muq::Approximation::FullTensorQuadrature Class Reference

Multivariate quadrature rule defined by the tensor product of 1d rules. More...

#include <FullTensorQuadrature.h>

Inheritance diagram for muq::Approximation::FullTensorQuadrature:

Detailed Description

Multivariate quadrature rule defined by the tensor product of 1d rules.

One of the most straightforward multivariate quadrature rules, a full tensor expansion. Creates a the complete tensor product of the points of the given order 1D quadrature rules for each dimension. The 1D quadrature order can be isotropic or vary per dimension. Note that an isotropic order does not mean isotropic number of points in each dimension, if different 1D quadrature rules are used.

Probably not the most useful class for actual analysis, because you have to know exactly what order you want, but is an important building block for sparse quadrature routines.

Definition at line 28 of file FullTensorQuadrature.h.

Public Member Functions
	FullTensorQuadrature (unsigned int dim, std::shared_ptr< Quadrature > const &rules)
	FullTensorQuadrature (unsigned int dim, std::shared_ptr< Quadrature > const &rules, unsigned int order)
	FullTensorQuadrature (std::vector< std::shared_ptr< Quadrature >> const &rules, Eigen::RowVectorXi orders=Eigen::RowVectorXi())
virtual	~FullTensorQuadrature ()=default
virtual void	Compute (unsigned int order) override
virtual void	Compute (Eigen::RowVectorXi const &orders) override
virtual unsigned int	Exactness (unsigned int quadOrder) const override
Public Member Functions inherited from muq::Approximation::Quadrature
	Quadrature (unsigned int dimIn)
virtual	~Quadrature ()=default
virtual unsigned int	Dim () const
virtual Eigen::MatrixXd const &	Points () const
virtual Eigen::VectorXd const &	Weights () const

Constructor & Destructor Documentation

FullTensorQuadrature() [1/3]

FullTensorQuadrature::FullTensorQuadrature	(	unsigned int	dim,
		std::shared_ptr< Quadrature > const &	rules
	)

Sets up a tensor product of quadrature rules in dim dimensions. Does not compute the tensor product because no order is specified.

Definition at line 14 of file FullTensorQuadrature.cpp.

FullTensorQuadrature() [2/3]

FullTensorQuadrature::FullTensorQuadrature	(	unsigned int	dim,
		std::shared_ptr< Quadrature > const &	rules,
		unsigned int	order
	)

Sets up and solves a tensor product of 1d quadrature rules.

Definition at line 9 of file FullTensorQuadrature.cpp.

FullTensorQuadrature() [3/3]

FullTensorQuadrature::FullTensorQuadrature	(	std::vector< std::shared_ptr< Quadrature >> const &	rules,
		Eigen::RowVectorXi	orders = Eigen::RowVectorXi()
	)

Sets up a tensor product of quadrature rules with potentially different rules in each dimension. If the orders row vector is specified, then the tensor product rule is also computed, otherwise an additional call to "Compute" is required.

Definition at line 18 of file FullTensorQuadrature.cpp.

References Compute(), and rules.

~FullTensorQuadrature()

virtual muq::Approximation::FullTensorQuadrature::~FullTensorQuadrature ( )

virtualdefault

Member Function Documentation

Compute() [1/2]

void FullTensorQuadrature::Compute ( Eigen::RowVectorXi const &  orders )

overridevirtual

Base implementation of Compute. Assumes the quadrature rule is 1d and then calls Compute with the first component of the orders vector.

Multivariate quadrature rules should override this function.

Reimplemented from muq::Approximation::Quadrature.

Definition at line 37 of file FullTensorQuadrature.cpp.

References muq::Approximation::Quadrature::dim, muq::Approximation::Quadrature::pts, rules, and muq::Approximation::Quadrature::wts.

Compute() [2/2]

void FullTensorQuadrature::Compute ( unsigned int  order )

overridevirtual

Implements muq::Approximation::Quadrature.

Definition at line 32 of file FullTensorQuadrature.cpp.

References muq::Approximation::Quadrature::dim.

Referenced by muq::Approximation::AdaptiveSmolyakQuadrature::ComputeOneTerm(), FullTensorQuadrature(), muq::Approximation::AdaptiveSmolyakQuadrature::OneTermPoints(), and muq::Approximation::PCEFactory::Setup().

Exactness()

unsigned int FullTensorQuadrature::Exactness ( unsigned int  quadOrder ) const

overridevirtual

Returns the order of the polynomial that can be integrated exactly by this quadrature rule. An \(n\)-point Gauss quadrature rule integrates polynomials of order \(2n-1\) exactly. Thus, since \(n\)= quadOrder+1, for Gauss quadrature rules, this function will return 2*quadOrder+1.

In the multivariate tensor product rule, the maximum exactness across all dimensions is returned.

If not exactness information is known (or implemented) for a particular quadrature rule, an exception will be thrown.

Reimplemented from muq::Approximation::Quadrature.

Definition at line 72 of file FullTensorQuadrature.cpp.

References rules.

Member Data Documentation

rules

std::vector<std::shared_ptr<Quadrature> > muq::Approximation::FullTensorQuadrature::rules

private

Definition at line 62 of file FullTensorQuadrature.h.

Referenced by Compute(), Exactness(), and FullTensorQuadrature().

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The documentation for this class was generated from the following files:

• doxygen_prep/MUQ/Approximation/Quadrature/FullTensorQuadrature.h
• doxygen_prep/modules/Approximation/src/Quadrature/FullTensorQuadrature.cpp