# SPDX-License-Identifier: EPL-2.0 OR GPL-2.0-or-later
# SPDX-FileCopyrightText: Bradley M. Bell <bradbell@seanet.com>
# SPDX-FileContributor: 2003-22 Bradley M. Bell
# ----------------------------------------------------------------------------

{xrst_begin research}
{xrst_spell
   approximations
   distributive
   kasper
   kristensen
   py
   subgraphs
   symmertic
}

Research and Software Engineering Projects Related to CppAD
###########################################################

See Also
********
:ref:`wish_list-name`

Purpose
*******
This is a list of research topics,
and software engineering projects, related to CppAD.
If you know of published results for any of the research topics,
please contact the project manage
so a link to the answer can be added to the CppAD documentation.

Abs-Normal Form
***************
`Abs-normal <https://arxiv.org/abs/1701.00753>`_ forms are
recent advent in AD and algorithms related to it are an important
research topic.
The CppAD :ref:`abs_normal_fun-name` routine enables one to create approximations
for non-smooth functions that have higher than first order accuracy.
This opens the question of designing algorithms to take advantage of this.

Atomic Functions
****************
Mathematical formulas for, and implementation of,
:ref:`atomic functions<atomic_two-name>`
that make AD faster and or conserve on memory for special cases; e.g.,
special functions, sparse matrix operations.

Dynamic Parameters
******************
CppAD provides for :ref:`dynamic parameters<new_dynamic-name>`
in a unique way (they can depend on other dynamic parameters).
This opens the question of techniques that take advantage of this.
For example, see :ref:`base2ad.cpp-name` which uses this feature.

Multi-Threading
***************
Interesting algorithms and implementations that take advantage of
the CppAD :ref:`multi threading<multi_thread-name>` capability.

Optimization
************
There is no paper describing
the CppAD :ref:`optimization<optimize-name>` of a computational graph.
In particular, the optimization of
:ref:`conditional expressions<condexp-name>` is not well understood.
In addition, possible improvements to the optimization would be welcome.
For example, detecting places where the distributive law can be
used to reduce two multiplies and one addition to one multiply and
two additions.

Scripting Language
******************
It would be useful to make :ref:`addon-name` packages that
connect CppAD to a scripting languages.
The package
`cppad_swig <https://bradbell.github.io/cppad_py>`_
demonstrate how one could use swig to do this and
`cppad_py <https://bradbell.github.io/cppad_py>`_
is a preliminary version of such a connection to Python.

Sparsity
********

Sparsity Patterns
=================
There are forward, reverse and subgraph methods for computing a
:ref:`sparsity_pattern-name` .
It is unclear which is better for which cases.

Coloring Problem
================
Given the
:ref:`glossary@Sparsity Pattern` for a Jacobian or Hessian,
a graph coloring algorithm is used to determine which row or columns
can be evaluated at the same time; see
`color_general.hpp <https://github.com/coin-or/CppAD/blob/master/cppad/local/color_general.hpp>`_
and
`color_symmertic.hpp <https://github.com/coin-or/CppAD/blob/master/cppad/local/color_symmetric.hpp>`_.

Subgraphs
=========
The :ref:`subgraph_jac_rev-name` method use subgraphs to compute sparsity patterns
and to evaluate sparse derivatives.
This is a new technique that should be written up.
It was invented by
Kasper Kristensen, DTU Technical University of Denmark.
See the :ref:`wish_list@Subgraph` wish list items.

Speed
*****
CppAD provides for some :ref:`speed-name` comparisons between
different AD packages.
These comparisons could be improved, extended, and written up.

{xrst_end research}
