Class for computing Gauss Quadrature rules from an orthogonal polynomial family. More...

#include <GaussQuadrature.h>

Inheritance diagram for muq::Approximation::GaussQuadrature:

Detailed Description

Class for computing Gauss Quadrature rules from an orthogonal polynomial family.

Uses the Golub-Welsch algorithm to construct a Gauss Quadrature rule of a specified order.

Definition at line 20 of file GaussQuadrature.h.

Public Member Functions
	GaussQuadrature ()

virtual	~GaussQuadrature ()=default

	GaussQuadrature (std::shared_ptr< OrthogonalPolynomial > polyIn)

	GaussQuadrature (std::shared_ptr< OrthogonalPolynomial > polyIn, int polyOrderIn)

virtual void	Compute (unsigned int quadOrder) 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 void	Compute (Eigen::RowVectorXi const &orders)

virtual unsigned int	Dim () const

virtual Eigen::MatrixXd const &	Points () const

virtual Eigen::VectorXd const &	Weights () const

Constructor & Destructor Documentation

◆ GaussQuadrature() [1/3]

GaussQuadrature::GaussQuadrature ( )

Definition at line 5 of file GaussQuadrature.cpp.

◆ ~GaussQuadrature()

virtual muq::Approximation::GaussQuadrature::~GaussQuadrature ( )

virtualdefault

◆ GaussQuadrature() [2/3]

GaussQuadrature::GaussQuadrature ( std::shared_ptr< OrthogonalPolynomial > polyIn )

Definition at line 7 of file GaussQuadrature.cpp.

◆ GaussQuadrature() [3/3]

GaussQuadrature::GaussQuadrature	(	std::shared_ptr< OrthogonalPolynomial >	polyIn,
		int	polyOrderIn
	)

Definition at line 12 of file GaussQuadrature.cpp.

References Compute().

Member Function Documentation

◆ Compute()

void GaussQuadrature::Compute ( unsigned int quadOrder )

overridevirtual

Implements muq::Approximation::Quadrature.

Definition at line 19 of file GaussQuadrature.cpp.

References poly, polyOrder, muq::Approximation::Quadrature::pts, and muq::Approximation::Quadrature::wts.

Referenced by ConstructDensity(), and GaussQuadrature().

◆ Exactness()

virtual unsigned int muq::Approximation::GaussQuadrature::Exactness ( unsigned int quadOrder ) const

inlineoverridevirtual

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 35 of file GaussQuadrature.h.

Member Data Documentation

◆ poly

std::shared_ptr<OrthogonalPolynomial> muq::Approximation::GaussQuadrature::poly

private

Definition at line 39 of file GaussQuadrature.h.

Referenced by Compute().

◆ polyOrder

int muq::Approximation::GaussQuadrature::polyOrder