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FFTW's MPI interface also supports multi-dimensional DFTs of real cannam@95: data, similar to the serial r2c and c2r interfaces. (Parallel cannam@95: one-dimensional real-data DFTs are not currently supported; you must cannam@95: use a complex transform and set the imaginary parts of the inputs to cannam@95: zero.) cannam@95: cannam@95:
The key points to understand for r2c and c2r MPI transforms (compared cannam@95: to the MPI complex DFTs or the serial r2c/c2r transforms), are: cannam@95: cannam@95:
complex data, and then use the same distribution for the real cannam@95: data except that the last complex dimension is replaced by a (padded) cannam@95: real dimension of twice the length. cannam@95: cannam@95:
For example suppose we are performing an out-of-place r2c transform of cannam@95: L × M × N real data [padded to L × M × 2(N/2+1)], cannam@95: resulting in L × M × N/2+1 complex data. Similar to the cannam@95: example in 2d MPI example, we might do something like: cannam@95: cannam@95:
#include <fftw3-mpi.h>
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cannam@95: int main(int argc, char **argv)
cannam@95: {
cannam@95: const ptrdiff_t L = ..., M = ..., N = ...;
cannam@95: fftw_plan plan;
cannam@95: double *rin;
cannam@95: fftw_complex *cout;
cannam@95: ptrdiff_t alloc_local, local_n0, local_0_start, i, j, k;
cannam@95:
cannam@95: MPI_Init(&argc, &argv);
cannam@95: fftw_mpi_init();
cannam@95:
cannam@95: /* get local data size and allocate */
cannam@95: alloc_local = fftw_mpi_local_size_3d(L, M, N/2+1, MPI_COMM_WORLD,
cannam@95: &local_n0, &local_0_start);
cannam@95: rin = fftw_alloc_real(2 * alloc_local);
cannam@95: cout = fftw_alloc_complex(alloc_local);
cannam@95:
cannam@95: /* create plan for out-of-place r2c DFT */
cannam@95: plan = fftw_mpi_plan_dft_r2c_3d(L, M, N, rin, cout, MPI_COMM_WORLD,
cannam@95: FFTW_MEASURE);
cannam@95:
cannam@95: /* initialize rin to some function my_func(x,y,z) */
cannam@95: for (i = 0; i < local_n0; ++i)
cannam@95: for (j = 0; j < M; ++j)
cannam@95: for (k = 0; k < N; ++k)
cannam@95: rin[(i*M + j) * (2*(N/2+1)) + k] = my_func(local_0_start+i, j, k);
cannam@95:
cannam@95: /* compute transforms as many times as desired */
cannam@95: fftw_execute(plan);
cannam@95:
cannam@95: fftw_destroy_plan(plan);
cannam@95:
cannam@95: MPI_Finalize();
cannam@95: }
cannam@95:
cannam@95: Note that we allocated rin using fftw_alloc_real with an
cannam@95: argument of 2 * alloc_local: since alloc_local is the
cannam@95: number of complex values to allocate, the number of real
cannam@95: values is twice as many. The rin array is then
cannam@95: local_n0 × M × 2(N/2+1) in row-major order, so its
cannam@95: (i,j,k) element is at the index (i*M + j) * (2*(N/2+1)) +
cannam@95: k (see Multi-dimensional Array Format).
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As for the complex transforms, improved performance can be obtained by
cannam@95: specifying that the output is the transpose of the input or vice versa
cannam@95: (see Transposed distributions). In our L × M × N r2c
cannam@95: example, including FFTW_TRANSPOSED_OUT in the flags means that
cannam@95: the input would be a padded L × M × 2(N/2+1) real array
cannam@95: distributed over the L dimension, while the output would be a
cannam@95: M × L × N/2+1 complex array distributed over the M
cannam@95: dimension. To perform the inverse c2r transform with the same data
cannam@95: distributions, you would use the FFTW_TRANSPOSED_IN flag.
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