chi_math::QuadratureGaussLegendre Class Reference

#include <quadrature_gausslegendre.h>

Inheritance diagram for chi_math::QuadratureGaussLegendre:

Public Member Functions
	QuadratureGaussLegendre (const chi::InputParameters &params)
	QuadratureGaussLegendre (QuadratureOrder in_order, bool verbose=false, unsigned int max_iters=1000, double tol=1.0e-12)
	QuadratureGaussLegendre (unsigned int N, bool verbose=false, unsigned int max_iters=1000, double tol=1.0e-12)
Public Member Functions inherited from chi_math::Quadrature
const std::pair< double, double > &	GetRange () const
void	SetRange (const std::pair< double, double > &in_range)
Public Member Functions inherited from ChiObject
	ChiObject ()
	ChiObject (const chi::InputParameters &params)
void	SetStackID (size_t stack_id)
size_t	StackID () const
virtual void	PushOntoStack (std::shared_ptr< ChiObject > &new_object)
virtual	~ChiObject ()=default

Static Public Member Functions
static chi::InputParameters	GetInputParameters ()
Static Public Member Functions inherited from chi_math::Quadrature
static chi::InputParameters	GetInputParameters ()
Static Public Member Functions inherited from ChiObject
static chi::InputParameters	GetInputParameters ()

Private Member Functions
void	Initialize (unsigned int N, bool verbose, unsigned int max_iters, double tol)

Static Private Member Functions
static std::vector< double >	FindRoots (unsigned int N, unsigned int max_iters=1000, double tol=1.0e-12)

Additional Inherited Members
Data Fields inherited from chi_math::Quadrature
QuadratureOrder	order_
std::vector< chi_math::QuadraturePointXYZ >	qpoints_
std::vector< double >	weights_
Protected Member Functions inherited from chi_math::Quadrature
	Quadrature (const chi::InputParameters &params)
	Quadrature (QuadratureOrder in_order)
Protected Attributes inherited from chi_math::Quadrature
std::pair< double, double >	range_
bool	verbose_ = false

Detailed Description

Gauss-Legendre quadrature.

Definition at line 13 of file quadrature_gausslegendre.h.

Constructor & Destructor Documentation

QuadratureGaussLegendre() [1/3]

chi_math::QuadratureGaussLegendre::QuadratureGaussLegendre ( const chi::InputParameters &  params )

explicit

Definition at line 45 of file quadrature_gausslegendre.cc.

QuadratureGaussLegendre() [2/3]

chi_math::QuadratureGaussLegendre::QuadratureGaussLegendre ( QuadratureOrder  in_order, bool  verbose = false, unsigned int  max_iters = 1000, double  tol = 1.0e-12  )

explicit

Populates the abscissae and weights for a Gauss-Legendre quadrature given the degree of the mononomial such that the quadrature rule integrates exactly the weighted integrand , with , on the interval . The number of points generated will be ceil((O+1)/2).

Definition at line 79 of file quadrature_gausslegendre.cc.

QuadratureGaussLegendre() [3/3]

chi_math::QuadratureGaussLegendre::QuadratureGaussLegendre ( unsigned int  N, bool  verbose = false, unsigned int  max_iters = 1000, double  tol = 1.0e-12  )

explicit

Populates the abscissae and weights for a Gauss-Legendre quadrature given the number of desired quadrature points. The order of the quadrature will be 2N-1.

Definition at line 93 of file quadrature_gausslegendre.cc.

Member Function Documentation

FindRoots()

std::vector< double > chi_math::QuadratureGaussLegendre::FindRoots ( unsigned int  N, unsigned int  max_iters = 1000, double  tol = 1.0e-12  )

staticprivate

Finds the roots of the Legendre polynomial.

The algorithm is that depicted in:

[1] Barrera-Figueroa, et al., "Multiple root finder algorithm for Legendre and Chebyshev polynomials via Newton's method", Annales Mathematicae et Informaticae, 33 (2006) pp. 3-13.

Parameters

N	Is the order of the polynomial.
roots	Is a reference to the roots.
max_iters	Maximum newton iterations to perform for each root. Default: 1000.
tol	Tolerance at which the newton iteration will be terminated. Default: 1.0e-12.

Author

Jan

Definition at line 161 of file quadrature_gausslegendre.cc.

GetInputParameters()

chi::InputParameters chi_math::QuadratureGaussLegendre::GetInputParameters ( )

static

Definition at line 20 of file quadrature_gausslegendre.cc.

Initialize()

void chi_math::QuadratureGaussLegendre::Initialize ( unsigned int  N, bool  verbose, unsigned int  max_iters, double  tol  )

private

Populates the abscissae and weights for a Gauss-Legendre quadrature given the number of desired quadrature points.

Definition at line 105 of file quadrature_gausslegendre.cc.

---

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

• framework/math/Quadratures/quadrature_gausslegendre.h
• framework/math/Quadratures/quadrature_gausslegendre.cc