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A Tool for Custom Construction of QMC and RQMC Point Sets

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Monte Carlo and Quasi-Monte Carlo Methods (MCQMC 2020)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 387))

Abstract

We present LatNet Builder, a software tool to find good parameters for lattice rules, polynomial lattice rules, and digital nets in base 2, for quasi-Monte Carlo (QMC) and randomized quasi-Monte Carlo (RQMC) sampling over the s-dimensional unit hypercube. The selection criteria are figures of merit that give different weights to different subsets of coordinates. They are upper bounds on the worst-case error (for QMC) or variance (for RQMC) for integrands rescaled to have a norm of at most one in certain Hilbert spaces of functions. We summarize what are the various Hilbert spaces, discrepancies, types of weights, figures of merit, types of constructions, and search methods supported by LatNet Builder. We briefly discuss its organization and we provide simple illustrations of what it can do.

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Acknowledgements

This work has been supported by a NSERC Discovery Grant and an IVADO Grant to P. L’Ecuyer, and by a stipend from Corps des Mines to P. Marion. F. Puchhammer was supported by Spanish and Basque governments fundings through BCAM (ERDF, ESF, SEV-2017-0718, PID2019-108111RB-I00, PID2019-104927GB-C22, BERC 2018e2021, EXP. 2019/00432, KK-2020/00049), and the computing infrastructure of i2BASQUE and IZO-SGI SGIker (UPV). Yocheved Darmon wrote code for producing the output files.

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Authors and Affiliations

  1. Département d’Informatique et de Recherche Opérationnelle, Université de Montréal, Montreal, Quebec, Canada

    Pierre L’Ecuyer

  2. Laboratoire de Probabilités, Statistique et Modélisation, LPSM, Sorbonne Université, CNRS, 75005, Paris, France

    Pierre Marion

  3. Institut des Actuaires, Paris, France

    Maxime Godin

  4. Université de Montréal, Montreal, Quebec, Canada

    Florian Puchhammer

  5. Basque Center for Applied Mathematics, Bilbao, Spain

    Florian Puchhammer

Authors
  1. Pierre L’Ecuyer
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  2. Pierre Marion
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  3. Maxime Godin
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  4. Florian Puchhammer
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Corresponding author

Correspondence to Pierre Marion .

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Editors and Affiliations

  1. NVIDIA, Berlin, Germany

    Alexander Keller

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L’Ecuyer, P., Marion, P., Godin, M., Puchhammer, F. (2022). A Tool for Custom Construction of QMC and RQMC Point Sets. In: Keller, A. (eds) Monte Carlo and Quasi-Monte Carlo Methods. MCQMC 2020. Springer Proceedings in Mathematics & Statistics, vol 387. Springer, Cham. https://doi.org/10.1007/978-3-030-98319-2_3

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