Purely abstract class for metric handling. More...

#include <metric.hpp>

Inheritance diagram for Kadath::Metric:

Public Member Functions
	Metric (const Metric &)
	Copy constructor. More...

virtual	~Metric ()
	Destructor. 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 dd)
	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 &so, int ind) const
	Uses the `Metric` to manipulate one of the index of a `Term_eq` (i.e. More...

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

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

virtual int	give_type (int) const
	Returns the type of tensorial basis of the covariant representation, in a given `Domain`. 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
	Metric (const Space &)
	Constructor from a `Space` only (internal use only). More...

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_riemann (int) const
	Computes the Riemann tensor, 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_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 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...

Friends
class	System_of_eqs

class	Metric_flat

class	Metric_dirac

class	Metric_conf

class	Domain_nucleus

class	Domain_shell

class	Domain_compact

class	Domain_bispheric_rect

class	Domain_bispheric_chi_first

class	Domain_bispheric_eta_first

class	Domain_shell_outer_adapted

class	Domain_shell_inner_adapted

class	Domain_nucleus_symphi

class	Domain_shell_symphi

class	Domain_compact_symphi

Detailed Description

Purely abstract class for metric handling.

Can not be instanciated directly. One must use the various derived classes.

Definition at line 39 of file metric.hpp.

Constructor & Destructor Documentation

◆ Metric() [1/2]

Kadath::Metric::Metric ( const Space & sp )

protected

Constructor from a Space only (internal use only).

Definition at line 29 of file metric.cpp.

References espace, Kadath::Space::get_nbr_domains(), p_christo, p_det_cov, p_dirac, p_met_con, p_met_cov, p_ricci_scalar, p_ricci_tensor, and p_riemann.

◆ Metric() [2/2]

Kadath::Metric::Metric ( const Metric & so )

Copy constructor.

Definition at line 49 of file metric.cpp.

References espace, Kadath::Space::get_nbr_domains(), p_christo, p_det_cov, p_dirac, p_met_con, p_met_cov, p_ricci_scalar, p_ricci_tensor, and p_riemann.

◆ ~Metric()

Kadath::Metric::~Metric ( )

virtual

Destructor.

Definition at line 69 of file metric.cpp.

References espace, Kadath::Space::get_nbr_domains(), p_christo, p_det_cov, p_dirac, p_met_con, p_met_cov, p_ricci_scalar, p_ricci_tensor, and p_riemann.

Member Function Documentation

◆ compute_christo()

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

protectedvirtual

Computes the Christoffel symbols, in a given Domain.

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

Definition at line 407 of file metric.cpp.

References compute_con(), compute_cov(), espace, Kadath::Space::get_domain(), Kadath::Space::get_ndim(), Kadath::Index::inc(), p_christo, p_met_con, p_met_cov, Kadath::Tensor::set(), Kadath::Array< T >::set(), Kadath::Scalar::set_domain(), and type_tensor.

◆ compute_con()

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

protectedvirtual

Computes the contravariant representation, in a given Domain.

Reimplemented in Kadath::Metric_nophi_AADS_const, Kadath::Metric_nophi_AADS, Kadath::Metric_nophi_const, Kadath::Metric_nophi, Kadath::Metric_flat_nophi, Kadath::Metric_cfc, Kadath::Metric_conf_factor_const, Kadath::Metric_conf_factor, Kadath::Metric_dirac_const, Kadath::Metric_conf, Kadath::Metric_const, Kadath::Metric_general, Kadath::Metric_flat, Kadath::Metric_AADS, and Kadath::Metric_ADS.

Definition at line 740 of file metric.cpp.

◆ compute_cov()

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

protectedvirtual

Computes the covariant representation, in a given Domain.

Reimplemented in Kadath::Metric_nophi_AADS_const, Kadath::Metric_nophi_AADS, Kadath::Metric_nophi_const, Kadath::Metric_nophi, Kadath::Metric_flat_nophi, Kadath::Metric_cfc, Kadath::Metric_conf_factor_const, Kadath::Metric_conf_factor, Kadath::Metric_dirac_const, Kadath::Metric_conf, Kadath::Metric_const, Kadath::Metric_general, Kadath::Metric_flat, Kadath::Metric_AADS, and Kadath::Metric_ADS.

Definition at line 735 of file metric.cpp.

◆ compute_det_cov()

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

protectedvirtual

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

protectedvirtual

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::compute_ricci_scalar ( int dd ) const

protectedvirtual

Computes the Ricci scalar, in a given Domain.

Reimplemented in Kadath::Metric_harmonic, Kadath::Metric_dirac, Kadath::Metric_flat, Kadath::Metric_AADS, and Kadath::Metric_ADS.

Definition at line 590 of file metric.cpp.

References compute_con(), compute_cov(), compute_ricci_tensor(), espace, Kadath::Space::get_domain(), Kadath::Space::get_ndim(), p_met_con, p_met_cov, p_ricci_scalar, p_ricci_tensor, Kadath::Scalar::set_domain(), and type_tensor.

◆ compute_ricci_tensor()

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

protectedvirtual

Computes the Ricci tensor, in a given Domain.

Reimplemented in Kadath::Metric_nophi_AADS, Kadath::Metric_nophi, Kadath::Metric_cfc, Kadath::Metric_conf_factor, Kadath::Metric_harmonic, Kadath::Metric_dirac, Kadath::Metric_conf, Kadath::Metric_general, Kadath::Metric_flat, Kadath::Metric_AADS, and Kadath::Metric_ADS.

Definition at line 532 of file metric.cpp.

References compute_christo(), Kadath::Val_domain::der_abs(), espace, Kadath::Space::get_domain(), Kadath::Space::get_ndim(), Kadath::Index::inc(), p_christo, p_met_con, p_met_cov, p_ricci_tensor, Kadath::Tensor::set(), and Kadath::Scalar::set_domain().

◆ compute_riemann()

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

protectedvirtual

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

◆ derive()

Term_eq Kadath::Metric::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 in Kadath::Metric_nophi_AADS, Kadath::Metric_nophi, Kadath::Metric_flat_nophi, Kadath::Metric_cfc, Kadath::Metric_conf_factor, Kadath::Metric_conf, Kadath::Metric_general, Kadath::Metric_flat, Kadath::Metric_AADS, and Kadath::Metric_ADS.

Definition at line 290 of file metric.cpp.

References compute_christo(), Kadath::Term_eq::der_t, derive_partial(), Kadath::Tensor::do_summation_one_dom(), Kadath::Term_eq::get_dom(), Kadath::Tensor::get_index_type(), Kadath::Tensor::get_name_ind(), Kadath::Tensor::get_valence(), manipulate_ind(), p_christo, Kadath::Tensor::set_name_affected(), Kadath::Tensor::set_name_ind(), and Kadath::Term_eq::val_t.

◆ derive_flat()

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

virtual

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_partial()

Term_eq Kadath::Metric::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 in Kadath::Metric_flat_nophi, and Kadath::Metric_flat.

Definition at line 172 of file metric.cpp.

References compute_con(), compute_cov(), Kadath::Term_eq::der_t, Kadath::Tensor::do_summation_one_dom(), espace, Kadath::Tensor::get_basis(), Kadath::Base_tensor::get_basis(), Kadath::Term_eq::get_dom(), Kadath::Tensor::get_index_type(), Kadath::Tensor::get_name_ind(), Kadath::Term_eq::get_type_data(), Kadath::Tensor::get_valence(), Kadath::Index::inc(), Kadath::Tensor::is_name_affected(), manipulate_ind(), p_met_con, p_met_cov, Kadath::Tensor::set(), Kadath::Array< T >::set(), Kadath::Index::set(), Kadath::Scalar::set_domain(), Kadath::Tensor::set_name_affected(), Kadath::Tensor::set_name_ind(), type_tensor, and Kadath::Term_eq::val_t.

◆ get_background()

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

virtual

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

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

◆ give_det_cov()

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

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

◆ give_dirac()

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

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

◆ give_ricci_scalar()

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

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

◆ give_ricci_tensor()

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

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

◆ give_riemann()

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

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

◆ give_term()

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

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

◆ give_type()

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

virtual

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

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

Definition at line 118 of file metric.cpp.

References compute_cov(), and p_met_cov.

◆ manipulate_ind()

void Kadath::Metric::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 in Kadath::Metric_AADS, Kadath::Metric_ADS, Kadath::Metric_flat_nophi, and Kadath::Metric_flat.

Definition at line 645 of file metric.cpp.

References compute_con(), compute_cov(), Kadath::Term_eq::der_t, espace, Kadath::Term_eq::get_der_t(), Kadath::Term_eq::get_dom(), Kadath::Space::get_domain(), Kadath::Tensor::get_index_type(), Kadath::Tensor::get_name_ind(), Kadath::Space::get_ndim(), Kadath::Term_eq::get_val_t(), Kadath::Tensor::get_valence(), Kadath::Index::inc(), Kadath::Tensor::is_name_affected(), p_met_con, p_met_cov, Kadath::Tensor::set(), Kadath::Array< T >::set(), Kadath::Index::set(), Kadath::Term_eq::set_der_t(), Kadath::Scalar::set_domain(), Kadath::Tensor::set_name_affected(), Kadath::Tensor::set_name_ind(), Kadath::Term_eq::set_val_t(), type_tensor, and Kadath::Term_eq::val_t.

◆ update() [1/2]

void Kadath::Metric::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 in Kadath::Metric_flat_nophi, Kadath::Metric_AADS, Kadath::Metric_ADS, and Kadath::Metric_flat.

Definition at line 99 of file metric.cpp.

References espace, and Kadath::Space::get_nbr_domains().

◆ update() [2/2]

void Kadath::Metric::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 in Kadath::Metric_flat_nophi, Kadath::Metric_flat, Kadath::Metric_AADS, and Kadath::Metric_ADS.

Definition at line 82 of file metric.cpp.

References compute_christo(), compute_con(), compute_cov(), compute_det_cov(), compute_dirac(), compute_ricci_scalar(), compute_ricci_tensor(), compute_riemann(), p_christo, p_det_cov, p_dirac, p_met_con, p_met_cov, p_ricci_scalar, p_ricci_tensor, p_riemann, and type_tensor.

Member Data Documentation

◆ espace

const Space& Kadath::Metric::espace

protected

The associated Space.

Definition at line 42 of file metric.hpp.

◆ p_christo

MMPtr_array<Term_eq> Kadath::Metric::p_christo

mutableprotected

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

mutableprotected

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

mutableprotected

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

mutableprotected

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

mutableprotected

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

mutableprotected

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

mutableprotected

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

mutableprotected

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

protected

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

protected

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

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Metric() [1/2]

◆ Metric() [2/2]

◆ ~Metric()

Member Function Documentation

◆ compute_christo()

◆ compute_con()

◆ compute_cov()

◆ compute_det_cov()

◆ compute_dirac()

◆ compute_ricci_scalar()

◆ compute_ricci_tensor()

◆ compute_riemann()

◆ derive()

◆ derive_flat()

◆ derive_partial()

◆ get_background()

◆ give_christo()

◆ give_det_cov()

◆ give_dirac()

◆ give_ricci_scalar()

◆ give_ricci_tensor()

◆ give_riemann()

◆ give_term()

◆ give_type()

◆ manipulate_ind()

◆ update() [1/2]

◆ update() [2/2]

Member Data Documentation

◆ 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