Bound on the average weighted \(\mathcal P_\alpha\) discrepancy. More...

#include <PAlphaDPW08.h>

Public Member Functions
	PAlphaDPW08 (unsigned int alpha, const LatticeTester::Weights &weights, Real normType)
	Constructor.
template<LatticeType LR, EmbeddingType L>
Real	value (Real lambda, const SizeParam< LR, L > &sizeParam, Dimension dimension, Real norm=1.0) const
std::string	name () const
Public Member Functions inherited from LatBuilder::Norm::NormAlphaBase< PAlphaDPW08 >
	NormAlphaBase (unsigned int alpha, Real normType)
	Constructor.
unsigned	alpha () const
Real	normType () const
Real	minExp () const
Real	maxExp () const
Real	value (Real lambda, const SizeParam< LR, L > &sizeParam, Dimension dimension, Real norm=1.0) const
	Returns the value of the bound.
Real	operator() (const SizeParam< LR, L > &sizeParam, Dimension dimension, Real norm=1.0) const
	Returns the smallest value of the bound for dimension `dimension`.
Real	minimum (const SizeParam< LR, L > &sizeParam, Dimension dimension, Real norm) const
	Returns the minimum value of the bound function.

Additional Inherited Members
Static Public Attributes inherited from LatBuilder::Norm::NormAlphaBase< PAlphaDPW08 >
static const unsigned	MINIMIZER_MAX_ITER
	Maximum number of iterations to be used with the minimizer.
static const int	MINIMIZER_PREC_BITS
	Relative precision on the minimum value to be used with the minimizer.

Detailed Description

Bound on the average weighted \(\mathcal P_\alpha\) discrepancy.

This is the bound

\[ \min_{1/\alpha < \lambda \leq 1} \overline{E}^2_{n,s,\alpha,\boldsymbol\gamma}(\lambda) \]

from Theorem 10 (with the minimization step proposed in Algorithm 2) in [8] .

Constructor & Destructor Documentation

LatBuilder::Norm::PAlphaDPW08::PAlphaDPW08	(	unsigned int	alpha,
		const LatticeTester::Weights &	weights,
		Real	normType )

Constructor.

Parameters

alpha	Smoothness level \(\alpha\) of the class of functions.
weights	Projection-dependent weights \( \gamma_{\mathfrak u} \).
normType	Type of cross-projection norm used by the figure of merit.

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