The class SphericalHarmonics_Coefficients. More...

#include "Headers/SphericalHarmonics_Coefficients.h"

Public Member Functions
double	real (const int n, const int bin=0)
	return the real part of the n-th coefficient of the expansion for a given separation bin More...

double	imag (const int n, const int bin=0)
	return the imaginary part of the n-th coefficient of the expansion for a given separation bin More...

void	initialize (const int norder, const int nbins=1)
	initialize the internal quantities More...

void	reset ()
	reset the internal quantities

std::vector< std::complex< double > >	alm (const double xx, const double yy, const double zz)
	compute the \( a_{lm}\) for the normalized coordinates \( \lbrace x, y, z \rbrace \) More...

void	add (const std::vector< std::complex< double >> alm, const double ww, const int bin=0)
	add the \( a_{lm}\) to a specific separation bin with a weight More...

void	add (const double xx, const double yy, const double zz, const double ww, const int bin=0)
	compute add the \( a_{lm}\) for the normalized coordinates \( \lbrace x, y, z \rbrace \) to a specific separation bin with a weight More...

double	power (const int l, const int bin1, const int bin2)
	compute the product of the \( a_{lm} \) in two separation bin More...

Constructors/destructors
	SphericalHarmonics_Coefficients ()
	default constructor

	SphericalHarmonics_Coefficients (const int norder, const int nbins=1)
	default constructor More...

	~SphericalHarmonics_Coefficients ()
	default descructor

Protected Attributes
int	m_nbins
	the number of separation bins

int	m_norder
	the number of multipoles, \( l_{max}+1 \)

int	m_lmax
	the maximum multipole \( l_{max} \)

int	m_n_sph
	the total number of spherical harmonics

std::vector< int >	m_n_sph_l
	the number of spherical harmonics for a given choice of \(l\)

std::vector< std::vector< std::complex< double > > >	m_alm
	the spherical harmonics expansion coefficients in separation bins

std::vector< double >	m_normalization
	the normalization

std::vector< double >	m_Plm
	vector for temporary computation of associated legendre polynomials

std::vector< std::complex< double > >	m_sph
	vector for temporary computation of spherical harmonics

Detailed Description

The class SphericalHarmonics_Coefficients.

This class is used to handle objects of type SphericalHarmonics_Coefficients . It contains all methods to compute coefficients of spherical harmonics expansion \(a_{lm}\) in any position of the unit sphere.

Coefficients can be binned according to the magnitude of the separation vector and accumulated.

Definition at line 57 of file SphericalHarmonics_Coefficients.h.

Constructor & Destructor Documentation

◆ SphericalHarmonics_Coefficients()

cbl::glob::SphericalHarmonics_Coefficients::SphericalHarmonics_Coefficients	(	const int	norder,
		const int	nbins = `1`
	)

inline

default constructor

Parameters

norder	the number of multipoles, \( l_{max}+1 \)
nbins	the number of separation bins

Definition at line 110 of file SphericalHarmonics_Coefficients.h.

Member Function Documentation

◆ add() [1/2]

void cbl::glob::SphericalHarmonics_Coefficients::add	(	const double	xx,
		const double	yy,
		const double	zz,
		const double	ww,
		const int	bin = `0`
	)

compute add the \( a_{lm}\) for the normalized coordinates \( \lbrace x, y, z \rbrace \) to a specific separation bin with a weight

Parameters

xx	the x coordinate
yy	the y coordinate
zz	the z coordinate
ww	the weight
bin	the separation bin

Definition at line 192 of file SphericalHarmonics_Coefficients.cpp.

◆ add() [2/2]

void cbl::glob::SphericalHarmonics_Coefficients::add	(	const std::vector< std::complex< double >>	alm,
		const double	ww,
		const int	bin = `0`
	)

add the \( a_{lm}\) to a specific separation bin with a weight

Parameters

alm	the spherical harmonics expansion coefficients
ww	the weight
bin	the separation bin

Definition at line 182 of file SphericalHarmonics_Coefficients.cpp.

◆ alm()

std::vector< std::complex< double > > cbl::glob::SphericalHarmonics_Coefficients::alm	(	const double	xx,
		const double	yy,
		const double	zz
	)

compute the \( a_{lm}\) for the normalized coordinates \( \lbrace x, y, z \rbrace \)

Parameters

xx	the x coordinate
yy	the y coordinate
zz	the z coordinate

Returns: vector containing the \( a_{lm}\) for the normalized coordinates \( \lbrace x, y, z \rbrace \)

Definition at line 89 of file SphericalHarmonics_Coefficients.cpp.

◆ imag()

double cbl::glob::SphericalHarmonics_Coefficients::imag	(	const int	n,
		const int	bin = `0`
	)

inline

return the imaginary part of the n-th coefficient of the expansion for a given separation bin

Parameters

n	the n-th coefficient of the spherical harmonics expansion
bin	the separation bin

Returns: the imaginary part of the n-th coefficient of the expansion for a given separation bin

Definition at line 147 of file SphericalHarmonics_Coefficients.h.

◆ initialize()

void cbl::glob::SphericalHarmonics_Coefficients::initialize	(	const int	norder,
		const int	nbins = `1`
	)

initialize the internal quantities

Parameters

norder	the number of multipoles, \( l_{max}+1 \)
nbins	the number of separation bins

Definition at line 46 of file SphericalHarmonics_Coefficients.cpp.

◆ power()

double cbl::glob::SphericalHarmonics_Coefficients::power	(	const int	l,
		const int	bin1,
		const int	bin2
	)

compute the product of the \( a_{lm} \) in two separation bin

This function computes the product of the \( a_{lm} \) in two separation bin:

\[ \zeta_l(r_1, r_2) = \sum_{m=-l}^l a_{lm}(r_1) a^*_{lm} (r_2) \]

Parameters

l	the coefficient order
bin1	the first separation bin
bin2	the second separation bin

Returns: the product of the \( a_{lm} \) in two separation bin

Definition at line 203 of file SphericalHarmonics_Coefficients.cpp.

◆ real()

double cbl::glob::SphericalHarmonics_Coefficients::real	(	const int	n,
		const int	bin = `0`
	)

inline

return the real part of the n-th coefficient of the expansion for a given separation bin

Parameters

n	the n-th coefficient of the spherical harmonics expansion
bin	the separation bin

Returns: the real part of the n-th coefficient of the expansion for a given separation bin

Definition at line 133 of file SphericalHarmonics_Coefficients.h.

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

Headers/SphericalHarmonics_Coefficients.h
Func/SphericalHarmonics_Coefficients.cpp

Public Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ SphericalHarmonics_Coefficients()

Member Function Documentation

◆ add() [1/2]

◆ add() [2/2]

◆ alm()

◆ imag()

◆ initialize()

◆ power()

◆ real()