20 Aug
2020
20 Aug
'20

8:17 p.m.

On Thu, 2020-08-20 at 17:08 -0600, Aaron Meurer wrote:

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

I am not sure anyone does it, but I certainly can think of ways to use this functionality:

``` def good_images(image_or_stack): """Filter dark images

image_or_stack : ndarray (..., N, M, 3)

Returns ------- good_images : ndarray (K, N, M, 3) Returns all good images as a one dimensional stack for further processing, where `K` is the number of good images. """ assert image_or_stack.ndim >= 3 assert image_or_stack.shape[-1] == 3 # 3 colors, fixed.

average_brightness = image_or_stack.mean((-3, -2, -1))

return image_or_stack[average_brigthness, ...] ```

Note that the above uses a single True/False if you pass in a single image.

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

I think they are perfectly fine semantically, but they definitely do require special handling. Although the reason for that special handling is that we have to implement boolean indices using integer array indices and that is not possible without additional logic.

If you browse the NumPy code, you will see there is a `HAS_0D_BOOL` macro (basically enum), to distinguish:

internal_indx = np.nonzero(False)

and:

internal_indx = np.nonzero([False])

because the first effectively inserts a new dimension and then indices it, while the former just indices an existing dimension.

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.

I hope the example above helps you, I think you should always remember the two rules of boolean indexing mentioned somewhere in the docs:

* A boolean array indexes into `arr.ndim` dimensions, and effectively removes them. * A boolean array index adds a single input array.

I guess, I should have written that mock-up code (maybe you can help improve the NumPy docs, although I guess this might be too technical):

``` def preprocess_boolean_indices(arr, indices): """Take an array and indices and returns a new array and new indices without any boolean ones.

NOTE: Code will not handle None or Ellipsis """ new_indices = [] for axis, index in enumerate(indices): if not is_boolean_index(index): new_indices.append(index)

# Check whether dimensions match here! new_indices.extend(np.nonzero(indices)) if index.ndim == 0: # nonzero result added an index, but we # should index into 0-dimensions, so add one. # (Ellipsis or None would mean `axis` is incorrect) arr = np.expand_dims(arr, axis)

return arr, indices

prep_arr, prep_indices = preprocess_boolean_indices(arr, indices) arr[indices] == prep_arr[prep_indices] ```

That is ugly, but the issue is not in the semantics of 0-D booleans, but rather in the translating boolean indices to integer indices.

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

Yeah, either always transpose or just refuse the "separated by" cases. It is an interesting angle to only support the cases where axis insertion can be done as "expected", I remember mainly the discussion to just always transpose.

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

Absolutely agree with that step (I don't know if you are careful with scalars and 0D arrays, it would be the only issue I can think of).

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.

Right, the implementation is likely straight forward. But the semantics of it is pretty weird (or impossible), almost any trial will show that, I think:

arr = np.arange(12).reshape(3, 4) arr # array([[ 0, 1, 2, 3], # [ 4, 5, 6, 7], # [ 8, 9, 10, 11]]) arr[[True, False, True], [True, False, False, False]] # array([0, 8])

OK, you can reason about that, but only because there is a single boolean True in the second array (and then gets broadcast.

arr[[True, False, True], [True, False, True, False]] # array([ 0, 10])

Ok, we can reason about this, but at that point we have to align the True values from the first index with those from the second (effectively convert the two indices to integer ones in our heads).

But what is the meaning of aligning true values? I am sure there is none, except in very special cases. To proof this, lets try:

arr[[True, True, True], [True, False, True, False]]

which gives a broadcasting error :).

So yeah, I guess you can find "meaning" for it but it seems just too strange, and even if you do using two integer indices will make things much clearer and less error prone.

- Sebastian

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

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