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InvJacobianOPoint< CombinedMapping< CircularToCartesian< R, Theta, X, Y >, CartesianToCircular< Xpc, Ypc, R, Theta > >, ddc::Coordinate< R, Theta > > Class Template Reference

A specialisation of InvJacobianOPoint for a combined mapping FoG where F is a circular mapping from logical to physical, and G is an inverse circular mapping from physical to logical. More...

Public Member Functions

KOKKOS_FUNCTION InvJacobianOPoint (Mapping const &mapping)
 The constructor of InvJacobianOPoint.
 
KOKKOS_INLINE_FUNCTION Matrix_2x2 operator() () const
 Compute the full inverse Jacobian matrix from a coordinate system (x_pc, y_pc) to a coordinate system (x, y).
 

Detailed Description

template<class X, class Y, class R, class Theta, class Xpc, class Ypc>
class InvJacobianOPoint< CombinedMapping< CircularToCartesian< R, Theta, X, Y >, CartesianToCircular< Xpc, Ypc, R, Theta > >, ddc::Coordinate< R, Theta > >

A specialisation of InvJacobianOPoint for a combined mapping FoG where F is a circular mapping from logical to physical, and G is an inverse circular mapping from physical to logical.

The combined mapping FoG therefore maps from a physical domain (Xpc, Ypc) to a physical domain (X,Y) (this mapping is equivalent to the identity).

Constructor & Destructor Documentation

◆ InvJacobianOPoint()

template<class X , class Y , class R , class Theta , class Xpc , class Ypc >
KOKKOS_FUNCTION InvJacobianOPoint< CombinedMapping< CircularToCartesian< R, Theta, X, Y >, CartesianToCircular< Xpc, Ypc, R, Theta > >, ddc::Coordinate< R, Theta > >::InvJacobianOPoint ( Mapping const &  mapping)
inlineexplicit

The constructor of InvJacobianOPoint.

Parameters
[in]mappingThe mapping for which the inverse of the Jacobian is calculated.

Member Function Documentation

◆ operator()()

template<class X , class Y , class R , class Theta , class Xpc , class Ypc >
KOKKOS_INLINE_FUNCTION Matrix_2x2 InvJacobianOPoint< CombinedMapping< CircularToCartesian< R, Theta, X, Y >, CartesianToCircular< Xpc, Ypc, R, Theta > >, ddc::Coordinate< R, Theta > >::operator() ( ) const
inline

Compute the full inverse Jacobian matrix from a coordinate system (x_pc, y_pc) to a coordinate system (x, y).

Here, as \( \mathcal{G}^{-1} = \mathcal{F} \), the Jacobian matrix of \((\mathcal{F} \circ \mathcal{G}^{-1})^{-1} \) is the identity matrix. So, the pseudo-Cartesian Jacobian matrix for a circular mapping is given by :

  • \( (J_{\mathcal{F}}J_{\mathcal{G}}^{-1})^{-1}_{11}(0, \theta) = 1, \)
  • \( (J_{\mathcal{F}}J_{\mathcal{G}}^{-1})^{-1}_{12}(0, \theta) = 0, \)
  • \( (J_{\mathcal{F}}J_{\mathcal{G}}^{-1})^{-1}_{21}(0, \theta) = 0, \)
  • \( (J_{\mathcal{F}}J_{\mathcal{G}}^{-1})^{-1}_{22}(0, \theta) = 1. \)
Returns
The matrix evaluated at the central point.
The documentation for this class was generated from the following file: