Scalar Class Reference
[Tensorial fields]

Tensor field of valence 0 (or component of a tensorial field). More...

#include <scalar.h>

Inheritance diagram for Scalar:

Public Member Functions
	Scalar (const Map &mpi)
	Constructor from mapping.
	Scalar (const Tensor &a)
	Constructor from a Tensor (must be of valence 0).
	Scalar (const Scalar &a)
	Copy constructor.
	Scalar (const Cmp &a)
	Constructor by conversion of a Cmp.
	Scalar (const Map &, const Mg3d &, FILE *)
	Constructor from a file (see `sauve(FILE*)` ).
virtual	~Scalar ()
	Destructor.
virtual void	set_etat_nondef ()
	Sets the logical state to `ETATNONDEF` (undefined).
virtual void	set_etat_zero ()
	Sets the logical state to `ETATZERO` (zero).
virtual void	set_etat_qcq ()
	Sets the logical state to `ETATQCQ` (ordinary state).
void	set_etat_one ()
	Sets the logical state to `ETATUN` (one).
virtual void	allocate_all ()
	Sets the logical state to `ETATQCQ` (ordinary state) and performs the memory allocation of all the elements, down to the `double` arrays of the `Tbl` s.
void	annule_hard ()
	Sets the `Scalar` to zero in a hard way.
int	get_etat () const
	Returns the logical state `ETATNONDEF` (undefined), `ETATZERO` (null) or `ETATQCQ` (ordinary).
int	get_dzpuis () const
	Returns `dzpuis`.
bool	dz_nonzero () const
	Returns `true` if the last domain is compactified and `*this` is not zero in this domain.
bool	check_dzpuis (int dzi) const
	Returns `false` if the last domain is compactified and `*this` is not zero in this domain and `dzpuis` is not equal to `dzi` , otherwise return true.
void	operator= (const Scalar &a)
	Assignment to another `Scalar` defined on the same mapping.
virtual void	operator= (const Tensor &a)
	Assignment to a `Tensor` (of valence 0).
void	operator= (const Cmp &a)
	Assignment to a `Cmp`.
void	operator= (const Valeur &a)
	Assignment to a `Valeur`.
void	operator= (const Mtbl &a)
	Assignment to a `Mtbl`.
void	operator= (double)
	Assignment to a `double`.
void	operator= (int)
	Assignment to an `int`.
	operator Cmp () const
	Conversion to a `Cmp`.
const Valeur &	get_spectral_va () const
	Returns `va` (read only version).
Valeur &	set_spectral_va ()
	Returns `va` (read/write version).
Tbl &	set_domain (int l)
	Read/write of the value in a given domain.
const Tbl &	domain (int l) const
	Read-only of the value in a given domain.
double	val_grid_point (int l, int k, int j, int i) const
	Returns the value of the field at a specified grid point.
double	val_point (double r, double theta, double phi) const
	Computes the value of the field at an arbitrary point $(r, \theta, \phi)$ , by means of the spectral expansion.
double &	set_grid_point (int l, int k, int j, int i)
	Setting the value of the field at a given grid point.
virtual void	annule (int l_min, int l_max)
	Sets the `Scalar` to zero in several domains.
void	set_inner_boundary (int l, double x)
	Sets the value of the `Scalar` at the inner boundary of a given domain.
void	set_outer_boundary (int l, double x)
	Sets the value of the `Scalar` at the outer boundary of a given domain.
Tbl	multipole_spectrum () const
	Gives the spectrum in terms of multipolar modes l .
Tbl	tbl_out_bound (int l_dom, bool leave_ylm=false)
	Returns the `Tbl` containing the values of angular coefficients at the outer boundary.
Tbl	tbl_in_bound (int n, bool leave_ylm=false)
	Returns the `Tbl` containing the values of angular coefficients at the inner boundary.
Scalar	scalar_out_bound (int n, bool leave_ylm=false)
	Returns the `Scalar` containing the values of angular coefficients at the outer boundary.
const Scalar &	dsdr () const
	Returns $\partial / \partial r$ of `*this` .
const Scalar &	srdsdt () const
	Returns $1/r \partial / \partial \theta$ of `*this` .
const Scalar &	srstdsdp () const
	Returns $1/(r\sin\theta) \partial / \partial \phi$ of `*this` .
const Scalar &	dsdt () const
	Returns $\partial / \partial \theta$ of `*this` .
const Scalar &	dsdradial () const
	Returns $\partial / \partial r$ of `this` if the mapping is affine (class `Map_af`) and $\partial / \partial \ln r$ of `this` if the mapping is logarithmic (class `Map_log`).
const Scalar &	dsdrho () const
	Returns $\partial / \partial \rho$ of `*this` .
const Scalar &	stdsdp () const
	Returns $1/\sin\theta \partial / \partial \phi$ of `*this` .
const Scalar &	dsdx () const
	Returns $\partial/\partial x$ of `*this` , where $x=r\sin\theta \cos\phi$ .
const Scalar &	dsdy () const
	Returns $\partial/\partial y$ of `*this` , where $y=r\sin\theta \sin\phi$ .
const Scalar &	dsdz () const
	Returns $\partial/\partial z$ of `*this` , where $z=r\cos\theta$ .
const Scalar &	deriv (int i) const
	Returns $\partial/\partial x_i$ of `*this` , where .
const Vector &	derive_cov (const Metric &gam) const
	Returns the gradient (1-form = covariant vector) of `*this`.
const Vector &	derive_con (const Metric &gam) const
	Returns the "contravariant" derivative of `*this` with respect to some metric $\gamma$ , by raising the index of the gradient (cf.
Scalar	derive_lie (const Vector &v) const
	Computes the derivative of `this` along a vector field `v`.
const Scalar &	laplacian (int ced_mult_r=4) const
	Returns the Laplacian of `*this`.
const Scalar &	lapang () const
	Returns the angular Laplacian $\Delta_{\theta\varphi}$ of `*this` , where $\Delta_{\theta\varphi} f = \frac{\partial^2 f} {\partial \theta^2} + \frac{1}{\tan \theta} \frac{\partial f} {\partial \theta} +\frac{1}{\sin^2 \theta}\frac{\partial^2 f} {\partial \varphi^2}$ .
void	div_r ()
	Division by r everywhere; `dzpuis` is not changed.
void	div_r_dzpuis (int ced_mult_r)
	Division by r everywhere but with the output flag `dzpuis` set to `ced_mult_r` .
void	div_r_ced ()
	Division by r in the compactified external domain (CED), the `dzpuis` flag is not changed.
void	mult_r ()
	Multiplication by r everywhere; `dzpuis` is not changed.
void	mult_r_dzpuis (int ced_mult_r)
	Multiplication by r everywhere but with the output flag `dzpuis` set to `ced_mult_r` .
void	mult_r_ced ()
	Multiplication by r in the compactified external domain (CED), the `dzpuis` flag is not changed.
void	mult_rsint ()
	Multiplication by $r\sin\theta$ everywhere; `dzpuis` is not changed.
void	mult_rsint_dzpuis (int ced_mult_r)
	Multiplication by $r\sin\theta$ but with the output flag `dzpuis` set to `ced_mult_r` .
void	div_rsint ()
	Division by $r\sin\theta$ everywhere; `dzpuis` is not changed.
void	div_rsint_dzpuis (int ced_mult_r)
	Division by $r\sin\theta$ but with the output flag `dzpuis` set to `ced_mult_r` .
void	mult_cost ()
	Multiplication by $\cos\theta$ .
void	div_cost ()
	Division by $\cos\theta$ .
void	mult_sint ()
	Multiplication by $\sin\theta$ .
void	div_sint ()
	Division by $\sin\theta$ .
void	div_tant ()
	Division by $\tan\theta$ .
Scalar	primr (bool null_infty=true) const
	Computes the radial primitive which vanishes for $r\to \infty$ .
double	integrale () const
	Computes the integral over all space of `*this` .
const Tbl &	integrale_domains () const
	Computes the integral in each domain of `*this` .
virtual void	dec_dzpuis (int dec=1)
	Decreases by `dec` units the value of `dzpuis` and changes accordingly the values of the `Scalar` 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 of the `Scalar` in the compactified external domain (CED).
virtual void	change_triad (const Base_vect &new_triad)
	Sets a new vectorial basis (triad) of decomposition and modifies the components accordingly.
void	filtre (int n)
	Sets the `n` lasts coefficients in r to 0 in the external domain.
void	filtre_r (int *nn)
	Sets the `n` lasts coefficients in r to 0 in all domains.
void	filtre_r (int n, int nzone)
	Sets the `n` last coefficients in r to 0 in the domain `nzone` .
virtual void	exponential_filter_r (int lzmin, int lzmax, int p, double alpha=-16.)
	Applies an exponential filter to the spectral coefficients in the radial direction.
void	sarra_filter_r (int lzmin, int lzmax, double p, double alpha=-1E-16)
	Applies an exponential filter to the spectral coefficients in the radial direction.
void	exp_filter_r_all_domains (Scalar &ss, int p, double alpha=-16.)
	Applies an exponential filter in radial direction in all domains.
void	sarra_filter_r_all_domains (double p, double alpha=1E-16)
	Applies an exponential filter in radial direction in all domains for the case where p is a double (see `Scalar:sarra_filter_r` ).
virtual void	exponential_filter_ylm (int lzmin, int lzmax, int p, double alpha=-16.)
	Applies an exponential filter to the spectral coefficients in the angular directions.
void	annule_l (int l_min, int l_max, bool ylm_output=false)
	Sets all the multipolar components between `l_min` and `l_max` to zero.
void	filtre_phi (int n, int zone)
	Sets the `n` lasts coefficients in $\Phi$ to 0 in the domain `zone` .
void	filtre_tp (int nn, int nz1, int nz2)
	Sets the `n` lasts coefficients in $\theta$ to 0 in the domain `nz1` to `nz2` when expressed in spherical harmonics.
void	fixe_decroissance (int puis)
	Substracts all the components behaving like $r^{-n}$ in the external domain, with n strictly lower than `puis` , so that `*this` decreases at least like $r^{\tt puis}$ at infinity.
void	smooth_decay (int k, int n)
	Performs a matching of the last non-compactified shell with a decaying function $\sum_{j=0}^k {\alpha_j \over r^{\ell+n+j}}$ where $\ell$ is the spherical harmonic index and n is some specifiable parameter.
void	raccord (int n)
	Performs the matching of the nucleus with respect to the first shell.
void	raccord_c1_zec (int puis, int nbre, int lmax)
	Performs the matching of the external domain with respect to the last shell using function like $\frac{1}{r^i}$ with ${\tt puis} \leq i \leq {\tt puis+nbre}$ for each spherical harmonics with $l \leq {\tt lmax}$ .
void	raccord_externe (int puis, int nbre, int lmax)
	Matching of the external domain with the outermost shell.
void	match_tau (Param &par_bc, Param *par_mat=0x0)
	Method for matching accross domains and imposing boundary condition.
void	match_tau_shell (Param &par_bc, Param *par_mat=0x0)
	Method for matching accross domains and imposing boundary condition.
void	match_collocation (Param &par_bc, Param *par_mat=0x0)
	Method for matching accross domains and imposing boundary condition.
virtual void	sauve (FILE *) const
	Save in a 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.
void	visu_section (const char section_type, double aa, double umin, double umax, double vmin, double vmax, const char title=0x0, const char filename=0x0, bool start_dx=true, int nu=200, int nv=200) const
	3D visualization via a plane section.
void	visu_section (const Tbl &plane, double umin, double umax, double vmin, double vmax, const char title=0x0, const char filename=0x0, bool start_dx=true, int nu=200, int nv=200) const
	3D visualization via a plane section.
void	visu_section_anim (const char section_type, double aa, double umin, double umax, double vmin, double vmax, int jtime, double ttime, int jgraph=1, const char title=0x0, const char filename_root=0x0, bool start_dx=false, int nu=200, int nv=200) const
	3D visualization via time evolving plane section (animation).
void	visu_box (double xmin, double xmax, double ymin, double ymax, double zmin, double zmax, const char title0=0x0, const char filename0=0x0, bool start_dx=true, int nx=40, int ny=40, int nz=40) const
	3D visualization (volume rendering) via OpenDX.
void	operator+= (const Scalar &)
	+= Scalar
void	operator-= (const Scalar &)
	-= Scalar
void	operator*= (const Scalar &)
	*= Scalar
virtual void	std_spectral_base ()
	Sets the spectral bases of the `Valeur` `va` to the standard ones for a scalar field.
virtual void	std_spectral_base_odd ()
	Sets the spectral bases of the `Valeur` `va` to the standard odd ones for a scalar field.
void	set_spectral_base (const Base_val &)
	Sets the spectral bases of the `Valeur` `va`.
const Base_val &	get_spectral_base () const
	Returns the spectral bases of the `Valeur` `va`.
void	set_dzpuis (int)
	Modifies the `dzpuis` flag.
Valeur **	asymptot (int n, const int flag=0) const
	Asymptotic expansion at r = infinity.
Scalar	poisson () const
	Solves the scalar Poisson equation with `*this` as a source.
void	poisson (Param &par, Scalar &uu) const
	Solves the scalar Poisson equation with `*this` as a source (version with parameters to control the resolution).
Scalar	poisson_tau () const
	Solves the scalar Poisson equation with `this` as a source using a real Tau method The source $\sigma$ of the equation $\Delta u = \sigma$ is represented by the `Scalar` `this` .
void	poisson_tau (Param &par, Scalar &uu) const
	Solves the scalar Poisson equation with `this` as a source using a real Tau method (version with parameters to control the resolution) The source $\sigma$ of the equation $\Delta u = \sigma$ is represented by the `Scalar` `this` .
Scalar	poisson_dirichlet (const Valeur &limite, int num) const
	Is identicall to `Scalar::poisson()` .
Scalar	poisson_neumann (const Valeur &, int) const
	Idem as `Scalar::poisson_dirichlet` , the boundary condition being on the radial derivative of the solution.
Scalar	poisson_dir_neu (const Valeur &limite, int num, double fact_dir, double fact_neu) const
	Is identicall to `Scalar::poisson()` .
Scalar	poisson_frontiere_double (const Valeur &, const Valeur &, int) const
	Idem as `Scalar::poisson_dirichlet` , the boundary condition being on both the function and its radial derivative.
void	poisson_regular (int k_div, int nzet, double unsgam1, Param &par, Scalar &uu, Scalar &uu_regu, Scalar &uu_div, Tensor &duu_div, Scalar &source_regu, Scalar &source_div) const
	Solves the scalar Poisson equation with `*this` as a source (version with parameters to control the resolution).
Tbl	test_poisson (const Scalar &uu, ostream &ostr, bool detail=false) const
	Checks if a Poisson equation with `*this` as a source has been correctly solved.
Scalar	poisson_angu (double lambda=0) const
	Solves the (generalized) angular Poisson equation with `*this` as source.
Scalar	avance_dalembert (Param &par, const Scalar &fJm1, const Scalar &source) const
	Performs one time-step integration (from $t=J \to J+1$ ) of the scalar d'Alembert equation with `*this` being the value of the function f at time J .
Scalar	sol_elliptic (Param_elliptic &params) const
	Resolution of a general elliptic equation, putting zero at infinity.
Scalar	sol_elliptic_boundary (Param_elliptic &params, const Mtbl_cf &bound, double fact_dir, double fact_neu) const
	Resolution of a general elliptic equation, putting zero at infinity and with inner boundary conditions.
Scalar	sol_elliptic_boundary (Param_elliptic &params, const Scalar &bound, double fact_dir, double fact_neu) const
	Resolution of general elliptic equation, with inner boundary conditions as Scalars on mono-domain angulare grids.
Scalar	sol_elliptic_2d (Param_elliptic &) const
	Solves the scalar 2-dimensional elliptic equation with `*this` as a source.
Scalar	sol_elliptic_pseudo_1d (Param_elliptic &) const
	Solves a pseudo-1d elliptic equation with `*this` as a source.
Scalar	sol_elliptic_no_zec (Param_elliptic &params, double val=0) const
	Resolution of a general elliptic equation, putting a given value at the outermost shell and not solving in the compactified domain.
Scalar	sol_elliptic_only_zec (Param_elliptic &params, double val) const
	Resolution of a general elliptic equation solving in the compactified domain and putting a given value at the inner boundary.
Scalar	sol_elliptic_sin_zec (Param_elliptic &params, double coefs, double phases) const
	General elliptic solver.
Scalar	sol_elliptic_fixe_der_zero (double val, Param_elliptic &params) const
	Resolution of a general elliptic equation fixing the dericative at the origin and relaxing one continuity condition.
Scalar	sol_divergence (int n) const
	Resolution of a divergence-like equation.
void	import (const Scalar &ci)
	Assignment to another `Scalar` defined on a different mapping.
void	import_symy (const Scalar &ci)
	Assignment to another `Scalar` defined on a different mapping.
void	import_asymy (const Scalar &ci)
	Assignment to another `Scalar` defined on a different mapping.
void	import (int nzet, const Scalar &ci)
	Assignment to another `Scalar` defined on a different mapping.
void	import_symy (int nzet, const Scalar &ci)
	Assignment to another `Scalar` defined on a different mapping.
void	import_asymy (int nzet, const Scalar &ci)
	Assignment to another `Scalar` defined on a different mapping.
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.
void	annule_extern_cn (int l_0, int deg)
	Performs a smooth (C^n) transition in a given domain to zero.
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.
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).
Protected Member Functions
void	del_t ()
	Logical destructor.
virtual void	del_deriv () const
	Logical destructor of the derivatives.
void	set_der_0x0 () const
	Sets the pointers for derivatives to 0x0.
void	import_gal (int nzet, const Scalar &ci)
	Assignment to another `Scalar` defined on a different mapping, when the two mappings do not have a particular relative orientation.
void	import_align (int nzet, const Scalar &ci)
	Assignment to another `Scalar` defined on a different mapping, when the two mappings have aligned Cartesian axis.
void	import_anti (int nzet, const Scalar &ci)
	Assignment to another `Scalar` defined on a different mapping, when the two mappings have anti-aligned Cartesian axis (i.e.
void	import_align_symy (int nzet, const Scalar &ci)
	Assignment to another `Scalar` defined on a different mapping, when the two mappings have aligned Cartesian axis.
void	import_anti_symy (int nzet, const Scalar &ci)
	Assignment to another `Scalar` defined on a different mapping, when the two mappings have anti-aligned Cartesian axis (i.e.
void	import_align_asymy (int nzet, const Scalar &ci)
	Assignment to another `Scalar` defined on a different mapping, when the two mappings have aligned Cartesian axis.
void	import_anti_asymy (int nzet, const Scalar &ci)
	Assignment to another `Scalar` defined on a different mapping, when the two mappings have anti-aligned Cartesian axis (i.e.
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	etat
	The logical state `ETATNONDEF` (undefined), `ETATZERO` (null), `ETATUN` (one), or `ETATQCQ` (ordinary).
int	dzpuis
	Power of r by which the quantity represented by `this` must be divided in the compactified external domain (CED) in order to get the correct physical values.
Valeur	va
	The numerical value of the `Scalar`.
Scalar *	p_dsdr
	Pointer on $\partial/\partial r$ of `*this` (0x0 if not up to date).
Scalar *	p_srdsdt
	Pointer on $1/r \partial/\partial \theta$ of `*this` (0x0 if not up to date).
Scalar *	p_srstdsdp
	Pointer on $1/(r\sin\theta) \partial/\partial \phi$ of `*this` (0x0 if not up to date).
Scalar *	p_dsdt
	Pointer on $\partial/\partial \theta$ of `*this` (0x0 if not up to date).
Scalar *	p_stdsdp
	Pointer on $1/\sin\theta \partial/\partial \phi$ of `*this` (0x0 if not up to date).
Scalar *	p_dsdx
	Pointer on $\partial/\partial x$ of `*this` , where $x=r\sin\theta \cos\phi$ (0x0 if not up to date).
Scalar *	p_dsdy
	Pointer on $\partial/\partial y$ of `*this` , where $y=r\sin\theta \sin\phi$ (0x0 if not up to date).
Scalar *	p_dsdz
	Pointer on $\partial/\partial z$ of `*this` , where $z=r\cos\theta$ (0x0 if not up to date).
Scalar *	p_lap
	Pointer on the Laplacian of `*this` (0x0 if not up to date).
Scalar *	p_lapang
	Pointer on the Laplacian of `*this` (0x0 if not up to date).
Scalar *	p_dsdradial
	Pointer on $\partial/\partial radial$ of `*this`.
Scalar *	p_dsdrho
	Pointer on $\partial/\partial \rho$ of `*this`.
int	ind_lap
	Power of r by which the last computed Laplacian has been multiplied in the compactified external domain.
Tbl *	p_integ
	Pointer on the space integral of `*this` (values in each domain) (0x0 if not up to date).
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
ostream &	operator<< (ostream &, const Scalar &)
	Display.
Scalar	operator- (const Scalar &)
Scalar	operator+ (const Scalar &, const Scalar &)
Scalar	operator+ (const Scalar &, const Mtbl &)
Scalar	operator+ (const Scalar &, double)
Scalar	operator- (const Scalar &, const Scalar &)
Scalar	operator- (const Scalar &, const Mtbl &)
Scalar	operator- (const Scalar &, double)
Scalar	operator* (const Scalar &, const Scalar &)
Scalar	operator% (const Scalar &, const Scalar &)
Scalar	operator\| (const Scalar &, const Scalar &)
Scalar	operator* (const Mtbl &, const Scalar &)
Scalar	operator* (double, const Scalar &)
Scalar	operator/ (const Scalar &, const Scalar &)
Scalar	operator/ (const Scalar &, const Mtbl &)
Scalar	operator/ (const Mtbl &, const Scalar &)
Scalar	operator/ (const Scalar &, double)
Scalar	operator/ (double, const Scalar &)
Scalar	sin (const Scalar &)
Scalar	cos (const Scalar &)
Scalar	tan (const Scalar &)
Scalar	asin (const Scalar &)
Scalar	acos (const Scalar &)
Scalar	atan (const Scalar &)
Scalar	exp (const Scalar &)
Scalar	Heaviside (const Scalar &)
Scalar	log (const Scalar &)
Scalar	log10 (const Scalar &)
Scalar	sqrt (const Scalar &)
Scalar	racine_cubique (const Scalar &)
Scalar	pow (const Scalar &, int)
Scalar	pow (const Scalar &, double)
Scalar	abs (const Scalar &)
double	totalmax (const Scalar &)
double	totalmin (const Scalar &)
Tbl	max (const Scalar &)
Tbl	min (const Scalar &)
Tbl	norme (const Scalar &)
Tbl	diffrel (const Scalar &a, const Scalar &b)
Tbl	diffrelmax (const Scalar &a, const Scalar &b)
class	Scalar
class	Vector
class	Sym_tensor
class	Tensor_sym
class	Metric
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_sym	operator* (const Tensor &, const Tensor_sym &)
Tensor_sym	operator* (const Tensor_sym &, const Tensor &)
Tensor_sym	operator* (const Tensor_sym &, const Tensor_sym &)
	Tensorial product of two symmetric tensors.

Detailed Description

Tensor field of valence 0 (or component of a tensorial field).

()

Definition at line 377 of file scalar.h.

Constructor & Destructor Documentation

Scalar::Scalar ( const Map & mpi ) [explicit]

Constructor from mapping.

Definition at line 197 of file scalar.C.

References Tensor::cmp, and set_der_0x0().

Scalar::Scalar ( const Tensor & a )

Constructor from a Tensor (must be of valence 0).

Definition at line 208 of file scalar.C.

References Tensor::cmp, set_der_0x0(), and Tensor::valence.

Scalar::Scalar ( const Scalar & a )

Copy constructor.

Definition at line 221 of file scalar.C.

References Tensor::cmp, and set_der_0x0().

Scalar::Scalar ( const Cmp & a )

Constructor by conversion of a Cmp.

Definition at line 231 of file scalar.C.

References Tensor::cmp, and set_der_0x0().

Scalar::Scalar	(	const Map &	mpi,
		const Mg3d &	mgi,
		FILE *	fd
	)

Constructor from a file (see sauve(FILE*) ).

Definition at line 241 of file scalar.C.

References Tensor::cmp, dzpuis, etat, fread_be(), Map::get_mg(), and set_der_0x0().

Scalar::~Scalar ( ) [virtual]

Destructor.

Definition at line 260 of file scalar.C.

References Tensor::cmp, and del_t().

Member Function Documentation

void Scalar::allocate_all ( ) [virtual]

Sets the logical state to ETATQCQ (ordinary state) and 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 from Tensor.

Definition at line 358 of file scalar.C.

References Valeur::c, Mtbl::get_nzone(), Valeur::set_etat_c_qcq(), Tbl::set_etat_qcq(), Mtbl::set_etat_qcq(), set_etat_qcq(), Mtbl::t, and va.

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

Sets the Scalar to zero in several domains.

Parameters:

	l_min	[input] The `Scalar` 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,va.mg->get_nzone()-1) is equivalent to set_etat_zero() .

Reimplemented from Tensor.

Definition at line 384 of file scalar.C.

References annule(), Valeur::annule(), etat, Mg3d::get_nzone(), Valeur::mg, p_dsdr, p_dsdradial, p_dsdt, p_dsdx, p_dsdy, p_dsdz, p_integ, p_lap, p_lapang, p_srdsdt, p_srstdsdp, p_stdsdp, set_etat_zero(), and va.

void Tensor::annule_domain ( int l ) [inherited]

Sets the Tensor to zero in a given domain.

Parameters:

l [input] Index of the domain in which the Tensor will be set (logically) to zero.

Definition at line 662 of file tensor.C.

References Tensor::annule().

void Tensor::annule_extern_cn	(	int	l_0,
		int	deg
	)			`[inherited]`

Performs a smooth (C^n) transition in a given domain to zero.

Parameters:

	l_0	[input] in the domain of index l0 the tensor is multiplied by the right polynomial (of degree 2n+1), to ensure continuty of the function and its n first derivative at both ends of this domain. The tensor is unchanged in the domains l < l_0 and set to zero in domains l > l_0.
	deg	[input] the degree n of smoothness of the transition.

Definition at line 686 of file tensor.C.

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

void Scalar::annule_hard ( )

Sets the Scalar to zero in a hard way.

1/ Sets the logical state to ETATQCQ , i.e. to an ordinary state. 2/ Fills the Valeur va with zeros. NB: this function must be used for debugging purposes only. For other operations, the functions set_etat_zero() or annule(int,int) must be perferred.

Definition at line 373 of file scalar.C.

References Valeur::annule_hard(), del_deriv(), etat, and va.

void Scalar::annule_l	(	int	l_min,
		int	l_max,
		bool	ylm_output = `false`
	)

Sets all the multipolar components between l_min and l_max to zero.

This is done for [ l_min , l_max ] and all relevant m in the spherical harmonics expansion basis. If ylm_output is set to true , then the spectral expansion basis of this is left to be that of spherical harmonics.

Definition at line 107 of file scalar_manip.C.

References Valeur::base, Valeur::c, Valeur::c_cf, etat, Mtbl_cf::get_etat(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Base_val::give_quant_numbers(), Tensor::mp, Mtbl_cf::set(), set_etat_zero(), va, Valeur::ylm(), and Valeur::ylm_i().

Valeur ** Scalar::asymptot	(	int	n,
		const int	flag = `0`
	)			const

Asymptotic expansion at r = infinity.

Determines the coefficients $a_k(\theta, \phi)$ of the expansion

$\sum_{k=0}^n {a_k(\theta, \phi) \over r^k}$

of *this when $r \rightarrow \infty$ .

Parameters:

	n	order of the expansion
	flag	: output

Returns:: Array of n +1 Valeur s on mg->angu describing the coefficients $a_k(\theta, \phi)$ . This array is allocated by the routine.

Definition at line 59 of file scalar_asymptot.C.

References Valeur::base, Valeur::c, dzpuis, Mg3d::get_angu(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Mg3d::get_type_r(), Tensor::mp, mult_r_ced(), Valeur::set(), Valeur::set_base(), Valeur::set_etat_c_qcq(), Tbl::set_etat_qcq(), Mtbl::set_etat_qcq(), Tbl::set_etat_zero(), Valeur::set_etat_zero(), set_grid_point(), Mtbl::t, va, and val_grid_point().

Scalar Scalar::avance_dalembert	(	Param &	par,
		const Scalar &	fJm1,
		const Scalar &	source
	)			const

Performs one time-step integration (from $t=J \to J+1$ ) of the scalar d'Alembert equation with *this being the value of the function f at time J .

Works only with an affine mapping (class Map_af ) and, if the last domain is a compactified one, it simply copies the value of the field in this last domain at the time-step J to the last domain of the returned solution.

Parameters:

par

[input/output] possible parameters to control the resolution of the d'Alembert equation:

par.get_double(0) : [input] the time step dt ,
par.get_int(0) : [input] the type of boundary conditions set at the outer boundary (0 : reflexion, 1 : Sommerfeld outgoing wave, valid only for l=0 components, 2 : Bayliss & Turkel outgoing wave, valid for l=0, 1, 2 components)
par.get_int_mod(0) : [input/output] set to 0 at first call, is used as a working flag after (must not be modified after first call)
par.get_tensor_mod(0) : [input] (optional) if the wave equation is on a curved space-time, this is the potential in front of the Laplace operator. It has to be a Scalar and updated at every time-step (for a potential depending on time). Note: there are many other working objects attached to this Param , so one should not modify it. There should be exactly one Param for each wave equation to be solved.

fJm1 [input] solution $f^{J-1}$ at time J-1

source [input] source $\sigma$ of the d'Alembert equation $\diamond u = \sigma$ .

Returns:: solution $f^{J+1}$ at time J+1 with boundary conditions defined by par.get_int(0) .

Definition at line 213 of file scalar_pde.C.

References Map::dalembert(), and Tensor::mp.

void Scalar::change_triad ( const Base_vect & new_triad ) [virtual]

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

Reimplemented from Tensor.

Definition at line 990 of file scalar.C.

bool Scalar::check_dzpuis ( int dzi ) const

Returns false if the last domain is compactified and *this is not zero in this domain and dzpuis is not equal to dzi , otherwise return true.

Definition at line 866 of file scalar.C.

References dz_nonzero(), and dzpuis.

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

Computes the Lie derivative of this with respect to some vector field v (protected method; the public interface is method derive_lie ).

Definition at line 335 of file tensor_calculus.C.

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

void Scalar::dec_dzpuis ( int dec = 1 ) [virtual]

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

Reimplemented from Tensor.

Definition at line 414 of file scalar_r_manip.C.

References Map::dec2_dzpuis(), Map::dec_dzpuis(), del_deriv(), etat, and Tensor::mp.

void Scalar::del_deriv ( ) const [protected, virtual]

Logical destructor of the derivatives.

Reimplemented from Tensor.

Definition at line 280 of file scalar.C.

References p_dsdr, p_dsdradial, p_dsdrho, p_dsdt, p_dsdx, p_dsdy, p_dsdz, p_integ, p_lap, p_lapang, p_srdsdt, p_srstdsdp, p_stdsdp, and set_der_0x0().

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

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

Reimplemented in Sym_tensor, and Vector.

Definition at line 410 of file tensor.C.

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

void Scalar::del_t ( ) [protected]

Logical destructor.

Definition at line 272 of file scalar.C.

References del_deriv(), Valeur::del_t(), Valeur::set_etat_nondef(), and va.

const Scalar & Scalar::deriv ( int i ) const

Returns $\partial/\partial x_i$ of *this , where $x_i = (x, y, z)$ .

If dzpuis is zero, then the returned Scalar has dzpuis = 2. It is increased by 1 otherwise.

Parameters:

i

[input] i=1 for x , i=2 for y , i=3 for z .

Definition at line 358 of file scalar_deriv.C.

References dsdx(), dsdy(), and dsdz().

const Vector & Scalar::derive_con ( const Metric & gam ) const

Returns the "contravariant" derivative of *this with respect to some metric $\gamma$ , by raising the index of the gradient (cf.

method derive_cov() ) with $\gamma$ .

Reimplemented from Tensor.

Definition at line 401 of file scalar_deriv.C.

const Vector & Scalar::derive_cov ( const Metric & gam ) const

Returns the gradient (1-form = covariant vector) of *this.

Parameters:

gam

metric components only used to get the triad with respect to which the components of the result are defined

Reimplemented from Tensor.

Definition at line 389 of file scalar_deriv.C.

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

Computes the derivative of this along a vector field v.

Reimplemented from Tensor.

Definition at line 418 of file scalar_deriv.C.

References Tensor::compute_derive_lie(), and Tensor::mp.

void Scalar::div_cost ( )

Division by $\cos\theta$ .

Definition at line 66 of file scalar_th_manip.C.

References del_deriv(), Map::div_cost(), and Tensor::mp.

void Scalar::div_r ( )

Division by r everywhere; dzpuis is not changed.

Definition at line 129 of file scalar_r_manip.C.

References del_deriv(), Map::div_r(), and Tensor::mp.

void Scalar::div_r_ced ( )

Division by r in the compactified external domain (CED), the dzpuis flag is not changed.

Definition at line 192 of file scalar_r_manip.C.

References del_deriv(), Map::div_r_zec(), and Tensor::mp.

void Scalar::div_r_dzpuis ( int ced_mult_r )

Division by r everywhere but with the output flag dzpuis set to ced_mult_r .

Parameters:

ced_mult_r [input] value of dzpuis of the result.

Definition at line 143 of file scalar_r_manip.C.

References allocate_all(), annule(), Valeur::base, dec_dzpuis(), del_deriv(), div_r(), domain(), dzpuis, etat, Valeur::get_base(), Map::get_mg(), Mg3d::get_nzone(), Mg3d::get_type_r(), inc_dzpuis(), Tensor::mp, set_domain(), set_etat_qcq(), set_spectral_base(), Base_val::sx(), and va.

void Scalar::div_rsint ( )

Division by $r\sin\theta$ everywhere; dzpuis is not changed.

Definition at line 344 of file scalar_r_manip.C.

References del_deriv(), Map::div_rsint(), and Tensor::mp.

void Scalar::div_rsint_dzpuis ( int ced_mult_r )

Division by $r\sin\theta$ but with the output flag dzpuis set to ced_mult_r .

Parameters:

ced_mult_r [input] value of dzpuis of the result.

Definition at line 358 of file scalar_r_manip.C.

References allocate_all(), annule(), Valeur::base, dec_dzpuis(), del_deriv(), div_rsint(), div_sint(), domain(), dzpuis, etat, Valeur::get_base(), Map::get_mg(), Mg3d::get_nzone(), Mg3d::get_type_r(), inc_dzpuis(), Tensor::mp, set_domain(), set_dzpuis(), set_etat_qcq(), set_spectral_base(), Base_val::ssint(), Base_val::sx(), and va.

void Scalar::div_sint ( )

Division by $\sin\theta$ .

Definition at line 94 of file scalar_th_manip.C.

References del_deriv(), Map::div_sint(), and Tensor::mp.

void Scalar::div_tant ( )

Division by $\tan\theta$ .

Definition at line 107 of file scalar_th_manip.C.

References del_deriv(), Map::div_tant(), and Tensor::mp.

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

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

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

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

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

Parameters:

gam

metric $\gamma$

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

Reimplemented in Sym_tensor, and Vector.

Definition at line 1051 of file tensor.C.

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

const Tbl& Scalar::domain ( int l ) const [inline]

Read-only of the value in a given domain.

Parameters:

l

[input] domain index

Returns:: Tbl containing the value of the field in domain l .

Definition at line 607 of file scalar.h.

References etat, and va.

Tensor Tensor::down	(	int	ind,
		const Metric &	gam
	)			const `[inherited]`

Computes a new tensor by lowering an index of *this.

Parameters:

ind

index to be lowered, with the following convention :

ind1 = 0 : first index of the tensor
ind1 = 1 : second index of the tensor
and so on... (ind must be of covariant type (CON )).

gam metric used to lower the index (contraction with the twice covariant form of the metric on the index ind ).

Definition at line 261 of file tensor_calculus.C.

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

const Scalar & Scalar::dsdr ( ) const

Returns $\partial / \partial r$ of *this .

If dzpuis is zero, then the returned Scalar has dzpuis = 2. It is increased by 1 otherwise.

Definition at line 112 of file scalar_deriv.C.

References Map::dsdr(), dzpuis, etat, Map::get_mg(), Mg3d::get_nzone(), Mg3d::get_type_r(), Tensor::mp, p_dsdr, Scalar(), set_dzpuis(), and set_etat_zero().

const Scalar & Scalar::dsdradial ( ) const

Returns $\partial / \partial r$ of *this if the mapping is affine (class Map_af) and $\partial / \partial \ln r$ of *this if the mapping is logarithmic (class Map_log).

If dzpuis is zero, then the returned Scalar has dzpuis = 2. It is increased by 1 otherwise.

Definition at line 490 of file scalar_deriv.C.

References Map::dsdradial(), dzpuis, etat, Map::get_mg(), Mg3d::get_nzone(), Mg3d::get_type_r(), Tensor::mp, p_dsdradial, Scalar(), set_dzpuis(), and set_etat_zero().

const Scalar & Scalar::dsdrho ( ) const

Returns $\partial / \partial \rho$ of *this .

If dzpuis is zero, then the returned Scalar has dzpuis = 2. It is increased by 1 otherwise.

Definition at line 521 of file scalar_deriv.C.

References dsdr(), dzpuis, etat, Map::get_mg(), Mg3d::get_nzone(), get_spectral_va(), Mg3d::get_type_r(), Tensor::mp, Valeur::mult_ct(), Valeur::mult_st(), p_dsdrho, Scalar(), set_dzpuis(), set_etat_zero(), and srdsdt().

const Scalar & Scalar::dsdt ( ) const

Returns $\partial / \partial \theta$ of *this .

Definition at line 207 of file scalar_deriv.C.

References Map::dsdt(), dzpuis, etat, Tensor::mp, p_dsdt, Scalar(), set_dzpuis(), and set_etat_zero().

const Scalar & Scalar::dsdx ( ) const

Returns $\partial/\partial x$ of *this , where $x=r\sin\theta \cos\phi$ .

If dzpuis is zero, then the returned Scalar has dzpuis = 2. It is increased by 1 otherwise.

Definition at line 265 of file scalar_deriv.C.

References Map::comp_x_from_spherical(), dsdr(), dzpuis, etat, Map::get_mg(), Mg3d::get_nzone(), Mg3d::get_type_r(), Tensor::mp, p_dsdx, Scalar(), set_dzpuis(), set_etat_zero(), srdsdt(), and srstdsdp().

const Scalar & Scalar::dsdy ( ) const

Returns $\partial/\partial y$ of *this , where $y=r\sin\theta \sin\phi$ .

If dzpuis is zero, then the returned Scalar has dzpuis = 2. It is increased by 1 otherwise.

Definition at line 296 of file scalar_deriv.C.

References Map::comp_y_from_spherical(), dsdr(), dzpuis, etat, Map::get_mg(), Mg3d::get_nzone(), Mg3d::get_type_r(), Tensor::mp, p_dsdy, Scalar(), set_dzpuis(), set_etat_zero(), srdsdt(), and srstdsdp().

const Scalar & Scalar::dsdz ( ) const

Returns $\partial/\partial z$ of *this , where $z=r\cos\theta$ .

If dzpuis is zero, then the returned Scalar has dzpuis = 2. It is increased by 1 otherwise.

Definition at line 327 of file scalar_deriv.C.

References Map::comp_z_from_spherical(), dsdr(), dzpuis, etat, Map::get_mg(), Mg3d::get_nzone(), Mg3d::get_type_r(), Tensor::mp, p_dsdz, Scalar(), set_dzpuis(), set_etat_zero(), and srdsdt().

bool Scalar::dz_nonzero ( ) const

Returns true if the last domain is compactified and *this is not zero in this domain.

Definition at line 807 of file scalar.C.

References Valeur::c, Valeur::c_cf, Valeur::etat, etat, Map::get_mg(), Mg3d::get_nzone(), Mg3d::get_type_r(), Tensor::mp, and va.

void Scalar::exp_filter_r_all_domains	(	Scalar &	ss,
		int	p,
		double	alpha = `-16.`
	)

Applies an exponential filter in radial direction in all domains.

(see Scalar:exponential_filter_r ). Note that this may cause regularity problems at the origin if applied in a nucleus.

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

Applies an exponential filter to the spectral coefficients in the radial direction.

The filter is of the type: $\forall n\leq N,\, b_n = \sigma(n/N ) a_n$ , with $\sigma(x) = \exp\left( -\ln (10^\alpha ) x^{2p} \right)$ and N the number of radial coefficients.

Parameters:

	lzmin,lzmax	[input] the indices of the domain where the filter is applied (in [`lzmin` , `lzmax` ])
	p	[input] the order of the filter
	alpha	[input] $\alpha$ appearing in the above formula.

Reimplemented from Tensor.

Definition at line 56 of file scalar_exp_filter.C.

References Valeur::c, Valeur::c_cf, Valeur::coef(), del_deriv(), Valeur::del_deriv(), etat, Map::get_mg(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Tensor::mp, Mtbl_cf::set(), and va.

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

Applies an exponential filter to the spectral coefficients in the angular directions.

The filter is of the type: $\forall \ell \leq \ell_{\rm max},\, \forall m,\, b_{\ell m} = \sigma(\ell/\ell_{\rm max} ) a_{\ell m}$ , with $\sigma(x)$ defined for Scalar::exponential_filter_r and $\ell_{\rm max}$ the number of spherical harmonics used.

Reimplemented from Tensor.

Definition at line 138 of file scalar_exp_filter.C.

References Valeur::base, Valeur::c, Valeur::c_cf, del_deriv(), Valeur::del_deriv(), etat, Map::get_mg(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Base_val::give_lmax(), Base_val::give_quant_numbers(), Tensor::mp, Mtbl_cf::set(), va, Valeur::ylm(), and Valeur::ylm_i().

void Scalar::filtre ( int n )

Sets the n lasts coefficients in r to 0 in the external domain.

Definition at line 147 of file scalar_manip.C.

References Valeur::c_cf, Valeur::coef(), del_deriv(), etat, Map::get_mg(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Tensor::mp, Mtbl_cf::set(), Valeur::set_etat_cf_qcq(), and va.

void Scalar::filtre_phi	(	int	n,
		int	zone
	)

Sets the n lasts coefficients in $\Phi$ to 0 in the domain zone .

Definition at line 245 of file scalar_manip.C.

References Valeur::c_cf, Valeur::coef(), del_deriv(), etat, Map::get_mg(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Tensor::mp, Mtbl_cf::set(), Valeur::set_etat_cf_qcq(), and va.

void Scalar::filtre_r	(	int	n,
		int	nzone
	)

Sets the n last coefficients in r to 0 in the domain nzone .

Definition at line 214 of file scalar_manip.C.

References Valeur::c, Valeur::c_cf, Valeur::coef(), del_deriv(), etat, Map::get_mg(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Tensor::mp, Mtbl_cf::set(), Valeur::set_etat_cf_qcq(), and va.

void Scalar::filtre_r ( int * nn )

Sets the n lasts coefficients in r to 0 in all domains.

Definition at line 176 of file scalar_manip.C.

References Valeur::c, Valeur::c_cf, Valeur::coef(), del_deriv(), etat, Map::get_mg(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Tensor::mp, Mtbl_cf::set(), Valeur::set_etat_cf_qcq(), and va.

void Scalar::filtre_tp	(	int	nn,
		int	nz1,
		int	nz2
	)

Sets the n lasts coefficients in $\theta$ to 0 in the domain nz1 to nz2 when expressed in spherical harmonics.

Definition at line 266 of file scalar_manip.C.

References Valeur::filtre_tp(), and va.

void Scalar::fixe_decroissance ( int puis )

Substracts all the components behaving like $r^{-n}$ in the external domain, with n strictly lower than puis , so that *this decreases at least like $r^{\tt puis}$ at infinity.

Definition at line 342 of file scalar_manip.C.

References Valeur::base, Valeur::c_cf, Valeur::coef(), dzpuis, Map_af::get_alpha(), Base_val::get_base_r(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Tensor::mp, mult_r_ced(), R_CHEBU, Mtbl_cf::set(), Valeur::set_etat_cf_qcq(), and va.

int Scalar::get_dzpuis ( ) const [inline]

Returns dzpuis.

Definition at line 546 of file scalar.h.

References dzpuis.

int Scalar::get_etat ( ) const [inline]

Returns the logical state ETATNONDEF (undefined), ETATZERO (null) or ETATQCQ (ordinary).

Definition at line 543 of file scalar.h.

References etat.

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

Returns the types of all the indices.

Returns:: 1-D array of integers (class Itbl ) of size valence containing the type of each index, COV for a covariant one and CON for a contravariant one.

Definition at line 892 of file tensor.h.

References Tensor::type_indice.

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

Gives the type (covariant or contravariant) of the index number i .

i must be strictly lower than valence and obey the following convention:

i = 0 : first index
i = 1 : second index
and so on...

Returns:: COV for a covariant index, CON for a contravariant one.

Definition at line 882 of file tensor.h.

References Tensor::type_indice.

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

Returns the mapping.

Definition at line 857 of file tensor.h.

References Tensor::mp.

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

Returns the number of stored components.

Definition at line 868 of file tensor.h.

References Tensor::n_comp.

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

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

Definition at line 439 of file tensor.C.

References Tensor::met_depend.

const Base_val& Scalar::get_spectral_base ( ) const [inline]

Returns the spectral bases of the Valeur va.

Definition at line 1277 of file scalar.h.

References Valeur::base, and va.

const Valeur& Scalar::get_spectral_va ( ) const [inline]

Returns va (read only version).

Definition at line 583 of file scalar.h.

References va.

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

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

Definition at line 862 of file tensor.h.

References Tensor::triad.

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

Returns the valence.

Definition at line 865 of file tensor.h.

References Tensor::valence.

void Scalar::import	(	int	nzet,
		const Scalar &	ci
	)

Assignment to another Scalar defined on a different mapping.

This assignment is performed point to point by means of the spectral expansion of the original Scalar.

Parameters:

	nzet	[input] Number of domains of the destination mapping (i.e. `this->mp` ) where the importation is performed: the assignment is done for the domains whose indices are between 0 and `nzet-1` . In the other domains, `*this` is set to zero.
	ci	[input] `Scalar` to be imported.

Definition at line 76 of file scalar_import.C.

References Map::get_bvect_cart(), Tensor::get_mp(), import_align(), import_anti(), import_gal(), and Tensor::mp.

void Scalar::import ( const Scalar & ci )

Assignment to another Scalar defined on a different mapping.

This assignment is performed point to point by means of the spectral expansion of the original Scalar.

Parameters:

ci [input] Scalar to be imported.

Definition at line 64 of file scalar_import.C.

References Map::get_mg(), Mg3d::get_nzone(), and Tensor::mp.

void Scalar::import_align	(	int	nzet,
		const Scalar &	ci
	)			`[protected]`

Assignment to another Scalar defined on a different mapping, when the two mappings have aligned Cartesian axis.

This assignment is performed point to point by means of the spectral expansion of the original Scalar.

Parameters:

	nzet	[input] Number of domains of the destination mapping (i.e. `this->mp` ) where the importation is performed: the assignment is done for the domains whose indices are between 0 and `nzet-1` . In the other domains, `*this` is set to zero.
	ci	[input] `Scalar` to be imported.

Definition at line 528 of file scalar_import.C.

References Param::add_double(), Param::add_int(), Param::add_int_mod(), annule(), Valeur::c, Valeur::c_cf, Valeur::coef(), del_t(), Map::get_bvect_cart(), get_dzpuis(), get_etat(), Map::get_mg(), Tensor::get_mp(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Map::get_ori_x(), Map::get_ori_y(), Map::get_ori_z(), get_spectral_va(), Tensor::mp, Map::phi, Map::r, set_dzpuis(), Valeur::set_etat_c_qcq(), set_etat_one(), Mtbl::set_etat_qcq(), set_etat_qcq(), set_etat_zero(), Tbl::t, Mtbl::t, Map::tet, va, Map::val_lx(), Mtbl_cf::val_point(), Map::x, Map::y, and Map::z.

void Scalar::import_align_asymy	(	int	nzet,
		const Scalar &	ci
	)			`[protected]`

Assignment to another Scalar defined on a different mapping, when the two mappings have aligned Cartesian axis.

Case where the Scalar is antisymmetric with respect to the plane y=0.

This assignment is performed point to point by means of the spectral expansion of the original Scalar.

Parameters:

	nzet	[input] Number of domains of the destination mapping (i.e. `this->mp` ) where the importation is performed: the assignment is done for the domains whose indices are between 0 and `nzet-1` . In the other domains, `*this` is set to zero.
	ci	[input] `Scalar` to be imported.

Definition at line 374 of file scalar_import_asymy.C.

References Param::add_double(), Param::add_int(), Param::add_int_mod(), annule(), Valeur::c, Valeur::c_cf, Valeur::coef(), del_t(), Map::get_bvect_cart(), get_dzpuis(), get_etat(), Map::get_mg(), Tensor::get_mp(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Map::get_ori_x(), Map::get_ori_y(), Map::get_ori_z(), get_spectral_va(), Mg3d::get_type_p(), Tensor::mp, Map::phi, Map::r, set_dzpuis(), Valeur::set_etat_c_qcq(), set_etat_one(), Mtbl::set_etat_qcq(), set_etat_qcq(), set_etat_zero(), Tbl::t, Mtbl::t, Map::tet, va, Map::val_lx(), Mtbl_cf::val_point_asymy(), Map::x, Map::y, and Map::z.

void Scalar::import_align_symy	(	int	nzet,
		const Scalar &	ci
	)			`[protected]`

Assignment to another Scalar defined on a different mapping, when the two mappings have aligned Cartesian axis.

Case where the Scalar is symmetric with respect to the plane y=0.

This assignment is performed point to point by means of the spectral expansion of the original Scalar.

Parameters:

	nzet	[input] Number of domains of the destination mapping (i.e. `this->mp` ) where the importation is performed: the assignment is done for the domains whose indices are between 0 and `nzet-1` . In the other domains, `*this` is set to zero.
	ci	[input] `Scalar` to be imported.

Definition at line 345 of file scalar_import_symy.C.

References Param::add_double(), Param::add_int(), Param::add_int_mod(), annule(), Valeur::c, Valeur::c_cf, Valeur::coef(), del_t(), Map::get_bvect_cart(), get_dzpuis(), get_etat(), Map::get_mg(), Tensor::get_mp(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Map::get_ori_x(), Map::get_ori_y(), Map::get_ori_z(), get_spectral_va(), Mg3d::get_type_p(), Tensor::mp, Map::phi, Map::r, set_dzpuis(), Valeur::set_etat_c_qcq(), set_etat_one(), Mtbl::set_etat_qcq(), set_etat_qcq(), set_etat_zero(), Tbl::t, Mtbl::t, Map::tet, va, Map::val_lx(), Mtbl_cf::val_point_symy(), Map::x, Map::y, and Map::z.

void Scalar::import_anti	(	int	nzet,
		const Scalar &	ci
	)			`[protected]`

Assignment to another Scalar defined on a different mapping, when the two mappings have anti-aligned Cartesian axis (i.e.

$x_1 = - x_2$ , $y_1 = - y_2$ , $z_1 = z_2$ ).

This assignment is performed point to point by means of the spectral expansion of the original Scalar.

Parameters:

	nzet	[input] Number of domains of the destination mapping (i.e. `this->mp` ) where the importation is performed: the assignment is done for the domains whose indices are between 0 and `nzet-1` . In the other domains, `*this` is set to zero.
	ci	[input] `Scalar` to be imported.

Definition at line 331 of file scalar_import.C.

References Param::add_double(), Param::add_int(), Param::add_int_mod(), annule(), Valeur::c, Valeur::c_cf, Valeur::coef(), del_t(), Map::get_bvect_cart(), get_dzpuis(), get_etat(), Map::get_mg(), Tensor::get_mp(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Map::get_ori_x(), Map::get_ori_y(), Map::get_ori_z(), get_spectral_va(), Tensor::mp, Map::phi, Map::r, set_dzpuis(), Valeur::set_etat_c_qcq(), set_etat_one(), Mtbl::set_etat_qcq(), set_etat_qcq(), set_etat_zero(), Tbl::t, Mtbl::t, Map::tet, va, Map::val_lx(), Mtbl_cf::val_point(), Map::x, Map::y, and Map::z.

void Scalar::import_anti_asymy	(	int	nzet,
		const Scalar &	ci
	)			`[protected]`

Assignment to another Scalar defined on a different mapping, when the two mappings have anti-aligned Cartesian axis (i.e.

$x_1 = - x_2$ , $y_1 = - y_2$ , $z_1 = z_2$ ). Case where the Scalar is antisymmetric with respect to the plane y=0.

This assignment is performed point to point by means of the spectral expansion of the original Scalar.

Parameters:

	nzet	[input] Number of domains of the destination mapping (i.e. `this->mp` ) where the importation is performed: the assignment is done for the domains whose indices are between 0 and `nzet-1` . In the other domains, `*this` is set to zero.
	ci	[input] `Scalar` to be imported.

Definition at line 127 of file scalar_import_asymy.C.

References Param::add_double(), Param::add_int(), Param::add_int_mod(), annule(), Valeur::c, Valeur::c_cf, Valeur::coef(), del_t(), Map::get_bvect_cart(), get_dzpuis(), get_etat(), Map::get_mg(), Tensor::get_mp(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Map::get_ori_x(), Map::get_ori_y(), Map::get_ori_z(), get_spectral_va(), Mg3d::get_type_p(), Tensor::mp, Map::phi, Map::r, set_dzpuis(), Valeur::set_etat_c_qcq(), set_etat_one(), Mtbl::set_etat_qcq(), set_etat_qcq(), set_etat_zero(), Tbl::t, Mtbl::t, Map::tet, va, Map::val_lx(), Mtbl_cf::val_point_asymy(), Map::x, Map::y, and Map::z.

void Scalar::import_anti_symy	(	int	nzet,
		const Scalar &	ci
	)			`[protected]`

Assignment to another Scalar defined on a different mapping, when the two mappings have anti-aligned Cartesian axis (i.e.

$x_1 = - x_2$ , $y_1 = - y_2$ , $z_1 = z_2$ ). Case where the Scalar is symmetric with respect to the plane y=0.

This assignment is performed point to point by means of the spectral expansion of the original Scalar.

Parameters:

	nzet	[input] Number of domains of the destination mapping (i.e. `this->mp` ) where the importation is performed: the assignment is done for the domains whose indices are between 0 and `nzet-1` . In the other domains, `*this` is set to zero.
	ci	[input] `Scalar` to be imported.

Definition at line 127 of file scalar_import_symy.C.

References Param::add_double(), Param::add_int(), Param::add_int_mod(), annule(), Valeur::c, Valeur::c_cf, Valeur::coef(), del_t(), Map::get_bvect_cart(), get_dzpuis(), get_etat(), Map::get_mg(), Tensor::get_mp(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Map::get_ori_x(), Map::get_ori_y(), Map::get_ori_z(), get_spectral_va(), Mg3d::get_type_p(), Tensor::mp, Map::phi, Map::r, set_dzpuis(), Valeur::set_etat_c_qcq(), set_etat_one(), Mtbl::set_etat_qcq(), set_etat_qcq(), set_etat_zero(), Tbl::t, Mtbl::t, Map::tet, va, Map::val_lx(), Mtbl_cf::val_point_symy(), Map::x, Map::y, and Map::z.

void Scalar::import_asymy	(	int	nzet,
		const Scalar &	ci
	)

Assignment to another Scalar defined on a different mapping.

Case where the Scalar is antisymmetric with respect to the plane y=0. This assignment is performed point to point by means of the spectral expansion of the original Scalar.

Parameters:

	nzet	[input] Number of domains of the destination mapping (i.e. `this->mp` ) where the importation is performed: the assignment is done for the domains whose indices are between 0 and `nzet-1` . In the other domains, `*this` is set to zero.
	ci	[input] `Scalar` to be imported.

Definition at line 80 of file scalar_import_asymy.C.

References Map::get_bvect_cart(), Tensor::get_mp(), import_align_asymy(), import_anti_asymy(), and Tensor::mp.

void Scalar::import_asymy ( const Scalar & ci )

Assignment to another Scalar defined on a different mapping.

Case where the Scalar is antisymmetric with respect to the plane y=0. This assignment is performed point to point by means of the spectral expansion of the original Scalar.

Parameters:

ci [input] Scalar to be imported.

Definition at line 68 of file scalar_import_asymy.C.

References Map::get_mg(), Mg3d::get_nzone(), and Tensor::mp.

void Scalar::import_gal	(	int	nzet,
		const Scalar &	ci
	)			`[protected]`

Assignment to another Scalar defined on a different mapping, when the two mappings do not have a particular relative orientation.

This assignment is performed point to point by means of the spectral expansion of the original Scalar.

Parameters:

	nzet	[input] Number of domains of the destination mapping (i.e. `this->mp` ) where the importation is performed: the assignment is done for the domains whose indices are between 0 and `nzet-1` . In the other domains, `*this` is set to zero.
	ci	[input] `Scalar` to be imported.

Definition at line 127 of file scalar_import.C.

References Param::add_double(), Param::add_int(), Param::add_int_mod(), annule(), Valeur::c, Valeur::coef(), del_t(), get_dzpuis(), get_etat(), Map::get_mg(), Tensor::get_mp(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Map::get_ori_x(), Map::get_ori_y(), Map::get_ori_z(), Map::get_rot_phi(), get_spectral_va(), Tensor::mp, Map::phi, Map::r, set_dzpuis(), Valeur::set_etat_c_qcq(), set_etat_one(), Mtbl::set_etat_qcq(), set_etat_qcq(), set_etat_zero(), Tbl::t, Mtbl::t, Map::tet, va, Map::val_lx(), Map::xa, Map::ya, and Map::za.

void Scalar::import_symy	(	int	nzet,
		const Scalar &	ci
	)

Assignment to another Scalar defined on a different mapping.

Case where the Scalar is symmetric with respect to the plane y=0. This assignment is performed point to point by means of the spectral expansion of the original Scalar.

Parameters:

	nzet	[input] Number of domains of the destination mapping (i.e. `this->mp` ) where the importation is performed: the assignment is done for the domains whose indices are between 0 and `nzet-1` . In the other domains, `*this` is set to zero.
	ci	[input] `Scalar` to be imported.

Definition at line 80 of file scalar_import_symy.C.

References Map::get_bvect_cart(), Tensor::get_mp(), import_align_symy(), import_anti_symy(), and Tensor::mp.

void Scalar::import_symy ( const Scalar & ci )

Assignment to another Scalar defined on a different mapping.

Case where the Scalar is symmetric with respect to the plane y=0. This assignment is performed point to point by means of the spectral expansion of the original Scalar.

Parameters:

ci [input] Scalar to be imported.

Definition at line 68 of file scalar_import_symy.C.

References Map::get_mg(), Mg3d::get_nzone(), and Tensor::mp.

void Scalar::inc_dzpuis ( int inc = 1 ) [virtual]

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

Reimplemented from Tensor.

Definition at line 466 of file scalar_r_manip.C.

References del_deriv(), etat, Map::inc2_dzpuis(), Map::inc_dzpuis(), and Tensor::mp.

Itbl Tensor::indices ( int pos ) const [virtual, inherited]

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 in Tensor_sym, and Vector.

Definition at line 535 of file tensor.C.

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

double Scalar::integrale ( ) const

Computes the integral over all space of *this .

The computed quantity is (u being the field represented by *this ) $\int u \, r^2 \sin\theta \, dr\, d\theta \, d\phi$ . Note that in the compactified external domain (CED), dzpuis must be 4 for the computation to take place.

Definition at line 57 of file scalar_integ.C.

References Map::get_mg(), Mg3d::get_nzone(), integrale_domains(), and Tensor::mp.

const Tbl & Scalar::integrale_domains ( ) const

Computes the integral in each domain of *this .

The computed quantity is (u being the field represented by *this ) $\int u \, r^2 \sin\theta \, dr\, d\theta \, d\phi$ in each domain. The result is returned a Tbl on the various domains. Note that in the compactified external domain (CED), dzpuis must be 4 for the computation to take place.

Definition at line 75 of file scalar_integ.C.

References etat, Map::integrale(), Tensor::mp, and p_integ.

const Scalar & Scalar::lapang ( ) const

Returns the angular Laplacian $\Delta_{\theta\varphi}$ of *this , where $\Delta_{\theta\varphi} f = \frac{\partial^2 f} {\partial \theta^2} + \frac{1}{\tan \theta} \frac{\partial f} {\partial \theta} +\frac{1}{\sin^2 \theta}\frac{\partial^2 f} {\partial \varphi^2}$ .

Definition at line 460 of file scalar_deriv.C.

References dzpuis, etat, Map::lapang(), Tensor::mp, p_lapang, Scalar(), set_dzpuis(), and set_etat_zero().

const Scalar & Scalar::laplacian ( int ced_mult_r = 4 ) const

Returns the Laplacian of *this.

Parameters:

ced_mult_r

[input] Determines the quantity computed in the compactified external domain (CED) (u in the field represented by *this ) :

ced_mult_r = 0 : $\Delta u$
ced_mult_r = 2 : $r^2 \, \Delta u$
ced_mult_r = 4 (default) : $r^4 \, \Delta u$

Definition at line 435 of file scalar_deriv.C.

References etat, ind_lap, Map::laplacien(), Tensor::mp, p_lap, and Scalar().

void Scalar::match_collocation	(	Param &	par_bc,
		Param *	par_mat = `0x0`
	)

Method for matching accross domains and imposing boundary condition.

Matching of the field represented by this accross domains and imposition of the boundary condition using the collocation method.

Parameters:

	par_bc	[input] `Param` to control the boundary conditions
	par_mat	[input/output] optional `Param` in which the matching matrices are stored (together with their LU decomposition).

void Scalar::match_tau	(	Param &	par_bc,
		Param *	par_mat = `0x0`
	)

Method for matching accross domains and imposing boundary condition.

Matching of the field represented by this accross domains and imposition of the boundary condition using the tau method.

Parameters:

	par_bc	[input] `Param` to control the boundary conditions par_bc must contain (at a minimum) a modifiable Tbl which specifies a physical boundary two integers, one specifying the domain that has the boundary the other specifying the number of conditions 1 -> Dirichlet 2 -> Robin (which may reduce to von Neumann, see below) two doubles, specifying the Robin BC parameters. If the first is zero, we see that Robin will reduce to von Neumann
	par_mat	[input/output] optional `Param` in which the matching matrices are stored (together with their LU decomposition).

Definition at line 62 of file scalar_match_tau.C.

References Param::add_matrice_mod(), Tbl::annule_hard(), Matrice::annule_hard(), annule_hard(), Valeur::c, Valeur::c_cf, Valeur::coef(), etat, Map_af::get_alpha(), Param::get_double_mod(), Param::get_int(), Param::get_matrice_mod(), Map::get_mg(), Param::get_n_double_mod(), Param::get_n_int(), Param::get_n_matrice_mod(), Param::get_n_tbl_mod(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), get_spectral_base(), Param::get_tbl_mod(), Mg3d::get_type_r(), Base_val::give_quant_numbers(), Matrice::inverse(), Tensor::mp, R_CHEBI, R_CHEBP, Mtbl_cf::set(), Tbl::set(), Matrice::set(), Matrice::set_lu(), va, and Valeur::ylm().

void Scalar::match_tau_shell	(	Param &	par_bc,
		Param *	par_mat = `0x0`
	)

Method for matching accross domains and imposing boundary condition.

Matching of the field represented by this accross domains and imposition of the boundary condition using the tau method.

Parameters:

	par_bc	[input] `Param` to control the boundary conditions
	par_mat	[input/output] optional `Param` in which the matching matrices are stored (together with their LU decomposition).

void Scalar::mult_cost ( )

Multiplication by $\cos\theta$ .

Definition at line 54 of file scalar_th_manip.C.

References del_deriv(), Tensor::mp, and Map::mult_cost().

void Scalar::mult_r ( )

Multiplication by r everywhere; dzpuis is not changed.

Definition at line 204 of file scalar_r_manip.C.

References del_deriv(), Tensor::mp, and Map::mult_r().

void Scalar::mult_r_ced ( )

Multiplication by r in the compactified external domain (CED), the dzpuis flag is not changed.

Definition at line 265 of file scalar_r_manip.C.

References del_deriv(), Tensor::mp, and Map::mult_r_zec().

void Scalar::mult_r_dzpuis ( int ced_mult_r )

Multiplication by r everywhere but with the output flag dzpuis set to ced_mult_r .

Parameters:

ced_mult_r [input] value of dzpuis of the result.

Definition at line 217 of file scalar_r_manip.C.

References allocate_all(), annule(), Valeur::base, dec_dzpuis(), del_deriv(), domain(), dzpuis, etat, Valeur::get_base(), Map::get_mg(), Mg3d::get_nzone(), Mg3d::get_type_r(), inc_dzpuis(), Tensor::mp, mult_r(), Base_val::mult_x(), set_domain(), set_etat_qcq(), set_spectral_base(), and va.

void Scalar::mult_rsint ( )

Multiplication by $r\sin\theta$ everywhere; dzpuis is not changed.

Definition at line 277 of file scalar_r_manip.C.

References del_deriv(), Tensor::mp, and Map::mult_rsint().

void Scalar::mult_rsint_dzpuis ( int ced_mult_r )

Multiplication by $r\sin\theta$ but with the output flag dzpuis set to ced_mult_r .

Parameters:

ced_mult_r [input] value of dzpuis of the result.

Definition at line 290 of file scalar_r_manip.C.

References allocate_all(), annule(), Valeur::base, dec_dzpuis(), del_deriv(), domain(), dzpuis, etat, Valeur::get_base(), Map::get_mg(), Mg3d::get_nzone(), Mg3d::get_type_r(), inc_dzpuis(), Tensor::mp, mult_rsint(), Base_val::mult_sint(), mult_sint(), Base_val::mult_x(), set_domain(), set_dzpuis(), set_etat_qcq(), set_spectral_base(), and va.

void Scalar::mult_sint ( )

Multiplication by $\sin\theta$ .

Definition at line 80 of file scalar_th_manip.C.

References del_deriv(), Tensor::mp, and Map::mult_sint().

Tbl Scalar::multipole_spectrum ( ) const

Gives the spectrum in terms of multipolar modes l .

Returns:: a Tbl of size (nzone, lmax), where lmax is the maximal multipolar momentum over all domains. The l -th element contains the L1 norm of the l -th multipole (i.e. a sum over all m of the norms (coefficient space) of the component of a given .

Definition at line 949 of file scalar.C.

References Tbl::annule_hard(), Mtbl_cf::base, Valeur::c_cf, Valeur::coef(), etat, Map::get_mg(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Tensor::mp, Tbl::set(), Tbl::set_etat_zero(), va, and Valeur::ylm().

Scalar::operator Cmp ( ) const

Conversion to a Cmp.

Definition at line 667 of file scalar.C.

References dzpuis, Tensor::mp, Cmp::set_dzpuis(), and va.

const Scalar & Tensor::operator()	(	int	i1,
		int	i2,
		int	i3,
		int	i4
	)			const `[inherited]`

Returns the value of a component for a tensor of valence 4 (read-only version).

Parameters:

	i1	value of the first index (1, 2 or 3)
	i2	value of the second index (1, 2 or 3)
	i3	value of the third index (1, 2 or 3)
	i4	value of the fourth index (1, 2 or 3)

Returns:: reference on the component specified by (i1,i2,i3,i4)

Definition at line 779 of file tensor.C.

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

const Scalar & Tensor::operator()	(	int	i1,
		int	i2,
		int	i3
	)			const `[inherited]`

Returns the value of a component for a tensor of valence 3 (read-only version).

Parameters:

	i1	value of the first index (1, 2 or 3)
	i2	value of the second index (1, 2 or 3)
	i3	value of the third index (1, 2 or 3)

Returns:: reference on the component specified by (i1,i2,i3)

Definition at line 767 of file tensor.C.

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

const Scalar & Tensor::operator()	(	int	i1,
		int	i2
	)			const `[inherited]`

Returns the value of a component for a tensor of valence 2 (read-only version).

Parameters:

	i1	value of the first index (1, 2 or 3)
	i2	value of the second index (1, 2 or 3)

Returns:: reference on the component specified by (i1,i2)

Definition at line 756 of file tensor.C.

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

const Scalar & Tensor::operator() ( const Itbl & ind ) const [inherited]

Returns the value of a component (read-only version).

Parameters:

ind

1-D Itbl of size valence containing the values of each index specifing the component, with the following storage convention:

ind(0) : value of the first index (1, 2 or 3)
ind(1) : value of the second index (1, 2 or 3)
and so on...

Returns:: reference on the component specified by ind

Definition at line 794 of file tensor.C.

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

void Scalar::operator*= ( const Scalar & ci )

*= Scalar

Definition at line 933 of file scalar_arithm.C.

References del_deriv(), dzpuis, etat, get_etat(), Tensor::get_mp(), Tensor::mp, operator=(), set_etat_nondef(), set_etat_zero(), and va.

void Scalar::operator+= ( const Scalar & ci )

+= Scalar

Reimplemented from Tensor.

Definition at line 829 of file scalar_arithm.C.

References del_deriv(), dz_nonzero(), dzpuis, etat, get_etat(), Tensor::get_mp(), Tensor::mp, set_dzpuis(), set_etat_nondef(), and va.

void Scalar::operator-= ( const Scalar & ci )

-= Scalar

Reimplemented from Tensor.

Definition at line 882 of file scalar_arithm.C.

References del_deriv(), dz_nonzero(), dzpuis, etat, get_etat(), Tensor::get_mp(), Tensor::mp, set_dzpuis(), set_etat_nondef(), and va.

void Scalar::operator= ( int n )

Assignment to an int.

Definition at line 646 of file scalar.C.

References del_deriv(), dzpuis, set_etat_one(), set_etat_qcq(), set_etat_zero(), and va.

void Scalar::operator= ( double x )

Assignment to a double.

Definition at line 625 of file scalar.C.

References del_deriv(), dzpuis, set_etat_one(), set_etat_qcq(), set_etat_zero(), and va.

void Scalar::operator= ( const Mtbl & a )

Assignment to a Mtbl.

Definition at line 585 of file scalar.C.

References Valeur::c, del_deriv(), Valeur::del_t(), Mtbl::get_etat(), set_etat_qcq(), set_etat_zero(), and va.

void Scalar::operator= ( const Valeur & a )

Assignment to a Valeur.

Definition at line 542 of file scalar.C.

References del_deriv(), Valeur::del_t(), Valeur::get_etat(), set_etat_qcq(), set_etat_zero(), and va.

void Scalar::operator= ( const Cmp & a )

Assignment to a Cmp.

Definition at line 492 of file scalar.C.

References del_deriv(), Valeur::del_t(), dzpuis, Cmp::get_dzpuis(), Cmp::get_etat(), Cmp::get_mp(), Tensor::mp, set_etat_nondef(), set_etat_qcq(), set_etat_zero(), Cmp::va, and va.

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

Assignment to a Tensor (of valence 0).

Definition at line 429 of file scalar.C.

References Tensor::cmp, operator=(), and Tensor::valence.

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

Assignment to another Scalar defined on the same mapping.

Reimplemented from Tensor.

Definition at line 439 of file scalar.C.

References del_deriv(), Valeur::del_t(), dzpuis, etat, Valeur::get_base(), Tensor::mp, Valeur::set_base(), set_etat_nondef(), set_etat_one(), set_etat_qcq(), set_etat_zero(), and va.

void Scalar::poisson	(	Param &	par,
		Scalar &	uu
	)			const

Solves the scalar Poisson equation with *this as a source (version with parameters to control the resolution).

The source $\sigma$ of the equation $\Delta u = \sigma$ is represented by the Scalar *this . Note that dzpuis must be equal to 2 or 4, i.e. that the quantity stored in *this is in fact $r^2 \sigma$ or $r^4 \sigma$ in the compactified external domain.

Parameters:

	par	[input/output] possible parameters
	uu	[input/output] solution u with the boundary condition u =0 at spatial infinity.

Definition at line 148 of file scalar_pde.C.

References Tensor::mp, and Map::poisson().

Scalar Scalar::poisson ( ) const

Solves the scalar Poisson equation with *this as a source.

The source $\sigma$ of the equation $\Delta u = \sigma$ is represented by the Scalar *this . Note that dzpuis must be equal to 2 or 4, i.e. that the quantity stored in *this is in fact $r^2 \sigma$ or $r^4 \sigma$ in the compactified external domain. The solution u with the boundary condition u =0 at spatial infinity is the returned Scalar.

Definition at line 132 of file scalar_pde.C.

References Tensor::mp, and Map::poisson().

Scalar Scalar::poisson_angu ( double lambda = 0 ) const

Solves the (generalized) angular Poisson equation with *this as source.

The generalized angular Poisson equation is $\Delta_{\theta\varphi} u + \lambda u = \sigma$ , where $\Delta_{\theta\varphi} u := \frac{\partial^2 u} {\partial \theta^2} + \frac{1}{\tan \theta} \frac{\partial u} {\partial \theta} +\frac{1}{\sin^2 \theta}\frac{\partial^2 u} {\partial \varphi^2}$ .

Parameters:

lambda

[input] coefficient $\lambda$ in the above equation (default value = 0)

Returns:: solution u .

Definition at line 196 of file scalar_pde.C.

References Tensor::mp, and Map::poisson_angu().

Scalar Scalar::poisson_dir_neu	(	const Valeur &	limite,
		int	num,
		double	fact_dir,
		double	fact_neu
	)			const

Is identicall to Scalar::poisson() .

The regularity condition at the origin is replace by a mixed boundary condition (Dirichlet + Neumann).

Parameters:

	limite	[input] : angular function. The boundary condition is given by `limite`[num] .
	num	[input] : index of the boudary at which the condition is to be fullfilled.
	fact_dir	[input] : double in front of $\Psi$ (if $\Psi$ is the variable solved).
	fact_neu	[input] : double in front of the radial derivative of $\Psi$ .

More precisely we impose $fact\_dir.\Psi + fact\_neu.\frac{\partial \Phi}{\partial r}$ is equal to the source at the boundary between the domains num and num+1 (the latter one being a shell).

Definition at line 76 of file scalar_pde_frontiere.C.

References Tensor::mp, Map::poisson_frontiere(), Cmp::set_dzpuis(), and Cmp::va.

Scalar Scalar::poisson_dirichlet	(	const Valeur &	limite,
		int	num
	)			const

Is identicall to Scalar::poisson() .

The regularity condition at the origin is replace by a boundary condition of the Dirichlet type.

Parameters:

	limite	[input] : angular function. The boundary condition is given by `limite`[num] .
	num	[input] : index of the boudary at which the condition is to be fullfilled.

More precisely we impose the solution is equal to limite[num] at the boundary between the domains num and num+1 (the latter one being a shell).

Definition at line 60 of file scalar_pde_frontiere.C.

References Tensor::mp, Map::poisson_frontiere(), Cmp::set_dzpuis(), and Cmp::va.

Scalar Scalar::poisson_frontiere_double	(	const Valeur &	lim_func,
		const Valeur &	lim_der,
		int	num_zone
	)			const

Idem as Scalar::poisson_dirichlet , the boundary condition being on both the function and its radial derivative.

The boundary condition at infinity is relaxed.

Definition at line 111 of file scalar_pde_frontiere.C.

References Tensor::mp.

Scalar Scalar::poisson_neumann	(	const Valeur &	limite,
		int	num_front
	)			const

Idem as Scalar::poisson_dirichlet , the boundary condition being on the radial derivative of the solution.

Definition at line 94 of file scalar_pde_frontiere.C.

References Tensor::mp, Map::poisson_frontiere(), Cmp::set_dzpuis(), and Cmp::va.

void Scalar::poisson_regular	(	int	k_div,
		int	nzet,
		double	unsgam1,
		Param &	par,
		Scalar &	uu,
		Scalar &	uu_regu,
		Scalar &	uu_div,
		Tensor &	duu_div,
		Scalar &	source_regu,
		Scalar &	source_div
	)			const

Solves the scalar Poisson equation with *this as a source (version with parameters to control the resolution).

The source $\sigma$ of the equation $\Delta u = \sigma$ is represented by the Scalar *this . The regularized source $\sigma_{\rm regu} = \sigma - \sigma_{\rm div}$ is constructed and solved. Note that dzpuis must be equal to 2 or 4, i.e. that the quantity stored in *this is in fact $r^2 \sigma$ or $r^4 \sigma$ in the compactified external domain.

Parameters:

	k_div	[input] regularization degree of the procedure
	nzet	[input] number of domains covering the star
	unsgam1	[input] parameter $1/(\gamma-1)$ where $\gamma$ denotes the adiabatic index
	par	[input/output] possible parameters
	uu	[input/output] solution
	uu_regu	[output] solution of the regular part of the source.
	uu_div	[output] solution of the diverging part of the source.
	duu_div	[output] derivative of the diverging potential.
	source_regu	[output] regularized source
	source_div	[output] diverging part of the source

Definition at line 57 of file scalar_poisson_regu.C.

References Tensor::get_triad(), Tensor::mp, Map::poisson_regular(), Tensor::set(), Tenseur::set(), Itbl::set(), Itbl::set_etat_qcq(), and Tenseur::set_etat_qcq().

void Scalar::poisson_tau	(	Param &	par,
		Scalar &	uu
	)			const

Solves the scalar Poisson equation with *this as a source using a real Tau method (version with parameters to control the resolution) The source $\sigma$ of the equation $\Delta u = \sigma$ is represented by the Scalar *this .

Note that dzpuis must be equal to 2, 3 or 4, i.e. that the quantity stored in *this is in fact $r^2 \sigma$ , $r^3 \sigma$ or $r^4 \sigma$ in the compactified external domain. The solution u with the boundary condition u =0 at spatial infinity is the returned Scalar.

Definition at line 180 of file scalar_pde.C.

References Tensor::mp, and Map::poisson_tau().

Scalar Scalar::poisson_tau ( ) const

Solves the scalar Poisson equation with *this as a source using a real Tau method The source $\sigma$ of the equation $\Delta u = \sigma$ is represented by the Scalar *this .

Note that dzpuis must be equal to 2, 3 or 4, i.e. that the quantity stored in *this is in fact $r^2 \sigma$ , $r^3 \sigma$ or $r^4 \sigma$ in the compactified external domain. The solution u with the boundary condition u =0 at spatial infinity is the returned Scalar.

Definition at line 165 of file scalar_pde.C.

References Tensor::mp, and Map::poisson_tau().

int Tensor::position ( const Itbl & ind ) const [virtual, inherited]

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 in Tensor_sym, and Vector.

Definition at line 521 of file tensor.C.

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

Scalar Scalar::primr ( bool null_infty = true ) const

Computes the radial primitive which vanishes for $r\to \infty$ .

i.e. the function $F(r,\theta,\varphi) = \int_r^\infty f(r',\theta,\varphi) \, dr'$ where f is the function represented by *this (and must have a dzpuis = 2).

Parameters:

null_infty

if true (default), the primitive is null at infinity (or on the grid boundary). F is null at the center otherwise

Returns:: function F

Definition at line 97 of file scalar_integ.C.

References Tensor::mp, and Map::primr().

void Scalar::raccord ( int n )

Performs the $C^n$ matching of the nucleus with respect to the first shell.

Definition at line 58 of file scalar_raccord.C.

References Tbl::annule_hard(), Valeur::base, Valeur::c_cf, Valeur::coef(), etat, Map_af::get_alpha(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Mg3d::get_type_r(), Matrice::inverse(), Tensor::mp, R_CHEBI, R_CHEBP, Mtbl_cf::set(), Tbl::set(), Valeur::set_etat_cf_qcq(), Mtbl_cf::t, va, Valeur::ylm(), and Valeur::ylm_i().

void Scalar::raccord_c1_zec	(	int	puis,
		int	nbre,
		int	lmax
	)

Performs the $C^1$ matching of the external domain with respect to the last shell using function like $\frac{1}{r^i}$ with ${\tt puis} \leq i \leq {\tt puis+nbre}$ for each spherical harmonics with $l \leq {\tt lmax}$ .

Definition at line 73 of file scalar_raccord_zec.C.

References Tbl::annule_hard(), Valeur::base, Valeur::c_cf, Valeur::coef(), dec_dzpuis(), dsdr(), etat, Map_af::get_alpha(), Base_val::get_base_r(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Matrice::inverse(), Tensor::mp, R_CHEB, Mtbl_cf::set(), Matrice::set(), Tbl::set(), Matrice::set_band(), set_dzpuis(), Valeur::set_etat_cf_qcq(), Matrice::set_etat_qcq(), Tbl::set_etat_qcq(), Matrice::set_lu(), Mtbl_cf::t, va, Valeur::ylm(), and Valeur::ylm_i().

void Scalar::raccord_externe	(	int	puis,
		int	nbre,
		int	lmax
	)

Matching of the external domain with the outermost shell.

Definition at line 62 of file scalar_raccord_externe.C.

References Tbl::annule_hard(), Valeur::base, Valeur::c_cf, Valeur::coef(), Map_af::get_alpha(), Map_af::get_beta(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Tensor::mp, Mtbl_cf::set(), Tbl::set(), Matrice::set(), set_dzpuis(), Valeur::set_etat_cf_qcq(), Mtbl_cf::set_etat_qcq(), Tbl::set_etat_qcq(), Matrice::set_etat_qcq(), Mtbl_cf::t, va, Valeur::ylm(), and Valeur::ylm_i().

void Scalar::sarra_filter_r	(	int	lzmin,
		int	lzmax,
		double	p,
		double	alpha = `-1E-16`
	)

Applies an exponential filter to the spectral coefficients in the radial direction.

The filter is of the type: $\forall n\leq N,\, b_n = \sigma(n/N ) a_n$ , with $\sigma(x) = \exp\left( \alpha x^{p} \right)$ and N the number of radial coefficients.

Parameters:

	lzmin,lzmax	[input] the indices of the domain where the filter is applied (in [`lzmin` , `lzmax` ])
	p	[input] the order of the filter
	alpha	[input] $\alpha$ appearing in the above formula.

Definition at line 92 of file scalar_exp_filter.C.

References Valeur::c, Valeur::c_cf, Valeur::coef(), del_deriv(), Valeur::del_deriv(), etat, Map::get_mg(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Tensor::mp, Mtbl_cf::set(), and va.

void Scalar::sarra_filter_r_all_domains	(	double	p,
		double	alpha = `1E-16`
	)

Applies an exponential filter in radial direction in all domains for the case where p is a double (see Scalar:sarra_filter_r ).

Note that this may cause regularity problems at the origin if applied in a nucleus.

Definition at line 132 of file scalar_exp_filter.C.

References Map::get_mg(), Tensor::get_mp(), Mg3d::get_nzone(), and sarra_filter_r().

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

Save in a file.

Reimplemented from Tensor.

Definition at line 679 of file scalar.C.

References dzpuis, etat, fwrite_be(), Valeur::sauve(), and va.

Scalar Scalar::scalar_out_bound	(	int	n,
		bool	leave_ylm = `false`
	)

Returns the Scalar containing the values of angular coefficients at the outer boundary.

Parameters:

	l_dom	[input] domain index
	leave_ylm	[input] flag to decide whether the coefficients are expressed in spherical harmonics or Fourier base

Definition at line 463 of file scalar_manip.C.

References Valeur::base, Valeur::c_cf, Valeur::coef(), etat, Base_val::get_base_t(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nt(), Tensor::mp, Map::mp_angu(), Base_val::set_base_t(), va, Mtbl_cf::val_out_bound_jk(), and Valeur::ylm().

Scalar & Tensor::set	(	int	i1,
		int	i2,
		int	i3,
		int	i4
	)			`[inherited]`

Returns the value of a component for a tensor of valence 4 (read/write version).

Parameters:

	i1	value of the first index (1, 2 or 3)
	i2	value of the second index (1, 2 or 3)
	i3	value of the third index (1, 2 or 3)
	i4	value of the fourth index (1, 2 or 3)

Returns:: modifiable reference on the component specified by (i1,i2,i3,i4)

Definition at line 633 of file tensor.C.

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

Scalar & Tensor::set	(	int	i1,
		int	i2,
		int	i3
	)			`[inherited]`

Returns the value of a component for a tensor of valence 3 (read/write version).

Parameters:

	i1	value of the first index (1, 2 or 3)
	i2	value of the second index (1, 2 or 3)
	i3	value of the third index (1, 2 or 3)

Returns:: modifiable reference on the component specified by (i1,i2,i3)

Definition at line 617 of file tensor.C.

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

Scalar & Tensor::set	(	int	i1,
		int	i2
	)			`[inherited]`

Returns the value of a component for a tensor of valence 2 (read/write version).

Parameters:

	i1	value of the first index (1, 2 or 3)
	i2	value of the second index (1, 2 or 3)

Returns:: modifiable reference on the component specified by (i1,i2)

Definition at line 602 of file tensor.C.

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

Scalar & Tensor::set ( const Itbl & ind ) [inherited]

Returns the value of a component (read/write version).

Parameters:

ind

1-D Itbl of size valence containing the values of each index specifing the component, with the following storage convention:

ind(0) : value of the first index (1, 2 or 3)
ind(1) : value of the second index (1, 2 or 3)
and so on...

Returns:: modifiable reference on the component specified by ind

Definition at line 650 of file tensor.C.

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

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

To be used to describe the fact that the derivatives members have been calculated with met .

First it sets a null element of met_depend to &met and puts this in the list of the dependancies of met .

Definition at line 449 of file tensor.C.

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

void Scalar::set_der_0x0 ( ) const [protected]

Sets the pointers for derivatives to 0x0.

Reimplemented from Tensor.

Definition at line 299 of file scalar.C.

References ind_lap, p_dsdr, p_dsdradial, p_dsdrho, p_dsdt, p_dsdx, p_dsdy, p_dsdz, p_integ, p_lap, p_lapang, p_srdsdt, p_srstdsdp, and p_stdsdp.

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

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

.. to 0x0.

Reimplemented in Sym_tensor, and Vector.

Definition at line 429 of file tensor.C.

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

Tbl& Scalar::set_domain ( int l ) [inline]

Read/write of the value in a given domain.

This method should be used only to set the value in a given domain (it performs a call to del_deriv); for reading the value in a domain without changing it, the method domain(int ) is preferable.

Parameters:

l

[input] domain index

Returns:: writable Tbl containing the value of the field in domain l .

Definition at line 597 of file scalar.h.

References del_deriv(), etat, Valeur::set(), and va.

void Scalar::set_dzpuis ( int dzi )

Modifies the dzpuis flag.

NB: this method does not change the field values stored in the compactified external domain (use methods dec_dzpuis() , etc... for this purpose).

Definition at line 801 of file scalar.C.

References dzpuis.

void Scalar::set_etat_nondef ( ) [virtual]

Sets the logical state to ETATNONDEF (undefined).

Calls the logical destructor of the Valeur va * deallocates the memory occupied by all the derivatives.

Reimplemented from Tensor.

Definition at line 337 of file scalar.C.

References del_t(), and etat.

void Scalar::set_etat_one ( )

Sets the logical state to ETATUN (one).

Fills the Valeur va with ones and deallocates the memory occupied by all the derivatives.

Definition at line 327 of file scalar.C.

References del_deriv(), etat, and va.

void Scalar::set_etat_qcq ( ) [virtual]

Sets the logical state to ETATQCQ (ordinary state).

If the state is already ETATQCQ , this function does nothing. Otherwise, it calls the logical destructor of the Valeur va and deallocates the memory occupied by all the derivatives.

Reimplemented from Tensor.

Definition at line 346 of file scalar.C.

References del_t(), and etat.

void Scalar::set_etat_zero ( ) [virtual]

Sets the logical state to ETATZERO (zero).

Calls the logical destructor of the Valeur va and deallocates the memory occupied by all the derivatives.

Reimplemented from Tensor.

Definition at line 317 of file scalar.C.

References del_deriv(), etat, Valeur::set_etat_zero(), and va.

double& Scalar::set_grid_point	(	int	l,
		int	k,
		int	j,
		int	i
	)			`[inline]`

Setting the value of the field at a given grid point.

CAUTION: to gain in efficiency (especially when this method is invoqued inside a loop), the method del_deriv() (to delete the derived members) is not called by set_grid_point . It must thus be invoqued by the user, after all the calls to set_grid_point have been performed.

Parameters:

	l	[input] domain index
	k	[input] $\phi$ index
	j	[input] $\theta$ index
	i	[input] r ( $\xi$ ) index

Returns:: writable value of the field at the specified grid point

Definition at line 666 of file scalar.h.

References etat, Valeur::set(), and va.

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

Sets the types of all the indices.

Returns:: a reference on the 1-D array of integers (class Itbl ) of size valence that can be modified (COV for a covariant one and CON for a contravariant one)

Definition at line 914 of file tensor.h.

References Tensor::type_indice.

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

Sets the type of the index number i .

i must be strictly lower than valence and obey the following convention:

i = 0 : first index
i = 1 : second index
and so on...

Returns:: reference on the type that can be modified (COV for a covariant index, CON for a contravariant one)

Definition at line 905 of file tensor.h.

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

void Scalar::set_inner_boundary	(	int	l,
		double	x
	)

Sets the value of the Scalar at the inner boundary of a given domain.

Parameters:

	l	[input] domain index
	x	[input] (constant) value at the inner boundary of domain no. `l`

Definition at line 279 of file scalar_manip.C.

References annule_hard(), Valeur::coef_i(), del_deriv(), etat, Map::get_mg(), Mg3d::get_np(), Mg3d::get_nt(), Tensor::mp, Valeur::set(), Valeur::set_etat_c_qcq(), and va.

void Scalar::set_outer_boundary	(	int	l,
		double	x
	)

Sets the value of the Scalar at the outer boundary of a given domain.

Parameters:

	l	[input] domain index
	x	[input] (constant) value at the outer boundary of domain no. `l`

Definition at line 311 of file scalar_manip.C.

References annule_hard(), Valeur::coef_i(), del_deriv(), etat, Map::get_mg(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Tensor::mp, Valeur::set(), Valeur::set_etat_c_qcq(), and va.

void Scalar::set_spectral_base ( const Base_val & bi )

Sets the spectral bases of the Valeur va.

Definition at line 790 of file scalar.C.

References Valeur::set_base(), and va.

Valeur& Scalar::set_spectral_va ( ) [inline]

Returns va (read/write version).

Definition at line 586 of file scalar.h.

References va.

void Tensor::set_triad ( const Base_vect & new_triad ) [inherited]

Assigns a new vectorial basis (triad) of decomposition.

NB: this function modifies only the member triad and leave unchanged the components (member cmp ). In order to change them coherently with the new basis, the function change_triad(const Base_vect& ) must be called instead.

Definition at line 515 of file tensor.C.

References Tensor::triad.

void Scalar::smooth_decay	(	int	k,
		int	n
	)

Performs a $C^k$ matching of the last non-compactified shell with a decaying function $\sum_{j=0}^k {\alpha_j \over r^{\ell+n+j}}$ where $\ell$ is the spherical harmonic index and n is some specifiable parameter.

Definition at line 209 of file scalar_raccord_zec.C.

References Valeur::c, Valeur::c_cf, Valeur::coef(), dsdr(), etat, Valeur::get_base(), get_dzpuis(), get_etat(), Valeur::get_etat(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Mg3d::get_type_r(), Matrice::inverse(), Tensor::mp, Map::r, Matrice::set(), Tbl::set(), Matrice::set_band(), Valeur::set_base(), Valeur::set_base_r(), Valeur::set_etat_cf_qcq(), Matrice::set_etat_qcq(), Mtbl_cf::set_etat_qcq(), set_etat_qcq(), Tbl::set_etat_qcq(), Tbl::set_etat_zero(), Matrice::set_lu(), std_spectral_base(), Mtbl_cf::t, va, val_grid_point(), Valeur::ylm(), and Valeur::ylm_i().

Scalar Scalar::sol_divergence ( int n ) const

Resolution of a divergence-like equation.

The equation solved reads: $\frac{\partial \phi}{\partial r} + \frac{n}{r} \phi = \sigma$ , with $\phi$ the unknown and $\sigma$ the source represented by this.

Parameters:

n

[input] the coefficient in front of the 1/r term.

Returns:: the solution to the equation.

Definition at line 64 of file scalar_sol_div.C.

References Tbl::annule_hard(), Mtbl_cf::annule_hard(), Valeur::c_cf, check_dzpuis(), etat, Map_af::get_alpha(), Map_af::get_beta(), Diff_sx::get_matrice(), Diff_dsdx::get_matrice(), Diff_xdsdx::get_matrice(), Mtbl_cf::get_mg(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), get_spectral_base(), Mg3d::get_type_r(), Base_val::give_quant_numbers(), Matrice::inverse(), Tensor::mp, Base_val::mult_x(), R_CHEB, R_CHEBI, R_CHEBP, R_CHEBU, Mtbl_cf::set(), Matrice::set(), Tbl::set(), Valeur::set_etat_cf_qcq(), Tbl::set_etat_qcq(), Matrice::set_etat_qcq(), set_etat_qcq(), set_etat_zero(), Matrice::set_lu(), set_spectral_base(), set_spectral_va(), va, and Valeur::ylm_i().

Scalar Scalar::sol_elliptic ( Param_elliptic & params ) const

Resolution of a general elliptic equation, putting zero at infinity.

Parameters:

params

[input] the operators and variables to be used.

Definition at line 230 of file scalar_pde.C.

References Tensor::mp, set_etat_qcq(), and Map_af::sol_elliptic().

Scalar Scalar::sol_elliptic_2d ( Param_elliptic & ope_var ) const

Solves the scalar 2-dimensional elliptic equation with *this as a source.

Note that dzpuis must be equal to 2, 3 or 4, i.e. The solution u with the boundary condition u =0 at spatial infinity is the returned Scalar.

Definition at line 405 of file scalar_pde.C.

References Tensor::mp, set_etat_qcq(), and Map_af::sol_elliptic_2d().

Scalar Scalar::sol_elliptic_boundary	(	Param_elliptic &	params,
		const Scalar &	bound,
		double	fact_dir,
		double	fact_neu
	)			const

Resolution of general elliptic equation, with inner boundary conditions as Scalars on mono-domain angulare grids.

Definition at line 278 of file scalar_pde.C.

References Tensor::mp, set_etat_qcq(), and Map_af::sol_elliptic_boundary().

Scalar Scalar::sol_elliptic_boundary	(	Param_elliptic &	params,
		const Mtbl_cf &	bound,
		double	fact_dir,
		double	fact_neu
	)			const

Resolution of a general elliptic equation, putting zero at infinity and with inner boundary conditions.

Parameters:

	params	[input] the operators and variables to be used.
	bound	[input] : the boundary condition
	fact_dir	: 1 Dirchlet condition, 0 Neumann condition
	fact_neu	: 0 Dirchlet condition, 1 Neumann condition

Definition at line 252 of file scalar_pde.C.

References Tensor::mp, set_etat_qcq(), and Map_af::sol_elliptic_boundary().

Scalar Scalar::sol_elliptic_fixe_der_zero	(	double	val,
		Param_elliptic &	params
	)			const

Resolution of a general elliptic equation fixing the dericative at the origin and relaxing one continuity condition.

Parameters:

	val	[input] value of the derivative.
	params	[input] the operators and variables to be used.

Definition at line 382 of file scalar_pde.C.

References Tensor::mp, set_etat_qcq(), and Map_af::sol_elliptic_fixe_der_zero().

Scalar Scalar::sol_elliptic_no_zec	(	Param_elliptic &	params,
		double	val = `0`
	)			const

Resolution of a general elliptic equation, putting a given value at the outermost shell and not solving in the compactified domain.

Parameters:

	params	[input] the operators and variables to be used.
	val	[input] value at the last shell.

Definition at line 310 of file scalar_pde.C.

References Tensor::mp, set_etat_qcq(), and Map_af::sol_elliptic_no_zec().

Scalar Scalar::sol_elliptic_only_zec	(	Param_elliptic &	params,
		double	val
	)			const

Resolution of a general elliptic equation solving in the compactified domain and putting a given value at the inner boundary.

Parameters:

	params	[input] the operators and variables to be used.
	val	[input] value at the inner boundary of the external domain.

Definition at line 337 of file scalar_pde.C.

References Tensor::mp, set_etat_qcq(), and Map_af::sol_elliptic_only_zec().

Scalar Scalar::sol_elliptic_pseudo_1d ( Param_elliptic & ope_var ) const

Solves a pseudo-1d elliptic equation with *this as a source.

Definition at line 426 of file scalar_pde.C.

References Tensor::mp, set_etat_qcq(), and Map_af::sol_elliptic_pseudo_1d().

Scalar Scalar::sol_elliptic_sin_zec	(	Param_elliptic &	params,
		double *	coefs,
		double *	phases
	)			const

General elliptic solver.

The equation is not solved in the compactified domain and the matching is done with an homogeneous solution.

Parameters:

	params	[input] the operators and variables to be used.
	coef	[output] : coefficient of the oscillatory solution in the external domain.
	phases	[output] : phases (i.e. choice of the homogeneous solution to match with).

Definition at line 359 of file scalar_pde.C.

References Tensor::mp, set_etat_qcq(), and Map_af::sol_elliptic_sin_zec().

void Scalar::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.

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 from Tensor.

Definition at line 734 of file scalar.C.

References Valeur::display_coef(), dzpuis, etat, and va.

const Scalar & Scalar::srdsdt ( ) const

Returns $1/r \partial / \partial \theta$ of *this .

If dzpuis is zero, then the returned Scalar has dzpuis = 2. It is increased by 1 otherwise.

Definition at line 144 of file scalar_deriv.C.

References dzpuis, etat, Map::get_mg(), Mg3d::get_nzone(), Mg3d::get_type_r(), Tensor::mp, p_srdsdt, Scalar(), set_dzpuis(), set_etat_zero(), and Map::srdsdt().

const Scalar & Scalar::srstdsdp ( ) const

Returns $1/(r\sin\theta) \partial / \partial \phi$ of *this .

If dzpuis is zero, then the returned Scalar has dzpuis = 2. It is increased by 1 otherwise.

Definition at line 176 of file scalar_deriv.C.

References dzpuis, etat, Map::get_mg(), Mg3d::get_nzone(), Mg3d::get_type_r(), Tensor::mp, p_srstdsdp, Scalar(), set_dzpuis(), set_etat_zero(), and Map::srstdsdp().

void Scalar::std_spectral_base ( ) [virtual]

Sets the spectral bases of the Valeur va to the standard ones for a scalar field.

Reimplemented from Tensor.

Definition at line 777 of file scalar.C.

References Valeur::std_base_scal(), and va.

void Scalar::std_spectral_base_odd ( ) [virtual]

Sets the spectral bases of the Valeur va to the standard odd ones for a scalar field.

Reimplemented from Tensor.

Definition at line 784 of file scalar.C.

References Valeur::std_base_scal_odd(), and va.

const Scalar & Scalar::stdsdp ( ) const

Returns $1/\sin\theta \partial / \partial \phi$ of *this .

Definition at line 237 of file scalar_deriv.C.

References dzpuis, etat, Tensor::mp, p_stdsdp, Scalar(), set_dzpuis(), set_etat_zero(), and Map::stdsdp().

Tbl Scalar::tbl_in_bound	(	int	n,
		bool	leave_ylm = `false`
	)

Returns the Tbl containing the values of angular coefficients at the inner boundary.

Parameters:

	l_dom	[input] domain index
	leave_ylm	[input] flag to decide whether the coefficients are expressed in spherical harmonics or Fourier base

Definition at line 444 of file scalar_manip.C.

References Valeur::c_cf, Valeur::coef(), etat, Map::get_mg(), Mg3d::get_np(), Mg3d::get_nt(), Mg3d::get_type_r(), Tensor::mp, Tbl::set(), Tbl::set_etat_qcq(), Tbl::set_etat_zero(), va, Mtbl_cf::val_in_bound_jk(), and Valeur::ylm().

Tbl Scalar::tbl_out_bound	(	int	l_dom,
		bool	leave_ylm = `false`
	)

Returns the Tbl containing the values of angular coefficients at the outer boundary.

Parameters:

	l_dom	[input] domain index
	leave_ylm	[input] flag to decide whether the coefficients are expressed in spherical harmonics or Fourier base

Definition at line 426 of file scalar_manip.C.

References Valeur::c_cf, Valeur::coef(), etat, Map::get_mg(), Mg3d::get_np(), Mg3d::get_nt(), Tensor::mp, Tbl::set(), Tbl::set_etat_qcq(), Tbl::set_etat_zero(), va, Mtbl_cf::val_out_bound_jk(), and Valeur::ylm().

Tbl Scalar::test_poisson	(	const Scalar &	uu,
		ostream &	ostr,
		bool	detail = `false`
	)			const

Checks if a Poisson equation with *this as a source has been correctly solved.

Parameters:

uu [input] Solution u of the Poisson equation $\Delta u = \sigma$ , $\sigma$ being represented by the Scalar *this .

ostr [input/output] Output stream used for displaying err .

detail

[input]

if true displays err(0,*) , err(1,*) and err(2,*)
if false (default), displays only the relative error err(0,*) .

Returns:

2-D Tbl err decribing the errors in each domain:

err(0,l) : Relative error in domain no. l , defined as the maximum value of $|\Delta u - \sigma|$ in that domain divided by M , where M is the maximum value of $|\sigma|$ over all domains if dzpuis = 0 or $\sigma$ is zero in the compactified external domain (CED). If dzpuis != 0 and $\sigma$ does not vanish in the CED, the value of M used in the non-compactified domains is the maximum value over these domains, whereas the value of M used in the compactified external domain is the maximum value on that particular domain.
err(1,l) : Maximum value of the absolute error $|\Delta u - \sigma|$ in domain no. l
err(2,l) : Maximum value of $|\sigma|$ in domain no. l

Definition at line 56 of file scalar_test_poisson.C.

References check_dzpuis(), dzpuis, Map::get_mg(), Tensor::get_mp(), Mg3d::get_nzone(), laplacian(), Tensor::mp, Tbl::set(), and Tbl::set_etat_qcq().

Scalar Tensor::trace ( const Metric & gam ) const [inherited]

Trace with respect to a given metric for a valence 2 tensor.

Parameters:

gam

metric used to raise or lower one of the indices, in order to take the trace

Definition at line 193 of file tensor_calculus.C.

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

Scalar Tensor::trace ( ) const [inherited]

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

Definition at line 176 of file tensor_calculus.C.

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

Tensor Tensor::trace	(	int	ind1,
		int	ind2,
		const Metric &	gam
	)			const `[inherited]`

Trace with respect to a given metric.

Parameters:

ind1

first index for the contraction, with the following convention :

ind1 = 0 : first index of the tensor
ind1 = 1 : second index of the tensor
and so on...

ind2 second index for the contraction

gam metric used to raise or lower ind1 in order that it has a opposite type than ind2

Definition at line 149 of file tensor_calculus.C.

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

Tensor Tensor::trace	(	int	ind1,
		int	ind2
	)			const `[inherited]`

Trace on two different type indices.

Parameters:

ind1

first index for the contraction, with the following convention :

ind1 = 0 : first index of the tensor
ind1 = 1 : second index of the tensor
and so on...

ind2 second index for the contraction

Definition at line 90 of file tensor_calculus.C.

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

Tensor Tensor::up	(	int	ind,
		const Metric &	gam
	)			const `[inherited]`

Computes a new tensor by raising an index of *this.

Parameters:

ind

index to be raised, with the following convention :

ind1 = 0 : first index of the tensor
ind1 = 1 : second index of the tensor
and so on... (ind must be of covariant type (COV )).

gam metric used to raise the index (contraction with the twice contravariant form of the metric on the index ind ).

Definition at line 221 of file tensor_calculus.C.

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

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

Computes a new tensor by raising or lowering all the indices of *this .

Parameters:

gam

metric used to lower the contravariant indices and raising the covariant ones.

Definition at line 301 of file tensor_calculus.C.

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

double Scalar::val_grid_point	(	int	l,
		int	k,
		int	j,
		int	i
	)			const `[inline]`

Returns the value of the field at a specified grid point.

Parameters:

	l	[input] domain index
	k	[input] $\phi$ index
	j	[input] $\theta$ index
	i	[input] r ( $\xi$ ) index

Definition at line 619 of file scalar.h.

References etat, and va.

double Scalar::val_point	(	double	r,
		double	theta,
		double	phi
	)			const

Computes the value of the field at an arbitrary point $(r, \theta, \phi)$ , by means of the spectral expansion.

NB: if $(r, \theta, \phi)$ is a point of the spectral grid, the method val_grid_point is to be preferred, being much more efficient.

Parameters:

	r	[input] value of the coordinate r
	theta	[input] value of the coordinate $\theta$
	phi	[input] value of the coordinate $\phi$

Returns:: value at the point $(r, \theta, \phi)$ of the field represented by *this . NB: in the compactified external domain, the returned value is the actual value of the field, i.e. the stored value divided by $r^{\rm dzpuis}$ .

Definition at line 883 of file scalar.C.

References dzpuis, etat, Map::get_mg(), Mg3d::get_nzone(), Tensor::mp, va, Map::val_lx(), and Valeur::val_point().

void Scalar::visu_box	(	double	xmin,
		double	xmax,
		double	ymin,
		double	ymax,
		double	zmin,
		double	zmax,
		const char *	title0 = `0x0`,
		const char *	filename0 = `0x0`,
		bool	start_dx = `true`,
		int	nx = `40`,
		int	ny = `40`,
		int	nz = `40`
	)			const

3D visualization (volume rendering) via OpenDX.

Prepares files for visualization by OpenDX of the values of the field in some rectangular box.

Parameters:

	xmin	[input] defines with `xmax` the x range of the visualization box
	xmax	[input] defines with `xmin` the x range of the visualization box
	ymin	[input] defines with `ymax` the y range of the visualization box
	ymax	[input] defines with `ymin` the y range of the visualization box
	zmin	[input] defines with `zmax` the z range of the visualization box
	zmax	[input] defines with `zmin` the z range of the visualization box
	title	[input] title for the graph (for OpenDX legend)
	filename	[input] name for the file which will be the input for OpenDX; the default 0x0 is transformed into "scalar_box"
	start_dx	[input] determines whether OpenDX must be launched (as a subprocess) to view the field; if set to `false` , only input files for future usage of OpenDX are created
	nx	[input] number of points in the x direction (uniform sampling)
	ny	[input] number of points in the y direction (uniform sampling)
	nz	[input] number of points in the z direction (uniform sampling)

Definition at line 338 of file scalar_visu.C.

References Valeur::c_cf, check_dzpuis(), Valeur::coef(), Map::convert_absolute(), dec_dzpuis(), dzpuis, Tensor::mp, Scalar(), va, Map::val_lx(), and Mtbl_cf::val_point().

void Scalar::visu_section	(	const Tbl &	plane,
		double	umin,
		double	umax,
		double	vmin,
		double	vmax,
		const char *	title = `0x0`,
		const char *	filename = `0x0`,
		bool	start_dx = `true`,
		int	nu = `200`,
		int	nv = `200`
	)			const

3D visualization via a plane section.

Prepares files for visualization by OpenDX of the values of the field in any given plane.

Parameters:

	plane	[input] : 2D `Tbl` defining the section plane: `plane` must of dimension 3x3 with the following content: `plane(0,i)` : absolute Cartesian coordinates (xa0,ya0,za0) of some point in the plane considered as the origin for the plane coordinates (u,v): `plane(0,0)` = xa0 , `plane(0,1)` = ya0 , `plane(0,2)` = za0 `plane(1,i)` : components w.r.t. absolute Cartesian coordinates of the u-coordinate unit vector in the section plane `plane(2,i)` : components w.r.t. absolute Cartesian coordinates of the v-coordinate unit vector in the section plane
	umin	[input] defines with `umax` the range of the plane coordinate u
	umax	[input] defines with `umin` the range of the plane coordinate u
	vmin	[input] defines with `vmax` the range of the plane coordinate v
	vmax	[input] defines with `vmin` the range of the plane coordinate v
	title	[input] title for the graph (for OpenDX legend)
	filename	[input] name for the file which will be the input for OpenDX; the default 0x0 is transformed into "scalar_section"
	start_dx	[input] determines whether OpenDX must be launched (as a subprocess) to view the field; if set to `false` , only input files for future usage of OpenDX are created
	nu	[input] number of points in the u direction (uniform sampling)
	nv	[input] number of points in the v direction (uniform sampling)

Definition at line 152 of file scalar_visu.C.

References Valeur::c_cf, Valeur::coef(), Map::convert_absolute(), Tensor::mp, va, Map::val_lx(), and Mtbl_cf::val_point().

void Scalar::visu_section	(	const char	section_type,
		double	aa,
		double	umin,
		double	umax,
		double	vmin,
		double	vmax,
		const char *	title = `0x0`,
		const char *	filename = `0x0`,
		bool	start_dx = `true`,
		int	nu = `200`,
		int	nv = `200`
	)			const

3D visualization via a plane section.

Prepares files for visualization by OpenDX of the values of the field in a plane x=const, y=const or z=const

Parameters:

	section_type	[input] defines the type of section : 'x' for a plane x = a with a = const (parameter `aa` ) 'y' for a plane y = a with a = const (parameter `aa` ) 'z' for a plane z = a with a = const (parameter `aa` )
	aa	[input] constant a defining the section plane
	umin	[input] defines with `umax` the range of the plane coordinate u
	umax	[input] defines with `umin` the range of the plane coordinate u
	vmin	[input] defines with `vmax` the range of the plane coordinate v
	vmax	[input] defines with `vmin` the range of the plane coordinate v
	title	[input] title for the graph (for OpenDX legend)
	filename	[input] name for the file which will be the input for OpenDX; the default 0x0 is transformed into "scalar_section"
	start_dx	[input] determines whether OpenDX must be launched (as a subprocess) to view the field; if set to `false` , only input files for future usage of OpenDX are created
	nu	[input] number of points in the u direction (uniform sampling)
	nv	[input] number of points in the v direction (uniform sampling)

Definition at line 74 of file scalar_visu.C.

References Tbl::set(), and Tbl::set_etat_qcq().

void Scalar::visu_section_anim	(	const char	section_type,
		double	aa,
		double	umin,
		double	umax,
		double	vmin,
		double	vmax,
		int	jtime,
		double	ttime,
		int	jgraph = `1`,
		const char *	title = `0x0`,
		const char *	filename_root = `0x0`,
		bool	start_dx = `false`,
		int	nu = `200`,
		int	nv = `200`
	)			const

3D visualization via time evolving plane section (animation).

Prepares files for visualization by OpenDX of the values of the field in a plane x=const, y=const or z=const at successive time steps

Parameters:

	section_type	[input] defines the type of section : 'x' for a plane x = a with a = const (parameter `aa` ) 'y' for a plane y = a with a = const (parameter `aa` ) 'z' for a plane z = a with a = const (parameter `aa` )
	aa	[input] constant a defining the section plane
	umin	[input] defines with `umax` the range of the plane coordinate u
	umax	[input] defines with `umin` the range of the plane coordinate u
	vmin	[input] defines with `vmax` the range of the plane coordinate v
	vmax	[input] defines with `vmin` the range of the plane coordinate v
	jtime	[input] time step label
	ttime	[input] time t corresponding to `jtime`
	jgraph	[input] number of time steps between two graphs: the graph will be generated only if `jtime` is a multiple of `jgraph`
	title	[input] title for the graph (for OpenDX legend)
	filename_root	[input] beginning of the names for the files which will be the input for OpenDX (the end of names will be automatically generated from the time steps); the default 0x0 is transformed into "anim"
	start_dx	[input] determines whether OpenDX must be launched (as a subprocess) to view the field; if set to `false` , only input files for future usage of OpenDX are created
	nu	[input] number of points in the u direction (uniform sampling)
	nv	[input] number of points in the v direction (uniform sampling)

Definition at line 531 of file scalar_visu.C.

References visu_section().

Friends And Related Function Documentation

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

Tensorial product of two symmetric tensors.

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

Definition at line 147 of file tensor_sym_calculus.C.

ostream& operator<<	(	ostream &	,
		const Scalar &
	)			`[friend]`

Display.

Reimplemented from Tensor.

Member Data Documentation

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

Array of size n_comp of pointers onto the components.

Definition at line 311 of file tensor.h.

int Scalar::dzpuis [protected]

Power of r by which the quantity represented by this must be divided in the compactified external domain (CED) in order to get the correct physical values.

Definition at line 393 of file scalar.h.

int Scalar::etat [protected]

The logical state ETATNONDEF (undefined), ETATZERO (null), ETATUN (one), or ETATQCQ (ordinary).

Definition at line 386 of file scalar.h.

int Scalar::ind_lap [mutable, protected]

Power of r by which the last computed Laplacian has been multiplied in the compactified external domain.

Definition at line 453 of file scalar.h.

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

Array on the Metric 's which were used to compute derived quantities, like p_derive_cov , etc.

.. The i-th element of this array is the Metric used to compute the i-th element of p_derive_cov , etc..

Definition at line 323 of file tensor.h.

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

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

Definition at line 291 of file tensor.h.

int Tensor::n_comp [protected, inherited]

Number of stored components, depending on the symmetry.

Definition at line 308 of file tensor.h.

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

Array of pointers on the contravariant derivatives of this with respect to various metrics.

See the comments of met_depend . See also the comments of method derive_con() for a precise definition of a "contravariant" derivative.

Definition at line 339 of file tensor.h.

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

Array of pointers on the covariant derivatives of this with respect to various metrics.

See the comments of met_depend . See also the comments of method derive_cov() for the index convention of the covariant derivation.

Definition at line 331 of file tensor.h.

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

Array of pointers on the divergence of this with respect to various metrics.

See the comments of met_depend . See also the comments of method divergence() for a precise definition of a the divergence with respect to a given metric.

Definition at line 347 of file tensor.h.

Scalar* Scalar::p_dsdr [mutable, protected]

Pointer on $\partial/\partial r$ of *this (0x0 if not up to date).

Definition at line 401 of file scalar.h.

Scalar* Scalar::p_dsdradial [mutable, protected]

Pointer on $\partial/\partial radial$ of *this.

Definition at line 445 of file scalar.h.

Scalar* Scalar::p_dsdrho [mutable, protected]

Pointer on $\partial/\partial \rho$ of *this.

Definition at line 448 of file scalar.h.

Scalar* Scalar::p_dsdt [mutable, protected]

Pointer on $\partial/\partial \theta$ of *this (0x0 if not up to date).

Definition at line 414 of file scalar.h.

Scalar* Scalar::p_dsdx [mutable, protected]

Pointer on $\partial/\partial x$ of *this , where $x=r\sin\theta \cos\phi$ (0x0 if not up to date).

Definition at line 424 of file scalar.h.

Scalar* Scalar::p_dsdy [mutable, protected]

Pointer on $\partial/\partial y$ of *this , where $y=r\sin\theta \sin\phi$ (0x0 if not up to date).

Definition at line 429 of file scalar.h.

Scalar* Scalar::p_dsdz [mutable, protected]

Pointer on $\partial/\partial z$ of *this , where $z=r\cos\theta$ (0x0 if not up to date).

Definition at line 434 of file scalar.h.

Tbl* Scalar::p_integ [mutable, protected]

Pointer on the space integral of *this (values in each domain) (0x0 if not up to date).

Definition at line 458 of file scalar.h.

Scalar* Scalar::p_lap [mutable, protected]

Pointer on the Laplacian of *this (0x0 if not up to date).

Definition at line 438 of file scalar.h.

Scalar* Scalar::p_lapang [mutable, protected]

Pointer on the Laplacian of *this (0x0 if not up to date).

Definition at line 442 of file scalar.h.

Scalar* Scalar::p_srdsdt [mutable, protected]

Pointer on $1/r \partial/\partial \theta$ of *this (0x0 if not up to date).

Definition at line 406 of file scalar.h.

Scalar* Scalar::p_srstdsdp [mutable, protected]

Pointer on $1/(r\sin\theta) \partial/\partial \phi$ of *this (0x0 if not up to date).

Definition at line 411 of file scalar.h.

Scalar* Scalar::p_stdsdp [mutable, protected]

Pointer on $1/\sin\theta \partial/\partial \phi$ of *this (0x0 if not up to date).

Definition at line 419 of file scalar.h.

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

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

Definition at line 299 of file tensor.h.

Itbl Tensor::type_indice [protected, inherited]

1D array of integers (class Itbl ) of size valence containing the type of each index: COV for a covariant one and CON for a contravariant one.

Definition at line 306 of file tensor.h.

Valeur Scalar::va [protected]

The numerical value of the Scalar.

Definition at line 395 of file scalar.h.

int Tensor::valence [protected, inherited]

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

Definition at line 294 of file tensor.h.

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

Scalar Class Reference [Tensorial fields]

Public Member Functions

Protected Member Functions

Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation

Scalar Class Reference
[Tensorial fields]