tools.numdiff.approx_fprime_cs()

statsmodels.tools.numdiff.approx_fprime_cs

statsmodels.tools.numdiff.approx_fprime_cs(x, f, epsilon=None, args=(), kwargs={}) [source]

Calculate gradient or Jacobian with complex step derivative approximation

Parameters:	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.
Returns:	partials : ndarray array of partial derivatives, Gradient or Jacobian

Notes

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.