Gauss-Legendre's polar quadrature. More...

#include "src/Quadrature.h"

Public Member Functions
	GLPolarQuad ()
	Dummy constructor calls the parent constructor.

void	setNumPolarAngles (size_t num_polar)
	Set the number of polar angles to initialize. More...

void	useCorrectedWeights (bool use_corrected_weights)
	Indicates whether to correct weights based on altered polar angles. More...

void	initialize ()
	Routine to initialize the polar quadrature. More...

void	precomputeWeights (bool solve_3D)
	Calculates total weights for every azimuthal/polar combination based on the Gauss-Legendre polar quadrature. More...

DoubleVec	getCorrectedWeights (size_t azim) const
	Calculates the weights to be used in numerical integration. More...

Public Member Functions inherited from Quadrature
	Quadrature ()
	Dummy constructor sets the default number of angles to zero.

size_t	getNumPolarAngles () const
	Returns the number of polar angles. More...

size_t	getNumAzimAngles () const
	Returns the number of azimuthal angles. More...

double	getSinTheta (size_t azim, size_t polar) const
	Returns the $sin(\theta)$ value for a particular polar angle. More...

double	getSinThetaInline (size_t azim, size_t polar) const
	Returns the $sin(\theta)$ value for a particular polar angle. More...

double	getTheta (size_t azim, size_t polar) const
	Returns the polar angle in radians for a given azimuthal and polar angle index. More...

double	getPhi (size_t azim) const
	Returns the azimuthal angle value in radians. More...

double	getAzimWeight (size_t azim) const
	Returns the azimuthal angle weight value for a particular azimuthal angle. More...

double	getPolarWeight (size_t azim, size_t polar) const
	Returns the polar weight for a particular azimuthal and polar angle. More...

double	getWeight (size_t azim, size_t polar) const
	Returns the total weight for Tracks with the given azimuthal and polar indexes. More...

double	getWeightInline (size_t azim, size_t polar) const
	Returns the total weight for Tracks with the given azimuthal and polar indexes without error checking and inlined. More...

const std::vector< DoubleVec > &	getSinThetas () const
	Returns a pointer to the Quadrature's vector of polar angle sines $sin\theta_{p}$ . More...

const std::vector< DoubleVec > &	getThetas () const
	Returns a reference to the Quadrature's vector of polar angles $\theta_{p}$ . More...

const DoubleVec &	getPhis () const
	Returns a pointer to the Quadrature's vector of azimuthal angles $\phi$ . More...

const DoubleVec &	getAzimWeights () const
	Returns a pointer to the Quadrature's vector of azimuthal weights. More...

const std::vector< DoubleVec > &	getPolarWeights () const
	Returns a pointer to the Quadrature's vector of polar weights. More...

QuadratureType	getQuadratureType () const
	Returns the type of Quadrature created. More...

const DoubleVec &	getAzimSpacings () const
	Returns an vector of adjusted azimuthal spacings. More...

double	getAzimSpacing (size_t azim) const
	Returns the adjusted azimuthal spacing at the requested azimuthal angle index. More...

const std::vector< DoubleVec > &	getPolarSpacings () const
	Returns a 2D vector of adjusted polar spacings. More...

double	getPolarSpacing (size_t azim, size_t polar) const
	Returns the adjusted polar spacing at the requested azimuthal angle index and polar angle index. More...

virtual void	setNumAzimAngles (size_t num_azim)
	Set the number of azimuthal angles to initialize. More...

void	setThetas (const DoubleVec &thetas)
	Sets the Quadrature's vector of polar angles. More...

void	setPolarWeights (const DoubleVec &weights)
	Set the Quadrature's vector of polar weights. More...

void	setTheta (double theta, size_t azim, size_t polar)
	Sets the polar angle for the given indexes. More...

void	setPhi (double phi, size_t azim)
	Sets the azimuthal angle for the given index. More...

void	setAzimSpacing (double spacing, size_t azim)
	Sets the azimuthal spacing for the given index. More...

void	setPolarSpacing (double spacing, size_t azim, size_t polar)
	Sets the polar spacing for the given indexes. More...

void	setAzimWeight (double weight, size_t azim)
	Sets the azimuthal weight for the given index. More...

void	setPolarWeight (double weight, size_t azim, size_t polar)
	Sets the polar weight for the given indexes. More...

std::string	toString () const
	Converts this Quadrature to a character vector of its attributes. More...

Static Public Member Functions
static double	legendrePolynomial (size_t n, double x)
	the Legendre polynomial of degree n evaluated at x More...

static double	logDerivLegendre (size_t n, double x)
	The first logarithmic derivative of a Legendre polynomial. More...

static double	secondLogDerivLegendre (size_t n, double x)
	The second logarithmic derivative of a Legendre polynomial. More...

static double	getSingleWeight (double root, size_t n)
	Calculates the weights to be used in Gauss-Legendre Quadrature. More...

static DoubleVec	getLegendreRoots (size_t n)
	Finds the roots of Legendre polynomial of order n. More...

static DoubleVec	getGLWeights (const DoubleVec &roots, size_t n)
	Calculates the weights to be used in Gauss-Legendre Quadrature. More...

Additional Inherited Members
Protected Member Functions inherited from Quadrature
template<typename T >
void	setPolarValues (std::vector< std::vector< T > > &vec, size_t azim_index, size_t polar_index, T value)

template<typename T >
void	setAzimuthalValues (std::vector< T > &vec, size_t azim_index, T value)

Static Protected Member Functions inherited from Quadrature
template<typename T >
static void	resize2D (std::vector< std::vector< T > > &vec, size_t dim1, size_t dim2)

Protected Attributes inherited from Quadrature
QuadratureType	_quad_type

size_t	_num_azim

size_t	_num_polar

std::vector< DoubleVec >	_sin_thetas

std::vector< DoubleVec >	_thetas

DoubleVec	_phis

DoubleVec	_azim_spacings

DoubleVec	_azim_weights

std::vector< DoubleVec >	_polar_spacings

std::vector< DoubleVec >	_polar_weights

std::vector< DoubleVec >	_total_weights

Detailed Description

Gauss-Legendre's polar quadrature.

Member Function Documentation

◆ getCorrectedWeights()

DoubleVec GLPolarQuad::getCorrectedWeights ( size_t azim ) const

Calculates the weights to be used in numerical integration.

assumes the function will be integrated over (-1, 1)

azim the azimuthal angle index

Returns: the vector of weights

◆ getGLWeights()

DoubleVec GLPolarQuad::getGLWeights	(	const DoubleVec &	roots,
		size_t	n
	)

static

Calculates the weights to be used in Gauss-Legendre Quadrature.

Parameters

roots	a vector containing the roots of the Legendre polynomial
n	the order of the Legendre Polynomial

Returns: a vector of weights matched by index to the vector of roots

◆ getLegendreRoots()

DoubleVec GLPolarQuad::getLegendreRoots ( size_t n )

static

Finds the roots of Legendre polynomial of order n.

Guesses for positive roots are set at logarithmic intervals. Positive roots are found simultaneously using an Alberth-Householder-n method. Each guess is successively nudged towards a true root. Only the positive roots are calculated

Parameters

n	the order of the polynomial

Returns: a list of the roots of the polynomial

◆ getSingleWeight()

double GLPolarQuad::getSingleWeight	(	double	root,
		size_t	n
	)

static

Calculates the weights to be used in Gauss-Legendre Quadrature.

Parameters

root	the root of the Legendre polynomial
n	the order of the Legendre Polynomial

Returns: a vector of weights matched by index to the vector of roots

◆ initialize()

void GLPolarQuad::initialize ( )

virtual

Routine to initialize the polar quadrature.

This routine uses the tabulated values for the Gauss-Legendre polar angle quadrature, including the sine thetas and weights.

Reimplemented from Quadrature.

◆ legendrePolynomial()

double GLPolarQuad::legendrePolynomial	(	size_t	n,
		double	x
	)

static

the Legendre polynomial of degree n evaluated at x

Parameters

n	an integer >=0: the order of the polynomial
x	in (-1,1), the point at which to evaluate the polynomial

Returns: the value of the Legendre polynomial of degree n at x

◆ logDerivLegendre()

double GLPolarQuad::logDerivLegendre	(	size_t	n,
		double	x
	)

static

The first logarithmic derivative of a Legendre polynomial.

Parameters

n	the order of the polynomial
x	point at which to evaluate the logarithmic derivative

Returns: the value of the logarithmic derivative at x

◆ precomputeWeights()

void GLPolarQuad::precomputeWeights ( bool solve_3D )

virtual

Calculates total weights for every azimuthal/polar combination based on the Gauss-Legendre polar quadrature.

Parameters

solve_3D Boolean indicating whether this is a 3D quadrature

Reimplemented from Quadrature.

◆ secondLogDerivLegendre()

double GLPolarQuad::secondLogDerivLegendre	(	size_t	n,
		double	x
	)

static

The second logarithmic derivative of a Legendre polynomial.

Parameters

n	the order of the polynomial
x	point at which to evaluate the logarithmic derivative

Returns: the value of the logarithmic derivative at x

◆ setNumPolarAngles()

void GLPolarQuad::setNumPolarAngles ( size_t num_polar )

virtual

Set the number of polar angles to initialize.

Parameters

num_polar the number of polar angles (maximum 20)

Reimplemented from Quadrature.

◆ useCorrectedWeights()

void GLPolarQuad::useCorrectedWeights ( bool use_corrected_weights )

Indicates whether to correct weights based on altered polar angles.

Parameters

use_corrected_weights Whether to alter the weights

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

/home/guillaume/Research/OpenMOC/src/Quadrature.h
/home/guillaume/Research/OpenMOC/src/Quadrature.cpp

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ getCorrectedWeights()

◆ getGLWeights()

◆ getLegendreRoots()

◆ getSingleWeight()

◆ initialize()

◆ legendrePolynomial()

◆ logDerivLegendre()

◆ precomputeWeights()

◆ secondLogDerivLegendre()

◆ setNumPolarAngles()

◆ useCorrectedWeights()