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