如果可能的话，如何进行 fftw3 MPI“转置”2D 变换？

Question

考虑 L x M（列主设置）形式的 2D 变换，从复杂数组src到实数数组tgt。或者，用 Fortranese 语言来说，

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

对应的指针是

type(C_PTR) :: csrc,ctgt   .

我会按以下方式分配它们：

  ! The complex array first
    alloc_local = fftw_mpi_local_size_2d(M,L/2+1,MPI_COMM_WORLD,local_M,local_offset1)
    csrc = fftw_alloc_complex(alloc_local)
    call c_f_pointer(csrc, src, [L/2,local_M])

    ! Now the real array
    alloc_local = fftw_mpi_local_size_2d(2*(L/2+1),M, &
                                   MPI_COMM_WORLD,local_L,local_offset2)
    ctgt = fftw_alloc_real(alloc_local)
    call c_f_pointer(ctgt, tgt, [M,local_L])

现在，该计划将创建为：

! Create c-->r transform with one transposition left out
plan =  fftw_mpi_plan_dft_c2r_2d(M,L,src,tgt, MPI_COMM_WORLD, & 
                                           ior(FFTW_MEASURE,FFTW_MPI_TRANSPOSED_OUT))

最后，变换将执行为：

call fftw_mpi_execute_dft_c2r(plan, src, tgt)

然而，这个方子并不起作用。最后一次调用导致分段错误。起初，我认为这可能与我分配src和tgt数组的方式有关，但使用分配给tgt的不同内存量并没有给出任何结果。所以，我要么在做一些非常愚蠢的事情，要么根本不可能做到。

编辑：简约的可编译示例

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(M,L/2+1, MPI_COMM_WORLD, &
       local_M, local_offset1)

  csrc = fftw_alloc_complex(alloc_local)
  call c_f_pointer(csrc, src, [L/2,local_M])


  alloc_local = fftw_mpi_local_size_2d(2*(L/2+1),M, MPI_COMM_WORLD, &
       &                               local_L, local_offset2)

  ctgt = fftw_alloc_real(alloc_local)
  call c_f_pointer(ctgt, tgt, [M,local_L])

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

  call fftw_mpi_execute_dft_c2r(plan, src, tgt)

  call mpi_finalize(ierr)


end program trashingfftw

Answer 1

答案是：

对于 mpi 实数变换，仅允许两种转置和方向组合：

• 实数到复数变换和 FFTW_MPI_TRANSPOSED_OUT
• 复杂到实数变换和 FFTW_MPI_TRANSPOSED_IN

我在挖掘 fftw3 版本时发现了这一点。3.3.4代码，文件“rdft2-problem.c”，注释在第120行。

编辑：

最小的可编译和工作示例：

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