Lattice Tester is a C++ software library offering tools to measure the uniformity of lattices in \({\mathbb {Z}}^t\) , the t-dimensional integers. Such lattices occur for quasi-Monte Carlo point sets and from multiple recursive linear random number generators, for example. The uniformity measures include the length of a shortest nonzero vector in the lattice or in its dual (the spectral test), and figures of merit that use normalized versions of these lengths for projections of the lattice onto several subsets of coordinates, and take the worst-case over the considered projections. This paper gives a brief tour of Lattice Tester, its algorithms, its design, and numerical illustrations. More details and examples can be found in the user’s guide. The code is freely available on GitHub.

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Lattice Tester: A Software Tool to Analyze Integral Lattices

  • Pierre L’Ecuyer,
  • Christian Weiß

摘要

Lattice Tester is a C++ software library offering tools to measure the uniformity of lattices in \({\mathbb {Z}}^t\) , the t-dimensional integers. Such lattices occur for quasi-Monte Carlo point sets and from multiple recursive linear random number generators, for example. The uniformity measures include the length of a shortest nonzero vector in the lattice or in its dual (the spectral test), and figures of merit that use normalized versions of these lengths for projections of the lattice onto several subsets of coordinates, and take the worst-case over the considered projections. This paper gives a brief tour of Lattice Tester, its algorithms, its design, and numerical illustrations. More details and examples can be found in the user’s guide. The code is freely available on GitHub.