ewald_spline_util.F

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!--------------------------------------------------------------------------------------------------!
!   CP2K: A general program to perform molecular dynamics simulations                              !
!   Copyright 2000-2024 CP2K developers group <https://cp2k.org>                                   !
!                                                                                                  !
!   SPDX-License-Identifier: GPL-2.0-or-later                                                      !
!--------------------------------------------------------------------------------------------------!
 
! **************************************************************************************************
!> \brief Setting up the Spline coefficients used to Interpolate the G-Term
!>      in Ewald sums
!> \par History
!>      12.2005 created [tlaino]
!> \author Teodoro Laino
! **************************************************************************************************
MODULE ewald_spline_util
   USE cell_methods,                    ONLY: cell_create
   USE cell_types,                      ONLY: cell_release,&
                                              cell_type
   USE cp_log_handling,                 ONLY: cp_get_default_logger,&
                                              cp_logger_type
   USE cp_output_handling,              ONLY: cp_print_key_finished_output,&
                                              cp_print_key_unit_nr
   USE input_section_types,             ONLY: section_vals_get_subs_vals,&
                                              section_vals_type,&
                                              section_vals_val_get
   USE kinds,                           ONLY: dp
   USE message_passing,                 ONLY: mp_para_env_type
   USE pw_grid_types,                   ONLY: halfspace,&
                                              pw_grid_type
   USE pw_grids,                        ONLY: pw_grid_create,&
                                              pw_grid_setup
   USE pw_methods,                      ONLY: pw_zero
   USE pw_pool_types,                   ONLY: pw_pool_create,&
                                              pw_pool_type
   USE pw_spline_utils,                 ONLY: &
        eval_interp_spl3_pbc, eval_d_interp_spl3_pbc, find_coeffs, pw_spline_do_precond, &
        pw_spline_precond_create, pw_spline_precond_release, pw_spline_precond_set_kind, &
        pw_spline_precond_type, spl3_pbc
   USE pw_types,                        ONLY: pw_r3d_rs_type
!NB parallelization
#include "./base/base_uses.f90"
 
   IMPLICIT NONE
   PRIVATE
 
   LOGICAL, PRIVATE, PARAMETER :: debug_this_module = .true.
   CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'ewald_spline_util'
   PUBLIC :: setup_ewald_spline
 
CONTAINS
 
! **************************************************************************************************
!> \brief Setup of the G-space Ewald Term Spline Coefficients
!> \param pw_grid ...
!> \param pw_pool ...
!> \param coeff ...
!> \param LG ...
!> \param gx ...
!> \param gy ...
!> \param gz ...
!> \param hmat ...
!> \param npts ...
!> \param param_section ...
!> \param tag ...
!> \param print_section ...
!> \param para_env ...
!> \par History
!>      12.2005 created [tlaino]
!> \author Teodoro Laino
! **************************************************************************************************
   SUBROUTINE setup_ewald_spline(pw_grid, pw_pool, coeff, LG, gx, gy, gz, hmat, npts, &
                                 param_section, tag, print_section, para_env)
      TYPE(pw_grid_type), POINTER                        :: pw_grid
      TYPE(pw_pool_type), POINTER                        :: pw_pool
      TYPE(pw_r3d_rs_type), POINTER                      :: coeff
      REAL(kind=dp), DIMENSION(:), POINTER               :: lg, gx, gy, gz
      REAL(kind=dp), INTENT(IN)                          :: hmat(3, 3)
      INTEGER, INTENT(IN)                                :: npts(3)
      TYPE(section_vals_type), POINTER                   :: param_section
      CHARACTER(LEN=*), INTENT(IN)                       :: tag
      TYPE(section_vals_type), POINTER                   :: print_section
      TYPE(mp_para_env_type), POINTER                    :: para_env
 
      INTEGER                                            :: bo(2, 3), iounit
      TYPE(cell_type), POINTER                           :: cell
      TYPE(cp_logger_type), POINTER                      :: logger
      TYPE(pw_r3d_rs_type)                               :: pw
 
!
! Setting Up Fit Procedure
!
 
      cpassert(.NOT. ASSOCIATED(pw_grid))
      cpassert(.NOT. ASSOCIATED(pw_pool))
      cpassert(.NOT. ASSOCIATED(coeff))
      NULLIFY (cell)
 
      CALL cell_create(cell, hmat=hmat, periodic=(/1, 1, 1/))
      CALL pw_grid_create(pw_grid, para_env, local=.true.)
      logger => cp_get_default_logger()
      iounit = cp_print_key_unit_nr(logger, print_section, "", &
                                    extension=".Log")
      bo(1, 1:3) = 0
      bo(2, 1:3) = npts(1:3) - 1
      CALL pw_grid_setup(cell%hmat, pw_grid, grid_span=halfspace, bounds=bo, iounit=iounit)
 
      CALL cp_print_key_finished_output(iounit, logger, print_section, &
                                        "")
      ! pw_pool initialized
      CALL pw_pool_create(pw_pool, pw_grid=pw_grid)
      ALLOCATE (coeff)
      CALL pw_pool%create_pw(pw)
      CALL pw_pool%create_pw(coeff)
      ! Evaluate function on grid
      CALL eval_pw_tablr(pw, pw_pool, coeff, lg, gx, gy, gz, hmat_mm=hmat, &
                         param_section=param_section, tag=tag)
      CALL pw_pool%give_back_pw(pw)
      CALL cell_release(cell)
 
   END SUBROUTINE setup_ewald_spline
 
! **************************************************************************************************
!> \brief Evaluates the function G-Term in reciprocal space on the grid
!>      and find the coefficients of the Splines
!> \param grid ...
!> \param pw_pool ...
!> \param TabLR ...
!> \param Lg ...
!> \param gx ...
!> \param gy ...
!> \param gz ...
!> \param hmat_mm ...
!> \param param_section ...
!> \param tag ...
!> \par History
!>      12.2005 created [tlaino]
!> \author Teodoro Laino
! **************************************************************************************************
   SUBROUTINE eval_pw_tablr(grid, pw_pool, TabLR, Lg, gx, gy, gz, hmat_mm, &
                            param_section, tag)
      TYPE(pw_r3d_rs_type), INTENT(INOUT)                :: grid
      TYPE(pw_pool_type), POINTER                        :: pw_pool
      TYPE(pw_r3d_rs_type), POINTER                      :: tablr
      REAL(kind=dp), DIMENSION(:), POINTER               :: lg, gx, gy, gz
      REAL(kind=dp), DIMENSION(3, 3)                     :: hmat_mm
      TYPE(section_vals_type), POINTER                   :: param_section
      CHARACTER(LEN=*), INTENT(IN)                       :: tag
 
      CHARACTER(len=*), PARAMETER                        :: routinen = 'eval_pw_TabLR'
 
      INTEGER :: act_nx, act_ny, aint_precond, handle, i, iii, is, j, js, k, ks, lg_loc_max, &
         lg_loc_min, max_iter, my_i, my_j, my_k, n1, n2, n3, n_extra, nlg_loc, nxlim, nylim, &
         nzlim, precond_kind
      INTEGER, DIMENSION(2, 3)                           :: gbo
      LOGICAL                                            :: success
      REAL(kind=dp)                                      :: dr1, dr2, dr3, eps_r, eps_x, xs1, xs2, &
                                                            xs3
      REAL(kind=dp), ALLOCATABLE                         :: cos_gx(:, :), cos_gy(:, :), &
                                                            cos_gz(:, :), lhs(:, :), rhs(:, :), &
                                                            sin_gx(:, :), sin_gy(:, :), &
                                                            sin_gz(:, :)
      TYPE(pw_spline_precond_type)                       :: precond
      TYPE(section_vals_type), POINTER                   :: interp_section
 
!NB pull expensive Cos() out of inner looop
!NB temporaries for holding stuff so that dgemm can be used
 
      EXTERNAL :: dgemm
 
      CALL timeset(routinen, handle)
      n1 = grid%pw_grid%npts(1)
      n2 = grid%pw_grid%npts(2)
      n3 = grid%pw_grid%npts(3)
      dr1 = grid%pw_grid%dr(1)
      dr2 = grid%pw_grid%dr(2)
      dr3 = grid%pw_grid%dr(3)
      gbo = grid%pw_grid%bounds
      nxlim = floor(real(n1, kind=dp)/2.0_dp)
      nylim = floor(real(n2, kind=dp)/2.0_dp)
      nzlim = floor(real(n3, kind=dp)/2.0_dp)
      is = 0
      js = 0
      ks = 0
      IF (2*nxlim /= n1) is = 1
      IF (2*nylim /= n2) js = 1
      IF (2*nzlim /= n3) ks = 1
      CALL pw_zero(grid)
 
      ! Used the full symmetry to reduce the evaluation to 1/64th
      !NB parallelization
      iii = 0
      !NB allocate temporaries for Cos refactoring
      ALLOCATE (cos_gx(SIZE(lg), gbo(1, 1):gbo(2, 1)))
      ALLOCATE (sin_gx(SIZE(lg), gbo(1, 1):gbo(2, 1)))
      ALLOCATE (cos_gy(SIZE(lg), gbo(1, 2):gbo(2, 2)))
      ALLOCATE (sin_gy(SIZE(lg), gbo(1, 2):gbo(2, 2)))
      ALLOCATE (cos_gz(SIZE(lg), gbo(1, 3):gbo(2, 3)))
      ALLOCATE (sin_gz(SIZE(lg), gbo(1, 3):gbo(2, 3)))
      !NB precalculate Cos(gx*xs1) etc for Cos refactoring
      DO k = gbo(1, 3), gbo(2, 3)
         my_k = k - gbo(1, 3)
         xs3 = real(my_k, dp)*dr3
         IF (k > nzlim) cycle
         cos_gz(1:SIZE(lg), k) = cos(gz(1:SIZE(lg))*xs3)
         sin_gz(1:SIZE(lg), k) = sin(gz(1:SIZE(lg))*xs3)
      END DO ! k
      xs2 = 0.0_dp
      DO j = gbo(1, 2), gbo(2, 2)
         IF (j > nylim) cycle
         cos_gy(1:SIZE(lg), j) = cos(gy(1:SIZE(lg))*xs2)
         sin_gy(1:SIZE(lg), j) = sin(gy(1:SIZE(lg))*xs2)
         xs2 = xs2 + dr2
      END DO ! j
      xs1 = 0.0_dp
      DO i = gbo(1, 1), gbo(2, 1)
         IF (i > nxlim) cycle
         cos_gx(1:SIZE(lg), i) = cos(gx(1:SIZE(lg))*xs1)
         sin_gx(1:SIZE(lg), i) = sin(gx(1:SIZE(lg))*xs1)
         xs1 = xs1 + dr1
      END DO ! i
 
      !NB use DGEMM to compute sum over kg for each i, j, k
      ! number of elements per node, round down
      nlg_loc = SIZE(lg)/grid%pw_grid%para%group_size
      ! number of extra elements not yet accounted for
      n_extra = mod(SIZE(lg), grid%pw_grid%para%group_size)
      ! first n_extra nodes get NLg_loc+1, remaining get NLg_loc
      IF (grid%pw_grid%para%my_pos < n_extra) THEN
         lg_loc_min = (nlg_loc + 1)*grid%pw_grid%para%my_pos + 1
         lg_loc_max = lg_loc_min + (nlg_loc + 1) - 1
      ELSE
         lg_loc_min = (nlg_loc + 1)*n_extra + nlg_loc*(grid%pw_grid%para%my_pos - n_extra) + 1
         lg_loc_max = lg_loc_min + nlg_loc - 1
      END IF
      ! shouldn't be necessary
      lg_loc_max = min(SIZE(lg), lg_loc_max)
      nlg_loc = lg_loc_max - lg_loc_min + 1
 
      IF (nlg_loc > 0) THEN ! some work for this node
 
         act_nx = min(gbo(2, 1), nxlim) - gbo(1, 1) + 1
         act_ny = min(gbo(2, 2), nylim) - gbo(1, 2) + 1
         !NB temporaries for DGEMM use
         ALLOCATE (lhs(act_nx, nlg_loc))
         ALLOCATE (rhs(act_ny, nlg_loc))
 
         ! do cos(gx) cos(gy+gz) term
         DO i = gbo(1, 1), gbo(2, 1)
            IF (i > nxlim) cycle
            lhs(i - gbo(1, 1) + 1, 1:nlg_loc) = lg(lg_loc_min:lg_loc_max)*cos_gx(lg_loc_min:lg_loc_max, i)
         END DO
         DO k = gbo(1, 3), gbo(2, 3)
            IF (k > nzlim) cycle
            DO j = gbo(1, 2), gbo(2, 2)
               IF (j > nylim) cycle
               rhs(j - gbo(1, 2) + 1, 1:nlg_loc) = cos_gy(lg_loc_min:lg_loc_max, j)*cos_gz(lg_loc_min:lg_loc_max, k) - &
                                                   sin_gy(lg_loc_min:lg_loc_max, j)*sin_gz(lg_loc_min:lg_loc_max, k)
            END DO
            CALL dgemm('N', 'T', act_nx, act_ny, nlg_loc, 1.0d0, lhs(1, 1), act_nx, rhs(1, 1), act_ny, 0.0d0, &
                       grid%array(gbo(1, 1), gbo(1, 2), k), SIZE(grid%array, 1))
         END DO
 
         ! do sin(gx) sin(gy+gz) term
         DO i = gbo(1, 1), gbo(2, 1)
            IF (i > nxlim) cycle
            lhs(i - gbo(1, 1) + 1, 1:nlg_loc) = -lg(lg_loc_min:lg_loc_max)*sin_gx(lg_loc_min:lg_loc_max, i)
         END DO
         DO k = gbo(1, 3), gbo(2, 3)
            IF (k > nzlim) cycle
            DO j = gbo(1, 2), gbo(2, 2)
               IF (j > nylim) cycle
               rhs(j - gbo(1, 2) + 1, 1:nlg_loc) = cos_gy(lg_loc_min:lg_loc_max, j)*sin_gz(lg_loc_min:lg_loc_max, k) + &
                                                   sin_gy(lg_loc_min:lg_loc_max, j)*cos_gz(lg_loc_min:lg_loc_max, k)
            END DO
            CALL dgemm('N', 'T', act_nx, act_ny, nlg_loc, 1.0d0, lhs(1, 1), act_nx, rhs(1, 1), act_ny, 1.0d0, &
                       grid%array(gbo(1, 1), gbo(1, 2), k), SIZE(grid%array, 1))
         END DO
 
         !NB deallocate temporaries for DGEMM use
         DEALLOCATE (lhs)
         DEALLOCATE (rhs)
         !NB deallocate temporaries for Cos refactoring
         DEALLOCATE (cos_gx)
         DEALLOCATE (sin_gx)
         DEALLOCATE (cos_gy)
         DEALLOCATE (sin_gy)
         DEALLOCATE (cos_gz)
         DEALLOCATE (sin_gz)
         !NB parallelization
      ELSE ! no work for this node, just zero contribution
         grid%array(gbo(1, 1):nxlim, gbo(1, 2):nylim, gbo(1, 3):nzlim) = 0.0_dp
      END IF ! NLg_loc > 0
 
      CALL grid%pw_grid%para%group%sum(grid%array(gbo(1, 1):nxlim, gbo(1, 2):nylim, gbo(1, 3):nzlim))
 
      fake_loopongrid: DO k = gbo(1, 3), gbo(2, 3)
         my_k = k
         IF (k > nzlim) my_k = nzlim - abs(nzlim - k) + ks
         DO j = gbo(1, 2), gbo(2, 2)
            my_j = j
            IF (j > nylim) my_j = nylim - abs(nylim - j) + js
            DO i = gbo(1, 1), gbo(2, 1)
               my_i = i
               IF (i > nxlim) my_i = nxlim - abs(nxlim - i) + is
               grid%array(i, j, k) = grid%array(my_i, my_j, my_k)
            END DO
         END DO
      END DO fake_loopongrid
      !
      ! Solve for spline coefficients
      !
      interp_section => section_vals_get_subs_vals(param_section, "INTERPOLATOR")
      CALL section_vals_val_get(interp_section, "aint_precond", i_val=aint_precond)
      CALL section_vals_val_get(interp_section, "precond", i_val=precond_kind)
      CALL section_vals_val_get(interp_section, "max_iter", i_val=max_iter)
      CALL section_vals_val_get(interp_section, "eps_r", r_val=eps_r)
      CALL section_vals_val_get(interp_section, "eps_x", r_val=eps_x)
      !
      ! Solve for spline coefficients
      !
      CALL pw_spline_precond_create(precond, precond_kind=aint_precond, &
                                    pool=pw_pool, pbc=.true., transpose=.false.)
      CALL pw_spline_do_precond(precond, grid, tablr)
      CALL pw_spline_precond_set_kind(precond, precond_kind)
      success = find_coeffs(values=grid, coeffs=tablr, &
                            linop=spl3_pbc, preconditioner=precond, pool=pw_pool, &
                            eps_r=eps_r, eps_x=eps_x, &
                            max_iter=max_iter)
      cpassert(success)
      CALL pw_spline_precond_release(precond)
      !
      ! Check for the interpolation Spline
      !
      CALL check_spline_interp_tablr(hmat_mm, lg, gx, gy, gz, tablr, param_section, &
                                     tag)
      CALL timestop(handle)
   END SUBROUTINE eval_pw_tablr
 
! **************************************************************************************************
!> \brief Routine to check the accuracy for the Spline Interpolation
!> \param hmat_mm ...
!> \param Lg ...
!> \param gx ...
!> \param gy ...
!> \param gz ...
!> \param TabLR ...
!> \param param_section ...
!> \param tag ...
!> \par History
!>      12.2005 created [tlaino]
!> \author Teodoro Laino
! **************************************************************************************************
   SUBROUTINE check_spline_interp_tablr(hmat_mm, Lg, gx, gy, gz, TabLR, &
                                        param_section, tag)
      REAL(kind=dp), DIMENSION(3, 3)                     :: hmat_mm
      REAL(kind=dp), DIMENSION(:), POINTER               :: lg, gx, gy, gz
      TYPE(pw_r3d_rs_type), POINTER                      :: tablr
      TYPE(section_vals_type), POINTER                   :: param_section
      CHARACTER(LEN=*), INTENT(IN)                       :: tag
 
      CHARACTER(len=*), PARAMETER :: routinen = 'check_spline_interp_TabLR'
 
      INTEGER                                            :: handle, i, iw, kg, npoints
      REAL(kind=dp)                                      :: dn(3), dr1, dr2, dr3, dxterm, dyterm, &
                                                            dzterm, errd, errf, fterm, maxerrord, &
                                                            maxerrorf, na, nn, term, tmp1, tmp2, &
                                                            vec(3), xs1, xs2, xs3
      TYPE(cp_logger_type), POINTER                      :: logger
 
      NULLIFY (logger)
      logger => cp_get_default_logger()
      iw = cp_print_key_unit_nr(logger, param_section, "check_spline", &
                                extension="."//trim(tag)//"Log")
      CALL timeset(routinen, handle)
      IF (iw > 0) THEN
         npoints = 100
         errf = 0.0_dp
         maxerrorf = 0.0_dp
         errd = 0.0_dp
         maxerrord = 0.0_dp
         dr1 = hmat_mm(1, 1)/real(npoints, kind=dp)
         dr2 = hmat_mm(2, 2)/real(npoints, kind=dp)
         dr3 = hmat_mm(3, 3)/real(npoints, kind=dp)
         xs1 = 0.0_dp
         xs2 = 0.0_dp
         xs3 = 0.0_dp
         WRITE (iw, '(A,T5,A15,4X,A17,T50,4X,A,5X,A,T80,A,T85,A15,4X,A17,T130,4X,A,5X,A)') &
            "#", "Analytical Term", "Interpolated Term", "Error", "MaxError", &
            "*", " Analyt Deriv  ", "Interp Deriv Mod ", "Error", "MaxError"
         DO i = 1, npoints + 1
            term = 0.0_dp
            dxterm = 0.0_dp
            dyterm = 0.0_dp
            dzterm = 0.0_dp
            ! Sum over k vectors
            DO kg = 1, SIZE(lg)
               vec = (/real(gx(kg), kind=dp), real(gy(kg), kind=dp), real(gz(kg), kind=dp)/)
               term = term + lg(kg)*cos(vec(1)*xs1 + vec(2)*xs2 + vec(3)*xs3)
               dxterm = dxterm - lg(kg)*sin(vec(1)*xs1 + vec(2)*xs2 + vec(3)*xs3)*vec(1)
               dyterm = dyterm - lg(kg)*sin(vec(1)*xs1 + vec(2)*xs2 + vec(3)*xs3)*vec(2)
               dzterm = dzterm - lg(kg)*sin(vec(1)*xs1 + vec(2)*xs2 + vec(3)*xs3)*vec(3)
            END DO
            na = sqrt(dxterm*dxterm + dyterm*dyterm + dzterm*dzterm)
            dn = eval_d_interp_spl3_pbc((/xs1, xs2, xs3/), tablr)
            nn = sqrt(dot_product(dn, dn))
            fterm = eval_interp_spl3_pbc((/xs1, xs2, xs3/), tablr)
            tmp1 = abs(term - fterm)
            tmp2 = sqrt(dot_product(dn - (/dxterm, dyterm, dzterm/), dn - (/dxterm, dyterm, dzterm/)))
            errf = errf + tmp1
            maxerrorf = max(maxerrorf, tmp1)
            errd = errd + tmp2
            maxerrord = max(maxerrord, tmp2)
            WRITE (iw, '(T5,F15.10,5X,F15.10,T50,2F12.9,T80,A,T85,F15.10,5X,F15.10,T130,2F12.9)') &
               term, fterm, tmp1, maxerrorf, "*", na, nn, tmp2, maxerrord
            xs1 = xs1 + dr1
            xs2 = xs2 + dr2
            xs3 = xs3 + dr3
         END DO
         WRITE (iw, '(A,T5,A,T50,F12.9,T130,F12.9)') "#", "Averages", errf/real(npoints, kind=dp), &
            errd/real(npoints, kind=dp)
      END IF
      CALL timestop(handle)
      CALL cp_print_key_finished_output(iw, logger, param_section, "check_spline")
 
   END SUBROUTINE check_spline_interp_tablr
 
END MODULE ewald_spline_util