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6.13 FFTW MPI Fortran Interface

The FFTW MPI interface is callable from modern Fortran compilers supporting the Fortran 2003 iso_c_binding standard for calling C functions. As described in Calling FFTW from Modern Fortran, this means that you can directly call FFTW’s C interface from Fortran with only minor changes in syntax. There are, however, a few things specific to the MPI interface to keep in mind:

For example, here is a Fortran code snippet to perform a distributed L × M complex DFT in-place. (This assumes you have already initialized MPI with MPI_init and have also performed call fftw_mpi_init.)

  use, intrinsic :: iso_c_binding
  include 'fftw3-mpi.f03'
  integer(C_INTPTR_T), parameter :: L = ...
  integer(C_INTPTR_T), parameter :: M = ...
  type(C_PTR) :: plan, cdata
  complex(C_DOUBLE_COMPLEX), pointer :: data(:,:)
  integer(C_INTPTR_T) :: i, j, alloc_local, local_M, local_j_offset

!   get local data size and allocate (note dimension reversal)
  alloc_local = fftw_mpi_local_size_2d(M, L, MPI_COMM_WORLD, &
                                       local_M, local_j_offset)
  cdata = fftw_alloc_complex(alloc_local)
  call c_f_pointer(cdata, data, [L,local_M])

!   create MPI plan for in-place forward DFT (note dimension reversal)
  plan = fftw_mpi_plan_dft_2d(M, L, data, data, MPI_COMM_WORLD, &
                              FFTW_FORWARD, FFTW_MEASURE)

! initialize data to some function my_function(i,j)
  do j = 1, local_M
    do i = 1, L
      data(i, j) = my_function(i, j + local_j_offset)
    end do
  end do

! compute transform (as many times as desired)
  call fftw_mpi_execute_dft(plan, data, data)

  call fftw_destroy_plan(plan)
  call fftw_free(cdata)

Note that when we called fftw_mpi_local_size_2d and fftw_mpi_plan_dft_2d with the dimensions in reversed order, since a L × M Fortran array is viewed by FFTW in C as a M × L array. This means that the array was distributed over the M dimension, the local portion of which is a L × local_M array in Fortran. (You must not use an allocate statement to allocate an L × local_M array, however; you must allocate alloc_local complex numbers, which may be greater than L * local_M, in order to reserve space for intermediate steps of the transform.) Finally, we mention that because C’s array indices are zero-based, the local_j_offset argument can conveniently be interpreted as an offset in the 1-based j index (rather than as a starting index as in C).

If instead you had used the ior(FFTW_MEASURE, FFTW_MPI_TRANSPOSED_OUT) flag, the output of the transform would be a transposed M × local_L array, associated with the same cdata allocation (since the transform is in-place), and which you could declare with:

  complex(C_DOUBLE_COMPLEX), pointer :: tdata(:,:)
  ...
  call c_f_pointer(cdata, tdata, [M,local_L])

where local_L would have been obtained by changing the fftw_mpi_local_size_2d call to:

  alloc_local = fftw_mpi_local_size_2d_transposed(M, L, MPI_COMM_WORLD, &
                           local_M, local_j_offset, local_L, local_i_offset)

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