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