This class implements searches to find the best rank-1 lattices with respect to a given discrepancy, using component-by-component (CBC) searches, random or exhaustive for each component. More...
Public Member Functions | |
| SearcherCBC (Discrepancy disc, boolean primeN) | |
| The number of points \(n\), the dimension \(s\), and possibly the \(s\) weight factors \(\gamma_j\) must be given in disc. | |
| double | exhaust (int s) |
| Exhaustive CBC search to find the lattice with the best (the smallest) discrepancy in dimension \(s\). | |
| double | exhaustPrime (int s) |
Similar to exhaust(s), except that only values of \(a_j\) relatively prime to \(n\) are considered. | |
| double | random (int s, int k) |
| Random CBC search to find the lattice with the best (the smallest) discrepancy in dimension \(s\). | |
| double | randomPrime (int s, int k) |
Similar to random(s, k), except that only values of \(a_j\) relatively prime to \(n\) are considered. | |
| double[] | getBestVals () |
| Returns the best value of the discrepancy found in the last search, in each dimension up to \(s\). | |
| Public Member Functions inherited from umontreal.ssj.discrepancy.Searcher | |
| Searcher (Discrepancy disc, boolean primeN) | |
| The number of points \(n\), the dimension \(s\), and possibly the \(s\) weight factors \(\gamma_j\) must be given in disc. | |
| double | getBestVal () |
| Returns the best value of the discrepancy found in the last search. | |
| int[] | getBestAs () |
| Returns the generator of the lattice which gave the best value of the discrepancy in the last search. | |
| void | initGen (int seed) |
| Initializes the random number generator used in random searches with the starting seed seed. | |
Detailed Description
This class implements searches to find the best rank-1 lattices with respect to a given discrepancy, using component-by-component (CBC) searches, random or exhaustive for each component.
That is, one searches for the best lattice by varying only one component at a time for each dimension. Once the best component has been found for a given dimension, then this value is fixed and we pass to the search for the next component.
The discrepancy object in the SearcherCBC constructor must fix the number of points \(n\), the maximal dimension \(s\) of the lattice and possibly, the weight factors \(\gamma_j\). Then the search program will examine different lattices with \(n\), \(s\) and \(\gamma_j\) fixed in order to find the best amongst those examined.
Definition at line 46 of file SearcherCBC.java.
Constructor & Destructor Documentation
◆ SearcherCBC()
| umontreal.ssj.discrepancy.SearcherCBC.SearcherCBC | ( | Discrepancy | disc, |
| boolean | primeN ) |
The number of points \(n\), the dimension \(s\), and possibly the \(s\) weight factors \(\gamma_j\) must be given in disc.
The \(n\) points of the lattice will be generated in the search. The flag primeN indicates whether \(n\) is a prime number (true) or not (false). This is used in the *Prime methods.
Definition at line 141 of file SearcherCBC.java.
Member Function Documentation
◆ exhaust()
| double umontreal.ssj.discrepancy.SearcherCBC.exhaust | ( | int | s | ) |
Exhaustive CBC search to find the lattice with the best (the smallest) discrepancy in dimension \(s\).
The search runs over all values \( a_j = 1, 2, …, (n-1)\) for a given dimension \(j\). Once the best lattice has been found in dimension \(j\), that coefficient \(a_j\) is fixed and the search runs over all values of \(a_{j+1}\) for the next dimension. The first component
\(a_0\) is always set to 1. The method returns the best value of the discrepancy in dimension \(s\).
Reimplemented from umontreal.ssj.discrepancy.Searcher.
Definition at line 158 of file SearcherCBC.java.
◆ exhaustPrime()
| double umontreal.ssj.discrepancy.SearcherCBC.exhaustPrime | ( | int | s | ) |
Similar to exhaust(s), except that only values of \(a_j\) relatively prime to \(n\) are considered.
Reimplemented from umontreal.ssj.discrepancy.Searcher.
Definition at line 166 of file SearcherCBC.java.
◆ getBestVals()
| double[] umontreal.ssj.discrepancy.SearcherCBC.getBestVals | ( | ) |
Returns the best value of the discrepancy found in the last search, in each dimension up to \(s\).
The values returned are \(V_j\), for \(j = 0, 1, …, (s-1)\).
Definition at line 202 of file SearcherCBC.java.
◆ random()
| double umontreal.ssj.discrepancy.SearcherCBC.random | ( | int | s, |
| int | k ) |
Random CBC search to find the lattice with the best (the smallest) discrepancy in dimension \(s\).
\(k\) random values \(a_j\) are examined for each dimension \(j\). Each random component
\(a_j\) takes values over the integers \(1, 2, …, (n-1)\). The first component \(a_0\) is always set to 1. The method returns the best value of the discrepancy in dimension \(s\).
Reimplemented from umontreal.ssj.discrepancy.Searcher.
Definition at line 182 of file SearcherCBC.java.
◆ randomPrime()
| double umontreal.ssj.discrepancy.SearcherCBC.randomPrime | ( | int | s, |
| int | k ) |
Similar to random(s, k), except that only values of \(a_j\) relatively prime to \(n\) are considered.
Reimplemented from umontreal.ssj.discrepancy.Searcher.
Definition at line 190 of file SearcherCBC.java.
The documentation for this class was generated from the following file:
- src/main/java/umontreal/ssj/discrepancy/SearcherCBC.java
