This class implements searches to find the best Korobov lattices with respect to a given discrepancy. More...

Inheritance diagram for SearcherKorobov:

Collaboration diagram for SearcherKorobov:

Public Member Functions
	SearcherKorobov (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`. More...

double	exhaust (int s)
	Exhaustive search to find the best Korobov lattice (i.e. More...

double	exhaustPrime (int s)
	Similar to exhaust(s), except that only values of \(a\) relatively prime to \(n\) are considered.

double	random (int s, int k)
	Random search to find the best Korobov lattice (with the smallest discrepancy) in dimension \(s\). More...

double	randomPrime (int s, int k)
	Similar to random(s, k), except that only values of \(a\) relatively prime to \(n\) are considered.

int	getBestA ()
	Returns the generator \(a\) of the lattice which gave the best value of the discrepancy in the last search.

Public Member Functions inherited from 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`. More...

double	exhaust (int s)
	Exhaustive search to find the lattice with the best (the smallest) discrepancy in dimension \(s\). More...

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 search to find the lattice with the best (the smallest) discrepancy in dimension \(s\). More...

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	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. More...

void	initGen (int seed)
	Initializes the random number generator used in random searches with the starting seed `seed`. More...

Protected Member Functions
void	print (int y)

Protected Member Functions inherited from Searcher
void	print (int[] y, int s)

Protected Attributes
int	bestA

Protected Attributes inherited from Searcher
Discrepancy	disc

PointSet	lat

double []	gamma

double	bestVal

int []	bestAs

boolean	primeN = false

boolean	power2F = false

Additional Inherited Members
Static Protected Attributes inherited from Searcher
static RandomStream	gen = new LFSR113()

Detailed Description

This class implements searches to find the best Korobov lattices with respect to a given discrepancy.

Given a positive integer \(n\) and a multiplier \(a\), the points are defined by

\[ \mathbf{u}_i = (i/n)(1, a, a^2, …, a^{s-1}) \bmod1 \]

for \(i=0,…,n-1\).

The discrepancy object in the 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.

Constructor & Destructor Documentation

◆ SearcherKorobov()

SearcherKorobov	(	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.

Member Function Documentation

◆ exhaust()

double exhaust ( int s )

Exhaustive search to find the best Korobov lattice (i.e.

with the smallest discrepancy) in dimension \(s\). The search runs exhaustively over all values \( a = 2, 3, …, (n-1)\), where \(a\) is the generator of the lattice. The method returns the best value found for the discrepancy.

◆ random()

double random	(	int	s,
		int	k
	)

Random search to find the best Korobov lattice (with the smallest discrepancy) in dimension \(s\).

\(k\) random values \(a\) are examined as generator of the lattice. The \(a\) takes values over the integers \( a = 2, 3, …, (n-1)\). The method returns the best value found for the discrepancy.

The documentation for this class was generated from the following file:

SearcherKorobov.java

Public Member Functions

Protected Member Functions