Base class for coordinate mappings. More...

#include <map.h>

Inheritance diagram for Lorene::Map:

Public Member Functions
virtual	~Map ()
	Destructor. More...

virtual void	sauve (FILE *) const
	Save in a file. More...

const Mg3d *	get_mg () const
	Gives the `Mg3d` on which the mapping is defined. More...

double	get_ori_x () const
	Returns the x coordinate of the origin. More...

double	get_ori_y () const
	Returns the y coordinate of the origin. More...

double	get_ori_z () const
	Returns the z coordinate of the origin. More...

double	get_rot_phi () const
	Returns the angle between the x –axis and X –axis. More...

const Base_vect_spher &	get_bvect_spher () const
	Returns the orthonormal vectorial basis $(\partial/\partial r,1/r\partial/\partial \theta, 1/(r\sin\theta)\partial/\partial \phi)$ associated with the coordinates $(r, \theta, \phi)$ of the mapping. More...

const Base_vect_cart &	get_bvect_cart () const
	Returns the Cartesian basis $(\partial/\partial x,\partial/\partial y,\partial/\partial z)$ associated with the coordinates (x,y,z) of the mapping, i.e. More...

const Metric_flat &	flat_met_spher () const
	Returns the flat metric associated with the spherical coordinates and with components expressed in the triad `bvect_spher`. More...

const Metric_flat &	flat_met_cart () const
	Returns the flat metric associated with the Cartesian coordinates and with components expressed in the triad `bvect_cart`. More...

const Cmp &	cmp_zero () const
	Returns the null `Cmp` defined on `*this`. More...

virtual const Map_af &	mp_angu (int) const =0
	Returns the "angular" mapping for the outside of domain `l_zone`. More...

void	convert_absolute (double xx, double yy, double zz, double &rr, double &theta, double &pphi) const
	Determines the coordinates $(r,\theta,\phi)$ corresponding to given absolute Cartesian coordinates (X,Y,Z). More...

virtual double	val_r (int l, double xi, double theta, double pphi) const =0
	Returns the value of the radial coordinate r for a given $(\xi, \theta', \phi')$ in a given domain. More...

virtual void	val_lx (double rr, double theta, double pphi, int &l, double &xi) const =0
	Computes the domain index l and the value of $\xi$ corresponding to a point given by its physical coordinates $(r, \theta, \phi)$ . More...

virtual void	val_lx (double rr, double theta, double pphi, const Param &par, int &l, double &xi) const =0
	Computes the domain index l and the value of $\xi$ corresponding to a point given by its physical coordinates $(r, \theta, \phi)$ . More...

virtual bool	operator== (const Map &) const =0
	Comparison operator (egality) More...

void	set_ori (double xa0, double ya0, double za0)
	Sets a new origin. More...

void	set_rot_phi (double phi0)
	Sets a new rotation angle. More...

virtual void	homothetie (double lambda)=0
	Sets a new radial scale. More...

virtual void	resize (int l, double lambda)=0
	Rescales the outer boundary of one domain. More...

virtual void	operator= (const Map_af &)=0
	Assignment to an affine mapping. More...

virtual void	adapt (const Cmp &ent, const Param &par, int nbr=0)=0
	Adaptation of the mapping to a given scalar field. More...

virtual void	reevaluate (const Map *mp_prev, int nzet, Cmp &uu) const =0
	Recomputes the values of a `Cmp` at the collocation points after a change in the mapping. More...

virtual void	reevaluate_symy (const Map *mp_prev, int nzet, Cmp &uu) const =0
	Recomputes the values of a `Cmp` at the collocation points after a change in the mapping. More...

virtual void	reevaluate (const Map *mp_prev, int nzet, Scalar &uu) const =0
	Recomputes the values of a `Scalar` at the collocation points after a change in the mapping. More...

virtual void	reevaluate_symy (const Map *mp_prev, int nzet, Scalar &uu) const =0
	Recomputes the values of a `Scalar` at the collocation points after a change in the mapping. More...

virtual void	dsdxi (const Cmp &ci, Cmp &resu) const =0
	Computes $\partial/ \partial \xi$ of a `Cmp` . More...

virtual void	dsdr (const Cmp &ci, Cmp &resu) const =0
	Computes $\partial/ \partial r$ of a `Cmp` . More...

virtual void	srdsdt (const Cmp &ci, Cmp &resu) const =0
	Computes $1/r \partial/ \partial \theta$ of a `Cmp` . More...

virtual void	srstdsdp (const Cmp &ci, Cmp &resu) const =0
	Computes $1/(r\sin\theta) \partial/ \partial \phi$ of a `Cmp` . More...

virtual void	dsdxi (const Scalar &uu, Scalar &resu) const =0
	Computes $\partial/ \partial xi$ of a `Scalar` . More...

virtual void	dsdr (const Scalar &uu, Scalar &resu) const =0
	Computes $\partial/ \partial r$ of a `Scalar` . More...

virtual void	dsdradial (const Scalar &uu, Scalar &resu) const =0
	Computes $\partial/ \partial r$ of a `Scalar` if the description is affine and $\partial/ \partial \ln r$ if it is logarithmic. More...

virtual void	srdsdt (const Scalar &uu, Scalar &resu) const =0
	Computes $1/r \partial/ \partial \theta$ of a `Scalar` . More...

virtual void	srstdsdp (const Scalar &uu, Scalar &resu) const =0
	Computes $1/(r\sin\theta) \partial/ \partial \phi$ of a `Scalar` . More...

virtual void	dsdt (const Scalar &uu, Scalar &resu) const =0
	Computes $\partial/ \partial \theta$ of a `Scalar` . More...

virtual void	stdsdp (const Scalar &uu, Scalar &resu) const =0
	Computes $1/\sin\theta \partial/ \partial \varphi$ of a `Scalar` . More...

virtual void	laplacien (const Scalar &uu, int zec_mult_r, Scalar &lap) const =0
	Computes the Laplacian of a scalar field. More...

virtual void	laplacien (const Cmp &uu, int zec_mult_r, Cmp &lap) const =0
	Computes the Laplacian of a scalar field (`Cmp` version). More...

virtual void	lapang (const Scalar &uu, Scalar &lap) const =0
	Computes the angular Laplacian of a scalar field. More...

virtual void	primr (const Scalar &uu, Scalar &resu, bool null_infty) const =0
	Computes the radial primitive which vanishes for $r\to \infty$ . More...

virtual void	mult_r (Scalar &uu) const =0
	Multiplication by r of a `Scalar` , the `dzpuis` of `uu` is not changed. More...

virtual void	mult_r (Cmp &ci) const =0
	Multiplication by r of a `Cmp` . More...

virtual void	mult_r_zec (Scalar &) const =0
	Multiplication by r (in the compactified external domain only) of a `Scalar`. More...

virtual void	mult_rsint (Scalar &) const =0
	Multiplication by $r\sin\theta$ of a `Scalar`. More...

virtual void	div_rsint (Scalar &) const =0
	Division by $r\sin\theta$ of a `Scalar`. More...

virtual void	div_r (Scalar &) const =0
	Division by r of a `Scalar`. More...

virtual void	div_r_zec (Scalar &) const =0
	Division by r (in the compactified external domain only) of a `Scalar`. More...

virtual void	mult_cost (Scalar &) const =0
	Multiplication by $\cos\theta$ of a `Scalar`. More...

virtual void	div_cost (Scalar &) const =0
	Division by $\cos\theta$ of a `Scalar`. More...

virtual void	mult_sint (Scalar &) const =0
	Multiplication by $\sin\theta$ of a `Scalar`. More...

virtual void	div_sint (Scalar &) const =0
	Division by $\sin\theta$ of a `Scalar`. More...

virtual void	div_tant (Scalar &) const =0
	Division by $\tan\theta$ of a `Scalar`. More...

virtual void	comp_x_from_spherical (const Scalar &v_r, const Scalar &v_theta, const Scalar &v_phi, Scalar &v_x) const =0
	Computes the Cartesian x component (with respect to `bvect_cart` ) of a vector given by its spherical components with respect to `bvect_spher` . More...

virtual void	comp_x_from_spherical (const Cmp &v_r, const Cmp &v_theta, const Cmp &v_phi, Cmp &v_x) const =0
	`Cmp` version More...

virtual void	comp_y_from_spherical (const Scalar &v_r, const Scalar &v_theta, const Scalar &v_phi, Scalar &v_y) const =0
	Computes the Cartesian y component (with respect to `bvect_cart` ) of a vector given by its spherical components with respect to `bvect_spher` . More...

virtual void	comp_y_from_spherical (const Cmp &v_r, const Cmp &v_theta, const Cmp &v_phi, Cmp &v_y) const =0
	`Cmp` version More...

virtual void	comp_z_from_spherical (const Scalar &v_r, const Scalar &v_theta, Scalar &v_z) const =0
	Computes the Cartesian z component (with respect to `bvect_cart` ) of a vector given by its spherical components with respect to `bvect_spher` . More...

virtual void	comp_z_from_spherical (const Cmp &v_r, const Cmp &v_theta, Cmp &v_z) const =0
	`Cmp` version More...

virtual void	comp_r_from_cartesian (const Scalar &v_x, const Scalar &v_y, const Scalar &v_z, Scalar &v_r) const =0
	Computes the Spherical r component (with respect to `bvect_spher` ) of a vector given by its cartesian components with respect to `bvect_cart` . More...

virtual void	comp_r_from_cartesian (const Cmp &v_x, const Cmp &v_y, const Cmp &v_z, Cmp &v_r) const =0
	`Cmp` version More...

virtual void	comp_t_from_cartesian (const Scalar &v_x, const Scalar &v_y, const Scalar &v_z, Scalar &v_t) const =0
	Computes the Spherical $\theta$ component (with respect to `bvect_spher` ) of a vector given by its cartesian components with respect to `bvect_cart` . More...

virtual void	comp_t_from_cartesian (const Cmp &v_x, const Cmp &v_y, const Cmp &v_z, Cmp &v_t) const =0
	`Cmp` version More...

virtual void	comp_p_from_cartesian (const Scalar &v_x, const Scalar &v_y, Scalar &v_p) const =0
	Computes the Spherical $\phi$ component (with respect to `bvect_spher` ) of a vector given by its cartesian components with respect to `bvect_cart` . More...

virtual void	comp_p_from_cartesian (const Cmp &v_x, const Cmp &v_y, Cmp &v_p) const =0
	`Cmp` version More...

virtual void	dec_dzpuis (Scalar &) const =0
	Decreases by 1 the value of `dzpuis` of a `Scalar` and changes accordingly its values in the compactified external domain (CED). More...

virtual void	dec2_dzpuis (Scalar &) const =0
	Decreases by 2 the value of `dzpuis` of a `Scalar` and changes accordingly its values in the compactified external domain (CED). More...

virtual void	inc_dzpuis (Scalar &) const =0
	Increases by 1 the value of `dzpuis` of a `Scalar` and changes accordingly its values in the compactified external domain (CED). More...

virtual void	inc2_dzpuis (Scalar &) const =0
	Increases by 2 the value of `dzpuis` of a `Scalar` and changes accordingly its values in the compactified external domain (CED). More...

virtual Tbl *	integrale (const Cmp &) const =0
	Computes the integral over all space of a `Cmp` . More...

virtual void	poisson (const Cmp &source, Param &par, Cmp &uu) const =0
	Computes the solution of a scalar Poisson equation. More...

virtual void	poisson_tau (const Cmp &source, Param &par, Cmp &uu) const =0
	Computes the solution of a scalar Poisson equationwith a Tau method. More...

virtual void	poisson_falloff (const Cmp &source, Param &par, Cmp &uu, int k_falloff) const =0

virtual void	poisson_ylm (const Cmp &source, Param &par, Cmp &pot, int nylm, double *intvec) const =0

virtual void	poisson_regular (const Cmp &source, int k_div, int nzet, double unsgam1, Param &par, Cmp &uu, Cmp &uu_regu, Cmp &uu_div, Tenseur &duu_div, Cmp &source_regu, Cmp &source_div) const =0
	Computes the solution of a scalar Poisson equation. More...

virtual void	poisson_compact (const Cmp &source, const Cmp &aa, const Tenseur &bb, const Param &par, Cmp &psi) const =0
	Resolution of the elliptic equation $a \Delta\psi + {\bf b} \cdot \nabla \psi = \sigma$ in the case where the stellar interior is covered by a single domain. More...

virtual void	poisson_compact (int nzet, const Cmp &source, const Cmp &aa, const Tenseur &bb, const Param &par, Cmp &psi) const =0
	Resolution of the elliptic equation $a \Delta\psi + {\bf b} \cdot \nabla \psi = \sigma$ in the case of a multidomain stellar interior. More...

virtual void	poisson_angu (const Scalar &source, Param &par, Scalar &uu, double lambda=0) const =0
	Computes the solution of the generalized angular Poisson equation. More...

virtual void	poisson_angu (const Cmp &source, Param &par, Cmp &uu, double lambda=0) const =0

virtual Param *	donne_para_poisson_vect (Param &para, int i) const =0
	Function intended to be used by `Map::poisson_vect` and `Map::poisson_vect_oohara` . More...

virtual void	poisson_frontiere (const Cmp &source, const Valeur &limite, int raccord, int num_front, Cmp &pot, double=0., double=0.) const =0
	Computes the solution of a Poisson equation from the domain `num_front+1` . More...

virtual void	poisson_frontiere_double (const Cmp &source, const Valeur &lim_func, const Valeur &lim_der, int num_zone, Cmp &pot) const =0

virtual void	poisson_interne (const Cmp &source, const Valeur &limite, Param &par, Cmp &pot) const =0
	Computes the solution of a Poisson equation in the shell, imposing a boundary condition at the surface of the star. More...

virtual void	poisson2d (const Cmp &source_mat, const Cmp &source_quad, Param &par, Cmp &uu) const =0
	Computes the solution of a 2-D Poisson equation. More...

virtual void	dalembert (Param &par, Scalar &fJp1, const Scalar &fJ, const Scalar &fJm1, const Scalar &source) const =0
	Performs one time-step integration of the d'Alembert scalar equation. More...

Public Attributes
Coord	r
	r coordinate centered on the grid More...

Coord	tet
	$\theta$ coordinate centered on the grid More...

Coord	phi
	$\phi$ coordinate centered on the grid More...

Coord	sint
	$\sin\theta$ More...

Coord	cost
	$\cos\theta$ More...

Coord	sinp
	$\sin\phi$ More...

Coord	cosp
	$\cos\phi$ More...

Coord	x
	x coordinate centered on the grid More...

Coord	y
	y coordinate centered on the grid More...

Coord	z
	z coordinate centered on the grid More...

Coord	xa
	Absolute x coordinate. More...

Coord	ya
	Absolute y coordinate. More...

Coord	za
	Absolute z coordinate. More...

Protected Member Functions
	Map (const Mg3d &)
	Constructor from a multi-domain 3D grid. More...

	Map (const Map &)
	Copy constructor. More...

	Map (const Mg3d &, FILE *)
	Constructor from a file (see `sauve(FILE* )` ) More...

virtual void	reset_coord ()
	Resets all the member `Coords`. More...

Protected Attributes
const Mg3d *	mg
	Pointer on the multi-grid `Mgd3` on which `this` is defined. More...

double	ori_x
	Absolute coordinate x of the origin. More...

double	ori_y
	Absolute coordinate y of the origin. More...

double	ori_z
	Absolute coordinate z of the origin. More...

double	rot_phi
	Angle between the x –axis and X –axis. More...

Base_vect_spher	bvect_spher
	Orthonormal vectorial basis $(\partial/\partial r,1/r\partial/\partial \theta, 1/(r\sin\theta)\partial/\partial \phi)$ associated with the coordinates $(r, \theta, \phi)$ of the mapping. More...

Base_vect_cart	bvect_cart
	Cartesian basis $(\partial/\partial x,\partial/\partial y,\partial/\partial z)$ associated with the coordinates (x,y,z) of the mapping, i.e. More...

Metric_flat *	p_flat_met_spher
	Pointer onto the flat metric associated with the spherical coordinates and with components expressed in the triad `bvect_spher`. More...

Metric_flat *	p_flat_met_cart
	Pointer onto the flat metric associated with the Cartesian coordinates and with components expressed in the triad `bvect_cart`. More...

Cmp *	p_cmp_zero
	The null Cmp. More...

Map_af *	p_mp_angu
	Pointer on the "angular" mapping. More...

Private Member Functions
virtual ostream &	operator>> (ostream &) const =0
	Operator >> More...

Friends
ostream &	operator<< (ostream &, const Map &)
	Operator <<. More...

Detailed Description

Base class for coordinate mappings.

()

This class is the basic class for describing the mapping between the grid coordinates $(\xi, \theta', \phi')$ and the physical coordinates $(r, \theta, \phi)$ [cf. Bonazzola, Gourgoulhon & Marck, Phys. Rev. D 58, 104020 (1998)]. The class Map is an abstract one: it cannot be instanciated. Specific implementation of coordinate mappings will be performed by derived classes of Map.

The class Map and its derived classes determine the methods for partial derivatives with respect to the physical coordinates, as well as resolution of basic partial differential equations (e.g. Poisson equations).

The mapping is defined with respect to some `‘absolute’' reference frame, whose Cartesian coordinates are denoted by (X,Y,Z). The coordinates (X, Y, Z) of center of the mapping (i.e. the point r =0) are given by the data members (ori_x,ori_y,ori_z). The Cartesian coordinate relative to the mapping (i.e. defined from $(r, \theta, \phi)$ by the usual formul $x=r\sin\theta\cos\phi, \ldots$ ) are denoted by (x,y,z). The planes (x,y) and (X,Y) are supposed to coincide, so that the relative orientation of the mapping with respect to the absolute reference frame is described by only one angle (the data member rot_phi).

Definition at line 682 of file map.h.

Constructor & Destructor Documentation

◆ Map() [1/3]

Lorene::Map::Map ( const Mg3d & mgi )

explicitprotected

Constructor from a multi-domain 3D grid.

Definition at line 142 of file map.C.

References p_cmp_zero, and Lorene::Cmp::set_etat_zero().

◆ Map() [2/3]

Lorene::Map::Map ( const Map & mp )

protected

Copy constructor.

Definition at line 160 of file map.C.

References p_cmp_zero, and Lorene::Cmp::set_etat_zero().

◆ Map() [3/3]

Lorene::Map::Map	(	const Mg3d &	mgi,
		FILE *	fd
	)

protected

Constructor from a file (see sauve(FILE* ) )

Definition at line 179 of file map.C.

References bvect_cart, bvect_spher, Lorene::fread_be(), mg, ori_x, ori_y, ori_z, p_cmp_zero, rot_phi, Lorene::Cmp::set_etat_zero(), Lorene::Base_vect_spher::set_ori(), Lorene::Base_vect_cart::set_rot_phi(), and Lorene::Base_vect_spher::set_rot_phi().

◆ ~Map()

Lorene::Map::~Map ( )

virtual

Destructor.

Definition at line 216 of file map.C.

References p_cmp_zero, p_flat_met_cart, p_flat_met_spher, and p_mp_angu.

Member Function Documentation

◆ adapt()

virtual void Lorene::Map::adapt	(	const Cmp &	ent,
		const Param &	par,
		int	nbr = `0`
	)

pure virtual

Adaptation of the mapping to a given scalar field.

This is a virtual function: see the actual implementations in the derived classes for the meaning of the various parameters.

Implemented in Lorene::Map_eps, Lorene::Map_star, Lorene::Map_log, Lorene::Map_et, and Lorene::Map_af.

◆ cmp_zero()

const Cmp& Lorene::Map::cmp_zero ( ) const

inline

Returns the null Cmp defined on *this.

To be used by the Tenseur class when necessary to return a null Cmp .

Definition at line 819 of file map.h.

References p_cmp_zero.

◆ comp_p_from_cartesian() [1/2]

virtual void Lorene::Map::comp_p_from_cartesian	(	const Scalar &	v_x,
		const Scalar &	v_y,
		Scalar &	v_p
	)		const

pure virtual

Computes the Spherical $\phi$ component (with respect to bvect_spher ) of a vector given by its cartesian components with respect to bvect_cart .

Parameters

v_x	[input] x-component of the vector
v_y	[input] y-component of the vector
v_p	[output] $\phi$ -component of the vector

Implemented in Lorene::Map_radial.

◆ comp_p_from_cartesian() [2/2]

virtual void Lorene::Map::comp_p_from_cartesian	(	const Cmp &	v_x,
		const Cmp &	v_y,
		Cmp &	v_p
	)		const

pure virtual

Cmp version

Implemented in Lorene::Map_radial.

◆ comp_r_from_cartesian() [1/2]

virtual void Lorene::Map::comp_r_from_cartesian	(	const Scalar &	v_x,
		const Scalar &	v_y,
		const Scalar &	v_z,
		Scalar &	v_r
	)		const

pure virtual

Computes the Spherical r component (with respect to bvect_spher ) of a vector given by its cartesian components with respect to bvect_cart .

Parameters

v_x	[input] x-component of the vector
v_y	[input] y-component of the vector
v_z	[input] z-component of the vector
v_r	[output] r -component of the vector

Implemented in Lorene::Map_radial.

◆ comp_r_from_cartesian() [2/2]

virtual void Lorene::Map::comp_r_from_cartesian	(	const Cmp &	v_x,
		const Cmp &	v_y,
		const Cmp &	v_z,
		Cmp &	v_r
	)		const

pure virtual

Cmp version

Implemented in Lorene::Map_radial.

◆ comp_t_from_cartesian() [1/2]

virtual void Lorene::Map::comp_t_from_cartesian	(	const Scalar &	v_x,
		const Scalar &	v_y,
		const Scalar &	v_z,
		Scalar &	v_t
	)		const

pure virtual

Computes the Spherical $\theta$ component (with respect to bvect_spher ) of a vector given by its cartesian components with respect to bvect_cart .

Parameters

v_x	[input] x-component of the vector
v_y	[input] y-component of the vector
v_z	[input] z-component of the vector
v_t	[output] $\theta$ -component of the vector

Implemented in Lorene::Map_radial.

◆ comp_t_from_cartesian() [2/2]

virtual void Lorene::Map::comp_t_from_cartesian	(	const Cmp &	v_x,
		const Cmp &	v_y,
		const Cmp &	v_z,
		Cmp &	v_t
	)		const

pure virtual

Cmp version

Implemented in Lorene::Map_radial.

◆ comp_x_from_spherical() [1/2]

virtual void Lorene::Map::comp_x_from_spherical	(	const Scalar &	v_r,
		const Scalar &	v_theta,
		const Scalar &	v_phi,
		Scalar &	v_x
	)		const

pure virtual

Computes the Cartesian x component (with respect to bvect_cart ) of a vector given by its spherical components with respect to bvect_spher .

Parameters

v_r	[input] r -component of the vector
v_theta	[input] $\theta$ -component of the vector
v_phi	[input] $\phi$ -component of the vector
v_x	[output] x-component of the vector

Implemented in Lorene::Map_radial.

◆ comp_x_from_spherical() [2/2]

virtual void Lorene::Map::comp_x_from_spherical	(	const Cmp &	v_r,
		const Cmp &	v_theta,
		const Cmp &	v_phi,
		Cmp &	v_x
	)		const

pure virtual

Cmp version

Implemented in Lorene::Map_radial.

◆ comp_y_from_spherical() [1/2]

virtual void Lorene::Map::comp_y_from_spherical	(	const Scalar &	v_r,
		const Scalar &	v_theta,
		const Scalar &	v_phi,
		Scalar &	v_y
	)		const

pure virtual

Computes the Cartesian y component (with respect to bvect_cart ) of a vector given by its spherical components with respect to bvect_spher .

Parameters

v_r	[input] r -component of the vector
v_theta	[input] $\theta$ -component of the vector
v_phi	[input] $\phi$ -component of the vector
v_y	[output] y-component of the vector

Implemented in Lorene::Map_radial.

◆ comp_y_from_spherical() [2/2]

virtual void Lorene::Map::comp_y_from_spherical	(	const Cmp &	v_r,
		const Cmp &	v_theta,
		const Cmp &	v_phi,
		Cmp &	v_y
	)		const

pure virtual

Cmp version

Implemented in Lorene::Map_radial.

◆ comp_z_from_spherical() [1/2]

virtual void Lorene::Map::comp_z_from_spherical	(	const Scalar &	v_r,
		const Scalar &	v_theta,
		Scalar &	v_z
	)		const

pure virtual

Computes the Cartesian z component (with respect to bvect_cart ) of a vector given by its spherical components with respect to bvect_spher .

Parameters

v_r	[input] r -component of the vector
v_theta	[input] $\theta$ -component of the vector
v_z	[output] z-component of the vector

Implemented in Lorene::Map_radial.

◆ comp_z_from_spherical() [2/2]

virtual void Lorene::Map::comp_z_from_spherical	(	const Cmp &	v_r,
		const Cmp &	v_theta,
		Cmp &	v_z
	)		const

pure virtual

Cmp version

Implemented in Lorene::Map_radial.

◆ convert_absolute()

void Lorene::Map::convert_absolute	(	double	xx,
		double	yy,
		double	zz,
		double &	rr,
		double &	theta,
		double &	pphi
	)		const

Determines the coordinates $(r,\theta,\phi)$ corresponding to given absolute Cartesian coordinates (X,Y,Z).

Parameters

xx	[input] value of the coordinate x (absolute frame)
yy	[input] value of the coordinate y (absolute frame)
zz	[input] value of the coordinate z (absolute frame)
rr	[output] value of r
theta	[output] value of $\theta$
pphi	[output] value of $\phi$

Definition at line 305 of file map.C.

References ori_x, ori_y, ori_z, rot_phi, and Lorene::sqrt().

◆ dalembert()

virtual void Lorene::Map::dalembert	(	Param &	par,
		Scalar &	fJp1,
		const Scalar &	fJ,
		const Scalar &	fJm1,
		const Scalar &	source
	)		const

pure virtual

Performs one time-step integration of the d'Alembert scalar equation.

Parameters

par	[input/output] possible parameters to control the resolution of the wave equation. See the actual implementation in the derived class of `Map` for documentation. Note that, at least, param must contain the time step as first `double` parameter.
fJp1	[output] solution $f^{J+1}$ at time J+1 with boundary conditions of outgoing radiation (not exact!)
fJ	[input] solution at time J
fJm1	[input] solution $f^{J-1}$ at time J-1
source	[input] source $\sigma$ of the d'Alembert equation $\diamond u = \sigma$ .

Implemented in Lorene::Map_eps, Lorene::Map_star, Lorene::Map_log, Lorene::Map_et, and Lorene::Map_af.

◆ dec2_dzpuis()

virtual void Lorene::Map::dec2_dzpuis ( Scalar & ) const

pure virtual

Decreases by 2 the value of dzpuis of a Scalar
and changes accordingly its values in the
compactified external domain (CED).

Implemented in Lorene::Map_radial.

◆ dec_dzpuis()

virtual void Lorene::Map::dec_dzpuis ( Scalar & ) const

pure virtual

Decreases by 1 the value of dzpuis of a Scalar
and changes accordingly its values in the
compactified external domain (CED).

Implemented in Lorene::Map_radial.

◆ div_cost()

virtual void Lorene::Map::div_cost ( Scalar & ) const

pure virtual

Division by $\cos\theta$ of a Scalar.

Implemented in Lorene::Map_radial.

◆ div_r()

virtual void Lorene::Map::div_r ( Scalar & ) const

pure virtual

Division by r of a Scalar.

Implemented in Lorene::Map_radial.

◆ div_r_zec()

virtual void Lorene::Map::div_r_zec ( Scalar & ) const

pure virtual

Division by r (in the compactified external domain only) of a Scalar.

Implemented in Lorene::Map_radial.

◆ div_rsint()

virtual void Lorene::Map::div_rsint ( Scalar & ) const

pure virtual

Division by $r\sin\theta$ of a Scalar.

Implemented in Lorene::Map_radial.

◆ div_sint()

virtual void Lorene::Map::div_sint ( Scalar & ) const

pure virtual

Division by $\sin\theta$ of a Scalar.

Implemented in Lorene::Map_radial.

◆ div_tant()

virtual void Lorene::Map::div_tant ( Scalar & ) const

pure virtual

Division by $\tan\theta$ of a Scalar.

Implemented in Lorene::Map_radial.

◆ donne_para_poisson_vect()

virtual Param* Lorene::Map::donne_para_poisson_vect	(	Param &	para,
		int	i
	)		const

pure virtual

Function intended to be used by Map::poisson_vect and Map::poisson_vect_oohara .

It constructs the sets of parameters used for each scalar Poisson equation from the one for the vectorial one.

Parameters

para	[input] : the `Param` used for the resolution of the vectorial Poisson equation : \ `para.int()` maximum number of iteration.\ `para.double(0)` relaxation parameter.\ `para.double(1)` required precision. \ `para.tenseur_mod()` source of the vectorial part at the previous step.\ `para.cmp_mod()` source of the scalar part at the previous step.
i	[input] number of the scalar Poisson equation that is being solved (values from 0 to 2 for the componants of the vectorial part and 3 for the scalar one).

Returns: the pointer on the parameter set used for solving the scalar Poisson equation labelled by i .

Implemented in Lorene::Map_eps, Lorene::Map_star, Lorene::Map_log, Lorene::Map_et, and Lorene::Map_af.

◆ dsdr() [1/2]

virtual void Lorene::Map::dsdr	(	const Cmp &	ci,
		Cmp &	resu
	)		const

pure virtual

Computes $\partial/ \partial r$ of a Cmp .

Note that in the compactified external domain (CED), it computes $-\partial/ \partial u = r^2 \partial/ \partial r$ .

Parameters

ci	[input] field to consider
resu	[output] derivative of `ci`

Implemented in Lorene::Map_eps, Lorene::Map_star, Lorene::Map_log, Lorene::Map_et, and Lorene::Map_af.

◆ dsdr() [2/2]

virtual void Lorene::Map::dsdr	(	const Scalar &	uu,
		Scalar &	resu
	)		const

pure virtual

Computes $\partial/ \partial r$ of a Scalar .

Note that in the compactified external domain (CED), the dzpuis flag of the output is 2 if the input has dzpuis = 0, and is increased by 1 in other cases.

Parameters

uu	[input] field to consider
resu	[output] derivative of `uu`

Implemented in Lorene::Map_eps, Lorene::Map_star, Lorene::Map_log, Lorene::Map_et, and Lorene::Map_af.

◆ dsdradial()

virtual void Lorene::Map::dsdradial	(	const Scalar &	uu,
		Scalar &	resu
	)		const

pure virtual

Computes $\partial/ \partial r$ of a Scalar if the description is affine and $\partial/ \partial \ln r$ if it is logarithmic.

Note that in the compactified external domain (CED), the dzpuis flag of the output is 2 if the input has dzpuis = 0, and is increased by 1 in other cases.

Parameters

uu	[input] field to consider
resu	[output] derivative of `uu`

Implemented in Lorene::Map_eps, Lorene::Map_star, Lorene::Map_log, Lorene::Map_et, and Lorene::Map_af.

◆ dsdt()

virtual void Lorene::Map::dsdt	(	const Scalar &	uu,
		Scalar &	resu
	)		const

pure virtual

Computes $\partial/ \partial \theta$ of a Scalar .

Parameters

uu	[input] scalar field
resu	[output] derivative of `uu`

Implemented in Lorene::Map_eps, Lorene::Map_star, Lorene::Map_log, Lorene::Map_et, and Lorene::Map_af.

◆ dsdxi() [1/2]

virtual void Lorene::Map::dsdxi	(	const Cmp &	ci,
		Cmp &	resu
	)		const

pure virtual

Computes $\partial/ \partial \xi$ of a Cmp .

Note that in the compactified external domain (CED), it computes $-\partial/ \partial u = \xi^2 \partial/ \partial \xi$ .

Parameters

ci	[input] field to consider
resu	[output] derivative of `ci`

Implemented in Lorene::Map_eps, Lorene::Map_star, Lorene::Map_log, Lorene::Map_et, and Lorene::Map_af.

◆ dsdxi() [2/2]

virtual void Lorene::Map::dsdxi	(	const Scalar &	uu,
		Scalar &	resu
	)		const

pure virtual

Computes $\partial/ \partial xi$ of a Scalar .

Note that in the compactified external domain (CED), the dzpuis flag of the output is 2 if the input has dzpuis = 0, and is increased by 1 in other cases.

Parameters

uu	[input] field to consider
resu	[output] derivative of `uu`

Implemented in Lorene::Map_eps, Lorene::Map_star, Lorene::Map_log, Lorene::Map_et, and Lorene::Map_af.

◆ flat_met_cart()

const Metric_flat & Lorene::Map::flat_met_cart ( ) const

Returns the flat metric associated with the Cartesian coordinates and with components expressed in the triad bvect_cart.

Definition at line 334 of file map.C.

References bvect_cart, and p_flat_met_cart.

◆ flat_met_spher()

const Metric_flat & Lorene::Map::flat_met_spher ( ) const

Returns the flat metric associated with the spherical coordinates and with components expressed in the triad bvect_spher.

Definition at line 324 of file map.C.

References bvect_spher, and p_flat_met_spher.

◆ get_bvect_cart()

const Base_vect_cart& Lorene::Map::get_bvect_cart ( ) const

inline

Returns the Cartesian basis $(\partial/\partial x,\partial/\partial y,\partial/\partial z)$ associated with the coordinates (x,y,z) of the mapping, i.e.

the Cartesian coordinates related to $(r, \theta, \phi)$ by means of usual formulae.

Definition at line 803 of file map.h.

References bvect_cart.

◆ get_bvect_spher()

const Base_vect_spher& Lorene::Map::get_bvect_spher ( ) const

inline

Returns the orthonormal vectorial basis $(\partial/\partial r,1/r\partial/\partial \theta, 1/(r\sin\theta)\partial/\partial \phi)$ associated with the coordinates $(r, \theta, \phi)$ of the mapping.

Definition at line 795 of file map.h.

References bvect_spher.

◆ get_mg()

const Mg3d* Lorene::Map::get_mg ( ) const

inline

Gives the Mg3d on which the mapping is defined.

Definition at line 777 of file map.h.

References mg.

◆ get_ori_x()

double Lorene::Map::get_ori_x ( ) const

inline

Returns the x coordinate of the origin.

Definition at line 780 of file map.h.

References ori_x.

◆ get_ori_y()

double Lorene::Map::get_ori_y ( ) const

inline

Returns the y coordinate of the origin.

Definition at line 782 of file map.h.

References ori_y.

◆ get_ori_z()

double Lorene::Map::get_ori_z ( ) const

inline

Returns the z coordinate of the origin.

Definition at line 784 of file map.h.

References ori_z.

◆ get_rot_phi()

double Lorene::Map::get_rot_phi ( ) const

inline

Returns the angle between the x –axis and X –axis.

Definition at line 787 of file map.h.

References rot_phi.

◆ homothetie()

virtual void Lorene::Map::homothetie ( double lambda )

pure virtual

Sets a new radial scale.

Parameters

lambda [input] factor by which the value of r is to be multiplied

Implemented in Lorene::Map_eps, Lorene::Map_star, Lorene::Map_log, Lorene::Map_et, and Lorene::Map_af.

◆ inc2_dzpuis()

virtual void Lorene::Map::inc2_dzpuis ( Scalar & ) const

pure virtual

Increases by 2 the value of dzpuis of a Scalar
and changes accordingly its values in the
compactified external domain (CED).

Implemented in Lorene::Map_radial.

◆ inc_dzpuis()

virtual void Lorene::Map::inc_dzpuis ( Scalar & ) const

pure virtual

Increases by 1 the value of dzpuis of a Scalar
and changes accordingly its values in the
compactified external domain (CED).

Implemented in Lorene::Map_radial.

◆ integrale()

virtual Tbl* Lorene::Map::integrale ( const Cmp & ) const

pure virtual

Computes the integral over all space of a Cmp .

The computed quantity is $\int u \, r^2 \sin\theta \, dr\, d\theta \, d\phi$ . The routine allocates a Tbl (size: mg->nzone ) to store the result (partial integral) in each domain and returns a pointer to it.

Implemented in Lorene::Map_eps, Lorene::Map_star, Lorene::Map_log, Lorene::Map_et, and Lorene::Map_af.

◆ lapang()

virtual void Lorene::Map::lapang	(	const Scalar &	uu,
		Scalar &	lap
	)		const

pure virtual

Computes the angular Laplacian of a scalar field.

Parameters

uu	[input] Scalar field u (represented as a `Scalar` ) the Laplacian $\Delta u$ of which is to be computed
lap	[output] Angular Laplacian of u (see documentation of `Scalar`

Implemented in Lorene::Map_eps, Lorene::Map_star, Lorene::Map_log, Lorene::Map_et, and Lorene::Map_af.

◆ laplacien() [1/2]

virtual void Lorene::Map::laplacien	(	const Scalar &	uu,
		int	zec_mult_r,
		Scalar &	lap
	)		const

pure virtual

Computes the Laplacian of a scalar field.

Parameters

uu	[input] Scalar field u (represented as a `Scalar` ) the Laplacian $\Delta u$ of which is to be computed
zec_mult_r	[input] Determines the quantity computed in the compactified external domain (CED) : \ zec_mult_r = 0 : $\Delta u$ \ zec_mult_r = 2 : $r^2 \, \Delta u$ \ zec_mult_r = 4 (default) : $r^4 \, \Delta u$
lap	[output] Laplacian of u

Implemented in Lorene::Map_eps, Lorene::Map_star, Lorene::Map_log, Lorene::Map_et, and Lorene::Map_af.

◆ laplacien() [2/2]

virtual void Lorene::Map::laplacien	(	const Cmp &	uu,
		int	zec_mult_r,
		Cmp &	lap
	)		const

pure virtual

Computes the Laplacian of a scalar field (Cmp version).

Implemented in Lorene::Map_eps, Lorene::Map_star, Lorene::Map_log, Lorene::Map_et, and Lorene::Map_af.

◆ mp_angu()

virtual const Map_af& Lorene::Map::mp_angu ( int ) const

pure virtual

Returns the "angular" mapping for the outside of domain l_zone.

Valid only for the class Map_af.

Implemented in Lorene::Map_eps, Lorene::Map_star, Lorene::Map_log, Lorene::Map_et, and Lorene::Map_af.

◆ mult_cost()

virtual void Lorene::Map::mult_cost ( Scalar & ) const

pure virtual

Multiplication by $\cos\theta$ of a Scalar.

Implemented in Lorene::Map_radial.

◆ mult_r() [1/2]

virtual void Lorene::Map::mult_r ( Scalar & uu ) const

pure virtual

Multiplication by r of a Scalar , the dzpuis
of uu is not changed.

Implemented in Lorene::Map_radial.

◆ mult_r() [2/2]

virtual void Lorene::Map::mult_r ( Cmp & ci ) const

pure virtual

Multiplication by r of a Cmp .

In the CED, there is only a decrement of dzpuis

Implemented in Lorene::Map_radial.

◆ mult_r_zec()

virtual void Lorene::Map::mult_r_zec ( Scalar & ) const

pure virtual

Multiplication by r (in the compactified external domain only) of a Scalar.

Implemented in Lorene::Map_radial.

◆ mult_rsint()

virtual void Lorene::Map::mult_rsint ( Scalar & ) const

pure virtual

Multiplication by $r\sin\theta$ of a Scalar.

Implemented in Lorene::Map_radial.

◆ mult_sint()

virtual void Lorene::Map::mult_sint ( Scalar & ) const

pure virtual

Multiplication by $\sin\theta$ of a Scalar.

Implemented in Lorene::Map_radial.

◆ operator=()

virtual void Lorene::Map::operator= ( const Map_af & )

pure virtual

Assignment to an affine mapping.

Implemented in Lorene::Map_eps, Lorene::Map_star, Lorene::Map_log, Lorene::Map_et, Lorene::Map_af, and Lorene::Map_radial.

◆ operator==()

virtual bool Lorene::Map::operator== ( const Map & ) const

pure virtual

Comparison operator (egality)

Implemented in Lorene::Map_eps, Lorene::Map_star, Lorene::Map_log, Lorene::Map_et, Lorene::Map_af, and Lorene::Map_radial.

◆ operator>>()

virtual ostream& Lorene::Map::operator>> ( ostream & ) const

privatepure virtual

Operator >>

Implemented in Lorene::Map_eps, Lorene::Map_star, Lorene::Map_log, Lorene::Map_et, and Lorene::Map_af.

◆ poisson()

virtual void Lorene::Map::poisson	(	const Cmp &	source,
		Param &	par,
		Cmp &	uu
	)		const

pure virtual

Computes the solution of a scalar Poisson equation.

Parameters

source	[input] source $\sigma$ of the Poisson equation $\Delta u = \sigma$ .
par	[input/output] possible parameters to control the resolution of the Poisson equation. See the actual implementation in the derived class of `Map` for documentation.
uu	[input/output] solution u with the boundary condition u =0 at spatial infinity.

Implemented in Lorene::Map_eps, Lorene::Map_star, Lorene::Map_log, Lorene::Map_et, and Lorene::Map_af.

◆ poisson2d()

virtual void Lorene::Map::poisson2d	(	const Cmp &	source_mat,
		const Cmp &	source_quad,
		Param &	par,
		Cmp &	uu
	)		const

pure virtual

Computes the solution of a 2-D Poisson equation.

The 2-D Poisson equation writes

${\partial^2 u\over\partial r^2} + {1\over r} {\partial u \over \partial r} + {1\over r^2} {\partial^2 u\over\partial \theta^2} = \sigma \ .$

Parameters

source_mat	[input] Compactly supported part of the source $\sigma$ of the 2-D Poisson equation (typically matter terms)
source_quad	[input] Non-compactly supported part of the source $\sigma$ of the 2-D Poisson equation (typically quadratic terms)
par	[input/output] possible parameters to control the resolution of the Poisson equation. See the actual implementation in the derived class of `Map` for documentation.
uu	[input/output] solution u with the boundary condition u =0 at spatial infinity.

Implemented in Lorene::Map_eps, Lorene::Map_star, Lorene::Map_log, Lorene::Map_et, and Lorene::Map_af.

◆ poisson_angu()

virtual void Lorene::Map::poisson_angu	(	const Scalar &	source,
		Param &	par,
		Scalar &	uu,
		double	lambda = `0`
	)		const

pure virtual

Computes the solution of the generalized angular Poisson equation.

The generalized angular Poisson equation is $\Delta_{\theta\varphi} u + \lambda u = \sigma$ , where $\Delta_{\theta\varphi} u := \frac{\partial^2 u} {\partial \theta^2} + \frac{1}{\tan \theta} \frac{\partial u} {\partial \theta} +\frac{1}{\sin^2 \theta}\frac{\partial^2 u} {\partial \varphi^2}$ .

Parameters

source	[input] source $\sigma$ of the equation $\Delta_{\theta\varphi} u + \lambda u = \sigma$ .
par	[input/output] possible parameters to control the resolution of the Poisson equation. See the actual implementation in the derived class of `Map` for documentation.
uu	[input/output] solution u
lambda	[input] coefficient $\lambda$ in the above equation (default value = 0)

Implemented in Lorene::Map_eps, Lorene::Map_star, Lorene::Map_log, Lorene::Map_et, and Lorene::Map_af.

◆ poisson_compact() [1/2]

virtual void Lorene::Map::poisson_compact	(	const Cmp &	source,
		const Cmp &	aa,
		const Tenseur &	bb,
		const Param &	par,
		Cmp &	psi
	)		const

pure virtual

Resolution of the elliptic equation $a \Delta\psi + {\bf b} \cdot \nabla \psi = \sigma$ in the case where the stellar interior is covered by a single domain.

Parameters

source	[input] source $\sigma$ of the above equation
aa	[input] factor a in the above equation
bb	[input] vector b in the above equation
par	[input/output] possible parameters to control the resolution of the equation. See the actual implementation in the derived class of `Map` for documentation.
psi	[input/output] solution $\psi$ which satisfies $\psi(0)=0$ .

Implemented in Lorene::Map_radial.

◆ poisson_compact() [2/2]

virtual void Lorene::Map::poisson_compact	(	int	nzet,
		const Cmp &	source,
		const Cmp &	aa,
		const Tenseur &	bb,
		const Param &	par,
		Cmp &	psi
	)		const

pure virtual

Resolution of the elliptic equation $a \Delta\psi + {\bf b} \cdot \nabla \psi = \sigma$ in the case of a multidomain stellar interior.

Parameters

nzet	[input] number of domains covering the stellar interior
source	[input] source $\sigma$ of the above equation
aa	[input] factor a in the above equation
bb	[input] vector b in the above equation
par	[input/output] possible parameters to control the resolution of the equation. See the actual implementation in the derived class of `Map` for documentation.
psi	[input/output] solution $\psi$ which satisfies $\psi(0)=0$ .

Implemented in Lorene::Map_radial.

◆ poisson_frontiere()

virtual void Lorene::Map::poisson_frontiere	(	const Cmp &	source,
		const Valeur &	limite,
		int	raccord,
		int	num_front,
		Cmp &	pot,
		double	= `0.`,
		double	= `0.`
	)		const

pure virtual

Computes the solution of a Poisson equation from the domain num_front+1 .

imposing a boundary condition at the boundary between the domains num_front and num_front+1 .

Parameters

source	[input] : source of the equation.
limite	[input] : `limite`[num_front] contains the angular function being the boudary condition.
raccord	[input] : 1 for the Dirichlet problem and 2 for the Neumann one and 3 for Dirichlet-Neumann.
num_front	[input] : index of the boudary at which the boundary condition has to be imposed.
pot	[output] : result.
fact_dir	[input] : Valeur by which we multiply the quantity we solve. (in the case of Dirichlet-Neumann boundary condition.)
fact_neu	[input] : Valeur by which we multiply the radial derivative of the quantity we solve. (in the case of Dirichlet-Neumann boundary condition.)

Implemented in Lorene::Map_eps, Lorene::Map_star, Lorene::Map_log, Lorene::Map_et, and Lorene::Map_af.

◆ poisson_interne()

virtual void Lorene::Map::poisson_interne	(	const Cmp &	source,
		const Valeur &	limite,
		Param &	par,
		Cmp &	pot
	)		const

pure virtual

Computes the solution of a Poisson equation in the shell, imposing a boundary condition at the surface of the star.

Parameters

source	[input] : source of the equation.
limite	[input] : `limite`[num_front] contains the angular function being the boudary condition.
par	[input] : parameters of the computation.
pot	[output] : result.

Implemented in Lorene::Map_eps, Lorene::Map_star, Lorene::Map_log, Lorene::Map_et, and Lorene::Map_af.

◆ poisson_regular()

virtual void Lorene::Map::poisson_regular	(	const Cmp &	source,
		int	k_div,
		int	nzet,
		double	unsgam1,
		Param &	par,
		Cmp &	uu,
		Cmp &	uu_regu,
		Cmp &	uu_div,
		Tenseur &	duu_div,
		Cmp &	source_regu,
		Cmp &	source_div
	)		const

pure virtual

Computes the solution of a scalar Poisson equation.

The regularized source

Parameters

source	[input] source $\sigma$ of the Poisson equation $\Delta u = \sigma$ .
k_div	[input] regularization degree of the procedure
nzet	[input] number of domains covering the star
unsgam1	[input] parameter $1/(\gamma-1)$ where $\gamma$ denotes the adiabatic index.
par	[input/output] possible parameters to control the resolution of the Poisson equation. See the actual implementation in the derived class of `Map` for documentation.
uu	[input/output] solution u with the boundary condition u =0 at spatial infinity.
uu_regu	[output] solution of the regular part of the source.
uu_div	[output] solution of the diverging part of the source.
duu_div	[output] derivative of the diverging potential
source_regu	[output] regularized source
source_div	[output] diverging part of the source

Implemented in Lorene::Map_eps, Lorene::Map_star, Lorene::Map_log, Lorene::Map_et, and Lorene::Map_af.

◆ poisson_tau()

virtual void Lorene::Map::poisson_tau	(	const Cmp &	source,
		Param &	par,
		Cmp &	uu
	)		const

pure virtual

Computes the solution of a scalar Poisson equationwith a Tau method.

Parameters

source	[input] source $\sigma$ of the Poisson equation $\Delta u = \sigma$ .
par	[input/output] possible parameters to control the resolution of the Poisson equation. See the actual implementation in the derived class of `Map` for documentation.
uu	[input/output] solution u with the boundary condition u =0 at spatial infinity.

Implemented in Lorene::Map_eps, Lorene::Map_star, Lorene::Map_log, Lorene::Map_et, and Lorene::Map_af.

◆ primr()

virtual void Lorene::Map::primr	(	const Scalar &	uu,
		Scalar &	resu,
		bool	null_infty
	)		const

pure virtual

Computes the radial primitive which vanishes for $r\to \infty$ .

i.e. the function $F(r,\theta,\varphi) = \int_r^\infty f(r',\theta,\varphi) \, dr'$

Parameters

uu	[input] function f (must have a `dzpuis` = 2)
resu	[input] function F
null_infty	if true (default), the primitive is null at infinity (or on the grid boundary). F is null at the center otherwise

Implemented in Lorene::Map_eps, Lorene::Map_star, Lorene::Map_log, Lorene::Map_et, and Lorene::Map_af.

◆ reevaluate() [1/2]

virtual void Lorene::Map::reevaluate	(	const Map *	mp_prev,
		int	nzet,
		Cmp &	uu
	)		const

pure virtual

Recomputes the values of a Cmp at the collocation points after a change in the mapping.

Parameters

mp_prev	[input] Previous value of the mapping.
nzet	[input] Number of domains where the computation must be done: the computation is performed for the domains of index $0\le {\tt l} \le {\tt nzet-1}$ ; `uu` is set to zero in the other domains.
uu	[input/output] input : `Cmp` previously computed on the mapping `mp_prev` ; ouput : values of (logically) the same `Cmp` at the grid points defined by `this`.

Implemented in Lorene::Map_radial.

◆ reevaluate() [2/2]

virtual void Lorene::Map::reevaluate	(	const Map *	mp_prev,
		int	nzet,
		Scalar &	uu
	)		const

pure virtual

Recomputes the values of a Scalar at the collocation points after a change in the mapping.

Parameters

mp_prev	[input] Previous value of the mapping.
nzet	[input] Number of domains where the computation must be done: the computation is performed for the domains of index $0\le {\tt l} \le {\tt nzet-1}$ ; `uu` is set to zero in the other domains.
uu	[input/output] input : `Scalar` previously computed on the mapping `mp_prev` ; ouput : values of (logically) the same `Scalae` at the grid points defined by `this`.

Implemented in Lorene::Map_radial.

◆ reevaluate_symy() [1/2]

virtual void Lorene::Map::reevaluate_symy	(	const Map *	mp_prev,
		int	nzet,
		Cmp &	uu
	)		const

pure virtual

Recomputes the values of a Cmp at the collocation points after a change in the mapping.

Case where the Cmp is symmetric with respect the plane y=0.

Parameters

mp_prev	[input] Previous value of the mapping.
nzet	[input] Number of domains where the computation must be done: the computation is performed for the domains of index $0\le {\tt l} \le {\tt nzet-1}$ ; `uu` is set to zero in the other domains.
uu	[input/output] input : `Cmp` previously computed on the mapping `mp_prev` ; ouput : values of (logically) the same `Cmp` at the grid points defined by `this`.

Implemented in Lorene::Map_radial.

◆ reevaluate_symy() [2/2]

virtual void Lorene::Map::reevaluate_symy	(	const Map *	mp_prev,
		int	nzet,
		Scalar &	uu
	)		const

pure virtual

Recomputes the values of a Scalar at the collocation points after a change in the mapping.

Case where the Scalar is symmetric with respect the plane y=0.

Parameters

mp_prev	[input] Previous value of the mapping.
nzet	[input] Number of domains where the computation must be done: the computation is performed for the domains of index $0\le {\tt l} \le {\tt nzet-1}$ ; `uu` is set to zero in the other domains.
uu	[input/output] input : `Scalar` previously computed on the mapping `mp_prev` ; ouput : values of (logically) the same `Scalar` at the grid points defined by `this`.

Implemented in Lorene::Map_radial.

◆ reset_coord()

void Lorene::Map::reset_coord ( )

protectedvirtual

Resets all the member Coords.

Reimplemented in Lorene::Map_et, and Lorene::Map_radial.

Definition at line 279 of file map.C.

References cosp, cost, Lorene::Coord::del_t(), phi, r, sinp, sint, tet, x, xa, y, ya, z, and za.

◆ resize()

virtual void Lorene::Map::resize	(	int	l,
		double	lambda
	)

pure virtual

Rescales the outer boundary of one domain.

The inner boundary is unchanged. The inner boundary of the next domain is changed to match the new outer boundary.

Parameters

l	[input] index of the domain
lambda	[input] factor by which the value of $R(\theta, \varphi)$ defining the outer boundary of the domain is to be multiplied.

Implemented in Lorene::Map_eps, Lorene::Map_star, Lorene::Map_log, Lorene::Map_et, and Lorene::Map_af.

◆ sauve()

void Lorene::Map::sauve ( FILE * fd ) const

virtual

Save in a file.

Reimplemented in Lorene::Map_eps, Lorene::Map_star, Lorene::Map_log, Lorene::Map_et, Lorene::Map_af, and Lorene::Map_radial.

Definition at line 227 of file map.C.

References Lorene::fwrite_be(), mg, ori_x, ori_y, ori_z, rot_phi, and Lorene::Mg3d::sauve().

◆ set_ori()

void Lorene::Map::set_ori	(	double	xa0,
		double	ya0,
		double	za0
	)

Sets a new origin.

Definition at line 256 of file map.C.

References bvect_spher, ori_x, ori_y, ori_z, reset_coord(), and Lorene::Base_vect_spher::set_ori().

◆ set_rot_phi()

void Lorene::Map::set_rot_phi ( double phi0 )

Sets a new rotation angle.

Definition at line 266 of file map.C.

References bvect_cart, bvect_spher, reset_coord(), rot_phi, Lorene::Base_vect_cart::set_rot_phi(), and Lorene::Base_vect_spher::set_rot_phi().

◆ srdsdt() [1/2]

virtual void Lorene::Map::srdsdt	(	const Cmp &	ci,
		Cmp &	resu
	)		const

pure virtual

Computes $1/r \partial/ \partial \theta$ of a Cmp .

Note that in the compactified external domain (CED), it computes $1/u \partial/ \partial \theta = r \partial/ \partial \theta$ .

Parameters

ci	[input] field to consider
resu	[output] derivative of `ci`

Implemented in Lorene::Map_eps, Lorene::Map_star, Lorene::Map_log, Lorene::Map_et, and Lorene::Map_af.

◆ srdsdt() [2/2]

virtual void Lorene::Map::srdsdt	(	const Scalar &	uu,
		Scalar &	resu
	)		const

pure virtual

Computes $1/r \partial/ \partial \theta$ of a Scalar .

Note that in the compactified external domain (CED), the dzpuis flag of the output is 2 if the input has dzpuis = 0, and is increased by 1 in other cases.

Parameters

uu	[input] field to consider
resu	[output] derivative of `uu`

Implemented in Lorene::Map_eps, Lorene::Map_star, Lorene::Map_log, Lorene::Map_et, and Lorene::Map_af.

◆ srstdsdp() [1/2]

virtual void Lorene::Map::srstdsdp	(	const Cmp &	ci,
		Cmp &	resu
	)		const

pure virtual

Computes $1/(r\sin\theta) \partial/ \partial \phi$ of a Cmp .

Note that in the compactified external domain (CED), it computes $1/(u\sin\theta) \partial/ \partial \phi = r/\sin\theta \partial/ \partial \phi$ .

Parameters

ci	[input] field to consider
resu	[output] derivative of `ci`

Implemented in Lorene::Map_eps, Lorene::Map_star, Lorene::Map_log, Lorene::Map_et, and Lorene::Map_af.

◆ srstdsdp() [2/2]

virtual void Lorene::Map::srstdsdp	(	const Scalar &	uu,
		Scalar &	resu
	)		const

pure virtual

Computes $1/(r\sin\theta) \partial/ \partial \phi$ of a Scalar .

Note that in the compactified external domain (CED), the dzpuis flag of the output is 2 if the input has dzpuis = 0, and is increased by 1 in other cases.

Parameters

uu	[input] field to consider
resu	[output] derivative of `uu`

Implemented in Lorene::Map_eps, Lorene::Map_star, Lorene::Map_log, Lorene::Map_et, and Lorene::Map_af.

◆ stdsdp()

virtual void Lorene::Map::stdsdp	(	const Scalar &	uu,
		Scalar &	resu
	)		const

pure virtual

Computes $1/\sin\theta \partial/ \partial \varphi$ of a Scalar .

Parameters

uu	[input] scalar field
resu	[output] derivative of `uu`

Implemented in Lorene::Map_eps, Lorene::Map_star, Lorene::Map_log, Lorene::Map_et, and Lorene::Map_af.

◆ val_lx() [1/2]

virtual void Lorene::Map::val_lx	(	double	rr,
		double	theta,
		double	pphi,
		int &	l,
		double &	xi
	)		const

pure virtual

Computes the domain index l and the value of $\xi$ corresponding to a point given by its physical coordinates $(r, \theta, \phi)$ .

Parameters

rr	[input] value of r
theta	[input] value of $\theta$
pphi	[input] value of $\phi$
l	[output] value of the domain index
xi	[output] value of $\xi$

Implemented in Lorene::Map_eps, Lorene::Map_star, Lorene::Map_log, Lorene::Map_et, and Lorene::Map_af.

◆ val_lx() [2/2]

virtual void Lorene::Map::val_lx	(	double	rr,
		double	theta,
		double	pphi,
		const Param &	par,
		int &	l,
		double &	xi
	)		const

pure virtual

Computes the domain index l and the value of $\xi$ corresponding to a point given by its physical coordinates $(r, \theta, \phi)$ .

This version enables to pass some parameters to control the accuracy of the computation.

Parameters

rr	[input] value of r
theta	[input] value of $\theta$
pphi	[input] value of $\phi$
par	[input/output] parameters to control the accuracy of the computation
l	[output] value of the domain index
xi	[output] value of $\xi$

Implemented in Lorene::Map_eps, Lorene::Map_star, Lorene::Map_log, Lorene::Map_et, and Lorene::Map_af.

◆ val_r()

virtual double Lorene::Map::val_r	(	int	l,
		double	xi,
		double	theta,
		double	pphi
	)		const

pure virtual

Returns the value of the radial coordinate r for a given $(\xi, \theta', \phi')$ in a given domain.

Parameters

l	[input] index of the domain
xi	[input] value of $\xi$
theta	[input] value of $\theta'$
pphi	[input] value of $\phi'$

Returns: value of $r=R_l(\xi, \theta', \phi')$

Implemented in Lorene::Map_eps, Lorene::Map_star, Lorene::Map_log, Lorene::Map_et, and Lorene::Map_af.

Friends And Related Function Documentation

◆ operator<<

ostream& operator<<	(	ostream &	o,
		const Map &	cv
	)

friend

Operator <<.

Definition at line 242 of file map.C.

Member Data Documentation

◆ bvect_cart

Base_vect_cart Lorene::Map::bvect_cart

protected

Cartesian basis $(\partial/\partial x,\partial/\partial y,\partial/\partial z)$ associated with the coordinates (x,y,z) of the mapping, i.e.

the Cartesian coordinates related to $(r, \theta, \phi)$ by means of usual formulae.

Definition at line 709 of file map.h.

◆ bvect_spher

Base_vect_spher Lorene::Map::bvect_spher

protected

Orthonormal vectorial basis $(\partial/\partial r,1/r\partial/\partial \theta, 1/(r\sin\theta)\partial/\partial \phi)$ associated with the coordinates $(r, \theta, \phi)$ of the mapping.

Definition at line 701 of file map.h.

◆ cosp

Coord Lorene::Map::cosp

$\cos\phi$

Definition at line 736 of file map.h.

◆ cost

Coord Lorene::Map::cost

$\cos\theta$

Definition at line 734 of file map.h.

◆ mg

const Mg3d* Lorene::Map::mg

protected

Pointer on the multi-grid Mgd3 on which this is defined.

Definition at line 688 of file map.h.

◆ ori_x

double Lorene::Map::ori_x

protected

Absolute coordinate x of the origin.

Definition at line 690 of file map.h.

◆ ori_y

double Lorene::Map::ori_y

protected

Absolute coordinate y of the origin.

Definition at line 691 of file map.h.

◆ ori_z

double Lorene::Map::ori_z

protected

Absolute coordinate z of the origin.

Definition at line 692 of file map.h.

◆ p_cmp_zero

Cmp* Lorene::Map::p_cmp_zero

protected

The null Cmp.

To be used by the Tenseur class when necessary to return a null Cmp .

Definition at line 725 of file map.h.

◆ p_flat_met_cart

Metric_flat* Lorene::Map::p_flat_met_cart

mutableprotected

Pointer onto the flat metric associated with the Cartesian coordinates and with components expressed in the triad bvect_cart.

Definition at line 719 of file map.h.

◆ p_flat_met_spher

Metric_flat* Lorene::Map::p_flat_met_spher

mutableprotected

Pointer onto the flat metric associated with the spherical coordinates and with components expressed in the triad bvect_spher.

Definition at line 714 of file map.h.

◆ p_mp_angu

Map_af* Lorene::Map::p_mp_angu

mutableprotected

Pointer on the "angular" mapping.

Definition at line 727 of file map.h.

◆ phi

Coord Lorene::Map::phi

$\phi$ coordinate centered on the grid

Definition at line 732 of file map.h.

◆ r

Coord Lorene::Map::r

r coordinate centered on the grid

Definition at line 730 of file map.h.

◆ rot_phi

double Lorene::Map::rot_phi

protected

Angle between the x –axis and X –axis.

Definition at line 693 of file map.h.

◆ sinp

Coord Lorene::Map::sinp

$\sin\phi$

Definition at line 735 of file map.h.

◆ sint

Coord Lorene::Map::sint

$\sin\theta$

Definition at line 733 of file map.h.

◆ tet

Coord Lorene::Map::tet

$\theta$ coordinate centered on the grid

Definition at line 731 of file map.h.

◆ x

Coord Lorene::Map::x

x coordinate centered on the grid

Definition at line 738 of file map.h.

◆ xa

Coord Lorene::Map::xa

Absolute x coordinate.

Definition at line 742 of file map.h.

◆ y

Coord Lorene::Map::y

y coordinate centered on the grid

Definition at line 739 of file map.h.

◆ ya

Coord Lorene::Map::ya

Absolute y coordinate.

Definition at line 743 of file map.h.

◆ z

Coord Lorene::Map::z

z coordinate centered on the grid

Definition at line 740 of file map.h.

◆ za

Coord Lorene::Map::za

Absolute z coordinate.

Definition at line 744 of file map.h.

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

map.h
map.C

Public Member Functions

Public Attributes

Protected Member Functions

Protected Attributes

Private Member Functions

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Map() [1/3]

◆ Map() [2/3]

◆ Map() [3/3]

◆ ~Map()

Member Function Documentation

◆ adapt()

◆ cmp_zero()

◆ comp_p_from_cartesian() [1/2]

◆ comp_p_from_cartesian() [2/2]

◆ comp_r_from_cartesian() [1/2]

◆ comp_r_from_cartesian() [2/2]

◆ comp_t_from_cartesian() [1/2]

◆ comp_t_from_cartesian() [2/2]

◆ comp_x_from_spherical() [1/2]

◆ comp_x_from_spherical() [2/2]

◆ comp_y_from_spherical() [1/2]

◆ comp_y_from_spherical() [2/2]

◆ comp_z_from_spherical() [1/2]

◆ comp_z_from_spherical() [2/2]

◆ convert_absolute()

◆ dalembert()

◆ dec2_dzpuis()

◆ dec_dzpuis()

◆ div_cost()

◆ div_r()

◆ div_r_zec()

◆ div_rsint()

◆ div_sint()

◆ div_tant()

◆ donne_para_poisson_vect()

◆ dsdr() [1/2]

◆ dsdr() [2/2]

◆ dsdradial()

◆ dsdt()

◆ dsdxi() [1/2]

◆ dsdxi() [2/2]

◆ flat_met_cart()

◆ flat_met_spher()

◆ get_bvect_cart()

◆ get_bvect_spher()

◆ get_mg()

◆ get_ori_x()

◆ get_ori_y()

◆ get_ori_z()

◆ get_rot_phi()

◆ homothetie()

◆ inc2_dzpuis()

◆ inc_dzpuis()

◆ integrale()

◆ lapang()

◆ laplacien() [1/2]

◆ laplacien() [2/2]

◆ mp_angu()

◆ mult_cost()

◆ mult_r() [1/2]

◆ mult_r() [2/2]

◆ mult_r_zec()

◆ mult_rsint()

◆ mult_sint()

◆ operator=()

◆ operator==()

◆ operator>>()

◆ poisson()

◆ poisson2d()

◆ poisson_angu()

◆ poisson_compact() [1/2]

◆ poisson_compact() [2/2]

◆ poisson_frontiere()

◆ poisson_interne()

◆ poisson_regular()

◆ poisson_tau()

◆ primr()