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find_weibull.f90
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find_weibull.f90
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! Simple program for finding the Weibull distribution parameters
! k shape factor and c scale factor.
! The file with the example wind measurement data set comes
! from the measurement mast US Virgin Islands St. Thomas Bovoni and
! was downloaded from the site
! https://midcdmz.nrel.gov/apps/sitehome.pl?site=USVILONA.
!
! Roberts, O.; Andreas, A.; (1997). United States Virgin Islands:
! St. Thomas & St. Croix (Data); NREL Report No. DA-5500-64451.
! http://dx.doi.org/10.7799/1183464
! https://midcdmz.nrel.gov/
!
! https://midcdmz.nrel.gov/
!
! Sorting function from
! https://fortran-lang.discourse.group/t/modern-fortran-sample-code/2019/4
!
program find_weibull
implicit none
integer, parameter :: maxread = 10**6
logical :: file_exists
character(len=9999) :: fname
integer :: i, nread
integer :: funit, ierr
integer :: niter
real :: k ! shape factor
real :: c ! scale factor
real :: ws_mean, ws_median
real :: kmax, kmin
real :: eps
real, allocatable :: rtemp(:), ws(:)
! check if an argument is present
if(command_argument_count() < 1) stop 'Usage: find_weibull.out <filename>'
! get a filename from an argument
call get_command_argument(1, fname)
! check if file exists
inquire(file = fname, exist = file_exists)
if(.not. file_exists) stop 'File does not exist!'
allocate(rtemp(maxread))
nread = maxread
open(newunit = funit, file = fname, action = "read", status = "old")
read(funit, *) ! read the header
do i = 1, maxread
read(funit, *, iostat = ierr) rtemp(i)
if (ierr /= 0) then ! reached end of file
nread = i - 1
exit
end if
end do
close(funit)
allocate(ws(nread), source=rtemp(:nread))
deallocate(rtemp)
! range for searching k and c
kmin = 1.0
kmax = 8.0
! accuracy
eps = 0.000001
! number of iterations
niter = 50
! shape factor
k = bisection(ws, kmin, kmax, eps, niter)
! mean wind speed
ws_mean = sum(ws) / nread
! scale factor
c = ws_mean * (0.586 + 0.433/k)**(-1/k)
! median wind speed
ws_median = median(ws)
print*, "Found Weibull distribution parameters:"
print*
write(*, "(A,F4.2,A)") " shape factor k: ", k
write(*, "(A,F4.2,A)") " scale factor c: ", c
print*
write(*, "(A,F4.2,A)") " Mean wind speed: ", ws_mean, " m/s"
write(*, "(A,F4.2,A)") " Median wind speed: ", ws_median, " m/s"
deallocate(ws)
contains
! k estimator
pure real function k_estimator(x, kin) result(res)
real, intent(in) :: x(:)
real, intent(in) :: kin
integer :: n
n = size(x)
res = (sum(x**3) / n) / ((sum(x) / n)**3)
res = res * (gamma(1.0+1.0/kin)**3) - gamma(1.0 + 3.0/kin)
end function k_estimator
real function bisection(x, ikmin, ikmax, eps, iter) result (k)
real, intent(in) :: x(:)
real, intent(in) :: ikmin, ikmax, eps
integer, intent(in) :: iter
!real :: k
integer :: j
real :: fk, fkk
real :: fkmin, fkmax
real :: kmin, kmax
! initial values
kmin = ikmin
kmax = ikmax
fkmin = k_estimator(x, kmin)
fkmax = k_estimator(x, kmax)
if (fkmin * fkmax > 0) then
print *, "Error: Both estimated k values are greater than zero!"
k = 0
stop
end if
do j = 1, iter
k = (kmin + kmax) / 2
fk = k_estimator(x, k)
fkk = (fkmax - fkmin) / (kmax - kmin)
if (abs(fk/fkk) - eps > 0) then
if (fk*fkmin < 0) then
kmax = k
fkmax = fk
else
if (fk * fkmin == 0) then
return
end if
kmin = k
fkmin = fk
end if
else
return
end if
end do
k = 0
end function bisection
pure real function median(x) result(res)
real, intent(in) :: x(:)
real :: xs(size(x))
integer :: n
xs = qsort(x)
n = size(x)
if (mod(n, 2) == 0) then
res = (xs(n/2) + xs(n/2+1)) / 2
else
res = xs((n+1)/2)
end if
end function median
! sorting function from
! https://fortran-lang.discourse.group/t/modern-fortran-sample-code/2019/4
pure recursive function qsort(data) result(sorted)
real, intent(in) :: data(:)
real :: sorted(size(data))
if (size(data) > 1) then
sorted = [qsort(pack(data(2:),data(2:)<data(1))), data(1), &
qsort(pack(data(2:),data(2:)>=data(1)))]
else
sorted = data
end if
end function qsort
end program find_weibull