statsmodels.tools.numdiff.approx_fprime

statsmodels.tools.numdiff.approx_fprime(x, f, epsilon=None, args=(), kwargs={}, centered=False)

Gradient of function, or Jacobian if function f returns 1d array

Parameters

xarray

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. This is EPS**(1/2)*x for centered == False and EPS**(1/3)*x for centered == True.

argstuple

Tuple of additional arguments for function f.

kwargsdict

Dictionary of additional keyword arguments for function f.

centeredbool

Whether central difference should be returned. If not, does forward differencing.

Returns

gradarray

gradient or Jacobian

Notes

If f returns a 1d array, it returns a Jacobian. If a 2d array is returned by f (e.g., with a value for each observation), it returns a 3d array with the Jacobian of each observation with shape xk x nobs x xk. I.e., the Jacobian of the first observation would be [:, 0, :]