Lattice Builder Manual Software Package for Constructing Rank-1 Lattices

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

#include <PAlphaDPW08.h>

## Public Member Functions

PAlphaDPW08 (unsigned int alpha, const LatCommon::Weights &weights, Real normType)
Constructor. More...

template<LatType L>
Real value (Real lambda, const SizeParam< L > &sizeParam, Dimension dimension, Real norm=1.0) const

std::string name () const Public Member Functions inherited from LatBuilder::Norm::PAlphaBase< PAlphaDPW08 >
PAlphaBase (unsigned int alpha, Real normType)
Constructor. More...

unsigned alpha () const

Real normType () const

Real minExp () const

Real maxExp () const

Real value (Real lambda, const SizeParam< L > &sizeParam, Dimension dimension, Real norm=1.0) const
Returns the value of the bound. More...

Real operator() (const SizeParam< L > &sizeParam, Dimension dimension, Real norm=1.0) const
Returns the smallest value of the bound for dimension dimension. More...

Real minimum (const SizeParam< L > &sizeParam, Dimension dimension, Real norm) const
Returns the minimum value of the bound function. More... Static Public Attributes inherited from LatBuilder::Norm::PAlphaBase< 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  .

## Constructor & Destructor Documentation

 LatBuilder::Norm::PAlphaDPW08::PAlphaDPW08 ( unsigned int alpha, const LatCommon::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: