ope_sec_order_solh.C
/*
* Copyright (c) 2003 Philippe Grandclement
*
* 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 version 2
* as published by the Free Software Foundation.
*
* 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 ope_sec_order_solh_C[] = "$Header: /cvsroot/Lorene/C++/Source/Ope_elementary/Ope_sec_order/ope_sec_order_solh.C,v 1.4 2014/10/13 08:53:36 j_novak Exp $" ;
/*
* $Id: ope_sec_order_solh.C,v 1.4 2014/10/13 08:53:36 j_novak Exp $
* $Header: /cvsroot/Lorene/C++/Source/Ope_elementary/Ope_sec_order/ope_sec_order_solh.C,v 1.4 2014/10/13 08:53:36 j_novak Exp $
*
*/
#include <cmath>
#include <cstdlib>
#include "proto.h"
#include "ope_elementary.h"
//------------------------------------
// Routine pour les cas non prevus --
//------------------------------------
namespace Lorene {
Tbl _solh_sec_order_pas_prevu (int, double, double,double,double,double,Tbl&) {
cout << "Homogeneous solution not implemented in Sec_order : "<< endl ;
abort() ;
exit(-1) ;
Tbl res(1) ;
return res;
}
//-------------------
//-- R_CHEB ------
//-------------------
Tbl _solh_sec_order_r_cheb (int n, double alpha, double beta,
double a, double b, double c, Tbl& val_lim) {
// Stuff to compute the coefs...
Tbl res(2,n) ;
res.set_etat_qcq() ;
double* coloc = new double[n] ;
int * deg = new int[3] ;
deg[0] = 1 ;
deg[1] = 1 ;
deg[2] = n ;
// Array on the radius
double* sigma = new double[n] ;
for (int i=0 ; i<n ; i++)
sigma[i] = alpha*(-cos(M_PI*i/(n-1))) + beta ;
double sigma_minus = beta-alpha ;
double sigma_plus = beta+alpha ;
// Determinant :
double delta = b*b-4*a*c ;
int signe = 0 ;
if (delta > 0)
signe = + 1 ;
if (delta < 0)
signe = -1 ;
if (fabs(delta) < 1e-14)
signe = 0 ;
switch (signe) {
case 1: {
// Two real solutions
double lambda_one = (-b + sqrt(delta)) / 2./a ;
double lambda_two = (-b - sqrt(delta)) / 2./a ;
// First SH
for (int i=0 ; i<n ; i++)
coloc[i] = exp(sigma[i]*lambda_one) ;
cfrcheb(deg, deg, coloc, deg, coloc) ;
for (int i=0 ; i<n ;i++)
res.set(0,i) = coloc[i] ;
// Second SH
for (int i=0 ; i<n ; i++)
coloc[i] = exp(sigma[i]*lambda_two) ;
cfrcheb(deg, deg, coloc, deg, coloc) ;
for (int i=0 ; i<n ;i++)
res.set(1,i) = coloc[i] ;
// Limit on the boundaries :
val_lim.set(0,0) = exp(sigma_minus*lambda_one) ;
val_lim.set(0,1) = lambda_one*exp(sigma_minus*lambda_one)
/exp(sigma_minus) ;
val_lim.set(0,2) = exp(sigma_plus*lambda_one) ;
val_lim.set(0,3) = lambda_one*exp(sigma_plus*lambda_one)
/exp(sigma_plus) ;
val_lim.set(1,0) = exp(sigma_minus*lambda_two) ;
val_lim.set(1,1) = lambda_two*exp(sigma_minus*lambda_two)/
exp(sigma_minus);
val_lim.set(1,2) = exp(sigma_plus*lambda_two) ;
val_lim.set(1,3) = lambda_two*exp(sigma_plus*lambda_two)
/exp(sigma_plus) ;
val_lim /= sqrt(double(2)) ;
break ;
}
case 0: {
// Only one solution :
double lambda = -b/2./a ;
// First SH
for (int i=0 ; i<n ; i++)
coloc[i] = exp(sigma[i]*lambda) ;
cfrcheb(deg, deg, coloc, deg, coloc) ;
for (int i=0 ; i<n ;i++)
res.set(0,i) = coloc[i] ;
// Second SH
for (int i=0 ; i<n ; i++)
coloc[i] = sigma[i]*exp(sigma[i]*lambda) ;
cfrcheb(deg, deg, coloc, deg, coloc) ;
for (int i=0 ; i<n ;i++)
res.set(1,i) = coloc[i] ;
// Limit on the boundaries :
val_lim.set(0,0) = exp(sigma_minus*lambda) ;
val_lim.set(0,1) = lambda*exp(sigma_minus*lambda)/exp(sigma_minus) ;
val_lim.set(0,2) = exp(sigma_plus*lambda) ;
val_lim.set(0,3) = lambda*exp(sigma_plus*lambda)/exp(sigma_plus) ;
val_lim.set(1,0) = sigma_minus*exp(sigma_minus*lambda) ;
val_lim.set(1,1) = exp(sigma_minus*lambda)* (lambda*sigma_minus+1)
/exp(sigma_minus);
val_lim.set(1,2) = sigma_plus*exp(sigma_plus*lambda) ;
val_lim.set(1,3) = exp(sigma_plus*lambda)* (lambda*sigma_plus+1)/
exp(sigma_plus) ;
val_lim /= sqrt(double(2)) ;
break ;
}
case -1:{
// Two imaginary solutions :
double real_part = -b/2./a ;
double imag_part = sqrt(-delta)/2./a ;
// First SH
for (int i=0 ; i<n ; i++)
coloc[i] = exp(sigma[i]*real_part)*cos(imag_part*sigma[i]) ;
cfrcheb(deg, deg, coloc, deg, coloc) ;
for (int i=0 ; i<n ;i++)
res.set(0,i) = coloc[i] ;
// Second SH
for (int i=0 ; i<n ; i++)
coloc[i] = exp(sigma[i]*real_part)*sin(imag_part*sigma[i]) ;
cfrcheb(deg, deg, coloc, deg, coloc) ;
for (int i=0 ; i<n ;i++)
res.set(1,i) = coloc[i] ;
// Limit on the boundaries :
val_lim.set(0,0) = exp(sigma_minus*real_part)*cos(imag_part*sigma_minus) ;
val_lim.set(0,1) = (real_part*cos(imag_part*sigma_minus) -
imag_part*sin(imag_part*sigma_minus)) * exp(real_part*sigma_minus)
/exp(sigma_minus);
val_lim.set(0,2) = exp(sigma_plus*real_part)*cos(imag_part*sigma_plus) ;
val_lim.set(0,3) = (real_part*cos(imag_part*sigma_plus) -
imag_part*sin(imag_part*sigma_plus)) * exp(real_part*sigma_plus)
/exp(sigma_plus) ;
val_lim.set(1,0) = exp(sigma_minus*real_part)*sin(imag_part*sigma_minus) ;
val_lim.set(1,1) = (real_part*sin(imag_part*sigma_minus) +
imag_part*cos(imag_part*sigma_minus)) * exp(real_part*sigma_minus)
/exp(sigma_minus);
val_lim.set(1,2) = exp(sigma_plus*real_part)*sin(imag_part*sigma_plus);
val_lim.set(1,3) = (real_part*sin(imag_part*sigma_plus) +
imag_part*cos(imag_part*sigma_plus)) * exp(real_part*sigma_plus)
/exp(sigma_plus) ;
val_lim /= sqrt(double(2)) ;
break ;
}
default:
cout << "What are you doing here ? Get out or I call the police !" << endl;
abort() ;
break ;
}
delete [] deg ;
delete [] coloc ;
delete [] sigma ;
return res ;
}
Tbl Ope_sec_order::get_solh () const {
// Routines de derivation
static Tbl (*solh_sec_order[MAX_BASE]) (int, double, double,
double, double, double, Tbl&) ;
static int nap = 0 ;
// Premier appel
if (nap==0) {
nap = 1 ;
for (int i=0 ; i<MAX_BASE ; i++) {
solh_sec_order[i] = _solh_sec_order_pas_prevu ;
}
// Les routines existantes
solh_sec_order[R_CHEB >> TRA_R] = _solh_sec_order_r_cheb ;
}
Tbl val_lim (2,4) ;
val_lim.set_etat_qcq() ;
Tbl res(solh_sec_order[base_r](nr,alpha,beta,a_param,b_param,c_param,
val_lim)) ;
s_one_minus = val_lim(0,0) ;
ds_one_minus = val_lim(0,1) ;
s_one_plus = val_lim(0,2) ;
ds_one_plus = val_lim(0,3) ;
s_two_minus = val_lim(1,0) ;
ds_two_minus = val_lim(1,1) ;
s_two_plus = val_lim(1,2) ;
ds_two_plus = val_lim(1,3) ;
return res ;
}
}
Lorene::Cmp::set
Tbl & set(int l)
Read/write of the value in a given domain.
Definition cmp.h:724
Lorene::Ope_elementary::ds_two_minus
double ds_two_minus
Value of the derivative of the second homogeneous solution at the inner boundary.
Definition ope_elementary.h:160
Lorene::Ope_elementary::s_two_plus
double s_two_plus
Value of the second homogeneous solution at the outer boundary.
Definition ope_elementary.h:146
Lorene::Ope_elementary::s_one_minus
double s_one_minus
Value of the first homogeneous solution at the inner boundary.
Definition ope_elementary.h:131
Lorene::Ope_elementary::beta
double beta
Parameter of the associated mapping.
Definition ope_elementary.h:109
Lorene::Ope_elementary::ds_one_plus
double ds_one_plus
Value of the derivative of the first homogeneous solution at the outer boundary.
Definition ope_elementary.h:136
Lorene::Ope_elementary::ds_one_minus
double ds_one_minus
Value of the derivative of the first homogeneous solution at the inner boundary.
Definition ope_elementary.h:141
Lorene::Ope_elementary::alpha
double alpha
Parameter of the associated mapping.
Definition ope_elementary.h:108
Lorene::Ope_elementary::s_two_minus
double s_two_minus
Value of the second homogeneous solution at the inner boundary.
Definition ope_elementary.h:150
Lorene::Ope_elementary::base_r
int base_r
Radial basis of decomposition.
Definition ope_elementary.h:107
Lorene::Ope_elementary::s_one_plus
double s_one_plus
Value of the first homogeneous solution at the outer boundary.
Definition ope_elementary.h:127
Lorene::Ope_elementary::ds_two_plus
double ds_two_plus
Value of the derivative of the second homogeneous solution at the outer boundary.
Definition ope_elementary.h:155
Lorene::Ope_elementary::nr
int nr
Number of radial points.
Definition ope_elementary.h:106
Lorene::Ope_sec_order::b_param
double b_param
The parameter .
Definition ope_elementary.h:570
Lorene::Ope_sec_order::get_solh
virtual Tbl get_solh() const
Computes the homogeneous solutions(s).
Definition ope_sec_order_solh.C:207
Lorene::Ope_sec_order::a_param
double a_param
The parameter .
Definition ope_elementary.h:569
Lorene::Ope_sec_order::c_param
double c_param
The parameter .
Definition ope_elementary.h:571
Lorene::Tbl
Basic array class.
Definition tbl.h:161
Lorene::Tbl::set_etat_qcq
void set_etat_qcq()
Sets the logical state to ETATQCQ (ordinary state).
Definition tbl.C:361
Lorene::sqrt
Cmp sqrt(const Cmp &)
Square root.
Definition cmp_math.C:220
Lorene::exp
Cmp exp(const Cmp &)
Exponential.
Definition cmp_math.C:270
Lorene::sin
Cmp sin(const Cmp &)
Sine.
Definition cmp_math.C:69
Lorene::cos
Cmp cos(const Cmp &)
Cosine.
Definition cmp_math.C:94
MAX_BASE
#define MAX_BASE
Nombre max. de bases differentes.
Definition type_parite.h:144
TRA_R
#define TRA_R
Translation en R, used for a bitwise shift (in hex).
Definition type_parite.h:158
R_CHEB
#define R_CHEB
base de Chebychev ordinaire (fin)
Definition type_parite.h:166
Lorene
Lorene prototypes.
Definition app_hor.h:64