MAINT: Disallow complex covariances in multivariate_normal

[hameerabbasi]

This commit disallows complex covariances in multivariate_normal
as passing them can silently lead to incorrect results.

[bashtage]

Looks good, except I would remove the word "yet" since there is no promise that this function will ever support complex gaussian (and IMO it should not, a complex gaussian should have its own method, but this is another discussion).

[bashtage]

Of course, needs a test to make sure that it is triggered.

[hameerabbasi]

this is another discussion

Let's have the discussion somewhere, because it's the difference between a ValueError and a NotImplementedError.

[hameerabbasi]

I have no clue why this is failing. It fails locally too.

[zoj613]

I have no clue why this is failing. It fails locally too.

seems like the line added to the tests gives this warning: numpy.ComplexWarning: Casting complex values to real discards the imaginary part, causing the test to fail.

[eric-wieser]

This only checks the covariance and not the mean - is that deliberate? If so, I think the message could be clearer

[eric-wieser]

Worth being aware of these lines:
https://github.com/numpy/numpy/pull/14733/files#diff-6599d3132920de62ea7e896a318d8803R3481-R3482

[hameerabbasi]

seems like the line added to the tests gives this warning: numpy.ComplexWarning: Casting complex values to real discards the imaginary part, causing the test to fail.

Worth being aware of these lines:
https://github.com/numpy/numpy/pull/14733/files#diff-6599d3132920de62ea7e896a318d8803R3481-R3482

The check is above that, and should raise an exception before the warning ever happens.

[charris]

Needs rebase.

[WarrenWeckesser]

This looks like a pretty straightforward fix; can we revive it and get it merged?

I agree with @bashtage's comment--there is no plan to make this method accept complex inputs--so the error should be a TypeError. See, for example, what happens when you pass a complex array to multinomial:

In [8]: rng.multinomial(3, [0.25, 0.5, 0.25+0j])
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-8-d28a44019b56> in <module>
----> 1 rng.multinomial(3, [0.25, 0.5, 0.25+0j])

_generator.pyx in numpy.random._generator.Generator.multinomial()

TypeError: can't convert complex to float

Also @eric-wieser's comment should be followed up with a change that also raises an exception if mean is complex.

[charris]

Somewhat related, there was a PR to introduce a complex multivariate implementation. I don't recall what the replacement for the ordinary covariance matrix was, but apparently there is a standard approach somewhere out there in the numerical world.

[charris]

@WarrenWeckesser Feel free to take this over.

[WarrenWeckesser]

This PR was continued in #21779, which has been merged.