Guru vector and transform sizes - FFTW 3.2.2
Description: FFTW 3.2.2

Next: Guru Complex DFTs, Previous: Interleaved and split arrays, Up: Guru Interface

#### 4.5.2 Guru vector and transform sizes

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

         typedef struct {
              int n;
              int is;
              int os;
         } fftw_iodim;

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

The meaning of the stride parameter depends on the type of the array that the stride refers to. If the array is interleaved complex, strides are expressed in units of complex numbers (`fftw_complex`). If the array is split complex or real, strides are expressed in units of real numbers (`double`). This convention is consistent with the usual pointer arithmetic in the C language. An interleaved array is denoted by a pointer `p` to `fftw_complex`, so that `p+1` points to the next complex number. Split arrays are denoted by pointers to `double`, in which case pointer arithmetic operates in units of `sizeof(double)`. The guru planner interfaces all take a (`rank`, `dims[rank]`) pair describing the transform size, and a (`howmany_rank`, `howmany_dims[howmany_rank]`) pair describing the “vector” size (a multi-dimensional loop of transforms to perform), where `dims` and `howmany_dims` are arrays of `fftw_iodim`.

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

A row-major multidimensional array with dimensions `n[rank]` (see Row-major Format) corresponds to `dims[i].n` = `n[i]` and the recurrence `dims[i].is` = `n[i+1] * dims[i+1].is` (similarly for `os`). The stride of the last (`i=rank-1`) dimension is the overall stride of the array. e.g. to be equivalent to the advanced complex-DFT interface, you would have `dims[rank-1].is` = `istride` and `dims[rank-1].os` = `ostride`. In general, we only guarantee FFTW to return a non-`NULL` plan if the vector and transform dimensions correspond to a set of distinct indices, and for in-place transforms the input/output strides should be the same.