MediumCalculusca-201

Finite-Difference Gradient Check

Problem

Gradient checking compares an analytic gradient against central finite differences with step h = 1e-6.

For f(x) = sum(coeffs[j] * x_j^2), verify that the supplied gradient matches numerically: return True only if every component differs by at most tol (default 1e-6).

Hint

Perturb one coordinate at a time and compare the symmetric difference quotient.

Test cases

case 1

in: [[1,2],[3,4],[6,16]]

expected: true

case 2

in: [[1,2],[3,4],[6,15]]

expected: false

case 3

in: [[0,0.5],[2,-1],[0,-1]]

expected: true

case 4

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

expected: true

Starter codePython

def finite_difference_check(coeffs, x, grad, tol=1e-6):
    # Your code here
    pass

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