FFTW 3.3.5: Guru vector and transform sizes

The guru interface introduces one basic new data structure, cannam@127: fftw_iodim, that is used to specify sizes and strides for cannam@127: multi-dimensional transforms and vectors: cannam@127:

cannam@127:

typedef struct {
cannam@127:      int n;
cannam@127:      int is;
cannam@127:      int os;
cannam@127: } fftw_iodim;
cannam@127:

Here, n is the size of the dimension, and is and os cannam@127: are the strides of that dimension for the input and output arrays. (The cannam@127: stride is the separation of consecutive elements along this dimension.) cannam@127:

The meaning of the stride parameter depends on the type of the array cannam@127: that the stride refers to. If the array is interleaved complex, cannam@127: strides are expressed in units of complex numbers cannam@127: (fftw_complex). If the array is split complex or real, strides cannam@127: are expressed in units of real numbers (double). This cannam@127: convention is consistent with the usual pointer arithmetic in the C cannam@127: language. An interleaved array is denoted by a pointer p to cannam@127: fftw_complex, so that p+1 points to the next complex cannam@127: number. Split arrays are denoted by pointers to double, in cannam@127: which case pointer arithmetic operates in units of cannam@127: sizeof(double). cannam@127: cannam@127:

The guru planner interfaces all take a (rank, dims[rank]) cannam@127: pair describing the transform size, and a (howmany_rank, cannam@127: howmany_dims[howmany_rank]) pair describing the “vector” size (a cannam@127: multi-dimensional loop of transforms to perform), where dims and cannam@127: howmany_dims are arrays of fftw_iodim. cannam@127:

For example, the howmany parameter in the advanced complex-DFT cannam@127: interface corresponds to howmany_rank = 1, cannam@127: howmany_dims[0].n = howmany, howmany_dims[0].is = cannam@127: idist, and howmany_dims[0].os = odist. cannam@127: cannam@127: cannam@127: (To compute a single transform, you can just use howmany_rank = 0.) cannam@127:

A row-major multidimensional array with dimensions n[rank] cannam@127: (see Row-major Format) corresponds to dims[i].n = cannam@127: n[i] and the recurrence dims[i].is =

n[i+1] *
cannam@127: dims[i+1].is

(similarly for os). The stride of the last cannam@127: (i=rank-1) dimension is the overall stride of the array. cannam@127: e.g. to be equivalent to the advanced complex-DFT interface, you would cannam@127: have dims[rank-1].is = istride and cannam@127: dims[rank-1].os = ostride. cannam@127: cannam@127:

In general, we only guarantee FFTW to return a non-NULL plan if cannam@127: the vector and transform dimensions correspond to a set of distinct cannam@127: indices, and for in-place transforms the input/output strides should cannam@127: be the same. cannam@127:

4.5.2 Guru vector and transform sizes