[Numpy-discussion] Is this a bug?

Nathaniel Smith njs at pobox.com
Tue Sep 16 19:32:32 EDT 2014


On Tue, Sep 16, 2014 at 6:56 PM, Jaime Fernández del Río
<jaime.frio at gmail.com> wrote:
> On Tue, Sep 16, 2014 at 3:26 PM, Charles R Harris
> <charlesr.harris at gmail.com> wrote:
>>
>> On Tue, Sep 16, 2014 at 2:51 PM, Nathaniel Smith <njs at pobox.com> wrote:
>>>
>>> On Tue, Sep 16, 2014 at 4:31 PM, Jaime Fernández del Río
>>> <jaime.frio at gmail.com> wrote:
>>> > If it is a bug, it is an extended one, because it is the same behavior
>>> > of
>>> > einsum:
>>> >
>>> >>>> np.einsum('i,i', [1,1,1], [1])
>>> > 3
>>> >>>> np.einsum('i,i', [1,1,1], [1,1])
>>> > Traceback (most recent call last):
>>> >   File "<stdin>", line 1, in <module>
>>> > ValueError: operands could not be broadcast together with remapped
>>> > shapes
>>> > [origi
>>> > nal->remapped]: (3,)->(3,) (2,)->(2,)
>>> >
>>> > And I think it is a conscious design decision, there is a comment about
>>> > broadcasting missing core dimensions here:
>>> >
>>> >
>>> > https://github.com/numpy/numpy/blob/master/numpy/core/src/umath/ufunc_object.c#L1940
>>>
>>> "intentional" and "sensible" are not always the same thing :-). That
>>> said, it isn't totally obvious to me what the correct behaviour for
>>> einsum is in this case.
>>>
>>> > and the code makes it very explicit that input argument dimensions with
>>> > the
>>> > same label are broadcast to a common shape, see here:
>>> >
>>> >
>>> > https://github.com/numpy/numpy/blob/master/numpy/core/src/umath/ufunc_object.c#L1956
>>> >
>>> > I kind of expect numpy to broadcast whenever possible, so this doesn't
>>> > feel
>>> > wrong to me.
>>>
>>> The case Chuck is talking about is like if we allowed matrix
>>> multiplication between an array with shape (n, 1) with an array with
>>> (k, m), because (n, 1) can be broadcast to (n, k). This feels VERY
>>> wrong to me, will certainly hide many bugs, and is definitely not how
>>> it works right now (for np.dot, anyway; apparently it does work that
>>> way for the brand-new gufunc np.linalg.matrix_multiply, but this must
>>> be an accident).
>>>
>>> > That said, it is hard to come up with convincing examples of how this
>>> > behavior would be useful in any practical context. But changing
>>> > something
>>> > that has been working like that for so long seems like a risky thing.
>>> > And I
>>> > cannot come with a convincing example of why it would be harmful
>>> > either.
>>>
>>> gufuncs are very new.
>>>
>>
>> Or at least newly used. They've been sitting around for years with little
>> use and less testing. This is probably (easily?) fixable as the shape of the
>> operands is available.
>>
>> In [22]: [d.shape for d in nditer([[1,1,1], [[1,1,1]]*3]).operands]
>> Out[22]: [(3,), (3, 3)]
>>
>> In [23]: [d.shape for d in nditer([[[1,1,1]], [[1,1,1]]*3]).operands]
>> Out[23]: [(1, 3), (3, 3)]
>>
>
> If we agree that it is broken, which I still am not fully sure of, then yes,
> it is very easy to fix. I have been looking into that code quite a bit
> lately, so I could patch something up pretty quick.
>
> Are we OK with the appending of size 1 dimensions to complete the core
> dimensions? That is, should matrix_multiply([1,1,1], [[1],[1],[1]]) work, or
> should it complain about the first argument having less dimensions than the
> core dimensions in the signature?

I think that by default, gufuncs should definitely *not* allow this.

Example case 1: qr can be applied equally well to a (1, n) array or an
(n, 1) array, but with different results. If the user passes in an
(n,) array, then how do we know which one they wanted?

Example case 2: matrix multiplication, as you know :-), is a case
where I do think we should allow for a bit more cleverness with the
core dimensions... but the appropriate cleverness is much more subtle
than just "prepend size 1 dimensions until things fit". Instead, for
the first argument you need to prepend, for the second argument you
need to append, and then you need to remove the corresponding
dimensions from the output. Specific cases:

# Your version gives:
matmul([1, 1, 1], [[1], [1], [1]]).shape == (1, 1)
# But this should be (1,) (try it with np.dot)

# Your version gives:
matmul([[1, 1, 1]], [1, 1, 1]) -> error, (1, 3) and (1, 3) are not conformable
# But this should work (second argument should be treated as (3, 1), not (1, 3))

So the default should be to be strict about core dimensions, unless
explicitly requested otherwise by the person defining the gufunc.

> Lastly, there is an interesting side effect of the way this broadcasting is
> handled: if a gufunc specifies a core dimension in an output argument only,
> and an `out` kwarg is not passed in, then the output array will have that
> core dimension set to be of size 1, e.g. if the signature of `f` is
> '(),()->(a)', then f(1, 2).shape is (1,). This has always felt funny to me,
> and I think that an unspecified dimension in an output array should either
> be specified by a passed out array, or raise an error about an unspecified
> core dimension or something like that. Does this sound right?

Does this have any use cases? My vote is that we simply disallow this
until we have concrete uses and can decide how to do it properly. That
way there won't be any backcompat concerns to deal with later.

-n

-- 
Nathaniel J. Smith
Postdoctoral researcher - Informatics - University of Edinburgh
http://vorpus.org



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