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! $Header$
#include "cctk.h"
module conversion
implicit none
private
public make_cylindrical2cartesian
public make_spherical2cartesian
public make_cartesian2spherical
contains
subroutine make_cylindrical2cartesian (xx, tt)
CCTK_REAL, intent(in) :: xx(3)
CCTK_REAL, intent(out) :: tt(3,3)
CCTK_REAL, parameter :: eps = 1.0d-20
CCTK_REAL :: x,y,z
CCTK_REAL :: rho
! cylindrical coordinates: rho phi z
! Cartesian coordinates: x y z
! rho^2 = x^2 + y^2
! tan(phi) = y/x
! A[cart](p)_i = TT(p)_i^j A[cyl](p)_j
! where p = p[cart]
! Transformation:
! x = rho cos(phi)
! y = rho sin(phi)
! z = z
! rho = sqrt(x^2+y^2)
! phi = atan(y/x)
! z = z
! Jacobian:
! drho/dx = x/rho
! drho/dy = y/rho
! drho/dz = 0
! dphi/dx = -y/rho^2
! dphi/dy = x/rho^2
! dphi/dz = 0
! dz /dx = 0
! dz /dy = 0
! dz /dz = 1
x = xx(1)
y = xx(2)
z = xx(3)
rho = sqrt(x**2+y**2)
tt(1,1) = x/(rho+eps)
tt(2,1) = y/(rho+eps)
tt(3,1) = 0
tt(1,2) = -y/(rho**2+eps)
tt(2,2) = x/(rho**2+eps)
tt(3,2) = 0
tt(1,3) = 0
tt(2,3) = 0
tt(3,3) = 1
end subroutine make_cylindrical2cartesian
subroutine make_spherical2cartesian (xx, tt)
CCTK_REAL, intent(in) :: xx(3)
CCTK_REAL, intent(out) :: tt(3,3)
CCTK_REAL, parameter :: eps = 1.0d-20
CCTK_REAL :: x,y,z
CCTK_REAL :: rho,r
! Cartesian coordinates: x y z
! spherical coordinates: r theta phi
! r^2 = x^2 + y^2 + z^2
! cos(theta) = z/r
! tan(phi) = y/x
! A[cart](p)_i = TT(p)_i^j A[spher](p)_j
! where p = p[cart]
! Definition:
! rho = r sin(theta)
! z/rho = cos(theta) / sin(theta)
! Transformation:
! x = r sin(theta) cos(phi)
! y = r sin(theta) sin(phi)
! z = r cos(theta)
! r = sqrt(x^2+y^2+z^2)
! theta = acos(z/r)
! phi = atan(y/x)
! Jacobian:
! dr /dx = x/r
! dr /dy = y/r
! dr /dz = z/r
! dtheta/dx = xz/r^2rho ! 0
! dtheta/dy = yz/r^2rho ! 0
! dtheta/dz = -rho/r^2 ! 1/rho
! dphi /dx = -y/rho^2
! dphi /dy = x/rho^2
! dphi /dz = 0
x = xx(1)
y = xx(2)
z = xx(3)
rho = sqrt(x**2+y**2)
r = sqrt(x**2+y**2+z**2)
tt(1,1) = x/(r+eps)
tt(2,1) = y/(r+eps)
tt(3,1) = z/(r+eps)
tt(1,2) = x*z/(r**2*rho+eps)
tt(2,2) = y*z/(r**2*rho+eps)
tt(3,2) = -rho**2/(r**2*rho+eps)
tt(1,3) = -y/(rho**2+eps)
tt(2,3) = x/(rho**2+eps)
tt(3,3) = 0
end subroutine make_spherical2cartesian
subroutine make_cartesian2spherical (xx, tt)
CCTK_REAL, intent(in) :: xx(3)
CCTK_REAL, intent(out) :: tt(3,3)
CCTK_REAL, parameter :: eps = 1.0d-20
CCTK_REAL :: x,y,z
CCTK_REAL :: rho,r
! Cartesian coordinates: x y z
! spherical coordinates: r theta phi
! r^2 = x^2 + y^2 + z^2
! cos(theta) = z/r
! tan(phi) = y/x
! A[spher](p)_i = TT(p)_i^j A[cart](p)_j
! where p = p[cart]
! Definition:
! rho = r sin(theta)
! z/rho = cos(theta) / sin(theta)
! Transformation:
! x = r sin(theta) cos(phi)
! y = r sin(theta) sin(phi)
! z = r cos(theta)
! r = sqrt(x^2+y^2+z^2)
! theta = acos(z/r)
! phi = atan(y/x)
! Jacobian:
! dx/dr = sin(theta) cos(phi) = x/r
! dx/dtheta = r cos(theta) cos(phi) = x z/rho
! dx/dphi = - r sin(theta) sin(phi) = -y
! dy/dr = sin(theta) sin(phi) = y/r
! dy/dtheta = r cos(theta) sin(phi) = y z/rho
! dy/dphi = r sin(theta) cos(phi) = x
! dz/dr = cos(theta) = z/r
! dz/dtheta = - r sin(theta) = -rho
! dz/dphi = 0 = 0
x = xx(1)
y = xx(2)
z = xx(3)
rho = sqrt(x**2+y**2)
r = sqrt(x**2+y**2+z**2)
tt(1,1) = x/(r+eps)
tt(2,1) = x * z/(rho+eps)
tt(3,1) = -y
tt(1,2) = y/(r+eps)
tt(2,2) = y * z/(rho+eps)
tt(3,2) = x
tt(1,3) = z/(r+eps)
tt(2,3) = -rho
tt(3,3) = 0
end subroutine make_cartesian2spherical
end module conversion
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