statsmodels.tools.numdiff.approx_hess_cs#

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

Calculate Hessian with complex-step derivative approximation

Parameters:

xnumpy:array_like: value at which function derivative is evaluated
fcallable: function of one array f(x)
epsilonfloat, optional: stepsize, if None, then stepsize is automatically chosen
argstuple, optional: Arguments for function f.
kwargsdict, optional: Keyword arguments for function f.

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.