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:¶

xndarray

parameters at which the derivative is evaluated

ffunction

f(*((x,)+args), **kwargs) returning either one value or 1d array

epsilonfloat, optional

Stepsize, if None, optimal stepsize is used. Optimal step-size is EPS*x. See note.

argstuple

Tuple of additional arguments for function f.

kwargsdict

Dictionary of additional keyword arguments for function f.

Returns:¶

partialsndarray

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.