FFTW 3.3.5: 2d MPI example

Before we document the FFTW MPI interface in detail, we begin with a Chris@42: simple example outlining how one would perform a two-dimensional Chris@42: N0 by N1 complex DFT. Chris@42:

Chris@42:

#include <fftw3-mpi.h>
Chris@42: 
Chris@42: int main(int argc, char **argv)
Chris@42: {
Chris@42:     const ptrdiff_t N0 = ..., N1 = ...;
Chris@42:     fftw_plan plan;
Chris@42:     fftw_complex *data;
Chris@42:     ptrdiff_t alloc_local, local_n0, local_0_start, i, j;
Chris@42: 
Chris@42:     MPI_Init(&argc, &argv);
Chris@42:     fftw_mpi_init();
Chris@42: 
Chris@42:     /* get local data size and allocate */
Chris@42:     alloc_local = fftw_mpi_local_size_2d(N0, N1, MPI_COMM_WORLD,
Chris@42:                                          &local_n0, &local_0_start);
Chris@42:     data = fftw_alloc_complex(alloc_local);
Chris@42: 
Chris@42:     /* create plan for in-place forward DFT */
Chris@42:     plan = fftw_mpi_plan_dft_2d(N0, N1, data, data, MPI_COMM_WORLD,
Chris@42:                                 FFTW_FORWARD, FFTW_ESTIMATE);    
Chris@42: 
Chris@42:     /* initialize data to some function my_function(x,y) */
Chris@42:     for (i = 0; i < local_n0; ++i) for (j = 0; j < N1; ++j)
Chris@42:        data[i*N1 + j] = my_function(local_0_start + i, j);
Chris@42: 
Chris@42:     /* compute transforms, in-place, as many times as desired */
Chris@42:     fftw_execute(plan);
Chris@42: 
Chris@42:     fftw_destroy_plan(plan);
Chris@42: 
Chris@42:     MPI_Finalize();
Chris@42: }
Chris@42:

As can be seen above, the MPI interface follows the same basic style Chris@42: of allocate/plan/execute/destroy as the serial FFTW routines. All of Chris@42: the MPI-specific routines are prefixed with ‘fftw_mpi_’ instead Chris@42: of ‘fftw_’. There are a few important differences, however: Chris@42:

First, we must call fftw_mpi_init() after calling Chris@42: MPI_Init (required in all MPI programs) and before calling any Chris@42: other ‘fftw_mpi_’ routine. Chris@42: Chris@42: Chris@42:

Second, when we create the plan with fftw_mpi_plan_dft_2d, Chris@42: analogous to fftw_plan_dft_2d, we pass an additional argument: Chris@42: the communicator, indicating which processes will participate in the Chris@42: transform (here MPI_COMM_WORLD, indicating all processes). Chris@42: Whenever you create, execute, or destroy a plan for an MPI transform, Chris@42: you must call the corresponding FFTW routine on all processes Chris@42: in the communicator for that transform. (That is, these are Chris@42: collective calls.) Note that the plan for the MPI transform Chris@42: uses the standard fftw_execute and fftw_destroy routines Chris@42: (on the other hand, there are MPI-specific new-array execute functions Chris@42: documented below). Chris@42: Chris@42: Chris@42: Chris@42:

Third, all of the FFTW MPI routines take ptrdiff_t arguments Chris@42: instead of int as for the serial FFTW. ptrdiff_t is a Chris@42: standard C integer type which is (at least) 32 bits wide on a 32-bit Chris@42: machine and 64 bits wide on a 64-bit machine. This is to make it easy Chris@42: to specify very large parallel transforms on a 64-bit machine. (You Chris@42: can specify 64-bit transform sizes in the serial FFTW, too, but only Chris@42: by using the ‘guru64’ planner interface. See 64-bit Guru Interface.) Chris@42: Chris@42: Chris@42:

Fourth, and most importantly, you don’t allocate the entire Chris@42: two-dimensional array on each process. Instead, you call Chris@42: fftw_mpi_local_size_2d to find out what portion of the Chris@42: array resides on each processor, and how much space to allocate. Chris@42: Here, the portion of the array on each process is a local_n0 by Chris@42: N1 slice of the total array, starting at index Chris@42: local_0_start. The total number of fftw_complex numbers Chris@42: to allocate is given by the alloc_local return value, which Chris@42: may be greater than local_n0 * N1 (in case some Chris@42: intermediate calculations require additional storage). The data Chris@42: distribution in FFTW’s MPI interface is described in more detail by Chris@42: the next section. Chris@42: Chris@42: Chris@42:

Given the portion of the array that resides on the local process, it Chris@42: is straightforward to initialize the data (here to a function Chris@42: myfunction) and otherwise manipulate it. Of course, at the end Chris@42: of the program you may want to output the data somehow, but Chris@42: synchronizing this output is up to you and is beyond the scope of this Chris@42: manual. (One good way to output a large multi-dimensional distributed Chris@42: array in MPI to a portable binary file is to use the free HDF5 Chris@42: library; see the HDF home page.) Chris@42: Chris@42: Chris@42:

6.3 2d MPI example