! Copyright (c) 2004-2024 Lars Nerger ! ! This file is part of PDAF. ! ! PDAF is free software: you can redistribute it and/or modify ! it under the terms of the GNU Lesser General Public License ! as published by the Free Software Foundation, either version ! 3 of the License, or (at your option) any later version. ! ! PDAF 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 Lesser General Public License for more details. ! ! You should have received a copy of the GNU Lesser General Public ! License along with PDAF. If not, see <http://www.gnu.org/licenses/>. ! !$Id$ !BOP ! ! !ROUTINE: PDAF_3dvar_costf_cvt --- Evaluate cost function and its gradient ! ! !INTERFACE: SUBROUTINE PDAF_3dvar_costf_cvt(step, iter, dim_p, dim_cvec_p, dim_obs_p, & obs_p, dy_p, v_p, J_tot, gradJ, & U_prodRinvA, U_cvt, U_cvt_adj, U_obs_op_lin, U_obs_op_adj, & opt_parallel) ! !DESCRIPTION: ! Routine to evaluate the cost function and its gradient ! for the incremental 3D-Var with variable transformation ! ! Variant for domain decomposed states. ! ! ! This is a core routine of PDAF and ! should not be changed by the user ! ! ! !REVISION HISTORY: ! 2021-03 - Lars Nerger - Initial code ! Later revisions - see svn log ! ! !USES: ! Include definitions for real type of different precision ! (Defines BLAS/LAPACK routines and MPI_REALTYPE) #include "typedefs.h" USE PDAF_timer, & ONLY: PDAF_timeit USE PDAF_memcounting, & ONLY: PDAF_memcount USE PDAF_mod_filtermpi, & ONLY: MPIerr, COMM_filter, MPI_SUM, MPI_REALTYPE USE PDAF_mod_filter, & ONLY: debug IMPLICIT NONE ! !ARGUMENTS: INTEGER, INTENT(in) :: step ! Current time step INTEGER, INTENT(in) :: iter ! Optimization iteration INTEGER, INTENT(in) :: dim_p ! PE-local state dimension INTEGER, INTENT(in) :: dim_cvec_p ! PE-local size of control vector INTEGER, INTENT(in) :: dim_obs_p ! PE-local dimension of observation vector REAL, INTENT(in) :: obs_p(dim_obs_p) ! Vector of observations REAL, INTENT(in) :: dy_p(dim_obs_p) ! background innovation REAL, INTENT(in) :: v_p(dim_cvec_p) ! control vector REAL, INTENT(out) :: J_tot ! on exit: Value of cost function REAL, INTENT(out) :: gradJ(dim_cvec_p) ! on exit: PE-local gradient of J INTEGER, INTENT(in) :: opt_parallel ! Whether to use a decomposed control vector ! ! External subroutines ! ! (PDAF-internal names, real names are defined in the call to PDAF) EXTERNAL :: U_prodRinvA, & ! Provide product R^-1 A U_cvt, & ! Apply control vector transform matrix to control vector U_cvt_adj, & ! Apply adjoint control vector transform matrix U_obs_op_lin, & ! Linearized observation operator U_obs_op_adj ! Adjoint observation operator ! !CALLING SEQUENCE: ! Called by: PDAF_3dvar_analysis_cvt ! Calls: U_prodRinvA ! Calls: PDAF_timeit ! Calls: PDAF_memcount ! Calls: gemvTYPE (BLAS; dgemv or sgemv dependent on precision) !EOP ! *** local variables *** INTEGER :: i ! Counter INTEGER, SAVE :: allocflag = 0 ! Flag whether first time allocation is done REAL, ALLOCATABLE :: Vv_p(:) ! PE-local product V deltav REAL, ALLOCATABLE :: HVv_p(:) ! PE-local product HV deltav REAL, ALLOCATABLE :: RiHVv_p(:,:) ! PE-local observation residual REAL, ALLOCATABLE :: gradJ_p(:) ! PE-local part of gradJ (partial sums) REAL :: J_B_p, J_B, J_obs_p, J_obs ! Cost function terms ! ********************** ! *** INITIALIZATION *** ! ********************** IF (debug>0) & WRITE (*,*) '++ PDAF-debug: ', debug, 'PDAF_3dvar_costf_cvt -- START: iteration', iter ! Allocate arrays ALLOCATE(Vv_p(dim_p)) ALLOCATE(HVv_p(dim_obs_p)) ALLOCATE(RiHVv_p(dim_obs_p, 1)) ALLOCATE(gradJ_p(dim_cvec_p)) IF (allocflag == 0) CALL PDAF_memcount(3, 'r', 2*dim_obs_p + dim_cvec_p + dim_p) ! ******************************************* ! *** Observation part of cost function *** ! ******************************************* CALL PDAF_timeit(55, 'new') CALL PDAF_timeit(56, 'new') ! Apply V to control vector v_p IF (debug>0) & WRITE (*,*) '++ PDAF-debug: ', debug, 'PDAF_3dvar_costf_cvt -- call cvt' CALL PDAF_timeit(60, 'new') CALL U_cvt(iter, dim_p, dim_cvec_p, v_p, Vv_p) CALL PDAF_timeit(60, 'old') IF (debug>0) THEN WRITE (*,*) '++ PDAF-debug PDAF_3dvar_costf_cvt:', debug, & 'state increment after CVT dX(1:min(dim_p,6))', Vv_p(1:min(dim_p,6)) WRITE (*,*) '++ PDAF-debug PDAF_3dvar_costf_cvt:', debug, & 'MIN/MAX dX', MINVAL(Vv_p), MAXVAL(Vv_p) END IF ! Apply linearized observation operator IF (debug>0) & WRITE (*,*) '++ PDAF-debug: ', debug, 'PDAF_3dvar_costf_cvt -- call obs_op_lin' CALL PDAF_timeit(64, 'new') CALL U_obs_op_lin(step, dim_p, dim_obs_p, Vv_p, HVv_p) CALL PDAF_timeit(64, 'old') IF (debug>0) THEN WRITE (*,*) '++ PDAF-debug PDAF_3dvar_costf_cvt:', debug, & 'observed state after CVT (1:min(dim_obs_p,6))', HVv_p(1:min(dim_obs_p,6)) WRITE (*,*) '++ PDAF-debug PDAF_3dvar_costf_cvt:', debug, & 'MIN/MAX HdX', MINVAL(HVv_p), MAXVAL(HVv_p) END IF ! HVv - dy CALL PDAF_timeit(51, 'new') HVv_p = HVv_p - dy_p CALL PDAF_timeit(51, 'old') IF (debug>0) THEN WRITE (*,*) '++ PDAF-debug PDAF_3dvar_costf_cvt:', debug, & 'process local residual d (1:min(dim_obs_p,6))', HVv_p(1:min(dim_obs_p,6)) WRITE (*,*) '++ PDAF-debug PDAF_3dvar_costf_cvt:', debug, & 'MIN/MAX d', MINVAL(HVv_p), MAXVAL(HVv_p) END IF ! *** RiHVv = Rinv HVv ! *** This is implemented as a subroutine thus that ! *** Rinv does not need to be allocated explicitly. IF (debug>0) & WRITE (*,*) '++ PDAF-debug: ', debug, 'PDAF_3dvar_costf_cvt -- call prodRinvA' CALL PDAF_timeit(48, 'new') CALL U_prodRinvA(step, dim_obs_p, 1, obs_p, HVv_p, RiHVv_p) CALL PDAF_timeit(48, 'old') IF (debug>0) THEN WRITE (*,*) '++ PDAF-debug PDAF_3dvar_costf_cvt:', debug, & 'R^-1 d (1:min(dim_obs_p,6))', RiHVv_p(1:min(dim_obs_p,6),1) WRITE (*,*) '++ PDAF-debug PDAF_3dvar_costf_cvt:', debug, & 'MIN/MAX R^-1 d', MINVAL(RiHVv_p), MAXVAL(RiHVv_p) END IF ! *** Compute J_obs *** CALL PDAF_timeit(51, 'new') J_obs_p = 0.0 DO i = 1, dim_obs_p J_obs_p = J_obs_p + HVv_p(i)*RiHVv_p(i,1) END DO J_obs_p = 0.5*J_obs_p IF (debug>0) & WRITE (*,*) '++ PDAF-debug PDAF_3dvar_costf_cvt:', debug, & 'process local observation cost J_obs', J_obs_p ! Get global value CALL MPI_Allreduce(J_obs_p, J_obs, 1, MPI_REALTYPE, MPI_SUM, & COMM_filter, MPIerr) IF (debug>0) & WRITE (*,*) '++ PDAF-debug PDAF_3dvar_costf_cvt:', debug, & 'global observation cost J_obs', J_obs CALL PDAF_timeit(51, 'old') CALL PDAF_timeit(56, 'old') ! ****************************************** ! *** Background part of cost function *** ! ****************************************** CALL PDAF_timeit(57, 'new') CALL PDAF_timeit(51, 'new') J_B_p = 0.0 DO i = 1, dim_cvec_p J_B_p = J_B_p + v_p(i)*v_p(i) END DO J_B_p = 0.5 * J_B_p IF (debug>0) & WRITE (*,*) '++ PDAF-debug PDAF_3dvar_costf_cvt:', debug, & 'process local CV cost J_B', J_B_p IF (opt_parallel==1) THEN ! Get global value CALL MPI_Allreduce(J_B_p, J_B, 1, MPI_REALTYPE, MPI_SUM, & COMM_filter, MPIerr) ELSE J_B = J_B_p END IF IF (debug>0) & WRITE (*,*) '++ PDAF-debug PDAF_3dvar_costf_cvt:', debug, & 'global CV cost J_B', J_B CALL PDAF_timeit(57, 'old') ! ***************************** ! *** Total cost function *** ! ***************************** J_tot = J_B + J_obs CALL PDAF_timeit(51, 'old') CALL PDAF_timeit(55, 'old') ! ************************** ! *** Compute gradient *** ! ************************** CALL PDAF_timeit(58, 'new') ! Apply adjoint of observation operator IF (debug>0) & WRITE (*,*) '++ PDAF-debug: ', debug, 'PDAF_3dvar_costf_cvt -- call obs_op_adj' CALL PDAF_timeit(65, 'new') Vv_p = 0.0 CALL U_obs_op_adj(step, dim_p, dim_obs_p, RiHVv_p, Vv_p) CALL PDAF_timeit(65, 'old') IF (debug>0) THEN WRITE (*,*) '++ PDAF-debug PDAF_3dvar_costf_cvt:', debug, & 'H^TR^-1 d (1:min(dim_p,6))', Vv_p(1:min(dim_p,6)) WRITE (*,*) '++ PDAF-debug PDAF_3dvar_costf_cvt:', debug, & 'MIN/MAX H^TR^-1 d', MINVAL(Vv_p), MAXVAL(Vv_p) END IF ! Apply V^T to vector IF (debug>0) & WRITE (*,*) '++ PDAF-debug: ', debug, 'PDAF_3dvar_costf_cvt -- call cvt_adj' CALL PDAF_timeit(62, 'new') CALL U_cvt_adj(iter, dim_p, dim_cvec_p, Vv_p, gradJ) CALL PDAF_timeit(62, 'old') IF (debug>0) THEN WRITE (*,*) '++ PDAF-debug PDAF_3dvar_costf_cvt:', debug, & 'CVT(H^TR^-1 d) (1:min(dim_cvec_p,6))', gradJ(1:min(dim_cvec_p,6)) WRITE (*,*) '++ PDAF-debug PDAF_3dvar_costf_cvt:', debug, & 'MIN/MAX CVT(H^TR^-1 d)', MINVAL(gradJ), MAXVAL(gradJ) END IF ! Complete gradient adding v_p CALL PDAF_timeit(51, 'new') gradJ = v_p + gradJ CALL PDAF_timeit(51, 'old') IF (debug>0) THEN WRITE (*,*) '++ PDAF-debug PDAF_3dvar_costf_cvt:', debug, & 'process local gradient gradJ (1:min(dim_cvec_p,6))', gradJ(1:min(dim_cvec_p,6)) WRITE (*,*) '++ PDAF-debug PDAF_3dvar_costf_cvt:', debug, & 'MIN/MAX gradJ', MINVAL(gradJ), MAXVAL(gradJ) END IF CALL PDAF_timeit(58, 'old') ! ******************** ! *** Finishing up *** ! ******************** DEALLOCATE(Vv_p, HVv_p, RiHVv_p, gradJ_p) IF (allocflag == 0) allocflag = 1 IF (debug>0) & WRITE (*,*) '++ PDAF-debug: ', debug, 'PDAF_3dvar_costf_cvt -- END' END SUBROUTINE PDAF_3dvar_costf_cvt