MediumCalculusca-026

Numerical Gradient of 2D Function

Problem

Compute the numerical gradient of f(x, y) = x^3 + a * x * y^2 at (x, y) using central differences with h = 1e-6.

Return [df/dx, df/dy] where each partial uses the symmetric difference quotient. The analytic gradient is [3*x^2 + a*y^2, 2*a*x*y].

Hint

Perturb one variable at a time and keep the step symmetric around the point.

case 1

in: [1,2,1]

expected: [13,4]

case 2

in: [0,-2,3]

expected: [12,0]

case 3

in: [2,0,5]

expected: [50,0]

case 4

in: [-1,1,2]

expected: [-1,-4]

Starter codePython

def numerical_gradient_2d(a, x, y, h=1e-6):
    # Return [df_dx, df_dy]
    # Your code here
    pass

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