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similarity_module.f90 5.89 KiB
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module similarity_module
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  use iso_c_binding, only: c_int, c_double
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  use, intrinsic :: ieee_arithmetic
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  implicit none
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  abstract interface
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    function objective_fun(sim, obs, n) result(val)
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      use iso_c_binding, only: c_int, c_double
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      implicit none
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      integer(c_int), intent(in) :: n
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      real(c_double), intent(in) :: sim(n), obs(n)
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      real(c_double) :: val
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    end function objective_fun
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  end interface
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  procedure(objective_fun), pointer :: FUN => null()
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contains
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  subroutine set_objective_function(crit)
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    implicit none
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    integer(c_int), intent(in) :: crit
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    select case (crit)
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      case(1)
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        FUN => kge
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      case(2)
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        FUN => rmse
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      case(3)
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        FUN => invkge
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      case(4)
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        FUN => invrmse
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      case default
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        FUN => invkge
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    end select
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  end subroutine set_objective_function
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  subroutine similarity(Rn, nt, nb, crit, nthreads, sim_matrix) bind(C, name="similarity")
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    use, intrinsic :: ieee_arithmetic
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    use omp_lib
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    implicit none
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    integer(c_int), value :: nt, nb, crit, nthreads
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    real(c_double), intent(in) :: Rn(nt,nb)
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    real(c_double), intent(out) :: sim_matrix(nb,nb)
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    integer(c_int) :: i, j
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    real(c_double) :: val, nan_val
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    nan_val = ieee_value(0.0_c_double, ieee_quiet_nan)
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    call set_objective_function(crit)
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    if (.not. associated(FUN)) then
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      sim_matrix = nan_val
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      return
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    end if
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    select case (crit)
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      case(2, 4) ! if symetric, like RMSE
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        !$omp parallel do num_threads(nthreads) default(shared) private(i, j) schedule(static)
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        do i = 1, nb
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          do j = i, nb
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            sim_matrix(i,j) = FUN(Rn(:,i), Rn(:,j), nt)
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            sim_matrix(j,i) = sim_matrix(i,j)
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          end do
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        end do
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        !$omp end parallel do
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      case default ! if not symetric, like KGE
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        !$omp parallel do num_threads(nthreads) default(shared) private(i, j) schedule(static)
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        do i = 1, nb
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          do j = 1, nb
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sim_matrix(i,j) = FUN(Rn(:,i), Rn(:,j), nt) end do end do !$omp end parallel do end select end subroutine similarity function kge(sim, obs, n) result(kge_val) use, intrinsic :: ieee_arithmetic implicit none integer, intent(in) :: n real(c_double), dimension(n), intent(in) :: sim, obs real(c_double) :: kge_val integer :: i, count real(c_double) :: sum_obs, sum_sim, sum_obs2, sum_sim2, sum_obs_sim real(c_double) :: mean_obs, mean_sim, std_obs, std_sim, r, beta, gamma, diff real(c_double) :: nan_val, eps eps = 1.0e-12_c_double count = 0 sum_obs = 0.0_c_double sum_sim = 0.0_c_double sum_obs2 = 0.0_c_double sum_sim2 = 0.0_c_double sum_obs_sim = 0.0_c_double nan_val = ieee_value(0.0_c_double, ieee_quiet_nan) ! Loop to filter NaN values and accumulate sums do i = 1, n if (.not. ieee_is_nan(obs(i)) .and. .not. ieee_is_nan(sim(i))) then count = count + 1 sum_obs = sum_obs + obs(i) sum_sim = sum_sim + sim(i) sum_obs2 = sum_obs2 + obs(i) * obs(i) sum_sim2 = sum_sim2 + sim(i) * sim(i) sum_obs_sim = sum_obs_sim + obs(i) * sim(i) end if end do ! Return NA if the common period is not long enough if (count <= 1) then kge_val = nan_val return end if ! Compute means mean_obs = sum_obs / count mean_sim = sum_sim / count ! Check to avoid division by zero if (abs(mean_obs) < eps) then kge_val = nan_val return end if ! Compute standard deviations (using Welford's correction) std_obs = sqrt((sum_obs2 - sum_obs * mean_obs) / (count - 1)) std_sim = sqrt((sum_sim2 - sum_sim * mean_sim) / (count - 1)) ! Check standard deviations if (std_obs < eps .or. std_sim < eps) then kge_val = nan_val return end if ! Compute correlation r = ((sum_obs_sim - count * mean_obs * mean_sim) / (count - 1)) / (std_obs * std_sim) ! Compute KGE components
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beta = mean_sim / mean_obs gamma = (std_sim / mean_sim) / (std_obs / mean_obs) ! Final KGE computation diff = (r - 1.0_c_double)**2 + (beta - 1.0_c_double)**2 + (gamma - 1.0_c_double)**2 kge_val = 1.0_c_double - sqrt(diff) if (abs(kge_val - 1.0_c_double) < eps) kge_val = 1.0_c_double end function kge function rmse(sim, obs, n) result(res) integer, intent(in) :: n real(c_double), dimension(n), intent(in) :: sim, obs real(c_double) :: res integer :: i, count real(c_double) :: sum_sq, diff real(c_double) :: nan_val, eps nan_val = ieee_value(0.0_c_double, ieee_quiet_nan) eps = 1.0e-12_c_double count = 0 sum_sq = 0.0_c_double do i = 1, n if (.not. ieee_is_nan(obs(i)) .and. .not. ieee_is_nan(sim(i))) then count = count + 1 diff = sim(i) - obs(i) sum_sq = sum_sq + diff**2 end if end do if (count == 0) then res = nan_val return end if res = sqrt(sum_sq / count) if (res < eps) res = 0.0_c_double end function rmse function invrmse(sim, obs, n) result(res) integer, intent(in) :: n real(c_double), dimension(n), intent(in) :: sim, obs real(c_double) :: rmse_val, res real(c_double) :: inf_val, eps inf_val = ieee_value(0.0_c_double, ieee_positive_inf) eps = 1.0e-12_c_double rmse_val = rmse(obs, sim, n) if (rmse_val < eps) then res = inf_val else res = 1.0_c_double / rmse_val end if end function invrmse function invkge(sim, obs, n) result(res) integer, intent(in) :: n real(c_double), dimension(n), intent(in) :: sim, obs real(c_double) :: kge_val, res real(c_double) :: inf_val, eps inf_val = ieee_value(0.0_c_double, ieee_positive_inf) eps = 1.0e-12_c_double kge_val = kge(obs, sim, n) if (abs(kge_val - 1.0_c_double) < eps) then res = inf_val else res = 1.0_c_double / (1-kge_val) end if end function invkge
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end module similarity_module