finite_diff_hessian_auto()

template<typename F >

void stan::math::internal::finite_diff_hessian_auto	(	const F &	f,
		const Eigen::VectorXd &	x,
		double &	fx,
		Eigen::VectorXd &	grad_fx,
		Eigen::MatrixXd &	hess_fx
	)

Calculate the value and the Hessian of the specified function at the specified argument using first-order finite difference of gradients, automatically setting the stepsize between the function evaluations along a dimension.

The functor must implement

double operator()(const Eigen::VectorXd&)

For details of the algorithm, see "Central difference approximation", under "Second-order derivatives based on gradient", in: https://v8doc.sas.com/sashtml/ormp/chap5/sect28.htm

Step size for dimension i is set automatically using stan::math::finite_diff_stepsize(x(i)).

2n gradient calls are needed for the algorithm.

Template Parameters

F	Type of function

Parameters

[in]	f	Function
[in]	x	Argument to function
[out]	fx	Function applied to argument
[out]	grad_fx	Gradient of function at argument
[out]	hess_fx	Hessian of function at argument

Definition at line 43 of file finite_diff_hessian_auto.hpp.