Chris@19: Chris@19: Chris@19: Transposed distributions - FFTW 3.3.4 Chris@19: Chris@19: Chris@19: Chris@19: Chris@19: Chris@19: Chris@19: Chris@19: Chris@19: Chris@19: Chris@19: Chris@19: Chris@19: Chris@19:
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6.4.3 Transposed distributions

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Internally, FFTW's MPI transform algorithms work by first computing Chris@19: transforms of the data local to each process, then by globally Chris@19: transposing the data in some fashion to redistribute the data Chris@19: among the processes, transforming the new data local to each process, Chris@19: and transposing back. For example, a two-dimensional n0 by Chris@19: n1 array, distributed across the n0 dimension, is Chris@19: transformd by: (i) transforming the n1 dimension, which are Chris@19: local to each process; (ii) transposing to an n1 by n0 Chris@19: array, distributed across the n1 dimension; (iii) transforming Chris@19: the n0 dimension, which is now local to each process; (iv) Chris@19: transposing back. Chris@19: Chris@19: Chris@19:

However, in many applications it is acceptable to compute a Chris@19: multidimensional DFT whose results are produced in transposed order Chris@19: (e.g., n1 by n0 in two dimensions). This provides a Chris@19: significant performance advantage, because it means that the final Chris@19: transposition step can be omitted. FFTW supports this optimization, Chris@19: which you specify by passing the flag FFTW_MPI_TRANSPOSED_OUT Chris@19: to the planner routines. To compute the inverse transform of Chris@19: transposed output, you specify FFTW_MPI_TRANSPOSED_IN to tell Chris@19: it that the input is transposed. In this section, we explain how to Chris@19: interpret the output format of such a transform. Chris@19: Chris@19: Chris@19:

Suppose you have are transforming multi-dimensional data with (at Chris@19: least two) dimensions n0 × n1 × n2 × … × nd-1. As always, it is distributed along Chris@19: the first dimension n0. Now, if we compute its DFT with the Chris@19: FFTW_MPI_TRANSPOSED_OUT flag, the resulting output data are stored Chris@19: with the first two dimensions transposed: n1 × n0 × n2 ×…× nd-1, Chris@19: distributed along the n1 dimension. Conversely, if we take the Chris@19: n1 × n0 × n2 ×…× nd-1 data and transform it with the Chris@19: FFTW_MPI_TRANSPOSED_IN flag, then the format goes back to the Chris@19: original n0 × n1 × n2 × … × nd-1 array. Chris@19: Chris@19:

There are two ways to find the portion of the transposed array that Chris@19: resides on the current process. First, you can simply call the Chris@19: appropriate ‘local_size’ function, passing n1 × n0 × n2 ×…× nd-1 (the Chris@19: transposed dimensions). This would mean calling the ‘local_size’ Chris@19: function twice, once for the transposed and once for the Chris@19: non-transposed dimensions. Alternatively, you can call one of the Chris@19: ‘local_size_transposed’ functions, which returns both the Chris@19: non-transposed and transposed data distribution from a single call. Chris@19: For example, for a 3d transform with transposed output (or input), you Chris@19: might call: Chris@19: Chris@19: 

     ptrdiff_t fftw_mpi_local_size_3d_transposed(
Chris@19:                      ptrdiff_t n0, ptrdiff_t n1, ptrdiff_t n2, MPI_Comm comm,
Chris@19:                      ptrdiff_t *local_n0, ptrdiff_t *local_0_start,
Chris@19:                      ptrdiff_t *local_n1, ptrdiff_t *local_1_start);
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Chris@19: Here, local_n0 and local_0_start give the size and Chris@19: starting index of the n0 dimension for the Chris@19: non-transposed data, as in the previous sections. For Chris@19: transposed data (e.g. the output for Chris@19: FFTW_MPI_TRANSPOSED_OUT), local_n1 and Chris@19: local_1_start give the size and starting index of the n1 Chris@19: dimension, which is the first dimension of the transposed data Chris@19: (n1 by n0 by n2). Chris@19: Chris@19:

(Note that FFTW_MPI_TRANSPOSED_IN is completely equivalent to Chris@19: performing FFTW_MPI_TRANSPOSED_OUT and passing the first two Chris@19: dimensions to the planner in reverse order, or vice versa. If you Chris@19: pass both the FFTW_MPI_TRANSPOSED_IN and Chris@19: FFTW_MPI_TRANSPOSED_OUT flags, it is equivalent to swapping the Chris@19: first two dimensions passed to the planner and passing neither Chris@19: flag.) Chris@19: Chris@19: Chris@19: