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#### 6.12.4 MPI Data Distribution Functions

As described above (see MPI Data Distribution), in order to allocate your arrays, before creating a plan, you must first call one of the following routines to determine the required allocation size and the portion of the array locally stored on a given process. The `MPI_Comm` communicator passed here must be equivalent to the communicator used below for plan creation.

The basic interface for multidimensional transforms consists of the functions:

    ptrdiff_t fftw_mpi_local_size_2d(ptrdiff_t n0, ptrdiff_t n1, MPI_Comm comm,
                                     ptrdiff_t *local_n0, ptrdiff_t *local_0_start);
    ptrdiff_t fftw_mpi_local_size_3d(ptrdiff_t n0, ptrdiff_t n1, ptrdiff_t n2,
                                     MPI_Comm comm,
                                     ptrdiff_t *local_n0, ptrdiff_t *local_0_start);
    ptrdiff_t fftw_mpi_local_size(int rnk, const ptrdiff_t *n, MPI_Comm comm,
                                  ptrdiff_t *local_n0, ptrdiff_t *local_0_start);

    ptrdiff_t fftw_mpi_local_size_2d_transposed(ptrdiff_t n0, ptrdiff_t n1, MPI_Comm comm,
                                                ptrdiff_t *local_n0, ptrdiff_t *local_0_start,
                                                ptrdiff_t *local_n1, ptrdiff_t *local_1_start);
    ptrdiff_t fftw_mpi_local_size_3d_transposed(ptrdiff_t n0, ptrdiff_t n1, ptrdiff_t n2,
                                                MPI_Comm comm,
                                                ptrdiff_t *local_n0, ptrdiff_t *local_0_start,
                                                ptrdiff_t *local_n1, ptrdiff_t *local_1_start);
    ptrdiff_t fftw_mpi_local_size_transposed(int rnk, const ptrdiff_t *n, MPI_Comm comm,
                                             ptrdiff_t *local_n0, ptrdiff_t *local_0_start,
                                             ptrdiff_t *local_n1, ptrdiff_t *local_1_start);

These functions return the number of elements to allocate (complex numbers for DFT/r2c/c2r plans, real numbers for r2r plans), whereas the `local_n0` and `local_0_start` return the portion (`local_0_start` to `local_0_start + local_n0 - 1`) of the first dimension of an n0 × n1 × n2 × … × nd-1 array that is stored on the local process. See Basic and advanced distribution interfaces. For `FFTW_MPI_TRANSPOSED_OUT` plans, the ‘`_transposed`’ variants are useful in order to also return the local portion of the first dimension in the n1 × n0 × n2 ×…× nd-1 transposed output. See Transposed distributions. The advanced interface for multidimensional transforms is:

    ptrdiff_t fftw_mpi_local_size_many(int rnk, const ptrdiff_t *n, ptrdiff_t howmany,
                                       ptrdiff_t block0, MPI_Comm comm,
                                       ptrdiff_t *local_n0, ptrdiff_t *local_0_start);
    ptrdiff_t fftw_mpi_local_size_many_transposed(int rnk, const ptrdiff_t *n, ptrdiff_t howmany,
                                                  ptrdiff_t block0, ptrdiff_t block1, MPI_Comm comm,
                                                  ptrdiff_t *local_n0, ptrdiff_t *local_0_start,
                                                  ptrdiff_t *local_n1, ptrdiff_t *local_1_start);

These differ from the basic interface in only two ways. First, they allow you to specify block sizes `block0` and `block1` (the latter for the transposed output); you can pass `FFTW_MPI_DEFAULT_BLOCK` to use FFTW’s default block size as in the basic interface. Second, you can pass a `howmany` parameter, corresponding to the advanced planning interface below: this is for transforms of contiguous `howmany`-tuples of numbers (`howmany = 1` in the basic interface).

The corresponding basic and advanced routines for one-dimensional transforms (currently only complex DFTs) are:

    ptrdiff_t fftw_mpi_local_size_1d(
                 ptrdiff_t n0, MPI_Comm comm, int sign, unsigned flags,
                 ptrdiff_t *local_ni, ptrdiff_t *local_i_start,
                 ptrdiff_t *local_no, ptrdiff_t *local_o_start);
    ptrdiff_t fftw_mpi_local_size_many_1d(
                 ptrdiff_t n0, ptrdiff_t howmany,
                 MPI_Comm comm, int sign, unsigned flags,
                 ptrdiff_t *local_ni, ptrdiff_t *local_i_start,
                 ptrdiff_t *local_no, ptrdiff_t *local_o_start);

As above, the return value is the number of elements to allocate (complex numbers, for complex DFTs). The `local_ni` and `local_i_start` arguments return the portion (`local_i_start` to `local_i_start + local_ni - 1`) of the 1d array that is stored on this process for the transform input, and `local_no` and `local_o_start` are the corresponding quantities for the input. The `sign` (`FFTW_FORWARD` or `FFTW_BACKWARD`) and `flags` must match the arguments passed when creating a plan. Although the inputs and outputs have different data distributions in general, it is guaranteed that the output data distribution of an `FFTW_FORWARD` plan will match the input data distribution of an `FFTW_BACKWARD` plan and vice versa; similarly for the `FFTW_MPI_SCRAMBLED_OUT` and `FFTW_MPI_SCRAMBLED_IN` flags. See One-dimensional distributions.

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