21 Aug
2020
21 Aug
'20

12:08 a.m.

On Thu, Aug 20, 2020 at 4:38 PM Sebastian Berg sebastian@sipsolutions.net wrote:

On Thu, 2020-08-20 at 16:00 -0600, Aaron Meurer wrote:

Just to be clear, what exactly do you think should be deprecated? Boolean scalar indices in general, or just boolean scalars combined with other arrays, or something else?

My angle is that we should allow only:

Any number of integer array indices (ideally only explicitly with `arr.vindex[]`, but we do not have that luxury right now.)

A single boolean index (array or scalar is identical)

but no mix of the above (including multiple boolean indices).

Because I think they are at least one level more confusing than multiple advanced indices.

I admit, I forgot that the broadcasting logic is fine in this case:

arr = np.zeros((2, 3)) arr[[True], np.array(3)]

where the advanced index is also a scalar index. In that case the result is straight forward, since broadcasting does not affect `np.array(3)`.

I am happy to be wrong about that assessment, but I think your opinion on it could likely push us towards just doing a Deprecation. The only use case for "multiple boolean indices" that I could think of was this:

`arr = np.diag([1, 2, 3, 4]) # 2-d square array indx = arr.diagonal() > 2 # mask for each row and column masked_diagonal = arr[indx, indx] print(repr(masked_diagonal)) # array([3, 4])`

and my guess is that the reaction to that code is a: "Wait what?!"

That code might seem reasonable, but it only works if you have the exact same number of `True` values in the two indices. And if you have the exact same number but two different arrays, then I fail to reason about the result without doing the `nonzero` step, which I think indicates that there just is no logical concept for it.

So, I think we may be better of forcing the few power-user who may have found a use for this type of nugget to use `np.nonzero()` or find another solution.

Well I'm cautious because despite implementing the logic for all this, I'm a bit divorced from most use-cases. So I don't have a great feeling for what is currently being used. For example, is it possible to have a situation where you build a mask out of an expression, like a[x > 0] or whatever, where the mask expression could be any number of dimensions depending on the input values? And if so, does the current logic for scalar booleans do the right thing when the number of dimensions happens to be 0.

Mixing nonscalar boolean and integer arrays seems fine, as far as the logic is concerned. I'm not really sure if it makes sense semantically. I'll have to think about it more. The thing that has the most odd corner cases in the indexing logic is boolean scalars. It would be nice if you could treat them uniformly with the same logic as other boolean arrays, but they have special cases everywhere. This is in contrast with integer scalars which perfectly match the logic of integer arrays with the shape == (). Maybe I'm just not looking at it from the right angle. I don't know.

In ndindex, I've left the "arrays separated by slices, ellipses, or newaxes" case unimplemented. Travis Oliphant told me he thinks it was a mistake and it would be better to not allow it. I've also left boolean scalars mixed with other arrays unimplemented because I don't want to waste more time trying to figure out what is going on in the example I posted earlier (though what you wrote helps). I have nonscalar boolean arrays mixed with integer arrays working just fine, and the logic isn't really any different than it would be if I only supported them separately.

Aaron Meurer

- Sebastian
Aaron Meurer

On Thu, Aug 20, 2020 at 3:56 PM Sebastian Berg sebastian@sipsolutions.net wrote:

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.

- Convert all boolean indices into a series of integer indices
using `np.nonzero(index)`

- 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).

- 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. > > Aaron Meurer > _______________________________________________ > NumPy-Discussion mailing list > NumPy-Discussion@python.org > https://mail.python.org/mailman/listinfo/numpy-discussion >

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