[Numpy-discussion] What is up with raw boolean indices (like a[False])?

Sebastian Berg sebastian at sipsolutions.net
Thu Aug 20 20:17:32 EDT 2020

```On Thu, 2020-08-20 at 17:08 -0600, Aaron Meurer wrote:
> On Thu, Aug 20, 2020 at 4:38 PM Sebastian Berg
> <sebastian at 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
> >
> > 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
> >
> >     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]
> >     # 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

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])

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