Implementation of Simplicial Complexes for CPA Functions in C++11 using the Armadillo Linear Algebra Library

Sigurdur Freyr Hafstein

2013

Abstract

Continuous, piecewise affine (CPA) functions can be algorithmically parameterized to deliver Lyapunov functions for compact invariant sets. We discuss flexible structures and algorithms to manipulate CPA functions for these purposes and discuss their implementation in C++11 using the Armadillo linear algebra library. Especially, we discuss some of the new language features in C++11 that lead to simpler and more readable code. The implementation was developed in the freeware Visual Studio Express 2012 for Windows Desktop (VS2012). Apart from a detailed description and code examples for the construction and manipulation of the simplicial complex that serves as a basis for CPA functions, this contribution includes some discussion on practical implementation details when using VS2012, C++11, and the linking to and use of the excellent Armadillo linear algebra library. Thus, some parts of this paper, especially Section 3, might be useful not only for those interested in the implementation of the simplicial complex for computing CPA Lyapunov functions, but also for those generally interested in using the free Armadillo library for computations in VS2012.

References

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Paper Citation


in Harvard Style

Freyr Hafstein S. (2013). Implementation of Simplicial Complexes for CPA Functions in C++11 using the Armadillo Linear Algebra Library . In Proceedings of the 3rd International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH, ISBN 978-989-8565-69-3, pages 49-57. DOI: 10.5220/0004423400490057


in Bibtex Style

@conference{simultech13,
author={Sigurdur Freyr Hafstein},
title={Implementation of Simplicial Complexes for CPA Functions in C++11 using the Armadillo Linear Algebra Library},
booktitle={Proceedings of the 3rd International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,},
year={2013},
pages={49-57},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004423400490057},
isbn={978-989-8565-69-3},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 3rd International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,
TI - Implementation of Simplicial Complexes for CPA Functions in C++11 using the Armadillo Linear Algebra Library
SN - 978-989-8565-69-3
AU - Freyr Hafstein S.
PY - 2013
SP - 49
EP - 57
DO - 10.5220/0004423400490057