This class implements Minkowski’s theoretical LOWER bound on the length of the shortest non-zero vector in a lattice. More...
#include <latticetester/NormaMinkowski.h>
Inherits LatticeTester::Normalizer< RedDbl >.
Public Member Functions | |
| NormaMinkowski (RedDbl &logDensity, int t, double beta=1) | |
| Constructor for the bounds obtained for Minkowski lattices. More... | |
| double | getGamma (int j) const |
| Returns the value of the lattice constant \(\gamma_j\) in dimension \(j\). More... | |
 Public Member Functions inherited from LatticeTester::Normalizer< RedDbl > | |
| Normalizer (RedDbl &logDensity, int t, std::string Name, NormType norm=L2NORM, double beta=1) | |
Complete constructor for a Normalizer. More... | |
| Normalizer (int t, std::string Name, NormType norm=L2NORM, double beta=1) | |
| Constructor that does not take the density as an argument. More... | |
| virtual | ~Normalizer () |
| Destructor. More... | |
| virtual void | init (RedDbl &logDensity, double beta) |
| This is a method that will initialize the bounds this normalizer can return. More... | |
| std::string | ToString () const |
| Returns a string that describes this object. More... | |
| NormType | getNorm () const |
| Returns the norm associated with this object. More... | |
| void | setLogDensity (RedDbl logDensity) |
Sets the log-density associated with this object to logDensity. More... | |
| RedDbl | getLogDensity () const |
Returns the logDensity associated with this object. More... | |
| void | setNorm (NormType norm) |
Sets the norm associated with this object to norm. More... | |
| int | getDim () const |
| Returns the maximal dimension for this object. More... | |
| double | getPreComputedBound (int j) const |
Returns the bound for dimension j as computed in Normalizer::init(). More... | |
| virtual RedDbl | getBound (int j) const |
Calculates and returns the bound on the length of the shortest nonzero vector in dimension j. More... | |
Additional Inherited Members | |
| Static Public Attributes inherited from LatticeTester::Normalizer< RedDbl > | |
| static const int | MAX_DIM = 48 |
| The maximum dimension of the lattices for which this class can give an upper bound. More... | |
| Protected Attributes inherited from LatticeTester::Normalizer< RedDbl > | |
| std::string | m_name |
| Name of the normalizer. More... | |
| NormType | m_norm |
| Norm associated with this object. More... | |
| RedDbl | m_logDensity |
| log of the density, ie log of the number of points of the lattice per unit of volume. More... | |
| int | m_maxDim |
Only elements 1 to m_maxDim (inclusive) of m_bounds bellow will be pre-computed. More... | |
| double | m_beta |
| Beta factor used to give more or less importance to some of the dimensions. More... | |
| double * | m_bounds |
| Contains the bounds on the length of the shortest nonzero vector in the lattice in each dimension. More... | |
Detailed Description
template<typename RedDbl>
class LatticeTester::NormaMinkowski< RedDbl >
This class implements Minkowski’s theoretical LOWER bound on the length of the shortest non-zero vector in a lattice.
The length of a vector is computed using the \({\mathcal{L}}_2\) norm. The bounding lengths, for a lattice containing \(n\) points per unit volume in dimension \(t\), are given by \(\ell_t^* = \gamma_t^{1/2} n^{-1/t}\), where the \(\gamma_t\) are the Minkowski lattice constants.
Constructor & Destructor Documentation
◆ NormaMinkowski()
| LatticeTester::NormaMinkowski< RedDbl >::NormaMinkowski | ( | RedDbl & | logDensity, |
| int | t, | ||
| double | beta = 1 |
||
| ) |
Constructor for the bounds obtained for Minkowski lattices.
The lattices have \(n\) points per unit volume, in all dimensions \(\le t\). The bias factor beta \(= \beta\) gives more weight to some of the dimensions. Note this class stores the log value of the density to handle larger values. Restriction: \(t \le48\).
Member Function Documentation
◆ getGamma()
|
inlinevirtual |
Returns the value of the lattice constant \(\gamma_j\) in dimension \(j\).
Reimplemented from LatticeTester::Normalizer< RedDbl >.
The documentation for this class was generated from the following file:
- include/latticetester/NormaMinkowski.h
