Weighted figure of merit. More...

#include <WeightedFigureOfMerit.h>

Public Member Functions
	WeightedFigureOfMerit (Real normType, std::unique_ptr< LatticeTester::Weights > weights, PROJDEP projdep=PROJDEP())
	Constructor.
bool	symmetric () const
	Returns `true` if the value of the figure of merit is invariant under the transormation \(a_j \mapsto n - a_j\) for any \(j=1,\dots,s\), where \(n\) and \(s\) are, respectively, the number of points and the dimension of the lattice and \(a_j\) is the \(j\)-th component of the generating vector \(\boldsymbol a = (a_1, \dots, a_s)\).
Real	normType () const
const LatticeTester::Weights &	weights () const
	Returns the projection-dependent weights \(\gamma_{\mathfrak u}\).
const ProjDepMerit::Base< PROJDEP > &	projDepMerit () const
	Returns the projection-dependent figure of merit \(D_{\mathfrak u}\).
template<LatticeType LR, EmbeddingType ET, Compress COMPRESS, PerLevelOrder PLO>
WeightedFigureOfMeritEvaluator< WeightedFigureOfMerit, LR, ET, COMPRESS, PLO >	evaluator (Storage< LR, ET, COMPRESS, PLO > storage) const
	Creates an evaluator for the figure of merit.
std::string	name () const
Public Member Functions inherited from LatBuilder::FigureOfMerit
virtual	~FigureOfMerit ()
	Destructor.

Static Public Member Functions
static constexpr Compress	suggestedCompression ()
template<typename T>
static Accumulator< ACC, T >	accumulator (T initialValue)
	Creates a new accumulator.
static std::string	evaluationName ()

Detailed Description

template<class PROJDEP, template< typename > class ACC>
class LatBuilder::WeightedFigureOfMerit< PROJDEP, ACC >

Weighted figure of merit.

This class implements generic weighted average-case figures of merit of the form

\[ D(P_n) = \left[ \mathop{\mathcal K}_{\mathfrak u \in \mathcal J} \left\{ \gamma_{\mathfrak u}^q D_{\mathfrak u}^q(P_n(\mathfrak u)) \right\} \right]^{1/q}, \]

where \(\mathcal K\) is an operator that combines the set elements (typically a sum on its elements or the extraction of the maximum element), using the given projection-dependent weights \(\gamma_{\mathfrak u}\) and a projection-dependent figure of merit \(D_{\mathfrak u}^2\), for all projections \(\mathfrak u\) in a given set of coordinate sets \(\mathcal J\).

The set of projections under consideration will typically be

\[ \mathcal J = \left\{ \mathfrak u \::\: \mathfrak u \subseteq \{1,\dots,s\} \right\} \]

for an exhaustive search over lattices of dimension \(s\), or

\[ \mathcal J = \left\{ \mathfrak u \cup \{s\} \::\: \mathfrak u \subseteq \{1,\dots,s\} \right\} \]

for a CBC search for the \(s\)th coordinate of a lattice.

Template Parameters

PROJDEP	Type of projection-dependent figure of merit.
ACC	Type of binary operator to use for the accumulator that defines the operator \(\mathcal K\) on the set elements. For example, Functor::Max or Functor::Sum.

Note: The WeightedFigureOfMeritEvaluator object returned by the evaluator() function produces a square merit value.

Examples: tutorial/MeritSeqCBC.cc, tutorial/MeritSeqCBCSignals.cc, tutorial/WeightedFigureOfMerit.cc, tutorial/WeightedFigureOfMeritCBC.cc, and tutorial/WeightedFigureOfMeritSignals.cc.

Constructor & Destructor Documentation

◆ WeightedFigureOfMerit()

template<class PROJDEP, template< typename > class ACC>

LatBuilder::WeightedFigureOfMerit< PROJDEP, ACC >::WeightedFigureOfMerit	(	Real	normType,
		std::unique_ptr< LatticeTester::Weights >	weights,
		PROJDEP	projdep = PROJDEP() )

inline

Constructor.

Parameters

normType	Value of \(q\) as in the \(q\)-norm taken over all projections.
weights	Weights \(\gamma_{\mathfrak u}^q\), already raised to the power \(q\).
projdep	Projection-dependent figure of merit (evaluates to a square merit value).

References weights().

Member Function Documentation

◆ accumulator()

template<class PROJDEP, template< typename > class ACC>

template<typename T>

Accumulator< ACC, T > LatBuilder::WeightedFigureOfMerit< PROJDEP, ACC >::accumulator ( T initialValue )

inlinestatic

Creates a new accumulator.

Parameters

initialValue Initial accumulator value.

◆ name()

template<class PROJDEP, template< typename > class ACC>

std::string LatBuilder::WeightedFigureOfMerit< PROJDEP, ACC >::name ( ) const

inlinevirtual

Implements LatBuilder::FigureOfMerit.

◆ normType()

template<class PROJDEP, template< typename > class ACC>

Real LatBuilder::WeightedFigureOfMerit< PROJDEP, ACC >::normType ( ) const

inlinevirtual

Implements LatBuilder::FigureOfMerit.

◆ symmetric()

template<class PROJDEP, template< typename > class ACC>

bool LatBuilder::WeightedFigureOfMerit< PROJDEP, ACC >::symmetric ( ) const

inlinevirtual

Returns true if the value of the figure of merit is invariant under the transormation \(a_j \mapsto n - a_j\) for any \(j=1,\dots,s\), where \(n\) and \(s\) are, respectively, the number of points and the dimension of the lattice and \(a_j\) is the \(j\)-th component of the generating vector \(\boldsymbol a = (a_1, \dots, a_s)\).

Implements LatBuilder::FigureOfMerit.

References projDepMerit().