gradient-check-one-parameter — Google case

Google-inspired optimization team is debugging a custom differentiable component whose analytical gradient may be wrong. You need to compute a numerical finite-difference gradient for one parameter so the team can compare it with the implementation.

Estimate the derivative of the function f with respect to the first coordinate of x by a centred finite difference, ${\displaystyle \frac{f(x+h{e}_1)-f(x-h{e}_1)}{2h}}\backslash dfrac\{f(x+h\; e\_1)-f(x-h\; e\_1)\}\{2h\}$, and compare it with the claimed analytic derivative analytic[0]. f takes an array and returns a scalar; h defaults to ${10}^{-5}10^\{-5\}$.

Implement solve(f, x, analytic, h=1e-5).

Returns. Return a tuple (numeric, analytic, abs_error) of Python floats.

Examples

Example 1

Input:

solve(lambda v: float(np.sum(v ** 2)), [1.5], [3.0])

Output:

(3.0, 3.0, 1.96532e-11)

Example 2

Input:

solve(lambda v: float(np.sum(v ** 2)), [1.5], [2.0])

Output:

(3.0, 2.0, 1.0)