Tensor_sym Class Reference
[Tensorial fields]

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

#include <tensor.h>

Inheritance diagram for Tensor_sym:

Tensor Sym_tensor Sym_tensor_trans Sym_tensor_tt List of all members.

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 &)
 Tensorial product with symmetries.
Tensor_sym operator * (const Tensor_sym &, const Tensor &)
 Tensorial product with symmetries.
class Scalar
class Vector
class Sym_tensor
class Tensor_sym
class Metric
ostream & operator<< (ostream &, const Tensor &)
Scalar operator+ (const Tensor &, const Scalar &)
 Tensor + Scalar. The Tensor must be of valence 0.
Scalar operator+ (const Scalar &, const Tensor &)
 Scalar + Tensor. The Tensor must be of valence 0.
Scalar operator- (const Tensor &, const Scalar &)
 Tensor - Scalar. The Tensor must be of valence 0.
Scalar operator- (const Scalar &, const Tensor &)
 Scalar - Tensor. The Tensor must be of valence 0.
Tensor operator * (const Tensor &, const Tensor &)
 Tensorial product.
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 1027 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 62 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 90 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 113 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 145 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 167 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 182 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 495 of file tensor.C.

References 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 658 of file tensor.C.

References Tensor::cmp, 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 653 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 677 of file tensor.C.

References Itbl::annule_hard(), FIN, Map::get_mg(), Mg3d::get_nr(), Mg3d::get_nzone(), Mg3d::get_type_r(), Tensor::mp, Itbl::set(), 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 70 of file tensor_change_triad.C.

References 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 332 of file tensor_calculus.C.

References Tensor::cmp, Map::flat_met_cart(), Map::flat_met_spher(), Tensor::get_triad(), Tensor::mp, Tensor::n_comp, Tensor::triad, 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 795 of file tensor.C.

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

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 385 of file tensor.C.

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

void Tensor::del_derive_met (  int   )  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 401 of file tensor.C.

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

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 197 of file tensor_sym_calculus.C.

References Tensor::derive_con().

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 185 of file tensor_sym_calculus.C.

References Tensor::derive_cov().

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 212 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 1043 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 258 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 1054 of file tensor.C.

References Tensor::cmp, Map::get_bvect_cart(), Base_vect::identify(), Tensor::mp, 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 1067 of file tensor.C.

References Tensor::cmp, Map::get_bvect_cart(), Base_vect::identify(), Tensor::mp, 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 886 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 876 of file tensor.h.

References Tensor::type_indice.

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

Returns the mapping.

Definition at line 851 of file tensor.h.

References Tensor::mp.

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

Returns the number of stored components.

Definition at line 862 of file tensor.h.

References Tensor::n_comp.

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

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

Definition at line 430 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 856 of file tensor.h.

References Tensor::triad.

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

Returns the valence.

Definition at line 859 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 803 of file tensor.C.

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

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 303 of file tensor_sym.C.

References 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 770 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 758 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 747 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 785 of file tensor.C.

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

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

+= Tensor

Definition at line 558 of file tensor.C.

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

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

-= Tensor

Definition at line 574 of file tensor.C.

References Tensor::cmp, 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 from Tensor.

Reimplemented in Sym_tensor, Sym_tensor_trans, and Sym_tensor_tt.

Definition at line 211 of file tensor_sym.C.

References Tensor::cmp, 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 in Sym_tensor, Sym_tensor_trans, and Sym_tensor_tt.

Definition at line 191 of file tensor_sym.C.

References Tensor::cmp, 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 238 of file tensor_sym.C.

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

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

Save in a binary file.

Reimplemented from Tensor.

Definition at line 365 of file tensor_sym.C.

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

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 624 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 608 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 593 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 641 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 &   )  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 440 of file tensor.C.

References Tensor::met_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 394 of file tensor.C.

References Tensor::set_der_met_0x0().

void Tensor::set_der_met_0x0 (  int   )  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 420 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 476 of file tensor.C.

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

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

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

Reimplemented in Scalar.

Definition at line 468 of file tensor.C.

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

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

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

Reimplemented in Scalar.

Definition at line 484 of file tensor.C.

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

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 908 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 899 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 506 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 861 of file tensor.C.

References 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 914 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, 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 970 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 1139 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 1144 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 190 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 173 of file tensor_calculus.C.

References Tensor::mp, 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 146 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 87 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 218 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 298 of file tensor_calculus.C.

References 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 144 of file tensor_sym_calculus.C.

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

Tensorial product.

Definition at line 100 of file tensor_calculus_ext.C.

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

Tensorial product with symmetries.

Reimplemented from Tensor.

Definition at line 61 of file tensor_sym_calculus.C.

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

Tensorial product with symmetries.

Reimplemented from Tensor.

Definition at line 101 of file tensor_sym_calculus.C.

Scalar operator+ (  const Scalar &  a,
const Tensor &  b
)  [friend, inherited]
 

Scalar + Tensor. The Tensor must be of valence 0.

Definition at line 122 of file tensor_arithm.C.

Scalar operator+ (  const Tensor &  a,
const Scalar &  b
)  [friend, inherited]
 

Tensor + Scalar. The Tensor must be of valence 0.

Definition at line 113 of file tensor_arithm.C.

Scalar operator- (  const Scalar &  a,
const Tensor &  b
)  [friend, inherited]
 

Scalar - Tensor. The Tensor must be of valence 0.

Definition at line 166 of file tensor_arithm.C.

Scalar operator- (  const Tensor &  a,
const Scalar &  b
)  [friend, inherited]
 

Tensor - Scalar. The Tensor must be of valence 0.

Definition at line 157 of file tensor_arithm.C.

Member Data Documentation

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

Array of size n_comp of pointers onto the components.

Definition at line 305 of file tensor.h.

int Tensor_sym::id_sym1 [protected]
 

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

Definition at line 1034 of file tensor.h.

int Tensor_sym::id_sym2 [protected]
 

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

Definition at line 1039 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 317 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 285 of file tensor.h.

int Tensor::n_comp [protected, inherited]
 

Number of stored components, depending on the symmetry.

Definition at line 302 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 333 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 325 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 341 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 293 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 300 of file tensor.h.

int Tensor::valence [protected, inherited]
 

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

Definition at line 288 of file tensor.h.

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