LatNet Builder Manual  2.0.1-11
Software Package for Constructing Highly Uniform Point Sets
Figures of merit

This page describes how the various figures of merit can be specified.

  • Figures of merit for ordinary lattice rules:

    • the \(\mathcal P_{\alpha}\) discrepancy:
      –figure-of-merit Palpha with \(\alpha\)=alpha,
    • the \(\mathcal R_{\alpha}\) criterion:
      –figure-of-merit Ralpha with \(\alpha\)=alpha,

    For the two last figures of merit, the CU prefix may be added to fasten the computations by using the coordinate-uniform evaluation algorithm when an \(\ell_2\) norm is used.

    • the spectral figure of merit:
      –figure-of-merit spectral;
  • Figures of merit for polynomial lattice rules:

    • the \(\mathcal P_{\alpha}\) discrepancy:
      –figure-of-merit Palpha with \(\alpha\)=alpha,
    • the \(\mathcal R\) criterion:
      –figure-of-merit R;

    For both figures of merit, the CU prefix may be added to fasten the computations by using the coordinate-uniform evaluation algorithm when an \(\ell_2\) norm is used.

  • Figures of merit for digital nets:
    • the \(\mathcal P_{\alpha}\) discrepancy:
      Only with the coordinate-uniform evaluation algorithm and an \(\ell_2\) norm.
      –figure-of-merit CU:Palpha –norm-type 2 with \(\alpha\)=alpha,
    • the \(\mathcal R\) criterion:
      Only with the coordinate-uniform evaluation algorithm and an \(\ell_2\) norm.
      –figure-of-merit CU:R –norm-type 2,
    • the t-value merit:
      –figure-of-merit t-value,
    • the projection-dependent t-value merit:
      –figure-of-merit projdep:t-value,
    • the projection-dependent t-value based star discrepancy bound merit
      –figure-of-merit projdep:t-value:starDisc,
    • the projection-dependent resolution-gap merit:
      –figure-of-merit projdep:resolution-gap;
  • Figures of merit for interlaced polynomial lattice rules and interlaced digital nets:

    • the \(B_{\alpha, d, (1)}\) interlaced discrepancy:
      Only with an \(\ell_1\) norm.
      –figure-of-merit CU:IAalpha –norm-type 1 with \(\alpha\)=alpha,
    • the \(B_{d, (2)}\) interlaced discrepancy:
      Only with an \(\ell_1\) norm. –figure-of-merit CU:IB –norm-type 1.

    For both figures of merit, the CU prefix may be added to fasten the computations by using the coordinate-uniform evaluation algorithm.