Tensor_sym Class Reference
[Tensorial fields]

Symmetric tensors (with respect to two of their arguments). More...

#include <tensor.h>

Inheritance diagram for Tensor_sym:

Public Member Functions
	Tensor_sym (const Map &map, int val, const Itbl &tipe, const Base_vect &triad_i, int index_sym1, int index_sym2)
	Standard constructor.
	Tensor_sym (const Map &map, int val, int tipe, const Base_vect &triad_i, int index_sym1, int index_sym2)
	Standard constructor when all the indices are of the same type.
	Tensor_sym (const Map &map, int tipe0, int tipe1, int tipe2, const Base_vect &triad_i, int index_sym1, int index_sym2)
	Constructor for a valence 3 symmetric tensor.
	Tensor_sym (const Tensor_sym &a)
	Copy constructor.
	Tensor_sym (const Map &map, const Base_vect &triad_i, FILE *fich)
	Constructor from a file (see `sauve(FILE*)` ).
virtual	~Tensor_sym ()
	Destructor.
virtual void	operator= (const Tensor_sym &a)
	Assignment to another `Tensor_sym`.
virtual void	operator= (const Tensor &a)
	Assignment to a `Tensor` NB: the symmetry about the indices `id_sym1` and `id_sym2` of the input tensor is assumed but is not checked.
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.
Tensor_sym	derive_lie (const Vector &v) const
	Computes the Lie derivative of `this` with respect to some vector field `v`.
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).
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 Tensor &	divergence (const Metric &gam) const
	Computes the divergence of `this` with respect to some metric $\gamma$ .
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) const
	Logical destructor of the derivatives depending on the i-th element of `met_depend` .
void	set_der_met_0x0 (int) const
	Sets all the i-th components of `met_depend` , `p_derive_cov` , etc.
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
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.
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
Tensor_sym	operator* (const Tensor &, const Tensor_sym &)
Tensor_sym	operator* (const Tensor_sym &, const Tensor &)
class	Scalar
class	Vector
class	Sym_tensor
class	Tensor_sym
class	Metric
ostream &	operator<< (ostream &, const Tensor &)
Scalar	operator+ (const Tensor &, const Scalar &)
Scalar	operator+ (const Scalar &, const Tensor &)
Scalar	operator- (const Tensor &, const Scalar &)
Scalar	operator- (const Scalar &, const Tensor &)
Tensor	operator* (const Tensor &, const Tensor &)
Tensor_sym	operator* (const Tensor &, const Tensor_sym &)
Tensor_sym	operator* (const Tensor_sym &, const Tensor &)
Tensor_sym	operator* (const Tensor_sym &, const Tensor_sym &)
	Tensorial product of two symmetric tensors.

Detailed Description

Symmetric tensors (with respect to two of their arguments).

This subclass of Tensor is intended to store the components of a tensorial field with respect to a specific basis (triad), in the case the tensor has a valence at least 2 and is symmetric with respect to two of its arguments (or in other words, the components are symmetric with respect to two of their indices). ()

Definition at line 1033 of file tensor.h.

Constructor & Destructor Documentation

Tensor_sym::Tensor_sym	(	const Map &	map,
		int	val,
		const Itbl &	tipe,
		const Base_vect &	triad_i,
		int	index_sym1,
		int	index_sym2
	)

Standard constructor.

Parameters:

	map	the mapping
	val	valence of the tensor (must be at least 2)
	tipe	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, with the following storage convention: `tipe(0)` : type of the first index `tipe(1)` : type of the second index and so on...
	triad_i	vectorial basis (triad) with respect to which the tensor components are defined
	index_sym1	number of the first symmetric index (`0<=` `index_sym1` < `valence` )
	index_sym2	number of the second symmetric index (`index_sym1` < `index_sym2` < `valence` )

Definition at line 65 of file tensor_sym.C.

References id_sym1, id_sym2, and Tensor::valence.

Tensor_sym::Tensor_sym	(	const Map &	map,
		int	val,
		int	tipe,
		const Base_vect &	triad_i,
		int	index_sym1,
		int	index_sym2
	)

Standard constructor when all the indices are of the same type.

Parameters:

	map	the mapping
	val	valence of the tensor (must be at least 2)
	tipe	the type (`COV` or `CON` ) of the indices.
	triad_i	vectorial basis (triad) with respect to which the tensor components are defined.
	index_sym1	number of the first symmetric index (`0<=` `index_sym1` < `valence` )
	index_sym2	number of the second symmetric index (`index_sym1` < `index_sym2` < `valence` )

Definition at line 93 of file tensor_sym.C.

References id_sym1, id_sym2, and Tensor::valence.

Tensor_sym::Tensor_sym	(	const Map &	map,
		int	tipe0,
		int	tipe1,
		int	tipe2,
		const Base_vect &	triad_i,
		int	index_sym1,
		int	index_sym2
	)

Constructor for a valence 3 symmetric tensor.

Parameters:

	map	the mapping
	tipe0	type (`COV` or `CON` ) of the first index.
	tipe1	type (`COV` or `CON` ) of the second index.
	tipe2	type (`COV` or `CON` ) of the third index.
	triad_i	vectorial basis (triad) with respect to which the tensor components are defined.
	index_sym1	number of the first symmetric index (`0<=` `index_sym1` `<=2` )
	index_sym2	number of the second symmetric index (`index_sym1` < `index_sym2` `<=2` )

Definition at line 116 of file tensor_sym.C.

References id_sym1, id_sym2, Itbl::set(), and Tensor::type_indice.

Tensor_sym::Tensor_sym ( const Tensor_sym & a )

Copy constructor.

Definition at line 148 of file tensor_sym.C.

References Tensor::cmp, indices(), Tensor::n_comp, and position().

Tensor_sym::Tensor_sym	(	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 created by the function `sauve(FILE*)`.

Definition at line 170 of file tensor_sym.C.

References fread_be(), id_sym1, id_sym2, and Tensor::type_indice.

Tensor_sym::~Tensor_sym ( ) [virtual]

Destructor.

Definition at line 185 of file tensor_sym.C.

Member Function Documentation

void Tensor::allocate_all ( ) [virtual, inherited]

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 Scalar.

Definition at line 504 of file tensor.C.

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

void Tensor::annule	(	int	l_min,
		int	l_max
	)			`[virtual, inherited]`

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 Scalar.

Definition at line 667 of file tensor.C.

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

void 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 662 of file tensor.C.

References Tensor::annule().

void 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 686 of file tensor.C.

References Scalar::allocate_all(), Scalar::annule(), Itbl::annule_hard(), Tensor::cmp, Tensor::del_deriv(), Map::get_mg(), Mg3d::get_nr(), Mg3d::get_nzone(), Mg3d::get_type_r(), Tensor::mp, Tensor::n_comp, pow(), Map::r, Tbl::set(), Itbl::set(), Scalar::set_domain(), Tbl::set_etat_qcq(), Scalar::std_spectral_base(), and Map::val_r().

void Tensor::change_triad ( const Base_vect & new_triad ) [virtual, inherited]

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

Reimplemented in Scalar, and Vector.

Definition at line 73 of file tensor_change_triad.C.

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

void Tensor::compute_derive_lie	(	const Vector &	v,
		Tensor &	resu
	)			const `[protected, inherited]`

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 335 of file tensor_calculus.C.

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

void Tensor::dec_dzpuis ( int dec = 1 ) [virtual, inherited]

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

Reimplemented in Scalar.

Definition at line 804 of file tensor.C.

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

void Tensor::del_deriv ( ) const [protected, virtual, inherited]

Deletes the derived quantities.

Reimplemented in Scalar, Sym_tensor, Sym_tensor_trans, Sym_tensor_tt, Vector, and Vector_divfree.

Definition at line 394 of file tensor.C.

References Tensor::del_derive_met(), and Tensor::set_der_0x0().

void Tensor::del_derive_met ( int j ) const [protected, virtual, inherited]

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

Reimplemented in Sym_tensor, and Vector.

Definition at line 410 of file tensor.C.

References Tensor::met_depend, Tensor::p_derive_con, Tensor::p_derive_cov, Tensor::p_divergence, Tensor::set_der_met_0x0(), and Metric::tensor_depend.

const Tensor_sym & 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.

method derive_cov() ) with $\gamma$ .

Reimplemented from Tensor.

Definition at line 200 of file tensor_sym_calculus.C.

const Tensor_sym & Tensor_sym::derive_cov ( const Metric & gam ) const

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 $\gamma$

Reimplemented from Tensor.

Definition at line 188 of file tensor_sym_calculus.C.

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

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

Reimplemented from Tensor.

Reimplemented in Sym_tensor.

Definition at line 215 of file tensor_sym_calculus.C.

References Tensor::compute_derive_lie(), id_sym1, id_sym2, Tensor::mp, Tensor::triad, Tensor::type_indice, and Tensor::valence.

const Tensor & Tensor::divergence ( const Metric & gam ) const [inherited]

Computes the divergence of this with respect to some metric $\gamma$ .

The divergence is taken with respect of the last index of this which thus must be contravariant. For instance if the tensor $T$ represented by this is a twice contravariant tensor, whose components w.r.t. the triad $e_i$ are $T^{ij}$ : $T = T^{ij} \; e_i \otimes e_j$ , the divergence of $T$ w.r.t. $\gamma$ is the vector

${\rm div}\, T = \nabla_k T^{ik} \; e_i$

where $\nabla$ denotes the connection associated with the metric $\gamma$ .

Parameters:

gam

metric $\gamma$

Returns:: divergence of this with respect to $\gamma$ .

Reimplemented in Sym_tensor, and Vector.

Definition at line 1051 of file tensor.C.

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

Tensor 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 261 of file tensor_calculus.C.

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

void Tensor::exponential_filter_r	(	int	lzmin,
		int	lzmax,
		int	p,
		double	alpha = `-16.`
	)			`[virtual, inherited]`

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

Works only for Cartesian components.

Reimplemented in Scalar, Sym_tensor, and Vector.

Definition at line 1062 of file tensor.C.

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

void Tensor::exponential_filter_ylm	(	int	lzmin,
		int	lzmax,
		int	p,
		double	alpha = `-16.`
	)			`[virtual, inherited]`

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

Works only for Cartesian components.

Reimplemented in Scalar, Sym_tensor, and Vector.

Definition at line 1075 of file tensor.C.

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

Itbl Tensor::get_index_type ( ) const [inline, inherited]

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 892 of file tensor.h.

References Tensor::type_indice.

int Tensor::get_index_type ( int i ) const [inline, inherited]

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 882 of file tensor.h.

References Tensor::type_indice.

const Map& Tensor::get_mp ( ) const [inline, inherited]

Returns the mapping.

Definition at line 857 of file tensor.h.

References Tensor::mp.

int Tensor::get_n_comp ( ) const [inline, inherited]

Returns the number of stored components.

Definition at line 868 of file tensor.h.

References Tensor::n_comp.

int Tensor::get_place_met ( const Metric & metre ) const [protected, inherited]

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

Definition at line 439 of file tensor.C.

References Tensor::met_depend.

const Base_vect* Tensor::get_triad ( ) const [inline, inherited]

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

Definition at line 862 of file tensor.h.

References Tensor::triad.

int Tensor::get_valence ( ) const [inline, inherited]

Returns the valence.

Definition at line 865 of file tensor.h.

References Tensor::valence.

void Tensor::inc_dzpuis ( int inc = 1 ) [virtual, inherited]

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

Reimplemented in Scalar.

Definition at line 812 of file tensor.C.

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

Itbl Tensor_sym::indices ( int pos ) const [virtual]

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 Tensor.

Definition at line 306 of file tensor_sym.C.

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

const Scalar & 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 779 of file tensor.C.

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

const Scalar & 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 767 of file tensor.C.

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

const Scalar & 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 756 of file tensor.C.

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

const Scalar & 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 794 of file tensor.C.

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

void Tensor::operator+= ( const Tensor & t ) [inherited]

+= Tensor

Reimplemented in Scalar.

Definition at line 567 of file tensor.C.

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

void Tensor::operator-= ( const Tensor & t ) [inherited]

-= Tensor

Reimplemented in Scalar.

Definition at line 583 of file tensor.C.

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

void Tensor_sym::operator= ( const Tensor & a ) [virtual]

Assignment to a Tensor NB: the symmetry about the indices id_sym1 and id_sym2 of the input tensor is assumed but is not checked.

Reimplemented in Sym_tensor, Sym_tensor_trans, and Sym_tensor_tt.

Definition at line 214 of file tensor_sym.C.

References Tensor::cmp, Tensor::del_deriv(), Tensor::get_triad(), Tensor::get_valence(), id_sym1, id_sym2, indices(), Tensor::n_comp, Tensor::position(), Tensor::triad, Tensor::type_indice, and Tensor::valence.

void Tensor_sym::operator= ( const Tensor_sym & a ) [virtual]

Assignment to another Tensor_sym.

Reimplemented from Tensor.

Reimplemented in Sym_tensor, Sym_tensor_trans, and Sym_tensor_tt.

Definition at line 194 of file tensor_sym.C.

References Tensor::cmp, Tensor::del_deriv(), id_sym1, id_sym2, indices(), Tensor::n_comp, position(), Tensor::triad, Tensor::type_indice, and Tensor::valence.

int Tensor_sym::position ( const Itbl & ind ) const [virtual]

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 Tensor.

Definition at line 241 of file tensor_sym.C.

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

void Tensor_sym::sauve ( FILE * fd ) const [virtual]

Save in a binary file.

Reimplemented from Tensor.

Definition at line 368 of file tensor_sym.C.

References fwrite_be(), id_sym1, and id_sym2.

Scalar & 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 633 of file tensor.C.

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

Scalar & 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 617 of file tensor.C.

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

Scalar & 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 602 of file tensor.C.

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

Scalar & 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 650 of file tensor.C.

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

void Tensor::set_dependance ( const Metric & met ) const [protected, inherited]

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 449 of file tensor.C.

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

void Tensor::set_der_0x0 ( ) const [protected, inherited]

Sets the pointers on derived quantities to 0x0.

Reimplemented in Scalar, Sym_tensor, Sym_tensor_trans, Sym_tensor_tt, Vector, and Vector_divfree.

Definition at line 403 of file tensor.C.

References Tensor::set_der_met_0x0().

void Tensor::set_der_met_0x0 ( int i ) const [protected, inherited]

Sets all the i-th components of met_depend , p_derive_cov , etc.

.. to 0x0.

Reimplemented in Sym_tensor, and Vector.

Definition at line 429 of file tensor.C.

References Tensor::met_depend, Tensor::p_derive_con, Tensor::p_derive_cov, and Tensor::p_divergence.

void Tensor::set_etat_nondef ( ) [virtual, inherited]

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

Reimplemented in Scalar.

Definition at line 485 of file tensor.C.

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

void Tensor::set_etat_qcq ( ) [virtual, inherited]

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

Reimplemented in Scalar.

Definition at line 477 of file tensor.C.

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

void Tensor::set_etat_zero ( ) [virtual, inherited]

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

Reimplemented in Scalar.

Definition at line 493 of file tensor.C.

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

Itbl& Tensor::set_index_type ( ) [inline, inherited]

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 914 of file tensor.h.

References Tensor::type_indice.

int& Tensor::set_index_type ( int i ) [inline, inherited]

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 905 of file tensor.h.

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

void 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 515 of file tensor.C.

References Tensor::triad.

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

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 Scalar.

Definition at line 870 of file tensor.C.

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

void Tensor::std_spectral_base ( ) [virtual, inherited]

Sets the standard spectal bases of decomposition for each component.

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

Reimplemented in Scalar, and Vector.

Definition at line 922 of file tensor.C.

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

void Tensor::std_spectral_base_odd ( ) [virtual, inherited]

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

Currently only implemented for a scalar.

Reimplemented in Scalar.

Definition at line 978 of file tensor.C.

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

int Tensor_sym::sym_index1 ( ) const [inline]

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

Definition at line 1145 of file tensor.h.

References id_sym1.

int Tensor_sym::sym_index2 ( ) const [inline]

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

Definition at line 1150 of file tensor.h.

References id_sym2.

Scalar 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 193 of file tensor_calculus.C.

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

Scalar Tensor::trace ( ) const [inherited]

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

Definition at line 176 of file tensor_calculus.C.

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

Tensor 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 149 of file tensor_calculus.C.

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

Tensor 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 90 of file tensor_calculus.C.

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

Tensor 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 221 of file tensor_calculus.C.

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

Tensor 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 301 of file tensor_calculus.C.

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

Friends And Related Function Documentation

Tensor_sym operator*	(	const Tensor_sym &	a,
		const Tensor_sym &	b
	)			`[friend, inherited]`

Tensorial product of two symmetric tensors.

NB: the output is an object of class Tensor_sym , with the two symmetric indices corresponding to the symmetric indices of tensor a . This means that the symmetries of tensor b indices are not used in the storage, since there is currently no class in Lorene to manage tensors with more than two symmetric indices.

Definition at line 147 of file tensor_sym_calculus.C.

Member Data Documentation

Scalar** Tensor::cmp [protected, inherited]

Array of size n_comp of pointers onto the components.

Definition at line 311 of file tensor.h.

int Tensor_sym::id_sym1 [protected]

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

Definition at line 1040 of file tensor.h.

int Tensor_sym::id_sym2 [protected]

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

Definition at line 1045 of file tensor.h.

const Metric* Tensor::met_depend[N_MET_MAX] [mutable, protected, inherited]

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 323 of file tensor.h.

const Map* const Tensor::mp [protected, inherited]

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

Definition at line 291 of file tensor.h.

int Tensor::n_comp [protected, inherited]

Number of stored components, depending on the symmetry.

Definition at line 308 of file tensor.h.

Tensor* Tensor::p_derive_con[N_MET_MAX] [mutable, protected, inherited]

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 339 of file tensor.h.

Tensor* Tensor::p_derive_cov[N_MET_MAX] [mutable, protected, inherited]

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 331 of file tensor.h.

Tensor* Tensor::p_divergence[N_MET_MAX] [mutable, protected, inherited]

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 347 of file tensor.h.

const Base_vect* Tensor::triad [protected, inherited]

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

Definition at line 299 of file tensor.h.

Itbl Tensor::type_indice [protected, inherited]

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 306 of file tensor.h.

int Tensor::valence [protected, inherited]

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

Definition at line 294 of file tensor.h.

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

Tensor_sym Class Reference [Tensorial fields]

Public Member Functions

Protected Member Functions

Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation

Tensor_sym Class Reference
[Tensorial fields]