, f, epsilon=None, args=(), kwargs={})[source]

Calculate gradient or Jacobian with complex step derivative approximation

  • x (array) – parameters at which the derivative is evaluated
  • f (function) – f(*((x,)+args), **kwargs) returning either one value or 1d array
  • epsilon (float, optional) – Stepsize, if None, optimal stepsize is used. Optimal step-size is EPS*x. See note.
  • args (tuple) – Tuple of additional arguments for function f.
  • kwargs (dict) – Dictionary of additional keyword arguments for function f.

partials – array of partial derivatives, Gradient or Jacobian

Return type:



The complex-step derivative has truncation error O(epsilon**2), so truncation error can be eliminated by choosing epsilon to be very small. The complex-step derivative avoids the problem of round-off error with small epsilon because there is no subtraction.