block-diag-ilu 0.2.1

block_diag_ilu is a C++ implementation of an incomplete LU factorization.

block_diag_ilu
==============

.. image:: http://hera.physchem.kth.se:9090/api/badges/chemreac/block_diag_ilu/status.svg
:target: http://hera.physchem.kth.se:9090/chemreac/block_diag_ilu
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``block_diag_ilu`` is an open source `C++ single header-file implementeation
<https://github.com/chemreac/block_diag_ilu/tree/master/include>`_ of an
incomplete LU decomposition routine suitable for diagonally dominant (square) block diagonal
matrices with sub- and super diagonals of small magnitude. It is useful for
preconditioning linear systems. The usecase in mind is for integrating discretized PDEs of mixed
chemical kinetics / diffusion problems where the diffusion process may be accurately
considered a mild perturbation.

A picture is woth a thousant words, so if your matrix looks anything like this:

.. image:: https://raw.githubusercontent.com/bjodah/block_diag_ilu/master/scripts/matrix.png
:scale: 50%
:alt: Diagnoally dominant block diagonal matrix with sub- and super-diagnoals

its LU decomposition then looks like this:

.. image:: https://raw.githubusercontent.com/bjodah/block_diag_ilu/master/scripts/lu.png
:scale: 50%
:alt: LU decomposition of same matrix

then ``block_diag_ilu`` should be able to save quite a bit of time when
solving linear systems approximately, *e.g.* for preconditioning.

Conditional compilation
-----------------------
The following macros affect the compilation:

+--------------------------+-----------------------------------------------+---------------+
|Macro name |Action (when defined) |Default |
+==========================+===============================================+===============+
|NDEBUG |use ``std::unique_ptr`` instead of |undefined |
| |``std::vector`` as underlying data structure. | |
+--------------------------+-----------------------------------------------+---------------+
|WITH_BLOCK_DIAG_ILU_DGETRF|Use unblocked (parallell) internal |undefined |
| |implementation of LAPACK's ``dgetrf`` (uses | |
| |OpenMP) | |
+--------------------------+-----------------------------------------------+---------------+


License
-------
The source code is Open Source and is released under the very permissive
"simplified (2-clause) BSD license". See ``LICENSE.txt`` for further details.

Contributors are welcome to suggest improvements at https://github.com/chemreac/block_diag_ilu

Author
------
Björn Dahlgren, contact:
- gmail adress: bjodah
- kth.se adress: bda