.. _examplesection:

Examples
========

Examples can be found in `pyomo/contrib/parmest/examples` and include:

* Reactor design example [PyomoBookIII]_
* Semibatch example [AM00]_
* Rooney Biegler example [RB01]_

Each example includes a Python file that contains the Pyomo model and a
Python file to run parameter estimation.

Additional use cases include:

* Data reconciliation (reactor design example)
* Parameter estimation using data with duplicate sensors and time-series
  data (reactor design example)
* Parameter estimation using mpi4py, the example saves results to a file
  for later analysis/graphics (semibatch example)

The example below uses the reactor design example.  The file
**reactor_design.py** includes a function which returns an populated
instance of the Pyomo model.  Note that the model is defined to maximize
`cb` and that `k1`, `k2`, and `k3` are fixed.  The _main_ program is
included for easy testing of the model declaration.

.. literalinclude:: /../../pyomo/contrib/parmest/examples/reactor_design/reactor_design.py
   :language: python

The file **parameter_estimation_example.py** uses parmest to estimate values of `k1`,
`k2`, and `k3` by minimizing the sum of squared error between model and
observed values of `ca`, `cb`, `cc`, and `cd`.  Additional example files use
parmest to run parameter estimation with bootstrap resampling and
perform a likelihood ratio test over a range of theta values.

.. literalinclude:: /../../pyomo/contrib/parmest/examples/reactor_design/parameter_estimation_example.py
   :language: python

The semibatch and Rooney Biegler examples are defined in a similar
manner.