statsmodels.tools.numdiff.approx_hess_cs¶

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

Calculate Hessian with complex-step derivative approximation

Parameters:¶

x : array_like¶

value at which function derivative is evaluated

f : function¶

function of one array f(x)

epsilon : float¶

stepsize, if None, then stepsize is automatically chosen

Returns:¶

hess – array of partial second derivatives, Hessian

Return type:¶

ndarray

Notes

based on equation 10 in M. S. RIDOUT: Statistical Applications of the Complex-step Method of Numerical Differentiation, University of Kent, Canterbury, Kent, U.K.

The stepsize is the same for the complex and the finite difference part.