LORENE
et_bin_bhns_extr_ylm.C
1/*
2 * Method of class Et_bin_bhns_extr to construct spherical harmonics
3 *
4 * (see file et_bin_bhns_extr.h for documentation).
5 *
6 */
7
8/*
9 * Copyright (c) 2004 Joshua A. Faber
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: et_bin_bhns_extr_ylm.C,v 1.6 2016/12/05 16:17:52 j_novak Exp $
32 * $Log: et_bin_bhns_extr_ylm.C,v $
33 * Revision 1.6 2016/12/05 16:17:52 j_novak
34 * Suppression of some global variables (file names, loch, ...) to prevent redefinitions
35 *
36 * Revision 1.5 2014/10/13 08:52:55 j_novak
37 * Lorene classes and functions now belong to the namespace Lorene.
38 *
39 * Revision 1.4 2014/10/06 15:13:08 j_novak
40 * Modified #include directives to use c++ syntax.
41 *
42 * Revision 1.3 2005/02/28 23:18:07 k_taniguchi
43 * Change the functions to constant ones
44 *
45 * Revision 1.2 2005/01/03 19:52:56 k_taniguchi
46 * Change a factor multiplied/divided by sqrt(2).
47 *
48 * Revision 1.1 2004/12/29 16:30:46 k_taniguchi
49 * *** empty log message ***
50 *
51 *
52 * $Header: /cvsroot/Lorene/C++/Source/Etoile/et_bin_bhns_extr_ylm.C,v 1.6 2016/12/05 16:17:52 j_novak Exp $
53 *
54 */
55
56// C headers
57#include <cstdlib>
58#include <cmath>
59
60// Lorene headers
61#include "map.h"
62#include "tenseur.h"
63#include "et_bin_bhns_extr.h"
64
65namespace Lorene {
66void Et_bin_bhns_extr::get_ylm(int nylm, Cmp** ylmvec) const {
67
68 // IMPORTANT NOTE:
69 // For Y_lm with m>=1, we have the real and imaginary parts,
70 // not Y_{l,m} and Y_{l,-m}. This changes the normalization
71 // properties. In order to normalize properly, we multiply
72 // all fields in get_integrals below by a factor of 2.0 when
73 // m>=1.
74
75 cout << "Constructing ylm" << endl;
76
77 int nz = mp.get_mg()->get_nzone() ;
78 int nr = mp.get_mg()->get_nr(0) ;
79 int np = mp.get_mg()->get_np(0) ;
80 int nt = mp.get_mg()->get_nt(0) ;
81
82 for (int l=0 ; l<nz ; l++) {
83
84 Mtbl Xabs (mp.x) ;
85 Mtbl Yabs (mp.y) ;
86 Mtbl Zabs (mp.z) ;
87
88 for (int k=0 ; k<np ; k++) {
89 for (int j=0 ; j<nt ; j++) {
90 for (int i=0 ; i<nr ; i++) {
91
92 double xval=Xabs(l,k,j,i);
93 double yval=Yabs(l,k,j,i);
94 double zval=Zabs(l,k,j,i);
95 double rval=sqrt(xval*xval+yval*yval+zval*zval);
96
97 // cout <<l<<" "<<k<<" "<<j<<" "<<i<<endl;
98
99 //l=0,m=0
100 ylmvec[0]->set(l,k,j,i)=1.0*sqrt(1.0/4.0/M_PI);
101 // cout << " 0 " << endl;
102 // l=1 included?
103 if (nylm>1 ) {
104 if (nylm <4) {abort();} else {
105 //l=1,m=0
106 ylmvec[1]->set(l,k,j,i)=zval*sqrt(3.0/4.0/M_PI);
107 //l=1,m=1
108 ylmvec[2]->set(l,k,j,i)=-1.0*xval*sqrt(3.0/8.0/M_PI);
109 ylmvec[3]->set(l,k,j,i)=-1.0*yval*sqrt(3.0/8.0/M_PI);
110 }
111 }
112 // l=2 included?
113 if (nylm>4 ) {
114 if (nylm <9) {abort();} else {
115 //l=2,m=0
116 ylmvec[4]->set(l,k,j,i)=(3.0*zval*zval-rval*rval)*sqrt(5.0/16.0/M_PI);
117 //l=2,m=1
118 ylmvec[5]->set(l,k,j,i)=-1.0*zval*xval*sqrt(15.0/8.0/M_PI);
119 ylmvec[6]->set(l,k,j,i)=-1.0*zval*yval*sqrt(15.0/8.0/M_PI);
120 //l=2,m=2
121 ylmvec[7]->set(l,k,j,i)=(xval*xval-yval*yval)*sqrt(15.0/32.0/M_PI);
122 ylmvec[8]->set(l,k,j,i)=2.0*xval*yval*sqrt(15.0/32.0/M_PI);
123 }
124 }
125 // l=3 included?
126 if (nylm>9 ) {
127 if (nylm <16) {abort();} else {
128 //l=3,m=0
129 ylmvec[9]->set(l,k,j,i)=(5.0*pow(zval,3)-3.0*zval*rval*rval)*
130 sqrt(7.0/16.0/M_PI);
131 //l=3,m=1
132 ylmvec[10]->set(l,k,j,i)=-1.0*(5.0*zval*zval-rval*rval)*xval*
133 sqrt(21.0/64.0/M_PI);
134 ylmvec[11]->set(l,k,j,i)=-1.0*(5.0*zval*zval-rval*rval)*yval*
135 sqrt(21.0/64.0/M_PI);
136 //l=3,m=2
137 ylmvec[12]->set(l,k,j,i)=zval*(xval*xval-yval*yval)*
138 sqrt(105./32.0/M_PI);
139 ylmvec[13]->set(l,k,j,i)=zval*(2.0*xval*yval)*
140 sqrt(105./32.0/M_PI);
141 //l=3,m=3
142 ylmvec[14]->set(l,k,j,i)=-1.0*(pow(xval,3)-3.0*xval*yval*yval)*
143 sqrt(35.0/64.0/M_PI);
144 ylmvec[15]->set(l,k,j,i)=-1.0*(3.0*xval*xval*yval-pow(yval,3))*
145 sqrt(35.0/64.0/M_PI);
146 }
147 }
148 // l=4 included?
149 if (nylm>16 ) {
150 if (nylm <25) {abort();} else {
151 //l=4,m=0
152 ylmvec[16]->set(l,k,j,i)=(35.0*pow(zval,4)-30.0*zval*zval*rval*rval+3*pow(rval,4))*
153 sqrt(9.0/256.0/M_PI);
154 //l=4,m=1
155 ylmvec[17]->set(l,k,j,i)=-1.0*(7.0*pow(zval,3)-3*zval*rval*rval)*xval*
156 sqrt(45.0/64.0/M_PI);
157 ylmvec[18]->set(l,k,j,i)=-1.0*(7.0*pow(zval,3)-3*zval*rval*rval)*yval*
158 sqrt(45.0/64.0/M_PI);
159 //l=4,m=2
160 ylmvec[19]->set(l,k,j,i)=(7.0*zval*zval-rval*rval)*(xval*xval-yval*yval)*
161 sqrt(45./128.0/M_PI);
162 ylmvec[20]->set(l,k,j,i)=(7.0*zval*zval-rval*rval)*(2.0*xval*yval)*
163 sqrt(45./128.0/M_PI);
164 //l=4,m=3
165 ylmvec[21]->set(l,k,j,i)=-1.0*zval*(pow(xval,3)-3.0*xval*yval*yval)*
166 sqrt(315.0/64.0/M_PI);
167 ylmvec[22]->set(l,k,j,i)=-1.0*zval*(3.0*xval*xval*yval-pow(yval,3))*
168 sqrt(315.0/64.0/M_PI);
169 //l=4,m=4
170 ylmvec[23]->set(l,k,j,i)=(pow(xval,4)-6*xval*xval*yval*yval+pow(yval,4))*
171 sqrt(315.0/512.0/M_PI);
172 ylmvec[24]->set(l,k,j,i)=4.0*xval*yval*(xval*xval-yval*yval)*
173 sqrt(315.0/512.0/M_PI);
174 }
175 }
176 // l=5 included?
177 if (nylm>25 ) {
178 if (nylm <36) {abort();} else {
179 //l=5,m=0
180 ylmvec[25]->set(l,k,j,i)=(63.0*pow(zval,5)-70.0*pow(zval,3)*rval*rval+15*zval*pow(rval,4))*
181 sqrt(11.0/256.0/M_PI);
182 //l=5,m=1
183 ylmvec[26]->set(l,k,j,i)=-1.0*(21.0*pow(zval,4)-14*zval*zval*rval*rval+pow(rval,4))*xval*
184 sqrt(165.0/512.0/M_PI);
185 ylmvec[27]->set(l,k,j,i)=-1.0*(21.0*pow(zval,4)-14*zval*zval*rval*rval+pow(rval,4))*yval*
186 sqrt(165.0/512.0/M_PI);
187 //l=5,m=2
188 ylmvec[28]->set(l,k,j,i)=(3.0*pow(zval,3)-zval*rval*rval)*(xval*xval-yval*yval)*
189 sqrt(1155./128.0/M_PI);
190 ylmvec[29]->set(l,k,j,i)=(3.0*pow(zval,3)-zval*rval*rval)*(2.0*xval*yval)*
191 sqrt(1155./128.0/M_PI);
192 //l=5,m=3
193 ylmvec[30]->set(l,k,j,i)=-1.0*(9.0*zval*zval-rval*rval)*(pow(xval,3)-3.0*xval*yval*yval)*
194 sqrt(385.0/1024.0/M_PI);
195 ylmvec[31]->set(l,k,j,i)=-1.0*(9.0*zval*zval-rval*rval)*(3.0*xval*xval*yval-pow(yval,3))*
196 sqrt(385.0/1024.0/M_PI);
197 //l=5,m=4
198 ylmvec[32]->set(l,k,j,i)=zval*(pow(xval,4)-6*xval*xval*yval*yval+pow(yval,4))*
199 sqrt(3465.0/512.0/M_PI);
200 ylmvec[33]->set(l,k,j,i)=zval*4.0*xval*yval*(xval*xval-yval*yval)*
201 sqrt(3465.0/512.0/M_PI);
202 //l=5,m=5
203 ylmvec[34]->set(l,k,j,i)=-1.0*(pow(xval,5)-10.0*pow(xval,3)*yval*yval+5.0*xval*pow(yval,4))*
204 sqrt(693.0/1024.0/M_PI);
205 ylmvec[35]->set(l,k,j,i)=-1.0*(5.0*pow(xval,4)*yval-10.0*xval*xval*pow(yval,3)+pow(yval,5))*
206 sqrt(693.0/1024.0/M_PI);
207 }
208 }
209 // l=6 included?
210 if (nylm>36 ) {
211 if (nylm <49) {abort();} else {
212 //l=6,m=0
213 ylmvec[36]->set(l,k,j,i)=(231.0*pow(zval,6)-315.0*pow(zval,4)*rval*rval+105.0*zval*zval*pow(rval,4)-5.0*pow(rval,6))*
214 sqrt(13.0/1024.0/M_PI);
215 //l=6,m=1
216 ylmvec[37]->set(l,k,j,i)=-1.0*(33.0*pow(zval,5)-30.0*pow(zval,3)*rval*rval+5.0*zval*pow(rval,4))*xval*
217 sqrt(273.0/512.0/M_PI);
218 ylmvec[38]->set(l,k,j,i)=-1.0*(33.0*pow(zval,5)-30.0*pow(zval,3)*rval*rval+5.0*zval*pow(rval,4))*yval*
219 sqrt(273.0/512.0/M_PI);
220 //l=6,m=2
221 ylmvec[39]->set(l,k,j,i)=(33.0*pow(zval,4)-18.0*zval*zval*rval*rval+pow(rval,4))*(xval*xval-yval*yval)*
222 sqrt(1365./4096.0/M_PI);
223 ylmvec[40]->set(l,k,j,i)=(33.0*pow(zval,4)-18.0*zval*zval*rval*rval+pow(rval,4))*(2.0*xval*yval)*
224 sqrt(1365./4096.0/M_PI);
225 //l=6,m=3
226 ylmvec[41]->set(l,k,j,i)=-1.0*(11.0*pow(zval,3)-3.0*zval*rval*rval)*(pow(xval,3)-3.0*xval*yval*yval)*
227 sqrt(1365.0/1024.0/M_PI);
228 ylmvec[42]->set(l,k,j,i)=-1.0*(11.0*pow(zval,3)-3.0*zval*rval*rval)*(3.0*xval*xval*yval-pow(yval,3))*
229 sqrt(1365.0/1024.0/M_PI);
230 //l=6,m=4
231 ylmvec[43]->set(l,k,j,i)=(11.0*zval*zval-rval*rval)*(pow(xval,4)-6*xval*xval*yval*yval+pow(yval,4))*
232 sqrt(819.0/2048.0/M_PI);
233 ylmvec[44]->set(l,k,j,i)=(11.0*zval*zval-rval*rval)*4.0*xval*yval*(xval*xval-yval*yval)*
234 sqrt(819.0/2048.0/M_PI);
235 //l=6,m=5
236 ylmvec[45]->set(l,k,j,i)=-1.0*zval*(pow(xval,5)-10.0*pow(xval,3)*yval*yval+5.0*xval*pow(yval,4))*
237 sqrt(9009.0/1024.0/M_PI);
238 ylmvec[46]->set(l,k,j,i)=-1.0*zval*(5.0*pow(xval,4)*yval-10.0*xval*xval*pow(yval,3)+pow(yval,5))*
239 sqrt(9009.0/1024.0/M_PI);
240 //l=6,m=6
241 ylmvec[47]->set(l,k,j,i)=(pow(xval,6)-15.0*pow(xval,4)*yval*yval+15.0*xval*xval*pow(yval,4)-pow(yval,6))*
242 sqrt(3003.0/4096.0/M_PI);
243 ylmvec[48]->set(l,k,j,i)=(6.0*pow(xval,5)*yval-20.0*pow(xval,3)*pow(yval,3)+6.0*xval*pow(yval,5))*
244 sqrt(3003.0/4096.0/M_PI);
245 }
246 }
247 if(nylm >49) {
248 cout << "l>6 not implemented!!!!!!!"<< endl;
249 abort();
250 }
251 }
252 }
253 }
254 }
255
256}
257
258void Et_bin_bhns_extr::get_integrals(int nylm, double* intvec, Cmp** ylmvec,
259 Cmp source) const {
260
261 // As mentioned in the comment before get_ylm, our real/imaginary
262 // representation of the Y_lm Cmp's does not agree with the normalization
263 // used to define
264 // the spherical harmonic decomposition of Cmp arrays. Thus, we multiply
265 // all terms with m>=1 by a factor of 2.0 in order to
266 // produce the correct decomposition.
267
268 int nz=mp.get_mg()->get_nzone() ;
269
270 Map_af mapping (mp);
271
272 const double* a1 = mapping.get_alpha() ;
273 const double* b1 = mapping.get_beta() ;
274
275 double rlim=a1[nz-1]+b1[nz-1];
276
277 int ll=0;
278 int mm=0;
279 int ncount=0;
280 for (int n=0; n<nylm; n++) {
281
282 Cmp ylmsource=(*ylmvec[n]*source);
283 int symcheck=1;
284 for (int l=0; l<nz; l++) {
285 int symc=ylmsource.va.base.get_base_t(l);
286 if(symc!=2304 && symc!=1280)symcheck=0;
287 }
288 if(symcheck==1) {
289 intvec[n]=ylmsource.integrale()/(2.0*ll+1.0)/sqrt(2.0*M_PI)/pow(rlim,ll+1);
290 } else {
291 intvec[n]=0;
292 }
293 if(mm>=1)intvec[n]*=2.0;
294
295 int lnew=0;
296 int mnew=0;
297 int nnew=0;
298 if(mm<ll) {
299 if(mm==0) {
300 lnew=ll;
301 mnew=mm+1;
302 nnew=0;
303 }
304 if(mm>0&&ncount==0) {
305 lnew=ll;
306 mnew=mm;
307 nnew=1;
308 }
309 if(mm>0&&ncount==1) {
310 lnew=ll;
311 mnew=mm+1;
312 nnew=0;
313 }
314 }
315 if(mm==ll) {
316 if(mm==0) {
317 lnew=ll+1;
318 mnew=0;
319 nnew=0;
320 }
321 if(mm>0&&ncount==0) {
322 lnew=ll;
323 mnew=mm;
324 nnew=1;
325 }
326 if(mm>0&&ncount==1) {
327 lnew=ll+1;
328 mnew=0;
329 nnew=0;
330 }
331 }
332 ll=lnew;
333 mm=mnew;
334 ncount=nnew;
335 }
336}
337}
Lorene::Base_val::get_base_t
int get_base_t(int l) const
Returns the expansion basis for functions in the domain of index l (e.g.
Definition base_val.h:414
Lorene::Cmp
Component of a tensorial field *** DEPRECATED : use class Scalar instead ***.
Definition cmp.h:446
Lorene::Cmp::va
Valeur va
The numerical value of the Cmp.
Definition cmp.h:464
Lorene::Cmp::set
Tbl & set(int l)
Read/write of the value in a given domain.
Definition cmp.h:724
Lorene::Cmp::integrale
double integrale() const
Computes the integral over all space of *this .
Definition cmp_integ.C:58
Lorene::Et_bin_bhns_extr::get_ylm
void get_ylm(int nylm, Cmp **ylmvec) const
Constructs spherical harmonics.
Definition et_bin_bhns_extr_ylm.C:66
Lorene::Et_bin_bhns_extr::get_integrals
void get_integrals(int nylm, double *intvec, Cmp **ylmvec, Cmp source) const
Computes multipole moments.
Definition et_bin_bhns_extr_ylm.C:258
Lorene::Etoile::mp
Map & mp
Mapping associated with the star.
Definition etoile.h:432
Lorene::Map_af
Affine radial mapping.
Definition map.h:2042
Lorene::Map_af::get_beta
const double * get_beta() const
Returns the pointer on the array beta.
Definition map_af.C:608
Lorene::Map_af::get_alpha
const double * get_alpha() const
Returns the pointer on the array alpha.
Definition map_af.C:604
Lorene::Mtbl
Multi-domain array.
Definition mtbl.h:118
Lorene::Valeur::base
Base_val base
Bases on which the spectral expansion is performed.
Definition valeur.h:315
Lorene::sqrt
Cmp sqrt(const Cmp &)
Square root.
Definition cmp_math.C:223
Lorene::pow
Cmp pow(const Cmp &, int)
Power .
Definition cmp_math.C:351
Lorene
Lorene prototypes.
Definition app_hor.h:67