Trk::JacobianThetaPToCotThetaPt Class Reference

This is the 5x5 jacobian for the transformation of track parameters and errors having the new standard momentum representation of \( (\phi, \theta, q/p) \) to the representation of \( (\phi, cot\theta, q/p_{T}) \), while the first two variables that express the local position representation keep unchanged. More...

#include <JacobianThetaPToCotThetaPt.h>

Inheritance diagram for Trk::JacobianThetaPToCotThetaPt:

Collaboration diagram for Trk::JacobianThetaPToCotThetaPt:

Public Member Functions
	JacobianThetaPToCotThetaPt (const double theta, const double qp)

Detailed Description

This is the 5x5 jacobian for the transformation of track parameters and errors having the new standard momentum representation of \( (\phi, \theta, q/p) \) to the representation of \( (\phi, cot\theta, q/p_{T}) \), while the first two variables that express the local position representation keep unchanged.

Mathematical motivation:
assuming \( u_{\mu} = (d_{0}', z_{0}', \phi_{0}', cot\theta, q/p_{T}) \) and \( v_{\mu} = (d_{0}, z_{0}, \phi_{0}, \theta, q/p)\), the set of \( v_{\mu}\) parameters can be expressed by the set of \( u_{\mu} \) parameters by following functions:

• \( u_{1} = d_{0}' = d_{0} \)
• \( u_{2} = z_{0}' = z_{0} \)
• \( u_{3} = \phi_{0}' = \phi_{0} \)
• \( u_{4} = cot\theta = cot(\theta) \)
• \( u_{5} = q/p_{T} = \frac{q}{p \cdot sin(\theta)} \)
  this results in three non-trivial terms of the corresponding jacobian:
• \( \frac{\partial cot\theta}{\partial \theta} = - \frac{1}{sin^{2}\theta} \)
• \( \frac{\partial (q/p_{T})}{\partial \theta} = - (q/p) \frac{cos(\theta)}{sin^2(\theta)} \)
• \( \frac{\partial (q/p_{T})}{\partial (q/p)} = 1./sin\theta \)

Author

Andre.nosp@m.as.S.nosp@m.alzbu.nosp@m.rger.nosp@m.@cern.nosp@m..ch

Definition at line 41 of file JacobianThetaPToCotThetaPt.h.

Constructor & Destructor Documentation

JacobianThetaPToCotThetaPt()

Trk::JacobianThetaPToCotThetaPt::JacobianThetaPToCotThetaPt	(	const double	theta,
		const double	qp )

Definition at line 12 of file JacobianThetaPToCotThetaPt.cxx.

                                                                                            :
  AmgMatrix(5,5)()
{
   // initialize to zero
   this->setIdentity();
 
   double sintheta = std::sin(theta);
   (*this)(3,3) = - 1./(sintheta*sintheta);
   (*this)(4,3) = - qp * std::cos(theta)/(sintheta*sintheta);
   (*this)(4,4) = 1.0 / sintheta;
}

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The documentation for this class was generated from the following files:

• JacobianThetaPToCotThetaPt.h
• JacobianThetaPToCotThetaPt.cxx