Lattice Builder Manual
Software Package for Constructing Rank-1 Lattices
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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 () |
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 \(\alpha\).
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inline |
Constructor.
alpha | Value of \(\alpha\). |