FFTW 3.3.5: Advanced Complex DFTs

Chris@42:

fftw_plan fftw_plan_many_dft(int rank, const int *n, int howmany,
Chris@42:                              fftw_complex *in, const int *inembed,
Chris@42:                              int istride, int idist,
Chris@42:                              fftw_complex *out, const int *onembed,
Chris@42:                              int ostride, int odist,
Chris@42:                              int sign, unsigned flags);
Chris@42:

This routine plans multiple multidimensional complex DFTs, and it Chris@42: extends the fftw_plan_dft routine (see Complex DFTs) to Chris@42: compute howmany transforms, each having rank rank and size Chris@42: n. In addition, the transform data need not be contiguous, but Chris@42: it may be laid out in memory with an arbitrary stride. To account for Chris@42: these possibilities, fftw_plan_many_dft adds the new parameters Chris@42: howmany, {i,o}nembed, Chris@42: {i,o}stride, and Chris@42: {i,o}dist. The FFTW basic interface Chris@42: (see Complex DFTs) provides routines specialized for ranks 1, 2, Chris@42: and 3, but the advanced interface handles only the general-rank Chris@42: case. Chris@42:

howmany is the number of transforms to compute. The resulting Chris@42: plan computes howmany transforms, where the input of the Chris@42: k-th transform is at location in+k*idist (in C pointer Chris@42: arithmetic), and its output is at location out+k*odist. Plans Chris@42: obtained in this way can often be faster than calling FFTW multiple Chris@42: times for the individual transforms. The basic fftw_plan_dft Chris@42: interface corresponds to howmany=1 (in which case the dist Chris@42: parameters are ignored). Chris@42: Chris@42: Chris@42:

Each of the howmany transforms has rank rank and size Chris@42: n, as in the basic interface. In addition, the advanced Chris@42: interface allows the input and output arrays of each transform to be Chris@42: row-major subarrays of larger rank-rank arrays, described by Chris@42: inembed and onembed parameters, respectively. Chris@42: {i,o}nembed must be arrays of length rank, Chris@42: and n should be elementwise less than or equal to Chris@42: {i,o}nembed. Passing NULL for an Chris@42: nembed parameter is equivalent to passing n (i.e. same Chris@42: physical and logical dimensions, as in the basic interface.) Chris@42:

The stride parameters indicate that the j-th element of Chris@42: the input or output arrays is located at j*istride or Chris@42: j*ostride, respectively. (For a multi-dimensional array, Chris@42: j is the ordinary row-major index.) When combined with the Chris@42: k-th transform in a howmany loop, from above, this means Chris@42: that the (j,k)-th element is at j*stride+k*dist. Chris@42: (The basic fftw_plan_dft interface corresponds to a stride of 1.) Chris@42: Chris@42:

For in-place transforms, the input and output stride and Chris@42: dist parameters should be the same; otherwise, the planner may Chris@42: return NULL. Chris@42:

Arrays n, inembed, and onembed are not used after Chris@42: this function returns. You can safely free or reuse them. Chris@42:

Examples: Chris@42: One transform of one 5 by 6 array contiguous in memory: Chris@42:

Chris@42:

   int rank = 2;
Chris@42:    int n[] = {5, 6};
Chris@42:    int howmany = 1;
Chris@42:    int idist = odist = 0; /* unused because howmany = 1 */
Chris@42:    int istride = ostride = 1; /* array is contiguous in memory */
Chris@42:    int *inembed = n, *onembed = n;
Chris@42:

Transform of three 5 by 6 arrays, each contiguous in memory, Chris@42: stored in memory one after another: Chris@42:

Chris@42:

   int rank = 2;
Chris@42:    int n[] = {5, 6};
Chris@42:    int howmany = 3;
Chris@42:    int idist = odist = n[0]*n[1]; /* = 30, the distance in memory
Chris@42:                                      between the first element
Chris@42:                                      of the first array and the
Chris@42:                                      first element of the second array */
Chris@42:    int istride = ostride = 1; /* array is contiguous in memory */
Chris@42:    int *inembed = n, *onembed = n;
Chris@42:

Chris@42:

   int rank = 1; /* not 2: we are computing 1d transforms */
Chris@42:    int n[] = {10}; /* 1d transforms of length 10 */
Chris@42:    int howmany = 3;
Chris@42:    int idist = odist = 1;
Chris@42:    int istride = ostride = 3; /* distance between two elements in 
Chris@42:                                  the same column */
Chris@42:    int *inembed = n, *onembed = n;
Chris@42:

4.4.1 Advanced Complex DFTs