# 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
xarray_like

value at which function derivative is evaluated

ffunction

function of one array f(x)

epsilonfloat

stepsize, if None, then stepsize is automatically chosen

Returns
hessndarray

array of partial second derivatives, Hessian

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.