LatBuilder::Functor::IAAlpha Class Reference

One-dimensional merit function for the interlaced \(\mathcal B_{\alpha, d, \gamma, (1)}\) discrepancy in base 2 [rGOD13a]. More...

#include <IAAlpha.h>

Public Types
typedef Real	value_type
typedef Real	result_type

Public Member Functions
	IAAlpha (unsigned int alpha, unsigned int interlacingFactor)
	Constructor.
unsigned int	alpha () const
unsigned int	interlacingFactor () const
bool	symmetric () const
template<typename MODULUS>
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 interlaced \(\mathcal B_{\alpha, d, \gamma, (1)}\) discrepancy in base 2 [rGOD13a].

This merit function is defined as:

\[ \phi_{\alpha, d, (1)}(x) = \frac{1 - 2^{(\min(\alpha, d) -1) \lfloor \log_2(x) \rfloor} (2^{\min(\alpha, d)} -1)}{2^{(\alpha+2)/2} (2^{\min(\alpha, d) - 1} -1) } \]

with \( \min(\alpha, d) > 1 \) where we set \(2^{\lfloor \log_2(0) \rfloor} = 0\).

Constructor & Destructor Documentation

IAAlpha()

LatBuilder::Functor::IAAlpha::IAAlpha ( unsigned int alpha, unsigned int interlacingFactor )

inline

Constructor.

Parameters

alpha	Value of \(\alpha\).
interlacingFactor	Value of \(d\).

References LatBuilder::intPow().

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

• include/latbuilder/Functor/IAAlpha.h