! 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: PDAF_lseik_analysis_trans.F90 1147 2023-03-12 16:14:34Z lnerger $ !BOP ! ! !ROUTINE: PDAF_lseik_analysis_trans --- LSEIK analysis/transformation ! ! !INTERFACE: SUBROUTINE PDAF_lseik_analysis_trans(domain_p, step, dim_l, dim_obs_f, dim_obs_l, & dim_ens, rank, state_l, Uinv_l, ens_l, HX_f, & HXbar_f, state_inc_l, OmegaT_in, forget, U_g2l_obs, & U_init_obs_l, U_prodRinvA_l, U_init_obsvar_l, U_init_n_domains_p, & screen, incremental, type_forget, type_sqrt, flag) ! !DESCRIPTION: ! Analysis step of the LSEIK filter with direct ! transformation of the forecast into the ! analysis ensemble. This variant does not ! compute the analysis state, but only the ! analysis ensemble, whose mean is the analysis ! state. ! Supported is also the adaptive forgetting factor. ! ! Variant for domain decomposed states. ! ! ! This is a core routine of PDAF and ! should not be changed by the user ! ! ! !REVISION HISTORY: ! 2009-07 - 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_filter, & ONLY: Nm1vsN, obs_member, debug USE PDAF_mod_filtermpi, & ONLY: mype USE PDAFomi, & ONLY: omi_omit_obs => omit_obs #if defined (_OPENMP) USE omp_lib, & ONLY: omp_get_num_threads, omp_get_thread_num #endif IMPLICIT NONE ! !ARGUMENTS: ! ! Variable naming scheme: ! ! suffix _p: Denotes a full variable on the PE-local domain ! ! suffix _l: Denotes a local variable on the current analysis domain INTEGER, INTENT(in) :: domain_p ! Current local analysis domain INTEGER, INTENT(in) :: step ! Current time step INTEGER, INTENT(in) :: dim_l ! State dimension on local analysis domain INTEGER, INTENT(in) :: dim_obs_f ! PE-local dimension of full observation vector INTEGER, INTENT(in) :: dim_obs_l ! Size of obs. vector on local ana. domain INTEGER, INTENT(in) :: dim_ens ! Size of ensemble INTEGER, INTENT(in) :: rank ! Rank of initial covariance matrix REAL, INTENT(inout) :: state_l(dim_l) ! on exit: state on local analysis domain REAL, INTENT(inout) :: Uinv_l(rank, rank) ! Inverse of matrix U - temporary use only REAL, INTENT(inout) :: ens_l(dim_l, dim_ens) ! Local state ensemble REAL, INTENT(in) :: HX_f(dim_obs_f, dim_ens) ! PE-local full observed state ens. REAL, INTENT(in) :: HXbar_f(dim_obs_f) ! PE-local full observed ens. mean REAL, INTENT(in) :: state_inc_l(dim_l) ! Local state increment REAL, INTENT(inout) :: OmegaT_in(rank, dim_ens) ! Matrix Omega REAL, INTENT(inout) :: forget ! Forgetting factor INTEGER, INTENT(in) :: screen ! Verbosity flag INTEGER, INTENT(in) :: incremental ! Control incremental updating INTEGER, INTENT(in) :: type_forget ! Type of forgetting factor INTEGER, INTENT(in) :: type_sqrt ! Type of square-root of A ! (0): symmetric sqrt; (1): Cholesky decomposition INTEGER, INTENT(inout) :: flag ! Status flag ! ! External subroutines ! ! (PDAF-internal names, real names are defined in the call to PDAF) EXTERNAL :: U_g2l_obs, & ! Restrict full obs. vector to local analysis domain U_init_obs_l, & ! Init. observation vector on local analysis domain U_init_obsvar_l, & ! Initialize local mean observation error variance U_init_n_domains_p, & ! Provide PE-local number of local analysis domains U_prodRinvA_l ! Provide product R^-1 A for local analysis domain ! !CALLING SEQUENCE: ! Called by: PDAF_lseik_update ! Calls: U_g2l_obs ! Calls: U_init_obs_l ! Calls: U_prodRinvA_l ! Calls: PDAF_set_forget_local ! Calls: PDAF_seik_matrixT ! Calls: PDAF_seik_Uinv ! Calls: PDAF_seik_TtimesA ! Calls: gemmTYPE (BLAS; dgemm or sgemm dependent on precision) ! Calls: gemvTYPE (BLAS; dgemv or sgemv dependent on precision) ! Calls: gesvTYPE (LAPACK; dgesv or sgesv dependent on precision) ! Calls: syevTYPE (LAPACK; dsyev or ssyev dependent on precision) ! Calls: potrfTYPE (LAPACK; dpotrf or spotrf dependent on precision) ! Calls: trtrsTYPE (LAPACK; dtrtrs or strtrs dependent on precision) !EOP ! *** local variables *** INTEGER :: i, j, member, col, row ! Counters INTEGER, SAVE :: allocflag = 0 ! Flag whether first time allocation is done INTEGER :: lib_info ! Status flag for LAPACK calls INTEGER :: ldwork ! Size of work array for SYEV INTEGER :: maxblksize, blkupper, blklower ! Variables for blocked ensemble update REAL :: fac ! Temporary variable sqrt(dim_ens) or sqrt(rank) INTEGER, SAVE :: lastdomain = -1 ! store domain index LOGICAL, SAVE :: screenout = .true. ! Whether to print information to stdout REAL, ALLOCATABLE :: HL_l(:,:) ! Temporary matrices for analysis REAL, ALLOCATABLE :: RiHL_l(:,:) ! Temporary matrices for analysis REAL, ALLOCATABLE :: resid_l(:) ! observation residual REAL, ALLOCATABLE :: obs_l(:) ! local observation vector REAL, ALLOCATABLE :: HXbar_l(:) ! state projected onto obs. space REAL, ALLOCATABLE :: RiHLd_l(:) ! local RiHLd REAL, ALLOCATABLE :: VRiHLd_l(:) ! Temporary vector for analysis REAL, ALLOCATABLE :: tmp_Uinv_l(:,:) ! Temporary storage of Uinv REAL, ALLOCATABLE :: OmegaT(:,:) ! Transpose of Omega REAL, ALLOCATABLE :: TA(:,:) ! Temporary matrix REAL, ALLOCATABLE :: ens_blk(:,:) ! Temporary blocked state ensemble REAL, ALLOCATABLE :: svals(:) ! Singular values of Uinv REAL, ALLOCATABLE :: work(:) ! Work array for SYEV INTEGER, ALLOCATABLE :: ipiv(:) ! vector of pivot indices for GESV INTEGER, SAVE :: mythread, nthreads ! Thread variables for OpenMP INTEGER :: incremental_dummy ! Dummy variable to avoid compiler warning REAL :: state_inc_l_dummy(1) ! Dummy variable to avoid compiler warning !$OMP THREADPRIVATE(mythread, nthreads, lastdomain, allocflag, screenout) ! ******************* ! *** Preparation *** ! ******************* CALL PDAF_timeit(51, 'new') ! Initialize variable to prevent compiler warning incremental_dummy = incremental state_inc_l_dummy(1) = state_inc_l(1) #if defined (_OPENMP) nthreads = omp_get_num_threads() mythread = omp_get_thread_num() #else nthreads = 1 mythread = 0 #endif ! Control screen output IF (lastdomain<domain_p .AND. lastdomain>-1) THEN screenout = .false. ELSE screenout = .true. ! In case of OpenMP, let only thread 0 write output to the screen IF (mythread>0) screenout = .false. ! Output, only in case of OpenMP parallelization #if defined (_OPENMP) IF (screenout) THEN WRITE (*,'(a, 5x,a,i5,a)') & 'PDAF', '--- Use OpenMP parallelization with ', nthreads, ' threads' END IF #endif END IF IF (debug>0) & WRITE (*,*) '++ PDAF-debug: ', debug, 'PDAF_lseik_analysis -- START' CALL PDAF_timeit(51, 'old') ! ************************ ! *** Compute residual *** ! *** d = y - H x *** ! ************************ CALL PDAF_timeit(12, 'new') haveobsB: IF (dim_obs_l > 0) THEN ! *** The residual only exists for domains with observations *** ALLOCATE(resid_l(dim_obs_l)) ALLOCATE(obs_l(dim_obs_l)) ALLOCATE(HXbar_l(dim_obs_l)) IF (allocflag == 0) CALL PDAF_memcount(3, 'r', 3 * dim_obs_l) ! Restrict mean obs. state onto local observation space IF (debug>0) & WRITE (*,*) '++ PDAF-debug: ', debug, 'PDAF_lseik_analysis -- call g2l_obs for mean' CALL PDAF_timeit(46, 'new') obs_member = 0 CALL U_g2l_obs(domain_p, step, dim_obs_f, dim_obs_l, HXbar_f, HXbar_l) CALL PDAF_timeit(46, 'old') ! get local observation vector IF (debug>0) & WRITE (*,*) '++ PDAF-debug: ', debug, 'PDAF_lseik_analysis -- call init_obs_l' CALL PDAF_timeit(47, 'new') CALL U_init_obs_l(domain_p, step, dim_obs_l, obs_l) CALL PDAF_timeit(47, 'old') ! Get residual as difference of observation and observed state CALL PDAF_timeit(51, 'new') resid_l = obs_l - HXbar_l CALL PDAF_timeit(51, 'old') IF (debug>0) & WRITE (*,*) '++ PDAF-debug PDAF_lseik_analysis:', debug, ' innovation d_l', resid_l ! Omit observations with too high innovation IF (omi_omit_obs) CALL PDAFomi_omit_by_inno_l_cb(domain_p, dim_obs_l, resid_l, obs_l) END IF haveobsB CALL PDAF_timeit(12, 'old') ! ************************************************* ! *** Compute analyzed matrix Uinv *** ! *** *** ! *** -1 T T -1 *** ! *** U = forget fac T T + (HL) R (HL) *** ! *** i i i i *** ! *** *** ! *** Here FAC is a scaling factor according *** ! *** to the definition of the ensemble *** ! *** covariance scaled by N^-1 (original SEIK) *** ! *** (N-1)^-1 (SEIK as ensemble KF) *** ! ************************************************* CALL PDAF_timeit(10, 'new') haveobsA: IF (dim_obs_l > 0) THEN ! *** The contribution of observation matrix ist only *** ! *** computed for domains with observations *** CALL PDAF_timeit(30, 'new') ! *** Compute HL = [Hx_1 ... Hx_N] T ALLOCATE(HL_l(dim_obs_l, dim_ens)) IF (allocflag == 0) CALL PDAF_memcount(3, 'r', dim_obs_l * dim_ens) CALL PDAF_timeit(46, 'new') IF (debug>0) & WRITE (*,*) '++ PDAF-debug: ', debug, 'PDAF_lseik_analysis -- call g2l_obs', dim_ens, 'times' ENS: DO member = 1, dim_ens ! Store member index obs_member = member ! [Hx_1 ... Hx_(r+1)] for local analysis domain CALL U_g2l_obs(domain_p, step, dim_obs_f, dim_obs_l, HX_f(:, member), & HL_l(:, member)) END DO ENS CALL PDAF_timeit(46, 'old') ! *** Set the value of the forgetting factor *** ! *** Inserted here, because HL_l is required *** CALL PDAF_timeit(51, 'new') IF (type_forget == 2) THEN CALL PDAF_set_forget_local(domain_p, step, dim_obs_l, dim_ens, HL_l, & HXbar_l, resid_l, obs_l, U_init_n_domains_p, U_init_obsvar_l, & forget) ENDIF DEALLOCATE(HXbar_l) ! Complete HL = [Hx_1 ... Hx_(r+1)] T CALL PDAF_seik_matrixT(dim_obs_l, dim_ens, HL_l) IF (debug>0) & WRITE (*,*) '++ PDAF-debug PDAF_lseik_analysis:', debug, ' HXT_l', HL_l(:, 1:dim_ens-1) CALL PDAF_timeit(51, 'old') CALL PDAF_timeit(30, 'old') CALL PDAF_timeit(31, 'new') ! *** RiHL = Rinv HL *** ! *** this is implemented as a subroutine thus that *** ! *** Rinv does not need to be allocated explicitly *** IF (debug>0) & WRITE (*,*) '++ PDAF-debug: ', debug, 'PDAF_lseik_analysis -- call prodRinvA_l' ALLOCATE(RiHL_l(dim_obs_l, rank)) IF (allocflag == 0) CALL PDAF_memcount(3, 'r', dim_obs_l * rank) CALL PDAF_timeit(48, 'new') CALL U_prodRinvA_l(domain_p, step, dim_obs_l, rank, obs_l, HL_l, RiHL_l) CALL PDAF_timeit(48, 'old') IF (debug>0) & WRITE (*,*) '++ PDAF-debug PDAF_lseik_analysis:', debug, ' R^-1(HXT_l)', RiHL_l DEALLOCATE(obs_l) CALL PDAF_timeit(51, 'new') ! *** Initialize Uinv = fac T^T T *** CALL PDAF_seik_Uinv(rank, Uinv_l) ! *** T *** ! *** Compute HL RiHL *** ALLOCATE(tmp_Uinv_l(rank, rank)) IF (allocflag == 0) CALL PDAF_memcount(3, 'r', rank**2) CALL gemmTYPE('t', 'n', rank, rank, dim_obs_l, & 1.0, HL_l, dim_obs_l, RiHL_l, dim_obs_l, & 0.0, tmp_Uinv_l, rank) DEALLOCATE(HL_l) CALL PDAF_timeit(51, 'old') ELSE haveobsA ! *** For domains with dim_obs_l=0 there is no *** ! *** direct observation-contribution to Uinv *** CALL PDAF_timeit(31, 'new') CALL PDAF_timeit(51, 'new') ! Initialize Uinv = fac T^T T CALL PDAF_seik_Uinv(rank, Uinv_l) ! No observation-contribution to Uinv from this domain ALLOCATE(tmp_Uinv_l(rank, rank)) IF (allocflag == 0) CALL PDAF_memcount(3, 'r', rank**2) tmp_Uinv_l = 0.0 CALL PDAF_timeit(51, 'old') END IF haveobsA ! *** Complete computation of Uinv *** ! *** -1 -1 T *** ! *** U = forget U + HL RiHL *** CALL PDAF_timeit(51, 'new') Uinv_l = forget * Uinv_l + tmp_Uinv_l CALL PDAF_timeit(51, 'old') IF (debug>0) & WRITE (*,*) '++ PDAF-debug PDAF_lseik_analysis:', debug, ' U^-1_l', Uinv_l CALL PDAF_timeit(31, 'old') CALL PDAF_timeit(10, 'old') ! *********************************************** ! *** Compute weight for model state update *** ! *** *** ! *** T f *** ! *** w = U RiHL d with d = (y - H x ) *** ! *********************************************** CALL PDAF_timeit(13, 'new') CALL PDAF_timeit(51, 'new') ! *** Computer RiHLd = RiHV^T d *** ALLOCATE(RiHLd_l(rank)) IF (allocflag == 0) CALL PDAF_memcount(3, 'r', rank) haveobsC: IF (dim_obs_l > 0) THEN ! *** RiHLd_p/=0 only with observations *** CALL gemvTYPE('t', dim_obs_l, rank, 1.0, RiHL_l, & dim_obs_l, resid_l, 1, 0.0, RiHLd_l, 1) IF (debug>0) & WRITE (*,*) '++ PDAF-debug PDAF_lseik_analysis:', debug, ' (HXT_l R^-1)^T d_l', RiHLd_l DEALLOCATE(RiHL_l, resid_l) ELSE haveobsC RiHLd_l = 0.0 END IF haveobsC ! *** Compute weight vector for state analysis: *** ! *** w = U RiHLd *** ! *** For this, two variants are implemented: *** ! *** 1. solve for w in: *** ! *** -1 *** ! *** U w = RiHLd *** ! *** We use the LAPACK routine GESV *** ! *** 2. Compute singular value decomposition *** ! *** of Uinv: Uinv = ASB^T *** ! *** Then: U = A S^(-1) B *** ! *** This is combined with a symmetric *** ! *** square-root for the ensemble transformation *** typeuinv1: IF (type_sqrt==1) THEN ! *** Variant 1: Solve Uinv w= RiHLd for w ALLOCATE(ipiv(rank)) IF (allocflag == 0) CALL PDAF_memcount(3, 'i', rank) ! save matrix Uinv tmp_Uinv_l = Uinv_l IF (debug>0) & WRITE (*,*) '++ PDAF-debug PDAF_lseik_analysis:', debug, & ' Invert U^-1_l using solver GESV' ! call solver (GESV - LU solver) CALL gesvTYPE(rank, 1, tmp_Uinv_l, rank, ipiv, & RiHLd_l, rank, lib_info) DEALLOCATE(ipiv) ELSE typeuinv1 ! *** Variant 2: Invert Uinv using SVD ALLOCATE(svals(rank)) ALLOCATE(work(3 * rank)) ldwork = 3 * rank IF (allocflag == 0) CALL PDAF_memcount(3, 'r', 4 * rank) IF (debug>0) & WRITE (*,*) '++ PDAF-debug PDAF_lseik_analysis:', debug, & ' Compute eigenvalue decomposition of U^-1_l' ! Compute SVD of Uinv CALL syevTYPE('v', 'l', rank, Uinv_l, rank, svals, work, ldwork, lib_info) DEALLOCATE(work) ! Compute product U RiHLd IF (lib_info==0) THEN IF (debug>0) & WRITE (*,*) '++ PDAF-debug PDAF_lseik_analysis:', debug, ' eigenvalues', svals ALLOCATE(VRiHLd_l(rank)) IF (allocflag == 0) CALL PDAF_memcount(3, 'r', rank) CALL gemvTYPE('t', rank, rank, 1.0, Uinv_l, & rank, RiHLd_l, 1, 0.0, VRiHLd_l, 1) DO row = 1,rank VRiHLd_l(row) = VRiHLd_l(row) / svals(row) END DO CALL gemvTYPE('n', rank, rank, 1.0, Uinv_l, & rank, VRiHLd_l, 1, 0.0, RiHLd_l, 1) IF (debug>0) & WRITE (*,*) '++ PDAF-debug PDAF_lseik_analysis:', debug, ' U(HXT_l R^-1)^T d_l', RiHLd_l DEALLOCATE(VRiHLd_l) END IF END IF typeuinv1 CALL PDAF_timeit(13, 'old') ! *** check whether SVD was successful IF (lib_info == 0) THEN flag = 0 ELSE WRITE (*, '(/5x, a, i10, a/)') & 'PDAF-ERROR(1): Domain ', domain_p, ' Problem in computation of analysis weights !!!' flag = 1 END IF ! **************************************************************** ! *** Transform state ensemble *** ! *** a _f f *** ! *** X = X + X W *** ! *** with -T T *** ! *** W = T (RiHLd + sqrt(FAC) C Omega ) *** ! *** Here FAC depends on the use definition of the covariance *** ! *** matrix P using a factor (r+1)^-1 or r^-1. *** ! **************************************************************** ! *** Prepare weight matrix for ensemble transformation *** check1: IF (flag == 0) THEN ! allocate fields ALLOCATE(OmegaT(rank, dim_ens)) IF (allocflag == 0) CALL PDAF_memcount(3, 'r', rank * dim_ens) IF (mype == 0 .AND. screen > 0 .AND. screenout) THEN WRITE (*, '(a, 5x, a)') 'PDAF', 'Transform state ensemble' IF (type_sqrt == 1) THEN WRITE (*, '(a, 5x, a)') 'PDAF', '--- use Cholesky square-root of U' ELSE WRITE (*, '(a, 5x, a)') 'PDAF', '--- use symmetric square-root of U' END IF END IF CALL PDAF_timeit(20, 'new') CALL PDAF_timeit(32, 'new') ! Part 1: square-root of U typeuinv2: IF (type_sqrt == 1) THEN ! Variant, if Uinv has been inverted above by solving ! Store Uinv for temporary use tmp_Uinv_l(:, :) = Uinv_l(:, :) IF (debug>0) & WRITE (*,*) '++ PDAF-debug PDAF_lseik_analysis:', debug, & ' Compute Cholesky decomposition of U^-1_l' ! Cholesky decomposition of tmp_Uinv_l = C C^T CALL potrfTYPE('l', rank, tmp_Uinv_l, rank, lib_info) ! check if Cholesky decomposition was successful CholeskyOK: IF (lib_info == 0) THEN ! Decomposition OK, continue flag = 0 ELSE ! Decomposition failed WRITE (*, '(/5x, a, i10, a/)') & 'PDAF-ERROR(3): Problem with Cholesky decomposition of Uinv - domain ', & domain_p, ' !!!' flag = 3 ENDIF CholeskyOK ELSE typeuinv2 ! Variant, if SVD inversion of Uinv has been performed ! Use OmegaT as temporary array DO col = 1, rank DO row = 1, rank OmegaT(row, col) = Uinv_l(row, col) / SQRT(svals(col)) END DO END DO CALL gemmTYPE('n', 't', rank, rank, rank, & 1.0, OmegaT, rank, Uinv_l, rank, & 0.0, tmp_Uinv_l, rank) DEALLOCATE(svals) ! Set flag flag = 0 END IF typeuinv2 CALL PDAF_timeit(32, 'old') END IF check1 check2: IF (flag == 0) THEN ! *** Part 2: Product U^(1/2) Omega *** CALL PDAF_timeit(34, 'new') IF (type_sqrt == 1) THEN ! Initialize the matrix Omega from argument OmegaT_in OmegaT = OmegaT_in ! A = (Omega C^(-1)) by solving Ct A = OmegaT for A CALL trtrsTYPE('l', 't', 'n', rank, dim_ens, & tmp_Uinv_l, rank, OmegaT, rank, lib_info) ELSE ! TEMP_UINV already contains matrix C (no more inversion) CALL gemmTYPE('n', 'n', rank, dim_ens, rank, & 1.0, tmp_Uinv_l, rank, OmegaT_in, rank, & 0.0, OmegaT, rank) lib_info = 0 END IF IF (debug>0) & WRITE (*,*) '++ PDAF-debug PDAF_lseik_analysis:', debug, & ' transform for perturbations', OmegaT CALL PDAF_timeit(34, 'old') ! check whether solve was successful solveOK: IF (lib_info == 0) THEN ! Solve for A OK, continue flag = 0 ELSE ! Solve for A failed WRITE (*, '(/5x, a, i10, a/)') & 'PDAF-ERROR(2): Problem in computation of transformation matrix - domain ', & domain_p, ' !!!' flag = 2 CALL PDAF_timeit(20, 'old') END IF solveOK END IF check2 check3: IF (flag == 0) THEN CALL PDAF_timeit(35, 'new') ! *** Part 4: Add RiHLd and multiply by scaling factor IF (Nm1vsN == 1) THEN ! Use factor (N-1)^-1 fac = SQRT(REAL(dim_ens - 1)) ELSE ! Use factor N^-1 fac = SQRT(REAL(dim_ens)) END IF ! *** Add RiHLd to A^T stored in OmegaT DO j = 1, dim_ens DO i = 1, rank OmegaT(i, j) = fac * OmegaT(i, j) + RiHLd_l(i) END DO END DO DEALLOCATE(RiHLd_l) ! *** T A^T (A^T stored in OmegaT_l) *** ALLOCATE(TA(dim_ens, dim_ens)) IF (allocflag == 0) CALL PDAF_memcount(3, 'r', dim_ens**2) CALL PDAF_seik_TtimesA(rank, dim_ens, OmegaT, TA) IF (debug>0) & WRITE (*,*) '++ PDAF-debug PDAF_lseik_analysis:', debug, ' transform', TA CALL PDAF_timeit(35, 'old') CALL PDAF_timeit(20, 'old') ! *** Perform ensemble transformation *** ! Use block formulation for transformation maxblksize = 200 IF (mype == 0 .AND. screen > 0 .AND. screenout) & WRITE (*, '(a, 5x, a, i5)') & 'PDAF', '--- use blocking with size ', maxblksize ALLOCATE(ens_blk(maxblksize, dim_ens)) IF (allocflag == 0) CALL PDAF_memcount(3, 'r', maxblksize * dim_ens) blocking: DO blklower = 1, dim_l, maxblksize blkupper = MIN(blklower + maxblksize - 1, dim_l) ! Store old state ensemble CALL PDAF_timeit(21, 'new') DO col = 1, dim_ens ens_blk(1 : blkupper - blklower + 1, col) & = ens_l(blklower : blkupper, col) END DO DO col = 1, dim_ens ens_l(blklower : blkupper, col) = state_l(blklower : blkupper) END DO CALL PDAF_timeit(21, 'old') ! a _f f T ! Transform ensemble: X = X + X T(A ) CALL PDAF_timeit(22, 'new') CALL gemmTYPE('n', 'n', blkupper - blklower + 1, dim_ens, dim_ens, & 1.0, ens_blk, maxblksize, TA, dim_ens, & 1.0, ens_l(blklower, 1), dim_l) CALL PDAF_timeit(22, 'old') END DO blocking DEALLOCATE(ens_blk, TA) DEALLOCATE(OmegaT) END IF check3 CALL PDAF_timeit(51, 'old') ! ******************** ! *** Finishing up *** ! ******************** DEALLOCATE(tmp_Uinv_l) IF (allocflag == 0) allocflag = 1 ! Store domain index lastdomain = domain_p IF (debug>0) & WRITE (*,*) '++ PDAF-debug: ', debug, 'PDAF_lseik_analysis -- END' END SUBROUTINE PDAF_lseik_analysis_trans