= PDAF3_assimilate_lnetf_nondiagR =

This page documents the routine `PDAF3_assimilate_lnetf_nondiagR`. The routine is part of the advanced [wiki:PDAF3_interface PDAF3 interface] that was introduced with PDAF V3.0. 

The routine is used to execute the analysis step of the local nonlinear ensemble transform filter LNETF with PDAF-OMI for the case of a non-diagonal observation error covariance matrix.

The routine is typically called in `assimilate_pdaf` or directly in the model code.

The general aspects of the filter specific routines `PDAF3_assimilate_*` are described on the page [ModifyModelforEnsembleIntegration Modification of the model code for the ensemble integration] and its sub-page on [InsertAnalysisStep inserting the analysis step]. The routine is used in both the fully-parallel and the flexible parallelization variant of the data assimilation system. 

The interface for the routine `PDAF3_assimilate_lnetf_nondiagR` contains names for routines that operate on the local analysis domains (marked by the suffix `_l`). 

The interface is:
{{{
  SUBROUTINE PDAF3_assimilate_lnetf_nondiagR(U_collect_state, U_distribute_state, &
                                  U_init_dim_obs_pdafomi, U_obs_op_pdafomi, &
                                  U_init_n_domains, U_init_dim_l, &
                                  U_init_dim_obs_l_pdafomi, U_likelihood_l_pdafomi, &
                                  U_prepoststep, U_next_observation, status)
}}}
with the following arguments:
 * `U_collect_state`: [[BR]]The name of the user-supplied routine that initializes a state vector from the array holding the ensemble of model states from the model fields. This is basically the inverse operation to `U_distribute_state` used in [ModifyModelforEnsembleIntegration#PDAF_get_state PDAF_get_state] and also here.
 * `U_distribute_state`:  [[BR]]The name of a user supplied routine that initializes the model fields from the array holding the ensemble of model state vectors.
 * `U_init_dim_obs_pdafomi`: [[BR]]The name of the user-supplied routine that initializes the observation information and provides the size of observation vector. This routine is part of an OMI observation module.
 * `U_obs_op_pdafomi`: [[BR]]The name of the user-supplied routine that acts as the observation operator on some state vector. This routine is part of an OMI observation module.
 * `U_init_n_domains`: [[BR]]The name of the routine that provides the number of local analysis domains
 * `U_init_dim_l`: [[BR]]The name of the user-supplied routine that provides the state dimension for a local analysis domain
 * `U_init_dim_obs_l_pdafomi`: [[BR]]The name of the user-supplied routine that initializes the size of the observation vector for a local analysis domain. This routine is part of an OMI observation module.
 * `U_prodRinvA_l_pdafomi`: [[BR]]The name of the user-supplied routine that computes the product of the inverse of the observation error covariance matrix with some matrix provided to the routine by PDAF.  This routine is part of an OMI observation module.
 * `U_likelihood_l_pdafomi`: [[BR]]The name of the user-supplied routine that computes the local likelihood of an ensemble state.  This routine is part of an OMI observation module.
 * `U_prepoststep`: [[BR]]The name of the user-supplied pre/poststep routine as in `PDAF_get_state`
 * `U_next_observation`: [[BR]]The name of the user-supplied routine that initializes the variables `nsteps`, `timenow`, and `doexit`. The same routine is also used in `PDAF_get_state`.
 * `status`: [[BR]]The integer status flag. It is zero, if the routine is exited without errors.



Notes:
 * The order of the routine names does not show the order in which these routines are executed. See the [ImplementAnalysisLocal#Executionorderofuser-suppliedroutines section on the order of the execution] on the page on implementing the analysis step of the local filter algorithms. 
 * The difference to the routine `PDAF3_assimilate_local` used for diagdonal R-matrices is only in the additonal argument `U_likelihood_l_pdafomi`.
 * The local filters LESTKF, LETKF, and LSEIK use the separate routine [wiki:PDAF3_assimilate_local_nondiagR].
 * The filter LKNETF uses the separate routine [wiki:PDAF3_assimilate_lknetf_nondiagR]
 * It is recommended that the value of `status_pdaf` is checked in the program after this routine is executed. Only if its value is 0 the initialization was successful.

The user-supplied call-back routines are described on the page on [ImplementAnalysisLocal implementing the analysis step of the local filters].