1 /**************************************************************************
2 * Copyright(c) 2006-07, ALICE Experiment at CERN, All rights reserved. *
4 * Author: The ALICE Off-line Project. *
5 * Contributors are mentioned in the code where appropriate. *
7 * Permission to use, copy, modify and distribute this software and its *
8 * documentation strictly for non-commercial purposes is hereby granted *
9 * without fee, provided that the above copyright notice appears in all *
10 * copies and that both the copyright notice and this permission notice *
11 * appear in the supporting documentation. The authors make no claims *
12 * about the suitability of this software for any purpose. It is *
13 * provided "as is" without express or implied warranty. *
14 **************************************************************************/
16 //-------------------------------------------------------------------------
17 // Implementation of the AliSplineFit class
18 // The class performs a spline fit on an incoming TGraph. The graph is
19 // divided into several parts (identified by knots between each part).
20 // Spline fits are performed on each part. According to user parameters,
21 // the function, first and second derivative are requested to be continuous
23 // Origin: Marian Ivanov, CERN, Marian.Ivanov@cern.ch
24 // Adjustments by Haavard Helstrup, Haavard.Helstrup@cern.ch
25 //-------------------------------------------------------------------------
28 #include "AliSplineFit.h"
30 ClassImp(AliSplineFit)
32 TLinearFitter* AliSplineFit::fitterStatic()
34 static TLinearFitter* fit = new TLinearFitter(4,"pol3","");
38 AliSplineFit::AliSplineFit() :
56 // Default constructor
62 AliSplineFit::AliSplineFit(const AliSplineFit& source) :
64 fBDump (source.fBDump),
65 fGraph (source.fGraph),
67 fMinPoints (source.fMinPoints),
68 fSigma (source.fSigma),
69 fMaxDelta (source.fMaxDelta),
79 fChi2I (source.fChi2I)
84 fIndex = new Int_t[fN0];
85 fParams = new TClonesArray("TVectorD",fN0);
86 fCovars = new TClonesArray("TMatrixD",fN0);
87 fParams = (TClonesArray*)source.fParams->Clone();
88 fCovars = (TClonesArray*)source.fCovars->Clone();
89 for (Int_t i=0; i<fN0; i++) fIndex[i] = source.fIndex[i];
91 fX = new Double_t[fN];
92 fY0 = new Double_t[fN];
93 fY1 = new Double_t[fN];
94 fChi2I = new Double_t[fN];
95 for (Int_t i=0; i<fN; i++){
97 fY0[i] = source.fY0[i];
98 fY1[i] = source.fY1[i];
99 fChi2I[i] = source.fChi2I[i];
102 AliSplineFit& AliSplineFit::operator=(const AliSplineFit& source){
104 // assignment operator
106 if (&source == this) return *this;
109 // reassign memory as previous fit could have a different size
112 if ( fN0 != source.fN0) {
119 fIndex = new Int_t[fN0];
120 fParams = new TClonesArray("TVectorD",fN0);
121 fCovars = new TClonesArray("TMatrixD",fN0);
123 if ( fN != source.fN) {
130 fX = new Double_t[fN];
131 fY0 = new Double_t[fN];
132 fY1 = new Double_t[fN];
133 fChi2I = new Double_t[fN];
136 // use copy constructor (without reassigning memory) to copy values
138 new (this) AliSplineFit(source);
144 AliSplineFit::~AliSplineFit(){
146 // destructor. Don't delete fGraph, as this normally comes as input parameter
157 Double_t AliSplineFit::Eval(Double_t x, Int_t deriv) const{
159 // evaluate value at x
160 // deriv = 0: function value
161 // = 1: first derivative
162 // = 2: 2nd derivative
163 // = 3: 3rd derivative
165 // a2 = -(3*a0 -3*b0 + 2*a1*dx +b1*dx)/(dx*dx)
166 // a3 = -(-2*a0+2*b0 - a1*dx - b1*dx)/(dx*dx*dx)
168 Int_t index = TMath::BinarySearch(fN,fX,x);
169 if (index<0) index =0;
170 if (index>fN-2) index =fN-2;
172 Double_t dx = x-fX[index];
173 Double_t dxc = fX[index+1]-fX[index];
174 if (dxc<=0) return fY0[index];
175 Double_t y0 = fY0[index];
176 Double_t y1 = fY1[index];
177 Double_t y01 = fY0[index+1];
178 Double_t y11 = fY1[index+1];
179 Double_t y2 = -(3.*y0-3.*y01+2*y1*dxc+y11*dxc)/(dxc*dxc);
180 Double_t y3 = -(-2.* y0 + 2*y01 - y1*dxc - y11*dxc) /(dxc*dxc*dxc);
181 Double_t val = y0+y1*dx+y2*dx*dx+y3*dx*dx*dx;
182 if (deriv==1) val = y1+2.*y2*dx+3.*y3*dx*dx;
183 if (deriv==2) val = 2.*y2+6.*y3*dx;
184 if (deriv==3) val = 6*y3;
189 TGraph * AliSplineFit::GenerGraph(Int_t npoints, Double_t fraction, Double_t s1, Double_t s2, Double_t s3, Int_t der){
191 // generate random graph
194 // s1, s2, s3 - sigma of derivative
197 Double_t *value = new Double_t[npoints];
198 Double_t *time = new Double_t[npoints];
199 Double_t d0=0, d1=0,d2=0,d3=0;
202 for(Int_t i=1; i<npoints; i++){
203 Double_t dtime = 1./npoints;
204 Double_t dd1 = dtime;
205 Double_t dd2 = dd1*dd1;
206 Double_t dd3 = dd2*dd1;
207 d0 += d1*dd1 + d2*dd2/2. + d3*dd3/6.;
208 d1 += d2*dd1 +d3*dd2/2;
211 time[i] = time[i-1]+dtime;
212 d1 =(1.-fraction)*d1+fraction*(gRandom->Exp(s1))*(gRandom->Rndm()-0.5);
213 d2 =(1.-fraction)*d2+fraction*(gRandom->Exp(s2))*(gRandom->Rndm()-0.5);
214 d3 =(1.-fraction)*d3+fraction*(gRandom->Exp(s3))*(gRandom->Rndm()-0.5);
215 if (gRandom->Rndm()<fraction) d3 =(1.-fraction)*d3+fraction*(gRandom->BreitWigner(0,s3));
217 Double_t dmean = (value[npoints-1]-value[0])/(time[npoints-1]-time[0]);
218 Double_t min = value[0];
219 Double_t max = value[0];
220 for (Int_t i=0; i<npoints; i++){
221 value[i] = value[i]-dmean*(time[i]-time[0]);
222 if (value[i]<min) min=value[i];
223 if (value[i]>max) max=value[i];
226 for (Int_t i=0; i<npoints; i++){
227 value[i] = (value[i]-min)/(max-min);
229 if (der==1) for (Int_t i=1; i<npoints; i++){
230 value[i-1] = (value[i]-value[i-1])/(time[i]-time[i-1]);
233 TGraph * graph = new TGraph(npoints,time,value);
241 TGraph * AliSplineFit::GenerNoise(TGraph * graph0, Double_t sigma0){
243 // add noise to graph
246 Int_t npoints=graph0->GetN();
247 Double_t *value = new Double_t[npoints];
248 Double_t *time = new Double_t[npoints];
249 for(Int_t i=0; i<npoints; i++){
250 time[i] = graph0->GetX()[i];
251 value[i] = graph0->GetY()[i]+gRandom->Gaus(0,sigma0);
253 TGraph * graph = new TGraph(npoints,time,value);
261 TGraph * AliSplineFit::MakeGraph(Double_t xmin, Double_t xmax, Int_t npoints, Int_t deriv) const {
263 // if npoints<=0 draw derivative
268 if (deriv<=0) return new TGraph(fN,fX,fY0);
269 if (deriv==1) return new TGraph(fN,fX,fY1);
270 if (deriv>2) return new TGraph(fN-1,fX,fChi2I);
272 Double_t * x = new Double_t[npoints+1];
273 Double_t * y = new Double_t[npoints+1];
274 for (Int_t ip=0; ip<=npoints; ip++){
275 x[ip] = xmin+ (xmax-xmin)*(Double_t(ip)/Double_t(npoints));
276 y[ip] = Eval(x[ip],deriv);
279 graph = new TGraph(npoints,x,y);
285 TGraph * AliSplineFit::MakeDiff(TGraph * graph0) const {
287 // Make graph of difference to reference graph
290 Int_t npoints=graph0->GetN();
292 Double_t * x = new Double_t[npoints];
293 Double_t * y = new Double_t[npoints];
294 for (Int_t ip=0; ip<npoints; ip++){
295 x[ip] = graph0->GetX()[ip];
296 y[ip] = Eval(x[ip],0)-graph0->GetY()[ip];
298 graph = new TGraph(npoints,x,y);
305 TH1F * AliSplineFit::MakeDiffHisto(TGraph * graph0) const {
307 // Make histogram of difference to reference graph
310 Int_t npoints=graph0->GetN();
311 Float_t min=1e38,max=-1e38;
312 for (Int_t ip=0; ip<npoints; ip++){
313 Double_t x = graph0->GetX()[ip];
314 Double_t y = Eval(x,0)-graph0->GetY()[ip];
324 TH1F *his = new TH1F("hdiff","hdiff", 100, min, max);
325 for (Int_t ip=0; ip<npoints; ip++){
326 Double_t x = graph0->GetX()[ip];
327 Double_t y = Eval(x,0)-graph0->GetY()[ip];
336 void AliSplineFit::InitKnots(TGraph * graph, Int_t min, Int_t iter, Double_t maxDelta){
338 // initialize knots + estimate sigma of noise + make initial parameters
342 const Double_t kEpsilon = 1.e-7;
345 fMaxDelta = maxDelta;
346 Int_t npoints = fGraph->GetN();
348 // Make simple spline if too few points in graph
350 if (npoints < fMinPoints ) {
355 fN0 = (npoints/fNmin)+1;
356 Float_t delta = Double_t(npoints)/Double_t(fN0-1);
358 fParams = new TClonesArray("TVectorD",fN0);
359 fCovars = new TClonesArray("TMatrixD",fN0);
360 fIndex = new Int_t[fN0];
361 TLinearFitter fitterLocal(4,"pol3"); // local fitter
365 Double_t yMin=graph->GetY()[0];
366 Double_t yMax=graph->GetY()[0];
368 for (Int_t iKnot=0; iKnot<fN0; iKnot++){
369 Int_t index0 = TMath::Nint(Double_t(iKnot)*Double_t(delta));
370 Int_t index1 = TMath::Min(TMath::Nint(Double_t(iKnot+1)*Double_t(delta)),npoints-1);
371 Int_t indexM = (iKnot>0) ? fIndex[iKnot-1]:index0;
372 fIndex[iKnot]=TMath::Min(index0, npoints-1);
373 Float_t startX =graph->GetX()[fIndex[iKnot]];
375 for (Int_t ipoint=indexM; ipoint<index1; ipoint++){
376 Double_t dxl =graph->GetX()[ipoint]-startX;
377 Double_t y = graph->GetY()[ipoint];
380 fitterLocal.AddPoint(&dxl,y,1);
384 sigma2 += fitterLocal.GetChisquare()/Double_t((index1-indexM)-4.);
385 TMatrixD * covar = new ((*fCovars)[iKnot]) TMatrixD(4,4);
386 TVectorD * param = new ((*fParams)[iKnot]) TVectorD(4);
387 fitterLocal.GetParameters(*param);
388 fitterLocal.GetCovarianceMatrix(*covar);
389 fitterLocal.ClearPoints();
391 fSigma =TMath::Sqrt(sigma2/Double_t(fN0)); // mean sigma
392 Double_t tDiff = ((yMax-yMin)+TMath::Abs(yMax)+TMath::Abs(yMin))*kEpsilon;
393 fSigma += tDiff+fMaxDelta/TMath::Sqrt(npoints);
395 for (Int_t iKnot=0; iKnot<fN0; iKnot++){
396 TMatrixD & cov = *((TMatrixD*)fCovars->At(iKnot));
402 for (Int_t iKnot=0; iKnot<fN0; iKnot++) if (fIndex[iKnot]>=0) fN++;
403 fX = new Double_t[fN];
404 fY0 = new Double_t[fN];
405 fY1 = new Double_t[fN];
406 fChi2I = new Double_t[fN];
408 for (Int_t i=0; i<fN0; i++){
409 if (fIndex[i]<0) continue;
411 printf("AliSplineFit::InitKnots: Knot number > Max knot number\n");
414 TVectorD * param = (TVectorD*) fParams->At(i);
415 fX[iKnot] = fGraph->GetX()[fIndex[i]];
416 fY0[iKnot] = (*param)(0);
417 fY1[iKnot] = (*param)(1);
424 Int_t AliSplineFit::OptimizeKnots(Int_t nIter){
428 const Double_t kMaxChi2= 5;
430 TTreeSRedirector cstream("SplineIter.root");
431 for (Int_t iIter=0; iIter<nIter; iIter++){
432 if (fBDump) cstream<<"Fit"<<
437 for (Int_t iKnot=1; iKnot<fN0-1; iKnot++){
438 if (fIndex[iKnot]<0) continue; //disabled knot
439 Double_t chi2 = CheckKnot(iKnot);
440 Double_t startX = fGraph->GetX()[fIndex[iKnot]];
442 TMatrixD * covar = (TMatrixD*)fCovars->At(iKnot);
443 TVectorD * param = (TVectorD*)fParams->At(iKnot);
453 if (chi2>kMaxChi2) { nKnots++;continue;}
455 Int_t iPrevious=iKnot-1;
456 Int_t iNext =iKnot+1;
457 while (fIndex[iPrevious]<0) iPrevious--;
458 while (fIndex[iNext]<0) iNext++;
459 RefitKnot(iPrevious);
462 while (iKnot<fN0-1&& fIndex[iKnot]<0) iKnot++;
469 Bool_t AliSplineFit::RefitKnot(Int_t iKnot){
474 Int_t iPrevious=(iKnot>0) ?iKnot-1: 0;
475 Int_t iNext =(iKnot<fN0)?iKnot+1: fN0-1;
476 while (iPrevious>0&&fIndex[iPrevious]<0) iPrevious--;
477 while (iNext<fN0&&fIndex[iNext]<0) iNext++;
478 if (iPrevious<0) iPrevious=0;
479 if (iNext>=fN0) iNext=fN0-1;
481 Double_t startX = fGraph->GetX()[fIndex[iKnot]];
482 AliSplineFit::fitterStatic()->ClearPoints();
483 Int_t indPrev = fIndex[iPrevious];
484 Int_t indNext = fIndex[iNext];
485 Double_t *graphX = fGraph->GetX();
486 Double_t *graphY = fGraph->GetY();
488 // make arrays for points to fit (to save time)
490 Int_t nPoints = indNext-indPrev;
491 Double_t *xPoint = new Double_t[3*nPoints];
492 Double_t *yPoint = &xPoint[nPoints];
493 Double_t *ePoint = &xPoint[2*nPoints];
495 for (Int_t iPoint=indPrev; iPoint<indNext; iPoint++, indVec++){
496 Double_t dxl = graphX[iPoint]-startX;
497 Double_t y = graphY[iPoint];
498 xPoint[indVec] = dxl;
500 ePoint[indVec] = fSigma;
501 // ePoint[indVec] = fSigma+TMath::Abs(y)*kEpsilon;
502 // AliSplineFit::fitterStatic.AddPoint(&dxl,y,fSigma+TMath::Abs(y)*kEpsilon);
504 AliSplineFit::fitterStatic()->AssignData(nPoints,1,xPoint,yPoint,ePoint);
505 AliSplineFit::fitterStatic()->Eval();
507 // delete temporary arrays
511 TMatrixD * covar = (TMatrixD*)fCovars->At(iKnot);
512 TVectorD * param = (TVectorD*)fParams->At(iKnot);
513 AliSplineFit::fitterStatic()->GetParameters(*param);
514 AliSplineFit::fitterStatic()->GetCovarianceMatrix(*covar);
519 Float_t AliSplineFit::CheckKnot(Int_t iKnot){
524 Int_t iPrevious=iKnot-1;
525 Int_t iNext =iKnot+1;
526 while (fIndex[iPrevious]<0) iPrevious--;
527 while (fIndex[iNext]<0) iNext++;
528 TVectorD &pPrevious = *((TVectorD*)fParams->At(iPrevious));
529 TVectorD &pNext = *((TVectorD*)fParams->At(iNext));
530 TVectorD &pKnot = *((TVectorD*)fParams->At(iKnot));
531 TMatrixD &cPrevious = *((TMatrixD*)fCovars->At(iPrevious));
532 TMatrixD &cNext = *((TMatrixD*)fCovars->At(iNext));
533 TMatrixD &cKnot = *((TMatrixD*)fCovars->At(iKnot));
534 Double_t xPrevious = fGraph->GetX()[fIndex[iPrevious]];
535 Double_t xNext = fGraph->GetX()[fIndex[iNext]];
536 Double_t xKnot = fGraph->GetX()[fIndex[iKnot]];
538 // extra variables introduced to save processing time
540 Double_t dxc = xNext-xPrevious;
541 Double_t invDxc = 1./dxc;
542 Double_t invDxc2 = invDxc*invDxc;
543 TMatrixD tPrevious(4,4);
546 tPrevious(0,0) = 1; tPrevious(1,1) = 1;
547 tPrevious(2,0) = -3.*invDxc2;
548 tPrevious(2,1) = -2.*invDxc;
549 tPrevious(3,0) = 2.*invDxc2*invDxc;
550 tPrevious(3,1) = 1.*invDxc2;
551 tNext(2,0) = 3.*invDxc2; tNext(2,1) = -1*invDxc;
552 tNext(3,0) = -2.*invDxc2*invDxc; tNext(3,1) = 1.*invDxc2;
553 TMatrixD tpKnot(4,4);
554 TMatrixD tpNext(4,4);
555 Double_t dx = xKnot-xPrevious;
556 tpKnot(0,0) = 1; tpKnot(1,1) = 1; tpKnot(2,2) = 1; tpKnot(3,3) = 1;
557 tpKnot(0,1) = dx; tpKnot(0,2) = dx*dx; tpKnot(0,3) = dx*dx*dx;
558 tpKnot(1,2) = 2.*dx; tpKnot(1,3) = 3.*dx*dx;
560 Double_t dxn = xNext-xPrevious;
561 tpNext(0,0) = 1; tpNext(1,1) = 1; tpNext(2,2) = 1; tpNext(3,3) = 1;
562 tpNext(0,1) = dxn; tpNext(0,2) = dxn*dxn; tpNext(0,3) = dxn*dxn*dxn;
563 tpNext(1,2) = 2.*dxn; tpNext(1,3) = 3.*dxn*dxn;
564 tpNext(2,3) = 3.*dxn;
567 // matrix and vector at previous
570 TVectorD sPrevious = tPrevious*pPrevious+tNext*pNext;
571 TVectorD sKnot = tpKnot*sPrevious;
572 TVectorD sNext = tpNext*sPrevious;
574 TMatrixD csPrevious00(tPrevious, TMatrixD::kMult,cPrevious);
575 csPrevious00 *= tPrevious.T();
576 TMatrixD csPrevious01(tNext,TMatrixD::kMult,cNext);
577 csPrevious01*=tNext.T();
578 TMatrixD csPrevious(csPrevious00,TMatrixD::kPlus,csPrevious01);
579 TMatrixD csKnot(tpKnot,TMatrixD::kMult,csPrevious);
581 TMatrixD csNext(tpNext,TMatrixD::kMult,csPrevious);
584 TVectorD dPrevious = pPrevious-sPrevious;
585 TVectorD dKnot = pKnot-sKnot;
586 TVectorD dNext = pNext-sNext;
590 prec(0,0) = (fMaxDelta*fMaxDelta);
591 prec(1,1) = prec(0,0)*invDxc2;
592 prec(2,2) = prec(1,1)*invDxc2;
593 prec(3,3) = prec(2,2)*invDxc2;
595 // prec(0,0) = (fMaxDelta*fMaxDelta);
596 // prec(1,1) = (fMaxDelta*fMaxDelta)/(dxc*dxc);
597 // prec(2,2) = (fMaxDelta*fMaxDelta)/(dxc*dxc*dxc*dxc);
598 // prec(3,3) = (fMaxDelta*fMaxDelta)/(dxc*dxc*dxc*dxc*dxc*dxc);
600 csPrevious+=cPrevious;
603 Double_t chi2P = dPrevious*(csPrevious*dPrevious);
608 Double_t chi2K = dKnot*(csKnot*dKnot);
613 Double_t chi2N = dNext*(csNext*dNext);
615 return (chi2P+chi2K+chi2N)/8.;
620 void AliSplineFit::SplineFit(Int_t nder){
622 // Cubic spline fit of graph
625 // nder<0 - no continuity requirement
626 // =0 - continous 0 derivative
627 // =1 - continous 1 derivative
628 // >1 - continous 2 derivative
631 TGraph * graph = fGraph;
634 if (nknots < 2 ) return;
635 Int_t npoints = graph->GetN();
636 if (npoints < fMinPoints ) return;
640 // each knot 4 parameters
642 TMatrixD *pmatrix = 0;
643 TVectorD *pvalues = 0;
645 pmatrix = new TMatrixD(4*(nknots-1)+3*(nknots-2), 4*(nknots-1)+3*(nknots-2));
646 pvalues = new TVectorD(4*(nknots-1)+3*(nknots-2));
649 pmatrix = new TMatrixD(4*(nknots-1)+2*(nknots-2), 4*(nknots-1)+2*(nknots-2));
650 pvalues = new TVectorD(4*(nknots-1)+2*(nknots-2));
653 pmatrix = new TMatrixD(4*(nknots-1)+1*(nknots-2), 4*(nknots-1)+1*(nknots-2));
654 pvalues = new TVectorD(4*(nknots-1)+1*(nknots-2));
657 pmatrix = new TMatrixD(4*(nknots-1)+0*(nknots-2), 4*(nknots-1)+0*(nknots-2));
658 pvalues = new TVectorD(4*(nknots-1)+0*(nknots-2));
662 TMatrixD &matrix = *pmatrix;
663 TVectorD &values = *pvalues;
666 // defined extra variables (current4 etc.) to save processing time.
667 // fill normal matrices, then copy to sparse matrix.
669 Double_t *graphX = graph->GetX();
670 Double_t *graphY = graph->GetY();
671 for (Int_t ip=0;ip<npoints;ip++){
672 if (current<nknots-2&&graphX[ip]>fX[current+1]) current++;
673 Double_t xmiddle = (fX[current+1]+fX[current])*0.5;
674 Double_t x1 = graphX[ip]- xmiddle;
680 Double_t y = graphY[ip];
681 Int_t current4 = 4*current;
683 matrix(current4 , current4 )+=1;
684 matrix(current4 , current4+1)+=x1;
685 matrix(current4 , current4+2)+=x2;
686 matrix(current4 , current4+3)+=x3;
688 matrix(current4+1, current4 )+=x1;
689 matrix(current4+1, current4+1)+=x2;
690 matrix(current4+1, current4+2)+=x3;
691 matrix(current4+1, current4+3)+=x4;
693 matrix(current4+2, current4 )+=x2;
694 matrix(current4+2, current4+1)+=x3;
695 matrix(current4+2, current4+2)+=x4;
696 matrix(current4+2, current4+3)+=x5;
698 matrix(current4+3, current4 )+=x3;
699 matrix(current4+3, current4+1)+=x4;
700 matrix(current4+3, current4+2)+=x5;
701 matrix(current4+3, current4+3)+=x6;
703 values(current4 ) += y;
704 values(current4+1) += y*x1;
705 values(current4+2) += y*x2;
706 values(current4+3) += y*x3;
711 Int_t offset =4*(nknots-1)-1;
712 if (nder>=0) for (Int_t iknot = 1; iknot<nknots-1; iknot++){
714 Double_t dxm = (fX[iknot]-fX[iknot-1])*0.5;
715 Double_t dxp = -(fX[iknot+1]-fX[iknot])*0.5;
716 Double_t dxm2 = dxm*dxm;
717 Double_t dxp2 = dxp*dxp;
718 Double_t dxm3 = dxm2*dxm;
719 Double_t dxp3 = dxp2*dxp;
720 Int_t iknot4 = 4*iknot;
721 Int_t iknot41 = 4*(iknot-1);
722 Int_t offsKnot = offset+iknot;
726 // a0[i] = a0m[i-1] + a1m[i-1]*dxm + a2m[i-1]*dxm^2 + a3m[i-1]*dxm^3
727 // a0[i] = a0m[i-0] + a1m[i-0]*dxp + a2m[i-0]*dxp^2 + a3m[i-0]*dxp^3
728 // (a0m[i-1] + a1m[i-1]*dxm + a2m[i-1]*dxm^2 + a3m[i-1]*dxm^3) -
729 // (a0m[i-0] + a1m[i-0]*dxp + a2m[i-0]*dxp^2 + a3m[i-0]*dxp^3) = 0
731 matrix(offsKnot, iknot41 )=1;
732 matrix(offsKnot, iknot4 )=-1;
734 matrix(offsKnot, iknot41+1)=dxm;
735 matrix(offsKnot, iknot4 +1)=-dxp;
737 matrix(offsKnot, iknot41+2)=dxm2;
738 matrix(offsKnot, iknot4 +2)=-dxp2;
740 matrix(offsKnot, iknot41+3)=dxm3;
741 matrix(offsKnot, iknot4 +3)=-dxp3;
743 matrix(iknot41 , offsKnot)=1;
744 matrix(iknot41+1, offsKnot)=dxm;
745 matrix(iknot41+2, offsKnot)=dxm2;
746 matrix(iknot41+3, offsKnot)=dxm3;
747 matrix(iknot4 , offsKnot)=-1;
748 matrix(iknot4+1, offsKnot)=-dxp;
749 matrix(iknot4+2, offsKnot)=-dxp2;
750 matrix(iknot4+3, offsKnot)=-dxp3;
755 offset =4*(nknots-1)-1+(nknots-2);
756 if (nder>=1)for (Int_t iknot = 1; iknot<nknots-1; iknot++){
758 Double_t dxm = (fX[iknot]-fX[iknot-1])*0.5;
759 Double_t dxp = -(fX[iknot+1]-fX[iknot])*0.5;
760 Double_t dxm2 = dxm*dxm;
761 Double_t dxp2 = dxp*dxp;
762 Int_t iknot4 = 4*iknot;
763 Int_t iknot41 = 4*(iknot-1);
764 Int_t offsKnot = offset+iknot;
766 // condition on knot derivation
768 // a0d[i] = a1m[i-1] + 2*a2m[i-1]*dxm + 3*a3m[i-1]*dxm^2
769 // a0d[i] = a1m[i-0] + 2*a2m[i-0]*dxp + 3*a3m[i-0]*dxp^2
772 matrix(offsKnot, iknot41+1)= 1;
773 matrix(offsKnot, iknot4 +1)=-1;
775 matrix(offsKnot, iknot41+2)= 2.*dxm;
776 matrix(offsKnot, iknot4 +2)=-2.*dxp;
778 matrix(offsKnot, iknot41+3)= 3.*dxm2;
779 matrix(offsKnot, iknot4 +3)=-3.*dxp2;
781 matrix(iknot41+1, offsKnot)=1;
782 matrix(iknot41+2, offsKnot)=2.*dxm;
783 matrix(iknot41+3, offsKnot)=3.*dxm2;
785 matrix(iknot4+1, offsKnot)=-1.;
786 matrix(iknot4+2, offsKnot)=-2.*dxp;
787 matrix(iknot4+3, offsKnot)=-3.*dxp2;
792 offset =4*(nknots-1)-1+2*(nknots-2);
793 if (nder>=2) for (Int_t iknot = 1; iknot<nknots-1; iknot++){
795 Double_t dxm = (fX[iknot]-fX[iknot-1])*0.5;
796 Double_t dxp = -(fX[iknot+1]-fX[iknot])*0.5;
797 Int_t iknot4 = 4*iknot;
798 Int_t iknot41 = 4*(iknot-1);
799 Int_t offsKnot = offset+iknot;
801 // condition on knot second derivative
803 // a0dd[i] = 2*a2m[i-1] + 6*a3m[i-1]*dxm
804 // a0dd[i] = 2*a2m[i-0] + 6*a3m[i-0]*dxp
807 matrix(offsKnot, iknot41+2)= 2.;
808 matrix(offsKnot, iknot4 +2)=-2.;
810 matrix(offsKnot, iknot41+3)= 6.*dxm;
811 matrix(offsKnot, iknot4 +3)=-6.*dxp;
813 matrix(iknot41+2, offsKnot)=2.;
814 matrix(iknot41+3, offsKnot)=6.*dxm;
816 matrix(iknot4+2, offsKnot)=-2.;
817 matrix(iknot4+3, offsKnot)=-6.*dxp;
820 // sparse matrix to do fit
822 TMatrixDSparse smatrix(matrix);
823 TDecompSparse svd(smatrix,0);
825 const TVectorD results = svd.Solve(values,ok);
827 for (Int_t iknot = 0; iknot<nknots-1; iknot++){
829 Double_t dxm = -(fX[iknot+1]-fX[iknot])*0.5;
831 fY0[iknot] = results(4*iknot)+ results(4*iknot+1)*dxm+results(4*iknot+2)*dxm*dxm+
832 results(4*iknot+3)*dxm*dxm*dxm;
834 fY1[iknot] = results(4*iknot+1)+2.*results(4*iknot+2)*dxm+
835 3*results(4*iknot+3)*dxm*dxm;
837 Int_t iknot2= nknots-1;
838 Int_t iknot = nknots-2;
839 Double_t dxm = (fX[iknot2]-fX[iknot2-1])*0.5;
841 fY0[iknot2] = results(4*iknot)+ results(4*iknot+1)*dxm+results(4*iknot+2)*dxm*dxm+
842 results(4*iknot+3)*dxm*dxm*dxm;
844 fY1[iknot2] = results(4*iknot+1)+2.*results(4*iknot+2)*dxm+
845 3*results(4*iknot+3)*dxm*dxm;
856 void AliSplineFit::MakeKnots0(TGraph * graph, Double_t maxdelta, Int_t minpoints){
858 // make knots - restriction max distance and minimum points
861 Int_t npoints = graph->GetN();
862 Double_t *xknots = new Double_t[npoints];
868 for (Int_t ip=0;ip<npoints;ip++){
869 if (graph->GetX()[ip]-xknots[nknots-1]>maxdelta && ipoints>minpoints){
870 xknots[nknots] = graph->GetX()[ip];
876 if (npoints-ipoints>minpoints){
877 xknots[nknots] = graph->GetX()[npoints-1];
880 xknots[nknots-1] = graph->GetX()[npoints-1];
884 fX = new Double_t[nknots];
885 fY0 = new Double_t[nknots];
886 fY1 = new Double_t[nknots];
887 fChi2I= new Double_t[nknots];
888 for (Int_t i=0; i<nknots; i++) fX[i]= xknots[i];
895 void AliSplineFit::MakeSmooth(TGraph * graph, Float_t ratio, Option_t * type){
897 // Interface to GraphSmooth
901 Int_t npoints2 = TMath::Nint(graph->GetN()*ratio);
902 TGraph * graphT0 = smooth.SmoothKern(graph,type,ratio);
903 if (!graphT0) return;
904 TGraph graphT1(npoints2);
905 for (Int_t ipoint=0; ipoint<npoints2; ipoint++){
906 Int_t pointS = TMath::Nint(ipoint/ratio);
907 if (ipoint==npoints2-1) pointS=graph->GetN()-1;
908 graphT1.SetPoint(ipoint, graphT0->GetX()[pointS] , graphT0->GetY()[pointS]);
910 TSpline3 spline2("spline", &graphT1);
911 Update(&spline2, npoints2);
915 void AliSplineFit::Update(TSpline3 *spline, Int_t nknots){
921 fX = new Double_t[nknots];
922 fY0 = new Double_t[nknots];
923 fY1 = new Double_t[nknots];
926 for (Int_t i=0; i<nknots; i++) {
927 spline->GetCoeff(i,fX[i],fY0[i], fY1[i],d0,d1);
934 void AliSplineFit::Test(Int_t npoints, Int_t ntracks, Float_t snoise){
944 TTreeSRedirector *pcstream = new TTreeSRedirector("TestSmooth.root");
945 for (Int_t i=0; i<ntracks; i++){
946 graph0 = AliSplineFit::GenerGraph(npoints,0.05,0,0,1,0);
947 graph1 = AliSplineFit::GenerNoise(graph0,snoise);
948 fit.InitKnots(graph1, 10,10, 0.00);
949 TGraph *d0 = fit.MakeDiff(graph0);
950 TGraph *g0 = fit.MakeGraph(0,1,1000,0);
952 TH1F * h2 = fit.MakeDiffHisto(graph0);
953 TGraph *d2 = fit.MakeDiff(graph0);
954 TGraph *g2 = fit.MakeGraph(0,1,1000,0);
956 TH1F * h1 = fit.MakeDiffHisto(graph0);
957 TGraph *d1 = fit.MakeDiff(graph0);
958 TGraph *g1 = fit.MakeGraph(0,1,1000,0);
960 Float_t ratio = Float_t(fit.fN)/Float_t(npoints);
961 fitS.MakeSmooth(graph1,ratio,"box");
962 TGraph *dS = fitS.MakeDiff(graph0);
963 TGraph *gS = fit.MakeGraph(0,1,1000,0);
965 TH1F * hS = fitS.MakeDiffHisto(graph0);
966 Double_t mean2 = h2->GetMean();
967 Double_t sigma2 = h2->GetRMS();
968 Double_t mean1 = h1->GetMean();
969 Double_t sigma1 = h1->GetRMS();
970 Double_t meanS = hS->GetMean();
971 Double_t sigmaS = hS->GetRMS();
974 sprintf(fname,"pol%d",fit.fN);
976 sprintf(fname,"pol%d",19);
978 TF1 fpol("fpol",fname);
980 TGraph dpol(*graph1);
981 TGraph gpol(*graph1);
982 for (Int_t ipoint=0; ipoint<graph1->GetN(); ipoint++){
983 dpol.GetY()[ipoint]= graph0->GetY()[ipoint]-
984 fpol.Eval(graph0->GetX()[ipoint]);
985 gpol.GetY()[ipoint]= fpol.Eval(graph0->GetX()[ipoint]);
987 (*pcstream)<<"Test"<<
1001 "Npoints="<<fit.fN<<
1022 void AliSplineFit::Cleanup(){
1024 // deletes extra information to reduce amount of information stored on the data
1027 // delete fGraph; fGraph=0; // Don't delete fGraph -- input parameter
1028 delete fParams; fParams=0;
1029 delete fCovars; fCovars=0;
1030 delete [] fIndex; fIndex=0;
1031 delete [] fChi2I; fChi2I=0;
1035 void AliSplineFit::CopyGraph() {
1037 // enter graph points directly to fit parameters
1038 // (to bee used when too few points are available)
1040 fN = fGraph->GetN();
1041 fX = new Double_t[fN];
1042 fY0 = new Double_t[fN];
1043 fY1 = new Double_t[fN];
1044 for (Int_t i=0; i<fN; i++ ) {
1045 fX[i] = fGraph->GetX()[i];
1046 fY0[i] = fGraph->GetY()[i];