LatticeBuilder: A General Software Tool for Constructing Rank-1 Lattice Rules

Abstract : We introduce a new software tool and library named Lattice Builder, written in C++, that implements a variety of construction algorithms for good rank-1 lattice rules. It supports exhaustive and random searches, as well as component-by-component (CBC) and random CBC constructions, for any number of points, and for various measures of (non)uniformity of the points. The measures currently implemented are all shift-invariant and represent the worst-case integration error for certain classes of integrands. They include for example the weighted Pα square discrepancy, the Rα criterion, and figures of merit based on the spectral test, with projection-dependent weights. Each of these measures can be computed as a finite sum. For the Pα and Rα criteria, efficient specializations of the CBC algorithm are provided for projection-dependent, order-dependent and product weights. For numbers of points that are integer powers of a prime base, the construction of embedded rank-1 lattice rules is supported through any of the above algorithms, and also through a fast CBC algorithm, with a variety of possibilities for the normalization of the merit values of individual embedded levels and for their combination into a single merit value. The library is extensible, thanks to the decomposition of the algorithms into decoupled components, which makes it easy to implement new types of weights, new search domains, new figures of merit, etc.
Type de document :
Article dans une revue
ACM Transactions on Mathematical Software, Association for Computing Machinery, 2016
Liste complète des métadonnées

Littérature citée [32 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/hal-01240168
Contributeur : Bruno Tuffin <>
Soumis le : mercredi 9 décembre 2015 - 14:10:22
Dernière modification le : mercredi 16 mai 2018 - 11:23:18
Document(s) archivé(s) le : jeudi 10 mars 2016 - 11:40:07

Fichier

latbuilder.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01240168, version 1

Citation

Pierre L'Ecuyer, David Munger. LatticeBuilder: A General Software Tool for Constructing Rank-1 Lattice Rules. ACM Transactions on Mathematical Software, Association for Computing Machinery, 2016. 〈hal-01240168〉

Partager

Métriques

Consultations de la notice

489

Téléchargements de fichiers

151