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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. Each n field must be positive for dims and nonnegative for howmany_dims, while both rank and howmany_rank must be nonnegative.

For example, the howmany parameter in the advanced complex-DFT interface corresponds to howmany_rank = 1, howmany_dims.n = howmany, howmany_dims.is = idist, and howmany_dims.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.

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