This class implements lower bounds on the Hermite constants based on the Minkowski-Hlawka theorem [mHLA43a]. More...
Inheritance diagram for LatticeTester::NormaMinkHlaw:
Public Member Functions | |
| NormaMinkHlaw (double logm, int64_t k, int64_t maxDim, NormType norm=L2NORM) | |
| This constructor assumes that the rescaled primal lattice has scaling factor \(m\) and order \(k\), so its density is \(m^{k-t}\) for \(t\geq k\), and cannot exceed 1 for projections in \(s < k\) dimensions. | |
| NormaMinkHlaw (double logDensity, int64_t maxDim, NormType norm=L2NORM) | |
Constructs a NormaMinkHlaw for up to maxDim dimensions, by assuming that the log density is logDensity in all dimensions and the lattice was not rescaled. | |
| double | getGamma (int64_t j) const |
| Returns the value of the lattice constant \(\gamma_j\) in dimension \(j\). | |
| Public Member Functions inherited from LatticeTester::Normalizer | |
| Normalizer (double logm, int64_t k, int64_t maxDim, NormType norm=L2NORM) | |
| This is the preferred constructor in all the subclasses. | |
| Normalizer (double logDensity, int64_t maxDim, NormType norm=L2NORM) | |
| This old (legacy) constructor assumes that the lattice is not rescaled and that the (log)density is the same in all dimensions, which is practically never true when rescaling. | |
| Normalizer (int64_t maxDim, NormType norm=L2NORM) | |
| This constructor creates a Normalizer object without computing any bounds. | |
| virtual | ~Normalizer () |
| Destructor. | |
| void | computeBounds (double logm, int64_t k) |
| This method computes the bounds that this normalizer will return, by assuming that the primal lattice was rescaled by the factor \(m\) and has order \(k\), so its density is \(m^{k-t}\) for \(t\geq k\), and cannot exceed \(m^s\) for projections in \(s < k\) dimensions. | |
| virtual void | computeBounds (double logDensity) |
This method computes bounds by assuming that the log density is logDensity for all dimensions up to the maximal dimension maxDim, which is rarely true. | |
| std::string | toString () const |
| Returns a string that describes this object. | |
| NormType | getNorm () const |
| Returns the norm associated with this object. | |
| int64_t | getMaxDim () const |
| Returns the maximal dimension for this object. | |
| virtual double * | getBounds () const |
| Returns the array that contains the bounds on the lengths of the shortest nonzero vectors. | |
| virtual double | getBound (int64_t j) const |
Returns the bound on the length of the shortest nonzero vector in j dimensions. | |
Additional Inherited Members | |
| Static Public Attributes inherited from LatticeTester::Normalizer | |
| static const int64_t | MAX_DIM = 48 |
| The maximum dimension of the lattices for which this class can compute a bound. | |
| Protected Attributes inherited from LatticeTester::Normalizer | |
| std::string | m_name |
| Name of the normalizer. | |
| NormType | m_norm |
| Norm type associated with this object. | |
| int64_t | m_maxDim |
| Maximum dimension. | |
| double * | m_bounds |
Contains the bounds on the length of the shortest nonzero vector in the lattice in each dimension up to maxDim. | |
Detailed Description
This class implements lower bounds on the Hermite constants based on the Minkowski-Hlawka theorem [mHLA43a].
The Hermite constants are approximated by the \(\gamma_t^{(Z)}\) given in the guide. These lower bounds are all smaller than the lower bounds from NormaBestLat.
Constructor & Destructor Documentation
◆ NormaMinkHlaw() [1/2]
| LatticeTester::NormaMinkHlaw::NormaMinkHlaw | ( | double | logm, |
| int64_t | k, | ||
| int64_t | maxDim, | ||
| NormType | norm = L2NORM ) |
This constructor assumes that the rescaled primal lattice has scaling factor \(m\) and order \(k\), so its density is \(m^{k-t}\) for \(t\geq k\), and cannot exceed 1 for projections in \(s < k\) dimensions.
◆ NormaMinkHlaw() [2/2]
| LatticeTester::NormaMinkHlaw::NormaMinkHlaw | ( | double | logDensity, |
| int64_t | maxDim, | ||
| NormType | norm = L2NORM ) |
Constructs a NormaMinkHlaw for up to maxDim dimensions, by assuming that the log density is logDensity in all dimensions and the lattice was not rescaled.
Restriction: maxDim \( \le 48\).
Member Function Documentation
◆ getGamma()
|
inlinevirtual |
Returns the value of the lattice constant \(\gamma_j\) in dimension \(j\).
Reimplemented from LatticeTester::Normalizer.
The documentation for this class was generated from the following file:
- include/latticetester/NormaMinkHlaw.h
