Base_val Class Reference
[Spectral representation.]

Bases of the spectral expansions. More...

#include <base_val.h>

Public Member Functions
	Base_val (int nb_of_domains)
	Standard constructor.
	Base_val (const Base_val &)
	Copy constructor.
	Base_val (FILE *)
	Constructor from a file (see `sauve(FILE*)` ).
	~Base_val ()
	Destructor.
void	set_base_nondef ()
	Sets the spectral bases to `NONDEF`.
void	set_base_r (int l, int base_r)
	Sets the expansion basis for r ( $\xi$ ) functions in a given domain.
void	set_base_t (int base_t)
	Sets the expansion basis for $\theta$ functions in all domains.
void	set_base_p (int base_p)
	Sets the expansion basis for $\phi$ functions in all domains.
void	operator= (const Base_val &)
	Assignment.
bool	operator== (const Base_val &) const
	Comparison operator.
int	get_b (int l) const
	Returns the code for the expansion basis in domain no. `l`.
int	get_base_r (int l) const
	Returns the expansion basis for r ( $\xi$ ) functions in the domain of index `l` (e.g.
int	get_base_t (int l) const
	Returns the expansion basis for $\theta$ functions in the domain of index `l` (e.g.
int	get_base_p (int l) const
	Returns the expansion basis for $\phi$ functions in the domain of index `l` (e.g.
void	name_r (int l, int k, int j, int i, char *basename) const
	Name of the basis function in r ( $\xi$ ).
void	name_theta (int l, int k, int j, char *basename) const
	Name of the basis function in $\theta$ .
void	name_phi (int l, int k, char *basename) const
	Name of the basis function in $\varphi$ .
const Tbl &	theta_functions (int l, int nt) const
	Values of the theta basis functions at the theta collocation points.
const Tbl &	phi_functions (int l, int np) const
	Values of the phi basis functions at the phi collocation points.
int	get_nzone () const
	Returns the number of domains.
void	dsdx ()
	The basis is transformed as with a $\frac{\partial}{\partial \xi}$ operation.
void	sx ()
	The basis is transformed as with a $\frac{1}{\xi}$ multiplication.
void	mult_x ()
	The basis is transformed as with a multiplication by $\xi$ .
void	dsdt ()
	The basis is transformed as with a $\frac{\partial}{\partial \theta}$ operation.
void	ssint ()
	The basis is transformed as with a $\frac{1}{\sin \theta}$ multiplication.
void	mult_sint ()
	The basis is transformed as with a $\sin \theta$ multiplication.
void	mult_cost ()
	The basis is transformed as with a $\cos \theta$ multiplication.
void	ylm ()
	The basis is transformed as with a transformation to basis.
void	give_quant_numbers (int, int, int, int &, int &, int &) const
	Computes the various quantum numbers and 1d radial base.
int	give_lmax (const Mg3d &mgrid, int lz) const
	Returns the highest multipole for a given grid.
void	sauve (FILE *) const
	Save in a file.
Public Attributes
int *	b
	Array (size: `nzone` ) of the spectral basis in each domain.
Protected Attributes
int	nzone
	Number of domains (zones).
Friends
ostream &	operator<< (ostream &, const Base_val &)
	Display.
Base_val	operator* (const Base_val &, const Base_val &)

Detailed Description

Bases of the spectral expansions.

()

The class Base_val describes, in each domain, on which basis the spectral expansion of a given function is performed. The corresponding coefficients will be stored in a Mtbl_cf.

The various bases in each of the three dimensions r , $\theta$ and $\phi$ are identified by an integer defined by a macro in the file type_parite.h. These three integers are then merged (by means of the bitwise OR operator) to give a single integer, stored in Base_val::b[l], l being the domain index. The bases in r , $\theta$ and $\phi$ can be restored by applying the bitwise AND operator with the masks MSQ_R, MSQ_T and MSQ_P defined in type_parite.h.

The basis functions for expansion with respect to the radial coordinate $\xi$ are coded as follows, m being the order of the Fourier expansion in $\phi$ :

R_CHEB (0x00000001) : Chebyshev polynomials (r -sampling: FIN);
R_CHEBP (0x00000002) : Even Chebyshev polynomials (r -sampling: RARE);
R_CHEBI (0x00000003) : Odd Chebyshev polynomials (r -sampling: RARE );
R_CHEBPI_P (0x00000004) : Even (resp. odd) Chebyshev polynomials for l (spherical harmonic index) even (resp. odd) (r -sampling: RARE );
R_CHEBPI_I (0x00000005) : Odd (resp. even) Chebyshev polynomials for l (spherical harmonic index) even (resp. odd) (r -sampling: RARE ) ;
R_CHEBPIM_P (0x00000006) : Even (resp. odd) Chebyshev polynomials for m even (resp. odd) (r -sampling: RARE );
R_CHEBPIM_I (0x00000007) : Odd (resp. even) Chebyshev polynomials for m even (resp. odd) (r -sampling: RARE ) ;
R_CHEBU (0x00000008) : Chebyshev polynomials (r -sampling: UNSURR ) ;
R_LEG (0x00000009) : Legendre polynomials (r -sampling: FIN);
R_LEGP (0x0000000a) : Even Legendre polynomials (r -sampling: RARE);
R_LEGI (0x0000000b) : Odd Legendre polynomials (r -sampling: RARE);
R_JACO02 (0x0000000c) : Jacobi(0,2) polynomials (r -sampling: FIN).

The basis functions for expansion with respect to the co-latitude coordinate $\theta$ are coded as follows, m being the order of the Fourier expansion in $\phi$ :

T_COSSIN_C (0x00000100) : $\cos(j \theta)$ for m even, $\sin(j \theta)$ for m odd ( $\theta$ -sampling: NONSYM);
T_COSSIN_S (0x00000200) : $\sin(j \theta)$ for m even, $\cos(j \theta)$ for m odd ( $\theta$ -sampling: NONSYM);
T_COS (0x00000300) : $\cos(j \theta)$ m being always even and ( $\theta$ -sampling: NONSYM);
T_SIN (0x00000400) : $\sin(j \theta)$ m being always even, ( $\theta$ -sampling: NONSYM);
T_COS_P (0x00000500) : $\cos(2j \theta)$ ( $\theta$ -sampling: SYM);
T_SIN_P (0x00000600) : $\sin(2j \theta)$ ( $\theta$ -sampling: SYM);
T_COS_I (0x00000700) : $\cos((2j+1) \theta)$ ( $\theta$ -sampling: SYM);
T_SIN_I (0x00000800) : $\sin((2j+1) \theta)$ ( $\theta$ -sampling: SYM);
T_COSSIN_CP (0x00000900) : $\cos(2j \theta)$ for m even, $\sin((2j+1) \theta)$ for m odd ( $\theta$ -sampling: SYM);
T_COSSIN_SP (0x00000a00) : $\sin(2j \theta)$ for m even, $\cos((2j+1) \theta)$ for m odd ( $\theta$ -sampling: SYM);
T_COSSIN_CI (0x00000b00) : $\cos((2j+1) \theta)$ for m even, $\sin(2j \theta)$ for m odd ( $\theta$ -sampling: SYM);
T_COSSIN_SI (0x00000c00) : $\sin((2j+1) \theta)$ for m even, $\cos(2j \theta)$ for m odd ( $\theta$ -sampling: SYM);
T_LEG_P (0x00000d00) : Associated Legendre functions $P_{2j}^m(\cos\theta)$ for m even, $P_{2j+1}^m(\cos\theta)$ for m odd ( $\theta$ -sampling: SYM);
T_LEG_PP (0x00000e00) : Associated Legendre functions $P_{2j}^m(\cos\theta)$ , m being always even ( $\theta$ -sampling: SYM);
T_LEG_I (0x00000f00) : Associated Legendre functions $P_{2j+1}^m(\cos\theta)$ for m even, $P_{2j}^m(\cos\theta)$ for m odd ( $\theta$ -sampling: SYM);
T_LEG_IP (0x00001000) : Associated Legendre functions $P_{2j+1}^m(\cos\theta)$ , m being always even ( $\theta$ -sampling: SYM);
T_LEG_PI (0x00001100) : Associated Legendre functions $P_{2j+1}^m(\cos\theta)$ , m being always odd ( $\theta$ -sampling: SYM);
T_LEG_II (0x00001200) : Associated Legendre functions $P_{2j}^m(\cos\theta)$ , m being always odd ( $\theta$ -sampling: SYM);
T_LEG (0x00001700) : Associated Legendre functions $P_l^m(\cos\theta)$ of all types ;
T_LEG_MP (0x00001800) : Associated Legendre functions $P_l^m(\cos\theta)$ m being always even ( $\theta$ -sampling: NONSYM );
T_LEG_MI (0x00001900) : Associated Legendre functions $P_l^m(\cos\theta)$ m being always odd ( $\theta$ -sampling: NONSYM );

The basis functions for expansion with respect to the azimuthal coordinate $\phi$ are coded as follows

P_COSSIN (0x00010000) : Fourrier series $(\cos(m\phi),\ \sin(m\phi))$ ( $\phi$ -sampling: NONSYM);
P_COSSIN_P (0x00020000) : Fourrier series $(\cos(m\phi),\ \sin(m\phi))$ with even harmonics only (i.e. m even) ( $\phi$ -sampling: SYM);
P_COSSIN_I (0x00030000) : Fourrier series $(\cos(m\phi),\ \sin(m\phi))$ with odd harmonics only (i.e. m odd) ( $\phi$ -sampling: SYM);

Definition at line 318 of file base_val.h.

Constructor & Destructor Documentation

Base_val::Base_val ( int nb_of_domains ) [explicit]

Standard constructor.

Definition at line 146 of file base_val.C.

References b, NONDEF, and nzone.

Base_val::Base_val ( const Base_val & bi )

Copy constructor.

Definition at line 154 of file base_val.C.

References b, and nzone.

Base_val::Base_val ( FILE * fd ) [explicit]

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

Definition at line 162 of file base_val.C.

References b, fread_be(), and nzone.

Base_val::~Base_val ( )

Destructor.

Definition at line 173 of file base_val.C.

References b.

Member Function Documentation

void Base_val::dsdt ( )

The basis is transformed as with a $\frac{\partial}{\partial \theta}$ operation.

Definition at line 165 of file base_val_manip.C.

References get_base_t(), set_base_t(), T_COS, T_COS_I, T_COS_P, T_COSSIN_C, T_COSSIN_CI, T_COSSIN_CP, T_COSSIN_S, T_COSSIN_SI, T_COSSIN_SP, T_SIN, T_SIN_I, and T_SIN_P.

void Base_val::dsdx ( )

The basis is transformed as with a $\frac{\partial}{\partial \xi}$ operation.

Definition at line 84 of file base_val_manip.C.

References get_base_r(), R_CHEBI, R_CHEBP, R_CHEBPI_I, R_CHEBPI_P, R_CHEBPIM_I, R_CHEBPIM_P, and set_base_r().

int Base_val::get_b ( int l ) const [inline]

Returns the code for the expansion basis in domain no. l.

Definition at line 385 of file base_val.h.

References b, and nzone.

int Base_val::get_base_p ( int l ) const [inline]

Returns the expansion basis for $\phi$ functions in the domain of index l (e.g.

P_COSSIN , etc..., see general documentation of class Base_val for denomination of the various bases).

Definition at line 418 of file base_val.h.

References b, MSQ_P, and nzone.

int Base_val::get_base_r ( int l ) const [inline]

Returns the expansion basis for r ( $\xi$ ) functions in the domain of index l (e.g.

R_CHEB_P , etc..., see general documentation of class Base_val for denomination of the various bases).

Definition at line 396 of file base_val.h.

References b, MSQ_R, and nzone.

int Base_val::get_base_t ( int l ) const [inline]

Returns the expansion basis for $\theta$ functions in the domain of index l (e.g.

T_COS_P , etc..., see general documentation of class Base_val for denomination of the various bases).

Definition at line 407 of file base_val.h.

References b, MSQ_T, and nzone.

int Base_val::get_nzone ( ) const [inline]

Returns the number of domains.

Definition at line 504 of file base_val.h.

References nzone.

int Base_val::give_lmax	(	const Mg3d &	mgrid,
		int	lz
	)			const

Returns the highest multipole for a given grid.

Parameters:

	mgrid	: the `Mg3d`
	lz	: the domain to consider

Returns:: the highest multipolar momentum l that can be described by this base on the grid.

Definition at line 290 of file base_val_quantum.C.

References get_base_t(), Mg3d::get_np(), Mg3d::get_nt(), Mg3d::get_nzone(), T_CL_COS_I, T_CL_COS_P, T_CL_SIN_I, T_CL_SIN_P, T_COS, T_COS_I, T_COS_P, T_COSSIN_C, T_COSSIN_CI, T_COSSIN_CP, T_COSSIN_S, T_COSSIN_SI, T_COSSIN_SP, T_LEG, T_LEG_I, T_LEG_II, T_LEG_IP, T_LEG_MI, T_LEG_MP, T_LEG_P, T_LEG_PI, T_LEG_PP, T_SIN_I, and T_SIN_P.

void Base_val::give_quant_numbers	(	int	l,
		int	k,
		int	j,
		int &	m_quant,
		int &	l_quant,
		int &	base_r_1d
	)			const

Computes the various quantum numbers and 1d radial base.

Definition at line 77 of file base_val_quantum.C.

References get_base_p(), get_base_r(), get_base_t(), P_COSSIN, P_COSSIN_I, P_COSSIN_P, R_CHEB, R_CHEBI, R_CHEBP, R_CHEBPI_I, R_CHEBPI_P, R_CHEBPIM_I, R_CHEBPIM_P, R_CHEBU, R_JACO02, R_LEG, R_LEGI, R_LEGP, T_CL_COS_I, T_CL_COS_P, T_CL_SIN_I, T_CL_SIN_P, T_COS, T_COS_I, T_COS_P, T_COSSIN_C, T_COSSIN_CI, T_COSSIN_CP, T_COSSIN_S, T_COSSIN_SI, T_COSSIN_SP, T_LEG, T_LEG_I, T_LEG_II, T_LEG_IP, T_LEG_MI, T_LEG_MP, T_LEG_P, T_LEG_PI, T_LEG_PP, T_SIN_I, and T_SIN_P.

void Base_val::mult_cost ( )

The basis is transformed as with a $\cos \theta$ multiplication.

Definition at line 309 of file base_val_manip.C.

References get_base_t(), set_base_t(), T_COS, T_COS_I, T_COS_P, T_COSSIN_C, T_COSSIN_CI, T_COSSIN_CP, T_COSSIN_S, T_COSSIN_SI, T_COSSIN_SP, T_SIN, T_SIN_I, and T_SIN_P.

void Base_val::mult_sint ( )

The basis is transformed as with a $\sin \theta$ multiplication.

Definition at line 261 of file base_val_manip.C.

References get_base_t(), set_base_t(), T_COS, T_COS_I, T_COS_P, T_COSSIN_C, T_COSSIN_CI, T_COSSIN_CP, T_COSSIN_S, T_COSSIN_SI, T_COSSIN_SP, T_SIN, T_SIN_I, and T_SIN_P.

void Base_val::mult_x ( )

The basis is transformed as with a multiplication by $\xi$ .

Definition at line 138 of file base_val_manip.C.

References get_base_r(), R_CHEBI, R_CHEBP, R_CHEBPI_I, R_CHEBPI_P, R_CHEBPIM_I, R_CHEBPIM_P, and set_base_r().

void Base_val::name_phi	(	int	l,
		int	k,
		char *	basename
	)			const

Name of the basis function in $\varphi$ .

Parameters:

	l	[input] domain index
	k	[input] phi index
	basename	[output] string containing the name of the basis function; this `char` array must have a size of (at least) 8 elements and must have been allocated before the call to `name_phi` .

Definition at line 65 of file base_val_name_phi.C.

References b, MAX_BASE_2, MSQ_P, nzone, P_COSSIN, P_COSSIN_I, P_COSSIN_P, and TRA_P.

void Base_val::name_r	(	int	l,
		int	k,
		int	j,
		int	i,
		char *	basename
	)			const

Name of the basis function in r ( $\xi$ ).

Parameters:

	l	[input] domain index
	k	[input] phi index (for the basis in r may depend upon the phi index)
	j	[input] theta index (for the basis in r may depend upon the theta index)
	i	[input] r index
	basename	[output] string containing the name of the basis function; this `char` array must have a size of (at least) 8 elements and must have been allocated before the call to `name_r` .

Definition at line 80 of file base_val_name_r.C.

References b, MAX_BASE, MSQ_R, nzone, R_CHEB, R_CHEBI, R_CHEBP, R_CHEBPI_I, R_CHEBPI_P, R_CHEBPIM_I, R_CHEBPIM_P, R_CHEBU, R_JACO02, R_LEG, R_LEGI, R_LEGP, and TRA_R.

void Base_val::name_theta	(	int	l,
		int	k,
		int	j,
		char *	basename
	)			const

Name of the basis function in $\theta$ .

Parameters:

	l	[input] domain index
	k	[input] phi index (for the basis in $\theta$ may depend upon the phi index)
	j	[input] theta index
	basename	[output] string containing the name of the basis function; this `char` array must have a size of (at least) 8 elements and must have been allocated before the call to `name_theta` .

Definition at line 110 of file base_val_name_theta.C.

References b, MAX_BASE, MSQ_T, nzone, T_CL_COS_I, T_CL_COS_P, T_CL_SIN_I, T_CL_SIN_P, T_COS, T_COS_I, T_COS_P, T_COSSIN_C, T_COSSIN_CI, T_COSSIN_CP, T_COSSIN_S, T_COSSIN_SI, T_COSSIN_SP, T_LEG, T_LEG_I, T_LEG_II, T_LEG_IP, T_LEG_MI, T_LEG_MP, T_LEG_P, T_LEG_PI, T_LEG_PP, T_SIN, T_SIN_I, T_SIN_P, and TRA_T.

void Base_val::operator= ( const Base_val & bi )

Assignment.

Definition at line 211 of file base_val.C.

References b, and nzone.

bool Base_val::operator== ( const Base_val & c2 ) const

Comparison operator.

Definition at line 331 of file base_val.C.

References b.

const Tbl & Base_val::phi_functions	(	int	l,
		int	np
	)			const

Values of the phi basis functions at the phi collocation points.

Parameters:

	l	[input] domain index
	np	[input] number of phi collocation points (or equivalently number of phi basis functions) in the domain of index `l`

Returns:: resu : Tbl 2-D containing the values $B_i(\phi_k)$ of the np phi basis functions at the np collocation points $\phi_k$ in the domain of index l . The storage convention is the following one : \ resu(i,k) = $B_i(\phi_k)$ .

Definition at line 84 of file base_val_phi_funct.C.

References b, MAX_BASE_2, MSQ_P, P_COSSIN, P_COSSIN_I, P_COSSIN_P, and TRA_P.

void Base_val::sauve ( FILE * fd ) const

Save in a file.

Definition at line 224 of file base_val.C.

References b, fwrite_be(), and nzone.

void Base_val::set_base_nondef ( )

Sets the spectral bases to NONDEF.

Definition at line 322 of file base_val.C.

References b, and NONDEF.

void Base_val::set_base_p ( int base_p )

Sets the expansion basis for $\phi$ functions in all domains.

Parameters:

base_p type of basis functions in $\phi$ (e.g. P_COSSIN , etc..., see general documentation of class Base_val for denomination of the various bases).

Definition at line 200 of file base_val.C.

References b, MSQ_R, MSQ_T, and nzone.

void Base_val::set_base_r	(	int	l,
		int	base_r
	)

Sets the expansion basis for r ( $\xi$ ) functions in a given domain.

Parameters:

	l	Domain index
	base_r	type of basis functions in r ( $\xi$ ) (e.g. `R_CHEB_P` , etc..., see general documentation of class `Base_val` for denomination of the various bases).

Definition at line 181 of file base_val.C.

References b, MSQ_P, MSQ_T, and nzone.

void Base_val::set_base_t ( int base_t )

Sets the expansion basis for $\theta$ functions in all domains.

Parameters:

base_t type of basis functions in $\theta$ (e.g. T_COS_P , etc..., see general documentation of class Base_val for denomination of the various bases).

Definition at line 191 of file base_val.C.

References b, MSQ_P, MSQ_R, and nzone.

void Base_val::ssint ( )

The basis is transformed as with a $\frac{1}{\sin \theta}$ multiplication.

Definition at line 213 of file base_val_manip.C.

References get_base_t(), set_base_t(), T_COS, T_COS_I, T_COS_P, T_COSSIN_C, T_COSSIN_CI, T_COSSIN_CP, T_COSSIN_S, T_COSSIN_SI, T_COSSIN_SP, T_SIN, T_SIN_I, and T_SIN_P.

void Base_val::sx ( )

The basis is transformed as with a $\frac{1}{\xi}$ multiplication.

Definition at line 111 of file base_val_manip.C.

References get_base_r(), R_CHEBI, R_CHEBP, R_CHEBPI_I, R_CHEBPI_P, R_CHEBPIM_I, R_CHEBPIM_P, and set_base_r().

const Tbl & Base_val::theta_functions	(	int	l,
		int	nt
	)			const

Values of the theta basis functions at the theta collocation points.

Parameters:

	l	[input] domain index
	nt	[input] number of theta collocation points (or equivalently number of theta basis functions) in the domain of index `l`

Returns:: resu : Tbl 3-D containing the values $B_i(\theta_j)$ of the nt theta basis functions at the nt collocation points $\theta_j$ in the domain of index l . The storage convention is the following one : \ resu(ind_phi,i,j) = $B_i(\theta_j)$ with ind_phi being a supplementary dimension in case of a dependence in phi of the theta basis : for example, if the theta basis is T_COS_P (no dependence in phi), resu.get_dim(2) = 1 and ind_phi can take only the value 0; if the theta basis is T_COSSIN_CP , resu.get_dim(2) = 2, with ind_phi = 0 for m even and ind_phi = 1 for m odd.