Complex-Step Derivative

Problem

The complex-step derivative avoids subtractive cancellation entirely:

f'(x) = Im(f(x + i*h)) / h

Using h = 1e-20 gives near machine precision. Apply this to the polynomial f(x) = sum(coeffs[i] * x^i) and return the derivative estimate.

Hint

The imaginary part of a complex evaluation carries the derivative with no cancellation error.

case 1

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

expected: 6

case 2

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

expected: 13.999999999999998

case 3

in: [[5],1]

expected: 0

case 4

in: [[0,1],1]

expected: 1

Starter codePython

def complex_step_derivative(coeffs, x, h=1e-20):
    # Your code here
    pass

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