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fftw_plan fftw_plan_many_dft(int rank, const int *n, int howmany, Chris@19: fftw_complex *in, const int *inembed, Chris@19: int istride, int idist, Chris@19: fftw_complex *out, const int *onembed, Chris@19: int ostride, int odist, Chris@19: int sign, unsigned flags); Chris@19:Chris@19:
Chris@19: This routine plans multiple multidimensional complex DFTs, and it
Chris@19: extends the fftw_plan_dft routine (see Complex DFTs) to
Chris@19: compute howmany transforms, each having rank rank and size
Chris@19: n. In addition, the transform data need not be contiguous, but
Chris@19: it may be laid out in memory with an arbitrary stride. To account for
Chris@19: these possibilities, fftw_plan_many_dft adds the new parameters
Chris@19: howmany, {i,o}nembed,
Chris@19: {i,o}stride, and
Chris@19: {i,o}dist. The FFTW basic interface
Chris@19: (see Complex DFTs) provides routines specialized for ranks 1, 2,
Chris@19: and 3, but the advanced interface handles only the general-rank
Chris@19: case.
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howmany is the number of transforms to compute. The resulting
Chris@19: plan computes howmany transforms, where the input of the
Chris@19: k-th transform is at location in+k*idist (in C pointer
Chris@19: arithmetic), and its output is at location out+k*odist. Plans
Chris@19: obtained in this way can often be faster than calling FFTW multiple
Chris@19: times for the individual transforms. The basic fftw_plan_dft
Chris@19: interface corresponds to howmany=1 (in which case the dist
Chris@19: parameters are ignored).
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Each of the howmany transforms has rank rank and size
Chris@19: n, as in the basic interface. In addition, the advanced
Chris@19: interface allows the input and output arrays of each transform to be
Chris@19: row-major subarrays of larger rank-rank arrays, described by
Chris@19: inembed and onembed parameters, respectively.
Chris@19: {i,o}nembed must be arrays of length rank,
Chris@19: and n should be elementwise less than or equal to
Chris@19: {i,o}nembed. Passing NULL for an
Chris@19: nembed parameter is equivalent to passing n (i.e. same
Chris@19: physical and logical dimensions, as in the basic interface.)
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The stride parameters indicate that the j-th element of
Chris@19: the input or output arrays is located at j*istride or
Chris@19: j*ostride, respectively. (For a multi-dimensional array,
Chris@19: j is the ordinary row-major index.) When combined with the
Chris@19: k-th transform in a howmany loop, from above, this means
Chris@19: that the (j,k)-th element is at j*stride+k*dist.
Chris@19: (The basic fftw_plan_dft interface corresponds to a stride of 1.)
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For in-place transforms, the input and output stride and
Chris@19: dist parameters should be the same; otherwise, the planner may
Chris@19: return NULL.
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Arrays n, inembed, and onembed are not used after
Chris@19: this function returns. You can safely free or reuse them.
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Examples: Chris@19: One transform of one 5 by 6 array contiguous in memory: Chris@19:
int rank = 2;
Chris@19: int n[] = {5, 6};
Chris@19: int howmany = 1;
Chris@19: int idist = odist = 0; /* unused because howmany = 1 */
Chris@19: int istride = ostride = 1; /* array is contiguous in memory */
Chris@19: int *inembed = n, *onembed = n;
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Chris@19: Transform of three 5 by 6 arrays, each contiguous in memory, Chris@19: stored in memory one after another: Chris@19:
int rank = 2;
Chris@19: int n[] = {5, 6};
Chris@19: int howmany = 3;
Chris@19: int idist = odist = n[0]*n[1]; /* = 30, the distance in memory
Chris@19: between the first element
Chris@19: of the first array and the
Chris@19: first element of the second array */
Chris@19: int istride = ostride = 1; /* array is contiguous in memory */
Chris@19: int *inembed = n, *onembed = n;
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Chris@19: Transform each column of a 2d array with 10 rows and 3 columns: Chris@19:
int rank = 1; /* not 2: we are computing 1d transforms */
Chris@19: int n[] = {10}; /* 1d transforms of length 10 */
Chris@19: int howmany = 3;
Chris@19: int idist = odist = 1;
Chris@19: int istride = ostride = 3; /* distance between two elements in
Chris@19: the same column */
Chris@19: int *inembed = n, *onembed = n;
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