cannam@95: Next: FFTW Fortran type reference, cannam@95: Previous: Overview of Fortran interface, cannam@95: Up: Calling FFTW from Modern Fortran cannam@95:
A minor annoyance in calling FFTW from Fortran is that FFTW's array cannam@95: dimensions are defined in the C convention (row-major order), while cannam@95: Fortran's array dimensions are the opposite convention (column-major cannam@95: order). See Multi-dimensional Array Format. This is just a cannam@95: bookkeeping difference, with no effect on performance. The only cannam@95: consequence of this is that, whenever you create an FFTW plan for a cannam@95: multi-dimensional transform, you must always reverse the cannam@95: ordering of the dimensions. cannam@95: cannam@95:
For example, consider the three-dimensional (L × M × N) arrays: cannam@95: cannam@95:
complex(C_DOUBLE_COMPLEX), dimension(L,M,N) :: in, out cannam@95:cannam@95:
To plan a DFT for these arrays using fftw_plan_dft_3d, you could do:
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plan = fftw_plan_dft_3d(N,M,L, in,out, FFTW_FORWARD,FFTW_ESTIMATE) cannam@95:cannam@95:
That is, from FFTW's perspective this is a N × M × L array.
cannam@95: No data transposition need occur, as this is only
cannam@95: notation. Similarly, to use the more generic routine
cannam@95: fftw_plan_dft with the same arrays, you could do:
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integer(C_INT), dimension(3) :: n = [N,M,L] cannam@95: plan = fftw_plan_dft_3d(3, n, in,out, FFTW_FORWARD,FFTW_ESTIMATE) cannam@95:cannam@95:
Note, by the way, that this is different from the legacy Fortran cannam@95: interface (see Fortran-interface routines), which automatically cannam@95: reverses the order of the array dimension for you. Here, you are cannam@95: calling the C interface directly, so there is no “translation” layer. cannam@95: cannam@95:
An important thing to keep in mind is the implication of this for cannam@95: multidimensional real-to-complex transforms (see Multi-Dimensional DFTs of Real Data). In C, a multidimensional real-to-complex DFT cannam@95: chops the last dimension roughly in half (N × M × L real input cannam@95: goes to N × M × L/2+1 complex output). In Fortran, because cannam@95: the array dimension notation is reversed, the first dimension of cannam@95: the complex data is chopped roughly in half. For example consider the cannam@95: ‘r2c’ transform of L × M × N real input in Fortran: cannam@95: cannam@95:
type(C_PTR) :: plan cannam@95: real(C_DOUBLE), dimension(L,M,N) :: in cannam@95: complex(C_DOUBLE_COMPLEX), dimension(L/2+1,M,N) :: out cannam@95: plan = fftw_plan_dft_r2c_3d(N,M,L, in,out, FFTW_ESTIMATE) cannam@95: ... cannam@95: call fftw_execute_dft_r2c(plan, in, out) cannam@95:cannam@95:
Alternatively, for an in-place r2c transform, as described in the C cannam@95: documentation we must pad the first dimension of the cannam@95: real input with an extra two entries (which are ignored by FFTW) so as cannam@95: to leave enough space for the complex output. The input is cannam@95: allocated as a 2[L/2+1] × M × N array, even though only cannam@95: L × M × N of it is actually used. In this example, we will cannam@95: allocate the array as a pointer type, using ‘fftw_alloc’ to cannam@95: ensure aligned memory for maximum performance (see Allocating aligned memory in Fortran); this also makes it easy to reference the cannam@95: same memory as both a real array and a complex array. cannam@95: cannam@95:
real(C_DOUBLE), pointer :: in(:,:,:) cannam@95: complex(C_DOUBLE_COMPLEX), pointer :: out(:,:,:) cannam@95: type(C_PTR) :: plan, data cannam@95: data = fftw_alloc_complex(int((L/2+1) * M * N, C_SIZE_T)) cannam@95: call c_f_pointer(data, in, [2*(L/2+1),M,N]) cannam@95: call c_f_pointer(data, out, [L/2+1,M,N]) cannam@95: plan = fftw_plan_dft_r2c_3d(N,M,L, in,out, FFTW_ESTIMATE) cannam@95: ... cannam@95: call fftw_execute_dft_r2c(plan, in, out) cannam@95: ... cannam@95: call fftw_destroy_plan(plan) cannam@95: call fftw_free(data) cannam@95:cannam@95: cannam@95: cannam@95: