--- /dev/null
+/**************************************************************************
+ * Copyright(c) 2006-07, ALICE Experiment at CERN, All rights reserved. *
+ * *
+ * Author: The ALICE Off-line Project. *
+ * Contributors are mentioned in the code where appropriate. *
+ * *
+ * Permission to use, copy, modify and distribute this software and its *
+ * documentation strictly for non-commercial purposes is hereby granted *
+ * without fee, provided that the above copyright notice appears in all *
+ * copies and that both the copyright notice and this permission notice *
+ * appear in the supporting documentation. The authors make no claims *
+ * about the suitability of this software for any purpose. It is *
+ * provided "as is" without express or implied warranty. *
+ **************************************************************************/
+
+
+#include "AliSplineFit.h"
+
+ClassImp(AliSplineFit);
+
+TLinearFitter AliSplineFit::fitterStatic = TLinearFitter(4,"pol3","");
+
+AliSplineFit::AliSplineFit() :
+ fBDump(kFALSE),
+ fGraph (0),
+ fNmin (0),
+ fSigma (0),
+ fMaxDelta (0),
+ fN0 (0),
+ fParams (0),
+ fCovars (0),
+ fIndex (0),
+ fN (0),
+ fChi2 (0.0),
+ fX (0),
+ fY0 (0),
+ fY1 (0),
+ fChi2I (0)
+ //
+ // Default constructor
+ //
+{ }
+
+
+
+AliSplineFit::AliSplineFit(const AliSplineFit& source) :
+ TObject(source),
+ fBDump (source.fBDump),
+ fGraph (source.fGraph),
+ fNmin (source.fNmin),
+ fSigma (source.fSigma),
+ fMaxDelta (source.fMaxDelta),
+ fN0 (source.fN0),
+ fN (source.fN),
+ fChi2 (source.fChi2)
+{
+//
+// Copy constructor
+//
+ fIndex = new Int_t[fN0];
+ fParams = new TClonesArray("TVectorD",fN0);
+ fCovars = new TClonesArray("TMatrixD",fN0);
+ fParams = (TClonesArray*)source.fParams->Clone();
+ fCovars = (TClonesArray*)source.fCovars->Clone();
+ for (Int_t i=0; i<fN0; i++) fIndex[i] = source.fIndex[i];
+
+ fX = new Double_t[fN];
+ fY0 = new Double_t[fN];
+ fY1 = new Double_t[fN];
+ fChi2I = new Double_t[fN];
+ for (Int_t i=0; i<fN; i++){
+ fX[i] = source.fX[i];
+ fY0[i] = source.fY0[i];
+ fY1[i] = source.fY1[i];
+ }
+}
+AliSplineFit& AliSplineFit::operator=(const AliSplineFit& source){
+//
+// assignment operator
+//
+ if (&source == this) return *this;
+
+//
+// reassign memory as previous fit could have a different size
+//
+
+ if ( fN0 != source.fN0) {
+
+ delete fParams;
+ delete fCovars;
+ delete []fIndex;
+
+ fN0 = source.fN0;
+ fIndex = new Int_t[fN0];
+ fParams = new TClonesArray("TVectorD",fN0);
+ fCovars = new TClonesArray("TMatrixD",fN0);
+ }
+ if ( fN != source.fN) {
+
+ delete []fX;
+ delete []fY0;
+ delete []fY1;
+ delete []fChi2I;
+ fN = source.fN;
+ fX = new Double_t[fN];
+ fY0 = new Double_t[fN];
+ fY1 = new Double_t[fN];
+ fChi2I = new Double_t[fN];
+ }
+
+// use copy constructor (without reassigning memory) to copy values
+
+ new (this) AliSplineFit(source);
+
+ return *this;
+}
+
+
+AliSplineFit::~AliSplineFit(){
+ //
+ // destructor. Don't delete fGraph, as this normally comes as input parameter
+ //
+ delete []fX;
+ delete []fY0;
+ delete []fY1;
+ delete []fChi2I;
+ delete fParams;
+ delete fCovars;
+ delete []fIndex;
+}
+
+Double_t AliSplineFit::Eval(Double_t x, Int_t deriv) const{
+ //
+ // evaluate value at x
+ // deriv = 0: function value
+ // = 1: first derivative
+ // = 2: 2nd derivative
+ // = 3: 3rd derivative
+ //
+ // a2 = -(3*a0 -3*b0 + 2*a1*dx +b1*dx)/(dx*dx)
+ // a3 = -(-2*a0+2*b0 - a1*dx - b1*dx)/(dx*dx*dx)
+
+ Int_t index = TMath::BinarySearch(fN,fX,x);
+ if (index<0) index =0;
+ if (index>fN-2) index =fN-2;
+ //
+ Double_t dx = x-fX[index];
+ Double_t dxc = fX[index+1]-fX[index];
+ Double_t y0 = fY0[index];
+ Double_t y1 = fY1[index];
+ Double_t y01 = fY0[index+1];
+ Double_t y11 = fY1[index+1];
+ Double_t y2 = -(3.*y0-3.*y01+2*y1*dxc+y11*dxc)/(dxc*dxc);
+ Double_t y3 = -(-2.* y0 + 2*y01 - y1*dxc - y11*dxc) /(dxc*dxc*dxc);
+ Double_t val = y0+y1*dx+y2*dx*dx+y3*dx*dx*dx;
+ if (deriv==1) val = y1+2.*y2*dx+3.*y3*dx*dx;
+ if (deriv==2) val = 2.*y2+6.*y3*dx;
+ if (deriv==3) val = 6*y3;
+ return val;
+}
+
+
+TGraph * AliSplineFit::GenerGraph(Int_t npoints, Double_t fraction, Double_t s1, Double_t s2, Double_t s3, Int_t der){
+ //
+ // generate random graph
+ // xrange 0,1
+ // yrange 0,1
+ // s1, s2, s3 - sigma of derivative
+ // fraction -
+
+ Double_t *value = new Double_t[npoints];
+ Double_t *time = new Double_t[npoints];
+ Double_t d0=0, d1=0,d2=0,d3=0;
+ value[0] = d0;
+ time[0] = 0;
+ for(Int_t i=1; i<npoints; i++){
+ Double_t dtime = 1./npoints;
+ Double_t dd1 = dtime;
+ Double_t dd2 = dd1*dd1;
+ Double_t dd3 = dd2*dd1;
+ d0 += d1*dd1 + d2*dd2/2. + d3*dd3/6.;
+ d1 += d2*dd1 +d3*dd2/2;
+ d2 += d3*dd1;
+ value[i] = d0;
+ time[i] = time[i-1]+dtime;
+ d1 =(1.-fraction)*d1+fraction*(gRandom->Exp(s1))*(gRandom->Rndm()-0.5);
+ d2 =(1.-fraction)*d2+fraction*(gRandom->Exp(s2))*(gRandom->Rndm()-0.5);
+ d3 =(1.-fraction)*d3+fraction*(gRandom->Exp(s3))*(gRandom->Rndm()-0.5);
+ if (gRandom->Rndm()<fraction) d3 =(1.-fraction)*d3+fraction*(gRandom->BreitWigner(0,s3));
+ }
+ Double_t dmean = (value[npoints-1]-value[0])/(time[npoints-1]-time[0]);
+ Double_t min = value[0];
+ Double_t max = value[0];
+ for (Int_t i=0; i<npoints; i++){
+ value[i] = value[i]-dmean*(time[i]-time[0]);
+ if (value[i]<min) min=value[i];
+ if (value[i]>max) max=value[i];
+ }
+
+ for (Int_t i=0; i<npoints; i++){
+ value[i] = (value[i]-min)/(max-min);
+ }
+ if (der==1) for (Int_t i=1; i<npoints; i++){
+ value[i-1] = (value[i]-value[i-1])/(time[i]-time[i-1]);
+ }
+
+ TGraph * graph = new TGraph(npoints,time,value);
+
+ delete [] value;
+ delete [] time;
+ return graph;
+}
+
+
+TGraph * AliSplineFit::GenerNoise(TGraph * graph0, Double_t sigma0){
+ //
+ // add noise to graph
+ //
+
+ Int_t npoints=graph0->GetN();
+ Double_t *value = new Double_t[npoints];
+ Double_t *time = new Double_t[npoints];
+ for(Int_t i=0; i<npoints; i++){
+ time[i] = graph0->GetX()[i];
+ value[i] = graph0->GetY()[i]+gRandom->Gaus(0,sigma0);
+ }
+ TGraph * graph = new TGraph(npoints,time,value);
+
+ delete [] value;
+ delete [] time;
+ return graph;
+}
+
+
+TGraph * AliSplineFit::MakeGraph(Double_t xmin, Double_t xmax, Int_t npoints, Int_t deriv) const {
+ //
+ // if npoints<=0 draw derivative
+ //
+
+ TGraph *graph =0;
+ if (npoints<=0) {
+ if (deriv<=0) return new TGraph(fN,fX,fY0);
+ if (deriv==1) return new TGraph(fN,fX,fY1);
+ if (deriv>2) return new TGraph(fN-1,fX,fChi2I);
+ }
+ Double_t * x = new Double_t[npoints+1];
+ Double_t * y = new Double_t[npoints+1];
+ for (Int_t ip=0; ip<=npoints; ip++){
+ x[ip] = xmin+ (xmax-xmin)*(Double_t(ip)/Double_t(npoints));
+ y[ip] = Eval(x[ip],deriv);
+ }
+
+ graph = new TGraph(npoints,x,y);
+ delete [] x;
+ delete [] y;
+ return graph;
+}
+
+TGraph * AliSplineFit::MakeDiff(TGraph * graph0) const {
+ //
+ // Make graph of difference to reference graph
+ //
+
+ Int_t npoints=graph0->GetN();
+ TGraph *graph =0;
+ Double_t * x = new Double_t[npoints];
+ Double_t * y = new Double_t[npoints];
+ for (Int_t ip=0; ip<npoints; ip++){
+ x[ip] = graph0->GetX()[ip];
+ y[ip] = Eval(x[ip],0)-graph0->GetY()[ip];
+ }
+ graph = new TGraph(npoints,x,y);
+ delete [] x;
+ delete [] y;
+ return graph;
+}
+
+
+TH1F * AliSplineFit::MakeDiffHisto(TGraph * graph0) const {
+ //
+ // Make histogram of difference to reference graph
+ //
+
+ Int_t npoints=graph0->GetN();
+ Float_t min=1e+39,max=-1e+39;
+ for (Int_t ip=0; ip<npoints; ip++){
+ Double_t x = graph0->GetX()[ip];
+ Double_t y = Eval(x,0)-graph0->GetY()[ip];
+ if (ip==0) {
+ min = y;
+ max = y;
+ }else{
+ if (y<min) min=y;
+ if (y>max) max=y;
+ }
+ }
+
+ TH1F *his = new TH1F("hdiff","hdiff", 100, min, max);
+ for (Int_t ip=0; ip<npoints; ip++){
+ Double_t x = graph0->GetX()[ip];
+ Double_t y = Eval(x,0)-graph0->GetY()[ip];
+ his->Fill(y);
+ }
+
+ return his;
+}
+
+
+
+void AliSplineFit::InitKnots(TGraph * graph, Int_t min, Int_t iter, Double_t maxDelta){
+ //
+ // initialize knots + estimate sigma of noise + make initial parameters
+ //
+ //
+
+ const Double_t kEpsilon = 1.e-7;
+ fGraph = graph;
+ fNmin = min;
+ fMaxDelta = maxDelta;
+ Int_t npoints = fGraph->GetN();
+ fN0 = (npoints/fNmin)+1;
+ Float_t delta = Double_t(npoints)/Double_t(fN0-1);
+
+ fParams = new TClonesArray("TVectorD",fN0);
+ fCovars = new TClonesArray("TMatrixD",fN0);
+ fIndex = new Int_t[fN0];
+ TLinearFitter fitterLocal(4,"pol3"); // local fitter
+ Double_t sigma2 =0;
+
+
+ Double_t yMin=graph->GetY()[0];
+ Double_t yMax=graph->GetY()[0];
+
+ for (Int_t iKnot=0; iKnot<fN0; iKnot++){
+ Int_t index0 = TMath::Nint(Double_t(iKnot)*Double_t(delta));
+ Int_t index1 = TMath::Min(TMath::Nint(Double_t(iKnot+1)*Double_t(delta)),npoints-1);
+ Int_t indexM = (iKnot>0) ? fIndex[iKnot-1]:index0;
+ fIndex[iKnot]=TMath::Min(index0, npoints-1);
+ Float_t startX =graph->GetX()[fIndex[iKnot]];
+
+ for (Int_t ipoint=indexM; ipoint<index1; ipoint++){
+ Double_t dxl =graph->GetX()[ipoint]-startX;
+ Double_t y = graph->GetY()[ipoint];
+ if (y<yMin) yMin=y;
+ if (y>yMax) yMax=y;
+ fitterLocal.AddPoint(&dxl,y,1);
+ }
+
+ fitterLocal.Eval();
+ sigma2 += fitterLocal.GetChisquare()/Double_t((index1-indexM)-4.);
+ TMatrixD * covar = new ((*fCovars)[iKnot]) TMatrixD(4,4);
+ TVectorD * param = new ((*fParams)[iKnot]) TVectorD(4);
+ fitterLocal.GetParameters(*param);
+ fitterLocal.GetCovarianceMatrix(*covar);
+ fitterLocal.ClearPoints();
+ }
+ fSigma =TMath::Sqrt(sigma2/Double_t(fN0)); // mean sigma
+ Double_t tDiff = ((yMax-yMin)+TMath::Abs(yMax)+TMath::Abs(yMin))*kEpsilon;
+ fSigma += tDiff+fMaxDelta/TMath::Sqrt(npoints);
+ fMaxDelta +=tDiff;
+ for (Int_t iKnot=0; iKnot<fN0; iKnot++){
+ TMatrixD & cov = *((TMatrixD*)fCovars->At(iKnot));
+ cov*=fSigma*fSigma;
+ }
+ OptimizeKnots(iter);
+
+ fN = 0;
+ for (Int_t iKnot=0; iKnot<fN0; iKnot++) if (fIndex[iKnot]>=0) fN++;
+ fX = new Double_t[fN];
+ fY0 = new Double_t[fN];
+ fY1 = new Double_t[fN];
+ fChi2I = new Double_t[fN];
+ Int_t iKnot=0;
+ for (Int_t i=0; i<fN0; i++){
+ if (fIndex[i]<0) continue;
+ if (iKnot>=fN) {
+ printf("AliSplineFit::InitKnots: Knot number > Max knot number\n");
+ break;
+ }
+ TVectorD * param = (TVectorD*) fParams->At(i);
+ fX[iKnot] = fGraph->GetX()[fIndex[i]];
+ fY0[iKnot] = (*param)(0);
+ fY1[iKnot] = (*param)(1);
+ fChi2I[iKnot] = 0;
+ iKnot++;
+ }
+}
+
+
+Int_t AliSplineFit::OptimizeKnots(Int_t nIter){
+ //
+ //
+ //
+ const Double_t kMaxChi2= 5;
+ Int_t nKnots=0;
+ TTreeSRedirector cstream("SplineIter.root");
+ for (Int_t iIter=0; iIter<nIter; iIter++){
+ if (fBDump) cstream<<"Fit"<<
+ "iIter="<<iIter<<
+ "fit.="<<this<<
+ "\n";
+ nKnots=2;
+ for (Int_t iKnot=1; iKnot<fN0-1; iKnot++){
+ if (fIndex[iKnot]<0) continue; //disabled knot
+ Double_t chi2 = CheckKnot(iKnot);
+ Double_t startX = fGraph->GetX()[fIndex[iKnot]];
+ if (fBDump) {
+ TMatrixD * covar = (TMatrixD*)fCovars->At(iKnot);
+ TVectorD * param = (TVectorD*)fParams->At(iKnot);
+ cstream<<"Chi2"<<
+ "iIter="<<iIter<<
+ "iKnot="<<iKnot<<
+ "chi2="<<chi2<<
+ "x="<<startX<<
+ "param="<<param<<
+ "covar="<<covar<<
+ "\n";
+ }
+ if (chi2>kMaxChi2) { nKnots++;continue;}
+ fIndex[iKnot]*=-1;
+ Int_t iPrevious=iKnot-1;
+ Int_t iNext =iKnot+1;
+ while (fIndex[iPrevious]<0) iPrevious--;
+ while (fIndex[iNext]<0) iNext++;
+ RefitKnot(iPrevious);
+ RefitKnot(iNext);
+ iKnot++;
+ while (iKnot<fN0-1&& fIndex[iKnot]<0) iKnot++;
+ }
+ }
+ return nKnots;
+}
+
+
+Bool_t AliSplineFit::RefitKnot(Int_t iKnot){
+ //
+ //
+ //
+ const Double_t kEpsilon = 1.e-7;
+
+ Int_t iPrevious=(iKnot>0) ?iKnot-1: 0;
+ Int_t iNext =(iKnot<fN0)?iKnot+1: fN0-1;
+ while (iPrevious>0&&fIndex[iPrevious]<0) iPrevious--;
+ while (iNext<fN0&&fIndex[iNext]<0) iNext++;
+ if (iPrevious<0) iPrevious=0;
+ if (iNext>=fN0) iNext=fN0-1;
+
+ Double_t startX = fGraph->GetX()[fIndex[iKnot]];
+ AliSplineFit::fitterStatic.ClearPoints();
+ Int_t indPrev = fIndex[iPrevious];
+ Int_t indNext = fIndex[iNext];
+ Double_t *graphX = fGraph->GetX();
+ Double_t *graphY = fGraph->GetY();
+
+ // make arrays for points to fit (to save time)
+
+ Int_t nPoints = indNext-indPrev;
+ Double_t *xPoint = new Double_t[3*nPoints];
+ Double_t *yPoint = &xPoint[nPoints];
+ Double_t *ePoint = &xPoint[2*nPoints];
+ Int_t indVec=0;
+ for (Int_t iPoint=indPrev; iPoint<indNext; iPoint++, indVec++){
+ Double_t dxl = graphX[iPoint]-startX;
+ Double_t y = graphY[iPoint];
+ xPoint[indVec] = dxl;
+ yPoint[indVec] = y;
+ ePoint[indVec] = fSigma;
+// ePoint[indVec] = fSigma+TMath::Abs(y)*kEpsilon;
+// AliSplineFit::fitterStatic.AddPoint(&dxl,y,fSigma+TMath::Abs(y)*kEpsilon);
+ }
+ AliSplineFit::fitterStatic.AssignData(nPoints,1,xPoint,yPoint,ePoint);
+ AliSplineFit::fitterStatic.Eval();
+
+// delete temporary arrays
+
+ delete [] xPoint;
+
+ TMatrixD * covar = (TMatrixD*)fCovars->At(iKnot);
+ TVectorD * param = (TVectorD*)fParams->At(iKnot);
+ AliSplineFit::fitterStatic.GetParameters(*param);
+ AliSplineFit::fitterStatic.GetCovarianceMatrix(*covar);
+ return 0;
+}
+
+
+Float_t AliSplineFit::CheckKnot(Int_t iKnot){
+ //
+ //
+ //
+
+ Int_t iPrevious=iKnot-1;
+ Int_t iNext =iKnot+1;
+ while (fIndex[iPrevious]<0) iPrevious--;
+ while (fIndex[iNext]<0) iNext++;
+ TVectorD &pPrevious = *((TVectorD*)fParams->At(iPrevious));
+ TVectorD &pNext = *((TVectorD*)fParams->At(iNext));
+ TVectorD &pKnot = *((TVectorD*)fParams->At(iKnot));
+ TMatrixD &cPrevious = *((TMatrixD*)fCovars->At(iPrevious));
+ TMatrixD &cNext = *((TMatrixD*)fCovars->At(iNext));
+ TMatrixD &cKnot = *((TMatrixD*)fCovars->At(iKnot));
+ Double_t xPrevious = fGraph->GetX()[fIndex[iPrevious]];
+ Double_t xNext = fGraph->GetX()[fIndex[iNext]];
+ Double_t xKnot = fGraph->GetX()[fIndex[iKnot]];
+
+ // extra variables introduced to save processing time
+
+ Double_t dxc = xNext-xPrevious;
+ Double_t invDxc = 1./dxc;
+ Double_t invDxc2 = invDxc*invDxc;
+ TMatrixD tPrevious(4,4);
+ TMatrixD tNext(4,4);
+
+ tPrevious(0,0) = 1; tPrevious(1,1) = 1;
+ tPrevious(2,0) = -3.*invDxc2;
+ tPrevious(2,1) = -2.*invDxc;
+ tPrevious(3,0) = 2.*invDxc2*invDxc;
+ tPrevious(3,1) = 1.*invDxc2;
+ tNext(2,0) = 3.*invDxc2; tNext(2,1) = -1*invDxc;
+ tNext(3,0) = -2.*invDxc2*invDxc; tNext(3,1) = 1.*invDxc2;
+ TMatrixD tpKnot(4,4);
+ TMatrixD tpNext(4,4);
+ Double_t dx = xKnot-xPrevious;
+ tpKnot(0,0) = 1; tpKnot(1,1) = 1; tpKnot(2,2) = 1; tpKnot(3,3) = 1;
+ tpKnot(0,1) = dx; tpKnot(0,2) = dx*dx; tpKnot(0,3) = dx*dx*dx;
+ tpKnot(1,2) = 2.*dx; tpKnot(1,3) = 3.*dx*dx;
+ tpKnot(2,3) = 3.*dx;
+ Double_t dxn = xNext-xPrevious;
+ tpNext(0,0) = 1; tpNext(1,1) = 1; tpNext(2,2) = 1; tpNext(3,3) = 1;
+ tpNext(0,1) = dxn; tpNext(0,2) = dxn*dxn; tpNext(0,3) = dxn*dxn*dxn;
+ tpNext(1,2) = 2.*dxn; tpNext(1,3) = 3.*dxn*dxn;
+ tpNext(2,3) = 3.*dxn;
+
+ //
+ // matrix and vector at previous
+ //
+
+ TVectorD sPrevious = tPrevious*pPrevious+tNext*pNext;
+ TVectorD sKnot = tpKnot*sPrevious;
+ TVectorD sNext = tpNext*sPrevious;
+
+ TMatrixD csPrevious00(tPrevious, TMatrixD::kMult,cPrevious);
+ csPrevious00 *= tPrevious.T();
+ TMatrixD csPrevious01(tNext,TMatrixD::kMult,cNext);
+ csPrevious01*=tNext.T();
+ TMatrixD csPrevious(csPrevious00,TMatrixD::kPlus,csPrevious01);
+ TMatrixD csKnot(tpKnot,TMatrixD::kMult,csPrevious);
+ csKnot*=tpKnot.T();
+ TMatrixD csNext(tpNext,TMatrixD::kMult,csPrevious);
+ csNext*=tpNext.T();
+
+ TVectorD dPrevious = pPrevious-sPrevious;
+ TVectorD dKnot = pKnot-sKnot;
+ TVectorD dNext = pNext-sNext;
+ //
+ //
+ TMatrixD prec(4,4);
+ prec(0,0) = (fMaxDelta*fMaxDelta);
+ prec(1,1) = prec(0,0)*invDxc2;
+ prec(2,2) = prec(1,1)*invDxc2;
+ prec(3,3) = prec(2,2)*invDxc2;
+
+// prec(0,0) = (fMaxDelta*fMaxDelta);
+// prec(1,1) = (fMaxDelta*fMaxDelta)/(dxc*dxc);
+// prec(2,2) = (fMaxDelta*fMaxDelta)/(dxc*dxc*dxc*dxc);
+// prec(3,3) = (fMaxDelta*fMaxDelta)/(dxc*dxc*dxc*dxc*dxc*dxc);
+
+ csPrevious+=cPrevious;
+ csPrevious+=prec;
+ csPrevious.Invert();
+ Double_t chi2P = dPrevious*(csPrevious*dPrevious);
+
+ csKnot+=cKnot;
+ csKnot+=prec;
+ csKnot.Invert();
+ Double_t chi2K = dKnot*(csKnot*dKnot);
+
+ csNext+=cNext;
+ csNext+=prec;
+ csNext.Invert();
+ Double_t chi2N = dNext*(csNext*dNext);
+
+ return (chi2P+chi2K+chi2N)/8.;
+
+
+}
+
+void AliSplineFit::SplineFit(Int_t nder){
+ //
+ // Cubic spline fit of graph
+ //
+ // nder
+ // nder<0 - no continuity requirement
+ // =0 - continous 0 derivative
+ // =1 - continous 1 derivative
+ // >1 - continous 2 derivative
+ //
+ if (!fGraph) return;
+ TGraph * graph = fGraph;
+ if (nder>1) nder=2;
+ Int_t nknots = fN;
+ Int_t npoints = graph->GetN();
+ //
+ //
+ // spline fit
+ // each knot 4 parameters
+ //
+ TMatrixD *pmatrix = 0;
+ TVectorD *pvalues = 0;
+ if (nder>1){
+ pmatrix = new TMatrixD(4*(nknots-1)+3*(nknots-2), 4*(nknots-1)+3*(nknots-2));
+ pvalues = new TVectorD(4*(nknots-1)+3*(nknots-2));
+ }
+ if (nder==1){
+ pmatrix = new TMatrixD(4*(nknots-1)+2*(nknots-2), 4*(nknots-1)+2*(nknots-2));
+ pvalues = new TVectorD(4*(nknots-1)+2*(nknots-2));
+ }
+ if (nder==0){
+ pmatrix = new TMatrixD(4*(nknots-1)+1*(nknots-2), 4*(nknots-1)+1*(nknots-2));
+ pvalues = new TVectorD(4*(nknots-1)+1*(nknots-2));
+ }
+ if (nder<0){
+ pmatrix = new TMatrixD(4*(nknots-1)+0*(nknots-2), 4*(nknots-1)+0*(nknots-2));
+ pvalues = new TVectorD(4*(nknots-1)+0*(nknots-2));
+ }
+
+
+ TMatrixD &matrix = *pmatrix;
+ TVectorD &values = *pvalues;
+ Int_t current = 0;
+//
+// defined extra variables (current4 etc.) to save processing time.
+// fill normal matrices, then copy to sparse matrix.
+//
+ Double_t *graphX = graph->GetX();
+ Double_t *graphY = graph->GetY();
+ for (Int_t ip=0;ip<npoints;ip++){
+ if (current<nknots-2&&graphX[ip]>fX[current+1]) current++;
+ Double_t xmiddle = (fX[current+1]+fX[current])*0.5;
+ Double_t x1 = graphX[ip]- xmiddle;
+ Double_t x2 = x1*x1;
+ Double_t x3 = x2*x1;
+ Double_t x4 = x2*x2;
+ Double_t x5 = x3*x2;
+ Double_t x6 = x3*x3;
+ Double_t y = graphY[ip];
+ Int_t current4 = 4*current;
+
+ matrix(current4 , current4 )+=1;
+ matrix(current4 , current4+1)+=x1;
+ matrix(current4 , current4+2)+=x2;
+ matrix(current4 , current4+3)+=x3;
+ //
+ matrix(current4+1, current4 )+=x1;
+ matrix(current4+1, current4+1)+=x2;
+ matrix(current4+1, current4+2)+=x3;
+ matrix(current4+1, current4+3)+=x4;
+ //
+ matrix(current4+2, current4 )+=x2;
+ matrix(current4+2, current4+1)+=x3;
+ matrix(current4+2, current4+2)+=x4;
+ matrix(current4+2, current4+3)+=x5;
+ //
+ matrix(current4+3, current4 )+=x3;
+ matrix(current4+3, current4+1)+=x4;
+ matrix(current4+3, current4+2)+=x5;
+ matrix(current4+3, current4+3)+=x6;
+ //
+ values(current4 ) += y;
+ values(current4+1) += y*x1;
+ values(current4+2) += y*x2;
+ values(current4+3) += y*x3;
+ }
+ //
+ // constraint 0
+ //
+ Int_t offset =4*(nknots-1)-1;
+ if (nder>=0) for (Int_t iknot = 1; iknot<nknots-1; iknot++){
+
+ Double_t dxm = (fX[iknot]-fX[iknot-1])*0.5;
+ Double_t dxp = -(fX[iknot+1]-fX[iknot])*0.5;
+ Double_t dxm2 = dxm*dxm;
+ Double_t dxp2 = dxp*dxp;
+ Double_t dxm3 = dxm2*dxm;
+ Double_t dxp3 = dxp2*dxp;
+ Int_t iknot4 = 4*iknot;
+ Int_t iknot41 = 4*(iknot-1);
+ Int_t offsKnot = offset+iknot;
+ //
+ // condition on knot
+ //
+ // a0[i] = a0m[i-1] + a1m[i-1]*dxm + a2m[i-1]*dxm^2 + a3m[i-1]*dxm^3
+ // a0[i] = a0m[i-0] + a1m[i-0]*dxp + a2m[i-0]*dxp^2 + a3m[i-0]*dxp^3
+ // (a0m[i-1] + a1m[i-1]*dxm + a2m[i-1]*dxm^2 + a3m[i-1]*dxm^3) -
+ // (a0m[i-0] + a1m[i-0]*dxp + a2m[i-0]*dxp^2 + a3m[i-0]*dxp^3) = 0
+
+ matrix(offsKnot, iknot41 )=1;
+ matrix(offsKnot, iknot4 )=-1;
+
+ matrix(offsKnot, iknot41+1)=dxm;
+ matrix(offsKnot, iknot4 +1)=-dxp;
+
+ matrix(offsKnot, iknot41+2)=dxm2;
+ matrix(offsKnot, iknot4 +2)=-dxp2;
+
+ matrix(offsKnot, iknot41+3)=dxm3;
+ matrix(offsKnot, iknot4 +3)=-dxp3;
+
+ matrix(iknot41 , offsKnot)=1;
+ matrix(iknot41+1, offsKnot)=dxm;
+ matrix(iknot41+2, offsKnot)=dxm2;
+ matrix(iknot41+3, offsKnot)=dxm3;
+ matrix(iknot4 , offsKnot)=-1;
+ matrix(iknot4+1, offsKnot)=-dxp;
+ matrix(iknot4+2, offsKnot)=-dxp2;
+ matrix(iknot4+3, offsKnot)=-dxp3;
+ }
+ //
+ // constraint 1
+ //
+ offset =4*(nknots-1)-1+(nknots-2);
+ if (nder>=1)for (Int_t iknot = 1; iknot<nknots-1; iknot++){
+
+ Double_t dxm = (fX[iknot]-fX[iknot-1])*0.5;
+ Double_t dxp = -(fX[iknot+1]-fX[iknot])*0.5;
+ Double_t dxm2 = dxm*dxm;
+ Double_t dxp2 = dxp*dxp;
+ Int_t iknot4 = 4*iknot;
+ Int_t iknot41 = 4*(iknot-1);
+ Int_t offsKnot = offset+iknot;
+ //
+ // condition on knot derivation
+ //
+ // a0d[i] = a1m[i-1] + 2*a2m[i-1]*dxm + 3*a3m[i-1]*dxm^2
+ // a0d[i] = a1m[i-0] + 2*a2m[i-0]*dxp + 3*a3m[i-0]*dxp^2
+
+ //
+ matrix(offsKnot, iknot41+1)= 1;
+ matrix(offsKnot, iknot4 +1)=-1;
+
+ matrix(offsKnot, iknot41+2)= 2.*dxm;
+ matrix(offsKnot, iknot4 +2)=-2.*dxp;
+
+ matrix(offsKnot, iknot41+3)= 3.*dxm2;
+ matrix(offsKnot, iknot4 +3)=-3.*dxp2;
+
+ matrix(iknot41+1, offsKnot)=1;
+ matrix(iknot41+2, offsKnot)=2.*dxm;
+ matrix(iknot41+3, offsKnot)=3.*dxm2;
+
+ matrix(iknot4+1, offsKnot)=-1.;
+ matrix(iknot4+2, offsKnot)=-2.*dxp;
+ matrix(iknot4+3, offsKnot)=-3.*dxp2;
+ }
+ //
+ // constraint 2
+ //
+ offset =4*(nknots-1)-1+2*(nknots-2);
+ if (nder>=2) for (Int_t iknot = 1; iknot<nknots-1; iknot++){
+
+ Double_t dxm = (fX[iknot]-fX[iknot-1])*0.5;
+ Double_t dxp = -(fX[iknot+1]-fX[iknot])*0.5;
+ Int_t iknot4 = 4*iknot;
+ Int_t iknot41 = 4*(iknot-1);
+ Int_t offsKnot = offset+iknot;
+ //
+ // condition on knot second derivative
+ //
+ // a0dd[i] = 2*a2m[i-1] + 6*a3m[i-1]*dxm
+ // a0dd[i] = 2*a2m[i-0] + 6*a3m[i-0]*dxp
+ //
+ //
+ matrix(offsKnot, iknot41+2)= 2.;
+ matrix(offsKnot, iknot4 +2)=-2.;
+
+ matrix(offsKnot, iknot41+3)= 6.*dxm;
+ matrix(offsKnot, iknot4 +3)=-6.*dxp;
+
+ matrix(iknot41+2, offsKnot)=2.;
+ matrix(iknot41+3, offsKnot)=6.*dxm;
+
+ matrix(iknot4+2, offsKnot)=-2.;
+ matrix(iknot4+3, offsKnot)=-6.*dxp;
+ }
+
+// sparse matrix to do fit
+
+ TMatrixDSparse smatrix(matrix);
+ TDecompSparse svd(smatrix,0);
+ Bool_t ok;
+ const TVectorD results = svd.Solve(values,ok);
+
+ for (Int_t iknot = 0; iknot<nknots-1; iknot++){
+
+ Double_t dxm = -(fX[iknot+1]-fX[iknot])*0.5;
+
+ fY0[iknot] = results(4*iknot)+ results(4*iknot+1)*dxm+results(4*iknot+2)*dxm*dxm+
+ results(4*iknot+3)*dxm*dxm*dxm;
+
+ fY1[iknot] = results(4*iknot+1)+2.*results(4*iknot+2)*dxm+
+ 3*results(4*iknot+3)*dxm*dxm;
+ }
+ Int_t iknot2= nknots-1;
+ Int_t iknot = nknots-2;
+ Double_t dxm = (fX[iknot2]-fX[iknot2-1])*0.5;
+
+ fY0[iknot2] = results(4*iknot)+ results(4*iknot+1)*dxm+results(4*iknot+2)*dxm*dxm+
+ results(4*iknot+3)*dxm*dxm*dxm;
+
+ fY1[iknot2] = results(4*iknot+1)+2.*results(4*iknot+2)*dxm+
+ 3*results(4*iknot+3)*dxm*dxm;
+
+ delete pmatrix;
+ delete pvalues;
+
+}
+
+
+
+
+
+void AliSplineFit::MakeKnots0(TGraph * graph, Double_t maxdelta, Int_t minpoints){
+ //
+ // make knots - restriction max distance and minimum points
+ //
+
+ Int_t npoints = graph->GetN();
+ Double_t *xknots = new Double_t[npoints];
+ Int_t nknots =0;
+ Int_t ipoints =0;
+ //
+ // generate knots
+ //
+ for (Int_t ip=0;ip<npoints;ip++){
+ if (graph->GetX()[ip]-xknots[nknots-1]>maxdelta && ipoints>minpoints){
+ xknots[nknots] = graph->GetX()[ip];
+ ipoints=1;
+ nknots++;
+ }
+ ipoints++;
+ }
+ if (npoints-ipoints>minpoints){
+ xknots[nknots] = graph->GetX()[npoints-1];
+ nknots++;
+ }else{
+ xknots[nknots-1] = graph->GetX()[npoints-1];
+ }
+
+ fN = nknots;
+ fX = new Double_t[nknots];
+ fY0 = new Double_t[nknots];
+ fY1 = new Double_t[nknots];
+ fChi2I= new Double_t[nknots];
+ for (Int_t i=0; i<nknots; i++) fX[i]= xknots[i];
+ delete [] xknots;
+}
+
+
+
+
+void AliSplineFit::MakeSmooth(TGraph * graph, Float_t ratio, char * type){
+ //
+ // Interface to GraphSmooth
+ //
+
+ TGraphSmooth smooth;
+ Int_t npoints2 = TMath::Nint(graph->GetN()*ratio);
+ TGraph * graphT0 = smooth.SmoothKern(graph,type,ratio);
+ if (!graphT0) return;
+ TGraph graphT1(npoints2);
+ for (Int_t ipoint=0; ipoint<npoints2; ipoint++){
+ Int_t pointS = TMath::Nint(ipoint/ratio);
+ if (ipoint==npoints2-1) pointS=graph->GetN()-1;
+ graphT1.SetPoint(ipoint, graphT0->GetX()[pointS] , graphT0->GetY()[pointS]);
+ }
+ TSpline3 spline2("spline", &graphT1);
+ Update(&spline2, npoints2);
+}
+
+
+void AliSplineFit::Update(TSpline3 *spline, Int_t nknots){
+ //
+ //
+ //
+
+ fN = nknots;
+ fX = new Double_t[nknots];
+ fY0 = new Double_t[nknots];
+ fY1 = new Double_t[nknots];
+ Double_t d0, d1;
+ fChi2I= 0;
+ for (Int_t i=0; i<nknots; i++) {
+ spline->GetCoeff(i,fX[i],fY0[i], fY1[i],d0,d1);
+ }
+}
+
+
+
+
+void AliSplineFit::Test(Int_t npoints, Int_t ntracks, Float_t snoise){
+ //
+ // test function
+ //
+
+ AliSplineFit fit;
+ AliSplineFit fitS;
+ TGraph * graph0=0;
+ TGraph * graph1=0;
+
+ TTreeSRedirector *pcstream = new TTreeSRedirector("TestSmooth.root");
+ for (Int_t i=0; i<ntracks; i++){
+ graph0 = AliSplineFit::GenerGraph(npoints,0.05,0,0,1,0);
+ graph1 = AliSplineFit::GenerNoise(graph0,snoise);
+ fit.InitKnots(graph1, 10,10, 0.00);
+ TGraph *d0 = fit.MakeDiff(graph0);
+ TGraph *g0 = fit.MakeGraph(0,1,1000,0);
+ fit.SplineFit(2);
+ TH1F * h2 = fit.MakeDiffHisto(graph0);
+ TGraph *d2 = fit.MakeDiff(graph0);
+ TGraph *g2 = fit.MakeGraph(0,1,1000,0);
+ fit.SplineFit(1);
+ TH1F * h1 = fit.MakeDiffHisto(graph0);
+ TGraph *d1 = fit.MakeDiff(graph0);
+ TGraph *g1 = fit.MakeGraph(0,1,1000,0);
+
+ Float_t ratio = Float_t(fit.fN)/Float_t(npoints);
+ fitS.MakeSmooth(graph1,ratio,"box");
+ TGraph *dS = fitS.MakeDiff(graph0);
+ TGraph *gS = fit.MakeGraph(0,1,1000,0);
+
+ TH1F * hS = fitS.MakeDiffHisto(graph0);
+ Double_t mean2 = h2->GetMean();
+ Double_t sigma2 = h2->GetRMS();
+ Double_t mean1 = h1->GetMean();
+ Double_t sigma1 = h1->GetRMS();
+ Double_t meanS = hS->GetMean();
+ Double_t sigmaS = hS->GetRMS();
+ char fname[100];
+ if (fit.fN<20){
+ sprintf(fname,"pol%d",fit.fN);
+ }else{
+ sprintf(fname,"pol%d",19);
+ }
+ TF1 fpol("fpol",fname);
+ graph1->Fit(&fpol);
+ TGraph dpol(*graph1);
+ TGraph gpol(*graph1);
+ for (Int_t ipoint=0; ipoint<graph1->GetN(); ipoint++){
+ dpol.GetY()[ipoint]= graph0->GetY()[ipoint]-
+ fpol.Eval(graph0->GetX()[ipoint]);
+ gpol.GetY()[ipoint]= fpol.Eval(graph0->GetX()[ipoint]);
+ }
+ (*pcstream)<<"Test"<<
+ "Event="<<i<<
+ "Graph0.="<<graph0<<
+ "Graph1.="<<graph1<<
+ "G0.="<<g0<<
+ "G1.="<<g1<<
+ "G2.="<<g2<<
+ "GS.="<<gS<<
+ "GP.="<<&gpol<<
+ "D0.="<<d0<<
+ "D1.="<<d1<<
+ "D2.="<<d2<<
+ "DS.="<<dS<<
+ "DP.="<<&dpol<<
+ "Npoints="<<fit.fN<<
+ "Mean1="<<mean1<<
+ "Mean2="<<mean2<<
+ "MeanS="<<meanS<<
+ "Sigma1="<<sigma1<<
+ "Sigma2="<<sigma2<<
+ "SigmaS="<<sigmaS<<
+ "\n";
+
+ delete graph0;
+ delete graph1;
+ delete g1;
+ delete g2;
+ delete gS;
+ delete h1;
+ delete h2;
+ delete hS;
+ }
+ delete pcstream;
+}
git://git.uio.no / u / mrichter / AliRoot.git / commitdiff