= PDAF3_assimilate_global_nondiagR =

This page documents the routine `PDAF3_assimilate_global_nondiagR` of PDAF. The routine is part of the advanced PDAF3 interface that was introduced with PDAF V3.0. 

The routine is used to execute the analysis step of all global ensemble filters ESTKF, ETKF, and SEIK 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 using the global filters (`PDAF_localfilter()=0`) is:
{{{
  SUBROUTINE PDAF3_assimilate_global_nondiagR(U_collect_state, U_distribute_state, &
                                 U_init_dim_obs_pdafomi, U_obs_op_pdafomi, &
                                 U_prodRinvA_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 `PDAF_get_state` as well as 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. This is the inverse operation to `U_collect_state`.
 * `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_prodRinvA_pdafomi`: 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_prepoststep`: [[BR]]The name of the user-supplied pre/poststep routine as in `PDAF_get_state`
 * `U_next_observation`: [[BR]]The name of a 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 difference to the routine `PDAF3_assimilate_global` used for diagonal R-matrices is only in the additional argument `U_prodRinvA_pdafomi`.
 * The routine is identical to the routine `PDAFomi_assimilate_global_nondiagR` of PDAF 2. The new name reflects consistency with `PDAF3_assimilate_global_nondiagR`. If one has used `PDAFomi_assimilate_global_nondiagR` before one can just adapt the name of the called routine.
 * The filters EnKF and LEnKF use the separate routine [wiki:PDAFomi_assimilate_enkf_nondiagR PDAFomi_assimilate_enkf_nondiagR].
 * The filters NETF and PF use the separate routine [wiki:PDAFomi_assimilate_nonlin_nondiagR PDAFomi_assimilate_nonlin_nondiagR].
 * It is recommended that the value of `status_pdaf` is checked in the program after the 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 [ImplementAnalysisGlobal implementing the analysis step of the global filters].