Implementation of local interpolation based on COG points
authorabercuci <abercuci@f7af4fe6-9843-0410-8265-dc069ae4e863>
Mon, 10 Sep 2007 09:54:57 +0000 (09:54 +0000)
committerabercuci <abercuci@f7af4fe6-9843-0410-8265-dc069ae4e863>
Mon, 10 Sep 2007 09:54:57 +0000 (09:54 +0000)
STAT/TKDInterpolator.cxx

index 1724ac0..9be1a2f 100644 (file)
@@ -6,9 +6,12 @@
 #include "TH2.h"
 #include "TObjArray.h"
 #include "TObjString.h"
+#include "TPad.h"
 #include "TBox.h"
 #include "TGraph.h"
 #include "TMarker.h"
+#include "TRandom.h"
+#include "TROOT.h"
 
 
 
@@ -33,6 +36,8 @@ TKDInterpolator::TKDInterpolator() : TKDTreeIF()
        ,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.
 }
 
 //_________________________________________________________________
@@ -45,6 +50,8 @@ TKDInterpolator::TKDInterpolator(Int_t npoints, Int_t ndim, UInt_t bsize, Float_
        ,fKDhelper(0x0)
        ,fFitter(0x0)
 {
+// Wrapper constructor for the similar TKDTree one.
+       
        Build();
 }
 
@@ -65,24 +72,26 @@ TKDInterpolator::TKDInterpolator(TTree *t, const Char_t *var, const Char_t *cut,
 //
 // 
 
-       fNpoints = t->GetEntriesFast();
        TObjArray *vars = TString(var).Tokenize(":");
        fNDim = vars->GetEntriesFast();
-       if(fNDim > 6/*kDimMax*/) Warning("TKDInterpolator(TTree*, UInt_t, const Char_t)", Form("Variable number exceed maximum dimension %d. Results are unpredictable.", 6/*kDimMax*/));
+       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;
 
-       printf("Allocating %d points in %d dimensions.\n", fNpoints, fNDim);
-       Float_t *mem = new Float_t[fNDim*fNpoints];
-       fData = new Float_t*[fNDim];
-       for(int idim=0; idim<fNDim; idim++) fData[idim] = &mem[idim*fNpoints];
-       kDataOwner = kTRUE;
-       
+       Int_t np;
        Double_t *v;
        for(int idim=0; idim<fNDim; idim++){
-               if(!(t->Draw(((TObjString*)(*vars)[idim])->GetName(), cut, "goff"))){
-                       Warning("TKDInterpolator(TTree*, UInt_t, const Char_t)", Form("Can not access data for %s", ((TObjString*)(*vars)[idim])->GetName() ));
+               if(!(np = t->Draw(((TObjString*)(*vars)[idim])->GetName(), cut, "goff"))){
+                       Warning("TKDInterpolator(TTree*, const Char_t, const Char_t, UInt_t)", Form("Can not access data for %s", ((TObjString*)(*vars)[idim])->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));
+                       //Float_t *mem = new Float_t[fNDim*fNpoints];
+                       fData = new Float_t*[fNDim];
+                       for(int idim=0; idim<fNDim; idim++) fData[idim] = new Float_t[fNpoints]; //&mem[idim*fNpoints];
+                       kDataOwner = kTRUE;
+               }
                v = t->GetV1();
                for(int ip=0; ip<fNpoints; ip++) fData[idim][ip] = (Float_t)v[ip];
        }
@@ -108,6 +117,10 @@ TKDInterpolator::~TKDInterpolator()
 //_________________________________________________________________
 void TKDInterpolator::Build()
 {
+// Fill interpolator's data array i.e.
+//  - estimation points 
+//  - corresponding PDF values
+
        if(!fBoundaries) MakeBoundaries();
        
        // allocate memory for data
@@ -150,63 +163,87 @@ void TKDInterpolator::Build()
 }
 
 //_________________________________________________________________
-Double_t TKDInterpolator::Eval(Float_t *point)
+Double_t TKDInterpolator::Eval(const Double_t *point, Int_t npoints)
 {
-
-       // calculate number of parameters in the parabolic expresion
-       Int_t kNN = 1 + fNDim + fNDim*(fNDim+1)/2;
-
+// Evaluate PDF at k-dimensional position "point". The initial number of
+// neighbour estimation points is set to "npoints"
+       
+       //Int_t npoints = Int_t(alpha * fNTNodes);
+       //printf("Params : %d NPoints %d\n", lambda, npoints);
        // prepare workers
        if(!fTmpPoint) fTmpPoint = new Double_t[fNDim];
-       if(!fKDhelper) fKDhelper = new TKDTreeIF(GetNTerminalNodes(), fNDim, kNN, fRefPoints);
+       if(!fKDhelper) fKDhelper = new TKDTreeIF(GetNTerminalNodes(), fNDim, npoints, fRefPoints);
        if(!fFitter){
-               // generate formula for nD
+               // generate parabolic for nD
+               
+               // calculate number of parameters in the parabolic expresion
+               Int_t lambda = 1 + fNDim + fNDim*(fNDim+1)/2;
+               //Float_t alpha = Float_t(2*lambda + 1) / fNTNodes; // the bandwidth or smoothing parameter
                TString formula("1");
                for(int idim=0; idim<fNDim; idim++){
                        formula += Form("++x[%d]", idim);
                        for(int jdim=idim; jdim<fNDim; jdim++) formula += Form("++x[%d]*x[%d]", idim, jdim);
                }
-               fFitter = new TLinearFitter(kNN, formula.Data());
+               fFitter = new TLinearFitter(lambda, formula.Data());
+               Info("Eval(const Double_t*, Int_t)", Form("Using %s for local interpolation.", formula.Data()));
        }
-       
-       Int_t kNN_old = 0;
+
+       Float_t pointF[50];
+       for(int idim=0; idim<fNDim; idim++) pointF[idim] = point[idim];
+       Int_t istart = 0;
        Int_t *index;
-       Float_t dist;
+       Float_t dist, d0, w0, w;
+       Double_t uncertainty = TMath::Sqrt(1./fBucketSize); 
        fFitter->ClearPoints();
        do{
-               if(!fKDhelper->FindNearestNeighbors(point, kNN, index, dist)){
-                       Error("Eval()", Form("Failed retriving %d neighbours for point:", kNN));
+               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;
                }
-               for(int in=kNN_old; in<kNN; in++){
-                       for(int idim=0; idim<fNDim; idim++) fTmpPoint[idim] = fRefPoints[idim][index[in]];
-                       fFitter->AddPoint(fTmpPoint, TMath::Log(fRefValues[index[in]]), 1.);
+               for(int in=istart; in<npoints; in++){
+                       //printf("%d index[%2d] x(", in, index[in]);
+                       d0 = 0.;
+                       for(int idim=0; idim<fNDim; idim++){
+                               fTmpPoint[idim] = fRefPoints[idim][index[in]];
+                               //printf("%6.4f ", fTmpPoint[idim]);
+                               d0 += TMath::Abs(fTmpPoint[idim] - point[idim]);
+                       }
+                       d0 /= dist;
+                       w0 = (1. - d0*d0*d0);
+                       w = w0*w0*w0;
+
+                       //printf(") f = %f [%f] d0 = %6.4f   w = %6.4f  \n", fRefValues[index[in]], TMath::Log(fRefValues[index[in]]), d0, w);
+                       fFitter->AddPoint(fTmpPoint, TMath::Log(fRefValues[index[in]]), uncertainty/w);
                }
-               kNN_old = kNN;
-               kNN += 4;
+               istart = npoints;
+               npoints += 4;
        } while(fFitter->Eval());
 
        // calculate evaluation
-       TVectorD par(kNN);
-       fFitter->GetParameters(par);
-       Double_t result = par[0];
        Int_t ipar = 0;
+       Double_t result = fFitter->GetParameter(ipar++);
        for(int idim=0; idim<fNDim; idim++){
-               result += par[++ipar]*point[idim];
-               for(int jdim=idim; jdim<fNDim; jdim++) result += par[++ipar]*point[idim]*point[jdim];
+               result += fFitter->GetParameter(ipar++)*point[idim];
+               for(int jdim=idim; jdim<fNDim; jdim++) result += fFitter->GetParameter(ipar++)*point[idim]*point[jdim];
        }
+       //printf("\tResult : %f [%f]\n", TMath::Exp(result), result);
        return TMath::Exp(result);
 }
 
 
 //_________________________________________________________________
-void TKDInterpolator::DrawNodes(Int_t depth, Int_t ax1, Int_t ax2)
+void TKDInterpolator::DrawNodes(UInt_t ax1, UInt_t ax2, Int_t depth)
 {
 // 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();
 
@@ -221,12 +258,14 @@ void TKDInterpolator::DrawNodes(Int_t depth, Int_t ax1, Int_t ax2)
 
        //printf("depth %d nodes %d\n", depth, nnodes);
        
-       //TH2 *h2 = new TH2S("hframe", "", 100, fRange[2*ax1], fRange[2*ax1+1], 100, fRange[2*ax2], fRange[2*ax2+1]);
-       TH2 *h2 = new TH2S("hframe", "", 100, 0., 1., 100, 0., 1.);
+       TH2 *h2 = 0x0;
+       if(!(h2 = (TH2S*)gROOT->FindObject("hNodes"))) 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 border = 0.;//1.E-4;
-       TBox **node_array = new TBox*[nnodes], *node;
+       TBox *node_array = new TBox[nnodes], *node;
        Float_t *bounds = 0x0;
        nnodes = 0;
        for(int inode = 0; inode <= 2*fNnodes; inode++){
@@ -234,18 +273,19 @@ void TKDInterpolator::DrawNodes(Int_t depth, Int_t ax1, Int_t ax2)
                        if(!IsTerminal(inode)) continue;
                } else if((inode+1) >> depth != 1) continue;
 
-               node = node_array[nnodes++];
+               node = &node_array[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+Int_t(gRandom->Uniform()*50.));
                bounds = GetBoundary(inode);
-               node = new TBox(bounds[2*ax1]+border, bounds[2*ax2]+border, bounds[2*ax1+1]-border, bounds[2*ax2+1]-border);
-               node->SetFillStyle(0);  
-               node->SetFillColor(51+inode);
-               node->Draw();
+               node->DrawBox(bounds[2*ax1]+border, bounds[2*ax2]+border, bounds[2*ax1+1]-border, bounds[2*ax2+1]-border);
        }
        if(depth != -1) return;
 
        // Draw reference points
        TGraph *ref = new TGraph(GetNTerminalNodes());
-       ref->SetMarkerStyle(2);
+       ref->SetMarkerStyle(3);
+       ref->SetMarkerSize(.7);
        ref->SetMarkerColor(2);
        for(int inode = 0; inode < GetNTerminalNodes(); inode++) ref->SetPoint(inode, fRefPoints[ax1][inode], fRefPoints[ax2][inode]);
        ref->Draw("p");
@@ -253,43 +293,43 @@ void TKDInterpolator::DrawNodes(Int_t depth, Int_t ax1, Int_t ax2)
 }
 
 //_________________________________________________________________
-void TKDInterpolator::DrawNode(Int_t tnode, Int_t ax1, Int_t ax2)
+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 >= GetNTerminalNodes()){
                Warning("DrawNode()", Form("Terminal node %d outside defined range.", tnode));
                return;
        }
 
-       //TH2 *h2 = new TH2S("hframe", "", 1, fRange[2*ax1], fRange[2*ax1+1], 1, fRange[2*ax2], fRange[2*ax2+1]);
-       TH2 *h2 = new TH2S("hframe", "", 1, 0., 1., 1, 0., 1.);
-       h2->Draw();
-
        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;
 
-       printf("true index %d points %d\n", tnode, nPoints);
-
        // draw data points
        TGraph *g = new TGraph(nPoints);
-       g->SetMarkerStyle(3);
-       g->SetMarkerSize(.8);
+       g->SetMarkerStyle(7);
        for(int ip = 0; ip<nPoints; ip++) g->SetPoint(ip, fData[ax1][index[ip]], fData[ax2][index[ip]]);
-       g->Draw("p");
 
        // draw estimation point
-       TMarker *m=new TMarker(fRefPoints[ax1][inode], fRefPoints[ax2][inode], 2);
+       TMarker *m=new TMarker(fRefPoints[ax1][inode], fRefPoints[ax2][inode], 20);
        m->SetMarkerColor(2);
-       m->Draw();
+       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);
+
+       if(gPad) gPad->Clear(); 
+       g->Draw("ap");
+       m->Draw();
        n->Draw();
        
        return;