I have a list of 3D points stored in numpy array A with shape (N,3) and a rotation matrix R with shape (3,3). I'd like to compute the dot product of R.x for each point x in A in-place. Naively I can do this:
for n in xrange(N):
A[n,:] = dot(R, A[n,:])
Is there a way to vectorize this with a native numpy call? If it matters, N is on order of a couple thousand.
You can multiply A with the transpose of the rotation matrix:
A = dot(A, R.T)
There's a couple of minor updates/points of clarification to add to Aapo Kyrola's (correct) answer. First, the syntax of the matrix multiplication can be slightly simplified using the recently added matrix multiplication operator @:
A = A @ R.T
Also, you can arrange the transformation in the standard form (rotation matrix first) by taking the transpose of A prior to the multiplication, then transposing the result:
A = (R @ A.T).T
You can check that both forms of the transformation produce the same results via the following assertion:
np.testing.assert_array_equal((R @ A.T).T, A @ R.T)
