Dot product of every element with every other element of an array

Question

Is there an easy way to take the dot product of one element of an array with every other? So given:

array([[1, 2, 3],
       [4, 5, 6],
       [7, 8, 9]])

I would like to get the result:

array([  32.,   50.,  122.])

I.e. a[0] dot a[1], a[0] dot a[2], a[1] dot a[2].

The array I am working with will NOT be square; that's just an example.

Thanks!

Answer 1

>>> X = scipy.matrix('1 2 3; 4 5 6; 7 8 9')
>>> X*X.T
matrix([[ 14,  32,  50],
        [ 32,  77, 122],
        [ 50, 122, 194]])

It gives you more than what you wanted, but it's undeniably easy.

Or

>>> X = scipy.array([[1,2,3], [4,5,6], [7,8,9]])
>>> scipy.dot(X, X.T)
array([[ 14,  32,  50],
       [ 32,  77, 122],
       [ 50, 122, 194]])

Answer 2

Since it looks like you are using numpy:

from itertools import combinations
import numpy as np

dot_products = [np.dot(*v) for v in combinations(vectors, 2)]

I checked this out and it appears to work on my python install.

Answer 3

Here's another one:

>>> a = numpy.array([[1, 2, 3],
...        [4, 5, 6],
...        [7, 8, 9]])
>>> numpy.array([numpy.dot(a[i], a[j]) for i in range(len(a)) for j in range(i + 1, len(a))])
array([ 32,  50, 122])