finite_diff_grad_hessian_auto()

template<typename F >

void stan::math::finite_diff_grad_hessian_auto ( const F &  f, const Eigen::VectorXd &  x, double &  fx, Eigen::MatrixXd &  hess, std::vector< Eigen::MatrixXd > &  grad_hess_fx  )

inline

Calculate the value, Hessian, and the gradient of the Hessian of the specified function at the specified argument using second-order autodiff and first-order finite difference.

The functor must implement

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

Reference for finite difference to compute gradient:

De Levie: An improved numerical approximation for the first derivative, page 3

Step size for dimension i is set automatically using stan::math::finite_diff_stepsize(H(i, j)); the nested finite differences are over entries in the Hessian.

Evaluating this function involves 6 calls to the Hessian autodiff function for each entry in the Hessian.

Template Parameters

F	Type of function

Parameters

[in]	f	Function
[in]	x	Argument to function
[out]	fx	Function applied to argument
[out]	hess	Hessian matrix
[out]	grad_hess_fx	gradient of Hessian of function at argument

Definition at line 44 of file finite_diff_grad_hessian_auto.hpp.