[Numpy-discussion] Consider improving numpy.outer's behavior with zero-dimensional vectors

josef.pktd at gmail.com josef.pktd at gmail.com
Fri Apr 17 15:18:16 EDT 2015 

On Fri, Apr 17, 2015 at 2:56 PM, Sebastian Berg
<sebastian at sipsolutions.net> wrote:
> On Fr, 2015-04-17 at 12:40 -0400, josef.pktd at gmail.com wrote:
>> On Fri, Apr 17, 2015 at 12:16 PM, Neil Girdhar <mistersheik at gmail.com> wrote:
>> >
>> >
>> > On Fri, Apr 17, 2015 at 12:09 PM, <josef.pktd at gmail.com> wrote:
>> >>
>> >> On Fri, Apr 17, 2015 at 11:22 AM, Neil Girdhar <mistersheik at gmail.com>
>> >> wrote:
>> >> >
>> >> >
>> >> > On Fri, Apr 17, 2015 at 10:47 AM, <josef.pktd at gmail.com> wrote:
>> >> >>
>> >> >> On Fri, Apr 17, 2015 at 10:07 AM, Sebastian Berg
>> >> >> <sebastian at sipsolutions.net> wrote:
>> >> >> > On Do, 2015-04-16 at 15:28 -0700, Matthew Brett wrote:
>> >> >> >> Hi,
>> >> >> >>
>> >> >> > <snip>
>> >> >> >>
>> >> >> >> So, how about a slight modification of your proposal?
>> >> >> >>
>> >> >> >> 1) Raise deprecation warning for np.outer for non 1D arrays for a
>> >> >> >> few
>> >> >> >> versions, with depraction in favor of np.multiply.outer, then
>> >> >> >> 2) Raise error for np.outer on non 1D arrays
>> >> >> >>
>> >> >> >
>> >> >> > I think that was Neil's proposal a bit earlier, too. +1 for it in any
>> >> >> > case, since at least for the moment I doubt outer is used a lot for
>> >> >> > non
>> >> >> > 1-d arrays. Possible step 3) make it work on higher dims after a long
>> >> >> > period.
>> >> >>
>> >> >> sounds ok to me
>> >> >>
>> >> >> Some random comments of what I remember or guess in terms of usage
>> >> >>
>> >> >> I think there are at most very few np.outer usages with 2d or higher
>> >> >> dimension.
>> >> >> (statsmodels has two models that switch between 2d and 1d
>> >> >> parameterization where we don't use outer but it has similar
>> >> >> characteristics. However, we need to control the ravel order, which
>> >> >> IIRC is Fortran)
>> >> >>
>> >> >> The current behavior of 0-D scalars in the initial post might be
>> >> >> useful if a numpy function returns a scalar instead of a 1-D array in
>> >> >> size=1. np.diag which is a common case, doesn't return a scalar (in my
>> >> >> version of numpy).
>> >> >>
>> >> >> I don't know any use case where I would ever want to have the 2d
>> >> >> behavior of np.multiply.outer.
>> >> >
>> >>
>> >> I only understand part of your example, but it looks similar to what
>> >> we are doing in statsmodels.
>> >>
>> >> >
>> >> > My use case is pretty simple.  Given an input vector x, and a weight
>> >> > matrix
>> >> > W, and a model y=Wx, I calculate the gradient of the loss L with respect
>> >> > W.
>> >> > It is the outer product of x with the vector of gradients dL/dy.  So the
>> >> > code is simply:
>> >> >
>> >> > W -= outer(x, dL_by_dy)
>> >>
>> >> if you sum/subtract over all the values, isn't this the same as
>> >> np.dot(x, dL_by_dy)
>> >>
>> >
>> > What?  Matrix subtraction is element-wise:
>> >
>> > In [1]: x = np.array([2,3,4])
>> >
>> > In [2]: dL_by_dy = np.array([7,9])
>> >
>> > In [5]: W = np.zeros((3, 2))
>> >
>> > In [6]: W -= np.outer(x, dL_by_dy)
>> >
>> > In [7]: W
>> > Out[7]:
>> > array([[-14., -18.],
>> >        [-21., -27.],
>> >        [-28., -36.]])
>>
>>
>> Ok, different use case
>>
>> mine are more like variations on the following
>>
>> >>> a1 = np.arange(18).reshape(6,3)
>> >>> a2 = np.arange(12).reshape(6, 2)
>> >>> index = [1, 2, 5]
>>
>>
>> text book version
>> >>> np.sum([np.outer(a1[i], a2[i]) for i in index], 0)
>> array([[180, 204],
>>        [196, 223],
>>        [212, 242]])
>>
>> simpler
>> >>> np.dot(a1[index].T, a2[index])
>> array([[180, 204],
>>        [196, 223],
>>        [212, 242]])
>>
>>
>> >
>> >> >
>> >> > Sometimes, I have some x_indices and y_indices.  Now I want to do:
>> >> >
>> >> > W[x_indices, y_indices] -= outer(x[x_indices], dL_by_dy[y_indices])
>> >> >
>> >> > Unfortunately, if x_indices or y_indices are "int" or slice in some way
>> >> > that
>> >> > removes a dimension, the left side will have fewer dimensions than the
>> >> > right.  np.multipy.outer does the right thing without the ugly cases:
>> >> >
>> >> > if isinstance(x_indices, int): … # ugly hacks follow.
>> >>
>> >> My usual hacks are either to use np.atleast_1d or np.atleast_1d or
>> >> np.squeeze if there is shape mismatch in some cases.
>> >
>> >
>> > Yes, but in this case, the left side is the problem, which has too few
>> > dimensions.  So atleast_1d doesn't work.  I was conditionally squeezing, but
>> > that is extremely ugly.  Especially if you're conditionally squeezing based
>> > on both x_indices and y_indices.
>>
>> I don't remember if I ever used something like this
>>
>> >>> a1[0, 1]
>> 1
>> >>> a1[np.atleast_1d(0), np.atleast_1d(1)]
>> array([1])
>>
>> >>> a1[np.atleast_1d(0), np.atleast_1d(1)] = [[100]]
>>
>> >>> a1[0, 1]  = [[100]]
>> Traceback (most recent call last):
>>   File "<pyshell#314>", line 1, in <module>
>>     a1[0, 1]  = [[100]]
>> ValueError: setting an array element with a sequence.
>>
>
> Hehe, yeah, that difference. But if you really want that, you can
> usually do a1[0, 1, ...] if you don't mind the ugliness.

I'm not sure what you mean, although it sounds like a nice trick.
This doesn't work for me

>>> a1[0, 1, ...]  = [[100]]
Traceback (most recent call last):
  File "<pyshell#315>", line 1, in <module>
    a1[0, 1, ...]  = [[100]]
ValueError: assignment to 0-d array

>>> np.__version__
'1.9.2rc1'
>>> a1[0, 1,

Josef



>
>> Josef
>>
>>
>> >
>> >>
>> >>
>> >> >
>> >> >> I guess we will or would have applications for outer along an axis,
>> >> >> for example if x.shape = (100, 10), then we have
>> >> >> x[:,None, :] * x[:, :, None]     (I guess)
>> >> >> Something like this shows up reasonably often in econometrics as
>> >> >> "Outer Product". However in most cases we can avoid constructing this
>> >> >> matrix and get the final results in a more memory efficient or faster
>> >> >> way.
>> >> >> (example an array of covariance matrices)
>> >> >
>> >> >
>> >> > Not sure I see this.  outer(a, b) should return something that has
>> >> > shape:
>> >> > (a.shape + b.shape).  If you're doing it "along an axis", you mean
>> >> > you're
>> >> > reshuffling the resulting shape vector?
>> >>
>> >> No I'm not reshaping the full tensor product.
>> >>
>> >> It's a vectorized version of looping over independent outer products
>> >>
>> >> np.array([outer(xi, yi) for xi,yi in zip(x, y)])
>> >> (which I would never use with outer)
>> >>
>> >> but I have code that works similar for a reduce (or reduce_at) loop over
>> >> this.
>> >>
>> >> Josef
>> >>
>> >>
>> >> >>
>> >> >>
>> >> >> Josef
>> >> >>
>> >> >>
>> >> >>
>> >> >>
>> >> >> >
>> >> >> > - Sebastian
>> >> >> >
>> >> >> >
>> >> >> >> Best,
>> >> >> >>
>> >> >> >> Matthew
>> >> >> >> _______________________________________________
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>> >> >> >>
>> >> >> >
>> >> >> >
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>> >> >
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