LORENE
scalar_sol_div.C
1 /*
2  * Resolution of the divergence ODE: df/df + n*f/r = source (source must have dzpuis =2)
3  *
4  * (see file scalar.h for documentation).
5  *
6  */
7 
8 /*
9  * Copyright (c) 2005 Jerome Novak
10  *
11  * This file is part of LORENE.
12  *
13  * LORENE is free software; you can redistribute it and/or modify
14  * it under the terms of the GNU General Public License version 2
15  * as published by the Free Software Foundation.
16  *
17  * LORENE is distributed in the hope that it will be useful,
18  * but WITHOUT ANY WARRANTY; without even the implied warranty of
19  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
20  * GNU General Public License for more details.
21  *
22  * You should have received a copy of the GNU General Public License
23  * along with LORENE; if not, write to the Free Software
24  * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
25  *
26  */
27 
28 
29 
30 /*
31  * $Id: scalar_sol_div.C,v 1.6 2016/12/05 16:18:19 j_novak Exp $
32  * $Log: scalar_sol_div.C,v $
33  * Revision 1.6 2016/12/05 16:18:19 j_novak
34  * Suppression of some global variables (file names, loch, ...) to prevent redefinitions
35  *
36  * Revision 1.5 2014/10/13 08:53:47 j_novak
37  * Lorene classes and functions now belong to the namespace Lorene.
38  *
39  * Revision 1.4 2014/10/06 15:16:16 j_novak
40  * Modified #include directives to use c++ syntax.
41  *
42  * Revision 1.3 2005/09/16 14:33:00 j_novak
43  * Added #include <math.h>.
44  *
45  * Revision 1.2 2005/09/16 12:49:52 j_novak
46  * The case with dzpuis=1 is added.
47  *
48  * Revision 1.1 2005/06/08 12:35:22 j_novak
49  * New method for solving divergence-like ODEs.
50  *
51  *
52  * $Header: /cvsroot/Lorene/C++/Source/Tensor/Scalar/scalar_sol_div.C,v 1.6 2016/12/05 16:18:19 j_novak Exp $
53  *
54  */
55 
56 // C headers
57 #include <cassert>
58 #include <cmath>
59 
60 //Lorene headers
61 #include "tensor.h"
62 #include "diff.h"
63 #include "proto.h"
64 
65 // Local prototypes
66 namespace Lorene {
67 void _sx_r_chebp(Tbl* , int& ) ;
68 void _sx_r_chebi(Tbl* , int& ) ;
69 
70 
71 Scalar Scalar::sol_divergence(int n_factor) const {
72 
73  assert(etat != ETATNONDEF) ;
74  const Map_af* mpaff = dynamic_cast<const Map_af*>(mp) ;
75  assert( mpaff != 0x0) ;
76 
77  Scalar result(*mp) ;
78 
79  if ( etat == ETATZERO )
80  result.set_etat_zero() ;
81  else { //source not zero
82  Base_val base_resu = get_spectral_base() ;
83  base_resu.mult_x() ;
84  const Mg3d* mg = mp->get_mg() ;
85  result.set_etat_qcq() ; result.set_spectral_base(base_resu) ;
86  result.set_spectral_va().set_etat_cf_qcq() ;
87  Valeur sigma(va) ;
88  sigma.ylm_i() ; // work on Fourier basis
89  const Mtbl_cf& source = *sigma.c_cf ;
90 
91  // Checks on the type of domains
92  int nz = mg->get_nzone() ;
93  bool ced = (mg->get_type_r(nz-1) == UNSURR ) ;
94  assert ( (!ced) || (check_dzpuis(2)) || (check_dzpuis(1)) ) ;
95  assert (mg->get_type_r(0) == RARE) ;
96  int nt = mg->get_nt(0) ;
97  int np = mg->get_np(0) ;
98 #ifndef NDEBUG
99  for (int lz = 0; lz<nz; lz++)
100  assert( (mg->get_nt(lz) == nt) && (mg->get_np(lz) == np) ) ;
101 #endif
102  int nr, base_r,l_quant, m_quant;
103  Tbl *so ;
104  Tbl *s_hom ;
105  Tbl *s_part ;
106 
107  // Working objects and initialization
108  Mtbl_cf sol_part(mg, base_resu) ;
109  Mtbl_cf sol_hom(mg, base_resu) ;
110  Mtbl_cf& resu = *result.set_spectral_va().c_cf ;
111  sol_part.annule_hard();
112  sol_hom.annule_hard() ;
113  resu.annule_hard() ;
114 
115  //---------------
116  //-- NUCLEUS ---
117  //---------------
118  int lz = 0 ;
119  nr = mg->get_nr(lz) ;
120 
121  int dege = 1 ; // the operator is degenerate
122  int nr0 = nr - dege ;
123  Tbl vect1(3, 1, nr) ;
124  Tbl vect2(3, 1, nr) ;
125  int base_pipo = 0 ;
126  double alpha = mpaff->get_alpha()[lz] ;
127  double beta = 0. ;
128  Matrice ope_even(nr0, nr0) ; //when the *result* is decomposed on R_CHEBP
129  ope_even.set_etat_qcq() ;
130  for (int i=dege; i<nr; i++) {
131  vect1.annule_hard() ;
132  vect2.annule_hard() ;
133  vect1.set(0,0,i) = 1. ; vect2.set(0,0,i) = 1. ;
134  _dsdx_r_chebp(&vect1, base_pipo) ;
135  _sx_r_chebp(&vect2, base_pipo) ;
136  for (int j=0; j<nr0; j++)
137  ope_even.set(j,i-dege) = (vect1(0,0,j) + n_factor*vect2(0,0,j)) / alpha ;
138  }
139  ope_even.set_lu() ;
140  Matrice ope_odd(nr0, nr0) ; //when the *result* is decomposed on R_CHEBI
141  ope_odd.set_etat_qcq() ;
142  for (int i=0; i<nr0; i++) {
143  vect1.annule_hard() ;
144  vect2.annule_hard() ;
145  vect1.set(0,0,i) = 1. ; vect2.set(0,0,i) = 1. ;
146  _dsdx_r_chebi(&vect1, base_pipo) ;
147  _sx_r_chebi(&vect2, base_pipo) ;
148  for (int j=0; j<nr0; j++)
149  ope_odd.set(j,i) = (vect1(0,0,j) + n_factor*vect2(0,0,j)) / alpha ;
150  }
151  ope_odd.set_lu() ;
152 
153  for (int k=0 ; k<np+1 ; k++)
154  for (int j=0 ; j<nt ; j++) {
155  // to get the spectral base
156  base_resu.give_quant_numbers(lz, k, j, m_quant, l_quant, base_r) ;
157  assert ( (base_r == R_CHEBP) || (base_r == R_CHEBI) ) ;
158  const Matrice& operateur = (( base_r == R_CHEBP ) ?
159  ope_even : ope_odd ) ;
160  // particular solution
161  so = new Tbl(nr0) ;
162  so->set_etat_qcq() ;
163  for (int i=0 ; i<nr0 ; i++)
164  so->set(i) = source(lz, k, j, i) ;
165 
166  s_part = new Tbl(operateur.inverse(*so)) ;
167 
168  // Putting to Mtbl_cf
169  double somme = 0 ;
170  for (int i=0 ; i<nr0 ; i++) {
171  if (base_r == R_CHEBP) {
172  resu.set(lz, k, j, i+dege) = (*s_part)(i) ;
173  somme += ((i+dege)%2 == 0 ? 1 : -1)*(*s_part)(i) ;
174  }
175  else
176  resu.set(lz,k,j,i) = (*s_part)(i) ;
177  }
178  if (base_r == R_CHEBI)
179  for (int i=nr0; i<nr; i++)
180  resu.set(lz,k,j,i) = 0 ;
181  if (base_r == R_CHEBP) //result must vanish at r=0
182  resu.set(lz, k, j, 0) -= somme ;
183 
184  delete so ;
185  delete s_part ;
186 
187  }
188 
189  //---------------------
190  //-- SHELLS --
191  //---------------------
192  int nz0 = (ced ? nz - 1 : nz) ;
193  for (lz=1 ; lz<nz0 ; lz++) {
194  nr = mg->get_nr(lz) ;
195  alpha = mpaff->get_alpha()[lz] ;
196  beta = mpaff->get_beta()[lz];
197  double ech = beta / alpha ;
198  Diff_id id(R_CHEB, nr) ; const Matrice& mid = id.get_matrice() ;
199  Diff_xdsdx xd(R_CHEB, nr) ; const Matrice& mxd = xd.get_matrice() ;
200  Diff_dsdx dx(R_CHEB, nr) ; const Matrice& mdx = dx.get_matrice() ;
201  Matrice operateur = mxd + ech*mdx + n_factor*mid ;
202  operateur.set_lu() ;
203  // homogeneous solution
204  s_hom = new Tbl(solh(nr, n_factor-1, ech, R_CHEB)) ;
205 
206  for (int k=0 ; k<np+1 ; k++)
207  for (int j=0 ; j<nt ; j++) {
208  // to get the spectral base
209  base_resu.give_quant_numbers(lz, k, j, m_quant, l_quant, base_r) ;
210  assert (base_r == R_CHEB) ;
211 
212  so = new Tbl(nr) ;
213  so->set_etat_qcq() ;
214  // particular solution
215  Tbl tmp(nr) ;
216  tmp.set_etat_qcq() ;
217  for (int i=0 ; i<nr ; i++)
218  tmp.set(i) = source(lz, k, j, i) ;
219  for (int i=0; i<nr; i++) so->set(i) = beta*tmp(i) ;
220  multx_1d(nr, &tmp.t, R_CHEB) ;
221  for (int i=0; i<nr; i++) so->set(i) += alpha*tmp(i) ;
222 
223  s_part = new Tbl (operateur.inverse(*so)) ;
224 
225  // cleaning things...
226  for (int i=0 ; i<nr ; i++) {
227  sol_part.set(lz, k, j, i) = (*s_part)(i) ;
228  sol_hom.set(lz, k, j, i) = (*s_hom)(1,i) ;
229  }
230 
231  delete so ;
232  delete s_part ;
233  }
234  delete s_hom ;
235  }
236  if (ced) {
237  //---------------
238  //-- CED -----
239  //---------------
240  int dzp = ( check_dzpuis(2) ? 2 : 1) ;
241  nr = source.get_mg()->get_nr(nz-1) ;
242  alpha = mpaff->get_alpha()[nz-1] ;
243  beta = mpaff->get_beta()[nz-1] ;
244  dege = dzp ;
245  nr0 = nr - dege ;
246  Diff_dsdx dx(R_CHEBU, nr) ; const Matrice& mdx = dx.get_matrice() ;
247  Diff_sx sx(R_CHEBU, nr) ; const Matrice& msx = sx.get_matrice() ;
248  Diff_xdsdx xdx(R_CHEBU, nr) ; const Matrice& mxdx = xdx.get_matrice() ;
249  Diff_id id(R_CHEBU, nr) ; const Matrice& mid = id.get_matrice() ;
250  Matrice operateur(nr0, nr0) ;
251  operateur.set_etat_qcq() ;
252  if (dzp == 2)
253  for (int lin=0; lin<nr0; lin++)
254  for (int col=dege; col<nr; col++)
255  operateur.set(lin,col-dege) = (-mdx(lin,col)
256  + n_factor*msx(lin, col)) / alpha ;
257  else {
258  for (int lin=0; lin<nr0; lin++) {
259  for (int col=dege; col<nr; col++)
260  operateur.set(lin,col-dege) = (-mxdx(lin,col)
261  + n_factor*mid(lin, col)) ;
262  }
263  }
264  operateur.set_lu() ;
265  // homogeneous solution
266  s_hom = new Tbl(solh(nr, n_factor-1, 0., R_CHEBU)) ;
267  for (int k=0 ; k<np+1 ; k++)
268  for (int j=0 ; j<nt ; j++) {
269  base_resu.give_quant_numbers(lz, k, j, m_quant, l_quant, base_r) ;
270  assert(base_r == R_CHEBU) ;
271 
272  // particular solution
273  so = new Tbl(nr0) ;
274  so->set_etat_qcq() ;
275  for (int i=0 ; i<nr0 ; i++)
276  so->set(i) = source(nz-1, k, j, i) ;
277  s_part = new Tbl(operateur.inverse(*so)) ;
278 
279  // cleaning
280  double somme = 0 ;
281  for (int i=0 ; i<nr0 ; i++) {
282  sol_part.set(nz-1, k, j, i+dege) = (*s_part)(i) ;
283  somme += (*s_part)(i) ;
284  sol_hom.set(nz-1, k, j, i) = (*s_hom)(i) ;
285  }
286  for (int i=nr0; i<nr; i++)
287  sol_hom.set(nz-1, k, j, i) = (*s_hom)(i) ;
288  //result must vanish at infinity
289  sol_part.set(nz-1, k, j, 0) = -somme ;
290  delete so ;
291  delete s_part ;
292  }
293  delete s_hom ;
294  }
295 
296  //-------------------------
297  //-- matching solutions ---
298  //-------------------------
299  if (nz > 1) {
300  Tbl echelles(nz-1) ;
301  echelles.set_etat_qcq() ;
302  for (lz=1; lz<nz; lz++)
303  echelles.set(lz-1)
304  = pow ( (mpaff->get_beta()[lz]/mpaff->get_alpha()[lz] -1),
305  n_factor) ;
306  if (ced) echelles.set(nz-2) = 1./pow(-2., n_factor) ;
307 
308  for (int k=0 ; k<np+1 ; k++)
309  for (int j=0 ; j<nt ; j++) {
310  for (lz=1; lz<nz; lz++) {
311  double val1 = 0 ;
312  double valm1 = 0 ;
313  double valhom1 = 0 ;
314  int nr_prec = mg->get_nr(lz-1) ;
315  nr = mg->get_nr(lz) ;
316  for (int i=0; i<nr_prec; i++)
317  val1 += resu(lz-1, k, j, i) ;
318  for (int i=0; i<nr; i++) {
319  valm1 += ( i%2 == 0 ? 1 : -1)*sol_part(lz, k, j, i) ;
320  valhom1 += ( i%2 == 0 ? 1 : -1)*sol_hom(lz, k, j, i) ;
321  }
322  double lambda = (val1 - valm1) * echelles(lz-1) ;
323  for (int i=0; i<nr; i++)
324  resu.set(lz, k, j, i) = sol_part(lz, k, j, i)
325  + lambda*sol_hom(lz, k, j, i) ;
326 
327  }
328  }
329  }
330  }
331  return result ;
332 }
333 
334 }
const Base_val & get_spectral_base() const
Returns the spectral bases of the Valeur va.
Definition: scalar.h:1328
virtual const Matrice & get_matrice() const
Returns the matrix associated with the operator.
Definition: diff_sx.C:103
Mtbl_cf * c_cf
Coefficients of the spectral expansion of the function.
Definition: valeur.h:312
const double * get_alpha() const
Returns the pointer on the array alpha.
Definition: map_af.C:604
void ylm_i()
Inverse of ylm()
Definition: valeur_ylm_i.C:134
int get_np(int l) const
Returns the number of points in the azimuthal direction ( ) in domain no. l.
Definition: grilles.h:479
void set_etat_cf_qcq()
Sets the logical state to ETATQCQ (ordinary state) for values in the configuration space (Mtbl_cf c_c...
Definition: valeur.C:715
virtual void set_etat_zero()
Sets the logical state to ETATZERO (zero).
Definition: scalar.C:330
void give_quant_numbers(int, int, int, int &, int &, int &) const
Computes the various quantum numbers and 1d radial base.
void set_lu() const
Calculate the LU-representation, assuming the band-storage has been done.
Definition: matrice.C:395
Lorene prototypes.
Definition: app_hor.h:67
Tbl & set(int l)
Read/write of the Tbl containing the coefficients in a given domain.
Definition: mtbl_cf.h:304
Tbl inverse(const Tbl &sec_membre) const
Solves the linear system represented by the matrix.
Definition: matrice.C:427
const Mg3d * get_mg() const
Gives the Mg3d on which the mapping is defined.
Definition: map.h:777
double & set(int i)
Read/write of a particular element (index i) (1D case)
Definition: tbl.h:301
virtual const Matrice & get_matrice() const
Returns the matrix associated with the operator.
Definition: diff_dsdx.C:97
Tensor field of valence 0 (or component of a tensorial field).
Definition: scalar.h:393
Values and coefficients of a (real-value) function.
Definition: valeur.h:297
Class for the elementary differential operator (see the base class Diff ).
Definition: diff.h:129
Scalar sol_divergence(int n) const
Resolution of a divergence-like equation.
virtual void set_etat_qcq()
Sets the logical state to ETATQCQ (ordinary state).
Definition: scalar.C:359
const Mg3d * get_mg() const
Returns the Mg3d on which the Mtbl_cf is defined.
Definition: mtbl_cf.h:463
void set_etat_qcq()
Sets the logical state to ETATQCQ (ordinary state).
Definition: tbl.C:364
Class for the elementary differential operator Identity (see the base class Diff ).
Definition: diff.h:210
friend Scalar pow(const Scalar &, int)
Power .
Definition: scalar_math.C:454
#define R_CHEBI
base de Cheb. impaire (rare) seulement
Definition: type_parite.h:170
#define R_CHEBP
base de Cheb. paire (rare) seulement
Definition: type_parite.h:168
Matrix handling.
Definition: matrice.h:152
const double * get_beta() const
Returns the pointer on the array beta.
Definition: map_af.C:608
int get_nzone() const
Returns the number of domains.
Definition: grilles.h:465
Valeur va
The numerical value of the Scalar.
Definition: scalar.h:411
double & set(int j, int i)
Read/write of a particuliar element.
Definition: matrice.h:277
void set_spectral_base(const Base_val &)
Sets the spectral bases of the Valeur va
Definition: scalar.C:803
int get_nr(int l) const
Returns the number of points in the radial direction ( ) in domain no. l.
Definition: grilles.h:469
Multi-domain grid.
Definition: grilles.h:279
Bases of the spectral expansions.
Definition: base_val.h:325
void annule_hard()
Sets the Mtbl_cf to zero in a hard way.
Definition: mtbl_cf.C:315
Affine radial mapping.
Definition: map.h:2042
Class for the elementary differential operator (see the base class Diff ).
Definition: diff.h:409
int etat
The logical state ETATNONDEF (undefined), ETATZERO (null), ETATUN (one), or ETATQCQ (ordinary)...
Definition: scalar.h:402
void mult_x()
The basis is transformed as with a multiplication by .
Coefficients storage for the multi-domain spectral method.
Definition: mtbl_cf.h:196
void set_etat_qcq()
Sets the logical state to ETATQCQ (ordinary state).
Definition: matrice.C:178
Basic array class.
Definition: tbl.h:164
int get_nt(int l) const
Returns the number of points in the co-latitude direction ( ) in domain no. l.
Definition: grilles.h:474
Valeur & set_spectral_va()
Returns va (read/write version)
Definition: scalar.h:610
#define R_CHEBU
base de Chebychev ordinaire (fin), dev. en 1/r
Definition: type_parite.h:180
Class for the elementary differential operator division by (see the base class Diff )...
Definition: diff.h:329
int get_type_r(int l) const
Returns the type of sampling in the radial direction in domain no.
Definition: grilles.h:491
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 n...
Definition: scalar.C:879
const Map *const mp
Mapping on which the numerical values at the grid points are defined.
Definition: tensor.h:301
void annule_hard()
Sets the Tbl to zero in a hard way.
Definition: tbl.C:375
virtual const Matrice & get_matrice() const
Returns the matrix associated with the operator.
Definition: diff_xdsdx.C:101
#define R_CHEB
base de Chebychev ordinaire (fin)
Definition: type_parite.h:166