Radial mapping of rather general form. More...

#include <map.h>

Inheritance diagram for Lorene::Map_et:

Public Member Functions
	Map_et (const Mg3d &mgrille, const double *r_limits)
	Standard Constructor. More...

	Map_et (const Mg3d &mgrille, const double *r_limits, const Tbl &tab)
	Constructor using the equation of the surface of the star. More...

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

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

virtual	~Map_et ()
	Destructor. More...

virtual void	operator= (const Map_et &mp)
	Assignment to another `Map_et`. More...

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

void	set_ff (const Valeur &)
	Assigns a given value to the function $F(\theta',\phi')$ . More...

void	set_gg (const Valeur &)
	Assigns a given value to the function $G(\theta',\phi')$ . More...

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

const double *	get_alpha () const
	Returns a pointer on the array `alpha` (values of $\alpha$ in each domain) More...

const double *	get_beta () const
	Returns a pointer on the array `beta` (values of $\beta$ in each domain) More...

const Valeur &	get_ff () const
	Returns a (constant) reference to the function $F(\theta',\phi')$ . More...

const Valeur &	get_gg () const
	Returns a (constant) reference to the function $G(\theta',\phi')$ . More...

virtual double	val_r (int l, double xi, double theta, double pphi) const
	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
	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
	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
	Comparison operator (egality) More...

virtual double	val_r_jk (int l, double xi, int j, int k) const
	Returns the value of the radial coordinate r for a given $\xi$ and a given collocation point in $(\theta', \phi')$ in a given domain. More...

virtual void	val_lx_jk (double rr, int j, int k, const Param &par, int &l, double &xi) const
	Computes the domain index l and the value of $\xi$ corresponding to a point of arbitrary r but collocation values of $(\theta, \phi)$ . More...

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

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

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

void	resize_extr (double lambda)
	Rescales the outer boundary of the outermost domain in the case of non-compactified external domain. More...

void	set_alpha (double alpha0, int l)
	Modifies the value of $\alpha$ in domain no. l. More...

void	set_beta (double beta0, int l)
	Modifies the value of $\beta$ in domain no. l. More...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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
	Computes the solution of a scalar Poisson equation. More...

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

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

virtual void	poisson_frontiere (const Cmp &, const Valeur &, int, int, Cmp &, double=0., double=0.) const
	Not yet implemented. More...

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

virtual void	poisson_interne (const Cmp &source, const Valeur &limite, Param &par, Cmp &pot) const
	Computes the solution of a Poisson equation in the shell . More...

virtual void	poisson2d (const Cmp &source_mat, const Cmp &source_quad, Param &par, Cmp &uu) const
	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
	Not yet implemented. More...

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

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

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

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

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

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

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

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

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

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

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

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

virtual void	div_tant (Scalar &) const
	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
	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
	`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
	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
	`Cmp` version More...

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

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

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

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

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...

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...

Public Attributes
Coord	rsxdxdr
	$1/(\partial R/\partial \xi) R/\xi$ in the nucleus; \ $1/(\partial R/\partial \xi) R/(\xi + \beta/\alpha)$ in the shells; \ $1/(\partial U/\partial \xi) U/(\xi-1)$ in the outermost compactified domain. More...

Coord	rsx2drdx
	$[ R/ (\alpha \xi + \beta) ]^2 (\partial R/\partial \xi) / \alpha$ in the nucleus and the shells; \ $\partial U/\partial \xi / \alpha$ in the outermost compactified domain. More...

Coord	xsr
	$\xi/R$ in the nucleus; \ 1/R in the non-compactified shells; \ $(\xi-1)/U$ in the compactified outer domain. More...

Coord	dxdr
	$1/(\partial R/\partial\xi) = \partial \xi /\partial r$ in the nucleus and in the non-compactified shells; \ $-1/(\partial U/\partial\xi) = - \partial \xi /\partial u$ in the compactified outer domain. More...

Coord	drdt
	$\partial R/\partial\theta'$ in the nucleus and in the non-compactified shells; \ $-\partial U/\partial\theta'$ in the compactified external domain (CED). More...

Coord	stdrdp
	${1\over\sin\theta} \partial R/\partial\varphi'$ in the nucleus and in the non-compactified shells; \ $-{1\over\sin\theta}\partial U/\partial\varphi'$ in the compactified external domain (CED). More...

Coord	srdrdt
	$1/R \times (\partial R/\partial\theta')$ in the nucleus and in the non-compactified shells; \ $-1/U \times (\partial U/\partial\theta)$ in the compactified outer domain. More...

Coord	srstdrdp
	$1/(R\sin\theta) \times (\partial R/\partial\varphi')$ in the nucleus and in the non-compactified shells; \ $-1/(U\sin\theta) \times (\partial U/\partial\varphi')$ in the compactified outer domain. More...

Coord	sr2drdt
	$1/R^2 \times (\partial R/\partial\theta')$ in the nucleus and in the non-compactified shells; \ $-1/U^2 \times (\partial U/\partial\theta')$ in the compactified outer domain. More...

Coord	sr2stdrdp
	$1/(R^2\sin\theta) \times (\partial R/\partial\varphi')$ in the nucleus and in the non-compactified shells; \ $-1/(U^2\sin\theta) \times (\partial U/\partial\varphi')$ in the compactified outer domain. More...

Coord	d2rdx2
	$\partial^2 R/\partial\xi^2$ in the nucleus and in the non-compactified shells; \ $-\partial^2 U/\partial\xi^2$ in the compactified outer domain. More...

Coord	lapr_tp
	$1/R^2 \times [ 1/\sin(\theta)\times \partial /\partial\theta' (\sin\theta \partial R /\partial\theta') + 1/\sin^2\theta \partial^2 R /\partial{\varphi'}^2]$ in the nucleus and in the non-compactified shells; \ $- 1/U^2 \times [ 1/\sin(\theta)\times \partial /\partial\theta' (\sin\theta \partial U /\partial\theta') + 1/\sin^2\theta \partial^2 U /\partial{\varphi'}^2]$ in the compactified outer domain. More...

Coord	d2rdtdx
	$\partial^2 R/\partial\xi\partial\theta'$ in the nucleus and in the non-compactified shells; \ $-\partial^2 U/\partial\xi\partial\theta'$ in the compactified outer domain. More...

Coord	sstd2rdpdx
	$1/\sin\theta \times \partial^2 R/\partial\xi\partial\varphi'$ in the nucleus and in the non-compactified shells; \ $-1/\sin\theta \times \partial^2 U/\partial\xi\partial\varphi'$ in the compactified outer domain. More...

Coord	sr2d2rdt2
	$1/R^2 \partial^2 R/\partial{\theta'}^2$ in the nucleus and in the non-compactified shells; \ $-1/U^2 \partial^2 U/\partial{\theta'}^2$ in the compactified outer domain. More...

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
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
void	set_coord ()
	Assignement of the building functions to the member `Coords`. More...

void	fait_poly ()
	Construction of the polynomials $A(\xi)$ and $B(\xi)$ . More...

virtual ostream &	operator>> (ostream &) const
	Operator >> More...

Private Attributes
double *	alpha
	Array (size: `mg->nzone` ) of the values of $\alpha$ in each domain. More...

double *	beta
	Array (size: `mg->nzone` ) of the values of $\beta$ in each domain. More...

Tbl **	aa
	Array (size: `mg->nzone` ) of `Tbl` which stores the values of $A(\xi)$ in each domain. More...

Tbl **	daa
	Array (size: `mg->nzone` ) of `Tbl` which stores the values of $A'(\xi)$ in each domain. More...

Tbl **	ddaa
	Array (size: `mg->nzone` ) of `Tbl` which stores the values of $A''(\xi)$ in each domain. More...

Tbl	aasx
	Values at the `nr` collocation points of $A(\xi)/\xi$ in the nucleus. More...

Tbl	aasx2
	Values at the `nr` collocation points of $A(\xi)/\xi^2$ in the nucleus. More...

Tbl	zaasx
	Values at the `nr` collocation points of $A(\xi)/(\xi-1)$ in the outermost compactified domain. More...

Tbl	zaasx2
	Values at the `nr` collocation points of $A(\xi)/(\xi-1)^2$ in the outermost compactified domain. More...

Tbl **	bb
	Array (size: `mg->nzone` ) of `Tbl` which stores the values of $B(\xi)$ in each domain. More...

Tbl **	dbb
	Array (size: `mg->nzone` ) of `Tbl` which stores the values of $B'(\xi)$ in each domain. More...

Tbl **	ddbb
	Array (size: `mg->nzone` ) of `Tbl` which stores the values of $B''(\xi)$ in each domain. More...

Tbl	bbsx
	Values at the `nr` collocation points of $B(\xi)/\xi$ in the nucleus. More...

Tbl	bbsx2
	Values at the `nr` collocation points of $B(\xi)/\xi^2$ in the nucleus. More...

Valeur	ff
	Values of the function $F(\theta', \phi')$ at the `nt*np` angular collocation points in each domain. More...

Valeur	gg
	Values of the function $G(\theta', \phi')$ at the `nt*np` angular collocation points in each domain. More...

Friends
Mtbl *	map_et_fait_r (const Map *)

Mtbl *	map_et_fait_tet (const Map *)

Mtbl *	map_et_fait_phi (const Map *)

Mtbl *	map_et_fait_sint (const Map *)

Mtbl *	map_et_fait_cost (const Map *)

Mtbl *	map_et_fait_sinp (const Map *)

Mtbl *	map_et_fait_cosp (const Map *)

Mtbl *	map_et_fait_x (const Map *)

Mtbl *	map_et_fait_y (const Map *)

Mtbl *	map_et_fait_z (const Map *)

Mtbl *	map_et_fait_xa (const Map *)

Mtbl *	map_et_fait_ya (const Map *)

Mtbl *	map_et_fait_za (const Map *)

Mtbl *	map_et_fait_xsr (const Map *)

Mtbl *	map_et_fait_dxdr (const Map *)

Mtbl *	map_et_fait_drdt (const Map *)

Mtbl *	map_et_fait_stdrdp (const Map *)

Mtbl *	map_et_fait_srdrdt (const Map *)

Mtbl *	map_et_fait_srstdrdp (const Map *)

Mtbl *	map_et_fait_sr2drdt (const Map *)

Mtbl *	map_et_fait_sr2stdrdp (const Map *)

Mtbl *	map_et_fait_d2rdx2 (const Map *)

Mtbl *	map_et_fait_lapr_tp (const Map *)

Mtbl *	map_et_fait_d2rdtdx (const Map *)

Mtbl *	map_et_fait_sstd2rdpdx (const Map *)

Mtbl *	map_et_fait_sr2d2rdt2 (const Map *)

Mtbl *	map_et_fait_rsxdxdr (const Map *)

Mtbl *	map_et_fait_rsx2drdx (const Map *)

Detailed Description

Radial mapping of rather general form.

()

This mapping relates the grid coordinates $(\xi, \theta', \phi')$ and the physical coordinates $(r, \theta, \phi)$ in the following manner [see Bonazzola, Gourgoulhon & Marck, Phys. Rev. D 58 , 104020 (1998) for details]: $\theta=\theta'$ , $\phi=\phi'$ and

$r = \alpha [\xi + A(\xi) F(\theta', \phi') + B(\xi) G(\theta', \phi')] + \beta$ in non-compactified domains,
$u={1\over r} = \alpha [\xi + A(\xi) F(\theta', \phi')] + \beta$ in the (usually outermost) compactified domain, where $\alpha$ and $\beta$ are constant in each domain, $A(\xi)$ and $B(\xi)$ are constant polynomials defined by
$A(\xi) = 3 \xi^4 - 2 \xi^6$ and $B(\xi) = (5\xi^3 - 3\xi^5)/2$ in the nucleus (innermost domain which contains r =0);
$A(\xi) = (\xi^3 - 3\xi + 2)/4$ and $B(\xi) = (-\xi^3 + 3\xi +2)/4$ in the other domains. The functions $F(\theta', \phi')$ and $G(\theta', \phi')$ depend on the domain under consideration and define the boundaries of this domain.

Definition at line 2770 of file map.h.

Constructor & Destructor Documentation

◆ Map_et() [1/4]

Lorene::Map_et::Map_et	(	const Mg3d &	mgrille,
		const double *	r_limits
	)

Standard Constructor.

Parameters

mgrille	[input] Multi-domain grid on which the mapping is defined
r_limits	[input] Array (size: number of domains + 1) of the value of r at the boundaries of the various domains : `r_limits`[l] : inner boundary of the domain no. `l` `r_limits`[l+1] : outer boundary of the domain no. `l`

Definition at line 155 of file map_et.C.

References alpha, beta, Lorene::Mg3d::get_nzone(), Lorene::Mg3d::get_type_r(), Lorene::Map::mg, and set_coord().

◆ Map_et() [2/4]

Lorene::Map_et::Map_et	(	const Mg3d &	mgrille,
		const double *	r_limits,
		const Tbl &	tab
	)

Constructor using the equation of the surface of the star.

Parameters

mgrille	[input] Multi-domain grid on which the mapping is defined It must contains at least one shell.
r_limits	[input] Array (size: number of domains + 1) of the value of r at the boundaries of the various domains : `r_limits`[l] : inner boundary of the domain no. `l` `r_limits`[l+1] : outer boundary of the domain no. `l` The first value is not used.
tab	[input] equation of the surface between the nucleus and the first shell in the form : ${\rm tab}(k,j) = r(\phi_k,\theta_j)$ , where $\phi_k$ and $\theta_j$ are the values of the angular colocation points.

Definition at line 229 of file map_et.C.

References alpha, Lorene::Valeur::annule(), Lorene::Valeur::annule_hard(), beta, fait_poly(), ff, Lorene::Base_val::get_base_p(), Lorene::Tbl::get_dim(), Lorene::Tbl::get_ndim(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_nzone(), gg, Lorene::max(), Lorene::min(), P_COSSIN, P_COSSIN_P, Lorene::Tbl::set(), Lorene::Valeur::set(), set_coord(), Lorene::Valeur::set_etat_c_qcq(), Lorene::Tbl::set_etat_qcq(), Lorene::Valeur::std_base_scal(), and Lorene::Mg3d::std_base_scal().

◆ Map_et() [3/4]

Lorene::Map_et::Map_et ( const Map_et & mpi )

Copy constructor.

Definition at line 411 of file map_et.C.

References alpha, beta, fait_poly(), Lorene::Mg3d::get_nzone(), Lorene::Map::mg, and set_coord().

◆ Map_et() [4/4]

Lorene::Map_et::Map_et	(	const Mg3d &	mgi,
		FILE *	fich
	)

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

Definition at line 472 of file map_et.C.

References alpha, beta, fait_poly(), Lorene::fread_be(), Lorene::Mg3d::get_nzone(), Lorene::Map::mg, and set_coord().

◆ ~Map_et()

Lorene::Map_et::~Map_et ( )

virtual

Destructor.

Definition at line 509 of file map_et.C.

References aa, alpha, bb, beta, daa, dbb, ddaa, ddbb, Lorene::Mg3d::get_nzone(), and Lorene::Map::mg.

Member Function Documentation

◆ adapt()

void Lorene::Map_et::adapt	(	const Cmp &	ent,
		const Param &	par,
		int	nbr_filtre = `0`
	)

virtual

Adaptation of the mapping to a given scalar field.

Computes the functions $F(\theta',\phi')$ and $G(\theta',\phi')$ as well as the factors $\alpha$ and $\beta$ , so that the boundaries of some domains coincide with isosurfaces of the scalar field ent .

Parameters

ent	[input] scalar field, the isosurfaces of which are used to determine the mapping
par	[input/output] parameters of the computation: \ `par.get_int(0)` : maximum number of iterations to locate zeros by the secant method \ `par.get_int(1)` : number of domains where the adjustment to the isosurfaces of `ent` is to be performed \ `par.get_int(2)` : number of domains `nz_search` where the isosurfaces will be searched : the routine scans the `nz_search` innermost domains, starting from the domain of index `nz_search-1` . NB: the field `ent` must be continuous over these domains \ `par.get_int(3)` : 1 = performs the full computation, 0 = performs only the rescaling by the factor `par.get_double_mod(0)` \ `par.get_int(4)` : theta index of the collocation point $(\theta_, \phi_)$ [using the notations of Bonazzola, Gourgoulhon & Marck, Phys. Rev. D 58 , 104020 (1998)] defining an isosurface of `ent` \ `par.get_int(5)` : phi index of the collocation point $(\theta_, \phi_)$ [using the notations of Bonazzola, Gourgoulhon & Marck, Phys. Rev. D 58 , 104020 (1998)] defining an isosurface of `ent` \ `par.get_int_mod(0)` [output] : number of iterations actually used in the secant method \ `par.get_double(0)` : required absolute precision in the determination of zeros by the secant method \ `par.get_double(1)` : factor by which the values of $\lambda$ and $\mu$ [using the notations of Bonazzola, Gourgoulhon & Marck, Phys. Rev. D 58 , 104020 (1998)] will be multiplied : 1 = regular mapping, 0 = contracting mapping \ `par.get_double(2)` : factor by which all the radial distances will be multiplied \ `par.get_tbl(0)` : array of values of the field `ent` to define the isosurfaces.
nbr_filtre	[input] Number of the last coefficients in $\varphi$ set to zero.

Implements Lorene::Map.

Definition at line 111 of file map_et_adapt.C.

References Lorene::Param::get_double(), Lorene::Tbl::get_etat(), Lorene::Param::get_int(), Lorene::Param::get_int_mod(), Lorene::Cmp::get_mp(), Lorene::Tbl::get_ndim(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_nzone(), Lorene::Tbl::get_taille(), Lorene::Param::get_tbl(), and Lorene::Map::mg.

◆ cmp_zero()

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

inlineinherited

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 Lorene::Map::p_cmp_zero.

◆ comp_p_from_cartesian() [1/2]

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

virtualinherited

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

Implements Lorene::Map.

Definition at line 186 of file map_radial_comp_rtp.C.

References Lorene::Scalar::get_etat().

◆ comp_p_from_cartesian() [2/2]

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

virtualinherited

Cmp version

Implements Lorene::Map.

Definition at line 179 of file map_radial_comp_rtp.C.

References Lorene::Map_radial::comp_p_from_cartesian().

◆ comp_r_from_cartesian() [1/2]

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

virtualinherited

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

Implements Lorene::Map.

Definition at line 75 of file map_radial_comp_rtp.C.

References Lorene::Scalar::get_etat().

◆ comp_r_from_cartesian() [2/2]

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

virtualinherited

Cmp version

Implements Lorene::Map.

Definition at line 68 of file map_radial_comp_rtp.C.

References Lorene::Map_radial::comp_r_from_cartesian().

◆ comp_t_from_cartesian() [1/2]

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

virtualinherited

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

Implements Lorene::Map.

Definition at line 131 of file map_radial_comp_rtp.C.

References Lorene::Scalar::get_etat().

◆ comp_t_from_cartesian() [2/2]

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

virtualinherited

Cmp version

Implements Lorene::Map.

Definition at line 124 of file map_radial_comp_rtp.C.

References Lorene::Map_radial::comp_t_from_cartesian().

◆ comp_x_from_spherical() [1/2]

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

virtualinherited

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

Implements Lorene::Map.

Definition at line 79 of file map_radial_comp_xyz.C.

References Lorene::Scalar::get_etat().

◆ comp_x_from_spherical() [2/2]

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

virtualinherited

Cmp version

Implements Lorene::Map.

Definition at line 71 of file map_radial_comp_xyz.C.

References Lorene::Map_radial::comp_x_from_spherical().

◆ comp_y_from_spherical() [1/2]

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

virtualinherited

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

Implements Lorene::Map.

Definition at line 138 of file map_radial_comp_xyz.C.

References Lorene::Scalar::get_etat().

◆ comp_y_from_spherical() [2/2]

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

virtualinherited

Cmp version

Implements Lorene::Map.

Definition at line 129 of file map_radial_comp_xyz.C.

References Lorene::Map_radial::comp_y_from_spherical().

◆ comp_z_from_spherical() [1/2]

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

virtualinherited

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

Implements Lorene::Map.

Definition at line 195 of file map_radial_comp_xyz.C.

References Lorene::Scalar::get_etat().

◆ comp_z_from_spherical() [2/2]

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

virtualinherited

Cmp version

Implements Lorene::Map.

Definition at line 187 of file map_radial_comp_xyz.C.

References Lorene::Map_radial::comp_z_from_spherical().

◆ convert_absolute()

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

inherited

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

◆ dalembert()

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

virtual

Not yet implemented.

Implements Lorene::Map.

Definition at line 72 of file map_et_dalembert.C.

References Lorene::Scalar::get_etat().

◆ dec2_dzpuis()

void Lorene::Map_radial::dec2_dzpuis ( Scalar & ci ) const

virtualinherited

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

Implements Lorene::Map.

Definition at line 751 of file map_radial_r_manip.C.

References Lorene::Scalar::get_etat().

◆ dec_dzpuis()

void Lorene::Map_radial::dec_dzpuis ( Scalar & ci ) const

virtualinherited

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

Implements Lorene::Map.

Definition at line 646 of file map_radial_r_manip.C.

References Lorene::Scalar::get_etat().

◆ div_cost()

void Lorene::Map_radial::div_cost ( Scalar & ci ) const

virtualinherited

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

Implements Lorene::Map.

Definition at line 88 of file map_radial_th_manip.C.

References Lorene::Scalar::get_etat().

◆ div_r()

void Lorene::Map_radial::div_r ( Scalar & ci ) const

virtualinherited

Division by r of a Scalar.

Implements Lorene::Map.

Definition at line 517 of file map_radial_r_manip.C.

References Lorene::Scalar::get_etat().

◆ div_r_zec()

void Lorene::Map_radial::div_r_zec ( Scalar & uu ) const

virtualinherited

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

Implements Lorene::Map.

Definition at line 588 of file map_radial_r_manip.C.

References Lorene::Scalar::get_etat().

◆ div_rsint()

void Lorene::Map_radial::div_rsint ( Scalar & ci ) const

virtualinherited

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

Implements Lorene::Map.

Definition at line 437 of file map_radial_r_manip.C.

References Lorene::Scalar::get_etat().

◆ div_sint()

void Lorene::Map_radial::div_sint ( Scalar & ci ) const

virtualinherited

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

Implements Lorene::Map.

Definition at line 136 of file map_radial_th_manip.C.

References Lorene::Scalar::get_etat().

◆ div_tant()

void Lorene::Map_radial::div_tant ( Scalar & ci ) const

virtualinherited

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

Implements Lorene::Map.

Definition at line 161 of file map_radial_th_manip.C.

References Lorene::Scalar::get_etat().

◆ donne_para_poisson_vect()

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

virtual

Internal 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 .

Implements Lorene::Map.

Definition at line 78 of file map_poisson_vect.C.

References Lorene::Param::add_cmp_mod(), Lorene::Param::add_double(), Lorene::Param::add_int(), Lorene::Param::add_int_mod(), Lorene::Param::get_cmp_mod(), Lorene::Param::get_double(), Lorene::Param::get_int(), Lorene::Param::get_int_mod(), Lorene::Param::get_tenseur_mod(), and Lorene::Tenseur::set().

◆ dsdr() [1/2]

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

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`

Implements Lorene::Map.

Definition at line 190 of file map_et_deriv.C.

References Lorene::Cmp::get_etat().

◆ dsdr() [2/2]

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

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`

Implements Lorene::Map.

Definition at line 218 of file map_et_deriv.C.

References Lorene::Scalar::get_etat().

◆ dsdradial()

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

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`

Implements Lorene::Map.

Definition at line 277 of file map_et_deriv.C.

References Lorene::Scalar::get_etat().

◆ dsdt()

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

virtual

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

Parameters

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

Implements Lorene::Map.

Definition at line 632 of file map_et_deriv.C.

References Lorene::Scalar::get_etat().

◆ dsdxi() [1/2]

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

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`

Implements Lorene::Map.

Definition at line 98 of file map_et_deriv.C.

References Lorene::Cmp::get_etat().

◆ dsdxi() [2/2]

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

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`

Implements Lorene::Map.

Definition at line 126 of file map_et_deriv.C.

References Lorene::Scalar::get_etat().

◆ fait_poly()

void Lorene::Map_et::fait_poly ( )

private

Construction of the polynomials $A(\xi)$ and $B(\xi)$ .

Definition at line 668 of file map_et.C.

References aa, bb, daa, dbb, ddaa, ddbb, Lorene::Mg3d::get_nr(), Lorene::Mg3d::get_nzone(), Lorene::Mg3d::get_type_r(), and Lorene::Map::mg.

◆ flat_met_cart()

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

inherited

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 Lorene::Map::bvect_cart, and Lorene::Map::p_flat_met_cart.

◆ flat_met_spher()

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

inherited

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 Lorene::Map::bvect_spher, and Lorene::Map::p_flat_met_spher.

◆ get_alpha()

const double * Lorene::Map_et::get_alpha ( ) const

Returns a pointer on the array alpha (values of $\alpha$ in each domain)

Definition at line 1049 of file map_et.C.

References alpha.

◆ get_beta()

const double * Lorene::Map_et::get_beta ( ) const

Returns a pointer on the array beta (values of $\beta$ in each domain)

Definition at line 1053 of file map_et.C.

References beta.

◆ get_bvect_cart()

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

inlineinherited

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 Lorene::Map::bvect_cart.

◆ get_bvect_spher()

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

inlineinherited

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 Lorene::Map::bvect_spher.

◆ get_ff()

const Valeur & Lorene::Map_et::get_ff ( ) const

Returns a (constant) reference to the function $F(\theta',\phi')$ .

Definition at line 1057 of file map_et.C.

References ff.

◆ get_gg()

const Valeur & Lorene::Map_et::get_gg ( ) const

Returns a (constant) reference to the function $G(\theta',\phi')$ .

Definition at line 1061 of file map_et.C.

References gg.

◆ get_mg()

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

inlineinherited

Gives the Mg3d on which the mapping is defined.

Definition at line 777 of file map.h.

References Lorene::Map::mg.

◆ get_ori_x()

double Lorene::Map::get_ori_x ( ) const

inlineinherited

Returns the x coordinate of the origin.

Definition at line 780 of file map.h.

References Lorene::Map::ori_x.

◆ get_ori_y()

double Lorene::Map::get_ori_y ( ) const

inlineinherited

Returns the y coordinate of the origin.

Definition at line 782 of file map.h.

References Lorene::Map::ori_y.

◆ get_ori_z()

double Lorene::Map::get_ori_z ( ) const

inlineinherited

Returns the z coordinate of the origin.

Definition at line 784 of file map.h.

References Lorene::Map::ori_z.

◆ get_rot_phi()

double Lorene::Map::get_rot_phi ( ) const

inlineinherited

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

Definition at line 787 of file map.h.

References Lorene::Map::rot_phi.

◆ homothetie()

void Lorene::Map_et::homothetie ( double lambda )

virtual

Sets a new radial scale.

Parameters

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

Implements Lorene::Map.

Definition at line 928 of file map_et.C.

References Lorene::Mg3d::get_nzone(), Lorene::Mg3d::get_type_r(), and Lorene::Map::mg.

◆ inc2_dzpuis()

void Lorene::Map_radial::inc2_dzpuis ( Scalar & ci ) const

virtualinherited

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

Implements Lorene::Map.

Definition at line 802 of file map_radial_r_manip.C.

References Lorene::Scalar::get_etat().

◆ inc_dzpuis()

void Lorene::Map_radial::inc_dzpuis ( Scalar & ci ) const

virtualinherited

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

Implements Lorene::Map.

Definition at line 699 of file map_radial_r_manip.C.

References Lorene::Scalar::get_etat().

◆ integrale()

Tbl * Lorene::Map_et::integrale ( const Cmp & ci ) const

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.

Implements Lorene::Map.

Definition at line 77 of file map_et_integ.C.

References Lorene::Cmp::get_etat().

◆ lapang()

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

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`

Implements Lorene::Map.

Definition at line 286 of file map_et_lap.C.

◆ laplacien() [1/2]

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

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

Implements Lorene::Map.

Definition at line 78 of file map_et_lap.C.

References Lorene::Scalar::get_etat().

◆ laplacien() [2/2]

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

virtual

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

Implements Lorene::Map.

Definition at line 183 of file map_et_lap.C.

References Lorene::Cmp::get_etat().

◆ mp_angu()

const Map_af & Lorene::Map_et::mp_angu ( int ) const

virtual

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

Valid only for the class Map_af.

Implements Lorene::Map.

Definition at line 1068 of file map_et.C.

References Lorene::c_est_pas_fait(), and Lorene::Map::p_mp_angu.

◆ mult_cost()

void Lorene::Map_radial::mult_cost ( Scalar & ci ) const

virtualinherited

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

Implements Lorene::Map.

Definition at line 64 of file map_radial_th_manip.C.

References Lorene::Scalar::get_etat().

◆ mult_r() [1/2]

void Lorene::Map_radial::mult_r ( Scalar & uu ) const

virtualinherited

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

Implements Lorene::Map.

Definition at line 147 of file map_radial_r_manip.C.

References Lorene::Scalar::get_etat().

◆ mult_r() [2/2]

void Lorene::Map_radial::mult_r ( Cmp & ci ) const

virtualinherited

Multiplication by r of a Cmp.

In the CED, there is only a decrement of dzpuis

Implements Lorene::Map.

Definition at line 222 of file map_radial_r_manip.C.

References Lorene::Cmp::get_etat().

◆ mult_r_zec()

void Lorene::Map_radial::mult_r_zec ( Scalar & ci ) const

virtualinherited

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

Implements Lorene::Map.

Definition at line 299 of file map_radial_r_manip.C.

References Lorene::Scalar::get_etat().

◆ mult_rsint()

void Lorene::Map_radial::mult_rsint ( Scalar & ci ) const

virtualinherited

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

Implements Lorene::Map.

Definition at line 358 of file map_radial_r_manip.C.

References Lorene::Scalar::get_etat().

◆ mult_sint()

void Lorene::Map_radial::mult_sint ( Scalar & ci ) const

virtualinherited

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

Implements Lorene::Map.

Definition at line 112 of file map_radial_th_manip.C.

References Lorene::Scalar::get_etat().

◆ operator=() [1/2]

void Lorene::Map_et::operator= ( const Map_et & mp )

virtual

Assignment to another Map_et.

Definition at line 536 of file map_et.C.

References alpha, beta, ff, get_alpha(), get_beta(), Lorene::Map::get_mg(), Lorene::Mg3d::get_nzone(), Lorene::Map::get_ori_x(), Lorene::Map::get_ori_y(), Lorene::Map::get_ori_z(), Lorene::Map::get_rot_phi(), gg, Lorene::Map::mg, reset_coord(), Lorene::Map::set_ori(), and Lorene::Map::set_rot_phi().

◆ operator=() [2/2]

void Lorene::Map_et::operator= ( const Map_af & mpa )

virtual

Assignment to an affine mapping.

Implements Lorene::Map_radial.

Definition at line 562 of file map_et.C.

References alpha, beta, ff, Lorene::Map_af::get_alpha(), Lorene::Map_af::get_beta(), Lorene::Map::get_mg(), Lorene::Mg3d::get_nzone(), Lorene::Map::get_ori_x(), Lorene::Map::get_ori_y(), Lorene::Map::get_ori_z(), Lorene::Map::get_rot_phi(), gg, Lorene::Map::mg, reset_coord(), Lorene::Map::set_ori(), and Lorene::Map::set_rot_phi().

◆ operator==()

bool Lorene::Map_et::operator== ( const Map & mpi ) const

virtual

Comparison operator (egality)

Implements Lorene::Map_radial.

Definition at line 1007 of file map_et.C.

References alpha, beta, Lorene::Map::bvect_cart, Lorene::Map::bvect_spher, Lorene::diffrelmax(), ff, Lorene::Map::get_bvect_cart(), Lorene::Map::get_bvect_spher(), Lorene::Map::get_mg(), Lorene::Mg3d::get_nzone(), Lorene::Map::get_ori_x(), Lorene::Map::get_ori_y(), Lorene::Map::get_ori_z(), gg, Lorene::max(), Lorene::Map::mg, Lorene::Map::ori_x, Lorene::Map::ori_y, and Lorene::Map::ori_z.

◆ operator>>()

ostream & Lorene::Map_et::operator>> ( ostream & ost ) const

privatevirtual

Operator >>

Implements Lorene::Map.

Definition at line 821 of file map_et.C.

References Lorene::Valeur::affiche_seuil(), alpha, beta, ff, Lorene::Mg3d::get_nzone(), Lorene::Mg3d::get_type_p(), Lorene::Mg3d::get_type_t(), gg, Lorene::Map::mg, and val_r().

◆ poisson()

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

virtual

Computes the solution of a scalar Poisson equation.

Following the method explained in Sect. III.C of Bonazzola, Gourgoulhon & Marck, Phys. Rev. D 58 , 104020 (1998),
the Poisson equation $\Delta u = \sigma$ is re-written as $a \tilde\Delta u = \sigma + R(u)$ , where $\tilde\Delta$ is the Laplacian in an affine mapping and R(u) contains the terms generated by the deviation of the mapping *this from spherical symmetry. This equation is solved by iterations. At each step J the equation effectively solved is $\tilde\Delta u^{J+1} = s^J$ where

$s^J = 1/a_l^{\rm max} \{ {\tt source} + R(u^J) + (a_l^{\rm max}-a) [ \lambda s^{J-1} + (1-\lambda) s^{J-2} ] \} \ ,$

with $a_l^{\rm max} := \max(a)$ in domain no. l and $\lambda$ is a relaxation parameter.

Parameters

source	[input] source $\sigma$ of the Poisson equation
par	[input/output] parameters for the iterative method: \ `par.get_int(0)` : [input] maximum number of iterations \ `par.get_double(0)` : [input] relaxation parameter $\lambda$ \ `par.get_double(1)` : [input] required precision: the iterative method is stopped as soon as the relative difference between and $u^{J-1}$ is greater than `par.get_double(1)` \ `par.get_cmp_mod(0)` : [input/output] input : `Cmp` containing $s^{J-1}$ (cf. the above equation) to start the iteration (if nothing is known a priori, this `Cmp` must be set to zero); output: value of $s^{J-1}$ , to used in a next call to the routine \ `par.get_int_mod(0)` : [output] number of iterations actually used to get the solution.
uu	[input/output] input : previously computed value of u to start the iteration (term R(u) ) (if nothing is known a priori, `uu` must be set to zero); output: solution u with the boundary condition u =0 at spatial infinity.

Implements Lorene::Map.

Definition at line 108 of file map_et_poisson.C.

References Lorene::Cmp::get_etat().

◆ poisson2d()

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

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] Parameters to control the resolution : \ `par.get_double_mod(0)` : [output] constant `lambda` such that the source of the equation effectively solved is `source_mat` + lambda * source_quad , in order to fulfill the virial identity GRV2. \ If the theta basis is `T_SIN_I` , the following arguments are required: \ `par.get_int(0)` : [input] maximum number of iterations \ `par.get_double(0)` : [input] relaxation parameter \ `par.get_double(1)` : [input] required precision: the iterative method is stopped as soon as the relative difference between and $u^{J-1}$ is greater than `par.get_double(1)` \ `par.get_cmp_mod(0)` : [input/output] input : `Cmp` containing $s^{J-1}$ to start the iteration (if nothing is known a priori, this `Cmp` must be set to zero); output: value of $s^{J-1}$ , to used in a next call to the routine \ `par.get_int_mod(0)` : [output] number of iterations actually used to get the solution.
uu	[input/output] solution u with the boundary condition u =0 at spatial infinity.

Implements Lorene::Map.

Definition at line 83 of file map_et_poisson2d.C.

References Lorene::Cmp::get_etat().

◆ poisson_angu()

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

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)

Implements Lorene::Map.

Definition at line 599 of file map_et_poisson.C.

References alpha, Lorene::Map_radial::dxdr, Lorene::Scalar::get_dzpuis(), Lorene::Scalar::get_etat(), Lorene::Tensor::get_mp(), Lorene::Mg3d::get_nr(), Lorene::Mg3d::get_nzone(), Lorene::max(), Lorene::Map::mg, Lorene::Cmp::set_dzpuis(), Lorene::Scalar::set_dzpuis(), Lorene::Mtbl::set_etat_qcq(), Lorene::Scalar::set_spectral_va(), Lorene::Map_radial::srdrdt, Lorene::Map_radial::srstdrdp, and Lorene::Mtbl::t.

◆ poisson_compact() [1/2]

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

virtualinherited

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] parameters of the iterative method of resolution : \ `par.get_int(0)` : [input] maximum number of iterations \ `par.get_double(0)` : [input] required precision: the iterative method is stopped as soon as the relative difference between $\psi^J$ and $\psi^{J-1}$ is greater than `par.get_double(0)` \ `par.get_double(1)` : [input] relaxation parameter $\lambda$ \ `par.get_int_mod(0)` : [output] number of iterations actually used to get the solution.
psi	[input/output]: input : previously computed value of $\psi$ to start the iteration (if nothing is known a priori, `psi` must be set to zero); output: solution $\psi$ which satisfies $\psi(0)=0$ .

Implements Lorene::Map.

Definition at line 158 of file map_radial_poisson_cpt.C.

References Lorene::Cmp::get_etat().

◆ poisson_compact() [2/2]

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

virtualinherited

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 $\psi(0)=0$ .

Implements Lorene::Map.

Definition at line 456 of file map_radial_poisson_cpt.C.

References Lorene::Cmp::get_etat(), and Lorene::Map_radial::poisson_compact().

◆ poisson_frontiere()

void Lorene::Map_et::poisson_frontiere	(	const Cmp &	,
		const Valeur &	,
		int	,
		int	,
		Cmp &	,
		double	= `0.`,
		double	= `0.`
	)		const

virtual

Not yet implemented.

Implements Lorene::Map.

Definition at line 127 of file cmp_pde_frontiere.C.

◆ poisson_interne()

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

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.

Implements Lorene::Map.

Definition at line 277 of file cmp_pde_frontiere.C.

References Lorene::Cmp::get_etat().

◆ poisson_regular()

void Lorene::Map_et::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

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] parameters for the iterative method: \ `par.get_int(0)` : [input] maximum number of iterations \ `par.get_double(0)` : [input] relaxation parameter $\lambda$ \ `par.get_double(1)` : [input] required precision: the iterative method is stopped as soon as the relative difference between and $u^{J-1}$ is greater than `par.get_double(1)` \ `par.get_cmp_mod(0)` : [input/output] input : `Cmp` containing $s^{J-1}$ (cf. the above equation) to start the iteration (if nothing is known a priori, this `Cmp` must be set to zero); output: value of $s^{J-1}$ , to used in a next call to the routine \ `par.get_int_mod(0)` : [output] number of iterations actually used to get the solution.
uu	[input/output] input : previously computed value of u to start the iteration (term R(u) ) (if nothing is known a priori, `uu` must be set to zero); 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

Implements Lorene::Map.

Definition at line 88 of file map_et_poisson_regu.C.

References Lorene::Cmp::get_etat().

◆ poisson_tau()

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

virtual

Computes the solution of a scalar Poisson equation with a Tau method.

Following the method explained in Sect. III.C of Bonazzola, Gourgoulhon & Marck, Phys. Rev. D 58 , 104020 (1998),
the Poisson equation $\Delta u = \sigma$ is re-written as $a \tilde\Delta u = \sigma + R(u)$ , where $\tilde\Delta$ is the Laplacian in an affine mapping and R(u) contains the terms generated by the deviation of the mapping *this from spherical symmetry. This equation is solved by iterations. At each step J the equation effectively solved is $\tilde\Delta u^{J+1} = s^J$ where

$s^J = 1/a_l^{\rm max} \{ {\tt source} + R(u^J) + (a_l^{\rm max}-a) [ \lambda s^{J-1} + (1-\lambda) s^{J-2} ] \} \ ,$

with $a_l^{\rm max} := \max(a)$ in domain no. l and $\lambda$ is a relaxation parameter.

Parameters

source	[input] source $\sigma$ of the Poisson equation
par	[input/output] parameters for the iterative method: \ `par.get_int(0)` : [input] maximum number of iterations \ `par.get_double(0)` : [input] relaxation parameter $\lambda$ \ `par.get_double(1)` : [input] required precision: the iterative method is stopped as soon as the relative difference between and $u^{J-1}$ is greater than `par.get_double(1)` \ `par.get_cmp_mod(0)` : [input/output] input : `Cmp` containing $s^{J-1}$ (cf. the above equation) to start the iteration (if nothing is known a priori, this `Cmp` must be set to zero); output: value of $s^{J-1}$ , to used in a next call to the routine \ `par.get_int_mod(0)` : [output] number of iterations actually used to get the solution.
uu	[input/output] input : previously computed value of u to start the iteration (term R(u) ) (if nothing is known a priori, `uu` must be set to zero); output: solution u with the boundary condition u =0 at spatial infinity.

Implements Lorene::Map.

Definition at line 357 of file map_et_poisson.C.

References Lorene::Cmp::get_etat().

◆ primr()

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

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

Implements Lorene::Map.

Definition at line 113 of file map_et_integ.C.

◆ reevaluate() [1/2]

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

virtualinherited

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`.

Implements Lorene::Map.

Definition at line 64 of file map_radial_reevaluate.C.

References Lorene::Cmp::get_dzpuis(), Lorene::Cmp::get_etat(), Lorene::Cmp::get_mp(), Lorene::Mg3d::get_nzone(), and Lorene::Map::mg.

◆ reevaluate() [2/2]

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

virtualinherited

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 `Scalar` at the grid points defined by `this`.

Implements Lorene::Map.

Definition at line 179 of file map_radial_reevaluate.C.

References Lorene::Scalar::get_dzpuis(), Lorene::Scalar::get_etat(), Lorene::Tensor::get_mp(), Lorene::Mg3d::get_nzone(), and Lorene::Map::mg.

◆ reevaluate_symy() [1/2]

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

virtualinherited

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

Case where the Cmp is symmetric with respect to 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`.

Implements Lorene::Map.

Definition at line 65 of file map_radial_reeval_symy.C.

References Lorene::Cmp::get_dzpuis(), Lorene::Cmp::get_etat(), Lorene::Cmp::get_mp(), Lorene::Mg3d::get_nzone(), and Lorene::Map::mg.

◆ reevaluate_symy() [2/2]

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

virtualinherited

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

Case where the Scalar is symmetric with respect to 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`.

Implements Lorene::Map.

Definition at line 199 of file map_radial_reeval_symy.C.

References Lorene::Scalar::get_dzpuis(), Lorene::Scalar::get_etat(), Lorene::Tensor::get_mp(), Lorene::Mg3d::get_nzone(), and Lorene::Map::mg.

◆ reset_coord()

void Lorene::Map_et::reset_coord ( )

protectedvirtual

Resets all the member Coords.

Reimplemented from Lorene::Map_radial.

Definition at line 651 of file map_et.C.

References Lorene::Coord::del_t(), Lorene::Map_radial::reset_coord(), rsx2drdx, and rsxdxdr.

◆ resize()

void Lorene::Map_et::resize	(	int	l,
		double	lambda
	)

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.

Implements Lorene::Map.

Definition at line 951 of file map_et.C.

References Lorene::Mg3d::get_type_r(), and Lorene::Map::mg.

◆ resize_extr()

void Lorene::Map_et::resize_extr ( double lambda )

Rescales the outer boundary of the outermost domain in the case of non-compactified external domain.

The inner boundary is unchanged.

Parameters

lambda [input] factor by which the value of the radius of the outermost domain is to be multiplied.

Definition at line 58 of file map_et_resize_extr.C.

References Lorene::Mg3d::get_nzone(), Lorene::Mg3d::get_type_r(), and Lorene::Map::mg.

◆ sauve()

void Lorene::Map_et::sauve ( FILE * fich ) const

virtual

Save in a file.

Reimplemented from Lorene::Map_radial.

Definition at line 802 of file map_et.C.

References alpha, beta, ff, Lorene::fwrite_be(), Lorene::Mg3d::get_nzone(), gg, Lorene::Map::mg, Lorene::Valeur::sauve(), and Lorene::Map_radial::sauve().

◆ set_alpha()

void Lorene::Map_et::set_alpha	(	double	alpha0,
		int	l
	)

Modifies the value of $\alpha$ in domain no. l.

Definition at line 447 of file map_et.C.

References alpha, and reset_coord().

◆ set_beta()

void Lorene::Map_et::set_beta	(	double	beta0,
		int	l
	)

Modifies the value of $\beta$ in domain no. l.

Definition at line 458 of file map_et.C.

References beta, and reset_coord().

◆ set_coord()

void Lorene::Map_et::set_coord ( )

private

Assignement of the building functions to the member Coords.

Definition at line 607 of file map_et.C.

◆ set_ff()

void Lorene::Map_et::set_ff ( const Valeur & ffi )

Assigns a given value to the function $F(\theta',\phi')$ .

Definition at line 585 of file map_et.C.

References ff, and reset_coord().

◆ set_gg()

void Lorene::Map_et::set_gg ( const Valeur & ggi )

Assigns a given value to the function $G(\theta',\phi')$ .

Definition at line 593 of file map_et.C.

References gg, and reset_coord().

◆ set_ori()

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

inherited

Sets a new origin.

Definition at line 256 of file map.C.

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

◆ set_rot_phi()

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

inherited

Sets a new rotation angle.

Definition at line 266 of file map.C.

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

◆ srdsdt() [1/2]

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

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`

Implements Lorene::Map.

Definition at line 340 of file map_et_deriv.C.

References Lorene::Cmp::get_etat().

◆ srdsdt() [2/2]

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

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`

Implements Lorene::Map.

Definition at line 394 of file map_et_deriv.C.

References Lorene::Scalar::get_etat().

◆ srstdsdp() [1/2]

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

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`

Implements Lorene::Map.

Definition at line 488 of file map_et_deriv.C.

References Lorene::Cmp::get_etat().

◆ srstdsdp() [2/2]

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

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`

Implements Lorene::Map.

Definition at line 543 of file map_et_deriv.C.

References Lorene::Scalar::get_etat().

◆ stdsdp()

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

virtual

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

Parameters

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

Implements Lorene::Map.

Definition at line 677 of file map_et_deriv.C.

References Lorene::Scalar::get_etat().

◆ val_lx() [1/2]

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

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 $\xi$

Implements Lorene::Map.

Definition at line 149 of file map_et_radius.C.

References Lorene::Param::add_double(), Lorene::Param::add_int(), and Lorene::Param::add_int_mod().

◆ val_lx() [2/2]

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

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: \ `par.get_int(0)` : [input] maximum number of iterations in the secant method to locate $\xi$ \ `par.get_int_mod(0)` : [output] effective number of iterations used \ `par.get_double(0)` : [input] absolute precision in the secant method to locate $\xi$
l	[output] value of the domain index
xi	[output] value of $\xi$

Implements Lorene::Map.

Definition at line 172 of file map_et_radius.C.

References Lorene::Param::get_double(), Lorene::Param::get_int(), Lorene::Param::get_int_mod(), Lorene::Mg3d::get_nzone(), Lorene::Mg3d::get_type_r(), and Lorene::Map::mg.

◆ val_lx_jk()

void Lorene::Map_et::val_lx_jk	(	double	rr,
		int	j,
		int	k,
		const Param &	par,
		int &	l,
		double &	xi
	)		const

virtual

Computes the domain index l and the value of $\xi$ corresponding to a point of arbitrary r but collocation values of $(\theta, \phi)$ .

Parameters

rr	[input] value of r
j	[input] index of the collocation point in $\theta$
k	[input] index of the collocation point in $\phi$
par	[input/output] parameters to control the accuracy of the computation: \ `par.get_int(0)` : [input] maximum number of iterations in the secant method to locate $\xi$ \ `par.get_int_mod(0)` : [output] effective number of iterations used \ `par.get_double(0)` : [input] absolute precision in the secant method to locate $\xi$
l	[output] value of the domain index
xi	[output] value of $\xi$

Implements Lorene::Map_radial.

Definition at line 421 of file map_et_radius.C.

References Lorene::Param::get_double(), Lorene::Param::get_int(), Lorene::Param::get_int_mod(), Lorene::Mg3d::get_nzone(), Lorene::Mg3d::get_type_r(), and Lorene::Map::mg.

◆ val_r()

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

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 $r=R_l(\xi, \theta', \phi')$

Implements Lorene::Map.

Definition at line 95 of file map_et_radius.C.

References ff, Lorene::Mg3d::get_type_r(), Lorene::Map::mg, and Lorene::Valeur::val_point().

◆ val_r_jk()

double Lorene::Map_et::val_r_jk	(	int	l,
		double	xi,
		int	j,
		int	k
	)		const

virtual

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

Parameters

l	[input] index of the domain
xi	[input] value of $\xi$
j	[input] index of the collocation point in $\theta'$
k	[input] index of the collocation point in $\phi'$

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

Implements Lorene::Map_radial.

Definition at line 370 of file map_et_radius.C.

References ff, Lorene::Mg3d::get_type_r(), and Lorene::Map::mg.

Member Data Documentation

◆ aa

Tbl** Lorene::Map_et::aa

private

Array (size: mg->nzone ) of Tbl which stores the values of $A(\xi)$ in each domain.

Definition at line 2783 of file map.h.

◆ aasx

Tbl Lorene::Map_et::aasx

private

Values at the nr collocation points of $A(\xi)/\xi$ in the nucleus.

Definition at line 2796 of file map.h.

◆ aasx2

Tbl Lorene::Map_et::aasx2

private

Values at the nr collocation points of $A(\xi)/\xi^2$ in the nucleus.

Definition at line 2799 of file map.h.

◆ alpha

double* Lorene::Map_et::alpha

private

Array (size: mg->nzone ) of the values of $\alpha$ in each domain.

Definition at line 2776 of file map.h.

◆ bb

Tbl** Lorene::Map_et::bb

private

Array (size: mg->nzone ) of Tbl which stores the values of $B(\xi)$ in each domain.

Definition at line 2814 of file map.h.

◆ bbsx

Tbl Lorene::Map_et::bbsx

private

Values at the nr collocation points of $B(\xi)/\xi$ in the nucleus.

Definition at line 2827 of file map.h.

◆ bbsx2

Tbl Lorene::Map_et::bbsx2

private

Values at the nr collocation points of $B(\xi)/\xi^2$ in the nucleus.

Definition at line 2830 of file map.h.

◆ beta

double* Lorene::Map_et::beta

private

Array (size: mg->nzone ) of the values of $\beta$ in each domain.

Definition at line 2778 of file map.h.

◆ bvect_cart

Base_vect_cart Lorene::Map::bvect_cart

protectedinherited

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

protectedinherited

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

inherited

$\cos\phi$

Definition at line 736 of file map.h.

◆ cost

Coord Lorene::Map::cost

inherited

$\cos\theta$

Definition at line 734 of file map.h.

◆ d2rdtdx

Coord Lorene::Map_radial::d2rdtdx

inherited

$\partial^2 R/\partial\xi\partial\theta'$ in the nucleus and in the non-compactified shells; \ $-\partial^2 U/\partial\xi\partial\theta'$ in the compactified outer domain.

Definition at line 1655 of file map.h.

◆ d2rdx2

Coord Lorene::Map_radial::d2rdx2

inherited

$\partial^2 R/\partial\xi^2$ in the nucleus and in the non-compactified shells; \ $-\partial^2 U/\partial\xi^2$ in the compactified outer domain.

Definition at line 1634 of file map.h.

◆ daa

Tbl** Lorene::Map_et::daa

private

Array (size: mg->nzone ) of Tbl which stores the values of $A'(\xi)$ in each domain.

Definition at line 2788 of file map.h.

◆ dbb

Tbl** Lorene::Map_et::dbb

private

Array (size: mg->nzone ) of Tbl which stores the values of $B'(\xi)$ in each domain.

Definition at line 2819 of file map.h.

◆ ddaa

Tbl** Lorene::Map_et::ddaa

private

Array (size: mg->nzone ) of Tbl which stores the values of $A''(\xi)$ in each domain.

Definition at line 2793 of file map.h.

◆ ddbb

Tbl** Lorene::Map_et::ddbb

private

Array (size: mg->nzone ) of Tbl which stores the values of $B''(\xi)$ in each domain.

Definition at line 2824 of file map.h.

◆ drdt

Coord Lorene::Map_radial::drdt

inherited

$\partial R/\partial\theta'$ in the nucleus and in the non-compactified shells; \ $-\partial U/\partial\theta'$ in the compactified external domain (CED).

Definition at line 1583 of file map.h.

◆ dxdr

Coord Lorene::Map_radial::dxdr

inherited

$1/(\partial R/\partial\xi) = \partial \xi /\partial r$ in the nucleus and in the non-compactified shells; \ $-1/(\partial U/\partial\xi) = - \partial \xi /\partial u$ in the compactified outer domain.

Definition at line 1575 of file map.h.

◆ ff

Valeur Lorene::Map_et::ff

private

Values of the function $F(\theta', \phi')$ at the nt*np angular collocation points in each domain.

The Valeur ff is defined on the multi-grid mg->g_angu (cf. class Mg3d ).

Definition at line 2837 of file map.h.

◆ gg

Valeur Lorene::Map_et::gg

private

Values of the function $G(\theta', \phi')$ at the nt*np angular collocation points in each domain.

The Valeur gg is defined on the multi-grid mg->g_angu (cf. class Mg3d ).

Definition at line 2844 of file map.h.

◆ lapr_tp

Coord Lorene::Map_radial::lapr_tp

inherited

$1/R^2 \times [ 1/\sin(\theta)\times \partial /\partial\theta' (\sin\theta \partial R /\partial\theta') + 1/\sin^2\theta \partial^2 R /\partial{\varphi'}^2]$ in the nucleus and in the non-compactified shells; \ $- 1/U^2 \times [ 1/\sin(\theta)\times \partial /\partial\theta' (\sin\theta \partial U /\partial\theta') + 1/\sin^2\theta \partial^2 U /\partial{\varphi'}^2]$ in the compactified outer domain.

Definition at line 1646 of file map.h.

◆ mg

const Mg3d* Lorene::Map::mg

protectedinherited

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

protectedinherited

Absolute coordinate x of the origin.

Definition at line 690 of file map.h.

◆ ori_y

double Lorene::Map::ori_y

protectedinherited

Absolute coordinate y of the origin.

Definition at line 691 of file map.h.

◆ ori_z

double Lorene::Map::ori_z

protectedinherited

Absolute coordinate z of the origin.

Definition at line 692 of file map.h.

◆ p_cmp_zero

Cmp* Lorene::Map::p_cmp_zero

protectedinherited

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

mutableprotectedinherited

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

mutableprotectedinherited

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

mutableprotectedinherited

Pointer on the "angular" mapping.

Definition at line 727 of file map.h.

◆ phi

Coord Lorene::Map::phi

inherited

$\phi$ coordinate centered on the grid

Definition at line 732 of file map.h.

◆ r

Coord Lorene::Map::r

inherited

r coordinate centered on the grid

Definition at line 730 of file map.h.

◆ rot_phi

double Lorene::Map::rot_phi

protectedinherited

Angle between the x –axis and X –axis.

Definition at line 693 of file map.h.

◆ rsx2drdx

Coord Lorene::Map_et::rsx2drdx

$[ R/ (\alpha \xi + \beta) ]^2 (\partial R/\partial \xi) / \alpha$ in the nucleus and the shells; \ $\partial U/\partial \xi / \alpha$ in the outermost compactified domain.

Definition at line 2859 of file map.h.

◆ rsxdxdr

Coord Lorene::Map_et::rsxdxdr

$1/(\partial R/\partial \xi) R/\xi$ in the nucleus; \ $1/(\partial R/\partial \xi) R/(\xi + \beta/\alpha)$ in the shells; \ $1/(\partial U/\partial \xi) U/(\xi-1)$ in the outermost compactified domain.

Definition at line 2852 of file map.h.

◆ sinp

Coord Lorene::Map::sinp

inherited

$\sin\phi$

Definition at line 735 of file map.h.

◆ sint

Coord Lorene::Map::sint

inherited

$\sin\theta$

Definition at line 733 of file map.h.

◆ sr2d2rdt2

Coord Lorene::Map_radial::sr2d2rdt2

inherited

$1/R^2 \partial^2 R/\partial{\theta'}^2$ in the nucleus and in the non-compactified shells; \ $-1/U^2 \partial^2 U/\partial{\theta'}^2$ in the compactified outer domain.

Definition at line 1672 of file map.h.

◆ sr2drdt

Coord Lorene::Map_radial::sr2drdt

inherited

$1/R^2 \times (\partial R/\partial\theta')$ in the nucleus and in the non-compactified shells; \ $-1/U^2 \times (\partial U/\partial\theta')$ in the compactified outer domain.

Definition at line 1615 of file map.h.

◆ sr2stdrdp

Coord Lorene::Map_radial::sr2stdrdp

inherited

$1/(R^2\sin\theta) \times (\partial R/\partial\varphi')$ in the nucleus and in the non-compactified shells; \ $-1/(U^2\sin\theta) \times (\partial U/\partial\varphi')$ in the compactified outer domain.

Definition at line 1623 of file map.h.

◆ srdrdt

Coord Lorene::Map_radial::srdrdt

inherited

$1/R \times (\partial R/\partial\theta')$ in the nucleus and in the non-compactified shells; \ $-1/U \times (\partial U/\partial\theta)$ in the compactified outer domain.

Definition at line 1599 of file map.h.

◆ srstdrdp

Coord Lorene::Map_radial::srstdrdp

inherited

$1/(R\sin\theta) \times (\partial R/\partial\varphi')$ in the nucleus and in the non-compactified shells; \ $-1/(U\sin\theta) \times (\partial U/\partial\varphi')$ in the compactified outer domain.

Definition at line 1607 of file map.h.

◆ sstd2rdpdx

Coord Lorene::Map_radial::sstd2rdpdx

inherited

$1/\sin\theta \times \partial^2 R/\partial\xi\partial\varphi'$ in the nucleus and in the non-compactified shells; \ $-1/\sin\theta \times \partial^2 U/\partial\xi\partial\varphi'$ in the compactified outer domain.

Definition at line 1663 of file map.h.

◆ stdrdp

Coord Lorene::Map_radial::stdrdp

inherited

${1\over\sin\theta} \partial R/\partial\varphi'$ in the nucleus and in the non-compactified shells; \ $-{1\over\sin\theta}\partial U/\partial\varphi'$ in the compactified external domain (CED).

Definition at line 1591 of file map.h.

◆ tet

Coord Lorene::Map::tet

inherited

$\theta$ coordinate centered on the grid

Definition at line 731 of file map.h.

◆ x

Coord Lorene::Map::x

inherited

x coordinate centered on the grid

Definition at line 738 of file map.h.

◆ xa

Coord Lorene::Map::xa

inherited

Absolute x coordinate.

Definition at line 742 of file map.h.

◆ xsr

Coord Lorene::Map_radial::xsr

inherited

$\xi/R$ in the nucleus; \ 1/R in the non-compactified shells; \ $(\xi-1)/U$ in the compactified outer domain.

Definition at line 1564 of file map.h.

◆ y

Coord Lorene::Map::y

inherited

y coordinate centered on the grid

Definition at line 739 of file map.h.

◆ ya

Coord Lorene::Map::ya

inherited

Absolute y coordinate.

Definition at line 743 of file map.h.

◆ z

Coord Lorene::Map::z

inherited

z coordinate centered on the grid

Definition at line 740 of file map.h.

◆ za

Coord Lorene::Map::za

inherited

Absolute z coordinate.

Definition at line 744 of file map.h.

◆ zaasx

Tbl Lorene::Map_et::zaasx

private

Values at the nr collocation points of $A(\xi)/(\xi-1)$ in the outermost compactified domain.

Definition at line 2804 of file map.h.

◆ zaasx2

Tbl Lorene::Map_et::zaasx2

private

Values at the nr collocation points of $A(\xi)/(\xi-1)^2$ in the outermost compactified domain.

Definition at line 2809 of file map.h.

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

Public Member Functions

Public Attributes

Protected Member Functions

Protected Attributes

Private Member Functions

Private Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Map_et() [1/4]

◆ Map_et() [2/4]

◆ Map_et() [3/4]

◆ Map_et() [4/4]

◆ ~Map_et()

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]

◆ fait_poly()

◆ flat_met_cart()

◆ flat_met_spher()

◆ get_alpha()

◆ get_beta()

◆ get_bvect_cart()

◆ get_bvect_spher()

◆ get_ff()

◆ get_gg()

◆ 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=() [1/2]

◆ operator=() [2/2]

◆ operator==()

◆ operator>>()

◆ poisson()

◆ poisson2d()