statsmodels.tools.numdiff.approx_hess1¶
-
statsmodels.tools.numdiff.approx_hess1(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
- ffunction
function of one array f(x, *args, **kwargs)
- epsilonfloat or array-like, optional
Stepsize used, if None, then stepsize is automatically chosen according to EPS**(1/3)*x.
- argstuple
Arguments for function f.
- kwargsdict
Keyword arguments for function f.
- return_gradbool
Whether or not to also return the gradient
- Returns
- hessndarray
array of partial second derivatives, Hessian
- gradnparray
Gradient if return_grad == True
Notes
Equation (7) in Ridout. Computes the Hessian as:
1/(d_j*d_k) * ((f(x + d[j]*e[j] + d[k]*e[k]) - f(x + d[j]*e[j])))
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