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|
/*
* Methods of the class Map_et relative to the function
* r = R_l(xi, theta', phi')
*/
/*
* Copyright (c) 1999-2001 Eric Gourgoulhon
*
* This file is part of LORENE.
*
* LORENE is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* LORENE is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with LORENE; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*
*/
char map_et_radius_C[] = "$Header: /cvsroot/Lorene/C++/Source/Map/map_et_radius.C,v 1.6 2014/10/13 08:53:05 j_novak Exp $" ;
/*
* $Id: map_et_radius.C,v 1.6 2014/10/13 08:53:05 j_novak Exp $
* $Log: map_et_radius.C,v $
* Revision 1.6 2014/10/13 08:53:05 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.5 2013/06/05 15:10:42 j_novak
* Suppression of FINJAC sampling in r. This Jacobi(0,2) base is now
* available by setting colloc_r to BASE_JAC02 in the Mg3d constructor.
*
* Revision 1.4 2008/08/27 08:49:16 jl_cornou
* Added R_JACO02 case
*
* Revision 1.3 2004/01/26 16:58:35 j_novak
* Added initialization to avoid compiler warning.
*
* Revision 1.2 2003/12/19 16:21:43 j_novak
* Shadow hunt
*
* Revision 1.1.1.1 2001/11/20 15:19:27 e_gourgoulhon
* LORENE
*
* Revision 1.5 2000/10/20 13:14:47 eric
* Map_et::val_lx : la valeur par defaut de precis est desormais 1e-14
* (et non plus 1e-15).
*
* Revision 1.4 2000/01/04 13:05:47 eric
* \Corrections dans val_lx et val_lx_jk : initialisation de ftp/gtp
* par double(0) dans les cas ou il ne sont pas calcules.
*
* Revision 1.3 1999/12/17 11:03:36 eric
* Fonctions val_r_jk et val_lx_jk operationnelles.
*
* Revision 1.2 1999/12/17 09:29:22 eric
* val_lx : initialisation de niter a 0.
*
* Revision 1.1 1999/12/16 14:19:39 eric
* Initial revision
*
*
* $Header: /cvsroot/Lorene/C++/Source/Map/map_et_radius.C,v 1.6 2014/10/13 08:53:05 j_novak Exp $
*
*/
// Headers Lorene
#include "map.h"
#include "param.h"
#include "nbr_spx.h"
#include "utilitaires.h"
// Local prototypes
namespace Lorene {
double fonc_invr_map_et_noyau(double, const Param&) ;
double fonc_invr_map_et_coq(double, const Param&) ;
double fonc_invr_map_et_zec(double, const Param&) ;
//------------------------------//
// val_r //
//------------------------------//
double Map_et::val_r(int l, double xi, double theta, double pphi) const {
assert( l>=0 ) ;
assert( l<mg->get_nzone() ) ;
double resu ;
double ftp = ff.val_point(l, 0, theta, pphi) ; // value of F_l(theta,phi)
switch( mg->get_type_r(l) ) {
case RARE: {
double gtp = gg.val_point(l, 0, theta, pphi) ;
double xi_2 = xi * xi ;
double xi_3 = xi * xi_2 ;
double a = xi_2 * xi_2 * (3. - 2.*xi_2) ;
double b = ( 2.5 - 1.5 * xi_2 ) * xi_3 ;
resu = alpha[l] * ( xi + a * ftp + b * gtp ) + beta[l] ;
break ;
}
case FIN: {
double gtp = gg.val_point(l, 0, theta, pphi) ;
double xm1 = xi - 1. ;
double xp1 = xi + 1. ;
double a = 0.25* xm1 * xm1 * (xi + 2.) ;
double b = 0.25* xp1 * xp1 * (2. - xi) ;
resu = alpha[l] * ( xi + a * ftp + b * gtp ) + beta[l] ;
break ;
}
case UNSURR: {
double xm1 = xi - 1. ;
double a = 0.25* xm1 * xm1 * (xi + 2.) ;
resu = double(1) / ( alpha[l] * ( xi + a * ftp ) + beta[l] ) ;
break ;
}
default: {
cout << "Map_et::val_r: unknown type_r ! " << endl ;
abort () ;
}
}
return resu ;
}
//------------------------------//
// val_lx //
//------------------------------//
//-------------------------------
// Version with default precision
//-------------------------------
void Map_et::val_lx(double rr, double theta, double pphi,
int& lz, double& xi) const {
int nitermax = 100 ; // Maximum number of iteration in the secant method
int niter ;
double precis = 1e-14 ; // Absolute precision in the secant method
Param par ;
par.add_int(nitermax) ;
par.add_int_mod(niter) ;
par.add_double(precis) ;
// Call of the version with precision parameters
val_lx(rr, theta, pphi, par, lz, xi) ;
}
//---------------------------------
// Version with specified precision
//---------------------------------
void Map_et::val_lx(double rr, double theta, double pphi,
const Param& par, int& lz, double& xi) const {
int nz = mg->get_nzone() ;
// Precision in the secant method :
// ------------------------------
int nitermax = par.get_int() ;
int& niter = par.get_int_mod() ;
niter = 0 ; // initialisation
double precis = par.get_double() ;
// Particular case of r = infinity
//--------------------------------
if (rr == __infinity) {
if ( (mg->get_type_r(nz-1) == UNSURR) &&
(alpha[nz-1] == - beta[nz-1]) ) {
lz = nz - 1 ;
xi = 1 ;
}
else {
cout.precision(16);
cout.setf(ios::showpoint);
cout << "Map_et::val_lx: the domain containing r = " << rr <<
" has not been found ! "
<< endl ;
abort () ;
}
return ;
}
// In which domain is located r ?
// ----------------------------
lz = - 1 ;
double rmax = 0. ;
double ftp = double(0) ;
double gtp = double(0) ;
for (int l=0; l<nz; l++) {
switch( mg->get_type_r(l) ) {
case RARE: {
ftp = ff.val_point(l, 0, theta, pphi) ; // value of F_l(theta,phi)
gtp = gg.val_point(l, 0, theta, pphi) ; // value of G_l(theta,phi)
rmax = alpha[l] * ( double(1) + ftp + gtp ) + beta[l] ;
break ;
}
case FIN: {
ftp = double(0) ;
gtp = gg.val_point(l, 0, theta, pphi) ;
rmax = alpha[l] * ( double(1) + gtp ) + beta[l] ;
break ;
}
case UNSURR: {
ftp = double(0) ;
gtp = double(0) ;
rmax = double(1) / ( alpha[l] + beta[l] ) ;
break ;
}
default: {
cout << "Map_et::val_lx: unknown type_r ! " << endl ;
abort() ;
}
} // end of switch on type_r
if ( rr <= rmax + 1.e-14 ) {
lz = l ;
if (ftp == double(0)) ftp = ff.val_point(l, 0, theta, pphi) ;
if (gtp == double(0)) gtp = gg.val_point(l, 0, theta, pphi) ;
break ;
}
} // End of loop onto the domains
if (lz == -1) { // The domain has not been found
cout.precision(16);
cout.setf(ios::showpoint);
cout << "Map_et::val_lx: the domain containing r = " << rr <<
" has not been found ! "
<< endl ;
for (int l=0; l<nz; l++) {
ftp = ff.val_point(l, 0, theta, pphi) ;
gtp = gg.val_point(l, 0, theta, pphi) ;
switch( mg->get_type_r(l) ) {
case RARE: {
rmax = alpha[l] * ( double(1) + ftp + gtp ) + beta[l] ;
break ;
}
case FIN: {
rmax = alpha[l] * ( double(1) + gtp ) + beta[l] ;
break ;
}
case UNSURR: {
rmax = double(1) / ( alpha[l] + beta[l] ) ;
break ;
}
default: {
cout << "Map_et::val_lx: unknown type_r ! " << endl ;
abort () ;
}
} // end of switch on type_r
cout << "domain: " << l << " theta = " << theta << " phi = "
<< pphi << " : rmax = " << rmax << endl ;
}
abort() ;
}
// Computation of xi
// -----------------
if ( (rr >= rmax) && ( rr <= rmax + 1.e-14) ) {
xi = double(1) ;
}
else {
// Search of xi by the secant method
// ---------------------------------
Param parzerosec ;
parzerosec.add_double(rr, 0) ;
parzerosec.add_double(ftp, 1) ;
parzerosec.add_double(gtp, 2) ;
parzerosec.add_double(alpha[lz], 3) ;
parzerosec.add_double(beta[lz], 4) ;
switch( mg->get_type_r(lz) ) {
case RARE: {
if ( (ff.get_etat()==ETATZERO) && (gg.get_etat()==ETATZERO) ) {
xi = ( rr - beta[lz] ) / alpha[lz] ;
}
else {
double xmin = 0 ;
double xmax = 1 ;
xi = zerosec(fonc_invr_map_et_noyau, parzerosec, xmin, xmax,
precis, nitermax, niter) ;
}
break ;
}
case FIN: {
if ( (ff.get_etat()==ETATZERO) && (gg.get_etat()==ETATZERO) ) {
xi = ( rr - beta[lz] ) / alpha[lz] ;
}
else {
double xmin = -1 ;
double xmax = 1 ;
xi = zerosec(fonc_invr_map_et_coq, parzerosec, xmin, xmax,
precis, nitermax, niter) ;
}
break ;
}
case UNSURR: {
if ( (ff.get_etat()==ETATZERO) ) {
xi = ( double(1)/rr - beta[lz] ) / alpha[lz] ;
}
else {
assert(ff.get_etat()==ETATQCQ) ;
if ( ff.c->t[lz]->get_etat() == ETATZERO) {
xi = ( double(1) / rr - beta[lz] ) / alpha[lz] ;
}
else {
double xmin = -1 ;
double xmax = 1 ;
xi = zerosec(fonc_invr_map_et_zec, parzerosec, xmin, xmax,
precis, nitermax, niter) ;
}
}
break ;
}
default: {
cout << "Map_et::val_lx: unknown type_r ! " << endl ;
abort () ;
}
}
} // End of search by the secant method
}
//------------------------------//
// val_r_jk //
//------------------------------//
double Map_et::val_r_jk(int l, double xi, int j, int k) const {
assert( l>=0 ) ;
assert( l<mg->get_nzone() ) ;
double resu ;
double ftp = ff(l, k, j, 0) ; // value of F_l(theta_j, phi_k)
switch( mg->get_type_r(l) ) {
case RARE: {
double gtp = gg(l, k, j, 0) ; // value of G_l(theta_j, phi_k)
double xi_2 = xi * xi ;
double xi_3 = xi * xi_2 ;
double a = xi_2 * xi_2 * (3. - 2.*xi_2) ;
double b = ( 2.5 - 1.5 * xi_2 ) * xi_3 ;
resu = alpha[l] * ( xi + a * ftp + b * gtp ) + beta[l] ;
break ;
}
case FIN: {
double gtp = gg(l, k, j, 0) ; // value of G_l(theta_j, phi_k)
double xm1 = xi - 1. ;
double xp1 = xi + 1. ;
double a = 0.25* xm1 * xm1 * (xi + 2.) ;
double b = 0.25* xp1 * xp1 * (2. - xi) ;
resu = alpha[l] * ( xi + a * ftp + b * gtp ) + beta[l] ;
break ;
}
case UNSURR: {
double xm1 = xi - 1. ;
double a = 0.25* xm1 * xm1 * (xi + 2.) ;
resu = double(1) / ( alpha[l] * ( xi + a * ftp ) + beta[l] ) ;
break ;
}
default: {
cout << "Map_et::val_r_jk: unknown type_r ! " << endl ;
abort () ;
}
}
return resu ;
}
//------------------------------//
// val_lx_jk //
//------------------------------//
void Map_et::val_lx_jk(double rr, int j, int k, const Param& par,
int& lz, double& xi) const {
int nz = mg->get_nzone() ;
// Precision in the secant method :
// ------------------------------
int nitermax = par.get_int() ;
int& niter = par.get_int_mod() ;
niter = 0 ; // initialisation
double precis = par.get_double() ;
// Particular case of r = infinity
//--------------------------------
if (rr == __infinity) {
if ( (mg->get_type_r(nz-1) == UNSURR) &&
(alpha[nz-1] == - beta[nz-1]) ) {
lz = nz - 1 ;
xi = 1 ;
}
else {
cout.precision(16);
cout.setf(ios::showpoint);
cout << "Map_et::val_lx_jk: the domain containing r = " << rr <<
" has not been found ! "
<< endl ;
abort () ;
}
return ;
}
// In which domain is located r ?
// ----------------------------
lz = - 1 ;
double rmax = 0 ;
double ftp = double(0) ;
double gtp = double(0) ;
for (int l=0; l<nz; l++) {
switch( mg->get_type_r(l) ) {
case RARE: {
ftp = ff(l, k, j, 0) ; // value of F_l(theta_j, phi_k)
gtp = gg(l, k, j, 0) ; // value of G_l(theta_j, phi_k)
rmax = alpha[l] * ( double(1) + ftp + gtp ) + beta[l] ;
break ;
}
case FIN: {
ftp = double(0) ;
gtp = gg(l, k, j, 0) ; // value of G_l(theta_j, phi_k)
rmax = alpha[l] * ( double(1) + gtp ) + beta[l] ;
break ;
}
case UNSURR: {
ftp = double(0) ;
gtp = double(0) ;
rmax = double(1) / ( alpha[l] + beta[l] ) ;
break ;
}
default: {
cout << "Map_et::val_lx_jk: unknown type_r ! " << endl ;
abort() ;
}
} // end of switch on type_r
if ( rr <= rmax + 1.e-14 ) {
lz = l ;
if (ftp == double(0)) ftp = ff(l, k, j, 0) ;
if (gtp == double(0)) gtp = gg(l, k, j, 0) ;
break ;
}
} // End of loop onto the domains
if (lz == -1) { // The domain has not been found
cout.precision(16);
cout.setf(ios::showpoint);
cout << "Map_et::val_lx_jk: the domain containing r = " << rr <<
" has not been found ! "
<< endl ;
for (int l=0; l<nz; l++) {
ftp = ff(l, k, j, 0) ;
gtp = gg(l, k, j, 0) ;
switch( mg->get_type_r(l) ) {
case RARE: {
rmax = alpha[l] * ( double(1) + ftp + gtp ) + beta[l] ;
break ;
}
case FIN: {
rmax = alpha[l] * ( double(1) + gtp ) + beta[l] ;
break ;
}
case UNSURR: {
rmax = double(1) / ( alpha[l] + beta[l] ) ;
break ;
}
default: {
cout << "Map_et::val_lx_jk: unknown type_r ! " << endl ;
abort () ;
}
} // end of switch on type_r
cout << "domain: " << l << " j = " << j << " k = " << k
<< " : rmax = " << rmax << endl ;
}
abort() ;
}
// Computation of xi
// -----------------
if ( (rr >= rmax) && ( rr <= rmax + 1.e-14) ) {
xi = double(1) ;
}
else {
// Search of xi by the secant method
// ---------------------------------
Param parzerosec ;
parzerosec.add_double(rr, 0) ;
parzerosec.add_double(ftp, 1) ;
parzerosec.add_double(gtp, 2) ;
parzerosec.add_double(alpha[lz], 3) ;
parzerosec.add_double(beta[lz], 4) ;
switch( mg->get_type_r(lz) ) {
case RARE: {
if ( (ff.get_etat()==ETATZERO) && (gg.get_etat()==ETATZERO) ) {
xi = ( rr - beta[lz] ) / alpha[lz] ;
}
else {
double xmin = 0 ;
double xmax = 1 ;
xi = zerosec(fonc_invr_map_et_noyau, parzerosec, xmin, xmax,
precis, nitermax, niter) ;
}
break ;
}
case FIN: {
if ( (ff.get_etat()==ETATZERO) && (gg.get_etat()==ETATZERO) ) {
xi = ( rr - beta[lz] ) / alpha[lz] ;
}
else {
double xmin = -1 ;
double xmax = 1 ;
xi = zerosec(fonc_invr_map_et_coq, parzerosec, xmin, xmax,
precis, nitermax, niter) ;
}
break ;
}
case UNSURR: {
if ( (ff.get_etat()==ETATZERO) ) {
xi = ( double(1)/rr - beta[lz] ) / alpha[lz] ;
}
else {
assert(ff.get_etat()==ETATQCQ) ;
if ( ff.c->t[lz]->get_etat() == ETATZERO) {
xi = ( double(1) / rr - beta[lz] ) / alpha[lz] ;
}
else {
double xmin = -1 ;
double xmax = 1 ;
xi = zerosec(fonc_invr_map_et_zec, parzerosec, xmin, xmax,
precis, nitermax, niter) ;
}
}
break ;
}
default: {
cout << "Map_et::val_lx_jk: unknown type_r ! " << endl ;
abort () ;
}
}
} // End of search by the secant method
}
//=============================================================================//
// Auxilary functions //
//=============================================================================//
double fonc_invr_map_et_noyau(double x, const Param& par) {
double r = par.get_double(0) ;
double f = par.get_double(1) ;
double g = par.get_double(2) ;
double alp = par.get_double(3) ;
double bet = par.get_double(4) ;
double x_2 = x * x ;
double x_3 = x_2 * x ;
double a = x_2 * x_2 * (3. - 2.*x_2) ;
double b = ( 2.5 - 1.5 * x_2 ) * x_3 ;
return alp * ( x + a * f + b * g ) + bet - r ;
}
//****************************************************************************
double fonc_invr_map_et_coq(double x, const Param& par) {
double r = par.get_double(0) ;
double f = par.get_double(1) ;
double g = par.get_double(2) ;
double alp = par.get_double(3) ;
double bet = par.get_double(4) ;
double xm1 = x - 1. ;
double xp1 = x + 1. ;
double a = 0.25* xm1 * xm1 * (x + 2.) ;
double b = 0.25* xp1 * xp1 * (2. - x) ;
return alp * ( x + a * f + b * g ) + bet - r ;
}
//****************************************************************************
double fonc_invr_map_et_zec(double x, const Param& par) {
double r = par.get_double(0) ;
double f = par.get_double(1) ;
double alp = par.get_double(3) ;
double bet = par.get_double(4) ;
double xm1 = x - 1. ;
double a = 0.25* xm1 * xm1 * (x + 2.) ;
return alp * ( x + a * f ) + bet - double(1) / r ;
}
}
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