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