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

Fri Apr 17 14:56:26 EDT 2015

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.

> 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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> >> >> >> NumPy-Discussion at scipy.org
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> >> >> >>
> >> >> >
> >> >> >
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> >> >> >
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> >> >
> >> >
> >> >
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