoints%fBucketSize;
- counts = counts ? counts : fBucketSize;
- Int_t inode = fNTNodes - 1, tnode = inode + fNnodes;
- fTNodes[inode].fRefValue = Float_t(counts)/fNpoints;
- bounds = GetBoundary(tnode);
- for(int idim=0; idim<fNDim; idim++) fTNodes[inode].fRefValue /= (bounds[2*idim+1] - bounds[2*idim]);
-
- // loop points in this terminal node
- indexPoints = GetPointsIndexes(tnode);
- for(int idim=0; idim<fNDim; idim++){
- fTNodes[inode].fRefPoint[idim] = 0.;
- for(int ip = 0; ip<counts; ip++) fTNodes[inode].fRefPoint[idim] += fData[idim][indexPoints[ip]];
- fTNodes[inode].fRefPoint[idim] /= counts;
- }
-}
-
-//__________________________________________________________________
-void TKDInterpolator::GetStatus()
-{
-// Prints the status of the interpolator
-
- printf("Interpolator Status :\n");
- printf(" Method : %s\n", fStatus&1 ? "INT" : "COG");
- printf(" Store : %s\n", fStatus&2 ? "YES" : "NO");
- printf(" Weights: %s\n", fStatus&4 ? "YES" : "NO");
- return;
-
- printf("fNTNodes %d\n", fNTNodes); //Number of evaluation data points
- for(int i=0; i<fNTNodes; i++){
- printf("%d ", i);
- for(int idim=0; idim<fNDim; idim++) printf("%f ", fTNodes[i].fRefPoint[idim]);
- printf("[%f] %s\n", fTNodes[i].fRefValue, fTNodes[i].fCov ? "true" : "false");
- printf("Fit parameters : ");
- if(!fTNodes[i].fPar){
- printf("Not defined.\n");
- continue;
- }
- for(int ip=0; ip<3; ip++) printf("p%d[%f] ", ip, (*fTNodes[i].fPar)(ip));
- printf("\n");
- }
-}
-
-//_________________________________________________________________
-Double_t TKDInterpolator::Eval(const Double_t *point, Double_t &result, Double_t &error, Bool_t force)
-{
-// Evaluate PDF for "point". The result is returned in "result" and error in "error". The function returns the chi2 of the fit.
-//
-// Observations:
-//
-// 1. The default method used for interpolation is kCOG.
-// 2. The initial number of neighbors used for the estimation is set to Int(alpha*fLambda) (alpha = 1.5)
-
- Float_t pointF[50]; // local Float_t conversion for "point"
- for(int idim=0; idim<fNDim; idim++) pointF[idim] = (Float_t)point[idim];
- Int_t node = FindNode(pointF) - fNnodes;
- if((fStatus&1) && fTNodes[node].fCov && !force) return fTNodes[node].CookPDF(point, result, error);
-
- // Allocate memory
- if(!fBuffer) fBuffer = new Double_t[2*fLambda];
- if(!fKDhelper){
- fRefPoints = new Float_t*[fNDim];
- for(int id=0; id<fNDim; id++){
- fRefPoints[id] = new Float_t[fNTNodes];
- for(int in=0; in<fNTNodes; in++) fRefPoints[id][in] = fTNodes[in].fRefPoint[id];
- }
-// for(int in=0; in<fNTNodes; in++){
-// printf("%3d ", in);
-// for(int id=0; id<fNDim; id++) printf("%6.3f ", fTNodes[in].fRefPoint[id]/*fRefPoints[id][in]*/);
-// printf("\n");
-// }
- fKDhelper = new TKDTreeIF(fNTNodes, fNDim, 30, fRefPoints);
- fKDhelper->MakeBoundaries();
- }
- if(!fFitter) fFitter = new TLinearFitter(fLambda, Form("hyp%d", fLambda-1));
-
- // generate parabolic for nD
- //Float_t alpha = Float_t(2*lambda + 1) / fNTNodes; // the bandwidth or smoothing parameter
- //Int_t npoints = Int_t(alpha * fNTNodes);
- //printf("Params : %d NPoints %d\n", lambda, npoints);
- // prepare workers
-
- Int_t *index, // indexes of NN
- ipar, // local looping variable
- npoints = Int_t((1.+fAlpha)*fLambda); // number of data points used for interpolation
- Float_t *dist, // distances of NN
- d, // NN normalized distance
- w0, // work
- w; // tri-cubic weight function
- Double_t sig // bucket error
- = TMath::Sqrt(1./fBucketSize);
-
- do{
- // find nearest neighbors
- for(int idim=0; idim<fNDim; idim++) pointF[idim] = (Float_t)point[idim];
- if(!fKDhelper->FindNearestNeighbors(pointF, npoints+1, index, dist)){
- Error("Eval()", Form("Failed retriving %d neighbours for point:", npoints));
- for(int idim=0; idim<fNDim; idim++) printf("%f ", point[idim]);
- printf("\n");
- return -1;
- }
- // add points to fitter
- fFitter->ClearPoints();
- TKDNodeInfo *node = 0x0;
- for(int in=0; in<npoints; in++){
- node = &fTNodes[index[in]];
- if(fStatus&1){ // INT
- Float_t *bounds = GetBoundary(FindNode(node->fRefPoint));
- ipar = 0;
- for(int idim=0; idim<fNDim; idim++){
- fBuffer[ipar++] = .5*(bounds[2*idim] + bounds[2*idim+1]);
- fBuffer[ipar++] = (bounds[2*idim]*bounds[2*idim] + bounds[2*idim] * bounds[2*idim+1] + bounds[2*idim+1] * bounds[2*idim+1])/3.;
- for(int jdim=idim+1; jdim<fNDim; jdim++) fBuffer[ipar++] = (bounds[2*idim] + bounds[2*idim+1]) * (bounds[2*jdim] + bounds[2*jdim+1]) * .25;
- }
- } else { // COG
- Float_t *p = node->fRefPoint;
- ipar = 0;
- for(int idim=0; idim<fNDim; idim++){
- fBuffer[ipar++] = p[idim];
- for(int jdim=idim; jdim<fNDim; jdim++) fBuffer[ipar++] = p[idim]*p[jdim];
- }
- }
-
- // calculate tri-cubic weighting function
- if(fStatus&4){
- d = dist[in]/ dist[npoints];
- w0 = (1. - d*d*d); w = w0*w0*w0;
- } else w = 1.;
-
- //for(int idim=0; idim<fNDim; idim++) printf("%f ", fBuffer[idim]);
- //printf("\nd[%f] w[%f] sig[%f]\n", d, w, sig);
- fFitter->AddPoint(fBuffer, node->fRefValue, node->fRefValue*sig/w);
- }
- npoints += 4;
- } while(fFitter->Eval());
-
- // retrive fitter results
- TMatrixD cov(fLambda, fLambda);
- TVectorD par(fLambda);
- fFitter->GetCovarianceMatrix(cov);
- fFitter->GetParameters(par);
- Double_t chi2 = fFitter->GetChisquare()/(npoints - 4 - fLambda);
-
- // store results
- if(fStatus&2 && fStatus&1) fTNodes[node].Store(par, cov);
-
- // Build df/dpi|x values
- Double_t *fdfdp = &fBuffer[fLambda];
- ipar = 0;
- fdfdp[ipar++] = 1.;
- for(int idim=0; idim<fNDim; idim++){
- fdfdp[ipar++] = point[idim];
- for(int jdim=idim; jdim<fNDim; jdim++) fdfdp[ipar++] = point[idim]*point[jdim];
+ if(!fTNodes){
+ printf("W - TKDInterpolator::SetNode() : Node array not defined.\n");
+ return;
}
- // calculate estimation
- result =0.; error = 0.;
- for(int i=0; i<fLambda; i++){
- result += fdfdp[i]*par(i);
- for(int j=0; j<fLambda; j++) error += fdfdp[i]*fdfdp[j]*cov(i,j);
- }
- error = TMath::Sqrt(error);
-
- return chi2;
+ new((*fTNodes)[fNTNodes++]) TKDNodeInfo(node);
}
//_________________________________________________________________
-void TKDInterpolator::DrawNodes(UInt_t ax1, UInt_t ax2, Int_t depth)
+void TKDInterpolator::Build(Int_t npoints, Int_t ndim)
{
-// Draw nodes structure projected on plane "ax1:ax2". The parameter
-// "depth" specifies the bucket size per node. If depth == -1 draw only
-// terminal nodes and evaluation points (default -1 i.e. bucket size per node equal bucket size specified by the user)
-//
-// Observation:
-// This function creates the nodes (TBox) array for the specified depth
-// but don't delete it. Abusing this function may cause memory leaks !
-
-
- if(!fBoundaries) MakeBoundaries();
-
- // Count nodes in specific view
- Int_t nnodes = 0;
- for(int inode = 0; inode <= 2*fNnodes; inode++){
- if(depth == -1){
- if(!IsTerminal(inode)) continue;
- } else if((inode+1) >> depth != 1) continue;
- nnodes++;
- }
-
- //printf("depth %d nodes %d\n", depth, nnodes);
-
- TH2 *h2 = new TH2S("hNodes", "", 100, fRange[2*ax1], fRange[2*ax1+1], 100, fRange[2*ax2], fRange[2*ax2+1]);
- h2->GetXaxis()->SetTitle(Form("x_{%d}", ax1));
- h2->GetYaxis()->SetTitle(Form("x_{%d}", ax2));
- h2->Draw();
-
- const Float_t kBorder = 0.;//1.E-4;
- TBox *nodeArray = new TBox[nnodes], *node;
- Float_t *bounds = 0x0;
- nnodes = 0;
- for(int inode = 0; inode <= 2*fNnodes; inode++){
- if(depth == -1){
- if(!IsTerminal(inode)) continue;
- } else if((inode+1) >> depth != 1) continue;
-
- node = &nodeArray[nnodes++];
- //node = new TBox(bounds[2*ax1]+border, bounds[2*ax2]+border, bounds[2*ax1+1]-border, bounds[2*ax2+1]-border);
- node->SetFillStyle(3002);
- node->SetFillColor(50+inode/*Int_t(gRandom->Uniform()*50.)*/);
- bounds = GetBoundary(inode);
- node->DrawBox(bounds[2*ax1]+kBorder, bounds[2*ax2]+kBorder, bounds[2*ax1+1]-kBorder, bounds[2*ax2+1]-kBorder);
- }
- if(depth != -1) return;
-
- // Draw reference points
- TGraph *ref = new TGraph(fNTNodes);
- ref->SetMarkerStyle(3);
- ref->SetMarkerSize(.7);
- ref->SetMarkerColor(2);
- for(int inode = 0; inode < fNTNodes; inode++) ref->SetPoint(inode, fTNodes[inode].fRefPoint[ax1], fTNodes[inode].fRefPoint[ax2]);
- ref->Draw("p");
- return;
+ fNSize = ndim;
+ TKDInterpolatorBase::Build(npoints);
}
//_________________________________________________________________
-void TKDInterpolator::DrawNode(Int_t tnode, UInt_t ax1, UInt_t ax2)
-{
-// Draw node "node" and the data points within.
-//
-// Observation:
-// This function creates some graphical objects
-// but don't delete it. Abusing this function may cause memory leaks !
-
- if(tnode < 0 || tnode >= fNTNodes){
- Warning("DrawNode()", Form("Terminal node %d outside defined range.", tnode));
- return;
+Int_t TKDInterpolator::GetNodeIndex(const Float_t *p)
+{
+/* printf("TKDInterpolator::GetNodeIndex() ...\n");
+ printf("Looking for p[");
+ for(int i=0; i<fNSize; i++) printf("%f ", p[i]);
+ printf("] ...\n");*/
+ TKDNodeInfo *node;
+ for(int inode=0; inode<fNTNodes; inode++){
+ node = (TKDNodeInfo*)(*fTNodes)[inode];
+ //node->Print();
+ if(node->Has(p)) return inode;
}
-
- Int_t inode = tnode;
- tnode += fNnodes;
- // select zone of interest in the indexes array
- Int_t *index = GetPointsIndexes(tnode);
- Int_t nPoints = (tnode == 2*fNnodes) ? fNpoints%fBucketSize : fBucketSize;
-
- // draw data points
- TGraph *g = new TGraph(nPoints);
- g->SetMarkerStyle(7);
- for(int ip = 0; ip<nPoints; ip++) g->SetPoint(ip, fData[ax1][index[ip]], fData[ax2][index[ip]]);
-
- // draw estimation point
- TMarker *m=new TMarker(fTNodes[inode].fRefPoint[ax1], fTNodes[inode].fRefPoint[ax2], 20);
- m->SetMarkerColor(2);
- m->SetMarkerSize(1.7);
-
- // draw node contour
- Float_t *bounds = GetBoundary(tnode);
- TBox *n = new TBox(bounds[2*ax1], bounds[2*ax2], bounds[2*ax1+1], bounds[2*ax2+1]);
- n->SetFillStyle(0);
-
- g->Draw("ap");
- m->Draw();
- n->Draw();
-
- return;
-}
-
-
-//__________________________________________________________________
-void TKDInterpolator::SetInterpolationMethod(const Bool_t on)
-{
-// Set interpolation bit to "on".
-
- if(on) fStatus += fStatus&1 ? 0 : 1;
- else fStatus += fStatus&1 ? -1 : 0;
+ return -1;
}
//_________________________________________________________________
-void TKDInterpolator::SetStore(const Bool_t on)
+Bool_t TKDInterpolator::SetNode(const Int_t inode, const TKDNodeInfo &ref)
{
-// Set store bit to "on"
-
- if(on) fStatus += fStatus&2 ? 0 : 2;
- else fStatus += fStatus&2 ? -2 : 0;
+ if(!fTNodes){
+ printf("W - TKDInterpolator::SetNode() : Node array not defined.\n");
+ return kFALSE;
+ }
+ if(inode >= fNTNodes){
+ printf("W - TKDInterpolator::SetNode() : Node array defined up to %d.\n", fNTNodes);
+ return kFALSE;
+ }
+ TKDNodeInfo *node = (TKDNodeInfo*)(*fTNodes)[inode];
+ (*node) = ref;
}
-//_________________________________________________________________
-void TKDInterpolator::SetWeights(const Bool_t on)
-{
-// Set weights bit to "on"
-
- if(on) fStatus += fStatus&4 ? 0 : 4;
- else fStatus += fStatus&4 ? -4 : 0;
-}
#ifndef ROOT_TKDInterpolator
#define ROOT_TKDInterpolator
-#ifndef ROOT_TKDTree
-#include "TKDTree.h"
+#ifndef ROOT_TKDInterpolatorBase
+#include "TKDInterpolatorBase.h"
#endif
-// Non parametric interpolation class based on local polinomial regression.
-// The class can be used to approximate PDF together with TKDTree or for
-// general regression when the data points are given.
-
-template <typename Value> class TVectorT;
-typedef struct TVectorT<Double_t> TVectorD;
-template <typename Value> class TMatrixT;
-typedef class TMatrixT<Double_t> TMatrixD;
-template <typename Index, typename Value> class TKDTree;
-typedef class TKDTree<Int_t, Float_t> TKDTreeIF;
-class TTree;
-class TLinearFitter;
-class TKDInterpolator : public TKDTreeIF
+class TKDInterpolator : public TKDInterpolatorBase
{
public:
TKDInterpolator();
- TKDInterpolator(TTree *t, const Char_t *var, const Char_t *cut = 0, UInt_t bsize = 100, Long64_t nentries = 1000000000, Long64_t firstentry = 0);
- TKDInterpolator(Int_t npoints, Int_t ndim, UInt_t bsize, Float_t **data);
+ TKDInterpolator(Int_t ndim, Int_t npoints=0);
~TKDInterpolator();
+ void AddNode(const TKDNodeInfo &ref);
+ void Build(Int_t npoints, Int_t ndim);
+ Int_t GetNodeIndex(const Float_t *p);
+ Bool_t SetNode(const Int_t i, const TKDNodeInfo &ref);
- Double_t Eval(const Double_t *point, Double_t &result, Double_t &error, Bool_t force = kFALSE);
- Float_t GetAlpha() const {return fAlpha;}
- inline Bool_t GetCOGPoint(Int_t node, Float_t *coord, Float_t &val, Float_t &error) const;
- inline Bool_t GetDataPoint(Int_t n, Float_t *p) const;
- TKDTreeIF* GetHelper() {return fKDhelper;}
- Bool_t GetInterpolationMethod() const {return fStatus&1;}
- Int_t GetNTNodes() const {return fNTNodes;}
- Bool_t GetStore() const {return fStatus&2;}
- Bool_t GetWeights() const {return fStatus&4;}
-
- void DrawNodes(UInt_t ax1 = 0, UInt_t ax2 = 1, Int_t depth = -1);
- void DrawNode(Int_t tnode, UInt_t ax1 = 0, UInt_t ax2 = 1);
- void GetStatus();
- void SetAlpha(const Float_t a){if(a>0.) fAlpha = a;}
- void SetInterpolationMethod(const Bool_t on = kTRUE);
- void SetStore(const Bool_t on = kTRUE);
- void SetWeights(const Bool_t on = kTRUE);
-
private:
TKDInterpolator(const TKDInterpolator &);
TKDInterpolator& operator=(const TKDInterpolator &);
- void Build();
-
-public:
- class TKDNodeInfo
- {
- public:
- TKDNodeInfo(const Int_t ndim = 0);
- virtual ~TKDNodeInfo();
- void Build(const Int_t ndim);
- Double_t CookPDF(const Double_t *point, Double_t &result, Double_t &error);
- void Store(const TVectorD &par, const TMatrixD &cov);
-
- Int_t fNDim; // data dimension
- Float_t *fRefPoint; //[fNDim] node's COG
- Float_t fRefValue; // measured value for node
- TMatrixD *fCov; // interpolator covariance matrix
- TVectorD *fPar; // interpolator parameters
-
- private:
- TKDNodeInfo(const TKDNodeInfo &);
- TKDNodeInfo& operator=(const TKDNodeInfo &);
-
- ClassDef(TKDNodeInfo, 1) // node info for interpolator
- };
-
-protected:
- Int_t fNTNodes; //Number of evaluation data points
- TKDNodeInfo *fTNodes; //[fNTNodes] interpolation node
private:
- UChar_t fStatus; // status of the interpolator
- UChar_t fLambda; // number of parameters in polynom
- Short_t fDepth; //! depth of the KD Tree structure used
- Float_t fAlpha; // alpha parameter
- Float_t **fRefPoints; //! temporary storage of COG data
- Double_t *fBuffer; //! working space [2*fLambda]
- TKDTreeIF *fKDhelper; //! kNN finder
- TLinearFitter *fFitter; //! linear fitter
-
- ClassDef(TKDInterpolator, 1) // data interpolator based on KD tree
+
+ ClassDef(TKDInterpolator, 1) // LOWESS data interpolator
};
-//__________________________________________________________________
-Bool_t TKDInterpolator::GetCOGPoint(Int_t node, Float_t *coord, Float_t &val, Float_t &err) const
-{
- if(node < 0 || node > fNTNodes) return kFALSE;
-
- for(int idim=0; idim<fNDim; idim++) coord[idim] = fTNodes[node].fRefPoint[idim];
- val = fTNodes[node].fRefValue;
- err = fTNodes[node].fRefValue/TMath::Sqrt(fBucketSize);
- return kTRUE;
-}
-
-//__________________________________________________________________
-Bool_t TKDInterpolator::GetDataPoint(Int_t n, Float_t *p) const
-{
- if(n < 0 || n >= fNpoints) return kFALSE;
- if(!fData) return kFALSE;
-
- for(int i=0; i<fNDim; i++) p[i] = fData[i][n];
- return kTRUE;
-}
-
#endif
--- /dev/null
+#include "TKDInterpolatorBase.h"
+#include "TKDNodeInfo.h"
+#include "TKDTree.h"
+
+#include "TClonesArray.h"
+#include "TLinearFitter.h"
+#include "TTree.h"
+#include "TH2.h"
+#include "TObjArray.h"
+#include "TObjString.h"
+#include "TBox.h"
+#include "TGraph.h"
+#include "TMarker.h"
+#include "TMath.h"
+#include "TVectorD.h"
+#include "TMatrixD.h"
+
+ClassImp(TKDInterpolatorBase)
+
+/////////////////////////////////////////////////////////////////////
+// Memory setup of protected data members
+// fRefPoints : evaluation point of PDF for each terminal node of underlying KD Tree.
+// | 1st terminal node (fNDim point coordinates) | 2nd terminal node (fNDim point coordinates) | ...
+//
+// fRefValues : evaluation value/error of PDF for each terminal node of underlying KD Tree.
+// | 1st terminal node (value) | 2nd terminal node (value) | ... | 1st terminal node (error) | 2nd terminal node (error) | ...
+//
+// status = |0|0|0|0|0|1(tri-cubic weights)|1(STORE)|1 INT(0 COG )|
+/////////////////////////////////////////////////////////////////////
+
+
+//_________________________________________________________________
+TKDInterpolatorBase::TKDInterpolatorBase(const Int_t dim) :
+ fNSize(dim)
+ ,fNTNodes(0)
+ ,fTNodes(0x0)
+ ,fStatus(4)
+ ,fLambda(1 + dim + (dim*(dim+1)>>1))
+ ,fDepth(-1)
+ ,fAlpha(.5)
+ ,fRefPoints(0x0)
+ ,fBuffer(0x0)
+ ,fKDhelper(0x0)
+ ,fFitter(0x0)
+{
+// Default constructor. To be used with care since in this case building
+// of data structure is completly left to the user responsability.
+}
+
+//_________________________________________________________________
+void TKDInterpolatorBase::Build(const Int_t n)
+{
+ // allocate memory for data
+
+ if(fTNodes) delete fTNodes;
+ fNTNodes = n;
+ fTNodes = new TClonesArray("TKDNodeInfo", fNTNodes);
+ for(int in=0; in<fNTNodes; in++) new ((*fTNodes)[in]) TKDNodeInfo(fNSize);
+}
+
+//_________________________________________________________________
+TKDInterpolatorBase::~TKDInterpolatorBase()
+{
+ if(fFitter) delete fFitter;
+ if(fKDhelper) delete fKDhelper;
+ if(fBuffer) delete [] fBuffer;
+
+ if(fRefPoints){
+ for(int idim=0; idim<fNSize; idim++) delete [] fRefPoints[idim] ;
+ delete [] fRefPoints;
+ }
+ if(fTNodes) delete fTNodes;
+}
+
+
+//__________________________________________________________________
+Bool_t TKDInterpolatorBase::GetCOGPoint(Int_t inode, Float_t *&coord, Float_t &val, Float_t &err) const
+{
+ if(inode < 0 || inode > fNTNodes) return kFALSE;
+
+ TKDNodeInfo *node = (TKDNodeInfo*)(*fTNodes)[inode];
+ coord = &(node->fData[0]);
+ val = node->fVal[0];
+ err = node->fVal[1];
+ return kTRUE;
+}
+
+//_________________________________________________________________
+TKDNodeInfo* TKDInterpolatorBase::GetNodeInfo(const Int_t inode) const
+{
+ if(!fTNodes || inode >= fNTNodes) return 0x0;
+ return (TKDNodeInfo*)(*fTNodes)[inode];
+}
+
+
+//__________________________________________________________________
+void TKDInterpolatorBase::GetStatus()
+{
+// Prints the status of the interpolator
+
+ printf("Interpolator Status :\n");
+ printf(" Dim : %d [%d]\n", fNSize, fLambda);
+ printf(" Method : %s\n", fStatus&1 ? "INT" : "COG");
+ printf(" Store : %s\n", fStatus&2 ? "YES" : "NO");
+ printf(" Weights: %s\n", fStatus&4 ? "YES" : "NO");
+
+ printf("fNTNodes %d\n", fNTNodes); //Number of evaluation data points
+ for(int i=0; i<fNTNodes; i++){
+ TKDNodeInfo *node = (TKDNodeInfo*)(*fTNodes)[i];
+ printf("%d ", i); node->Print();
+ }
+}
+
+//_________________________________________________________________
+Double_t TKDInterpolatorBase::Eval(const Double_t *point, Double_t &result, Double_t &error, Bool_t force)
+{
+// Evaluate PDF for "point". The result is returned in "result" and error in "error". The function returns the chi2 of the fit.
+//
+// Observations:
+//
+// 1. The default method used for interpolation is kCOG.
+// 2. The initial number of neighbors used for the estimation is set to Int(alpha*fLambda) (alpha = 1.5)
+
+ Float_t pointF[50]; // local Float_t conversion for "point"
+ for(int idim=0; idim<fNSize; idim++) pointF[idim] = (Float_t)point[idim];
+ Int_t nodeIndex = GetNodeIndex(pointF);
+ if(nodeIndex<0){
+ result = 0.;
+ error = 1.E10;
+ return 0.;
+ }
+ TKDNodeInfo *node = (TKDNodeInfo*)(*fTNodes)[nodeIndex];
+ if((fStatus&1) && node->fCov && !force) return node->CookPDF(point, result, error);
+
+ // Allocate memory
+ if(!fBuffer) fBuffer = new Double_t[2*fLambda];
+ if(!fKDhelper){
+ fRefPoints = new Float_t*[fNSize];
+ for(int id=0; id<fNSize; id++){
+ fRefPoints[id] = new Float_t[fNTNodes];
+ for(int in=0; in<fNTNodes; in++) fRefPoints[id][in] = ((TKDNodeInfo*)(*fTNodes)[in])->fData[id];
+ }
+ fKDhelper = new TKDTreeIF(fNTNodes, fNSize, 30, fRefPoints);
+ fKDhelper->MakeBoundaries();
+ }
+ if(!fFitter) fFitter = new TLinearFitter(fLambda, Form("hyp%d", fLambda-1));
+
+ // generate parabolic for nD
+ //Float_t alpha = Float_t(2*lambda + 1) / fNTNodes; // the bandwidth or smoothing parameter
+ //Int_t npoints = Int_t(alpha * fNTNodes);
+ //printf("Params : %d NPoints %d\n", lambda, npoints);
+ // prepare workers
+
+ Int_t *index, // indexes of NN
+ ipar, // local looping variable
+ npoints = Int_t((1.+fAlpha)*fLambda); // number of data points used for interpolation
+ Float_t *dist, // distances of NN
+ d, // NN normalized distance
+ w0, // work
+ w; // tri-cubic weight function
+
+ do{
+ // find nearest neighbors
+ for(int idim=0; idim<fNSize; idim++) pointF[idim] = (Float_t)point[idim];
+ if(!fKDhelper->FindNearestNeighbors(pointF, npoints+1, index, dist)){
+ Error("Eval()", Form("Failed retriving %d neighbours for point:", npoints));
+ for(int idim=0; idim<fNSize; idim++) printf("%f ", point[idim]);
+ printf("\n");
+ return -1;
+ }
+ // add points to fitter
+ fFitter->ClearPoints();
+ TKDNodeInfo *tnode = 0x0;
+ for(int in=0; in<npoints; in++){
+ tnode = (TKDNodeInfo*)(*fTNodes)[index[in]];
+ //tnode->Print();
+ if(fStatus&1){ // INT
+ Float_t *bounds = &(tnode->fData[fNSize]);
+ ipar = 0;
+ for(int idim=0; idim<fNSize; idim++){
+ fBuffer[ipar++] = .5*(bounds[2*idim] + bounds[2*idim+1]);
+ fBuffer[ipar++] = (bounds[2*idim]*bounds[2*idim] + bounds[2*idim] * bounds[2*idim+1] + bounds[2*idim+1] * bounds[2*idim+1])/3.;
+ 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;
+ }
+ } else { // COG
+ Float_t *p = &(tnode->fData[0]);
+ ipar = 0;
+ for(int idim=0; idim<fNSize; idim++){
+ fBuffer[ipar++] = p[idim];
+ for(int jdim=idim; jdim<fNSize; jdim++) fBuffer[ipar++] = p[idim]*p[jdim];
+ }
+ }
+
+ // calculate tri-cubic weighting function
+ if(fStatus&4){
+ d = dist[in]/ dist[npoints];
+ w0 = (1. - d*d*d); w = w0*w0*w0;
+ } else w = 1.;
+
+// printf("x[");
+// for(int idim=0; idim<fLambda-1; idim++) printf("%f ", fBuffer[idim]);
+// printf("] v[%f +- %f] (%f, %f)\n", tnode->fVal[0], tnode->fVal[1]/w, tnode->fVal[1], w);
+ fFitter->AddPoint(fBuffer, tnode->fVal[0], tnode->fVal[1]/w);
+ }
+ npoints += 4;
+ } while(fFitter->Eval());
+
+ // retrive fitter results
+ TMatrixD cov(fLambda, fLambda);
+ TVectorD par(fLambda);
+ fFitter->GetCovarianceMatrix(cov);
+ fFitter->GetParameters(par);
+ Double_t chi2 = fFitter->GetChisquare()/(npoints - 4 - fLambda);
+
+ // store results
+ if(fStatus&2 && fStatus&1) node->Store(par, cov);
+
+ // Build df/dpi|x values
+ Double_t *fdfdp = &fBuffer[fLambda];
+ ipar = 0;
+ fdfdp[ipar++] = 1.;
+ for(int idim=0; idim<fNSize; idim++){
+ fdfdp[ipar++] = point[idim];
+ for(int jdim=idim; jdim<fNSize; jdim++) fdfdp[ipar++] = point[idim]*point[jdim];
+ }
+
+ // calculate estimation
+ result =0.; error = 0.;
+ for(int i=0; i<fLambda; i++){
+ result += fdfdp[i]*par(i);
+ for(int j=0; j<fLambda; j++) error += fdfdp[i]*fdfdp[j]*cov(i,j);
+ }
+ error = TMath::Sqrt(error);
+
+ return chi2;
+}
+
+//_________________________________________________________________
+void TKDInterpolatorBase::DrawBins(UInt_t ax1, UInt_t ax2, Float_t ax1min, Float_t ax1max, Float_t ax2min, Float_t ax2max)
+{
+// Draw nodes structure projected on plane "ax1:ax2". The parameter
+// "depth" specifies the bucket size per node. If depth == -1 draw only
+// terminal nodes and evaluation points (default -1 i.e. bucket size per node equal bucket size specified by the user)
+//
+// Observation:
+// This function creates the nodes (TBox) array for the specified depth
+// but don't delete it. Abusing this function may cause memory leaks !
+
+
+
+ TH2 *h2 = new TH2S("hNodes", "", 100, ax1min, ax1max, 100, ax2min, ax2max);
+ h2->GetXaxis()->SetTitle(Form("x_{%d}", ax1));
+ h2->GetYaxis()->SetTitle(Form("x_{%d}", ax2));
+ h2->Draw();
+
+ const Float_t kBorder = 0.;//1.E-4;
+ TBox *boxArray = new TBox[fNTNodes], *box;
+ Float_t *bounds = 0x0;
+ for(int inode = 0; inode < fNTNodes; inode++){
+ box = &boxArray[inode];
+ box->SetFillStyle(3002);
+ box->SetFillColor(50+inode/*Int_t(gRandom->Uniform()*50.)*/);
+
+ bounds = &(((TKDNodeInfo*)(*fTNodes)[inode])->fData[fNSize]);
+ box->DrawBox(bounds[2*ax1]+kBorder, bounds[2*ax2]+kBorder, bounds[2*ax1+1]-kBorder, bounds[2*ax2+1]-kBorder);
+ }
+
+ // Draw reference points
+ TGraph *ref = new TGraph(fNTNodes);
+ ref->SetMarkerStyle(3);
+ ref->SetMarkerSize(.7);
+ ref->SetMarkerColor(2);
+ for(int inode = 0; inode < fNTNodes; inode++){
+ TKDNodeInfo *node = (TKDNodeInfo*)(*fTNodes)[inode];
+ ref->SetPoint(inode, node->fData[ax1], node->fData[ax2]);
+ }
+ ref->Draw("p");
+ return;
+}
+
+//__________________________________________________________________
+void TKDInterpolatorBase::SetInterpolationMethod(const Bool_t on)
+{
+// Set interpolation bit to "on".
+
+ if(on) fStatus += fStatus&1 ? 0 : 1;
+ else fStatus += fStatus&1 ? -1 : 0;
+}
+
+
+//_________________________________________________________________
+void TKDInterpolatorBase::SetStore(const Bool_t on)
+{
+// Set store bit to "on"
+
+ if(on) fStatus += fStatus&2 ? 0 : 2;
+ else fStatus += fStatus&2 ? -2 : 0;
+}
+
+//_________________________________________________________________
+void TKDInterpolatorBase::SetWeights(const Bool_t on)
+{
+// Set weights bit to "on"
+
+ if(on) fStatus += fStatus&4 ? 0 : 4;
+ else fStatus += fStatus&4 ? -4 : 0;
+}
--- /dev/null
+#ifndef ROOT_TKDInterpolatorBase
+#define ROOT_TKDInterpolatorBase
+
+#ifndef ROOT_Rtypes
+#include "Rtypes.h"
+#endif
+
+///////////////////////////////////////////////////////////////
+//
+// Base non parametric interpolation algorithm.
+// The class implements local polynomial regression (LOWESS).
+// The user will work with daughter classes which implements
+// particular data configurations.
+//
+///////////////////////////////////////////////////////////////
+
+template <typename Value> class TVectorT;
+typedef struct TVectorT<Double_t> TVectorD;
+template <typename Value> class TMatrixT;
+typedef class TMatrixT<Double_t> TMatrixD;
+template <typename Index, typename Value> class TKDTree;
+typedef class TKDTree<Int_t, Float_t> TKDTreeIF;
+class TLinearFitter;
+class TClonesArray;
+class TKDNodeInfo;
+class TKDInterpolatorBase
+{
+public:
+ TKDInterpolatorBase(const Int_t size = 0);
+ virtual ~TKDInterpolatorBase();
+
+ Double_t Eval(const Double_t *point, Double_t &result, Double_t &error, Bool_t force = kFALSE);
+ virtual Int_t GetNodeIndex(const Float_t *p) = 0;
+ Float_t GetAlpha() const {return fAlpha;}
+ Bool_t GetCOGPoint(Int_t node, Float_t *&coord, Float_t &val, Float_t &error) const;
+ Bool_t GetInterpolationMethod() const {return fStatus&1;}
+ TKDNodeInfo* GetNodeInfo(const Int_t inode) const;
+ Int_t GetNTNodes() const {return fNTNodes;}
+ void GetStatus();
+ Bool_t GetStore() const {return fStatus&2;}
+ Bool_t GetWeights() const {return fStatus&4;}
+
+ void DrawBins(UInt_t ax1 = 0, UInt_t ax2 = 1, Float_t ax1min=-1., Float_t ax1max=1., Float_t ax2min=-1., Float_t ax2max=1.);
+ void SetAlpha(const Float_t a){if(a>0.) fAlpha = a;}
+ void SetInterpolationMethod(const Bool_t on = kTRUE);
+ void SetStore(const Bool_t on = kTRUE);
+ void SetWeights(const Bool_t on = kTRUE);
+
+protected:
+ virtual void Build(const Int_t nnodes);
+
+private:
+ TKDInterpolatorBase(const TKDInterpolatorBase &);
+ TKDInterpolatorBase& operator=(const TKDInterpolatorBase &);
+
+protected:
+ Int_t fNSize; // data dimension
+ Int_t fNTNodes; //Number of evaluation data points
+ TClonesArray *fTNodes; //interpolation nodes
+
+//private:
+ UChar_t fStatus; // status of the interpolator
+ UChar_t fLambda; // number of parameters in polynom
+ Short_t fDepth; //! depth of the KD Tree structure used
+ Float_t fAlpha; // alpha parameter
+ Float_t **fRefPoints; //! temporary storage of COG data
+ Double_t *fBuffer; //! working space [2*fLambda]
+ TKDTree<Int_t, Float_t> *fKDhelper; //! kNN finder
+ TLinearFitter *fFitter; //! linear fitter
+
+ ClassDef(TKDInterpolatorBase, 1) // data interpolator based on KD tree
+};
+
+
+#endif
+
--- /dev/null
+#include "TKDNodeInfo.h"
+
+#include "TVectorD.h"
+#include "TMatrixD.h"
+#include "TMath.h"
+
+ClassImp(TKDNodeInfo)
+
+
+//_________________________________________________________________
+TKDNodeInfo::TKDNodeInfo(const Int_t dim):
+ TObject()
+ ,fNDim(3*dim)
+ ,fData(0x0)
+ ,fCov(0x0)
+ ,fPar(0x0)
+{
+ fVal[0] = 0.; fVal[1] = 0.;
+ Build(dim);
+}
+
+//_________________________________________________________________
+TKDNodeInfo::TKDNodeInfo(const TKDNodeInfo &ref):
+ TObject((TObject&) ref)
+ ,fNDim(fNDim)
+ ,fData(0x0)
+ ,fCov(0x0)
+ ,fPar(0x0)
+{
+ Build(fNDim/3);
+
+ memcpy(fData, ref.fData, fNDim*sizeof(Float_t));
+ fVal[0] = ref.fVal[0];
+ fVal[1] = ref.fVal[1];
+ if(ref.fCov) (*fCov) = (*ref.fCov);
+ if(ref.fPar) (*fPar) = (*ref.fPar);
+}
+
+
+//_________________________________________________________________
+TKDNodeInfo::~TKDNodeInfo()
+{
+ if(fData) delete [] fData;
+ if(fCov){
+ delete fPar;
+ delete fCov;
+ }
+}
+
+//_________________________________________________________________
+TKDNodeInfo& TKDNodeInfo::operator=(const TKDNodeInfo & ref)
+{
+// Info("operator==()", "...");
+
+ Int_t ndim = fNDim/3;
+ if(fNDim != ref.fNDim){
+ fNDim = ref.fNDim;
+ Build(ndim);
+ }
+ memcpy(fData, ref.fData, fNDim*sizeof(Float_t));
+ fVal[0] = ref.fVal[0];
+ fVal[1] = ref.fVal[1];
+ if(ref.fCov) (*fCov) = (*ref.fCov);
+ if(ref.fPar) (*fPar) = (*ref.fPar);
+
+ return *this;
+}
+
+//_________________________________________________________________
+void TKDNodeInfo::Build(const Int_t dim)
+{
+// Allocate/Reallocate space for this node.
+
+// Info("Build()", "...");
+
+ if(!dim) return;
+
+ Int_t lambda = Int_t(1 + dim + .5*dim*(dim+1));
+ if(fData) delete [] fData;
+ fData = new Float_t[fNDim];
+ if(fCov){
+ fCov->ResizeTo(lambda, lambda);
+ fPar->ResizeTo(lambda);
+ }
+ return;
+}
+
+//_________________________________________________________________
+void TKDNodeInfo::Print()
+{
+ Int_t dim = fNDim/3;
+ printf("x[");
+ for(int idim=0; idim<dim; idim++) printf("%f ", fData[idim]);
+ printf("] f = [%f +- %f]\n", fVal[0], fVal[1]);
+
+ Float_t *bounds = &fData[dim];
+ printf("range[");
+ for(int idim=0; idim<dim; idim++) printf("(%f %f) ", fData[2*idim], fData[2*idim+1]);
+ printf("]\n");
+
+ printf("Fit parameters : ");
+ if(!fCov){
+ printf("Not defined.\n");
+ return;
+ }
+
+ Int_t lambda = Int_t(1 + dim + .5*dim*(dim+1));
+ for(int ip=0; ip<3; ip++) printf("p%d[%f] ", ip, (*fPar)(ip));
+ printf("\n");
+}
+
+//_________________________________________________________________
+void TKDNodeInfo::Store(const TVectorD &par, const TMatrixD &cov)
+{
+ if(!fCov){
+ fCov = new TMatrixD(cov.GetNrows(), cov.GetNrows());
+ fPar = new TVectorD(par.GetNrows());
+ }
+ (*fPar) = par;
+ (*fCov) = cov;
+}
+
+//_________________________________________________________________
+Double_t TKDNodeInfo::CookPDF(const Double_t *point, Double_t &result, Double_t &error)
+{
+// Recalculate the PDF for one node from the results of interpolation (parameters and covariance matrix)
+
+ Int_t ndim = fNDim/3;
+ if(ndim>10) return 0.; // support only up to 10 dimensions
+
+ Int_t lambda = 1 + ndim + (ndim*(ndim+1)>>1);
+ Double_t fdfdp[66];
+ Int_t ipar = 0;
+ fdfdp[ipar++] = 1.;
+ for(int idim=0; idim<ndim; idim++){
+ fdfdp[ipar++] = point[idim];
+ for(int jdim=idim; jdim<ndim; jdim++) fdfdp[ipar++] = point[idim]*point[jdim];
+ }
+
+ // calculate estimation
+ result =0.; error = 0.;
+ for(int i=0; i<lambda; i++){
+ result += fdfdp[i]*(*fPar)(i);
+ for(int j=0; j<lambda; j++) error += fdfdp[i]*fdfdp[j]*(*fCov)(i,j);
+ }
+ error = TMath::Sqrt(error);
+
+ //printf("TKDNodeInfo::CookPDF() : %6.3f +- %6.3f\n", result, error);
+
+ return 0.;
+}
+
--- /dev/null
+#ifndef ROOT_TKDNodeInfo
+#define ROOT_TKDNodeInfo
+
+#ifndef ROOT_TObject
+#include "TObject.h"
+#endif
+
+template <typename Value> class TVectorT;
+typedef struct TVectorT<Double_t> TVectorD;
+template <typename Value> class TMatrixT;
+typedef class TMatrixT<Double_t> TMatrixD;
+class TKDInterpolatorBase;
+class TKDNodeInfo : public TObject
+{
+friend class TKDInterpolatorBase;
+public:
+ TKDNodeInfo(const Int_t ndim = 0);
+ TKDNodeInfo(const TKDNodeInfo &);
+ TKDNodeInfo& operator=(const TKDNodeInfo &);
+ virtual ~TKDNodeInfo();
+ Double_t CookPDF(const Double_t *point, Double_t &result, Double_t &error);
+ inline Bool_t Has(const Float_t *p);
+ void Print();
+ void Store(const TVectorD &par, const TMatrixD &cov);
+
+protected:
+ void Build(const Int_t ndim);
+
+public:
+ Int_t fNDim; // 3 times data dimension
+ Float_t *fData; //[fNDim] node's data
+ Float_t fVal[2]; // measured value for node
+ TMatrixD *fCov; // interpolator covariance matrix
+ TVectorD *fPar; // interpolator parameters
+
+ ClassDef(TKDNodeInfo, 1) // node info for interpolator
+};
+
+//_____________________________________________________________________
+Bool_t TKDNodeInfo::Has(const Float_t *p)
+{
+ Int_t n = 0;
+ Int_t ndim = fNDim/3;
+ for(int id=0; id<ndim; id++) if(p[id]>=fData[ndim+2*id] && p[id]<fData[ndim+2*id+1]) n++;
+ if(n==ndim) return kTRUE;
+ return kFALSE;
+}
+
+
+#endif
+
--- /dev/null
+#include "TKDPDF.h"
+#include "TKDNodeInfo.h"
+
+#include "TClonesArray.h"
+#include "TTree.h"
+#include "TH2.h"
+#include "TObjArray.h"
+#include "TObjString.h"
+#include "TBox.h"
+#include "TGraph.h"
+#include "TMarker.h"
+
+ClassImp(TKDPDF)
+
+
+
+//_________________________________________________________________
+TKDPDF::TKDPDF() :
+ TKDTreeIF()
+ ,TKDInterpolatorBase()
+{
+// Default constructor. To be used with care since in this case building
+// of data structure is completly left to the user responsability.
+}
+
+//_________________________________________________________________
+TKDPDF::TKDPDF(Int_t npoints, Int_t ndim, UInt_t bsize, Float_t **data) :
+ TKDTreeIF(npoints, ndim, bsize, data)
+ ,TKDInterpolatorBase(ndim)
+{
+// Wrapper constructor for the TKDTree.
+
+ Build();
+}
+
+
+//_________________________________________________________________
+TKDPDF::TKDPDF(TTree *t, const Char_t *var, const Char_t *cut, UInt_t bsize, Long64_t nentries, Long64_t firstentry) :
+ TKDTreeIF()
+ ,TKDInterpolatorBase()
+{
+// Alocate data from a tree. The variables which have to be analysed are
+// defined in the "var" parameter as a colon separated list. The format should
+// be identical to that used by TTree::Draw().
+//
+//
+
+ TObjArray *vars = TString(var).Tokenize(":");
+ fNDim = vars->GetEntriesFast(); fNDimm = 2*fNDim;
+ fNSize = fNDim;
+ if(fNDim > 6/*kDimMax*/) Warning("TKDPDF(TTree*, const Char_t, const Char_t, UInt_t)", Form("Variable number exceed maximum dimension %d. Results are unpredictable.", 6/*kDimMax*/));
+ fBucketSize = bsize;
+
+ Int_t np;
+ Double_t *v;
+ for(int idim=0; idim<fNDim; idim++){
+ if(!(np = t->Draw(((TObjString*)(*vars)[idim])->GetName(), cut, "goff", nentries, firstentry))){
+ Warning("TKDPDF(TTree*, const Char_t, const Char_t, UInt_t)", Form("Can not access data for keys %s. Key defined on tree :", ((TObjString*)(*vars)[idim])->GetName() ));
+ TIterator *it = (t->GetListOfLeaves())->MakeIterator();
+ TObject *o;
+ while((o = (*it)())) printf("\t%s\n", o->GetName());
+ continue;
+ }
+ if(!fNpoints){
+ fNpoints = np;
+ //Info("TKDPDF(TTree*, const Char_t, const Char_t, UInt_t)", Form("Allocating %d data points in %d dimensions.", fNpoints, fNDim));
+ fData = new Float_t*[fNDim];
+ for(int idim=0; idim<fNDim; idim++) fData[idim] = new Float_t[fNpoints];
+ kDataOwner = kTRUE;
+ }
+ v = t->GetV1();
+ for(int ip=0; ip<fNpoints; ip++) fData[idim][ip] = (Float_t)v[ip];
+ }
+ TKDTreeIF::Build();
+ Build();
+}
+
+//_________________________________________________________________
+TKDPDF::~TKDPDF()
+{
+}
+
+//_________________________________________________________________
+void TKDPDF::Build()
+{
+// Fill interpolator's data array i.e.
+// - estimation points
+// - corresponding PDF values
+
+ fNTNodes = fNpoints/fBucketSize + ((fNpoints%fBucketSize)?1:0);/*TKDTreeIF::GetNTNodes();*/
+ if(!fBoundaries) MakeBoundaries();
+ fLambda = 1 + fNDim + (fNDim*(fNDim+1)>>1);
+ //printf("after MakeBoundaries() %d\n", memory());
+
+ // allocate interpolation nodes
+ TKDInterpolatorBase::Build(fNTNodes);
+
+ TKDNodeInfo *node = 0x0;
+ Float_t *bounds = 0x0;
+ Int_t *indexPoints;
+ for(int inode=0, tnode = fNnodes; inode<fNTNodes-1; inode++, tnode++){
+ node = (TKDNodeInfo*)(*fTNodes)[inode];
+ node->fVal[0] = Float_t(fBucketSize)/fNpoints;
+ bounds = GetBoundary(tnode);
+ for(int idim=0; idim<fNDim; idim++) node->fVal[0] /= (bounds[2*idim+1] - bounds[2*idim]);
+ node->fVal[1] = node->fVal[0]/TMath::Sqrt(float(fBucketSize));
+
+ indexPoints = GetPointsIndexes(tnode);
+ // loop points in this terminal node
+ for(int idim=0; idim<fNDim; idim++){
+ node->fData[idim] = 0.;
+ for(int ip = 0; ip<fBucketSize; ip++) node->fData[idim] += fData[idim][indexPoints[ip]];
+ node->fData[idim] /= fBucketSize;
+ }
+ memcpy(&(node->fData[fNDim]), bounds, fNDimm*sizeof(Float_t));
+ }
+
+ // analyze last (incomplete) terminal node
+ Int_t counts = fNpoints%fBucketSize;
+ counts = counts ? counts : fBucketSize;
+ Int_t inode = fNTNodes - 1, tnode = inode + fNnodes;
+ node = (TKDNodeInfo*)(*fTNodes)[inode];
+ node->fVal[0] = Float_t(counts)/fNpoints;
+ bounds = GetBoundary(tnode);
+ for(int idim=0; idim<fNDim; idim++) node->fVal[0] /= (bounds[2*idim+1] - bounds[2*idim]);
+ node->fVal[1] = node->fVal[0]/TMath::Sqrt(float(counts));
+
+ // loop points in this terminal node
+ indexPoints = GetPointsIndexes(tnode);
+ for(int idim=0; idim<fNDim; idim++){
+ node->fData[idim] = 0.;
+ for(int ip = 0; ip<counts; ip++) node->fData[idim] += fData[idim][indexPoints[ip]];
+ node->fData[idim] /= counts;
+ }
+ memcpy(&(node->fData[fNDim]), bounds, fNDimm*sizeof(Float_t));
+
+ delete [] fBoundaries;
+ fBoundaries = 0x0;
+}
+
+
+//_________________________________________________________________
+void TKDPDF::DrawNode(Int_t tnode, UInt_t ax1, UInt_t ax2)
+{
+// Draw node "node" and the data points within.
+//
+// Observation:
+// This function creates some graphical objects
+// but don't delete it. Abusing this function may cause memory leaks !
+
+ if(tnode < 0 || tnode >= fNTNodes){
+ Warning("DrawNode()", Form("Terminal node %d outside defined range.", tnode));
+ return;
+ }
+
+ Int_t inode = tnode;
+ tnode += fNnodes;
+ // select zone of interest in the indexes array
+ Int_t *index = GetPointsIndexes(tnode);
+ Int_t nPoints = (tnode == 2*fNnodes) ? fNpoints%fBucketSize : fBucketSize;
+
+ // draw data points
+ TGraph *g = new TGraph(nPoints);
+ g->SetMarkerStyle(7);
+ for(int ip = 0; ip<nPoints; ip++) g->SetPoint(ip, fData[ax1][index[ip]], fData[ax2][index[ip]]);
+
+ // draw estimation point
+ TKDNodeInfo *node = (TKDNodeInfo*)(*fTNodes)[inode];
+ TMarker *m=new TMarker(node->fData[ax1], node->fData[ax2], 20);
+ m->SetMarkerColor(2);
+ m->SetMarkerSize(1.7);
+
+ // draw node contour
+ Float_t *bounds = GetBoundary(tnode);
+ TBox *n = new TBox(bounds[2*ax1], bounds[2*ax2], bounds[2*ax1+1], bounds[2*ax2+1]);
+ n->SetFillStyle(0);
+
+ g->Draw("ap");
+ m->Draw();
+ n->Draw();
+
+ return;
+}
+
--- /dev/null
+#ifndef ROOT_TKDPDF
+#define ROOT_TKDPDF
+
+#ifndef ROOT_TKDTree
+#include "TKDTree.h"
+#endif
+
+#ifndef ROOT_TKDInterpolatorBase
+#include "TKDInterpolatorBase.h"
+#endif
+
+// Non parametric interpolation class based on local polinomial regression.
+// The class can be used to approximate PDF together with TKDTree or for
+// general regression when the data points are given.
+
+template <typename Index, typename Value> class TKDTree;
+typedef class TKDTree<Int_t, Float_t> TKDTreeIF;
+class TTree;
+class TLinearFitter;
+class TKDPDF : public TKDTreeIF, public TKDInterpolatorBase
+{
+public:
+ TKDPDF();
+ TKDPDF(TTree *t, const Char_t *var, const Char_t *cut = 0, UInt_t bsize = 100, Long64_t nentries = 1000000000, Long64_t firstentry = 0);
+ TKDPDF(Int_t npoints, Int_t ndim, UInt_t bsize, Float_t **data);
+ ~TKDPDF();
+
+ inline Bool_t GetDataPoint(Int_t n, Float_t *p) const;
+ inline Int_t GetNodeIndex(const Float_t *p);
+ void DrawNode(Int_t tnode, UInt_t ax1=0, UInt_t ax2=1);
+
+private:
+ TKDPDF(const TKDPDF &);
+ TKDPDF& operator=(const TKDPDF &);
+ void Build();
+
+
+ ClassDef(TKDPDF, 1) // data interpolator based on KD tree
+};
+
+
+//__________________________________________________________________
+Bool_t TKDPDF::GetDataPoint(Int_t n, Float_t *p) const
+{
+ if(n < 0 || n >= fNpoints) return kFALSE;
+ if(!fData) return kFALSE;
+
+ for(int i=0; i<fNDim; i++) p[i] = fData[i][n];
+ return kTRUE;
+}
+
+//__________________________________________________________________
+Int_t TKDPDF::GetNodeIndex(const Float_t *p)
+{
+ return FindNode(p) - fNnodes;
+}
+
+#endif
+
#include "TKDSpline.h"
-
ClassImp(TKDSpline)
-/////////////////////////////////////////////////////////////////////
-// Memory setup of protected data memebers
-// fRefPoints : evaluation point of PDF for each terminal node of underlying KD Tree.
-// | 1st terminal node (fNDim point coordinates) | 2nd terminal node (fNDim point coordinates) | ...
-//
-// fRefValues : evaluation value/error of PDF for each terminal node of underlying KD Tree.
-// | 1st terminal node (value) | 2nd terminal node (value) | ... | 1st terminal node (error) | 2nd terminal node (error) | ...
-/////////////////////////////////////////////////////////////////////
//_________________________________________________________________
-TKDSpline::TKDSpline() : TKDInterpolator()
+TKDSpline::TKDSpline() :
+ TKDInterpolator()
{
}
//_________________________________________________________________
-TKDSpline::TKDSpline(Int_t npoints, Int_t ndim, UInt_t bsize, Float_t **data) : TKDInterpolator(npoints, ndim, bsize, data)
-{
- Build();
-}
-
-
-//_________________________________________________________________
-TKDSpline::TKDSpline(TTree *t, const Char_t *var, const Char_t *cut, UInt_t bsize) : TKDInterpolator(t, var, cut, bsize)
+TKDSpline::TKDSpline(Int_t npoints, Int_t ndim) :
+ TKDInterpolator(npoints, ndim)
{
Build();
}
{
public:
TKDSpline();
- TKDSpline(TTree *t, const Char_t *var, const Char_t *cut = 0, UInt_t bsize=100);
- TKDSpline(Int_t npoints, Int_t ndim, UInt_t bsize, Float_t **data);
+ TKDSpline(Int_t npoints, Int_t ndim);
private:
void Build();
// traverse tree
UChar_t ax;
Value val, dif;
- Int_t nAllNodes = fNnodes + GetNTNodes();
+ Int_t nAllNodes = fNnodes + fNpoints/fBucketSize + ((fNpoints%fBucketSize)?1:0);
Int_t nodeStack[128], nodeIn[128];
Index currentIndex = 0;
nodeStack[0] = inode;
if(range) memcpy(fRange, range, fNDimm*sizeof(Value));
// total number of nodes including terminal nodes
- Int_t totNodes = fNnodes + GetNTNodes();
+ Int_t totNodes = fNnodes + fNpoints/fBucketSize + ((fNpoints%fBucketSize)?1:0);
fBoundaries = new Value[totNodes*fNDimm];
//Info("MakeBoundaries(Value*)", Form("Allocate boundaries for %d nodes", totNodes));
inline UChar_t GetNodeAxis(Int_t id) const {return (id < 0 || id >= fNnodes) ? 0 : fAxis[id];}
inline Value GetNodeValue(Int_t id) const {return (id < 0 || id >= fNnodes) ? 0 : fValue[id];}
inline Int_t GetNNodes() const {return fNnodes;}
- inline Int_t GetNTNodes() const {return fNpoints/fBucketSize + ((fNpoints%fBucketSize)?1:0);}
inline Value* GetBoundaries();
inline Value* GetBoundary(const Int_t node);
static Int_t GetIndex(Int_t row, Int_t collumn){return collumn+(1<<row);}
SRCS= TKDTree.cxx \
- TKDInterpolator.cxx \
+ TKDInterpolatorBase.cxx \
+ TKDNodeInfo.cxx \
+ TKDPDF.cxx \
+ TKDInterpolator.cxx \
TKDSpline.cxx \
AliTMinuitToolkit.cxx \
TStatToolkit.cxx
git://git.uio.no / u / mrichter / AliRoot.git / commitdiff