| 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 \(\alpha\). |