Lattice Builder Manual Software Package for Constructing Rank-1 Lattices

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LatBuilder::Functor::PAlpha Class Reference

One-dimensional merit function for the \(\mathcal P_\alpha\) discrepancy. More...

`#include <PAlpha.h>`

## Public Types
typedef Real | value_type
typedef Real | result_type

## Public Member Functions
| PAlpha (unsigned int alpha)
| Constructor. More...
unsigned int | alpha () const
bool | symmetric () const
result_type | operator() (const value_type &x, Modulus n=0) const
| Returns the one-dimensional function evaluated at `x`.
std::string | name () const

## Static Public Member Functions
static constexpr Compress | suggestedCompression ()

## Detailed Description

One-dimensional merit function for the \(\mathcal P_\alpha\) discrepancy.

This merit function is defined as

\[ \omega(x) = -\frac{(-4\pi^2)^{\alpha/2}}{\alpha!} \, B_\alpha(x), \]

for even integers \(\alpha\), where \(B_\alpha(x)\) is the Bernoulli polynomial of degree \(\alpha\).

## Constructor & Destructor Documentation

LatBuilder::Functor::PAlpha::PAlpha | ( | unsigned int | alpha | ) |
| inline

Constructor.

Parameters

  alpha | Value of \(\alpha\).

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

- latbuilder/include/latbuilder/Functor/PAlpha.h