What is up with raw boolean indices (like a[False])?
I've been trying to figure out this behavior. It doesn't seem to be documented at https://numpy.org/doc/stable/reference/arrays.indexing.html
a = np.empty((2, 3)) a.shape
(2, 5)
a[True].shape
(1, 2, 5)
a[False].shape
(0, 2, 5)
It seems like indexing with a raw boolean (True or False) adds an axis with a dimension 1 or 0, resp.
Except it only works once:
a[:,False]
array([], shape=(2, 0, 3), dtype=float64)
a[:,False, False]
array([], shape=(2, 0, 3), dtype=float64)
a[:,False,True].shape
(2, 0, 3)
a[:,True,False].shape
(2, 0, 3)
The docs say "A single boolean index array is practically identical to x[obj.nonzero()]". I have a hard time seeing this as an extension of that, since indexing by `np.nonzero(False)` or `np.nonzero(True)` *replaces* the given axis.
a[np.nonzero(True)].shape
(1, 3)
a[np.nonzero(False)].shape
(0, 3)
I think at best this behavior should be documented. I'm trying to understand the motivation for it, or if it's even intentional. And in particular, why do multiple boolean indices not insert multiple axes? It would actually be useful to be able to generically add length 0 axes using an index, similar to how `newaxis` adds a length 1 axis.
Aaron Meurer
On Mon, 20200706 at 12:39 0600, Aaron Meurer wrote:
I've been trying to figure out this behavior. It doesn't seem to be documented at https://numpy.org/doc/stable/reference/arrays.indexing.html
a = np.empty((2, 3)) a.shape
(2, 5)
a[True].shape
(1, 2, 5)
a[False].shape
(0, 2, 5)
It seems like indexing with a raw boolean (True or False) adds an axis with a dimension 1 or 0, resp.
Except it only works once:
a[:,False]
array([], shape=(2, 0, 3), dtype=float64)
a[:,False, False]
array([], shape=(2, 0, 3), dtype=float64)
a[:,False,True].shape
(2, 0, 3)
a[:,True,False].shape
(2, 0, 3)
The docs say "A single boolean index array is practically identical to x[obj.nonzero()]". I have a hard time seeing this as an extension of that, since indexing by `np.nonzero(False)` or `np.nonzero(True)` *replaces* the given axis.
a[np.nonzero(True)].shape
(1, 3)
a[np.nonzero(False)].shape
(0, 3)
I think at best this behavior should be documented. I'm trying to understand the motivation for it, or if it's even intentional. And in particular, why do multiple boolean indices not insert multiple axes? It would actually be useful to be able to generically add length 0 axes using an index, similar to how `newaxis` adds a length 1 axis.
Its fully intentional as it is the correct generalization from an ND boolean index to include a 0D boolean index. To be fair, there is a footnote in the "Detailed notes" saying that: "the nonzero equivalence for Boolean arrays does not hold for zero dimensional boolean arrays.", this is for technical reasons since `nonzero` does not do useful things for 0D input.
In any case, a boolean index always does the following:
1. It will *remove as many dimensions as the index has, because this is the number of dimensions effectively indexed by it* 2. It will add a single new dimension at the same place. The length of this new dimension is the number of `True` elements. 3. If you have multiple advanced indexing you get annoying broadcasting of all of these. That is *always* confusing for boolean indices. 0D should not be too special there...
And this generalizes to 0D just as well, even if it may be a bit surprising at first.
I have written much of this more clearly once before in this NEP, which may be a good read to _really_ understand it:
https://numpy.org/neps/nep0021advancedindexing.html
In general, I wonder if going into much depth about how 0D arrays are not actually really handled very special is good. Yes, its confusing on its own, but it seems also a bit like overloading the user with unnecessary knowledge?
Cheers,
Sebastian
Aaron Meurer _______________________________________________ NumPyDiscussion mailing list NumPyDiscussion@python.org https://mail.python.org/mailman/listinfo/numpydiscussion
Its fully intentional as it is the correct generalization from an ND boolean index to include a 0D boolean index. To be fair, there is a footnote in the "Detailed notes" saying that: "the nonzero equivalence for Boolean arrays does not hold for zero dimensional boolean arrays.", this is for technical reasons since `nonzero` does not do useful things for 0D input.
In any case, a boolean index always does the following:
 It will *remove as many dimensions as the index has, because this is the number of dimensions effectively indexed by it*
 It will add a single new dimension at the same place. The length of this new dimension is the number of `True` elements.
 If you have multiple advanced indexing you get annoying broadcasting of all of these. That is *always* confusing for boolean indices. 0D should not be too special there...
And this generalizes to 0D just as well, even if it may be a bit surprising at first.
I guess if those are the base rules for boolean indices this makes sense. So that brings up the question then, is there a way to add arbitrary empty dimensions using an index?
I have written much of this more clearly once before in this NEP, which may be a good read to _really_ understand it: https://numpy.org/neps/nep0021advancedindexing.html In general, I wonder if going into much depth about how 0D arrays are not actually really handled very special is good. Yes, its confusing on its own, but it seems also a bit like overloading the user with unnecessary knowledge?
The page I referenced is already written like a very highly technical document, so I think it should embrace that and fully describe the spec of NumPy indexing. NumPy could use more userfriendly documentation for indexing, but that page ain't it. FWIW, I wrote some documentation on slices of my own here https://quansight.github.io/ndindex/slices.html. I eventually plan to extend this to all forms of NumPy indexing. Anyway, the three bullet points you mentioned above would be helpful to include in the docs.
Cheers, Sebastian
 If you have multiple advanced indexing you get annoying broadcasting of all of these. That is *always* confusing for boolean indices. 0D 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:
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 1dimensional, 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.
From what I can tell, the logic is that all integer and boolean arrays
(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
On Wed, 20200819 at 18:07 0600, Aaron Meurer wrote:
 If you have multiple advanced indexing you get annoying
broadcasting of all of these. That is *always* confusing for boolean indices. 0D 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 1dimensional, 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 0D 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 _______________________________________________ NumPyDiscussion mailing list NumPyDiscussion@python.org https://mail.python.org/mailman/listinfo/numpydiscussion
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.
Aaron Meurer
On Wed, Aug 19, 2020 at 6:55 PM Sebastian Berg sebastian@sipsolutions.net wrote:
On Wed, 20200819 at 18:07 0600, Aaron Meurer wrote:
 If you have multiple advanced indexing you get annoying
broadcasting of all of these. That is *always* confusing for boolean indices. 0D 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 1dimensional, 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 0D 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 _______________________________________________ NumPyDiscussion mailing list NumPyDiscussion@python.org https://mail.python.org/mailman/listinfo/numpydiscussion
NumPyDiscussion mailing list NumPyDiscussion@python.org https://mail.python.org/mailman/listinfo/numpydiscussion
On Thu, 20200820 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 mockup/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):
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, 20200819 at 18:07 0600, Aaron Meurer wrote:
 If you have multiple advanced indexing you get annoying
broadcasting of all of these. That is *always* confusing for boolean indices. 0D 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 1dimensional, 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 _______________________________________________ NumPyDiscussion mailing list NumPyDiscussion@python.org https://mail.python.org/mailman/listinfo/numpydiscussion
NumPyDiscussion mailing list NumPyDiscussion@python.org https://mail.python.org/mailman/listinfo/numpydiscussion
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On Thu, 20200820 at 16:50 0500, Sebastian Berg wrote:
On Thu, 20200820 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 mockup/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 preprocessing.
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, 20200819 at 18:07 0600, Aaron Meurer wrote:
 If you have multiple advanced indexing you get annoying
broadcasting of all of these. That is *always* confusing for boolean indices. 0D 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 1dimensional, 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 _______________________________________________ NumPyDiscussion mailing list NumPyDiscussion@python.org https://mail.python.org/mailman/listinfo/numpydiscussion
NumPyDiscussion mailing list NumPyDiscussion@python.org https://mail.python.org/mailman/listinfo/numpydiscussion
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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?
Aaron Meurer
On Thu, Aug 20, 2020 at 3:56 PM Sebastian Berg sebastian@sipsolutions.net wrote:
On Thu, 20200820 at 16:50 0500, Sebastian Berg wrote:
On Thu, 20200820 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 mockup/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 preprocessing.
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, 20200819 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. > 0D 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 1dimensional, 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 _______________________________________________ NumPyDiscussion mailing list NumPyDiscussion@python.org https://mail.python.org/mailman/listinfo/numpydiscussion
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On Thu, 20200820 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]) # 2d 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 poweruser who may have found a use for this type of nugget to use `np.nonzero()` or find another solution.
 Sebastian
Aaron Meurer
On Thu, Aug 20, 2020 at 3:56 PM Sebastian Berg sebastian@sipsolutions.net wrote:
On Thu, 20200820 at 16:50 0500, Sebastian Berg wrote:
On Thu, 20200820 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 mockup/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 preprocessing.
 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, 20200819 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. > > 0D 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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On Thu, Aug 20, 2020 at 4:38 PM Sebastian Berg sebastian@sipsolutions.net wrote:
On Thu, 20200820 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]) # 2d 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 poweruser 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 usecases. 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, 20200820 at 16:50 0500, Sebastian Berg wrote:
On Thu, 20200820 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 mockup/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 preprocessing.
 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, 20200819 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. > > > 0D 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 > _______________________________________________ > NumPyDiscussion mailing list > NumPyDiscussion@python.org > https://mail.python.org/mailman/listinfo/numpydiscussion >
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On Thu, 20200820 at 17:08 0600, Aaron Meurer wrote:
On Thu, Aug 20, 2020 at 4:38 PM Sebastian Berg sebastian@sipsolutions.net wrote:
On Thu, 20200820 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]) # 2d 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 poweruser 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 usecases. 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 mockup 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 0dimensions, 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 0D 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, 20200820 at 16:50 0500, Sebastian Berg wrote:
On Thu, 20200820 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 mockup/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 preprocessing.
 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, 20200819 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. > > > > 0D 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 > > _______________________________________________ > > NumPyDiscussion mailing list > > NumPyDiscussion@python.org > > https://mail.python.org/mailman/listinfo/numpydiscussion > > > > _______________________________________________ > NumPyDiscussion mailing list > NumPyDiscussion@python.org > https://mail.python.org/mailman/listinfo/numpydiscussion _______________________________________________ NumPyDiscussion mailing list NumPyDiscussion@python.org https://mail.python.org/mailman/listinfo/numpydiscussion
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NumPyDiscussion mailing list NumPyDiscussion@python.org https://mail.python.org/mailman/listinfo/numpydiscussion
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Aaron Meurer

Sebastian Berg