HardCalculusca-367

Normalized Linear Norm Gradient

Problem

For f(x) = ||W x|| with a constant matrix W, the gradient with respect to x is W^T W x / ||W x||.

Given W as nested rows and a nonzero x, return the gradient list.

Hint

Differentiate the norm as (Wx)/||Wx|| and apply the chain rule for W.

case 1

in: [[[1,0],[0,1]],[1,1]]

expected: [0.7071067811865475,0.7071067811865475]

case 2

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

expected: [1,2]

case 3

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

expected: [0,1]

Starter codePython

def normalized_linear_norm_gradient(w, x):
    # Your code here
    pass

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