MediumCalculusca-002

Numerical Gradient

Problem

Compute the numerical gradient of f(x) = sum(x_i^2) at a given point using central differences with h = 1e-6.

Returns a list grad where grad[i] = (f(point + h*e_i) - f(point - h*e_i)) / (2h).

Hint

For each dimension i, perturb only that coordinate by ±h.

case 1

in: [[1,2,3]]

expected: [2,4,6]

case 2

in: [[0,0]]

expected: [0,0]

case 3

in: [[5]]

expected: [10]

case 4

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

expected: [2,2,2,2]

Starter codePython

def numerical_gradient(point, h=1e-6):
    # f(x) = sum(x_i ** 2)
    # Your code here
    pass

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