Class that deals with flat metric. More...

#include <metric.hpp>

Inheritance diagram for Kadath::Metric_flat:

Public Member Functions
	Metric_flat (const Space &sp, const Base_tensor &bb)
	Standard constructor. More...

	Metric_flat (const Metric_flat &)
	Copye constructor. More...

virtual void	update ()
	Updates the derived quantities (Christoffels etc..) This is done only for the ones that are needed, i.e. More...

virtual void	update (int)
	Updates the derived quantities (Christoffels etc..) in a given `Domain` This is done only for the ones that are needed, i.e. More...

virtual void	manipulate_ind (Term_eq &, int) const
	Uses the `Metric` to manipulate one of the index of a `Term_eq` (i.e. More...

virtual Term_eq	derive_partial (int, char, const Term_eq &) const
	Computes the partial derivative of a `Term_eq` (assumes Cartesian basis of decomposition). More...

virtual Term_eq	derive (int, char, const Term_eq &) const
	Computes the covariant derivative of a `Term_eq` (assumes Cartesian basis of decomposition). More...

Term_eq	derive_with_other (int tder, char indder, const Term_eq &so, const Metric *othermet) const
	Computes the flat covariant derivative. More...

virtual void	set_system (System_of_eqs &syst, const char *name)
	Associate the metric to a given system of equations. More...

virtual int	give_type (int) const
	Returns the type of tensorial basis of the covariant representation, in a given `Domain`. More...

virtual Term_eq	derive_flat (int typeder, char nameder, const Term_eq &so) const
	Computes the covariant flat derivative of a `Term_eq`. More...

virtual const Metric *	get_background () const
	Returns a pointer on the background metric, if it exists. More...

const Term_eq *	give_term (int typemet, int dd) const
	Gives one representation of the metric, in a `Domain`. More...

const Term_eq *	give_christo (int dd) const
	Gives the Christoffel symbols, in a `Domain`. More...

const Term_eq *	give_riemann (int dd) const
	Gives the Riemann tensor, in a `Domain`. More...

const Term_eq *	give_ricci_tensor (int dd) const
	Gives the Ricci tensor, in a `Domain`. More...

const Term_eq *	give_ricci_scalar (int dd) const
	Gives the Ricci scalar, in a `Domain`. More...

const Term_eq *	give_dirac (int dd) const
	Gives the potential of the Dirac gauge, in a `Domain`. More...

const Term_eq *	give_det_cov (int dd) const
	Gives the determinant of the covariant metric, in a `Domain`. More...

Protected Member Functions
virtual void	compute_con (int) const
	Computes the contravariant representation, in a given `Domain`. More...

virtual void	compute_cov (int) const
	Computes the covariant representation, in a given `Domain`. More...

virtual void	compute_christo (int) const
	Computes the Christoffel symbols, in a given `Domain`. More...

virtual void	compute_ricci_tensor (int) const
	Computes the Ricci tensor, in a given `Domain`. More...

virtual void	compute_ricci_scalar (int) const
	Computes the Ricci scalar, in a given `Domain`. More...

virtual void	compute_riemann (int) const
	Computes the Riemann tensor, in a given `Domain`. More...

virtual void	compute_dirac (int) const
	Computes the Dirac gauge term, in a given `Domain`. More...

virtual void	compute_det_cov (int) const
	Computes the determinant of the covariant representation, in a given `Domain`. More...

Protected Attributes
const Base_tensor &	basis
	The tensorial basis used. More...

const Space &	espace
	The associated `Space`. More...

const System_of_eqs *	syst
	Pointer of the system of equations where the metric is used (only one for now). More...

MMPtr_array< Term_eq >	p_met_cov
	Array of pointers on various `Term_eq`. More...

MMPtr_array< Term_eq >	p_met_con
	Array of pointers on various `Term_eq`. More...

MMPtr_array< Term_eq >	p_christo
	Array of pointers on various `Term_eq`. More...

MMPtr_array< Term_eq >	p_riemann
	Array of pointers on various `Term_eq`. More...

MMPtr_array< Term_eq >	p_ricci_tensor
	Array of pointers on various `Term_eq`. More...

MMPtr_array< Term_eq >	p_ricci_scalar
	Array of pointers on various `Term_eq`. More...

MMPtr_array< Term_eq >	p_dirac
	Array of pointers on various `Term_eq`. More...

MMPtr_array< Term_eq >	p_det_cov
	Array of pointers on various `Term_eq`. More...

int	type_tensor
	States if one works in the CON or COV representation. More...

Private Member Functions
Term_eq	derive_partial_spher (int tder, char indder, const Term_eq &so) const
	Computes the partial derivative part of the covariant derivative, in orthonormal spherical coordinates. More...

Term_eq	derive_partial_cart (int tder, char indder, const Term_eq &so) const
	Computes the partial derivative part of the covariant derivative, in Cartesian coordinates. More...

Term_eq	derive_partial_mtz (int tder, char indder, const Term_eq &so) const
	Computes the partial derivative part of the covariant derivative, in orthonormal coordinates where the constant radii sections have a negative curvature. More...

Term_eq	derive_spher (int tder, char indder, const Term_eq &so) const
	Computes the flat covariant derivative, in orthonormal spherical coordinates. More...

Term_eq	derive_cart (int tder, char indder, const Term_eq &so) const
	Computes the flat covariant derivative, in Cartesian coordinates. More...

Term_eq	derive_mtz (int tder, char indder, const Term_eq &so) const
	Computes the flat covariant derivative, in orthonormal coordinates where the constant radii sections have a negative curvature. More...

Term_eq	derive_with_other_spher (int tder, char indder, const Term_eq &so, const Metric *othermet) const
	Computes the flat covariant derivative, in orthonormal spherical coordinates. More...

Term_eq	derive_with_other_mtz (int tder, char indder, const Term_eq &so, const Metric *othermet) const
	Computes the flat covariant derivative, in orthonormal coordinates where the constant radii sections have a negative curvature. More...

Term_eq	derive_with_other_cart (int tder, char indder, const Term_eq &so, const Metric *othermet) const
	Computes the flat covariant derivative, in Cartesian coordinates. More...

Detailed Description

Class that deals with flat metric.

Definition at line 222 of file metric.hpp.

Constructor & Destructor Documentation

◆ Metric_flat() [1/2]

Kadath::Metric_flat::Metric_flat	(	const Space &	sp,
		const Base_tensor &	bb
	)

Standard constructor.

Parameters

sp	: the associated `Space`.
bb	: the tensorial basis.

Definition at line 30 of file metric_flat.cpp.

◆ Metric_flat() [2/2]

Kadath::Metric_flat::Metric_flat ( const Metric_flat & so )

Copye constructor.

Definition at line 33 of file metric_flat.cpp.

Member Function Documentation

◆ compute_christo()

void Kadath::Metric_flat::compute_christo ( int dd ) const

protectedvirtual

Computes the Christoffel symbols, in a given Domain.

Reimplemented from Kadath::Metric.

Definition at line 77 of file metric_flat.cpp.

◆ compute_con()

void Kadath::Metric_flat::compute_con ( int ) const

protectedvirtual

Computes the contravariant representation, in a given Domain.

Reimplemented from Kadath::Metric.

Definition at line 63 of file metric_flat.cpp.

References basis, Kadath::Metric::espace, Kadath::Space::get_ndim(), Kadath::Metric::p_met_con, Kadath::Tensor::set(), Kadath::Scalar::set_domain(), and Kadath::Tensor::std_base().

◆ compute_cov()

void Kadath::Metric_flat::compute_cov ( int ) const

protectedvirtual

Computes the covariant representation, in a given Domain.

Reimplemented from Kadath::Metric.

Definition at line 44 of file metric_flat.cpp.

References basis, Kadath::Metric::espace, Kadath::Space::get_ndim(), Kadath::Metric::p_met_cov, Kadath::Tensor::set(), Kadath::Scalar::set_domain(), and Kadath::Tensor::std_base().

◆ compute_det_cov()

void Kadath::Metric::compute_det_cov ( int ) const

protectedvirtualinherited

Computes the determinant of the covariant representation, in a given Domain.

Reimplemented in Kadath::Metric_harmonic.

Definition at line 750 of file metric.cpp.

◆ compute_dirac()

void Kadath::Metric::compute_dirac ( int ) const

protectedvirtualinherited

Computes the Dirac gauge term, in a given Domain.

Reimplemented in Kadath::Metric_conf, and Kadath::Metric_general.

Definition at line 745 of file metric.cpp.

◆ compute_ricci_scalar()

void Kadath::Metric_flat::compute_ricci_scalar ( int dd ) const

protectedvirtual

Computes the Ricci scalar, in a given Domain.

Reimplemented from Kadath::Metric.

Definition at line 113 of file metric_flat.cpp.

References basis, Kadath::Metric::espace, Kadath::Base_tensor::get_basis(), Kadath::Space::get_domain(), Kadath::Domain::get_radius(), Kadath::Metric::p_ricci_scalar, Kadath::Scalar::set_domain(), and Kadath::Scalar::std_base().

◆ compute_ricci_tensor()

void Kadath::Metric_flat::compute_ricci_tensor ( int dd ) const

protectedvirtual

Computes the Ricci tensor, in a given Domain.

Reimplemented from Kadath::Metric.

Definition at line 82 of file metric_flat.cpp.

References Kadath::Scalar::annule_hard(), basis, Kadath::Metric::espace, Kadath::Base_tensor::get_basis(), Kadath::Space::get_domain(), Kadath::Domain::get_radius(), Kadath::Metric::p_ricci_tensor, Kadath::Tensor::set(), Kadath::Scalar::set_domain(), and Kadath::Tensor::std_base().

◆ compute_riemann()

void Kadath::Metric::compute_riemann ( int dd ) const

protectedvirtualinherited

Computes the Riemann tensor, in a given Domain.

Reimplemented in Kadath::Metric_nophi_AADS, Kadath::Metric_nophi, Kadath::Metric_cfc, Kadath::Metric_conf_factor, Kadath::Metric_conf, Kadath::Metric_general, and Kadath::Metric_ADS.

Definition at line 476 of file metric.cpp.

References Kadath::Metric::compute_christo(), Kadath::Val_domain::der_abs(), Kadath::Metric::espace, Kadath::Space::get_domain(), Kadath::Space::get_ndim(), Kadath::Index::inc(), Kadath::Metric::p_christo, Kadath::Metric::p_met_con, Kadath::Metric::p_met_cov, Kadath::Metric::p_riemann, Kadath::Tensor::set(), Kadath::Array< T >::set(), and Kadath::Scalar::set_domain().

◆ derive()

Term_eq Kadath::Metric_flat::derive	(	int	typeder,
		char	nameder,
		const Term_eq &	so
	)		const

virtual

Computes the covariant derivative of a Term_eq (assumes Cartesian basis of decomposition).

The index corresponding to the derivation is given a name. If need be inner summation is performed.

Parameters

typeder	: the result is either or
nameder	: the name given as the derivation index.
so	: the `Term_eq` to be derived.

Returns: : the covariant derivative.

Reimplemented from Kadath::Metric.

Definition at line 422 of file metric_flat.cpp.

References basis, compute_con(), compute_cov(), derive_cart(), derive_mtz(), derive_spher(), Kadath::Base_tensor::get_basis(), Kadath::Term_eq::get_dom(), Kadath::Term_eq::get_type_data(), Kadath::Metric::p_met_con, and Kadath::Metric::p_met_cov.

◆ derive_cart()

Term_eq Kadath::Metric_flat::derive_cart	(	int	tder,
		char	indder,
		const Term_eq &	so
	)		const

private

Computes the flat covariant derivative, in Cartesian coordinates.

If need be inner summation of the result is performed and index manipulated.

Parameters

tder	: type of the result (COV or CON)
indder	: name of the index corresponding to the derivative.
so	: the field to be derived.

Returns: : the result as a Term_eq.

Definition at line 315 of file metric_flat.cpp.

References derive_partial().

◆ derive_flat()

Term_eq Kadath::Metric::derive_flat	(	int	typeder,
		char	nameder,
		const Term_eq &	so
	)		const

virtualinherited

Computes the covariant flat derivative of a Term_eq.

The index corresponding to the derivation is given a name. If need be inner summation is performed.

Parameters

typeder	: the result is either $\bar{D}_i$ or $\bar{D}^i$
nameder	: the name given as the derivation index.
so	: the `Term_eq` to be derived.

Returns: : the covariant flat derivative.

Reimplemented in Kadath::Metric_nophi_AADS, Kadath::Metric_nophi, Kadath::Metric_cfc, Kadath::Metric_conf_factor, Kadath::Metric_conf, and Kadath::Metric_general.

Definition at line 402 of file metric.cpp.

◆ derive_mtz()

Term_eq Kadath::Metric_flat::derive_mtz	(	int	tder,
		char	indder,
		const Term_eq &	so
	)		const

private

Computes the flat covariant derivative, in orthonormal coordinates where the constant radii sections have a negative curvature.

If need be inner summation of the result is performed and index manipulated.

Parameters

tder	: type of the result (COV or CON)
indder	: name of the index corresponding to the derivative.
so	: the field to be derived.

Returns: : the result as a Term_eq.

Definition at line 370 of file metric_flat.cpp.

References Kadath::Domain::connection_mtz(), Kadath::Term_eq::der_t, derive_partial(), Kadath::Tensor::do_summation_one_dom(), Kadath::Metric::espace, Kadath::Term_eq::get_dom(), Kadath::Space::get_domain(), Kadath::Tensor::get_name_ind(), Kadath::Tensor::get_valence(), Kadath::Tensor::is_name_affected(), manipulate_ind(), Kadath::Tensor::set_name_affected(), Kadath::Tensor::set_name_ind(), and Kadath::Term_eq::val_t.

◆ derive_partial()

Term_eq Kadath::Metric_flat::derive_partial	(	int	typeder,
		char	nameder,
		const Term_eq &	so
	)		const

virtual

Computes the partial derivative of a Term_eq (assumes Cartesian basis of decomposition).

The index corresponding to the derivation is given a name. If need be inner summation is performed.

Parameters

typeder	: the result is either $\partial_i$ or $\partial^i$
nameder	: the name given as the derivation index.
so	: the `Term_eq` to be derived.

Returns: : the derivative.

Reimplemented from Kadath::Metric.

Definition at line 287 of file metric_flat.cpp.

References basis, compute_con(), compute_cov(), derive_partial_cart(), derive_partial_mtz(), derive_partial_spher(), Kadath::Base_tensor::get_basis(), Kadath::Term_eq::get_dom(), Kadath::Term_eq::get_type_data(), Kadath::Metric::p_met_con, and Kadath::Metric::p_met_cov.

◆ derive_partial_cart()

Term_eq Kadath::Metric_flat::derive_partial_cart	(	int	tder,
		char	indder,
		const Term_eq &	so
	)		const

private

Computes the partial derivative part of the covariant derivative, in Cartesian coordinates.

If need be inner summation of the result is performed and index manipulated.

Parameters

tder	: type of the result (COV or CON)
indder	: name of the index corresponding to the derivative.
so	: the field to be derived.

Returns: : the result as a Term_eq.

Definition at line 148 of file metric_flat.cpp.

References Kadath::Term_eq::der_t, Kadath::Tensor::do_summation_one_dom(), Kadath::Metric::espace, Kadath::Term_eq::get_dom(), Kadath::Space::get_domain(), Kadath::Tensor::get_name_ind(), Kadath::Tensor::get_valence(), Kadath::Tensor::is_name_affected(), manipulate_ind(), Kadath::Domain::partial_cart(), Kadath::Tensor::set_name_affected(), Kadath::Tensor::set_name_ind(), and Kadath::Term_eq::val_t.

◆ derive_partial_mtz()

Term_eq Kadath::Metric_flat::derive_partial_mtz	(	int	tder,
		char	indder,
		const Term_eq &	so
	)		const

private

Computes the partial derivative part of the covariant derivative, in orthonormal coordinates where the constant radii sections have a negative curvature.

The result is $\partial_r, \frac{\cos \theta}{r}\partial_\theta, \frac{\cos \theta}{r\sin\theta}\partial_\varphi$ . If need be inner summation of the result is performed and index manipulated.

Parameters

tder	: type of the result (COV or CON)
indder	: name of the index corresponding to the derivative.
so	: the field to be derived.

Returns: : the result as a Term_eq.

Definition at line 240 of file metric_flat.cpp.

References Kadath::Term_eq::der_t, Kadath::Tensor::do_summation_one_dom(), Kadath::Metric::espace, Kadath::Term_eq::get_dom(), Kadath::Space::get_domain(), Kadath::Tensor::get_name_ind(), Kadath::Tensor::get_valence(), Kadath::Tensor::is_name_affected(), manipulate_ind(), Kadath::Domain::partial_mtz(), Kadath::Tensor::set_name_affected(), Kadath::Tensor::set_name_ind(), and Kadath::Term_eq::val_t.

◆ derive_partial_spher()

Term_eq Kadath::Metric_flat::derive_partial_spher	(	int	tder,
		char	indder,
		const Term_eq &	so
	)		const

private

Computes the partial derivative part of the covariant derivative, in orthonormal spherical coordinates.

The result is $\partial_r, \frac{1}{r}\partial_\theta, \frac{1}{r\sin\theta}\partial_\varphi$ . If need be inner summation of the result is performed and index manipulated.

Parameters

tder	: type of the result (COV or CON)
indder	: name of the index corresponding to the derivative.
so	: the field to be derived.

Returns: : the result as a Term_eq.

Definition at line 195 of file metric_flat.cpp.

References Kadath::Term_eq::der_t, Kadath::Tensor::do_summation_one_dom(), Kadath::Metric::espace, Kadath::Term_eq::get_dom(), Kadath::Space::get_domain(), Kadath::Tensor::get_name_ind(), Kadath::Tensor::get_valence(), Kadath::Tensor::is_name_affected(), manipulate_ind(), Kadath::Domain::partial_spher(), Kadath::Tensor::set_name_affected(), Kadath::Tensor::set_name_ind(), and Kadath::Term_eq::val_t.

◆ derive_spher()

Term_eq Kadath::Metric_flat::derive_spher	(	int	tder,
		char	indder,
		const Term_eq &	so
	)		const

private

Computes the flat covariant derivative, in orthonormal spherical coordinates.

If need be inner summation of the result is performed and index manipulated.

Parameters

tder	: type of the result (COV or CON)
indder	: name of the index corresponding to the derivative.
so	: the field to be derived.

Returns: : the result as a Term_eq.

Definition at line 319 of file metric_flat.cpp.

References Kadath::Domain::connection_spher(), Kadath::Term_eq::der_t, derive_partial(), Kadath::Tensor::do_summation_one_dom(), Kadath::Metric::espace, Kadath::Term_eq::get_dom(), Kadath::Space::get_domain(), Kadath::Tensor::get_name_ind(), Kadath::Tensor::get_valence(), Kadath::Tensor::is_name_affected(), manipulate_ind(), Kadath::Tensor::set_name_affected(), Kadath::Tensor::set_name_ind(), and Kadath::Term_eq::val_t.

◆ derive_with_other()

Term_eq Kadath::Metric_flat::derive_with_other	(	int	tder,
		char	indder,
		const Term_eq &	so,
		const Metric *	othermet
	)		const

Computes the flat covariant derivative.

If need be inner summation of the result is performed. If the CON derivative is asked for, the index is NOT manipulated by the flat metric but by an arbitrary one.

Parameters

tder	: type of the result (COV or CON)
indder	: name of the index corresponding to the derivative.
so	: the field to be derived.
othermet	: pointer on the `Metric` used for index manipulation.

Returns: : the result as a Term_eq.

Definition at line 470 of file metric_flat.cpp.

References basis, compute_con(), compute_cov(), derive_with_other_cart(), derive_with_other_mtz(), derive_with_other_spher(), Kadath::Base_tensor::get_basis(), Kadath::Term_eq::get_dom(), Kadath::Term_eq::get_type_data(), Kadath::Metric::p_met_con, and Kadath::Metric::p_met_cov.

◆ derive_with_other_cart()

Term_eq Kadath::Metric_flat::derive_with_other_cart	(	int	tder,
		char	indder,
		const Term_eq &	so,
		const Metric *	othermet
	)		const

private

Computes the flat covariant derivative, in Cartesian coordinates.

If need be inner summation of the result is performed. If the CON derivative is asked for, the index is NOT manipulated by the flat metric but by an arbitrary one.

Parameters

tder	: type of the result (COV or CON)
indder	: name of the index corresponding to the derivative.
so	: the field to be derived.
othermet	: pointer on the `Metric` used for index manipulation.

Returns: : the result as a Term_eq.

Definition at line 450 of file metric_flat.cpp.

References Kadath::Domain::derive_flat_cart(), Kadath::Term_eq::get_dom(), Kadath::Space::get_domain(), Kadath::Tensor::get_space(), and Kadath::Term_eq::val_t.

◆ derive_with_other_mtz()

Term_eq Kadath::Metric_flat::derive_with_other_mtz	(	int	tder,
		char	indder,
		const Term_eq &	so,
		const Metric *	othermet
	)		const

private

Computes the flat covariant derivative, in orthonormal coordinates where the constant radii sections have a negative curvature.

If need be inner summation of the result is performed. If the CON derivative is asked for, the index is NOT manipulated by the flat metric but by an arbitrary one.

Parameters

tder	: type of the result (COV or CON)
indder	: name of the index corresponding to the derivative.
so	: the field to be derived.
othermet	: pointer on the `Metric` used for index manipulation.

Returns: : the result as a Term_eq.

Definition at line 463 of file metric_flat.cpp.

References Kadath::Domain::derive_flat_mtz(), Kadath::Term_eq::get_dom(), Kadath::Space::get_domain(), Kadath::Tensor::get_space(), and Kadath::Term_eq::val_t.

◆ derive_with_other_spher()

Term_eq Kadath::Metric_flat::derive_with_other_spher	(	int	tder,
		char	indder,
		const Term_eq &	so,
		const Metric *	othermet
	)		const

private

Computes the flat covariant derivative, in orthonormal spherical coordinates.

If need be inner summation of the result is performed. If the CON derivative is asked for, the index is NOT manipulated by the flat metric but by an arbitrary one.

Parameters

tder	: type of the result (COV or CON)
indder	: name of the index corresponding to the derivative.
so	: the field to be derived.
othermet	: pointer on the `Metric` used for index manipulation.

Returns: : the result as a Term_eq.

Definition at line 456 of file metric_flat.cpp.

References Kadath::Domain::derive_flat_spher(), Kadath::Term_eq::get_dom(), Kadath::Space::get_domain(), Kadath::Tensor::get_space(), and Kadath::Term_eq::val_t.

◆ get_background()

const Metric * Kadath::Metric::get_background ( ) const

virtualinherited

Returns a pointer on the background metric, if it exists.

Reimplemented in Kadath::Metric_AADS.

Definition at line 167 of file metric.cpp.

◆ give_christo()

const Term_eq * Kadath::Metric::give_christo ( int dd ) const

inherited

Gives the Christoffel symbols, in a Domain.

This is the Term_eq version.

Parameters

dd	: in which `Domain`.

Returns: : pointer on the result (being a Term_eq).

Definition at line 124 of file metric.cpp.

References Kadath::Metric::compute_christo(), Kadath::Metric::espace, Kadath::Space::get_nbr_domains(), and Kadath::Metric::p_christo.

◆ give_det_cov()

const Term_eq * Kadath::Metric::give_det_cov ( int dd ) const

inherited

Gives the determinant of the covariant metric, in a Domain.

This is the Term_eq version.

Parameters

dd	: in which `Domain`.

Returns: : pointer on the result (being a Term_eq).

Definition at line 159 of file metric.cpp.

References Kadath::Metric::compute_det_cov(), Kadath::Metric::espace, Kadath::Space::get_nbr_domains(), and Kadath::Metric::p_det_cov.

◆ give_dirac()

const Term_eq * Kadath::Metric::give_dirac ( int dd ) const

inherited

Gives the potential of the Dirac gauge, in a Domain.

This is the Term_eq version.

Parameters

dd	: in which `Domain`.

Returns: : pointer on the result (being a Term_eq).

Definition at line 152 of file metric.cpp.

References Kadath::Metric::compute_dirac(), Kadath::Metric::espace, Kadath::Space::get_nbr_domains(), and Kadath::Metric::p_dirac.

◆ give_ricci_scalar()

const Term_eq * Kadath::Metric::give_ricci_scalar ( int dd ) const

inherited

Gives the Ricci scalar, in a Domain.

This is the Term_eq version.

Parameters

dd	: in which `Domain`.

Returns: : pointer on the result (being a Term_eq).

Definition at line 145 of file metric.cpp.

References Kadath::Metric::compute_ricci_scalar(), Kadath::Metric::espace, Kadath::Space::get_nbr_domains(), and Kadath::Metric::p_ricci_scalar.

◆ give_ricci_tensor()

const Term_eq * Kadath::Metric::give_ricci_tensor ( int dd ) const

inherited

Gives the Ricci tensor, in a Domain.

This is the Term_eq version.

Parameters

dd	: in which `Domain`.

Returns: : pointer on the result (being a Term_eq).

Definition at line 138 of file metric.cpp.

References Kadath::Metric::compute_ricci_tensor(), Kadath::Metric::espace, Kadath::Space::get_nbr_domains(), and Kadath::Metric::p_ricci_tensor.

◆ give_riemann()

const Term_eq * Kadath::Metric::give_riemann ( int dd ) const

inherited

Gives the Riemann tensor, in a Domain.

This is the Term_eq version.

Parameters

dd	: in which `Domain`.

Returns: : pointer on the result (being a Term_eq).

Definition at line 131 of file metric.cpp.

References Kadath::Metric::compute_riemann(), Kadath::Metric::espace, Kadath::Space::get_nbr_domains(), and Kadath::Metric::p_riemann.

◆ give_term()

const Term_eq * Kadath::Metric::give_term	(	int	typemet,
		int	dd
	)		const

inherited

Gives one representation of the metric, in a Domain.

This is the Term_eq version.

Parameters

typemet	: CON or COV.
dd	: in which `Domain`.

Returns: : pointer on the result (being a Term_eq).

Definition at line 103 of file metric.cpp.

References Kadath::Metric::compute_con(), Kadath::Metric::compute_cov(), Kadath::Metric::espace, Kadath::Space::get_nbr_domains(), Kadath::Metric::p_met_con, and Kadath::Metric::p_met_cov.

◆ give_type()

int Kadath::Metric_flat::give_type ( int dd ) const

virtual

Returns the type of tensorial basis of the covariant representation, in a given Domain.

Reimplemented from Kadath::Metric.

Definition at line 59 of file metric_flat.cpp.

References basis, and Kadath::Base_tensor::get_basis().

◆ manipulate_ind()

void Kadath::Metric_flat::manipulate_ind	(	Term_eq &	so,
		int	ind
	)		const

virtual

Uses the Metric to manipulate one of the index of a Term_eq (i.e.

moves the index up or down)

Parameters

so	: the `Term_eq` to be manipulated.
ind	: index number.

Reimplemented from Kadath::Metric.

Definition at line 140 of file metric_flat.cpp.

References Kadath::Term_eq::set_der_t(), and Kadath::Term_eq::set_val_t().

◆ set_system()

void Kadath::Metric_flat::set_system	(	System_of_eqs &	syst,
		const char *	name
	)

virtual

Associate the metric to a given system of equations.

Parameters

syst	: the `System_of_eqs`.
name	: name by which the metric will be known in the system (like "g", "f"...)

Definition at line 499 of file metric_flat.cpp.

References Kadath::System_of_eqs::met, Kadath::System_of_eqs::name_met, and Kadath::Metric::syst.

◆ update() [1/2]

void Kadath::Metric_flat::update ( )

virtual

Updates the derived quantities (Christoffels etc..) This is done only for the ones that are needed, i.e.

for the ones that have already been computed.

Reimplemented from Kadath::Metric.

Definition at line 36 of file metric_flat.cpp.

◆ update() [2/2]

void Kadath::Metric_flat::update ( int dd )

virtual

Updates the derived quantities (Christoffels etc..) in a given Domain This is done only for the ones that are needed, i.e.

for the ones that have already been computed.

Parameters

dd	: the index of the `Domain`.

Reimplemented from Kadath::Metric.

Definition at line 40 of file metric_flat.cpp.

Member Data Documentation

◆ basis

const Base_tensor& Kadath::Metric_flat::basis

protected

The tensorial basis used.

Definition at line 225 of file metric.hpp.

◆ espace

const Space& Kadath::Metric::espace

protectedinherited

The associated Space.

Definition at line 42 of file metric.hpp.

◆ p_christo

MMPtr_array<Term_eq> Kadath::Metric::p_christo

mutableprotectedinherited

Array of pointers on various Term_eq.

Each one points onto one component of the Christoffel symbols, in a given Domain.

Definition at line 60 of file metric.hpp.

◆ p_det_cov

MMPtr_array<Term_eq> Kadath::Metric::p_det_cov

mutableprotectedinherited

Array of pointers on various Term_eq.

Each one points onto determinant of the covariant representation, in a given Domain.

Definition at line 85 of file metric.hpp.

◆ p_dirac

MMPtr_array<Term_eq> Kadath::Metric::p_dirac

mutableprotectedinherited

Array of pointers on various Term_eq.

Each one points onto the potential of the Dirac gauge, in a given Domain.

Definition at line 80 of file metric.hpp.

◆ p_met_con

MMPtr_array<Term_eq> Kadath::Metric::p_met_con

mutableprotectedinherited

Array of pointers on various Term_eq.

Each one points onto one component of the contravariant representation of the Metric, in a given Domain.

Definition at line 55 of file metric.hpp.

◆ p_met_cov

MMPtr_array<Term_eq> Kadath::Metric::p_met_cov

mutableprotectedinherited

Array of pointers on various Term_eq.

Each one points onto one component of the covariant representation of the Metric, in a given Domain.

Definition at line 50 of file metric.hpp.

◆ p_ricci_scalar

MMPtr_array<Term_eq> Kadath::Metric::p_ricci_scalar

mutableprotectedinherited

Array of pointers on various Term_eq.

Each one points onto the Ricci scalar, in a given Domain.

Definition at line 75 of file metric.hpp.

◆ p_ricci_tensor

MMPtr_array<Term_eq> Kadath::Metric::p_ricci_tensor

mutableprotectedinherited

Array of pointers on various Term_eq.

Each one points onto one component of the Ricci tensor, in a given Domain.

Definition at line 70 of file metric.hpp.

◆ p_riemann

MMPtr_array<Term_eq> Kadath::Metric::p_riemann

mutableprotectedinherited

Array of pointers on various Term_eq.

Each one points onto one component of the Riemann tensor, in a given Domain.

Definition at line 65 of file metric.hpp.

◆ syst

const System_of_eqs* Kadath::Metric::syst

protectedinherited

Pointer of the system of equations where the metric is used (only one for now).

Definition at line 44 of file metric.hpp.

◆ type_tensor

int Kadath::Metric::type_tensor

protectedinherited

States if one works in the CON or COV representation.

Definition at line 86 of file metric.hpp.

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

Public Member Functions

Protected Member Functions

Protected Attributes

Private Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ Metric_flat() [1/2]

◆ Metric_flat() [2/2]

Member Function Documentation

◆ compute_christo()

◆ compute_con()

◆ compute_cov()

◆ compute_det_cov()

◆ compute_dirac()

◆ compute_ricci_scalar()

◆ compute_ricci_tensor()

◆ compute_riemann()

◆ derive()

◆ derive_cart()

◆ derive_flat()

◆ derive_mtz()

◆ derive_partial()

◆ derive_partial_cart()

◆ derive_partial_mtz()

◆ derive_partial_spher()

◆ derive_spher()

◆ derive_with_other()

◆ derive_with_other_cart()

◆ derive_with_other_mtz()

◆ derive_with_other_spher()

◆ get_background()

◆ give_christo()

◆ give_det_cov()

◆ give_dirac()

◆ give_ricci_scalar()

◆ give_ricci_tensor()

◆ give_riemann()

◆ give_term()

◆ give_type()

◆ manipulate_ind()

◆ set_system()

◆ update() [1/2]

◆ update() [2/2]

Member Data Documentation

◆ basis

◆ espace

◆ p_christo

◆ p_det_cov

◆ p_dirac

◆ p_met_con

◆ p_met_cov

◆ p_ricci_scalar

◆ p_ricci_tensor

◆ p_riemann

◆ syst

◆ type_tensor