lines 8-46 of file: example/python/mixed/fix_constraint_xam.py

{xrst_begin mixed_fix_constraint_xam.py}

fix_constraint: Example and Test
################################

Random Effects
**************
For this example there is no random effects.

fix_likelihood
**************
For this example, the fixed likelihood is

.. math::

   f( \theta ) = ( \theta - 1 )^2

fix_constraint
**************
For this example, the fixed constraint is

.. math::

   g( \theta ) = ( \theta + 2)^2

Fixed Constraint Bounds
***********************
For this example, there is no fixed constraint upper bound
and the lower bound is :math:`g^L \leq g(\theta)`

Optimal Fixed Effects
*********************
If :math:`g^L \leq g(1) = 9`, the optimal value for the fixed effects is
:math:`\hat{\theta} = 1`.
Otherwise, the optimal value satisfies the equation
:math:`c ( \hat{\theta} ) = g^L`; i.e,
:math:`\hat{\theta} = \sqrt{g^L} - 2`.

{xrst_end mixed_fix_constraint_xam.py}