CODEWITHSUNDEEP
python-3.xnumpytensor
Junk Warrior
Junk Warrior

Reputation: 101

Numpy: How to perform the outer product of four vectors and then summing them?

A = [a1, a2], B = [b1, b2], C = [c1, c2], D = [d1, d2].

The outer product of A, B, C, D is just:

[
    [
        [[a1*b1*c1*d1, a1*b1*c1*d2], [a1*b1*c1*d1, a1*b1*c2*d2]], 
        [[a1*b2*c2*d1, a1*b2*c1*d2], [a1*b2*c2*d1, a1*b2*c2*d2]]
    ],
    [
        [[a2*b1*c1*d1, a2*b1*c1*d2], [a2*b1*c2*d1, a2*b1*c2*d2]], 
        [[a2*b2*c1*d1, a2*b2*c1*d2], [a2*b2*c2*d1, a2*b2*c2*d2]]
    ]
]

In numpy, the outer product is thus an array of shape (2, 2, 2, 2). I know how to do this. The problem is, I have 100 this kind of A, B, C, D. They are taken from A_k, B_k, C_k, D_k by fixing k. So they are actually array of shape (2, 100) or (100, 2). Actually may be (20, 100) or (100, 20). I use 2 to simplify the writing. What I want to do is: do this kind of outer product for 100 times and then sum them up. That is: to sum 100 arrays of shape (2, 2, 2, 2). How can I do this efficiently with numpy? If better, is there any GPU acceleration way of doing this?

If A, B, C, D are just 1d array, I know how to do this. The following one-line code works fine:

a[:, None, None, None] * b[None, :, None, None] * c[None, None, :, None] * d[None, None, None, :]

Upvotes: 0

Views: 169

Answers (1)

NLi10Me
NLi10Me

Reputation: 3302

numpy.einsum plus numpy.sum with careful selection of axes should give you what you need.

Upvotes: 1

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