absorption.cc

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/* Copyright (C) 2000-2012
   Stefan Buehler  <sbuehler@ltu.se>
   Axel von Engeln <engeln@uni-bremen.de>
 
   This program 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, or (at your option) any
   later version.
 
   This program 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 this program; if not, write to the Free Software
   Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307,
   USA. */
 
#include "arts.h"
#include <map>
#include <cfloat>
#include <algorithm>
#include <cmath>
#include <cstdlib>
#include "file.h"
#include "absorption.h"
#include "math_funcs.h"
#include "messages.h"
#include "logic.h"
#include "interpolation_poly.h"
 
#include "global_data.h"
 
 
std::map<String, Index> SpeciesMap;
 
 
// member fct of isotopologuerecord, calculates the partition fct at the
// given temperature  from the partition fct coefficients (3rd order
// polynomial in temperature)
Numeric IsotopologueRecord::CalculatePartitionFctAtTempFromCoeff( Numeric
                                                    temperature ) const
{
  Numeric result = 0.;
  Numeric exponent = 1.;
 
  Vector::const_iterator it;
 
//      cout << "T: " << temperature << "\n";
  for (it=mqcoeff.begin(); it != mqcoeff.end(); ++it)
    {
      result += *it * exponent;
      exponent *= temperature;
//      cout << "it: " << it << "\n";
//      cout << "res: " << result << ", exp: " << exponent << "\n";
    }
  return result;
}
 
 
// member fct of isotopologuerecord, calculates the partition fct at the
// given temperature  from the partition fct coefficients (3rd order
// polynomial in temperature)
Numeric IsotopologueRecord::CalculatePartitionFctAtTempFromData( Numeric
temperature ) const
{
    GridPosPoly gp;
    gridpos_poly( gp, mqcoeffgrid, temperature, mqcoeffinterporder);
    Vector itw;
    interpweights(itw, gp );
    return interp(  itw, mqcoeff, gp );
}
 
 
void SpeciesAuxData::initParams(Index nparams)
{
    using global_data::species_data;
 
    mparams.resize(species_data.nelem());
 
    for (Index isp = 0; isp < species_data.nelem(); isp++)
    {
        mparams[isp].resize(species_data[isp].Isotopologue().nelem(), nparams);
        mparams[isp] = NAN;
    }
}
 
 
bool SpeciesAuxData::ReadFromStream(String& artsid, istream& is, Index nparams, const Verbosity& verbosity)
{
    CREATE_OUT3;
 
    // Global species lookup data:
    using global_data::species_data;
 
    // We need a species index sorted by Arts identifier. Keep this in a
    // static variable, so that we have to do this only once.  The ARTS
    // species index is ArtsMap[<Arts String>].
    static map<String, SpecIsoMap> ArtsMap;
 
    // Remember if this stuff has already been initialized:
    static bool hinit = false;
 
    if ( !hinit )
    {
 
        out3 << "  ARTS index table:\n";
 
        for ( Index i=0; i<species_data.nelem(); ++i )
        {
            const SpeciesRecord& sr = species_data[i];
 
 
            for ( Index j=0; j<sr.Isotopologue().nelem(); ++j)
            {
 
                SpecIsoMap indicies(i,j);
                String buf = sr.Name()+"-"+sr.Isotopologue()[j].Name();
 
                ArtsMap[buf] = indicies;
 
                // Print the generated data structures (for debugging):
                // The explicit conversion of Name to a c-String is
                // necessary, because setw does not work correctly for
                // stl Strings.
                const Index& i1 = ArtsMap[buf].Speciesindex();
                const Index& i2 = ArtsMap[buf].Isotopologueindex();
 
                out3 << "  Arts Identifier = " << buf << "   Species = "
                << setw(10) << setiosflags(ios::left)
                << species_data[i1].Name().c_str()
                << "iso = "
                << species_data[i1].Isotopologue()[i2].Name().c_str()
                << "\n";
 
            }
        }
        hinit = true;
    }
 
 
    // This always contains the rest of the line to parse. At the
    // beginning the entire line. Line gets shorter and shorter as we
    // continue to extract stuff from the beginning.
    String line;
 
    // Look for more comments?
    bool comment = true;
 
    while (comment)
    {
        // Return true if eof is reached:
        if (is.eof()) return true;
 
        // Throw runtime_error if stream is bad:
        if (!is) throw runtime_error ("Stream bad.");
 
        // Read line from file into linebuffer:
        getline(is,line);
 
        // It is possible that we were exactly at the end of the file before
        // calling getline. In that case the previous eof() was still false
        // because eof() evaluates only to true if one tries to read after the
        // end of the file. The following check catches this.
        if (line.nelem() == 0 && is.eof()) return true;
 
        // @ as first character marks catalogue entry
        char c;
        extract(c,line,1);
 
        // check for empty line
        if (c == '@')
        {
            comment = false;
        }
    }
 
 
    // read the arts identifier String
    istringstream icecream(line);
 
    icecream >> artsid;
 
    if (artsid.length() != 0)
    {
        Index mspecies;
        Index misotopologue;
 
        // ok, now for the cool index map:
        // is this arts identifier valid?
        const map<String, SpecIsoMap>::const_iterator i = ArtsMap.find(artsid);
        if ( i == ArtsMap.end() )
        {
            ostringstream os;
            os << "ARTS Tag: " << artsid << " is unknown.";
            throw runtime_error(os.str());
        }
 
        SpecIsoMap id = i->second;
 
 
        // Set mspecies:
        mspecies = id.Speciesindex();
 
        // Set misotopologue:
        misotopologue = id.Isotopologueindex();
 
        Matrix& params = mparams[mspecies];
        // Extract accuracies:
        try
        {
            Numeric p;
            for (Index ip = 0; ip < nparams; ip++)
            {
                icecream >> double_imanip() >> p;
                params(misotopologue, ip) = p;
            }
        }
        catch (runtime_error)
        {
            throw runtime_error("Error reading SpeciesAuxData.");
        }
    }
    
    // That's it!
    return false;
}
 
 
void checkIsotopologueRatios(const ArrayOfArrayOfSpeciesTag& abs_species,
                             const SpeciesAuxData& isoratios)
{
    using global_data::species_data;
    
    // Check total number of species:
    if (species_data.nelem() != isoratios.getParams().nelem())
      {
        ostringstream os;
        os << "Number of species in SpeciesAuxData (" << isoratios.getParams().nelem()
        << "does not fit builtin species data (" << species_data.nelem() << ").";
        throw runtime_error(os.str());
      }
    
    // For the selected species, we check all isotopes by looping over the
    // species data. (Trying to check only the isotopes actually used gets
    // quite complicated, actually, so we do the simple thing here.)
    
    // Loop over the absorption species:
    for (Index i=0; i<abs_species.nelem(); i++)
      {
        // sp is the index of this species in the internal lookup table
        const Index sp = abs_species[i][0].Species();
        
        // Get handle on species data for this species:
        const SpeciesRecord& this_sd = species_data[sp];
     
        // Check number of isotopologues:
        if (this_sd.Isotopologue().nelem() != isoratios.getParams()[sp].nrows())
          {
            ostringstream os;
            os << "Incorrect number of isotopologues in isotopologue data.\n"
            << "Species: " << this_sd.Name() << ".\n"
            << "Number of isotopes in SpeciesAuxData ("
            << isoratios.getParams()[i].nrows() << ") "
            << "does not fit builtin species data (" << this_sd.Isotopologue().nelem() << ").";
            throw runtime_error(os.str());
          }
        
        for (Index iso = 0; iso < this_sd.Isotopologue().nelem(); ++iso)
          {
            // For "real" species (not representing continau) the isotopologue
            // ratio must not be NAN or below zero.
            if (!this_sd.Isotopologue()[iso].isContinuum()) {
                if (isnan(isoratios.getParam(sp, iso, 0)) ||
                    isoratios.getParam(sp, iso, 0) < 0.) {
                    
                    ostringstream os;
                    os << "Invalid isotopologue ratio.\n"
                    << "Species: " << this_sd.Name() << "-"
                    << this_sd.Isotopologue()[iso].Name() << "\n"
                    << "Ratio:   " << isoratios.getParam(sp, iso, 0);
                    throw runtime_error(os.str());
                }
            }
          }
      }
}
 
 
void fillSpeciesAuxDataWithIsotopologueRatiosFromSpeciesData(SpeciesAuxData& sad)
{
    using global_data::species_data;
 
    sad.initParams(1);
 
    for (Index isp = 0; isp < species_data.nelem(); isp++)
        for (Index iiso = 0; iiso < species_data[isp].Isotopologue().nelem(); iiso++)
        {
            sad.setParam(isp, iiso, 0, species_data[isp].Isotopologue()[iiso].Abundance());
        }
}
 
 
void define_species_map()
{
  using global_data::species_data;
 
  for ( Index i=0 ; i<species_data.nelem() ; ++i)
    {
      SpeciesMap[species_data[i].Name()] = i;
    }
}
 
 
ostream& operator<< (ostream& os, const SpeciesRecord& sr)
{
  for ( Index j=0; j<sr.Isotopologue().nelem(); ++j)
    {
      os << sr.Name() << "-" << sr.Isotopologue()[j].Name() << "\n";
    }
  return os;
}
 
      
ostream& operator<< (ostream& os, const SpeciesAuxData& sad)
{
  os << sad.getParams();
  return os;
}
 
 
 
void find_broad_spec_locations(ArrayOfIndex& broad_spec_locations,
                                const ArrayOfArrayOfSpeciesTag& abs_species,
                                const Index this_species)
{
  // Make sure this_species points to somewhere inside abs_species:
  assert(this_species>=0);
  assert(this_species<abs_species.nelem());
  
  // Number of broadening species:
  const Index nbs = LineRecord::NBroadSpec();
  
  // Resize output array:
  broad_spec_locations.resize(nbs);
  
//  // Set broadening species names, using the enums defined in absorption.h.
//  // This is hardwired here and quite primitive, but should do the job.
//  ArrayOfString broad_spec_names(nbs);
//  broad_spec_names[LineRecord::SPEC_POS_N2]  = "N2";
//  broad_spec_names[LineRecord::SPEC_POS_O2]  = "O2";
//  broad_spec_names[LineRecord::SPEC_POS_H2O] = "H2O";
//  broad_spec_names[LineRecord::SPEC_POS_CO2] = "CO2";
//  broad_spec_names[LineRecord::SPEC_POS_H2]  = "H2";
//  broad_spec_names[LineRecord::SPEC_POS_He]  = "He";
  
  // Loop over all broadening species and see if we can find them in abs_species.
  for (Index i=0; i<nbs; ++i) {
    // Find associated internal species index (we do the lookup by index, not by name).
    const Index isi = LineRecord::BroadSpecSpecIndex(i);
    
    // First check if this broadening species is the same as this_species
    if ( isi == abs_species[this_species][0].Species() )
      broad_spec_locations[i] = -2;
    else
    {
      // Find position of broadening species isi in abs_species. The called
      // function returns -1 if not found, which is already the correct
      // treatment for this case that we also want here.
      broad_spec_locations[i] = find_first_species_tg(abs_species,isi);
    }
  }
}
 
void calc_gamma_and_deltaf_artscat4(Numeric& gamma,
                                    Numeric& deltaf,
                                    const Numeric p,
                                    const Numeric t,
                                    ConstVectorView vmrs,
                                    const Index this_species,
                                    const ArrayOfIndex& broad_spec_locations,
                                    const LineRecord& l_l,
                                    const Verbosity& verbosity)
{
    CREATE_OUT2;
 
    // Number of broadening species:
    const Index nbs = LineRecord::NBroadSpec();
    assert(nbs==broad_spec_locations.nelem());
 
    // Theta is reference temperature divided by local temperature. Used in
    // several place by the broadening and shift formula.
    const Numeric theta = l_l.Ti0() / t;
    
    // Split total pressure in self and foreign part:
    const Numeric p_self    = vmrs[this_species] * p;
    const Numeric p_foreign = p-p_self;
    
    // Calculate sum of VMRs of all available foreign broadening species (we need this
    // for normalization). The species "Self" will not be included in the sum!
    Numeric broad_spec_vmr_sum = 0;
 
    // Gamma is the line width. We first initialize gamma with the self width
    gamma =  l_l.Sgam() * pow(theta, l_l.Nself()) * p_self;
 
    // and treat foreign width separately:
    Numeric gamma_foreign = 0;
    
    // There is no self shift parameter (or rather, we do not have it), so
    // we do not need separate treatment of self and foreign for the shift:
    deltaf = 0;
    
    // Add up foreign broadening species, where available:
    for (Index i=0; i<nbs; ++i) {
        if ( broad_spec_locations[i] < -1 ) {
            // -2 means that this broadening species is identical to Self.
            // Throw runtime errors if the parameters are not identical.
            if (l_l.Gamma_foreign(i)!=l_l.Sgam() ||
                l_l.N_foreign(i)!=l_l.Nself())
              {
                ostringstream os;
                os << "Inconsistency in LineRecord, self broadening and line "
                   << "broadening for " << LineRecord::BroadSpecName(i) << "\n"
                   << "should be identical.\n"
                   << "LineRecord:\n"
                   << l_l;
                throw runtime_error(os.str());
              }
        } else if ( broad_spec_locations[i] >= 0 ) {
 
            // Add to VMR sum:
            broad_spec_vmr_sum += vmrs[broad_spec_locations[i]];
 
            // foreign broadening:
            gamma_foreign +=  l_l.Gamma_foreign(i) * pow(theta, l_l.N_foreign(i))
                              * vmrs[broad_spec_locations[i]];
         
            // Pressure shift:
            // The T dependence is connected to that of the corresponding
            // broadening parameter by:
            // n_shift = .25 + 1.5 * n_gamma
            deltaf += l_l.Delta_foreign(i)
                      * pow( theta , (Numeric).25 + (Numeric)1.5*l_l.N_foreign(i) )
                      * vmrs[broad_spec_locations[i]];
        }
    }
 
    // Check that sum of self and all foreign VMRs is not too far from 1:
    if ( abs(vmrs[this_species]+broad_spec_vmr_sum-1) > 0.1
         && out2.sufficient_priority() )
      {
        ostringstream os;
        os << "Warning: The total VMR of all your defined broadening\n"
             << "species (including \"self\") is "
             << vmrs[this_species]+broad_spec_vmr_sum
             << ", more than 10% " << "different from 1.\n";
        out2 << os.str();
      }
    
    // Normalize foreign gamma and deltaf with the foreign VMR sum (but only if
    // we have any foreign broadening species):
    if (broad_spec_vmr_sum != 0.)
      {
        gamma_foreign /= broad_spec_vmr_sum;
        deltaf        /= broad_spec_vmr_sum;
      }
    else if (p_self > 0.)
    // If there are no foreign broadening species present, the best assumption
    // we can make is to use gamma_self in place of gamma_foreign. for deltaf
    // there is no equivalent solution, as we don't have a Delta_self and don't
    // know which other Delta we should apply (in this case delta_f gets 0,
    // which should be okayish):
      {
        gamma_foreign = gamma/p_self;
      }
    // It can happen that broad_spec_vmr_sum==0 AND p_self==0 (e.g., when p_grid
    // exceeds the given atmosphere and zero-padding is applied). In this case,
    // both gamma_foreign and deltaf are 0 and we leave it like that.
 
    // Multiply by pressure. For the width we take only the foreign pressure.
    // This is consistent with that we have scaled with the sum of all foreign
    // broadening VMRs. In this way we make sure that the total foreign broadening
    // scales with the total foreign pressure.
    gamma_foreign  *= p_foreign;
    // For the shift we simply take the total pressure, since there is no self part.
    deltaf *= p;
 
    // For the width, add foreign parts:
    gamma += gamma_foreign;
    
    // That's it, we're done.
}
 
void xsec_species( MatrixView               xsec_attenuation,
                   MatrixView               xsec_phase,
                   ConstVectorView          f_grid,
                   ConstVectorView          abs_p,
                   ConstVectorView          abs_t,
                   ConstMatrixView          all_vmrs,
                   const ArrayOfArrayOfSpeciesTag& abs_species,
                   const Index              this_species,
                   const ArrayOfLineRecord& abs_lines,
                   const Index              ind_ls,
                   const Index              ind_lsn,
                   const Numeric            cutoff,
                   const SpeciesAuxData&    isotopologue_ratios,
                   const Verbosity&         verbosity )
{
  // Make lineshape and species lookup data visible:
  using global_data::lineshape_data;
  using global_data::lineshape_norm_data;
 
  // speed of light constant
  extern const Numeric SPEED_OF_LIGHT;
 
  // Boltzmann constant
  extern const Numeric BOLTZMAN_CONST;
 
  // Avogadros constant
  extern const Numeric AVOGADROS_NUMB;
 
  // Planck constant
  extern const Numeric PLANCK_CONST;
 
  // sqrt(ln(2))
  // extern const Numeric SQRT_NAT_LOG_2;
 
  // Constant within the Doppler Broadening calculation:
  const Numeric doppler_const = sqrt( 2.0 * BOLTZMAN_CONST *
                                      AVOGADROS_NUMB) / SPEED_OF_LIGHT; 
 
  // dimension of f_grid, abs_lines
  const Index nf = f_grid.nelem();
  const Index nl = abs_lines.nelem();
 
  // number of pressure levels:
  const Index np = abs_p.nelem();
 
  // Define the vector for the line shape function and the
  // normalization factor of the lineshape here, so that we don't need
  // so many free store allocations.  the last element is used to
  // calculate the value at the cutoff frequency
  Vector ls_attenuation(nf+1);
  Vector ls_phase(nf+1);
  Vector fac(nf+1);
 
  const bool cut = (cutoff != -1) ? true : false;
 
  const bool calc_phase = lineshape_data[ind_ls].Phase();
 
  // Check that the frequency grid is sorted in the case of lineshape
  // with cutoff. Duplicate frequency values are allowed.
  if (cut)
    {
      if ( ! is_sorted( f_grid ) )
        {
          ostringstream os;
          os << "If you use a lineshape function with cutoff, your\n"
             << "frequency grid *f_grid* must be sorted.\n"
             << "(Duplicate values are allowed.)";
          throw runtime_error(os.str());
        }
    }
  
  // Check that all temperatures are non-negative
  bool negative = false;
  
  for (Index i = 0; !negative && i < abs_t.nelem (); i++)
    {
      if (abs_t[i] < 0.)
        negative = true;
    }
  
  if (negative)
    {
      ostringstream os;
      os << "abs_t contains at least one negative temperature value.\n"
         << "This is not allowed.";
      throw runtime_error(os.str());
    }
  
  // We need a local copy of f_grid which is 1 element longer, because
  // we append a possible cutoff to it.
  // The initialization of this has to be inside the line loop!
  Vector f_local( nf + 1 );
 
  // Voigt generally needs a different frequency grid. If we allocate
  // that in the outer loop, instead of in voigt, we don't have the
  // free store allocation at each lineshape call. Calculation is
  // still done in the voigt routine itself, this is just an auxillary
  // parameter, passed to lineshape. For selected lineshapes (e.g.,
  // Rosenkranz) it is used additionally to pass parameters needed in
  // the lineshape (e.g., overlap, ...). Consequently we have to
  // assure that aux has a dimension not less then the number of
  // parameters passed.
  Index ii = (nf+1 < 10) ? 10 : nf+1;
  Vector aux(ii);
 
  // Check that abs_p, abs_t, and abs_vmrs have consistent
  // dimensions. This could be a user error, so we throw a
  // runtime_error. 
 
  if ( abs_t.nelem() != np )
    {
      ostringstream os;
      os << "Variable abs_t must have the same dimension as abs_p.\n"
         << "abs_t.nelem() = " << abs_t.nelem() << '\n'
         << "abs_p.nelem() = " << np;
      throw runtime_error(os.str());
    }
 
  // all_vmrs should have dimensions [nspecies, np]:
  
  if ( all_vmrs.ncols() != np )
    {
      ostringstream os;
      os << "Number of columns of all_vmrs must match abs_p.\n"
         << "all_vmrs.ncols() = " << all_vmrs.ncols() << '\n'
         << "abs_p.nelem() = " << np;
      throw runtime_error(os.str());
    }
 
  const Index nspecies = abs_species.nelem();
  
  if ( all_vmrs.nrows() != nspecies)
  {
    ostringstream os;
    os << "Number of rows of all_vmrs must match abs_species.\n"
    << "all_vmrs.nrows() = " << all_vmrs.nrows() << '\n'
    << "abs_species.nelem() = " << nspecies;
    throw runtime_error(os.str());
  }
 
  // With abs_h2o it is different. We do not really need this in most
  // cases, only the Rosenkranz lineshape for oxygen uses it. There is
  // a global (scalar) default value of -1, that we are expanding to a
  // vector here if we find it. The Rosenkranz lineshape does a check
  // to make sure that the value is actually set, and not the default
  // value. 
//  Vector abs_h2o(np);
//  if ( abs_h2o_orig.nelem() == np )
//    {
//      abs_h2o = abs_h2o_orig;
//    }
//  else
//    {
//      if ( ( 1   == abs_h2o_orig.nelem()) && 
//           ( -.99 > abs_h2o_orig[0]) )
//        {
//          // We have found the global default value. Expand this to a
//          // vector with the right length, by copying -1 to all
//          // elements of abs_h2o.
//          abs_h2o = -1;         
//        }
//      else
//        {
//          ostringstream os;
//          os << "Variable abs_h2o must have default value -1 or the\n"
//             << "same dimension as abs_p.\n"
//             << "abs_h2o.nelem() = " << abs_h2o.nelem() << '\n'
//             << "abs_p.nelem() = " << np;
//          throw runtime_error(os.str());
//        }
//    }
 
  // Check that the dimension of xsec is indeed [f_grid.nelem(),
  // abs_p.nelem()]:
  if ( xsec_attenuation.nrows() != nf || xsec_attenuation.ncols() != np )
    {
      ostringstream os;
      os << "Variable xsec must have dimensions [f_grid.nelem(),abs_p.nelem()].\n"
         << "[xsec_attenuation.nrows(),xsec_attenuation.ncols()] = [" << xsec_attenuation.nrows()
         << ", " << xsec_attenuation.ncols() << "]\n"
         << "f_grid.nelem() = " << nf << '\n'
         << "abs_p.nelem() = " << np;
      throw runtime_error(os.str());
    }
   if ( xsec_phase.nrows() != nf || xsec_phase.ncols() != np )
    {
      ostringstream os;
      os << "Variable xsec must have dimensions [f_grid.nelem(),abs_p.nelem()].\n"
         << "[xsec_phase.nrows(),xsec_phase.ncols()] = [" << xsec_phase.nrows()
         << ", " << xsec_phase.ncols() << "]\n"
         << "f_grid.nelem() = " << nf << '\n'
         << "abs_p.nelem() = " << np;
      throw runtime_error(os.str());
    } 
  
  // Find the location of all broadening species in abs_species. Set to -1 if
  // not found. The length of array broad_spec_locations is the number of allowed
  // broadening species (in ARTSCAT-4 Self, N2, O2, H2O, CO2, H2, He). The value
  // means:
  // -1 = not in abs_species
  // -2 = in abs_species, but should be ignored because it is identical to Self
  // N  = species is number N in abs_species
  ArrayOfIndex broad_spec_locations;
  find_broad_spec_locations(broad_spec_locations,
                            abs_species,
                            this_species);
 
  String fail_msg;
  bool failed = false;
 
  // Loop all pressures:
  if (np)
#pragma omp parallel for                    \
  if (!arts_omp_in_parallel()               \
      && np >= arts_omp_get_max_threads())  \
  firstprivate(ls_attenuation, ls_phase, fac, f_local, aux)
  for ( Index i=0; i<np; ++i )
    {
      if (failed) continue;
 
      // Store input profile variables, this is perhaps slightly faster.
      const Numeric p_i       = abs_p[i];
      const Numeric t_i       = abs_t[i];
      const Numeric vmr_i     = all_vmrs(this_species,i);
    
      //out3 << "  p = " << p_i << " Pa\n";
 
      // Calculate total number density from pressure and temperature.
      // n = n0*T0/p0 * p/T or n = p/kB/t, ideal gas law
      //      const Numeric n = p_i / BOLTZMAN_CONST / t_i;
      // This is not needed anymore, since we now calculate true cross
      // sections, which do not contain the n.
 
      // For the pressure broadening, we also need the partial pressure:
      const Numeric p_partial = p_i * vmr_i;
 
      // Get handle on xsec for this pressure level i.
      // Watch out! This is output, we have to be careful not to
      // introduce race conditions when writing to it.
      VectorView xsec_i_attenuation = xsec_attenuation(Range(joker),i);
      VectorView xsec_i_phase = xsec_phase(Range(joker),i);
 
      
//       if (omp_in_parallel())
//         cout << "omp_in_parallel: true\n";
//       else
//         cout << "omp_in_parallel: false\n";
 
 
      // Prepare a variable that can be used by the individual LBL
      // threads to add up absorption:
      Index n_lbl_threads;
      if (arts_omp_in_parallel())
        {
          // If we already are running parallel, then the LBL loop
          // will not be parallelized.
          n_lbl_threads = 1;
        }
      else
        {
          n_lbl_threads = arts_omp_get_max_threads();
        }
      Matrix xsec_accum_attenuation(n_lbl_threads, xsec_i_attenuation.nelem(), 0);
      Matrix xsec_accum_phase(n_lbl_threads, xsec_i_phase.nelem(), 0);
 
 
      // Loop all lines:
      if (nl)
#pragma omp parallel for                   \
  if (!arts_omp_in_parallel()               \
      && nl >= arts_omp_get_max_threads())  \
  firstprivate(ls_attenuation, ls_phase, fac, f_local, aux)
      for ( Index l=0; l< nl; ++l )
        {
          // Skip remaining iterations if an error occurred
          if (failed) continue;
 
//           if (omp_in_parallel())
//             cout << "LBL: omp_in_parallel: true\n";
//           else
//             cout << "LBL: omp_in_parallel: false\n";
 
 
          // The try block here is necessary to correctly handle
          // exceptions inside the parallel region. 
          try
            {
              // Copy f_grid to the beginning of f_local. There is one
              // element left at the end of f_local.  
              // THIS HAS TO BE INSIDE THE LINE LOOP, BECAUSE THE CUTOFF
              // FREQUENCY IS ALWAYS PUT IN A DIFFERENT PLACE!
              f_local[Range(0,nf)] = f_grid;
 
              // This will hold the actual number of frequencies to add to
              // xsec later on:
              Index nfl = nf;
 
              // This will hold the actual number of frequencies for the
              // call to the lineshape functions later on:
              Index nfls = nf;      
 
              // abs_lines[l] is used several times, this construct should be
              // faster (Oliver Lemke)
              const LineRecord& l_l = abs_lines[l];  // which line are we dealing with
              
              // Make sure that catalogue version is either 3 or 4 (no other
              // versions are supported yet):
              if ( 3!=l_l.Version() && 4!=l_l.Version() )
              {
                ostringstream os;
                os << "Unknown spectral line catalogue version (artscat-"
                << l_l.Version() << ").\n"
                << "Allowed are artscat-3 and artscat-4.";
                throw runtime_error(os.str());
              }
              
              // Center frequency in vacuum:
              Numeric F0 = l_l.F();
 
              // Intensity is already in the right units (Hz*m^2). It also
              // includes already the isotopologue ratio. Needs only to be
              // coverted to the actual temperature and multiplied by total
              // number density and lineshape.
              Numeric intensity = l_l.I0();
 
              // Lower state energy is already in the right unit (Joule).
              Numeric e_lower = l_l.Elow();
 
              // Upper state energy:
              Numeric e_upper = e_lower + F0 * PLANCK_CONST;
 
              // Get the ratio of the partition function.
              // This will throw a runtime error if no data exists.
              // Important: This function needs both the reference
              // temperature and the actual temperature, because the
              // reference temperature can be different for each line,
              // even of the same species.
              Numeric part_fct_ratio =
                l_l.IsotopologueData().CalculatePartitionFctRatio( l_l.Ti0(),
                                                              t_i );
 
              // Boltzmann factors
              Numeric nom = exp(- e_lower / ( BOLTZMAN_CONST * t_i ) ) - 
                exp(- e_upper / ( BOLTZMAN_CONST * t_i ) );
 
              Numeric denom = exp(- e_lower / ( BOLTZMAN_CONST * l_l.Ti0() ) ) - 
                exp(- e_upper / ( BOLTZMAN_CONST * l_l.Ti0() ) );
 
 
              // intensity at temperature
              // (calculate the line intensity according to the standard 
              // expression given in HITRAN)
              intensity *= part_fct_ratio * nom / denom;
 
              if (lineshape_norm_data[ind_lsn].Name() == "quadratic")
                {
                  // in case of the quadratic normalization factor use the 
                  // so called 'microwave approximation' of the line intensity 
                  // given by 
                  // P. W. Rosenkranz, Chapter 2, Eq.(2.16), in M. A. Janssen, 
                  // Atmospheric Remote Sensing by Microwave Radiometry, 
                  // John Wiley & Sons, Inc., 1993
                  Numeric mafac = (PLANCK_CONST * F0) / (2.000e0 * BOLTZMAN_CONST
                                                         * t_i);
                  intensity     = intensity * mafac / sinh(mafac);
                }
 
              // 2. Calculate the pressure broadened line width and the pressure
              // shifted center frequency.
              //
              // Here there is a difference betweeen catalogue version 4
              // (from ESA planetary study) and earlier catalogue versions.
              Numeric gamma;     // The line width.
              Numeric deltaf;    // Pressure shift.
              if (l_l.Version() == 4)
                {
                  calc_gamma_and_deltaf_artscat4(gamma,
                                                 deltaf,
                                                 p_i,
                                                 t_i,
                                                 all_vmrs(joker,i),
                                                 this_species,
                                                 broad_spec_locations,
                                                 l_l,
                                                 verbosity);
                }
              else if (l_l.Version() == 3)
                {
                  //                  Numeric Tgam;
                  //                  Numeric Nair;
                  //                  Numeric Agam;
                  //                  Numeric Sgam;
                  //                  Numeric Nself;
                  //                  Numeric Psf;
                  
                  //              if (l_l.Version() == 3)
                  //              {
                  const Numeric Tgam = l_l.Tgam();
                  const Numeric Agam = l_l.Agam();
                  const Numeric Nair = l_l.Nair();
                  const Numeric Sgam = l_l.Sgam();
                  const Numeric Nself = l_l.Nself();
                  const Numeric Psf = l_l.Psf();
                  //              }
                  //              else
                  //              {
                  //                static bool warn = false;
                  //                if (!warn)
                  //                {
                  //                  CREATE_OUT0;
                  //                  warn = true;
                  //                  out0 << "  WARNING: Using artscat version 4 for calculations is currently\n"
                  //                       << "           just a hack and results are most likely wrong!!!\n";
                  //                }
                  //                Tgam = l_l.Tgam();
                  //                // Use hardcoded mixing ratios for air
                  //                Agam = l_l.Gamma_N2() * 0.79 + l_l.Gamma_O2() * 0.21;
                  //                Nair = l_l.Gam_N_N2() * 0.79 + l_l.Gam_N_O2() * 0.21;
                  //                Sgam = l_l.Gamma_self();
                  //                Nself = l_l.Gam_N_self();
                  //                Psf = l_l.Delta_N2() * 0.79 + l_l.Delta_O2() * 0.21;
                  //              }
                  
                  // Get pressure broadened line width:
                  // (Agam is in Hz/Pa, abs_p is in Pa, gamma is in Hz)
                  const Numeric theta = Tgam / t_i;
                  const Numeric theta_Nair = pow(theta, Nair);
                  
                  gamma =   Agam * theta_Nair  * (p_i - p_partial)
                  + Sgam * pow(theta, Nself) * p_partial;
                  
                  
                  // Pressure shift:
                  // The T dependence is connected to that of agam by:
                  // n_shift = .25 + 1.5 * n_agam
                  // Theta has been initialized above.
                  deltaf = Psf * p_i *
                  std::pow( theta , (Numeric).25 + (Numeric)1.5*Nair );
                  
                }
              else
                {
                  // There is a runtime error check for allowed artscat versions
                  // further up.
                  assert(false);
                }
              
              // Apply pressure shift:
              F0 += deltaf;
              
              // 3. Doppler broadening without the sqrt(ln(2)) factor, which
              // seems to be redundant.
              const Numeric sigma = F0 * doppler_const *
                sqrt( t_i / l_l.IsotopologueData().Mass());
 
//              cout << l_l.IsotopologueData().Name() << " " << l_l.F() << " "
//                   << Nair << " " << Agam << " " << Sgam << " " << Nself << endl;
 
              
 
              // Indices pointing at begin/end frequencies of f_grid or at
              // the elements that have to be calculated in case of cutoff
              Index i_f_min = 0;            
              Index i_f_max = nf-1;         
 
              // cutoff ?
              if ( cut )
                {
                  // Check whether we have elements in ls that can be
                  // ignored at lower frequencies of f_grid.
                  //
                  // Loop through all frequencies, finding min value and
                  // set all values to zero on that way.
                  while ( i_f_min < nf && (F0 - cutoff) > f_grid[i_f_min] )
                    {
                      //              ls[i_f_min] = 0;
                      ++i_f_min;
                    }
              
 
                  // Check whether we have elements in ls that can be
                  // ignored at higher frequencies of f_grid.
                  //
                  // Loop through all frequencies, finding max value and
                  // set all values to zero on that way.
                  while ( i_f_max >= 0 && (F0 + cutoff) < f_grid[i_f_max] )
                    {
                      //              ls[i_f_max] = 0;
                      --i_f_max;
                    }
              
                  // Append the cutoff frequency to f_local:
                  ++i_f_max;
                  f_local[i_f_max] = F0 + cutoff;
 
                  // Number of frequencies to calculate:
                  nfls = i_f_max - i_f_min + 1; // Add one because indices
                  // are pointing to first and
                  // last valid element. This
                  // is for the lineshape
                  // calls. 
                  nfl = nfls -1;              // This is for xsec.
                }
              else
                {
                  // Nothing to do here. Note that nfl and nfls are both still set to nf.
                }
 
              //          cout << "nf, nfl, nfls = " << nf << ", " << nfl << ", " << nfls << ".\n";
        
              // Maybe there are no frequencies left to compute?  Note that
              // the number that counts here is nfl, since only these are
              // the `real' frequencies, for which xsec is changed. nfls
              // will always be at least one, because it contains the cutoff.
              if ( nfl > 0 )
                {
                  //               cout << ls << endl
                  //                    << "aux / F0 / gamma / sigma" << aux << "/" << F0 << "/" << gamma << "/" << sigma << endl
                  //                    << f_local[Range(i_f_min,nfls)] << endl
                  //                    << nfls << endl;
 
                  // Calculate the line shape:
                  lineshape_data[ind_ls].Function()(ls_attenuation,ls_phase,
                                                    aux,F0,gamma,sigma,
                                                    f_local[Range(i_f_min,nfls)]);
 
                  // Calculate the chosen normalization factor:
                  lineshape_norm_data[ind_lsn].Function()(fac,F0,
                                                          f_local[Range(i_f_min,nfls)],
                                                          t_i);
 
                  // Get a handle on the range of xsec that we want to change.
                  // We use nfl here, which could be one less than nfls.
                  VectorView this_xsec_attenuation      = xsec_accum_attenuation(arts_omp_get_thread_num(), Range(i_f_min,nfl));
                  VectorView this_xsec_phase            = xsec_accum_phase(arts_omp_get_thread_num(), Range(i_f_min,nfl));
 
                  // Get handles on the range of ls and fac that we need.
                  VectorView this_ls_attenuation  = ls_attenuation[Range(0,nfl)];
                  VectorView this_ls_phase  = ls_phase[Range(0,nfl)];
                  VectorView this_fac = fac[Range(0,nfl)];
 
                  // cutoff ?
                  if ( cut )
                    {
                      // Subtract baseline for cutoff frequency
                      // The index nfls-1 should be exactly the index pointing
                      // to the value at the cutoff frequency.
                      // Subtract baseline from xsec. 
                      // this_xsec -= base;
                      this_ls_attenuation -= ls_attenuation[nfls-1];
                      if (calc_phase) this_ls_phase -= ls_phase[nfls-1];
                    }
 
                  // Add line to xsec. 
                  {
                    // To make the loop a bit faster, precompute all constant
                    // factors. These are:
                    // 1. Total number density of the air. --> Not
                    //    anymore, we now to real cross-sections
                    // 2. Line intensity.
                    // 3. Isotopologue ratio.
                    //
                    // The isotopologue ratio must be applied here, since we are
                    // summing up lines belonging to different isotopologues.
 
                    //                const Numeric factors = n * intensity * l_l.IsotopologueData().Abundance();
//                    const Numeric factors = intensity * l_l.IsotopologueData().Abundance();
                      const Numeric factors = intensity
                          * isotopologue_ratios.getParam(l_l.Species(), l_l.Isotopologue(), 0);
 
                    // We have to do:
                    // xsec(j,i) += factors * ls[j] * fac[j];
                    //
                    // We use ls as a dummy to compute the product, then add it
                    // to this_xsec.
 
                    this_ls_attenuation *= this_fac;
                    this_ls_attenuation *= factors;
                    this_xsec_attenuation += this_ls_attenuation;
 
                    if (calc_phase)
                      {
                        this_ls_phase *= this_fac;
                        this_ls_phase *= factors;
                        this_xsec_phase += this_ls_phase;
                      }
                  }
                }
 
            } // end of try block
          catch (runtime_error e)
            {
#pragma omp critical (xsec_species_fail)
                { fail_msg = e.what(); failed = true; }
            }
 
        } // end of parallel LBL loop
 
      // Bail out if an error occurred in the LBL loop
      if (failed) continue;
 
      // Now we just have to add up all the rows of xsec_accum:
      for (Index j=0; j<xsec_accum_attenuation.nrows(); ++j)
        {
          xsec_i_attenuation += xsec_accum_attenuation(j, Range(joker));
        }
 
      if (calc_phase)
        for (Index j=0; j<xsec_accum_phase.nrows(); ++j)
          {
            xsec_i_phase += xsec_accum_phase(j, Range(joker));
          }
    } // end of parallel pressure loop
 
  if (failed) throw runtime_error("Run-time error in function: xsec_species\n" + fail_msg);
 
}
 
 
 
 
 
Numeric wavenumber_to_joule(Numeric e)
{
  // Planck constant [Js]
  extern const Numeric PLANCK_CONST;
 
  // Speed of light [m/s]
  extern const Numeric SPEED_OF_LIGHT;
 
  // Constant to convert lower state energy from cm^-1 to J
  const Numeric lower_energy_const = PLANCK_CONST * SPEED_OF_LIGHT * 1E2;
 
  return e*lower_energy_const; 
}
 
 
//======================================================================
//             Functions related to species
//======================================================================
 
 
Index species_index_from_species_name( String name )
{
  // For the return value:
  Index mspecies;
 
  // Trim whitespace
  name.trim();
 
  //  cout << "name / def = " << name << " / " << def << endl;
 
  // Look for species name in species map:
  map<String, Index>::const_iterator mi = SpeciesMap.find(name);
  if ( mi != SpeciesMap.end() )
    {
      // Ok, we've found the species. Set mspecies.
      mspecies = mi->second;
    }
  else
    {
      // The species does not exist!
      mspecies = -1;
    }
 
  return mspecies;
}
 
 
 
String species_name_from_species_index( const Index spec_ind )
{
    // Species lookup data:
    using global_data::species_data;
 
    // Assert that spec_ind is inside species data. (This is an assertion,
    // because species indices should never be user input, but set by the
    // program automatically, based on species names.)
    assert( spec_ind>=0 );
    assert( spec_ind<species_data.nelem() );
    
    // A reference to the relevant record of the species data:
    const  SpeciesRecord& spr = species_data[spec_ind];
    
    return spr.Name();
}
 
 
//======================================================================
//        Functions to convert the accuracy index to ARTS units
//======================================================================
 
// ********* for HITRAN database *************
//convert HITRAN index for line position accuracy to ARTS
//units (Hz).
 
void convHitranIERF(     
                    Numeric&     mdf,
              const Index&       df 
                    )
{
  switch ( df )
    {
    case 0:
      { 
        mdf = -1;
        break; 
      }
    case 1:
      {
        mdf = 30*1E9;
        break; 
      }
    case 2:
      {
        mdf = 3*1E9;
        break; 
      }
    case 3:
      {
        mdf = 300*1E6;
        break; 
      }
    case 4:
      {
        mdf = 30*1E6;
        break; 
      }
    case 5:
      {
        mdf = 3*1E6;
        break; 
      }
    case 6:
      {
        mdf = 0.3*1E6;
        break; 
      }
    }
}
                    
//convert HITRAN index for intensity and halfwidth accuracy to ARTS
//units (relative difference).
void convHitranIERSH(     
                    Numeric&     mdh,
              const Index&       dh 
                    )
{
  switch ( dh )
    {
    case 0:
      { 
        mdh = -1;
        break; 
      }
    case 1:
      {
        mdh = -1;
        break; 
      }
    case 2:
      {
        mdh = -1;
        break; 
      }
    case 3:
      {
        mdh = 30;
        break; 
      }
    case 4:
      {
        mdh = 20;
        break; 
      }
    case 5:
      {
        mdh = 10;
        break; 
      }
    case 6:
      {
        mdh =5;
        break; 
      }
    case 7:
      {
        mdh =2;
        break; 
      }
    case 8:
      {
        mdh =1;
        break; 
      }
    }
  mdh=mdh/100;              
}
 
// ********* for MYTRAN database ************* 
//convert MYTRAN index for intensity and halfwidth accuracy to ARTS
//units (relative difference).
void convMytranIER(     
                    Numeric&     mdh,
              const Index  &      dh 
                    )
{
  switch ( dh )
    {
    case 0:
      { 
        mdh = 200;
        break; 
      }
    case 1:
      {
        mdh = 100;
        break; 
      }
    case 2:
      {
        mdh = 50;
        break; 
      }
    case 3:
      {
        mdh = 30;
        break; 
      }
    case 4:
      {
        mdh = 20;
        break; 
      }
    case 5:
      {
        mdh = 10;
        break; 
      }
    case 6:
      {
        mdh =5;
        break; 
      }
    case 7:
      {
        mdh = 2;
        break; 
      }
    case 8:
      {
        mdh = 1;
        break; 
      }
    case 9:
      {
        mdh = 0.5;
        break; 
      }
    }
  mdh=mdh/100;              
}
 
ostream& operator<< (ostream &os, const LineshapeSpec& lsspec)
{
    os << "LineshapeSpec Index: " << lsspec.Ind_ls() << ", NormIndex: " << lsspec.Ind_lsn()
    << ", Cutoff: " << lsspec.Cutoff() << endl;
 
    return os;
}
 
 
void xsec_species_line_mixing_wrapper(  MatrixView               xsec_attenuation,
                                        MatrixView               xsec_phase,
                                        const ArrayOfArrayOfLineMixingRecord& line_mixing_data,
                                        const ArrayOfArrayOfIndex& line_mixing_data_lut,
                                        ConstVectorView          f_grid,
                                        ConstVectorView          abs_p,
                                        ConstVectorView          abs_t,
                                        ConstMatrixView          all_vmrs,
                                        const ArrayOfArrayOfSpeciesTag& abs_species,
                                        const Index              this_species,
                                        const ArrayOfLineRecord& abs_lines,
                                        const Index              ind_ls,
                                        const Index              ind_lsn,
                                        const Numeric            cutoff,
                                        const SpeciesAuxData&    isotopologue_ratios,
                                        const Verbosity&         verbosity )
{
    if(abs_species[this_species][0].LineMixingType() == SpeciesTag::LINE_MIXING_TYPE_NONE) // If no linemixing data exists
        xsec_species(xsec_attenuation, xsec_phase, f_grid, abs_p, abs_t, all_vmrs,
                     abs_species, this_species, abs_lines, ind_ls, ind_lsn, cutoff,
                     isotopologue_ratios, verbosity);
        else // If linemixing data exists
    {
        switch(abs_species[this_species][0].LineMixingType())
        {
            case SpeciesTag::LINE_MIXING_TYPE_2NDORDER:
                xsec_species_line_mixing_2nd_order(xsec_attenuation, xsec_phase, line_mixing_data, 
                                                   line_mixing_data_lut, f_grid, abs_p, abs_t, all_vmrs,
                                                   abs_species, this_species, abs_lines, ind_ls, ind_lsn, 
                                                   cutoff, isotopologue_ratios, verbosity);
                break;
                //             default:
                //                 //ERROR
        }
    }
    
}
 
 
void xsec_species_line_mixing_2nd_order(MatrixView               xsec_attenuation,
                                        MatrixView               xsec_phase,
                                        const ArrayOfArrayOfLineMixingRecord& line_mixing_data,
                                        const ArrayOfArrayOfIndex& line_mixing_data_lut,
                                        ConstVectorView          f_grid,
                                        ConstVectorView          abs_p,
                                        ConstVectorView          abs_t,
                                        ConstMatrixView          all_vmrs,
                                        const ArrayOfArrayOfSpeciesTag& abs_species,
                                        const Index              this_species,
                                        const ArrayOfLineRecord& abs_lines,
                                        const Index              ind_ls,
                                        const Index              ind_lsn,
                                        const Numeric            cutoff,
                                        const SpeciesAuxData&    isotopologue_ratios,
                                        const Verbosity&         verbosity )
{
    // Must have the phase
    using global_data::lineshape_data;
    if (! lineshape_data[ind_ls].Phase())
    {
        ostringstream os;
        os <<  "This is an error message. You are using " << lineshape_data[ind_ls].Name() <<
        ".\n"<<"This line shape does not include phase in its calculations and\nis therefore invalid for " <<
        "second order line mixing.\n\n";
        throw runtime_error(os.str());
    }
    const ArrayOfLineMixingRecord& data = line_mixing_data[this_species];
    const ArrayOfIndex&  lut  = line_mixing_data_lut[this_species];
    
    // Helper variables
    Matrix attenuation(f_grid.nelem(),1), phase(f_grid.nelem(),1);
    
    //Since we need to be able to modify the line.
    ArrayOfLineRecord ll;
    ll.resize(1);
    // Variable containing modifying elements
    Vector a(2);
    
    for(Index jj=0;jj<abs_p.nelem(); jj++)
    {
        const Numeric p = abs_p[jj], t = abs_t[jj];
        
        for(Index ii = 0; ii < lut.nelem(); ii++)
        {
            // Since we need cross section per line to do the mixing.
            ll[0] = abs_lines[ii];//Possible speed-up by separating all non-split lines and doing those as a batch?
            
            // Since we need line mixing only for selected lines the rest should ignore by doing nothing.
            a=0;
            
            if(lut[ii]!=-1)
            {
                const Vector& dat = data[lut[ii]].Data();
                if( dat.nelem() != 10 )
                {
                    ostringstream os;
                    os <<  "This is an error message. You have not defined the linemixing data vector " << 
                    "properly. It should be of length 10, yet your version is of length: " << dat.nelem() << ".\n" << 
                    "The structure of the line mixing data Vector should be as follows:\n" << 
                    "data[0] is the first order zeroth phase correction\n" << 
                    "data[1] is the first order first phase correction\n" << 
                    "data[2] is the second order zeroth phase correction\n" << 
                    "data[3] is the second order first phase correction \n" << 
                    "data[4] is the second order zeroth frequency correction\n" << 
                    "data[5] is the second order first frequency correction \n" << 
                    "data[6] is the reference temperature\n" << 
                    "data[7] is the first order phase correction temperature dependence exponent\n" << 
                    "data[8] is the second order attenuation correction temperature dependence exponent\n" << 
                    "data[9] is the second order frequency correction temperature dependence exponent";
                    throw std::runtime_error(os.str());
                }
                
                // First order phase correction
                a[0] =              p 
                * ( ( dat[0] + dat[1] * ( dat[6]/t-1. ) ) 
                * pow( dat[6]/t, dat[7] ) );
                
                // Second order attenuation correction
                a[1] =      p * p 
                * ( ( dat[2] + dat[3] * ( dat[6]/t-1. ) ) 
                * pow( dat[6]/t, dat[8] ) );
                
                // Second order line-center correction
                ll[0].setF( p * p 
                * ( ( dat[4] +  dat[5] * ( dat[6]/t-1. ) ) 
                * pow( dat[6]/t, dat[9] ) ) + ll[0].F());
            }
            
            attenuation=0;
            phase=0;
            
            Vector P(1,p),T(1,t);
            Matrix V(all_vmrs.nrows(),1);V(joker,0)=all_vmrs(joker,jj);
            
            xsec_species(attenuation, phase, f_grid, P, T, V,
                        abs_species, this_species, ll, ind_ls, ind_lsn, cutoff,
                        isotopologue_ratios, verbosity);
            
            // Do the actual line mixing and add this to xsec_attenuation.
            xsec_phase(joker,jj) += phase(joker,0);
            phase *= a[0];
            xsec_attenuation(joker,jj) += phase(joker,0);       // First order phase correction
            xsec_attenuation(joker,jj) += attenuation(joker,0); // Zeroth order attenuation
            attenuation *= a[1];
            xsec_attenuation(joker,jj) += attenuation(joker,0); // Second order attenuation correction
            
        }
    }
}