How to do a fftw3 MPI “transposed” 2D transform if possible at all?

Question

Consider a 2D transform of the form L x M (column major setup), from a complex array src to a real array tgt. Or , in Fortranese,

complex(C         


        

Answer 1

And the answer is:

For mpi real transforms, there are only two allowed combinations of transpositions and directions:

• real to complex transform and FFTW_MPI_TRANSPOSED_OUT
• complex to real transform and FFTW_MPI_TRANSPOSED_IN

I have found this while digging inside the fftw3 ver. 3.3.4 code, file "rdft2-problem.c", comment on the line 120.

EDIT:

MINIMAL COMPILABLE AND WORKING EXAMPLE:

program trashingfftw
  use, intrinsic :: iso_c_binding
  use MPI

  implicit none
  include 'fftw3-mpi.f03'

  integer(C_INTPTR_T), parameter :: L = 256
  integer(C_INTPTR_T), parameter :: M = 256

  type(C_PTR) :: plan, ctgt, csrc

  complex(C_DOUBLE_COMPLEX), pointer :: src(:,:)
  real(8), pointer :: tgt(:,:)

  integer(C_INTPTR_T) :: alloc_local, local_M, &
                         & local_L,local_offset1,local_offset2

  integer :: ierr,id


  call mpi_init(ierr)

  call mpi_comm_rank(MPI_COMM_WORLD,id,ierr)

  call fftw_mpi_init()


  alloc_local = fftw_mpi_local_size_2d(L/2+1,M, MPI_COMM_WORLD, &
       local_l, local_offset1)

  print *, id, "alloc complex=",alloc_local, local_l

  csrc = fftw_alloc_complex(alloc_local)
  call c_f_pointer(csrc, src, [M,local_l])

  !Caveat: Must partition the real storage according to complex layout, this is why
  ! I am using M and L/2+1 instead of M, 2*(L/2+1) as it was done in the original post
  alloc_local = fftw_mpi_local_size_2d(M,L/2+1, MPI_COMM_WORLD, &
      &                               local_M, local_offset2)

  print *, id, "alloc real=",alloc_local, local_m
  ! Two reals per complex
  ctgt = fftw_alloc_real(2*alloc_local)
  ! Only the first L are relevant, the rest is just dangling space (see fftw3 docs) 
  !caveat: since the padding is in the first index, the 2d data is laid out non-contiguously 
  !(L sensible reals, padding, padding, L sensible reals, padding, padding, ....)
  call c_f_pointer(ctgt, tgt, [2*(L/2+1),local_m])


  plan =  fftw_mpi_plan_dft_c2r_2d(M,L,src,tgt, MPI_COMM_WORLD, & 
       ior(FFTW_MEASURE, FFTW_MPI_TRANSPOSED_IN))

  ! Should be non-null
  print *, 'plan:', plan

  src(3,2)=(1.,0)
  call fftw_mpi_execute_dft_c2r(plan, src, tgt) 

  call mpi_finalize(ierr)
end program thrashingfftw