ThirdHitPredictionFromInvParabola Class Reference

#include <ThirdHitPredictionFromInvParabola.h>

Classes
class	MappedPoint

Public Types
typedef PixelRecoRange< float >	Range
typedef TkRotation< double >	Rotation

Public Member Functions
void	init (const GlobalPoint &P1, const GlobalPoint &P2, double ip, double curv)
Range	operator() (double radius, int charge) const
Range	rangeRPhi (double radius, int charge) const
Range	rangeRPhiSlow (double radius, int charge, int nIter=5) const
	ThirdHitPredictionFromInvParabola (const GlobalPoint &P1, const GlobalPoint &P2, double ip, double curv, double tolerance)

Private Types
typedef MappedPoint< double >	PointUV

Private Member Functions
double	coeffA (double impactParameter, int charge) const
double	coeffB (double impactParameter, int charge) const
PointUV	findPointAtCurve (double radius, int charge, double ip) const
double	ipFromCurvature (double curvature, int charge) const
double	predV (double u, double ip, int charge) const

Private Attributes
PointUV	p1
PointUV	p2
Range	theIpRangeMinus
Range	theIpRangePlus
Rotation	theRotation
double	theTolerance

Detailed Description

Definition at line 24 of file ThirdHitPredictionFromInvParabola.h.

Member Typedef Documentation

typedef MappedPoint<double> ThirdHitPredictionFromInvParabola::PointUV

private

Definition at line 79 of file ThirdHitPredictionFromInvParabola.h.

typedef PixelRecoRange<float> ThirdHitPredictionFromInvParabola::Range

Definition at line 29 of file ThirdHitPredictionFromInvParabola.h.

typedef TkRotation<double> ThirdHitPredictionFromInvParabola::Rotation

Definition at line 28 of file ThirdHitPredictionFromInvParabola.h.

Constructor & Destructor Documentation

ThirdHitPredictionFromInvParabola::ThirdHitPredictionFromInvParabola	(	const GlobalPoint &	P1,
		const GlobalPoint &	P2,
		double	ip,
		double	curv,
		double	tolerance
	)

Definition at line 25 of file ThirdHitPredictionFromInvParabola.cc.

References init().

  : theTolerance(torlerance)
{
  init(P1,P2,ip,fabs(curv));
}

Member Function Documentation

double ThirdHitPredictionFromInvParabola::coeffA ( double  impactParameter, int  charge  ) const

inlineprivate

Definition at line 91 of file ThirdHitPredictionFromInvParabola.h.

References p1, p2, ThirdHitPredictionFromInvParabola::MappedPoint< T >::u(), and ThirdHitPredictionFromInvParabola::MappedPoint< T >::v().

Referenced by findPointAtCurve(), and predV().

{
  double u1u2 = p1.u()*p2.u();
  double du = p2.u() - p1.u();
  double pv = p1.v()*p2.u() - p2.v()*p1.u();
  return -charge*pv/du - u1u2*impactParameter;
}

double ThirdHitPredictionFromInvParabola::coeffB ( double  impactParameter, int  charge  ) const

inlineprivate

Definition at line 100 of file ThirdHitPredictionFromInvParabola.h.

References p1, p2, ThirdHitPredictionFromInvParabola::MappedPoint< T >::u(), and ThirdHitPredictionFromInvParabola::MappedPoint< T >::v().

Referenced by findPointAtCurve(), and predV().

{
  double dv = p2.v() - p1.v();
  double du = p2.u() - p1.u();
  double su = p2.u() + p1.u();
  return charge*dv/du - su*impactParameter;
}

ThirdHitPredictionFromInvParabola::PointUV ThirdHitPredictionFromInvParabola::findPointAtCurve ( double  radius, int  charge, double  ip  ) const

private

Definition at line 61 of file ThirdHitPredictionFromInvParabola.cc.

References funct::A, alpha, coeffA(), coeffB(), delta, csvReporter::r, mathSSE::sqrt(), theRotation, and v.

Referenced by rangeRPhi().

{
  //
  // assume u=(1-alpha^2/2)/r v=alpha/r
  // solve qudratic equation neglecting aplha^4 term
  //
  double A = coeffA(ip,c);
  double B = coeffB(ip,c);

  double overR = 1./r;
  double ipOverR = ip*overR;

  double delta = 1-4*(0.5*B+ipOverR)*(-B+A*r-ipOverR);
  double sqrtdelta = (delta > 0) ? std::sqrt(delta) : 0.;
  double alpha = (c>0)?  (-c+sqrtdelta)/(B+2*ipOverR) :  (-c-sqrtdelta)/(B+2*ipOverR);

  double v = alpha*overR;
  double d2 = overR*overR - v*v;
  double u = (d2 > 0) ? std::sqrt(d2) : 0.;

  return PointUV(u,v,&theRotation);
}

void ThirdHitPredictionFromInvParabola::init	(	const GlobalPoint &	P1,
		const GlobalPoint &	P2,
		double	ip,
		double	curv
	)

Definition at line 34 of file ThirdHitPredictionFromInvParabola.cc.

References abs, PixelRecoRange< T >::intersection(), ipFromCurvature(), p1, p2, PixelRecoRange< T >::sort(), theIpRangeMinus, theIpRangePlus, theRotation, Vector3DBase< T, FrameTag >::unit(), PV3DBase< T, PVType, FrameType >::x(), and PV3DBase< T, PVType, FrameType >::y().

Referenced by ThirdHitPredictionFromInvParabola().

{
//  GlobalVector aX = GlobalVector( P2.x()-P1.x(), P2.y()-P1.y(), 0.).unit();
  GlobalVector aX = GlobalVector( P1.x(), P1.y(), 0.).unit();
  GlobalVector aY( -aX.y(), aX.x(), 0.); 
  GlobalVector aZ( 0., 0., 1.);
  theRotation = Rotation(aX,aY,aZ); 

  p1 = PointUV(Point2D(P1.x(),P1.y()), &theRotation);
  p2 = PointUV(Point2D(P2.x(),P2.y()), &theRotation);

  Range ipRange(-ip, ip); 
  ipRange.sort();
  
  double ipIntyPlus = ipFromCurvature(0.,1);
  double ipCurvPlus = ipFromCurvature(std::abs(curv), 1);
  double ipCurvMinus = ipFromCurvature(std::abs(curv), -1);

  
  Range ipRangePlus = Range(ipIntyPlus, ipCurvPlus); ipRangePlus.sort();
  Range ipRangeMinus = Range(-ipIntyPlus, ipCurvMinus); ipRangeMinus.sort();

  theIpRangePlus  = ipRangePlus.intersection(ipRange);
  theIpRangeMinus = ipRangeMinus.intersection(ipRange);
}

double ThirdHitPredictionFromInvParabola::ipFromCurvature ( double  curvature, int  charge  ) const

private

Definition at line 165 of file ThirdHitPredictionFromInvParabola.cc.

References p1, p2, ThirdHitPredictionFromInvParabola::MappedPoint< T >::u(), and ThirdHitPredictionFromInvParabola::MappedPoint< T >::v().

Referenced by init().

{
  double u1u2 = p1.u()*p2.u();
  double du = p2.u() - p1.u();
  double pv = p1.v()*p2.u() - p2.v()*p1.u();

  double inInf = -charge*pv/(du*u1u2);
  return inInf-curvature/(2.*u1u2);
}

Range ThirdHitPredictionFromInvParabola::operator() ( double  radius, int  charge  ) const

inline

Definition at line 35 of file ThirdHitPredictionFromInvParabola.h.

References rangeRPhi().

{ return rangeRPhi(radius,charge); } 

double ThirdHitPredictionFromInvParabola::predV ( double  u, double  ip, int  charge  ) const

private

Definition at line 178 of file ThirdHitPredictionFromInvParabola.cc.

References coeffA(), coeffB(), and funct::sqr().

Referenced by rangeRPhiSlow().

{
  return -charge*( coeffA(ip,charge) - coeffB(ip,charge)*u - ip*sqr(u));
}

ThirdHitPredictionFromInvParabola::Range ThirdHitPredictionFromInvParabola::rangeRPhi	(	double	radius,
		int	charge
	)		const

Definition at line 85 of file ThirdHitPredictionFromInvParabola.cc.

References PixelRecoRange< T >::empty(), findPointAtCurve(), PixelRecoRange< T >::intersection(), M_PI, PixelRecoRange< T >::max(), PixelRecoRange< T >::min(), Basic2DVector< T >::phi(), csvReporter::r, PixelRecoRange< T >::sort(), theIpRangeMinus, theIpRangePlus, theTolerance, ThirdHitPredictionFromInvParabola::MappedPoint< T >::unmap(), and ThirdHitPredictionFromInvParabola::MappedPoint< T >::v().

Referenced by operator()().

{
  Range predRPhi(1.,-1.);
  Range ip = (charge > 0) ? theIpRangePlus : theIpRangeMinus;

  PointUV pred_tmp1 = findPointAtCurve(radius,charge,ip.min());
  PointUV pred_tmp2 = findPointAtCurve(radius,charge,ip.max());

  double phi1 = pred_tmp1.unmap().phi();
  while ( phi1 >= M_PI) phi1 -= 2*M_PI;
  while ( phi1 < -M_PI) phi1 += 2*M_PI;
  double phi2 = phi1+radius*(pred_tmp2.v()-pred_tmp1.v()); 
  
  if (ip.empty()) {
    Range r1(phi1*radius-theTolerance, phi1*radius+theTolerance); 
    Range r2(phi2*radius-theTolerance, phi2*radius+theTolerance); 
    predRPhi = r1.intersection(r2);
  } else {
    Range r(phi1, phi2); 
    r.sort();
    predRPhi= Range(radius*r.min()-theTolerance, radius*r.max()+theTolerance);
  }

  return predRPhi;
}

ThirdHitPredictionFromInvParabola::Range ThirdHitPredictionFromInvParabola::rangeRPhiSlow	(	double	radius,
		int	charge,
		int	nIter = 5
	)		const

Definition at line 113 of file ThirdHitPredictionFromInvParabola.cc.

References DeDxDiscriminatorTools::charge(), PixelRecoRange< T >::empty(), i, PixelRecoRange< T >::intersection(), M_PI, PixelRecoRange< T >::max(), PixelRecoRange< T >::min(), Basic2DVector< T >::phi(), predV(), csvReporter::r, CosmicsPD_Skims::radius, PixelRecoRange< T >::sort(), funct::sqr(), mathSSE::sqrt(), theIpRangeMinus, theIpRangePlus, theRotation, theTolerance, ThirdHitPredictionFromInvParabola::MappedPoint< T >::unmap(), and v.

{
  Range predRPhi(1.,-1.);

  double invr2 = 1/radius/radius;
  double u = sqrt(invr2);
  double v = 0.;

  Range ip = (charge > 0) ? theIpRangePlus : theIpRangeMinus;

  for (int i=0; i < nIter; ++i) {
    v = predV(u, ip.min(), charge); 
    double d2 = invr2-sqr(v);
    u = (d2 > 0) ? sqrt(d2) : 0.;
  }
  PointUV  pred_tmp1(u, v,  &theRotation);
  double phi1 = pred_tmp1.unmap().phi(); 
  while ( phi1 >= M_PI) phi1 -= 2*M_PI;
  while ( phi1 < -M_PI) phi1 += 2*M_PI;


  u = sqrt(invr2); 
  v=0;
  for (int i=0; i < nIter; ++i) {
    v = predV(u, ip.max(), charge); 
    double d2 = invr2-sqr(v);
    u = (d2 > 0) ? sqrt(d2) : 0.;
  }
  PointUV  pred_tmp2(u, v,  &theRotation);
  double phi2 = pred_tmp2.unmap().phi(); 
  while ( phi2-phi1 >= M_PI) phi2 -= 2*M_PI;
  while ( phi2-phi1 < -M_PI) phi2 += 2*M_PI;

// check faster alternative, without while(..) it is enough to:
//  phi2 = phi1+radius*(pred_tmp2.v()-pred_tmp1.v()); 

  if (ip.empty()) {
    Range r1(phi1*radius-theTolerance, phi1*radius+theTolerance); 
    Range r2(phi2*radius-theTolerance, phi2*radius+theTolerance); 
    predRPhi = r1.intersection(r2);
  } else {
    Range r(phi1, phi2); 
    r.sort();
    predRPhi= Range(radius*r.min()-theTolerance, radius*r.max()+theTolerance);
  }
  return predRPhi;

}

Member Data Documentation

PointUV ThirdHitPredictionFromInvParabola::p1

private

Definition at line 80 of file ThirdHitPredictionFromInvParabola.h.

Referenced by coeffA(), coeffB(), init(), and ipFromCurvature().

PointUV ThirdHitPredictionFromInvParabola::p2

private

Definition at line 80 of file ThirdHitPredictionFromInvParabola.h.

Referenced by coeffA(), coeffB(), init(), and ipFromCurvature().

Range ThirdHitPredictionFromInvParabola::theIpRangeMinus

private

Definition at line 83 of file ThirdHitPredictionFromInvParabola.h.

Referenced by init(), rangeRPhi(), and rangeRPhiSlow().

Range ThirdHitPredictionFromInvParabola::theIpRangePlus

private

Definition at line 83 of file ThirdHitPredictionFromInvParabola.h.

Referenced by init(), rangeRPhi(), and rangeRPhiSlow().

Rotation ThirdHitPredictionFromInvParabola::theRotation

private

Definition at line 78 of file ThirdHitPredictionFromInvParabola.h.

Referenced by findPointAtCurve(), init(), and rangeRPhiSlow().

double ThirdHitPredictionFromInvParabola::theTolerance

private

Definition at line 84 of file ThirdHitPredictionFromInvParabola.h.

Referenced by rangeRPhi(), and rangeRPhiSlow().