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utils_mod.F90
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MODULE utils_mod
interface quicksort
MODULE procedure quicksort_single
MODULE procedure quicksort_double
MODULE procedure quicksort_int32
END interface quicksort
CONTAINS
!--------------------------------------------------
SUBROUTINE insert_into_sorted_list1 (x, n, list, iloc, is_new_out)
IMPLICIT NONE
integer, intent(in) :: x
integer, intent(inout) :: n
integer, intent(inout) :: list(:)
integer, intent(out) :: iloc
logical, intent(out), optional :: is_new_out
logical :: is_new
! Local variables
integer :: iright, ileft
IF (n == 0) THEN
iloc = 1
is_new = .true.
ELSEIF (x <= list(1)) THEN
iloc = 1
is_new = (x /= list(1))
ELSEIF (x > list(n)) THEN
iloc = n + 1
is_new = .true.
ELSEIF (x == list(n)) THEN
iloc = n
is_new = .false.
ELSE
iright = 1
ileft = n
DO WHILE (.true.)
IF (ileft - iright > 1) THEN
iloc = (iright + ileft) / 2
IF (x > list(iloc)) THEN
iright = iloc
ELSEIF (x < list(iloc)) THEN
ileft = iloc
ELSE
is_new = .false.
EXIT
ENDIF
ELSE
iloc = ileft
is_new = .true.
EXIT
ENDIF
ENDDO
ENDIF
IF (is_new) THEN
IF (iloc <= n) THEN
list(iloc+1:n+1) = list(iloc:n)
ENDIF
list(iloc) = x
n = n + 1
ENDIF
IF (present(is_new_out)) THEN
is_new_out = is_new
ENDIF
END SUBROUTINE insert_into_sorted_list1
!--------------------------------------------------
SUBROUTINE insert_into_sorted_list2 (x, y, n, xlist, ylist, iloc, is_new_out)
IMPLICIT NONE
integer, intent(in) :: x, y
integer, intent(inout) :: n
integer, intent(inout) :: xlist(:), ylist(:)
integer, intent(out) :: iloc
logical, intent(out), optional :: is_new_out
! Local variables
logical :: is_new
integer :: ileft, iright
IF (n == 0) THEN
iloc = 1
is_new = .true.
ELSEIF ((y < ylist(1)) .or. ((y == ylist(1)) .and. (x <= xlist(1)))) THEN
iloc = 1
is_new = (x /= xlist(1)) .or. (y /= ylist(1))
ELSEIF ((y > ylist(n)) .or. ((y == ylist(n)) .and. (x > xlist(n)))) THEN
iloc = n + 1
is_new = .true.
ELSEIF ((x == xlist(n)) .and. (y == ylist(n))) THEN
iloc = n
is_new = .false.
ELSE
ileft = 1
iright = n
DO WHILE (.true.)
IF (iright - ileft > 1) THEN
iloc = (ileft + iright) / 2
IF ((y > ylist(iloc)) .or. ((y == ylist(iloc)) .and. (x > xlist(iloc)))) THEN
ileft = iloc
ELSEIF ((y < ylist(iloc)) .or. ((y == ylist(iloc)) .and. (x < xlist(iloc)))) THEN
iright = iloc
ELSE
is_new = .false.
EXIT
ENDIF
ELSE
iloc = iright
is_new = .true.
EXIT
ENDIF
ENDDO
ENDIF
IF (is_new) THEN
IF (iloc <= n) THEN
xlist(iloc+1:n+1) = xlist(iloc:n)
ylist(iloc+1:n+1) = ylist(iloc:n)
ENDIF
xlist(iloc) = x
ylist(iloc) = y
n = n + 1
ENDIF
IF (present(is_new_out)) THEN
is_new_out = is_new
ENDIF
END SUBROUTINE insert_into_sorted_list2
!--------------------------------------------------
FUNCTION find_in_sorted_list1 (x, n, list) result(iloc)
IMPLICIT NONE
integer :: iloc
integer, intent(in) :: x
integer, intent(in) :: n
integer, intent(in) :: list (n)
! Local variables
integer :: i, ileft, iright
iloc = 0
IF (n > 0) THEN
IF ((x >= list(1)) .and. (x <= list(n))) THEN
IF (x == list(1)) THEN
iloc = 1
ELSEIF (x == list(n)) THEN
iloc = n
ELSE
ileft = 1
iright = n
DO WHILE (iright - ileft > 1)
i = (ileft + iright) / 2
IF (x == list(i)) THEN
iloc = i
EXIT
ELSEIF (x > list(i)) THEN
ileft = i
ELSEIF (x < list(i)) THEN
iright = i
ENDIF
ENDDO
ENDIF
ENDIF
ENDIF
END FUNCTION find_in_sorted_list1
!--------------------------------------------------
FUNCTION find_in_sorted_list2 (x, y, n, xlist, ylist) result(iloc)
IMPLICIT NONE
integer :: iloc
integer, intent(in) :: x, y
integer, intent(in) :: n
integer, intent(in) :: xlist(:), ylist(:)
! Local variables
integer :: i, ileft, iright
iloc = 0
IF (n < 1) RETURN
IF ((y < ylist(1)) .or. ((y == ylist(1)) .and. (x < xlist(1)))) THEN
iloc = 0
ELSEIF ((y > ylist(n)) .or. ((y == ylist(n)) .and. (x > xlist(n)))) THEN
iloc = 0
ELSEIF ((x == xlist(1)) .and. (y == ylist(1))) THEN
iloc = 1
ELSEIF ((x == xlist(n)) .and. (y == ylist(n))) THEN
iloc = n
ELSE
ileft = 1
iright = n
DO WHILE (.true.)
IF (iright - ileft > 1) THEN
i = (ileft + iright) / 2
IF ((y == ylist(i)) .and. (x == xlist(i))) THEN
iloc = i
EXIT
ELSEIF ((y > ylist(i)) .or. ((y == ylist(i)) .and. (x > xlist(i)))) THEN
ileft = i
ELSEIF ((y < ylist(i)) .or. ((y == ylist(i)) .and. (x < xlist(i)))) THEN
iright = i
ENDIF
ELSE
iloc = 0
EXIT
ENDIF
ENDDO
ENDIF
END FUNCTION find_in_sorted_list2
!-----------------------------------------------------
SUBROUTINE find_floor_lat (y, n, lat, iloc, yinc)
USE precision
IMPLICIT NONE
real(r8), intent(in) :: y
integer, intent(in) :: n
real(r8), intent(in) :: lat (n)
integer, intent(out) :: iloc
integer, intent(out), optional :: yinc
! Local variables
integer :: i, iright, ileft
IF (lat(1) < lat(n)) THEN
IF (present(yinc)) yinc = 1
IF (y <= lat(1)) THEN
iloc = 1
ELSEIF (y >= lat(n)) THEN
iloc = n
ELSE
ileft = 1; iright = n
DO WHILE (iright - ileft > 1)
i = (iright + ileft) / 2
IF (y >= lat(i)) THEN
ileft = i
ELSE
iright = i
ENDIF
ENDDO
iloc = ileft
ENDIF
ELSE
IF (present(yinc)) yinc = -1
IF (y >= lat(1)) THEN
iloc = 1
ELSEIF (y <= lat(n)) THEN
iloc = n
ELSE
ileft = 1; iright = n
DO WHILE (iright - ileft > 1)
i = (iright + ileft) / 2
IF (y >= lat(i)) THEN
iright = i
ELSE
ileft = i
ENDIF
ENDDO
iloc = iright
ENDIF
ENDIF
END SUBROUTINE find_floor_lat
!-----------------------------------------------------
SUBROUTINE find_ceiling_lat (y, n, lat, iloc, yinc)
USE precision
IMPLICIT NONE
real(r8), intent(in) :: y
integer, intent(in) :: n
real(r8), intent(in) :: lat (n)
integer, intent(out) :: iloc
integer, intent(out), optional :: yinc
! Local variables
integer :: i, iright, ileft
IF (lat(1) < lat(n)) THEN
IF (present(yinc)) yinc = 1
IF (y <= lat(1)) THEN
iloc = 1
ELSEIF (y >= lat(n)) THEN
iloc = n
ELSE
ileft = 1; iright = n
DO WHILE (iright - ileft > 1)
i = (iright + ileft) / 2
IF (y > lat(i)) THEN
ileft = i
ELSE
iright = i
ENDIF
ENDDO
iloc = ileft
ENDIF
ELSE
IF (present(yinc)) yinc = -1
IF (y >= lat(1)) THEN
iloc = 1
ELSEIF (y <= lat(n)) THEN
iloc = n
ELSE
ileft = 1; iright = n
DO WHILE (iright - ileft > 1)
i = (iright + ileft) / 2
IF (y > lat(i)) THEN
iright = i
ELSE
ileft = i
ENDIF
ENDDO
iloc = iright
ENDIF
ENDIF
END SUBROUTINE find_ceiling_lat
!-----------------------------------------------------
SUBROUTINE find_floor_lon (x, n, lon, iloc)
USE precision
IMPLICIT NONE
real(r8), intent(in) :: x
integer, intent(in) :: n
real(r8), intent(in) :: lon (n)
integer, intent(out) :: iloc
! Local variables
integer :: i, iright, ileft
IF (lon(1) >= lon(n)) THEN
! for the cast 0~180 -> -180~0
IF ((x >= lon(n)) .and. (x < lon(1))) THEN
iloc = n; RETURN
ENDIF
ELSE
! for the CASE -180~180
IF ((x < lon(1)) .or. (x >= lon(n))) THEN
iloc = n; RETURN
ENDIF
ENDIF
ileft = 1; iright = n
DO WHILE (iright - ileft > 1)
i = (iright + ileft)/2
IF (lon(iright) > lon(i)) THEN
IF (x >= lon(i)) THEN
ileft = i
ELSE
iright = i
ENDIF
ELSE
IF ((x < lon(iright)) .or. (x >= lon(i))) THEN
ileft = i
ELSE
iright = i
ENDIF
ENDIF
ENDDO
iloc = ileft
END SUBROUTINE find_floor_lon
!-----------------------------------------
FUNCTION max_lon (lon1, lon2) result (lon)
USE precision
IMPLICIT NONE
real(r8) :: lon
real(r8), intent(in) :: lon1, lon2
real(r8) :: lonr, lonl
lonr = max(lon1,lon2); lonl = min(lon1,lon2)
IF (lonr - lonl > 180.0) THEN
lon = lonl
ELSE
lon = lonr
ENDIF
END FUNCTION max_lon
!-----------------------------------------
FUNCTION min_lon (lon1, lon2) result (lon)
USE precision
IMPLICIT NONE
real(r8) :: lon
real(r8), intent(in) :: lon1, lon2
real(r8) :: lonr, lonl
lonr = max(lon1,lon2); lonl = min(lon1,lon2)
IF (lonr - lonl > 180.0) THEN
lon = lonr
ELSE
lon = lonl
ENDIF
END FUNCTION min_lon
!-----------------------------------------------------
SUBROUTINE find_ceiling_lon (x, n, lon, iloc)
USE precision
IMPLICIT NONE
real(r8), intent(in) :: x
integer, intent(in) :: n
real(r8), intent(in) :: lon (n)
integer, intent(out) :: iloc
! Local variables
integer :: i, iright, ileft
IF (lon(1) >= lon(n)) THEN
! for the cast 0~180 -> -180~0
IF ((x > lon(n)) .and. (x <= lon(1))) THEN
iloc = 1; RETURN
ENDIF
ELSE
! for the CASE -180~180
IF ((x <= lon(1)) .or. (x > lon(n))) THEN
iloc = 1; RETURN
ENDIF
ENDIF
ileft = 1; iright = n
DO WHILE (iright - ileft > 1)
i = (iright + ileft)/2
IF (lon(iright) > lon(i)) THEN
IF (x > lon(i)) THEN
ileft = i
ELSE
iright = i
ENDIF
ELSE
IF ((x <= lon(iright)) .or. (x > lon(i))) THEN
ileft = i
ELSE
iright = i
ENDIF
ENDIF
ENDDO
iloc = iright
END SUBROUTINE find_ceiling_lon
!-----------------------------------------------------
recursive SUBROUTINE quicksort_single (nA, A, order)
USE precision
IMPLICIT NONE
integer, intent(in) :: nA
real(4), intent(inout) :: A (nA)
integer, intent(inout) :: order (nA)
! Local variables
integer :: left, right
real(4) :: pivot
integer :: marker
real(4) :: rtemp
integer :: itemp
IF (nA > 1) THEN
pivot = A (nA/2)
left = 0
right = nA + 1
DO WHILE (left < right)
right = right - 1
DO WHILE (A(right) > pivot)
right = right - 1
ENDDO
left = left + 1
DO WHILE (A(left) < pivot)
left = left + 1
ENDDO
IF (left < right) THEN
rtemp = A(left)
A(left) = A(right)
A(right) = rtemp
itemp = order(left)
order(left) = order(right)
order(right) = itemp
ENDIF
ENDDO
IF (left == right) THEN
marker = left + 1
ELSE
marker = left
ENDIF
CALL quicksort_single (marker-1, A(:marker-1), order(:marker-1))
CALL quicksort_single (nA-marker+1, A(marker:), order(marker:) )
ENDIF
END SUBROUTINE quicksort_single
!-----------------------------------------------------
recursive SUBROUTINE quicksort_double (nA, A, order)
USE precision
IMPLICIT NONE
integer , intent(in) :: nA
real(r8), intent(inout) :: A (nA)
integer , intent(inout) :: order (nA)
! Local variables
integer :: left, right
real(r8) :: pivot
integer :: marker
real(r8) :: rtemp
integer :: itemp
IF (nA > 1) THEN
pivot = A (nA/2)
left = 0
right = nA + 1
DO WHILE (left < right)
right = right - 1
DO WHILE (A(right) > pivot)
right = right - 1
ENDDO
left = left + 1
DO WHILE (A(left) < pivot)
left = left + 1
ENDDO
IF (left < right) THEN
rtemp = A(left)
A(left) = A(right)
A(right) = rtemp
itemp = order(left)
order(left) = order(right)
order(right) = itemp
ENDIF
ENDDO
IF (left == right) THEN
marker = left + 1
ELSE
marker = left
ENDIF
CALL quicksort_double (marker-1, A(:marker-1), order(:marker-1))
CALL quicksort_double (nA-marker+1, A(marker:), order(marker:) )
ENDIF
END SUBROUTINE quicksort_double
!-----------------------------------------------------
recursive SUBROUTINE quicksort_int32 (nA, A, order)
USE precision
IMPLICIT NONE
integer, intent(in) :: nA
integer, intent(inout) :: A (nA)
integer, intent(inout) :: order (nA)
! Local variables
integer :: left, right
real(r8) :: pivot
integer :: marker
integer :: itemp
IF (nA > 1) THEN
pivot = A (nA/2)
left = 0
right = nA + 1
DO WHILE (left < right)
right = right - 1
DO WHILE (A(right) > pivot)
right = right - 1
ENDDO
left = left + 1
DO WHILE (A(left) < pivot)
left = left + 1
ENDDO
IF (left < right) THEN
itemp = A(left)
A(left) = A(right)
A(right) = itemp
itemp = order(left)
order(left) = order(right)
order(right) = itemp
ENDIF
ENDDO
IF (left == right) THEN
marker = left + 1
ELSE
marker = left
ENDIF
CALL quicksort_int32 (marker-1, A(:marker-1), order(:marker-1))
CALL quicksort_int32 (nA-marker+1, A(marker:), order(marker:) )
ENDIF
END SUBROUTINE quicksort_int32
!-----------------------------------------------------
recursive FUNCTION quickselect (nA, A, k) result(selected)
USE precision
IMPLICIT NONE
real(r8) :: selected
integer , intent(in) :: nA
real(r8), intent(inout) :: A (nA)
integer, intent(in) :: k
! Local variables
integer :: left, right
real(r8) :: pivot
integer :: marker
real(r8) :: rtemp
IF (nA > 1) THEN
pivot = A (nA/2)
left = 0
right = nA + 1
DO WHILE (left < right)
right = right - 1
DO WHILE (A(right) > pivot)
right = right - 1
ENDDO
left = left + 1
DO WHILE (A(left) < pivot)
left = left + 1
ENDDO
IF (left < right) THEN
rtemp = A(left)
A(left) = A(right)
A(right) = rtemp
ENDIF
ENDDO
IF (left == right) THEN
marker = left + 1
ELSE
marker = left
ENDIF
IF (k < marker) THEN
selected = quickselect (marker-1, A(:marker-1), k)
ELSE
selected = quickselect (nA-marker+1, A(marker:), k-marker+1)
ENDIF
ELSE
selected = A(1)
ENDIF
END FUNCTION quickselect
! ------------------------
FUNCTION median(x, n) result(mval)
USE precision
IMPLICIT NONE
real(r8) :: mval
integer, intent(in) :: n
real(r8), intent(in) :: x(n)
real(r8), allocatable :: xtemp(:)
allocate (xtemp(n))
xtemp = x
IF (mod(n,2) == 0) THEN
mval = (quickselect(n,xtemp,n/2) + quickselect(n,xtemp,n/2+1)) / 2.0_r8
ELSE
mval = quickselect(n,xtemp,n/2+1)
ENDIF
deallocate (xtemp)
END FUNCTION median
!-----------------------------------------------------
FUNCTION areaquad (lat0, lat1, lon0, lon1) result(area)
USE precision
USE MathConstants, only : deg2rad
IMPLICIT NONE
real(r8), parameter :: re = 6.37122e3 ! kilometer
real(r8) :: area
real(r8), intent(in) :: lat0, lat1, lon0, lon1
real(r8) :: dx, dy
IF (lon1 < lon0) THEN
dx = (lon1 + 360 -lon0) * deg2rad
ELSE
dx = (lon1 - lon0) * deg2rad
ENDIF
dy = sin(lat1 * deg2rad) - sin(lat0 * deg2rad)
area = dx * dy * re * re
END FUNCTION areaquad
END MODULE utils_mod