finite_diff_grad_hessian()

template<typename F >

void stan::math::finite_diff_grad_hessian ( const F &  f, const Eigen::VectorXd &  x, double &  fx, Eigen::MatrixXd &  hess, std::vector< Eigen::MatrixXd > &  grad_hess_fx, double  epsilon = 1e-04  )

inline

Calculate the value 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::Matrix<double, Eigen::Dynamic, 1>&)

Reference:

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

4 calls to the function, f.

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
[in]	epsilon	perturbation size

Definition at line 41 of file finite_diff_grad_hessian.hpp.