Summary of Command-Line Options

The latnetbuilder executable supports the following command-line options:

--version

Optional. Shows the version of the software.

--help / -h

Optional. Shows a light version of this page in the console.

--set-type / -t

Required. Specifies the point set type. Takes one of the following values:

• lattice to search for rank-1 lattices; or
• net to search for digital nets.
  

--construction / -c

Required. Specifies the construction type. Takes one of the following values:

• For lattices (–set-type lattice):
  • ordinary to search for ordinary lattices; or
  • polynomial to search for polynomial lattices.
• For digital nets (–set-type net):
  • sobol to search for Sobol' nets; or
  • polynomial to search for polynomial lattice rules; or
  • explicit to search for digital nets with explicit generating matrices.

You can learn more on the different point set types and constructions here. Details on how to use the two options above can be find here.

--dimension / -d

Required. Specifies the dimension of the searched point sets. Takes an integer argument.

--size-parameter / -s

Required. Specifies the size parameter of the point sets. Takes an argument of the form:

• For lattices (–set-type lattice):
  • –size-parameter modulus; or
  • –size-parameter primeBase^power; or
  • –size-parameter 2^k (even for polynomial lattice rules).
• For digital nets (–set-type net):
  • –size-parameter 2^k; or
  • –size-parameter modulus (only for polynomial lattice rules); or
  • –size-parameter primeBase^power (only for polynomial lattice rules).

See here for additional details.

--exploration-method / -e

Required. Specifies the exploration method. Takes an argument of the form:

• evaluate:point-set-description to compute the merit value of the point set described by point-set-description. See here for details about point-set-description.
• exhaustive for exhaustive search;
• random:samples for a random search with samples random samples;
• full-CBC for a component-by-component search;
• random-CBC:samples for a random component-by-component search with samples random samples per coordinate;

Specific to lattices (–set-type lattice ):

• Korobov for a Korobov search;
• random-Korobov:samples for a random Korobov search with samples random samples;

• fast-CBC for a fast CBC search (requires a coordinate-uniform implementation of the selected figure of merit);

  Recall that the implementation of the fast CBC algorithm only supports modulus that are a power of a prime base in the ordinary case and irreducible modulus in the polynomial case.

• extend:modulus:genVec to extend the lattice to a lattice with modulus modulus and generating vector genVec specified as a dash-separated list of integers/polynomials. See here for details about genVec.

Specific to digital nets (–set-type net ):

• mixed-CBC:samples:nbFull for a full-CBC search for the first nbFull coordinates and then a random-CBC search with samples random samples for the remaining coordinates.

When the random variant of a search is used with a filter (see the --filters option below), the candidate samples that are rejected by the filter pipeline are not considered as valid samples, meaning that the user-specified number of random samples only corresponds to the number of accepted candidates.

--figure-of-merit / -f

Required. Specifies the figure of merit to be used. Takes an argument of either of the following forms:

• figure
• CU:figure where the optional prefix CU: indicates that a coordinate-uniform implementation of the evaluation algorithm should be used (only available for Palpha, R1, R with –norm-type 2 and IAalpha, IB with –norm-type 1)

and where figure is one of:

• Palpha for the weighted \(\mathcal P_\alpha\) discrepancy with \(\alpha=\)alpha (the figures of merit are different for ordinary and polynomial lattice rules but have the same name);
• spectral for the spectral figure of merit (only available with ordinary lattice rules);
• Ralpha for the weighted \(\mathcal R_\alpha\) figure of merit with \(\alpha=\)alpha (only available with ordinary lattice rules); or
• R for the weighted \(\mathcal R\) figure of merit (only available with polynomial lattice rules and digital nets);
• t-value for the t-value merit (only available with digital nets and incompatible with CBC explorations);
• projdep:t-value for the projection-dependent t-value merit (only available wih digital nets);
• projdep:resolution-gap for the projection-dependent resolution-gap (only available wih digital nets);
• IAalpha for the interlaced \(B_{\alpha, d, (1)}\) discrepancy with \(\alpha=\)alpha (only available for interlaced polynomial lattice rules and digital nets); or
• IB for the interlaced \(B_{d, (2)}\) discrepancy (only available for interlaced polynomial lattice rules and digital nets).

The definitions of all these figures of merit can be find here. More details on how to use this option are available on this page.

--interlacing-factor / -i

Optional (default:1). Specifies the interlacing factor. Takes a positive integer value. If set to a value greater than 1, the search point set will be an interlaced digital net / polynomial lattice rule set. Requires to use the appropriate figures of merit and the corresponding norm-type. See here for the definition of interlaced digital nets and polynomial lattice rules and Interlaced digital nets and polynomial lattice rules for details about constructing such point sets with the command-line tool.

--norm-type / -q

Required. Specifies the type of the \(\ell_q\) norm to combine the merit values across projections. Takes an argument of the form:

• realNumber for a finite positive number;
• inf for infinity. The value of this option must be compatible with the type of figure of merit, especially regarding the use of the coordinate-uniform evaluation algorithm.

See Figures of merit for additional details on this parameter.

--weights / -w

Required. Specifies the type(s) of weights and their values. Takes a whitespace-separated list of arguments, each of which specifying a type of weights with its values. (The actual weights are the sum of these.) Takes argument of the form:

• product:default:list for product weights with the weights for the first coordinates specified by the comma-separated list of weights list, and with weight default for the other coordinates;
• order-dependent:default:list for order-dependent weights with the weights for the first orders specified by the comma-separated list of weights list (starting at order 1), and with weight default for the other orders;
• POD:default1:list1:default2:list2 for POD weights, where default1 and list1 specify the default and individual order-dependent weights, and where default2 and list2 specify the default and individual product weights.
• projection-dependent:proj:weight:...:proj:weight for projection-dependent weights where proj is a projection (comma-separated list of coordinates) and weight the associated weight.
  Alternatively, a file containing the weights can be used: –weights file:path_to_file to assign the weight weight to all other where path_to_file is the path to the file containing the weights. The file must consist of lines of the form:
  • coordinates: weight to assign the weight weight to the projection defined by the comma-separated list of coordinates coordinates;
  • order order: weight to assign the weight weight to all other projections of order order;
  • default: weight projections;
  • #comment to ignore comment.

The way to specify the different types of weights is explained here.

--weights-power / -p

Optional (default: same value as for the –norm-type option). Specifies that the weights passed by option –weights have already been elevated to that power.

By default, the weights are assumed to have been elevated to the same power as specified by option –norm-type. A value of inf is mapped to 1. See the definition of \(p\) in the first paragraph of this page for additional details.

--multilevel / -M

Optional (default: false). Specifies if the searched point sets are multilevel point sets. Takes one of the following values:

• false to search for unilevel point sets; or
• true to search for multilevel point sets.

--combiner / -C

Optional. Selects a combiner for multilevel figures of merit. Takes one of the following values:

• sum to sum the individual merit values of all nested levels;
• max to select the maximum individual merit value across all nested levels;
• level:max to select the individual merit value of the nested level with the largest number of points (the highest level);
• level:m to select the individual merit value of the \(m\)th nested level.

--filters / -F

Optional. Configures filters for merit values. Only supported when –set-type lattice is set. Takes a whitespace-separated list of arguments of the form:

• norm:type for a normalizer of type specified by type;
• low-pass:threshold for a low-pass filter with threshold value threshold.

If the option –multilevel true is set, in the case of a normalization filter, weights can be optionally specified by appending :select:minLevel,maxLevel to the filter specification, which sets positive weights across all levels ranging from minLevel through maxLevel, and a zero weight for other levels.

--repeat / -r

Optional (default 1). Number of times the exploration must be executed (can be useful to obtain different results from random exploration). Takes an integer argument.

--verbose / -v

Optional (default 0). Specifies the verbosity level. Ranges between 0 (quite quiet) and 3 (pretty chatty) Takes an integer argument.

--output-folder / -o

Optional. Specify a path to a folder where to store the log files of the search. The path can be absolute or relative. If the folder does not exist, it will be created. If the folder already exists, some existing files may be lost.

--merit-digits-displayed

Optional. Sets the number of significant figures to use when displaying merit values. Takes a positive integer as its argument.