! 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_enkf_Tleft --- Operate matrix T from left to some matrix ! ! !INTERFACE: SUBROUTINE PDAF_enkf_Tleft(dim_ens, dim, A) ! !DESCRIPTION: ! Operate matrix T on another matrix as ! B = T A\\ ! \\ ! T is a symmetric dim_ens x dim_ens matrix with zero column ! sums defined as: ! diag(T)=1-1/dim_ens; nondiag(T)=-1/dim_ens ! Applied from the left to a matrix A, T subtracts the ! mean over the rows of A from this matrix. In this routine, T ! is not explicitly constructed, but its operation on the ! matrix A is implemented. ! ! ! 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: USE PDAF_memcounting, & ONLY: PDAF_memcount IMPLICIT NONE ! !ARGUMENTS: INTEGER, INTENT(in) :: dim_ens ! Rank of initial covariance matrix INTEGER, INTENT(in) :: dim ! Number of columns in A and B REAL, INTENT(inout) :: A(dim_ens, dim) ! Input/output matrix ! !CALLING SEQUENCE: ! Called by: User-provided prepoststep routines for ETKF ! Called by: PDAF_etkf_analysis_T ! Called by: PDAF_letkf_analysis_T ! Calls: PDAF_memcount !EOP ! *** local variables *** INTEGER :: row, col ! counters REAL :: invdimens ! Inversize of ensemble size INTEGER, SAVE :: allocflag = 0 ! Flag for dynamic allocation REAL, ALLOCATABLE :: colmean(:) ! Mean values of columns of A ! ********************** ! *** INITIALIZATION *** ! ********************** ALLOCATE(colmean(dim)) IF (allocflag == 0) THEN ! count allocated memory CALL PDAF_memcount(3, 'r', dim) allocflag = 1 END IF colmean = 0.0 invdimens = 1.0 / REAL(dim_ens) ! *** Compute column means of A *** DO col = 1, dim DO row = 1, dim_ens colmean(col) = colmean(col) + A(row, col) END DO END DO colmean = invdimens * colmean ! **************************************************** ! *** Operate T on A *** ! *** *** ! *** Tv_1 = (v_11-mean(v_1), ... ,v_r1-mean(v_1)) *** ! *** with v_1 = (v_11,v_21, ... ,v_N) *** ! **************************************************** ! first DIM rows DO col = 1, dim DO row = 1, dim_ens A(row, col) = A(row, col) - colmean(col) END DO END DO ! ******************** ! *** FINISHING UP *** ! ******************** DEALLOCATE(colmean) END SUBROUTINE PDAF_enkf_Tleft