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GNU Info (fftw.info)Array Dimensions for Real Multi-dimensional TransformsArray Dimensions for Real Multi-dimensional Transforms ------------------------------------------------------ The output of a multi-dimensional transform of real data contains symmetries that, in principle, make half of the outputs redundant (Note: What RFFTWND Really Computes.). In practice, it is not possible to entirely realize these savings in an efficient and understandable format. Instead, the output of the rfftwnd transforms is *slightly* over half of the output of the corresponding complex transform. We do not "pack" the data in any way, but store it as an ordinary array of `fftw_complex' values. In fact, this data is simply a subsection of what would be the array in the corresponding complex transform. Specifically, for a real transform of dimensions n1 x n2 x ... x nd, the complex data is an n1 x n2 x ... x (nd/2+1) array of `fftw_complex' values in row-major order (with the division rounded down). That is, we only store the lower half (plus one element) of the last dimension of the data from the ordinary complex transform. (We could have instead taken half of any other dimension, but implementation turns out to be simpler if the last, contiguous, dimension is used.) Since the complex data is slightly larger than the real data, some complications arise for in-place transforms. In this case, the final dimension of the real data must be padded with extra values to accommodate the size of the complex data--two extra if the last dimension is even and one if it is odd. That is, the last dimension of the real data must physically contain 2 * (nd/2+1) `fftw_real' values (exactly enough to hold the complex data). This physical array size does not, however, change the *logical* array size--only nd values are actually stored in the last dimension, and nd is the last dimension passed to `rfftwnd_create_plan'. automatically generated by info2www version 1.2.2.9 |