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.
- return_gradbool
Whether or not to also return the gradient
- Returns
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