gas_abs_lookup.cc

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/* Copyright (C) 2002-2008 Stefan Buehler <sbuehler@ltu.se>
 
   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 <cmath>
#include "gas_abs_lookup.h"
#include "interpolation.h"
#include "interpolation_poly.h"
#include "make_vector.h"
#include "logic.h"
#include "check_input.h"
#include "messages.h"
#include "physics_funcs.h"
 
 
void find_new_grid_in_old_grid( ArrayOfIndex& pos,
                                ConstVectorView old_grid,
                                ConstVectorView new_grid,
                                const Verbosity& verbosity )
{
  CREATE_OUT3
  
  const Index n_new_grid = new_grid.nelem();
  const Index n_old_grid = old_grid.nelem();
 
  // Make sure that pos has the right size:
  assert( n_new_grid == pos.nelem() );
 
  // The frequency difference in Hz that we are willing to tolerate. 1
  // Hz seems to be on the safe side.
  const Numeric tolerance = 1;
 
  // Old grid position:
  Index j = 0;
 
  // Loop the new frequencies:
  for ( Index i=0; i<n_new_grid; ++i )
    {
      // We have done runtime checks that both the new and the old
      // frequency gris are sorted in GasAbsLookup::Adapt, so we can
      // use the fact here.
 
      while ( abs(new_grid[i]-old_grid[j]) > tolerance )
        {
          ++j;
          if ( j>=n_old_grid )
            {
              ostringstream os;
              os << "Cannot find new frequency " << i
                 << " (" << new_grid[i] << "Hz) in the lookup table frequency grid.";
              throw runtime_error( os.str() );
            }
        }
 
      pos[i] = j;
      out3 << "    " << new_grid[i] << " found, index = " << pos[i] << ".\n";
    }
}
 
 
void GasAbsLookup::Adapt( const ArrayOfArrayOfSpeciesTag& current_species,
                          ConstVectorView current_f_grid,
                          const Verbosity& verbosity )
{
  CREATE_OUT2
  CREATE_OUT3
  
  // Some constants we will need:
  const Index n_current_species = current_species.nelem();
  const Index n_current_f_grid  = current_f_grid.nelem();
 
  const Index n_species         = species.nelem();
  const Index n_nls             = nonlinear_species.nelem();
  const Index n_nls_pert        = nls_pert.nelem();
  const Index n_f_grid          = f_grid.nelem();
  const Index n_p_grid          = p_grid.nelem();
  
  out2 << "  Original table: " << n_species << " species, "
       << n_f_grid << " frequencies.\n"
       << "  Adapt to:       " << n_current_species << " species, "
       << n_current_f_grid << " frequencies.\n";
 
  if ( 0 == n_nls )
    {
      out2 << "  Table contains no nonlinear species.\n";
    }
 
  // Set up a logical array for the nonlinear species
  ArrayOfIndex non_linear(n_species,0);
  for ( Index s=0; s<n_nls; ++s )
    {
      non_linear[nonlinear_species[s]] = 1;
    }
 
  if ( 0 == t_pert.nelem() )
    {
      out2 << "  Table contains no temperature perturbations.\n";
    }
 
  // We are constructing a new lookup table, containing just the
  // species and frequencies that are necessary for the current
  // calculation. We will build it in this local variable, then copy
  // it back to *this in the end.
  GasAbsLookup new_table;
 
  // First some checks on the lookup table itself:
 
  // Species:
  if ( 0 == n_species )
    {
      ostringstream os;
      os << "The lookup table should have at least one species.";
      throw runtime_error( os.str() );
    }
  
  // Nonlinear species:
  // They should be unique ...
  if ( !is_unique(nonlinear_species) )
    {
      ostringstream os;
      os << "The table must not have duplicate nonlinear species.\n"
         << "Value of *nonlinear_species*: " << nonlinear_species;
      throw runtime_error( os.str() );
    }
 
  // ... and pointing at valid species. 
  for ( Index i=0; i<n_nls; ++i )
    {
      ostringstream os;
      os << "nonlinear_species[" << i << "]";
      chk_if_in_range( os.str(),
                       nonlinear_species[i],
                       0,
                       n_species-1 );
    }
 
  // Frequency grid:
  chk_if_increasing( "f_grid", f_grid );
 
  // Pressure grid:
  chk_if_decreasing( "p_grid", p_grid );
 
  // Reference VMRs:
  chk_matrix_nrows( "vmrs_ref", vmrs_ref, n_species );
  chk_matrix_ncols( "vmrs_ref", vmrs_ref, n_p_grid );
 
  // Reference temperatur:
  chk_vector_length( "t_ref", t_ref, n_p_grid );
 
  // Temperature perturbations:
  // Nothing to check for t_pert, it seems.
 
  // Perturbations for nonlinear species:
  // Check that nls_pert is empty if and only if nonlinear_species is
  // empty:
  if ( 0 == n_nls )
    {
      chk_vector_length( "nls_pert", nls_pert, 0 );
    }
  else
    {
      if ( 0 == n_nls_pert )
        {
          ostringstream os;
          os << "The vector nls_pert should contain the perturbations\n"
             << "for the nonlinear species, but it is empty.";
          throw runtime_error( os.str() );
        }
    }
 
  // The table itself, xsec:
  //
  // We have to separtely consider the 3 cases described in the
  // documentation of GasAbsLookup.
  //
  //     Dimension: [ a, b, c, d ]
  //
  if ( 0==n_nls )
    {
      if ( 0==t_pert.nelem() )
        {
          //     Simplest case (no temperature perturbations,
          //     no vmr perturbations):
          //     a = 1
          //     b = n_species
          //     c = n_f_grid 
          //     d = n_p_grid
          chk_size( "xsec", xsec,
                    1,
                    n_species,
                    n_f_grid,
                    n_p_grid );
        }
      else
        {
          //     Standard case (temperature perturbations,
          //     but no vmr perturbations):
          //     a = n_t_pert
          //     b = n_species
          //     c = n_f_grid
          //     d = n_p_grid
          chk_size( "xsec", xsec,
                    t_pert.nelem(),
                    n_species,
                    n_f_grid,
                    n_p_grid );
        }
    }
  else
    {
      //     Full case (with temperature perturbations and
      //     vmr perturbations):
      //     a = n_t_pert
      //     b = n_species + n_nonlinear_species * ( n_nls_pert - 1 )
      //     c = n_f_grid
      //     d = n_p_grid
      Index a = t_pert.nelem();
      Index b = n_species
        + n_nls * ( n_nls_pert - 1 );
      Index c = n_f_grid;
      Index d = n_p_grid;
 
      chk_size( "xsec", xsec, a, b, c, d );
    }
 
  // We also need indices to the positions of the original species
  // data in xsec. Nonlinear species take more space, therefor the
  // position in xsec is not the same as the position in species.
  ArrayOfIndex original_spec_pos_in_xsec(n_species);
  for (Index i=0,sp=0; i<n_species; ++i)
    {
      original_spec_pos_in_xsec[i] = sp;
      if (non_linear[i]) sp += n_nls_pert;
      else               sp += 1;
    }
 
 
 
  // Now some checks on the input data:
 
  // The list of current species should not be empty:
  if ( 0==n_current_species )
    {
      ostringstream os;
      os << "The list of current species should not be empty.";
      throw runtime_error( os.str() );
    }
 
  // The grid of current frequencies should be monotonically sorted:
  chk_if_increasing( "current_f_grid", current_f_grid );
 
 
  // 1. Find and remember the indices of the current species in the
  //    lookup table. At the same time verify that each species is
  //    included in the table exactly once.
  ArrayOfIndex i_current_species(n_current_species);
  out3 << "  Looking for species in lookup table:\n";
  for ( Index i=0; i<n_current_species; ++i )
    {
      out3 << "  " << get_tag_group_name( current_species[i] ) << ": ";
      // We need no error checking for the next statement, since the
      // chk_contains function throws a runtime error if the species
      // is not found exactly once.
      i_current_species[i] =
        chk_contains( "species", species, current_species[i] );
      out3 << "found.\n";
    }
 
  // 1a. Find out which of the current species are nonlinear species:
  Index n_current_nonlinear_species = 0;        // Number of current nonlinear species
  ArrayOfIndex current_non_linear(n_current_species,0); // A logical array to
                                                        // flag which of the
                                                        // current species are
                                                        // nonlinear.
 
  out3 << "  Finding out which of the current species are nonlinear:\n";
  for ( Index i=0; i<n_current_species; ++i )
    {
      // Check if this is a nonlinear species:
      if (non_linear[i_current_species[i]])
        {
          out3 << "  " << get_tag_group_name( current_species[i] ) << "\n";
 
          current_non_linear[i] = 1;
          ++n_current_nonlinear_species;
        }
    }
 
  // 2. Find and remember the frequencies of the current calculation in
  //    the lookup table. At the same time verify that all frequencies are
  //    included and that no frequency occurs twice.
 
  // FIXME: This is a bit tricky, because we are comparing
  // Numerics. Let's see how well this works in practice.
 
  ArrayOfIndex i_current_f_grid(n_current_f_grid);
  out3 << "  Looking for Frequencies in lookup table:\n";
 
  // We need no error checking for the next statement, since the
  // function called throws a runtime error if a frequency
  // is not found, or if the grids are not ok.
  find_new_grid_in_old_grid( i_current_f_grid,
                             f_grid,
                             current_f_grid,
                             verbosity );
 
 
  // 3. Use the species and frequency index lists to build the new lookup
  // table.
 
  // Species:
  new_table.species.resize( n_current_species );
  for ( Index i=0; i<n_current_species; ++i )
    {
      new_table.species[i] = species[i_current_species[i]];
 
      // Is this a nonlinear species?
      if (current_non_linear[i])
        new_table.nonlinear_species.push_back( i );
    }
 
  // Frequency grid:
  new_table.f_grid.resize( n_current_f_grid );
  for ( Index i=0; i<n_current_f_grid; ++i )
    {
      new_table.f_grid[i] = f_grid[i_current_f_grid[i]];
    }
 
  // Pressure grid:
  //  new_table.p_grid.resize( n_p_grid ); 
  new_table.p_grid = p_grid;
 
  // Reference VMR profiles:
  new_table.vmrs_ref.resize( n_current_species,
                             n_p_grid     );
  for ( Index i=0; i<n_current_species; ++i )
    {
      new_table.vmrs_ref( i,
                          Range(joker) )
        = vmrs_ref( i_current_species[i],
                    Range(joker)          );
    }
 
  // Reference temperature profile:
  //  new_table.t_ref.resize( t_ref.nelem() );
  new_table.t_ref = t_ref;
 
  // Vector of temperature perturbations:
  //  new_table.t_pert.resize( t_pert.nelem() );
  new_table.t_pert = t_pert;
 
  // Vector of perturbations for the VMRs of the nonlinear species: 
  // (Should stay empty if we have no nonlinear species)
  if ( 0 != new_table.nonlinear_species.nelem() )
    {
      //      new_table.nls_pert.resize( n_nls_pert );
      new_table.nls_pert = nls_pert;
    }
 
  // Absorption coefficients:
  new_table.xsec.resize( xsec.nbooks(),
                         n_current_species+n_current_nonlinear_species*(n_nls_pert-1),
                         n_current_f_grid,
                         xsec.ncols()        );
 
  // We have to copy the right species and frequencies from the old to
  // the new table. Temperature perturbations and pressure grid remain
  // the same.
 
  // Do species:
  for ( Index i_s=0,sp=0; i_s<n_current_species; ++i_s )
    {
      // n_v is the number of VMR perturbations
      Index n_v;
      if (current_non_linear[i_s])
        n_v = n_nls_pert;
      else
        n_v = 1;
 
//      cout << "i_s / sp / n_v = " << i_s << " / " << sp << " / " << n_v << endl;
//      cout << "orig_pos = " << original_spec_pos_in_xsec[i_current_species[i_s]] << endl;
 
      // Do frequencies:
      for ( Index i_f=0; i_f<n_current_f_grid; ++i_f )
        {
          new_table.xsec( Range(joker),
                          Range(sp,n_v),
                          i_f,
                          Range(joker) )
            =
            xsec( Range(joker),
                  Range(original_spec_pos_in_xsec[i_current_species[i_s]],n_v),
                  i_current_f_grid[i_f],
                  Range(joker) );
 
//           cout << "result: " << xsec( Range(joker),
//                                       Range(original_spec_pos_in_xsec[i_current_species[i_s]],n_v),
//                                       i_current_f_grid[i_f],
//                                       Range(joker) ) << endl;
 
        }
 
      sp += n_v;
    }
 
 
  // 4. Replace original table by the new one.
  *this = new_table;
 
  // 5. Initialize log_p_grid.
  log_p_grid.resize( n_p_grid );
  transform( log_p_grid,
             log,
             p_grid );
}
 
 
void GasAbsLookup::Extract( Matrix&         sga,
                            const Index&    p_interp_order,
                            const Index&    t_interp_order,
                            const Index&    h2o_interp_order,
                            const Index&    f_index,
                            const Numeric&  p,
                            const Numeric&  T,
                            ConstVectorView abs_vmrs ) const
{
  // 1. Obtain some properties of the lookup table:
  
  // Number of gas species in the table:
  const Index n_species = species.nelem();
 
  // Number of nonlinear species:
  const Index n_nls = nonlinear_species.nelem();
 
  // Number of frequencies in the table:
  const Index n_f_grid = f_grid.nelem();
 
  // Number of pressure grid points in the table:
  const Index n_p_grid = p_grid.nelem();
 
  // Number of temperature perturbations:
  const Index n_t_pert = t_pert.nelem();
 
  // Number of nonlinear species perturbations:
  const Index n_nls_pert = nls_pert.nelem();
 
 
  // 2. First some checks on the lookup table itself:
 
  // Most checks here are asserts, because they check the internal
  // consistency of the lookup table. They should never fail if the
  // table has been created with ARTS.
 
  // If there are nonlinear species, then at least one species must be
  // H2O. We will use that to perturb in the case of nonlinear
  // species.
  Index h2o_index = -1;
  if (n_nls>0)
    {
      h2o_index = find_first_species_tg( species,
                                         species_index_from_species_name("H2O") );
 
      // This is a runtime error, even though it would be more logical
      // for it to be an assertion, since it is an internal check on
      // the table. The reason is that it is somewhat awkward to check
      // for this in other places.
      if ( h2o_index == -1 )
        {
          ostringstream os;
          os << "With nonlinear species, at least one species must be a H2O species.";
          throw runtime_error( os.str() );
        }
    }
 
  // Check that the dimension of vmrs_ref is consistent with species and p_grid:
  assert( is_size( vmrs_ref, n_species, n_p_grid) );
 
  // Check dimension of t_ref:
  assert( is_size( t_ref, n_p_grid) );
 
  // Check dimension of xsec:
  DEBUG_ONLY({
      Index a,b,c,d;
      if ( 0 == n_t_pert ) a = 1;
      else a = n_t_pert;
      b = n_species + n_nls * ( n_nls_pert - 1 );
      c = n_f_grid;
      d = n_p_grid;
//       cout << "xsec: "
//            << xsec.nbooks() << ", "
//            << xsec.npages() << ", "
//            << xsec.nrows() << ", "
//            << xsec.ncols() << "\n";
//       cout << "a b c d: "
//            << a << ", "
//            << b << ", "
//            << c << ", "
//            << d << "\n";
      assert( is_size( xsec, a, b, c, d ) );
    })
 
  // Make sure that log_p_grid is initialized:
  if (log_p_grid.nelem() != n_p_grid)
    {
      ostringstream os;
      os << "The lookup table internal variable log_p_grid is not initialized.\n"
         << "Use the abs_lookupAdapt method!";
      throw runtime_error( os.str() );
    }
 
  // Verify that we have enough pressure, temperature and humdity grid points
  // for the desired interpolation orders. This check is not only
  // table internal, since abs_nls_interp_order and abs_t_interp_order
  // are separate WSVs that could have been modified. Hence, these are
  // runtime errors.
 
  if ( (n_p_grid < p_interp_order+1) )
    {
      ostringstream os;
      os << "The number of pressure grid points in the table ("
         << n_p_grid << ") is not enough for the desired order of interpolation ("
         << p_interp_order << ").";
      throw runtime_error( os.str() );
    }
 
  if ( (n_nls_pert != 0) && (n_nls_pert < h2o_interp_order+1) )
    {
      ostringstream os;
      os << "The number of humidity perturbation grid points in the table ("
         << n_nls_pert << ") is not enough for the desired order of interpolation ("
         << h2o_interp_order << ").";
      throw runtime_error( os.str() );
    }
 
  if ( (n_t_pert != 0) && (n_t_pert < t_interp_order+1) )
    {
      ostringstream os;
      os << "The number of temperature perturbation grid points in the table ("
         << n_t_pert << ") is not enough for the desired order of interpolation ("
         << t_interp_order << ").";
      throw runtime_error( os.str() );
    }
 
 
  // 3. Checks on the input variables:
 
  // Assert that abs_vmrs has the right dimension:
  if ( !is_size( abs_vmrs, n_species ) )
    {
      ostringstream os;
      os << "Number of species in lookup table does not match number\n"
         << "of species for which you want to extract absorption.\n"
         << "Have you used abs_lookupAdapt?";
      throw runtime_error( os.str() );
    }
 
 
  // 4. Set up some things we will need later on: 
 
  // Set the start and extent for the frequency loop:
  Index f_start, f_extent;
  if ( f_index < 0 )
    {
      // This means we should extract for all frequencies.
 
      f_start  = 0;
      f_extent = n_f_grid;
    }
  else
    {
      // This means we should extract only for one frequency.
 
      // Check that f_index is inside f_grid:
      if ( f_index >= n_f_grid )
      {
        ostringstream os;
        os << "Problem with gas absorption lookup table.\n"
           << "Frequency index f_index is too high, you have " << f_index
           << ", the largest allowed value is " << n_f_grid-1 << ".";
        throw runtime_error( os.str() );
      }
      
      f_start  = f_index;
      f_extent = 1;
    }
  const Range f_range(f_start,f_extent);
 
 
  // Set up a logical array for the nonlinear species
  ArrayOfIndex non_linear(n_species,0);
  for ( Index s=0; s<n_nls; ++s )
    {
      non_linear[nonlinear_species[s]] = 1;
    }
 
 
  // Calculate the number density for the given pressure and
  // temperature: 
  // n = n0*T0/p0 * p/T or n = p/kB/t, ideal gas law
  const Numeric n = number_density( p, T );
 
  
  // 5. Determine pressure grid position and interpolation weights:
 
  // Check that p is inside the grid. (p_grid is sorted in decreasing order.)
  {
    const Numeric p_max = p_grid[0] + 0.5*(p_grid[0]-p_grid[1]); 
    const Numeric p_min = p_grid[n_p_grid-1] - 0.5*(p_grid[n_p_grid-2]-p_grid[n_p_grid-1]);
    if ( ( p > p_max ) ||
         ( p < p_min ) )
    {
      ostringstream os;
      os << "Problem with gas absorption lookup table.\n"
         << "Pressure p is outside the range covered by the lookup table.\n" 
         << "Your p value is " << p << " Pa.\n"
         << "The allowed range is " << p_min << " to " << p_max << ".\n"
         << "The pressure grid range in the table is " << p_grid[n_p_grid-1]
         << " to " << p_grid[0] << ".\n"
         << "We allow a bit of extrapolation, but NOT SO MUCH!";
      throw runtime_error( os.str() );
    }
  }
  
 
  // For sure, we need to store the pressure grid position. 
  // We do the interpolation in log(p). Test have shown that this
  // gives slightly better accuracy than interpolating in p directly. 
  ArrayOfGridPosPoly pgp(1);
  gridpos_poly( pgp,
                log_p_grid,
                log(p),
                p_interp_order );
 
  // Pressure interpolation weights:
  Vector pitw;
  pitw.resize(p_interp_order+1);
  interpweights(pitw,pgp[0]);
 
 
  // 6. We do the T and VMR interpolation for the pressure levels
  // that are used in the pressure interpolation. (How many depends on
  // p_interp_order.)  
  
  // To store the interpolated result for the p_interp_order+1
  // pressure levels:
  Tensor3 xsec_pre_interpolated;
  xsec_pre_interpolated.resize( p_interp_order+1, f_extent, n_species );
 
  for ( Index pi=0; pi<p_interp_order+1; ++pi )
    {
      // Index into p_grid:
      const Index this_p_grid_index = pgp[0].idx[pi];
 
      // Flag for temperature interpolation, if this is not 0 we want
      // to do T interpolation: 
      const Index do_T = n_t_pert;
 
      // Determine temperature grid position. This is only done if we
      // want temperature interpolation, but the variable tgp has to
      // be visible also outside for later use:
      ArrayOfGridPosPoly tgp(1);       // only a scalar
      if (do_T)
        {
            
          // Temperature in the atmosphere is altitude
          // dependent. When we do the interpolation for the pressure level
          // below and above our point, we should correct the target value of
          // the interpolation to the altitude (pressure) difference. This
          // ensures that there is for example no T interpolation if the
          // desired T is right on the reference profile curve.
          //
          // I explicitly compared this with the old option to calculate
          // the temperature offset relative to the temperature at
          // this level. The performance in both cases is very
          // similar. The reason, why I decided to keep this new
          // version, is that it avoids the problem of needing
          // oversized temperature perturbations if the pressure
          // grid is coarse.
          //
          // No! The above approach leads to problems when combined with
          // higher order pressure interpolation. The problem is that
          // the reference T and VMR profiles may be very
          // irregular. (For example the H2O profile often has a big
          // jump near the bottom.) That sometimes leads to negative
          // effective reference values when the reference profile is
          // interpolated. I therefore reverted back to the original
          // version of using the real temperature and humidity, not
          // the interpolated one.
 
          //          const Numeric effective_T_ref = interp(pitw,t_ref,pgp);
          const Numeric effective_T_ref = t_ref[this_p_grid_index];
 
          // Convert temperature to offset from t_ref:
          const Numeric T_offset = T - effective_T_ref;
 
          //          cout << "T_offset = " << T_offset << endl;
 
          // Check that temperature offset is inside the allowed range.
          {
            const Numeric t_min = t_pert[0] - 0.5*(t_pert[1]-t_pert[0]); 
            const Numeric t_max = t_pert[n_t_pert-1] + 0.5*(t_pert[n_t_pert-1]-t_pert[n_t_pert-2]);
            if ( ( T_offset > t_max ) ||
                 ( T_offset < t_min ) )
            {
              ostringstream os;
              os << "Problem with gas absorption lookup table.\n"
                 << "Temperature T is outside the range covered by the lookup table.\n" 
                 << "Your temperature was " << T
                 << " K at a pressure of " << p << " Pa.\n"
                 << "The temperature offset value is " << T_offset << ".\n"
                 << "The allowed range is " << t_min << " to " << t_max << ".\n"
                 << "The temperature perturbation grid range in the table is "
                 << t_pert[0] << " to " << t_pert[n_t_pert-1] << ".\n"
                 << "We allow a bit of extrapolation, but NOT SO MUCH!";
                throw runtime_error( os.str() );
            }
          }
 
          gridpos_poly( tgp, t_pert, T_offset, t_interp_order );
        }
 
      // Determine the H2O VMR grid position. We need to do this only
      // once, since the only species who's VMR is interpolated is
      // H2O. We do this only if there are nonlinear species, but the
      // variable has to be visible later.
      ArrayOfGridPosPoly vgp(1);       // only a scalar
      if (n_nls>0)
        {
          // Similar to the T case, we first interpolate the reference
          // VMR to the pressure of extraction, then compare with
          // the extraction VMR to determine the offset/fractional
          // difference for the VMR interpolation.
          //
          // No! The above approach leads to problems when combined with
          // higher order pressure interpolation. The problem is that
          // the reference T and VMR profiles may be very
          // irregular. (For example the H2O profile often has a big
          // jump near the bottom.) That sometimes leads to negative
          // effective reference values when the reference profile is
          // interpolated. I therefore reverted back to the original
          // version of using the real temperature and humidity, not
          // the interpolated one.
          
//           const Numeric effective_vmr_ref = interp(pitw,
//                                                    vmrs_ref(h2o_index, Range(joker)),
//                                                    pgp);
          const Numeric effective_vmr_ref = vmrs_ref(h2o_index, this_p_grid_index);
 
              
          // Fractional VMR:
          const Numeric VMR_frac = abs_vmrs[h2o_index] / effective_vmr_ref;
 
          // Check that VMR_frac is inside the allowed range.
          {
            // FIXME: This check depends on how I interpolate VMR.
            const Numeric x_min = nls_pert[0] - 0.5*(nls_pert[1]-nls_pert[0]); 
            const Numeric x_max = nls_pert[n_nls_pert-1]
              + 0.5*(nls_pert[n_nls_pert-1]-nls_pert[n_nls_pert-2]);
 
            if ( ( VMR_frac > x_max ) ||
                 ( VMR_frac < x_min ) )
              {
                ostringstream os;
                os << "Problem with gas absorption lookup table.\n"
                   << "VMR for H2O (species " << h2o_index
                   << ") is outside the range covered by the lookup table.\n" 
                   << "Your VMR was " << abs_vmrs[h2o_index]
                   << " at a pressure of " << p << " Pa.\n"
                   << "The reference VMR value there is " << effective_vmr_ref << "\n"
                   << "The fractional VMR relative to the reference value is "
                   << VMR_frac << ".\n"
                   << "The allowed range is " << x_min << " to " << x_max << ".\n"
                   << "The fractional VMR perturbation grid range in the table is "
                   << nls_pert[0] << " to " << nls_pert[n_nls_pert-1] << ".\n"
                   << "We allow a bit of extrapolation, but NOT SO MUCH!";
                throw runtime_error( os.str() );
              }
          }
 
          // For now, do linear interpolation in the fractional VMR.
          gridpos_poly( vgp, nls_pert, VMR_frac, h2o_interp_order );
        }
 
      // 7. Loop species:
      Index fpi=0;
      for ( Index si=0; si<n_species; ++si )
        {
          // Flag for VMR interpolation, if this is not 0 we want to
          // do VMR interpolation:
          const Index do_VMR = non_linear[si];
 
          // We now have everything that we need to handle all
          // different interpolation cases.
 
          // 8. Do the interpolation in T and/or VMR. Here are
          // handlers for 4 different cases (all possible
          // combinations). 
 
          // For interpolation result.
          // Fixed pressure level and species.
          // Free dimension is frequency.
          VectorView res(xsec_pre_interpolated(pi,Range(joker),si));
 
          if (do_T)
            if (do_VMR)
              {
                // With T and VMR
 
                // This is a "red" 2D interpolation case.
 
                Vector itw;
                itw.resize( (t_interp_order+1)*
                            (h2o_interp_order+1) );
                
                interpweights(itw,tgp[0],vgp[0]);
 
                // Get the right view on xsec:
                ConstTensor3View this_xsec
                  = xsec( Range(joker),          // Temperature range
                          Range(fpi,n_nls_pert), // VMR profile range
                          f_range,               // Frequency range
                          this_p_grid_index );   // Pressure index 
 
                // We must do the same interpolation for all
                // frequencies. Instead of playing with interp and
                // Views and looping the whole thing over frequency, I
                // choose to do this explicitly here, but directly for
                // all frequencies. This should be much more efficient.
 
                // Initialize result to zero:
                res = 0;
                Index iti = 0;
                for ( Index r=0; r<t_interp_order+1; ++r )
                  for ( Index c=0; c<h2o_interp_order+1; ++c )
                    {
                      for ( Index f=0; f<f_extent; ++f )
                        res[f] += itw[iti] * this_xsec( tgp[0].idx[r], vgp[0].idx[c], f );
                      
                      ++iti;
                    }
              }
            else
              {
                // With T no VMR
 
                // This is a "red" 1D interpolation case.
 
                Vector itw;
                itw.resize(t_interp_order+1);
                
                interpweights(itw,tgp[0]);
 
                // Get the right view on xsec:
                ConstMatrixView this_xsec
                  = xsec( Range(joker),          // Temperature range
                          fpi,                   // the matching species
                          f_range,               // Frequency range
                          this_p_grid_index );   // Pressure index 
 
                // We must do the same interpolation for all
                // frequencies. Instead of playing with interp and
                // Views and looping the whole thing over frequency, I
                // choose to do this explicitly here, but directly for
                // all frequencies. This should be much more efficient.
 
                // Initialize result to zero:
                res = 0;
                Index iti = 0;
                for ( Index r=0; r<t_interp_order+1; ++r )
                  {
                    for ( Index f=0; f<f_extent; ++f )
                      res[f] += itw[iti] * this_xsec( tgp[0].idx[r], f );
 
                    ++iti;
                  }
              }
          else
            if (do_VMR)
              {
                // No T with VMR
 
                // This is a "red" 1D interpolation case.
 
                Vector itw;
                itw.resize(h2o_interp_order+1);
                
                interpweights(itw,vgp[0]);
 
                // Get the right view on xsec:
                ConstMatrixView this_xsec
                  = xsec( 0,                     // no T variations
                          Range(fpi,n_nls_pert), // VMR profile range
                          f_range,               // Frequency range
                          this_p_grid_index );   // Pressure index 
 
                // We must do the same interpolation for all
                // frequencies. Instead of playing with interp and
                // Views and looping the whole thing over frequency, I
                // choose to do this explicitly here, but directly for
                // all frequencies. This should be much more efficient.
 
                // Initialize result to zero:
                res = 0;
                Index iti = 0;
                for ( Index c=0; c<h2o_interp_order+1; ++c )
                  {
                    for ( Index f=0; f<f_extent; ++f )                      
                      res[f] += itw[iti] * this_xsec( vgp[0].idx[c], f );             
                      
                    ++iti;
                  }
              }
            else
              {
                // No T no VMR
 
                // No need to interpolate anything here, actually.
                // We can copy all frequencies simultaneously, using
                // the range variable f_range.
                res = xsec(0,fpi,f_range,this_p_grid_index);
              }
 
          // Increase fpi. fpi marks the position of the first profile
          // of the current species in xsec. This is needed to find
          // the right subsection of xsec in the presence of nonlinear species.
          if (do_VMR)
            fpi += n_nls_pert;
          else
            fpi++;
 
        } // End of species loop 
 
      // fpi should have reached the end of that dimension of xsec. Check
      // this with an assertion:
      assert( fpi==xsec.npages() );
 
    } // End of pressure index loop (below and above gp)
 
  // Now we have to interpolate between the p_interp_order+1 pressure levels
 
  // It is a "red" 1D interpolation case we are talking about here.
  // (But for a matrix in frequency and species.) Doing a loop over
  // frequency and species with an interp call inside would be
  // unefficient, so we do this by hand here.
  sga.resize(f_extent, n_species);
  sga = 0;
  for ( Index pi=0; pi<p_interp_order+1; ++pi )
    {
      // Multiply pre interpolated quantities with pressure interpolation weights:
      xsec_pre_interpolated(pi,Range(joker),Range(joker)) *= pitw[pi];
 
      // Add up in sga:
      sga += xsec_pre_interpolated(pi,Range(joker),Range(joker));
    }
 
  // Watch out, this is not yet the final result, we
  // need to multiply with the number density of the species, i.e.,
  // with the total number density n, times the VMR of the
  // species: 
  for ( Index si=0; si<n_species; ++si )
    sga(Range(joker),si) *= ( n * abs_vmrs[si] );
 
  // That's it, we're done!
}
 
 
const Vector&  GasAbsLookup::GetFgrid() const
{
  return f_grid;
}
 
 
const Vector&  GasAbsLookup::GetPgrid() const
{
  return p_grid;
}
 
 
ostream& operator<< (ostream& os, const GasAbsLookup& /* gal */)
{
  os << "GasAbsLookup: Output operator not implemented";
  return os;
}