[Numpy-discussion] dot/tensordot limitations
Charles R Harris
charlesr.harris@gmail....
Wed Apr 30 02:16:07 CDT 2008
On Tue, Apr 29, 2008 at 4:41 PM, Anne Archibald <peridot.faceted@gmail.com>
wrote:
> Timothy Hochberg has proposed a generalization of the matrix mechanism
> to support manipulating arrays of linear algebra objects. For example,
> one might have an array of matrices one wants to apply to an array of
> vectors, to yield an array of vectors:
>
> In [88]: A = np.repeat(np.eye(3)[np.newaxis,...],2,axis=0)
>
> In [89]: A
> Out[89]:
> array([[[ 1., 0., 0.],
> [ 0., 1., 0.],
> [ 0., 0., 1.]],
>
> [[ 1., 0., 0.],
> [ 0., 1., 0.],
> [ 0., 0., 1.]]])
>
> In [90]: V = np.array([[1,0,0],[0,1,0]])
>
> Currently, it is very clumsy to handle this kind of situation even
> with arrays, keeping track of dimensions by hand. For example if one
> wants to multiply A by V "elementwise", one cannot simply use dot:
>
Let A have dimensions LxMxN and b dimensions LxN, then sum(A*b[:,newaxis,:],
axis=-1) will do the trick.
Example:
In [1]: A = ones((2,2,2))
In [2]: b = array([[1,2],[3,4]])
In [3]: A*b[:,newaxis,:]
Out[3]:
array([[[ 1., 2.],
[ 1., 2.]],
[[ 3., 4.],
[ 3., 4.]]])
In [4]: sum(A*b[:,newaxis,:], axis=-1)
Out[4]:
array([[ 3., 3.],
[ 7., 7.]])
Chuck
Chuck
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