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Chris@10: The most important concept to understand in using FFTW's MPI interface Chris@10: is the data distribution. With a serial or multithreaded FFT, all of Chris@10: the inputs and outputs are stored as a single contiguous chunk of Chris@10: memory. With a distributed-memory FFT, the inputs and outputs are Chris@10: broken into disjoint blocks, one per process. Chris@10: Chris@10:
In particular, FFTW uses a 1d block distribution of the data, Chris@10: distributed along the first dimension. For example, if you Chris@10: want to perform a 100 × 200 complex DFT, distributed over 4 Chris@10: processes, each process will get a 25 × 200 slice of the data. Chris@10: That is, process 0 will get rows 0 through 24, process 1 will get rows Chris@10: 25 through 49, process 2 will get rows 50 through 74, and process 3 Chris@10: will get rows 75 through 99. If you take the same array but Chris@10: distribute it over 3 processes, then it is not evenly divisible so the Chris@10: different processes will have unequal chunks. FFTW's default choice Chris@10: in this case is to assign 34 rows to processes 0 and 1, and 32 rows to Chris@10: process 2. Chris@10: Chris@10: Chris@10:
FFTW provides several ‘fftw_mpi_local_size’ routines that you can
Chris@10: call to find out what portion of an array is stored on the current
Chris@10: process. In most cases, you should use the default block sizes picked
Chris@10: by FFTW, but it is also possible to specify your own block size. For
Chris@10: example, with a 100 × 200 array on three processes, you can
Chris@10: tell FFTW to use a block size of 40, which would assign 40 rows to
Chris@10: processes 0 and 1, and 20 rows to process 2. FFTW's default is to
Chris@10: divide the data equally among the processes if possible, and as best
Chris@10: it can otherwise. The rows are always assigned in “rank order,”
Chris@10: i.e. process 0 gets the first block of rows, then process 1, and so
Chris@10: on. (You can change this by using MPI_Comm_split to create a
Chris@10: new communicator with re-ordered processes.) However, you should
Chris@10: always call the ‘fftw_mpi_local_size’ routines, if possible,
Chris@10: rather than trying to predict FFTW's distribution choices.
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In particular, it is critical that you allocate the storage size that Chris@10: is returned by ‘fftw_mpi_local_size’, which is not Chris@10: necessarily the size of the local slice of the array. The reason is Chris@10: that intermediate steps of FFTW's algorithms involve transposing the Chris@10: array and redistributing the data, so at these intermediate steps FFTW Chris@10: may require more local storage space (albeit always proportional to Chris@10: the total size divided by the number of processes). The Chris@10: ‘fftw_mpi_local_size’ functions know how much storage is required Chris@10: for these intermediate steps and tell you the correct amount to Chris@10: allocate. Chris@10: Chris@10:
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