LatNet Builder Manual
2.0.1-11
Software Package for Constructing Highly Uniform Point Sets
|
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 () |
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 \(2^{\lfloor \log_2(0) \rfloor} = 0\).
|
inline |
Constructor.
alpha | Value of \(\alpha\). |
interlacingFactor | Value of \(d\). |