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! $Header$
#include "cctk.h"
module timederivs
implicit none
private
public abs2
public timederiv
public timederiv2
public timederiv_uneven
public timederiv2_uneven
public operator(.outer.)
public operator(.dot.)
interface timederiv
module procedure rtimederiv
end interface
interface timederiv2
module procedure rtimederiv2
end interface
interface timederiv_uneven
module procedure rtimederiv_uneven
module procedure ctimederiv_uneven
end interface
interface timederiv2_uneven
module procedure rtimederiv2_uneven
module procedure ctimederiv2_uneven
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
elemental function abs2 (a)
CCTK_COMPLEX, intent(in) :: a
CCTK_REAL :: abs2
abs2 = a * conjg(a)
end function abs2
! Calculate a time derivate from several time levels
elemental function rtimederiv (f0, f1, f2, dt) result (fdot)
CCTK_REAL, intent(in) :: f0, f1, f2
CCTK_REAL, intent(in) :: dt
CCTK_REAL :: fdot
CCTK_REAL :: dt1, dt2
CCTK_REAL :: fdot1, fdot2
dt1 = dt
dt2 = 2*dt
! 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 function rtimederiv
elemental function rtimederiv2 (f0, f1, f2, dt) result (fdotdot)
CCTK_REAL, intent(in) :: f0, f1, f2
CCTK_REAL, intent(in) :: dt
CCTK_REAL :: fdotdot
CCTK_REAL :: dt1, dt2
CCTK_REAL :: fdotdot1, fdotdot2
dt1 = dt
dt2 = 2*dt
! 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 function rtimederiv2
! Calculate a time derivate from several time levels with uneven spacing
elemental function rtimederiv_uneven (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
CCTK_INT, intent(in) :: ce0, ce1, ce2
CCTK_REAL :: fdot
CCTK_REAL :: dt1, dt2
CCTK_REAL :: fdot1, fdot2
!!$ dt1 = ih_time(hn) - ih_time_p(hn)
!!$ dt2 = ih_time(hn) - ih_time_p_p(hn)
dt1 = t0 - t1
dt2 = t0 - t2
if (ce1/=0) then
fdot = 0
else if (ce2/=0) 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_uneven
elemental function ctimederiv_uneven (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
CCTK_INT, intent(in) :: ce0, ce1, ce2
CCTK_COMPLEX :: fdot
fdot = cmplx(timederiv_uneven(real(f0),real(f1),real(f2), t0,t1,t2, ce0,ce1,ce2), &
& timederiv_uneven(aimag(f0),aimag(f1),aimag(f2), t0,t1,t2, ce0,ce1,ce2), &
& kind(fdot))
end function ctimederiv_uneven
elemental function rtimederiv2_uneven (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
CCTK_INT, intent(in) :: ce0, ce1, ce2
CCTK_REAL :: fdotdot
CCTK_REAL :: dt1, dt2
CCTK_REAL :: fdotdot1, fdotdot2
!!$ dt1 = ih_time(hn) - ih_time_p(hn)
!!$ dt2 = ih_time(hn) - ih_time_p_p(hn)
dt1 = t0 - t1
dt2 = t0 - t2
if (ce1/=0) then
fdotdot = 0
else if (ce2/=0) 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_uneven
elemental function ctimederiv2_uneven (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
CCTK_INT, intent(in) :: ce0, ce1, ce2
CCTK_COMPLEX :: fdotdot
fdotdot = cmplx(timederiv2_uneven(real(f0),real(f1),real(f2), t0,t1,t2, ce0,ce1,ce2), &
& timederiv2_uneven(aimag(f0),aimag(f1),aimag(f2), t0,t1,t2, ce0,ce1,ce2), &
& kind(fdotdot))
end function ctimederiv2_uneven
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
end module timederivs
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