= PDAFomi_get_interp_coeff_lin =

This page documents the routine `PDAFomi_get_interp_coeff_lne` of PDAF-OMI.

The routine is called in `init_dim_obs_OBSTYPE of an obseration module to initialize interpolation coefficients in 1, 2, or 3 dimensions. It is used if the observation operator performs linear interpolation (usually `PDAFomi_obs_op_interp_lin`).

|| See the [wiki:OMI_observation_operators page describing PDAF-OMI observation operators] for a general overview.||

The interface is:
{{{
  SUBROUTINE PDAFomi_get_interp_coeff_lin(num_gp, n_dim, gcoords, ocoord, icoeff)

    INTEGER, INTENT(in) :: num_gp         ! Length of icoeff
    INTEGER, INTENT(in) :: n_dim          ! Number of dimensions in interpolation
    REAL, INTENT(in)    :: gcoords(:,:)   ! Coordinates of grid points
    REAL, INTENT(in)    :: ocoord(:)      ! Coordinates of observation
    REAL, INTENT(inout) :: icoeff(:)      ! Interpolation coefficients (num_gp)
}}}

'''Notes:'''
 * It is required that num_gp=2 for n_dim=1; num_gp=4 for n_dim=2; num_gp=8 for n_dim=3.
 * In the array `gcoords`, the first index specifies the grid point while the second specifies the coordinate, thus `gcoords(1,1)` is the first coordinate for grid point 1, `gcoords(1,2)` is the second coordiate for grid point 1, while `gcoords(2,1)` is the first coordiate for grid point 2. The coordinates need to be consistent with the indices specified in `thisobs%id_obs_p` since these specify the elements of the state vector that are interpolated. Only the first `n_dim` entries of ocoord will be used for the interpolation.
 * `ocoord(:,i)` holds the list of the coordinates for the observation with index i (different from the use in `gcoords`)
 * The order of the coordinates and coefficients is the following:
{{{
                       (7)------(8) 
                       /|       /|    with
                     (5)+-----(6)|       - column 1
                      | |      | |       / column 2
                      |(3)-----+(4)      | column 3
                      |/       |/
                     (1) ---- (2)

   thus gcoords(1,1)/=gcoords(2,1),        but  gcoords(1,1)=gcoords(3,1)=gcoords(5,1),
        gcoords(1,2)/=gcoords(3,2),             gcoords(1,2)=gcoords(2,2)=gcoords(5,2), 
        gcoords(1,3)/=gcoords(5,3)              gcoords(1,3)=gcoords(2,3)=gcoords(3,3)
}}}
 * For 1D linear interpolation (n_dim=1) only the coordinates for grid points 1 and 2 are used to compute the coefficients
 * For bi-linear interpolation (n_dim=2) only the coordinates for grid points 1, 2, and 3 are used to compute the coefficients
 * For tri-linear interpolation (n_dim=3) only the coordinates for grid points 1, 2, 3, and 5 are used to compute the coefficients