Class intended to describe valence-2 symmetric tensors. More...

#include <sym_tensor.h>

Inheritance diagram for Lorene::Sym_tensor:

Public Member Functions
	Sym_tensor (const Map &map, const Itbl &tipe, const Base_vect &triad_i)
	Standard constructor.
	Sym_tensor (const Map &map, int tipe, const Base_vect &triad_i)
	Standard constructor when both indices are of the same type.
	Sym_tensor (const Sym_tensor &a)
	Copy constructor.
	Sym_tensor (const Tensor &a)
	Constructor from a `Tensor` .
	Sym_tensor (const Map &map, const Base_vect &triad_i, FILE *fich)
	Constructor from a file (see `sauve(FILE*)` ).
virtual	~Sym_tensor ()
	Destructor.
virtual void	operator= (const Sym_tensor &a)
	Assignment to another `Sym_tensor`.
virtual void	operator= (const Tensor_sym &a)
	Assignment to a `Tensor_sym`.
virtual void	operator= (const Tensor &a)
	Assignment to a `Tensor` .
void	set_longit_trans (const Vector &v, const Sym_tensor_trans &a)
	Assigns the derived members `p_longit_pot` and `p_transverse` and updates the components accordingly.
void	set_auxiliary (const Scalar &trr, const Scalar &eta_over_r, const Scalar &mu_over_r, const Scalar &www, const Scalar &xxx, const Scalar &ttt)
	Assigns the component $T^{rr}$ and the derived members `p_eta` , `p_mu` , `p_www`, `p_xxx` and `p_ttt` , fro, their values and $\eta / r$ , $\mu / r$ .
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` ).
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` ).
const Vector &	divergence (const Metric &) const
	Returns the divergence of `this` with respect to a `Metric` .
Sym_tensor	derive_lie (const Vector &v) const
	Computes the Lie derivative of `this` with respect to some vector field `v`.
const Sym_tensor_trans &	transverse (const Metric &gam, Param *par=0x0, int method_poisson=6) const
	Computes the transverse part ${}^t T^{ij}$ of the tensor with respect to a given metric, transverse meaning divergence-free with respect to that metric.
const Vector &	longit_pot (const Metric &gam, Param *par=0x0, int method_poisson=6) const
	Computes the vector potential of longitudinal part of the tensor (see documentation of method `transverse()` above).
virtual const Scalar &	eta (Param *par=0x0) const
	Gives the field $\eta$ (see member `p_eta` ).
const Scalar &	mu (Param *par=0x0) const
	Gives the field $\mu$ (see member `p_mu` ).
const Scalar &	www () const
	Gives the field W (see member `p_www` ).
const Scalar &	xxx () const
	Gives the field X (see member `p_xxx` ).
const Scalar &	ttt () const
	Gives the field T (see member `p_ttt` ).
const Scalar &	compute_A (bool output_ylm=true, Param *par=0x0) const
	Gives the field A (see member `p_aaa` ).
const Scalar &	compute_tilde_B (bool output_ylm=true, Param *par=0x0) const
	Gives the field $\tilde{B}$ (see member `p_tilde_b` ).
Scalar	compute_tilde_B_tt (bool output_ylm=true, Param *par=0x0) const
	Gives the field $\tilde{B}$ (see member `p_tilde_b` ) associated with the TT-part of the `Sym_tensor` .
const Scalar &	compute_tilde_C (bool output_ylm=true, Param *par=0x0) const
	Gives the field $\tilde{C}$ (see member `p_tilde_c` ).
int	sym_index1 () const
	Number of the first symmetric index (`0<=` `id_sym1` < `valence` ).
int	sym_index2 () const
	Number of the second symmetric index (`id_sym1` < `id_sym2` < `valence` ).
virtual int	position (const Itbl &ind) const
	Returns the position in the array `cmp` of a component given by its indices.
virtual Itbl	indices (int pos) const
	Returns the indices of a component given by its position in the array `cmp` .
virtual void	sauve (FILE *) const
	Save in a binary file.
const Tensor_sym &	derive_cov (const Metric &gam) const
	Returns the covariant derivative of `this` with respect to some metric $\gamma$ .
const Tensor_sym &	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.
virtual void	set_etat_nondef ()
	Sets the logical state of all components to `ETATNONDEF` (undefined state).
virtual void	set_etat_zero ()
	Sets the logical state of all components to `ETATZERO` (zero state).
virtual void	set_etat_qcq ()
	Sets the logical state of all components to `ETATQCQ` (ordinary state).
virtual void	allocate_all ()
	Performs the memory allocation of all the elements, down to the `double` arrays of the `Tbl` s.
virtual void	change_triad (const Base_vect &new_triad)
	Sets a new vectorial basis (triad) of decomposition and modifies the components accordingly.
void	set_triad (const Base_vect &new_triad)
	Assigns a new vectorial basis (triad) of decomposition.
Scalar &	set (const Itbl &ind)
	Returns the value of a component (read/write version).
Scalar &	set (int i1, int i2)
	Returns the value of a component for a tensor of valence 2 (read/write version).
Scalar &	set (int i1, int i2, int i3)
	Returns the value of a component for a tensor of valence 3 (read/write version).
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).
void	annule_domain (int l)
	Sets the `Tensor` to zero in a given domain.
virtual void	annule (int l_min, int l_max)
	Sets the `Tensor` to zero in several domains.
void	annule_extern_cn (int l_0, int deg)
	Performs a smooth (C^n) transition in a given domain to zero.
virtual void	std_spectral_base ()
	Sets the standard spectal bases of decomposition for each component.
virtual void	std_spectral_base_odd ()
	Sets the standard odd spectal bases of decomposition for each component.
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).
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).
Tensor	up (int ind, const Metric &gam) const
	Computes a new tensor by raising an index of `*this`.
Tensor	down (int ind, const Metric &gam) const
	Computes a new tensor by lowering an index of `*this`.
Tensor	up_down (const Metric &gam) const
	Computes a new tensor by raising or lowering all the indices of `*this` .
Tensor	trace (int ind1, int ind2) const
	Trace on two different type indices.
Tensor	trace (int ind1, int ind2, const Metric &gam) const
	Trace with respect to a given metric.
Scalar	trace () const
	Trace on two different type indices for a valence 2 tensor.
Scalar	trace (const Metric &gam) const
	Trace with respect to a given metric for a valence 2 tensor.
const Map &	get_mp () const
	Returns the mapping.
const Base_vect *	get_triad () const
	Returns the vectorial basis (triad) on which the components are defined.
int	get_valence () const
	Returns the valence.
int	get_n_comp () const
	Returns the number of stored components.
int	get_index_type (int i) const
	Gives the type (covariant or contravariant) of the index number `i` .
Itbl	get_index_type () const
	Returns the types of all the indices.
int &	set_index_type (int i)
	Sets the type of the index number `i` .
Itbl &	set_index_type ()
	Sets the types of all the indices.
const Scalar &	operator() (const Itbl &ind) const
	Returns the value of a component (read-only version).
const Scalar &	operator() (int i1, int i2) const
	Returns the value of a component for a tensor of valence 2 (read-only version).
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).
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).
void	operator+= (const Tensor &)
	+= Tensor
void	operator-= (const Tensor &)
	-= Tensor
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.

Protected Member Functions
virtual void	del_deriv () const
	Deletes the derived quantities.
void	set_der_0x0 () const
	Sets the pointers on derived quantities to 0x0.
virtual void	del_derive_met (int i) const
	Logical destructor of the derivatives depending on the i-th element of `met_depend` specific to the class `Sym_tensor` (`p_transverse` , etc...).
void	set_der_met_0x0 (int i) const
	Sets all the i-th components of `met_depend` specific to the class `Sym_tensor` (`p_transverse` , etc...) to 0x0.
Scalar	get_tilde_B_from_TT_trace (const Scalar &tilde_B_tt_in, const Scalar &trace) const
	Computes $\tilde{B}$ (see `Sym_tensor::p_tilde_b` ) from its transverse-traceless part and the trace.
Sym_tensor *	inverse () const
	Returns a pointer on the inverse of the `Sym_tensor` (seen as a matrix).
void	set_dependance (const Metric &) const
	To be used to describe the fact that the derivatives members have been calculated with `met` .
int	get_place_met (const Metric &) const
	Returns the position of the pointer on `metre` in the array `met_depend` .
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` ).

Protected Attributes
Sym_tensor_trans *	p_transverse [N_MET_MAX]
	Array of the transverse part ${}^t T^{ij}$ of the tensor with respect to various metrics, transverse meaning divergence-free with respect to a metric.
Vector *	p_longit_pot [N_MET_MAX]
	Array of the vector potential of the longitudinal part of the tensor with respect to various metrics (see documentation of member `p_transverse`.
Scalar *	p_eta
	Field $\eta$ such that the components $(T^{r\theta}, T^{r\varphi})$ of the tensor are written (has only meaning with spherical components!):
Scalar *	p_mu
	Field $\mu$ such that the components $(T^{r\theta}, T^{r\varphi})$ of the tensor are written (has only meaning with spherical components!):
Scalar *	p_www
	Field W such that the components $T^{\theta\theta}, T^{\varphi\varphi}$ and $T^{\theta\varphi}$ of the tensor are written (has only meaning with spherical components!):
Scalar *	p_xxx
	Field X such that the components $T^{\theta\theta}, T^{\varphi\varphi}$ and $T^{\theta\varphi}$ of the tensor are written (has only meaning with spherical components!):
Scalar *	p_ttt
	Field T defined as $T = T^{\theta\theta} + T^{\varphi\varphi}$ .
Scalar *	p_aaa
	Field A defined from X and $\mu$ insensitive to the longitudinal part of the `Sym_tensor` (only for $\ell \geq 2$ ).
Scalar *	p_tilde_b
	Field $\tilde{B}$ defined from $h^{rr}, \eta, W$ and h insensitive to the longitudinal part of the `Sym_tensor`.
Scalar *	p_tilde_c
	Field $\tilde{C}$ defined from $h^{rr}, \eta, W$ and h insensitive to the longitudinal part of the `Sym_tensor`.
int	id_sym1
	Number of the first symmetric index (`0<=` `id_sym1` < `valence` ).
int	id_sym2
	Number of the second symmetric index (`id_sym1` < `id_sym2` < `valence` ).
const Map *const	mp
	Mapping on which the numerical values at the grid points are defined.
int	valence
	Valence of the tensor (0 = scalar, 1 = vector, etc...).
const Base_vect *	triad
	Vectorial basis (triad) with respect to which the tensor components are defined.
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.
int	n_comp
	Number of stored components, depending on the symmetry.
Scalar **	cmp
	Array of size `n_comp` of pointers onto the components.
const Metric *	met_depend [N_MET_MAX]
	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.
Tensor *	p_derive_cov [N_MET_MAX]
	Array of pointers on the covariant derivatives of `this` with respect to various metrics.
Tensor *	p_derive_con [N_MET_MAX]
	Array of pointers on the contravariant derivatives of `this` with respect to various metrics.
Tensor *	p_divergence [N_MET_MAX]
	Array of pointers on the divergence of `this` with respect to various metrics.

Friends
class	Metric

Detailed Description

Class intended to describe valence-2 symmetric tensors.

The storage and the calculations are different and quicker than with an usual Tensor .

The valence must be 2.()

Definition at line 223 of file sym_tensor.h.

Constructor & Destructor Documentation

◆ Sym_tensor() [1/5]

Lorene::Sym_tensor::Sym_tensor	(	const Map &	map,
		const Itbl &	tipe,
		const Base_vect &	triad_i )

Standard constructor.

Parameters

map	the mapping
tipe	1-D array of integers (class `Itbl` ) of size 2 containing the type of each index, `COV` for a covariant one and `CON` for a contravariant one, with the following storage convention: `tipe(0)` : type of the first index `tipe(1)` : type of the second index
triad_i	vectorial basis (triad) with respect to which the tensor components are defined

Definition at line 142 of file sym_tensor.C.

References Lorene::Map(), set_der_0x0(), and Lorene::Tensor_sym::Tensor_sym().

◆ Sym_tensor() [2/5]

Lorene::Sym_tensor::Sym_tensor	(	const Map &	map,
		int	tipe,
		const Base_vect &	triad_i )

Standard constructor when both indices are of the same type.

Parameters

map	the mapping
tipe	the type of the indices.
triad_i	vectorial basis (triad) with respect to which the tensor components are defined

Definition at line 152 of file sym_tensor.C.

References Lorene::Map(), set_der_0x0(), and Lorene::Tensor_sym::Tensor_sym().

◆ Sym_tensor() [3/5]

Lorene::Sym_tensor::Sym_tensor ( const Sym_tensor & a )

Copy constructor.

Definition at line 160 of file sym_tensor.C.

References Lorene::Tensor::get_place_met(), Lorene::Tensor::met_depend, p_eta, p_longit_pot, p_mu, p_transverse, p_www, p_xxx, Lorene::Tensor::set_dependance(), set_der_0x0(), Sym_tensor(), and Lorene::Tensor_sym::Tensor_sym().

◆ Sym_tensor() [4/5]

Lorene::Sym_tensor::Sym_tensor ( const Tensor & a )

Constructor from a Tensor .

The symmetry of the input tensor is assumed but is not checked.

Definition at line 193 of file sym_tensor.C.

References Lorene::Tensor::cmp, Lorene::Tensor_sym::indices(), Lorene::Tensor::mp, Lorene::Tensor::n_comp, Lorene::Tensor::position(), set_der_0x0(), Lorene::Tensor_sym::Tensor_sym(), Lorene::Tensor::triad, Lorene::Tensor::type_indice, and Lorene::Tensor::valence.

◆ Sym_tensor() [5/5]

Lorene::Sym_tensor::Sym_tensor	(	const Map &	map,
		const Base_vect &	triad_i,
		FILE *	fich )

Constructor from a file (see 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.
fich	file which has been used by the function `sauve(FILE*)` .

Definition at line 210 of file sym_tensor.C.

References Lorene::Map(), Lorene::Tensor::n_comp, set_der_0x0(), Lorene::Tensor_sym::Tensor_sym(), and Lorene::Tensor::valence.

◆ ~Sym_tensor()

Lorene::Sym_tensor::~Sym_tensor ( )

virtual

Destructor.

Definition at line 222 of file sym_tensor.C.

References del_deriv().

Member Function Documentation

◆ compute_A()

const Scalar & Lorene::Sym_tensor::compute_A	(	bool	output_ylm = true,
		Param *	par = 0x0 ) const

Gives the field A (see member p_aaa ).

Parameters

output_ylm a flag to control the spectral decomposition base of the result: if true (default) the spherical harmonics base is used.

Definition at line 316 of file sym_tensor_aux.C.

References Lorene::Scalar::div_r_dzpuis(), Lorene::Scalar::div_tant(), Lorene::dsdr(), Lorene::Scalar::dsdt(), Lorene::Scalar::get_dzpuis(), Lorene::Tensor::mp, Lorene::Tensor::operator()(), p_aaa, Lorene::Scalar::poisson_angu(), Lorene::Scalar::stdsdp(), Lorene::Tensor::triad, and xxx().

◆ compute_tilde_B()

const Scalar & Lorene::Sym_tensor::compute_tilde_B	(	bool	output_ylm = true,
		Param *	par = 0x0 ) const

Gives the field $\tilde{B}$ (see member p_tilde_b ).

Parameters

output_ylm a flag to control the spectral decomposition base of the result: if true (default) the spherical harmonics base is used.

Definition at line 362 of file sym_tensor_aux.C.

References Lorene::Scalar::annule_hard(), Lorene::Valeur::c_cf, Lorene::Scalar::div_r_dzpuis(), Lorene::Scalar::div_tant(), Lorene::Scalar::dsdr(), Lorene::Scalar::dsdt(), Lorene::Scalar::get_dzpuis(), Lorene::Scalar::get_etat(), Lorene::Scalar::get_spectral_base(), Lorene::Scalar::get_spectral_va(), Lorene::Base_val::give_quant_numbers(), Lorene::Tensor::mp, Lorene::Tensor::operator()(), p_tilde_b, Lorene::Scalar::poisson_angu(), Lorene::Scalar::set_spectral_va(), Lorene::Scalar::stdsdp(), Lorene::Tensor::triad, ttt(), www(), and Lorene::Valeur::ylm().

◆ compute_tilde_B_tt()

Scalar Lorene::Sym_tensor::compute_tilde_B_tt	(	bool	output_ylm = true,
		Param *	par = 0x0 ) const

Gives the field $\tilde{B}$ (see member p_tilde_b ) associated with the TT-part of the Sym_tensor .

Parameters

output_ylm a flag to control the spectral decomposition base of the result: if true (default) the spherical harmonics base is used.

Definition at line 478 of file sym_tensor_aux.C.

References Lorene::Scalar::annule_hard(), Lorene::Valeur::c, Lorene::Valeur::c_cf, compute_tilde_B(), Lorene::Scalar::div_r_dzpuis(), Lorene::Scalar::dsdr(), Lorene::Scalar::get_dzpuis(), Lorene::Scalar::get_etat(), Lorene::Scalar::get_spectral_base(), Lorene::Scalar::get_spectral_va(), Lorene::Base_val::give_quant_numbers(), Lorene::Tensor::mp, Lorene::Tensor::operator()(), Lorene::Mtbl_cf::set(), Lorene::Scalar::set_dzpuis(), Lorene::Scalar::set_spectral_va(), ttt(), Lorene::Valeur::ylm(), and Lorene::Valeur::ylm_i().

◆ compute_tilde_C()

const Scalar & Lorene::Sym_tensor::compute_tilde_C	(	bool	output_ylm = true,
		Param *	par = 0x0 ) const

Gives the field $\tilde{C}$ (see member p_tilde_c ).

Parameters

output_ylm a flag to control the spectral decomposition base of the result: if true (default) the spherical harmonics base is used.

Definition at line 596 of file sym_tensor_aux.C.

References Lorene::Scalar::annule_hard(), Lorene::Valeur::c_cf, Lorene::Scalar::div_r_dzpuis(), Lorene::Scalar::div_tant(), Lorene::Scalar::dsdr(), Lorene::Scalar::dsdt(), Lorene::Scalar::get_dzpuis(), Lorene::Scalar::get_etat(), Lorene::Scalar::get_spectral_base(), Lorene::Scalar::get_spectral_va(), Lorene::Base_val::give_quant_numbers(), Lorene::Tensor::mp, Lorene::Tensor::operator()(), p_tilde_c, Lorene::Scalar::poisson_angu(), Lorene::Scalar::set_spectral_va(), Lorene::Scalar::stdsdp(), Lorene::Tensor::triad, ttt(), www(), and Lorene::Valeur::ylm().

◆ del_deriv()

void Lorene::Sym_tensor::del_deriv ( ) const

protectedvirtual

Deletes the derived quantities.

Reimplemented from Lorene::Tensor.

Reimplemented in Lorene::Sym_tensor_trans, and Lorene::Sym_tensor_tt.

Definition at line 286 of file sym_tensor.C.

References Lorene::Tensor::del_deriv(), del_derive_met(), p_aaa, p_eta, p_mu, p_tilde_b, p_tilde_c, p_ttt, p_www, p_xxx, and set_der_0x0().

◆ del_derive_met()

void Lorene::Sym_tensor::del_derive_met ( int i ) const

protectedvirtual

Logical destructor of the derivatives depending on the i-th element of met_depend specific to the class Sym_tensor (p_transverse , etc...).

Reimplemented from Lorene::Tensor.

Definition at line 320 of file sym_tensor.C.

References Lorene::Tensor::del_derive_met(), Lorene::Tensor::met_depend, p_longit_pot, p_transverse, and set_der_met_0x0().

◆ derive_lie()

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

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

Definition at line 360 of file sym_tensor.C.

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

◆ divergence()

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

Returns the divergence of this with respect to a Metric .

The indices are assumed to be contravariant.

Definition at line 349 of file sym_tensor.C.

References Lorene::Tensor::divergence().

◆ eta()

const Scalar & Lorene::Sym_tensor::eta ( Param * par = 0x0 ) const

virtual

Gives the field $\eta$ (see member p_eta ).

Reimplemented in Lorene::Sym_tensor_tt.

Definition at line 111 of file sym_tensor_aux.C.

References Lorene::Scalar::div_tant(), Lorene::Scalar::dsdt(), Lorene::Scalar::get_dzpuis(), Lorene::Tensor::mp, Lorene::Scalar::mult_r_dzpuis(), Lorene::Tensor::operator()(), p_eta, Lorene::Scalar::poisson_angu(), Lorene::Scalar::stdsdp(), and Lorene::Tensor::triad.

◆ exponential_filter_r()

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

virtual

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

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

Reimplemented from Lorene::Tensor.

Definition at line 446 of file sym_tensor.C.

References Lorene::Tensor::cmp, Lorene::Scalar::div_r(), eta(), Lorene::Scalar::exponential_filter_r(), exponential_filter_r(), Lorene::Tensor::mp, mu(), Lorene::Tensor::n_comp, Lorene::Tensor::operator()(), set_auxiliary(), Lorene::Tensor::triad, ttt(), www(), and xxx().

◆ exponential_filter_ylm()

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

virtual

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, $\eta$ , $\mu$ , W, X, T for spherical components.

Reimplemented from Lorene::Tensor.

Definition at line 471 of file sym_tensor.C.

References Lorene::Tensor::cmp, Lorene::Scalar::div_r(), eta(), Lorene::Scalar::exponential_filter_ylm(), exponential_filter_ylm(), Lorene::Tensor::mp, mu(), Lorene::Tensor::n_comp, Lorene::Tensor::operator()(), set_auxiliary(), Lorene::Tensor::triad, ttt(), www(), and xxx().

◆ get_tilde_B_from_TT_trace()

Scalar Lorene::Sym_tensor::get_tilde_B_from_TT_trace	(	const Scalar &	tilde_B_tt_in,
		const Scalar &	trace ) const

protected

Computes $\tilde{B}$ (see Sym_tensor::p_tilde_b ) from its transverse-traceless part and the trace.

Definition at line 531 of file sym_tensor_aux.C.

References Lorene::Scalar::annule_hard(), Lorene::Tbl::annule_hard(), Lorene::Valeur::c, Lorene::Valeur::c_cf, Lorene::Scalar::div_r_dzpuis(), Lorene::Scalar::dsdr(), Lorene::Scalar::get_dzpuis(), Lorene::Scalar::get_etat(), Lorene::Scalar::get_spectral_base(), Lorene::Scalar::get_spectral_va(), Lorene::Base_val::give_quant_numbers(), Lorene::Tensor::mp, Lorene::Base_val::mult_x(), Lorene::Tensor::operator()(), Lorene::Mtbl_cf::set(), Lorene::Scalar::set_dzpuis(), Lorene::Scalar::set_spectral_base(), Lorene::Scalar::set_spectral_va(), Lorene::Tensor::triad, and Lorene::Valeur::ylm().

◆ inverse()

Sym_tensor * Lorene::Sym_tensor::inverse ( ) const

protected

Returns a pointer on the inverse of the Sym_tensor
(seen as a matrix).

Definition at line 372 of file sym_tensor.C.

References Lorene::Tensor::mp, Lorene::Tensor::operator()(), Lorene::Tensor::set(), Sym_tensor(), Lorene::Tensor::triad, and Lorene::Tensor::type_indice.

◆ longit_pot()

const Vector & Lorene::Sym_tensor::longit_pot	(	const Metric &	gam,
		Param *	par = 0x0,
		int	method_poisson = 6 ) const

Computes the vector potential $W^i$ of longitudinal part of the tensor (see documentation of method transverse() above).

Parameters

gam	metric with respect to the transverse decomposition is performed
par	parameters for the vector Poisson equation
method_poisson	type of method for solving the vector Poisson equation to get the longitudinal part (see method `Vector::poisson`)

Definition at line 143 of file sym_tensor_decomp.C.

References Lorene::Tensor::dec_dzpuis(), Lorene::Tensor::derive_con(), Lorene::diffrel(), divergence(), Lorene::Tensor::divergence(), Lorene::Vector::divergence(), Lorene::Tensor::get_place_met(), Lorene::maxabs(), Lorene::Tensor::mp, p_longit_pot, Lorene::Vector::poisson(), and Lorene::Tensor::set_dependance().

◆ mu()

const Scalar & Lorene::Sym_tensor::mu ( Param * par = 0x0 ) const

Gives the field $\mu$ (see member p_mu ).

Definition at line 151 of file sym_tensor_aux.C.

References Lorene::Scalar::div_tant(), Lorene::Scalar::dsdt(), Lorene::Scalar::get_dzpuis(), Lorene::Tensor::mp, Lorene::Scalar::mult_r_dzpuis(), Lorene::Tensor::operator()(), p_mu, Lorene::Scalar::poisson_angu(), Lorene::Scalar::stdsdp(), and Lorene::Tensor::triad.

◆ operator=() [1/3]

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

virtual

Assignment to another Sym_tensor.

Reimplemented in Lorene::Sym_tensor_trans, and Lorene::Sym_tensor_tt.

Definition at line 234 of file sym_tensor.C.

References del_deriv(), Lorene::Tensor::get_place_met(), Lorene::Tensor::met_depend, Lorene::Tensor_sym::operator=(), p_eta, p_longit_pot, p_mu, p_transverse, p_www, p_xxx, Lorene::Tensor::set_dependance(), and Sym_tensor().

◆ operator=() [2/3]

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

virtual

Assignment to a Tensor .

The symmetry is assumed but not checked.

Reimplemented from Lorene::Tensor_sym.

Reimplemented in Lorene::Sym_tensor_trans, and Lorene::Sym_tensor_tt.

Definition at line 275 of file sym_tensor.C.

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

◆ operator=() [3/3]

void Lorene::Sym_tensor::operator= ( const Tensor_sym & a )

virtual

Assignment to a Tensor_sym.

Reimplemented from Lorene::Tensor_sym.

Reimplemented in Lorene::Sym_tensor_trans, and Lorene::Sym_tensor_tt.

Definition at line 267 of file sym_tensor.C.

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

◆ set_auxiliary()

void Lorene::Sym_tensor::set_auxiliary	(	const Scalar &	trr,
		const Scalar &	eta_over_r,
		const Scalar &	mu_over_r,
		const Scalar &	www,
		const Scalar &	xxx,
		const Scalar &	ttt )

Assigns the component $T^{rr}$ and the derived members p_eta , p_mu , p_www, p_xxx and p_ttt , fro, their values and $\eta / r$ , $\mu / r$ .

It updates the other components accordingly.

Definition at line 266 of file sym_tensor_aux.C.

References Lorene::Scalar::check_dzpuis(), del_deriv(), Lorene::Scalar::dsdt(), Lorene::Scalar::get_dzpuis(), Lorene::Scalar::lapang(), p_eta, p_mu, p_ttt, p_www, p_xxx, Lorene::Tensor::set(), Lorene::Scalar::set_spectral_va(), Lorene::Scalar::stdsdp(), Lorene::Tensor::triad, and Lorene::Valeur::ylm_i().

◆ set_der_0x0()

void Lorene::Sym_tensor::set_der_0x0 ( ) const

protected

Sets the pointers on derived quantities to 0x0.

Definition at line 305 of file sym_tensor.C.

References p_aaa, p_eta, p_mu, p_tilde_b, p_tilde_c, p_ttt, p_www, p_xxx, and set_der_met_0x0().

◆ set_der_met_0x0()

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

protected

Sets all the i-th components of met_depend specific to the class Sym_tensor (p_transverse , etc...) to 0x0.

Definition at line 335 of file sym_tensor.C.

References p_longit_pot, and p_transverse.

◆ set_longit_trans()

void Lorene::Sym_tensor::set_longit_trans	(	const Vector &	v,
		const Sym_tensor_trans &	a )

Assigns the derived members p_longit_pot and p_transverse and updates the components accordingly.

(see the documentation of these derived members for details)

Definition at line 88 of file sym_tensor_decomp.C.

References Lorene::dec_dzpuis(), del_deriv(), Lorene::Tensor::get_index_type(), Lorene::Sym_tensor_trans::get_met_div(), Lorene::Tensor::get_place_met(), Lorene::Vector::ope_killing(), p_longit_pot, p_transverse, and Lorene::Tensor::set_dependance().

◆ transverse()

const Sym_tensor_trans & Lorene::Sym_tensor::transverse	(	const Metric &	gam,
		Param *	par = 0x0,
		int	method_poisson = 6 ) const

Computes the transverse part ${}^t T^{ij}$ of the tensor with respect to a given metric, transverse meaning divergence-free with respect to that metric.

Denoting *this by $T^{ij}$ , we then have

$\‍[ T^{ij} = {}^t T^{ij} + \nabla^i W^j + \nabla^j W^i \qquad\mbox{with}\quad \nabla_j {}^t T^{ij} = 0 *\‍]$

where $\nabla_i$ denotes the covariant derivative with respect to the given metric and $W^i$ is the vector potential of the longitudinal part of $T^{ij}$ (function longit_pot() below)

Parameters

gam	metric with respect to the transverse decomposition is performed
par	parameters for the vector Poisson equation
method_poisson	type of method for solving the vector Poisson equation to get the longitudinal part (see method `Vector::poisson`)

Definition at line 110 of file sym_tensor_decomp.C.

References Lorene::Tensor::cmp, Lorene::Tensor::get_place_met(), Lorene::Tensor::inc_dzpuis(), longit_pot(), Lorene::Tensor::mp, Lorene::Tensor::n_comp, Lorene::Vector::ope_killing(), p_transverse, Lorene::Tensor::set_dependance(), Sym_tensor(), Lorene::Tensor::triad, and Lorene::Tensor::type_indice.

◆ ttt()

const Scalar & Lorene::Sym_tensor::ttt ( ) const

Gives the field T (see member p_ttt ).

Definition at line 190 of file sym_tensor_aux.C.

References p_ttt, and Lorene::Tensor::triad.

◆ www()

const Scalar & Lorene::Sym_tensor::www ( ) const

Gives the field W (see member p_www ).

Definition at line 209 of file sym_tensor_aux.C.

References Lorene::Scalar::div_tant(), Lorene::Scalar::dsdt(), Lorene::Tensor::operator()(), p_www, Lorene::Scalar::poisson_angu(), Lorene::Scalar::stdsdp(), and Lorene::Tensor::triad.

◆ xxx()

const Scalar & Lorene::Sym_tensor::xxx ( ) const

Gives the field X (see member p_xxx ).

Definition at line 240 of file sym_tensor_aux.C.

References Lorene::Scalar::div_tant(), Lorene::Scalar::dsdt(), Lorene::Tensor::operator()(), p_xxx, Lorene::Scalar::poisson_angu(), Lorene::Scalar::stdsdp(), and Lorene::Tensor::triad.

◆ Metric

friend class Metric

friend

Definition at line 588 of file sym_tensor.h.

Member Data Documentation

◆ p_aaa

Scalar* Lorene::Sym_tensor::p_aaa

mutableprotected

Field A defined from X and $\mu$ insensitive to the longitudinal part of the Sym_tensor (only for $\ell \geq 2$ ).

Its definition reads

$\‍[A = \frac{\partial X}{\partial r} - \frac{\mu}{r^2}. \‍]$

Definition at line 322 of file sym_tensor.h.

◆ p_eta

Scalar* Lorene::Sym_tensor::p_eta

mutableprotected

Field $\eta$ such that the components $(T^{r\theta}, T^{r\varphi})$ of the tensor are written (has only meaning with spherical components!):

$\‍[ T^{r\theta} = {1\over r} \left( {\partial \eta \over \partial\theta} - {1\over\sin\theta} {\partial \mu \over \partial\varphi} \right) *\‍]$

$\‍[ T^{r\varphi} = {1\over r} \left( {1\over\sin\theta} {\partial \eta \over \partial\varphi} + {\partial \mu \over \partial\theta} \right) *\‍]$

Definition at line 260 of file sym_tensor.h.

◆ p_longit_pot

Vector* Lorene::Sym_tensor::p_longit_pot[N_MET_MAX]

mutableprotected

Array of the vector potential of the longitudinal part of the tensor with respect to various metrics (see documentation of member p_transverse.

Definition at line 246 of file sym_tensor.h.

◆ p_mu

Scalar* Lorene::Sym_tensor::p_mu

mutableprotected

Field $\mu$ such that the components $(T^{r\theta}, T^{r\varphi})$ of the tensor are written (has only meaning with spherical components!):

$\‍[ T^{r\theta} = {1\over r} \left( {\partial \eta \over \partial\theta} - {1\over\sin\theta} {\partial \mu \over \partial\varphi} \right) *\‍]$

$\‍[ T^{r\varphi} = {1\over r} \left( {1\over\sin\theta} {\partial \eta \over \partial\varphi} + {\partial \mu \over \partial\theta} \right) *\‍]$

Definition at line 274 of file sym_tensor.h.

◆ p_tilde_b

Scalar* Lorene::Sym_tensor::p_tilde_b

mutableprotected

Field $\tilde{B}$ defined from $h^{rr}, \eta, W$ and h insensitive to the longitudinal part of the Sym_tensor.

It is defined for each multipolar momentum $\ell \geq 2$ by

$\‍[\tilde{B} = (\ell + 2) \frac{\partial W}{\partial r} + \ell(\ell + 2) \frac{W}{r} - \frac{2\eta}{r^2} + \frac{(\ell +2)T}{2r(\ell + 1)} + \frac{1}{2(\ell + 1)} \frac{\partial T}{\partial r} - \frac{h^{rr}} {(\ell + 1)r}. \‍]$

Definition at line 334 of file sym_tensor.h.

◆ p_tilde_c

Scalar* Lorene::Sym_tensor::p_tilde_c

mutableprotected

Field $\tilde{C}$ defined from $h^{rr}, \eta, W$ and h insensitive to the longitudinal part of the Sym_tensor.

It is defined for each multipolar momentum $\ell \geq 2$ by

$\‍[\tilde{C} = - (\ell - 1) \frac{\partial W}{\partial r} + (\ell + 1)(\ell - 1) \frac{W}{r} - \frac{2\eta}{r^2} + \frac{(\ell - 1)T}{2r\ell} - \frac{1}{2 \ell } \frac{\partial T}{\partial r} - \frac{h^{rr}} {\ell r}. \‍]$

Definition at line 346 of file sym_tensor.h.

◆ p_transverse

Sym_tensor_trans* Lorene::Sym_tensor::p_transverse[N_MET_MAX]

mutableprotected

Array of the transverse part ${}^t T^{ij}$ of the tensor with respect to various metrics, transverse meaning divergence-free with respect to a metric.

Denoting *this by $T^{ij}$ , we then have

$\‍[ T^{ij} = {}^t T^{ij} + \nabla^i W^j + \nabla^j W^i \qquad\mbox{with}\quad \nabla_j {}^t T^{ij} = 0 *\‍]$

where $\nabla_i$ denotes the covariant derivative with respect to the given metric and $W^i$ is the vector potential of the longitudinal part of $T^{ij}$ (member p_longit_pot below)

Definition at line 239 of file sym_tensor.h.

◆ p_ttt

Scalar* Lorene::Sym_tensor::p_ttt

mutableprotected

Field T defined as $T = T^{\theta\theta} + T^{\varphi\varphi}$ .

Definition at line 315 of file sym_tensor.h.

◆ p_www

Scalar* Lorene::Sym_tensor::p_www

mutableprotected

Field W such that the components $T^{\theta\theta}, T^{\varphi\varphi}$ and $T^{\theta\varphi}$ of the tensor are written (has only meaning with spherical components!):

$\‍[ \frac{1}{2}\left(T^{\theta\theta} - T^{\varphi\varphi} \right) = \frac{\partial^2 W}{\partial\theta^2} - \frac{1}{\tan \theta} \frac{\partial W}{\partial \theta} - \frac{1}{\sin^2 \theta} \frac{\partial^2 W}{\partial \varphi^2} - 2\frac{\partial}{\partial \theta} \left( \frac{1}{\sin \theta} \frac{\partial X}{\partial \varphi} \right) , *\‍]$

$\‍[ T^{\theta\varphi} = \frac{\partial^2 X}{\partial\theta^2} - \frac{1}{\tan \theta} \frac{\partial X}{\partial \theta} - \frac{1}{\sin^2 \theta} \frac{\partial^2 X}{\partial \varphi^2} + 2\frac{\partial}{\partial \theta} \left( \frac{1}{\sin \theta} \frac{\partial W}{\partial \varphi} \right) . *\‍]$

Definition at line 293 of file sym_tensor.h.

◆ p_xxx

Scalar* Lorene::Sym_tensor::p_xxx

mutableprotected

Field X such that the components $T^{\theta\theta}, T^{\varphi\varphi}$ and $T^{\theta\varphi}$ of the tensor are written (has only meaning with spherical components!):

$\‍[ \frac{1}{2}\left(T^{\theta\theta} - T^{\varphi\varphi} \right) = \frac{\partial^2 W}{\partial\theta^2} - \frac{1}{\tan \theta} \frac{\partial W}{\partial \theta} - \frac{1}{\sin^2 \theta} \frac{\partial^2 W}{\partial \varphi^2} - 2\frac{\partial}{\partial \theta} \left( \frac{1}{\sin \theta} \frac{\partial X}{\partial \varphi} \right) , *\‍]$

$\‍[ T^{\theta\varphi} = \frac{\partial^2 X}{\partial\theta^2} - \frac{1}{\tan \theta} \frac{\partial X}{\partial \theta} - \frac{1}{\sin^2 \theta} \frac{\partial^2 X}{\partial \varphi^2} + 2\frac{\partial}{\partial \theta} \left( \frac{1}{\sin \theta} \frac{\partial W}{\partial \varphi} \right) . *\‍]$

Definition at line 312 of file sym_tensor.h.

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

Public Member Functions

Protected Member Functions

Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Sym_tensor() [1/5]

◆ Sym_tensor() [2/5]

◆ Sym_tensor() [3/5]

◆ Sym_tensor() [4/5]

◆ Sym_tensor() [5/5]

◆ ~Sym_tensor()

Member Function Documentation

◆ compute_A()

◆ compute_tilde_B()

◆ compute_tilde_B_tt()

◆ compute_tilde_C()

◆ del_deriv()

◆ del_derive_met()

◆ derive_lie()

◆ divergence()

◆ eta()

◆ exponential_filter_r()

◆ exponential_filter_ylm()

◆ get_tilde_B_from_TT_trace()

◆ inverse()

◆ longit_pot()

◆ mu()

◆ operator=() [1/3]

◆ operator=() [2/3]

◆ operator=() [3/3]

◆ set_auxiliary()

◆ set_der_0x0()

◆ set_der_met_0x0()

◆ set_longit_trans()

◆ transverse()

◆ ttt()

◆ www()

◆ xxx()

Friends And Related Symbol Documentation

◆ Metric

Member Data Documentation

◆ p_aaa

◆ p_eta

◆ p_longit_pot

◆ p_mu

◆ p_tilde_b

◆ p_tilde_c

◆ p_transverse

◆ p_ttt

◆ p_www

◆ p_xxx