et_bin_bhns_extr_ylm.C
/*
* Method of class Et_bin_bhns_extr to construct spherical harmonics
*
* (see file et_bin_bhns_extr.h for documentation).
*
*/
/*
* Copyright (c) 2004 Joshua A. Faber
*
* 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 et_bin_bhns_extr_ylm_C[] = "$Header: /cvsroot/Lorene/C++/Source/Etoile/et_bin_bhns_extr_ylm.C,v 1.5 2014/10/13 08:52:55 j_novak Exp $" ;
/*
* $Id: et_bin_bhns_extr_ylm.C,v 1.5 2014/10/13 08:52:55 j_novak Exp $
* $Log: et_bin_bhns_extr_ylm.C,v $
* Revision 1.5 2014/10/13 08:52:55 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.4 2014/10/06 15:13:08 j_novak
* Modified #include directives to use c++ syntax.
*
* Revision 1.3 2005/02/28 23:18:07 k_taniguchi
* Change the functions to constant ones
*
* Revision 1.2 2005/01/03 19:52:56 k_taniguchi
* Change a factor multiplied/divided by sqrt(2).
*
* Revision 1.1 2004/12/29 16:30:46 k_taniguchi
* *** empty log message ***
*
*
* $Header: /cvsroot/Lorene/C++/Source/Etoile/et_bin_bhns_extr_ylm.C,v 1.5 2014/10/13 08:52:55 j_novak Exp $
*
*/
// C headers
#include <cstdlib>
#include <cmath>
// Lorene headers
#include "map.h"
#include "tenseur.h"
#include "et_bin_bhns_extr.h"
namespace Lorene {
void Et_bin_bhns_extr::get_ylm(int nylm, Cmp** ylmvec) const {
// IMPORTANT NOTE:
// For Y_lm with m>=1, we have the real and imaginary parts,
// not Y_{l,m} and Y_{l,-m}. This changes the normalization
// properties. In order to normalize properly, we multiply
// all fields in get_integrals below by a factor of 2.0 when
// m>=1.
cout << "Constructing ylm" << endl;
int nz = mp.get_mg()->get_nzone() ;
int nr = mp.get_mg()->get_nr(0) ;
int np = mp.get_mg()->get_np(0) ;
int nt = mp.get_mg()->get_nt(0) ;
for (int l=0 ; l<nz ; l++) {
Mtbl Xabs (mp.x) ;
Mtbl Yabs (mp.y) ;
Mtbl Zabs (mp.z) ;
for (int k=0 ; k<np ; k++) {
for (int j=0 ; j<nt ; j++) {
for (int i=0 ; i<nr ; i++) {
double xval=Xabs(l,k,j,i);
double yval=Yabs(l,k,j,i);
double zval=Zabs(l,k,j,i);
double rval=sqrt(xval*xval+yval*yval+zval*zval);
// cout <<l<<" "<<k<<" "<<j<<" "<<i<<endl;
//l=0,m=0
ylmvec[0]->set(l,k,j,i)=1.0*sqrt(1.0/4.0/M_PI);
// cout << " 0 " << endl;
// l=1 included?
if (nylm>1 ) {
if (nylm <4) {abort();} else {
//l=1,m=0
ylmvec[1]->set(l,k,j,i)=zval*sqrt(3.0/4.0/M_PI);
//l=1,m=1
ylmvec[2]->set(l,k,j,i)=-1.0*xval*sqrt(3.0/8.0/M_PI);
ylmvec[3]->set(l,k,j,i)=-1.0*yval*sqrt(3.0/8.0/M_PI);
}
}
// l=2 included?
if (nylm>4 ) {
if (nylm <9) {abort();} else {
//l=2,m=0
ylmvec[4]->set(l,k,j,i)=(3.0*zval*zval-rval*rval)*sqrt(5.0/16.0/M_PI);
//l=2,m=1
ylmvec[5]->set(l,k,j,i)=-1.0*zval*xval*sqrt(15.0/8.0/M_PI);
ylmvec[6]->set(l,k,j,i)=-1.0*zval*yval*sqrt(15.0/8.0/M_PI);
//l=2,m=2
ylmvec[7]->set(l,k,j,i)=(xval*xval-yval*yval)*sqrt(15.0/32.0/M_PI);
ylmvec[8]->set(l,k,j,i)=2.0*xval*yval*sqrt(15.0/32.0/M_PI);
}
}
// l=3 included?
if (nylm>9 ) {
if (nylm <16) {abort();} else {
//l=3,m=0
ylmvec[9]->set(l,k,j,i)=(5.0*pow(zval,3)-3.0*zval*rval*rval)*
sqrt(7.0/16.0/M_PI);
//l=3,m=1
ylmvec[10]->set(l,k,j,i)=-1.0*(5.0*zval*zval-rval*rval)*xval*
sqrt(21.0/64.0/M_PI);
ylmvec[11]->set(l,k,j,i)=-1.0*(5.0*zval*zval-rval*rval)*yval*
sqrt(21.0/64.0/M_PI);
//l=3,m=2
ylmvec[12]->set(l,k,j,i)=zval*(xval*xval-yval*yval)*
sqrt(105./32.0/M_PI);
ylmvec[13]->set(l,k,j,i)=zval*(2.0*xval*yval)*
sqrt(105./32.0/M_PI);
//l=3,m=3
ylmvec[14]->set(l,k,j,i)=-1.0*(pow(xval,3)-3.0*xval*yval*yval)*
sqrt(35.0/64.0/M_PI);
ylmvec[15]->set(l,k,j,i)=-1.0*(3.0*xval*xval*yval-pow(yval,3))*
sqrt(35.0/64.0/M_PI);
}
}
// l=4 included?
if (nylm>16 ) {
if (nylm <25) {abort();} else {
//l=4,m=0
ylmvec[16]->set(l,k,j,i)=(35.0*pow(zval,4)-30.0*zval*zval*rval*rval+3*pow(rval,4))*
sqrt(9.0/256.0/M_PI);
//l=4,m=1
ylmvec[17]->set(l,k,j,i)=-1.0*(7.0*pow(zval,3)-3*zval*rval*rval)*xval*
sqrt(45.0/64.0/M_PI);
ylmvec[18]->set(l,k,j,i)=-1.0*(7.0*pow(zval,3)-3*zval*rval*rval)*yval*
sqrt(45.0/64.0/M_PI);
//l=4,m=2
ylmvec[19]->set(l,k,j,i)=(7.0*zval*zval-rval*rval)*(xval*xval-yval*yval)*
sqrt(45./128.0/M_PI);
ylmvec[20]->set(l,k,j,i)=(7.0*zval*zval-rval*rval)*(2.0*xval*yval)*
sqrt(45./128.0/M_PI);
//l=4,m=3
ylmvec[21]->set(l,k,j,i)=-1.0*zval*(pow(xval,3)-3.0*xval*yval*yval)*
sqrt(315.0/64.0/M_PI);
ylmvec[22]->set(l,k,j,i)=-1.0*zval*(3.0*xval*xval*yval-pow(yval,3))*
sqrt(315.0/64.0/M_PI);
//l=4,m=4
ylmvec[23]->set(l,k,j,i)=(pow(xval,4)-6*xval*xval*yval*yval+pow(yval,4))*
sqrt(315.0/512.0/M_PI);
ylmvec[24]->set(l,k,j,i)=4.0*xval*yval*(xval*xval-yval*yval)*
sqrt(315.0/512.0/M_PI);
}
}
// l=5 included?
if (nylm>25 ) {
if (nylm <36) {abort();} else {
//l=5,m=0
ylmvec[25]->set(l,k,j,i)=(63.0*pow(zval,5)-70.0*pow(zval,3)*rval*rval+15*zval*pow(rval,4))*
sqrt(11.0/256.0/M_PI);
//l=5,m=1
ylmvec[26]->set(l,k,j,i)=-1.0*(21.0*pow(zval,4)-14*zval*zval*rval*rval+pow(rval,4))*xval*
sqrt(165.0/512.0/M_PI);
ylmvec[27]->set(l,k,j,i)=-1.0*(21.0*pow(zval,4)-14*zval*zval*rval*rval+pow(rval,4))*yval*
sqrt(165.0/512.0/M_PI);
//l=5,m=2
ylmvec[28]->set(l,k,j,i)=(3.0*pow(zval,3)-zval*rval*rval)*(xval*xval-yval*yval)*
sqrt(1155./128.0/M_PI);
ylmvec[29]->set(l,k,j,i)=(3.0*pow(zval,3)-zval*rval*rval)*(2.0*xval*yval)*
sqrt(1155./128.0/M_PI);
//l=5,m=3
ylmvec[30]->set(l,k,j,i)=-1.0*(9.0*zval*zval-rval*rval)*(pow(xval,3)-3.0*xval*yval*yval)*
sqrt(385.0/1024.0/M_PI);
ylmvec[31]->set(l,k,j,i)=-1.0*(9.0*zval*zval-rval*rval)*(3.0*xval*xval*yval-pow(yval,3))*
sqrt(385.0/1024.0/M_PI);
//l=5,m=4
ylmvec[32]->set(l,k,j,i)=zval*(pow(xval,4)-6*xval*xval*yval*yval+pow(yval,4))*
sqrt(3465.0/512.0/M_PI);
ylmvec[33]->set(l,k,j,i)=zval*4.0*xval*yval*(xval*xval-yval*yval)*
sqrt(3465.0/512.0/M_PI);
//l=5,m=5
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))*
sqrt(693.0/1024.0/M_PI);
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))*
sqrt(693.0/1024.0/M_PI);
}
}
// l=6 included?
if (nylm>36 ) {
if (nylm <49) {abort();} else {
//l=6,m=0
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))*
sqrt(13.0/1024.0/M_PI);
//l=6,m=1
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*
sqrt(273.0/512.0/M_PI);
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*
sqrt(273.0/512.0/M_PI);
//l=6,m=2
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)*
sqrt(1365./4096.0/M_PI);
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)*
sqrt(1365./4096.0/M_PI);
//l=6,m=3
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)*
sqrt(1365.0/1024.0/M_PI);
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))*
sqrt(1365.0/1024.0/M_PI);
//l=6,m=4
ylmvec[43]->set(l,k,j,i)=(11.0*zval*zval-rval*rval)*(pow(xval,4)-6*xval*xval*yval*yval+pow(yval,4))*
sqrt(819.0/2048.0/M_PI);
ylmvec[44]->set(l,k,j,i)=(11.0*zval*zval-rval*rval)*4.0*xval*yval*(xval*xval-yval*yval)*
sqrt(819.0/2048.0/M_PI);
//l=6,m=5
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))*
sqrt(9009.0/1024.0/M_PI);
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))*
sqrt(9009.0/1024.0/M_PI);
//l=6,m=6
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))*
sqrt(3003.0/4096.0/M_PI);
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))*
sqrt(3003.0/4096.0/M_PI);
}
}
if(nylm >49) {
cout << "l>6 not implemented!!!!!!!"<< endl;
abort();
}
}
}
}
}
}
void Et_bin_bhns_extr::get_integrals(int nylm, double* intvec, Cmp** ylmvec,
Cmp source) const {
// As mentioned in the comment before get_ylm, our real/imaginary
// representation of the Y_lm Cmp's does not agree with the normalization
// used to define
// the spherical harmonic decomposition of Cmp arrays. Thus, we multiply
// all terms with m>=1 by a factor of 2.0 in order to
// produce the correct decomposition.
int nz=mp.get_mg()->get_nzone() ;
Map_af mapping (mp);
const double* a1 = mapping.get_alpha() ;
const double* b1 = mapping.get_beta() ;
double rlim=a1[nz-1]+b1[nz-1];
int ll=0;
int mm=0;
int ncount=0;
for (int n=0; n<nylm; n++) {
Cmp ylmsource=(*ylmvec[n]*source);
int symcheck=1;
for (int l=0; l<nz; l++) {
int symc=ylmsource.va.base.get_base_t(l);
if(symc!=2304 && symc!=1280)symcheck=0;
}
if(symcheck==1) {
intvec[n]=ylmsource.integrale()/(2.0*ll+1.0)/sqrt(2.0*M_PI)/pow(rlim,ll+1);
} else {
intvec[n]=0;
}
if(mm>=1)intvec[n]*=2.0;
int lnew=0;
int mnew=0;
int nnew=0;
if(mm<ll) {
if(mm==0) {
lnew=ll;
mnew=mm+1;
nnew=0;
}
if(mm>0&&ncount==0) {
lnew=ll;
mnew=mm;
nnew=1;
}
if(mm>0&&ncount==1) {
lnew=ll;
mnew=mm+1;
nnew=0;
}
}
if(mm==ll) {
if(mm==0) {
lnew=ll+1;
mnew=0;
nnew=0;
}
if(mm>0&&ncount==0) {
lnew=ll;
mnew=mm;
nnew=1;
}
if(mm>0&&ncount==1) {
lnew=ll+1;
mnew=0;
nnew=0;
}
}
ll=lnew;
mm=mnew;
ncount=nnew;
}
}
}
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:411
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:55
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:63
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:255
Lorene::Etoile::mp
Map & mp
Mapping associated with the star.
Definition etoile.h:429
Lorene::Map_af
Affine radial mapping.
Definition map.h:2027
Lorene::Map_af::get_beta
const double * get_beta() const
Returns the pointer on the array beta.
Definition map_af.C:481
Lorene::Map_af::get_alpha
const double * get_alpha() const
Returns the pointer on the array alpha.
Definition map_af.C:477
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:305
Lorene::sqrt
Cmp sqrt(const Cmp &)
Square root.
Definition cmp_math.C:220
Lorene::pow
Cmp pow(const Cmp &, int)
Power .
Definition cmp_math.C:348
Lorene
Lorene prototypes.
Definition app_hor.h:64