LatNet Builder Manual
2.0.1-11
Software Package for Constructing Highly Uniform Point Sets
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Base class for bounds on the \(\mathcal P_\alpha\) values. More...
#include <NormAlphaBase.h>
Public Member Functions | |
NormAlphaBase (unsigned int alpha, Real normType) | |
Constructor. More... | |
unsigned | alpha () const |
Real | normType () const |
Real | minExp () const |
Real | maxExp () const |
template<LatticeType LR, EmbeddingType L> | |
Real | value (Real lambda, const SizeParam< LR, L > &sizeParam, Dimension dimension, Real norm=1.0) const |
Returns the value of the bound. More... | |
template<LatticeType LR, EmbeddingType L> | |
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... | |
template<LatticeType LR, EmbeddingType L> | |
Real | minimum (const SizeParam< LR, L > &sizeParam, Dimension dimension, Real norm) const |
Returns the minimum value of the bound function. More... | |
Static Public Attributes | |
static const unsigned | MINIMIZER_MAX_ITER = 1000u |
Maximum number of iterations to be used with the minimizer. | |
static const int | MINIMIZER_PREC_BITS = 18 |
Relative precision on the minimum value to be used with the minimizer. | |
Base class for bounds on the \(\mathcal P_\alpha\) values.
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inline |
Constructor.
alpha | Smoothness level \(\alpha\) of the class of functions. |
normType | Type of cross-projection norm used by the figure of merit. |
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inline |
Returns the minimum value of the bound function.
Uses BrentMinimizer to minimize the bound function. The value of \(\lambda\) at which the minimum is reached is not returned.
Referenced by LatBuilder::Norm::NormAlphaBase< IB >::operator()().
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inline |
Returns the smallest value of the bound for dimension dimension
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sizeParam | Size parameter for the lattices. |
dimension | Dimension. |
norm | Additional normalization \( c \). |
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inline |
Returns the value of the bound.
lambda | Value of \(\lambda = \). |
sizeParam | Size parameter for the lattices. |
dimension | Dimension. |
norm | Additional normalization \( c \). |