fftw3: Advanced Complex DFTs
4.4.1 Advanced Complex DFTs
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fftw_plan fftw_plan_many_dft(int rank, const int *n, int howmany,
fftw_complex *in, const int *inembed,
int istride, int idist,
fftw_complex *out, const int *onembed,
int ostride, int odist,
int sign, unsigned flags);
This routine plans multiple multidimensional complex DFTs, and it
extends the 'fftw_plan_dft' routine (
Complex DFTs) to compute
'howmany' transforms, each having rank 'rank' and size 'n'. In
addition, the transform data need not be contiguous, but it may be laid
out in memory with an arbitrary stride. To account for these
possibilities, 'fftw_plan_many_dft' adds the new parameters 'howmany',
{'i','o'}'nembed', {'i','o'}'stride', and {'i','o'}'dist'. The FFTW
basic interface (Complex DFTs) provides routines specialized for
ranks 1, 2, and 3, but the advanced interface handles only the
general-rank case.
'howmany' is the number of transforms to compute. The resulting plan
computes 'howmany' transforms, where the input of the 'k'-th transform
is at location 'in+k*idist' (in C pointer arithmetic), and its output is
at location 'out+k*odist'. Plans obtained in this way can often be
faster than calling FFTW multiple times for the individual transforms.
The basic 'fftw_plan_dft' interface corresponds to 'howmany=1' (in which
case the 'dist' parameters are ignored).
Each of the 'howmany' transforms has rank 'rank' and size 'n', as in
the basic interface. In addition, the advanced interface allows the
input and output arrays of each transform to be row-major subarrays of
larger rank-'rank' arrays, described by 'inembed' and 'onembed'
parameters, respectively. {'i','o'}'nembed' must be arrays of length
'rank', and 'n' should be elementwise less than or equal to
{'i','o'}'nembed'. Passing 'NULL' for an 'nembed' parameter is
equivalent to passing 'n' (i.e. same physical and logical dimensions,
as in the basic interface.)
The 'stride' parameters indicate that the 'j'-th element of the input
or output arrays is located at 'j*istride' or 'j*ostride', respectively.
(For a multi-dimensional array, 'j' is the ordinary row-major index.)
When combined with the 'k'-th transform in a 'howmany' loop, from above,
this means that the ('j','k')-th element is at 'j*stride+k*dist'. (The
basic 'fftw_plan_dft' interface corresponds to a stride of 1.)
For in-place transforms, the input and output 'stride' and 'dist'
parameters should be the same; otherwise, the planner may return 'NULL'.
Arrays 'n', 'inembed', and 'onembed' are not used after this function
returns. You can safely free or reuse them.
*Examples*: One transform of one 5 by 6 array contiguous in memory:
int rank = 2;
int n[] = {5, 6};
int howmany = 1;
int idist = odist = 0; /* unused because howmany = 1 */
int istride = ostride = 1; /* array is contiguous in memory */
int *inembed = n, *onembed = n;
Transform of three 5 by 6 arrays, each contiguous in memory, stored
in memory one after another:
int rank = 2;
int n[] = {5, 6};
int howmany = 3;
int idist = odist = n[0]*n[1]; /* = 30, the distance in memory
between the first element
of the first array and the
first element of the second array */
int istride = ostride = 1; /* array is contiguous in memory */
int *inembed = n, *onembed = n;
Transform each column of a 2d array with 10 rows and 3 columns:
int rank = 1; /* not 2: we are computing 1d transforms */
int n[] = {10}; /* 1d transforms of length 10 */
int howmany = 3;
int idist = odist = 1;
int istride = ostride = 3; /* distance between two elements in
the same column */
int *inembed = n, *onembed = n;
Info Catalog
fftw3: Advanced Interface
fftw3: Advanced Interface
fftw3: Advanced Real-data DFTs