cp_fm_elpa.F

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!--------------------------------------------------------------------------------------------------!
!   CP2K: A general program to perform molecular dynamics simulations                              !
!   Copyright 2000-2025 CP2K developers group <https://cp2k.org>                                   !
!                                                                                                  !
!   SPDX-License-Identifier: GPL-2.0-or-later                                                      !
!--------------------------------------------------------------------------------------------------!
 
! **************************************************************************************************
!> \brief Wrapper for ELPA
!> \author Ole Schuett
! **************************************************************************************************
MODULE cp_fm_elpa
   USE cp_log_handling, ONLY: cp_to_string
   USE machine, ONLY: m_cpuid, &
                      machine_x86, &
                      machine_cpu_generic, &
                      machine_x86_sse4, &
                      machine_x86_avx, &
                      machine_x86_avx2
   USE cp_blacs_env, ONLY: cp_blacs_env_type
   USE cp_fm_basic_linalg, ONLY: cp_fm_uplo_to_full
   USE cp_fm_diag_utils, ONLY: cp_fm_redistribute_start, &
                               cp_fm_redistribute_end, &
                               cp_fm_redistribute_info
   USE cp_fm_struct, ONLY: cp_fm_struct_get
   USE cp_fm_types, ONLY: cp_fm_type, &
                          cp_fm_to_fm, &
                          cp_fm_release, &
                          cp_fm_create, &
                          cp_fm_write_info
   USE cp_log_handling, ONLY: cp_get_default_logger, &
                              cp_logger_get_default_io_unit, &
                              cp_logger_type
   USE kinds, ONLY: default_string_length, &
                    dp
   USE message_passing, ONLY: mp_comm_type
   USE omp_lib, ONLY: omp_get_max_threads
 
#include "../base/base_uses.f90"
 
#if defined (__ELPA)
   USE elpa_constants, ONLY: elpa_2stage_real_invalid, &
                             elpa_2stage_real_default, &
                             elpa_2stage_real_generic, &
                             elpa_2stage_real_generic_simple, &
                             elpa_2stage_real_bgp, &
                             elpa_2stage_real_bgq, &
                             elpa_2stage_real_sse_assembly, &
                             elpa_2stage_real_sse_block2, &
                             elpa_2stage_real_sse_block4, &
                             elpa_2stage_real_sse_block6, &
                             elpa_2stage_real_avx_block2, &
                             elpa_2stage_real_avx_block4, &
                             elpa_2stage_real_avx_block6, &
                             elpa_2stage_real_avx2_block2, &
                             elpa_2stage_real_avx2_block4, &
                             elpa_2stage_real_avx2_block6, &
                             elpa_2stage_real_avx512_block2, &
                             elpa_2stage_real_avx512_block4, &
                             elpa_2stage_real_avx512_block6, &
                             elpa_2stage_real_nvidia_gpu, &
                             elpa_2stage_real_amd_gpu, &
                             elpa_2stage_real_intel_gpu_sycl
 
   USE elpa, ONLY: elpa_t, elpa_solver_2stage, &
                   elpa_init, elpa_uninit, &
                   elpa_allocate, elpa_deallocate, elpa_ok
#endif
 
   IMPLICIT NONE
 
   PRIVATE
 
   CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'cp_fm_elpa'
 
#if defined(__ELPA)
   INTEGER, DIMENSION(21), PARAMETER :: elpa_kernel_ids = [ &
                                        elpa_2stage_real_invalid, & ! auto
                                        elpa_2stage_real_generic, &
                                        elpa_2stage_real_generic_simple, &
                                        elpa_2stage_real_bgp, &
                                        elpa_2stage_real_bgq, &
                                        elpa_2stage_real_sse_assembly, &
                                        elpa_2stage_real_sse_block2, &
                                        elpa_2stage_real_sse_block4, &
                                        elpa_2stage_real_sse_block6, &
                                        elpa_2stage_real_avx_block2, &
                                        elpa_2stage_real_avx_block4, &
                                        elpa_2stage_real_avx_block6, &
                                        elpa_2stage_real_avx2_block2, &
                                        elpa_2stage_real_avx2_block4, &
                                        elpa_2stage_real_avx2_block6, &
                                        elpa_2stage_real_avx512_block2, &
                                        elpa_2stage_real_avx512_block4, &
                                        elpa_2stage_real_avx512_block6, &
                                        elpa_2stage_real_nvidia_gpu, &
                                        elpa_2stage_real_amd_gpu, &
                                        elpa_2stage_real_intel_gpu_sycl]
 
   CHARACTER(len=14), DIMENSION(SIZE(elpa_kernel_ids)), PARAMETER :: &
      elpa_kernel_names = [character(len=14) :: &
                           "AUTO", &
                           "GENERIC", &
                           "GENERIC_SIMPLE", &
                           "BGP", &
                           "BGQ", &
                           "SSE", &
                           "SSE_BLOCK2", &
                           "SSE_BLOCK4", &
                           "SSE_BLOCK6", &
                           "AVX_BLOCK2", &
                           "AVX_BLOCK4", &
                           "AVX_BLOCK6", &
                           "AVX2_BLOCK2", &
                           "AVX2_BLOCK4", &
                           "AVX2_BLOCK6", &
                           "AVX512_BLOCK2", &
                           "AVX512_BLOCK4", &
                           "AVX512_BLOCK6", &
                           "NVIDIA_GPU", &
                           "AMD_GPU", &
                           "INTEL_GPU"]
 
   CHARACTER(len=44), DIMENSION(SIZE(elpa_kernel_ids)), PARAMETER :: &
      elpa_kernel_descriptions = [character(len=44) :: &
                                  "Automatically selected kernel", &
                                  "Generic kernel", &
                                  "Simplified generic kernel", &
                                  "Kernel optimized for IBM BGP", &
                                  "Kernel optimized for IBM BGQ", &
                                  "Kernel optimized for x86_64/SSE", &
                                  "Kernel optimized for x86_64/SSE (block=2)", &
                                  "Kernel optimized for x86_64/SSE (block=4)", &
                                  "Kernel optimized for x86_64/SSE (block=6)", &
                                  "Kernel optimized for Intel AVX (block=2)", &
                                  "Kernel optimized for Intel AVX (block=4)", &
                                  "Kernel optimized for Intel AVX (block=6)", &
                                  "Kernel optimized for Intel AVX2 (block=2)", &
                                  "Kernel optimized for Intel AVX2 (block=4)", &
                                  "Kernel optimized for Intel AVX2 (block=6)", &
                                  "Kernel optimized for Intel AVX-512 (block=2)", &
                                  "Kernel optimized for Intel AVX-512 (block=4)", &
                                  "Kernel optimized for Intel AVX-512 (block=6)", &
                                  "Kernel targeting Nvidia GPUs", &
                                  "Kernel targeting AMD GPUs", &
                                  "Kernel targeting Intel GPUs"]
 
#else
   INTEGER, DIMENSION(1), PARAMETER :: elpa_kernel_ids = [-1]
   CHARACTER(len=14), DIMENSION(1), PARAMETER :: elpa_kernel_names = ["AUTO"]
   CHARACTER(len=44), DIMENSION(1), PARAMETER :: elpa_kernel_descriptions = ["Automatically selected kernel"]
#endif
 
#if defined(__ELPA)
   INTEGER, SAVE :: elpa_kernel = elpa_kernel_ids(1) ! auto
#endif
   LOGICAL, SAVE :: elpa_qr = .false., &
                    elpa_qr_unsafe = .false., &
                    elpa_should_print = .false.
 
   PUBLIC :: cp_fm_diag_elpa, &
             set_elpa_kernel, &
             set_elpa_qr, &
             set_elpa_print, &
             elpa_kernel_ids, &
             elpa_kernel_names, &
             elpa_kernel_descriptions, &
             initialize_elpa_library, &
             finalize_elpa_library
 
CONTAINS
 
! **************************************************************************************************
!> \brief Initialize the ELPA library
! **************************************************************************************************
   SUBROUTINE initialize_elpa_library()
#if defined(__ELPA)
      IF (elpa_init(20180525) /= elpa_ok) &
         cpabort("The linked ELPA library does not support the required API version")
#else
      cpabort("Initialization of ELPA library requested but not enabled during build")
#endif
   END SUBROUTINE
 
! **************************************************************************************************
!> \brief Finalize the ELPA library
! **************************************************************************************************
   SUBROUTINE finalize_elpa_library()
#if defined(__ELPA)
      CALL elpa_uninit()
#else
      cpabort("Finalization of ELPA library requested but not enabled during build")
#endif
   END SUBROUTINE
 
! **************************************************************************************************
!> \brief Sets the active ELPA kernel.
!> \param requested_kernel one of the elpa_kernel_ids
! **************************************************************************************************
   SUBROUTINE set_elpa_kernel(requested_kernel)
      INTEGER, INTENT(IN)                                :: requested_kernel
 
#if defined (__ELPA)
      INTEGER                                            :: cpuid
 
      elpa_kernel = requested_kernel
 
      ! Resolve AUTO kernel.
      IF (elpa_kernel == elpa_2stage_real_invalid) THEN
         cpuid = m_cpuid()
         IF ((machine_cpu_generic .LT. cpuid) .AND. (cpuid .LE. machine_x86)) THEN
            SELECT CASE (cpuid)
            CASE (machine_x86_sse4)
               elpa_kernel = elpa_2stage_real_sse_block4
            CASE (machine_x86_avx)
               elpa_kernel = elpa_2stage_real_avx_block4
            CASE (machine_x86_avx2)
               elpa_kernel = elpa_2stage_real_avx2_block4
            CASE DEFAULT
               elpa_kernel = elpa_2stage_real_avx512_block4
            END SELECT
         END IF
 
         ! Prefer GPU kernel if available.
#if defined (__ELPA_NVIDIA_GPU)
         elpa_kernel = elpa_2stage_real_nvidia_gpu
#endif
#if defined (__ELPA_AMD_GPU)
         elpa_kernel = elpa_2stage_real_amd_gpu
#endif
#if defined (__ELPA_INTEL_GPU)
         elpa_kernel = elpa_2stage_real_intel_gpu_sycl
#endif
 
         ! If we could not find a suitable kernel then use ELPA_2STAGE_REAL_DEFAULT.
         IF (elpa_kernel == elpa_2stage_real_invalid) THEN
            elpa_kernel = elpa_2stage_real_default
         END IF
      END IF
#else
      mark_used(requested_kernel)
#endif
   END SUBROUTINE set_elpa_kernel
 
! **************************************************************************************************
!> \brief Sets flags that determines if ELPA should try to use QR during diagonalization
!>        If use_qr = .TRUE., the QR step is performed only if the size of the input matrix is
!>        suitable. Check cp_fm_diag_elpa for further details.
!> \param use_qr the logical flag
!> \param use_qr_unsafe logical which determines if block size checks should be bypassed for some
!>                      ELPA versions, potentially leading to incorrect eigenvalues
! **************************************************************************************************
   SUBROUTINE set_elpa_qr(use_qr, use_qr_unsafe)
      LOGICAL, INTENT(IN)                                :: use_qr, use_qr_unsafe
 
      elpa_qr = use_qr
      elpa_qr_unsafe = use_qr_unsafe
   END SUBROUTINE set_elpa_qr
 
! **************************************************************************************************
!> \brief Sets a flag that determines if additional information about the ELPA diagonalization
!>        should be printed when the diagonalization routine is called.
!> \param flag the logical flag
! **************************************************************************************************
   SUBROUTINE set_elpa_print(flag)
      LOGICAL, INTENT(IN)                                :: flag
 
      elpa_should_print = flag
   END SUBROUTINE set_elpa_print
 
! **************************************************************************************************
!> \brief Driver routine to diagonalize a FM matrix with the ELPA library.
!> \param matrix the matrix that is diagonalized
!> \param eigenvectors eigenvectors of the input matrix
!> \param eigenvalues eigenvalues of the input matrix
! **************************************************************************************************
   SUBROUTINE cp_fm_diag_elpa(matrix, eigenvectors, eigenvalues)
      TYPE(cp_fm_type), INTENT(IN)          :: matrix, eigenvectors
      REAL(kind=dp), DIMENSION(:), INTENT(OUT) :: eigenvalues
 
#if defined(__ELPA)
      CHARACTER(len=*), PARAMETER :: routinen = 'cp_fm_diag_elpa'
 
      INTEGER                                  :: handle
      TYPE(cp_fm_type)                         :: eigenvectors_new, matrix_new
      TYPE(cp_fm_redistribute_info)            :: rdinfo
 
      CALL timeset(routinen, handle)
 
      ! Determine if the input matrix needs to be redistributed before diagonalization.
      ! Heuristics are used to determine the optimal number of CPUs for diagonalization.
      ! The redistributed matrix is stored in matrix_new, which is just a pointer
      ! to the original matrix if no redistribution is required.
      ! With ELPA, we have to make sure that all processor columns have nonzero width
      CALL cp_fm_redistribute_start(matrix, eigenvectors, matrix_new, eigenvectors_new, &
                                    caller_is_elpa=.true., redist_info=rdinfo)
 
      ! Call ELPA on CPUs that hold the new matrix
      IF (ASSOCIATED(matrix_new%matrix_struct)) &
         CALL cp_fm_diag_elpa_base(matrix_new, eigenvectors_new, eigenvalues, rdinfo)
 
      ! Redistribute results and clean up
      CALL cp_fm_redistribute_end(matrix, eigenvectors, eigenvalues, matrix_new, eigenvectors_new)
 
      CALL timestop(handle)
#else
      mark_used(matrix)
      mark_used(eigenvectors)
      mark_used(eigenvalues)
 
      cpabort("CP2K compiled without the ELPA library.")
#endif
   END SUBROUTINE cp_fm_diag_elpa
 
#if defined(__ELPA)
! **************************************************************************************************
!> \brief Actual routine that calls ELPA to diagonalize a FM matrix.
!> \param matrix the matrix that is diagonalized
!> \param eigenvectors eigenvectors of the input matrix
!> \param eigenvalues eigenvalues of the input matrix
!> \param rdinfo ...
! **************************************************************************************************
   SUBROUTINE cp_fm_diag_elpa_base(matrix, eigenvectors, eigenvalues, rdinfo)
 
      TYPE(cp_fm_type), INTENT(IN)                       :: matrix, eigenvectors
      REAL(kind=dp), DIMENSION(:), INTENT(OUT)           :: eigenvalues
      TYPE(cp_fm_redistribute_info), INTENT(IN)          :: rdinfo
 
      CHARACTER(len=*), PARAMETER :: routinen = 'cp_fm_diag_elpa_base'
 
      INTEGER                                            :: handle
 
      CLASS(elpa_t), POINTER                   :: elpa_obj
      CHARACTER(len=default_string_length)     :: kernel_name
      TYPE(mp_comm_type) :: group
      INTEGER                                  :: i, &
                                                  mypcol, myprow, n, &
                                                  n_rows, n_cols, &
                                                  nblk, neig, io_unit, &
                                                  success
      LOGICAL                                  :: use_qr, check_eigenvalues
      REAL(kind=dp), DIMENSION(:), ALLOCATABLE :: eval, eval_noqr
      TYPE(cp_blacs_env_type), POINTER         :: context
      TYPE(cp_fm_type)                         :: matrix_noqr, eigenvectors_noqr
      TYPE(cp_logger_type), POINTER            :: logger
      REAL(kind=dp), PARAMETER                 :: th = 1.0e-14_dp
      INTEGER, DIMENSION(:), POINTER           :: ncol_locals
 
      CALL timeset(routinen, handle)
      NULLIFY (logger)
      NULLIFY (ncol_locals)
 
      check_eigenvalues = .false.
 
      logger => cp_get_default_logger()
      io_unit = cp_logger_get_default_io_unit(logger)
 
      n = matrix%matrix_struct%nrow_global
      context => matrix%matrix_struct%context
      group = matrix%matrix_struct%para_env
 
      myprow = context%mepos(1)
      mypcol = context%mepos(2)
 
      ! elpa needs the full matrix
      CALL cp_fm_uplo_to_full(matrix, eigenvectors)
 
      CALL cp_fm_struct_get(matrix%matrix_struct, &
                            local_leading_dimension=n_rows, &
                            ncol_local=n_cols, &
                            nrow_block=nblk, &
                            ncol_locals=ncol_locals)
 
      ! ELPA will fail in 'solve_tridi', with no useful error message, fail earlier
      IF (io_unit > 0 .AND. any(ncol_locals == 0)) THEN
         CALL rdinfo%write(io_unit)
         CALL cp_fm_write_info(matrix, io_unit)
         cpabort("ELPA [pre-fail]: Problem contains processor column with zero width.")
      END IF
 
      neig = SIZE(eigenvalues, 1)
      ! Decide if matrix is suitable for ELPA to use QR
      ! The definition of what is considered a suitable matrix depends on the ELPA version
      ! The relevant ELPA files to check are
      !     - Proper matrix order:  src/elpa2/elpa2_template.F90
      !     - Proper block size:    test/Fortran/test.F90
      ! Note that the names of these files might change in different ELPA versions
      ! Matrix order must be even
      use_qr = elpa_qr .AND. (modulo(n, 2) .EQ. 0)
      ! Matrix order and block size must be greater than or equal to 64
      IF (.NOT. elpa_qr_unsafe) &
         use_qr = use_qr .AND. (n .GE. 64) .AND. (nblk .GE. 64)
 
      ! Check if eigenvalues computed with ELPA_QR_UNSAFE should be verified
      IF (use_qr .AND. elpa_qr_unsafe .AND. elpa_should_print) &
         check_eigenvalues = .true.
 
      CALL matrix%matrix_struct%para_env%bcast(check_eigenvalues)
 
      IF (check_eigenvalues) THEN
         ! Allocate and initialize needed temporaries to compute eigenvalues without ELPA QR
         ALLOCATE (eval_noqr(n))
         CALL cp_fm_create(matrix=matrix_noqr, matrix_struct=matrix%matrix_struct)
         CALL cp_fm_to_fm(matrix, matrix_noqr)
         CALL cp_fm_create(matrix=eigenvectors_noqr, matrix_struct=eigenvectors%matrix_struct)
         CALL cp_fm_uplo_to_full(matrix_noqr, eigenvectors_noqr)
      END IF
 
      IF (io_unit > 0 .AND. elpa_should_print) THEN
         WRITE (unit=io_unit, fmt="(/,T2,A)") &
            "ELPA| Matrix diagonalization information"
 
         ! Find name for given kernel id.
         ! In case ELPA_2STAGE_REAL_DEFAULT was used it might not be in our elpa_kernel_ids list.
         kernel_name = "id: "//trim(adjustl(cp_to_string(elpa_kernel)))
         DO i = 1, SIZE(elpa_kernel_ids)
            IF (elpa_kernel_ids(i) == elpa_kernel) THEN
               kernel_name = elpa_kernel_names(i)
            END IF
         END DO
 
         WRITE (unit=io_unit, fmt="(T2,A,T71,I10)") &
            "ELPA| Matrix order (NA) ", n, &
            "ELPA| Matrix block size (NBLK) ", nblk, &
            "ELPA| Number of eigenvectors (NEV) ", neig, &
            "ELPA| Local rows (LOCAL_NROWS) ", n_rows, &
            "ELPA| Local columns (LOCAL_NCOLS) ", n_cols
         WRITE (unit=io_unit, fmt="(T2,A,T61,A20)") &
            "ELPA| Kernel ", adjustr(trim(kernel_name))
         IF (elpa_qr) THEN
            WRITE (unit=io_unit, fmt="(T2,A,T78,A3)") &
               "ELPA| QR step requested ", "YES"
         ELSE
            WRITE (unit=io_unit, fmt="(T2,A,T79,A2)") &
               "ELPA| QR step requested ", "NO"
         END IF
 
         IF (elpa_qr) THEN
            IF (elpa_qr_unsafe) THEN
               WRITE (unit=io_unit, fmt="(T2,A,T78,A3)") &
                  "ELPA| Use potentially unsafe QR ", "YES"
            ELSE
               WRITE (unit=io_unit, fmt="(T2,A,T79,A2)") &
                  "ELPA| Use potentially unsafe QR ", "NO"
            END IF
            IF (use_qr) THEN
               WRITE (unit=io_unit, fmt="(T2,A,T78,A3)") &
                  "ELPA| Matrix is suitable for QR ", "YES"
            ELSE
               WRITE (unit=io_unit, fmt="(T2,A,T79,A2)") &
                  "ELPA| Matrix is suitable for QR ", "NO"
            END IF
            IF (.NOT. use_qr) THEN
               IF (modulo(n, 2) /= 0) THEN
                  WRITE (unit=io_unit, fmt="(T2,A)") &
                     "ELPA| Matrix order is NOT even"
               END IF
               IF ((nblk < 64) .AND. (.NOT. elpa_qr_unsafe)) THEN
                  WRITE (unit=io_unit, fmt="(T2,A)") &
                     "ELPA| Matrix block size is NOT 64 or greater"
               END IF
            ELSE
               IF ((nblk < 64) .AND. elpa_qr_unsafe) THEN
                  WRITE (unit=io_unit, fmt="(T2,A)") &
                     "ELPA| Matrix block size check was bypassed"
               END IF
            END IF
         END IF
      END IF
 
      ! the full eigenvalues vector is needed
      ALLOCATE (eval(n))
 
      elpa_obj => elpa_allocate()
 
      CALL elpa_obj%set("na", n, success)
      cpassert(success == elpa_ok)
 
      CALL elpa_obj%set("nev", neig, success)
      cpassert(success == elpa_ok)
 
      CALL elpa_obj%set("local_nrows", n_rows, success)
      cpassert(success == elpa_ok)
 
      CALL elpa_obj%set("local_ncols", n_cols, success)
      cpassert(success == elpa_ok)
 
      CALL elpa_obj%set("nblk", nblk, success)
      cpassert(success == elpa_ok)
 
      CALL elpa_obj%set("mpi_comm_parent", group%get_handle(), success)
      cpassert(success == elpa_ok)
 
      CALL elpa_obj%set("process_row", myprow, success)
      cpassert(success == elpa_ok)
 
      CALL elpa_obj%set("process_col", mypcol, success)
      cpassert(success == elpa_ok)
 
      success = elpa_obj%setup()
      cpassert(success == elpa_ok)
 
      CALL elpa_obj%set("solver", elpa_solver_2stage, success)
      cpassert(success == elpa_ok)
 
      ! enabling the GPU must happen before setting the kernel
      IF (elpa_kernel == elpa_2stage_real_nvidia_gpu) THEN
         CALL elpa_obj%set("nvidia-gpu", 1, success)
         cpassert(success == elpa_ok)
      END IF
      IF (elpa_kernel == elpa_2stage_real_amd_gpu) THEN
         CALL elpa_obj%set("amd-gpu", 1, success)
         cpassert(success == elpa_ok)
      END IF
      IF (elpa_kernel == elpa_2stage_real_intel_gpu_sycl) THEN
         CALL elpa_obj%set("intel-gpu", 1, success)
         cpassert(success == elpa_ok)
      END IF
 
      CALL elpa_obj%set("real_kernel", elpa_kernel, success)
      cpwarn_if(success /= elpa_ok, "Setting real_kernel for ELPA failed")
 
      IF (use_qr) THEN
         CALL elpa_obj%set("qr", 1, success)
         cpassert(success == elpa_ok)
      END IF
 
      ! Set number of threads only when ELPA was built with OpenMP support.
      IF (elpa_obj%can_set("omp_threads", omp_get_max_threads()) == elpa_ok) THEN
         CALL elpa_obj%set("omp_threads", omp_get_max_threads(), success)
         cpassert(success == elpa_ok)
      END IF
 
      CALL elpa_obj%eigenvectors(matrix%local_data, eval, eigenvectors%local_data, success)
      IF (success /= elpa_ok) &
         cpabort("ELPA failed to diagonalize a matrix")
 
      IF (check_eigenvalues) THEN
         ! run again without QR
         CALL elpa_obj%set("qr", 0, success)
         cpassert(success == elpa_ok)
 
         CALL elpa_obj%eigenvectors(matrix_noqr%local_data, eval_noqr, eigenvectors_noqr%local_data, success)
         IF (success /= elpa_ok) &
            cpabort("ELPA failed to diagonalize a matrix even without QR decomposition")
 
         IF (any(abs(eval(1:neig) - eval_noqr(1:neig)) .GT. th)) &
            cpabort("Eigenvalues calculated with QR decomp. in ELPA are wrong. Disable ELPA_QR_UNSAFE.")
 
         DEALLOCATE (eval_noqr)
         CALL cp_fm_release(matrix_noqr)
         CALL cp_fm_release(eigenvectors_noqr)
      END IF
 
      CALL elpa_deallocate(elpa_obj, success)
      cpassert(success == elpa_ok)
 
      eigenvalues(1:neig) = eval(1:neig)
      DEALLOCATE (eval)
 
      CALL timestop(handle)
 
   END SUBROUTINE cp_fm_diag_elpa_base
#endif
 
END MODULE cp_fm_elpa