[Numpy-discussion] new MaskedArray class

[Warren Weckesser]

On 6/24/19, Marten van Kerkwijk <m.h.vankerkwijk at gmail.com> wrote:
> Hi Eric,
>
> The easiest definitely is for the mask to just propagate, which that even
> if just one point is masked, all points in the fft will be masked.
>
> On the direct point I made, I think it is correct that since one can think
> of the Fourier transform of a sine/cosine fit, then there is a solution
> even in the presence of some masked data, and this solution is distinct
> from that for a specific choice of fill value. But of course it is also
> true that the solution will be at least partially degenerate in its result
> and possibly indeterminate (e.g., for the extreme example of a real
> transform for which all but the first point are masked, all cosine term
> amplitudes are equal to the value of the first term, and are completely
> degenerate with each other, and all sine term amplitudes are indeterminate;
> one has only one piece of information, after all). Yet the inverse of any
> of those choices reproduces the input. That said, clearly there is a choice
> to be made whether this solution is at all interesting, which means that
> you are right that it needs an explicit user decision.
>

FWIW: The discrete Fourier transform is equivalent to a matrix
multiplication (https://en.wikipedia.org/wiki/DFT_matrix,
https://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.dft.html),
so whatever behavior you define for a nonmasked array times a masked
vector also applies to the FFT of a masked vector.

Warren


> All the best,
>
> Marten
>