#include <tensor.h>
Public Member Functions | |
Tensor (const Map &map, int val, const Itbl &tipe, const Base_vect &triad_i) | |
Standard constructor. | |
Tensor (const Map &map, int val, const Itbl &tipe, const Base_vect *triad_i) | |
Standard constructor with the triad passed as a pointer. | |
Tensor (const Map &map, int val, int tipe, const Base_vect &triad_i) | |
Standard constructor when all the indices are of the same type. | |
Tensor (const Tensor &) | |
Copy constructor. | |
Tensor (const Map &map, const Base_vect &triad_i, FILE *fich) | |
Constructor from a file (see sauve(FILE*) ). | |
virtual | ~Tensor () |
Destructor. | |
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. | |
virtual void | operator= (const Tensor &) |
Assignment to a Tensor . | |
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 & | derive_cov (const Metric &gam) const |
Returns the covariant derivative of this with respect to some metric . | |
const Tensor & | derive_con (const Metric &gam) const |
Returns the "contravariant" derivative of this with respect to some metric , by raising the last index of the covariant derivative (cf. | |
const Tensor & | divergence (const Metric &gam) const |
Computes the divergence of this with respect to some metric . | |
Tensor | derive_lie (const Vector &v) const |
Computes the Lie derivative of this with respect to some vector field v . | |
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. | |
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 . | |
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 | sauve (FILE *) const |
Save in a binary file. | |
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 | |
Tensor (const Map &map) | |
Constructor for a scalar field: to be used only by the derived class Scalar . | |
Tensor (const Map &map, int val, const Itbl &tipe, int n_comp_i, const Base_vect &triad_i) | |
Constructor to be used by derived classes, with symmetries among the components. | |
Tensor (const Map &map, int val, int tipe, int n_comp_i, const Base_vect &triad_i) | |
Constructor used by derived classes, with symmetries among the components, when all the indices are of the same type. | |
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 | |
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 | |
class | Scalar |
class | Vector |
class | Sym_tensor |
class | Tensor_sym |
class | Metric |
ostream & | operator<< (ostream &, const Tensor &) |
Scalar | operator+ (const Tensor &, const Scalar &) |
Scalar | operator+ (const Scalar &, const Tensor &) |
Scalar | operator- (const Tensor &, const Scalar &) |
Scalar | operator- (const Scalar &, const Tensor &) |
Tensor | operator* (const Tensor &, const Tensor &) |
Tensor_sym | operator* (const Tensor &, const Tensor_sym &) |
Tensor_sym | operator* (const Tensor_sym &, const Tensor &) |
Tensor_sym | operator* (const Tensor_sym &, const Tensor_sym &) |
Tensorial product of two symmetric tensors. |
Tensor handling.
()
This class has been devised to replace Tenseur
and Cmp
(the latter via the derived class Scalar
).
The Tensor
class is intended to store the components of a tensorial field with respect to a specific basis (triad).
All this is 3D meaning that the indices go from 1 to 3.
Definition at line 284 of file tensor.h.
Standard constructor.
map | the mapping | |
val | valence of the tensor | |
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:
| |
triad_i | vectorial basis (triad) with respect to which the tensor components are defined |
Definition at line 198 of file tensor.C.
References cmp, Itbl::get_dim(), Itbl::get_ndim(), n_comp, set_der_0x0(), and valence.
Standard constructor with the triad passed as a pointer.
map | the mapping | |
val | valence of the tensor | |
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:
| |
triad_i | pointer on the vectorial basis (triad) with respect to which the tensor components are defined (can be set to 0x0 for a scalar field) |
Definition at line 221 of file tensor.C.
References cmp, Itbl::get_dim(), Itbl::get_ndim(), n_comp, set_der_0x0(), and valence.
Standard constructor when all the indices are of the same type.
map | the mapping | |
val | valence of the tensor | |
tipe | the type (COV or CON ) of the indices. | |
triad_i | vectorial basis (triad) with respect to which the tensor components are defined. |
Definition at line 247 of file tensor.C.
References cmp, n_comp, set_der_0x0(), type_indice, and valence.
Tensor::Tensor | ( | const Tensor & | source | ) |
Copy constructor.
Definition at line 267 of file tensor.C.
References cmp, indices(), n_comp, position(), pow(), set_der_0x0(), and valence.
Constructor from a file (see sauve(FILE*)
).
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 291 of file tensor.C.
References Base_vect::bvect_from_file(), cmp, fread_be(), Map::get_mg(), mp, n_comp, set_der_0x0(), triad, and valence.
Tensor::Tensor | ( | const Map & | map | ) | [explicit, protected] |
Tensor::Tensor | ( | const Map & | map, | |
int | val, | |||
const Itbl & | tipe, | |||
int | n_comp_i, | |||
const Base_vect & | triad_i | |||
) | [protected] |
Constructor to be used by derived classes, with symmetries among the components.
The number of independent components is given as an argument (n_comp_i
), and not computed from the valence, as in the standard constructor.
map | the mapping | |
val | valence of the tensor | |
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:
| |
n_comp_i | number of components to be stored | |
triad_i | vectorial basis (triad) with respect to which the tensor components are defined |
Definition at line 330 of file tensor.C.
References cmp, Itbl::get_dim(), Itbl::get_ndim(), n_comp, set_der_0x0(), and valence.
Tensor::Tensor | ( | const Map & | map, | |
int | val, | |||
int | tipe, | |||
int | n_comp_i, | |||
const Base_vect & | triad_i | |||
) | [protected] |
Constructor used by derived classes, with symmetries among the components, when all the indices are of the same type.
The number of independent components is given as a argument (n_comp_i
), and not computed from the valence, as in the standard constructor.
map | the mapping | |
val | valence of the tensor | |
tipe | the type of the indices. | |
n_comp_i | number of components to be stored | |
triad_i | vectorial basis (triad) with respect to which the tensor components are defined |
Definition at line 355 of file tensor.C.
References cmp, n_comp, set_der_0x0(), type_indice, and valence.
Tensor::~Tensor | ( | ) | [virtual] |
void Tensor::allocate_all | ( | ) | [virtual] |
Performs the memory allocation of all the elements, down to the double
arrays of the Tbl
s.
This function performs in fact recursive calls to set_etat_qcq()
on each element of the chain Scalar
-> Valeur
-> Mtbl
-> Tbl
.
Reimplemented in Scalar.
Definition at line 504 of file tensor.C.
References Scalar::allocate_all(), cmp, del_deriv(), and n_comp.
void Tensor::annule | ( | int | l_min, | |
int | l_max | |||
) | [virtual] |
Sets the Tensor
to zero in several domains.
l_min | [input] The Tensor will be set (logically) to zero in the domains whose indices are in the range [l_min,l_max] . | |
l_max | [input] see the comments for l_min . |
Note that annule
(0,nz-1) , where nz
is the total number of domains, is equivalent to set_etat_zero()
.
Reimplemented in Scalar.
Definition at line 667 of file tensor.C.
References Scalar::annule(), cmp, del_deriv(), Map::get_mg(), Mg3d::get_nzone(), mp, n_comp, and set_etat_zero().
void Tensor::annule_domain | ( | int | l | ) |
void Tensor::annule_extern_cn | ( | int | l_0, | |
int | deg | |||
) |
Performs a smooth (C^n) transition in a given domain to zero.
l_0 | [input] in the domain of index l0 the tensor is multiplied by the right polynomial (of degree 2n+1), to ensure continuty of the function and its n first derivative at both ends of this domain. The tensor is unchanged in the domains l < l_0 and set to zero in domains l > l_0. | |
deg | [input] the degree n of smoothness of the transition. |
Definition at line 686 of file tensor.C.
References Scalar::allocate_all(), Scalar::annule(), Itbl::annule_hard(), cmp, del_deriv(), Map::get_mg(), Mg3d::get_nr(), Mg3d::get_nzone(), Mg3d::get_type_r(), mp, n_comp, pow(), Map::r, Tbl::set(), Itbl::set(), Scalar::set_domain(), Tbl::set_etat_qcq(), Scalar::std_spectral_base(), and Map::val_r().
void Tensor::change_triad | ( | const Base_vect & | new_triad | ) | [virtual] |
Sets a new vectorial basis (triad) of decomposition and modifies the components accordingly.
Reimplemented in Scalar, and Vector.
Definition at line 73 of file tensor_change_triad.C.
References Map::comp_p_from_cartesian(), Map::comp_r_from_cartesian(), Map::comp_t_from_cartesian(), Map::comp_x_from_spherical(), Map::comp_y_from_spherical(), Map::comp_z_from_spherical(), Base_vect_cart::get_align(), Map::get_bvect_cart(), Map::get_bvect_spher(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nt(), Mg3d::get_nzone(), mp, set(), triad, type_indice, and valence.
Computes the Lie derivative of this
with respect to some vector field v
(protected method; the public interface is method derive_lie
).
Definition at line 335 of file tensor_calculus.C.
References cmp, contract(), Scalar::dec_dzpuis(), derive_cov(), Map::flat_met_cart(), Map::flat_met_spher(), Scalar::get_dzpuis(), get_n_comp(), get_triad(), indices(), mp, n_comp, operator()(), set(), Itbl::set(), triad, type_indice, and valence.
void Tensor::dec_dzpuis | ( | int | dec = 1 |
) | [virtual] |
void Tensor::del_deriv | ( | ) | const [protected, virtual] |
Deletes the derived quantities.
Reimplemented in Scalar, Sym_tensor, Sym_tensor_trans, Sym_tensor_tt, Vector, and Vector_divfree.
Definition at line 394 of file tensor.C.
References del_derive_met(), and set_der_0x0().
void Tensor::del_derive_met | ( | int | j | ) | const [protected, virtual] |
Logical destructor of the derivatives depending on the i-th element of met_depend
.
Reimplemented in Sym_tensor, and Vector.
Definition at line 410 of file tensor.C.
References met_depend, p_derive_con, p_derive_cov, p_divergence, set_der_met_0x0(), and Metric::tensor_depend.
Returns the "contravariant" derivative of this
with respect to some metric , by raising the last index of the covariant derivative (cf.
method derive_cov()
) with .
Reimplemented in Scalar, and Tensor_sym.
Definition at line 1010 of file tensor.C.
References Metric::con(), contract(), derive_cov(), get_index_type(), get_place_met(), mp, p_derive_con, Itbl::set(), set_dependance(), Tensor_sym::sym_index1(), Tensor_sym::sym_index2(), Tensor(), triad, and valence.
Returns the covariant derivative of this
with respect to some metric .
denoting the tensor represented by this
and its covariant derivative with respect to the metric , the extra index (with respect to the indices of ) of is chosen to be the last one. This convention agrees with that of MTW (see Eq. (10.17) of MTW). For instance, if is a 1-form, whose components w.r.t. the triad are : , then the covariant derivative of is the bilinear form whose components are such that
gam | metric |
this
with respect to the connection associated with the metric Reimplemented in Scalar, and Tensor_sym.
Definition at line 998 of file tensor.C.
References Metric::connect(), get_place_met(), Connection::p_derive_cov(), p_derive_cov, and set_dependance().
Computes the Lie derivative of this
with respect to some vector field v
.
Reimplemented in Scalar, Sym_tensor, and Tensor_sym.
Definition at line 477 of file tensor_calculus.C.
References compute_derive_lie(), mp, triad, type_indice, and valence.
Computes the divergence of this
with respect to some metric .
The divergence is taken with respect of the last index of this
which thus must be contravariant. For instance if the tensor represented by this
is a twice contravariant tensor, whose components w.r.t. the triad are : , the divergence of w.r.t. is the vector
where denotes the connection associated with the metric .
gam | metric |
this
with respect to . Reimplemented in Sym_tensor, and Vector.
Definition at line 1051 of file tensor.C.
References Metric::connect(), get_place_met(), Connection::p_divergence(), p_divergence, and set_dependance().
Computes a new tensor by lowering an index of *this
.
ind | index to be lowered, with the following convention :
| |
gam | metric used to lower the index (contraction with the twice covariant form of the metric on the index ind ). |
Definition at line 261 of file tensor_calculus.C.
References contract(), Metric::cov(), indices(), mp, n_comp, set(), Itbl::set(), triad, type_indice, and valence.
void Tensor::exponential_filter_r | ( | int | lzmin, | |
int | lzmax, | |||
int | p, | |||
double | alpha = -16. | |||
) | [virtual] |
Applies exponential filters to all components (see Scalar::exponential_filter_r
).
Works only for Cartesian components.
Reimplemented in Scalar, Sym_tensor, and Vector.
Definition at line 1062 of file tensor.C.
References cmp, Map::get_bvect_cart(), Base_vect::identify(), mp, n_comp, and triad.
void Tensor::exponential_filter_ylm | ( | int | lzmin, | |
int | lzmax, | |||
int | p, | |||
double | alpha = -16. | |||
) | [virtual] |
Applies exponential filters to all components (see Scalar::exponential_filter_ylm
).
Works only for Cartesian components.
Reimplemented in Scalar, Sym_tensor, and Vector.
Definition at line 1075 of file tensor.C.
References cmp, Map::get_bvect_cart(), Base_vect::identify(), mp, n_comp, and triad.
Itbl Tensor::get_index_type | ( | ) | const [inline] |
Returns the types of all the indices.
Itbl
) of size valence
containing the type of each index, COV
for a covariant one and CON
for a contravariant one. Definition at line 892 of file tensor.h.
References type_indice.
int Tensor::get_index_type | ( | int | i | ) | const [inline] |
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 Definition at line 882 of file tensor.h.
References type_indice.
const Map& Tensor::get_mp | ( | ) | const [inline] |
int Tensor::get_n_comp | ( | ) | const [inline] |
int Tensor::get_place_met | ( | const Metric & | metre | ) | const [protected] |
Returns the position of the pointer on metre
in the array met_depend
.
Definition at line 439 of file tensor.C.
References met_depend.
const Base_vect* Tensor::get_triad | ( | ) | const [inline] |
int Tensor::get_valence | ( | ) | const [inline] |
void Tensor::inc_dzpuis | ( | int | inc = 1 |
) | [virtual] |
Itbl Tensor::indices | ( | int | pos | ) | const [virtual] |
Returns the indices of a component given by its position in the array cmp
.
pos | [input] position in the array cmp of the pointer to the Scalar representing a component |
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) Reimplemented in Tensor_sym, and Vector.
Definition at line 535 of file tensor.C.
References n_comp, Itbl::set(), and valence.
const Scalar & Tensor::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).
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) |
(i1,i2,i3,i4) Definition at line 779 of file tensor.C.
References cmp, position(), Itbl::set(), and valence.
const Scalar & Tensor::operator() | ( | int | i1, | |
int | i2, | |||
int | i3 | |||
) | const |
Returns the value of a component for a tensor of valence 3 (read-only version).
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) |
(i1,i2,i3) Definition at line 767 of file tensor.C.
References cmp, position(), Itbl::set(), and valence.
const Scalar & Tensor::operator() | ( | int | i1, | |
int | i2 | |||
) | const |
Returns the value of a component for a tensor of valence 2 (read-only version).
i1 | value of the first index (1, 2 or 3) | |
i2 | value of the second index (1, 2 or 3) |
(i1,i2) Definition at line 756 of file tensor.C.
References cmp, position(), Itbl::set(), and valence.
Returns the value of a component (read-only version).
ind | 1-D Itbl of size valence containing the values of each index specifing the component, with the following storage convention:
|
ind
Definition at line 794 of file tensor.C.
References cmp, Itbl::get_dim(), Itbl::get_ndim(), position(), and valence.
void Tensor::operator+= | ( | const Tensor & | t | ) |
+= Tensor
Reimplemented in Scalar.
Definition at line 567 of file tensor.C.
References cmp, del_deriv(), indices(), n_comp, position(), triad, type_indice, and valence.
void Tensor::operator-= | ( | const Tensor & | t | ) |
-= Tensor
Reimplemented in Scalar.
Definition at line 583 of file tensor.C.
References cmp, del_deriv(), indices(), n_comp, position(), triad, type_indice, and valence.
void Tensor::operator= | ( | const Tensor & | t | ) | [virtual] |
Assignment to a Tensor
.
Reimplemented in Scalar, Sym_tensor, Sym_tensor_trans, Sym_tensor_tt, Tensor_sym, Vector, and Vector_divfree.
Definition at line 549 of file tensor.C.
References cmp, del_deriv(), indices(), n_comp, position(), triad, type_indice, and valence.
int Tensor::position | ( | const Itbl & | ind | ) | const [virtual] |
Returns the position in the array cmp
of a component given by its indices.
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:
|
cmp
of the pointer to the Scalar
containing the component specified by ind
Reimplemented in Tensor_sym, and Vector.
Definition at line 521 of file tensor.C.
References Itbl::get_dim(), Itbl::get_ndim(), and valence.
void Tensor::sauve | ( | FILE * | fd | ) | const [virtual] |
Save in a binary file.
Reimplemented in Scalar, and Tensor_sym.
Definition at line 902 of file tensor.C.
References cmp, fwrite_be(), n_comp, Base_vect::sauve(), Itbl::sauve(), triad, type_indice, and valence.
Scalar & Tensor::set | ( | int | i1, | |
int | i2, | |||
int | i3, | |||
int | i4 | |||
) |
Returns the value of a component for a tensor of valence 4 (read/write version).
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) |
(i1,i2,i3,i4) Definition at line 633 of file tensor.C.
References cmp, del_deriv(), position(), Itbl::set(), and valence.
Scalar & Tensor::set | ( | int | i1, | |
int | i2, | |||
int | i3 | |||
) |
Returns the value of a component for a tensor of valence 3 (read/write version).
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) |
(i1,i2,i3) Definition at line 617 of file tensor.C.
References cmp, del_deriv(), position(), Itbl::set(), and valence.
Scalar & Tensor::set | ( | int | i1, | |
int | i2 | |||
) |
Returns the value of a component for a tensor of valence 2 (read/write version).
i1 | value of the first index (1, 2 or 3) | |
i2 | value of the second index (1, 2 or 3) |
(i1,i2) Definition at line 602 of file tensor.C.
References cmp, del_deriv(), position(), Itbl::set(), and valence.
Returns the value of a component (read/write version).
ind | 1-D Itbl of size valence containing the values of each index specifing the component, with the following storage convention:
|
ind
Definition at line 650 of file tensor.C.
References cmp, del_deriv(), Itbl::get_dim(), Itbl::get_ndim(), position(), and valence.
void Tensor::set_dependance | ( | const Metric & | met | ) | const [protected] |
To be used to describe the fact that the derivatives members have been calculated with met
.
First it sets a null element of met_depend
to &met
and puts this
in the list of the dependancies of met
.
Definition at line 449 of file tensor.C.
References met_depend, and Metric::tensor_depend.
void Tensor::set_der_0x0 | ( | ) | const [protected] |
Sets the pointers on derived quantities to 0x0.
Reimplemented in Scalar, Sym_tensor, Sym_tensor_trans, Sym_tensor_tt, Vector, and Vector_divfree.
Definition at line 403 of file tensor.C.
References set_der_met_0x0().
void Tensor::set_der_met_0x0 | ( | int | i | ) | const [protected] |
Sets all the i-th components of met_depend
, p_derive_cov
, etc.
.. to 0x0.
Reimplemented in Sym_tensor, and Vector.
Definition at line 429 of file tensor.C.
References met_depend, p_derive_con, p_derive_cov, and p_divergence.
void Tensor::set_etat_nondef | ( | ) | [virtual] |
Sets the logical state of all components to ETATNONDEF
(undefined state).
Reimplemented in Scalar.
Definition at line 485 of file tensor.C.
References cmp, del_deriv(), n_comp, and Scalar::set_etat_nondef().
void Tensor::set_etat_qcq | ( | ) | [virtual] |
Sets the logical state of all components to ETATQCQ
(ordinary state).
Reimplemented in Scalar.
Definition at line 477 of file tensor.C.
References cmp, del_deriv(), n_comp, and Scalar::set_etat_qcq().
void Tensor::set_etat_zero | ( | ) | [virtual] |
Sets the logical state of all components to ETATZERO
(zero state).
Reimplemented in Scalar.
Definition at line 493 of file tensor.C.
References cmp, del_deriv(), n_comp, and Scalar::set_etat_zero().
Itbl& Tensor::set_index_type | ( | ) | [inline] |
Sets the types of all the indices.
Itbl
) of size valence
that can be modified (COV
for a covariant one and CON
for a contravariant one) Definition at line 914 of file tensor.h.
References type_indice.
int& Tensor::set_index_type | ( | int | i | ) | [inline] |
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 COV
for a covariant index, CON
for a contravariant one) Definition at line 905 of file tensor.h.
References Itbl::set(), and type_indice.
void Tensor::set_triad | ( | const Base_vect & | new_triad | ) |
Assigns a new vectorial basis (triad) of decomposition.
NB: this function modifies only the member triad
and leave unchanged the components (member cmp
). In order to change them coherently with the new basis, the function change_triad
(const Base_vect& ) must be called instead.
Definition at line 515 of file tensor.C.
References triad.
void Tensor::spectral_display | ( | const char * | comment = 0x0 , |
|
double | threshold = 1.e-7 , |
|||
int | precision = 4 , |
|||
ostream & | ostr = cout | |||
) | const [virtual] |
Displays the spectral coefficients and the associated basis functions of each component.
This function shows only the values greater than a given threshold.
comment | comment to be printed at top of the display (default: 0x0 = nothing printed) | |
threshold | [input] Value above which a coefficient is printed (default: 1.e-7) | |
precision | [input] Number of printed digits (default: 4) | |
ostr | [input] Output stream used for the printing (default: cout) |
Reimplemented in Scalar.
Definition at line 870 of file tensor.C.
References cmp, indices(), n_comp, Scalar::spectral_display(), and valence.
void Tensor::std_spectral_base | ( | ) | [virtual] |
Sets the standard spectal bases of decomposition for each component.
To be used only with valence
lower than or equal 2.
Reimplemented in Scalar, and Vector.
Definition at line 922 of file tensor.C.
References cmp, Map::get_bvect_cart(), Map::get_bvect_spher(), Map::get_mg(), Base_vect::identify(), indices(), mp, n_comp, Scalar::set_spectral_base(), Mg3d::std_base_vect_cart(), Mg3d::std_base_vect_spher(), Scalar::std_spectral_base(), triad, and valence.
void Tensor::std_spectral_base_odd | ( | ) | [virtual] |
Trace with respect to a given metric for a valence 2 tensor.
gam | metric used to raise or lower one of the indices, in order to take the trace |
Definition at line 193 of file tensor_calculus.C.
References Metric::con(), contract(), Metric::cov(), trace(), type_indice, and valence.
Scalar Tensor::trace | ( | ) | const |
Trace on two different type indices for a valence 2 tensor.
Definition at line 176 of file tensor_calculus.C.
References mp, operator()(), Scalar::set_etat_zero(), type_indice, and valence.
Trace with respect to a given metric.
ind1 | first index for the contraction, with the following convention :
| |
ind2 | second index for the contraction | |
gam | metric used to raise or lower ind1 in order that it has a opposite type than ind2 |
Definition at line 149 of file tensor_calculus.C.
References Metric::con(), contract(), Metric::cov(), trace(), type_indice, and valence.
Tensor Tensor::trace | ( | int | ind1, | |
int | ind2 | |||
) | const |
Trace on two different type indices.
ind1 | first index for the contraction, with the following convention :
| |
ind2 | second index for the contraction |
Definition at line 90 of file tensor_calculus.C.
References cmp, get_n_comp(), indices(), mp, position(), set(), Itbl::set(), Scalar::set_etat_zero(), triad, type_indice, and valence.
Computes a new tensor by raising an index of *this
.
ind | index to be raised, with the following convention :
| |
gam | metric used to raise the index (contraction with the twice contravariant form of the metric on the index ind ). |
Definition at line 221 of file tensor_calculus.C.
References Metric::con(), contract(), indices(), mp, n_comp, set(), Itbl::set(), triad, type_indice, and valence.
Computes a new tensor by raising or lowering all the indices of *this
.
gam | metric used to lower the contravariant indices and raising the covariant ones. |
Definition at line 301 of file tensor_calculus.C.
References down(), Tensor(), type_indice, up(), and valence.
Tensor_sym operator* | ( | const Tensor_sym & | a, | |
const Tensor_sym & | b | |||
) | [friend] |
Tensorial product of two symmetric tensors.
NB: the output is an object of class Tensor_sym
, with the two symmetric indices corresponding to the symmetric indices of tensor a
. This means that the symmetries of tensor b
indices are not used in the storage, since there is currently no class in Lorene to manage tensors with more than two symmetric indices.
Definition at line 147 of file tensor_sym_calculus.C.
Scalar** Tensor::cmp [protected] |
const Metric* Tensor::met_depend[N_MET_MAX] [mutable, protected] |
const Map* const Tensor::mp [protected] |
int Tensor::n_comp [protected] |
Tensor* Tensor::p_derive_con[N_MET_MAX] [mutable, protected] |
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.
Tensor* Tensor::p_derive_cov[N_MET_MAX] [mutable, protected] |
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.
Tensor* Tensor::p_divergence[N_MET_MAX] [mutable, protected] |
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.
const Base_vect* Tensor::triad [protected] |
Itbl Tensor::type_indice [protected] |
int Tensor::valence [protected] |