np.tensordot旋转点云？

Question

Rotation about the origin is a matrix product that can be done with numpy's dot function,

import numpy as np
points = np.random.rand(100,3)  # 100 X, Y, Z tuples.  shape = (100,3)
rotation = np.identity(3)  # null rotation for example
out = np.empty(points.shape)
for idx, point in enumerate(points):
    out[idx,:] = np.dot(rotation, point)

This involves a for loop, or numpy tile could be used to vectorize. I think there is an implementation involving np.tensordot, but the function is witchcraft to me. Is this possible?

Answer 1

There are several ways you can do that. With np.matmul you can do:

out = np.matmul(rotation, points[:, :, np.newaxis])[:, :, 0]

Or, equivalently, if you are using Python 3.5 or later:

out = (rotation @ points[:, :, np.newaxis])[:, :, 0]

Another way is with np.einsum :

out = np.einsum('ij,nj->ni', rotation, points)

Finally, as you suggested, you can also use np.tensordot :

out = np.tensordot(points, rotation, axes=[1, 1])

Note that in this case points is the first argument and rotation the second, otherwise the dimensions at the output would be reversed.