How do I turn 2 equal sized vectors into a matrix that's the pairwise product of the two vectors in Python?

Question

Surprised I can't find this answer, but I am looking to basically create a covariance matrix, but instead of each value being a covariance, I want each cell to be the product of the two vectors. So if I have 1x5 vector, I want to end up with a 5x5 matrix.

For example:

Input:

[1, 2, 3, 4, 5]

Output:

[[ 1,  2,  3,  4,  5],
 [ 2,  4,  6,  8, 10],
 [ 3,  6,  9, 12, 15],
 [ 4,  8, 12, 16, 20],
 [ 5, 10, 15, 20, 25]]

Is there a fast way without building a loop?

It's a duplicate of https://stackoverflow.com/questions/49946881/numpy-multiplication-table-ouptut, but this might be interesting, too: https://stackoverflow.com/questions/11144513/cartesian-product-of-x-and-y-array-points-into-single-array-of-2d-points — mkrieger1, Jun 01 '23 at 20:24
You can do a numpy matrix multiply between the array and the array transposed. A 5x1 multiplied by a 1x5 gives a 5z5. So, `result = a.T @ a`. — Tim Roberts, Jun 01 '23 at 20:30
Is `x` (5,), (1,5) or (5,1) shape? or is it really a 5 element list? — hpaulj, Jun 01 '23 at 20:38
For 1d arrays, `np.outer` works. Or elementwise multiplication `*` with the right mix of shapes to `broadcast` — hpaulj, Jun 01 '23 at 20:45
The `@` code works in the array is actually `(1,5)` shape, but not if it is (5,), a 1d array. `np.array([1,2,3,4,5])` is 1d — hpaulj, Jun 01 '23 at 22:47

MSS · Answer 1 · 2023-06-02T13:37:28.957

Simply use numpy.outer. It computes the outer product of two vectors.

a = np.array([1, 2, 3, 4, 5])
res = np.outer(a,a)
print(res)

array([[ 1,  2,  3,  4,  5],
       [ 2,  4,  6,  8, 10],
       [ 3,  6,  9, 12, 15],
       [ 4,  8, 12, 16, 20],
       [ 5, 10, 15, 20, 25]])

Or if you are ok with broadcasting then :

res = a[:,None]*a
print(res)

array([[ 1,  2,  3,  4,  5],
       [ 2,  4,  6,  8, 10],
       [ 3,  6,  9, 12, 15],
       [ 4,  8, 12, 16, 20],
       [ 5, 10, 15, 20, 25]])

How do I turn 2 equal sized vectors into a matrix that's the pairwise product of the two vectors in Python?

1 Answers1