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block_diag_ilu is a C++ implementation of an incomplete LU factorization, ILU(0).

Project description

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block_diag_ilu is an open source C++ single header-file implementation 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 use-case 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 worth a thousand words, so if your matrix looks anything like this:

Diagonally dominant block diagonal matrix with sub- and super-diagonals

then its LU decomposition then looks like this:

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 std::vector as underlying data structure. undefined
BLOCK_DIAG_ILUT_WITH_OPENMP factorize blocks in parallel. Set the environment variable BLOCK_DIAG_ILU_NUM_THREADS to control number of threads. undefined will set these when envinronment variables with those are set to “1”.


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


Björn Dahlgren, contact:
  • gmail adress: bjodah
  • adress: bda

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Files for block-diag-ilu, version 0.5.1
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