Gradient of Quadratic Form

Problem

Return the gradient of the scalar function f(x) = x^T A x with respect to x:

nabla f = (A + A^T) x

For symmetric A this simplifies to 2*A*x.

Hint

The gradient of x^T A x is (A + A^T)x, since only the symmetric part contributes.

case 1

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

expected: [5,7]

case 2

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

expected: [6,8]

case 3

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

expected: [2,5]

case 4

in: [[[0,1],[-1,0]],[1,2]]

expected: [0,0]

Starter codePython

def grad_quadratic(A, x):
    # Your code here
    pass

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