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cannam@95: The most important concept to understand in using FFTW's MPI interface cannam@95: is the data distribution. With a serial or multithreaded FFT, all of cannam@95: the inputs and outputs are stored as a single contiguous chunk of cannam@95: memory. With a distributed-memory FFT, the inputs and outputs are cannam@95: broken into disjoint blocks, one per process. cannam@95: cannam@95:
In particular, FFTW uses a 1d block distribution of the data, cannam@95: distributed along the first dimension. For example, if you cannam@95: want to perform a 100 × 200 complex DFT, distributed over 4 cannam@95: processes, each process will get a 25 × 200 slice of the data. cannam@95: That is, process 0 will get rows 0 through 24, process 1 will get rows cannam@95: 25 through 49, process 2 will get rows 50 through 74, and process 3 cannam@95: will get rows 75 through 99. If you take the same array but cannam@95: distribute it over 3 processes, then it is not evenly divisible so the cannam@95: different processes will have unequal chunks. FFTW's default choice cannam@95: in this case is to assign 34 rows to processes 0 and 1, and 32 rows to cannam@95: process 2. cannam@95: cannam@95: cannam@95:
FFTW provides several ‘fftw_mpi_local_size’ routines that you can
cannam@95: call to find out what portion of an array is stored on the current
cannam@95: process. In most cases, you should use the default block sizes picked
cannam@95: by FFTW, but it is also possible to specify your own block size. For
cannam@95: example, with a 100 × 200 array on three processes, you can
cannam@95: tell FFTW to use a block size of 40, which would assign 40 rows to
cannam@95: processes 0 and 1, and 20 rows to process 2. FFTW's default is to
cannam@95: divide the data equally among the processes if possible, and as best
cannam@95: it can otherwise. The rows are always assigned in “rank order,”
cannam@95: i.e. process 0 gets the first block of rows, then process 1, and so
cannam@95: on. (You can change this by using MPI_Comm_split to create a
cannam@95: new communicator with re-ordered processes.) However, you should
cannam@95: always call the ‘fftw_mpi_local_size’ routines, if possible,
cannam@95: 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 cannam@95: is returned by ‘fftw_mpi_local_size’, which is not cannam@95: necessarily the size of the local slice of the array. The reason is cannam@95: that intermediate steps of FFTW's algorithms involve transposing the cannam@95: array and redistributing the data, so at these intermediate steps FFTW cannam@95: may require more local storage space (albeit always proportional to cannam@95: the total size divided by the number of processes). The cannam@95: ‘fftw_mpi_local_size’ functions know how much storage is required cannam@95: for these intermediate steps and tell you the correct amount to cannam@95: allocate. cannam@95: cannam@95:
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