Divergence-free vectors. More...

#include <vector.h>

Inheritance diagram for Lorene::Vector_divfree:

Public Member Functions
	Vector_divfree (const Map &map, const Base_vect &triad_i, const Metric &met)
	Standard constructor. More...

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

	Vector_divfree (const Map &map, const Base_vect &triad_i, const Metric &met, FILE *fich)
	Constructor from a file (see `Tensor::sauve(FILE*)` ). More...

virtual	~Vector_divfree ()
	Destructor. More...

void	operator= (const Vector_divfree &a)
	Assignment from another `Vector_divfree`. More...

virtual void	operator= (const Vector &a)
	Assignment from a `Vector`. More...

virtual void	operator= (const Tensor &a)
	Assignment from a `Tensor`. More...

void	set_vr_mu (const Scalar &vr_i, const Scalar &mu_i)
	Sets the angular potentials $\mu$ (see member `p_mu` ), and the component of the vector. More...

void	set_vr_eta_mu (const Scalar &vr_i, const Scalar &eta_i, const Scalar &mu_i)
	Defines the components through , $\eta$ and $\mu$ . More...

void	set_A_mu (const Scalar &A_i, const Scalar &mu_i, const Param *par_bc)
	Defines the components through potentials and $\mu$ . More...

virtual const Scalar &	eta () const
	Gives the field $\eta$ such that the angular components $(V^\theta, V^\varphi)$ of the vector are written: $V^\theta = {\partial \eta \over \partial\theta} - {1\over\sin\theta} {\partial \mu \over \partial\varphi}$ $V^\varphi = {1\over\sin\theta} {\partial \eta \over \partial\varphi} + {\partial \mu \over \partial\theta}$ . More...

Vector_divfree	poisson () const
	Computes the solution of a vectorial Poisson equation with `*this` $= \vec{V}$ as a source: $\Delta \vec{W} = \vec{V}$ . More...

void	update_etavr ()
	Computes the components and $\eta$ from the potential A and the divergence-free condition, according to : ${\partial \eta \over \ partial r} + { \eta \over r} - {V^r \over r} = A$ ${\partial V^r \over \partial r} + {2 V^r \over r} + {1 \over r} \Delta_{\vartheta \varphi} \eta = 0$ . More...

Vector_divfree	poisson (Param &par) const
	Computes the solution of a vectorial Poisson equation with `*this` $= \vec{V}$ as a source: $\Delta \vec{W} = \vec{V}$ . More...

virtual void	change_triad (const Base_vect &)
	Sets a new vectorial basis (triad) of decomposition and modifies the components accordingly. More...

void	decompose_div (const Metric &) const
	Makes the Helmholtz decomposition (see documentation of `p_potential` ) of `this` with respect to a given `Metric` , only in the case of contravariant vectors. More...

const Scalar &	potential (const Metric &) const
	Returns the potential in the Helmholtz decomposition. More...

const Vector_divfree &	div_free (const Metric &) const
	Returns the div-free vector in the Helmholtz decomposition. More...

virtual void	exponential_filter_r (int lzmin, int lzmax, int p, double alpha=-16.)
	Applies exponential filters to all components (see `Scalar::exponential_filter_r` ). More...

virtual void	exponential_filter_ylm (int lzmin, int lzmax, int p, double alpha=-16.)
	Applies exponential filters to all components (see `Scalar::exponential_filter_ylm` ). More...

Scalar &	set (int)
	Read/write access to a component. More...

Scalar &	set (const Itbl &ind)
	Returns the value of a component (read/write version). More...

Scalar &	set (int i1, int i2)
	Returns the value of a component for a tensor of valence 2 (read/write version). More...

Scalar &	set (int i1, int i2, int i3)
	Returns the value of a component for a tensor of valence 3 (read/write version). More...

Scalar &	set (int i1, int i2, int i3, int i4)
	Returns the value of a component for a tensor of valence 4 (read/write version). More...

const Scalar &	operator() (int) const
	Readonly access to a component. More...

const Scalar &	operator() (const Itbl &ind) const
	Returns the value of a component (read-only version). More...

const Scalar &	operator() (int i1, int i2) const
	Returns the value of a component for a tensor of valence 2 (read-only version). More...

const Scalar &	operator() (int i1, int i2, int i3) const
	Returns the value of a component for a tensor of valence 3 (read-only version). More...

const Scalar &	operator() (int i1, int i2, int i3, int i4) const
	Returns the value of a component for a tensor of valence 4 (read-only version). More...

virtual int	position (const Itbl &idx) const
	Returns the position in the `Scalar` array `cmp` of a component given by its index. More...

virtual Itbl	indices (int place) const
	Returns the index of a component given by its position in the `Scalar` array `cmp` . More...

virtual void	std_spectral_base ()
	Sets the standard spectal bases of decomposition for each component. More...

virtual void	pseudo_spectral_base ()
	Sets the standard spectal bases of decomposition for each component for a pseudo_vector. More...

virtual const Scalar &	mu () const
	Gives the field $\mu$ such that the angular components $(V^\theta, V^\varphi)$ of the vector are written: $V^\theta = {\partial \eta \over \partial\theta} - {1\over\sin\theta} {\partial \mu \over \partial\varphi}$ $V^\varphi = {1\over\sin\theta} {\partial \eta \over \partial\varphi} + {\partial \mu \over \partial\theta}$ . More...

virtual const Scalar &	A () const
	Gives the field defined by $A = {\partial \eta \over \partial r} + { \eta \over r} - {V^r \over r}$ Related to the curl, A is insensitive to the longitudinal part of the vector. More...

void	update_vtvp ()
	Computes the components $V^\theta$ and $V^\varphi$ from the potential $\eta$ and $\mu$ , according to: $V^\theta = {\partial \eta \over \partial\theta} - {1\over\sin\theta} {\partial \mu \over \partial\varphi}$ $V^\varphi = {1\over\sin\theta} {\partial \eta \over \partial\varphi} + {\partial \mu \over \partial\theta}$ . More...

const Scalar &	divergence (const Metric &) const
	The divergence of `this` with respect to a `Metric` . More...

const Vector_divfree	curl () const
	The curl of `this` with respect to a (flat) `Metric` . More...

Vector	derive_lie (const Vector &v) const
	Computes the Lie derivative of `this` with respect to some vector field `v`. More...

Sym_tensor	ope_killing (const Metric &gam) const
	Computes the Killing operator associated with a given metric. More...

Sym_tensor	ope_killing_conf (const Metric &gam) const
	Computes the conformal Killing operator associated with a given metric. More...

Vector	poisson (double lambda, int method=6) const
	Solves the vector Poisson equation with `*this` as a source. More...

Vector	poisson (double lambda, const Metric_flat &met_f, int method=6) const
	Solves the vector Poisson equation with `*this` as a source. More...

Vector	poisson (const double lambda, Param &par, int method=6) const
	Solves the vector Poisson equation with `*this` as a source and parameters controlling the solution. More...

void	poisson_boundary (double lambda, const Mtbl_cf &limit_vr, const Mtbl_cf &limit_eta, const Mtbl_cf &limit_mu, int num_front, double fact_dir, double fact_neu, Vector &resu) const
	Solves the vector Poisson equation with `*this` as a source with a boundary condition on the excised sphere. More...

void	poisson_boundary2 (double lam, Vector &resu, Scalar boundvr, Scalar boundeta, Scalar boundmu, double dir_vr, double neum_vr, double dir_eta, double neum_eta, double dir_mu, double neum_mu) const
	Alternative to previous poisson_boundary method for vectors ; this uses method 6 for vectorial solving, updated version (as in the poisson_vector_block routine). More...

Vector	poisson_dirichlet (double lambda, const Valeur &limit_vr, const Valeur &limit_vt, const Valeur &limit_vp, int num_front) const

Vector	poisson_neumann (double lambda, const Valeur &limit_vr, const Valeur &limit_vt, const Valeur &limit_vp, int num_front) const
	Solves the vector Poisson equation with `*this` as a source with a boundary condition on the excised sphere. More...

Vector	poisson_robin (double lambda, const Valeur &limit_vr, const Valeur &limit_vt, const Valeur &limit_vp, double fact_dir, double fact_neu, int num_front) const
	Solves the vector Poisson equation with `*this` as a source with a boundary condition on the excised sphere. More...

double	flux (double radius, const Metric &met) const
	Computes the flux of the vector accross a sphere r = const. More...

void	poisson_block (double lambda, Vector &resu) const

void	visu_arrows (double xmin, double xmax, double ymin, double ymax, double zmin, double zmax, const char title0=0x0, const char filename0=0x0, bool start_dx=true, int nx=8, int ny=8, int nz=8) const
	3D visualization via OpenDX. More...

void	visu_streamline (double xmin, double xmax, double ymin, double ymax, double zmin, double zmax, const char title0=0x0, const char filename0=0x0, bool start_dx=true, int nx=8, int ny=8, int nz=8) const

virtual void	set_etat_nondef ()
	Sets the logical state of all components to `ETATNONDEF` (undefined state). More...

virtual void	set_etat_zero ()
	Sets the logical state of all components to `ETATZERO` (zero state). More...

virtual void	set_etat_qcq ()
	Sets the logical state of all components to `ETATQCQ` (ordinary state). More...

virtual void	allocate_all ()
	Performs the memory allocation of all the elements, down to the `double` arrays of the `Tbl` s. More...

void	set_triad (const Base_vect &new_triad)
	Assigns a new vectorial basis (triad) of decomposition. More...

void	annule_domain (int l)
	Sets the `Tensor` to zero in a given domain. More...

virtual void	annule (int l_min, int l_max)
	Sets the `Tensor` to zero in several domains. More...

void	annule_extern_cn (int l_0, int deg)
	Performs a smooth (C^n) transition in a given domain to zero. More...

virtual void	std_spectral_base_odd ()
	Sets the standard odd spectal bases of decomposition for each component. More...

virtual void	dec_dzpuis (int dec=1)
	Decreases by `dec` units the value of `dzpuis` and changes accordingly the values in the compactified external domain (CED). More...

virtual void	inc_dzpuis (int inc=1)
	Increases by `inc` units the value of `dzpuis` and changes accordingly the values in the compactified external domain (CED). More...

virtual void	exponential_filter_ylm_phi (int lzmin, int lzmax, int p_r, int p_tet, int p_phi, double alpha=-16.)
	Applies exponential filters to all components (see `Scalar::exponential_filter_ylm_phi` ). More...

const Tensor &	derive_cov (const Metric &gam) const
	Returns the covariant derivative of `this` with respect to some metric $\gamma$ . More...

const Tensor &	derive_con (const Metric &gam) const
	Returns the "contravariant" derivative of `this` with respect to some metric $\gamma$ , by raising the last index of the covariant derivative (cf. More...

Tensor	up (int ind, const Metric &gam) const
	Computes a new tensor by raising an index of `*this`. More...

Tensor	down (int ind, const Metric &gam) const
	Computes a new tensor by lowering an index of `*this`. More...

Tensor	up_down (const Metric &gam) const
	Computes a new tensor by raising or lowering all the indices of `*this` . More...

Tensor	trace (int ind1, int ind2) const
	Trace on two different type indices. More...

Tensor	trace (int ind1, int ind2, const Metric &gam) const
	Trace with respect to a given metric. More...

Scalar	trace () const
	Trace on two different type indices for a valence 2 tensor. More...

Scalar	trace (const Metric &gam) const
	Trace with respect to a given metric for a valence 2 tensor. More...

const Map &	get_mp () const
	Returns the mapping. More...

const Base_vect *	get_triad () const
	Returns the vectorial basis (triad) on which the components are defined. More...

int	get_valence () const
	Returns the valence. More...

int	get_n_comp () const
	Returns the number of stored components. More...

int	get_index_type (int i) const
	Gives the type (covariant or contravariant) of the index number `i` . More...

Itbl	get_index_type () const
	Returns the types of all the indices. More...

int &	set_index_type (int i)
	Sets the type of the index number `i` . More...

Itbl &	set_index_type ()
	Sets the types of all the indices. More...

void	operator+= (const Tensor &)
	+= Tensor More...

void	operator-= (const Tensor &)
	-= Tensor More...

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

virtual void	spectral_display (const char *comment=0x0, double threshold=1.e-7, int precision=4, ostream &ostr=cout) const
	Displays the spectral coefficients and the associated basis functions of each component. More...

Protected Member Functions
virtual void	del_deriv () const
	Deletes the derived quantities. More...

void	set_der_0x0 () const
	Sets the pointers on derived quantities to 0x0. More...

void	sol_Dirac_A (const Scalar &aaa, Scalar &eta, Scalar &vr, const Param *par_bc=0x0) const
	Solves a system of two-coupled first-order PDEs obtained from the divergence-free condition and the requirement that the potential A has a given value. More...

void	sol_Dirac_A_tau (const Scalar &aaa, Scalar &eta, Scalar &vr, const Param *par_bc=0x0) const
	Solves via a tau method a system of two-coupled first-order PDEs obtained from the divergence-free condition and the requirement that the potential A has a given value. More...

void	sol_Dirac_A_poisson (const Scalar &aaa, Scalar &eta, Scalar &vr, const Param *par_bc=0x0) const
	Solves via a poisson method a system of two-coupled first-order PDEs obtained from the divergence-free condition and the requirement that the potential A has a given value. More...

void	sol_Dirac_A_1z (const Scalar &aaa, Scalar &eta, Scalar &vr, const Param *par_bc=0x0) const
	Solves a one-domain system of two-coupled first-order PDEs obtained from the divergence-free condition and the requirement that the potential A has a given value. More...

virtual void	del_derive_met (int) const
	Logical destructor of the derivatives depending on the i-th element of `met_depend` in the class `Vector`. More...

void	set_der_met_0x0 (int) const
	Sets all the i-th components of `met_depend` in the class `Vector` (`p_potential` , etc...) to 0x0. More...

void	set_dependance (const Metric &) const
	To be used to describe the fact that the derivatives members have been calculated with `met` . More...

int	get_place_met (const Metric &) const
	Returns the position of the pointer on `metre` in the array `met_depend` . More...

void	compute_derive_lie (const Vector &v, Tensor &resu) const
	Computes the Lie derivative of `this` with respect to some vector field `v` (protected method; the public interface is method `derive_lie` ). More...

Protected Attributes
const Metric *const	met_div
	Metric with respect to which the divergence is defined. More...

Scalar *	p_potential [N_MET_MAX]
	The potential $\phi$ giving the gradient part in the Helmholtz decomposition of any 3D vector $\vec{V}: \quad \vec{V} = \vec{\nabla} \phi + \vec{\nabla} \wedge \vec{\psi}$ . More...

Vector_divfree *	p_div_free [N_MET_MAX]
	The divergence-free vector $\vec{W} = \vec{\nabla} \wedge \vec{\psi}$ of the Helmholtz decomposition of any 3D vector $\vec{V}: \quad \vec{V} = \vec{\nabla} \phi + \vec{\nabla} *\wedge \vec{\psi}$ . More...

Scalar *	p_eta
	Field $\eta$ such that the angular components $(V^\theta, V^\varphi)$ of the vector are written: $V^\theta = {\partial \eta \over \partial\theta} - {1\over\sin\theta} {\partial \mu \over \partial\varphi}$ $V^\varphi = {1\over\sin\theta} {\partial \eta \over \partial\varphi} + {\partial \mu \over \partial\theta}$ . More...

Scalar *	p_mu
	Field $\mu$ such that the angular components $(V^\theta, V^\varphi)$ of the vector are written: $V^\theta = {\partial \eta \over \partial\theta} - {1\over\sin\theta} {\partial \mu \over \partial\varphi}$ $V^\varphi = {1\over\sin\theta} {\partial \eta \over \partial\varphi} + {\partial \mu \over \partial\theta}$ . More...

Scalar *	p_A
	Field defined by $A = {\partial \eta \over \ partial r} + { \eta \over r} - {V^r \over r}$ Insensitive to the longitudinal part of the vector, related to the curl. More...

const Map *const	mp
	Mapping on which the numerical values at the grid points are defined. More...

int	valence
	Valence of the tensor (0 = scalar, 1 = vector, etc...) More...

const Base_vect *	triad
	Vectorial basis (triad) with respect to which the tensor components are defined. More...

Itbl	type_indice
	1D array of integers (class `Itbl` ) of size `valence` containing the type of each index: `COV` for a covariant one and `CON` for a contravariant one. More...

int	n_comp
	Number of stored components, depending on the symmetry. More...

Scalar **	cmp
	Array of size `n_comp` of pointers onto the components. More...

const Metric *	met_depend [N_MET_MAX]
	Array on the `Metric` 's which were used to compute derived quantities, like `p_derive_cov` , etc... More...

Tensor *	p_derive_cov [N_MET_MAX]
	Array of pointers on the covariant derivatives of `this` with respect to various metrics. More...

Tensor *	p_derive_con [N_MET_MAX]
	Array of pointers on the contravariant derivatives of `this` with respect to various metrics. More...

Tensor *	p_divergence [N_MET_MAX]
	Array of pointers on the divergence of `this` with respect to various metrics. More...

Detailed Description

Divergence-free vectors.

()

This class is designed to store divergence-free vectors, with the component expressed in a orthonormal spherical basis $(e_r,e_\theta,e_\varphi)$ .

Definition at line 724 of file vector.h.

Constructor & Destructor Documentation

◆ Vector_divfree() [1/3]

Lorene::Vector_divfree::Vector_divfree	(	const Map &	map,
		const Base_vect &	triad_i,
		const Metric &	met
	)

Standard constructor.

Parameters

map	the mapping
triad_i	vectorial basis (triad) with respect to which the vector components are defined
met	the metric with respect to which the divergence is defined

Definition at line 82 of file vector_divfree.C.

References set_der_0x0().

◆ Vector_divfree() [2/3]

Lorene::Vector_divfree::Vector_divfree ( const Vector_divfree & source )

Copy constructor.

Definition at line 94 of file vector_divfree.C.

References Lorene::Vector::p_eta, Lorene::Vector::p_mu, and set_der_0x0().

◆ Vector_divfree() [3/3]

Lorene::Vector_divfree::Vector_divfree	(	const Map &	map,
		const Base_vect &	triad_i,
		const Metric &	met,
		FILE *	fich
	)

Constructor from a file (see Tensor::sauve(FILE*) ).

Parameters

map	the mapping
triad_i	vectorial basis (triad) with respect to which the tensor components are defined. It will be checked that it coincides with the basis saved in the file.
met	the metric with respect to which the divergence is defined
fich	file which has been created by the function `sauve(FILE*)` .

Definition at line 106 of file vector_divfree.C.

References set_der_0x0().

◆ ~Vector_divfree()

Lorene::Vector_divfree::~Vector_divfree ( )

virtual

Destructor.

Definition at line 120 of file vector_divfree.C.

References del_deriv().

Member Function Documentation

◆ A()

const Scalar & Lorene::Vector::A ( ) const

virtualinherited

Gives the field $A$ defined by

$A = {\partial \eta \over \partial r} + { \eta \over r} - {V^r \over r}$

Related to the curl, A is insensitive to the longitudinal part of the vector.

Definition at line 138 of file vector_etamu.C.

References Lorene::Tensor::cmp, Lorene::Scalar::div_r_dzpuis(), Lorene::Scalar::dsdr(), Lorene::Vector::eta(), Lorene::Vector::p_A, Lorene::Vector::p_eta, Lorene::Scalar::set_dzpuis(), and Lorene::Tensor::triad.

◆ allocate_all()

void Lorene::Tensor::allocate_all ( )

virtualinherited

Performs the memory allocation of all the elements, down to the double arrays of the Tbl s.

This function performs in fact recursive calls to set_etat_qcq() on each element of the chain Scalar -> Valeur -> Mtbl -> Tbl .

Reimplemented in Lorene::Scalar.

Definition at line 517 of file tensor.C.

References Lorene::Scalar::allocate_all(), Lorene::Tensor::cmp, Lorene::Tensor::del_deriv(), and Lorene::Tensor::n_comp.

◆ annule()

void Lorene::Tensor::annule	(	int	l_min,
		int	l_max
	)

virtualinherited

Sets the Tensor to zero in several domains.

Parameters

l_min	[input] The `Tensor` will be set (logically) to zero in the domains whose indices are in the range [l_min,l_max] .
l_max	[input] see the comments for `l_min` .

Note that annule(0,nz-1) , where nz is the total number of domains, is equivalent to set_etat_zero() .

Reimplemented in Lorene::Scalar.

Definition at line 680 of file tensor.C.

References Lorene::Scalar::annule(), Lorene::Tensor::cmp, Lorene::Tensor::del_deriv(), Lorene::Map::get_mg(), Lorene::Mg3d::get_nzone(), Lorene::Tensor::mp, Lorene::Tensor::n_comp, and Lorene::Tensor::set_etat_zero().

◆ annule_domain()

void Lorene::Tensor::annule_domain ( int l )

inherited

Sets the Tensor to zero in a given domain.

Parameters

l	[input] Index of the domain in which the `Tensor` will be set (logically) to zero.

Definition at line 675 of file tensor.C.

References Lorene::Tensor::annule().

◆ annule_extern_cn()

void Lorene::Tensor::annule_extern_cn	(	int	l_0,
		int	deg
	)

inherited

Performs a smooth (C^n) transition in a given domain to zero.

Parameters

l_0	[input] in the domain of index l0 the tensor is multiplied by the right polynomial (of degree 2n+1), to ensure continuty of the function and its n first derivative at both ends of this domain. The tensor is unchanged in the domains l < l_0 and set to zero in domains l > l_0.
deg	[input] the degree n of smoothness of the transition.

Definition at line 699 of file tensor.C.

References Lorene::Map::get_mg(), Lorene::Mg3d::get_type_r(), and Lorene::Tensor::mp.

◆ change_triad()

void Lorene::Vector::change_triad ( const Base_vect & new_triad )

virtualinherited

Sets a new vectorial basis (triad) of decomposition and modifies the components accordingly.

Reimplemented from Lorene::Tensor.

Definition at line 78 of file vector_change_triad.C.

References Lorene::Tensor::cmp, Lorene::Map::comp_p_from_cartesian(), Lorene::Map::comp_r_from_cartesian(), Lorene::Map::comp_t_from_cartesian(), Lorene::Map::comp_x_from_spherical(), Lorene::Map::comp_y_from_spherical(), Lorene::Map::comp_z_from_spherical(), Lorene::Base_vect_cart::get_align(), Lorene::Map::get_bvect_cart(), Lorene::Map::get_bvect_spher(), Lorene::Map::get_mg(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_nzone(), Lorene::Tensor::mp, and Lorene::Tensor::triad.

◆ compute_derive_lie()

void Lorene::Tensor::compute_derive_lie	(	const Vector &	v,
		Tensor &	resu
	)		const

protectedinherited

Computes the Lie derivative of this with respect to some vector field v (protected method; the public interface is method derive_lie ).

Definition at line 342 of file tensor_calculus.C.

References Lorene::Tensor::cmp, Lorene::contract(), Lorene::Scalar::dec_dzpuis(), Lorene::Tensor::derive_cov(), Lorene::Map::flat_met_cart(), Lorene::Map::flat_met_spher(), Lorene::Scalar::get_dzpuis(), Lorene::Tensor::get_n_comp(), Lorene::Tensor::get_triad(), Lorene::Tensor::indices(), Lorene::Tensor::mp, Lorene::Tensor::n_comp, Lorene::Tensor::operator()(), Lorene::Itbl::set(), Lorene::Tensor::set(), Lorene::Tensor::triad, Lorene::Tensor::type_indice, and Lorene::Tensor::valence.

◆ curl()

const Vector_divfree Lorene::Vector::curl ( ) const

inherited

The curl of this with respect to a (flat) Metric .

The Vector is assumed to be contravariant.

Definition at line 408 of file vector.C.

References Lorene::Tensor::cmp, Lorene::Scalar::div_r(), Lorene::Scalar::div_tant(), Lorene::Scalar::dsdt(), Lorene::Scalar::dsdx(), Lorene::Scalar::dsdy(), Lorene::Scalar::dsdz(), Lorene::Map::flat_met_cart(), Lorene::Map::flat_met_spher(), Lorene::Map::get_bvect_cart(), Lorene::Map::get_bvect_spher(), Lorene::Base_vect::identify(), Lorene::Tensor::mp, Lorene::Scalar::mult_r(), Lorene::Vector::set(), Lorene::Tensor::set(), Lorene::Scalar::srstdsdp(), and Lorene::Tensor::triad.

◆ dec_dzpuis()

void Lorene::Tensor::dec_dzpuis ( int dec = 1 )

virtualinherited

Decreases by dec units the value of dzpuis and changes accordingly the values in the compactified external domain (CED).

Reimplemented in Lorene::Scalar.

Definition at line 817 of file tensor.C.

References Lorene::Tensor::cmp, Lorene::Tensor::del_deriv(), and Lorene::Tensor::n_comp.

◆ decompose_div()

void Lorene::Vector::decompose_div ( const Metric & metre ) const

inherited

Makes the Helmholtz decomposition (see documentation of p_potential ) of this with respect to a given Metric , only in the case of contravariant vectors.

Definition at line 522 of file vector.C.

References Lorene::Scalar::check_dzpuis(), Lorene::Tensor::cmp, Lorene::Vector::divergence(), Lorene::Scalar::get_dzpuis(), Lorene::Scalar::get_etat(), Lorene::Map::get_mg(), Lorene::Mg3d::get_nzone(), Lorene::Tensor::get_place_met(), Lorene::Tensor::mp, Lorene::Vector::p_div_free, Lorene::Vector::p_potential, Lorene::Tensor::set_dependance(), and Lorene::Tensor::type_indice.

◆ del_deriv()

void Lorene::Vector_divfree::del_deriv ( ) const

protectedvirtual

Deletes the derived quantities.

Reimplemented from Lorene::Vector.

Definition at line 131 of file vector_divfree.C.

References Lorene::Vector::del_deriv(), and set_der_0x0().

◆ del_derive_met()

void Lorene::Vector::del_derive_met ( int j ) const

protectedvirtualinherited

Logical destructor of the derivatives depending on the i-th element of met_depend in the class Vector.

Reimplemented from Lorene::Tensor.

Definition at line 248 of file vector.C.

References Lorene::Tensor::del_derive_met(), Lorene::Tensor::met_depend, Lorene::Vector::p_div_free, Lorene::Vector::p_potential, and Lorene::Vector::set_der_met_0x0().

◆ derive_con()

const Tensor & Lorene::Tensor::derive_con ( const Metric & gam ) const

inherited

Returns the "contravariant" derivative of this with respect to some metric $\gamma$ , by raising the last index of the covariant derivative (cf.

method derive_cov() ) with $\gamma$ .

Definition at line 1023 of file tensor.C.

References Lorene::Metric::con(), Lorene::contract(), Lorene::Tensor::derive_cov(), Lorene::Tensor::get_index_type(), Lorene::Tensor::get_place_met(), Lorene::Tensor::mp, Lorene::Tensor::p_derive_con, Lorene::Itbl::set(), Lorene::Tensor::set_dependance(), Lorene::Tensor_sym::sym_index1(), Lorene::Tensor_sym::sym_index2(), Lorene::Tensor::Tensor(), Lorene::Tensor::triad, and Lorene::Tensor::valence.

◆ derive_cov()

const Tensor & Lorene::Tensor::derive_cov ( const Metric & gam ) const

inherited

Returns the covariant derivative of this with respect to some metric $\gamma$ .

$T$ denoting the tensor represented by this and $\nabla T$ its covariant derivative with respect to the metric $\gamma$ , the extra index (with respect to the indices of $T$ ) of $\nabla T$ is chosen to be the last one. This convention agrees with that of MTW (see Eq. (10.17) of MTW). For instance, if $T$ is a 1-form, whose components w.r.t. the triad $e^i$ are $T_i$ : $T=T_i \; e^i$ , then the covariant derivative of $T$ is the bilinear form $\nabla T$ whose components $\nabla_j T_i$ are such that

$\nabla T = \nabla_j T_i \; e^i \otimes e^j$

Parameters

gam	metric $\gamma$

Returns: covariant derivative $\nabla T$ of this with respect to the connection $\nabla$ associated with the metric $\gamma$

Definition at line 1011 of file tensor.C.

References Lorene::Metric::connect(), Lorene::Tensor::get_place_met(), Lorene::Connection::p_derive_cov(), Lorene::Tensor::p_derive_cov, and Lorene::Tensor::set_dependance().

◆ derive_lie()

Vector Lorene::Vector::derive_lie ( const Vector & v ) const

inherited

Computes the Lie derivative of this with respect to some vector field v.

Definition at line 398 of file vector.C.

References Lorene::Tensor::compute_derive_lie(), Lorene::Tensor::mp, Lorene::Tensor::triad, and Lorene::Tensor::type_indice.

◆ div_free()

const Vector_divfree & Lorene::Vector::div_free ( const Metric & metre ) const

inherited

Returns the div-free vector in the Helmholtz decomposition.

It first makes the Helmholtz decomposition (see documentation of p_potential ) of this with respect to a given Metric and then returns $\vec{W}$ . Only in the case of contravariant vectors.

Definition at line 510 of file vector.C.

References Lorene::Vector::decompose_div(), Lorene::Tensor::get_place_met(), Lorene::Vector::p_div_free, and Lorene::Tensor::set_dependance().

◆ divergence()

const Scalar & Lorene::Vector::divergence ( const Metric & metre ) const

inherited

The divergence of this with respect to a Metric .

The Vector is assumed to be contravariant.

Definition at line 387 of file vector.C.

References Lorene::Tensor::divergence().

◆ down()

Tensor Lorene::Tensor::down	(	int	ind,
		const Metric &	gam
	)		const

inherited

Computes a new tensor by lowering an index of *this.

Parameters

ind	index to be lowered, with the following convention : `ind1` = 0 : first index of the tensor `ind1` = 1 : second index of the tensor and so on... (`ind` must be of covariant type (`CON` )).
gam	metric used to lower the index (contraction with the twice covariant form of the metric on the index `ind` ).

Definition at line 268 of file tensor_calculus.C.

References Lorene::contract(), Lorene::Metric::cov(), Lorene::Tensor::indices(), Lorene::Tensor::mp, Lorene::Tensor::n_comp, Lorene::Itbl::set(), Lorene::Tensor::set(), Lorene::Tensor::triad, Lorene::Tensor::type_indice, and Lorene::Tensor::valence.

◆ eta()

const Scalar & Lorene::Vector_divfree::eta ( ) const

virtual

Gives the field $\eta$ such that the angular components $(V^\theta, V^\varphi)$ of the vector are written:

$V^\theta = {\partial \eta \over \partial\theta} - {1\over\sin\theta} {\partial \mu \over \partial\varphi}$

$V^\varphi = {1\over\sin\theta} {\partial \eta \over \partial\varphi} + {\partial \mu \over \partial\theta}$

.

Reimplemented from Lorene::Vector.

Definition at line 196 of file vector_divfree.C.

References Lorene::Tensor::cmp, Lorene::Scalar::dsdr(), Lorene::Scalar::get_dzpuis(), Lorene::Scalar::mult_r_dzpuis(), Lorene::Vector::p_eta, Lorene::Scalar::poisson_angu(), and Lorene::Tensor::triad.

◆ exponential_filter_r()

void Lorene::Vector::exponential_filter_r	(	int	lzmin,
		int	lzmax,
		int	p,
		double	alpha = `-16.`
	)

virtualinherited

Applies exponential filters to all components (see Scalar::exponential_filter_r ).

Does a loop for Cartesian components, and works in terms of the r-component, $\eta$ and $\mu$ for spherical components.

Reimplemented from Lorene::Tensor.

Definition at line 856 of file vector.C.

References Lorene::Tensor::cmp, Lorene::Vector::eta(), Lorene::Scalar::exponential_filter_r(), Lorene::Map::get_bvect_cart(), Lorene::Map::get_bvect_spher(), Lorene::Base_vect::identify(), Lorene::Tensor::mp, Lorene::Vector::mu(), Lorene::Tensor::n_comp, Lorene::Vector::operator()(), Lorene::Vector::set_vr_eta_mu(), and Lorene::Tensor::triad.

◆ exponential_filter_ylm()

void Lorene::Vector::exponential_filter_ylm	(	int	lzmin,
		int	lzmax,
		int	p,
		double	alpha = `-16.`
	)

virtualinherited

Applies exponential filters to all components (see Scalar::exponential_filter_ylm ).

Does a loop for Cartesian components, and works in terms of the r-component, $\eta$ and $\mu$ for spherical components.

Reimplemented from Lorene::Tensor.

Definition at line 873 of file vector.C.

References Lorene::Tensor::cmp, Lorene::Vector::eta(), Lorene::Scalar::exponential_filter_ylm(), Lorene::Map::get_bvect_cart(), Lorene::Map::get_bvect_spher(), Lorene::Base_vect::identify(), Lorene::Tensor::mp, Lorene::Vector::mu(), Lorene::Tensor::n_comp, Lorene::Vector::operator()(), Lorene::Vector::set_vr_eta_mu(), and Lorene::Tensor::triad.

◆ exponential_filter_ylm_phi()

void Lorene::Tensor::exponential_filter_ylm_phi	(	int	lzmin,
		int	lzmax,
		int	p_r,
		int	p_tet,
		int	p_phi,
		double	alpha = `-16.`
	)

virtualinherited

Applies exponential filters to all components (see Scalar::exponential_filter_ylm_phi ).

Works only for Cartesian components.

Reimplemented in Lorene::Scalar.

Definition at line 1101 of file tensor.C.

References Lorene::Tensor::cmp, Lorene::Map::get_bvect_cart(), Lorene::Base_vect::identify(), Lorene::Tensor::mp, Lorene::Tensor::n_comp, and Lorene::Tensor::triad.

◆ flux()

double Lorene::Vector::flux	(	double	radius,
		const Metric &	met
	)		const

inherited

Computes the flux of the vector accross a sphere r = const.

Parameters

radius	radius of the sphere S on which the flux is to be taken; the center of S is assumed to be the center of the mapping (member `mp`). `radius` can take the value `__infinity` (to get the flux at spatial infinity).
met	metric $\gamma$ giving the area element of the sphere

Returns: $\oint_S V^i ds_i$ , where is the vector represented by *this and is the area element induced on S by $\gamma$ .

Definition at line 813 of file vector.C.

References Lorene::Vector::change_triad(), Lorene::Map::get_bvect_spher(), Lorene::Map_af::integrale_surface(), Lorene::Map_af::integrale_surface_infini(), Lorene::Tensor::mp, Lorene::Tensor::triad, Lorene::Tensor::type_indice, and Lorene::Vector::Vector().

◆ get_index_type() [1/2]

int Lorene::Tensor::get_index_type ( int i ) const

inlineinherited

Gives the type (covariant or contravariant) of the index number i .

i must be strictly lower than valence and obey the following convention:

i = 0 : first index
i = 1 : second index
and so on...

Returns: COV for a covariant index, CON for a contravariant one.

Definition at line 899 of file tensor.h.

References Lorene::Tensor::type_indice.

◆ get_index_type() [2/2]

Itbl Lorene::Tensor::get_index_type ( ) const

inlineinherited

Returns the types of all the indices.

Returns: 1-D array of integers (class Itbl ) of size valence
containing the type of each index, COV for a covariant one and CON
for a contravariant one.

Definition at line 909 of file tensor.h.

References Lorene::Tensor::type_indice.

◆ get_mp()

const Map& Lorene::Tensor::get_mp ( ) const

inlineinherited

Returns the mapping.

Definition at line 874 of file tensor.h.

References Lorene::Tensor::mp.

◆ get_n_comp()

int Lorene::Tensor::get_n_comp ( ) const

inlineinherited

Returns the number of stored components.

Definition at line 885 of file tensor.h.

References Lorene::Tensor::n_comp.

◆ get_place_met()

int Lorene::Tensor::get_place_met ( const Metric & metre ) const

protectedinherited

Returns the position of the pointer on metre in the array met_depend .

Definition at line 452 of file tensor.C.

References Lorene::Tensor::met_depend.

◆ get_triad()

const Base_vect* Lorene::Tensor::get_triad ( ) const

inlineinherited

Returns the vectorial basis (triad) on which the components are defined.

Definition at line 879 of file tensor.h.

References Lorene::Tensor::triad.

◆ get_valence()

int Lorene::Tensor::get_valence ( ) const

inlineinherited

Returns the valence.

Definition at line 882 of file tensor.h.

References Lorene::Tensor::valence.

◆ inc_dzpuis()

void Lorene::Tensor::inc_dzpuis ( int inc = 1 )

virtualinherited

Increases by inc units the value of dzpuis and changes accordingly the values in the compactified external domain (CED).

Reimplemented in Lorene::Scalar.

Definition at line 825 of file tensor.C.

References Lorene::Tensor::cmp, Lorene::Tensor::del_deriv(), and Lorene::Tensor::n_comp.

◆ indices()

virtual Itbl Lorene::Vector::indices ( int place ) const

inlinevirtualinherited

Returns the index of a component given by its position in the Scalar array cmp .

Returns: the index is stored in an 1-D array (Itbl ) of size 1 giving its value for the component located at the position place in the Scalar array cmp . The element of this Itbl
corresponds to a spatial index 1, 2 or 3.

Reimplemented from Lorene::Tensor.

Definition at line 411 of file vector.h.

◆ mu()

const Scalar & Lorene::Vector::mu ( ) const

virtualinherited

Gives the field $\mu$ such that the angular components $(V^\theta, V^\varphi)$ of the vector are written:

$V^\theta = {\partial \eta \over \partial\theta} - {1\over\sin\theta} {\partial \mu \over \partial\varphi}$

$V^\varphi = {1\over\sin\theta} {\partial \eta \over \partial\varphi} + {\partial \mu \over \partial\theta}$

.

Definition at line 107 of file vector_etamu.C.

References Lorene::Tensor::cmp, Lorene::Scalar::div_tant(), Lorene::Scalar::dsdt(), Lorene::Vector::p_mu, Lorene::Scalar::poisson_angu(), Lorene::Scalar::stdsdp(), and Lorene::Tensor::triad.

◆ ope_killing()

Sym_tensor Lorene::Vector::ope_killing ( const Metric & gam ) const

inherited

Computes the Killing operator associated with a given metric.

The Killing operator is defined by $ D^i V^j + D^j V^i $ for a contravariant vector and by $ D_i V_j + D_j V_i $ for a covariant vector.

Parameters

gam	metric with respect to which the covariant derivative is defined.

Definition at line 444 of file vector.C.

References Lorene::Tensor::derive_con(), Lorene::Tensor::derive_cov(), Lorene::Tensor::mp, Lorene::Tensor::set(), Lorene::Tensor::triad, and Lorene::Tensor::type_indice.

◆ ope_killing_conf()

Sym_tensor Lorene::Vector::ope_killing_conf ( const Metric & gam ) const

inherited

Computes the conformal Killing operator associated with a given metric.

The conformal Killing operator is defined by $D^i V^j + D^j V^i - \frac{2}{3} D_k V^k \, \gamma^{ij}$ for a contravariant vector and by $D_i V_j + D_j V_i - \frac{2}{3} D^k V_k \, \gamma_{ij}$ for a covariant vector.

Parameters

gam	metric $\gamma_{ij}$ with respect to which the covariant derivative is defined.

Definition at line 468 of file vector.C.

References Lorene::Metric::con(), Lorene::Metric::cov(), Lorene::Tensor::derive_con(), Lorene::Tensor::derive_cov(), Lorene::Vector::divergence(), Lorene::Tensor::mp, Lorene::Tensor::set(), Lorene::Tensor::trace(), Lorene::Tensor::triad, and Lorene::Tensor::type_indice.

◆ operator()() [1/5]

const Scalar & Lorene::Vector::operator() ( int index ) const

inherited

Readonly access to a component.

Definition at line 311 of file vector.C.

References Lorene::Tensor::cmp.

◆ operator()() [2/5]

const Scalar & Lorene::Tensor::operator() ( const Itbl & ind ) const

inherited

Returns the value of a component (read-only version).

Parameters

ind	1-D `Itbl` of size `valence` containing the values of each index specifing the component, with the following storage convention: `ind(0)` : value of the first index (1, 2 or 3) `ind(1)` : value of the second index (1, 2 or 3) and so on...

Returns: reference on the component specified by ind

Definition at line 807 of file tensor.C.

References Lorene::Tensor::cmp, Lorene::Itbl::get_dim(), Lorene::Itbl::get_ndim(), Lorene::Tensor::position(), and Lorene::Tensor::valence.

◆ operator()() [3/5]

const Scalar & Lorene::Tensor::operator()	(	int	i1,
		int	i2
	)		const

inherited

Returns the value of a component for a tensor of valence 2 (read-only version).

Parameters

i1	value of the first index (1, 2 or 3)
i2	value of the second index (1, 2 or 3)

Returns: reference on the component specified by (i1,i2)

Definition at line 769 of file tensor.C.

References Lorene::Tensor::cmp, Lorene::Tensor::position(), Lorene::Itbl::set(), and Lorene::Tensor::valence.

◆ operator()() [4/5]

const Scalar & Lorene::Tensor::operator()	(	int	i1,
		int	i2,
		int	i3
	)		const

inherited

Returns the value of a component for a tensor of valence 3 (read-only version).

Parameters

i1	value of the first index (1, 2 or 3)
i2	value of the second index (1, 2 or 3)
i3	value of the third index (1, 2 or 3)

Returns: reference on the component specified by (i1,i2,i3)

Definition at line 780 of file tensor.C.

References Lorene::Tensor::cmp, Lorene::Tensor::position(), Lorene::Itbl::set(), and Lorene::Tensor::valence.

◆ operator()() [5/5]

const Scalar & Lorene::Tensor::operator()	(	int	i1,
		int	i2,
		int	i3,
		int	i4
	)		const

inherited

Returns the value of a component for a tensor of valence 4 (read-only version).

Parameters

i1	value of the first index (1, 2 or 3)
i2	value of the second index (1, 2 or 3)
i3	value of the third index (1, 2 or 3)
i4	value of the fourth index (1, 2 or 3)

Returns: reference on the component specified by (i1,i2,i3,i4)

Definition at line 792 of file tensor.C.

References Lorene::Tensor::cmp, Lorene::Tensor::position(), Lorene::Itbl::set(), and Lorene::Tensor::valence.

◆ operator+=()

void Lorene::Tensor::operator+= ( const Tensor & t )

inherited

+= Tensor

Definition at line 580 of file tensor.C.

References Lorene::Tensor::cmp, Lorene::Tensor::del_deriv(), Lorene::Tensor::indices(), Lorene::Tensor::n_comp, Lorene::Tensor::position(), Lorene::Tensor::triad, Lorene::Tensor::type_indice, and Lorene::Tensor::valence.

◆ operator-=()

void Lorene::Tensor::operator-= ( const Tensor & t )

inherited

-= Tensor

Definition at line 596 of file tensor.C.

References Lorene::Tensor::cmp, Lorene::Tensor::del_deriv(), Lorene::Tensor::indices(), Lorene::Tensor::n_comp, Lorene::Tensor::position(), Lorene::Tensor::triad, Lorene::Tensor::type_indice, and Lorene::Tensor::valence.

◆ operator=() [1/3]

void Lorene::Vector_divfree::operator= ( const Vector_divfree & a )

Assignment from another Vector_divfree.

Definition at line 144 of file vector_divfree.C.

References del_deriv(), met_div, and Lorene::Vector::operator=().

◆ operator=() [2/3]

void Lorene::Vector_divfree::operator= ( const Vector & a )

virtual

Assignment from a Vector.

Reimplemented from Lorene::Vector.

Definition at line 156 of file vector_divfree.C.

References del_deriv(), and Lorene::Vector::operator=().

◆ operator=() [3/3]

void Lorene::Vector_divfree::operator= ( const Tensor & a )

virtual

Assignment from a Tensor.

Reimplemented from Lorene::Vector.

Definition at line 166 of file vector_divfree.C.

References del_deriv(), and Lorene::Vector::operator=().

◆ poisson() [1/5]

Vector Lorene::Vector::poisson	(	double	lambda,
		int	method = `6`
	)		const

inherited

Solves the vector Poisson equation with *this as a source.

The equation solved is $\Delta N^i +\lambda \nabla^i \nabla_k N^k = S^i$ . *this must be given with dzpuis = 4. It uses the Helmholtz decomposition (see documentation of p_potential ), with a flat metric, deduced from the triad.

Parameters

lambda	[input] $\lambda$ .
method	[input] method used to solve the equation (see Vector::poisson(double, Metric_flat, int) for details).

Returns: the solution .

Definition at line 521 of file vector_poisson.C.

References Lorene::Map::flat_met_cart(), Lorene::Map::flat_met_spher(), Lorene::Tensor::mp, and Lorene::Tensor::triad.

◆ poisson() [2/5]

Vector Lorene::Vector::poisson	(	double	lambda,
		const Metric_flat &	met_f,
		int	method = `6`
	)		const

inherited

Solves the vector Poisson equation with *this as a source.

The equation solved is $\Delta N^i +\lambda \nabla^i \nabla_k N^k = S^i$ . *this must be given with dzpuis = 4. It uses the Helmholtz decomposition (see documentation of p_potential ), with the flat metric met_f given in argument.

Parameters

lambda	[input] $\lambda$ .
met_f	[input] the flat metric for the Helmholtz decomposition.
method	[input] method used to solve the equation: 0 : It uses the Helmholtz decomposition (see documentation of `p_potential` ), with the flat metric `met_f` given in argument (the default). 1 : It solves, first for the divergence (calculated using `met_f` ), then the r -component, the $\eta$ potential, and fianlly the $\mu$ potential (see documentation of `Vector_div_free` . 2 : The sources is transformed to cartesian components and the equation is solved using Shibata method (see Granclement et al. JCPH 2001. 6 : Solves for the r -component and $\eta$ together in a system, and for the $\mu$ potential (which decouples). The solution is then built from these fields through the method `Vector::set_vr_eta_mu()`. It is the default method.

Returns: the solution .

Definition at line 133 of file vector_poisson.C.

References Lorene::Tensor::cmp.

◆ poisson() [3/5]

Vector Lorene::Vector::poisson	(	const double	lambda,
		Param &	par,
		int	method = `6`
	)		const

inherited

Solves the vector Poisson equation with *this as a source and parameters controlling the solution.

The equatiopn solved is $\Delta N^i +\lambda \nabla^i \nabla_k N^k = S^i$ . *this must be given with dzpuis = 4. It uses the Helmholtz decomposition (see documentation of p_potential ), with a flat metric, deduced from the triad.

Parameters

lambda	[input] $\lambda$ .
par	[input/output] possible parameters
uu	[input/output] solution u with the boundary condition u =0 at spatial infinity.

Definition at line 546 of file vector_poisson.C.

References Lorene::Param::add_cmp_mod(), Lorene::Param::add_double(), Lorene::Param::add_int(), Lorene::Param::add_int_mod(), Lorene::Cmp::annule_hard(), Lorene::Tensor::cmp, Lorene::Tensor::dec_dzpuis(), Lorene::Scalar::derive_con(), Lorene::Vector::div_free(), Lorene::Map::get_bvect_cart(), Lorene::Map::get_bvect_spher(), Lorene::Param::get_cmp_mod(), Lorene::Param::get_double(), Lorene::Param::get_int(), Lorene::Param::get_int_mod(), Lorene::Scalar::inc_dzpuis(), Lorene::Tensor::mp, poisson(), Lorene::Scalar::poisson(), Lorene::Vector::potential(), Lorene::Vector::set(), Lorene::Tenseur::set(), Lorene::Tenseur::set_etat_qcq(), Lorene::Scalar::set_etat_zero(), Lorene::Tenseur::set_std_base(), and Lorene::Tensor::triad.

◆ poisson() [4/5]

Vector_divfree Lorene::Vector_divfree::poisson ( ) const

Computes the solution of a vectorial Poisson equation with *this $= \vec{V}$ as a source:

$\Delta \vec{W} = \vec{V}$

.

Returns: solution $\vec{W}$ of the above equation with the boundary condition $\vec{W}=0$ at spatial infinity.

Definition at line 149 of file vector_df_poisson.C.

References Lorene::Tensor::cmp, met_div, Lorene::Tensor::mp, Lorene::Vector::mu(), Lorene::Scalar::poisson(), and Lorene::Tensor::triad.

◆ poisson() [5/5]

Vector_divfree Lorene::Vector_divfree::poisson ( Param & par ) const

Computes the solution of a vectorial Poisson equation with *this $= \vec{V}$ as a source:

$\Delta \vec{W} = \vec{V}$

.

Returns: solution $\vec{W}$ of the above equation with the boundary condition $\vec{W}=0$ at spatial infinity.

Definition at line 72 of file vector_df_poisson.C.

References Lorene::Param::add_cmp_mod(), Lorene::Param::add_double(), Lorene::Param::add_int(), Lorene::Param::add_int_mod(), Lorene::Tensor::cmp, Lorene::Scalar::div_r(), Lorene::Param::get_cmp_mod(), Lorene::Param::get_double(), Lorene::Param::get_int(), Lorene::Param::get_int_mod(), met_div, Lorene::Tensor::mp, Lorene::Vector::mu(), Lorene::Scalar::mult_r(), Lorene::Scalar::poisson(), Lorene::Scalar::set_etat_zero(), set_vr_mu(), and Lorene::Tensor::triad.

◆ poisson_boundary()

void Lorene::Vector::poisson_boundary	(	double	lambda,
		const Mtbl_cf &	limit_vr,
		const Mtbl_cf &	limit_eta,
		const Mtbl_cf &	limit_mu,
		int	num_front,
		double	fact_dir,
		double	fact_neu,
		Vector &	resu
	)		const

inherited

Solves the vector Poisson equation with *this as a source with a boundary condition on the excised sphere.

The equation solved is $\Delta N^i +\lambda \nabla^i \nabla_k N^k = S^i$ . *this must be given with dzpuis = 4. It uses the Helmholtz decomposition (see documentation of p_potential )

Parameters

lambda	[input] $\lambda$ .
resu	[output] the solution .

Definition at line 68 of file vector_poisson_boundary.C.

References Lorene::Tensor::cmp, Lorene::Map::get_mg(), Lorene::Mg3d::get_nzone(), Lorene::Mg3d::get_type_r(), Lorene::Tensor::mp, and Lorene::Tensor::triad.

◆ poisson_boundary2()

void Lorene::Vector::poisson_boundary2	(	double	lam,
		Vector &	resu,
		Scalar	boundvr,
		Scalar	boundeta,
		Scalar	boundmu,
		double	dir_vr,
		double	neum_vr,
		double	dir_eta,
		double	neum_eta,
		double	dir_mu,
		double	neum_mu
	)		const

inherited

Alternative to previous poisson_boundary method for vectors ; this uses method 6 for vectorial solving, updated version (as in the poisson_vector_block routine).

Boundary arguments are here required as scalar fields.

Definition at line 83 of file vector_poisson_boundary2.C.

References Lorene::Valeur::c_cf, Lorene::Tensor::cmp, Lorene::Map::get_mg(), Lorene::Mg3d::get_nzone(), Lorene::Scalar::get_spectral_va(), Lorene::Mg3d::get_type_r(), Lorene::Tensor::mp, Lorene::Scalar::set_spectral_va(), Lorene::Tensor::triad, and Lorene::Valeur::ylm().

◆ poisson_neumann()

Vector Lorene::Vector::poisson_neumann	(	double	lambda,
		const Valeur &	limit_vr,
		const Valeur &	limit_vt,
		const Valeur &	limit_vp,
		int	num_front
	)		const

inherited

Solves the vector Poisson equation with *this as a source with a boundary condition on the excised sphere.

The equation solved is $\Delta N^i +\lambda \nabla^i \nabla_k N^k = S^i$ . *this must be given with dzpuis = 4. It uses the Helmholtz decomposition (see documentation of p_potential )

Parameters

lambda	[input] $\lambda$ .
resu	[output] the solution .

Definition at line 694 of file vector_poisson_boundary.C.

References Lorene::Tensor::mp, Lorene::Vector::poisson_robin(), and Lorene::Tensor::triad.

◆ poisson_robin()

Vector Lorene::Vector::poisson_robin	(	double	lambda,
		const Valeur &	limit_vr,
		const Valeur &	limit_vt,
		const Valeur &	limit_vp,
		double	fact_dir,
		double	fact_neu,
		int	num_front
	)		const

inherited

Solves the vector Poisson equation with *this as a source with a boundary condition on the excised sphere.

The equation solved is $\Delta N^i +\lambda \nabla^i \nabla_k N^k = S^i$ . *this must be given with dzpuis = 4. It uses the Helmholtz decomposition (see documentation of p_potential )

Parameters

lambda	[input] $\lambda$ .
resu	[output] the solution .

Definition at line 705 of file vector_poisson_boundary.C.

References Lorene::Scalar::annule_hard(), Lorene::Valeur::base, Lorene::Valeur::c_cf, Lorene::Tensor::cmp, Lorene::Valeur::coef(), Lorene::Scalar::div_tant(), Lorene::Scalar::dsdt(), Lorene::Valeur::get_mg(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_nzone(), Lorene::Tensor::mp, Lorene::norme(), Lorene::Scalar::poisson_angu(), Lorene::Valeur::set(), Lorene::Valeur::set_base(), Lorene::Scalar::set_grid_point(), Lorene::Scalar::set_spectral_va(), Lorene::Scalar::stdsdp(), and Lorene::Valeur::ylm().

◆ position()

virtual int Lorene::Vector::position ( const Itbl & idx ) const

inlinevirtualinherited

Returns the position in the Scalar array cmp of a component given by its index.

Returns: position in the Scalar array cmp
corresponding to the index given in idx . idx must be a 1-D Itbl of size 1, the element of which must be one of the spatial indices 1, 2 or 3.

Reimplemented from Lorene::Tensor.

Definition at line 392 of file vector.h.

References Lorene::Itbl::get_dim(), and Lorene::Itbl::get_ndim().

◆ potential()

const Scalar & Lorene::Vector::potential ( const Metric & metre ) const

inherited

Returns the potential in the Helmholtz decomposition.

It first makes the Helmholtz decomposition (see documentation of p_potential ) of this with respect to a given Metric and then returns $\phi$ . Only in the case of contravariant vectors.

Definition at line 498 of file vector.C.

References Lorene::Vector::decompose_div(), Lorene::Tensor::get_place_met(), Lorene::Vector::p_potential, and Lorene::Tensor::set_dependance().

◆ pseudo_spectral_base()

void Lorene::Vector::pseudo_spectral_base ( )

virtualinherited

Sets the standard spectal bases of decomposition for each component for a pseudo_vector.

Definition at line 352 of file vector.C.

References Lorene::Tensor::cmp, Lorene::Map::get_bvect_cart(), Lorene::Map::get_bvect_spher(), Lorene::Map::get_mg(), Lorene::Base_vect::identify(), Lorene::Tensor::mp, Lorene::Mg3d::pseudo_base_vect_cart(), Lorene::Mg3d::pseudo_base_vect_spher(), Lorene::Scalar::set_spectral_base(), and Lorene::Tensor::triad.

◆ sauve()

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

virtualinherited

Save in a binary file.

Reimplemented in Lorene::Tensor_sym, and Lorene::Scalar.

Definition at line 915 of file tensor.C.

References Lorene::Tensor::cmp, Lorene::fwrite_be(), Lorene::Tensor::n_comp, Lorene::Base_vect::sauve(), Lorene::Itbl::sauve(), Lorene::Tensor::triad, Lorene::Tensor::type_indice, and Lorene::Tensor::valence.

◆ set() [1/5]

Scalar & Lorene::Vector::set ( int index )

inherited

Read/write access to a component.

Definition at line 302 of file vector.C.

References Lorene::Tensor::cmp, and Lorene::Vector::del_deriv().

◆ set() [2/5]

Scalar & Lorene::Tensor::set ( const Itbl & ind )

inherited

Returns the value of a component (read/write version).

Parameters

ind	1-D `Itbl` of size `valence` containing the values of each index specifing the component, with the following storage convention: `ind(0)` : value of the first index (1, 2 or 3) `ind(1)` : value of the second index (1, 2 or 3) and so on...

Returns: modifiable reference on the component specified by ind

Definition at line 663 of file tensor.C.

References Lorene::Tensor::cmp, Lorene::Tensor::del_deriv(), Lorene::Itbl::get_dim(), Lorene::Itbl::get_ndim(), Lorene::Tensor::position(), and Lorene::Tensor::valence.

◆ set() [3/5]

Scalar & Lorene::Tensor::set	(	int	i1,
		int	i2
	)

inherited

Returns the value of a component for a tensor of valence 2 (read/write version).

Parameters

i1	value of the first index (1, 2 or 3)
i2	value of the second index (1, 2 or 3)

Returns: modifiable reference on the component specified by (i1,i2)

Definition at line 615 of file tensor.C.

References Lorene::Tensor::cmp, Lorene::Tensor::del_deriv(), Lorene::Tensor::position(), Lorene::Itbl::set(), and Lorene::Tensor::valence.

◆ set() [4/5]

Scalar & Lorene::Tensor::set	(	int	i1,
		int	i2,
		int	i3
	)

inherited

Returns the value of a component for a tensor of valence 3 (read/write version).

Parameters

i1	value of the first index (1, 2 or 3)
i2	value of the second index (1, 2 or 3)
i3	value of the third index (1, 2 or 3)

Returns: modifiable reference on the component specified by (i1,i2,i3)

Definition at line 630 of file tensor.C.

References Lorene::Tensor::cmp, Lorene::Tensor::del_deriv(), Lorene::Tensor::position(), Lorene::Itbl::set(), and Lorene::Tensor::valence.

◆ set() [5/5]

Scalar & Lorene::Tensor::set	(	int	i1,
		int	i2,
		int	i3,
		int	i4
	)

inherited

Returns the value of a component for a tensor of valence 4 (read/write version).

Parameters

i1	value of the first index (1, 2 or 3)
i2	value of the second index (1, 2 or 3)
i3	value of the third index (1, 2 or 3)
i4	value of the fourth index (1, 2 or 3)

Returns: modifiable reference on the component specified by (i1,i2,i3,i4)

Definition at line 646 of file tensor.C.

References Lorene::Tensor::cmp, Lorene::Tensor::del_deriv(), Lorene::Tensor::position(), Lorene::Itbl::set(), and Lorene::Tensor::valence.

◆ set_A_mu()

void Lorene::Vector_divfree::set_A_mu	(	const Scalar &	A_i,
		const Scalar &	mu_i,
		const Param *	par_bc
	)

Defines the components through potentials $A$ and $\mu$ .

(see members p_A and p_mu ),

Parameters

A_i	[input] Angular potential
mu_i	[input] Angular potential $\mu$

Definition at line 123 of file vector_divfree_aux.C.

References Lorene::Tensor::cmp, del_deriv(), Lorene::Tensor::get_mp(), Lorene::Tensor::mp, Lorene::Vector::p_A, Lorene::Vector::p_eta, Lorene::Vector::p_mu, Lorene::Scalar::set_dzpuis(), sol_Dirac_A(), Lorene::Tensor::triad, and Lorene::Vector::update_vtvp().

◆ set_dependance()

void Lorene::Tensor::set_dependance ( const Metric & met ) const

protectedinherited

To be used to describe the fact that the derivatives members have been calculated with met .

First it sets a null element of met_depend to &met and puts this in the list of the dependancies of met .

Definition at line 462 of file tensor.C.

References Lorene::Tensor::met_depend, and Lorene::Metric::tensor_depend.

◆ set_der_0x0()

void Lorene::Vector_divfree::set_der_0x0 ( ) const

protected

Sets the pointers on derived quantities to 0x0.

Definition at line 138 of file vector_divfree.C.

◆ set_der_met_0x0()

void Lorene::Vector::set_der_met_0x0 ( int i ) const

protectedinherited

Sets all the i-th components of met_depend in the class Vector (p_potential , etc...) to 0x0.

Definition at line 264 of file vector.C.

References Lorene::Vector::p_div_free, and Lorene::Vector::p_potential.

◆ set_etat_nondef()

void Lorene::Tensor::set_etat_nondef ( )

virtualinherited

Sets the logical state of all components to ETATNONDEF
(undefined state).

Reimplemented in Lorene::Scalar.

Definition at line 498 of file tensor.C.

References Lorene::Tensor::cmp, Lorene::Tensor::del_deriv(), Lorene::Tensor::n_comp, and Lorene::Scalar::set_etat_nondef().

◆ set_etat_qcq()

void Lorene::Tensor::set_etat_qcq ( )

virtualinherited

Sets the logical state of all components to ETATQCQ
(ordinary state).

Reimplemented in Lorene::Scalar.

Definition at line 490 of file tensor.C.

References Lorene::Tensor::cmp, Lorene::Tensor::del_deriv(), Lorene::Tensor::n_comp, and Lorene::Scalar::set_etat_qcq().

◆ set_etat_zero()

void Lorene::Tensor::set_etat_zero ( )

virtualinherited

Sets the logical state of all components to ETATZERO
(zero state).

Reimplemented in Lorene::Scalar.

Definition at line 506 of file tensor.C.

References Lorene::Tensor::cmp, Lorene::Tensor::del_deriv(), Lorene::Tensor::n_comp, and Lorene::Scalar::set_etat_zero().

◆ set_index_type() [1/2]

int& Lorene::Tensor::set_index_type ( int i )

inlineinherited

Sets the type of the index number i .

i must be strictly lower than valence and obey the following convention:

i = 0 : first index
i = 1 : second index
and so on...

Returns: reference on the type that can be modified (COV for a covariant index, CON for a contravariant one)

Definition at line 922 of file tensor.h.

References Lorene::Itbl::set(), and Lorene::Tensor::type_indice.

◆ set_index_type() [2/2]

Itbl& Lorene::Tensor::set_index_type ( )

inlineinherited

Sets the types of all the indices.

Returns: a reference on the 1-D array of integers (class Itbl ) of size valence that can be modified (COV for a covariant one and CON for a contravariant one)

Definition at line 931 of file tensor.h.

References Lorene::Tensor::type_indice.

◆ set_triad()

void Lorene::Tensor::set_triad ( const Base_vect & new_triad )

inherited

Assigns a new vectorial basis (triad) of decomposition.

NB: this function modifies only the member triad and leave unchanged the components (member cmp ). In order to change them coherently with the new basis, the function change_triad(const Base_vect& ) must be called instead.

Definition at line 528 of file tensor.C.

References Lorene::Tensor::triad.

◆ set_vr_eta_mu()

void Lorene::Vector_divfree::set_vr_eta_mu	(	const Scalar &	vr_i,
		const Scalar &	eta_i,
		const Scalar &	mu_i
	)

Defines the components through $V_r$ , $\eta$ and $\mu$ .

(see members p_eta and p_mu ),

Parameters

vr_i	[input] r-component of the vector
eta_i	[input] Angular potential $\eta$
mu_i	[input] Angular potential $\mu$

Definition at line 99 of file vector_divfree_aux.C.

References Lorene::Tensor::cmp, Lorene::Tensor::get_mp(), Lorene::Vector::p_eta, Lorene::Vector::p_mu, Lorene::Tensor::triad, and Lorene::Vector::update_vtvp().

◆ set_vr_mu()

void Lorene::Vector_divfree::set_vr_mu	(	const Scalar &	vr_i,
		const Scalar &	mu_i
	)

Sets the angular potentials $\mu$ (see member p_mu ), and the $V^r$ component of the vector.

The potential $\eta$ is then deduced from $V^r$ by the divergence-free condition. The components $V^\theta$ and $V^\varphi$ are updated consistently by a call to the method update_vtvp() .

Parameters

vr_i	[input] component of the vector
mu_i	[input] angular potential $\mu$

Definition at line 177 of file vector_divfree.C.

References Lorene::Tensor::cmp, del_deriv(), eta(), Lorene::Vector::p_mu, Lorene::Tensor::triad, and Lorene::Vector::update_vtvp().

◆ sol_Dirac_A()

void Lorene::Vector_divfree::sol_Dirac_A	(	const Scalar &	aaa,
		Scalar &	eta,
		Scalar &	vr,
		const Param *	par_bc = `0x0`
	)		const

protected

Solves a system of two-coupled first-order PDEs obtained from the divergence-free condition and the requirement that the potential A has a given value.

The system reads :

${\partial \eta \over \partial r} + {\eta \over r} - {V^r \over r} = A$

${\partial V^r \over \partial r} + {2 V^r \over r} + {1 \over r}\Delta_{\vartheta \varphi}\eta = 0$

Definition at line 80 of file vector_divfree_A.C.

References Lorene::Map::get_mg(), Lorene::Mg3d::get_type_r(), and Lorene::Tensor::mp.

◆ sol_Dirac_A_1z()

void Lorene::Vector_divfree::sol_Dirac_A_1z	(	const Scalar &	aaa,
		Scalar &	eta,
		Scalar &	vr,
		const Param *	par_bc = `0x0`
	)		const

protected

Solves a one-domain system of two-coupled first-order PDEs obtained from the divergence-free condition and the requirement that the potential A has a given value.

The system reads :

${\partial \eta \over \partial r} + {\eta \over r} - {V^r \over r} = A$

${\partial V^r \over \partial r} + {2 V^r \over r} + {1 \over r}\Delta_{\vartheta \varphi}\eta = 0$

Definition at line 72 of file vector_divfree_A_1z.C.

References Lorene::Map::get_mg(), Lorene::Mg3d::get_type_r(), and Lorene::Tensor::mp.

◆ sol_Dirac_A_poisson()

void Lorene::Vector_divfree::sol_Dirac_A_poisson	(	const Scalar &	aaa,
		Scalar &	eta,
		Scalar &	vr,
		const Param *	par_bc = `0x0`
	)		const

protected

Solves via a poisson method a system of two-coupled first-order PDEs obtained from the divergence-free condition and the requirement that the potential A has a given value.

The system reads :

${\partial \eta \over \partial r} + {\eta \over r} - {V^r \over r} = A$

${\partial V^r \over \partial r} + {2 V^r \over r} + {1 \over r}\Delta_{\vartheta \varphi}\eta = 0$

Definition at line 71 of file vector_divfree_A_poisson.C.

References Lorene::Scalar::div_r(), Lorene::Scalar::dsdr(), Lorene::Scalar::lapang(), Lorene::Scalar::mult_r_dzpuis(), and Lorene::Scalar::poisson_tau().

◆ sol_Dirac_A_tau()

void Lorene::Vector_divfree::sol_Dirac_A_tau	(	const Scalar &	aaa,
		Scalar &	eta,
		Scalar &	vr,
		const Param *	par_bc = `0x0`
	)		const

protected

Solves via a tau method a system of two-coupled first-order PDEs obtained from the divergence-free condition and the requirement that the potential A has a given value.

The system reads :

${\partial \eta \over \partial r} + {\eta \over r} - {V^r \over r} = A$

${\partial V^r \over \partial r} + {2 V^r \over r} + {1 \over r}\Delta_{\vartheta \varphi}\eta = 0$

Definition at line 73 of file vector_divfree_A_tau.C.

References Lorene::Map::get_mg(), Lorene::Mg3d::get_type_r(), and Lorene::Tensor::mp.

◆ spectral_display()

void Lorene::Tensor::spectral_display	(	const char *	comment = `0x0`,
		double	threshold = `1.e-7`,
		int	precision = `4`,
		ostream &	ostr = `cout`
	)		const

virtualinherited

Displays the spectral coefficients and the associated basis functions of each component.

This function shows only the values greater than a given threshold.

Parameters

comment	comment to be printed at top of the display (default: 0x0 = nothing printed)
threshold	[input] Value above which a coefficient is printed (default: 1.e-7)
precision	[input] Number of printed digits (default: 4)
ostr	[input] Output stream used for the printing (default: cout)

Reimplemented in Lorene::Scalar.

Definition at line 883 of file tensor.C.

References Lorene::Tensor::cmp, Lorene::Tensor::indices(), Lorene::Tensor::n_comp, Lorene::Scalar::spectral_display(), and Lorene::Tensor::valence.

◆ std_spectral_base()

void Lorene::Vector::std_spectral_base ( )

virtualinherited

Sets the standard spectal bases of decomposition for each component.

Reimplemented from Lorene::Tensor.

Definition at line 322 of file vector.C.

References Lorene::Tensor::cmp, Lorene::Map::get_bvect_cart(), Lorene::Map::get_bvect_spher(), Lorene::Map::get_mg(), Lorene::Base_vect::identify(), Lorene::Tensor::mp, Lorene::Scalar::set_spectral_base(), Lorene::Mg3d::std_base_vect_cart(), Lorene::Mg3d::std_base_vect_spher(), and Lorene::Tensor::triad.

◆ std_spectral_base_odd()

void Lorene::Tensor::std_spectral_base_odd ( )

virtualinherited

Sets the standard odd spectal bases of decomposition for each component.

Currently only implemented for a scalar.

Reimplemented in Lorene::Scalar.

Definition at line 991 of file tensor.C.

References Lorene::Tensor::cmp, Lorene::Scalar::std_spectral_base_odd(), and Lorene::Tensor::valence.

◆ trace() [1/4]

Tensor Lorene::Tensor::trace	(	int	ind1,
		int	ind2
	)		const

inherited

Trace on two different type indices.

Parameters

ind1	first index for the contraction, with the following convention : `ind1` = 0 : first index of the tensor `ind1` = 1 : second index of the tensor and so on...
ind2	second index for the contraction

Definition at line 97 of file tensor_calculus.C.

References Lorene::Tensor::cmp, Lorene::Tensor::get_n_comp(), Lorene::Tensor::indices(), Lorene::Tensor::mp, Lorene::Tensor::position(), Lorene::Itbl::set(), Lorene::Tensor::set(), Lorene::Scalar::set_etat_zero(), Lorene::Tensor::triad, Lorene::Tensor::type_indice, and Lorene::Tensor::valence.

◆ trace() [2/4]

Tensor Lorene::Tensor::trace	(	int	ind1,
		int	ind2,
		const Metric &	gam
	)		const

inherited

Trace with respect to a given metric.

Parameters

ind1	first index for the contraction, with the following convention : `ind1` = 0 : first index of the tensor `ind1` = 1 : second index of the tensor and so on...
ind2	second index for the contraction
gam	metric used to raise or lower ind1 in order that it has a opposite type than ind2

Definition at line 156 of file tensor_calculus.C.

References Lorene::Metric::con(), Lorene::contract(), Lorene::Metric::cov(), Lorene::Tensor::trace(), Lorene::Tensor::type_indice, and Lorene::Tensor::valence.

◆ trace() [3/4]

Scalar Lorene::Tensor::trace ( ) const

inherited

Trace on two different type indices for a valence 2 tensor.

Definition at line 183 of file tensor_calculus.C.

References Lorene::Tensor::mp, Lorene::Tensor::operator()(), Lorene::Scalar::set_etat_zero(), Lorene::Tensor::type_indice, and Lorene::Tensor::valence.

◆ trace() [4/4]

Scalar Lorene::Tensor::trace ( const Metric & gam ) const

inherited

Trace with respect to a given metric for a valence 2 tensor.

Parameters

gam	metric used to raise or lower one of the indices, in order to take the trace

Definition at line 200 of file tensor_calculus.C.

References Lorene::Metric::con(), Lorene::contract(), Lorene::Metric::cov(), Lorene::Tensor::trace(), Lorene::Tensor::type_indice, and Lorene::Tensor::valence.

◆ up()

Tensor Lorene::Tensor::up	(	int	ind,
		const Metric &	gam
	)		const

inherited

Computes a new tensor by raising an index of *this.

Parameters

ind	index to be raised, with the following convention : `ind1` = 0 : first index of the tensor `ind1` = 1 : second index of the tensor and so on... (`ind` must be of covariant type (`COV` )).
gam	metric used to raise the index (contraction with the twice contravariant form of the metric on the index `ind` ).

Definition at line 228 of file tensor_calculus.C.

References Lorene::Metric::con(), Lorene::contract(), Lorene::Tensor::indices(), Lorene::Tensor::mp, Lorene::Tensor::n_comp, Lorene::Itbl::set(), Lorene::Tensor::set(), Lorene::Tensor::triad, Lorene::Tensor::type_indice, and Lorene::Tensor::valence.

◆ up_down()

Tensor Lorene::Tensor::up_down ( const Metric & gam ) const

inherited

Computes a new tensor by raising or lowering all the indices of *this .

Parameters

gam	metric used to lower the contravariant indices and raising the covariant ones.

Definition at line 308 of file tensor_calculus.C.

References Lorene::Tensor::down(), Lorene::Tensor::Tensor(), Lorene::Tensor::type_indice, Lorene::Tensor::up(), and Lorene::Tensor::valence.

◆ update_etavr()

void Lorene::Vector_divfree::update_etavr ( )

Computes the components $V^r$ and $\eta$ from the potential A and the divergence-free condition, according to :

${\partial \eta \over \ partial r} + { \eta \over r} - {V^r \over r} = A$

${\partial V^r \over \partial r} + {2 V^r \over r} + {1 \over r} \Delta_{\vartheta \varphi} \eta = 0$

.

Definition at line 76 of file vector_divfree_aux.C.

References Lorene::Tensor::cmp, Lorene::Vector::del_deriv(), Lorene::Tensor::mp, Lorene::Vector::p_A, Lorene::Vector::p_eta, and sol_Dirac_A().

◆ update_vtvp()

void Lorene::Vector::update_vtvp ( )

inherited

Computes the components $V^\theta$ and $V^\varphi$ from the potential $\eta$ and $\mu$ , according to:

$V^\theta = {\partial \eta \over \partial\theta} - {1\over\sin\theta} {\partial \mu \over \partial\varphi}$

$V^\varphi = {1\over\sin\theta} {\partial \eta \over \partial\varphi} + {\partial \mu \over \partial\theta}$

.

Definition at line 176 of file vector_etamu.C.

References Lorene::Tensor::cmp, Lorene::Vector::del_deriv(), Lorene::Scalar::dsdt(), Lorene::Vector::p_eta, Lorene::Vector::p_mu, and Lorene::Scalar::stdsdp().

◆ visu_arrows()

void Lorene::Vector::visu_arrows	(	double	xmin,
		double	xmax,
		double	ymin,
		double	ymax,
		double	zmin,
		double	zmax,
		const char *	title0 = `0x0`,
		const char *	filename0 = `0x0`,
		bool	start_dx = `true`,
		int	nx = `8`,
		int	ny = `8`,
		int	nz = `8`
	)		const

inherited

3D visualization via OpenDX.

Parameters

xmin	[input] defines with `xmax` the x range of the visualization box
xmax	[input] defines with `xmin` the x range of the visualization box
ymin	[input] defines with `ymax` the y range of the visualization box
ymax	[input] defines with `ymin` the y range of the visualization box
zmin	[input] defines with `zmax` the z range of the visualization box
zmax	[input] defines with `zmin` the z range of the visualization box
title	[input] title for the graph (for OpenDX legend)
filename	[input] name for the file which will be the input for OpenDX; the default 0x0 is transformed into "vector_arrows"
start_dx	[input] determines whether OpenDX must be launched (as a subprocess) to view the field; if set to `false` , only input files for future usage of OpenDX are created
nx	[input] number of points in the x direction (uniform sampling)
ny	[input] number of points in the y direction (uniform sampling)
nz	[input] number of points in the z direction (uniform sampling)

Definition at line 65 of file vector_visu.C.

References Lorene::Valeur::c_cf, Lorene::Vector::change_triad(), Lorene::Scalar::check_dzpuis(), Lorene::Valeur::coef(), Lorene::Map::convert_absolute(), Lorene::Scalar::dec_dzpuis(), Lorene::Map::get_bvect_cart(), Lorene::Map::get_bvect_spher(), Lorene::Scalar::get_dzpuis(), Lorene::Tensor::mp, Lorene::Vector::operator()(), Lorene::Vector::set(), Lorene::Tensor::triad, Lorene::Map::val_lx(), Lorene::Mtbl_cf::val_point(), and Lorene::Vector::Vector().

Member Data Documentation

◆ cmp

Scalar** Lorene::Tensor::cmp

protectedinherited

Array of size n_comp of pointers onto the components.

Definition at line 321 of file tensor.h.

◆ met_depend

const Metric* Lorene::Tensor::met_depend[N_MET_MAX]

mutableprotectedinherited

Array on the Metric 's which were used to compute derived quantities, like p_derive_cov , etc...

The i-th element of this array is the Metric used to compute the i-th element of p_derive_cov , etc..

Definition at line 333 of file tensor.h.

◆ met_div

const Metric* const Lorene::Vector_divfree::met_div

protected

Metric with respect to which the divergence is defined.

Definition at line 730 of file vector.h.

◆ mp

const Map* const Lorene::Tensor::mp

protectedinherited

Mapping on which the numerical values at the grid points are defined.

Definition at line 301 of file tensor.h.

◆ n_comp

int Lorene::Tensor::n_comp

protectedinherited

Number of stored components, depending on the symmetry.

Definition at line 318 of file tensor.h.

◆ p_A

Scalar* Lorene::Vector::p_A

mutableprotectedinherited

Field $A$ defined by

$A = {\partial \eta \over \ partial r} + { \eta \over r} - {V^r \over r}$

Insensitive to the longitudinal part of the vector, related to the curl.

Definition at line 241 of file vector.h.

◆ p_derive_con

Tensor* Lorene::Tensor::p_derive_con[N_MET_MAX]

mutableprotectedinherited

Array of pointers on the contravariant derivatives of this with respect to various metrics.

See the comments of met_depend . See also the comments of method derive_con() for a precise definition of a "contravariant" derivative.

Definition at line 349 of file tensor.h.

◆ p_derive_cov

Tensor* Lorene::Tensor::p_derive_cov[N_MET_MAX]

mutableprotectedinherited

Array of pointers on the covariant derivatives of this with respect to various metrics.

See the comments of met_depend . See also the comments of method derive_cov() for the index convention of the covariant derivation.

Definition at line 341 of file tensor.h.

◆ p_div_free

Vector_divfree* Lorene::Vector::p_div_free[N_MET_MAX]

mutableprotectedinherited

The divergence-free vector $\vec{W} = \vec{\nabla} \wedge \vec{\psi}$ of the Helmholtz decomposition of any 3D vector $\vec{V}: \quad \vec{V} = \vec{\nabla} \phi + \vec{\nabla} *\wedge \vec{\psi}$ .

Only in the case of contravariant vectors.

Definition at line 205 of file vector.h.

◆ p_divergence

Tensor* Lorene::Tensor::p_divergence[N_MET_MAX]

mutableprotectedinherited

Array of pointers on the divergence of this with respect to various metrics.

See the comments of met_depend . See also the comments of method divergence() for a precise definition of a the divergence with respect to a given metric.

Definition at line 357 of file tensor.h.

◆ p_eta

Scalar* Lorene::Vector::p_eta

mutableprotectedinherited

Field $\eta$ such that the angular components $(V^\theta, V^\varphi)$ of the vector are written:

$V^\theta = {\partial \eta \over \partial\theta} - {1\over\sin\theta} {\partial \mu \over \partial\varphi}$

$V^\varphi = {1\over\sin\theta} {\partial \eta \over \partial\varphi} + {\partial \mu \over \partial\theta}$

.

Definition at line 219 of file vector.h.

◆ p_mu

Scalar* Lorene::Vector::p_mu

mutableprotectedinherited

Field $\mu$ such that the angular components $(V^\theta, V^\varphi)$ of the vector are written:

$V^\theta = {\partial \eta \over \partial\theta} - {1\over\sin\theta} {\partial \mu \over \partial\varphi}$

$V^\varphi = {1\over\sin\theta} {\partial \eta \over \partial\varphi} + {\partial \mu \over \partial\theta}$

.

Definition at line 233 of file vector.h.

◆ p_potential

Scalar* Lorene::Vector::p_potential[N_MET_MAX]

mutableprotectedinherited

The potential $\phi$ giving the gradient part in the Helmholtz decomposition of any 3D vector $\vec{V}: \quad \vec{V} = \vec{\nabla} \phi + \vec{\nabla} \wedge \vec{\psi}$ .

Only in the case of contravariant vectors.

Definition at line 198 of file vector.h.

◆ triad

const Base_vect* Lorene::Tensor::triad

protectedinherited

Vectorial basis (triad) with respect to which the tensor components are defined.

Definition at line 309 of file tensor.h.

◆ type_indice

Itbl Lorene::Tensor::type_indice

protectedinherited

1D array of integers (class Itbl ) of size valence
containing the type of each index: COV for a covariant one and CON for a contravariant one.

Definition at line 316 of file tensor.h.

◆ valence

int Lorene::Tensor::valence

protectedinherited

Valence of the tensor (0 = scalar, 1 = vector, etc...)

Definition at line 304 of file tensor.h.

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

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Vector_divfree() [1/3]

◆ Vector_divfree() [2/3]

◆ Vector_divfree() [3/3]

◆ ~Vector_divfree()

Member Function Documentation

◆ A()

◆ allocate_all()

◆ annule()

◆ annule_domain()

◆ annule_extern_cn()

◆ change_triad()

◆ compute_derive_lie()

◆ curl()

◆ dec_dzpuis()

◆ decompose_div()

◆ del_deriv()

◆ del_derive_met()

◆ derive_con()

◆ derive_cov()

◆ derive_lie()

◆ div_free()

◆ divergence()

◆ down()

◆ eta()

◆ exponential_filter_r()

◆ exponential_filter_ylm()

◆ exponential_filter_ylm_phi()

◆ flux()

◆ get_index_type() [1/2]

◆ get_index_type() [2/2]

◆ get_mp()

◆ get_n_comp()

◆ get_place_met()

◆ get_triad()

◆ get_valence()

◆ inc_dzpuis()

◆ indices()

◆ mu()

◆ ope_killing()

◆ ope_killing_conf()

◆ operator()() [1/5]

◆ operator()() [2/5]

◆ operator()() [3/5]

◆ operator()() [4/5]

◆ operator()() [5/5]

◆ operator+=()

◆ operator-=()

◆ operator=() [1/3]

◆ operator=() [2/3]

◆ operator=() [3/3]

◆ poisson() [1/5]

◆ poisson() [2/5]

◆ poisson() [3/5]

◆ poisson() [4/5]

◆ poisson() [5/5]

◆ poisson_boundary()

◆ poisson_boundary2()

◆ poisson_neumann()

◆ poisson_robin()

◆ position()

◆ potential()

◆ pseudo_spectral_base()

◆ sauve()

◆ set() [1/5]

◆ set() [2/5]

◆ set() [3/5]

◆ set() [4/5]

◆ set() [5/5]

◆ set_A_mu()

◆ set_dependance()

◆ set_der_0x0()

◆ set_der_met_0x0()

◆ set_etat_nondef()

◆ set_etat_qcq()

◆ set_etat_zero()