FFTW 3.3.8: Guru vector and transform sizes

The guru interface introduces one basic new data structure, cannam@167: fftw_iodim, that is used to specify sizes and strides for cannam@167: multi-dimensional transforms and vectors: cannam@167:

cannam@167:

typedef struct {
cannam@167:      int n;
cannam@167:      int is;
cannam@167:      int os;
cannam@167: } fftw_iodim;
cannam@167:

Here, n is the size of the dimension, and is and os cannam@167: are the strides of that dimension for the input and output arrays. (The cannam@167: stride is the separation of consecutive elements along this dimension.) cannam@167:

The meaning of the stride parameter depends on the type of the array cannam@167: that the stride refers to. If the array is interleaved complex, cannam@167: strides are expressed in units of complex numbers cannam@167: (fftw_complex). If the array is split complex or real, strides cannam@167: are expressed in units of real numbers (double). This cannam@167: convention is consistent with the usual pointer arithmetic in the C cannam@167: language. An interleaved array is denoted by a pointer p to cannam@167: fftw_complex, so that p+1 points to the next complex cannam@167: number. Split arrays are denoted by pointers to double, in cannam@167: which case pointer arithmetic operates in units of cannam@167: sizeof(double). cannam@167: cannam@167:

The guru planner interfaces all take a (rank, dims[rank]) cannam@167: pair describing the transform size, and a (howmany_rank, cannam@167: howmany_dims[howmany_rank]) pair describing the “vector” size (a cannam@167: multi-dimensional loop of transforms to perform), where dims and cannam@167: howmany_dims are arrays of fftw_iodim. Each n field must cannam@167: be positive for dims and nonnegative for howmany_dims, while both cannam@167: rank and howmany_rank must be nonnegative. cannam@167:

For example, the howmany parameter in the advanced complex-DFT cannam@167: interface corresponds to howmany_rank = 1, cannam@167: howmany_dims[0].n = howmany, howmany_dims[0].is = cannam@167: idist, and howmany_dims[0].os = odist. cannam@167: cannam@167: cannam@167: (To compute a single transform, you can just use howmany_rank = 0.) cannam@167:

A row-major multidimensional array with dimensions n[rank] cannam@167: (see Row-major Format) corresponds to dims[i].n = cannam@167: n[i] and the recurrence dims[i].is =

n[i+1] *
cannam@167: dims[i+1].is

(similarly for os). The stride of the last cannam@167: (i=rank-1) dimension is the overall stride of the array. cannam@167: e.g. to be equivalent to the advanced complex-DFT interface, you would cannam@167: have dims[rank-1].is = istride and cannam@167: dims[rank-1].os = ostride. cannam@167: cannam@167:

In general, we only guarantee FFTW to return a non-NULL plan if cannam@167: the vector and transform dimensions correspond to a set of distinct cannam@167: indices, and for in-place transforms the input/output strides should cannam@167: be the same. cannam@167:

4.5.2 Guru vector and transform sizes