gas_abs_lookup.cc

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/* Copyright (C) 2002-2012 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 "gas_abs_lookup.h"
#include <cfloat>
#include <cmath>
#include "check_input.h"
#include "interpolation.h"
#include "logic.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:
  ARTS_ASSERT(n_new_grid == pos.nelem());
 
  // 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 grids are sorted in GasAbsLookup::Adapt, so we can
    // use the fact here.
 
    while (abs(new_grid[i] - old_grid[j]) >
           max(abs(new_grid[i]), abs(old_grid[j])) * DBL_EPSILON) {
      ++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 << "  " << current_species[i].Name() << ": ";
 
    try {
      i_current_species[i] =
          chk_contains("abs_species", species, current_species[i]);
 
    } catch (const runtime_error_not_found&) {
      // Is this one of the trivial species?
      const auto spec_type = current_species[i].Type();
      if (spec_type == Species::TagType::Zeeman ||
          spec_type == Species::TagType::FreeElectrons ||
          spec_type == Species::TagType::Particles) {
        // Set to -1 to flag that this needs special handling later on.
        i_current_species[i] = -1;
      } else {
        ostringstream os;
        os << "Species " << current_species[i].Name()
           << " is missing in absorption lookup table.";
        throw runtime_error(os.str());
      }
    }
 
    out3 << "found (or trivial).\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) {
    if (i_current_species[i] >= 0)  // Jump over trivial species here.
    {
      // Check if this is a nonlinear species:
      if (non_linear[i_current_species[i]]) {
        out3 << "  " << 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) {
    if (i_current_species[i] >= 0) {
      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);
    } else {
      // Here we handle the case of the trivial species, for which we simply
      // copy the name:
 
      new_table.species[i] = current_species[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) {
    if (i_current_species[i] >= 0) {
      new_table.vmrs_ref(i, Range(joker)) =
          vmrs_ref(i_current_species[i], Range(joker));
    } else {
      // Here we handle the case of the trivial species, for which we set
      // the reference VMR to NAN.
      new_table.vmrs_ref(i, Range(joker)) = NAN;
    }
  }
 
  // 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) {
      if (i_current_species[i_s] >= 0) {
        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));
      } else {
        // Here we handle the case of the trivial species, which we simply
        // set to NAN:
        new_table.xsec(Range(joker), Range(sp, n_v), i_f, Range(joker)) = NAN;
      }
 
      //           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);
 
  // 6. Initialize flag_default.
  flag_default = Interpolation::LagrangeVector(f_grid, f_grid, 0);
}
 
 
void GasAbsLookup::Extract(Matrix& sga,
                           const ArrayOfSpeciesTag& select_abs_species,
                           const Index& p_interp_order,
                           const Index& t_interp_order,
                           const Index& h2o_interp_order,
                           const Index& f_interp_order,
                           const Numeric& p,
                           const Numeric& T,
                           ConstVectorView abs_vmrs,
                           ConstVectorView new_f_grid,
                           const Numeric& extpolfac) 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();
 
  // Number of frequencies in new_f_grid, the frequency grid for which we
  // want to extract.
  const Index n_new_f_grid = new_f_grid.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(species, Species::Species::Water);
 
    // 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:
  ARTS_ASSERT(is_size(vmrs_ref, n_species, n_p_grid));
 
  // Check dimension of t_ref:
  ARTS_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";
    ARTS_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,humdity, and frequency 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());
  }
 
  if ((n_f_grid < f_interp_order + 1)) {
    ostringstream os;
    os << "The number of frequency grid points in the table (" << n_f_grid
       << ") is not enough for the desired order of interpolation ("
       << f_interp_order << ").";
    throw runtime_error(os.str());
  }
 
  // 3. Checks on the input variables:
 
  // Check 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? Or did you miss to add\n"
       << "some VRM fields (e.g. for free electrons or particles)?\n";
    throw runtime_error(os.str());
  }
 
  // 4. Set up some things we will need later on:
 
  // 4.a Frequency grid positions
 
  // Frequency grid positions. The pointer is used to save copying of the
  // default from the lookup table.
  const ArrayOfLagrangeInterpolation* flag;
  ArrayOfLagrangeInterpolation flag_local;
 
  // With f_interp_order 0 the frequency grid has to have the same size as in the
  // lookup table, or exactly one element. If it matches the lookup table, we
  // do no frequency interpolation at all. (We set the frequency grid positions
  // to the predefined ones that come with the lookup table.)
  if (f_interp_order == 0) {
 
    // We do some superficial checks below, to make sure that the
    // frequency grid is the same as in the lookup table (only first
    // and last element of f_grid are tested). As margin for
    // agreement, we pick a value that is just slightly smaller than
    // the perturbation that is used by the wind jacobian, which is 0.1.
    const Numeric allowed_f_margin = 0.09;
    
    if (n_new_f_grid == n_f_grid) {
      // Use the default flag that is stored in the lookup table itself
      // (which effectively means no frequency interpolation)
      flag = &flag_default;
 
      // Check first f_grid element:
      if (abs(f_grid[0] - new_f_grid[0]) > allowed_f_margin)
      {
        ostringstream os;
        os << "First frequency in f_grid inconsistent with lookup table.\n"
           << "f_grid[0]        = " << f_grid[0] << "\n"
           << "new_f_grid[0] = " << new_f_grid[0] << ".";
        throw runtime_error(os.str());
      }
 
      // Check last f_grid element:
      if (abs(f_grid[n_f_grid - 1] - new_f_grid[n_new_f_grid - 1]) > allowed_f_margin)
      {
        ostringstream os;
        os << "Last frequency in f_grid inconsistent with lookup table.\n"
           << "f_grid[n_f_grid-1]              = " << f_grid[n_f_grid - 1]
           << "\n"
           << "new_f_grid[n_new_f_grid-1] = " << new_f_grid[n_new_f_grid - 1]
           << ".";
        throw runtime_error(os.str());
      }
    } else if (n_new_f_grid == 1) {
      flag = &flag_local;
      flag_local = Interpolation::LagrangeVector(new_f_grid, f_grid, 0);
 
      // Check that we really are on a frequency grid point, for safety's sake.
      if (abs(f_grid[flag_local[0].pos] - new_f_grid[0]) > allowed_f_margin)
      {
        ostringstream os;
        os << "Cannot find a matching lookup table frequency for frequency "
           << new_f_grid[0] << ".\n"
           << "(This check has not been properly tested, so perhaps this is\n"
           << "a false alarm. Check for this in file gas_abs_lookup.cc.)";
        throw runtime_error(os.str());
      }
    } else {
      ostringstream os;
      os << "With f_interp_order 0 the frequency grid has to have the same\n"
         << "size as in the lookup table, or exactly one element.";
      throw runtime_error(os.str());
    }
  } else {
    const Numeric f_min = f_grid[0] - 0.5 * (f_grid[1] - f_grid[0]);
    const Numeric f_max = f_grid[n_f_grid - 1] +
                          0.5 * (f_grid[n_f_grid - 1] - f_grid[n_f_grid - 2]);
    if (new_f_grid[0] < f_min) {
      ostringstream os;
      os << "Problem with gas absorption lookup table.\n"
         << "At least one frequency is outside the range covered by the lookup table.\n"
         << "Your new frequency value is " << new_f_grid[0] << " Hz.\n"
         << "The allowed range is " << f_min << " to " << f_max << " Hz.";
      throw runtime_error(os.str());
    }
    if (new_f_grid[n_new_f_grid - 1] > f_max) {
      ostringstream os;
      os << "Problem with gas absorption lookup table.\n"
         << "At least one frequency is outside the range covered by the lookup table.\n"
         << "Your new frequency value is " << new_f_grid[n_new_f_grid - 1]
         << " Hz.\n"
         << "The allowed range is " << f_min << " to " << f_max << " Hz.";
      throw runtime_error(os.str());
    }
 
    // We do have real frequency interpolation (f_interp_order!=0).
    flag = &flag_local;
    flag_local = Interpolation::LagrangeVector(new_f_grid, f_grid, f_interp_order);
  }
 
  // 4.b Other stuff
 
  // Flag for temperature interpolation, if this is not 0 we want
  // to do T interpolation:
  const Index do_T = n_t_pert;
 
  // 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.
  const auto plag = Interpolation::LagrangeVector(log(p), log_p_grid, p_interp_order);
 
  // Pressure interpolation weights:
  const auto pitw = interpweights(plag[0]);
 
  // Define also other grid positions and interpolation weights here, so that
  // we do not have to allocate them over and over in the loops below.
 
  // Define the ArrayOfLagrangeInterpolation that corresponds to "no interpolation at all".
  const ArrayOfLagrangeInterpolation lag_trivial(1);
 
  // Temperature grid positions.
  ArrayOfLagrangeInterpolation tlag_withT(1);  // Only a scalar.
  const ArrayOfLagrangeInterpolation* tlag;  // Pointer to either tlag_withT or lag_trivial.
 
  // Set this_t_interp_order, depending on whether we do T interpolation or not.
  if (do_T) {
    tlag = &tlag_withT;
  } else {
    // For the !do_T case we simply take the single
    // temperature that is there, so we point tgp accordingly.
    tlag = &lag_trivial;
  }
 
  // H2O(VMR) grid positions. vlag is what will be used in the interpolation.
  // Depending on species, it is either pointed to lag_trivial, or to vlag_h2o.
  const ArrayOfLagrangeInterpolation* vlag;
  ArrayOfLagrangeInterpolation vlag_h2o(1);  // only a scalar
 
  // 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:
  // xsec dimensions are:
  //   Temperature
  //   H2O
  //   Frequency
  //   Pressure
  // Dimensions of pre_interpolated are:
  //   Pressure    (interpolation points)
  //   Species
  //   Temperature (always 1)
  //   H2O         (always 1)
  //   Frequency
 
  Tensor5 xsec_pre_interpolated;
  xsec_pre_interpolated.resize(
      p_interp_order + 1, n_species, 1, 1, n_new_f_grid);
 
  // Define variables for interpolation weights outside the loops.
  // We will make itw point to either the weights with H2O interpolation, or
  // the ones without.
  Tensor3OfTensor3 itw_withH2O(0,0,0), itw_noH2O(0,0,0);
  const Tensor3OfTensor3 *itw;
 
  for (Index pi = 0; pi < p_interp_order + 1; ++pi) {
    // Throw a runtime error if one of the reference VMR profiles is zero, but
    // abs_vmrs is not. (This means that the lookup table was calculated with a
    // reference profile of zero for that gas.)
    //      for (Index si=0; si<n_species; ++si)
    //        if ( (vmrs_ref(si,pi) == 0) &&
    //            (abs_vmrs[si]    != 0) )
    //        {
    //          ostringstream os;
    //          os << "Reference VMR profile is zero, you cannot extract\n"
    //          << "Absorption for this species.\n"
    //          << "Species: " << si
    //          << " (" << get_species_name(species[si]) << ")\n"
    //          << "Lookup table pressure level: " << pi
    //          << " (" <<  p_grid[pi] << " Pa).";
    //          throw runtime_error( os.str() );
    //        }
 
    // Index into p_grid:
    const Index this_p_grid_index = plag[0].pos + pi;
 
    // 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:
    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] - extpolfac * (t_pert[1] - t_pert[0]);
        const Numeric t_max =
            t_pert[n_t_pert - 1] +
            extpolfac * (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());
        }
      }
 
      tlag_withT[0] = LagrangeInterpolation(0, T_offset, t_pert, 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.
    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] - extpolfac * (nls_pert[1] - nls_pert[0]);
        const Numeric x_max =
            nls_pert[n_nls_pert - 1] +
            extpolfac * (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.
      vlag_h2o[0] = LagrangeInterpolation(0, VMR_frac, nls_pert, h2o_interp_order);
    }
 
    // Precalculate interpolation weights.
    if (n_nls < n_species) {
      // Precalculate weights without H2O interpolation if there are less
      // nonlinear species than total species. (So at least one species
      // without H2O interpolation.)
      itw_noH2O = interpweights(*tlag, lag_trivial, *flag);
    }
    if (n_nls > 0) {
      // Precalculate weights with H2O interpolation if there is at least
      // one nonlinear species.
      itw_withH2O = interpweights(*tlag, vlag_h2o, *flag);
    }
 
    // 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];
 
      // For interpolation result.
      // Fixed pressure level and species.
      // Free dimension is T, H2O, and frequency.
      Tensor3View res(xsec_pre_interpolated(
          pi, si, Range(joker), Range(joker), Range(joker)));
 
      // Ignore species such as Zeeman and free_electrons which are not
      // stored in the lookup table. For those the result is set to 0.
      if (species[si].Zeeman() or species[si].FreeElectrons() or species[si].Particles()) {
        if (do_VMR) {
          ostringstream os;
          os << "Problem with gas absorption lookup table.\n"
             << "VMR interpolation is not allowed for species \""
             << species[si][0].Name() << "\"";
          throw runtime_error(os.str());
        }
        res = 0.;
        fpi++;
        continue;
      }
 
      // Set h2o related interpolation parameters:
      Index this_h2o_extent;  // Range of H2O interpolation
      if (do_VMR) {
        vlag = &vlag_h2o;
        this_h2o_extent = n_nls_pert;
        itw = &itw_withH2O;
      } else {
        vlag = &lag_trivial;
        this_h2o_extent = 1;
        itw = &itw_noH2O;
      }
 
      // Get the right view on xsec.
      ConstTensor3View this_xsec =
          xsec(Range(joker),                 // Temperature range
               Range(fpi, this_h2o_extent),  // VMR profile range
               Range(joker),                 // Frequency range
               this_p_grid_index);           // Pressure index
 
      // Do interpolation.
      reinterp(res,        // result
               this_xsec,  // input
               *itw,       // weights
               *tlag,
               *vlag,
               *flag);  // grid positions
 
      // 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:
    ARTS_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(n_species, n_new_f_grid);
  sga = 0;
  for (Index pi = 0; pi < p_interp_order + 1; ++pi) {
    // Multiply pre interpolated quantities with pressure interpolation weights.
    // Dimensions of pre_interpolated are:
    //   Pressure    (interpolation points)
    //   Species
    //   Temperature (always 1)
    //   H2O         (always 1)
    //   Frequency
    xsec_pre_interpolated(
        pi, Range(joker), Range(joker), Range(joker), Range(joker)) *= pitw[pi];
 
    // Add up in sga.
    // Dimensions of sga are (species, frequency)
    sga += xsec_pre_interpolated(pi, Range(joker), 0, 0, 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) {
    if (select_abs_species.nelem()) {
      if (species[si] == select_abs_species)
        sga(si, Range(joker)) *= (n * abs_vmrs[si]);
      else
        sga(si, Range(joker)) = 0.;
    } else {
      sga(si, Range(joker)) *= (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;
}