Lattice Builder Manual
Software Package for Constructing Rank-1 Lattices
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
alphaValue of \(\alpha\).

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