eos_compose_fit_build.C

/*
 *  Methods of class Eos_compose_fit building.
 *
 *  (see file eos_compose_fit.h for documentation).
 *
 */

/*
 *   Copyright (c) 2022 Jerome Novak
 *
 *   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 as published by
 *   the Free Software Foundation; either version 2 of the License, or
 *   (at your option) any later version.
 *
 *   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: eos_compose_fit_build.C,v 1.6 2023/07/12 15:39:30 j_novak Exp $
 * $Log: eos_compose_fit_build.C,v $
 * Revision 1.6  2023/07/12 15:39:30  j_novak
 * Reversed order of matching the EoS fit: it now starts from the crust (polytrope) and adjusts the kappa of this crust so as to have the right pressure at the highest density in the original table.
 *
 * Revision 1.4  2023/03/17 16:10:46  j_novak
 * Better computation of gamma_low, to avoid jumps in sound speed.
 *
 * Revision 1.3  2023/01/27 16:10:35  j_novak
 * A polytrope (class Eos_poly) is used for low and high enthalpies.
 *
 * Revision 1.2  2022/07/21 12:34:18  j_novak
 * Corrected units
 *
 * Revision 1.1  2022/04/15 13:39:24  j_novak
 * New class Eos_compose_fit to generate fitted EoSs from CompOSE tables.
 *
 *
 * $Header: /cvsroot/Lorene/C++/Source/Eos/eos_compose_fit_build.C,v 1.6 2023/07/12 15:39:30 j_novak Exp $
 *
 */

// Headers Lorene
#include "eos_compose_fit.h"
#include "scalar.h"
#include "utilitaires.h"
#include "unites.h"
#include "graphique.h"

namespace Lorene {
  void Eos_compose_fit::read_compose_data(int& nbp, Tbl*& logh_read,
                      Tbl*& logp_read, Tbl*& loge_read,
                      Tbl*& lognb_read, Tbl*& gam1_read) {
    // Files containing data and a test
    //---------------------------------
  
    string file_nb = tablename + "eos.nb" ;
    string file_thermo = tablename + "eos.thermo" ;
    
    cout << "opening " << file_nb << " and " << file_thermo << " ... " << flush ;
    ifstream in_nb(file_nb.data()) ;
    if (!in_nb) {
      cerr << "Eos_compose_fit::read_compose_data:" << endl ;
      cerr << "Problem in opening the EOS file!" << endl ;
      cerr << "While trying to open " << file_nb << endl ;
      cerr << "Aborting..." << endl ;
      abort() ;
    }
    
    // obtaining the size of the tables for memory allocation
    //-------------------------------------------------------

    int index1, index2 ;
    in_nb >> index1 >> index2 ;
    nbp = index2 - index1 + 1 ;
    assert(nbp > 0) ;

    Tbl press(nbp) ; press.set_etat_qcq() ;
    Tbl nb(nbp) ; nb.set_etat_qcq() ;
    Tbl ener(nbp) ; ener.set_etat_qcq() ; 
    
    if (logh_read != nullptr) delete logh_read ;
    logh_read = new Tbl(nbp) ;
    logh_read->set_etat_qcq() ;
    if (logp_read != nullptr) delete logp_read ;
    logp_read = new Tbl(nbp) ;
    logp_read->set_etat_qcq() ;
    if (loge_read != nullptr) delete loge_read ;
    loge_read = new Tbl(nbp) ;
    loge_read->set_etat_qcq() ;
    if (lognb_read != nullptr) delete lognb_read ;
    lognb_read = new Tbl(nbp) ;
    lognb_read->set_etat_qcq() ;
    if (gam1_read != nullptr) delete gam1_read ;
    gam1_read = new Tbl(nbp) ;
    gam1_read->set_etat_qcq() ;
    
    // Variables and conversion
    //-------------------------
    double nb_fm3, rho_cgs, p_cgs, p_over_nb_comp, eps_comp ;
    double dummy_x ;
    int dummy_n ;
    
    //# Dealing with units could be optimized...
    double rhonuc_cgs = Unites::rhonuc_si * 1e-3 ;
    double c2_cgs = Unites::c_si * Unites::c_si * 1e4 ;
    double m_neutron_MeV, m_proton_MeV ;
    
    ifstream in_p_rho (file_thermo.data()) ;
    if (!in_p_rho) {
      cerr << "Reading CompOSE data: " << endl ;
      cerr << "Problem in opening the EOS file!" << endl ;
      cerr << "While trying to open " << file_thermo << endl ;
      cerr << "Aborting..." << endl ;
      abort() ;
    }
    in_p_rho >> m_neutron_MeV >> m_proton_MeV ; //Neutron and proton masses
    in_p_rho.ignore(1000, '\n') ;

    // Conversion from MeV/fm^3 to cgs
    double p_convert = Unites::mev_si * 1.e45 * 10. ;
    // From meV/fm^3 to g/cm^3
    double eps_convert = Unites::mev_si * 1.e42 / (Unites::c_si*Unites::c_si) ;
    
    cout << " done. " << endl ;
    cout << "Reading the table ... " << flush ;
  
    //--------------------------------------
    // Main loop reading the CompOSE tables
    //--------------------------------------
    for (int i=0; i<nbp; i++) {
      in_nb >> nb_fm3 ;
      in_p_rho >> dummy_n >> dummy_n >> dummy_n >> p_over_nb_comp ;
      in_p_rho >> dummy_x >> dummy_x >> dummy_x >> dummy_x >> dummy_x
           >> eps_comp ;
      in_p_rho.ignore(1000, '\n') ;
      p_cgs = p_over_nb_comp * nb_fm3 * p_convert ;
      rho_cgs = ( eps_comp + 1. ) * m_neutron_MeV * nb_fm3 * eps_convert ;
      
      if ( (nb_fm3 < 0) || (rho_cgs < 0) || (p_cgs < 0) ){
    cerr << "Eos_compose_fit::read_compose_data: " << endl ;
    cerr << "Negative value in table!" << endl ;
    cerr << "nb = " << nb_fm3 << ", rho = " << rho_cgs <<
      ", p = " << p_cgs << endl ;
    cerr << "Aborting..." << endl ;
    abort() ;
      }

      press.set(i) = p_cgs / c2_cgs ;
      nb.set(i)    = nb_fm3 ;
      ener.set(i)    = rho_cgs ;
      
      // log-quantities in cgs units
      logp_read->set(i) = log( press(i) / rhonuc_cgs ) ;
      loge_read->set(i) = log( ener(i) / rhonuc_cgs ) ; 
      lognb_read->set(i) = log( 10.* nb(i) ) ;
    }
    nb_max = nb(nbp-1) ;
    cout << " done." << endl ;  
    // -----------------------------------------
    // End of the reading of the CompOSE tables
    // -----------------------------------------
    
    cout << "Computation of derived quantities and file outputs.. " << flush ;
  
    // Computation of various derived quantities
    //-------------------------------------------
    
    // log-enthallpy, with a shift ensuring h=10^{-14} for the lowest density
    double ww = 0. ;
    for (int i=0; i<nbp; i++) {
      double h = log( (ener(i) + press(i)) / (10 * nb(i) * rhonuc_cgs) ) ;
      
      if (i==0) { ww = h ; }
      h = h - ww + 1.e-14 ;
      
      logh_read->set(i) = log( h ) ;
    }

    // d log(p) / d log(n) -> adiabatic index \Gamma_1
    compute_derivative((*lognb_read), (*logp_read), (*gam1_read) ) ;
    
    cout << "done" << endl ;
    
  } // End (read_compose_data)


  void Eos_compose_fit::adiabatic_index_fit(int i_min, int i_mid, const Tbl&
                        logh_read, const Tbl& logp_read,
                        const Tbl&, const Tbl&
                        lognb_read, const Tbl& gam1_read) {

    int nbp = logh_read.get_dim(0) ;
    double nb0_max = exp(lognb_read(nbp-1)) ;
    
    assert((mp != nullptr) && (mg != nullptr)) ;
    const Map_af& mpd = *mp ;
    int nz = mg->get_nzone() ;
    assert(nz == 2) ;
    int nr = mg->get_nr(0) ;
#ifndef NDEBUG 
    for (int l=1; l<nz; l++)
      assert(mg->get_nr(l) == nr) ;
#endif
    const Coord& xx = mpd.r ; // xx = log(h) = log(log(e+p/m_B n_B))
    double x_max = (+xx)(nz-1, 0, 0, nr-1) ;
    double x_mid = (+xx)(1, 0, 0, 0) ;
    double x_min = (+xx)(0, 0, 0, 0) ;
    
    if (log_p != nullptr) delete log_p ;
    if (log_e != nullptr) delete log_e ;
    if (log_nb != nullptr) delete log_nb ;
    if (log_cs2 != nullptr) delete log_cs2 ;
    
    int np_gam = 0 ;
    double mean_gam = 0. ;
    for (int i=0; i<i_min; i++) {
      mean_gam += gam1_read(i) ;
      np_gam++ ;
    }

    Scalar expexpx(mpd) ; // e^(e^x) , or simply (e+p)/(m_B n_B)
    expexpx = exp(exp(xx)) ;
    expexpx.std_spectral_base() ;
    Scalar expx(mpd) ; // e^x or simply h = log((e+p)/(m_B n_B))
    expx = exp(xx) ;
    expx.std_spectral_base() ;
    
    mean_gam /= double(np_gam) ;
    cout << "Mean Gamma_1 = " << mean_gam << endl ;
    
    // Fitting of the adiabatic index \Gamma_1
    Scalar gam1_spec(mpd) ;
    gam1_spec = mean_gam ;
    gam1_spec.std_spectral_base() ;
    
    // High density part : polynomial fit (polynomial regression)
    //--------------------------------------------------------------
    int ndata = nbp - i_mid ;
    Tbl xdata(ndata) ; xdata.set_etat_qcq() ;
    Tbl ydata(ndata) ; ydata.set_etat_qcq() ;
    for (int i=i_mid; i<nbp; i++) {
      xdata.set(i-i_mid) = 2.*(logh_read(i) - x_mid)
    / (x_max - x_mid) - 1. ;
      ydata.set(i-i_mid) = gam1_read(i) ;
    }
    
    Tbl tcoefs = poly_regression(xdata, ydata, n_coefs) ;
    
    // Putting coefficients to the 'Scalar' object 
    gam1_spec.set_spectral_va().coef() ;
    for (int i=0; i<=n_coefs; i++) {
      (*gam1_spec.set_spectral_va().c_cf).set(1, 0, 0, i) = tcoefs(i) ;
    }
    
    // Not nice, but only simple way to update values on grid points
    if (gam1_spec.set_spectral_va().c != nullptr) {
      delete gam1_spec.set_spectral_va().c ;
      gam1_spec.set_spectral_va().c = nullptr ;
    }
    gam1_spec.set_spectral_va().coef_i() ;
    
    // Intermediate part : linear interpolation
    //------------------------------------------
    Scalar interm(mpd) ;
    // Linear formula
    interm = mean_gam
      + (gam1_spec.val_grid_point(1, 0, 0, 0) - mean_gam)
      * (xx - x_min) / (x_mid - x_min) ;
    
    gam1_spec.set_domain(0) = interm.domain(0) ;
    
    // Low density part : polytrope, \Gamma_1 = const.
    //-------------------------------------------------
    
    Scalar YYY(mpd) ;
    // Determining kappa_low
    double p_min = exp(logp_read(i_min)) ;
    double ccc = (mean_gam - 1.) / mean_gam ;
    double kappa_low0 = pow(ccc*expm1(exp(x_min)), mean_gam)
      / pow(p_min, mean_gam*ccc)  ;
    double kappa_low1 = 0.1*kappa_low0 ;
    double logp_max0 = integrate_equations(kappa_low0, mean_gam, gam1_spec, expx,
                       expexpx, YYY) ;
    double logp_max = logp_read(nbp-1) ;
    
    // 'kappa_low' is determined to get the correct pressure at the higher end
    //-------------------------------------------------------------------------
    while(fabs(logp_max0 - logp_max)/logp_max > 1.e-3) {
      double logp_max1 = integrate_equations(kappa_low1, mean_gam, gam1_spec, expx,
                         expexpx, YYY) ;
      double kappa_low_new
    = (kappa_low0*(logp_max1 -logp_max)- kappa_low1*(logp_max0 - logp_max))
    / (logp_max1 - logp_max0) ;
      cout << "Kappa(new) = " << kappa_low_new << ", logp = " << logp_max1 << endl ;
      if (kappa_low_new < 0.) kappa_low_new = 0.01*kappa_low0 ;
      kappa_low0 = kappa_low1 ;
      logp_max0 = logp_max1 ;
      kappa_low1 = kappa_low_new ;
    }
    
    //des_profile(YYY, x_min, x_max, 0, 0) ;

    // sound speed : log(cs^2) = log(Y*\Gamma_1)
    log_cs2 = new Scalar(log(YYY*gam1_spec)) ;
    log_cs2->std_spectral_base();
    
    // Pressure
    Scalar spec_press = exp((*log_p)) ;
    spec_press.std_spectral_base( );
    
    // Energy density 
    Scalar spec_ener = spec_press*(1./YYY - 1.) ; spec_ener.std_spectral_base() ;
    log_e = new Scalar(log(spec_ener)) ;
    log_e->std_spectral_base() ;
    
    // Baryon density
    Scalar spec_nbar = spec_press / (YYY * expexpx) ; 
    cout << "Relative difference in baryon density at the last point" << endl ;
    cout << "(fitted computed / original tabulated)  : "
     << fabs(1. - spec_nbar.val_grid_point(nz-1, 0, 0, nr-1) / nb0_max)
     << endl ;
    log_nb = new Scalar(log(spec_nbar)) ;
    log_nb->std_spectral_base() ; // log_nb_spec = log(n_B)
    
    log_p->set_spectral_va().coef_i() ;
    log_e->set_spectral_va().coef_i() ;
    log_nb->set_spectral_va().coef_i() ;
    spec_nbar.set_spectral_va().coef_i() ;
    log_cs2->set_spectral_va().coef_i() ;
    
    // Matching to the high-density part polytrope
    //--------------------------------------------
    
    double gam_high = gam1_spec.val_grid_point(1, 0, 0, nr-1) ;
    double kappa_high = spec_press.val_grid_point(1, 0, 0, nr-1)
      / pow(spec_nbar.val_grid_point(1, 0, 0, nr-1), gam_high) ;
    
    double mu_high = (spec_ener.val_grid_point(1, 0, 0, nr-1)
              - kappa_high/(gam_high - 1.)
              * pow(spec_nbar.val_grid_point(1, 0, 0, nr-1), gam_high))
      / spec_nbar.val_grid_point(1, 0, 0, nr-1);
    
    if (p_eos_high != nullptr) delete p_eos_high ;
    p_eos_high = new Eos_poly(gam_high, kappa_high, mu_high, mu_high) ;
    
    cout << "... done (analytic representation)" << endl ;

  } // End (adiabatic_index_fit)

  double Eos_compose_fit::integrate_equations
  (double kappa_low, double mean_gam, const Scalar& gam1_spec,
   const Scalar& expx, const Scalar& expexpx, Scalar& YYY) {

    // Enthalpy at lower end of the grid
    double ent_min = expx.val_grid_point(0, 0, 0, 0) ;

    // The low-density part is defined through an "Eos_poly" object
    if (p_eos_low != nullptr) delete p_eos_low ;
    p_eos_low = new Eos_poly(mean_gam, kappa_low) ;

    // pressure & energy from th epolytropic EoS
    double p_min = p_eos_low->press_ent_p(ent_min) ;
    double e_min = p_eos_low->ener_ent_p(ent_min) ;

    // Solution of the differential equations to compute pressure, energy, etc
    //--------------------------------------------------------------------------
    // rhs: f = (\Gamma_1 - 1.)/\Gamma_1 * e^x * e^(e^x)
    Scalar fff = ((gam1_spec-1.)/gam1_spec)*expx*expexpx ;
    fff.std_spectral_base() ;
    
    // First integration
    //-------------------
    // F = primitive(f)
    Scalar FFF = fff.primr() ;
    FFF.std_spectral_base() ;
    // Integration constant
    double Y_min = p_min / (e_min + p_min) ;
    double A_min = expexpx.val_grid_point(0, 0, 0, 0)*Y_min
    - FFF.val_grid_point(0, 0, 0, 0) ;

    // Y is solution of Y' + Y e^x = f 
    YYY = (A_min + FFF)/expexpx ;

    // Second integration
    //--------------------
    // \Pi' = e^x / Y
    Scalar Pidot = expx / YYY ;
    if (log_p != nullptr) delete log_p ;
    log_p = new Scalar(Pidot.primr()) ; // log_p_spec = log(p)
    // Integration constant
    double lnp0 = log(p_min) -  log_p->val_grid_point(0, 0, 0, 0) ;
    (*log_p) = (*log_p) + lnp0 ;

    // returning the log of pressure at the higher end of the grid
    return log_p->val_grid_point(1, 0, 0, mg->get_nr(1)-1) ;
  }

}