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Lattice Builder Manual
Software Package for Constructing Rank-1 Lattices
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This class implements lattice bases built from a Korobov lattice rule. More...
#include <KorobovLattice.h>
Inherits LatCommon::IntLattice.
Public Member Functions | |
| KorobovLattice (const MScal &n, const MScal &a, int maxDim, NormType norm=L2NORM) | |
Constructs a Korobov lattice with \(n\) points, maximal dimension maxDim using the norm norm. | |
| KorobovLattice (const MScal &n, const MScal &a, int dim, int t, NormType norm=L2NORM) | |
| Constructor. More... | |
| KorobovLattice (const KorobovLattice &Lat) | |
| Copy constructor. | |
| KorobovLattice & | operator= (const KorobovLattice &Lat) |
Assigns Lat to this object. | |
| ~KorobovLattice () | |
| Destructor. | |
| std::string | toStringCoef () const |
| Returns the multiplier \(a\) as a string. | |
| void | buildBasis (int d) |
| Builds the basis in dimension \(d\). | |
| void | incDim () |
| Increments the dimension of the basis by 1. | |
| void | incDimSlow () |
| Increments the dimension of the basis by 1 by rebuilding the basis from scratch. More... | |
Public Member Functions inherited from LatCommon::IntLattice | |
| IntLattice (const MScal &m, int k, int maxDim, NormType norm=L2NORM) | |
| Constructor. More... | |
| IntLattice (const IntLattice &Lat) | |
| Copy constructor. More... | |
| IntLattice & | operator= (const IntLattice &Lat) |
Assigns Lat to this object. More... | |
| virtual | ~IntLattice () |
| Destructor. | |
| void | copy (const IntLattice &lattice) |
| Same as assignment operator above. | |
| int | getDim () const |
Returns actual dimension Dim. | |
| void | setDim (int d) |
| Sets actual dimension to \(d\). | |
| int | getMaxDim () const |
| Returns the maximal dimension of the lattice. | |
| NormType | getNorm () const |
| Returns the norm used by the lattice. | |
| MScal | getM () const |
| Returns the value of the modulus \(m\) of the recurrence (the number of points of the lattice). | |
| NScal | getM2 () const |
| Returns the square number of points in the lattice. | |
| int | getOrder () const |
| Returns the order. | |
| Normalizer * | getNormalizer (NormaType norma, int alpha) |
Creates and returns the normalizer corresponding to criterion norma. More... | |
| Base & | getPrimalBasis () |
Returns the primal basis V. | |
| Base & | getDualBasis () |
Returns the dual basis W. | |
| void | calcLgVolDual2 (bool dualF) |
Computes the logarithm of the normalization factor m_lgVolDual2 for the merit in all dimensions % \(\le \) maxDim for the dual lattice if dualF is true, and for the primal lattice if dualF is false. | |
| double | getLgVolDual2 (int i) const |
| bool | getXX (int i) const |
| void | setXX (bool val, int i) |
| void | sort (int d) |
| Sorts the basis vectors with indices from \(d+1\) to the dimension of the basis by increasing length. More... | |
| void | permute (int i, int j) |
| Exchanges vectors \(i\) and \(j\) in the basis and in the dual basis. | |
| void | write (const char *filename) const |
Writes this basis in file named filename. | |
| void | trace (char *msg) |
| For debugging purposes. | |
| void | write (int flag) |
| Writes this basis on standard output. More... | |
| void | dualize () |
| Exchanges basis \(V\) and its dual \(W\). | |
| bool | checkDuality () |
| Checks that the bases satisfy the duality relation \(V[i]\cdot W[j] = m\,\delta_{ij}\). More... | |
| bool | baseEquivalence (IntLattice &Lat) |
Checks that Lat's basis and this basis are equivalent. More... | |
| void | buildProjection (IntLattice *lattice, const Coordinates &proj) |
Builds the basis (and dual basis) of the projection proj for this lattice. More... | |
Protected Member Functions | |
| void | init () |
| Initialization. | |
Protected Member Functions inherited from LatCommon::IntLattice | |
| void | init () |
| void | kill () |
| Cleans and releases all the memory allocated for this lattice. | |
Protected Attributes | |
| MScal | m_a |
| The multiplier of the Korobov lattice rule. | |
| int | m_shift |
| The shift applied to the lattice rule. | |
Protected Attributes inherited from LatCommon::IntLattice | |
| int | m_order |
| The order of the basis. | |
| MScal | m_m |
Number of points per unit volume (m_m) and its square (m_m2). | |
| NScal | m_m2 |
| double | m_lgm2 |
| The logarithm \(\log_2 (m^2)\). | |
| Base | m_v |
| Primal basis of the lattice. | |
| Base | m_w |
| Dual basis of the lattice. | |
| double * | m_lgVolDual2 |
| bool * | m_xx |
| Work variables. | |
| MScal | m_t1 |
| MScal | m_t2 |
| MScal | m_t3 |
| BMat | m_vSI |
| Base | m_vTemp |
This class implements lattice bases built from a Korobov lattice rule.
For a given \(a\), a Korobov lattice basis is formed as follows:
\[ \mathbf{b_1} = (1, a, a^2, \ldots, a^{d-1}),\quad \mathbf{b_2} = (0, n, 0, \ldots, 0),\quad \ldots,\quad \mathbf{b_d} = (0, \ldots, 0, n). \]
incDim de facon efficace comme dans MRGLattice | LatCommon::KorobovLattice::KorobovLattice | ( | const MScal & | n, |
| const MScal & | a, | ||
| int | dim, | ||
| int | t, | ||
| NormType | norm = L2NORM |
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| ) |
Constructor.
Same as above, except the lattice is formed as follow:
\[ \mathbf{b_1} = (a^t, a^{t+1}, a^{t+2}, \ldots, a^{t+d-1}),\qquad \mathbf{b_2} = (0, n, 0, \ldots, 0),\qquad \ldots,\qquad \mathbf{b_d} = (0, \ldots, 0, n). \]
| void LatCommon::KorobovLattice::incDimSlow | ( | ) |
Increments the dimension of the basis by 1 by rebuilding the basis from scratch.
This is very slow. It can be used for verification of the fast incDim method above.