On small argument against the "by_n" approach is that both `"ortho"`
and `None` use the directional notion already implicitly. Since below
you would need the `ifft(x, norm="by_1")` to achieve the desired effect
here as None will normalize the `ifft` by default.
One option would be to change the default None to an alias "inverse" to make it clearer. This could be done without a deprecation cycle.
So using `by_n` or similar, works well, but may make a call without
`norm` slightly more confusing (you may expect no normalization at all
on the `ifft`)? Not sure its a big argument, though...
To me the least ambiguous naming are:
1. Related to the transforms themselves, as these have the most clearly understood usage and naming for most people in most FFT/IFFT contexts that I've seen; and
2. Can be passed to both functions the same way to achieve round-trip equality (i.e., np.allclose(ifft(fft(x,norm=norm),norm=norm),x)).
People who want to do something weird like no normalization in either direction are not the ones that I think should be prioritized here, as they are the exception and not the rule (far rarer I'd expect). So I'd prefer that the naming reflect the generally desirable round-trip equality. This makes it easiest for people working with FFT and IFFT pairs (or even using FFT and thinking about Parseval's relation of the resulting frequency-domain data) to understand what's going on. For example this is a pretty clear docstring to me (as is NumPy's
current one):
norm : {'forward', 'inverse', 'ortho', None}
The normalization to apply during the FFT or IFFT, each of which will ensure
round-trip numerical equivalence when the same value is passed to both forward
and inverse transform functions:
- "inverse" (default; same as None) will apply full normalization only during
the IFFT (1/N); this follows the standard definition of the discrete Fourier
transform and its inverse.
- "forward" will apply full normalization only during the FFT (1/N).
- "ortho" will apply half the normalization during the FFT and the IFFT
(1/sqrt(N)), thereby ortho-normalizing the bases.
One could argue that "ortho" could equivalently be "split" or "half" or something, but it already seems clear enough about what it will do (and even why it's potentially useful).
My 2c,
Eric