Efficiently rotate a set of points with a rotation matrix in numpy

Question

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.

Answer 1

You can multiply A with the transpose of the rotation matrix:

A = dot(A, R.T) 

Answer 2

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)