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On Thu, 2020-08-20 at 16:50 -0500, Sebastian Berg wrote:
On Thu, 2020-08-20 at 12:21 -0600, Aaron Meurer wrote:
You're right. I was confusing the broadcasting logic for boolean arrays.
However, I did find this example
np.arange(10).reshape((2, 5))[np.array([[0, 0, 0, 0, 0]], dtype=np.int64), False] Traceback (most recent call last): File "<stdin>", line 1, in <module> IndexError: shape mismatch: indexing arrays could not be broadcast together with shapes (1,5) (0,)
That certainly seems to imply there is some broadcasting being done.
Yes, it broadcasts the array after converting it with `nonzero`, i.e. its much the same as:
indices = [[0, 0, 0, 0, 0]], *np.nonzero(False) indices = np.broadcast_arrays(*indices)
will give the same result (see also `np.ix_` which converts booleans as well for this reason, to give you outer indexing). I was half way through a mock-up/pseudo code, but thought you likely wasn't sure it was ending up clear. It sounds like things are probably falling into place for you (if they are not, let me know what might help you):
Sorry editing error up there, in short I hope those steps sense to you, note that the broadcasting is basically part of a later "integer only" indexing step, and the `nonzero` part is pre-processing.
1. Convert all boolean indices into a series of integer indices using `np.nonzero(index)`
2. For True/False scalars, that doesn't work, because `np.nonzero()`.
`nonzero` gave us an index array (which is good, we obviously want
one), but we need to index into `boolean_index.ndim == 0` dimensions! So that won't work, the approach using `nonzero` cannot generalize
here, although boolean indices generalize perfectly.
The solution to the dilemma is simple: If we have to index one dimension, but should be indexing zero, then we simply add that dimension to the original array (or at least pretend there was an additional dimension).
3. Do normal indexing with the result *including broadcasting*, we forget it was converted.
The other way to solve it would be to always reshape the original array to combine all axes being indexed by a single boolean index into one axis and then index it using `np.flatnonzero`. (But that would get a different result if you try to broadcast!)
In any case, I am not sure I would bother with making sense of this, except for sports! Its pretty much nonsense and I think the time understanding it is probably better spend deprecating it. The only reason I did not Deprecate itt before, is that I tried to do be minimal in the changes when I rewrote advanced indexing (and generalized boolean scalars correctly) long ago. That was likely the right start/choice at the time, since there were much bigger fish to catch, but I do not think anything is holding us back now.
Cheers,
Sebastian
Aaron Meurer
On Wed, Aug 19, 2020 at 6:55 PM Sebastian Berg <sebastian@sipsolutions.net> wrote:
On Wed, 2020-08-19 at 18:07 -0600, Aaron Meurer wrote:
3. If you have multiple advanced indexing you get annoying broadcasting of all of these. That is *always* confusing for boolean indices. 0-D should not be too special there...
OK, now that I am learning more about advanced indexing, this statement is confusing to me. It seems that scalar boolean indices do not broadcast. For example:
Well, broadcasting means you broadcast the *nonzero result* unless I am very confused... There is a reason I dismissed it. We could (and arguably should) just deprecate it. And I have doubts anyone would even notice.
> np.arange(2)[False, np.array([True, False])] array([], dtype=int64) > np.arange(2)[tuple(np.broadcast_arrays(False, > np.array([True, > False])))] Traceback (most recent call last): File "<stdin>", line 1, in <module> IndexError: too many indices for array: array is 1-dimensional, but 2 were indexed
And indeed, the docs even say, as you noted, "the nonzero equivalence for Boolean arrays does not hold for zero dimensional boolean arrays," which I guess also applies to the broadcasting.
I actually think that probably also holds. Nonzero just behave weird for 0D because arrays (because it returns a tuple). But since broadcasting the nonzero result is so weird, and since 0- D booleans require some additional logic and don't generalize 100% (code wise), I won't rule out there are differences.
From what I can tell, the logic is that all integer and boolean arrays
Did you try that? Because as I said above, IIRC broadcasting the boolean array without first calling `nonzero` isn't really whats going on. And I don't know how it could be whats going on, since adding dimensions to a boolean index would have much more implications?
- Sebastian
(and scalar ints) are broadcast together, *except* for boolean scalars. Then the first boolean scalar is replaced with and(all boolean scalars) and the rest are removed from the index. Then that index adds a length 1 axis if it is True and 0 if it is False.
So they don't broadcast, but rather "fake broadcast". I still contend that it would be much more useful, if True were a synonym for newaxis and False worked like newaxis but instead added a length 0 axis. Alternately, True and False scalars should behave exactly like all other boolean arrays with no exceptions (i.e., work like np.nonzero(), broadcast, etc.). This would be less useful, but more consistent.
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