CbmRichRingFitterCOPLight.h

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#ifndef CBM_RICH_RING_FITTER_COP_LIGHT
#define CBM_RICH_RING_FITTER_COP_LIGHT 1

#include <vector>
#include "CbmRichRingLight.h"
#include <cmath>

class CbmRichRingFitterCOPLight
{
public:

   CbmRichRingFitterCOPLight(){
    fHitX.resize(MAX_NOF_HITS_IN_RING);
    fHitY.resize(MAX_NOF_HITS_IN_RING);
   }
   virtual ~CbmRichRingFitterCOPLight(){
     fHitX.clear();
     fHitY.clear();
   }
   void DoFit(CbmRichRingLight *ring);

private:
   void CalcChi2(CbmRichRingLight* ring);

  static const int MAX_NOF_HITS_IN_RING = 200;
  std::vector<float> fHitX;
  std::vector<float> fHitY;
  int fNofHits;
}; //class

#endif

inline void CbmRichRingFitterCOPLight::DoFit(CbmRichRingLight *ring)
{
  fNofHits = ring->GetNofHits();
  if (fNofHits < 3) {
    ring->SetRadius(0.);
    ring->SetCenterX(0.);
    ring->SetCenterY(0.);
    return;
  }

  if (fNofHits >= MAX_NOF_HITS_IN_RING) {
    //cout << "-E- CbmRichRingFitterCOP::DoFit() - Too many hits in the ring:"
    //<<fNofHits <<endl;
    ring->SetRadius(0.);
    ring->SetCenterX(0.);
    ring->SetCenterY(0.);
    return;
  }

  for (int i = 0; i < fNofHits; i++) {
    fHitX[i] = ring->GetHit(i).fX;
    fHitY[i] = ring->GetHit(i).fY;
  }

  float radius = 0.;
  float centerX = 0.;
  float centerY = 0.;

  int iterMax = 4;
  float Xi, Yi, Zi;
  float M0, Mx, My, Mz, Mxy, Mxx, Myy, Mxz, Myz, Mzz, Mxz2, Myz2, Cov_xy;
  float A0, A1, A2, A22;
  float epsilon = 0.00001;
  float Dy, xnew, xold, ynew, yold = 10000000.;

  M0 = fNofHits;
  Mx = My = 0.;

  //calculate center of gravity
  for (int i = 0; i < fNofHits; i++) {
    Mx += fHitX[i];
    My += fHitY[i];
  }
  Mx /= M0;
  My /= M0;

  //computing moments (note: all moments are normed, i.e. divided by N)
  Mxx = Myy = Mxy = Mxz = Myz = Mzz = 0.;

  for (int i = 0; i < fNofHits; i++) {
    Xi = fHitX[i] - Mx; //transform to center of gravity coordinate system
    Yi = fHitY[i] - My;
    Zi = Xi * Xi + Yi * Yi;

    Mxy += Xi * Yi;
    Mxx += Xi * Xi;
    Myy += Yi * Yi;
    Mxz += Xi * Zi;
    Myz += Yi * Zi;
    Mzz += Zi * Zi;
  }
  Mxx /= M0;
  Myy /= M0;
  Mxy /= M0;
  Mxz /= M0;
  Myz /= M0;
  Mzz /= M0;

  //computing the coefficients of the characteristic polynomial
  Mz = Mxx + Myy;
  Cov_xy = Mxx * Myy - Mxy * Mxy;
  Mxz2 = Mxz * Mxz;
  Myz2 = Myz * Myz;

  A2 = 4. * Cov_xy - 3. * Mz * Mz - Mzz;
  A1 = Mzz * Mz + 4. * Cov_xy * Mz - Mxz2 - Myz2 - Mz * Mz * Mz;
  A0 = Mxz2 * Myy + Myz2 * Mxx - Mzz * Cov_xy - 2. * Mxz * Myz * Mxy + Mz
      * Mz * Cov_xy;

  A22 = A2 + A2;
  xnew = 0.;

  //Newton's method starting at x=0
  int iter;
  for (iter = 0; iter < iterMax; iter++) {
    ynew = A0 + xnew * (A1 + xnew * (A2 + 4. * xnew * xnew));

    if (fabs(ynew) > fabs(yold)) {
      //  printf("Newton2 goes wrong direction: ynew=%f  yold=%f\n",ynew,yold);
      xnew = 0.;
      break;
    }

    Dy = A1 + xnew * (A22 + 16. * xnew * xnew);
    xold = xnew;
    xnew = xold - ynew / Dy;
    //cout << " xnew = " << xnew ;
    if (xnew == 0 || fabs((xnew - xold) / xnew) < epsilon){
      //cout << "iter = " << iter << " N = " << fNhits << endl;
      break;
    }
  }

  //if (iter == iterMax - 1) {
    //  printf("Newton2 does not converge in %d iterations\n",iterMax);
  //  xnew = 0.;
  //}

  //computing the circle parameters
  float GAM = -Mz - xnew - xnew;
  float DET = xnew * xnew - xnew * Mz + Cov_xy;
  if (DET != 0.) {
    centerX = (Mxz * (Myy - xnew) - Myz * Mxy) / DET / 2.;
    centerY = (Myz * (Mxx - xnew) - Mxz * Mxy) / DET / 2.;
    radius = sqrt(centerX * centerX + centerY * centerY - GAM);
    centerX += Mx;
    centerY += My;
  } else {
    centerX = 0.;
    centerY = 0.;
    radius = 0.;
  }

  ring->SetRadius(radius);
  ring->SetCenterX(centerX);
  ring->SetCenterY(centerY);

  CalcChi2(ring);
}

inline void CbmRichRingFitterCOPLight::CalcChi2(CbmRichRingLight* pRing)
{
    int fNhits=pRing->GetNofHits();

    if (fNhits < 4) {
      pRing->SetChi2(-1.);
      return;
    }

    float Xd2, Yd2;
    float chi2 = 0.;

    float Radius  = pRing->GetRadius();
    float Xcenter = pRing->GetCenterX();
    float Ycenter = pRing->GetCenterY();

    for (int i = 0; i < fNhits; i++) {
      Xd2 = Xcenter - fHitX[i];
    Yd2 = Ycenter - fHitY[i];
    Xd2 *= Xd2;
    Yd2 *= Yd2;

    float d = sqrt( Xd2 + Yd2 ) - Radius;
        chi2 += d*d;
    }

    pRing->SetChi2(chi2);
}