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.
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.
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.
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.

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

alpha	Smoothness level \(\alpha\) of the class of functions.
normType	Type 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.

References MINIMIZER_MAX_ITER, MINIMIZER_PREC_BITS, and value().

Referenced by 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

sizeParam	Size parameter for the lattices.
dimension	Dimension.
norm	Additional normalization \( c \).

References minimum().

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

lambda	Value of \(\lambda = \).
sizeParam	Size parameter for the lattices.
dimension	Dimension.
norm	Additional normalization \( c \).

Referenced by minimum().

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

• include/latbuilder/Norm/NormAlphaBase.h