[Numpy-discussion] Dot/inner products with broadcasting?

Jaakko Luttinen jaakko.luttinen@aalto...
Wed Mar 20 10:10:02 CDT 2013


Well, thanks to seberg, I finally noticed that there is a dot product
function in this new module numpy.core.gufuncs_linalg, it was just named
differently (matrix_multiply instead of dot).

However, I may have found a bug in it:

import numpy.core.gufuncs_linalg as gula
A = np.arange(2*2).reshape((2,2))
B = np.arange(2*1).reshape((2,1))
gula.matrix_multiply(A, B)
----
ValueError: On entry to DGEMM parameter number 10 had an illegal value

-Jaakko

On 03/20/2013 03:33 PM, Jaakko Luttinen wrote:
> I tried using this inner1d as an alternative to dot because it uses
> broadcasting. However, I found something surprising: Not only is inner1d
> much much slower than dot, it is also slower than einsum which is much
> more general:
> 
> In [68]: import numpy as np
> 
> In [69]: import numpy.core.gufuncs_linalg as gula
> 
> In [70]: K = np.random.randn(1000,1000)
> 
> In [71]: %timeit gula.inner1d(K[:,np.newaxis,:],
> np.swapaxes(K,-1,-2)[np.newaxis,:,:])
> 1 loops, best of 3: 6.05 s per loop
> 
> In [72]: %timeit np.dot(K,K)
> 1 loops, best of 3: 392 ms per loop
> 
> In [73]: %timeit np.einsum('ik,kj->ij', K, K)
> 1 loops, best of 3: 1.24 s per loop
> 
> Why is it so? I thought that the performance of inner1d would be
> somewhere in between dot and einsum, probably closer to dot. Now I don't
> see any reason to use inner1d instead of einsum..
> 
> -Jaakko
> 
> On 03/15/2013 04:22 PM, Oscar Villellas wrote:
>> In fact, there is already an inner1d implemented in
>> numpy.core.umath_tests.inner1d
>>
>> from numpy.core.umath_tests import inner1d
>>
>> It should do the trick :)
>>
>> On Thu, Mar 14, 2013 at 12:54 PM, Jaakko Luttinen
>> <jaakko.luttinen@aalto.fi> wrote:
>>> Answering to myself, this pull request seems to implement an inner
>>> product with broadcasting (inner1d) and many other useful functions:
>>> https://github.com/numpy/numpy/pull/2954/
>>> -J
>>>
>>> On 03/13/2013 04:21 PM, Jaakko Luttinen wrote:
>>>> Hi!
>>>>
>>>> How can I compute dot product (or similar multiply&sum operations)
>>>> efficiently so that broadcasting is utilized?
>>>> For multi-dimensional arrays, NumPy's inner and dot functions do not
>>>> match the leading axes and use broadcasting, but instead the result has
>>>> first the leading axes of the first input array and then the leading
>>>> axes of the second input array.
>>>>
>>>> For instance, I would like to compute the following inner-product:
>>>> np.sum(A*B, axis=-1)
>>>>
>>>> But numpy.inner gives:
>>>> A = np.random.randn(2,3,4)
>>>> B = np.random.randn(3,4)
>>>> np.inner(A,B).shape
>>>> # -> (2, 3, 3) instead of (2, 3)
>>>>
>>>> Similarly for dot product, I would like to compute for instance:
>>>> np.sum(A[...,:,:,np.newaxis]*B[...,np.newaxis,:,:], axis=-2)
>>>>
>>>> But numpy.dot gives:
>>>> In [12]: A = np.random.randn(2,3,4); B = np.random.randn(2,4,5)
>>>> In [13]: np.dot(A,B).shape
>>>> # -> (2, 3, 2, 5) instead of (2, 3, 5)
>>>>
>>>> I could use einsum for these operations, but I'm not sure whether that's
>>>> as efficient as using some BLAS-supported(?) dot products.
>>>>
>>>> I couldn't find any function which could perform this kind of
>>>> operations. NumPy's functions seem to either flatten the input arrays
>>>> (vdot, outer) or just use the axes of the input arrays separately (dot,
>>>> inner, tensordot).
>>>>
>>>> Any help?
>>>>
>>>> Best regards,
>>>> Jaakko
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>>>>
>>>
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