Other Multi-dimensional Real-data MPI Transforms

cannam@95: cannam@95: cannam@95: Other Multi-dimensional Real-data MPI Transforms - FFTW 3.3.3 cannam@95: cannam@95: cannam@95: cannam@95: cannam@95: cannam@95: cannam@95: cannam@95: cannam@95: cannam@95: cannam@95: cannam@95: cannam@95: cannam@95:

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6.6 Other multi-dimensional Real-Data MPI Transforms

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FFTW's MPI interface also supports multi-dimensional ‘r2r’ cannam@95: transforms of all kinds supported by the serial interface cannam@95: (e.g. discrete cosine and sine transforms, discrete Hartley cannam@95: transforms, etc.). Only multi-dimensional ‘r2r’ transforms, not cannam@95: one-dimensional transforms, are currently parallelized. cannam@95: cannam@95:

These are used much like the multidimensional complex DFTs discussed cannam@95: above, except that the data is real rather than complex, and one needs cannam@95: to pass an r2r transform kind (fftw_r2r_kind) for each cannam@95: dimension as in the serial FFTW (see More DFTs of Real Data). cannam@95: cannam@95:

For example, one might perform a two-dimensional L × M that is cannam@95: an REDFT10 (DCT-II) in the first dimension and an RODFT10 (DST-II) in cannam@95: the second dimension with code like: cannam@95: cannam@95:

         const ptrdiff_t L = ..., M = ...;
cannam@95:          fftw_plan plan;
cannam@95:          double *data;
cannam@95:          ptrdiff_t alloc_local, local_n0, local_0_start, i, j;
cannam@95:      
cannam@95:          /* get local data size and allocate */
cannam@95:          alloc_local = fftw_mpi_local_size_2d(L, M, MPI_COMM_WORLD,
cannam@95:                                               &local_n0, &local_0_start);
cannam@95:          data = fftw_alloc_real(alloc_local);
cannam@95:      
cannam@95:          /* create plan for in-place REDFT10 x RODFT10 */
cannam@95:          plan = fftw_mpi_plan_r2r_2d(L, M, data, data, MPI_COMM_WORLD,
cannam@95:                                      FFTW_REDFT10, FFTW_RODFT10, FFTW_MEASURE);
cannam@95:      
cannam@95:          /* initialize data to some function my_function(x,y) */
cannam@95:          for (i = 0; i < local_n0; ++i) for (j = 0; j < M; ++j)
cannam@95:             data[i*M + j] = my_function(local_0_start + i, j);
cannam@95:      
cannam@95:          /* compute transforms, in-place, as many times as desired */
cannam@95:          fftw_execute(plan);
cannam@95:      
cannam@95:          fftw_destroy_plan(plan);
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Notice that we use the same ‘local_size’ functions as we did for cannam@95: complex data, only now we interpret the sizes in terms of real rather cannam@95: than complex values, and correspondingly use fftw_alloc_real. cannam@95: cannam@95: cannam@95: cannam@95: