special_interp.cc

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#include <cmath>
#include <iostream>
#include <stdexcept>
#include "auto_md.h"
#include "check_input.h"
#include "math_funcs.h"
#include "messages.h"
#include "special_interp.h"
 
/*===========================================================================
  === Point interpolation functions for atmospheric grids and fields
  ===========================================================================*/
 
void interp_atmfield_gp2itw(Matrix& itw,
                            const Index& atmosphere_dim,
                            const ArrayOfGridPos& gp_p,
                            const ArrayOfGridPos& gp_lat,
                            const ArrayOfGridPos& gp_lon) {
  const Index n = gp_p.nelem();
 
  if (atmosphere_dim == 1) {
    itw.resize(n, 2);
    interpweights(itw, gp_p);
  }
 
  else if (atmosphere_dim == 2) {
    ARTS_ASSERT(gp_lat.nelem() == n);
    itw.resize(n, 4);
    interpweights(itw, gp_p, gp_lat);
  }
 
  else if (atmosphere_dim == 3) {
    ARTS_ASSERT(gp_lat.nelem() == n);
    ARTS_ASSERT(gp_lon.nelem() == n);
    itw.resize(n, 8);
    interpweights(itw, gp_p, gp_lat, gp_lon);
  }
}
 
void interp_atmfield_by_itw(VectorView x,
                            const Index& atmosphere_dim,
                            ConstTensor3View x_field,
                            const ArrayOfGridPos& gp_p,
                            const ArrayOfGridPos& gp_lat,
                            const ArrayOfGridPos& gp_lon,
                            ConstMatrixView itw) {
  ARTS_ASSERT(x.nelem() == gp_p.nelem());
 
  if (atmosphere_dim == 1) {
    ARTS_ASSERT(itw.ncols() == 2);
    interp(x, itw, x_field(Range(joker), 0, 0), gp_p);
  }
 
  else if (atmosphere_dim == 2) {
    ARTS_ASSERT(itw.ncols() == 4);
    interp(x, itw, x_field(Range(joker), Range(joker), 0), gp_p, gp_lat);
  }
 
  else if (atmosphere_dim == 3) {
    ARTS_ASSERT(itw.ncols() == 8);
    interp(x, itw, x_field, gp_p, gp_lat, gp_lon);
  }
}
 
void interp_atmfield_by_gp(VectorView x,
                           const Index& atmosphere_dim,
                           ConstTensor3View x_field,
                           const ArrayOfGridPos& gp_p,
                           const ArrayOfGridPos& gp_lat,
                           const ArrayOfGridPos& gp_lon) {
  Matrix itw;
 
  interp_atmfield_gp2itw(itw, atmosphere_dim, gp_p, gp_lat, gp_lon);
 
  interp_atmfield_by_itw(x, atmosphere_dim, x_field, gp_p, gp_lat, gp_lon, itw);
}
 
Numeric interp_atmfield_by_gp(const Index& atmosphere_dim,
                              ConstTensor3View x_field,
                              const GridPos& gp_p,
                              const GridPos& gp_lat,
                              const GridPos& gp_lon) {
  ArrayOfGridPos agp_p(1), agp_lat(0), agp_lon(0);
 
  gridpos_copy(agp_p[0], gp_p);
 
  if (atmosphere_dim > 1) {
    agp_lat.resize(1);
    gridpos_copy(agp_lat[0], gp_lat);
  }
 
  if (atmosphere_dim > 2) {
    agp_lon.resize(1);
    gridpos_copy(agp_lon[0], gp_lon);
  }
 
  Vector x(1);
 
  interp_atmfield_by_gp(x, atmosphere_dim, x_field, agp_p, agp_lat, agp_lon);
 
  return x[0];
}
 
void interp_cloudfield_gp2itw(VectorView itw,
                              GridPos& gp_p_out,
                              GridPos& gp_lat_out,
                              GridPos& gp_lon_out,
                              const GridPos& gp_p_in,
                              const GridPos& gp_lat_in,
                              const GridPos& gp_lon_in,
                              const Index& atmosphere_dim,
                              const ArrayOfIndex& cloudbox_limits) {
  // Shift grid positions to cloud box grids
  if (atmosphere_dim == 1) {
    gridpos_copy(gp_p_out, gp_p_in);
    gp_p_out.idx -= cloudbox_limits[0];
    gridpos_upperend_check(gp_p_out, cloudbox_limits[1] - cloudbox_limits[0]);
    ARTS_ASSERT(itw.nelem() == 2);
    interpweights(itw, gp_p_out);
  } else if (atmosphere_dim == 2) {
    gridpos_copy(gp_p_out, gp_p_in);
    gridpos_copy(gp_lat_out, gp_lat_in);
    gp_p_out.idx -= cloudbox_limits[0];
    gp_lat_out.idx -= cloudbox_limits[2];
    gridpos_upperend_check(gp_p_out, cloudbox_limits[1] - cloudbox_limits[0]);
    gridpos_upperend_check(gp_lat_out, cloudbox_limits[3] - cloudbox_limits[2]);
    ARTS_ASSERT(itw.nelem() == 4);
    interpweights(itw, gp_p_out, gp_lat_out);
  } else {
    gridpos_copy(gp_p_out, gp_p_in);
    gridpos_copy(gp_lat_out, gp_lat_in);
    gridpos_copy(gp_lon_out, gp_lon_in);
    gp_p_out.idx -= cloudbox_limits[0];
    gp_lat_out.idx -= cloudbox_limits[2];
    gp_lon_out.idx -= cloudbox_limits[4];
    gridpos_upperend_check(gp_p_out, cloudbox_limits[1] - cloudbox_limits[0]);
    gridpos_upperend_check(gp_lat_out, cloudbox_limits[3] - cloudbox_limits[2]);
    gridpos_upperend_check(gp_lon_out, cloudbox_limits[5] - cloudbox_limits[4]);
    ARTS_ASSERT(itw.nelem() == 8);
    interpweights(itw, gp_p_out, gp_lat_out, gp_lon_out);
  }
}
 
void interp_atmsurface_gp2itw(Matrix& itw,
                              const Index& atmosphere_dim,
                              const ArrayOfGridPos& gp_lat,
                              const ArrayOfGridPos& gp_lon) {
  if (atmosphere_dim == 1) {
    itw.resize(1, 1);
    itw = 1;
  }
 
  else if (atmosphere_dim == 2) {
    const Index n = gp_lat.nelem();
    itw.resize(n, 2);
    interpweights(itw, gp_lat);
  }
 
  else if (atmosphere_dim == 3) {
    const Index n = gp_lat.nelem();
    ARTS_ASSERT(n == gp_lon.nelem());
    itw.resize(n, 4);
    interpweights(itw, gp_lat, gp_lon);
  }
}
 
void interp_atmsurface_by_itw(VectorView x,
                              const Index& atmosphere_dim,
                              ConstMatrixView x_surface,
                              const ArrayOfGridPos& gp_lat,
                              const ArrayOfGridPos& gp_lon,
                              ConstMatrixView itw) {
  if (atmosphere_dim == 1) {
    ARTS_ASSERT(itw.ncols() == 1);
    x = x_surface(0, 0);
  }
 
  else if (atmosphere_dim == 2) {
    ARTS_ASSERT(x.nelem() == gp_lat.nelem());
    ARTS_ASSERT(itw.ncols() == 2);
    interp(x, itw, x_surface(Range(joker), 0), gp_lat);
  }
 
  else if (atmosphere_dim == 3) {
    ARTS_ASSERT(x.nelem() == gp_lat.nelem());
    ARTS_ASSERT(itw.ncols() == 4);
    interp(x, itw, x_surface, gp_lat, gp_lon);
  }
}
 
void interp_atmsurface_by_gp(VectorView x,
                             const Index& atmosphere_dim,
                             ConstMatrixView x_surface,
                             const ArrayOfGridPos& gp_lat,
                             const ArrayOfGridPos& gp_lon) {
  Matrix itw;
 
  interp_atmsurface_gp2itw(itw, atmosphere_dim, gp_lat, gp_lon);
 
  interp_atmsurface_by_itw(x, atmosphere_dim, x_surface, gp_lat, gp_lon, itw);
}
 
Numeric interp_atmsurface_by_gp(const Index& atmosphere_dim,
                                ConstMatrixView x_surface,
                                const GridPos& gp_lat,
                                const GridPos& gp_lon) {
  ArrayOfGridPos agp_lat(0), agp_lon(0);
 
  if (atmosphere_dim > 1) {
    agp_lat.resize(1);
    gridpos_copy(agp_lat[0], gp_lat);
  }
 
  if (atmosphere_dim > 2) {
    agp_lon.resize(1);
    gridpos_copy(agp_lon[0], gp_lon);
  }
 
  Vector x(1);
 
  interp_atmsurface_by_gp(x, atmosphere_dim, x_surface, agp_lat, agp_lon);
 
  return x[0];
}
 
/*===========================================================================
  === Regridding
  ===========================================================================*/
 
void regrid_atmfield_by_gp(Tensor3& field_new,
                           const Index& atmosphere_dim,
                           ConstTensor3View field_old,
                           const ArrayOfGridPos& gp_p,
                           const ArrayOfGridPos& gp_lat,
                           const ArrayOfGridPos& gp_lon) {
  const Index n1 = gp_p.nelem();
 
  if (atmosphere_dim == 1) {
    field_new.resize(n1, 1, 1);
    Matrix itw(n1, 2);
    interpweights(itw, gp_p);
    interp(field_new(joker, 0, 0), itw, field_old(joker, 0, 0), gp_p);
  } else if (atmosphere_dim == 2) {
    const Index n2 = gp_lat.nelem();
    field_new.resize(n1, n2, 1);
    Tensor3 itw(n1, n2, 4);
    interpweights(itw, gp_p, gp_lat);
    interp(field_new(joker, joker, 0),
           itw,
           field_old(joker, joker, 0),
           gp_p,
           gp_lat);
  } else if (atmosphere_dim == 3) {
    const Index n2 = gp_lat.nelem();
    const Index n3 = gp_lon.nelem();
    field_new.resize(n1, n2, n3);
    Tensor4 itw(n1, n2, n3, 8);
    interpweights(itw, gp_p, gp_lat, gp_lon);
    interp(field_new, itw, field_old, gp_p, gp_lat, gp_lon);
  }
}
 
void regrid_atmsurf_by_gp(Matrix& field_new,
                          const Index& atmosphere_dim,
                          ConstMatrixView field_old,
                          const ArrayOfGridPos& gp_lat,
                          const ArrayOfGridPos& gp_lon) {
  if (atmosphere_dim == 1) {
    field_new = field_old;
  } else if (atmosphere_dim == 2) {
    const Index n1 = gp_lat.nelem();
    field_new.resize(n1, 1);
    Matrix itw(n1, 2);
    interpweights(itw, gp_lat);
    interp(field_new(joker, 0), itw, field_old(joker, 0), gp_lat);
  } else if (atmosphere_dim == 3) {
    const Index n1 = gp_lat.nelem();
    const Index n2 = gp_lon.nelem();
    field_new.resize(n1, n2);
    Tensor3 itw(n1, n2, 4);
    interpweights(itw, gp_lat, gp_lon);
    interp(field_new, itw, field_old, gp_lat, gp_lon);
  }
}
 
void get_gp_atmgrids_to_rq(ArrayOfGridPos& gp_p,
                           ArrayOfGridPos& gp_lat,
                           ArrayOfGridPos& gp_lon,
                           const RetrievalQuantity& rq,
                           const Index& atmosphere_dim,
                           const Vector& p_grid,
                           const Vector& lat_grid,
                           const Vector& lon_grid) {
  gp_p.resize(rq.Grids()[0].nelem());
  p2gridpos(gp_p, p_grid, rq.Grids()[0], 0);
  //
  if (atmosphere_dim >= 2) {
    gp_lat.resize(rq.Grids()[1].nelem());
    gridpos(gp_lat, lat_grid, rq.Grids()[1], 0);
  } else {
    gp_lat.resize(0);
  }
  //
  if (atmosphere_dim >= 3) {
    gp_lon.resize(rq.Grids()[2].nelem());
    gridpos(gp_lon, lon_grid, rq.Grids()[2], 0);
  } else {
    gp_lon.resize(0);
  }
}
 
void get_gp_atmsurf_to_rq(ArrayOfGridPos& gp_lat,
                          ArrayOfGridPos& gp_lon,
                          const RetrievalQuantity& rq,
                          const Index& atmosphere_dim,
                          const Vector& lat_grid,
                          const Vector& lon_grid) {
  if (atmosphere_dim >= 2) {
    gp_lat.resize(rq.Grids()[0].nelem());
    gridpos(gp_lat, lat_grid, rq.Grids()[0], 0);
  } else {
    gp_lat.resize(0);
  }
  //
  if (atmosphere_dim >= 3) {
    gp_lon.resize(rq.Grids()[1].nelem());
    gridpos(gp_lon, lon_grid, rq.Grids()[1], 0);
  } else {
    gp_lon.resize(0);
  }
}
 
void get_gp_rq_to_atmgrids(ArrayOfGridPos& gp_p,
                           ArrayOfGridPos& gp_lat,
                           ArrayOfGridPos& gp_lon,
                           Index& n_p,
                           Index& n_lat,
                           Index& n_lon,
                           const ArrayOfVector& ret_grids,
                           const Index& atmosphere_dim,
                           const Vector& p_grid,
                           const Vector& lat_grid,
                           const Vector& lon_grid) {
  // We want here an extrapolation to infinity ->
  //                                        extremly high extrapolation factor
  const Numeric inf_proxy = 1.0e99;
 
  gp_p.resize(p_grid.nelem());
  n_p = ret_grids[0].nelem();
  if (n_p > 1) {
    p2gridpos(gp_p, ret_grids[0], p_grid, inf_proxy);
    jacobian_type_extrapol(gp_p);
  } else {
    gp4length1grid(gp_p);
  }
 
  if (atmosphere_dim >= 2) {
    gp_lat.resize(lat_grid.nelem());
    n_lat = ret_grids[1].nelem();
    if (n_lat > 1) {
      gridpos(gp_lat, ret_grids[1], lat_grid, inf_proxy);
      jacobian_type_extrapol(gp_lat);
    } else {
      gp4length1grid(gp_lat);
    }
  } else {
    gp_lat.resize(0);
    n_lat = 1;
  }
  //
  if (atmosphere_dim >= 3) {
    gp_lon.resize(lon_grid.nelem());
    n_lon = ret_grids[2].nelem();
    if (n_lon > 1) {
      gridpos(gp_lon, ret_grids[2], lon_grid, inf_proxy);
      jacobian_type_extrapol(gp_lon);
    } else {
      gp4length1grid(gp_lon);
    }
  } else {
    gp_lon.resize(0);
    n_lon = 1;
  }
}
 
void get_gp_rq_to_atmgrids(ArrayOfGridPos& gp_lat,
                           ArrayOfGridPos& gp_lon,
                           Index& n_lat,
                           Index& n_lon,
                           const ArrayOfVector& ret_grids,
                           const Index& atmosphere_dim,
                           const Vector& lat_grid,
                           const Vector& lon_grid) {
  // We want here an extrapolation to infinity ->
  //                                        extremly high extrapolation factor
  const Numeric inf_proxy = 1.0e99;
 
  if (atmosphere_dim >= 2) {
    gp_lat.resize(lat_grid.nelem());
    n_lat = ret_grids[0].nelem();
    if (n_lat > 1) {
      gridpos(gp_lat, ret_grids[0], lat_grid, inf_proxy);
      jacobian_type_extrapol(gp_lat);
    } else {
      gp4length1grid(gp_lat);
    }
  } else {
    gp_lat.resize(0);
    n_lat = 1;
  }
  //
  if (atmosphere_dim >= 3) {
    gp_lon.resize(lon_grid.nelem());
    n_lon = ret_grids[1].nelem();
    if (n_lon > 1) {
      gridpos(gp_lon, ret_grids[1], lon_grid, inf_proxy);
      jacobian_type_extrapol(gp_lon);
    } else {
      gp4length1grid(gp_lon);
    }
  } else {
    gp_lon.resize(0);
    n_lon = 1;
  }
}
 
void regrid_atmfield_by_gp_oem(Tensor3& field_new,
                               const Index& atmosphere_dim,
                               ConstTensor3View field_old,
                               const ArrayOfGridPos& gp_p,
                               const ArrayOfGridPos& gp_lat,
                               const ArrayOfGridPos& gp_lon) {
  const Index n1 = gp_p.nelem();
 
  const bool np_is1 = field_old.npages() == 1 ? true : false;
  const bool nlat_is1 =
      atmosphere_dim > 1 && field_old.nrows() == 1 ? true : false;
  const bool nlon_is1 =
      atmosphere_dim > 2 && field_old.ncols() == 1 ? true : false;
 
  // If no length 1, we can use standard function
  if (!np_is1 && !nlat_is1 && !nlon_is1) {
    regrid_atmfield_by_gp(
        field_new, atmosphere_dim, field_old, gp_p, gp_lat, gp_lon);
  } else {
    //--- 1D (1 possibilities left) -------------------------------------------
    if (atmosphere_dim == 1) {  // 1: No interpolation at all
      field_new.resize(n1, 1, 1);
      field_new(joker, 0, 0) = field_old(0, 0, 0);
    }
 
    //--- 2D (3 possibilities left) -------------------------------------------
    else if (atmosphere_dim == 2) {
      const Index n2 = gp_lat.nelem();
      field_new.resize(n1, n2, 1);
      //
      if (np_is1 && nlat_is1)  // 1: No interpolation at all
      {
        // Here we need no interpolation at all
        field_new(joker, joker, 0) = field_old(0, 0, 0);
      } else if (np_is1)  // 2: Latitude interpolation
      {
        Matrix itw(n2, 2);
        interpweights(itw, gp_lat);
        Vector tmp(n2);
        interp(tmp, itw, field_old(0, joker, 0), gp_lat);
        for (Index p = 0; p < n1; p++) {
          ARTS_ASSERT(gp_p[p].fd[0] < 1e-6);
          field_new(p, joker, 0) = tmp;
        }
      } else  // 3: Pressure interpolation
      {
        Matrix itw(n1, 2);
        interpweights(itw, gp_p);
        Vector tmp(n1);
        interp(tmp, itw, field_old(joker, 0, 0), gp_p);
        for (Index lat = 0; lat < n2; lat++) {
          ARTS_ASSERT(gp_lat[lat].fd[0] < 1e-6);
          field_new(joker, lat, 0) = tmp;
        }
      }
    }
 
    //--- 3D (7 possibilities left) -------------------------------------------
    else if (atmosphere_dim == 3) {
      const Index n2 = gp_lat.nelem();
      const Index n3 = gp_lon.nelem();
      field_new.resize(n1, n2, n3);
      //
      if (np_is1 && nlat_is1 && nlon_is1)  // 1: No interpolation at all
      {
        field_new(joker, joker, joker) = field_old(0, 0, 0);
      }
 
      else if (np_is1)  // No pressure interpolation --------------
      {
        if (nlat_is1)  // 2: Just longitude interpolation
        {
          Matrix itw(n3, 2);
          interpweights(itw, gp_lon);
          Vector tmp(n3);
          interp(tmp, itw, field_old(0, 0, joker), gp_lon);
          for (Index p = 0; p < n1; p++) {
            ARTS_ASSERT(gp_p[p].fd[0] < 1e-6);
            for (Index lat = 0; lat < n2; lat++) {
              ARTS_ASSERT(gp_lat[lat].fd[0] < 1e-6);
              field_new(p, lat, joker) = tmp;
            }
          }
        } else if (nlon_is1)  // 3: Just latitude interpolation
        {
          Matrix itw(n2, 2);
          interpweights(itw, gp_lat);
          Vector tmp(n2);
          interp(tmp, itw, field_old(0, joker, 0), gp_lat);
          for (Index p = 0; p < n1; p++) {
            ARTS_ASSERT(gp_p[p].fd[0] < 1e-6);
            for (Index lon = 0; lon < n3; lon++) {
              ARTS_ASSERT(gp_lon[lon].fd[0] < 1e-6);
              field_new(p, joker, lon) = tmp;
            }
          }
        } else  // 4: Both lat and lon interpolation
        {
          Tensor3 itw(n2, n3, 4);
          interpweights(itw, gp_lat, gp_lon);
          Matrix tmp(n2, n3);
          interp(tmp, itw, field_old(0, joker, joker), gp_lat, gp_lon);
          for (Index p = 0; p < n1; p++) {
            ARTS_ASSERT(gp_p[p].fd[0] < 1e-6);
            field_new(p, joker, joker) = tmp;
          }
        }
      }
 
      else  // Pressure interpolation --------------
      {
        if (nlat_is1 && nlon_is1)  // 5: Just pressure interpolatiom
        {
          Matrix itw(n1, 2);
          interpweights(itw, gp_p);
          Vector tmp(n1);
          interp(tmp, itw, field_old(joker, 0, 0), gp_p);
          for (Index lat = 0; lat < n2; lat++) {
            ARTS_ASSERT(gp_lat[lat].fd[0] < 1e-6);
            for (Index lon = 0; lon < n3; lon++) {
              ARTS_ASSERT(gp_lon[lon].fd[0] < 1e-6);
              field_new(joker, lat, lon) = tmp;
            }
          }
        } else if (nlat_is1)  // 6: Both p and lon interpolation
        {
          Tensor3 itw(n1, n3, 4);
          interpweights(itw, gp_p, gp_lon);
          Matrix tmp(n1, n3);
          interp(tmp, itw, field_old(joker, 0, joker), gp_p, gp_lon);
          for (Index lat = 0; lat < n2; lat++) {
            ARTS_ASSERT(gp_lat[lat].fd[0] < 1e-6);
            field_new(joker, lat, joker) = tmp;
          }
        } else  // 7: Both p and lat interpolation
        {
          Tensor3 itw(n1, n2, 4);
          interpweights(itw, gp_p, gp_lat);
          Matrix tmp(n1, n2);
          interp(tmp, itw, field_old(joker, joker, 0), gp_p, gp_lat);
          for (Index lon = 0; lon < n3; lon++) {
            ARTS_ASSERT(gp_lon[lon].fd[0] < 1e-6);
            field_new(joker, joker, lon) = tmp;
          }
        }
      }
    }
  }
}
 
/* So far just a temporary test */
void regrid_atmsurf_by_gp_oem(Matrix& field_new,
                              const Index& atmosphere_dim,
                              ConstMatrixView field_old,
                              const ArrayOfGridPos& gp_lat,
                              const ArrayOfGridPos& gp_lon) {
  // As 1D is so simple, let's do it here and not go to standard function
  if (atmosphere_dim == 1) {
    field_new = field_old;
  } else {
    const bool nlat_is1 = field_old.nrows() == 1 ? true : false;
    const bool nlon_is1 =
        atmosphere_dim > 2 && field_old.ncols() == 1 ? true : false;
 
    // If no length 1, we can use standard function
    if (!nlat_is1 && !nlon_is1) {
      regrid_atmsurf_by_gp(
          field_new, atmosphere_dim, field_old, gp_lat, gp_lon);
    } else {
      if (atmosphere_dim == 2) {  // 1: No interpolation at all
        const Index n1 = gp_lat.nelem();
        field_new.resize(n1, 1);
        field_new(joker, 0) = field_old(0, 0);
      } else {
        const Index n1 = gp_lat.nelem();
        const Index n2 = gp_lon.nelem();
        field_new.resize(n1, n2);
        //
        if (nlat_is1 && nlon_is1)  // 1: No interpolation at all
        {
          field_new(joker, joker) = field_old(0, 0);
        } else if (nlon_is1)  // 2: Just latitude interpolation
        {
          Matrix itw(n1, 2);
          interpweights(itw, gp_lat);
          Vector tmp(n1);
          interp(tmp, itw, field_old(joker, 0), gp_lat);
          for (Index lon = 0; lon < n2; lon++) {
            ARTS_ASSERT(gp_lon[lon].fd[0] < 1e-6);
            field_new(joker, lon) = tmp;
          }
        } else  // 2: Just longitude interpolation
        {
          Matrix itw(n2, 2);
          interpweights(itw, gp_lon);
          Vector tmp(n2);
          interp(tmp, itw, field_old(0, joker), gp_lon);
          for (Index lat = 0; lat < n1; lat++) {
            ARTS_ASSERT(gp_lat[lat].fd[0] < 1e-6);
            field_new(lat, joker) = tmp;
          }
        }
      }
    }
  }
}
 
/*===========================================================================
  === Conversion altitudes / pressure
  ===========================================================================*/
 
void itw2p(VectorView p_values,
           ConstVectorView p_grid,
           const ArrayOfGridPos& gp,
           ConstMatrixView itw) {
  ARTS_ASSERT(itw.ncols() == 2);
  ARTS_ASSERT(p_values.nelem() == itw.nrows());
 
  // Local variable to store log of the pressure grid:
  Vector logpgrid(p_grid.nelem());
 
  transform(logpgrid, log, p_grid);
 
  interp(p_values, itw, logpgrid, gp);
 
  transform(p_values, exp, p_values);
}
 
void p2gridpos(ArrayOfGridPos& gp,
               ConstVectorView old_pgrid,
               ConstVectorView new_pgrid,
               const Numeric& extpolfac) {
  // Local variable to store log of the pressure grids
  Vector logold(old_pgrid.nelem());
  Vector lognew(new_pgrid.nelem());
 
  transform(logold, log, old_pgrid);
  transform(lognew, log, new_pgrid);
 
  gridpos(gp, logold, lognew, extpolfac);
}
 
void rte_pos2gridpos(GridPos& gp_p,
                     GridPos& gp_lat,
                     GridPos& gp_lon,
                     const Index& atmosphere_dim,
                     ConstVectorView p_grid,
                     ConstVectorView lat_grid,
                     ConstVectorView lon_grid,
                     ConstTensor3View z_field,
                     ConstVectorView rte_pos) {
  chk_rte_pos(atmosphere_dim, rte_pos);
 
  if (atmosphere_dim == 1) {
    chk_interpolation_grids(
        "Altitude interpolation", z_field(joker, 0, 0), rte_pos[0]);
    gridpos(gp_p, z_field(joker, 0, 0), rte_pos[0]);
  } else {
    // Determine z at lat/lon (z_grid) by blue interpolation
    const Index np = p_grid.nelem();
    Vector z_grid(np);
    ArrayOfGridPos agp_z, agp_lat(np);
    //
    gridpos_1to1(agp_z, p_grid);
    //
    chk_interpolation_grids("Latitude interpolation", lat_grid, rte_pos[1]);
    gridpos(gp_lat, lat_grid, rte_pos[1]);
 
    if (atmosphere_dim == 2) {
      for (Index i = 0; i < np; i++) {
        agp_lat[i] = gp_lat;
      }
      Matrix itw(np, 4);
      interpweights(itw, agp_z, agp_lat);
      interp(z_grid, itw, z_field(joker, joker, 0), agp_z, agp_lat);
    } else {
      chk_interpolation_grids("Longitude interpolation", lon_grid, rte_pos[2]);
      gridpos(gp_lon, lon_grid, rte_pos[2]);
      ArrayOfGridPos agp_lon(np);
      for (Index i = 0; i < np; i++) {
        agp_lat[i] = gp_lat;
        agp_lon[i] = gp_lon;
      }
      Matrix itw(np, 8);
      interpweights(itw, agp_z, agp_lat, agp_lon);
      interp(z_grid, itw, z_field, agp_z, agp_lat, agp_lon);
    }
 
    // And use z_grid to get gp_p (gp_al and gp_lon determined above)
    chk_interpolation_grids("Altitude interpolation", z_grid, rte_pos[0]);
    gridpos(gp_p, z_grid, rte_pos[0]);
  }
}
 
void rte_pos2gridpos(GridPos& gp_lat,
                     GridPos& gp_lon,
                     const Index& atmosphere_dim,
                     ConstVectorView lat_grid,
                     ConstVectorView lon_grid,
                     ConstVectorView rte_pos) {
  chk_rte_pos(atmosphere_dim, rte_pos);
 
  if (atmosphere_dim == 1) {
  } else {
    chk_interpolation_grids("Latitude interpolation", lat_grid, rte_pos[1]);
    gridpos(gp_lat, lat_grid, rte_pos[1]);
 
    if (atmosphere_dim == 3) {
      chk_interpolation_grids("Longitude interpolation", lon_grid, rte_pos[2]);
      gridpos(gp_lon, lon_grid, rte_pos[2]);
    }
  }
}
 
void z_at_lat_2d(VectorView z,
                 ConstVectorView p_grid,
// FIXME only used in assertion
#ifndef NDEBUG
                 ConstVectorView lat_grid,
#else
                 ConstVectorView,
#endif
                 ConstMatrixView z_field,
                 const GridPos& gp_lat) {
  const Index np = p_grid.nelem();
 
  ARTS_ASSERT(z.nelem() == np);
  ARTS_ASSERT(z_field.nrows() == np);
  ARTS_ASSERT(z_field.ncols() == lat_grid.nelem());
 
  Matrix z_matrix(np, 1);
  ArrayOfGridPos gp_z(np), agp_lat(1);
  Tensor3 itw(np, 1, 4);
 
  gridpos_copy(agp_lat[0], gp_lat);
  gridpos(gp_z, p_grid, p_grid);
  interpweights(itw, gp_z, agp_lat);
  interp(z_matrix, itw, z_field, gp_z, agp_lat);
 
  z = z_matrix(Range(joker), 0);
}
 
void z_at_latlon(VectorView z,
                 ConstVectorView p_grid,
//FIXME only used in assertion
#ifndef NDEBUG
                 ConstVectorView lat_grid,
                 ConstVectorView lon_grid,
#else
                 ConstVectorView,
                 ConstVectorView,
#endif
                 ConstTensor3View z_field,
                 const GridPos& gp_lat,
                 const GridPos& gp_lon) {
  const Index np = p_grid.nelem();
 
  ARTS_ASSERT(z.nelem() == np);
  ARTS_ASSERT(z_field.npages() == np);
  ARTS_ASSERT(z_field.nrows() == lat_grid.nelem());
  ARTS_ASSERT(z_field.ncols() == lon_grid.nelem());
 
  Tensor3 z_tensor(np, 1, 1);
  ArrayOfGridPos agp_z(np), agp_lat(1), agp_lon(1);
  Tensor4 itw(np, 1, 1, 8);
 
  gridpos_copy(agp_lat[0], gp_lat);
  gridpos_copy(agp_lon[0], gp_lon);
  gridpos(agp_z, p_grid, p_grid);
  interpweights(itw, agp_z, agp_lat, agp_lon);
 
  interp(z_tensor, itw, z_field, agp_z, agp_lat, agp_lon);
 
  z = z_tensor(Range(joker), 0, 0);
}
 
/*===========================================================================
  === Interpolation of GriddedFields
  ===========================================================================*/
 
void complex_n_interp(MatrixView n_real,
                      MatrixView n_imag,
                      const GriddedField3& complex_n,
                      const String& varname,
                      ConstVectorView f_grid,
                      ConstVectorView t_grid) {
  // Set expected order of grids
  Index gfield_fID = 0;
  Index gfield_tID = 1;
  Index gfield_compID = 2;
 
  // Check of complex_n
  //
  complex_n.checksize_strict();
  //
  chk_griddedfield_gridname(complex_n, gfield_fID, "Frequency");
  chk_griddedfield_gridname(complex_n, gfield_tID, "Temperature");
  chk_griddedfield_gridname(complex_n, gfield_compID, "Complex");
  //
  if (complex_n.data.ncols() != 2) {
    ostringstream os;
    os << "The data in *" << varname
       << "* must have exactly two pages. One page "
       << "each\nfor the real and imaginary part of the complex refractive index.";
  }
 
  // Frequency and temperature grid sizes
  const Index nf_in = complex_n.data.npages();
  const Index nt_in = complex_n.data.nrows();
  const Index nf_out = f_grid.nelem();
  const Index nt_out = t_grid.nelem();
 
  //Assert size of output variables
  ARTS_ASSERT(n_real.nrows() == nf_out && n_real.ncols() == nt_out);
  ARTS_ASSERT(n_imag.nrows() == nf_out && n_imag.ncols() == nt_out);
 
  const Vector& f_grid_in = complex_n.get_numeric_grid(gfield_fID);
  const Vector& t_grid_in = complex_n.get_numeric_grid(gfield_tID);
 
  // Expand/interpolate in frequency dimension
  //
  Matrix nrf(nf_out, nt_in), nif(nf_out, nt_in);
  //
  if (nf_in == 1) {
    for (Index i = 0; i < nf_out; i++) {
      nrf(i, joker) = complex_n.data(0, joker, 0);
      nif(i, joker) = complex_n.data(0, joker, 1);
    }
  } else {
    chk_interpolation_grids("Frequency interpolation", f_grid_in, f_grid);
    //
    ArrayOfGridPos gp(nf_out);
    Matrix itw(nf_out, 2);
    gridpos(gp, f_grid_in, f_grid);
    interpweights(itw, gp);
    for (Index i = 0; i < nt_in; i++) {
      interp(nrf(joker, i), itw, complex_n.data(joker, i, 0), gp);
      interp(nif(joker, i), itw, complex_n.data(joker, i, 1), gp);
    }
  }
 
  // Expand/interpolate in temperature dimension
  //
  if (nt_in == 1) {
    for (Index i = 0; i < nt_out; i++) {
      n_real(joker, i) = nrf(joker, 0);
      n_imag(joker, i) = nif(joker, 0);
    }
  } else {
    chk_interpolation_grids("Temperature interpolation", t_grid_in, t_grid);
    //
    ArrayOfGridPos gp(nt_out);
    Matrix itw(nt_out, 2);
    gridpos(gp, t_grid_in, t_grid);
    interpweights(itw, gp);
    for (Index i = 0; i < nf_out; i++) {
      interp(n_real(i, joker), itw, nrf(i, joker), gp);
      interp(n_imag(i, joker), itw, nif(i, joker), gp);
    }
  }
}