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@(@\newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\W}[1]{ \; #1 \; }@)@ This is cppad_mixed--20220519 documentation: Here is a link to its current documentation .
Compute the Hessian of The Fixed Effects Objective

Syntax
Prototype
Purpose
mixed_object
fixed_vec
random_opt
hes_fixed_obj_rcv
Example

Syntax
hes_fixed_obj_rcv = mixed_object.hes_fixed_obj(
     fixed_vec, random_opt
)

Prototype 

CppAD::mixed::d_sparse_rcv cppad_mixed::hes_fixed_obj(
     const d_vector& fixed_vec            ,
     const d_vector& random_opt           )

Purpose
Compute the Hessian of the fixed effects objective function @(@ L ( \theta ) @)@; see fixed effects objective . The Hessian is @[@ L^{(2)} ( \hat{\theta} ) @]@ Absolute value terms in the negative log-density vector for the fix_likelihood are not include in this Hessian (because they do not have a derivative, let alone Hessian, at zero).

mixed_object
We use mixed_object to denote an object of a class that is derived from the cppad_mixed base class.

fixed_vec
is the vector of fixed effects @(@ \theta @)@ at which the Hessian is evaluated.

random_opt
is the optimal random effects corresponding to this value for the fixed effects; i.e., u^(theta) .

hes_fixed_obj_rcv
The return value is a d_sparse_rcv representation of the lower triangle of the Hessian. (The Hessian is symmetric and hence determined by its lower triangle.) Absolute value terms in the negative log-density vector for the fix_likelihood are not include in this Hessian because they do not have a derivative (let alone Hessian) at zero.

Example
The file hes_fixed_obj.cpp contains an example and test of this routine. It returns true for success and false for failure.
Input File: src/eigen/hes_fixed_obj.cpp