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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 plans multidimensional complex DFTs, and is exactly the same as
fftw_plan_dft except for the new parameters howmany,
{i,o}nembed, {i,o}stride,
and {i,o}dist.
howmany is the number of transforms to compute, where the
k-th transform is of the arrays starting at in+k*idist and
out+k*odist. The resulting plans 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).
The two nembed parameters (which should be arrays of length
rank) indicate the sizes of the input and output array
dimensions, respectively, where the transform is of a subarray of size
n. (Each dimension of n should be <= the
corresponding dimension of the nembed arrays.) That is, the
input and output arrays are stored in row-major order with size given by
nembed (not counting the strides and howmany multiplicities).
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.
So, for example, to transform a sequence of contiguous arrays, stored
one after another, one would use a stride of 1 and a dist
of N, where N is the product of the dimensions. In
another example, to transform an array of contiguous "vectors" of
length M, one would use a howmany of M, a
stride of M, and a dist of 1.