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cannam@167:Multi-dimensional transforms work much the same way as one-dimensional
cannam@167: transforms: you allocate arrays of fftw_complex (preferably
cannam@167: using fftw_malloc), create an fftw_plan, execute it as
cannam@167: many times as you want with fftw_execute(plan), and clean up
cannam@167: with fftw_destroy_plan(plan) (and fftw_free).
cannam@167:
FFTW provides two routines for creating plans for 2d and 3d transforms, cannam@167: and one routine for creating plans of arbitrary dimensionality. cannam@167: The 2d and 3d routines have the following signature: cannam@167:
fftw_plan fftw_plan_dft_2d(int n0, int n1, cannam@167: fftw_complex *in, fftw_complex *out, cannam@167: int sign, unsigned flags); cannam@167: fftw_plan fftw_plan_dft_3d(int n0, int n1, int n2, cannam@167: fftw_complex *in, fftw_complex *out, cannam@167: int sign, unsigned flags); cannam@167:
These routines create plans for n0 by n1 two-dimensional
cannam@167: (2d) transforms and n0 by n1 by n2 3d transforms,
cannam@167: respectively. All of these transforms operate on contiguous arrays in
cannam@167: the C-standard row-major order, so that the last dimension has the
cannam@167: fastest-varying index in the array. This layout is described further in
cannam@167: Multi-dimensional Array Format.
cannam@167:
FFTW can also compute transforms of higher dimensionality. In order to cannam@167: avoid confusion between the various meanings of the the word cannam@167: “dimension”, we use the term rank cannam@167: cannam@167: to denote the number of independent indices in an array.2 For cannam@167: example, we say that a 2d transform has rank 2, a 3d transform has cannam@167: rank 3, and so on. You can plan transforms of arbitrary rank by cannam@167: means of the following function: cannam@167:
cannam@167:fftw_plan fftw_plan_dft(int rank, const int *n, cannam@167: fftw_complex *in, fftw_complex *out, cannam@167: int sign, unsigned flags); cannam@167:
Here, n is a pointer to an array n[rank] denoting an
cannam@167: n[0] by n[1] by … by n[rank-1] transform.
cannam@167: Thus, for example, the call
cannam@167:
fftw_plan_dft_2d(n0, n1, in, out, sign, flags); cannam@167:
is equivalent to the following code fragment: cannam@167:
int n[2]; cannam@167: n[0] = n0; cannam@167: n[1] = n1; cannam@167: fftw_plan_dft(2, n, in, out, sign, flags); cannam@167:
fftw_plan_dft is not restricted to 2d and 3d transforms,
cannam@167: however, but it can plan transforms of arbitrary rank.
cannam@167:
You may have noticed that all the planner routines described so far
cannam@167: have overlapping functionality. For example, you can plan a 1d or 2d
cannam@167: transform by using fftw_plan_dft with a rank of 1
cannam@167: or 2, or even by calling fftw_plan_dft_3d with n0
cannam@167: and/or n1 equal to 1 (with no loss in efficiency). This
cannam@167: pattern continues, and FFTW’s planning routines in general form a
cannam@167: “partial order,” sequences of
cannam@167:
cannam@167: interfaces with strictly increasing generality but correspondingly
cannam@167: greater complexity.
cannam@167:
fftw_plan_dft is the most general complex-DFT routine that we
cannam@167: describe in this tutorial, but there are also the advanced and guru interfaces,
cannam@167:
cannam@167:
cannam@167: which allow one to efficiently combine multiple/strided transforms
cannam@167: into a single FFTW plan, transform a subset of a larger
cannam@167: multi-dimensional array, and/or to handle more general complex-number
cannam@167: formats. For more information, see FFTW Reference.
cannam@167:
The cannam@167: term “rank” is commonly used in the APL, FORTRAN, and Common Lisp cannam@167: traditions, although it is not so common in the C world.
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