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! $Header$
#ifndef TGR_INCLUDED
#include "cctk.h"
#include "cctk_Parameters.h"
module derivs
implicit none
private
public get_derivs
public get_derivs2
public get_derivs3
contains
#endif
subroutine get_derivs (a, f, pos, off, dx, order)
CCTK_REAL, intent(in) :: a(*)
CCTK_REAL, intent(out) :: f(3)
integer, intent(in) :: pos, off(3)
CCTK_REAL, intent(in) :: dx(3)
integer, intent(in), optional :: order
integer :: order1
integer :: i
order1 = 2
if (present(order)) order1 = order
select case (order1)
case (2)
do i=1,3
f(i) = (a(pos+off(i)) - a(pos-off(i))) / (2*dx(i))
end do
case (4)
do i=1,3
f(i) = (- a(pos+2*off(i)) + 8*a(pos+off(i)) - 8*a(pos-off(i)) + a(pos-2*off(i))) / (12*dx(i))
end do
case default
call CCTK_WARN (0, "Unsupported finite differencing order")
end select
end subroutine get_derivs
subroutine get_derivs2 (a, f, pos, off, dx, order)
CCTK_REAL, intent(in) :: a(*)
CCTK_REAL, intent(out) :: f(3,3)
integer, intent(in) :: pos, off(3)
CCTK_REAL, intent(in) :: dx(3)
integer, intent(in), optional :: order
integer :: order1
integer :: i
order1 = 2
if (present(order)) order1 = order
select case (order1)
case (2)
do i=1,3
f(i,i) = (a(pos+off(i)) - 2*a(pos) + a(pos-off(i))) / dx(i)**2
end do
f(1,2) = ( a(pos-off(1)-off(2)) - a(pos+off(1)-off(2)) &
& - a(pos-off(1)+off(2)) + a(pos+off(1)+off(2))) / (4*dx(1)*dx(2))
f(2,1) = f(1,2)
f(1,3) = ( a(pos-off(1)-off(3)) - a(pos+off(1)-off(3)) &
& - a(pos-off(1)+off(3)) + a(pos+off(1)+off(3))) / (4*dx(1)*dx(3))
f(3,1) = f(1,3)
f(2,3) = ( a(pos-off(2)-off(3)) - a(pos+off(2)-off(3)) &
& - a(pos-off(2)+off(3)) + a(pos+off(2)+off(3))) / (4*dx(2)*dx(3))
f(3,2) = f(2,3)
case (4)
do i=1,3
f(i,i) = (- a(pos-2*off(i)) + 16*a(pos-off(i)) - 30*a(pos) + 16*a(pos+off(i)) - a(pos+2*off(i))) / (12*dx(i)**2)
end do
f(1,2) = ( a(pos+2*off(1)+2*off(2)) - 8*a(pos+off(1)+2*off(2)) + 8*a(pos-off(1)+2*off(2)) - a(pos-2*off(1)+2*off(2)) &
& - 8*a(pos+2*off(1)+ off(2)) + 64*a(pos+off(1)+ off(2)) - 64*a(pos-off(1)+ off(2)) + 8*a(pos-2*off(1)+ off(2)) &
& + 8*a(pos+2*off(1)- off(2)) - 64*a(pos+off(1)- off(2)) + 64*a(pos-off(1)- off(2)) - 8*a(pos-2*off(1)- off(2)) &
& - a(pos+2*off(1)-2*off(2)) + 8*a(pos+off(1)-2*off(2)) - 8*a(pos-off(1)-2*off(2)) + a(pos-2*off(1)-2*off(2))) / (144*dx(1)*dx(2))
f(2,1) = f(1,2)
f(1,3) = ( a(pos+2*off(1)+2*off(3)) - 8*a(pos+off(1)+2*off(3)) + 8*a(pos-off(1)+2*off(3)) - a(pos-2*off(1)+2*off(3)) &
& - 8*a(pos+2*off(1)+ off(3)) + 64*a(pos+off(1)+ off(3)) - 64*a(pos-off(1)+ off(3)) + 8*a(pos-2*off(1)+ off(3)) &
& + 8*a(pos+2*off(1)- off(3)) - 64*a(pos+off(1)- off(3)) + 64*a(pos-off(1)- off(3)) - 8*a(pos-2*off(1)- off(3)) &
& - a(pos+2*off(1)-2*off(3)) + 8*a(pos+off(1)-2*off(3)) - 8*a(pos-off(1)-2*off(3)) + a(pos-2*off(1)-2*off(3))) / (144*dx(1)*dx(3))
f(3,1) = f(1,3)
f(2,3) = ( a(pos+2*off(2)+2*off(3)) - 8*a(pos+off(2)+2*off(3)) + 8*a(pos-off(2)+2*off(3)) - a(pos-2*off(2)+2*off(3)) &
& - 8*a(pos+2*off(2)+ off(3)) + 64*a(pos+off(2)+ off(3)) - 64*a(pos-off(2)+ off(3)) + 8*a(pos-2*off(2)+ off(3)) &
& + 8*a(pos+2*off(2)- off(3)) - 64*a(pos+off(2)- off(3)) + 64*a(pos-off(2)- off(3)) - 8*a(pos-2*off(2)- off(3)) &
& - a(pos+2*off(2)-2*off(3)) + 8*a(pos+off(2)-2*off(3)) - 8*a(pos-off(2)-2*off(3)) + a(pos-2*off(2)-2*off(3))) / (144*dx(2)*dx(3))
f(3,2) = f(2,3)
case default
call CCTK_WARN (0, "Unsupported finite differencing order")
end select
end subroutine get_derivs2
subroutine get_derivs3 (a, f, pos, off, dx, order)
CCTK_REAL, intent(in) :: a(*)
CCTK_REAL, intent(out) :: f(3,3,3)
integer, intent(in) :: pos, off(3)
CCTK_REAL, intent(in) :: dx(3)
integer, intent(in), optional :: order
integer :: order1
order1 = 2
if (present(order)) order1 = order
select case (order1)
case (2)
f(1,1,1) = (a(pos+2*off(1)) - 2*a(pos+off(1)) + 2*a(pos-off(1)) - a(pos-2*off(1))) / (2*dx(1)**3)
f(2,1,1) = (a(pos+off(1)+off(2)) - 2*a(pos+off(2)) + a(pos-off(1)+off(2)) - a(pos+off(1)-off(2)) + 2*a(pos-off(2)) - a(pos-off(1)-off(2))) / (2*dx(1)*dx(1)*dx(2))
f(3,1,1) = (a(pos+off(1)+off(3)) - 2*a(pos+off(3)) + a(pos-off(1)+off(3)) - a(pos+off(1)-off(3)) + 2*a(pos-off(3)) - a(pos-off(1)-off(3))) / (2*dx(1)*dx(1)*dx(3))
f(1,2,1) = f(2,1,1)
f(2,2,1) = (a(pos+off(1)+off(2)) - 2*a(pos+off(1)) + a(pos+off(1)-off(2)) - a(pos-off(1)+off(2)) + 2*a(pos-off(1)) - a(pos-off(1)-off(2))) / (2*dx(1)*dx(2)*dx(2))
f(3,2,1) = (a(pos+off(1)+off(2)+off(3)) - a(pos-off(1)+off(2)+off(3)) - a(pos+off(1)-off(2)+off(3)) + a(pos-off(1)-off(2)+off(3)) - a(pos+off(1)+off(2)-off(3)) + a(pos-off(1)+off(2)-off(3)) + a(pos+off(1)-off(2)-off(3)) - a(pos-off(1)-off(2)-off(3))) / (8*dx(1)*dx(2)*dx(3))
f(1,3,1) = f(3,1,1)
f(2,3,1) = f(3,2,1)
f(3,3,1) = (a(pos+off(1)+off(3)) - 2*a(pos+off(1)) + a(pos+off(1)-off(3)) - a(pos-off(1)+off(3)) + 2*a(pos-off(1)) - a(pos-off(1)-off(3))) / (2*dx(1)*dx(3)*dx(3))
f(:,1,2) = f(:,2,1)
f(1,2,2) = f(2,2,1)
f(2,2,2) = (a(pos+2*off(2)) - 2*a(pos+off(2)) + 2*a(pos-off(2)) - a(pos-2*off(2))) / (2*dx(2)**3)
f(3,2,2) = (a(pos+off(2)+off(3)) - 2*a(pos+off(3)) + a(pos-off(2)+off(3)) - a(pos+off(2)-off(3)) + 2*a(pos-off(3)) - a(pos-off(2)-off(3))) / (2*dx(2)*dx(2)*dx(3))
f(1,3,2) = f(3,1,2)
f(2,3,2) = f(3,2,2)
f(3,3,2) = (a(pos+off(2)+off(3)) - 2*a(pos+off(2)) + a(pos+off(2)-off(3)) - a(pos-off(2)+off(3)) + 2*a(pos-off(2)) - a(pos-off(2)-off(3))) / (2*dx(2)*dx(3)*dx(3))
f(:,1,3) = f(:,3,1)
f(:,2,3) = f(:,3,2)
f(1,3,3) = f(3,1,3)
f(2,3,3) = f(3,2,3)
f(3,3,3) = (a(pos+2*off(3)) - 2*a(pos+off(3)) + 2*a(pos-off(3)) - a(pos-2*off(3))) / (2*dx(3)**3)
case (4)
! [+1 -8 +13 0 -13 +8 -1] / 8
f(1,1,1) = (a(pos-3*off(1)) - 8*a(pos-2*off(1)) + 13*a(pos-off(1)) - 13*a(pos+off(1)) + 8*a(pos+2*off(1)) - a(pos+3*off(1))) / (8*dx(1)**3)
! [-1 +8 0 -8 +1] / 12
! [-1 +16 -30 +16 -1] / 12
f(2,1,1) = (+ a(pos-2*off(1)-2*off(2)) - 16*a(pos-off(1)-2*off(2)) + 30*a(pos-2*off(2)) - 16*a(pos+off(1)-2*off(2)) + a(pos+2*off(1)-2*off(2)) &
& - 8*a(pos-2*off(1)- off(2)) + 128*a(pos-off(1)- off(2)) - 240*a(pos- off(2)) + 128*a(pos+off(1)- off(2)) - 8*a(pos+2*off(1)- off(2)) &
& + 8*a(pos-2*off(1)+ off(2)) - 128*a(pos-off(1)+ off(2)) + 240*a(pos+ off(2)) - 128*a(pos+off(1)+ off(2)) + 8*a(pos+2*off(1)+ off(2)) &
& - a(pos-2*off(1)+2*off(2)) + 16*a(pos-off(1)+2*off(2)) - 30*a(pos+2*off(2)) + 16*a(pos+off(1)+2*off(2)) - a(pos+2*off(1)+2*off(2))) / (144*dx(1)**2*dx(2))
f(3,1,1) = (+ a(pos-2*off(1)-2*off(3)) - 16*a(pos-off(1)-2*off(3)) + 30*a(pos-2*off(3)) - 16*a(pos+off(1)-2*off(3)) + a(pos+2*off(1)-2*off(3)) &
& - 8*a(pos-2*off(1)- off(3)) + 128*a(pos-off(1)- off(3)) - 240*a(pos- off(3)) + 128*a(pos+off(1)- off(3)) - 8*a(pos+2*off(1)- off(3)) &
& + 8*a(pos-2*off(1)+ off(3)) - 128*a(pos-off(1)+ off(3)) + 240*a(pos+ off(3)) - 128*a(pos+off(1)+ off(3)) + 8*a(pos+2*off(1)+ off(3)) &
& - a(pos-2*off(1)+2*off(3)) + 16*a(pos-off(1)+2*off(3)) - 30*a(pos+2*off(3)) + 16*a(pos+off(1)+2*off(3)) - a(pos+2*off(1)+2*off(3))) / (144*dx(1)**2*dx(3))
f(1,2,1) = f(2,1,1)
f(2,2,1) = (+ a(pos-2*off(2)-2*off(1)) - 16*a(pos-off(2)-2*off(1)) + 30*a(pos-2*off(1)) - 16*a(pos+off(2)-2*off(1)) + a(pos+2*off(2)-2*off(1)) &
& - 8*a(pos-2*off(2)- off(1)) + 128*a(pos-off(2)- off(1)) - 240*a(pos- off(1)) + 128*a(pos+off(2)- off(1)) - 8*a(pos+2*off(2)- off(1)) &
& + 8*a(pos-2*off(2)+ off(1)) - 128*a(pos-off(2)+ off(1)) + 240*a(pos+ off(1)) - 128*a(pos+off(2)+ off(1)) + 8*a(pos+2*off(2)+ off(1)) &
& - a(pos-2*off(2)+2*off(1)) + 16*a(pos-off(2)+2*off(1)) - 30*a(pos+2*off(1)) + 16*a(pos+off(2)+2*off(1)) - a(pos+2*off(2)+2*off(1))) / (144*dx(2)**2*dx(1))
f(3,2,1) = (- a(pos-2*off(1)-2*off(2)-2*off(3)) + 8*a(pos-off(1)-2*off(2)-2*off(3)) - 8*a(pos+off(1)-2*off(2)-2*off(3)) + a(pos+2*off(1)-2*off(2)-2*off(3)) &
& + 8*a(pos-2*off(1)- off(2)-2*off(3)) - 64*a(pos-off(1)- off(2)-2*off(3)) + 64*a(pos+off(1)- off(2)-2*off(3)) - 8*a(pos+2*off(1)- off(2)-2*off(3)) &
& - 8*a(pos-2*off(1)+ off(2)-2*off(3)) + 64*a(pos-off(1)+ off(2)-2*off(3)) - 64*a(pos+off(1)+ off(2)-2*off(3)) + 8*a(pos+2*off(1)+ off(2)-2*off(3)) &
& + a(pos-2*off(1)+2*off(2)-2*off(3)) - 8*a(pos-off(1)+2*off(2)-2*off(3)) + 8*a(pos+off(1)+2*off(2)-2*off(3)) - a(pos+2*off(1)+2*off(2)-2*off(3)) &
& + 8*a(pos-2*off(1)-2*off(2)- off(3)) - 64*a(pos-off(1)-2*off(2)- off(3)) + 64*a(pos+off(1)-2*off(2)- off(3)) - 8*a(pos+2*off(1)-2*off(2)- off(3)) &
& - 64*a(pos-2*off(1)- off(2)- off(3)) + 512*a(pos-off(1)- off(2)- off(3)) - 512*a(pos+off(1)- off(2)- off(3)) + 64*a(pos+2*off(1)- off(2)- off(3)) &
& + 64*a(pos-2*off(1)+ off(2)- off(3)) - 512*a(pos-off(1)+ off(2)- off(3)) + 512*a(pos+off(1)+ off(2)- off(3)) - 64*a(pos+2*off(1)+ off(2)- off(3)) &
& - 8*a(pos-2*off(1)+2*off(2)- off(3)) + 64*a(pos-off(1)+2*off(2)- off(3)) - 64*a(pos+off(1)+2*off(2)- off(3)) + 8*a(pos+2*off(1)+2*off(2)- off(3)) &
& - 8*a(pos-2*off(1)-2*off(2)+ off(3)) + 64*a(pos-off(1)-2*off(2)+ off(3)) - 64*a(pos+off(1)-2*off(2)+ off(3)) + 8*a(pos+2*off(1)-2*off(2)+ off(3)) &
& + 64*a(pos-2*off(1)- off(2)+ off(3)) - 512*a(pos-off(1)- off(2)+ off(3)) + 512*a(pos+off(1)- off(2)+ off(3)) - 64*a(pos+2*off(1)- off(2)+ off(3)) &
& - 64*a(pos-2*off(1)+ off(2)+ off(3)) + 512*a(pos-off(1)+ off(2)+ off(3)) - 512*a(pos+off(1)+ off(2)+ off(3)) + 64*a(pos+2*off(1)+ off(2)+ off(3)) &
& + 8*a(pos-2*off(1)+2*off(2)+ off(3)) - 64*a(pos-off(1)+2*off(2)+ off(3)) + 64*a(pos+off(1)+2*off(2)+ off(3)) - 8*a(pos+2*off(1)+2*off(2)+ off(3)) &
& + a(pos-2*off(1)-2*off(2)+2*off(3)) - 8*a(pos-off(1)-2*off(2)+2*off(3)) + 8*a(pos+off(1)-2*off(2)+2*off(3)) - a(pos+2*off(1)-2*off(2)+2*off(3)) &
& - 8*a(pos-2*off(1)- off(2)+2*off(3)) + 64*a(pos-off(1)- off(2)+2*off(3)) - 64*a(pos+off(1)- off(2)+2*off(3)) + 8*a(pos+2*off(1)- off(2)+2*off(3)) &
& + 8*a(pos-2*off(1)+ off(2)+2*off(3)) - 64*a(pos-off(1)+ off(2)+2*off(3)) + 64*a(pos+off(1)+ off(2)+2*off(3)) - 8*a(pos+2*off(1)+ off(2)+2*off(3)) &
& - a(pos-2*off(1)+2*off(2)+2*off(3)) + 8*a(pos-off(1)+2*off(2)+2*off(3)) - 8*a(pos+off(1)+2*off(2)+2*off(3)) + a(pos+2*off(1)+2*off(2)+2*off(3))) / (512*dx(1)*dx(2)*dx(3))
f(1,3,1) = f(3,1,1)
f(2,3,1) = f(3,2,1)
f(3,3,1) = (+ a(pos-2*off(3)-2*off(1)) - 16*a(pos-off(3)-2*off(1)) + 30*a(pos-2*off(1)) - 16*a(pos+off(3)-2*off(1)) + a(pos+2*off(3)-2*off(1)) &
& - 8*a(pos-2*off(3)- off(1)) + 128*a(pos-off(3)- off(1)) - 240*a(pos- off(1)) + 128*a(pos+off(3)- off(1)) - 8*a(pos+2*off(3)- off(1)) &
& + 8*a(pos-2*off(3)+ off(1)) - 128*a(pos-off(3)+ off(1)) + 240*a(pos+ off(1)) - 128*a(pos+off(3)+ off(1)) + 8*a(pos+2*off(3)+ off(1)) &
& - a(pos-2*off(3)+2*off(1)) + 16*a(pos-off(3)+2*off(1)) - 30*a(pos+2*off(1)) + 16*a(pos+off(3)+2*off(1)) - a(pos+2*off(3)+2*off(1))) / (144*dx(3)**2*dx(1))
f(:,1,2) = f(:,2,1)
f(1,2,2) = f(2,2,1)
f(2,2,2) = (a(pos-3*off(2)) - 8*a(pos-2*off(2)) + 13*a(pos-off(2)) - 13*a(pos+off(2)) + 8*a(pos+2*off(2)) - a(pos+3*off(2))) / (8*dx(2)**3)
f(3,2,2) = (+ a(pos-2*off(2)-2*off(3)) - 16*a(pos-off(2)-2*off(3)) + 30*a(pos-2*off(3)) - 16*a(pos+off(2)-2*off(3)) + a(pos+2*off(2)-2*off(3)) &
& - 8*a(pos-2*off(2)- off(3)) + 128*a(pos-off(2)- off(3)) - 240*a(pos- off(3)) + 128*a(pos+off(2)- off(3)) - 8*a(pos+2*off(2)- off(3)) &
& + 8*a(pos-2*off(2)+ off(3)) - 128*a(pos-off(2)+ off(3)) + 240*a(pos+ off(3)) - 128*a(pos+off(2)+ off(3)) + 8*a(pos+2*off(2)+ off(3)) &
& - a(pos-2*off(2)+2*off(3)) + 16*a(pos-off(2)+2*off(3)) - 30*a(pos+2*off(3)) + 16*a(pos+off(2)+2*off(3)) - a(pos+2*off(2)+2*off(3))) / (144*dx(2)**2*dx(3))
f(1,3,2) = f(3,1,2)
f(2,3,2) = f(3,2,2)
f(3,3,2) = (+ a(pos-2*off(3)-2*off(2)) - 16*a(pos-off(3)-2*off(2)) + 30*a(pos-2*off(2)) - 16*a(pos+off(3)-2*off(2)) + a(pos+2*off(3)-2*off(2)) &
& - 8*a(pos-2*off(3)- off(2)) + 128*a(pos-off(3)- off(2)) - 240*a(pos- off(2)) + 128*a(pos+off(3)- off(2)) - 8*a(pos+2*off(3)- off(2)) &
& + 8*a(pos-2*off(3)+ off(2)) - 128*a(pos-off(3)+ off(2)) + 240*a(pos+ off(2)) - 128*a(pos+off(3)+ off(2)) + 8*a(pos+2*off(3)+ off(2)) &
& - a(pos-2*off(3)+2*off(2)) + 16*a(pos-off(3)+2*off(2)) - 30*a(pos+2*off(2)) + 16*a(pos+off(3)+2*off(2)) - a(pos+2*off(3)+2*off(2))) / (144*dx(3)**2*dx(2))
f(:,1,3) = f(:,3,1)
f(:,2,3) = f(:,3,2)
f(1,3,3) = f(3,1,3)
f(2,3,3) = f(3,2,3)
f(3,3,3) = (a(pos-3*off(3)) - 8*a(pos-2*off(3)) + 13*a(pos-off(3)) - 13*a(pos+off(3)) + 8*a(pos+2*off(3)) - a(pos+3*off(3))) / (8*dx(3)**3)
case default
call CCTK_WARN (0, "Unsupported finite differencing order")
end select
end subroutine get_derivs3
#ifndef TGR_INCLUDED
end module derivs
#endif
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