lines 909-971 of file: lib/python/cppad_py/mixed.py

   {xrst_begin mixed_hes_fixed_obj}
   {xrst_spell
      laplace
   }

   Hessian of Fixed Effects Objective
   ##################################

   Syntax
   ******
   {xrst_literal
      # BEGIN_HES_FIXED_OBJ
      # END_HES_FIXED_OBJ
   }

   Purpose
   *******
   We are given a value for the fixed effects :math:`\theta`
   and the corresponding optimal value for the random effects
   :math:`\hat{u} ( \theta )`.
   This routine computes the hessian, with respect to the fixed effects,
   of the negative log of the Laplace approximation for the
   fixed effects objective

   .. math::
      \B{p} ( z | \theta ) \B{p} ( \theta ) \int_{-\infty}^{+\infty}
         \B{p} ( y | \theta , u ) \B{p}( u | \theta ) \B{d} u

   If there is no data,  and not random effects,
   the return value is the Hessian of
   :math:`- \log [ \B{p} ( \theta ) ]` .

   hes_fixed_obj_rcv
   *****************
   The argument *hes_fixed_obj_rcv* is a
   :ref:`py_sparse_rcv <py_sparse_rcv-name>` matrix.
   The input value of this argument does not matter.
   Upon return it contains the lower triangle of the Hessian
   (the Hessian is symmetric).

   fixed_vec
   *********
   The argument *fixed_vec* is a numpy vector with ``float`` elements
   and length *n_fixed*. It contains the value of the fixed effects
   :math:`\theta` at which the Hessian is evaluated.
   This vector can't be ``None``.

   random_opt
   **********
   The argument *random_opt* is a numpy vector with ``float`` elements
   and length *n_random*.
   It contains the optional value for the random effects,
   which is a function of the fixed effects and denoted by
   :math:`\hat{u} ( \theta )` .
   This vector can't be ``None``.

   Examples
   ********
   {xrst_toc_list
      example/python/mixed/hes_fixed_obj_xam.py
   }

   {xrst_end mixed_hes_fixed_obj}