Avoid using for loop. Python 3

Question

I have an array of shape (3,2):

import numpy as np
arr = np.array([[0.,0.],[0.25,-0.125],[0.5,-0.125]])

I was trying to build a matrix (matrix) of dimensions (6,2), with the results of the outer product of the elements i,i of arr and arr.T. At the moment I am using a for loop such as:

size = np.shape(arr)
matrix = np.zeros((size[0]*size[1],size[1]))
for i in range(np.shape(arr)[0]):
    prod = np.outer(arr[i],arr[i].T)
    matrix[size[1]*i:size[1]+size[1]*i,:] = prod

Resulting:

matrix =array([[ 0.      ,  0.      ],
               [ 0.      ,  0.      ],
               [ 0.0625  , -0.03125 ],
               [-0.03125 ,  0.015625],
               [ 0.25    , -0.0625  ],
               [-0.0625  ,  0.015625]])

Is there any way to build this matrix without using a for loop (e.g. broadcasting)?

Divakar · Accepted Answer · 2017-11-23 23:08:54Z

3

Extend arrays to 3D with None/np.newaxis keeping the first axis aligned, while letting the second axis getting pair-wise multiplied, perform multiplication leveraging broadcasting and reshape to 2D -

matrix = (arr[:,None,:]*arr[:,:,None]).reshape(-1,arr.shape[1])

We can also use np.einsum -

matrix = np.einsum('ij,ik->ijk',arr,arr).reshape(-1,arr.shape[1])

einsum string representation might be more intuitive as it lets us visualize three things :

Axes that are aligned (axis=0 here).
Axes that are getting summed up (none here).
Axes that are kept i.e. element-wise multiplied (axis=1 here).

edited Nov 23, 2017 at 23:08

answered Nov 23, 2017 at 22:55

Divakar

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