grid_tools  1.13.0
Private Member Functions
pmat4::ctoz Interface Reference

Private Member Functions

subroutine ctoz (v, z, infz)
 Utility codes for various Mobius transformations. More...
 

Detailed Description

Definition at line 105 of file pmat4.f90.

Constructor & Destructor Documentation

◆ ctoz()

subroutine pmat4::ctoz::ctoz ( real(dp), dimension(3), intent(in)  v,
complex(dpc), intent(out)  z,
logical, intent(out)  infz 
)
private

Utility codes for various Mobius transformations.

If aa1,bb1,cc1,dd1 are the coefficients for one transformation, and aa2,bb2,cc2,dd2 are the coefficients for a second one, then the coefficients for the mapping of a test point, zz, by aa1 etc to zw, followed by a mapping of zw, by aa2 etc to zv, is equivalent to a single mapping zz–>zv by the transformatn with coefficients aa3,bb3,cc3,dd3, such that, as 2*2 complex matrices:

 [ aa3, bb3 ]   [ aa2, bb2 ]   [ aa1, bb1 ]
 [          ] = [          ] * [          ]
 [ cc3, dd3 ]   [ cc2, dd2 ]   [ cc1, dd1 ] .

Note that the determinant of these matrices is always +1. Given a cartesian 3-vector representation of a point on the Riemann unit sphere, return the stereographically equivalent complex number.

Parameters
[in]vcartesian 3-vector representation of point on Riemann sphere
[out]zcomplex point stereographically equivalent to v
[out]infzlogical indicator for z being the point at infinity
Author
R. J. Purser

Definition at line 2027 of file pmat4.f90.

The documentation for this interface was generated from the following file: