Is there a function for calculating all the pairwise dot products of the columns of a matrix, or between all pairs in a list of vectors?

Question

Say you have n. vectors of arbitrary (but equal) length m each. Is there a (numpy?) function, or a quick way, of calculating all pairwise dot products between these n. vectors?

My initial thought was that you could calculate A^TA and take the upper triangular portion, but I'm not sure if that matrix multiplication is slow/computationally intensive. Is there a quicker/efficient way? Or should I just define a function using a for loop for all combinations of pairs?

I you want to multiply all the columns of your 2-D array `arr` by all the other columns, use [tensordot](https://docs.scipy.org/doc/numpy/reference/generated/numpy.tensordot.html) : `np.tensordot(arr, arr, axes=(0,0))`. Result shape is `(n,n)` — Brenlla, Apr 24 '19 at 16:50
@Chgad Yes, the dot product or scalar product or inner product. — questionmark, Apr 24 '19 at 16:53
For more info see [here](https://stackoverflow.com/q/41870228/6091318) — Brenlla, Apr 24 '19 at 16:57
BTW, `A.T.dot(A)` should also work fine, no need to take triangular portions — Brenlla, Apr 24 '19 at 17:08

score 1 · Answer 1 · answered Sep 28 '21 at 22:08

1

As per @Brenila’s comment, use tensordot:

np.tensordot(arr, arr, axes=(0,0))

Result shape is (n, n) for n = arr.shape[-1]

answered Sep 28 '21 at 22:08

Cimbali

11,012
1
39
68

Is there a function for calculating all the pairwise dot products of the columns of a matrix, or between all pairs in a list of vectors?

1 Answers1

Linked