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lines 6-91 of file: src/eigen/information_mat.cpp
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{xrst_begin information_mat}

Compute the Observed Information For Fixed Effects
##################################################

Deprecated 2020-03-22
*********************
Use :ref:`hes_fixed_obj-name` instead.

Syntax
******

| *information_rcv* = *mixed_object* . ``information_mat`` (
| |tab| *solution* , *random_opt*
| )

Purpose
*******
Compute the observed information matrix.
We use :math:`L ( \theta )` to denote the
:ref:`fixed effects objective<theory@Objective@Fixed Effects Objective, L(theta)>` .
The observed information is

.. math::

   L^{(2)} ( \hat{\theta} )

Absolute value terms in the
:ref:`problem@Negative Log-Density Vector`
for the :ref:`fix_likelihood-name` are not include in this Hessian
(because they do not have a derivative, let alone Hessian, at zero).

mixed_object
************
We use :ref:`derived_ctor@mixed_object`
to denote an object of a class that is
derived from the ``cppad_mixed`` base class.

solution
********
is the :ref:`optimize_fixed@solution`
for a previous call to :ref:`optimize_fixed-name` .
Only the *solution* . ``fixed_opt`` field is used.

random_opt
**********
is the optimal random effects corresponding to the solution; i.e.

| |tab| *random_opt* = *mixed_object* . ``optimize_random`` (
| |tab| |tab| *random_options* ,
| |tab| |tab| *solution* . ``fixed_opt`` ,
| |tab| |tab| *random_lower* ,
| |tab| |tab| *random_upper* ,
| |tab| |tab| *random_in*
| |tab| )

*random_options* ,
*random_lower* ,
*random_upper* , and
*random_in* , are the same
as in the call to ``optimize_fixed`` that corresponds to *solution* .

information_rcv
***************
The return value has prototype

   ``CppAD::mixed::d_sparse_rcv`` *information_rcv*

see :ref:`typedef@Sparse Types@d_sparse_rcv` .
This is a sparse matrix representation for the
lower triangle of the observed information matrix,
which is symmetric and hence determined by its lower triangle.
Absolute value terms in the
:ref:`problem@Negative Log-Density Vector`
for the :ref:`fix_likelihood-name` are not include in this Hessian
because they do not have a derivative (let alone Hessian) at zero.
{xrst_toc_hidden
   example/user/information_mat.cpp
}

Example
*******
The file :ref:`information_mat.cpp-name` contains an example and
test of this routine. It returns true for success and false for failure.

{xrst_end information_mat}