How to get dot product of each array in (n,1,3) numpy array with all arrays of (n,3) array and get the resultant array of shape (n,n)?

Question

I tried einsum np.einsum but this is giving me error that the output cannot have same letters repeated.

np.einsum('aij,aj->aa', vector1, vector2)

Also tried np.dot method but that attempt is also futile.

(Broadcasting might be having an answer for this.)
Tried

np.sum(vector1[:,np.newaxis] * vector2, axis=axis)

But, this is also giving me an error Here are the vectors 1 and 2

vector1 = np.arange(12).reshape((4,1,3))
vector2 = np.arange(12).reshape((4,3))

Thank you everyone for the comments.Apologies for asking the question incorrectly. (I needed n,n shape rather than n,3).

I am able to achieve it in the following way: np.einsum(‘ijk,bk->ib’,vector1,vector2)

Please post the inputs for vector1 and vector2 so your problem can be replicated. Thank you. — Jesse Sealand
– Jesse Sealand, Commented Sep 5, 2023 at 10:24
Do you just want np.einsum('aij,aj->aj', vector1, vector2)? — Matt Pitkin
– Matt Pitkin, Commented Sep 5, 2023 at 10:45
With (n,1,3) and (n,3) arrays, what's the sum-of-products dimension? Looks like you want to preserve the '3'. A[:,0,:] *B would produce a (n,3) result without any sum's. einsum('aij,aj->aj' will use A.sum(axis=1) * B. Neither is a dot product. — hpaulj
– hpaulj, Commented Sep 5, 2023 at 16:15
Other answers make a (n,3,3) result, and then sum on one of the 3s. You suggested two arrays, but did not give a desired result. So the question is still ambiguous. — hpaulj
– hpaulj, Commented Sep 5, 2023 at 18:27

KamiSama · Accepted Answer · 2023-09-05 10:57:43Z

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Indeed my friend. Broadcasting is the answer. Try this

vector1 = np.arange(12).reshape((4, 1, 3))
vector2 = np.arange(12).reshape((4, 3))

result = np.sum(vector1 * vector2[:, np.newaxis], axis=2)

np.sum(..., axis=2) is like adding up the results from the previous step along the last dimension (axis 2). This gives you the dot product for each pair of arrays in vector1 and vector2.

answered Sep 5, 2023 at 10:57

KamiSama

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2 Comments

hpaulj Over a year ago

Your result is (4,1). An alternative is to sum on axis 1, which is size 1, giving a (4,3).

Devarapalli Vamsi Over a year ago

Hey thanks for the information. Please revisit the question once. Given the sol as well.

Jesse Sealand · Accepted Answer · 2023-09-05 10:50:18Z

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Solution:

The key here is to be able to control which axes are bring worked on. np.dot() and np.tensordot() are unsuitable for this use case. So your intuition for using np.einsum is correct your notation needs adjusted a bit. For example

import numpy as np

vector1 = np.arange(12).reshape((4,1,3))
vector2 = np.arange(12).reshape((4,3))

np.einsum('ijk,ij->ik',vector1,vector2)

answered Sep 5, 2023 at 10:50

Jesse Sealand

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