[Numpy-discussion] Apply transform to many small matrices

[Jorge Scandaliaris]

Jorge Scandaliaris <jorgesmbox-ml <at> yahoo.es> writes:

<...>
> I have an ndarray A of shape (M,2,2) representing M 2 x 2 matrices.
> Now I want to apply a transform T of shape (2,2) to each of matrix.
> The way I do this now is by iterating over all rows of A 
> multiplying the matrices using numpy.dot():
> 
> for row in np.arange(A.shape[0]):
>     A[row] = np.dot(A[row],T)
> 
> but this seems to be slow when M is large and I have the feeling 
> there must be a way of doing it better.
> 

Well, I think I getting close, but still don't understand exactly what
I am doing:

A = array([[[ 1,  2],
        [ 3,  4]],

       [[ 5,  6],
        [ 7,  8]],

       [[ 9, 10],
        [11, 12]]])
T = array([[1, 2],
       [3, 4]])

np.tensordot(a, T.T, axes=((2,),(1,))) gives 

array([[[ 7, 10],
        [15, 22]],

       [[23, 34],
        [31, 46]],

       [[39, 58],
        [47, 70]]])

which is what I want. The problem is that I only arrived at this result after
trying many axes combinations, and the transpose in T was just intuition (The
idea of using tensordot came from reading various posts in the list). Can
someone help grasp tensordot, the doc is a bit cryptic to me.

Thanks,

Jorges