MediumCalculusca-318

Bilinear Form Partial Gradients

Problem

For the scalar function f(p, q) = p^T A q with constant matrix A, the gradient with respect to p is A q and with respect to q is A^T p.

Given the vectors p and q and the matrix A as nested rows, return [A q, A^T p].

Hint

Treat A as constant and differentiate the scalar product in each vector.

case 1

in: [[1,2],[3,4],[[1,0],[0,1]]]

expected: [[3,4],[1,2]]

case 2

in: [[1,0],[1,1],[[2,3],[4,5]]]

expected: [[5,9],[2,3]]

case 3

in: [[2],[1,-1],[[1,2]]]

expected: [[-1],[2,4]]

Starter codePython

def bilinear_form_partial_gradients(p, q, a):
    # Your code here
    pass

3 test cases · run your code against them in the editor