ENH,DOC: np.max of a zero-sized array throws a ValueError

[ev-br]

Describe the issue:

np.max of a zero-sized array throws a ValueError

Reproduce the code example:

In [1]: import numpy as np

In [2]: a = np.zeros([])

In [3]: np.max(a)        # works
Out[3]: 0.0

In [4]: b = np.zeros((5, 0, 3))

In [5]: np.max(b)
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [5], in <cell line: 1>()
----> 1 np.max(b)

File <__array_function__ internals>:5, in amax(*args, **kwargs)

File ~/.virtualenvs/scipy-dev/lib/python3.8/site-packages/numpy/core/fromnumeric.py:2754, in amax(a, axis, out, keepdims, initial, where)
   2638 @array_function_dispatch(_amax_dispatcher)
   2639 def amax(a, axis=None, out=None, keepdims=np._NoValue, initial=np._NoValue,
   2640          where=np._NoValue):
   2641     """
   2642     Return the maximum of an array or maximum along an axis.
   2643 
   (...)
   2752     5
   2753     """
-> 2754     return _wrapreduction(a, np.maximum, 'max', axis, None, out,
   2755                           keepdims=keepdims, initial=initial, where=where)

File ~/.virtualenvs/scipy-dev/lib/python3.8/site-packages/numpy/core/fromnumeric.py:86, in _wrapreduction(obj, ufunc, method, axis, dtype, out, **kwargs)
     83         else:
     84             return reduction(axis=axis, out=out, **passkwargs)
---> 86 return ufunc.reduce(obj, axis, dtype, out, **passkwargs)

ValueError: zero-size array to reduction operation maximum which has no identity

Error message:

ValueError                                Traceback (most recent call last)
Input In [5], in <cell line: 1>()
----> 1 np.max(b)

File <__array_function__ internals>:5, in amax(*args, **kwargs)

File ~/.virtualenvs/scipy-dev/lib/python3.8/site-packages/numpy/core/fromnumeric.py:2754, in amax(a, axis, out, keepdims, initial, where)
   2638 @array_function_dispatch(_amax_dispatcher)
   2639 def amax(a, axis=None, out=None, keepdims=np._NoValue, initial=np._NoValue,
   2640          where=np._NoValue):
   2641     """
   2642     Return the maximum of an array or maximum along an axis.
   2643 
   (...)
   2752     5
   2753     """
-> 2754     return _wrapreduction(a, np.maximum, 'max', axis, None, out,
   2755                           keepdims=keepdims, initial=initial, where=where)

File ~/.virtualenvs/scipy-dev/lib/python3.8/site-packages/numpy/core/fromnumeric.py:86, in _wrapreduction(obj, ufunc, method, axis, dtype, out, **kwargs)
     83         else:
     84             return reduction(axis=axis, out=out, **passkwargs)
---> 86 return ufunc.reduce(obj, axis, dtype, out, **passkwargs)

ValueError: zero-size array to reduction operation maximum which has no identity

NumPy/Python version information:

In [8]: np.version
Out[8]: '1.21.1'

Context for the issue:

Seen as a part of scipy/scipy#17241 (comment). Can be worked around of course, am just reporting that it needs a workaround.

[eric-wieser]

This is by design; what would you expect instead?

[eric-wieser]

I suppose you could make the argument that it should return -inf

[ev-br]

On the face of it, -inf sounds reasonable, but I don't know enough to make a compelling argument.

From a user perspective, it would be best if these zero-sized arrays were either not allowed at all (raise on construction?) or behave consistently (for some definition of being consistent). The latter expectation is nicely expressed by Warren in scipy/scipy#17241 (comment).

Otherwise, they regularly need to be special-cased in user code. OTOH, this is all a minor annoyance anyway, and workarounds are not too difficult. Cf scipy/scipy#17305 for a typical example (this is just a recent one out of I don't remember how many; the gut feeling is that this corner case shows up "rarely but regularly", but I've no hard data).

[seberg]

This has been discussed a few times, I have no strong opinion either way. Also maybe a bit discussed here.

Just to be sure you are aware, you can also pass initial=-np.inf.

[ev-br]

Oh thanks, was not aware of the initial=-np.inf! And now that I am aware, I see that it's documented to solve exactly this issue, "Must be present to allow computation on empty slice."

A minor gripe is that this sentence is not very discoverable unless already known. Not that I have a good actionable suggestion though.

Using initial=-np.inf fixes the original downstream problem that lead me to reporting this, so this issue can be closed unless it's useful for a more general discussion of zero-sized arrays (which I doubt, but in case of ambiguity etc).

[seberg]

Well, for a long time it might have been a bit trick to have -inf as an identity. That would change after gh-20970.
So it isn't a bad time for someone with a mission to ask for a change :).