cbl::glob::LegendrePolynomials Class Reference

The class LegendrePolynomials. More...

#include "Headers/LegendrePolynomials.h"

Public Member Functions
void	set (const int lMax)
	set maximum order of expansion More...
double	operator() (const double x, const int ell)
	evaluate the Legendre polynomial of order ell at x More...
std::vector< double >	operator() (const double x)
	evaluate the Legendre polynomial up to lMax at x More...
double	integral (const double x_min, const double x_max, const int ell)
	evaluate the bin-averaged Legendre polynomial of order ell More...
std::vector< double >	integral (const double x_min, const double x_max)
	evaluate the bin-averaged Legendre polynomials More...
std::vector< std::vector< double > >	triangle (const double r12, const double r13, const double r23)
	evaluate the Legendre polynomials for triangle angles. More...
std::vector< double >	triangle_integral (const double r12_min, const double r12_max, const double r13_min, const double r13_max, const double r23_min, const double r23_max, const double rel_err=1.e-4, const int nevals=10000)
	evaluate the bin-averaged Legendre polynomials over a triangle. Triangle side can vary from a minimum to a maximum value More...
Constructors/destructors
	LegendrePolynomials ()
	Default constructor of LegendrePolynomials.
	LegendrePolynomials (const int lMax, const bool safe=false)
	Constructor of LegendrePolynomials. More...
	~LegendrePolynomials ()
	Default destructor.

Protected Member Functions
void	m_set_coefficients (const int lMax)
	set internal attribute m_coefficients More...

Protected Attributes
size_t	m_nOrders
	Number of Legendre polynomial.
Eigen::MatrixXd	m_coefficients
	Coefficients of the Legendre polynomials.

Detailed Description

The class LegendrePolynomials.

This class is used to handle Legendre polynomials. It contains all methods to compute Legendre polynomials as well as their integrals.

Definition at line 52 of file LegendrePolynomials.h.

Constructor & Destructor Documentation

LegendrePolynomials()

cbl::glob::LegendrePolynomials::LegendrePolynomials	(	const int	lMax,
		const bool	safe = false
	)

Constructor of LegendrePolynomials.

Parameters

lMax	maximum order of Legendre polynomials
safe	True \(\rightarrow \) check input range is among -1 a 1 False \( \rightarrow \) do not check input

Definition at line 88 of file LegendrePolynomials.cpp.

Member Function Documentation

integral() [1/2]

vector< double > cbl::glob::LegendrePolynomials::integral	(	const double	x_min,
		const double	x_max
	)

evaluate the bin-averaged Legendre polynomials

Parameters

x_min	the lower bin edge
x_max	the up bin edge

Returns

the bin-averaged Legendre polynomials

Definition at line 167 of file LegendrePolynomials.cpp.

integral() [2/2]

double cbl::glob::LegendrePolynomials::integral	(	const double	x_min,
		const double	x_max,
		const int	ell
	)

evaluate the bin-averaged Legendre polynomial of order ell

Parameters

x_min	the lower bin edge
x_max	the up bin edge
ell	the order of the Legendre polynomial

Returns

the bin-averaged Legendre polynomial of order ell

Definition at line 144 of file LegendrePolynomials.cpp.

m_set_coefficients()

void cbl::glob::LegendrePolynomials::m_set_coefficients ( const int  lMax )

protected

set internal attribute m_coefficients

Set the coefficients of the Legendre Polynomials according to the following recursive relation:

\[ P_{n}(x)=2^{n} \sum_{k=0}^{n} x^{k}\left(\begin{array}{l} n \\ k \end{array}\right)\left(\begin{array}{c} \frac{n+k-1}{2} \\ n \end{array}\right) \]

Parameters

lMax	maximum order of Legendre polynomials

Definition at line 48 of file LegendrePolynomials.cpp.

operator()() [1/2]

vector< double > cbl::glob::LegendrePolynomials::operator()

(

const double

x

)

evaluate the Legendre polynomial up to lMax at x

Parameters

x	the point to evaluate Legendre polynomials

Returns

vector containing the Legendre polynomials at x

Definition at line 124 of file LegendrePolynomials.cpp.

operator()() [2/2]

double cbl::glob::LegendrePolynomials::operator()	(	const double	x,
		const int	ell
	)

evaluate the Legendre polynomial of order ell at x

Parameters

x	the point to evaluate Legendre polynomial
ell	the order of the Legendre polynomial

Returns

the Legendre polynomial of order ell at x

Definition at line 107 of file LegendrePolynomials.cpp.

set()

void cbl::glob::LegendrePolynomials::set

(

const int

lMax

)

set maximum order of expansion

Parameters

lMax	maximum order of Legendre polynomials

Definition at line 98 of file LegendrePolynomials.cpp.

triangle()

vector< vector< double > > cbl::glob::LegendrePolynomials::triangle	(	const double	r12,
		const double	r13,
		const double	r23
	)

evaluate the Legendre polynomials for triangle angles.

Parameters

r12	first triangle side
r13	second triangle side
r23	third triangle side

Returns

the Legendre polynomials averaged over a triangle

Definition at line 192 of file LegendrePolynomials.cpp.

triangle_integral()

vector< double > cbl::glob::LegendrePolynomials::triangle_integral	(	const double	r12_min,
		const double	r12_max,
		const double	r13_min,
		const double	r13_max,
		const double	r23_min,
		const double	r23_max,
		const double	rel_err = 1.e-4,
		const int	nevals = 10000
	)

evaluate the bin-averaged Legendre polynomials over a triangle. Triangle side can vary from a minimum to a maximum value

Parameters

r12_min	the first side lower edge
r12_max	the first side upper edge
r13_min	the second side lower edge
r13_max	the second side upper edge
r23_min	the third side lower edge
r23_max	the third side upper edge
rel_err	the relative integration error
nevals	maximum number of function evaluation

Returns

the Legendre polynomials averaged over a triangle

Definition at line 210 of file LegendrePolynomials.cpp.

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

• Headers/LegendrePolynomials.h
• Func/LegendrePolynomials.cpp