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

#include <scalar.h>

Inheritance diagram for Lorene::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.
bool	is_nan (bool verbose=false) const
	Looks for NaNs (not a number) in the scalar field.
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.
virtual void	exponential_filter_ylm_phi (int lzmin, int lzmax, int p_r, int p_tet, int p_phi, 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_star (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).
void	operator+= (const Tensor &)
	+= Tensor
void	operator-= (const Tensor &)
	-= Tensor

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... to 0x0.
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... The i-th element of this array is the `Metric` used to compute the i-th element of `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 &ost, const Scalar &ci)
	Display.
Scalar	operator- (const Scalar &ci)
	`-` Scalar
Scalar	operator+ (const Scalar &c1, const Scalar &c2)
	Scalar + Scalar.
Scalar	operator+ (const Scalar &c1, const Mtbl &mi)
	Scalar + Mbtl.
Scalar	operator+ (const Scalar &t1, double x)
	Scalar + double.
Scalar	operator- (const Scalar &c1, const Scalar &c2)
	Scalar - Scalar.
Scalar	operator- (const Scalar &t1, const Mtbl &mi)
	Scalar - Mbtl.
Scalar	operator- (const Scalar &t1, double x)
	Scalar - double.
Scalar	operator* (const Scalar &c1, const Scalar &c2)
	Scalar * Scalar.
Scalar	operator% (const Scalar &c1, const Scalar &c2)
	Scalar * Scalar with desaliasing.
Scalar	operator\| (const Scalar &c1, const Scalar &c2)
	Scalar * Scalar with desaliasing only in r.
Scalar	operator* (const Mtbl &mi, const Scalar &c1)
	Mtbl * Scalar.
Scalar	operator* (double a, const Scalar &c1)
	double * Scalar
Scalar	operator/ (const Scalar &c1, const Scalar &c2)
	Scalar / Scalar.
Scalar	operator/ (const Scalar &c1, const Mtbl &mi)
	Scalar / Mtbl.
Scalar	operator/ (const Mtbl &mi, const Scalar &c2)
	Mtbl / Scalar.
Scalar	operator/ (const Scalar &c1, double x)
	Scalar / double.
Scalar	operator/ (double x, const Scalar &c2)
	double / Scalar
Scalar	sin (const Scalar &ci)
	Sine.
Scalar	cos (const Scalar &ci)
	Cosine.
Scalar	tan (const Scalar &ci)
	Tangent.
Scalar	asin (const Scalar &ci)
	Arcsine.
Scalar	acos (const Scalar &ci)
	Arccosine.
Scalar	atan (const Scalar &ci)
	Arctangent.
Scalar	exp (const Scalar &ci)
	Exponential.
Scalar	Heaviside (const Scalar &ci)
	Heaviside function.
Scalar	log (const Scalar &ci)
	Neperian logarithm.
Scalar	log10 (const Scalar &ci)
	Basis 10 logarithm.
Scalar	sqrt (const Scalar &ci)
	Square root.
Scalar	racine_cubique (const Scalar &ci)
	Cube root.
Scalar	pow (const Scalar &ci, int n)
	Power ${\tt Scalar}^{\tt int}$ .
Scalar	pow (const Scalar &ci, double x)
	Power ${\tt Scalar}^{\tt double}$ .
Scalar	abs (const Scalar &ci)
	Absolute value.
double	totalmax (const Scalar &ci)
	Maximum values of a `Scalar` in each domain.
double	totalmin (const Scalar &ci)
	Minimum values of a `Scalar` in each domain.
Tbl	max (const Scalar &ci)
	Maximum values of a `Scalar` in each domain.
Tbl	min (const Scalar &ci)
	Minimum values of a `Scalar` in each domain.
Tbl	norme (const Scalar &ci)
	Sums of the absolute values of all the values of the `Scalar` in each domain.
Tbl	diffrel (const Scalar &a, const Scalar &b)
	Relative difference between two `Scalar` (norme version).
Tbl	diffrelmax (const Scalar &a, const Scalar &b)
	Relative difference between two `Scalar` (max version).

Detailed Description

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

()

Definition at line 393 of file scalar.h.

Constructor & Destructor Documentation

◆ Scalar() [1/5]

Lorene::Scalar::Scalar ( const Map & mpi )

explicit

Constructor from mapping.

Definition at line 210 of file scalar.C.

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

◆ Scalar() [2/5]

Lorene::Scalar::Scalar ( const Tensor & a )

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

Definition at line 221 of file scalar.C.

References Lorene::Tensor::cmp, dzpuis, etat, Lorene::Tensor::mp, set_der_0x0(), Lorene::Tensor::Tensor(), va, and Lorene::Tensor::valence.

◆ Scalar() [3/5]

Lorene::Scalar::Scalar ( const Scalar & a )

Copy constructor.

Definition at line 234 of file scalar.C.

References Lorene::Tensor::cmp, dzpuis, etat, Lorene::Tensor::mp, Scalar(), set_der_0x0(), Lorene::Tensor::Tensor(), and va.

◆ Scalar() [4/5]

Lorene::Scalar::Scalar ( const Cmp & a )

Constructor by conversion of a Cmp.

Definition at line 244 of file scalar.C.

References Lorene::Tensor::cmp, dzpuis, etat, get_dzpuis(), get_etat(), Lorene::Tensor::get_mp(), set_der_0x0(), Lorene::Tensor::Tensor(), and va.

◆ Scalar() [5/5]

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

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

Definition at line 254 of file scalar.C.

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

◆ ~Scalar()

Lorene::Scalar::~Scalar ( )

virtual

Destructor.

Definition at line 273 of file scalar.C.

References Lorene::Tensor::cmp, and del_t().

Member Function Documentation

◆ allocate_all()

void Lorene::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 Lorene::Tensor.

Definition at line 371 of file scalar.C.

References Lorene::Mtbl::get_nzone(), Lorene::Mtbl::set_etat_qcq(), set_etat_qcq(), Lorene::Tbl::set_etat_qcq(), Lorene::Mtbl::t, and va.

◆ annule()

void Lorene::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 Lorene::Tensor.

Definition at line 397 of file scalar.C.

References etat, 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.

◆ annule_hard()

void Lorene::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 386 of file scalar.C.

References del_deriv(), etat, and va.

◆ annule_l()

void Lorene::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 117 of file scalar_manip.C.

References etat, get_etat(), Lorene::Base_val::give_quant_numbers(), Lorene::Tensor::mp, Lorene::Mtbl_cf::set(), set_etat_zero(), and va.

◆ asymptot()

Valeur ** Lorene::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 66 of file scalar_asymptot.C.

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

◆ avance_dalembert()

Scalar Lorene::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 220 of file scalar_pde.C.

References Lorene::Tensor::mp, and Scalar().

◆ change_triad()

void Lorene::Scalar::change_triad ( const Base_vect & new_triad )

virtual

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

Reimplemented from Lorene::Tensor.

Definition at line 1003 of file scalar.C.

◆ check_dzpuis()

bool Lorene::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 879 of file scalar.C.

References dz_nonzero(), and dzpuis.

◆ dec_dzpuis()

void Lorene::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 Lorene::Tensor.

Definition at line 421 of file scalar_r_manip.C.

References del_deriv(), etat, and Lorene::Tensor::mp.

◆ del_deriv()

void Lorene::Scalar::del_deriv ( ) const

protectedvirtual

Logical destructor of the derivatives.

Reimplemented from Lorene::Tensor.

Definition at line 293 of file scalar.C.

References Lorene::Tensor::del_deriv(), 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().

◆ del_t()

void Lorene::Scalar::del_t ( )

protected

Logical destructor.

Definition at line 285 of file scalar.C.

References del_deriv(), and va.

◆ deriv()

const Scalar & Lorene::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 359 of file scalar_deriv.C.

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

◆ derive_con()

const Vector & Lorene::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 $\gamma$ .

Definition at line 402 of file scalar_deriv.C.

References Lorene::Tensor::derive_con().

◆ derive_cov()

const Vector & Lorene::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

Definition at line 390 of file scalar_deriv.C.

References Lorene::Tensor::derive_cov().

◆ derive_lie()

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

Computes the derivative of this along a vector field v.

Definition at line 419 of file scalar_deriv.C.

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

◆ div_cost()

void Lorene::Scalar::div_cost ( )

Division by $\cos\theta$ .

Definition at line 73 of file scalar_th_manip.C.

References del_deriv(), and Lorene::Tensor::mp.

◆ div_r()

void Lorene::Scalar::div_r ( )

Division by r everywhere; dzpuis is not changed.

Definition at line 136 of file scalar_r_manip.C.

References del_deriv(), and Lorene::Tensor::mp.

◆ div_r_ced()

void Lorene::Scalar::div_r_ced ( )

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

Definition at line 199 of file scalar_r_manip.C.

References del_deriv(), and Lorene::Tensor::mp.

◆ div_r_dzpuis()

void Lorene::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 150 of file scalar_r_manip.C.

References allocate_all(), annule(), dec_dzpuis(), del_deriv(), div_r(), domain(), dzpuis, etat, inc_dzpuis(), Lorene::Tensor::mp, Scalar(), set_domain(), set_etat_qcq(), set_spectral_base(), Lorene::Base_val::sx(), and va.

◆ div_rsint()

void Lorene::Scalar::div_rsint ( )

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

Definition at line 351 of file scalar_r_manip.C.

References del_deriv(), and Lorene::Tensor::mp.

◆ div_rsint_dzpuis()

void Lorene::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 365 of file scalar_r_manip.C.

References allocate_all(), annule(), dec_dzpuis(), del_deriv(), div_rsint(), div_sint(), domain(), dzpuis, etat, inc_dzpuis(), Lorene::Tensor::mp, Scalar(), set_domain(), set_dzpuis(), set_etat_qcq(), set_spectral_base(), Lorene::Base_val::ssint(), Lorene::Base_val::sx(), and va.

◆ div_sint()

void Lorene::Scalar::div_sint ( )

Division by $\sin\theta$ .

Definition at line 101 of file scalar_th_manip.C.

References del_deriv(), and Lorene::Tensor::mp.

◆ div_tant()

void Lorene::Scalar::div_tant ( )

Division by $\tan\theta$ .

Definition at line 114 of file scalar_th_manip.C.

References del_deriv(), and Lorene::Tensor::mp.

◆ domain()

const Tbl & Lorene::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 631 of file scalar.h.

References etat, and va.

◆ dsdr()

const Scalar & Lorene::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 113 of file scalar_deriv.C.

References dzpuis, etat, Lorene::Tensor::mp, p_dsdr, and Scalar().

◆ dsdradial()

const Scalar & Lorene::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 491 of file scalar_deriv.C.

References dzpuis, etat, Lorene::Tensor::mp, p_dsdradial, and Scalar().

◆ dsdrho()

const Scalar & Lorene::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 522 of file scalar_deriv.C.

References dsdr(), dzpuis, etat, get_spectral_va(), Lorene::Tensor::mp, Lorene::Valeur::mult_ct(), Lorene::Valeur::mult_st(), p_dsdrho, Scalar(), and srdsdt().

◆ dsdt()

const Scalar & Lorene::Scalar::dsdt ( ) const

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

Definition at line 208 of file scalar_deriv.C.

References dzpuis, etat, Lorene::Tensor::mp, p_dsdt, and Scalar().

◆ dsdx()

const Scalar & Lorene::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 266 of file scalar_deriv.C.

References dsdr(), dzpuis, etat, Lorene::Tensor::mp, p_dsdx, Scalar(), srdsdt(), and srstdsdp().

◆ dsdy()

const Scalar & Lorene::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 297 of file scalar_deriv.C.

References dsdr(), dzpuis, etat, Lorene::Tensor::mp, p_dsdy, Scalar(), srdsdt(), and srstdsdp().

◆ dsdz()

const Scalar & Lorene::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 328 of file scalar_deriv.C.

References dsdr(), dzpuis, etat, Lorene::Tensor::mp, p_dsdz, Scalar(), and srdsdt().

◆ dz_nonzero()

bool Lorene::Scalar::dz_nonzero ( ) const

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

Definition at line 820 of file scalar.C.

References etat, Lorene::Mg3d::get_nzone(), Lorene::Mg3d::get_type_r(), Lorene::Tensor::mp, and va.

◆ exp_filter_r_all_domains()

void Lorene::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.

References Scalar().

◆ exponential_filter_r()

void Lorene::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 Lorene::Tensor.

Definition at line 72 of file scalar_exp_filter.C.

References del_deriv(), etat, exp, Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nr(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_nzone(), log, Lorene::Tensor::mp, pow, and va.

◆ exponential_filter_ylm()

void Lorene::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 Lorene::Tensor.

Definition at line 154 of file scalar_exp_filter.C.

References del_deriv(), etat, exp, Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nr(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_nzone(), Lorene::Base_val::give_lmax(), Lorene::Base_val::give_quant_numbers(), log, Lorene::Tensor::mp, pow, and va.

◆ exponential_filter_ylm_phi()

void Lorene::Scalar::exponential_filter_ylm_phi	(	int	lzmin,
		int	lzmax,
		int	p_r,
		int	p_tet,
		int	p_phi,
		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 Lorene::Tensor.

Definition at line 198 of file scalar_exp_filter.C.

References abs, del_deriv(), etat, exp, Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nr(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_nzone(), Lorene::Base_val::give_lmax(), Lorene::Base_val::give_quant_numbers(), log, Lorene::Tensor::mp, pow, and va.

◆ filtre()

void Lorene::Scalar::filtre ( int n )

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

Definition at line 157 of file scalar_manip.C.

References del_deriv(), etat, Lorene::Tensor::mp, and va.

◆ filtre_phi()

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

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

Definition at line 255 of file scalar_manip.C.

References del_deriv(), etat, Lorene::Tensor::mp, and va.

◆ filtre_r() [1/2]

void Lorene::Scalar::filtre_r ( int * nn )

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

Definition at line 186 of file scalar_manip.C.

References del_deriv(), etat, Lorene::Tensor::mp, and va.

◆ filtre_r() [2/2]

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

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

Definition at line 224 of file scalar_manip.C.

References del_deriv(), etat, Lorene::Tensor::mp, and va.

◆ filtre_tp()

void Lorene::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 276 of file scalar_manip.C.

References va.

◆ fixe_decroissance()

void Lorene::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 352 of file scalar_manip.C.

References Lorene::Valeur::base, Lorene::Valeur::c_cf, Lorene::Valeur::coef(), cos, dzpuis, Lorene::Map_af::get_alpha(), Lorene::Base_val::get_base_r(), Lorene::Tensor::mp, mult_r_ced(), pow, R_CHEBU, Scalar(), Lorene::Mtbl_cf::set(), Lorene::Valeur::set_etat_cf_qcq(), and va.

◆ get_dzpuis()

int Lorene::Scalar::get_dzpuis ( ) const

inline

Returns dzpuis.

Definition at line 563 of file scalar.h.

References dzpuis.

◆ get_etat()

int Lorene::Scalar::get_etat ( ) const

inline

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

Definition at line 560 of file scalar.h.

References etat.

◆ get_spectral_base()

const Base_val & Lorene::Scalar::get_spectral_base ( ) const

inline

Returns the spectral bases of the Valeur va.

Definition at line 1328 of file scalar.h.

References va.

◆ get_spectral_va()

const Valeur & Lorene::Scalar::get_spectral_va ( ) const

inline

Returns va (read only version).

Definition at line 607 of file scalar.h.

References va.

◆ import() [1/2]

void Lorene::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 71 of file scalar_import.C.

References Lorene::Tensor::mp, and Scalar().

◆ import() [2/2]

void Lorene::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 83 of file scalar_import.C.

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

◆ import_align()

void Lorene::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 535 of file scalar_import.C.

References Lorene::Param::add_double(), Lorene::Param::add_int(), Lorene::Param::add_int_mod(), annule(), Lorene::Valeur::c_cf, Lorene::Valeur::coef(), del_t(), get_dzpuis(), get_etat(), Lorene::Tensor::get_mp(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nr(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_nzone(), get_spectral_va(), Lorene::Map(), Lorene::Tensor::mp, Lorene::r, Scalar(), set_dzpuis(), set_etat_one(), set_etat_qcq(), set_etat_zero(), sqrt, Lorene::Mtbl::t, Lorene::Tbl::t, va, and Lorene::Mtbl_cf::val_point().

◆ import_align_asymy()

void Lorene::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 381 of file scalar_import_asymy.C.

References Lorene::Param::add_double(), Lorene::Param::add_int(), Lorene::Param::add_int_mod(), annule(), Lorene::Valeur::c_cf, Lorene::Valeur::coef(), del_t(), get_dzpuis(), get_etat(), Lorene::Tensor::get_mp(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nr(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_nzone(), get_spectral_va(), Lorene::Mg3d::get_type_p(), Lorene::Map(), Lorene::Tensor::mp, Lorene::r, Scalar(), set_dzpuis(), set_etat_one(), set_etat_qcq(), set_etat_zero(), sqrt, Lorene::Mtbl::t, Lorene::Tbl::t, va, and Lorene::Mtbl_cf::val_point_asymy().

◆ import_align_symy()

void Lorene::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 352 of file scalar_import_symy.C.

References Lorene::Param::add_double(), Lorene::Param::add_int(), Lorene::Param::add_int_mod(), annule(), Lorene::Valeur::c_cf, Lorene::Valeur::coef(), del_t(), get_dzpuis(), get_etat(), Lorene::Tensor::get_mp(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nr(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_nzone(), get_spectral_va(), Lorene::Mg3d::get_type_p(), Lorene::Map(), Lorene::Tensor::mp, Lorene::r, Scalar(), set_dzpuis(), set_etat_one(), set_etat_qcq(), set_etat_zero(), sqrt, Lorene::Mtbl::t, Lorene::Tbl::t, va, and Lorene::Mtbl_cf::val_point_symy().

◆ import_anti()

void Lorene::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 338 of file scalar_import.C.

References Lorene::Param::add_double(), Lorene::Param::add_int(), Lorene::Param::add_int_mod(), annule(), Lorene::Valeur::c_cf, Lorene::Valeur::coef(), del_t(), get_dzpuis(), get_etat(), Lorene::Tensor::get_mp(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nr(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_nzone(), get_spectral_va(), Lorene::Map(), Lorene::Tensor::mp, Lorene::r, Scalar(), set_dzpuis(), set_etat_one(), set_etat_qcq(), set_etat_zero(), sqrt, Lorene::Mtbl::t, Lorene::Tbl::t, va, and Lorene::Mtbl_cf::val_point().

◆ import_anti_asymy()

void Lorene::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 134 of file scalar_import_asymy.C.

References Lorene::Param::add_double(), Lorene::Param::add_int(), Lorene::Param::add_int_mod(), annule(), Lorene::Valeur::c_cf, Lorene::Valeur::coef(), del_t(), get_dzpuis(), get_etat(), Lorene::Tensor::get_mp(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nr(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_nzone(), get_spectral_va(), Lorene::Mg3d::get_type_p(), Lorene::Map(), Lorene::Tensor::mp, Lorene::r, Scalar(), set_dzpuis(), set_etat_one(), set_etat_qcq(), set_etat_zero(), sqrt, Lorene::Mtbl::t, Lorene::Tbl::t, va, and Lorene::Mtbl_cf::val_point_asymy().

◆ import_anti_symy()

void Lorene::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 134 of file scalar_import_symy.C.

References Lorene::Param::add_double(), Lorene::Param::add_int(), Lorene::Param::add_int_mod(), annule(), Lorene::Valeur::c_cf, Lorene::Valeur::coef(), del_t(), get_dzpuis(), get_etat(), Lorene::Tensor::get_mp(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nr(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_nzone(), get_spectral_va(), Lorene::Mg3d::get_type_p(), Lorene::Map(), Lorene::Tensor::mp, Lorene::r, Scalar(), set_dzpuis(), set_etat_one(), set_etat_qcq(), set_etat_zero(), sqrt, Lorene::Mtbl::t, Lorene::Tbl::t, va, and Lorene::Mtbl_cf::val_point_symy().

◆ import_asymy() [1/2]

void Lorene::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 75 of file scalar_import_asymy.C.

References import_asymy(), Lorene::Tensor::mp, and Scalar().

◆ import_asymy() [2/2]

void Lorene::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 87 of file scalar_import_asymy.C.

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

◆ import_gal()

void Lorene::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 134 of file scalar_import.C.

References Lorene::Param::add_double(), Lorene::Param::add_int(), Lorene::Param::add_int_mod(), annule(), Lorene::Valeur::c_cf, Lorene::Valeur::coef(), del_t(), get_dzpuis(), get_etat(), Lorene::Tensor::get_mp(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nr(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_nzone(), get_spectral_va(), Lorene::Map(), Lorene::Tensor::mp, Lorene::r, Scalar(), set_dzpuis(), set_etat_one(), set_etat_qcq(), set_etat_zero(), sqrt, Lorene::Mtbl::t, Lorene::Tbl::t, va, and Lorene::Mtbl_cf::val_point().

◆ import_symy() [1/2]

void Lorene::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 75 of file scalar_import_symy.C.

References import_symy(), Lorene::Tensor::mp, and Scalar().

◆ import_symy() [2/2]

void Lorene::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 87 of file scalar_import_symy.C.

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

◆ inc_dzpuis()

void Lorene::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 Lorene::Tensor.

Definition at line 473 of file scalar_r_manip.C.

References del_deriv(), etat, and Lorene::Tensor::mp.

◆ integrale()

double Lorene::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 64 of file scalar_integ.C.

References integrale_domains(), and Lorene::Tensor::mp.

◆ integrale_domains()

const Tbl & Lorene::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 82 of file scalar_integ.C.

References etat, Lorene::Tensor::mp, and p_integ.

◆ is_nan()

bool Lorene::Scalar::is_nan ( bool verbose = false ) const

Looks for NaNs (not a number) in the scalar field.

If at least one NaN is found, it returns true. If the flag verbose is set to true, it outputs to the standard output the indices where NaNs have been found.

Definition at line 1014 of file scalar.C.

References etat, Lorene::Tensor::mp, and va.

◆ lapang()

const Scalar & Lorene::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 461 of file scalar_deriv.C.

References dzpuis, etat, Lorene::Tensor::mp, p_lapang, and Scalar().

◆ laplacian()

const Scalar & Lorene::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 436 of file scalar_deriv.C.

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

◆ match_collocation()

void Lorene::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).

References Scalar().

◆ match_tau()

void Lorene::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 69 of file scalar_match_tau.C.

◆ match_tau_shell()

void Lorene::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).

◆ match_tau_star()

void Lorene::Scalar::match_tau_star	(	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 for a grid with Map_star mapping.

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).

◆ mult_cost()

void Lorene::Scalar::mult_cost ( )

Multiplication by $\cos\theta$ .

Definition at line 61 of file scalar_th_manip.C.

References del_deriv(), and Lorene::Tensor::mp.

◆ mult_r()

void Lorene::Scalar::mult_r ( )

Multiplication by r everywhere; dzpuis is not changed.

Definition at line 211 of file scalar_r_manip.C.

References del_deriv(), and Lorene::Tensor::mp.

◆ mult_r_ced()

void Lorene::Scalar::mult_r_ced ( )

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

Definition at line 272 of file scalar_r_manip.C.

References del_deriv(), and Lorene::Tensor::mp.

◆ mult_r_dzpuis()

void Lorene::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 224 of file scalar_r_manip.C.

References allocate_all(), annule(), dec_dzpuis(), del_deriv(), domain(), dzpuis, etat, inc_dzpuis(), Lorene::Tensor::mp, mult_r(), Lorene::Base_val::mult_x(), Scalar(), set_domain(), set_etat_qcq(), set_spectral_base(), and va.

◆ mult_rsint()

void Lorene::Scalar::mult_rsint ( )

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

Definition at line 284 of file scalar_r_manip.C.

References del_deriv(), and Lorene::Tensor::mp.

◆ mult_rsint_dzpuis()

void Lorene::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 297 of file scalar_r_manip.C.

References allocate_all(), annule(), dec_dzpuis(), del_deriv(), domain(), dzpuis, etat, inc_dzpuis(), Lorene::Tensor::mp, mult_rsint(), Lorene::Base_val::mult_sint(), mult_sint(), Lorene::Base_val::mult_x(), Scalar(), set_domain(), set_dzpuis(), set_etat_qcq(), set_spectral_base(), and va.

◆ mult_sint()

void Lorene::Scalar::mult_sint ( )

Multiplication by $\sin\theta$ .

Definition at line 87 of file scalar_th_manip.C.

References del_deriv(), and Lorene::Tensor::mp.

◆ multipole_spectrum()

Tbl Lorene::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 962 of file scalar.C.

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

◆ operator Cmp()

Lorene::Scalar::operator Cmp ( ) const

Conversion to a Cmp.

Definition at line 680 of file scalar.C.

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

◆ operator*=()

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

*= Scalar

Definition at line 940 of file scalar_arithm.C.

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

◆ operator+=()

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

+= Scalar

Definition at line 836 of file scalar_arithm.C.

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

◆ operator-=()

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

-= Scalar

Definition at line 889 of file scalar_arithm.C.

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

◆ operator=() [1/7]

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

Assignment to a Cmp.

Definition at line 505 of file scalar.C.

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

◆ operator=() [2/7]

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

Assignment to a Mtbl.

Definition at line 598 of file scalar.C.

References del_deriv(), Lorene::Mtbl::get_etat(), set_etat_qcq(), set_etat_zero(), and va.

◆ operator=() [3/7]

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

Assignment to another Scalar defined on the same mapping.

Definition at line 452 of file scalar.C.

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

◆ operator=() [4/7]

void Lorene::Scalar::operator= ( const Tensor & a )

virtual

Assignment to a Tensor (of valence 0).

Reimplemented from Lorene::Tensor.

Definition at line 442 of file scalar.C.

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

◆ operator=() [5/7]

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

Assignment to a Valeur.

Definition at line 555 of file scalar.C.

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

◆ operator=() [6/7]

void Lorene::Scalar::operator= ( double x )

Assignment to a double.

Definition at line 638 of file scalar.C.

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

◆ operator=() [7/7]

void Lorene::Scalar::operator= ( int n )

Assignment to an int.

Definition at line 659 of file scalar.C.

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

◆ poisson() [1/2]

Scalar Lorene::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 139 of file scalar_pde.C.

References Lorene::Tensor::mp, and Scalar().

◆ poisson() [2/2]

void Lorene::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 155 of file scalar_pde.C.

References Lorene::Tensor::mp, and Scalar().

◆ poisson_angu()

Scalar Lorene::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 $\Delta_{\theta\varphi} u := \frac{\partial^2 u} {\partial \theta^2} + \frac{1}{\tan \theta} \frac{\partial u} {\partial \theta} +\frac{1}{\sin^2 \theta}\frac{\partial^2 u} {\partial \varphi^2}$ .

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

Returns: solution u .

Definition at line 203 of file scalar_pde.C.

References Lorene::Tensor::mp, and Scalar().

◆ poisson_dir_neu()

Scalar Lorene::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 83 of file scalar_pde_frontiere.C.

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

◆ poisson_dirichlet()

Scalar Lorene::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 67 of file scalar_pde_frontiere.C.

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

◆ poisson_frontiere_double()

Scalar Lorene::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 118 of file scalar_pde_frontiere.C.

References Lorene::Tensor::mp, and Scalar().

◆ poisson_neumann()

Scalar Lorene::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 101 of file scalar_pde_frontiere.C.

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

◆ poisson_regular()

void Lorene::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 65 of file scalar_poisson_regu.C.

References Lorene::Tensor::get_triad(), Lorene::Tensor::mp, Scalar(), Lorene::Itbl::set(), Lorene::Tenseur::set(), Lorene::Tensor::set(), Lorene::Itbl::set_etat_qcq(), Lorene::Tenseur::set_etat_qcq(), and Lorene::Tensor::Tensor().

◆ poisson_tau() [1/2]

Scalar Lorene::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 172 of file scalar_pde.C.

References Lorene::Tensor::mp, and Scalar().

◆ poisson_tau() [2/2]

void Lorene::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 187 of file scalar_pde.C.

References Lorene::Tensor::mp, and Scalar().

◆ primr()

Scalar Lorene::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 104 of file scalar_integ.C.

References Lorene::Tensor::mp, and Scalar().

◆ raccord()

void Lorene::Scalar::raccord ( int n )

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

Definition at line 65 of file scalar_raccord.C.

References Lorene::Tbl::annule_hard(), etat, Lorene::Map_af::get_alpha(), Lorene::Matrice::inverse(), Lorene::Tensor::mp, R_CHEBI, R_CHEBP, Lorene::Tbl::set(), and va.

◆ raccord_c1_zec()

void Lorene::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 80 of file scalar_raccord_zec.C.

References Lorene::Tbl::annule_hard(), Lorene::Valeur::base, Lorene::Valeur::c_cf, Lorene::Valeur::coef(), cos, dec_dzpuis(), dsdr(), etat, Lorene::Map_af::get_alpha(), Lorene::Base_val::get_base_r(), Lorene::Matrice::inverse(), Lorene::Tensor::mp, pow, R_CHEB, Scalar(), Lorene::Matrice::set(), Lorene::Tbl::set(), Lorene::Matrice::set_band(), set_dzpuis(), Lorene::Matrice::set_etat_qcq(), Lorene::Tbl::set_etat_qcq(), Lorene::Matrice::set_lu(), Lorene::Mtbl_cf::t, va, and Lorene::Valeur::ylm().

◆ raccord_externe()

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

Matching of the external domain with the outermost shell.

Definition at line 69 of file scalar_raccord_externe.C.

References Lorene::Tbl::annule_hard(), cos, Lorene::Map_af::get_alpha(), Lorene::Map_af::get_beta(), Lorene::Tensor::mp, pow, Lorene::Matrice::set(), Lorene::Tbl::set(), set_dzpuis(), Lorene::Matrice::set_etat_qcq(), Lorene::Tbl::set_etat_qcq(), sqrt, and va.

◆ sarra_filter_r()

void Lorene::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 108 of file scalar_exp_filter.C.

References del_deriv(), etat, exp, Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nr(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_nzone(), Lorene::Tensor::mp, pow, and va.

◆ sarra_filter_r_all_domains()

void Lorene::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 148 of file scalar_exp_filter.C.

References Lorene::Tensor::get_mp(), and sarra_filter_r().

◆ sauve()

void Lorene::Scalar::sauve ( FILE * fd ) const

virtual

Save in a file.

Reimplemented from Lorene::Tensor.

Definition at line 692 of file scalar.C.

References dzpuis, etat, Lorene::fwrite_be(), and va.

◆ scalar_out_bound()

Scalar Lorene::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 473 of file scalar_manip.C.

References annule_hard(), Lorene::Valeur::c, Lorene::Valeur::c_cf, etat, get_spectral_base(), Lorene::Tensor::mp, Scalar(), Lorene::Mtbl_cf::set(), Lorene::Base_val::set_base_t(), set_etat_zero(), set_spectral_base(), set_spectral_va(), std_spectral_base(), and va.

◆ set_der_0x0()

void Lorene::Scalar::set_der_0x0 ( ) const

protected

Sets the pointers for derivatives to 0x0.

Definition at line 312 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.

◆ set_domain()

Tbl & Lorene::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 621 of file scalar.h.

References del_deriv(), etat, and va.

◆ set_dzpuis()

void Lorene::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 814 of file scalar.C.

References dzpuis.

◆ set_etat_nondef()

void Lorene::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 Lorene::Tensor.

Definition at line 350 of file scalar.C.

References del_t(), and etat.

◆ set_etat_one()

void Lorene::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 340 of file scalar.C.

References del_deriv(), etat, and va.

◆ set_etat_qcq()

void Lorene::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 Lorene::Tensor.

Definition at line 359 of file scalar.C.

References del_t(), and etat.

◆ set_etat_zero()

void Lorene::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 Lorene::Tensor.

Definition at line 330 of file scalar.C.

References del_deriv(), etat, and va.

◆ set_grid_point()

double & Lorene::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 690 of file scalar.h.

References etat, and va.

◆ set_inner_boundary()

void Lorene::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 289 of file scalar_manip.C.

References annule_hard(), del_deriv(), etat, Lorene::Tensor::mp, and va.

◆ set_outer_boundary()

void Lorene::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 321 of file scalar_manip.C.

References annule_hard(), del_deriv(), etat, Lorene::Tensor::mp, and va.

◆ set_spectral_base()

void Lorene::Scalar::set_spectral_base ( const Base_val & bi )

Sets the spectral bases of the Valeur va.

Definition at line 803 of file scalar.C.

References va.

◆ set_spectral_va()

Valeur & Lorene::Scalar::set_spectral_va ( )

inline

Returns va (read/write version).

Definition at line 610 of file scalar.h.

References va.

◆ smooth_decay()

void Lorene::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 216 of file scalar_raccord_zec.C.

References Lorene::Valeur::c_cf, Lorene::Valeur::coef(), dsdr(), etat, Lorene::Map_af::get_alpha(), Lorene::Valeur::get_base(), Lorene::Map_af::get_beta(), get_dzpuis(), get_etat(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nr(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_nzone(), Lorene::Mg3d::get_type_r(), Lorene::Matrice::inverse(), Lorene::Tensor::mp, pow, Lorene::r, Scalar(), Lorene::Matrice::set(), Lorene::Tbl::set(), Lorene::Matrice::set_band(), Lorene::Valeur::set_base(), Lorene::Valeur::set_base_r(), Lorene::Valeur::set_etat_cf_qcq(), Lorene::Matrice::set_etat_qcq(), Lorene::Mtbl_cf::set_etat_qcq(), set_etat_qcq(), Lorene::Tbl::set_etat_qcq(), Lorene::Tbl::set_etat_zero(), Lorene::Matrice::set_lu(), std_spectral_base(), Lorene::Mtbl_cf::t, va, and val_grid_point().

◆ sol_divergence()

Scalar Lorene::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 71 of file scalar_sol_div.C.

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

◆ sol_elliptic()

Scalar Lorene::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 237 of file scalar_pde.C.

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

◆ sol_elliptic_2d()

Scalar Lorene::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 412 of file scalar_pde.C.

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

◆ sol_elliptic_boundary() [1/2]

Scalar Lorene::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 259 of file scalar_pde.C.

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

◆ sol_elliptic_boundary() [2/2]

Scalar Lorene::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 285 of file scalar_pde.C.

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

◆ sol_elliptic_fixe_der_zero()

Scalar Lorene::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 389 of file scalar_pde.C.

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

◆ sol_elliptic_no_zec()

Scalar Lorene::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 317 of file scalar_pde.C.

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

◆ sol_elliptic_only_zec()

Scalar Lorene::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 344 of file scalar_pde.C.

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

◆ sol_elliptic_pseudo_1d()

Scalar Lorene::Scalar::sol_elliptic_pseudo_1d ( Param_elliptic & ope_var ) const

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

Definition at line 433 of file scalar_pde.C.

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

◆ sol_elliptic_sin_zec()

Scalar Lorene::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 366 of file scalar_pde.C.

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

◆ spectral_display()

void Lorene::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 Lorene::Tensor.

Definition at line 747 of file scalar.C.

References dzpuis, etat, and va.

◆ srdsdt()

const Scalar & Lorene::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 145 of file scalar_deriv.C.

References dzpuis, etat, Lorene::Tensor::mp, p_srdsdt, and Scalar().

◆ srstdsdp()

const Scalar & Lorene::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 177 of file scalar_deriv.C.

References dzpuis, etat, Lorene::Tensor::mp, p_srstdsdp, and Scalar().

◆ std_spectral_base()

void Lorene::Scalar::std_spectral_base ( )

virtual

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

Reimplemented from Lorene::Tensor.

Definition at line 790 of file scalar.C.

References va.

◆ std_spectral_base_odd()

void Lorene::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 Lorene::Tensor.

Definition at line 797 of file scalar.C.

References va.

◆ stdsdp()

const Scalar & Lorene::Scalar::stdsdp ( ) const

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

Definition at line 238 of file scalar_deriv.C.

References dzpuis, etat, Lorene::Tensor::mp, p_stdsdp, and Scalar().

◆ tbl_in_bound()

Tbl Lorene::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 454 of file scalar_manip.C.

References etat, Lorene::Tensor::mp, Lorene::Tbl::set(), Lorene::Tbl::set_etat_qcq(), Lorene::Tbl::set_etat_zero(), and va.

◆ tbl_out_bound()

Tbl Lorene::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 436 of file scalar_manip.C.

References etat, Lorene::Tensor::mp, Lorene::Tbl::set(), Lorene::Tbl::set_etat_qcq(), Lorene::Tbl::set_etat_zero(), and va.

◆ test_poisson()

Tbl Lorene::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 63 of file scalar_test_poisson.C.

References abs, check_dzpuis(), dzpuis, Lorene::Tensor::get_mp(), laplacian(), max, Lorene::Tensor::mp, Scalar(), Lorene::Tbl::set(), and Lorene::Tbl::set_etat_qcq().

◆ val_grid_point()

double Lorene::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 643 of file scalar.h.

References etat, and va.

◆ val_point()

double Lorene::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 896 of file scalar.C.

References dzpuis, etat, Lorene::Tensor::mp, Lorene::phi, Lorene::r, and va.

◆ visu_box()

void Lorene::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 345 of file scalar_visu.C.

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

◆ visu_section() [1/2]

void Lorene::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 81 of file scalar_visu.C.

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

◆ visu_section() [2/2]

void Lorene::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 159 of file scalar_visu.C.

References Lorene::Tensor::mp, va, Lorene::Mtbl_cf::val_point(), Lorene::xa, Lorene::ya, and Lorene::za.

◆ visu_section_anim()

void Lorene::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 538 of file scalar_visu.C.

References visu_section().

◆ abs

Scalar abs ( const Scalar & ci )

friend

Absolute value.

Definition at line 526 of file scalar_math.C.

References Lorene::abs(), get_etat(), Lorene::Tensor::get_mp(), Scalar(), set_etat_qcq(), and va.

◆ acos

Scalar acos ( const Scalar & ci )

friend

Arccosine.

Definition at line 202 of file scalar_math.C.

References Lorene::acos(), get_etat(), Lorene::Tensor::get_mp(), Scalar(), set_etat_qcq(), set_etat_zero(), and va.

◆ asin

Scalar asin ( const Scalar & ci )

friend

Arcsine.

Definition at line 170 of file scalar_math.C.

References Lorene::asin(), get_etat(), Lorene::Tensor::get_mp(), Scalar(), set_etat_qcq(), and va.

◆ atan

Scalar atan ( const Scalar & ci )

friend

Arctangent.

Definition at line 234 of file scalar_math.C.

References Lorene::atan(), get_etat(), Lorene::Tensor::get_mp(), Scalar(), set_etat_qcq(), and va.

◆ cos

Scalar cos ( const Scalar & ci )

friend

Cosine.

Definition at line 107 of file scalar_math.C.

References Lorene::cos(), get_etat(), Lorene::Tensor::get_mp(), Scalar(), set_etat_qcq(), and va.

◆ diffrel

Tbl diffrel	(	const Scalar &	a,
		const Scalar &	b )

friend

Relative difference between two Scalar (norme version).

Returns: 1-D Tbl of size the number of domains, the elements of which are norme[a(l)-b(l)]/norme[b(l)] if b(l)!=0 and norme[a(l)-b(l)] if b(l)=0 , where a(l) and b(l) denote symbolically the values of a and b
in domain no. l .

Definition at line 698 of file scalar_math.C.

References get_etat(), Lorene::Tbl::get_etat(), Lorene::Tensor::get_mp(), Lorene::norme(), Scalar(), Lorene::Tbl::set(), and Lorene::Tbl::set_etat_qcq().

◆ diffrelmax

Tbl diffrelmax	(	const Scalar &	a,
		const Scalar &	b )

friend

Relative difference between two Scalar (max version).

Returns: 1-D Tbl of size the number of domains, the elements of which are max[abs(a(l)-b(l))]/max[abs(b(l))] if b(l)!=0 and max[abs(a(l)-b(l))] if b(l)=0 , where a(l) and b(l) denote symbolically the values of a and b
in domain no. l .

Definition at line 733 of file scalar_math.C.

References Lorene::abs(), get_etat(), Lorene::Tbl::get_etat(), Lorene::Tensor::get_mp(), Lorene::max(), Scalar(), Lorene::Tbl::set(), and Lorene::Tbl::set_etat_qcq().

◆ exp

Scalar exp ( const Scalar & ci )

friend

Exponential.

Definition at line 326 of file scalar_math.C.

References Lorene::exp(), get_etat(), Lorene::Tensor::get_mp(), Scalar(), set_etat_one(), set_etat_qcq(), and va.

◆ Heaviside

Scalar Heaviside ( const Scalar & ci )

friend

Heaviside function.

Definition at line 358 of file scalar_math.C.

References get_etat(), Lorene::Tensor::get_mp(), Lorene::Heaviside(), Scalar(), set_etat_one(), set_etat_qcq(), set_etat_zero(), and va.

◆ log

Scalar log ( const Scalar & ci )

friend

Neperian logarithm.

Definition at line 388 of file scalar_math.C.

References get_etat(), Lorene::Tensor::get_mp(), Lorene::log(), Scalar(), set_etat_qcq(), set_etat_zero(), and va.

◆ log10

Scalar log10 ( const Scalar & ci )

friend

Basis 10 logarithm.

Definition at line 421 of file scalar_math.C.

References get_etat(), Lorene::Tensor::get_mp(), Lorene::log10(), Scalar(), set_etat_qcq(), set_etat_zero(), and va.

◆ max

Tbl max ( const Scalar & ci )

friend

Maximum values of a Scalar in each domain.

Returns: 1-D Tbl of size the number of domains, the elements of which are the set of the maximum values in each domain.

Definition at line 614 of file scalar_math.C.

References Lorene::Tbl::annule_hard(), get_etat(), Lorene::Tensor::get_mp(), Lorene::max(), Scalar(), and va.

◆ min

Tbl min ( const Scalar & ci )

friend

Minimum values of a Scalar in each domain.

Returns: 1-D Tbl of size the number of domains, the elements of which are the set of the minimum values in each domain.

Definition at line 642 of file scalar_math.C.

References Lorene::Tbl::annule_hard(), get_etat(), Lorene::Tensor::get_mp(), Lorene::min(), Scalar(), and va.

◆ norme

Tbl norme ( const Scalar & ci )

friend

Sums of the absolute values of all the values of the Scalar in each domain.

Returns: 1-D Tbl of size the number of domains, the elements of which are the set of the sums of the absolute values in each domain.

Definition at line 670 of file scalar_math.C.

References Lorene::Tbl::annule_hard(), get_etat(), Lorene::Tensor::get_mp(), Lorene::norme(), Scalar(), and va.

◆ operator%

Scalar operator%	(	const Scalar &	c1,
		const Scalar &	c2 )

friend

Scalar * Scalar with desaliasing.

Definition at line 460 of file scalar_arithm.C.

References get_dzpuis(), get_etat(), Lorene::Tensor::get_mp(), Lorene::r, Scalar(), and va.

◆ operator* [1/3]

Scalar operator*	(	const Mtbl &	mi,
		const Scalar &	c1 )

friend

Mtbl * Scalar.

Definition at line 530 of file scalar_arithm.C.

References get_dzpuis(), Lorene::Mtbl::get_etat(), get_etat(), Lorene::Tensor::get_mp(), Lorene::r, Scalar(), and va.

◆ operator* [2/3]

Scalar operator*	(	const Scalar &	c1,
		const Scalar &	c2 )

friend

Scalar * Scalar.

Definition at line 426 of file scalar_arithm.C.

References get_dzpuis(), get_etat(), Lorene::Tensor::get_mp(), Lorene::r, Scalar(), and va.

◆ operator* [3/3]

Scalar operator*	(	double	a,
		const Scalar &	c1 )

friend

double * Scalar

Definition at line 571 of file scalar_arithm.C.

References Lorene::Valeur::get_base(), get_dzpuis(), get_etat(), Lorene::Tensor::get_mp(), get_spectral_va(), Lorene::r, Scalar(), and va.

◆ operator+ [1/3]

Scalar operator+	(	const Scalar &	c1,
		const Mtbl &	mi )

friend

Scalar + Mbtl.

Definition at line 166 of file scalar_arithm.C.

References check_dzpuis(), Lorene::Mtbl::get_etat(), get_etat(), Scalar(), set_dzpuis(), and va.

◆ operator+ [2/3]

Scalar operator+	(	const Scalar &	c1,
		const Scalar &	c2 )

friend

Scalar + Scalar.

Definition at line 116 of file scalar_arithm.C.

References dz_nonzero(), get_dzpuis(), get_etat(), Lorene::Tensor::get_mp(), Lorene::r, Scalar(), and va.

◆ operator+ [3/3]

Scalar operator+	(	const Scalar &	t1,
		double	x )

friend

Scalar + double.

Definition at line 210 of file scalar_arithm.C.

References check_dzpuis(), get_etat(), Scalar(), set_dzpuis(), va, and Lorene::x.

◆ operator- [1/4]

Scalar operator-	(	const Scalar &	c1,
		const Scalar &	c2 )

friend

Scalar - Scalar.

Definition at line 273 of file scalar_arithm.C.

References dz_nonzero(), get_dzpuis(), get_etat(), Lorene::Tensor::get_mp(), Lorene::r, Scalar(), and va.

◆ operator- [2/4]

Scalar operator- ( const Scalar & ci )

friend

- Scalar

Definition at line 93 of file scalar_arithm.C.

References get_dzpuis(), get_etat(), Lorene::Tensor::get_mp(), Lorene::r, Scalar(), and va.

◆ operator- [3/4]

Scalar operator-	(	const Scalar &	t1,
		const Mtbl &	mi )

friend

Scalar - Mbtl.

Definition at line 323 of file scalar_arithm.C.

References check_dzpuis(), Lorene::Mtbl::get_etat(), get_etat(), Scalar(), set_dzpuis(), and va.

◆ operator- [4/4]

Scalar operator-	(	const Scalar &	t1,
		double	x )

friend

Scalar - double.

Definition at line 363 of file scalar_arithm.C.

References check_dzpuis(), get_etat(), Scalar(), set_dzpuis(), va, and Lorene::x.

◆ operator/ [1/5]

Scalar operator/	(	const Mtbl &	mi,
		const Scalar &	c2 )

friend

Mtbl / Scalar.

Definition at line 710 of file scalar_arithm.C.

References get_dzpuis(), Lorene::Mtbl::get_etat(), get_etat(), Lorene::Tensor::get_mp(), Lorene::r, Scalar(), and va.

◆ operator/ [2/5]

Scalar operator/	(	const Scalar &	c1,
		const Mtbl &	mi )

friend

Scalar / Mtbl.

Definition at line 678 of file scalar_arithm.C.

References get_dzpuis(), Lorene::Mtbl::get_etat(), get_etat(), Lorene::Tensor::get_mp(), Lorene::r, Scalar(), and va.

◆ operator/ [3/5]

Scalar operator/	(	const Scalar &	c1,
		const Scalar &	c2 )

friend

Scalar / Scalar.

Definition at line 640 of file scalar_arithm.C.

References get_dzpuis(), get_etat(), Lorene::Tensor::get_mp(), Lorene::r, Scalar(), and va.

◆ operator/ [4/5]

Scalar operator/	(	const Scalar &	c1,
		double	x )

friend

Scalar / double.

Definition at line 744 of file scalar_arithm.C.

References Lorene::Valeur::get_base(), get_dzpuis(), get_etat(), Lorene::Tensor::get_mp(), get_spectral_va(), Lorene::r, Scalar(), va, and Lorene::x.

◆ operator/ [5/5]

Scalar operator/	(	double	x,
		const Scalar &	c2 )

friend

double / Scalar

Definition at line 778 of file scalar_arithm.C.

References Lorene::Valeur::get_base(), get_dzpuis(), get_etat(), Lorene::Tensor::get_mp(), get_spectral_va(), Lorene::r, Scalar(), va, and Lorene::x.

◆ operator<<

ostream & operator<<	(	ostream &	ost,
		const Scalar &	ci )

friend

Display.

Definition at line 708 of file scalar.C.

References etat, get_dzpuis(), operator<<, Scalar(), and va.

◆ operator|

Scalar operator\|	(	const Scalar &	c1,
		const Scalar &	c2 )

friend

Scalar * Scalar with desaliasing only in r.

Definition at line 494 of file scalar_arithm.C.

References get_dzpuis(), get_etat(), Lorene::Tensor::get_mp(), Lorene::r, Scalar(), and va.

◆ pow [1/2]

Scalar pow	(	const Scalar &	ci,
		double	x )

friend

Power ${\tt Scalar}^{\tt double}$ .

Definition at line 490 of file scalar_math.C.

References get_etat(), Lorene::Tensor::get_mp(), Lorene::pow(), Scalar(), set_etat_qcq(), va, and Lorene::x.

◆ pow [2/2]

Scalar pow	(	const Scalar &	ci,
		int	n )

friend

Power ${\tt Scalar}^{\tt int}$ .

Definition at line 454 of file scalar_math.C.

References get_etat(), Lorene::Tensor::get_mp(), Lorene::pow(), Scalar(), set_etat_qcq(), and va.

◆ racine_cubique

Scalar racine_cubique ( const Scalar & ci )

friend

Cube root.

Definition at line 296 of file scalar_math.C.

References get_etat(), Lorene::Tensor::get_mp(), Lorene::racine_cubique(), Scalar(), set_etat_qcq(), and va.

◆ sin

Scalar sin ( const Scalar & ci )

friend

Sine.

Definition at line 75 of file scalar_math.C.

References get_etat(), Lorene::Tensor::get_mp(), Scalar(), set_etat_qcq(), Lorene::sin(), and va.

◆ sqrt

Scalar sqrt ( const Scalar & ci )

friend

Square root.

Definition at line 266 of file scalar_math.C.

References get_etat(), Lorene::Tensor::get_mp(), Scalar(), set_etat_qcq(), Lorene::sqrt(), and va.

◆ tan

Scalar tan ( const Scalar & ci )

friend

Tangent.

Definition at line 139 of file scalar_math.C.

References get_etat(), Lorene::Tensor::get_mp(), Scalar(), set_etat_qcq(), Lorene::tan(), and va.

◆ totalmax

double totalmax ( const Scalar & ci )

friend

Maximum values of a Scalar in each domain.

Returns: 1-D Tbl of size the number of domains, the elements of which are the set of the maximum values in each domain.

Definition at line 556 of file scalar_math.C.

References get_etat(), Scalar(), Lorene::totalmax(), and va.

◆ totalmin

double totalmin ( const Scalar & ci )

friend

Minimum values of a Scalar in each domain.

Returns: 1-D Tbl of size the number of domains, the elements of which are the set of the minimum values in each domain.

Definition at line 585 of file scalar_math.C.

References get_etat(), Scalar(), Lorene::totalmin(), and va.

Member Data Documentation

◆ dzpuis

int Lorene::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 409 of file scalar.h.

◆ etat

int Lorene::Scalar::etat

protected

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

Definition at line 402 of file scalar.h.

◆ ind_lap

int Lorene::Scalar::ind_lap

mutableprotected

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

Definition at line 469 of file scalar.h.

◆ p_dsdr

Scalar* Lorene::Scalar::p_dsdr

mutableprotected

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

Definition at line 417 of file scalar.h.

◆ p_dsdradial

Scalar* Lorene::Scalar::p_dsdradial

mutableprotected

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

Definition at line 461 of file scalar.h.

◆ p_dsdrho

Scalar* Lorene::Scalar::p_dsdrho

mutableprotected

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

Definition at line 464 of file scalar.h.

◆ p_dsdt

Scalar* Lorene::Scalar::p_dsdt

mutableprotected

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

Definition at line 430 of file scalar.h.

◆ p_dsdx

Scalar* Lorene::Scalar::p_dsdx

mutableprotected

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

Definition at line 440 of file scalar.h.

◆ p_dsdy

Scalar* Lorene::Scalar::p_dsdy

mutableprotected

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

Definition at line 445 of file scalar.h.

◆ p_dsdz

Scalar* Lorene::Scalar::p_dsdz

mutableprotected

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

Definition at line 450 of file scalar.h.

◆ p_integ

Tbl* Lorene::Scalar::p_integ

mutableprotected

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

Definition at line 474 of file scalar.h.

◆ p_lap

Scalar* Lorene::Scalar::p_lap

mutableprotected

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

Definition at line 454 of file scalar.h.

◆ p_lapang

Scalar* Lorene::Scalar::p_lapang

mutableprotected

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

Definition at line 458 of file scalar.h.

◆ p_srdsdt

Scalar* Lorene::Scalar::p_srdsdt

mutableprotected

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

Definition at line 422 of file scalar.h.

◆ p_srstdsdp

Scalar* Lorene::Scalar::p_srstdsdp

mutableprotected

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

Definition at line 427 of file scalar.h.

◆ p_stdsdp

Scalar* Lorene::Scalar::p_stdsdp

mutableprotected

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

Definition at line 435 of file scalar.h.

◆ va

Valeur Lorene::Scalar::va

protected

The numerical value of the Scalar.

Definition at line 411 of file scalar.h.

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

Public Member Functions

Protected Member Functions

Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Scalar() [1/5]

◆ Scalar() [2/5]

◆ Scalar() [3/5]

◆ Scalar() [4/5]

◆ Scalar() [5/5]

◆ ~Scalar()

Member Function Documentation

◆ allocate_all()

◆ annule()

◆ annule_hard()

◆ annule_l()

◆ asymptot()

◆ avance_dalembert()

◆ change_triad()

◆ check_dzpuis()

◆ dec_dzpuis()

◆ del_deriv()

◆ del_t()

◆ deriv()

◆ derive_con()

◆ derive_cov()

◆ derive_lie()

◆ div_cost()

◆ div_r()

◆ div_r_ced()

◆ div_r_dzpuis()

◆ div_rsint()

◆ div_rsint_dzpuis()

◆ div_sint()

◆ div_tant()

◆ domain()

◆ dsdr()

◆ dsdradial()

◆ dsdrho()

◆ dsdt()

◆ dsdx()

◆ dsdy()

◆ dsdz()

◆ dz_nonzero()

◆ exp_filter_r_all_domains()

◆ exponential_filter_r()

◆ exponential_filter_ylm()

◆ exponential_filter_ylm_phi()

◆ filtre()

◆ filtre_phi()

◆ filtre_r() [1/2]

◆ filtre_r() [2/2]

◆ filtre_tp()

◆ fixe_decroissance()

◆ get_dzpuis()

◆ get_etat()

◆ get_spectral_base()

◆ get_spectral_va()

◆ import() [1/2]

◆ import() [2/2]

◆ import_align()

◆ import_align_asymy()

◆ import_align_symy()

◆ import_anti()

◆ import_anti_asymy()

◆ import_anti_symy()

◆ import_asymy() [1/2]

◆ import_asymy() [2/2]

◆ import_gal()

◆ import_symy() [1/2]

◆ import_symy() [2/2]

◆ inc_dzpuis()

◆ integrale()

◆ integrale_domains()

◆ is_nan()

◆ lapang()

◆ laplacian()

◆ match_collocation()

◆ match_tau()