Filters and normalizations

This page describes how filters and normalizations can be specified.

The option –filters can take a space-separated list of normalizers and filters which must be specified as follows.

Normalizations

When a normalization is available with the selected figure of merit, one can simply use norm to tell LatNet Builder to use the default normalization.

Alternatively, it is possible to choose specific normalizations:

• Normalizations for the \(P_\alpha\) discrepancy (ordinary lattice rules):
  • norm:Palpha-SL10 with \(\alpha=\)alpha (default),
  • norm:Palpha with \(\alpha=\)alpha (alias for SL10),
  • norm:Palpha-DPW08 with \(\alpha=\)alpha (only for product weights);
• Normalizations for the \(P_\alpha\) discrepancy (polynomial lattice rules):
  • norm:Palpha with \(\alpha=\)alpha (default);
• Normalizations for the \(B_{\alpha, d, (1)}\) interlaced discrepancy:
  • norm:IAalpha with \(\alpha=\)alpha (default);
• Normalizations for the \(B_{d, (2)}\) interlaced discrepancy:
  • norm:IB (default).

Filters

Low-pass filters can be specified with low-pass:threshold for a low-pass filter with threshold value threshold.

Using multilevel filters and normalizations

Multilevel filters and normalizations are specified the same way as unilevel filters and normalizations. Note however that their behavior is different as they apply to the individual merit value of each embedding level and not to the combined merit value.

As explained here, when one uses a normalization, some per-level weights are computed. It is possible to select only a range of levels instead of all the levels. This is done by appending :select:minLevel,maxLevel to the filter specification, which sets positive weights across all levels ranging from minLevel to maxLevel, and a zero weight for other levels.

Note that when a level selector combiner (–combiner level:m or –combiner level:max) is used with a normalization, the software will automatically select ( i.e. set a positive per-level weight) the same level as the combiner, overriding any select token you may have appended to your normalization. This is required to have exactly the same behavior when one constructs a unilevel point set or a multilevel point set with a level selector combiner.