LatNet Builder Manual  2.0.1-11
Software Package for Constructing Highly Uniform Point Sets
LatBuilder::Functor::IAAlpha Class Reference


One-dimensional merit function for the interlaced \(\mathcal B_{\alpha, d, \gamma, (1)}\) discrepancy in base 2 [10]. 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. More...
 
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 [10].

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
alphaValue of \(\alpha\).
interlacingFactorValue of \(d\).

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