BUG: linalg.polar: empty array support

[redha2404]

Reference issue

Check the box "polar" in #20372

What does this implement/fix?

If a is empty, the polar function now returns p and u of the right types. Before, an error occurred on empty array.

Additional information

It is just a first PR for #20372 to see I understand the problem

[lucascolley]

thanks @redha2404 , can you add a regression test? Examples can be found in the test file changes in https://github.com/scipy/scipy/pull/20295/files.

[lucascolley]

Looks reasonable to me, thanks! I'll let @ev-br take a look. CI failure is unrelated.

[ev-br]

This is a good start but needs a tweak to properly account for integer inputs.

[redha2404]

I think the problem with int is now resolved

[ev-br]

Thanks. The dtype is indeed correct now.
However I've a follow-up concern, sorry for not thinking about it before.
Let's see:

In [44]: a
Out[44]: array([], shape=(0, 3), dtype=float32)

In [45]: u, p = polar(a)

In [46]: p
Out[46]: 
array([[ 8.6914245e-20,  3.0839777e-41,  0.0000000e+00],
       [ 0.0000000e+00,  2.8025969e-45,  0.0000000e+00],
       [           nan,            nan, -6.4903711e+32]], dtype=float32)

In [47]: u @ p
Out[47]: array([], shape=(0, 3), dtype=float32)

The dtype here is irrelevant, but the contents of p is. It is documented to be positive semidefinite, but what is returned clearly is not. There is a hint in the implementation: you use np.empty_like(a.T @ a). Can you explain why you used empty instead of e.g. a.T @ a itself?

[redha2404]

I didn't notice np.empty_like puts such values. I wanted to precise the dtype I want on p but I just noticed that a.T @ a does the conversion int_array -> (float64, float64)

>>> u = np.empty((0,3), dtype=int)
>>> p = a.T @ a
>>> p.dtype
dtype('float64')

So, should I just put e.g, u = np.copy(a) and p=a.T @ a for 'right' ?

[redha2404]

Oh, not for u. It doesn't transform int to float. I should not change the line for u

[redha2404]

I changed it as you suggested it

[melissawm]

Hi @redha2404 - did you mean to close this?

[ev-br]

I wanted to give it the last look-though before pressing the green button but the patch is now gone.

[redha2404]

I wanted to change the branch from which I merge because it was from my main branch. Should I make another PR with the same modifications ?

[lucascolley]

I wanted to change the branch from which I merge because it was from my main branch. Should I make another PR with the same modifications ?

Yeah, sounds good 👍