# statsmodels.tools.numdiff.approx_hess2¶

statsmodels.tools.numdiff.approx_hess2(x, f, epsilon=`None`, args=`()`, kwargs=`{}`, return_grad=`False`)[source]

Calculate Hessian with finite difference derivative approximation

Parameters:
xarray_like

value at which function derivative is evaluated

f`function`

function of one array f(x, *args, **kwargs)

epsilon`float` or array_like, `optional`

Stepsize used, if None, then stepsize is automatically chosen according to EPS**(1/3)*x.

args`tuple`

Arguments for function f.

kwargs`dict`

Keyword arguments for function f.

Whether or not to also return the gradient

Returns:
hess`ndarray`

array of partial second derivatives, Hessian

grad`ndarray`

Notes

Equation (8) in Ridout. Computes the Hessian as:

``````1/(2*d_j*d_k) * ((f(x + d[j]*e[j] + d[k]*e[k]) - f(x + d[j]*e[j])) -
(f(x + d[k]*e[k]) - f(x)) +
(f(x - d[j]*e[j] - d[k]*e[k]) - f(x + d[j]*e[j])) -
(f(x - d[k]*e[k]) - f(x)))
``````

where e[j] is a vector with element j == 1 and the rest are zero and d[i] is epsilon[i].

References

Ridout, M.S. (2009) Statistical applications of the complex-step method

of numerical differentiation. The American Statistician, 63, 66-74

Last update: Dec 14, 2023