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#include "cctk.h"
#include "cctk_Parameters.h"
module qlm_derivs
use classify
implicit none
private
public abs2
public operator(.outer.)
public operator(.dot.)
public deriv
public deriv2
public deriv3
public timederiv
public timederiv2
interface deriv
module procedure rderiv
end interface
interface deriv2
module procedure rderiv2
end interface
interface deriv3
module procedure rderiv3
end interface
interface timederiv
module procedure rtimederiv
module procedure ctimederiv
end interface
interface timederiv2
module procedure rtimederiv2
module procedure ctimederiv2
end interface
interface operator(.outer.)
module procedure router
module procedure couter
end interface
interface operator(.dot.)
module procedure rdot
module procedure cdot
end interface
contains
! abs(c)**2 for complex c without a square root
pure elemental function abs2 (a)
CCTK_COMPLEX, intent(in) :: a
CCTK_REAL :: abs2
abs2 = a * conjg(a)
end function abs2
function router (left, right) result (result)
CCTK_REAL, intent(in) :: left(:), right(:)
CCTK_REAL :: result(size(left,1),size(right,1))
integer :: i, j
forall (i=1:size(left,1), j=1:size(right,1))
result(i,j) = left(i) * right(j)
end forall
end function router
function couter (left, right) result (result)
CCTK_COMPLEX, intent(in) :: left(:), right(:)
CCTK_COMPLEX :: result(size(left,1),size(right,1))
integer :: i, j
forall (i=1:size(left,1), j=1:size(right,1))
result(i,j) = left(i) * right(j)
end forall
end function couter
function rdot (left, right) result (result)
CCTK_REAL, intent(in) :: left(:), right(:)
CCTK_REAL :: result
integer :: i
if (size(left,1) /= size(right,1)) then
call CCTK_WARN (0, "Array sizes must have the same sizes")
end if
!!$ result = sum((/( left(i) * right(i), i=1,size(left,1) )/))
result = 0
do i=1,size(left,1)
result = result + left(i) * right(i)
end do
end function rdot
function cdot (left, right) result (result)
CCTK_COMPLEX, intent(in) :: left(:), right(:)
CCTK_COMPLEX :: result
integer :: i
if (size(left,1) /= size(right,1)) then
call CCTK_WARN (0, "Array sizes must have the same sizes")
end if
!!$ result = sum((/( left(i) * right(i), i=1,size(left,1) )/))
result = 0
do i=1,size(left,1)
result = result + left(i) * right(i)
end do
end function cdot
! Calculate spatial derivatives
pure function rderiv (f, i, j, dx) result (df)
DECLARE_CCTK_PARAMETERS
CCTK_REAL, intent(in) :: f(:,:)
integer, intent(in) :: i, j
CCTK_REAL, intent(in) :: dx(2)
CCTK_REAL :: df(2)
select case (spatial_order)
case (2)
df(1) = (+ f(i+1,j) - f(i-1,j)) / (2 * dx(1))
df(2) = (+ f(i,j+1) - f(i,j-1)) / (2 * dx(2))
case (4)
df(1) = (- f(i+2,j) + 8*f(i+1,j) - 8*f(i-1,j) + f(i-2,j)) / (12 * dx(1))
df(2) = (- f(i,j+2) + 8*f(i,j+1) - 8*f(i,j-1) + f(i,j-2)) / (12 * dx(2))
case default
! call CCTK_WARN (0, "internal error")
df = TAT_nan()
end select
end function rderiv
pure function rderiv2 (f, i, j, dx) result (ddf)
DECLARE_CCTK_PARAMETERS
CCTK_REAL, intent(in) :: f(:,:)
integer, intent(in) :: i, j
CCTK_REAL, intent(in) :: dx(2)
CCTK_REAL :: ddf(2,2)
select case (spatial_order)
case (2)
ddf(1,1) = (+ f(i+1,j) - 2*f(i,j) + f(i-1,j)) / dx(1)**2
ddf(2,2) = (+ f(i,j+1) - 2*f(i,j) + f(i,j-1)) / dx(2)**2
ddf(1,2) = (+ f(i-1,j-1) - f(i+1,j-1) - f(i-1,j+1) + f(i+1,j+1)) &
& / (4 * dx(1) * dx(2))
ddf(2,1) = ddf(1,2)
case (4)
ddf(1,1) &
= (- f(i+2,j) + 16*f(i+1,j) - 30*f(i,j) + 16*f(i-1,j) - f(i-2,j)) &
& / (12 * dx(1)**2)
ddf(2,2) &
= (- f(i,j+2) + 16*f(i,j+1) - 30*f(i,j) + 16*f(i,j-1) - f(i,j-2)) &
& / (12 * dx(2)**2)
ddf(1,2) &
= (+ f(i+2,j+2) - 8*f(i+1,j+2) + 8*f(i-1,j+2) - f(i-2,j+2) &
& - 8*f(i+2,j+1) + 64*f(i+1,j+1) - 64*f(i-1,j+1) + 8*f(i-2,j+1) &
& + 8*f(i+2,j-1) - 64*f(i+1,j-1) + 64*f(i-1,j-1) - 8*f(i-2,j-1) &
& - f(i+2,j-2) + 8*f(i+1,j-2) - 8*f(i-1,j-2) + f(i-2,j-2)) &
& / (144 * dx(1) * dx(2))
ddf(2,1) = ddf(1,2)
case default
! call CCTK_WARN (0, "internal error")
ddf = TAT_nan()
end select
end function rderiv2
pure function rderiv3 (f, i, j, dx) result (dddf)
DECLARE_CCTK_PARAMETERS
CCTK_REAL, intent(in) :: f(:,:)
integer, intent(in) :: i, j
CCTK_REAL, intent(in) :: dx(2)
CCTK_REAL :: dddf(2,2,2)
select case (spatial_order)
case (2, 4)
! No separate 4th order stencil, since that would need 3 ghost
! zones
dddf(1,1,1) = (- f(i-2,j ) &
& + 2*f(i-1,j ) &
& - 2*f(i+1,j ) &
& + f(i+2,j )) / (2*dx(1)**3)
dddf(1,1,2) = ( f(i+1,j+1) &
& - 2*f(i ,j+1) &
& + f(i-1,j+1) &
& - f(i+1,j-1) &
& + 2*f(i ,j-1) &
& - f(i-1,j-1)) / (2 * dx(1)**2 * dx(2))
dddf(1,2,2) = ( f(i+1,j+1) &
& - 2*f(i+1,j ) &
& + f(i+1,j-1) &
& - f(i-1,j+1) &
& + 2*f(i-1,j ) &
& - f(i-1,j-1)) / (2 * dx(1) * dx(2)**2)
dddf(2,2,2) = (- f(i ,j-2) &
& + 2*f(i ,j-1) &
& - 2*f(i ,j+1) &
& + f(i ,j+2)) / (2*dx(2)**3)
dddf(1,2,1) = dddf(1,1,2)
dddf(2,1,1) = dddf(1,1,2)
dddf(2,1,2) = dddf(1,2,2)
dddf(2,2,1) = dddf(1,2,2)
case default
! call CCTK_WARN (0, "internal error")
dddf = TAT_nan()
end select
end function rderiv3
! Calculate a time derivate from several time levels
pure elemental function rtimederiv (f0, f1, f2, t0, t1, t2, ce0, ce1, ce2) result (fdot)
CCTK_REAL, intent(in) :: f0, f1, f2
CCTK_REAL, intent(in) :: t0, t1, t2
logical, intent(in) :: ce0, ce1, ce2
CCTK_REAL :: fdot
CCTK_REAL :: dt1, dt2
CCTK_REAL :: fdot1, fdot2
!!$ dt1 = qlm_time(hn) - qlm_time_p(hn)
!!$ dt2 = qlm_time(hn) - qlm_time_p_p(hn)
dt1 = t0 - t1
dt2 = t0 - t2
if (ce0 .or. ce1) then
fdot = 0
else if (ce2) then
fdot = (f0 - f1) / dt1
else
! f(dt1) = f(0) + dt1 f'(0) + dt1^2/2 f''(0)
! f(dt2) = f(0) + dt2 f'(0) + dt2^2/2 f''(0)
! f'(0) = [f(dt1) - f(0)] / dt1 - dt1/2 f''(0)
! f'(0) = [f(dt2) - f(0)] / dt2 - dt2/2 f''(0)
fdot1 = (f0 - f1) / dt1
fdot2 = (f0 - f2) / dt2
fdot = (fdot1 * dt2 - fdot2 * dt1) / (dt2 - dt1)
end if
end function rtimederiv
pure elemental function ctimederiv (f0, f1, f2, t0, t1, t2, ce0, ce1, ce2) result (fdot)
CCTK_COMPLEX, intent(in) :: f0, f1, f2
CCTK_REAL, intent(in) :: t0, t1, t2
logical, intent(in) :: ce0, ce1, ce2
CCTK_COMPLEX :: fdot
fdot = cmplx(timederiv(real(f0),real(f1),real(f2), t0,t1,t2, ce0,ce1,ce2), &
& timederiv(aimag(f0),aimag(f1),aimag(f2), t0,t1,t2, ce0,ce1,ce2), &
& kind(fdot))
end function ctimederiv
pure elemental function rtimederiv2 (f0, f1, f2, t0, t1, t2, ce0, ce1, ce2) result (fdotdot)
CCTK_REAL, intent(in) :: f0, f1, f2
CCTK_REAL, intent(in) :: t0, t1, t2
logical, intent(in) :: ce0, ce1, ce2
CCTK_REAL :: fdotdot
CCTK_REAL :: dt1, dt2
CCTK_REAL :: fdotdot1, fdotdot2
!!$ dt1 = qlm_time(hn) - qlm_time_p(hn)
!!$ dt2 = qlm_time(hn) - qlm_time_p_p(hn)
dt1 = t0 - t1
dt2 = t0 - t2
if (ce0 .or. ce1) then
fdotdot = 0
else if (ce2) then
fdotdot = 0
else
! f(dt1) = f(0) + dt1 f'(0) + dt1^2/2 f''(0)
! f(dt2) = f(0) + dt2 f'(0) + dt2^2/2 f''(0)
! f''(0) = [f(dt1) - f(0)] / [dt1^2/2] - f'(0) / [dt1/2]
! f''(0) = [f(dt2) - f(0)] / [dt2^2/2] - f'(0) / [dt2/2]
fdotdot1 = (f1 - f0) / (dt1**2/2)
fdotdot2 = (f2 - f0) / (dt2**2/2)
fdotdot = (fdotdot1 * dt1 - fdotdot2 * dt2) / (dt1 - dt2)
end if
end function rtimederiv2
pure elemental function ctimederiv2 (f0, f1, f2, t0, t1, t2, ce0, ce1, ce2) result (fdotdot)
CCTK_COMPLEX, intent(in) :: f0, f1, f2
CCTK_REAL, intent(in) :: t0, t1, t2
logical, intent(in) :: ce0, ce1, ce2
CCTK_COMPLEX :: fdotdot
fdotdot = cmplx(timederiv2(real(f0),real(f1),real(f2), t0,t1,t2, ce0,ce1,ce2), &
& timederiv2(aimag(f0),aimag(f1),aimag(f2), t0,t1,t2, ce0,ce1,ce2), &
& kind(fdotdot))
end function ctimederiv2
end module qlm_derivs
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