statsmodels.tools.numdiff.approx_fprime_cs¶
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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.