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. More...

	Sym_tensor (const Map &map, int tipe, const Base_vect &triad_i)
	Standard constructor when both indices are of the same type. More...

	Sym_tensor (const Sym_tensor &a)
	Copy constructor. More...

	Sym_tensor (const Tensor &a)
	Constructor from a `Tensor` . More...

	Sym_tensor (const Map &map, const Base_vect &triad_i, FILE *fich)
	Constructor from a file (see `sauve(FILE*)` ). More...

virtual	~Sym_tensor ()
	Destructor. More...

virtual void	operator= (const Sym_tensor &a)
	Assignment to another `Sym_tensor`. More...

virtual void	operator= (const Tensor_sym &a)
	Assignment to a `Tensor_sym`. More...

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

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. More...

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 $\eta / r$ , $\mu / r$ . 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...

const Vector &	divergence (const Metric &) const
	Returns the divergence of `this` with respect to a `Metric` . More...

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

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. More...

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). More...

virtual const Scalar &	eta (Param *par=0x0) const
	Gives the field $\eta$ (see member `p_eta` ). More...

const Scalar &	mu (Param *par=0x0) const
	Gives the field $\mu$ (see member `p_mu` ). More...

const Scalar &	www () const
	Gives the field W (see member `p_www` ). More...

const Scalar &	xxx () const
	Gives the field X (see member `p_xxx` ). More...

const Scalar &	ttt () const
	Gives the field T (see member `p_ttt` ). More...

const Scalar &	compute_A (bool output_ylm=true, Param *par=0x0) const
	Gives the field A (see member `p_aaa` ). More...

const Scalar &	compute_tilde_B (bool output_ylm=true, Param *par=0x0) const
	Gives the field $\tilde{B}$ (see member `p_tilde_b` ). More...

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` . More...

const Scalar &	compute_tilde_C (bool output_ylm=true, Param *par=0x0) const
	Gives the field $\tilde{C}$ (see member `p_tilde_c` ). More...

int	sym_index1 () const
	Number of the first symmetric index (`0<=` `id_sym1` < `valence` ) More...

int	sym_index2 () const
	Number of the second symmetric index (`id_sym1` < `id_sym2` < `valence` ) More...

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

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

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

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

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. More...

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...

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

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

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 ()
	Sets the standard spectal bases of decomposition for each component. 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...

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...

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...

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

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

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...). More...

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. More...

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. More...

Sym_tensor *	inverse () const
	Returns a pointer on the inverse of the `Sym_tensor` (seen as a matrix). 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
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. More...

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`. More...

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!): $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) $ . More...

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!): $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) $ . More...

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!): $\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) . $ . More...

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!): $\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) . $ . More...

Scalar *	p_ttt
	Field T defined as $T = T^{\theta\theta} + T^{\varphi\varphi}$ . More...

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

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

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

int	id_sym1
	Number of the first symmetric index (`0<=` `id_sym1` < `valence` ) More...

int	id_sym2
	Number of the second symmetric index (`id_sym1` < `id_sym2` < `valence` ) 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...

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 226 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 145 of file sym_tensor.C.

References set_der_0x0().

◆ 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 155 of file sym_tensor.C.

References set_der_0x0().

◆ Sym_tensor() [3/5]

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

Copy constructor.

Definition at line 163 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(), and set_der_0x0().

◆ 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 196 of file sym_tensor.C.

References Lorene::Tensor::cmp, Lorene::Tensor_sym::indices(), Lorene::Tensor::n_comp, Lorene::Tensor::position(), set_der_0x0(), 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 213 of file sym_tensor.C.

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

◆ ~Sym_tensor()

Lorene::Sym_tensor::~Sym_tensor ( )

virtual

Destructor.

Definition at line 225 of file sym_tensor.C.

References del_deriv().

Member Function Documentation

◆ 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::Tensor::change_triad ( const Base_vect & new_triad )

virtualinherited

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

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

Definition at line 80 of file tensor_change_triad.C.

References 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_np(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_nzone(), Lorene::Tensor::mp, Lorene::Tensor::set(), Lorene::Tensor::triad, Lorene::Tensor::type_indice, and Lorene::Tensor::valence.

◆ 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 319 of file sym_tensor_aux.C.

References Lorene::Scalar::annule_l(), Lorene::Scalar::div_r_dzpuis(), Lorene::Scalar::div_tant(), Lorene::Scalar::dsdt(), Lorene::Scalar::get_dzpuis(), Lorene::Tensor::mp, Lorene::Tensor::operator()(), p_aaa, Lorene::Map::poisson_angu(), Lorene::Scalar::poisson_angu(), Lorene::Scalar::set_spectral_va(), Lorene::Scalar::stdsdp(), Lorene::Tensor::triad, xxx(), Lorene::Valeur::ylm(), and Lorene::Valeur::ylm_i().

◆ 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.

◆ 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 365 of file sym_tensor_aux.C.

◆ 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 481 of file sym_tensor_aux.C.

References compute_tilde_B(), and Lorene::Scalar::get_etat().

◆ 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 599 of file sym_tensor_aux.C.

◆ 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.

◆ del_deriv()

void Lorene::Sym_tensor::del_deriv ( ) const

protectedvirtual

Deletes the derived quantities.

Reimplemented from Lorene::Tensor.

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

Definition at line 289 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 323 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_con()

const Tensor_sym & Lorene::Tensor_sym::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 207 of file tensor_sym_calculus.C.

References Lorene::Tensor::derive_con().

◆ derive_cov()

const Tensor_sym & Lorene::Tensor_sym::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).

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 195 of file tensor_sym_calculus.C.

References Lorene::Tensor::derive_cov().

◆ 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 363 of file sym_tensor.C.

References Lorene::Tensor::compute_derive_lie(), Lorene::Tensor::mp, 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 352 of file sym_tensor.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::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 114 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::Map::poisson_angu(), 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 449 of file sym_tensor.C.

References Lorene::Tensor::cmp, Lorene::Scalar::div_r(), eta(), Lorene::Scalar::exponential_filter_r(), Lorene::Map::get_bvect_cart(), Lorene::Map::get_bvect_spher(), Lorene::Base_vect::identify(), 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 474 of file sym_tensor.C.

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

◆ 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.

◆ 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_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 534 of file sym_tensor_aux.C.

References Lorene::Scalar::get_etat(), and Lorene::Tensor::triad.

◆ 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()

Itbl Lorene::Tensor_sym::indices ( int pos ) const

virtualinherited

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

Parameters

pos	[input] position in the array `cmp` of the pointer to the `Scalar` representing a component

Returns

1-D array of integers (class Itbl ) of size valence giving the value of each index for the component located at the position pos in the array cmp, with the following storage convention:

Itbl(0) : value of the first index (1, 2 or 3)
Itbl(1) : value of the second index (1, 2 or 3)
and so on...

Reimplemented from Lorene::Tensor.

Definition at line 313 of file tensor_sym.C.

References Lorene::Tensor_sym::id_sym1, Lorene::Tensor_sym::id_sym2, Lorene::Tensor::n_comp, Lorene::Itbl::set(), and Lorene::Tensor::valence.

◆ 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 375 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 149 of file sym_tensor_decomp.C.

References Lorene::Tensor::dec_dzpuis(), Lorene::Tensor::derive_con(), Lorene::Tensor_sym::derive_con(), Lorene::diffrel(), divergence(), Lorene::Tensor::divergence(), Lorene::Map::get_mg(), Lorene::Mg3d::get_nzone(), 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 154 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::Map::poisson_angu(), Lorene::Scalar::poisson_angu(), Lorene::Scalar::stdsdp(), and Lorene::Tensor::triad.

◆ operator()() [1/4]

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()() [2/4]

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()() [3/4]

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()() [4/4]

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

virtual

Assignment to another Sym_tensor.

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

Definition at line 237 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, and Lorene::Tensor::set_dependance().

◆ operator=() [2/3]

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_tt, and Lorene::Sym_tensor_trans.

Definition at line 270 of file sym_tensor.C.

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

◆ operator=() [3/3]

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_tt, and Lorene::Sym_tensor_trans.

Definition at line 278 of file sym_tensor.C.

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

◆ position()

int Lorene::Tensor_sym::position ( const Itbl & ind ) const

virtualinherited

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

Parameters

ind	[input] 1-D array of integers (class `Itbl` ) of size `valence` giving 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: position in the array cmp of the pointer to the Scalar containing the component specified by ind

Reimplemented from Lorene::Tensor.

Definition at line 248 of file tensor_sym.C.

References Lorene::Itbl::get_dim(), Lorene::Itbl::get_ndim(), Lorene::Tensor_sym::id_sym1, Lorene::Tensor_sym::id_sym2, Lorene::Itbl::set(), and Lorene::Tensor::valence.

◆ sauve()

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

virtualinherited

Save in a binary file.

Reimplemented from Lorene::Tensor.

Definition at line 375 of file tensor_sym.C.

References Lorene::fwrite_be(), Lorene::Tensor_sym::id_sym1, Lorene::Tensor_sym::id_sym2, and Lorene::Tensor::sauve().

◆ set() [1/4]

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() [2/4]

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() [3/4]

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() [4/4]

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_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 269 of file sym_tensor_aux.C.

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

◆ 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::Sym_tensor::set_der_0x0 ( ) const

protected

Sets the pointers on derived quantities to 0x0.

Definition at line 308 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 338 of file sym_tensor.C.

References p_longit_pot, and p_transverse.

◆ 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_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 94 of file sym_tensor_decomp.C.

References Lorene::Tensor::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().

◆ 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.

◆ 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::Tensor::std_spectral_base ( )

virtualinherited

Sets the standard spectal bases of decomposition for each component.

To be used only with valence lower than or equal 2.

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

Definition at line 935 of file tensor.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::indices(), Lorene::Tensor::mp, Lorene::Tensor::n_comp, Lorene::Scalar::set_spectral_base(), Lorene::Mg3d::std_base_vect_cart(), Lorene::Mg3d::std_base_vect_spher(), Lorene::Scalar::std_spectral_base(), Lorene::Tensor::triad, and Lorene::Tensor::valence.

◆ 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.

◆ sym_index1()

int Lorene::Tensor_sym::sym_index1 ( ) const

inlineinherited

Number of the first symmetric index (0<= id_sym1 < valence )

Definition at line 1162 of file tensor.h.

References Lorene::Tensor_sym::id_sym1.

◆ sym_index2()

int Lorene::Tensor_sym::sym_index2 ( ) const

inlineinherited

Number of the second symmetric index (id_sym1 < id_sym2 < valence )

Definition at line 1167 of file tensor.h.

References Lorene::Tensor_sym::id_sym2.

◆ 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.

◆ 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 116 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(), 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 193 of file sym_tensor_aux.C.

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

◆ 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.

◆ www()

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

Gives the field W (see member p_www ).

Definition at line 212 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 243 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.

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.

◆ id_sym1

int Lorene::Tensor_sym::id_sym1

protectedinherited

Number of the first symmetric index (0<= id_sym1 < valence )

Definition at line 1057 of file tensor.h.

◆ id_sym2

int Lorene::Tensor_sym::id_sym2

protectedinherited

Number of the second symmetric index (id_sym1 < id_sym2 < valence )

Definition at line 1062 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.

◆ 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_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 325 of file sym_tensor.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_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::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 263 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 249 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 277 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 337 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 349 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 242 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 318 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 296 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 315 of file sym_tensor.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

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

◆ allocate_all()

◆ annule()

◆ annule_domain()

◆ annule_extern_cn()

◆ change_triad()

◆ compute_A()

◆ compute_derive_lie()

◆ compute_tilde_B()

◆ compute_tilde_B_tt()

◆ compute_tilde_C()

◆ dec_dzpuis()

◆ del_deriv()

◆ del_derive_met()

◆ derive_con()

◆ derive_cov()

◆ derive_lie()

◆ divergence()

◆ down()

◆ eta()

◆ exponential_filter_r()

◆ exponential_filter_ylm()

◆ exponential_filter_ylm_phi()

◆ get_index_type() [1/2]

◆ get_index_type() [2/2]

◆ get_mp()

◆ get_n_comp()

◆ get_place_met()

◆ get_tilde_B_from_TT_trace()

◆ get_triad()

◆ get_valence()

◆ inc_dzpuis()

◆ indices()

◆ inverse()

◆ longit_pot()

◆ mu()

◆ operator()() [1/4]

◆ operator()() [2/4]

◆ operator()() [3/4]

◆ operator()() [4/4]

◆ operator+=()

◆ operator-=()

◆ operator=() [1/3]

◆ operator=() [2/3]

◆ operator=() [3/3]

◆ position()

◆ sauve()

◆ set() [1/4]

◆ set() [2/4]

◆ set() [3/4]

◆ set() [4/4]

◆ set_auxiliary()

◆ set_dependance()

◆ set_der_0x0()

◆ set_der_met_0x0()

◆ set_etat_nondef()

◆ set_etat_qcq()

◆ set_etat_zero()

◆ set_index_type() [1/2]

◆ set_index_type() [2/2]

◆ set_longit_trans()

◆ set_triad()

◆ spectral_display()

◆ std_spectral_base()

◆ std_spectral_base_odd()

◆ sym_index1()

◆ sym_index2()

◆ trace() [1/4]