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#include "cctk.h"
#include "cctk_Arguments.h"
#include "cctk_Functions.h"
#include "cctk_Parameters.h"
module qlm_killing_normalisation
use cctk
use constants
implicit none
DECLARE_CCTK_FUNCTIONS
DECLARE_CCTK_PARAMETERS
private
public killing_factor
contains
subroutine killing_factor (CCTK_ARGUMENTS, hn, theta, factor, nsteps)
DECLARE_CCTK_ARGUMENTS
integer, intent(in) :: hn
CCTK_REAL, intent(in) :: theta
CCTK_REAL, intent(out) :: factor
integer, intent(out) :: nsteps
CCTK_REAL :: lambda0, theta0, phi0
CCTK_REAL :: lambda1, theta1, phi1
character :: msg*1000
lambda0 = 0
theta0 = theta
phi0 = 0
phi1 = 2*pi
call killing_geodesic &
(CCTK_PASS_FTOF, hn, lambda0, theta0, phi0, phi1, lambda1, theta1, &
nsteps)
factor = (lambda1 - lambda0) / (2*pi)
if (veryverbose/=0) then
write (msg, '("Integrated at theta=",g16.6)') theta
call CCTK_INFO (msg)
write (msg, '(" Integrated in ",i4," steps")') nsteps
call CCTK_INFO (msg)
write (msg, '(" Theta error is ",g16.6)') theta1 - theta0
call CCTK_INFO (msg)
write (msg, '(" Normalisation factor is ",g16.6)') factor
call CCTK_INFO (msg)
end if
end subroutine killing_factor
subroutine killing_geodesic &
(CCTK_ARGUMENTS, hn, lambda0, theta0, phi0, phi1, lambda1, theta1, nsteps)
DECLARE_CCTK_ARGUMENTS
integer, intent(in) :: hn
CCTK_REAL, intent(in) :: lambda0, theta0, phi0, phi1
CCTK_REAL, intent(out) :: lambda1, theta1
integer, intent(out) :: nsteps
CCTK_REAL :: org_theta, org_phi, del_theta, del_phi
CCTK_REAL :: lambda
CCTK_REAL :: theta, phi
CCTK_REAL :: dlambda
CCTK_REAL :: dtheta, dphi
CCTK_REAL :: theta2, phi2
integer :: ierr1, ierr2
org_theta = qlm_origin_theta(hn)
org_phi = qlm_origin_phi(hn)
del_theta = qlm_delta_theta(hn)
del_phi = qlm_delta_phi(hn)
nsteps = 0
lambda = lambda0
theta = theta0
phi = phi0
dtheta = killing_interp (qlm_xi_t(:,:,hn), &
org_theta, org_phi, del_theta, del_phi, theta, phi, ierr1)
dphi = killing_interp (qlm_xi_p(:,:,hn), &
org_theta, org_phi, del_theta, del_phi, theta, phi, ierr2)
if (ierr1/=0 .or. ierr2/=0) then
call CCTK_WARN (2, "Integration path leaves the domain")
lambda1 = lambda0
theta1 = theta0
nsteps = -1
return
end if
if (abs(dphi) < 1.0d-8 .or. abs(dtheta) > abs(dphi)) then
call CCTK_WARN (2, "Integration path starts out too steep")
lambda1 = lambda0
theta1 = theta0
nsteps = -1
return
end if
dlambda = (qlm_delta_phi(hn) / dphi) / 2
do
dtheta = killing_interp (qlm_xi_t(:,:,hn), &
org_theta, org_phi, del_theta, del_phi, theta, phi, ierr1)
dphi = killing_interp (qlm_xi_p(:,:,hn), &
org_theta, org_phi, del_theta, del_phi, theta, phi, ierr2)
if (ierr1/=0 .or. ierr2/=0) then
call CCTK_WARN (2, "Integration path leaves the domain")
lambda1 = lambda0
theta1 = theta0
nsteps = -1
return
end if
theta2 = theta + dlambda * dtheta / 2
phi2 = phi + dlambda * dphi / 2
dtheta = killing_interp (qlm_xi_t(:,:,hn), &
org_theta, org_phi, del_theta, del_phi, theta2, phi2, ierr1)
dphi = killing_interp (qlm_xi_p(:,:,hn), &
org_theta, org_phi, del_theta, del_phi, theta2, phi2, ierr2)
if (ierr1/=0 .or. ierr2/=0) then
call CCTK_WARN (2, "Integration path leaves the domain")
lambda1 = lambda0
theta1 = theta0
nsteps = -1
return
end if
if (dphi<=0) then
call CCTK_WARN (2, "Integration path does not enclose the pole")
lambda1 = lambda0
theta1 = theta0
nsteps = -1
return
end if
theta2 = theta + dlambda * dtheta
phi2 = phi + dlambda * dphi
if (phi2 >= phi1) exit
if (nsteps > 100000) then
call CCTK_WARN (2, "Integration takes too many steps")
lambda1 = lambda0
theta1 = theta0
nsteps = -1
return
exit
end if
nsteps = nsteps + 1
lambda = lambda + dlambda
theta = theta2
phi = phi2
end do
dlambda = (phi1 - phi) / dphi
nsteps = nsteps + 1
lambda = lambda + dlambda
theta = theta + dlambda * dtheta
phi = phi + dlambda * dphi
lambda1 = lambda
theta1 = theta
end subroutine killing_geodesic
function killing_interp &
(array, origin_x1, origin_x2, delta_x1, delta_x2, x1, x2, ierr)
CCTK_REAL :: killing_interp
CCTK_REAL, intent(in) :: array(:,:)
CCTK_REAL, intent(in) :: origin_x1, origin_x2
CCTK_REAL, intent(in) :: delta_x1, delta_x2
CCTK_REAL, intent(in) :: x1, x2
integer, intent(out) :: ierr
CCTK_REAL, parameter :: eps = 1.0d-10
CCTK_REAL :: xx1, xx2
CCTK_REAL :: dx1, dx2
CCTK_REAL :: f1a, f1b, f1c
CCTK_REAL :: f2a, f2b, f2c
CCTK_REAL :: interp2a, interp2b, interp2c
integer :: i, j
xx1 = x1
xx2 = x2
i = nint((xx1 - origin_x1) / delta_x1) + 1
j = nint((xx2 - origin_x2) / delta_x2) + 1
i = max(2, min(size(array,1)-1, i))
if (j>size(array,2)-1) then
! periodicity in phi-direction
xx2 = xx2 - (size(array,2)-2) * delta_x2
j = j - size(array,2)-2
end if
j = max(2, min(size(array,2)-1, j))
dx1 = xx1 - (origin_x1 + (i-1) * delta_x1)
dx2 = xx2 - (origin_x2 + (j-1) * delta_x2)
if (abs(dx1)>(1+eps)*delta_x1/2 .or. abs(dx2)>(1+eps)*delta_x2/2) then
call CCTK_WARN (2, "interpolating out of bounds")
killing_interp = 0
ierr = 1
return
end if
f1a = (-dx1) * (1-dx1) / ( 2 * 1 )
f1b = (-1-dx1) * (1-dx1) / ( 1 * (-1))
f1c = (-1-dx1) * (-dx1) / ((-1) * (-2))
f2a = (-dx2) * (1-dx2) / ( 2 * 1 )
f2b = (-1-dx2) * (1-dx2) / ( 1 * (-1))
f2c = (-1-dx2) * (-dx2) / ((-1) * (-2))
interp2a = f1a * array(i-1,j-1) + f1b * array(i,j-1) + f1c * array(i+1,j-1)
interp2b = f1a * array(i-1,j ) + f1b * array(i,j ) + f1c * array(i+1,j )
interp2c = f1a * array(i-1,j+1) + f1b * array(i,j+1) + f1c * array(i+1,j+1)
killing_interp = f2a * interp2a + f2b * interp2b + f2c * interp2c
ierr = 0
end function killing_interp
end module qlm_killing_normalisation
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