!--------------------------------------------------------------------------------------------------!
!   CP2K: A general program to perform molecular dynamics simulations                              !
!   Copyright (C) 2000 - 2018  CP2K developers group                                               !
!--------------------------------------------------------------------------------------------------!

! **************************************************************************************************
!> \brief different utils that are useful to manipulate splines on the regular
!>      grid of a pw
!> \par History
!>      05.2003 created [fawzi]
!>      08.2004 removed spline evaluation method using more than 2 read streams
!>              (pw_compose_stripe_rs3), added linear solver based spline
!>              inversion [fawzi]
!> \author Fawzi Mohamed
! **************************************************************************************************
MODULE pw_spline_utils
   USE cp_log_handling,                 ONLY: cp_get_default_logger,&
                                              cp_logger_type,&
                                              cp_to_string
   USE kinds,                           ONLY: dp
   USE mathconstants,                   ONLY: twopi
   USE message_passing,                 ONLY: mp_alltoall,&
                                              mp_comm_compare,&
                                              mp_sendrecv,&
                                              mp_sum
   USE pw_grid_types,                   ONLY: FULLSPACE,&
                                              PW_MODE_LOCAL
   USE pw_methods,                      ONLY: pw_axpy,&
                                              pw_copy,&
                                              pw_integral_ab,&
                                              pw_zero
   USE pw_pool_types,                   ONLY: pw_pool_create_pw,&
                                              pw_pool_give_back_pw,&
                                              pw_pool_release,&
                                              pw_pool_retain,&
                                              pw_pool_type
   USE pw_types,                        ONLY: COMPLEXDATA1D,&
                                              REALDATA3D,&
                                              REALSPACE,&
                                              RECIPROCALSPACE,&
                                              pw_p_type,&
                                              pw_type
#include "../base/base_uses.f90"

   IMPLICIT NONE
   PRIVATE

   LOGICAL, PRIVATE, PARAMETER :: debug_this_module = .TRUE.
   CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'pw_spline_utils'

   INTEGER, PARAMETER, PUBLIC               :: no_precond = 0, &
                                               precond_spl3_aint = 1, &
                                               precond_spl3_1 = 2, &
                                               precond_spl3_aint2 = 3, &
                                               precond_spl3_2 = 4, &
                                               precond_spl3_3 = 5

   REAL(KIND=dp), PUBLIC, PARAMETER, DIMENSION(4) :: nn10_coeffs = &
                                                     (/125._dp/216._dp, 25._dp/432._dp, 5._dp/864._dp, 1._dp/1728._dp/), &
                                                     spline3_coeffs = &
                                                     (/8._dp/(27._dp), 2._dp/(27._dp), 1._dp/(27._dp*2._dp), &
                                                       1._dp/(27._dp*8._dp)/), &
                                                     spline2_coeffs = &
                                                     (/27._dp/(64._dp), 9._dp/(64._dp*2_dp), 3._dp/(64._dp*4._dp), &
                                                       1._dp/(64._dp*8._dp)/), &
                                                     nn50_coeffs = &
                                                     (/15625._dp/17576._dp, 625._dp/35152._dp, 25._dp/70304._dp, &
                                                       1._dp/140608._dp/), &
                                                     spl3_aint_coeff = &
                                                     (/46._dp/27._dp, -2._dp/(27._dp), -1._dp/(27._dp*2._dp), &
                                                       -1._dp/(27._dp*8._dp)/), &
                                                     spl3_precond1_coeff = &
                                                     (/64._dp/3._dp, -8._dp/3._dp, -1._dp/3._dp, -1._dp/24._dp/), &
                                                     spl3_1d_transf_coeffs = &
                                                     (/2._dp/3._dp, 23._dp/48._dp, 1._dp/6._dp, 1._dp/48._dp/)

   REAL(KIND=dp), PUBLIC, PARAMETER, DIMENSION(3) :: spline3_deriv_coeffs = &
                                                     (/2.0_dp/9.0_dp, 1.0_dp/18.0_dp, 1.0_dp/72.0_dp/), &
                                                     spline2_deriv_coeffs = &
                                                     (/9.0_dp/32.0_dp, 3.0_dp/64.0_dp, 1.0_dp/128.0_dp/), &
                                                     nn10_deriv_coeffs = &
                                                     (/25._dp/72._dp, 5._dp/144, 1._dp/288._dp/), &
                                                     nn50_deriv_coeffs = &
                                                     (/625._dp/1352._dp, 25._dp/2704._dp, 1._dp/5408._dp/), &
                                                     spl3_1d_coeffs0 = &
                                                     (/1._dp/6_dp, 2._dp/3._dp, 1._dp/6._dp/), &
                                                     spl3_1d_transf_border1 = &
                                                     (/0.517977704_dp, 0.464044595_dp, 0.17977701e-1_dp/)

   INTEGER, SAVE, PRIVATE :: last_precond_id = 0

   PUBLIC :: pw_spline3_interpolate_values_g, &
             pw_spline3_deriv_g
   PUBLIC :: pw_spline_scale_deriv
   PUBLIC :: pw_spline2_interpolate_values_g, &
             pw_spline2_deriv_g
   PUBLIC :: pw_nn_smear_r, pw_nn_deriv_r, &
             spl3_nopbc, spl3_pbc, spl3_nopbct
   PUBLIC :: add_fine2coarse, add_coarse2fine
   PUBLIC :: pw_spline_precond_create, &
             pw_spline_do_precond, &
             pw_spline_precond_set_kind, &
             find_coeffs, &
             pw_spline_precond_release, &
             pw_spline_precond_type, &
             Eval_Interp_Spl3_pbc, &
             Eval_d_Interp_Spl3_pbc

!***

! **************************************************************************************************
!> \brief stores information for the preconditioner used to calculate the
!>      coeffs of splines
!> \author fawzi
! **************************************************************************************************
   TYPE pw_spline_precond_type
      INTEGER :: ref_count, id_nr, kind
      REAL(kind=dp), DIMENSION(4) :: coeffs
      REAL(kind=dp), DIMENSION(3) :: coeffs_1d
      LOGICAL :: sharpen, normalize, pbc, transpose
      TYPE(pw_pool_type), POINTER :: pool
   END TYPE pw_spline_precond_type

CONTAINS

! **************************************************************************************************
!> \brief calculates the FFT of the coefficents of the quadratic spline that
!>      interpolates the given values
!> \param spline_g on entry the FFT of the values to interpolate as cc,
!>        will contain the FFT of the coefficents of the spline
!> \par History
!>      06.2003 created [fawzi]
!> \author Fawzi Mohamed
!> \note
!>      does not work with spherical cutoff
! **************************************************************************************************
   SUBROUTINE pw_spline2_interpolate_values_g(spline_g)
      TYPE(pw_type), POINTER                             :: spline_g

      CHARACTER(len=*), PARAMETER :: routineN = 'pw_spline2_interpolate_values_g', &
         routineP = moduleN//':'//routineN

      INTEGER                                            :: handle, i, ii, j, k
      INTEGER, DIMENSION(2, 3)                           :: gbo
      INTEGER, DIMENSION(3)                              :: n_tot
      REAL(KIND=dp)                                      :: c23, coeff
      REAL(KIND=dp), ALLOCATABLE, DIMENSION(:)           :: cosIVals, cosJVals, cosKVals

      CALL timeset(routineN, handle)

      n_tot(1:3) = spline_g%pw_grid%npts(1:3)
      gbo = spline_g%pw_grid%bounds

      CPASSERT(ASSOCIATED(spline_g))
      CPASSERT(spline_g%in_use == COMPLEXDATA1D)
      CPASSERT(spline_g%in_space == RECIPROCALSPACE)
      CPASSERT(.NOT. spline_g%pw_grid%spherical)
      CPASSERT(spline_g%pw_grid%grid_span == FULLSPACE)

      ALLOCATE (cosIVals(gbo(1, 1):gbo(2, 1)), cosJVals(gbo(1, 2):gbo(2, 2)), &
                cosKVals(gbo(1, 3):gbo(2, 3)))

      coeff = twopi/n_tot(1)
!$OMP     PARALLEL DO PRIVATE(i) DEFAULT(NONE) SHARED(cosIVals,coeff,gbo)
      DO i = gbo(1, 1), gbo(2, 1)
         cosIVals(i) = COS(coeff*REAL(i, dp))
      END DO
      coeff = twopi/n_tot(2)
!$OMP     PARALLEL DO PRIVATE(j) DEFAULT(NONE) SHARED(cosJVals,coeff,gbo)
      DO j = gbo(1, 2), gbo(2, 2)
         cosJVals(j) = COS(coeff*REAL(j, dp))
      END DO
      coeff = twopi/n_tot(3)
!$OMP     PARALLEL DO PRIVATE(k) DEFAULT(NONE) SHARED(cosKVals,coeff,gbo)
      DO k = gbo(1, 3), gbo(2, 3)
         cosKVals(k) = COS(coeff*REAL(k, dp))
      END DO

!$OMP     PARALLEL DO PRIVATE(i,j,k,ii,coeff,c23) DEFAULT(NONE) SHARED(spline_g,cosIVals,cosJVals,cosKVals)
      DO ii = 1, SIZE(spline_g%cc)
         i = spline_g%pw_grid%g_hat(1, ii)
         j = spline_g%pw_grid%g_hat(2, ii)
         k = spline_g%pw_grid%g_hat(3, ii)

         c23 = cosJVals(j)*cosKVals(k)
         coeff = 64.0_dp/(cosIVals(i)*c23+ &
                          (cosIVals(i)*cosJVals(j)+cosIVals(i)*cosKVals(k)+c23)*3.0_dp+ &
                          (cosIVals(i)+cosJVals(j)+cosKVals(k))*9.0_dp+ &
                          27.0_dp)

         spline_g%cc(ii) = spline_g%cc(ii)*coeff

      END DO
      DEALLOCATE (cosIVals, cosJVals, cosKVals)

      CALL timestop(handle)
   END SUBROUTINE pw_spline2_interpolate_values_g

! **************************************************************************************************
!> \brief calculates the FFT of the coefficents of the2 cubic spline that
!>      interpolates the given values
!> \param spline_g on entry the FFT of the values to interpolate as cc,
!>        will contain the FFT of the coefficents of the spline
!> \par History
!>      06.2003 created [fawzi]
!> \author Fawzi Mohamed
!> \note
!>      does not work with spherical cutoff
!>      stupid distribution for cos calculation, it should calculate only the
!>      needed cos, and avoid the mp_sum
! **************************************************************************************************
   SUBROUTINE pw_spline3_interpolate_values_g(spline_g)
      TYPE(pw_type), POINTER                             :: spline_g

      CHARACTER(len=*), PARAMETER :: routineN = 'pw_spline3_interpolate_values_g', &
         routineP = moduleN//':'//routineN

      INTEGER                                            :: handle, i, ii, j, k
      INTEGER, DIMENSION(2, 3)                           :: gbo
      INTEGER, DIMENSION(3)                              :: n_tot
      REAL(KIND=dp)                                      :: c23, coeff
      REAL(KIND=dp), ALLOCATABLE, DIMENSION(:)           :: cosIVals, cosJVals, cosKVals

      CALL timeset(routineN, handle)

      n_tot(1:3) = spline_g%pw_grid%npts(1:3)
      gbo = spline_g%pw_grid%bounds

      CPASSERT(ASSOCIATED(spline_g))
      CPASSERT(spline_g%in_use == COMPLEXDATA1D)
      CPASSERT(spline_g%in_space == RECIPROCALSPACE)
      CPASSERT(.NOT. spline_g%pw_grid%spherical)
      CPASSERT(spline_g%pw_grid%grid_span == FULLSPACE)

      ALLOCATE (cosIVals(gbo(1, 1):gbo(2, 1)), &
                cosJVals(gbo(1, 2):gbo(2, 2)), &
                cosKVals(gbo(1, 3):gbo(2, 3)))

      coeff = twopi/n_tot(1)
!$OMP     PARALLEL DO PRIVATE(i) DEFAULT(NONE) SHARED(cosIVals,coeff,gbo)
      DO i = gbo(1, 1), gbo(2, 1)
         cosIVals(i) = COS(coeff*REAL(i, dp))
      END DO
      coeff = twopi/n_tot(2)
!$OMP     PARALLEL DO PRIVATE(j) DEFAULT(NONE) SHARED(cosJVals,coeff,gbo)
      DO j = gbo(1, 2), gbo(2, 2)
         cosJVals(j) = COS(coeff*REAL(j, dp))
      END DO
      coeff = twopi/n_tot(3)
!$OMP     PARALLEL DO PRIVATE(k) DEFAULT(NONE) SHARED(cosKVals,coeff,gbo)
      DO k = gbo(1, 3), gbo(2, 3)
         cosKVals(k) = COS(coeff*REAL(k, dp))
      END DO

!$OMP     PARALLEL DO DEFAULT(NONE) PRIVATE(i,j,k,ii,coeff,c23) SHARED(spline_g,cosIVals,cosJVals,cosKVals)
      DO ii = 1, SIZE(spline_g%cc)
         i = spline_g%pw_grid%g_hat(1, ii)
         j = spline_g%pw_grid%g_hat(2, ii)
         k = spline_g%pw_grid%g_hat(3, ii)
         ! no opt
!FM                coeff=1.0/((cosVal(1)*cosVal(2)*cosVal(3))/27.0_dp+&
!FM                     (cosVal(1)*cosVal(2)+cosVal(1)*cosVal(3)+&
!FM                     cosVal(2)*cosVal(3))*2.0_dp/27.0_dp+&
!FM                     (cosVal(1)+cosVal(2)+cosVal(3))*4.0_dp/27.0_dp+&
!FM                     8.0_dp/27.0_dp)
         ! opt
         c23 = cosJVals(j)*cosKVals(k)
         coeff = 27.0_dp/(cosIVals(i)*c23+ &
                          (cosIVals(i)*cosJVals(j)+cosIVals(i)*cosKVals(k)+c23)*2.0_dp+ &
                          (cosIVals(i)+cosJVals(j)+cosKVals(k))*4.0_dp+ &
                          8.0_dp)

         spline_g%cc(ii) = spline_g%cc(ii)*coeff

      END DO
      DEALLOCATE (cosIVals, cosJVals, cosKVals)

      CALL timestop(handle)
   END SUBROUTINE pw_spline3_interpolate_values_g

! **************************************************************************************************
!> \brief rescales the derivatives from gridspacing=1 to the real derivatives
!> \param deriv_vals_r an array of x,y,z derivatives
!> \param transpose if true applies the transpose of the map (defaults to
!>        false)
!> \param scale a scaling factor (defaults to 1.0)
!> \par History
!>      06.2003 created [fawzi]
!> \author Fawzi Mohamed
! **************************************************************************************************
   SUBROUTINE pw_spline_scale_deriv(deriv_vals_r, transpose, scale)
      TYPE(pw_p_type), DIMENSION(3)                      :: deriv_vals_r
      LOGICAL, INTENT(in), OPTIONAL                      :: transpose
      REAL(KIND=dp), INTENT(in), OPTIONAL                :: scale

      CHARACTER(len=*), PARAMETER :: routineN = 'pw_spline_scale_deriv', &
         routineP = moduleN//':'//routineN

      INTEGER                                            :: handle, i, idir, j, k
      INTEGER, DIMENSION(2, 3)                           :: bo
      INTEGER, DIMENSION(3)                              :: n_tot
      LOGICAL                                            :: diag, my_transpose
      REAL(KIND=dp)                                      :: dVal1, dVal2, dVal3, my_scale, scalef
      REAL(KIND=dp), DIMENSION(3, 3)                     :: dh_inv, h_grid
      REAL(kind=dp), DIMENSION(:, :, :), POINTER         :: ddata, ddata2, ddata3

      CALL timeset(routineN, handle)

      my_transpose = .FALSE.
      IF (PRESENT(transpose)) my_transpose = transpose
      my_scale = 1.0_dp
      IF (PRESENT(scale)) my_scale = scale
      n_tot(1:3) = deriv_vals_r(1)%pw%pw_grid%npts(1:3)
      bo = deriv_vals_r(1)%pw%pw_grid%bounds_local
      dh_inv = deriv_vals_r(1)%pw%pw_grid%dh_inv

      ! map grid to real derivative
      diag = .TRUE.
      IF (my_transpose) THEN
         DO j = 1, 3
            DO i = 1, 3
               h_grid(j, i) = my_scale*dh_inv(i, j) ! REAL(n_tot(i),dp)*cell_h_inv(i,j)
               IF (i /= j .AND. h_grid(j, i) /= 0.0_dp) diag = .FALSE.
            END DO
         END DO
      ELSE
         DO j = 1, 3
            DO i = 1, 3
               h_grid(i, j) = my_scale*dh_inv(i, j) ! REAL(n_tot(i),dp)*cell_h_inv(i,j)
               IF (i /= j .AND. h_grid(i, j) /= 0.0_dp) diag = .FALSE.
            END DO
         END DO
      END IF

      IF (diag) THEN
         DO idir = 1, 3
            ddata => deriv_vals_r(idir)%pw%cr3d
            scalef = h_grid(idir, idir)
            CALL dscal((bo(2, 1)-bo(1, 1)+1)*(bo(2, 2)-bo(1, 2)+1)*(bo(2, 3)-bo(1, 3)+1), &
                       scalef, ddata, 1)
         END DO
      ELSE
         ddata => deriv_vals_r(1)%pw%cr3d
         ddata2 => deriv_vals_r(2)%pw%cr3d
         ddata3 => deriv_vals_r(3)%pw%cr3d
!$OMP        PARALLEL DO DEFAULT(NONE) PRIVATE(k,j,i,dVal1,dVal2,dVal3) &
!$OMP                 SHARED(ddata,ddata2,ddata3,h_grid,bo)
         DO k = bo(1, 3), bo(2, 3)
            DO j = bo(1, 2), bo(2, 2)
               DO i = bo(1, 1), bo(2, 1)

                  dVal1 = ddata(i, j, k)
                  dVal2 = ddata2(i, j, k)
                  dVal3 = ddata3(i, j, k)

                  ddata(i, j, k) = h_grid(1, 1)*dVal1+ &
                                   h_grid(2, 1)*dVal2+h_grid(3, 1)*dVal3
                  ddata2(i, j, k) = h_grid(1, 2)*dVal1+ &
                                    h_grid(2, 2)*dVal2+h_grid(3, 2)*dVal3
                  ddata3(i, j, k) = h_grid(1, 3)*dVal1+ &
                                    h_grid(2, 3)*dVal2+h_grid(3, 3)*dVal3

               END DO
            END DO
         END DO
      END IF

      CALL timestop(handle)
   END SUBROUTINE pw_spline_scale_deriv

! **************************************************************************************************
!> \brief calculates the FFT of the values of the x,y,z (idir=1,2,3)
!>      derivative of the cubic spline
!> \param spline_g on entry the FFT of the coefficents of the spline
!>        will contain the FFT of the derivative
!> \param idir direction of the derivative
!> \par History
!>      06.2003 created [fawzi]
!> \author Fawzi Mohamed
!> \note
!>      the distance between gridpoints is assumed to be 1
! **************************************************************************************************
   SUBROUTINE pw_spline3_deriv_g(spline_g, idir)
      TYPE(pw_type), POINTER                             :: spline_g
      INTEGER, INTENT(in)                                :: idir

      CHARACTER(len=*), PARAMETER :: routineN = 'pw_spline3_deriv_g', &
         routineP = moduleN//':'//routineN
      REAL(KIND=dp), PARAMETER                           :: inv9 = 1.0_dp/9.0_dp

      INTEGER                                            :: handle, i, ii, j, k
      INTEGER, DIMENSION(2, 3)                           :: bo, gbo
      INTEGER, DIMENSION(3)                              :: n, n_tot
      REAL(KIND=dp)                                      :: coeff, tmp
      REAL(KIND=dp), ALLOCATABLE, DIMENSION(:)           :: csIVals, csJVals, csKVals

      CALL timeset(routineN, handle)

      n(1:3) = spline_g%pw_grid%npts_local(1:3)
      n_tot(1:3) = spline_g%pw_grid%npts(1:3)
      bo = spline_g%pw_grid%bounds_local
      gbo = spline_g%pw_grid%bounds

      CPASSERT(ASSOCIATED(spline_g))
      CPASSERT(spline_g%in_use == COMPLEXDATA1D)
      CPASSERT(spline_g%in_space == RECIPROCALSPACE)
      CPASSERT(.NOT. spline_g%pw_grid%spherical)
      CPASSERT(spline_g%pw_grid%grid_span == FULLSPACE)

      ALLOCATE (csIVals(gbo(1, 1):gbo(2, 1)), &
                csJVals(gbo(1, 2):gbo(2, 2)), &
                csKVals(gbo(1, 3):gbo(2, 3)))

      coeff = twopi/n_tot(1)
      IF (idir == 1) THEN
!$OMP        PARALLEL DO PRIVATE(i) DEFAULT(NONE) SHARED(gbo,csIVals,coeff)
         DO i = gbo(1, 1), gbo(2, 1)
            csIVals(i) = SIN(coeff*REAL(i, dp))
         END DO
      ELSE
!$OMP        PARALLEL DO PRIVATE(i) DEFAULT(NONE) SHARED(gbo,csIVals,coeff)
         DO i = gbo(1, 1), gbo(2, 1)
            csIVals(i) = COS(coeff*REAL(i, dp))
         END DO
      END IF
      coeff = twopi/n_tot(2)
      IF (idir == 2) THEN
!$OMP        PARALLEL DO PRIVATE(j) DEFAULT(NONE) SHARED(gbo,csJVals,coeff)
         DO j = gbo(1, 2), gbo(2, 2)
            csJVals(j) = SIN(coeff*REAL(j, dp))
         END DO
      ELSE
!$OMP        PARALLEL DO PRIVATE(j) DEFAULT(NONE) SHARED(gbo,csJVals,coeff)
         DO j = gbo(1, 2), gbo(2, 2)
            csJVals(j) = COS(coeff*REAL(j, dp))
         END DO
      END IF
      coeff = twopi/n_tot(3)
      IF (idir == 3) THEN
!$OMP        PARALLEL DO PRIVATE(k) DEFAULT(NONE) SHARED(gbo,csKVals,coeff)
         DO k = gbo(1, 3), gbo(2, 3)
            csKVals(k) = SIN(coeff*REAL(k, dp))
         END DO
      ELSE
!$OMP        PARALLEL DO PRIVATE(k) DEFAULT(NONE) SHARED(gbo,csKVals,coeff)
         DO k = gbo(1, 3), gbo(2, 3)
            csKVals(k) = COS(coeff*REAL(k, dp))
         END DO
      END IF

      SELECT CASE (idir)
      CASE (1)
         ! x deriv
!$OMP        PARALLEL DO PRIVATE(ii,k,j,i,coeff,tmp) DEFAULT(NONE) SHARED(spline_g,csIVals,csJVals,csKVals)
         DO ii = 1, SIZE(spline_g%cc)
            i = spline_g%pw_grid%g_hat(1, ii)
            j = spline_g%pw_grid%g_hat(2, ii)
            k = spline_g%pw_grid%g_hat(3, ii)
!FM                ! formula
!FM                coeff=(sinVal(1)*cosVal(2)*cosVal(3))/9.0_dp+&
!FM                     (sinVal(1)*cosVal(2)+sinVal(1)*cosVal(3))*2.0_dp/9.0_dp+&
!FM                     sinVal(1)*4.0_dp/9.0_dp
            tmp = csIVals(i)*csJVals(j)
            coeff = (tmp*csKVals(k)+ &
                     (tmp+csIVals(i)*csKVals(k))*2.0_dp+ &
                     csIVals(i)*4.0_dp)*inv9

            spline_g%cc(ii) = spline_g%cc(ii)* &
                              CMPLX(0.0_dp, coeff, dp)
         END DO
      CASE (2)
         ! y deriv
!$OMP        PARALLEL DO PRIVATE(ii,k,j,i,coeff,tmp) DEFAULT(NONE) SHARED(spline_g,csIVals,csJVals,csKVals)
         DO ii = 1, SIZE(spline_g%cc)
            i = spline_g%pw_grid%g_hat(1, ii)
            j = spline_g%pw_grid%g_hat(2, ii)
            k = spline_g%pw_grid%g_hat(3, ii)

            tmp = csIVals(i)*csJVals(j)
            coeff = (tmp*csKVals(k)+ &
                     (tmp+csJVals(j)*csKVals(k))*2.0_dp+ &
                     csJVals(j)*4.0_dp)*inv9

            spline_g%cc(ii) = spline_g%cc(ii)* &
                              CMPLX(0.0_dp, coeff, dp)
         END DO
      CASE (3)
         ! z deriv
!$OMP        PARALLEL DO PRIVATE(ii,k,j,i,coeff,tmp) DEFAULT(NONE) SHARED(spline_g,csIVals,csJVals,csKVals)
         DO ii = 1, SIZE(spline_g%cc)
            i = spline_g%pw_grid%g_hat(1, ii)
            j = spline_g%pw_grid%g_hat(2, ii)
            k = spline_g%pw_grid%g_hat(3, ii)

            tmp = csIVals(i)*csKVals(k)
            coeff = (tmp*csJVals(j)+ &
                     (tmp+csJVals(j)*csKVals(k))*2.0_dp+ &
                     csKVals(k)*4.0_dp)*inv9

            spline_g%cc(ii) = spline_g%cc(ii)* &
                              CMPLX(0.0_dp, coeff, dp)
         END DO
      END SELECT

      DEALLOCATE (csIVals, csJVals, csKVals)

      CALL timestop(handle)
   END SUBROUTINE pw_spline3_deriv_g

! **************************************************************************************************
!> \brief calculates the FFT of the values of the x,y,z (idir=1,2,3)
!>      derivative of the quadratic spline
!> \param spline_g on entry the FFT of the coefficents of the spline
!>        will contain the FFT of the derivative
!> \param idir direction of the derivative
!> \par History
!>      06.2003 created [fawzi]
!> \author Fawzi Mohamed
!> \note
!>      the distance between gridpoints is assumed to be 1
! **************************************************************************************************
   SUBROUTINE pw_spline2_deriv_g(spline_g, idir)
      TYPE(pw_type), POINTER                             :: spline_g
      INTEGER, INTENT(in)                                :: idir

      CHARACTER(len=*), PARAMETER :: routineN = 'pw_spline2_deriv_g', &
         routineP = moduleN//':'//routineN
      REAL(KIND=dp), PARAMETER                           :: inv16 = 1.0_dp/16.0_dp

      INTEGER                                            :: handle, i, ii, j, k
      INTEGER, DIMENSION(2, 3)                           :: bo
      INTEGER, DIMENSION(3)                              :: n, n_tot
      REAL(KIND=dp)                                      :: coeff, tmp
      REAL(KIND=dp), ALLOCATABLE, DIMENSION(:)           :: csIVals, csJVals, csKVals

      CALL timeset(routineN, handle)

      n(1:3) = spline_g%pw_grid%npts_local(1:3)
      n_tot(1:3) = spline_g%pw_grid%npts(1:3)
      bo = spline_g%pw_grid%bounds

      CPASSERT(ASSOCIATED(spline_g))
      CPASSERT(spline_g%in_use == COMPLEXDATA1D)
      CPASSERT(spline_g%in_space == RECIPROCALSPACE)
      CPASSERT(.NOT. spline_g%pw_grid%spherical)
      CPASSERT(spline_g%pw_grid%grid_span == FULLSPACE)

      ALLOCATE (csIVals(bo(1, 1):bo(2, 1)), csJVals(bo(1, 2):bo(2, 2)), &
                csKVals(bo(1, 3):bo(2, 3)))

      coeff = twopi/n_tot(1)
      IF (idir == 1) THEN
!$OMP        PARALLEL DO PRIVATE(i) DEFAULT(NONE) SHARED(bo,coeff,csIVals)
         DO i = bo(1, 1), bo(2, 1)
            csIVals(i) = SIN(coeff*REAL(i, dp))
         END DO
      ELSE
!$OMP        PARALLEL DO PRIVATE(i) DEFAULT(NONE) SHARED(bo,coeff,csIVals)
         DO i = bo(1, 1), bo(2, 1)
            csIVals(i) = COS(coeff*REAL(i, dp))
         END DO
      END IF
      coeff = twopi/n_tot(2)
      IF (idir == 2) THEN
!$OMP        PARALLEL DO PRIVATE(j) DEFAULT(NONE) SHARED(bo,coeff,csJVals)
         DO j = bo(1, 2), bo(2, 2)
            csJVals(j) = SIN(coeff*REAL(j, dp))
         END DO
      ELSE
!$OMP        PARALLEL DO PRIVATE(j) DEFAULT(NONE) SHARED(bo,coeff,csJVals)
         DO j = bo(1, 2), bo(2, 2)
            csJVals(j) = COS(coeff*REAL(j, dp))
         END DO
      END IF
      coeff = twopi/n_tot(3)
      IF (idir == 3) THEN
!$OMP        PARALLEL DO PRIVATE(k) DEFAULT(NONE) SHARED(bo,coeff,csKVals)
         DO k = bo(1, 3), bo(2, 3)
            csKVals(k) = SIN(coeff*REAL(k, dp))
         END DO
      ELSE
!$OMP        PARALLEL DO PRIVATE(k) DEFAULT(NONE) SHARED(bo,coeff,csKVals)
         DO k = bo(1, 3), bo(2, 3)
            csKVals(k) = COS(coeff*REAL(k, dp))
         END DO
      END IF

      SELECT CASE (idir)
      CASE (1)
         ! x deriv
!$OMP        PARALLEL DO PRIVATE(ii,k,j,i,coeff,tmp) SHARED(spline_g,csIVals,csJVals,csKVals) DEFAULT(NONE)
         DO ii = 1, SIZE(spline_g%cc)
            i = spline_g%pw_grid%g_hat(1, ii)
            j = spline_g%pw_grid%g_hat(2, ii)
            k = spline_g%pw_grid%g_hat(3, ii)
!FM                ! formula
!FM                coeff=(sinVal(1)*cosVal(2)*cosVal(3))/16.0_dp+&
!FM                     (sinVal(1)*cosVal(2)+sinVal(1)*cosVal(3))*3.0_dp/16.0_dp+&
!FM                     sinVal(1)*9.0_dp/16.0_dp
            tmp = csIVals(i)*csJVals(j)
            coeff = (tmp*csKVals(k)+ &
                     (tmp+csIVals(i)*csKVals(k))*3.0_dp+ &
                     csIVals(i)*9.0_dp)*inv16

            spline_g%cc(ii) = spline_g%cc(ii)* &
                              CMPLX(0.0_dp, coeff, dp)
         END DO
      CASE (2)
         ! y deriv
!$OMP        PARALLEL DO PRIVATE(ii,k,j,i,coeff,tmp) DEFAULT(NONE) SHARED(spline_g,csIVals,csJVals,csKVals)
         DO ii = 1, SIZE(spline_g%cc)
            i = spline_g%pw_grid%g_hat(1, ii)
            j = spline_g%pw_grid%g_hat(2, ii)
            k = spline_g%pw_grid%g_hat(3, ii)

            tmp = csIVals(i)*csJVals(j)
            coeff = (tmp*csKVals(k)+ &
                     (tmp+csJVals(j)*csKVals(k))*3.0_dp+ &
                     csJVals(j)*9.0_dp)*inv16

            spline_g%cc(ii) = spline_g%cc(ii)* &
                              CMPLX(0.0_dp, coeff, dp)
         END DO
      CASE (3)
         ! z deriv
!$OMP        PARALLEL DO PRIVATE(ii,k,j,i,coeff,tmp) DEFAULT(NONE) SHARED(spline_g,csIVals,csJVals,csKVals)
         DO ii = 1, SIZE(spline_g%cc)
            i = spline_g%pw_grid%g_hat(1, ii)
            j = spline_g%pw_grid%g_hat(2, ii)
            k = spline_g%pw_grid%g_hat(3, ii)

            tmp = csIVals(i)*csKVals(k)
            coeff = (tmp*csJVals(j)+ &
                     (tmp+csJVals(j)*csKVals(k))*3.0_dp+ &
                     csKVals(k)*9.0_dp)*inv16

            spline_g%cc(ii) = spline_g%cc(ii)* &
                              CMPLX(0.0_dp, coeff, dp)
         END DO
      END SELECT

      DEALLOCATE (csIVals, csJVals, csKVals)

      CALL timestop(handle)
   END SUBROUTINE pw_spline2_deriv_g

! **************************************************************************************************
!> \brief applies a nearest neighbor linear operator to a stripe in x direction:
!>      out_val(i)=sum(weight(j)*in_val(i+j-1),j=0..2)
!> \param weights the weights of the linear operator
!> \param in_val the argument to the operator
!> \param in_val_first the first argument (needed to calculate out_val(1))
!> \param in_val_last the last argument (needed to calculate out_val(n_el))
!> \param out_val the place where the result is accumulated
!> \param n_el the number of elements in in_v and out_v
!> \par History
!>      04.2004 created [fawzi]
!> \author fawzi
!> \note
!>      uses 2 read streams and 1 write stream
! **************************************************************************************************
   SUBROUTINE pw_compose_stripe(weights, in_val, in_val_first, in_val_last, &
                                out_val, n_el)
      REAL(kind=dp), DIMENSION(0:2), INTENT(in)          :: weights
      REAL(kind=dp), DIMENSION(*), INTENT(in)            :: in_val
      REAL(kind=dp), INTENT(in)                          :: in_val_first, in_val_last
      REAL(kind=dp), DIMENSION(*), INTENT(inout)         :: out_val
      INTEGER                                            :: n_el

      CHARACTER(len=*), PARAMETER :: routineN = 'pw_compose_stripe', &
         routineP = moduleN//':'//routineN

      INTEGER                                            :: i
      REAL(kind=dp)                                      :: v0, v1, v2

!1:n_el), &
!1:n_el), &

      IF (n_el < 1) RETURN
      v0 = in_val_first
      v1 = in_val(1)
      IF (weights(1) == 0.0_dp) THEN
         ! optimized version for x deriv
         DO i = 1, n_el-3, 3
            v2 = in_val(i+1)
            out_val(i) = out_val(i)+ &
                         weights(0)*v0+ &
                         weights(2)*v2
            v0 = in_val(i+2)
            out_val(i+1) = out_val(i+1)+ &
                           weights(0)*v1+ &
                           weights(2)*v0
            v1 = in_val(i+3)
            out_val(i+2) = out_val(i+2)+ &
                           weights(0)*v2+ &
                           weights(2)*v1
         END DO
      ELSE
         ! generic version
         DO i = 1, n_el-3, 3
            v2 = in_val(i+1)
            out_val(i) = out_val(i)+ &
                         weights(0)*v0+ &
                         weights(1)*v1+ &
                         weights(2)*v2
            v0 = in_val(i+2)
            out_val(i+1) = out_val(i+1)+ &
                           weights(0)*v1+ &
                           weights(1)*v2+ &
                           weights(2)*v0
            v1 = in_val(i+3)
            out_val(i+2) = out_val(i+2)+ &
                           weights(0)*v2+ &
                           weights(1)*v0+ &
                           weights(2)*v1
         END DO
      END IF
      SELECT CASE (MODULO (n_el-1, 3))
      CASE (0)
         v2 = in_val_last
         out_val(n_el) = out_val(n_el)+ &
                         weights(0)*v0+ &
                         weights(1)*v1+ &
                         weights(2)*v2
      CASE (1)
         v2 = in_val(n_el)
         out_val(n_el-1) = out_val(n_el-1)+ &
                           weights(0)*v0+ &
                           weights(1)*v1+ &
                           weights(2)*v2
         v0 = in_val_last
         out_val(n_el) = out_val(n_el)+ &
                         weights(0)*v1+ &
                         weights(1)*v2+ &
                         weights(2)*v0
      CASE (2)
         v2 = in_val(n_el-1)
         out_val(n_el-2) = out_val(n_el-2)+ &
                           weights(0)*v0+ &
                           weights(1)*v1+ &
                           weights(2)*v2
         v0 = in_val(n_el)
         out_val(n_el-1) = out_val(n_el-1)+ &
                           weights(0)*v1+ &
                           weights(1)*v2+ &
                           weights(2)*v0
         v1 = in_val_last
         out_val(n_el) = out_val(n_el)+ &
                         weights(0)*v2+ &
                         weights(1)*v0+ &
                         weights(2)*v1
      END SELECT

   END SUBROUTINE pw_compose_stripe

! **************************************************************************************************
!> \brief private routine that computes pw_nn_compose_r (it seems that without
!>      passing arrays in this way either some compiler do a copyin/out (xlf)
!>      or by inlining suboptimal code is produced (nag))
!> \param weights a 3x3x3 array with the linear operator
!> \param in_val the argument for the linear operator
!> \param out_val place where the value of the linear oprator should be added
!> \param pw_in pw to be able to get the needed meta data about in_val and
!>        out_val
!> \param bo boundaries of in_val and out_val
!> \author fawzi
! **************************************************************************************************
   SUBROUTINE pw_nn_compose_r_work(weights, in_val, out_val, pw_in, bo)
      REAL(kind=dp), DIMENSION(0:2, 0:2, 0:2)            :: weights
      INTEGER, DIMENSION(2, 3)                           :: bo
      TYPE(pw_type), POINTER                             :: pw_in
      REAL(kind=dp), DIMENSION(bo(1, 1):bo(2, 1), bo(1, &
         2):bo(2, 2), bo(1, 3):bo(2, 3)), INTENT(inout)  :: out_val
      REAL(kind=dp), DIMENSION(bo(1, 1):bo(2, 1), bo(1, &
         2):bo(2, 2), bo(1, 3):bo(2, 3)), INTENT(in)     :: in_val

      CHARACTER(len=*), PARAMETER :: routineN = 'pw_nn_compose_r_work', &
         routineP = moduleN//':'//routineN

      INTEGER                                            :: i, j, jw, k, kw, myj, myk
      INTEGER, DIMENSION(2, 3)                           :: gbo
      INTEGER, DIMENSION(3)                              :: s
      LOGICAL                                            :: has_boundary, yderiv, zderiv
      REAL(kind=dp)                                      :: in_val_f, in_val_l
      REAL(kind=dp), DIMENSION(:, :), POINTER            :: l_boundary, tmp, u_boundary

      zderiv = ALL(weights(:, :, 1) == 0.0_dp)
      yderiv = ALL(weights(:, 1, :) == 0.0_dp)
      bo = pw_in%pw_grid%bounds_local
      gbo = pw_in%pw_grid%bounds
      DO i = 1, 3
         s(i) = bo(2, i)-bo(1, i)+1
      END DO
      IF (ANY(s < 1)) RETURN
      has_boundary = ANY(pw_in%pw_grid%bounds_local(:, 1) /= &
                         pw_in%pw_grid%bounds(:, 1))
      IF (has_boundary) THEN
         ALLOCATE (l_boundary(bo(1, 2):bo(2, 2), bo(1, 3):bo(2, 3)), &
                   u_boundary(bo(1, 2):bo(2, 2), bo(1, 3):bo(2, 3)), &
                   tmp(bo(1, 2):bo(2, 2), bo(1, 3):bo(2, 3)))
         tmp(:, :) = pw_in%cr3d(bo(2, 1), :, :)
         CALL mp_sendrecv(tmp, pw_in%pw_grid%para%pos_of_x( &
                          gbo(1, 1)+MODULO(bo(2, 1)+1-gbo(1, 1), gbo(2, 1)-gbo(1, 1)+1)), &
                          l_boundary, pw_in%pw_grid%para%pos_of_x( &
                          gbo(1, 1)+MODULO(bo(1, 1)-1-gbo(1, 1), gbo(2, 1)-gbo(1, 1)+1)), &
                          pw_in%pw_grid%para%group)
         tmp(:, :) = pw_in%cr3d(bo(1, 1), :, :)
         CALL mp_sendrecv(tmp, pw_in%pw_grid%para%pos_of_x( &
                          gbo(1, 1)+MODULO(bo(1, 1)-1-gbo(1, 1), gbo(2, 1)-gbo(1, 1)+1)), &
                          u_boundary, pw_in%pw_grid%para%pos_of_x( &
                          gbo(1, 1)+MODULO(bo(2, 1)+1-gbo(1, 1), gbo(2, 1)-gbo(1, 1)+1)), &
                          pw_in%pw_grid%para%group)
         DEALLOCATE (tmp)
      END IF

!$OMP   PARALLEL DO DEFAULT(NONE) PRIVATE(k,kw,myk,j,jw,myj,in_val_f,&
!$OMP       in_val_l) SHARED(zderiv,yderiv,bo,in_val,out_val,s,l_boundary,&
!$OMP       u_boundary,weights,has_boundary)
      DO k = 0, s(3)-1
         DO kw = 0, 2
            myk = bo(1, 3)+MODULO(k+kw-1, s(3))
            IF (zderiv .AND. kw == 1) CYCLE
            DO j = 0, s(2)-1
               DO jw = 0, 2
                  myj = bo(1, 2)+MODULO(j+jw-1, s(2))
                  IF (yderiv .AND. jw == 1) CYCLE
                  IF (has_boundary) THEN
                     in_val_f = l_boundary(myj, myk)
                     in_val_l = u_boundary(myj, myk)
                  ELSE
                     in_val_f = in_val(bo(2, 1), myj, myk)
                     in_val_l = in_val(bo(1, 1), myj, myk)
                  END IF
                  CALL pw_compose_stripe(weights=weights(:, jw, kw), &
                                         in_val=in_val(:, myj, myk), &
                                         in_val_first=in_val_f, in_val_last=in_val_l, &
                                         out_val=out_val(:, bo(1, 2)+j, bo(1, 3)+k), n_el=s(1))
               END DO
            END DO
         END DO
      END DO
      IF (has_boundary) THEN
         DEALLOCATE (l_boundary, u_boundary)
      END IF
   END SUBROUTINE pw_nn_compose_r_work

! **************************************************************************************************
!> \brief applies a nearest neighbor linear operator to a pw in real space
!> \param weights a 3x3x3 array with the linear operator
!> \param pw_in the argument for the linear operator
!> \param pw_out place where the value of the linear oprator should be added
!> \author fawzi
!> \note
!>      has specialized versions for derivative operator (with central values==0)
! **************************************************************************************************
   SUBROUTINE pw_nn_compose_r(weights, pw_in, pw_out)
      REAL(kind=dp), DIMENSION(0:2, 0:2, 0:2)            :: weights
      TYPE(pw_type), POINTER                             :: pw_in, pw_out

      CHARACTER(len=*), PARAMETER :: routineN = 'pw_nn_compose_r', &
         routineP = moduleN//':'//routineN

      INTEGER                                            :: handle

      CALL timeset(routineN, handle)
      CPASSERT(ASSOCIATED(pw_in))
      CPASSERT(pw_in%in_space == REALSPACE)
      CPASSERT(pw_in%in_use == REALDATA3D)
      CPASSERT(ASSOCIATED(pw_out))
      CPASSERT(pw_out%in_space == REALSPACE)
      CPASSERT(pw_out%in_use == REALDATA3D)
      IF (.NOT. ALL(pw_in%pw_grid%bounds_local(:, 2:3) == pw_in%pw_grid%bounds(:, 2:3))) THEN
         CPABORT("wrong pw distribution")
      END IF
      CALL pw_nn_compose_r_work(weights=weights, in_val=pw_in%cr3d, &
                                out_val=pw_out%cr3d, pw_in=pw_in, bo=pw_in%pw_grid%bounds_local)
      CALL timestop(handle)
   END SUBROUTINE pw_nn_compose_r

! **************************************************************************************************
!> \brief calculates the values of a nearest neighbor smearing
!> \param pw_in the argument for the linear operator
!> \param pw_out place where the smeared values should be added
!> \param coeffs array with the coefficent of the smearing, ordered with
!>        the distance from the center: coeffs(1) the coeff of the central
!>        element, coeffs(2) the coeff of the 6 element with distance 1,
!>        coeff(3) the coeff of the 12 elements at distance sqrt(2),
!>        coeff(4) the coeff of the 8 elements at distance sqrt(3).
!> \author Fawzi Mohamed
!> \note
!>      does not normalize the smear to 1.
!>      with coeff=(/ 8._dp/27._dp, 2._dp/27._dp, 1._dp/54._dp, 1._dp/216._dp /)
!>      is equivalent to pw_spline3_evaluate_values_g, with
!>      coeff=(/ 27._dp/64._dp, 9._dp/128._dp, 3._dp/256._dp, 1._dp/512._dp /)
! **************************************************************************************************
   SUBROUTINE pw_nn_smear_r(pw_in, pw_out, coeffs)
      TYPE(pw_type), POINTER                             :: pw_in, pw_out
      REAL(KIND=dp), DIMENSION(4), INTENT(in)            :: coeffs

      CHARACTER(len=*), PARAMETER :: routineN = 'pw_nn_smear_r', routineP = moduleN//':'//routineN

      INTEGER                                            :: i, j, k
      REAL(kind=dp), DIMENSION(-1:1, -1:1, -1:1)         :: weights

      DO k = -1, 1
         DO j = -1, 1
            DO i = -1, 1
               weights(i, j, k) = coeffs(ABS(i)+ABS(j)+ABS(k)+1)
            END DO
         END DO
      END DO

      CALL pw_nn_compose_r(weights=weights, pw_in=pw_in, pw_out=pw_out)
   END SUBROUTINE pw_nn_smear_r

! **************************************************************************************************
!> \brief calculates a nearest neighbor central derivative.
!>      for the x dir:
!>      pw_out%cr3d(i,j,k)=( pw_in(i+1,j,k)-pw_in(i-1,j,k) )*coeff(1)+
!>             ( pw_in(i+1,j(+-)1,k)-pw_in(i-1,j(+-)1,k)+
!>               pw_in(i+1,j,k(+-)1)-pw_in(i-1,j,k(+-)1) )*coeff(2)+
!>             ( pw_in(i+1,j(+-)1,k(+-)1)-pw_in(i-1,j(+-)1,k(+-)1)+
!>               pw_in(i+1,j(+-)1,k(-+)1)-pw_in(i-1,j(+-)1,k(-+)1) )*coeff(3)
!>      periodic boundary conditions are applied
!> \param pw_in the argument for the linear operator
!> \param pw_out place where the smeared values should be added
!> \param coeffs array with the coefficent of the front (positive) plane
!>        of the central derivative, ordered with
!>        the distance from the center: coeffs(1) the coeff of the central
!>        element, coeffs(2) the coeff of the 4 element with distance 1,
!>        coeff(3) the coeff of the 4 elements at distance sqrt(2)
!> \param idir ...
!> \author Fawzi Mohamed
!> \note
!>      with coeff=(/ 2.0_dp/9.0_dp,  1.0_dp/18.0_dp, 1.0_dp/72.0_dp /)
!>      is equivalent to pw_spline3_deriv_r, with
!>      coeff=(/ 9.0_dp/32.0_dp, 3.0_dp/64.0_dp, 1.0_dp/128.0_dp /)
!>      to pw_spline2_deriv_r
!>      coeff=(/ 25._dp/72._dp, 5._dp/144, 1._dp/288._dp /)
! **************************************************************************************************
   SUBROUTINE pw_nn_deriv_r(pw_in, pw_out, coeffs, idir)
      TYPE(pw_type), POINTER                             :: pw_in, pw_out
      REAL(KIND=dp), DIMENSION(3), INTENT(in)            :: coeffs
      INTEGER                                            :: idir

      CHARACTER(len=*), PARAMETER :: routineN = 'pw_nn_deriv_r', routineP = moduleN//':'//routineN

      INTEGER                                            :: i, idirVal, j, k
      REAL(kind=dp), DIMENSION(-1:1, -1:1, -1:1)         :: weights

      DO k = -1, 1
         DO j = -1, 1
            DO i = -1, 1
               SELECT CASE (idir)
               CASE (1)
                  idirVal = i
               CASE (2)
                  idirVal = j
               CASE (3)
                  idirVal = k
               CASE default
                  CPABORT("invalid idir ("//TRIM(cp_to_string(idir))//")")
               END SELECT
               IF (idirVal == 0) THEN
                  weights(i, j, k) = 0.0_dp
               ELSE
                  weights(i, j, k) = REAL(idirVal, dp)*coeffs(ABS(i)+ABS(j)+ABS(k))
               END IF
            END DO
         END DO
      END DO

      CALL pw_nn_compose_r(weights=weights, pw_in=pw_in, pw_out=pw_out)
   END SUBROUTINE pw_nn_deriv_r

! **************************************************************************************************
!> \brief low level function that adds a coarse grid
!>      to a fine grid.
!>      If pbc is true periodic boundary conditions are applied
!>
!>      It will add to
!>
!>        fine_values(2*coarse_bounds(1,1):2*coarse_bounds(2,1),
!>                    2*coarse_bounds(1,2):2*coarse_bounds(2,2),
!>                    2*coarse_bounds(1,3):2*coarse_bounds(2,3))
!>
!>      using
!>
!>        coarse_coeffs(coarse_bounds(1,1):coarse_bounds(2,1),
!>                      coarse_bounds(1,2):coarse_bounds(2,2),
!>                      coarse_bounds(1,3):coarse_bounds(2,3))
!>
!>      composed with the weights obtained by the direct product of the
!>      1d coefficents weights:
!>
!>      for i,j,k in -3..3
!>         w(i,j,k)=weights_1d(abs(i)+1)*weights_1d(abs(j)+1)*
!>                  weights_1d(abs(k)+1)
!> \param coarse_coeffs_pw the values of the coefficients
!> \param fine_values_pw where to add the values due to the
!>        coarse coeffs
!> \param weights_1d the weights of the 1d smearing
!> \param w_border0 the 1d weight at the border (when pbc is false)
!> \param w_border1 the 1d weights for a point one off the border
!>        (w_border1(1) is the weight of the coefficent at the border)
!>        (used if pbc is false)
!> \param pbc if periodic boundary conditions should be applied
!> \param safe_computation ...
!> \author fawzi
!> \note
!>      coarse looping is continuos, I did not check if keeping the fine looping
!>      contiguos is better.
!>      And I ask myself yet again why, why we use x-slice distribution,
!>      z-slice distribution would be much better performancewise
!>      (and would semplify this code enormously).
!>      fine2coarse has much more understandable parallel part (build up of
!>      send/rcv sizes,... but worse if you have really a lot of processors,
!>      probabily irrelevant because it is not critical) [fawzi].
! **************************************************************************************************
   SUBROUTINE add_coarse2fine(coarse_coeffs_pw, fine_values_pw, &
                              weights_1d, w_border0, w_border1, pbc, safe_computation)
      TYPE(pw_type), POINTER                             :: coarse_coeffs_pw, fine_values_pw
      REAL(kind=dp), DIMENSION(4), INTENT(in)            :: weights_1d
      REAL(kind=dp), INTENT(in)                          :: w_border0
      REAL(kind=dp), DIMENSION(3), INTENT(in)            :: w_border1
      LOGICAL, INTENT(in)                                :: pbc
      LOGICAL, INTENT(in), OPTIONAL                      :: safe_computation

      CHARACTER(len=*), PARAMETER :: routineN = 'add_coarse2fine', &
         routineP = moduleN//':'//routineN

      INTEGER :: coarse_slice_size, f_shift(3), fi, fi_lb, fi_ub, fj, fk, handle, handle2, i, ii, &
         ij, ik, ip, j, k, my_lb, my_ub, n_procs, p, p_lb, p_old, p_ub, rcv_tot_size, rest_b, &
         s(3), send_tot_size, sf, shift, ss, x, x_att, xx
      INTEGER, ALLOCATABLE, DIMENSION(:)                 :: rcv_offset, rcv_size, real_rcv_size, &
                                                            send_offset, send_size, sent_size
      INTEGER, DIMENSION(2, 3)                           :: coarse_bo, coarse_gbo, fine_bo, &
                                                            fine_gbo, my_coarse_bo
      INTEGER, DIMENSION(:), POINTER                     :: pos_of_x
      LOGICAL                                            :: has_i_lbound, has_i_ubound, is_split, &
                                                            safe_calc
      REAL(kind=dp)                                      :: v0, v1, v2, v3, wi, wj, wk
      REAL(kind=dp), ALLOCATABLE, DIMENSION(:)           :: rcv_buf, send_buf
      REAL(kind=dp), DIMENSION(3)                        :: w_0, ww0
      REAL(kind=dp), DIMENSION(4)                        :: w_1, ww1
      REAL(kind=dp), DIMENSION(:, :, :), POINTER         :: coarse_coeffs, fine_values

      CALL timeset(routineN, handle)
!    CALL timeset(routineN//"_pre",handle2)
      safe_calc = .FALSE.
      IF (PRESENT(safe_computation)) safe_calc = safe_computation
      CALL mp_comm_compare(coarse_coeffs_pw%pw_grid%para%group, &
                           fine_values_pw%pw_grid%para%group, ii)
      IF (ii > 1) THEN
         CPABORT("")
      END IF
      my_coarse_bo = coarse_coeffs_pw%pw_grid%bounds_local
      coarse_gbo = coarse_coeffs_pw%pw_grid%bounds
      fine_bo = fine_values_pw%pw_grid%bounds_local
      fine_gbo = fine_values_pw%pw_grid%bounds
      f_shift = fine_gbo(1, :)-2*coarse_gbo(1, :)
      DO j = 2, 3
         DO i = 1, 2
            coarse_bo(i, j) = FLOOR((fine_bo(i, j)-f_shift(j))/2.)
         END DO
      END DO
      IF (fine_bo(1, 1) <= fine_bo(2, 1)) THEN
         coarse_bo(1, 1) = FLOOR((fine_bo(1, 1)-2-f_shift(1))/2.)
         coarse_bo(2, 1) = FLOOR((fine_bo(2, 1)+3-f_shift(1))/2.)
      ELSE
         coarse_bo(1, 1) = coarse_gbo(2, 1)
         coarse_bo(2, 1) = coarse_gbo(2, 1)-1
      END IF
      is_split = ANY(coarse_gbo(:, 1) /= my_coarse_bo(:, 1))
      IF (.NOT. is_split .OR. .NOT. pbc) THEN
         coarse_bo(1, 1) = MAX(coarse_gbo(1, 1), coarse_bo(1, 1))
         coarse_bo(2, 1) = MIN(coarse_gbo(2, 1), coarse_bo(2, 1))
      END IF
      has_i_ubound = (fine_gbo(2, 1) /= fine_bo(2, 1)) .OR. pbc .AND. is_split
      has_i_lbound = (fine_gbo(1, 1) /= fine_bo(1, 1)) .OR. pbc .AND. is_split

      IF (pbc) THEN
         CPASSERT(ALL(fine_gbo(1, :) == 2*coarse_gbo(1, :)+f_shift))
         CPASSERT(ALL(fine_gbo(2, :) == 2*coarse_gbo(2, :)+1+f_shift))
      ELSE
         CPASSERT(ALL(fine_gbo(2, :) == 2*coarse_gbo(2, :)+f_shift))
         CPASSERT(ALL(fine_gbo(1, :) == 2*coarse_gbo(1, :)+f_shift))
      END IF

      coarse_coeffs => coarse_coeffs_pw%cr3d
      DO i = 1, 3
         s(i) = coarse_gbo(2, i)-coarse_gbo(1, i)+1
      END DO
!       CALL timestop(handle2)
      ! *** parallel case
      IF (is_split) THEN
         CALL timeset(routineN//"_comm", handle2)
         coarse_slice_size = (coarse_bo(2, 2)-coarse_bo(1, 2)+1)* &
                             (coarse_bo(2, 3)-coarse_bo(1, 3)+1)
         n_procs = coarse_coeffs_pw%pw_grid%para%group_size
         ALLOCATE (send_size(0:n_procs-1), send_offset(0:n_procs-1), &
                   sent_size(0:n_procs-1), rcv_size(0:n_procs-1), &
                   rcv_offset(0:n_procs-1), real_rcv_size(0:n_procs-1))

         ! ** rcv size count

         pos_of_x => coarse_coeffs_pw%pw_grid%para%pos_of_x
         p_old = pos_of_x(coarse_gbo(1, 1) &
                          +MODULO(coarse_bo(1, 1)-coarse_gbo(1, 1), s(1)))
         rcv_size = 0
         DO x = coarse_bo(1, 1), coarse_bo(2, 1)
            p = pos_of_x(coarse_gbo(1, 1)+MODULO(x-coarse_gbo(1, 1), s(1)))
            rcv_size(p) = rcv_size(p)+coarse_slice_size
         END DO

         ! ** send size count

         pos_of_x => fine_values_pw%pw_grid%para%pos_of_x
         sf = fine_gbo(2, 1)-fine_gbo(1, 1)+1
         fi_lb = 2*my_coarse_bo(1, 1)-3+f_shift(1)
         fi_ub = 2*my_coarse_bo(2, 1)+3+f_shift(1)
         IF (.NOT. pbc) THEN
            fi_lb = MAX(fi_lb, fine_gbo(1, 1))
            fi_ub = MIN(fi_ub, fine_gbo(2, 1))
         ELSE
            fi_ub = MIN(fi_ub, fi_lb+sf-1)
         END IF
         p_old = pos_of_x(fine_gbo(1, 1)+MODULO(fi_lb-fine_gbo(1, 1), sf))
         p_lb = FLOOR((fi_lb-2-f_shift(1))/2.)
         send_size = 0
         DO x = fi_lb, fi_ub
            p = pos_of_x(fine_gbo(1, 1)+MODULO(x-fine_gbo(1, 1), sf))
            IF (p /= p_old) THEN
               p_ub = FLOOR((x-1+3-f_shift(1))/2.)

               send_size(p_old) = send_size(p_old)+(MIN(p_ub, my_coarse_bo(2, 1)) &
                                                    -MAX(p_lb, my_coarse_bo(1, 1))+1)*coarse_slice_size

               IF (pbc) THEN
                  DO xx = p_lb, coarse_gbo(1, 1)-1
                     x_att = coarse_gbo(1, 1)+MODULO(xx-coarse_gbo(1, 1), s(1))
                     IF (x_att >= my_coarse_bo(1, 1) .AND. x_att <= my_coarse_bo(2, 1)) THEN
                        send_size(p_old) = send_size(p_old)+coarse_slice_size
                     END IF
                  END DO
                  DO xx = coarse_gbo(2, 1)+1, p_ub
                     x_att = coarse_gbo(1, 1)+MODULO(xx-coarse_gbo(1, 1), s(1))
                     IF (x_att >= my_coarse_bo(1, 1) .AND. x_att <= my_coarse_bo(2, 1)) THEN
                        send_size(p_old) = send_size(p_old)+coarse_slice_size
                     END IF
                  END DO
               END IF

               p_old = p
               p_lb = FLOOR((x-2-f_shift(1))/2.)
            END IF
         END DO
         p_ub = FLOOR((fi_ub+3-f_shift(1))/2.)

         send_size(p_old) = send_size(p_old)+(MIN(p_ub, my_coarse_bo(2, 1)) &
                                              -MAX(p_lb, my_coarse_bo(1, 1))+1)*coarse_slice_size

         IF (pbc) THEN
            DO xx = p_lb, coarse_gbo(1, 1)-1
               x_att = coarse_gbo(1, 1)+MODULO(xx-coarse_gbo(1, 1), s(1))
               IF (x_att >= my_coarse_bo(1, 1) .AND. x_att <= my_coarse_bo(2, 1)) THEN
                  send_size(p_old) = send_size(p_old)+coarse_slice_size
               END IF
            END DO
            DO xx = coarse_gbo(2, 1)+1, p_ub
               x_att = coarse_gbo(1, 1)+MODULO(xx-coarse_gbo(1, 1), s(1))
               IF (x_att >= my_coarse_bo(1, 1) .AND. x_att <= my_coarse_bo(2, 1)) THEN
                  send_size(p_old) = send_size(p_old)+coarse_slice_size
               END IF
            END DO
         END IF
         ! ** offsets & alloc send-rcv

         send_tot_size = 0
         DO ip = 0, n_procs-1
            send_offset(ip) = send_tot_size
            send_tot_size = send_tot_size+send_size(ip)
         END DO
         ALLOCATE (send_buf(0:send_tot_size-1))

         rcv_tot_size = 0
         DO ip = 0, n_procs-1
            rcv_offset(ip) = rcv_tot_size
            rcv_tot_size = rcv_tot_size+rcv_size(ip)
         END DO
         IF (.NOT. rcv_tot_size == (coarse_bo(2, 1)-coarse_bo(1, 1)+1)*coarse_slice_size) THEN
            CPABORT("Error calculating rcv_tot_size ")
         END IF
         ALLOCATE (rcv_buf(0:rcv_tot_size-1))

         ! ** fill send buffer

         p_old = pos_of_x(fine_gbo(1, 1)+MODULO(fi_lb-fine_gbo(1, 1), sf))
         p_lb = FLOOR((fi_lb-2-f_shift(1))/2.)
         sent_size(:) = send_offset
         ss = my_coarse_bo(2, 1)-my_coarse_bo(1, 1)+1
         DO x = fi_lb, fi_ub
            p = pos_of_x(fine_gbo(1, 1)+MODULO(x-fine_gbo(1, 1), sf))
            IF (p /= p_old) THEN
               shift = FLOOR((fine_gbo(1, 1)+MODULO(x-1-fine_gbo(1, 1), sf)-f_shift(1))/2._dp)- &
                       FLOOR((x-1-f_shift(1))/2._dp)
               p_ub = FLOOR((x-1+3-f_shift(1))/2._dp)

               IF (pbc) THEN
                  DO xx = p_lb+shift, coarse_gbo(1, 1)-1
                     x_att = coarse_gbo(1, 1)+MODULO(xx-coarse_gbo(1, 1), sf)
                     IF (x_att >= my_coarse_bo(1, 1) .AND. x_att <= my_coarse_bo(2, 1)) THEN
                        CALL dcopy(coarse_slice_size, &
                                   coarse_coeffs(x_att, my_coarse_bo(1, 2), &
                                                 my_coarse_bo(1, 3)), ss, send_buf(sent_size(p_old)), 1)
                        sent_size(p_old) = sent_size(p_old)+coarse_slice_size
                     END IF
                  END DO
               END IF

               ii = sent_size(p_old)
               DO k = coarse_bo(1, 3), coarse_bo(2, 3)
                  DO j = coarse_bo(1, 2), coarse_bo(2, 2)
                     DO i = MAX(p_lb+shift, my_coarse_bo(1, 1)), MIN(p_ub+shift, my_coarse_bo(2, 1))
                        send_buf(ii) = coarse_coeffs(i, j, k)
                        ii = ii+1
                     END DO
                  END DO
               END DO
               sent_size(p_old) = ii

               IF (pbc) THEN
                  DO xx = coarse_gbo(2, 1)+1, p_ub+shift
                     x_att = coarse_gbo(1, 1)+MODULO(xx-coarse_gbo(1, 1), s(1))
                     IF (x_att >= my_coarse_bo(1, 1) .AND. x_att <= my_coarse_bo(2, 1)) THEN
                        CALL dcopy(coarse_slice_size, &
                                   coarse_coeffs(x_att, my_coarse_bo(1, 2), &
                                                 my_coarse_bo(1, 3)), ss, &
                                   send_buf(sent_size(p_old)), 1)
                        sent_size(p_old) = sent_size(p_old)+coarse_slice_size
                     END IF
                  END DO
               END IF

               p_old = p
               p_lb = FLOOR((x-2-f_shift(1))/2.)
            END IF
         END DO
         shift = FLOOR((fine_gbo(1, 1)+MODULO(x-1-fine_gbo(1, 1), sf)-f_shift(1))/2._dp)- &
                 FLOOR((x-1-f_shift(1))/2._dp)
         p_ub = FLOOR((fi_ub+3-f_shift(1))/2.)

         IF (pbc) THEN
            DO xx = p_lb+shift, coarse_gbo(1, 1)-1
               x_att = coarse_gbo(1, 1)+MODULO(xx-coarse_gbo(1, 1), s(1))
               IF (x_att >= my_coarse_bo(1, 1) .AND. x_att <= my_coarse_bo(2, 1)) THEN
                  CALL dcopy(coarse_slice_size, &
                             coarse_coeffs(x_att, my_coarse_bo(1, 2), &
                                           my_coarse_bo(1, 3)), ss, send_buf(sent_size(p_old)), 1)
                  sent_size(p_old) = sent_size(p_old)+coarse_slice_size
               END IF
            END DO
         END IF

         ii = sent_size(p_old)
         DO k = coarse_bo(1, 3), coarse_bo(2, 3)
            DO j = coarse_bo(1, 2), coarse_bo(2, 2)
               DO i = MAX(p_lb+shift, my_coarse_bo(1, 1)), MIN(p_ub+shift, my_coarse_bo(2, 1))
                  send_buf(ii) = coarse_coeffs(i, j, k)
                  ii = ii+1
               END DO
            END DO
         END DO
         sent_size(p_old) = ii

         IF (pbc) THEN
            DO xx = coarse_gbo(2, 1)+1, p_ub+shift
               x_att = coarse_gbo(1, 1)+MODULO(xx-coarse_gbo(1, 1), s(1))
               IF (x_att >= my_coarse_bo(1, 1) .AND. x_att <= my_coarse_bo(2, 1)) THEN
                  CALL dcopy(coarse_slice_size, &
                             coarse_coeffs(x_att, my_coarse_bo(1, 2), &
                                           my_coarse_bo(1, 3)), ss, send_buf(sent_size(p_old)), 1)
                  sent_size(p_old) = sent_size(p_old)+coarse_slice_size
               END IF
            END DO
         END IF

         CPASSERT(ALL(sent_size(:n_procs-2) == send_offset(1:)))
         CPASSERT(sent_size(n_procs-1) == send_tot_size)
         ! test send/rcv sizes
         CALL mp_alltoall(send_size, real_rcv_size, 1, coarse_coeffs_pw%pw_grid%para%group)
         CPASSERT(ALL(real_rcv_size == rcv_size))
         ! all2all
         CALL mp_alltoall(sb=send_buf, scount=send_size, sdispl=send_offset, &
                          rb=rcv_buf, rcount=rcv_size, rdispl=rcv_offset, &
                          group=coarse_coeffs_pw%pw_grid%para%group)

         ! ** reorder rcv buffer
         ! (actually reordering should be needed only with pbc)

         ALLOCATE (coarse_coeffs(coarse_bo(1, 1):coarse_bo(2, 1), &
                                 coarse_bo(1, 2):coarse_bo(2, 2), &
                                 coarse_bo(1, 3):coarse_bo(2, 3)))

         my_lb = MAX(coarse_gbo(1, 1), coarse_bo(1, 1))
         my_ub = MIN(coarse_gbo(2, 1), coarse_bo(2, 1))
         pos_of_x => coarse_coeffs_pw%pw_grid%para%pos_of_x
         sent_size(:) = rcv_offset
         ss = coarse_bo(2, 1)-coarse_bo(1, 1)+1
         DO x = my_ub+1, coarse_bo(2, 1)
            p_old = pos_of_x(coarse_gbo(1, 1)+MODULO(x-coarse_gbo(1, 1), s(1)))
            CALL dcopy(coarse_slice_size, &
                       rcv_buf(sent_size(p_old)), 1, &
                       coarse_coeffs(x, coarse_bo(1, 2), &
                                     coarse_bo(1, 3)), ss)
            sent_size(p_old) = sent_size(p_old)+coarse_slice_size
         END DO
         p_old = pos_of_x(coarse_gbo(1, 1) &
                          +MODULO(my_lb-coarse_gbo(1, 1), s(1)))
         p_lb = my_lb
         DO x = my_lb, my_ub
            p = pos_of_x(coarse_gbo(1, 1)+MODULO(x-coarse_gbo(1, 1), s(1)))
            IF (p /= p_old) THEN
               p_ub = x-1

               ii = sent_size(p_old)
               DO k = coarse_bo(1, 3), coarse_bo(2, 3)
                  DO j = coarse_bo(1, 2), coarse_bo(2, 2)
                     DO i = p_lb, p_ub
                        coarse_coeffs(i, j, k) = rcv_buf(ii)
                        ii = ii+1
                     END DO
                  END DO
               END DO
               sent_size(p_old) = ii

               p_lb = x
               p_old = p
            END IF
            rcv_size(p) = rcv_size(p)+coarse_slice_size
         END DO
         p_ub = my_ub
         ii = sent_size(p_old)
         DO k = coarse_bo(1, 3), coarse_bo(2, 3)
            DO j = coarse_bo(1, 2), coarse_bo(2, 2)
               DO i = p_lb, p_ub
                  coarse_coeffs(i, j, k) = rcv_buf(ii)
                  ii = ii+1
               END DO
            END DO
         END DO
         sent_size(p_old) = ii
         DO x = coarse_bo(1, 1), my_lb-1
            p_old = pos_of_x(coarse_gbo(1, 1)+MODULO(x-coarse_gbo(1, 1), s(1)))
            CALL dcopy(coarse_slice_size, &
                       rcv_buf(sent_size(p_old)), 1, &
                       coarse_coeffs(x, coarse_bo(1, 2), &
                                     coarse_bo(1, 3)), ss)
            sent_size(p_old) = sent_size(p_old)+coarse_slice_size
         END DO

         CPASSERT(ALL(sent_size(0:n_procs-2) == rcv_offset(1:)))
         CPASSERT(sent_size(n_procs-1) == rcv_tot_size)

         ! dealloc
         DEALLOCATE (send_size, send_offset, rcv_size, rcv_offset)
         DEALLOCATE (send_buf, rcv_buf, real_rcv_size)
         CALL timestop(handle2)

      END IF
      fine_values => fine_values_pw%cr3d
      w_0 = (/weights_1d(3), weights_1d(1), weights_1d(3)/)
      w_1 = (/weights_1d(4), weights_1d(2), weights_1d(2), weights_1d(4)/)

      DO k = coarse_bo(1, 3), coarse_bo(2, 3)
         DO ik = -3, 3
            IF (pbc) THEN
               wk = weights_1d(ABS(ik)+1)
               fk = fine_gbo(1, 3)+MODULO(2*k+ik-fine_gbo(1, 3)+f_shift(3), 2*s(3))
            ELSE
               fk = 2*k+ik+f_shift(3)
               IF (fk <= fine_bo(1, 3)+1 .OR. fk >= fine_bo(2, 3)-1) THEN
                  IF (fk < fine_bo(1, 3) .OR. fk > fine_bo(2, 3)) CYCLE
                  IF (fk == fine_bo(1, 3) .OR. fk == fine_bo(2, 3)) THEN
                     IF (ik /= 0) CYCLE
                     wk = w_border0
                  ELSE IF (fk == 2*coarse_bo(1, 3)+1+f_shift(3)) THEN
                     SELECT CASE (ik)
                     CASE (1)
                        wk = w_border1(1)
                     CASE (-1)
                        wk = w_border1(2)
                     CASE (-3)
                        wk = w_border1(3)
                     CASE default
                        CPABORT("")
                        CYCLE
                     END SELECT
                  ELSE
                     SELECT CASE (ik)
                     CASE (3)
                        wk = w_border1(3)
                     CASE (1)
                        wk = w_border1(2)
                     CASE (-1)
                        wk = w_border1(1)
                     CASE default
                        CPABORT("")
                        CYCLE
                     END SELECT
                  END IF
               ELSE
                  wk = weights_1d(ABS(ik)+1)
               END IF
            END IF
            DO j = coarse_bo(1, 2), coarse_bo(2, 2)
               DO ij = -3, 3
                  IF (pbc) THEN
                     wj = weights_1d(ABS(ij)+1)*wk
                     fj = fine_gbo(1, 2)+MODULO(2*j+ij-fine_gbo(1, 2)+f_shift(2), 2*s(2))
                  ELSE
                     fj = 2*j+ij+f_shift(2)
                     IF (fj <= fine_bo(1, 2)+1 .OR. fj >= fine_bo(2, 2)-1) THEN
                        IF (fj < fine_bo(1, 2) .OR. fj > fine_bo(2, 2)) CYCLE
                        IF (fj == fine_bo(1, 2) .OR. fj == fine_bo(2, 2)) THEN
                           IF (ij /= 0) CYCLE
                           wj = w_border0*wk
                        ELSE IF (fj == 2*coarse_bo(1, 2)+1+f_shift(2)) THEN
                           SELECT CASE (ij)
                           CASE (1)
                              wj = w_border1(1)*wk
                           CASE (-1)
                              wj = w_border1(2)*wk
                           CASE (-3)
                              wj = w_border1(3)*wk
                           CASE default
                              CYCLE
                           END SELECT
                        ELSE
                           SELECT CASE (ij)
                           CASE (-1)
                              wj = w_border1(1)*wk
                           CASE (1)
                              wj = w_border1(2)*wk
                           CASE (3)
                              wj = w_border1(3)*wk
                           CASE default
                              CYCLE
                           END SELECT
                        END IF
                     ELSE
                        wj = weights_1d(ABS(ij)+1)*wk
                     END IF
                  END IF

                  IF (fine_bo(2, 1)-fine_bo(1, 1) < 7 .OR. safe_calc) THEN
!                      CALL timeset(routineN//"_safe",handle2)
                     DO i = coarse_bo(1, 1), coarse_bo(2, 1)
                        DO ii = -3, 3
                           IF (pbc .AND. .NOT. is_split) THEN
                              wi = weights_1d(ABS(ii)+1)*wj
                              fi = fine_gbo(1, 1)+MODULO(2*i+ii-fine_gbo(1, 1)+f_shift(1), 2*s(1))
                           ELSE
                              fi = 2*i+ii+f_shift(1)
                              IF (fi < fine_bo(1, 1) .OR. fi > fine_bo(2, 1)) CYCLE
                              IF (.NOT. pbc .AND. (fi <= fine_gbo(1, 1)+1 .OR. &
                                                   fi >= fine_gbo(2, 1)-1)) THEN
                                 IF (fi == fine_gbo(1, 1) .OR. fi == fine_gbo(2, 1)) THEN
                                    IF (ii /= 0) CYCLE
                                    wi = w_border0*wj
                                 ELSE IF (fi == fine_gbo(1, 1)+1) THEN
                                    SELECT CASE (ii)
                                    CASE (1)
                                       wi = w_border1(1)*wj
                                    CASE (-1)
                                       wi = w_border1(2)*wj
                                    CASE (-3)
                                       wi = w_border1(3)*wj
                                    CASE default
                                       CYCLE
                                    END SELECT
                                 ELSE
                                    SELECT CASE (ii)
                                    CASE (-1)
                                       wi = w_border1(1)*wj
                                    CASE (1)
                                       wi = w_border1(2)*wj
                                    CASE (3)
                                       wi = w_border1(3)*wj
                                    CASE default
                                       CYCLE
                                    END SELECT
                                 END IF
                              ELSE
                                 wi = weights_1d(ABS(ii)+1)*wj
                              END IF
                           END IF
                           fine_values(fi, fj, fk) = &
                              fine_values(fi, fj, fk)+ &
                              wi*coarse_coeffs(i, j, k)
                        END DO
                     END DO
!                      CALL timestop(handle2)
                  ELSE
!                      CALL timeset(routineN//"_core1",handle2)
                     ww0 = wj*w_0
                     ww1 = wj*w_1
                     IF (pbc .AND. .NOT. is_split) THEN
                        v3 = coarse_coeffs(coarse_bo(2, 1), j, k)
                        i = coarse_bo(1, 1)
                        fi = 2*i+f_shift(1)
                        v0 = coarse_coeffs(i, j, k)
                        v1 = coarse_coeffs(i+1, j, k)
                        fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                  ww0(1)*v3+ww0(2)*v0+ww0(3)*v1
                        v2 = coarse_coeffs(i+2, j, k)
                        fi = fi+1
                        fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                  ww1(1)*v3+ww1(2)*v0+ww1(3)*v1+ww1(4)*v2
                     ELSE IF (.NOT. has_i_lbound) THEN
                        i = coarse_bo(1, 1)
                        fi = 2*i+f_shift(1)
                        v0 = coarse_coeffs(i, j, k)
                        fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                  w_border0*wj*v0
                        v1 = coarse_coeffs(i+1, j, k)
                        v2 = coarse_coeffs(i+2, j, k)
                        fi = fi+1
                        fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                  wj*(w_border1(1)*v0+w_border1(2)*v1+ &
                                                      w_border1(3)*v2)
                     ELSE
                        i = coarse_bo(1, 1)
                        v0 = coarse_coeffs(i, j, k)
                        v1 = coarse_coeffs(i+1, j, k)
                        v2 = coarse_coeffs(i+2, j, k)
                        fi = 2*i+f_shift(1)+1
                        IF (.NOT. (fi+1 == fine_bo(1, 1) .OR. &
                                   fi+2 == fine_bo(1, 1))) THEN
                           CALL cp_abort(__LOCATION__, &
                                         "unexpected start index "// &
                                         TRIM(cp_to_string(coarse_bo(1, 1)))//" "// &
                                         TRIM(cp_to_string(fi)))
                        END IF
                     END IF
                     fi = fi+1
                     IF (fi >= fine_bo(1, 1)) THEN
                        fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                  ww0(1)*v0+ww0(2)*v1+ &
                                                  ww0(3)*v2
                     ELSE
                        CPASSERT(fi+1 == fine_bo(1, 1))
                     END IF
!                      CALL timestop(handle2)
!                      CALL timeset(routineN//"_core",handle2)
                     DO i = coarse_bo(1, 1)+3, FLOOR((fine_bo(2, 1)-f_shift(1))/2.)-3, 4
                        v3 = coarse_coeffs(i, j, k)
                        fi = fi+1
                        fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                  (ww1(1)*v0+ww1(2)*v1+ &
                                                   ww1(3)*v2+ww1(4)*v3)
                        fi = fi+1
                        fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                  (ww0(1)*v1+ww0(2)*v2+ &
                                                   ww0(3)*v3)
                        v0 = coarse_coeffs(i+1, j, k)
                        fi = fi+1
                        fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                  (ww1(4)*v0+ww1(1)*v1+ &
                                                   ww1(2)*v2+ww1(3)*v3)
                        fi = fi+1
                        fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                  (ww0(1)*v2+ww0(2)*v3+ &
                                                   ww0(3)*v0)
                        v1 = coarse_coeffs(i+2, j, k)
                        fi = fi+1
                        fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                  (ww1(3)*v0+ww1(4)*v1+ &
                                                   ww1(1)*v2+ww1(2)*v3)
                        fi = fi+1
                        fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                  (ww0(1)*v3+ww0(2)*v0+ &
                                                   ww0(3)*v1)
                        v2 = coarse_coeffs(i+3, j, k)
                        fi = fi+1
                        fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                  (ww1(2)*v0+ww1(3)*v1+ &
                                                   ww1(4)*v2+ww1(1)*v3)
                        fi = fi+1
                        fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                  (ww0(1)*v0+ww0(2)*v1+ &
                                                   ww0(3)*v2)
                     END DO
!                      CALL timestop(handle2)
!                      CALL timeset(routineN//"_clean",handle2)
                     rest_b = MODULO(FLOOR((fine_bo(2, 1)-f_shift(1))/2.)-coarse_bo(1, 1)-3+1, 4)
                     IF (rest_b > 0) THEN
                        i = FLOOR((fine_bo(2, 1)-f_shift(1))/2.)-rest_b+1
                        v3 = coarse_coeffs(i, j, k)
                        fi = fi+1
                        fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                  (ww1(1)*v0+ww1(2)*v1+ &
                                                   ww1(3)*v2+ww1(4)*v3)
                        fi = fi+1
                        fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                  (ww0(1)*v1+ww0(2)*v2+ &
                                                   ww0(3)*v3)
                        IF (rest_b > 1) THEN
                           v0 = coarse_coeffs(i+1, j, k)
                           fi = fi+1
                           fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                     (ww1(4)*v0+ww1(1)*v1+ &
                                                      ww1(2)*v2+ww1(3)*v3)
                           fi = fi+1
                           fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                     (ww0(1)*v2+ww0(2)*v3+ &
                                                      ww0(3)*v0)
                           IF (rest_b > 2) THEN
                              v1 = coarse_coeffs(i+2, j, k)
                              fi = fi+1
                              fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                        (ww1(3)*v0+ww1(4)*v1+ &
                                                         ww1(1)*v2+ww1(2)*v3)
                              fi = fi+1
                              fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                        (ww0(1)*v3+ww0(2)*v0+ &
                                                         ww0(3)*v1)
                              IF (pbc .AND. .NOT. is_split) THEN
                                 v2 = coarse_coeffs(coarse_bo(1, 1), j, k)
                                 fi = fi+1
                                 fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                           ww1(1)*v3+ww1(2)*v0+ww1(3)*v1+ww1(4)*v2
                                 fi = fi+1
                                 fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                           ww0(1)*v0+ww0(2)*v1+ww0(3)*v2
                                 v3 = coarse_coeffs(coarse_bo(1, 1)+1, j, k)
                                 fi = fi+1
                                 fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                           ww1(1)*v0+ww1(2)*v1+ww1(3)*v2+ww1(4)*v3
                              ELSE IF (has_i_ubound) THEN
                                 v2 = coarse_coeffs(i+3, j, k)
                                 fi = fi+1
                                 fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                           ww1(1)*v3+ww1(2)*v0+ww1(3)*v1+ww1(4)*v2
                                 fi = fi+1
                                 fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                           ww0(1)*v0+ww0(2)*v1+ww0(3)*v2
                                 IF (fi+1 == fine_bo(2, 1)) THEN
                                    v3 = coarse_coeffs(i+4, j, k)
                                    fi = fi+1
                                    fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                              ww1(1)*v0+ww1(2)*v1+ww1(3)*v2+ww1(4)*v3
                                 END IF
                              ELSE
                                 fi = fi+1
                                 fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                           wj*(w_border1(3)*v3+w_border1(2)*v0+ &
                                                               w_border1(1)*v1)
                                 fi = fi+1
                                 fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                           w_border0*wj*v1
                              END IF
                           ELSE IF (pbc .AND. .NOT. is_split) THEN
                              v1 = coarse_coeffs(coarse_bo(1, 1), j, k)
                              fi = fi+1
                              fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                        ww1(1)*v2+ww1(2)*v3+ww1(3)*v0+ww1(4)*v1
                              fi = fi+1
                              fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                        ww0(1)*v3+ww0(2)*v0+ww0(3)*v1
                              v2 = coarse_coeffs(coarse_bo(1, 1)+1, j, k)
                              fi = fi+1
                              fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                        ww1(1)*v3+ww1(2)*v0+ww1(3)*v1+ww1(4)*v2
                           ELSE IF (has_i_ubound) THEN
                              v1 = coarse_coeffs(i+2, j, k)
                              fi = fi+1
                              fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                        ww1(1)*v2+ww1(2)*v3+ww1(3)*v0+ww1(4)*v1
                              fi = fi+1
                              fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                        ww0(1)*v3+ww0(2)*v0+ww0(3)*v1
                              IF (fi+1 == fine_bo(2, 1)) THEN
                                 v2 = coarse_coeffs(i+3, j, k)
                                 fi = fi+1
                                 fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                           ww1(1)*v3+ww1(2)*v0+ww1(3)*v1+ww1(4)*v2
                              END IF
                           ELSE
                              fi = fi+1
                              fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                        wj*(w_border1(3)*v2+w_border1(2)*v3+ &
                                                            w_border1(1)*v0)
                              fi = fi+1
                              fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                        w_border0*wj*v0
                           END IF
                        ELSE IF (pbc .AND. .NOT. is_split) THEN
                           v0 = coarse_coeffs(coarse_bo(1, 1), j, k)
                           fi = fi+1
                           fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                     ww1(1)*v1+ww1(2)*v2+ww1(3)*v3+ww1(4)*v0
                           fi = fi+1
                           fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                     ww0(1)*v2+ww0(2)*v3+ww0(3)*v0
                           v1 = coarse_coeffs(coarse_bo(1, 1)+1, j, k)
                           fi = fi+1
                           fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                     ww1(1)*v2+ww1(2)*v3+ww1(3)*v0+ww1(4)*v1
                        ELSE IF (has_i_ubound) THEN
                           v0 = coarse_coeffs(i+1, j, k)
                           fi = fi+1
                           fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                     ww1(1)*v1+ww1(2)*v2+ww1(3)*v3+ww1(4)*v0
                           fi = fi+1
                           fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                     ww0(1)*v2+ww0(2)*v3+ww0(3)*v0
                           IF (fi+1 == fine_bo(2, 1)) THEN
                              v1 = coarse_coeffs(i+2, j, k)
                              fi = fi+1
                              fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                        ww1(1)*v2+ww1(2)*v3+ww1(3)*v0+ww1(4)*v1
                           END IF
                        ELSE
                           fi = fi+1
                           fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                     wj*(w_border1(3)*v1+w_border1(2)*v2+ &
                                                         w_border1(1)*v3)
                           fi = fi+1
                           fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                     w_border0*wj*v3
                        END IF
                     ELSE IF (pbc .AND. .NOT. is_split) THEN
                        v3 = coarse_coeffs(coarse_bo(1, 1), j, k)
                        fi = fi+1
                        fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                  ww1(1)*v0+ww1(2)*v1+ww1(3)*v2+ww1(4)*v3
                        fi = fi+1
                        fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                  ww0(1)*v1+ww0(2)*v2+ww0(3)*v3
                        v0 = coarse_coeffs(coarse_bo(1, 1)+1, j, k)
                        fi = fi+1
                        fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                  ww1(1)*v1+ww1(2)*v2+ww1(3)*v3+ww1(4)*v0
                     ELSE IF (has_i_ubound) THEN
                        v3 = coarse_coeffs(i, j, k)
                        fi = fi+1
                        fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                  ww1(1)*v0+ww1(2)*v1+ww1(3)*v2+ww1(4)*v3
                        fi = fi+1
                        fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                  ww0(1)*v1+ww0(2)*v2+ww0(3)*v3
                        IF (fi+1 == fine_bo(2, 1)) THEN
                           v0 = coarse_coeffs(i+1, j, k)
                           fi = fi+1
                           fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                     ww1(1)*v1+ww1(2)*v2+ww1(3)*v3+ww1(4)*v0
                        END IF
                     ELSE
                        fi = fi+1
                        fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                  wj*(w_border1(3)*v0+w_border1(2)*v1+ &
                                                      w_border1(1)*v2)
                        fi = fi+1
                        fine_values(fi, fj, fk) = fine_values(fi, fj, fk)+ &
                                                  w_border0*wj*v2
                     END IF
                     CPASSERT(fi == fine_bo(2, 1))
                  END IF
!                   CALL timestop(handle2)
               END DO
            END DO
         END DO
      END DO

      IF (is_split) THEN
         DEALLOCATE (coarse_coeffs)
      END IF
      CALL timestop(handle)
   END SUBROUTINE add_coarse2fine

! **************************************************************************************************
!> \brief low level function that adds a coarse grid (without boundary)
!>      to a fine grid.
!>
!>      It will add to
!>
!>        coarse_coeffs(coarse_bounds(1,1):coarse_bounds(2,1),
!>                      coarse_bounds(1,2):coarse_bounds(2,2),
!>                      coarse_bounds(1,3):coarse_bounds(2,3))
!>
!>      using
!>
!>        fine_values(2*coarse_bounds(1,1):2*coarse_bounds(2,1),
!>                    2*coarse_bounds(1,2):2*coarse_bounds(2,2),
!>                    2*coarse_bounds(1,3):2*coarse_bounds(2,3))
!>
!>      composed with the weights obtained by the direct product of the
!>      1d coefficents weights:
!>
!>      for i,j,k in -3..3
!>         w(i,j,k)=weights_1d(abs(i)+1)*weights_1d(abs(j)+1)*
!>                  weights_1d(abs(k)+1)
!> \param fine_values_pw 3d array where to add the values due to the
!>        coarse coeffs
!> \param coarse_coeffs_pw 3d array with boundary of size 1 with the values of the
!>        coefficients
!> \param weights_1d the weights of the 1d smearing
!> \param w_border0 the 1d weight at the border
!> \param w_border1 the 1d weights for a point one off the border
!>        (w_border1(1) is the weight of the coefficent at the border)
!> \param pbc ...
!> \param safe_computation ...
!> \author fawzi
!> \note
!>      see coarse2fine for some relevant notes
! **************************************************************************************************
   SUBROUTINE add_fine2coarse(fine_values_pw, coarse_coeffs_pw, &
                              weights_1d, w_border0, w_border1, pbc, safe_computation)
      TYPE(pw_type), POINTER                             :: fine_values_pw, coarse_coeffs_pw
      REAL(kind=dp), DIMENSION(4), INTENT(in)            :: weights_1d
      REAL(kind=dp), INTENT(in)                          :: w_border0
      REAL(kind=dp), DIMENSION(3), INTENT(in)            :: w_border1
      LOGICAL, INTENT(in)                                :: pbc
      LOGICAL, INTENT(in), OPTIONAL                      :: safe_computation

      CHARACTER(len=*), PARAMETER :: routineN = 'add_fine2coarse', &
         routineP = moduleN//':'//routineN

      INTEGER :: coarse_slice_size, f_shift(3), fi, fj, fk, handle, handle2, i, ii, ij, ik, ip, j, &
         k, n_procs, p, p_old, rcv_tot_size, rest_b, s(3), send_tot_size, ss, x, x_att
      INTEGER, ALLOCATABLE, DIMENSION(:)                 :: pp_lb, pp_ub, rcv_offset, rcv_size, &
                                                            real_rcv_size, send_offset, send_size, &
                                                            sent_size
      INTEGER, DIMENSION(2, 3)                           :: coarse_bo, coarse_gbo, fine_bo, &
                                                            fine_gbo, my_coarse_bo
      INTEGER, DIMENSION(:), POINTER                     :: pos_of_x
      LOGICAL                                            :: has_i_lbound, has_i_ubound, is_split, &
                                                            local_data, safe_calc
      REAL(kind=dp)                                      :: vv0, vv1, vv2, vv3, vv4, vv5, vv6, vv7, &
                                                            wi, wj, wk
      REAL(kind=dp), ALLOCATABLE, DIMENSION(:)           :: rcv_buf, send_buf
      REAL(kind=dp), DIMENSION(3)                        :: w_0, ww0
      REAL(kind=dp), DIMENSION(4)                        :: w_1, ww1
      REAL(kind=dp), DIMENSION(:, :, :), POINTER         :: coarse_coeffs, fine_values

      CALL timeset(routineN, handle)

      safe_calc = .FALSE.
      IF (PRESENT(safe_computation)) safe_calc = safe_computation

      my_coarse_bo = coarse_coeffs_pw%pw_grid%bounds_local
      coarse_gbo = coarse_coeffs_pw%pw_grid%bounds
      fine_bo = fine_values_pw%pw_grid%bounds_local
      fine_gbo = fine_values_pw%pw_grid%bounds
      f_shift = fine_gbo(1, :)-2*coarse_gbo(1, :)
      is_split = ANY(coarse_gbo(:, 1) /= my_coarse_bo(:, 1))
      coarse_bo = my_coarse_bo
      IF (fine_bo(1, 1) <= fine_bo(2, 1)) THEN
         coarse_bo(1, 1) = FLOOR(REAL(fine_bo(1, 1)-f_shift(1), dp)/2._dp)-1
         coarse_bo(2, 1) = FLOOR(REAL(fine_bo(2, 1)+1-f_shift(1), dp)/2._dp)+1
      ELSE
         coarse_bo(1, 1) = coarse_gbo(2, 1)
         coarse_bo(2, 1) = coarse_gbo(2, 1)-1
      END IF
      IF (.NOT. is_split .OR. .NOT. pbc) THEN
         coarse_bo(1, 1) = MAX(coarse_gbo(1, 1), coarse_bo(1, 1))
         coarse_bo(2, 1) = MIN(coarse_gbo(2, 1), coarse_bo(2, 1))
      END IF
      has_i_ubound = (fine_gbo(2, 1) /= fine_bo(2, 1)) .OR. pbc .AND. is_split
      has_i_lbound = (fine_gbo(1, 1) /= fine_bo(1, 1)) .OR. pbc .AND. is_split

      IF (pbc) THEN
         CPASSERT(ALL(fine_gbo(1, :) == 2*coarse_gbo(1, :)+f_shift))
         CPASSERT(ALL(fine_gbo(2, :) == 2*coarse_gbo(2, :)+f_shift+1))
      ELSE
         CPASSERT(ALL(fine_gbo(2, :) == 2*coarse_gbo(2, :)+f_shift))
         CPASSERT(ALL(fine_gbo(1, :) == 2*coarse_gbo(1, :)+f_shift))
      END IF
      CPASSERT(coarse_gbo(2, 1)-coarse_gbo(1, 2) > 1)
      local_data = is_split ! ANY(coarse_bo/=my_coarse_bo)
      IF (local_data) THEN
         ALLOCATE (coarse_coeffs(coarse_bo(1, 1):coarse_bo(2, 1), &
                                 coarse_bo(1, 2):coarse_bo(2, 2), &
                                 coarse_bo(1, 3):coarse_bo(2, 3)))
         coarse_coeffs = 0._dp
      ELSE
         coarse_coeffs => coarse_coeffs_pw%cr3d
      END IF

      fine_values => fine_values_pw%cr3d
      w_0 = (/weights_1d(3), weights_1d(1), weights_1d(3)/)
      w_1 = (/weights_1d(4), weights_1d(2), weights_1d(2), weights_1d(4)/)

      DO i = 1, 3
         s(i) = coarse_gbo(2, i)-coarse_gbo(1, i)+1
      END DO
      IF (ANY(s < 1)) RETURN

      DO k = coarse_bo(1, 3), coarse_bo(2, 3)
         DO ik = -3, 3
            IF (pbc) THEN
               wk = weights_1d(ABS(ik)+1)
               fk = fine_gbo(1, 3)+MODULO(2*k+ik-fine_gbo(1, 3)+f_shift(3), 2*s(3))
            ELSE
               fk = 2*k+ik+f_shift(3)
               IF (fk <= fine_bo(1, 3)+1 .OR. fk >= fine_bo(2, 3)-1) THEN
                  IF (fk < fine_bo(1, 3) .OR. fk > fine_bo(2, 3)) CYCLE
                  IF (fk == fine_bo(1, 3) .OR. fk == fine_bo(2, 3)) THEN
                     IF (ik /= 0) CYCLE
                     wk = w_border0
                  ELSE IF (fk == fine_bo(1, 3)+1) THEN
                     SELECT CASE (ik)
                     CASE (1)
                        wk = w_border1(1)
                     CASE (-1)
                        wk = w_border1(2)
                     CASE (-3)
                        wk = w_border1(3)
                     CASE default
                        CPABORT("")
                        CYCLE
                     END SELECT
                  ELSE
                     SELECT CASE (ik)
                     CASE (3)
                        wk = w_border1(3)
                     CASE (1)
                        wk = w_border1(2)
                     CASE (-1)
                        wk = w_border1(1)
                     CASE default
                        CPABORT("")
                        CYCLE
                     END SELECT
                  END IF
               ELSE
                  wk = weights_1d(ABS(ik)+1)
               END IF
            END IF
            DO j = coarse_bo(1, 2), coarse_bo(2, 2)
               DO ij = -3, 3
                  IF (pbc) THEN
                     fj = fine_gbo(1, 2)+MODULO(2*j+ij-fine_gbo(1, 2)+f_shift(2), &
                                                2*s(2))
                     wj = weights_1d(ABS(ij)+1)*wk
                  ELSE
                     fj = 2*j+ij+f_shift(2)
                     IF (fj <= fine_bo(1, 2)+1 .OR. fj >= fine_bo(2, 2)-1) THEN
                        IF (fj < fine_bo(1, 2) .OR. fj > fine_bo(2, 2)) CYCLE
                        IF (fj == fine_bo(1, 2) .OR. fj == fine_bo(2, 2)) THEN
                           IF (ij /= 0) CYCLE
                           wj = w_border0*wk
                        ELSE IF (fj == fine_bo(1, 2)+1) THEN
                           SELECT CASE (ij)
                           CASE (1)
                              wj = w_border1(1)*wk
                           CASE (-1)
                              wj = w_border1(2)*wk
                           CASE (-3)
                              wj = w_border1(3)*wk
                           CASE default
                              CPABORT("")
                              CYCLE
                           END SELECT
                        ELSE
                           SELECT CASE (ij)
                           CASE (-1)
                              wj = w_border1(1)*wk
                           CASE (1)
                              wj = w_border1(2)*wk
                           CASE (3)
                              wj = w_border1(3)*wk
                           CASE default
                              CPABORT("")
                              CYCLE
                           END SELECT
                        END IF
                     ELSE
                        wj = weights_1d(ABS(ij)+1)*wk
                     END IF
                  END IF

                  IF (coarse_bo(2, 1)-coarse_bo(1, 1) < 7 .OR. safe_calc) THEN
                     DO i = coarse_bo(1, 1), coarse_bo(2, 1)
                        DO ii = -3, 3
                           IF (pbc .AND. .NOT. is_split) THEN
                              wi = weights_1d(ABS(ii)+1)*wj
                              fi = fine_gbo(1, 1)+MODULO(2*i+ii-fine_gbo(1, 1)+f_shift(1), 2*s(1))
                           ELSE
                              fi = 2*i+ii+f_shift(1)
                              IF (fi < fine_bo(1, 1) .OR. fi > fine_bo(2, 1)) CYCLE
                              IF (((.NOT. pbc) .AND. fi <= fine_gbo(1, 1)+1) .OR. &
                                  ((.NOT. pbc) .AND. fi >= fine_gbo(2, 1)-1)) THEN
                                 IF (fi == fine_gbo(1, 1) .OR. fi == fine_gbo(2, 1)) THEN
                                    IF (ii /= 0) CYCLE
                                    wi = w_border0*wj
                                 ELSE IF (fi == fine_gbo(1, 1)+1) THEN
                                    SELECT CASE (ii)
                                    CASE (1)
                                       wi = w_border1(1)*wj
                                    CASE (-1)
                                       wi = w_border1(2)*wj
                                    CASE (-3)
                                       wi = w_border1(3)*wj
                                    CASE default
                                       CYCLE
                                    END SELECT
                                 ELSE
                                    SELECT CASE (ii)
                                    CASE (-1)
                                       wi = w_border1(1)*wj
                                    CASE (1)
                                       wi = w_border1(2)*wj
                                    CASE (3)
                                       wi = w_border1(3)*wj
                                    CASE default
                                       CYCLE
                                    END SELECT
                                 END IF
                              ELSE
                                 wi = weights_1d(ABS(ii)+1)*wj
                              END IF
                           END IF
                           coarse_coeffs(i, j, k) = &
                              coarse_coeffs(i, j, k)+ &
                              wi*fine_values(fi, fj, fk)
                        END DO
                     END DO
                  ELSE
                     ww0 = wj*w_0
                     ww1 = wj*w_1
                     IF (pbc .AND. .NOT. is_split) THEN
                        i = coarse_bo(1, 1)-1
                        vv2 = fine_values(fine_bo(2, 1)-2, fj, fk)
                        vv3 = fine_values(fine_bo(2, 1)-1, fj, fk)
                        vv4 = fine_values(fine_bo(2, 1), fj, fk)
                        fi = fine_bo(1, 1)
                        vv5 = fine_values(fi, fj, fk)
                        fi = fi+1
                        vv6 = fine_values(fi, fj, fk)
                        fi = fi+1
                        vv7 = fine_values(fi, fj, fk)
                        coarse_coeffs(i+1, j, k) = coarse_coeffs(i+1, j, k) &
                                                   +ww1(4)*vv2+ww0(3)*vv3+ww1(3)*vv4+ww0(2)*vv5+ww1(2)*vv6+ww0(1)*vv7
                        coarse_coeffs(i+2, j, k) = coarse_coeffs(i+2, j, k) &
                                                   +ww1(4)*vv4+ww0(3)*vv5+ww1(3)*vv6+ww0(2)*vv7
                        coarse_coeffs(i+3, j, k) = coarse_coeffs(i+3, j, k) &
                                                   +ww1(4)*vv6+ww0(3)*vv7
                     ELSE IF (has_i_lbound) THEN
                        i = coarse_bo(1, 1)
                        fi = fine_bo(1, 1)-1
                        IF (i+1 == FLOOR((fine_bo(1, 1)+1-f_shift(1))/2._dp)) THEN
                           fi = fi+1
                           vv0 = fine_values(fi, fj, fk)
                           coarse_coeffs(i, j, k) = coarse_coeffs(i, j, k)+ &
                                                    vv0*ww0(3)
                           coarse_coeffs(i+1, j, k) = coarse_coeffs(i+1, j, k)+ &
                                                      vv0*ww0(2)
                           coarse_coeffs(i+2, j, k) = coarse_coeffs(i+2, j, k)+ &
                                                      vv0*ww0(1)
                        END IF
                     ELSE
                        i = coarse_bo(1, 1)
                        fi = 2*i+f_shift(1)
                        vv0 = fine_values(fi, fj, fk)
                        fi = fi+1
                        vv1 = fine_values(fi, fj, fk)
                        fi = fi+1
                        vv2 = fine_values(fi, fj, fk)
                        coarse_coeffs(i, j, k) = coarse_coeffs(i, j, k)+ &
                                                 (vv0*w_border0+vv1*w_border1(1))*wj+vv2*ww0(1)
                        coarse_coeffs(i+1, j, k) = coarse_coeffs(i+1, j, k)+ &
                                                   wj*w_border1(2)*vv1+ww0(2)*vv2
                        coarse_coeffs(i+2, j, k) = coarse_coeffs(i+2, j, k)+ &
                                                   wj*w_border1(3)*vv1+ww0(3)*vv2
                     END IF
                     DO i = coarse_bo(1, 1)+3, FLOOR((fine_bo(2, 1)-f_shift(1))/2._dp)-3, 4
                        fi = fi+1
                        vv0 = fine_values(fi, fj, fk)
                        fi = fi+1
                        vv1 = fine_values(fi, fj, fk)
                        fi = fi+1
                        vv2 = fine_values(fi, fj, fk)
                        fi = fi+1
                        vv3 = fine_values(fi, fj, fk)
                        fi = fi+1
                        vv4 = fine_values(fi, fj, fk)
                        fi = fi+1
                        vv5 = fine_values(fi, fj, fk)
                        fi = fi+1
                        vv6 = fine_values(fi, fj, fk)
                        fi = fi+1
                        vv7 = fine_values(fi, fj, fk)
                        coarse_coeffs(i-3, j, k) = coarse_coeffs(i-3, j, k) &
                                                   +ww1(1)*vv0
                        coarse_coeffs(i-2, j, k) = coarse_coeffs(i-2, j, k) &
                                                   +ww1(2)*vv0+ww0(1)*vv1+ww1(1)*vv2
                        coarse_coeffs(i-1, j, k) = coarse_coeffs(i-1, j, k) &
                                                   +ww1(3)*vv0+ww0(2)*vv1+ww1(2)*vv2+ww0(1)*vv3+ww1(1)*vv4
                        coarse_coeffs(i, j, k) = coarse_coeffs(i, j, k) &
                                                 +ww1(4)*vv0+ww0(3)*vv1+ww1(3)*vv2+ww0(2)*vv3+ww1(2)*vv4+ww0(1)*vv5+ww1(1)*vv6
                        coarse_coeffs(i+1, j, k) = coarse_coeffs(i+1, j, k) &
                                                   +ww1(4)*vv2+ww0(3)*vv3+ww1(3)*vv4+ww0(2)*vv5+ww1(2)*vv6+ww0(1)*vv7
                        coarse_coeffs(i+2, j, k) = coarse_coeffs(i+2, j, k) &
                                                   +ww1(4)*vv4+ww0(3)*vv5+ww1(3)*vv6+ww0(2)*vv7
                        coarse_coeffs(i+3, j, k) = coarse_coeffs(i+3, j, k) &
                                                   +ww1(4)*vv6+ww0(3)*vv7
                     END DO
                     IF (.NOT. FLOOR((fine_bo(2, 1)-f_shift(1))/2._dp)-coarse_bo(1, 1) >= 4) THEN
                        CPABORT("FLOOR((fine_bo(2,1)-f_shift(1))/2._dp)-coarse_bo(1,1)>=4")
                     END IF
                     rest_b = MODULO(FLOOR((fine_bo(2, 1)-f_shift(1))/2._dp)-coarse_bo(1, 1)-6, 4)
                     i = FLOOR((fine_bo(2, 1)-f_shift(1))/2._dp)-3-rest_b+4
                     CPASSERT(fi == (i-2)*2+f_shift(1))
                     IF (rest_b > 0) THEN
                        fi = fi+1
                        vv0 = fine_values(fi, fj, fk)
                        fi = fi+1
                        vv1 = fine_values(fi, fj, fk)
                        coarse_coeffs(i-3, j, k) = coarse_coeffs(i-3, j, k) &
                                                   +ww1(1)*vv0
                        coarse_coeffs(i-2, j, k) = coarse_coeffs(i-2, j, k) &
                                                   +ww1(2)*vv0+ww0(1)*vv1
                        coarse_coeffs(i-1, j, k) = coarse_coeffs(i-1, j, k) &
                                                   +ww1(3)*vv0+ww0(2)*vv1
                        coarse_coeffs(i, j, k) = coarse_coeffs(i, j, k) &
                                                 +ww1(4)*vv0+ww0(3)*vv1
                        IF (rest_b > 1) THEN
                           fi = fi+1
                           vv2 = fine_values(fi, fj, fk)
                           fi = fi+1
                           vv3 = fine_values(fi, fj, fk)
                           coarse_coeffs(i-2, j, k) = coarse_coeffs(i-2, j, k) &
                                                      +ww1(1)*vv2
                           coarse_coeffs(i-1, j, k) = coarse_coeffs(i-1, j, k) &
                                                      +ww1(2)*vv2+ww0(1)*vv3
                           coarse_coeffs(i, j, k) = coarse_coeffs(i, j, k) &
                                                    +ww1(3)*vv2+ww0(2)*vv3
                           coarse_coeffs(i+1, j, k) = coarse_coeffs(i+1, j, k) &
                                                      +ww1(4)*vv2+ww0(3)*vv3
                           IF (rest_b > 2) THEN
                              fi = fi+1
                              vv4 = fine_values(fi, fj, fk)
                              fi = fi+1
                              vv5 = fine_values(fi, fj, fk)
                              fi = fi+1
                              vv6 = fine_values(fi, fj, fk)
                              fi = fi+1
                              vv7 = fine_values(fi, fj, fk)
                              coarse_coeffs(i-1, j, k) = coarse_coeffs(i-1, j, k) &
                                                         +ww1(1)*vv4
                              IF (has_i_ubound) THEN
                                 IF (coarse_bo(2, 1)-2 == FLOOR((fine_bo(2, 1)-f_shift(1))/2._dp)) THEN
                                    fi = fi+1
                                    vv0 = fine_values(fi, fj, fk)
                                    coarse_coeffs(i+4, j, k) = coarse_coeffs(i+4, j, k) &
                                                               +vv0*ww1(4)
                                 ELSE
                                    vv0 = 0._dp
                                 END IF
                                 coarse_coeffs(i, j, k) = coarse_coeffs(i, j, k) &
                                                          +ww1(2)*vv4+ww0(1)*vv5+ww1(1)*vv6
                                 coarse_coeffs(i+1, j, k) = coarse_coeffs(i+1, j, k) &
                                                            +ww1(3)*vv4+ww0(2)*vv5+ww1(2)*vv6+ww0(1)*vv7+vv0*ww1(1)
                                 coarse_coeffs(i+2, j, k) = coarse_coeffs(i+2, j, k) &
                                                            +ww1(4)*vv4+ww0(3)*vv5+ww1(3)*vv6+ww0(2)*vv7+vv0*ww1(2)
                                 coarse_coeffs(i+3, j, k) = coarse_coeffs(i+3, j, k) &
                                                            +ww1(4)*vv6+ww0(3)*vv7+vv0*ww1(3)
                              ELSEIF (pbc .AND. .NOT. is_split) THEN
                                 fi = fi+1
                                 vv0 = fine_values(fi, fj, fk)
                                 vv1 = fine_values(fine_bo(1, 1), fj, fk)
                                 vv2 = fine_values(fine_bo(1, 1)+1, fj, fk)
                                 coarse_coeffs(i, j, k) = coarse_coeffs(i, j, k) &
                                                          +ww1(2)*vv4+ww0(1)*vv5+ww1(1)*vv6
                                 coarse_coeffs(i+1, j, k) = coarse_coeffs(i+1, j, k) &
                                                            +ww1(3)*vv4+ww0(2)*vv5+ww1(2)*vv6+ww0(1)*vv7+vv0*ww1(1)
                                 coarse_coeffs(i+2, j, k) = coarse_coeffs(i+2, j, k) &
                                                            +ww1(4)*vv4+ww0(3)*vv5+ww1(3)*vv6+ww0(2)*vv7+vv0*ww1(2) &
                                                            +vv1*ww0(1)+vv2*ww1(1)
                              ELSE
                                 coarse_coeffs(i, j, k) = coarse_coeffs(i, j, k) &
                                                          +ww1(2)*vv4+ww0(1)*vv5+wj*w_border1(3)*vv6
                                 coarse_coeffs(i+1, j, k) = coarse_coeffs(i+1, j, k) &
                                                            +ww1(3)*vv4+ww0(2)*vv5+wj*w_border1(2)*vv6
                                 coarse_coeffs(i+2, j, k) = coarse_coeffs(i+2, j, k) &
                                                            +ww1(4)*vv4+ww0(3)*vv5+wj*w_border1(1)*vv6+w_border0*wj*vv7
                              END IF
                           ELSE
                              fi = fi+1
                              vv4 = fine_values(fi, fj, fk)
                              fi = fi+1
                              vv5 = fine_values(fi, fj, fk)
                              IF (has_i_ubound) THEN
                                 IF (coarse_bo(2, 1)-2 == FLOOR((fine_bo(2, 1)-f_shift(1))/2._dp)) THEN
                                    fi = fi+1
                                    vv6 = fine_values(fi, fj, fk)
                                    coarse_coeffs(i+3, j, k) = coarse_coeffs(i+3, j, k) &
                                                               +ww1(4)*vv6
                                 ELSE
                                    vv6 = 0._dp
                                 END IF
                                 coarse_coeffs(i-1, j, k) = coarse_coeffs(i-1, j, k) &
                                                            +ww1(1)*vv4
                                 coarse_coeffs(i, j, k) = coarse_coeffs(i, j, k) &
                                                          +ww1(2)*vv4+ww0(1)*vv5+ww1(1)*vv6
                                 coarse_coeffs(i+1, j, k) = coarse_coeffs(i+1, j, k) &
                                                            +ww1(3)*vv4+ww0(2)*vv5+ww1(2)*vv6
                                 coarse_coeffs(i+2, j, k) = coarse_coeffs(i+2, j, k) &
                                                            +ww1(4)*vv4+ww0(3)*vv5+ww1(3)*vv6
                              ELSEIF (pbc .AND. .NOT. is_split) THEN
                                 fi = fi+1
                                 vv6 = fine_values(fi, fj, fk)
                                 vv7 = fine_values(fine_bo(1, 1), fj, fk)
                                 vv0 = fine_values(fine_bo(1, 1)+1, fj, fk)
                                 coarse_coeffs(i-1, j, k) = coarse_coeffs(i-1, j, k) &
                                                            +ww1(1)*vv4
                                 coarse_coeffs(i, j, k) = coarse_coeffs(i, j, k) &
                                                          +ww1(4)*vv0+ww0(3)*vv1+ww1(3)*vv2+ww0(2)*vv3+ &
                                                          ww1(2)*vv4+ww0(1)*vv5+ww1(1)*vv6
                                 coarse_coeffs(i+1, j, k) = coarse_coeffs(i+1, j, k) &
                                                            +ww1(4)*vv2+ww0(3)*vv3+ww1(3)*vv4+ww0(2)*vv5+ww1(2)*vv6 &
                                                            +ww0(1)*vv7+ww1(1)*vv0
                              ELSE
                                 coarse_coeffs(i-1, j, k) = coarse_coeffs(i-1, j, k) &
                                                            +wj*w_border1(3)*vv4
                                 coarse_coeffs(i, j, k) = coarse_coeffs(i, j, k) &
                                                          +wj*w_border1(2)*vv4
                                 coarse_coeffs(i+1, j, k) = coarse_coeffs(i+1, j, k) &
                                                            +wj*(w_border1(1)*vv4+w_border0*vv5)
                              END IF
                           END IF
                        ELSE
                           fi = fi+1
                           vv2 = fine_values(fi, fj, fk)
                           fi = fi+1
                           vv3 = fine_values(fi, fj, fk)
                           IF (has_i_ubound) THEN
                              IF (coarse_bo(2, 1)-2 == FLOOR((fine_bo(2, 1)-f_shift(1))/2._dp)) THEN
                                 fi = fi+1
                                 vv4 = fine_values(fi, fj, fk)
                                 coarse_coeffs(i+2, j, k) = coarse_coeffs(i+2, j, k) &
                                                            +ww1(4)*vv4
                              ELSE
                                 vv4 = 0._dp
                              END IF
                              coarse_coeffs(i-2, j, k) = coarse_coeffs(i-2, j, k) &
                                                         +ww1(1)*vv2
                              coarse_coeffs(i-1, j, k) = coarse_coeffs(i-1, j, k) &
                                                         +ww1(2)*vv2+ww0(1)*vv3+ww1(1)*vv4
                              coarse_coeffs(i, j, k) = coarse_coeffs(i, j, k) &
                                                       +ww1(3)*vv2+ww0(2)*vv3+ww1(2)*vv4
                              coarse_coeffs(i+1, j, k) = coarse_coeffs(i+1, j, k) &
                                                         +ww1(4)*vv2+ww0(3)*vv3+ww1(3)*vv4
                           ELSEIF (pbc .AND. .NOT. is_split) THEN
                              fi = fi+1
                              vv4 = fine_values(fi, fj, fk)
                              vv5 = fine_values(fine_bo(1, 1), fj, fk)
                              vv6 = fine_values(fine_bo(1, 1)+1, fj, fk)
                              coarse_coeffs(i-2, j, k) = coarse_coeffs(i-2, j, k) &
                                                         +ww1(1)*vv2
                              coarse_coeffs(i-1, j, k) = coarse_coeffs(i-1, j, k) &
                                                         +ww1(2)*vv2+ww0(1)*vv3+ww1(1)*vv4
                              coarse_coeffs(i, j, k) = coarse_coeffs(i, j, k) &
                                                       +ww1(3)*vv2+ww0(2)*vv3+ww1(2)*vv4+vv5*ww0(1)+ww1(1)*vv6
                           ELSE
                              coarse_coeffs(i-2, j, k) = coarse_coeffs(i-2, j, k) &
                                                         +wj*w_border1(3)*vv2
                              coarse_coeffs(i-1, j, k) = coarse_coeffs(i-1, j, k) &
                                                         +wj*w_border1(2)*vv2
                              coarse_coeffs(i, j, k) = coarse_coeffs(i, j, k) &
                                                       +wj*(w_border1(1)*vv2+w_border0*vv3)
                           END IF
                        END IF
                     ELSE
                        fi = fi+1
                        vv0 = fine_values(fi, fj, fk)
                        fi = fi+1
                        vv1 = fine_values(fi, fj, fk)
                        IF (has_i_ubound) THEN
                           IF (coarse_bo(2, 1)-2 == FLOOR((fine_bo(2, 1)-f_shift(1))/2._dp)) THEN
                              fi = fi+1
                              vv2 = fine_values(fi, fj, fk)
                              coarse_coeffs(i+1, j, k) = coarse_coeffs(i+1, j, k) &
                                                         +ww1(4)*vv2
                           ELSE
                              vv2 = 0._dp
                           END IF
                           coarse_coeffs(i-3, j, k) = coarse_coeffs(i-3, j, k) &
                                                      +ww1(1)*vv0
                           coarse_coeffs(i-2, j, k) = coarse_coeffs(i-2, j, k) &
                                                      +ww1(2)*vv0+ww0(1)*vv1+ww1(1)*vv2
                           coarse_coeffs(i-1, j, k) = coarse_coeffs(i-1, j, k) &
                                                      +ww1(3)*vv0+ww0(2)*vv1+ww1(2)*vv2
                           coarse_coeffs(i, j, k) = coarse_coeffs(i, j, k) &
                                                    +ww1(4)*vv0+ww0(3)*vv1+ww1(3)*vv2
                        ELSEIF (pbc .AND. .NOT. is_split) THEN
                           fi = fi+1
                           vv2 = fine_values(fi, fj, fk)
                           vv3 = fine_values(fine_bo(1, 1), fk, fk)
                           vv4 = fine_values(fine_bo(1, 1)+1, fk, fk)
                           coarse_coeffs(i-3, j, k) = coarse_coeffs(i-3, j, k) &
                                                      +ww1(1)*vv0
                           coarse_coeffs(i-2, j, k) = coarse_coeffs(i-2, j, k) &
                                                      +ww1(2)*vv0+ww0(1)*vv1+ww1(1)*vv2
                           coarse_coeffs(i-1, j, k) = coarse_coeffs(i-1, j, k) &
                                                      +ww1(3)*vv0+ww0(2)*vv1+ww1(2)*vv2+ww0(1)*vv3+ww1(1)*vv4
                        ELSE
                           coarse_coeffs(i-3, j, k) = coarse_coeffs(i-3, j, k) &
                                                      +wj*w_border1(3)*vv0
                           coarse_coeffs(i-2, j, k) = coarse_coeffs(i-2, j, k) &
                                                      +wj*w_border1(2)*vv0
                           coarse_coeffs(i-1, j, k) = coarse_coeffs(i-1, j, k) &
                                                      +wj*(w_border1(1)*vv0+w_border0*vv1)
                        END IF
                     END IF
                     CPASSERT(fi == fine_bo(2, 1))
                  END IF
               END DO
            END DO
         END DO
      END DO

      ! *** parallel case
      IF (is_split) THEN
         CALL timeset(routineN//"_comm", handle2)
         coarse_slice_size = (coarse_bo(2, 2)-coarse_bo(1, 2)+1)* &
                             (coarse_bo(2, 3)-coarse_bo(1, 3)+1)
         n_procs = coarse_coeffs_pw%pw_grid%para%group_size
         ALLOCATE (send_size(0:n_procs-1), send_offset(0:n_procs-1), &
                   sent_size(0:n_procs-1), rcv_size(0:n_procs-1), &
                   rcv_offset(0:n_procs-1), pp_lb(0:n_procs-1), &
                   pp_ub(0:n_procs-1), real_rcv_size(0:n_procs-1))

         ! ** send size count

         pos_of_x => coarse_coeffs_pw%pw_grid%para%pos_of_x
         send_size = 0
         DO x = coarse_bo(1, 1), coarse_bo(2, 1)
            p = pos_of_x(coarse_gbo(1, 1)+MODULO(x-coarse_gbo(1, 1), s(1)))
            send_size(p) = send_size(p)+coarse_slice_size
         END DO

         ! ** rcv size count

         pos_of_x => fine_values_pw%pw_grid%para%pos_of_x
         p_old = pos_of_x(fine_gbo(1, 1))
         pp_lb = fine_gbo(2, 1)
         pp_ub = fine_gbo(2, 1)-1
         pp_lb(p_old) = fine_gbo(1, 1)
         DO x = fine_gbo(1, 1), fine_gbo(2, 1)
            p = pos_of_x(x)
            IF (p /= p_old) THEN
               pp_ub(p_old) = x-1
               pp_lb(p) = x
               p_old = p
            END IF
         END DO
         pp_ub(p_old) = fine_gbo(2, 1)

         DO ip = 0, n_procs-1
            IF (pp_lb(ip) <= pp_ub(ip)) THEN
               pp_lb(ip) = FLOOR(REAL(pp_lb(ip)-f_shift(1), dp)/2._dp)-1
               pp_ub(ip) = FLOOR(REAL(pp_ub(ip)+1-f_shift(1), dp)/2._dp)+1
            ELSE
               pp_lb(ip) = coarse_gbo(2, 1)
               pp_ub(ip) = coarse_gbo(2, 1)-1
            END IF
            IF (.NOT. is_split .OR. .NOT. pbc) THEN
               pp_lb(ip) = MAX(pp_lb(ip), coarse_gbo(1, 1))
               pp_ub(ip) = MIN(pp_ub(ip), coarse_gbo(2, 1))
            END IF
         END DO

         rcv_size = 0
         DO ip = 0, n_procs-1
            DO x = pp_lb(ip), coarse_gbo(1, 1)-1
               x_att = coarse_gbo(1, 1)+MODULO(x-coarse_gbo(1, 1), s(1))
               IF (x_att >= my_coarse_bo(1, 1) .AND. x_att <= my_coarse_bo(2, 1)) THEN
                  rcv_size(ip) = rcv_size(ip)+coarse_slice_size
               END IF
            END DO
            rcv_size(ip) = rcv_size(ip)+coarse_slice_size* &
                           MAX(0, &
                               MIN(pp_ub(ip), my_coarse_bo(2, 1))-MAX(pp_lb(ip), my_coarse_bo(1, 1))+1)
            DO x = coarse_gbo(2, 1)+1, pp_ub(ip)
               x_att = coarse_gbo(1, 1)+MODULO(x-coarse_gbo(1, 1), s(1))
               IF (x_att >= my_coarse_bo(1, 1) .AND. x_att <= my_coarse_bo(2, 1)) THEN
                  rcv_size(ip) = rcv_size(ip)+coarse_slice_size
               END IF
            END DO
         END DO

         ! ** offsets & alloc send-rcv

         send_tot_size = 0
         DO ip = 0, n_procs-1
            send_offset(ip) = send_tot_size
            send_tot_size = send_tot_size+send_size(ip)
         END DO
         IF (send_tot_size /= (coarse_bo(2, 1)-coarse_bo(1, 1)+1)*coarse_slice_size) &
            CPABORT("Error calculating send_tot_size")
         ALLOCATE (send_buf(0:send_tot_size-1))

         rcv_tot_size = 0
         DO ip = 0, n_procs-1
            rcv_offset(ip) = rcv_tot_size
            rcv_tot_size = rcv_tot_size+rcv_size(ip)
         END DO
         ALLOCATE (rcv_buf(0:rcv_tot_size-1))

         ! ** fill send buffer

         pos_of_x => coarse_coeffs_pw%pw_grid%para%pos_of_x
         p_old = pos_of_x(coarse_gbo(1, 1) &
                          +MODULO(coarse_bo(1, 1)-coarse_gbo(1, 1), s(1)))
         sent_size(:) = send_offset
         ss = coarse_bo(2, 1)-coarse_bo(1, 1)+1
         DO x = coarse_bo(1, 1), coarse_bo(2, 1)
            p = pos_of_x(coarse_gbo(1, 1)+MODULO(x-coarse_gbo(1, 1), s(1)))
            CALL dcopy(coarse_slice_size, &
                       coarse_coeffs(x, coarse_bo(1, 2), &
                                     coarse_bo(1, 3)), ss, send_buf(sent_size(p)), 1)
            sent_size(p) = sent_size(p)+coarse_slice_size
         END DO

         IF (ANY(sent_size(0:n_procs-2) /= send_offset(1:n_procs-1))) &
            CPABORT("error 1 filling send buffer")
         IF (sent_size(n_procs-1) /= send_tot_size) &
            CPABORT("error 2 filling send buffer")

         IF (local_data) THEN
            DEALLOCATE (coarse_coeffs)
         ELSE
            NULLIFY (coarse_coeffs)
         END IF

         CPASSERT(ALL(sent_size(:n_procs-2) == send_offset(1:)))
         CPASSERT(sent_size(n_procs-1) == send_tot_size)
         ! test send/rcv sizes
         CALL mp_alltoall(send_size, real_rcv_size, 1, coarse_coeffs_pw%pw_grid%para%group)

         CPASSERT(ALL(real_rcv_size == rcv_size))
         ! all2all
         CALL mp_alltoall(sb=send_buf, scount=send_size, sdispl=send_offset, &
                          rb=rcv_buf, rcount=rcv_size, rdispl=rcv_offset, &
                          group=coarse_coeffs_pw%pw_grid%para%group)

         ! ** sum & reorder rcv buffer

         sent_size(:) = rcv_offset
         DO ip = 0, n_procs-1

            DO x = pp_lb(ip), coarse_gbo(1, 1)-1
               x_att = coarse_gbo(1, 1)+MODULO(x-coarse_gbo(1, 1), s(1))
               IF (x_att >= my_coarse_bo(1, 1) .AND. x_att <= my_coarse_bo(2, 1)) THEN
                  ii = sent_size(ip)
                  DO k = coarse_bo(1, 3), coarse_bo(2, 3)
                     DO j = coarse_bo(1, 2), coarse_bo(2, 2)
                        coarse_coeffs_pw%cr3d(x_att, j, k) = coarse_coeffs_pw%cr3d(x_att, j, k)+rcv_buf(ii)
                        ii = ii+1
                     END DO
                  END DO
                  sent_size(ip) = ii
               END IF
            END DO

            ii = sent_size(ip)
            DO x_att = MAX(pp_lb(ip), my_coarse_bo(1, 1)), MIN(pp_ub(ip), my_coarse_bo(2, 1))
               DO k = coarse_bo(1, 3), coarse_bo(2, 3)
                  DO j = coarse_bo(1, 2), coarse_bo(2, 2)
                     coarse_coeffs_pw%cr3d(x_att, j, k) = coarse_coeffs_pw%cr3d(x_att, j, k)+rcv_buf(ii)
                     ii = ii+1
                  END DO
               END DO
            END DO
            sent_size(ip) = ii

            DO x = coarse_gbo(2, 1)+1, pp_ub(ip)
               x_att = coarse_gbo(1, 1)+MODULO(x-coarse_gbo(1, 1), s(1))
               IF (x_att >= my_coarse_bo(1, 1) .AND. x_att <= my_coarse_bo(2, 1)) THEN
                  ii = sent_size(ip)
                  DO k = coarse_bo(1, 3), coarse_bo(2, 3)
                     DO j = coarse_bo(1, 2), coarse_bo(2, 2)
                        coarse_coeffs_pw%cr3d(x_att, j, k) = coarse_coeffs_pw%cr3d(x_att, j, k)+rcv_buf(ii)
                        ii = ii+1
                     END DO
                  END DO
                  sent_size(ip) = ii
               END IF
            END DO

         END DO

         IF (ANY(sent_size(0:n_procs-2) /= rcv_offset(1:n_procs-1))) &
            CPABORT("error 1 handling the rcv buffer")
         IF (sent_size(n_procs-1) /= rcv_tot_size) &
            CPABORT("error 2 handling the rcv buffer")

         ! dealloc
         DEALLOCATE (send_size, send_offset, rcv_size, rcv_offset)
         DEALLOCATE (send_buf, rcv_buf, real_rcv_size)
         DEALLOCATE (pp_ub, pp_lb)
         CALL timestop(handle2)
      ELSE
         CPASSERT(.NOT. local_data)
      END IF

      CALL timestop(handle)
   END SUBROUTINE add_fine2coarse

! **************************************************************************************************
!> \brief ...
!> \param preconditioner the preconditioner to create
!> \param precond_kind the kind of preconditioner to use
!> \param pool a pool with grids of the same type as the elements to
!>        precondition
!> \param pbc if periodic boundary conditions should be applied
!> \param transpose ...
!> \author fawzi
! **************************************************************************************************
   SUBROUTINE pw_spline_precond_create(preconditioner, precond_kind, &
                                       pool, pbc, transpose)
      TYPE(pw_spline_precond_type), POINTER              :: preconditioner
      INTEGER, INTENT(in)                                :: precond_kind
      TYPE(pw_pool_type), POINTER                        :: pool
      LOGICAL, INTENT(in)                                :: pbc, transpose

      CHARACTER(len=*), PARAMETER :: routineN = 'pw_spline_precond_create', &
         routineP = moduleN//':'//routineN

      ALLOCATE (preconditioner)
      last_precond_id = last_precond_id+1
      preconditioner%id_nr = last_precond_id
      preconditioner%ref_count = 1
      preconditioner%kind = no_precond
      preconditioner%pool => pool
      preconditioner%pbc = pbc
      preconditioner%transpose = transpose
      CALL pw_pool_retain(pool)
      CALL pw_spline_precond_set_kind(preconditioner, precond_kind)
   END SUBROUTINE pw_spline_precond_create

! **************************************************************************************************
!> \brief switches the types of precoditioner to use
!> \param preconditioner the preconditioner to be changed
!> \param precond_kind the new kind of preconditioner to use
!> \param pbc ...
!> \param transpose ...
!> \author fawzi
! **************************************************************************************************
   SUBROUTINE pw_spline_precond_set_kind(preconditioner, precond_kind, pbc, &
                                         transpose)
      TYPE(pw_spline_precond_type), POINTER              :: preconditioner
      INTEGER, INTENT(in)                                :: precond_kind
      LOGICAL, INTENT(in), OPTIONAL                      :: pbc, transpose

      CHARACTER(len=*), PARAMETER :: routineN = 'pw_spline_precond_set_kind', &
         routineP = moduleN//':'//routineN

      LOGICAL                                            :: do_3d_coeff
      REAL(kind=dp)                                      :: s

      CPASSERT(ASSOCIATED(preconditioner))
      CPASSERT(preconditioner%ref_count > 0)
      IF (PRESENT(transpose)) preconditioner%transpose = transpose
      do_3d_coeff = .FALSE.
      preconditioner%kind = precond_kind
      IF (PRESENT(pbc)) preconditioner%pbc = pbc
      SELECT CASE (precond_kind)
      CASE (no_precond)
      CASE (precond_spl3_aint2)
         preconditioner%coeffs_1d = (/-1.66_dp*0.25_dp, 1.66_dp, -1.66_dp*0.25_dp/)
         preconditioner%sharpen = .FALSE.
         preconditioner%normalize = .FALSE.
         do_3d_coeff = .TRUE.
      CASE (precond_spl3_3)
         preconditioner%coeffs_1d(1) = -0.25_dp*1.6_dp
         preconditioner%coeffs_1d(2) = 1.6_dp
         preconditioner%coeffs_1d(3) = -0.25_dp*1.6_dp
         preconditioner%sharpen = .FALSE.
         preconditioner%normalize = .FALSE.
         do_3d_coeff = .TRUE.
      CASE (precond_spl3_2)
         preconditioner%coeffs_1d(1) = -0.26_dp*1.76_dp
         preconditioner%coeffs_1d(2) = 1.76_dp
         preconditioner%coeffs_1d(3) = -0.26_dp*1.76_dp
         preconditioner%sharpen = .FALSE.
         preconditioner%normalize = .FALSE.
         do_3d_coeff = .TRUE.
      CASE (precond_spl3_aint)
         preconditioner%coeffs_1d = spl3_1d_coeffs0
         preconditioner%sharpen = .TRUE.
         preconditioner%normalize = .TRUE.
         do_3d_coeff = .TRUE.
      CASE (precond_spl3_1)
         preconditioner%coeffs_1d(1) = 0.5_dp/3._dp**(1._dp/3._dp)
         preconditioner%coeffs_1d(2) = 4._dp/3._dp**(1._dp/3._dp)
         preconditioner%coeffs_1d(3) = 0.5_dp/3._dp**(1._dp/3._dp)
         preconditioner%sharpen = .TRUE.
         preconditioner%normalize = .FALSE.
         do_3d_coeff = .TRUE.
      CASE default
         CPABORT("")
      END SELECT
      IF (do_3d_coeff) THEN
         s = 1._dp
         IF (preconditioner%sharpen) s = -1._dp
         preconditioner%coeffs(1) = &
            s*preconditioner%coeffs_1d(2)* &
            preconditioner%coeffs_1d(2)* &
            preconditioner%coeffs_1d(2)
         preconditioner%coeffs(2) = &
            s*preconditioner%coeffs_1d(1)* &
            preconditioner%coeffs_1d(2)* &
            preconditioner%coeffs_1d(2)
         preconditioner%coeffs(3) = &
            s*preconditioner%coeffs_1d(1)* &
            preconditioner%coeffs_1d(1)* &
            preconditioner%coeffs_1d(2)
         preconditioner%coeffs(4) = &
            s*preconditioner%coeffs_1d(1)* &
            preconditioner%coeffs_1d(1)* &
            preconditioner%coeffs_1d(1)
         IF (preconditioner%sharpen) THEN
            IF (preconditioner%normalize) THEN
               preconditioner%coeffs(1) = 2._dp+ &
                                          preconditioner%coeffs(1)
            ELSE
               preconditioner%coeffs(1) = -preconditioner%coeffs(1)
            END IF
         END IF
      END IF
   END SUBROUTINE pw_spline_precond_set_kind

! **************************************************************************************************
!> \brief retains the preconditioner
!> \param preconditioner the preconditioner to retain
!> \author fawzi
! **************************************************************************************************
   SUBROUTINE pw_spline_precond_retain(preconditioner)
      TYPE(pw_spline_precond_type), POINTER              :: preconditioner

      CHARACTER(len=*), PARAMETER :: routineN = 'pw_spline_precond_retain', &
         routineP = moduleN//':'//routineN

      CPASSERT(ASSOCIATED(preconditioner))
      CPASSERT(preconditioner%ref_count > 1)
      preconditioner%ref_count = preconditioner%ref_count+1
   END SUBROUTINE pw_spline_precond_retain

! **************************************************************************************************
!> \brief releases the preconditioner
!> \param preconditioner the preconditioner to release
!> \author fawzi
! **************************************************************************************************
   SUBROUTINE pw_spline_precond_release(preconditioner)
      TYPE(pw_spline_precond_type), POINTER              :: preconditioner

      CHARACTER(len=*), PARAMETER :: routineN = 'pw_spline_precond_release', &
         routineP = moduleN//':'//routineN

      IF (ASSOCIATED(preconditioner)) THEN
         CPASSERT(preconditioner%ref_count > 0)
         preconditioner%ref_count = preconditioner%ref_count-1
         IF (preconditioner%ref_count == 0) THEN
            CALL pw_pool_release(preconditioner%pool)
            DEALLOCATE (preconditioner)
         END IF
      END IF
   END SUBROUTINE pw_spline_precond_release

! **************************************************************************************************
!> \brief applies the preconditioner to the system of equations to find the
!>      coefficents of the spline
!> \param preconditioner the preconditioner to apply
!> \param in_v the grid on which the preconditioner should be applied
!> \param out_v place to store the preconditioner applied on v_out
!> \author fawzi
! **************************************************************************************************
   SUBROUTINE pw_spline_do_precond(preconditioner, in_v, out_v)
      TYPE(pw_spline_precond_type), POINTER              :: preconditioner
      TYPE(pw_type), POINTER                             :: in_v, out_v

      CHARACTER(len=*), PARAMETER :: routineN = 'pw_spline_do_precond', &
         routineP = moduleN//':'//routineN

      CPASSERT(ASSOCIATED(preconditioner))
      CPASSERT(preconditioner%ref_count > 0)
      SELECT CASE (preconditioner%kind)
      CASE (no_precond)
         CALL pw_copy(in_v, out_v)
      CASE (precond_spl3_aint, precond_spl3_1)
         CALL pw_zero(out_v)
         IF (preconditioner%pbc) THEN
            CALL pw_nn_smear_r(pw_in=in_v, pw_out=out_v, &
                               coeffs=preconditioner%coeffs)
         ELSE
            CALL pw_nn_compose_r_no_pbc(weights_1d=preconditioner%coeffs_1d, &
                                        pw_in=in_v, pw_out=out_v, sharpen=preconditioner%sharpen, &
                                        normalize=preconditioner%normalize, &
                                        transpose=preconditioner%transpose)
         END IF
      CASE (precond_spl3_3, precond_spl3_2, precond_spl3_aint2)
         CALL pw_zero(out_v)
         IF (preconditioner%pbc) THEN
            CALL pw_nn_smear_r(pw_in=in_v, pw_out=out_v, &
                               coeffs=preconditioner%coeffs)
         ELSE
            CALL pw_nn_compose_r_no_pbc(weights_1d=preconditioner%coeffs_1d, &
                                        pw_in=in_v, pw_out=out_v, sharpen=preconditioner%sharpen, &
                                        normalize=preconditioner%normalize, smooth_boundary=.TRUE., &
                                        transpose=preconditioner%transpose)
         END IF
      CASE default
         CPABORT("")
      END SELECT
   END SUBROUTINE pw_spline_do_precond

! **************************************************************************************************
!> \brief solves iteratively (CG) a systmes of linear equations
!>           linOp(coeffs)=values
!>      (for example those needed to find the coefficents of a spline)
!>      Returns true if the it succeded to acheive the requested accuracy
!> \param values the right hand side of the system
!> \param coeffs will contain the solution of the system (and on entry
!>        it contains the starting point)
!> \param linOp the linear operator to be inverted
!> \param preconditioner the preconditioner to apply
!> \param pool a pool of grids (for the temporary objects)
!> \param eps_r the requested precision on the residual
!> \param eps_x the requested precision on the solution
!> \param max_iter maximum number of iteration allowed
!> \return ...
!> \author fawzi
! **************************************************************************************************
   FUNCTION find_coeffs(values, coeffs, linOp, preconditioner, pool, &
                        eps_r, eps_x, max_iter) RESULT(res)
      TYPE(pw_type), POINTER                             :: values, coeffs
      INTERFACE
! **************************************************************************************************
         SUBROUTINE linOp(pw_in, pw_out)
            USE pw_types, ONLY: pw_type
            TYPE(pw_type), POINTER :: pw_in, pw_out
         END SUBROUTINE linOp
      END INTERFACE
      TYPE(pw_spline_precond_type), POINTER              :: preconditioner
      TYPE(pw_pool_type), POINTER                        :: pool
      REAL(kind=dp), INTENT(in)                          :: eps_r, eps_x
      INTEGER, INTENT(in)                                :: max_iter
      LOGICAL                                            :: res

      CHARACTER(len=*), PARAMETER :: routineN = 'find_coeffs', routineP = moduleN//':'//routineN

      INTEGER                                            :: i, iiter, iter, j, k
      INTEGER, DIMENSION(2, 3)                           :: bo
      LOGICAL                                            :: last
      REAL(kind=dp)                                      :: alpha, beta, eps_r_att, eps_x_att, r_z, &
                                                            r_z_new
      TYPE(cp_logger_type), POINTER                      :: logger
      TYPE(pw_type), POINTER                             :: Ap, p, r, z

      last = .FALSE.

      res = .FALSE.
      logger => cp_get_default_logger()
      CALL pw_pool_create_pw(pool, r, use_data=REALDATA3D, in_space=REALSPACE)
      CALL pw_pool_create_pw(pool, z, use_data=REALDATA3D, in_space=REALSPACE)
      CALL pw_pool_create_pw(pool, p, use_data=REALDATA3D, in_space=REALSPACE)
      CALL pw_pool_create_pw(pool, Ap, use_data=REALDATA3D, in_space=REALSPACE)

      !CALL cp_add_iter_level(logger%iter_info,level_name="SPLINE_FIND_COEFFS")
      ext_do: DO iiter = 1, max_iter, 10
         CALL pw_zero(r)
         CALL linOp(pw_in=coeffs, pw_out=r)
         r%cr3d = -r%cr3d
         CALL pw_axpy(values, r)
         CALL pw_spline_do_precond(preconditioner, in_v=r, out_v=z)
         CALL pw_copy(z, p)
         r_z = pw_integral_ab(r, z)

         DO iter = iiter, MIN(iiter+9, max_iter)
            eps_r_att = SQRT(pw_integral_ab(r, r))
            IF (eps_r_att == 0._dp) THEN
               eps_x_att = 0._dp
               last = .TRUE.
            ELSE
               CALL pw_zero(Ap)
               CALL linOp(pw_in=p, pw_out=Ap)
               alpha = r_z/pw_integral_ab(Ap, p)

               CALL pw_axpy(p, coeffs, alpha=alpha)

               eps_x_att = alpha*SQRT(pw_integral_ab(p, p)) ! try to spare if unneded?
               IF (eps_r_att < eps_r .AND. eps_x_att < eps_x) last = .TRUE.
            END IF
            !CALL cp_iterate(logger%iter_info,last=last)
            IF (last) THEN
               res = .TRUE.
               EXIT ext_do
            END IF

            CALL pw_axpy(Ap, r, alpha=-alpha)

            CALL pw_spline_do_precond(preconditioner, in_v=r, out_v=z)

            r_z_new = pw_integral_ab(r, z)
            beta = r_z_new/r_z
            r_z = r_z_new

            bo = p%pw_grid%bounds_local
            DO k = bo(1, 3), bo(2, 3)
               DO j = bo(1, 2), bo(2, 2)
                  DO i = bo(1, 1), bo(2, 1)
                     p%cr3d(i, j, k) = z%cr3d(i, j, k)+beta*p%cr3d(i, j, k)
                  END DO
               END DO
            END DO

         END DO
      END DO ext_do
      !CALL cp_rm_iter_level(logger%iter_info,level_name="SPLINE_FIND_COEFFS")

      CALL pw_pool_give_back_pw(pool, r)
      CALL pw_pool_give_back_pw(pool, z)
      CALL pw_pool_give_back_pw(pool, p)
      CALL pw_pool_give_back_pw(pool, Ap)
   END FUNCTION find_coeffs

! **************************************************************************************************
!> \brief adds to pw_out pw_in composed with the weights
!>      pw_out%cr3d(i,j,k)=pw_out%cr3d(i,j,k)+sum(pw_in%cr3d(i+l,j+m,k+n)*
!>         weights_1d(abs(l)+1)*weights_1d(abs(m)+1)*weights_1d(abs(n)+1),
!>         l=-1..1,m=-1..1,n=-1..1)
!> \param weights_1d ...
!> \param pw_in ...
!> \param pw_out ...
!> \param sharpen ...
!> \param normalize ...
!> \param transpose ...
!> \param smooth_boundary ...
!> \author fawzi
! **************************************************************************************************
   SUBROUTINE pw_nn_compose_r_no_pbc(weights_1d, pw_in, pw_out, &
                                     sharpen, normalize, transpose, smooth_boundary)
      REAL(kind=dp), DIMENSION(-1:1)                     :: weights_1d
      TYPE(pw_type), POINTER                             :: pw_in, pw_out
      LOGICAL, INTENT(in), OPTIONAL                      :: sharpen, normalize, transpose, &
                                                            smooth_boundary

      CHARACTER(len=*), PARAMETER :: routineN = 'pw_nn_compose_r_no_pbc', &
         routineP = moduleN//':'//routineN

      INTEGER                                            :: first_index, i, j, jw, k, kw, &
                                                            last_index, myj, myk, n_els
      INTEGER, DIMENSION(2, 3)                           :: bo, gbo
      INTEGER, DIMENSION(3)                              :: s
      LOGICAL                                            :: has_l_boundary, has_u_boundary, &
                                                            is_split, my_normalize, my_sharpen, &
                                                            my_smooth_boundary, my_transpose
      REAL(kind=dp)                                      :: in_val_f, in_val_l, in_val_tmp, w_j, w_k
      REAL(kind=dp), DIMENSION(-1:1)                     :: w
      REAL(kind=dp), DIMENSION(:, :), POINTER            :: l_boundary, tmp, u_boundary
      REAL(kind=dp), DIMENSION(:, :, :), POINTER         :: in_val, out_val

      bo = pw_in%pw_grid%bounds_local
      gbo = pw_in%pw_grid%bounds
      in_val => pw_in%cr3d
      out_val => pw_out%cr3d
      my_sharpen = .FALSE.
      IF (PRESENT(sharpen)) my_sharpen = sharpen
      my_normalize = .FALSE.
      IF (PRESENT(normalize)) my_normalize = normalize
      my_transpose = .FALSE.
      IF (PRESENT(transpose)) my_transpose = transpose
      my_smooth_boundary = .FALSE.
      IF (PRESENT(smooth_boundary)) my_smooth_boundary = smooth_boundary
      CPASSERT(.NOT. my_normalize .OR. my_sharpen)
      CPASSERT(.NOT. my_smooth_boundary .OR. .NOT. my_sharpen)
      DO i = 1, 3
         s(i) = bo(2, i)-bo(1, i)+1
      END DO
      IF (ANY(s < 1)) RETURN
      is_split = ANY(pw_in%pw_grid%bounds_local(:, 1) /= &
                     pw_in%pw_grid%bounds(:, 1))
      has_l_boundary = (gbo(1, 1) == bo(1, 1))
      has_u_boundary = (gbo(2, 1) == bo(2, 1))
      IF (is_split) THEN
         ALLOCATE (l_boundary(bo(1, 2):bo(2, 2), bo(1, 3):bo(2, 3)), &
                   u_boundary(bo(1, 2):bo(2, 2), bo(1, 3):bo(2, 3)), &
                   tmp(bo(1, 2):bo(2, 2), bo(1, 3):bo(2, 3)))
         tmp(:, :) = pw_in%cr3d(bo(2, 1), :, :)
         CALL mp_sendrecv(tmp, pw_in%pw_grid%para%pos_of_x( &
                          gbo(1, 1)+MODULO(bo(2, 1)+1-gbo(1, 1), gbo(2, 1)-gbo(1, 1)+1)), &
                          l_boundary, pw_in%pw_grid%para%pos_of_x( &
                          gbo(1, 1)+MODULO(bo(1, 1)-1-gbo(1, 1), gbo(2, 1)-gbo(1, 1)+1)), &
                          pw_in%pw_grid%para%group)
         tmp(:, :) = pw_in%cr3d(bo(1, 1), :, :)
         CALL mp_sendrecv(tmp, pw_in%pw_grid%para%pos_of_x( &
                          gbo(1, 1)+MODULO(bo(1, 1)-1-gbo(1, 1), gbo(2, 1)-gbo(1, 1)+1)), &
                          u_boundary, pw_in%pw_grid%para%pos_of_x( &
                          gbo(1, 1)+MODULO(bo(2, 1)+1-gbo(1, 1), gbo(2, 1)-gbo(1, 1)+1)), &
                          pw_in%pw_grid%para%group)
         DEALLOCATE (tmp)
      END IF

      n_els = s(1)
      IF (has_l_boundary) THEN
         n_els = n_els-1
         first_index = bo(1, 1)+1
      ELSE
         first_index = bo(1, 1)
      END IF
      IF (has_u_boundary) THEN
         n_els = n_els-1
         last_index = bo(2, 1)-1
      ELSE
         last_index = bo(2, 1)
      END IF
!$OMP PARALLEL DO DEFAULT(NONE) &
!$OMP PRIVATE(k, kw, myk, j, jw, myj, in_val_f, in_val_l, w_k, w_j, in_val_tmp, w) &
!$OMP SHARED(bo, in_val, out_val, s, l_boundary, u_boundary, weights_1d, is_split, &
!$OMP        my_transpose, gbo, my_smooth_boundary, has_l_boundary, has_u_boundary, &
!$OMP        my_sharpen, last_index, first_index, my_normalize, n_els)
      DO k = bo(1, 3), bo(2, 3)
         DO kw = -1, 1
            myk = k+kw
            IF (my_transpose) THEN
               IF (k >= gbo(2, 3)-1 .OR. k <= gbo(1, 3)+1) THEN
                  IF (k == gbo(2, 3) .OR. k == gbo(1, 3)) THEN
                     IF (myk < gbo(2, 3) .AND. myk > gbo(1, 3)) THEN
                        w_k = weights_1d(kw)
                        IF (my_smooth_boundary) THEN
                           w_k = weights_1d(kw)/weights_1d(0)
                        END IF
                     ELSE IF (kw == 0) THEN
                        w_k = 1._dp
                     ELSE
                        CYCLE
                     END IF
                  ELSE
                     IF (myk == gbo(2, 3) .OR. myk == gbo(1, 3)) CYCLE
                     w_k = weights_1d(kw)
                  END IF
               ELSE
                  w_k = weights_1d(kw)
               END IF
            ELSE
               IF (k >= gbo(2, 3)-1 .OR. k <= gbo(1, 3)+1) THEN
                  IF (k == gbo(2, 3) .OR. k == gbo(1, 3)) THEN
                     IF (kw /= 0) CYCLE
                     w_k = 1._dp
                  ELSE
                     IF (my_smooth_boundary .AND. ((k == gbo(1, 3)+1 .AND. myk == gbo(1, 3)) .OR. &
                                                   (k == gbo(2, 3)-1 .AND. myk == gbo(2, 3)))) THEN
                        w_k = weights_1d(kw)/weights_1d(0)
                     ELSE
                        w_k = weights_1d(kw)
                     END IF
                  END IF
               ELSE
                  w_k = weights_1d(kw)
               END IF
            END IF
            DO j = bo(1, 2), bo(2, 2)
               DO jw = -1, 1
                  myj = j+jw
                  IF (j < gbo(2, 2)-1 .AND. j > gbo(1, 2)+1) THEN
                     w_j = w_k*weights_1d(jw)
                  ELSE
                     IF (my_transpose) THEN
                        IF (j == gbo(2, 2) .OR. j == gbo(1, 2)) THEN
                           IF (myj < gbo(2, 2) .AND. myj > gbo(1, 2)) THEN
                              w_j = weights_1d(jw)*w_k
                              IF (my_smooth_boundary) THEN
                                 w_j = weights_1d(jw)/weights_1d(0)*w_k
                              END IF
                           ELSE IF (jw == 0) THEN
                              w_j = w_k
                           ELSE
                              CYCLE
                           END IF
                        ELSE
                           IF (myj == gbo(2, 2) .OR. myj == gbo(1, 2)) CYCLE
                           w_j = w_k*weights_1d(jw)
                        END IF
                     ELSE
                        IF (j == gbo(2, 2) .OR. j == gbo(1, 2)) THEN
                           IF (jw /= 0) CYCLE
                           w_j = w_k
                        ELSE IF (my_smooth_boundary .AND. ((j == gbo(1, 2)+1 .AND. myj == gbo(1, 2)) .OR. &
                                                           (j == gbo(2, 2)-1 .AND. myj == gbo(2, 2)))) THEN
                           w_j = w_k*weights_1d(jw)/weights_1d(0)
                        ELSE
                           w_j = w_k*weights_1d(jw)
                        END IF
                     END IF
                  END IF

                  IF (has_l_boundary) THEN
                     IF (my_transpose) THEN
                        IF (s(1) == 1) THEN
                           CPASSERT(.NOT. has_u_boundary)
                           in_val_tmp = u_boundary(myj, myk)
                        ELSE
                           in_val_tmp = in_val(bo(1, 1)+1, myj, myk)
                        END IF
                        IF (my_sharpen) THEN
                           IF (kw == 0 .AND. jw == 0) THEN
                              IF (my_normalize) THEN
                                 out_val(bo(1, 1), j, k) = out_val(bo(1, 1), j, k)+ &
                                                           (2.0_dp-w_j)*in_val(bo(1, 1), myj, myk)- &
                                                           in_val_tmp*weights_1d(1)*w_j
                              ELSE
                                 out_val(bo(1, 1), j, k) = out_val(bo(1, 1), j, k)+ &
                                                           in_val(bo(1, 1), myj, myk)*w_j- &
                                                           in_val_tmp*weights_1d(1)*w_j
                              END IF
                           ELSE
                              out_val(bo(1, 1), j, k) = out_val(bo(1, 1), j, k)- &
                                                        in_val(bo(1, 1), myj, myk)*w_j- &
                                                        in_val_tmp*weights_1d(1)*w_j
                           END IF
                        ELSE IF (my_smooth_boundary) THEN
                           out_val(bo(1, 1), j, k) = out_val(bo(1, 1), j, k)+ &
                                                     w_j*(in_val(bo(1, 1), myj, myk)+ &
                                                          in_val_tmp*weights_1d(1)/weights_1d(0))
                        ELSE
                           out_val(bo(1, 1), j, k) = out_val(bo(1, 1), j, k)+ &
                                                     w_j*(in_val(bo(1, 1), myj, myk)+ &
                                                          in_val_tmp*weights_1d(1))
                        END IF
                        in_val_f = 0.0_dp
                     ELSE
                        in_val_f = in_val(bo(1, 1), myj, myk)
                        IF (my_sharpen) THEN
                           IF (kw == 0 .AND. jw == 0) THEN
                              IF (my_normalize) THEN
                                 out_val(bo(1, 1), j, k) = out_val(bo(1, 1), j, k)+ &
                                                           (2.0_dp-w_j)*in_val_f
                              ELSE
                                 out_val(bo(1, 1), j, k) = out_val(bo(1, 1), j, k)+ &
                                                           in_val_f*w_j
                              END IF
                           ELSE
                              out_val(bo(1, 1), j, k) = out_val(bo(1, 1), j, k)- &
                                                        in_val_f*w_j
                           END IF
                        ELSE
                           out_val(bo(1, 1), j, k) = out_val(bo(1, 1), j, k)+ &
                                                     in_val_f*w_j
                        END IF
                     END IF
                  ELSE
                     in_val_f = l_boundary(myj, myk)
                  END IF
                  IF (has_u_boundary) THEN
                     IF (my_transpose) THEN
                        in_val_l = in_val(bo(2, 1), myj, myk)
                        IF (s(1) == 1) THEN
                           CPASSERT(.NOT. has_l_boundary)
                           in_val_tmp = l_boundary(myj, myk)
                        ELSE
                           in_val_tmp = in_val(bo(2, 1)-1, myj, myk)
                        END IF
                        IF (my_sharpen) THEN
                           IF (kw == 0 .AND. jw == 0) THEN
                              IF (my_normalize) THEN
                                 out_val(bo(2, 1), j, k) = out_val(bo(2, 1), j, k)+ &
                                                           in_val_l*(2._dp-w_j)- &
                                                           in_val_tmp*weights_1d(1)*w_j
                              ELSE
                                 out_val(bo(2, 1), j, k) = out_val(bo(2, 1), j, k)+ &
                                                           in_val_l*w_j- &
                                                           in_val_tmp*weights_1d(1)*w_j
                              END IF
                           ELSE
                              out_val(bo(2, 1), j, k) = out_val(bo(2, 1), j, k)- &
                                                        w_j*in_val_l- &
                                                        in_val_tmp*weights_1d(1)*w_j
                           END IF
                        ELSE IF (my_smooth_boundary) THEN
                           out_val(bo(2, 1), j, k) = out_val(bo(2, 1), j, k)+ &
                                                     w_j*(in_val_l+in_val_tmp*weights_1d(1)/weights_1d(0))
                        ELSE
                           out_val(bo(2, 1), j, k) = out_val(bo(2, 1), j, k)+ &
                                                     w_j*(in_val_l+in_val_tmp*weights_1d(1))
                        END IF
                        in_val_l = 0._dp
                     ELSE
                        in_val_l = in_val(bo(2, 1), myj, myk)
                        IF (my_sharpen) THEN
                           IF (kw == 0 .AND. jw == 0) THEN
                              IF (my_normalize) THEN
                                 out_val(bo(2, 1), j, k) = out_val(bo(2, 1), j, k)+ &
                                                           in_val_l*(2._dp-w_j)
                              ELSE
                                 out_val(bo(2, 1), j, k) = out_val(bo(2, 1), j, k)+ &
                                                           in_val_l*w_j
                              END IF
                           ELSE
                              out_val(bo(2, 1), j, k) = out_val(bo(2, 1), j, k)- &
                                                        w_j*in_val_l
                           END IF
                        ELSE
                           out_val(bo(2, 1), j, k) = out_val(bo(2, 1), j, k)+ &
                                                     w_j*in_val_l
                        END IF
                     END IF
                  ELSE
                     in_val_l = u_boundary(myj, myk)
                  END IF
                  IF (last_index >= first_index) THEN
                     IF (my_transpose) THEN
                        IF (bo(1, 1)-1 == gbo(1, 1)) THEN
                           in_val_f = 0._dp
                        ELSE IF (bo(2, 1)+1 == gbo(2, 1)) THEN
                           in_val_l = 0._dp
                        END IF
                     END IF
                     IF (my_sharpen) THEN
                        w = -weights_1d*w_j
                        IF (kw == 0 .AND. jw == 0) THEN
                           IF (my_normalize) THEN
                              w(0) = w(0)+2._dp
                           ELSE
                              w(0) = -w(0)
                           END IF
                        END IF
                     ELSE
                        w = weights_1d*w_j
                     END IF
                     IF (my_smooth_boundary .AND. (.NOT. my_transpose)) THEN
                        IF (gbo(1, 1)+1 >= bo(1, 1) .AND. &
                            gbo(1, 1)+1 <= bo(2, 1) .AND. gbo(2, 1)-gbo(1, 1) > 2) THEN
                           IF (gbo(1, 1) >= bo(1, 1)) THEN
                              out_val(gbo(1, 1)+1, j, k) = out_val(gbo(1, 1)+1, j, k)+ &
                                                           in_val(gbo(1, 1), myj, myk)*w_j*weights_1d(-1)* &
                                                           (1._dp/weights_1d(0)-1._dp)
                           ELSE
                              out_val(gbo(1, 1)+1, j, k) = out_val(gbo(1, 1)+1, j, k)+ &
                                                           l_boundary(myj, myk)*w_j*weights_1d(-1)* &
                                                           (1._dp/weights_1d(0)-1._dp)
                           END IF
                        END IF
                     END IF
                     CALL pw_compose_stripe(weights=w, &
                                            in_val=in_val(first_index:last_index, myj, myk), &
                                            in_val_first=in_val_f, in_val_last=in_val_l, &
                                            out_val=out_val(first_index:last_index, j, k), &
                                            n_el=n_els)
!FM                   call pw_compose_stripe2(weights=w,&
!FM                        in_val=in_val,&
!FM                        in_val_first=in_val_f,in_val_last=in_val_l,&
!FM                        out_val=out_val,&
!FM                        first_val=first_index,last_val=last_index,&
!FM                        myj=myj,myk=myk,j=j,k=k)
                     IF (my_smooth_boundary .AND. (.NOT. my_transpose)) THEN
                        IF (gbo(2, 1)-1 >= bo(1, 1) .AND. &
                            gbo(2, 1)-1 <= bo(2, 1) .AND. gbo(2, 1)-gbo(1, 1) > 2) THEN
                           IF (gbo(2, 1) <= bo(2, 1)) THEN
                              out_val(gbo(2, 1)-1, j, k) = out_val(gbo(2, 1)-1, j, k)+ &
                                                           in_val(gbo(2, 1), myj, myk)*w_j*weights_1d(1)* &
                                                           (1._dp/weights_1d(0)-1._dp)
                           ELSE
                              out_val(gbo(2, 1)-1, j, k) = out_val(gbo(2, 1)-1, j, k)+ &
                                                           u_boundary(myj, myk)*w_j*weights_1d(1)* &
                                                           (1._dp/weights_1d(0)-1._dp)
                           END IF
                        END IF
                     END IF

                  END IF
               END DO
            END DO
         END DO
      END DO

      IF (is_split) THEN
         DEALLOCATE (l_boundary, u_boundary)
      END IF
   END SUBROUTINE pw_nn_compose_r_no_pbc

! **************************************************************************************************
!> \brief ...
!> \param pw_in ...
!> \param pw_out ...
! **************************************************************************************************
   SUBROUTINE spl3_nopbc(pw_in, pw_out)
      TYPE(pw_type), POINTER                             :: pw_in, pw_out

      CALL pw_zero(pw_out)
      CALL pw_nn_compose_r_no_pbc(weights_1d=spl3_1d_coeffs0, pw_in=pw_in, &
                                  pw_out=pw_out, sharpen=.FALSE., normalize=.FALSE.)
   END SUBROUTINE spl3_nopbc

! **************************************************************************************************
!> \brief ...
!> \param pw_in ...
!> \param pw_out ...
! **************************************************************************************************
   SUBROUTINE spl3_nopbct(pw_in, pw_out)
      TYPE(pw_type), POINTER                             :: pw_in, pw_out

      CALL pw_zero(pw_out)
      CALL pw_nn_compose_r_no_pbc(weights_1d=spl3_1d_coeffs0, pw_in=pw_in, &
                                  pw_out=pw_out, sharpen=.FALSE., normalize=.FALSE., transpose=.TRUE.)
   END SUBROUTINE spl3_nopbct

! **************************************************************************************************
!> \brief ...
!> \param pw_in ...
!> \param pw_out ...
! **************************************************************************************************
   SUBROUTINE spl3_pbc(pw_in, pw_out)
      TYPE(pw_type), POINTER                             :: pw_in, pw_out

      CALL pw_zero(pw_out)
      CALL pw_nn_smear_r(pw_in, pw_out, coeffs=spline3_coeffs)
   END SUBROUTINE spl3_pbc

! **************************************************************************************************
!> \brief Evaluates the PBC interpolated Spline (pw) function on the generic
!>      input vector (vec)
!> \param vec ...
!> \param pw ...
!> \return ...
!> \par History
!>      12.2007 Adapted for use with distributed grids [rdeclerck]
!> \author Teodoro Laino 12/2005 [tlaino]
!> \note
!>      Requires the Spline coefficients to be computed with PBC
! **************************************************************************************************
   FUNCTION Eval_Interp_Spl3_pbc(vec, pw) RESULT(val)
      REAL(KIND=dp), DIMENSION(3), INTENT(in)            :: vec
      TYPE(pw_type), POINTER                             :: pw
      REAL(KIND=dp)                                      :: val

      CHARACTER(len=*), PARAMETER :: routineN = 'Eval_Interp_Spl3_pbc', &
         routineP = moduleN//':'//routineN

      INTEGER                                            :: i, ivec(3), j, k, npts(3)
      INTEGER, DIMENSION(2, 3)                           :: bo, bo_l
      INTEGER, DIMENSION(4)                              :: ii, ij, ik
      LOGICAL                                            :: my_mpsum
      REAL(KIND=dp) :: a1, a2, a3, b1, b2, b3, c1, c2, c3, d1, d2, d3, dr1, dr2, dr3, e1, e2, e3, &
         f1, f2, f3, g1, g2, g3, h1, h2, h3, p1, p2, p3, q1, q2, q3, r1, r2, r3, s1, s2, s3, s4, &
         t1, t2, t3, t4, u1, u2, u3, v1, v2, v3, v4, xd1, xd2, xd3
      REAL(KIND=dp), DIMENSION(4, 4, 4)                  :: box
      REAL(KIND=dp), DIMENSION(:, :, :), POINTER         :: grid

      NULLIFY (grid)
      my_mpsum = (pw%pw_grid%para%mode /= PW_MODE_LOCAL)
      npts = pw%pw_grid%npts
      ivec = FLOOR(vec/pw%pw_grid%dr)
      dr1 = pw%pw_grid%dr(1)
      dr2 = pw%pw_grid%dr(2)
      dr3 = pw%pw_grid%dr(3)

      xd1 = (vec(1)/dr1)-REAL(ivec(1), kind=dp)
      xd2 = (vec(2)/dr2)-REAL(ivec(2), kind=dp)
      xd3 = (vec(3)/dr3)-REAL(ivec(3), kind=dp)
      grid => pw%cr3d(:, :, :)
      bo = pw%pw_grid%bounds
      bo_l = pw%pw_grid%bounds_local

      ik(1) = MODULO(ivec(3)-1, npts(3))+bo(1, 3)
      ik(2) = MODULO(ivec(3), npts(3))+bo(1, 3)
      ik(3) = MODULO(ivec(3)+1, npts(3))+bo(1, 3)
      ik(4) = MODULO(ivec(3)+2, npts(3))+bo(1, 3)

      ij(1) = MODULO(ivec(2)-1, npts(2))+bo(1, 2)
      ij(2) = MODULO(ivec(2), npts(2))+bo(1, 2)
      ij(3) = MODULO(ivec(2)+1, npts(2))+bo(1, 2)
      ij(4) = MODULO(ivec(2)+2, npts(2))+bo(1, 2)

      ii(1) = MODULO(ivec(1)-1, npts(1))+bo(1, 1)
      ii(2) = MODULO(ivec(1), npts(1))+bo(1, 1)
      ii(3) = MODULO(ivec(1)+1, npts(1))+bo(1, 1)
      ii(4) = MODULO(ivec(1)+2, npts(1))+bo(1, 1)

      DO k = 1, 4
         DO j = 1, 4
            DO i = 1, 4
               IF ( &
                  ii(i) >= bo_l(1, 1) .AND. &
                  ii(i) <= bo_l(2, 1) .AND. &
                  ij(j) >= bo_l(1, 2) .AND. &
                  ij(j) <= bo_l(2, 2) .AND. &
                  ik(k) >= bo_l(1, 3) .AND. &
                  ik(k) <= bo_l(2, 3) &
                  ) THEN
                  box(i, j, k) = grid(ii(i)+1-bo_l(1, 1), &
                                      ij(j)+1-bo_l(1, 2), &
                                      ik(k)+1-bo_l(1, 3))
               ELSE
                  box(i, j, k) = 0.0_dp
               END IF
            END DO
         END DO
      END DO

      a1 = 3.0_dp+xd1
      a2 = a1*a1
      a3 = a2*a1
      b1 = 2.0_dp+xd1
      b2 = b1*b1
      b3 = b2*b1
      c1 = 1.0_dp+xd1
      c2 = c1*c1
      c3 = c2*c1
      d1 = xd1
      d2 = d1*d1
      d3 = d2*d1
      e1 = 3.0_dp+xd2
      e2 = e1*e1
      e3 = e2*e1
      f1 = 2.0_dp+xd2
      f2 = f1*f1
      f3 = f2*f1
      g1 = 1.0_dp+xd2
      g2 = g1*g1
      g3 = g2*g1
      h1 = xd2
      h2 = h1*h1
      h3 = h2*h1
      p1 = 3.0_dp+xd3
      p2 = p1*p1
      p3 = p2*p1
      q1 = 2.0_dp+xd3
      q2 = q1*q1
      q3 = q2*q1
      r1 = 1.0_dp+xd3
      r2 = r1*r1
      r3 = r2*r1
      u1 = xd3
      u2 = u1*u1
      u3 = u2*u1

      t1 = 1.0_dp/6.0_dp*(64.0_dp-48.0_dp*a1+12.0_dp*a2-a3)
      t2 = -22.0_dp/3.0_dp+10.0_dp*b1-4.0_dp*b2+0.5_dp*b3
      t3 = 2.0_dp/3.0_dp-2.0_dp*c1+2.0_dp*c2-0.5_dp*c3
      t4 = 1.0_dp/6.0_dp*d3
      s1 = 1.0_dp/6.0_dp*(64.0_dp-48.0_dp*e1+12.0_dp*e2-e3)
      s2 = -22.0_dp/3.0_dp+10.0_dp*f1-4.0_dp*f2+0.5_dp*f3
      s3 = 2.0_dp/3.0_dp-2.0_dp*g1+2.0_dp*g2-0.5_dp*g3
      s4 = 1.0_dp/6.0_dp*h3
      v1 = 1.0_dp/6.0_dp*(64.0_dp-48.0_dp*p1+12.0_dp*p2-p3)
      v2 = -22.0_dp/3.0_dp+10.0_dp*q1-4.0_dp*q2+0.5_dp*q3
      v3 = 2.0_dp/3.0_dp-2.0_dp*r1+2.0_dp*r2-0.5_dp*r3
      v4 = 1.0_dp/6.0_dp*u3

      val = ((box(1, 1, 1)*t1+box(2, 1, 1)*t2+box(3, 1, 1)*t3+box(4, 1, 1)*t4)*s1+ &
             (box(1, 2, 1)*t1+box(2, 2, 1)*t2+box(3, 2, 1)*t3+box(4, 2, 1)*t4)*s2+ &
             (box(1, 3, 1)*t1+box(2, 3, 1)*t2+box(3, 3, 1)*t3+box(4, 3, 1)*t4)*s3+ &
             (box(1, 4, 1)*t1+box(2, 4, 1)*t2+box(3, 4, 1)*t3+box(4, 4, 1)*t4)*s4)*v1+ &
            ((box(1, 1, 2)*t1+box(2, 1, 2)*t2+box(3, 1, 2)*t3+box(4, 1, 2)*t4)*s1+ &
             (box(1, 2, 2)*t1+box(2, 2, 2)*t2+box(3, 2, 2)*t3+box(4, 2, 2)*t4)*s2+ &
             (box(1, 3, 2)*t1+box(2, 3, 2)*t2+box(3, 3, 2)*t3+box(4, 3, 2)*t4)*s3+ &
             (box(1, 4, 2)*t1+box(2, 4, 2)*t2+box(3, 4, 2)*t3+box(4, 4, 2)*t4)*s4)*v2+ &
            ((box(1, 1, 3)*t1+box(2, 1, 3)*t2+box(3, 1, 3)*t3+box(4, 1, 3)*t4)*s1+ &
             (box(1, 2, 3)*t1+box(2, 2, 3)*t2+box(3, 2, 3)*t3+box(4, 2, 3)*t4)*s2+ &
             (box(1, 3, 3)*t1+box(2, 3, 3)*t2+box(3, 3, 3)*t3+box(4, 3, 3)*t4)*s3+ &
             (box(1, 4, 3)*t1+box(2, 4, 3)*t2+box(3, 4, 3)*t3+box(4, 4, 3)*t4)*s4)*v3+ &
            ((box(1, 1, 4)*t1+box(2, 1, 4)*t2+box(3, 1, 4)*t3+box(4, 1, 4)*t4)*s1+ &
             (box(1, 2, 4)*t1+box(2, 2, 4)*t2+box(3, 2, 4)*t3+box(4, 2, 4)*t4)*s2+ &
             (box(1, 3, 4)*t1+box(2, 3, 4)*t2+box(3, 3, 4)*t3+box(4, 3, 4)*t4)*s3+ &
             (box(1, 4, 4)*t1+box(2, 4, 4)*t2+box(3, 4, 4)*t3+box(4, 4, 4)*t4)*s4)*v4

      IF (my_mpsum) CALL mp_sum(val, pw%pw_grid%para%group)

   END FUNCTION Eval_Interp_Spl3_pbc

! **************************************************************************************************
!> \brief Evaluates the derivatives of the PBC interpolated Spline (pw)
!>      function on the generic input vector (vec)
!> \param vec ...
!> \param pw ...
!> \return ...
!> \par History
!>      12.2007 Adapted for use with distributed grids [rdeclerck]
!> \author Teodoro Laino 12/2005 [tlaino]
!> \note
!>      Requires the Spline coefficients to be computed with PBC
! **************************************************************************************************
   FUNCTION Eval_d_Interp_Spl3_pbc(vec, pw) RESULT(val)
      REAL(KIND=dp), DIMENSION(3), INTENT(in)            :: vec
      TYPE(pw_type), POINTER                             :: pw
      REAL(KIND=dp)                                      :: val(3)

      CHARACTER(len=*), PARAMETER :: routineN = 'Eval_d_Interp_Spl3_pbc', &
         routineP = moduleN//':'//routineN

      INTEGER                                            :: i, ivec(3), j, k, npts(3)
      INTEGER, DIMENSION(2, 3)                           :: bo, bo_l
      INTEGER, DIMENSION(4)                              :: ii, ij, ik
      LOGICAL                                            :: my_mpsum
      REAL(KIND=dp) :: a1, a2, a3, b1, b2, b3, c1, c2, c3, d1, d2, d3, dr1, dr1i, dr2, dr2i, dr3, &
         dr3i, e1, e2, e3, f1, f2, f3, g1, g2, g3, h1, h2, h3, p1, p2, p3, q1, q2, q3, r1, r2, r3, &
         s1, s1d, s1o, s2, s2d, s2o, s3, s3d, s3o, s4, s4d, s4o, t1, t1d, t1o, t2, t2d, t2o, t3, &
         t3d, t3o, t4, t4d, t4o, u1, u2, u3, v1, v1d, v1o, v2, v2d, v2o, v3, v3d, v3o, v4, v4d, &
         v4o, xd1, xd2, xd3
      REAL(KIND=dp), DIMENSION(4, 4, 4)                  :: box
      REAL(KIND=dp), DIMENSION(:, :, :), POINTER         :: grid

      NULLIFY (grid)
      my_mpsum = (pw%pw_grid%para%mode /= PW_MODE_LOCAL)
      npts = pw%pw_grid%npts
      ivec = FLOOR(vec/pw%pw_grid%dr)
      dr1 = pw%pw_grid%dr(1)
      dr2 = pw%pw_grid%dr(2)
      dr3 = pw%pw_grid%dr(3)
      dr1i = 1.0_dp/dr1
      dr2i = 1.0_dp/dr2
      dr3i = 1.0_dp/dr3
      xd1 = (vec(1)/dr1)-REAL(ivec(1), kind=dp)
      xd2 = (vec(2)/dr2)-REAL(ivec(2), kind=dp)
      xd3 = (vec(3)/dr3)-REAL(ivec(3), kind=dp)
      grid => pw%cr3d(:, :, :)
      bo = pw%pw_grid%bounds
      bo_l = pw%pw_grid%bounds_local

      ik(1) = MODULO(ivec(3)-1, npts(3))+bo(1, 3)
      ik(2) = MODULO(ivec(3), npts(3))+bo(1, 3)
      ik(3) = MODULO(ivec(3)+1, npts(3))+bo(1, 3)
      ik(4) = MODULO(ivec(3)+2, npts(3))+bo(1, 3)

      ij(1) = MODULO(ivec(2)-1, npts(2))+bo(1, 2)
      ij(2) = MODULO(ivec(2), npts(2))+bo(1, 2)
      ij(3) = MODULO(ivec(2)+1, npts(2))+bo(1, 2)
      ij(4) = MODULO(ivec(2)+2, npts(2))+bo(1, 2)

      ii(1) = MODULO(ivec(1)-1, npts(1))+bo(1, 1)
      ii(2) = MODULO(ivec(1), npts(1))+bo(1, 1)
      ii(3) = MODULO(ivec(1)+1, npts(1))+bo(1, 1)
      ii(4) = MODULO(ivec(1)+2, npts(1))+bo(1, 1)

      DO k = 1, 4
         DO j = 1, 4
            DO i = 1, 4
               IF ( &
                  ii(i) >= bo_l(1, 1) .AND. &
                  ii(i) <= bo_l(2, 1) .AND. &
                  ij(j) >= bo_l(1, 2) .AND. &
                  ij(j) <= bo_l(2, 2) .AND. &
                  ik(k) >= bo_l(1, 3) .AND. &
                  ik(k) <= bo_l(2, 3) &
                  ) THEN
                  box(i, j, k) = grid(ii(i)+1-bo_l(1, 1), &
                                      ij(j)+1-bo_l(1, 2), &
                                      ik(k)+1-bo_l(1, 3))
               ELSE
                  box(i, j, k) = 0.0_dp
               END IF
            END DO
         END DO
      END DO

      a1 = 3.0_dp+xd1
      a2 = a1*a1
      a3 = a2*a1
      b1 = 2.0_dp+xd1
      b2 = b1*b1
      b3 = b2*b1
      c1 = 1.0_dp+xd1
      c2 = c1*c1
      c3 = c2*c1
      d1 = xd1
      d2 = d1*d1
      d3 = d2*d1
      e1 = 3.0_dp+xd2
      e2 = e1*e1
      e3 = e2*e1
      f1 = 2.0_dp+xd2
      f2 = f1*f1
      f3 = f2*f1
      g1 = 1.0_dp+xd2
      g2 = g1*g1
      g3 = g2*g1
      h1 = xd2
      h2 = h1*h1
      h3 = h2*h1
      p1 = 3.0_dp+xd3
      p2 = p1*p1
      p3 = p2*p1
      q1 = 2.0_dp+xd3
      q2 = q1*q1
      q3 = q2*q1
      r1 = 1.0_dp+xd3
      r2 = r1*r1
      r3 = r2*r1
      u1 = xd3
      u2 = u1*u1
      u3 = u2*u1

      t1o = 1.0_dp/6.0_dp*(64.0_dp-48.0_dp*a1+12.0_dp*a2-a3)
      t2o = -22.0_dp/3.0_dp+10.0_dp*b1-4.0_dp*b2+0.5_dp*b3
      t3o = 2.0_dp/3.0_dp-2.0_dp*c1+2.0_dp*c2-0.5_dp*c3
      t4o = 1.0_dp/6.0_dp*d3
      s1o = 1.0_dp/6.0_dp*(64.0_dp-48.0_dp*e1+12.0_dp*e2-e3)
      s2o = -22.0_dp/3.0_dp+10.0_dp*f1-4.0_dp*f2+0.5_dp*f3
      s3o = 2.0_dp/3.0_dp-2.0_dp*g1+2.0_dp*g2-0.5_dp*g3
      s4o = 1.0_dp/6.0_dp*h3
      v1o = 1.0_dp/6.0_dp*(64.0_dp-48.0_dp*p1+12.0_dp*p2-p3)
      v2o = -22.0_dp/3.0_dp+10.0_dp*q1-4.0_dp*q2+0.5_dp*q3
      v3o = 2.0_dp/3.0_dp-2.0_dp*r1+2.0_dp*r2-0.5_dp*r3
      v4o = 1.0_dp/6.0_dp*u3

      t1d = -8.0_dp+4.0_dp*a1-0.5_dp*a2
      t2d = 10.0_dp-8.0_dp*b1+1.5_dp*b2
      t3d = -2.0_dp+4.0_dp*c1-1.5_dp*c2
      t4d = 0.5_dp*d2
      s1d = -8.0_dp+4.0_dp*e1-0.5_dp*e2
      s2d = 10.0_dp-8.0_dp*f1+1.5_dp*f2
      s3d = -2.0_dp+4.0_dp*g1-1.5_dp*g2
      s4d = 0.5_dp*h2
      v1d = -8.0_dp+4.0_dp*p1-0.5_dp*p2
      v2d = 10.0_dp-8.0_dp*q1+1.5_dp*q2
      v3d = -2.0_dp+4.0_dp*r1-1.5_dp*r2
      v4d = 0.5_dp*u2

      t1 = t1d*dr1i
      t2 = t2d*dr1i
      t3 = t3d*dr1i
      t4 = t4d*dr1i
      s1 = s1o
      s2 = s2o
      s3 = s3o
      s4 = s4o
      v1 = v1o
      v2 = v2o
      v3 = v3o
      v4 = v4o
      val(1) = ((box(1, 1, 1)*t1+box(2, 1, 1)*t2+box(3, 1, 1)*t3+box(4, 1, 1)*t4)*s1+ &
                (box(1, 2, 1)*t1+box(2, 2, 1)*t2+box(3, 2, 1)*t3+box(4, 2, 1)*t4)*s2+ &
                (box(1, 3, 1)*t1+box(2, 3, 1)*t2+box(3, 3, 1)*t3+box(4, 3, 1)*t4)*s3+ &
                (box(1, 4, 1)*t1+box(2, 4, 1)*t2+box(3, 4, 1)*t3+box(4, 4, 1)*t4)*s4)*v1+ &
               ((box(1, 1, 2)*t1+box(2, 1, 2)*t2+box(3, 1, 2)*t3+box(4, 1, 2)*t4)*s1+ &
                (box(1, 2, 2)*t1+box(2, 2, 2)*t2+box(3, 2, 2)*t3+box(4, 2, 2)*t4)*s2+ &
                (box(1, 3, 2)*t1+box(2, 3, 2)*t2+box(3, 3, 2)*t3+box(4, 3, 2)*t4)*s3+ &
                (box(1, 4, 2)*t1+box(2, 4, 2)*t2+box(3, 4, 2)*t3+box(4, 4, 2)*t4)*s4)*v2+ &
               ((box(1, 1, 3)*t1+box(2, 1, 3)*t2+box(3, 1, 3)*t3+box(4, 1, 3)*t4)*s1+ &
                (box(1, 2, 3)*t1+box(2, 2, 3)*t2+box(3, 2, 3)*t3+box(4, 2, 3)*t4)*s2+ &
                (box(1, 3, 3)*t1+box(2, 3, 3)*t2+box(3, 3, 3)*t3+box(4, 3, 3)*t4)*s3+ &
                (box(1, 4, 3)*t1+box(2, 4, 3)*t2+box(3, 4, 3)*t3+box(4, 4, 3)*t4)*s4)*v3+ &
               ((box(1, 1, 4)*t1+box(2, 1, 4)*t2+box(3, 1, 4)*t3+box(4, 1, 4)*t4)*s1+ &
                (box(1, 2, 4)*t1+box(2, 2, 4)*t2+box(3, 2, 4)*t3+box(4, 2, 4)*t4)*s2+ &
                (box(1, 3, 4)*t1+box(2, 3, 4)*t2+box(3, 3, 4)*t3+box(4, 3, 4)*t4)*s3+ &
                (box(1, 4, 4)*t1+box(2, 4, 4)*t2+box(3, 4, 4)*t3+box(4, 4, 4)*t4)*s4)*v4

      t1 = t1o
      t2 = t2o
      t3 = t3o
      t4 = t4o
      s1 = s1d*dr2i
      s2 = s2d*dr2i
      s3 = s3d*dr2i
      s4 = s4d*dr2i
      v1 = v1o
      v2 = v2o
      v3 = v3o
      v4 = v4o
      val(2) = ((box(1, 1, 1)*t1+box(2, 1, 1)*t2+box(3, 1, 1)*t3+box(4, 1, 1)*t4)*s1+ &
                (box(1, 2, 1)*t1+box(2, 2, 1)*t2+box(3, 2, 1)*t3+box(4, 2, 1)*t4)*s2+ &
                (box(1, 3, 1)*t1+box(2, 3, 1)*t2+box(3, 3, 1)*t3+box(4, 3, 1)*t4)*s3+ &
                (box(1, 4, 1)*t1+box(2, 4, 1)*t2+box(3, 4, 1)*t3+box(4, 4, 1)*t4)*s4)*v1+ &
               ((box(1, 1, 2)*t1+box(2, 1, 2)*t2+box(3, 1, 2)*t3+box(4, 1, 2)*t4)*s1+ &
                (box(1, 2, 2)*t1+box(2, 2, 2)*t2+box(3, 2, 2)*t3+box(4, 2, 2)*t4)*s2+ &
                (box(1, 3, 2)*t1+box(2, 3, 2)*t2+box(3, 3, 2)*t3+box(4, 3, 2)*t4)*s3+ &
                (box(1, 4, 2)*t1+box(2, 4, 2)*t2+box(3, 4, 2)*t3+box(4, 4, 2)*t4)*s4)*v2+ &
               ((box(1, 1, 3)*t1+box(2, 1, 3)*t2+box(3, 1, 3)*t3+box(4, 1, 3)*t4)*s1+ &
                (box(1, 2, 3)*t1+box(2, 2, 3)*t2+box(3, 2, 3)*t3+box(4, 2, 3)*t4)*s2+ &
                (box(1, 3, 3)*t1+box(2, 3, 3)*t2+box(3, 3, 3)*t3+box(4, 3, 3)*t4)*s3+ &
                (box(1, 4, 3)*t1+box(2, 4, 3)*t2+box(3, 4, 3)*t3+box(4, 4, 3)*t4)*s4)*v3+ &
               ((box(1, 1, 4)*t1+box(2, 1, 4)*t2+box(3, 1, 4)*t3+box(4, 1, 4)*t4)*s1+ &
                (box(1, 2, 4)*t1+box(2, 2, 4)*t2+box(3, 2, 4)*t3+box(4, 2, 4)*t4)*s2+ &
                (box(1, 3, 4)*t1+box(2, 3, 4)*t2+box(3, 3, 4)*t3+box(4, 3, 4)*t4)*s3+ &
                (box(1, 4, 4)*t1+box(2, 4, 4)*t2+box(3, 4, 4)*t3+box(4, 4, 4)*t4)*s4)*v4

      t1 = t1o
      t2 = t2o
      t3 = t3o
      t4 = t4o
      s1 = s1o
      s2 = s2o
      s3 = s3o
      s4 = s4o
      v1 = v1d*dr3i
      v2 = v2d*dr3i
      v3 = v3d*dr3i
      v4 = v4d*dr3i
      val(3) = ((box(1, 1, 1)*t1+box(2, 1, 1)*t2+box(3, 1, 1)*t3+box(4, 1, 1)*t4)*s1+ &
                (box(1, 2, 1)*t1+box(2, 2, 1)*t2+box(3, 2, 1)*t3+box(4, 2, 1)*t4)*s2+ &
                (box(1, 3, 1)*t1+box(2, 3, 1)*t2+box(3, 3, 1)*t3+box(4, 3, 1)*t4)*s3+ &
                (box(1, 4, 1)*t1+box(2, 4, 1)*t2+box(3, 4, 1)*t3+box(4, 4, 1)*t4)*s4)*v1+ &
               ((box(1, 1, 2)*t1+box(2, 1, 2)*t2+box(3, 1, 2)*t3+box(4, 1, 2)*t4)*s1+ &
                (box(1, 2, 2)*t1+box(2, 2, 2)*t2+box(3, 2, 2)*t3+box(4, 2, 2)*t4)*s2+ &
                (box(1, 3, 2)*t1+box(2, 3, 2)*t2+box(3, 3, 2)*t3+box(4, 3, 2)*t4)*s3+ &
                (box(1, 4, 2)*t1+box(2, 4, 2)*t2+box(3, 4, 2)*t3+box(4, 4, 2)*t4)*s4)*v2+ &
               ((box(1, 1, 3)*t1+box(2, 1, 3)*t2+box(3, 1, 3)*t3+box(4, 1, 3)*t4)*s1+ &
                (box(1, 2, 3)*t1+box(2, 2, 3)*t2+box(3, 2, 3)*t3+box(4, 2, 3)*t4)*s2+ &
                (box(1, 3, 3)*t1+box(2, 3, 3)*t2+box(3, 3, 3)*t3+box(4, 3, 3)*t4)*s3+ &
                (box(1, 4, 3)*t1+box(2, 4, 3)*t2+box(3, 4, 3)*t3+box(4, 4, 3)*t4)*s4)*v3+ &
               ((box(1, 1, 4)*t1+box(2, 1, 4)*t2+box(3, 1, 4)*t3+box(4, 1, 4)*t4)*s1+ &
                (box(1, 2, 4)*t1+box(2, 2, 4)*t2+box(3, 2, 4)*t3+box(4, 2, 4)*t4)*s2+ &
                (box(1, 3, 4)*t1+box(2, 3, 4)*t2+box(3, 3, 4)*t3+box(4, 3, 4)*t4)*s3+ &
                (box(1, 4, 4)*t1+box(2, 4, 4)*t2+box(3, 4, 4)*t3+box(4, 4, 4)*t4)*s4)*v4

      IF (my_mpsum) CALL mp_sum(val, pw%pw_grid%para%group)

   END FUNCTION Eval_d_Interp_Spl3_pbc

END MODULE pw_spline_utils
