Combinations of values of column vectors

Question

I need help in storing the combinations of column vectors' values in a numpy array.

My problem consists of two column vectors, having size nx1 and mx1, with n=m, and finding n combinations.

I then vertical stacked these column vectors in a matrix, having size nx2.

I found the combinations with the itertools.combination function of python, but I struggle to store them in a numpy array, since itertools gives n rows of tuples.

The main example I found online is reported below:

import itertools
val = [1, 2, 3, 4]
com_set = itertools.combinations(val, 2)

for i in com_set:
 print(i)

Output:

(1, 2)
(1, 3)
(1, 4)
(2, 3)
(2, 4)
(3, 4)

Now, in my case, I have two vectors, val and val1, different from each other.

And, I would need the output in a numpy array, possible a matrix, so I can apply the maximum likelihood estimation method on these values.

Answer 1

You are looking for itertools.product instead of itertools.combinations.

x = [1, 2, 3]
y = [4, 5, 6]
z = list(itertools.product(x, y))
# z = [(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6)]

You can turn the result into a (n * n, 2) shaped array by simply passing the result to np.array:

result = np.array(z)
# array([[1, 4],
#        [1, 5],
#        [1, 6],
#        [2, 4],
#        [2, 5],
#        [2, 6],
#        [3, 4],
#        [3, 5],
#        [3, 6]])

Finally, you can also do this with numpy directly, albeit in a different order:

result = np.stack(np.meshgrid(x, y)).reshape(2, -1).T
# array([[1, 4],
#        [2, 4],
#        [3, 4],
#        [1, 5],
#        [2, 5],
#        [3, 5],
#        [1, 6],
#        [2, 6],
#        [3, 6]])