If I have two numpy array of shape (N, 3) like
array1 = np.array([[x1, y1, 1],
........
[xn, yn, 1]])
array2 = np.array([[u1, v1, 1],
........
[un, vn, 1]])
I want
A = np.array([[x1 * u1, x1 * v1, x1, y1 * u1, y1 * v1, y1, u1, v1, 1],
.........
[xn * un, xn * vn, xn, yn * un, yn * vn, yn, un, vn, 1]]
How should I do it without using for loops to iterate through?
You clearly want a broadcasted multiplication along the second dimension. The trick with all problems like these is to remember that numpy ravels/reshapes in C order by default.
Let's analyze the rows of the output to see how to arrange the product. You have
[x1 * u1, x1 * v1, x1 * 1, y1 * u1, y1 * v1, y1 * 1, u1, v1, 1]
This is the raveled version of
[[x1 * u1, x1 * v1, x1 * 1],
[y1 * u1, y1 * v1, y1 * 1],
[ 1 * u1, 1 * v1, 1 * 1]]
Which in turn is the product
array1[0][:, None] * array2[0][None, :]
So the product you want keeps the first dimension and broadcasts the second as shown above. Then you ravel the last two dimensions together to get the partial Kronecker product:
A = (array1[:, :, None] * array2[:, None, :]).reshape(array1.shape[0], -1)
This is called Kronecker product. You can do that using np.kron() function like:
import numpy as np
array1 = np.array([[1,2,1],
[3,4,1]])
array2 = np.array([[3,4,1],
[1,0,1]])
N = array1.shape[0]
result = np.kron(array1, array2)
# A (NxN) x 9 output
#array([[ 3, 4, 1, 6, 8, 2, 3, 4, 1],
# [ 1, 0, 1, 2, 0, 2, 1, 0, 1],
# [ 9, 12, 3, 12, 16, 4, 3, 4, 1],
# [ 3, 0, 3, 4, 0, 4, 1, 0, 1]])
If you want a one to one Kronecker product, you might also use:
# N x 9
np.kron(array1, array2)[0:N*N:N, :]
#array([[ 3, 4, 1, 6, 8, 2, 3, 4, 1],
# [ 9, 12, 3, 12, 16, 4, 3, 4, 1]])
which is not recommended if performance matters.
kron. It's useful and at the very least, quite relevant.