Declares multiindices as feasible if their entries for less important dimensions are not too high. More...

#include <MultiIndexLimiter.h>

Inheritance diagram for muq::Utilities::AnisotropicLimiter:

Detailed Description

Declares multiindices as feasible if their entries for less important dimensions are not too high.

Given a weight vector \( w = (w_i)_{i=1}^d \) with \( w_i \in [0,1] \) and a cutoff threshold \( \epsilon \in (0,1)\), this limiter declares a multiindex \( \nu = (\nu_i)_{i=1}^d \) as feasible if \( w^\nu := \prod_{i=1}^d w_i^{\nu_i} > \epsilon \). It thus implements the multiindex selection criterion for the construction of a priori anisotropic sparse grids as described in Algorithm 2 in

Zech, Jakob. Sparse-grid approximation of high-dimensional parametric PDEs. ETH Zurich, 2018.

See also: muq::Utilities::MultiIndexFactory::CreateAnisotropic

Definition at line 81 of file MultiIndexLimiter.h.

Public Member Functions
	AnisotropicLimiter (const Eigen::RowVectorXf &weightsIn, const double epsilonIn)

virtual bool	IsFeasible (std::shared_ptr< MultiIndex > multi) const override

Public Member Functions inherited from muq::Utilities::MultiIndexLimiter
virtual	~MultiIndexLimiter ()=default

Constructor & Destructor Documentation

◆ AnisotropicLimiter()

muq::Utilities::AnisotropicLimiter::AnisotropicLimiter	(	const Eigen::RowVectorXf &	weightsIn,
		const double	epsilonIn
	)

Definition at line 13 of file MultiIndexLimiter.cpp.

References epsilon, nlohmann::to_string(), and weights.

Member Function Documentation

◆ IsFeasible()

bool muq::Utilities::AnisotropicLimiter::IsFeasible ( std::shared_ptr< MultiIndex > multi ) const

overridevirtual

This function is overloaded by children to define what terms are included.

Implements muq::Utilities::MultiIndexLimiter.

Definition at line 25 of file MultiIndexLimiter.cpp.

Member Data Documentation

◆ epsilon

const double muq::Utilities::AnisotropicLimiter::epsilon

private

Definition at line 91 of file MultiIndexLimiter.h.

Referenced by AnisotropicLimiter().

◆ weights

const Eigen::RowVectorXf& muq::Utilities::AnisotropicLimiter::weights