fftw3: Real-to-Real Transforms
4.3.5 Real-to-Real Transforms
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fftw_plan fftw_plan_r2r_1d(int n, double *in, double *out,
fftw_r2r_kind kind, unsigned flags);
fftw_plan fftw_plan_r2r_2d(int n0, int n1, double *in, double *out,
fftw_r2r_kind kind0, fftw_r2r_kind kind1,
unsigned flags);
fftw_plan fftw_plan_r2r_3d(int n0, int n1, int n2,
double *in, double *out,
fftw_r2r_kind kind0,
fftw_r2r_kind kind1,
fftw_r2r_kind kind2,
unsigned flags);
fftw_plan fftw_plan_r2r(int rank, const int *n, double *in, double *out,
const fftw_r2r_kind *kind, unsigned flags);
Plan a real input/output (r2r) transform of various kinds in zero or
more dimensions, returning an 'fftw_plan' (
Using Plans).
Once you have created a plan for a certain transform type and
parameters, then creating another plan of the same type and parameters,
but for different arrays, is fast and shares constant data with the
first plan (if it still exists).
The planner returns 'NULL' if the plan cannot be created. A
non-'NULL' plan is always returned by the basic interface unless you are
using a customized FFTW configuration supporting a restricted set of
transforms, or for size-1 'FFTW_REDFT00' kinds (which are not defined).
Arguments
.........
* 'rank' is the dimensionality of the transform (it should be the
size of the arrays '*n' and '*kind'), and can be any non-negative
integer. The '_1d', '_2d', and '_3d' planners correspond to a
'rank' of '1', '2', and '3', respectively. A 'rank' of zero is
equivalent to a copy of one number from input to output.
* 'n', or 'n0'/'n1'/'n2', or 'n[rank]', respectively, gives the
(physical) size of the transform dimensions. They can be any
positive integer.
- Multi-dimensional arrays are stored in row-major order with
dimensions: 'n0' x 'n1'; or 'n0' x 'n1' x 'n2'; or 'n[0]' x
'n[1]' x ... x 'n[rank-1]'. Multi-dimensional Array
Format.
- FFTW is generally best at handling sizes of the form 2^a 3^b
5^c 7^d 11^e 13^f, where e+f is either 0 or 1, and the other
exponents are arbitrary. Other sizes are computed by means of
a slow, general-purpose algorithm (which nevertheless retains
O(n log n) performance even for prime sizes). (It is possible
to customize FFTW for different array sizes; see
Installation and Customization.) Transforms whose sizes are
powers of 2 are especially fast.
- For a 'REDFT00' or 'RODFT00' transform kind in a dimension of
size n, it is n-1 or n+1, respectively, that should be
factorizable in the above form.
* 'in' and 'out' point to the input and output arrays of the
transform, which may be the same (yielding an in-place transform).
These arrays are overwritten during planning, unless
'FFTW_ESTIMATE' is used in the flags. (The arrays need not be
initialized, but they must be allocated.)
* 'kind', or 'kind0'/'kind1'/'kind2', or 'kind[rank]', is the kind of
r2r transform used for the corresponding dimension. The valid kind
constants are described in Real-to-Real Transform Kinds.
In a multi-dimensional transform, what is computed is the separable
product formed by taking each transform kind along the
corresponding dimension, one dimension after another.
* 'flags' is a bitwise OR ('|') of zero or more planner flags, as
defined in Planner Flags.
Info Catalog
fftw3: Real-data DFT Array Format
fftw3: Basic Interface
fftw3: Real-to-Real Transform Kinds