LatNet Builder Manual  2.0.1-11
Software Package for Constructing Highly Uniform Point Sets
LatBuilder::Norm::NormAlphaBase< DERIVED > Class Template Reference

Base class for bounds on the \(\mathcal P_\alpha\) values. More...

#include <NormAlphaBase.h>

Public Member Functions

 NormAlphaBase (unsigned int alpha, Real normType)
 Constructor. More...
 
unsigned alpha () const
 
Real normType () const
 
Real minExp () const
 
Real maxExp () const
 
template<LatticeType LR, EmbeddingType L>
Real value (Real lambda, const SizeParam< LR, L > &sizeParam, Dimension dimension, Real norm=1.0) const
 Returns the value of the bound. More...
 
template<LatticeType LR, EmbeddingType L>
Real operator() (const SizeParam< LR, L > &sizeParam, Dimension dimension, Real norm=1.0) const
 Returns the smallest value of the bound for dimension dimension. More...
 
template<LatticeType LR, EmbeddingType L>
Real minimum (const SizeParam< LR, L > &sizeParam, Dimension dimension, Real norm) const
 Returns the minimum value of the bound function. More...
 

Static Public Attributes

static const unsigned MINIMIZER_MAX_ITER = 1000u
 Maximum number of iterations to be used with the minimizer.
 
static const int MINIMIZER_PREC_BITS = 18
 Relative precision on the minimum value to be used with the minimizer.
 

Detailed Description

template<class DERIVED>
class LatBuilder::Norm::NormAlphaBase< DERIVED >

Base class for bounds on the \(\mathcal P_\alpha\) values.

Constructor & Destructor Documentation

◆ NormAlphaBase()

template<class DERIVED>
LatBuilder::Norm::NormAlphaBase< DERIVED >::NormAlphaBase ( unsigned int  alpha,
Real  normType 
)
inline

Constructor.

Parameters
alphaSmoothness level \(\alpha\) of the class of functions.
normTypeType of cross-projection norm used by the figure of merit.

Member Function Documentation

◆ minimum()

template<class DERIVED>
template<LatticeType LR, EmbeddingType L>
Real LatBuilder::Norm::NormAlphaBase< DERIVED >::minimum ( const SizeParam< LR, L > &  sizeParam,
Dimension  dimension,
Real  norm 
) const
inline

Returns the minimum value of the bound function.

Uses BrentMinimizer to minimize the bound function. The value of \(\lambda\) at which the minimum is reached is not returned.

Referenced by LatBuilder::Norm::NormAlphaBase< IB >::operator()().

◆ operator()()

template<class DERIVED>
template<LatticeType LR, EmbeddingType L>
Real LatBuilder::Norm::NormAlphaBase< DERIVED >::operator() ( const SizeParam< LR, L > &  sizeParam,
Dimension  dimension,
Real  norm = 1.0 
) const
inline

Returns the smallest value of the bound for dimension dimension.

Parameters
sizeParamSize parameter for the lattices.
dimensionDimension.
normAdditional normalization \( c \).

◆ value()

template<class DERIVED>
template<LatticeType LR, EmbeddingType L>
Real LatBuilder::Norm::NormAlphaBase< DERIVED >::value ( Real  lambda,
const SizeParam< LR, L > &  sizeParam,
Dimension  dimension,
Real  norm = 1.0 
) const
inline

Returns the value of the bound.

Parameters
lambdaValue of \(\lambda = \).
sizeParamSize parameter for the lattices.
dimensionDimension.
normAdditional normalization \( c \).

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