[LORENE] New display of spectral coefficients

[Eric Gourgoulhon]

Dear All,

A new kind of display of the coefficients of spectral expansions
has been introduced in Lorene: instead of giving the coefficient
index (i,j,k), it shows the name of the basis function in
a "human readable" format, e.g.

T2   for the second order Chebyshev polynomial
cos3t   for cos(3 theta)
sin2p   for sin(2 phi)
P_2^1  for the associated Legendre function P_l^m(cos(theta)
            with l=2 and m=1
etc...

This new display relies on the new methods of class Base_val:

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

*These functions are used in the new method
*
void Mtbl_cf::display(double threshold = 1.e-7, int precision = 4,
        ostream& ostr = cout) const*

which itself is used at the Valeur and Scalar levels:

*void Valeur::display_coef(double threshold = 1.e-7, int precision = 4, 
	ostream& ostr = cout) const*

*void Scalar::spectral_display(double threshold = 1.e-7, int precision = 4, 
	ostream& ostr = cout) const*

These new functions can be used instead of affiche_seuil. 

Here is an example of usage:

#include <stdlib.h>
#include "tensor.h"

int main() {

	// Construction of a multi-grid  
	Mg3d mgrid(2, 9, 5, 8, SYM, NONSYM, false) ;
	
  	// Construction of an affine mapping
	double r_limits[] = {0., 1., 2.} ;   
	Map_af map(mgrid, r_limits) ; 
  
	// Construction of a scalar field
	const Coord& x = map.x ; 
	const Coord& y = map.y ; 
	const Coord& z = map.z ; 

	Scalar uu(map) ; 

	uu = 1 + x + 2*y - z*z + x*y + x*x*y - z*z*y  ; 	
		
	uu.std_spectral_base() ;   // sets the "standard" spectral basis 							
	cout << "uu : " << endl ; 
	uu.spectral_display() ; 	
	
	return EXIT_SUCCESS ; 
}

The output is:

uu :
Spectral expansion (Mtbl_cf, threshold for display = 1e-07)
Bases of spectral expansions:
  Domain #0 : r: R_CHEBPIM_P,  theta: T_COSSIN_CP,  phi: P_COSSIN
  Domain #1 : r: R_CHEB     ,  theta: T_COSSIN_CP,  phi: P_COSSIN

 --------- Domain no. 0 ------- nr x nt x np = 9 x 5 x 8 ------
# cos0p cos0t : 0.7500 T0 -0.2500 T2
# cos0p cos2t : -0.2500 T0 -0.2500 T2
# cos1p sin1t : 1.0000 T1
# sin1p sin1t : 1.953 T1 -0.01562 T3
# sin1p sin3t : -0.2344 T1 -0.07812 T3
# sin2p cos0t : 0.1250 T0 +0.1250 T2
# sin2p cos2t : -0.1250 T0 -0.1250 T2
# sin3p sin1t : 0.1406 T1 +0.04687 T3
# sin3p sin3t : -0.04688 T1 -0.01562 T3

 --------- Domain no. 1 ------- nr x nt x np = 9 x 5 x 8 ------
# cos0p cos0t : -0.1875 T0 -0.7500 T1 -0.06250 T2
# cos0p cos2t : -1.187 T0 -0.7500 T1 -0.06250 T2
# cos1p sin1t : 1.500 T0 +0.5000 T1
# sin1p sin1t : 2.754 T0 +0.7832 T1 -0.03516 T2 -0.001953 T3
# sin1p sin3t : -1.230 T0 -1.084 T1 -0.1758 T2 -0.009766 T3
# sin2p cos0t : 0.5937 T0 +0.3750 T1 +0.03125 T2
# sin2p cos2t : -0.5938 T0 -0.3750 T1 -0.03125 T2
# sin3p sin1t : 0.7383 T0 +0.6504 T1 +0.1055 T2 +0.005859 T3
# sin3p sin3t : -0.2461 T0 -0.2168 T1 -0.03516 T2 -0.001953 T3

Best wishes,

	Eric.

-- 
Eric Gourgoulhon
Laboratoire de l'Univers et de ses THeories (LUTH)
UMR 8102 du CNRS / Observatoire de Paris, F-92195 Meudon Cedex, France
tel: +33 1.45.07.74.33 (secretariat : +33 1.45.07.75.10)
e-mail: Eric.Gourgoulhon at obspm.fr    WWW: http://www.luth.obspm.fr/