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Multi-dimensional transforms work much the same way as one-dimensional
Chris@10: transforms: you allocate arrays of fftw_complex (preferably
Chris@10: using fftw_malloc), create an fftw_plan, execute it as
Chris@10: many times as you want with fftw_execute(plan), and clean up
Chris@10: with fftw_destroy_plan(plan) (and fftw_free).
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FFTW provides two routines for creating plans for 2d and 3d transforms, Chris@10: and one routine for creating plans of arbitrary dimensionality. Chris@10: The 2d and 3d routines have the following signature: Chris@10:
fftw_plan fftw_plan_dft_2d(int n0, int n1, Chris@10: fftw_complex *in, fftw_complex *out, Chris@10: int sign, unsigned flags); Chris@10: fftw_plan fftw_plan_dft_3d(int n0, int n1, int n2, Chris@10: fftw_complex *in, fftw_complex *out, Chris@10: int sign, unsigned flags); Chris@10:Chris@10:
Chris@10: These routines create plans for n0 by n1 two-dimensional
Chris@10: (2d) transforms and n0 by n1 by n2 3d transforms,
Chris@10: respectively. All of these transforms operate on contiguous arrays in
Chris@10: the C-standard row-major order, so that the last dimension has the
Chris@10: fastest-varying index in the array. This layout is described further in
Chris@10: Multi-dimensional Array Format.
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FFTW can also compute transforms of higher dimensionality. In order to Chris@10: avoid confusion between the various meanings of the the word Chris@10: “dimension”, we use the term rank Chris@10: to denote the number of independent indices in an array.1 For Chris@10: example, we say that a 2d transform has rank 2, a 3d transform has Chris@10: rank 3, and so on. You can plan transforms of arbitrary rank by Chris@10: means of the following function: Chris@10: Chris@10:
fftw_plan fftw_plan_dft(int rank, const int *n, Chris@10: fftw_complex *in, fftw_complex *out, Chris@10: int sign, unsigned flags); Chris@10:Chris@10:
Chris@10: Here, n is a pointer to an array n[rank] denoting an
Chris@10: n[0] by n[1] by ... by n[rank-1] transform.
Chris@10: Thus, for example, the call
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fftw_plan_dft_2d(n0, n1, in, out, sign, flags); Chris@10:Chris@10:
is equivalent to the following code fragment: Chris@10:
int n[2]; Chris@10: n[0] = n0; Chris@10: n[1] = n1; Chris@10: fftw_plan_dft(2, n, in, out, sign, flags); Chris@10:Chris@10:
fftw_plan_dft is not restricted to 2d and 3d transforms,
Chris@10: however, but it can plan transforms of arbitrary rank.
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You may have noticed that all the planner routines described so far
Chris@10: have overlapping functionality. For example, you can plan a 1d or 2d
Chris@10: transform by using fftw_plan_dft with a rank of 1
Chris@10: or 2, or even by calling fftw_plan_dft_3d with n0
Chris@10: and/or n1 equal to 1 (with no loss in efficiency). This
Chris@10: pattern continues, and FFTW's planning routines in general form a
Chris@10: “partial order,” sequences of
Chris@10: interfaces with strictly increasing generality but correspondingly
Chris@10: greater complexity.
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fftw_plan_dft is the most general complex-DFT routine that we
Chris@10: describe in this tutorial, but there are also the advanced and guru interfaces,
Chris@10: which allow one to efficiently combine multiple/strided transforms
Chris@10: into a single FFTW plan, transform a subset of a larger
Chris@10: multi-dimensional array, and/or to handle more general complex-number
Chris@10: formats. For more information, see FFTW Reference.
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[1] The Chris@10: term “rank” is commonly used in the APL, FORTRAN, and Common Lisp Chris@10: traditions, although it is not so common in the C world.
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