smile::CPotentialSpline Class Reference

spherical-harmonic expansion of potential with coefficients being spline functions of radius More...

#include <potential.h>

Inheritance diagram for smile::CPotentialSpline:

Collaboration diagram for smile::CPotentialSpline:

Public Member Functions
template<typename NumT >
	CPotentialSpline (size_t _Ncoefs_radial, size_t _Ncoefs_angular, const CPointMassSet< NumT > &points, SYMMETRYTYPE _sym=ST_TRIAXIAL, double smoothfactor=0, const vectord *_gridradii=NULL)
	init potential from N point masses with given assumed symmetry type, may also provide desired grid radii (otherwise assigned automatically)
	CPotentialSpline (const vectord &_gridradii, const std::vector< vectord > &_coefs)
	init potential from stored SHE coefficients at given radii
	CPotentialSpline (size_t _Ncoefs_radial, size_t _Ncoefs_angular, const CDensity *density, const vectord *_gridradii=NULL)
	init potential from analytic mass model, may also provide desired grid radii (if not given, assign automatically)
template<typename NumT >
	CPotentialSpline (size_t _Ncoefs_angular, const CPointMassSet< NumT > &points, const vectord *radii, std::vector< vectord > *coefsArray)
	not really a constructor, but a way to compute potential expansion coefficients for a set of discrete point masses at given radii. More...
virtual CPotential *	clone () const
	Return a pointer to a copy of this instance of potential. More...
virtual POTENTIALTYPE	PotentialType () const
	enumerable potential type
virtual const char *	PotentialName () const
	string representation of potential type
virtual double	Mass (const double r) const
	faster estimate of M(r) using l=0 terms only
size_t	getNcoefs_radial () const
	return the number of radial points in the spline (excluding r=0)
void	getCoefs (vectord *radii, std::vector< vectord > *coefsArray, bool useNodes=true) const
	compute SHE coefficients at given radii. More...
Public Member Functions inherited from smile::CPotentialSH
	CPotentialSH (size_t _Ncoefs_angular)
virtual SYMMETRYTYPE	symmetry () const
	returns symmetry type of this potential
virtual double	Rho (double X, double Y, double Z, double t=0) const
	returns density at given coordinates, this should obviously be overriden in derivative classes
virtual double	Phi (double X, double Y, double Z, double t=0) const
	Return potential at a given spatial point (possibly a time-varying one). More...
virtual void	Force (const double xyz[N_DIM], const double t, double *force, double *forceDeriv=NULL) const
	common function for all derivative classes
size_t	getNcoefs_angular () const
	return l_max – the order of angular expansion
Public Member Functions inherited from smile::CDensity
virtual double	totalMass () const
	returns estimated M(r=infinity) or -1 if mass is infinite
double	getRadiusByMass (const double m) const
	solves for Mass(r)=m
void	getRadiiByMass (const vectord &masses, vectord *radii) const
	solves for Mass(r)=m for an array of sorted values of m (more efficient than doing it one-by-one)
bool	checkMassMonotonic () const
	safety measure: check (roughly) that mass is increasing with radius
bool	checkDensityNonzero () const
	another safety measure: check that density doesn't drop to zero along any of three axes (important to assess spherical-harmonic approximation quality)
virtual double	getGamma () const
	returns inner density slope estimate (only used in BSE potential expansion for the automatic selection of shape parameter Alpha)

Static Public Member Functions
static const char *	myName ()

Private Member Functions
virtual void	computeSHCoefs (const double r, double coefsF[], double coefsdFdr[], double coefsd2Fdr2[]) const
	reimplemented function to compute the coefficients of angular expansion of potential at the given radius
void	checkSymmetry (const std::vector< vectord > &coefsArray)
	assigns symmetry class if some coefficients are (near-)zero. More...
void	initDefault ()
	called as a default initialization when everything else fails
void	initSpline (const vectord &radii, const std::vector< vectord > &coefsArray)
	create spline objects for all non-zero spherical harmonics from the supplied radii and coefficients. More...
template<typename NumT >
void	computeCoefsFromPoints (const CPointMassSet< NumT > &points, const vectord *srcradii, vectord *outradii, std::vector< vectord > *outcoefs)
	calculate (non-smoothed) spherical harmonic coefs for a discrete point mass set. More...
template<typename NumT >
void	prepareCoefsDiscrete (const CPointMassSet< NumT > &points, double smoothfactor, const vectord *userradii)
	create smoothing splines from the coefficients computed at each particle's radius. More...
void	prepareCoefsAnalytic (const CDensity *density, const vectord *srcradii)
	compute expansion coefficients from an analytical mass profile. More...
void	coef0 (double r, double *val, double *der, double *der2) const
	evaluate value and optionally up to two derivatives of l=0 coefficient, taking into account extrapolation beyond the grid definition range and log-scaling of splines
void	coeflm (size_t lm, double r, double xi, double *val, double *der, double *der2, double c0val, double c0der=0, double c0der2=0) const
	evaluate value, and optionally first and second derivative of l>0 coefficients (lm is the combined index of angular harmonic >0); corresponding values for 0th coef must be known

Private Attributes
size_t	Ncoefs_radial
	number of radial coefficients (excluding the one at r=0)
vectord	gridradii
	defines nodes of radial grid in splines
double	minr
double	maxr
	definition range of splines; extrapolation beyond this radius
double	gammain
double	coefin
	slope and coef. for extrapolating potential inside minr (spherically-symmetric part, l=0)
double	gammaout
double	coefout
double	der2out
	slope and coef. for extrapolating potential outside maxr (spherically-symmetric part, l=0)
double	potcenter
double	potmax
double	potminr
	(abs.value) potential in the center (for transformation of l=0 spline), at the outermost spline node, and at 1st spline node
std::vector< gsl_spline * >	splines
	spline coefficients at each harmonic
vectord	slopein
vectord	slopeout
	slope of coefs for l>0 for extrapolating inside rmin/outside rmax

Additional Inherited Members
Public Types inherited from smile::CDensity
enum	POTENTIALTYPE {   PT_UNKNOWN, PT_DIRECT, PT_COMPOSITE, PT_COEFS,   PT_NB, PT_BSE, PT_BSECOMPACT, PT_SPLINE,   PT_CYLSPLINE, PT_LOG, PT_HARMONIC, PT_SCALEFREE,   PT_SCALEFREESH, PT_SPHERICAL, PT_DEHNEN, PT_MIYAMOTONAGAI,   PT_FERRERS, PT_PLUMMER, PT_ISOCHRONE, PT_PERFECTELLIPSOID,   PT_NFW, PT_SERSIC, PT_EXPDISK, PT_ELLIPSOIDAL,   PT_MGE }
	list of all existing types of density or density/potential models, each of them implemented in its own class More...
enum	SYMMETRYTYPE {   ST_NONE = 0, ST_REFLECTION = 1, ST_PLANESYM = 2, ST_ZROTSYM = 4,   ST_SPHSYM = 8, ST_TRIAXIAL = ST_REFLECTION | ST_PLANESYM, ST_AXISYMMETRIC = ST_TRIAXIAL | ST_ZROTSYM, ST_SPHERICAL = ST_AXISYMMETRIC | ST_SPHSYM,   ST_DEFAULT = ST_TRIAXIAL }
	Type of symmetry. More...
Protected Member Functions inherited from smile::CPotentialSH
void	assignlmrange ()
	assigns the above variables based on mysymmetry, should be called whenever mysymmetry has changed
Protected Attributes inherited from smile::CPotentialSH
size_t	Ncoefs_angular
	l_max, the order of angular expansion (0 means spherically symmetric model)
SYMMETRYTYPE	mysymmetry
	may have different type of symmetry
int	lmax
int	lstep
int	mmin
int	mmax
int	mstep
	range of angular coefficients used for given symmetry

Detailed Description

spherical-harmonic expansion of potential with coefficients being spline functions of radius

Constructor & Destructor Documentation

template<typename NumT >

smile::CPotentialSpline::CPotentialSpline	(	size_t	_Ncoefs_angular,
		const CPointMassSet< NumT > &	points,
		const vectord *	radii,
		std::vector< vectord > *	coefsArray
	)

not really a constructor, but a way to compute potential expansion coefficients for a set of discrete point masses at given radii.

Parameters

[in]	points	contains the source set of point masses;
[in]	_Ncoefs_angular	is the order of angular expansion (l_max);
[in]	radii	contains the array of radii at which the coefficients should be computed;
[out]	coefsArray	contains the computed coefficients. Smoothing is not performed, splines are not initialized and the potential is not usable after this call!

Member Function Documentation

void smile::CPotentialSpline::checkSymmetry ( const std::vector< vectord > &  coefsArray )

private

assigns symmetry class if some coefficients are (near-)zero.

called on an intermediate step after computing coefs but before initializing splines

CPotential * smile::CPotentialSpline::clone ( ) const

virtual

Return a pointer to a copy of this instance of potential.

A standard copy constructor or assignment is disabled because of different amount of data needed to be copied in different derived classes).

Implements smile::CPotential.

template<typename NumT >

void smile::CPotentialSpline::computeCoefsFromPoints ( const CPointMassSet< NumT > &  points, const vectord *  srcradii, vectord *  outradii, std::vector< vectord > *  outcoefs  )

private

calculate (non-smoothed) spherical harmonic coefs for a discrete point mass set.

Parameters

[in]

points

contains the positions and masses of particles that serve as the input. There are two modes of operation, depending on the content of "outradii" vector:

• in the context of initialization of potential from a discrete point set, "srcradii"=NULL; "outradii" will be initialized with radii of all particles sorted in ascending order, and "outcoefs" will contain coefficients of SH expansion for all points, "outradii" and "outcoefs" should point to existing arrays; in case of error outcoefs is set to zero length.

  Note

  : the order of indexes in outcoefs is swapped w.r.t. standard convention in this file: outcoefs[coefind][pointind] - this is done to save memory by not allocating arrays for unused coefind'ices.

• in the context of SHgrid Schwarzschild modelling, this is called from a quasi-constructor for the purpose of computing SH coefs at a given set of radii. This set is passed as "srcradii" array, and coefs are returned in "outcoefs" in the standard way: outcoefs[pointind][coefind]. "outcoefs" should point to an existing array, in case of error it is filled with zeroes.

Parameters

[in]	srcradii	may contain user-defined set of radii to compute the expansion coefficients.
[out]	outradii	points to an existing array to be filled with radial grid points.
[out]	outcoefs	points to an existing 2d array that will contain computed coefficients.

void smile::CPotentialSpline::getCoefs	(	vectord *	radii,
		std::vector< vectord > *	coefsArray,
		bool	useNodes = true
	)		const

compute SHE coefficients at given radii.

Parameters

[in]	useNodes	tells whether the radii in question are the original spline nodes (true) or user-specified radii (true);
[in,out]	radii	if useNodes=true, this array is filled with spline nodes [output parameter, but must point to an existing array], otherwise the coefficients are computed at the supplied radii [input parameter];
[out]	coefsArray	is filled by the computed coefficients (must point to an existing array)

void smile::CPotentialSpline::initSpline ( const vectord &  radii, const std::vector< vectord > &  coefsArray  )

private

create spline objects for all non-zero spherical harmonics from the supplied radii and coefficients.

radii should have "Ncoefs_radial" elements and coefsArray - "Ncoefs_radial * (Ncoefs_angular+1)^2" elements

void smile::CPotentialSpline::prepareCoefsAnalytic ( const CDensity *  density, const vectord *  srcradii  )

private

compute expansion coefficients from an analytical mass profile.

Parameters

[in]	density	is the density profile to be approximated
[in]	srcradii	may contain the radial grid; if NULL then it is assigned automatically.

template<typename NumT >

void smile::CPotentialSpline::prepareCoefsDiscrete ( const CPointMassSet< NumT > &  points, double  smoothfactor, const vectord *  userradii  )

private

create smoothing splines from the coefficients computed at each particle's radius.

Parameters

[in]	points	is the array of particle coordinates and masses
[in]	userradii	may contain the radial grid to construct the splines; if it is NULL then the radial grid is constructed automatically taking into account the range of radii covered by source points.
[in]	smoothfactor	determines how much smoothing is applied to the spline (good results are obtained for smoothfactor=1-2).

!!FIXME: what happens if the outermost pointRadius is < outerBinRadius ?

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

• potential.h
• potential.cpp