star_QI_global.C

/*
 *  Methods of the class Star_QI to compute global quantities
 *
 *    (see file compobj.h for documentation).
 *
 */

/*
 *   Copyright (c) 2012 Claire Some, 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 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
 *
 */

 

/*
 * $Id: star_QI_global.C,v 1.4 2016/12/05 16:17:49 j_novak Exp $
 * $Log: star_QI_global.C,v $
 * Revision 1.4  2016/12/05 16:17:49  j_novak
 * Suppression of some global variables (file names, loch, ...) to prevent redefinitions
 *
 * Revision 1.3  2014/10/13 08:52:49  j_novak
 * Lorene classes and functions now belong to the namespace Lorene.
 *
 * Revision 1.2  2013/06/05 15:10:41  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 1.1  2012/11/21 14:54:13  c_some
 * First version
 *
 *
 *
 * $Header: /cvsroot/Lorene/C++/Source/Compobj/star_QI_global.C,v 1.4 2016/12/05 16:17:49 j_novak Exp $
 *
 */


// C headers
#include <cassert>
#include <cstdlib>

// Lorene headers
#include "compobj.h"
#include "unites.h"
#include "proto_f77.h"

            //------------------------//
            //  Gravitational mass    //
            //------------------------//

namespace Lorene {
double Star_QI::mass_g() const {

    if (p_mass_g == 0x0) {    // a new computation is required
    
        Scalar s_euler = stress_euler.trace(gamma) ; 
    
        //## alternative:
        // assert(*(stress_euler.get_triad()) == mp.get_bvect_spher()) ; 
        // Scalar s_euler = ( stress_euler(1,1) + stress_euler(2,2) ) / a_car 
        //  + stress_euler(3,3) / b_car ; 
            
        // Cf. Eq. (4.18) of arXiv:1003.5015v2 with (E+p) U = B * mom_euler(3)
        
        Scalar source = nn * (ener_euler + s_euler) 
                + 2 * b_car * mom_euler(3) 
                    * tnphi  ; 
        source = a_car * bbb * source ;
        source.std_spectral_base() ; 

        p_mass_g = new double( source.integrale() ) ;

    }
    
    return *p_mass_g ; 

} 
        

            //------------------------//
            //  Angular momentum      //
            //------------------------//

double Star_QI::angu_mom() const {

    if (p_angu_mom == 0x0) {    // a new computation is required
    
        // Cf. Eq. (4.39) of arXiv:1003.5015v2 with (E+p) U = B * mom_euler(3) 
        
        assert(*(mom_euler.get_triad()) == mp.get_bvect_spher()) ; 
    
        Scalar dens = mom_euler(3) ; 

        dens.mult_r() ;         //  Multiplication by
        dens.set_spectral_va() = (dens.get_spectral_va()).mult_st() ;   //    r sin(theta)

        dens = a_car * b_car * bbb * dens ; 

        p_angu_mom = new double( dens.integrale() ) ;

    }
    
    return *p_angu_mom ; 

}

            //--------------------//
            //       GRV2         //
            //--------------------//

double Star_QI::grv2() const {

      using namespace Unites ;  
      if (p_grv2 == 0x0) {    // a new computation is required
    
        assert( *(stress_euler.get_triad()) == mp.get_bvect_spher() ) ; 
        Scalar sou_m =  2 * qpig * a_car * b_car * stress_euler(3,3) ;
    
        Vector dlogn = logn.derive_cov( mp.flat_met_spher() ) ; 
        Scalar sou_q =  1.5 * ak_car
      - dlogn(1)*dlogn(1) - dlogn(2)*dlogn(2) - dlogn(3)*dlogn(3) ; 
    
        p_grv2 = new double( double(1) - lambda_grv2(sou_m, sou_q) ) ; 
    
      }
    
      return *p_grv2 ; 
      
}


            //--------------------//
            //       GRV3         //
            //--------------------//

double Star_QI::grv3(ostream* ost) const {

  using namespace Unites ;  
  
  if (p_grv3 == 0x0) {    // a new computation is required

    Scalar source(mp) ; 
    
    // Gravitational term [cf. Eq. (43) of Gourgoulhon & Bonazzola
    // ------------------       Class. Quantum Grav. 11, 443 (1994)]
    
    Vector dlogn = logn.derive_cov( mp.flat_met_spher() ) ;

      Scalar alpha = dzeta - logn ; 
      Scalar bet = log( bbb ) ; 
      bet.std_spectral_base() ; 
      
      Vector dalpha = alpha.derive_cov( mp.flat_met_spher() ) ;
      Vector dbet = bet.derive_cov( mp.flat_met_spher() ) ;

      source = 0.75 * ak_car 
    - dlogn(1)*dlogn(1) - dlogn(2)*dlogn(2) - dlogn(3)*dlogn(3) 
    + 0.5 * ( dalpha(1)*dbet(1) + dalpha(2)*dbet(2) + dalpha(3)*dbet(3) ) ; 
      
      Scalar aa = alpha - 0.5 * bet ; 
      Scalar daadt = aa.srdsdt() ;  // 1/r d/dth
        
      // What follows is valid only for a mapping of class Map_radial : 
      const Map_radial* mpr = dynamic_cast<const Map_radial*>(&mp) ; 
      if (mpr == 0x0) {
    cout << "Star_rot::grv3: the mapping does not belong"
         << " to the class Map_radial !" << endl ; 
    abort() ; 
      }
      
      // Computation of 1/tan(theta) * 1/r daa/dtheta
      if (daadt.get_etat() == ETATQCQ) {
    Valeur& vdaadt = daadt.set_spectral_va() ; 
    vdaadt = vdaadt.ssint() ;   // division by sin(theta)
    vdaadt = vdaadt.mult_ct() ; // multiplication by cos(theta)
      }
      
      Scalar temp = aa.dsdr() + daadt ; 
      temp = ( bbb - a_car/bbb ) * temp ; 
      temp.std_spectral_base() ; 
      
      // Division by r 
      Valeur& vtemp = temp.set_spectral_va() ; 
      vtemp = vtemp.sx() ;    // division by xi in the nucleus
      // Id in the shells
      // division by xi-1 in the ZEC
      vtemp = (mpr->xsr) * vtemp ; // multiplication by xi/r in the nucleus
      //          by 1/r in the shells
      //          by r(xi-1) in the ZEC
      
      // In the ZEC, a multiplication by r has been performed instead
      //   of the division:             
      temp.set_dzpuis( temp.get_dzpuis() + 2 ) ;  
      
      source = bbb * source + 0.5 * temp ; 
          
    source.std_spectral_base() ; 
    
    double int_grav = source.integrale() ; 
    
    // Matter term
    // -----------
    
    Scalar s_euler = stress_euler.trace(gamma) ; 
    
        //## alternative:
        // assert(*(stress_euler.get_triad()) == mp.get_bvect_spher()) ; 
        // Scalar s_euler = ( stress_euler(1,1) + stress_euler(2,2) ) / a_car 
        //  + stress_euler(3,3) / b_car ; 
            
    source  = qpig * a_car * bbb * s_euler ;
     
    source.std_spectral_base() ; 

    double int_mat = source.integrale() ; 
    
    // Virial error
    // ------------
    if (ost != 0x0) {
      *ost << "Star_rot::grv3 : gravitational term : " << int_grav 
       << endl ;
      *ost << "Star_rot::grv3 : matter term :        " << int_mat 
       << endl ;
    }
    
    p_grv3 = new double( (int_grav + int_mat) / int_mat ) ;      
    
  }
  
  return *p_grv3 ; 
  
}

            //----------------------------//
            //     Quadrupole moment      //
            //----------------------------//

double Star_QI::mom_quad() const {

  using namespace Unites ;
    if (p_mom_quad == 0x0) {    // a new computation is required
    
    // Source for of the Poisson equation for nu
    // -----------------------------------------

    Scalar source(mp) ; 
    
    Scalar s_euler = stress_euler.trace(gamma) ; 
    
        //## alternative:
        // assert(*(stress_euler.get_triad()) == mp.get_bvect_spher()) ; 
        // Scalar s_euler = ( stress_euler(1,1) + stress_euler(2,2) ) / a_car 
        //  + stress_euler(3,3) / b_car ; 

        Scalar bet = log(bbb) ; 
        bet.std_spectral_base() ; 
        
        Vector dlogn = logn.derive_cov( mp.flat_met_spher() ) ;
        Vector dlogn_bet = dlogn + bet.derive_cov( mp.flat_met_spher() ) ;

        source =  qpig * a_car *( ener_euler + s_euler ) + ak_car 
          - dlogn(1)*dlogn_bet(1) - dlogn(2)*dlogn_bet(2) - dlogn(3)*dlogn_bet(3)   ; 
    
    source.std_spectral_base() ;

    // Multiplication by -r^2 P_2(cos(theta))
    //  [cf Eq.(7) of Salgado et al. Astron. Astrophys. 291, 155 (1994) ]
    // ------------------------------------------------------------------
    
    // Multiplication by r^2 : 
    // ----------------------
    source.mult_r() ; 
    source.mult_r() ; 
    if (source.check_dzpuis(2)) {
        source.inc_dzpuis(2) ; 
    }
        
    // Muliplication by cos^2(theta) :
    // -----------------------------
    Scalar temp = source ; 
    
    // What follows is valid only for a mapping of class Map_radial : 
    assert( dynamic_cast<const Map_radial*>(&mp) != 0x0 ) ; 
        
    if (temp.get_etat() == ETATQCQ) {
        Valeur& vtemp = temp.set_spectral_va() ; 
        vtemp = vtemp.mult_ct() ;   // multiplication by cos(theta)
        vtemp = vtemp.mult_ct() ;   // multiplication by cos(theta)
    }
    
    // Muliplication by -P_2(cos(theta)) :
    // ----------------------------------
    source = 0.5 * source - 1.5 * temp ; 
    
    // Final result
    // ------------

    p_mom_quad = new double( source.integrale() / qpig ) ;   

    }
    
    return *p_mom_quad ; 

}


// Function Star_QI::lambda_grv2

double Star_QI::lambda_grv2(const Scalar& sou_m, const Scalar& sou_q) {

    const Map_radial* mprad = dynamic_cast<const Map_radial*>( &sou_m.get_mp() ) ;
    
    if (mprad == 0x0) {
        cout << "Star_rot::lambda_grv2: the mapping of sou_m does not"
             << endl << " belong to the class Map_radial !" << endl ;
        abort() ;
    }   

    assert( &sou_q.get_mp() == mprad ) ;
    
    sou_q.check_dzpuis(4) ;
    
    const Mg3d* mg = mprad->get_mg() ;
    int nz = mg->get_nzone() ;
        
    // Construction of a Map_af which coincides with *mp on the equator
    // ----------------------------------------------------------------

    double theta0 = M_PI / 2 ;      // Equator
    double phi0 = 0 ;

    Map_af mpaff(*mprad) ;

    for (int l=0 ; l<nz ; l++) {
        double rmax = mprad->val_r(l, double(1), theta0, phi0) ;
        switch ( mg->get_type_r(l) ) {
            case RARE:  {
                double rmin = mprad->val_r(l, double(0), theta0, phi0) ;
                mpaff.set_alpha(rmax - rmin, l) ;
                mpaff.set_beta(rmin, l) ;
                break ;
            }
    
            case FIN:   {
                double rmin = mprad->val_r(l, double(-1), theta0, phi0) ;
                mpaff.set_alpha( double(.5) * (rmax - rmin), l ) ;
                mpaff.set_beta( double(.5) * (rmax + rmin), l) ;
                break ;
            }

            case UNSURR: {
                double rmin = mprad->val_r(l, double(-1), theta0, phi0) ;
                double umax = double(1) / rmin ;
                double umin = double(1) / rmax ;
                mpaff.set_alpha( double(.5) * (umin - umax),  l) ;
                mpaff.set_beta( double(.5) * (umin + umax), l) ;
                break ;
            }
    
            default: {
                cout << "Star_rot::lambda_grv2: unknown type_r ! " << endl ;
                abort () ;
                break ;
            }
    
        }
    }


    // Reduced Jacobian of
    // the transformation  (r,theta,phi) <-> (dzeta,theta',phi')
    // ------------------------------------------------------------
    
    Mtbl jac = 1 / ( (mprad->xsr) * (mprad->dxdr) ) ;   
                                // R/x dR/dx in the nucleus
                                // R dR/dx   in the shells
                                // - U/(x-1) dU/dx in the ZEC                       
    for (int l=0; l<nz; l++) {
        switch ( mg->get_type_r(l) ) {
            case RARE:  {
                double a1 = mpaff.get_alpha()[l] ;
                *(jac.t[l]) =  *(jac.t[l]) / (a1*a1) ;
                break ;
            }
    
            case FIN:   {
                double a1 = mpaff.get_alpha()[l] ;
                double b1 = mpaff.get_beta()[l] ;
                assert( jac.t[l]->get_etat() == ETATQCQ ) ;
                double* tjac = jac.t[l]->t ;
                double* const xi = mg->get_grille3d(l)->x ;
                for (int k=0; k<mg->get_np(l); k++) {
                    for (int j=0; j<mg->get_nt(l); j++) {
                        for (int i=0; i<mg->get_nr(l); i++) {
                            *tjac = *tjac /
                                    (a1 * (a1 * xi[i] + b1) ) ;
                            tjac++ ;    
                        }
                    }
                }               
                
                break ;
            }
    
            case UNSURR: {
                double a1 = mpaff.get_alpha()[l] ;
                *(jac.t[l]) = - *(jac.t[l]) / (a1*a1) ;
                break ;
            }
    
            default: {
                cout << "Star_rot::lambda_grv2: unknown type_r ! " << endl ;
                abort () ;
                break ;
            }
    
        }
    
    }


    // Multiplication of the sources by the reduced Jacobian:
    // -----------------------------------------------------
        
    Mtbl s_m(mg) ;
    if ( sou_m.get_etat() == ETATZERO ) {
        s_m = 0 ;
    }
    else{
        assert(sou_m.get_spectral_va().get_etat() == ETATQCQ) ; 
        sou_m.get_spectral_va().coef_i() ;  
        s_m = *(sou_m.get_spectral_va().c) ;
    }
        
    Mtbl s_q(mg) ;
    if ( sou_q.get_etat() == ETATZERO ) {
        s_q = 0 ;
    }
    else{
        assert(sou_q.get_spectral_va().get_etat() == ETATQCQ) ; 
        sou_q.get_spectral_va().coef_i() ;  
        s_q = *(sou_q.get_spectral_va().c) ;
    }
            
    s_m *= jac ;
    s_q *= jac ;
        
    
    // Preparations for the call to the Fortran subroutine
    // ---------------------------------------------------                              
    
    int np1 = 1 ;       // Axisymmetry enforced
    int nt = mg->get_nt(0) ;
    int nt2 = 2*nt - 1 ;    // Number of points for the theta sampling
                            //  in [0,Pi], instead of [0,Pi/2]

    // Array NDL
    // ---------
    int* ndl = new int[nz+4] ;
    ndl[0] = nz ;
    for (int l=0; l<nz; l++) {
        ndl[1+l] = mg->get_nr(l) ;
    }
    ndl[1+nz] = nt2 ;
    ndl[2+nz] = np1 ;
    ndl[3+nz] = nz ;

    // Parameters NDR, NDT, NDP
    // ------------------------
    int nrmax = 0 ;
    for (int l=0; l<nz ; l++) {
        nrmax = ( ndl[1+l] > nrmax ) ? ndl[1+l] : nrmax ;
    }
    int ndr = nrmax + 5 ;
    int ndt = nt2 + 2 ;
    int ndp = np1 + 2 ;

    // Array ERRE
    // ----------

    double* erre = new double [nz*ndr] ;

    for (int l=0; l<nz; l++) {
        double a1 = mpaff.get_alpha()[l] ;
        double b1 = mpaff.get_beta()[l] ;
        for (int i=0; i<ndl[1+l]; i++) {
            double xi = mg->get_grille3d(l)->x[i] ;
            erre[ ndr*l + i ] = a1 * xi + b1 ;
        }
    }

    // Arrays containing the data
    // --------------------------

    int ndrt = ndr*ndt ;
    int ndrtp = ndr*ndt*ndp ;
    int taille = ndrtp*nz ;

    double* tsou_m = new double[ taille ] ;
    double* tsou_q = new double[ taille ] ;

    // Initialisation to zero :
    for (int i=0; i<taille; i++) {
        tsou_m[i] = 0 ;
        tsou_q[i] = 0 ;
    }

    // Copy of s_m into tsou_m
    // -----------------------

    for (int l=0; l<nz; l++) {
       for (int k=0; k<np1; k++) {
            for (int j=0; j<nt; j++) {
                for (int i=0; i<mg->get_nr(l); i++) {
                    double xx = s_m(l, k, j, i) ;
                    tsou_m[ndrtp*l + ndrt*k + ndr*j + i] = xx ;
                    // point symetrique par rapport au plan theta = pi/2 :
                    tsou_m[ndrtp*l + ndrt*k + ndr*(nt2-1-j) + i] = xx ;         
                }
            }
        }
    }

    // Copy of s_q into tsou_q
    // -----------------------

    for (int l=0; l<nz; l++) {
       for (int k=0; k<np1; k++) {
            for (int j=0; j<nt; j++) {
                for (int i=0; i<mg->get_nr(l); i++) {
                    double xx = s_q(l, k, j, i) ;
                    tsou_q[ndrtp*l + ndrt*k + ndr*j + i] = xx ;
                    // point symetrique par rapport au plan theta = pi/2 :
                    tsou_q[ndrtp*l + ndrt*k + ndr*(nt2-1-j) + i] = xx ;         
                }
            }
        }
    }

    
    // Computation of the integrals
    // ----------------------------

    double int_m, int_q ;
    F77_integrale2d(ndl, &ndr, &ndt, &ndp, erre, tsou_m, &int_m) ;
    F77_integrale2d(ndl, &ndr, &ndt, &ndp, erre, tsou_q, &int_q) ;

    // Cleaning
    // --------

    delete [] ndl ;
    delete [] erre ;
    delete [] tsou_m ;
    delete [] tsou_q ;

    // Computation of lambda
    // ---------------------

    double lambda ;
    if ( int_q != double(0) ) {
        lambda = - int_m / int_q ;
    }
    else{
        lambda = 0 ;
    }
    
    return lambda ;
    
}

}