LatNet Builder Manual
2.0.1-11
Software Package for Constructing Highly Uniform Point Sets
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Bound on the average weighted \(\mathcal P_\alpha\) discrepancy. More...
#include <PAlphaDPW08.h>
Inherits LatBuilder::Norm::NormAlphaBase< PAlphaDPW08 >.
Public Member Functions | |
PAlphaDPW08 (unsigned int alpha, const LatticeTester::Weights &weights, Real normType) | |
Constructor. More... | |
template<LatticeType LR, EmbeddingType L> | |
Real | value (Real lambda, const SizeParam< LR, L > &sizeParam, Dimension dimension, Real norm=1.0) const |
std::string | name () const |
Public Member Functions inherited from LatBuilder::Norm::NormAlphaBase< PAlphaDPW08 > | |
NormAlphaBase (unsigned int alpha, Real normType) | |
Constructor. More... | |
unsigned | alpha () const |
Real | normType () const |
Real | minExp () const |
Real | maxExp () const |
Real | value (Real lambda, const SizeParam< LR, L > &sizeParam, Dimension dimension, Real norm=1.0) const |
Returns the value of the bound. More... | |
Real | operator() (const SizeParam< LR, L > &sizeParam, Dimension dimension, Real norm=1.0) const |
Returns the smallest value of the bound for dimension dimension . More... | |
Real | minimum (const SizeParam< LR, L > &sizeParam, Dimension dimension, Real norm) const |
Returns the minimum value of the bound function. More... | |
Additional Inherited Members | |
Static Public Attributes inherited from LatBuilder::Norm::NormAlphaBase< PAlphaDPW08 > | |
static const unsigned | MINIMIZER_MAX_ITER |
Maximum number of iterations to be used with the minimizer. | |
static const int | MINIMIZER_PREC_BITS |
Relative precision on the minimum value to be used with the minimizer. | |
Bound on the average weighted \(\mathcal P_\alpha\) discrepancy.
This is the bound
\[ \min_{1/\alpha < \lambda \leq 1} \overline{E}^2_{n,s,\alpha,\boldsymbol\gamma}(\lambda) \]
from Theorem 10 (with the minimization step proposed in Algorithm 2) in [7] .
LatBuilder::Norm::PAlphaDPW08::PAlphaDPW08 | ( | unsigned int | alpha, |
const LatticeTester::Weights & | weights, | ||
Real | normType | ||
) |
Constructor.
alpha | Smoothness level \(\alpha\) of the class of functions. |
weights | Projection-dependent weights \( \gamma_{\mathfrak u} \). |
normType | Type of cross-projection norm used by the figure of merit. |