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417 lines
14 KiB
Fortran
417 lines
14 KiB
Fortran
!!$
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!!$ Parallel Sparse BLAS v2.0
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!!$ (C) Copyright 2006 Salvatore Filippone University of Rome Tor Vergata
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!!$ Alfredo Buttari University of Rome Tor Vergata
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!!$
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!!$ Redistribution and use in source and binary forms, with or without
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!!$ modification, are permitted provided that the following conditions
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!!$ are met:
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!!$ 1. Redistributions of source code must retain the above copyright
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!!$ notice, this list of conditions and the following disclaimer.
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!!$ 2. Redistributions in binary form must reproduce the above copyright
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!!$ notice, this list of conditions, and the following disclaimer in the
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!!$ documentation and/or other materials provided with the distribution.
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!!$ 3. The name of the PSBLAS group or the names of its contributors may
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!!$ not be used to endorse or promote products derived from this
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!!$ software without specific written permission.
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!!$
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!!$ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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!!$ ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
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!!$ TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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!!$ PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE PSBLAS GROUP OR ITS CONTRIBUTORS
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!!$ BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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!!$ CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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!!$ SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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!!$ INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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!!$ CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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!!$ ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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!!$ POSSIBILITY OF SUCH DAMAGE.
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!!$
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!!$
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!!$ CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
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!!$ C C
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!!$ C References: C
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!!$ C [1] Duff, I., Marrone, M., Radicati, G., and Vittoli, C. C
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!!$ C Level 3 basic linear algebra subprograms for sparse C
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!!$ C matrices: a user level interface C
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!!$ C ACM Trans. Math. Softw., 23(3), 379-401, 1997. C
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!!$ C C
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!!$ C C
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!!$ C [2] S. Filippone, M. Colajanni C
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!!$ C PSBLAS: A library for parallel linear algebra C
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!!$ C computation on sparse matrices C
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!!$ C ACM Trans. on Math. Softw., 26(4), 527-550, Dec. 2000. C
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!!$ C C
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!!$ C [3] M. Arioli, I. Duff, M. Ruiz C
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!!$ C Stopping criteria for iterative solvers C
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!!$ C SIAM J. Matrix Anal. Appl., Vol. 13, pp. 138-144, 1992 C
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!!$ C C
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!!$ C C
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!!$ C [4] R. Barrett et al C
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!!$ C Templates for the solution of linear systems C
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!!$ C SIAM, 1993 C
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!!$ C C
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!!$ C C
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!!$ C [5] G. Sleijpen, D. Fokkema C
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!!$ C BICGSTAB(L) for linear equations involving unsymmetric C
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!!$ C matrices with complex spectrum C
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!!$ C Electronic Trans. on Numer. Analysis, Vol. 1, pp. 11-32, C
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!!$ C Sep. 1993 C
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!!$ C C
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!!$ C C
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!!$ CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
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! File: psb_dcgstabl.f90
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!
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! Subroutine: psb_dcgstabl
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!
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! Parameters:
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! a - type(<psb_dspmat_type>). The sparse matrix containing A.
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! prec - type(<psb_prec_type>). The data structure containing the preconditioner.
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! b - real,dimension(:). The right hand side.
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! x - real,dimension(:). The vector of unknowns.
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! eps - real. The error tolerance.
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! desc_a - type(<psb_desc_type>). The communication descriptor.
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! info - integer. Eventually returns an error code.
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! itmax - integer(optional). The maximum number of iterations.
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! iter - integer(optional). The number of iterations performed.
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! err - real(optional). The error on return.
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! itrace - integer(optional). The unit to write messages onto.
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! istop - integer(optional). The stopping criterium.
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!
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Subroutine psb_dcgstabl(a,prec,b,x,eps,desc_a,info,&
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&itmax,iter,err,itrace,irst,istop)
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use psb_base_mod
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use psb_prec_mod
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implicit none
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!!$ parameters
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Type(psb_dspmat_type), Intent(in) :: a
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Type(psb_dprec_type), Intent(in) :: prec
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Type(psb_desc_type), Intent(in) :: desc_a
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Real(Kind(1.d0)), Intent(in) :: b(:)
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Real(Kind(1.d0)), Intent(inout) :: x(:)
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Real(Kind(1.d0)), Intent(in) :: eps
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integer, intent(out) :: info
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Integer, Optional, Intent(in) :: itmax, itrace, irst,istop
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Integer, Optional, Intent(out) :: iter
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Real(Kind(1.d0)), Optional, Intent(out) :: err
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!!$ local data
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Real(Kind(1.d0)), allocatable, target :: aux(:),wwrk(:,:),uh(:,:), rh(:,:)
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Real(Kind(1.d0)), Pointer :: ww(:), q(:), r(:), rt0(:), p(:), v(:), &
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& s(:), t(:), z(:), f(:), gamma(:), gamma1(:), gamma2(:), taum(:,:), sigma(:)
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Real(Kind(1.d0)) :: rerr
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Integer :: litmax, naux, m, mglob, it, itrace_,&
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& np,me, n_row, n_col, nl, err_act
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Character ::diagl, diagu
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Logical, Parameter :: exchange=.True., noexchange=.False.
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Integer, Parameter :: irmax = 8
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Integer :: itx, i, isvch, ich, ictxt,istop_,j, int_err(5)
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Logical, Parameter :: debug = .False.
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Real(Kind(1.d0)) :: alpha, beta, rho, rho_old, rni, xni, bni, ani,bn2,&
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& omega, tau
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character(len=20) :: name
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info = 0
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name = 'psb_dcgstabl'
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call psb_erractionsave(err_act)
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If (debug) Write(0,*) 'entering psb_dbicgstabl'
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ictxt = psb_cd_get_context(desc_a)
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Call psb_info(ictxt, me, np)
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If (debug) Write(0,*) 'psb_dbicgstabl: from gridinfo',np,me
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mglob = psb_cd_get_global_rows(desc_a)
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n_row = psb_cd_get_local_rows(desc_a)
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n_col = psb_cd_get_local_cols(desc_a)
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if (present(istop)) then
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istop_ = istop
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else
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istop_ = 1
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endif
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!
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! ISTOP_ = 1: Normwise backward error, infinity norm
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! ISTOP_ = 2: ||r||/||b|| norm 2
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!
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if ((istop_ < 1 ).or.(istop_ > 2 ) ) then
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write(0,*) 'psb_bicgstabl: invalid istop',istop_
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info=5001
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int_err=istop_
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err=info
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call psb_errpush(info,name,i_err=int_err)
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goto 9999
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endif
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If (Present(itmax)) Then
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litmax = itmax
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Else
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litmax = 1000
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Endif
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If (Present(itrace)) Then
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itrace_ = itrace
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Else
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itrace_ = 0
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End If
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If (Present(irst)) Then
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nl = irst
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If (debug) Write(0,*) 'present: irst: ',irst,nl
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Else
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nl = 1
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If (debug) Write(0,*) 'not present: irst: ',irst,nl
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Endif
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if (nl <=0 ) then
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write(0,*) 'psb_bicgstabl: invalid irst ',nl
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info=5001
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int_err(1)=nl
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err=info
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call psb_errpush(info,name,i_err=int_err)
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goto 9999
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endif
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naux=4*n_col
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Allocate(aux(naux),gamma(0:nl),gamma1(nl),&
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&gamma2(nl),taum(nl,nl),sigma(nl), stat=info)
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If (info.Ne.0) Then
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info=4000
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call psb_errpush(info,name)
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goto 9999
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End If
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if (info == 0) Call psb_geall(wwrk,desc_a,info,n=10)
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if (info == 0) Call psb_geall(uh,desc_a,info,n=nl+1)
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if (info == 0) Call psb_geall(rh,desc_a,info,n=nl+1)
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if (info == 0) Call psb_geasb(wwrk,desc_a,info)
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if (info == 0) Call psb_geasb(uh,desc_a,info)
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if (info == 0) Call psb_geasb(rh,desc_a,info)
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if (info.ne.0) Then
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info=4011
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call psb_errpush(info,name)
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goto 9999
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End If
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q => wwrk(:,1)
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r => wwrk(:,2)
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p => wwrk(:,3)
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v => wwrk(:,4)
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f => wwrk(:,5)
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s => wwrk(:,6)
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t => wwrk(:,7)
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z => wwrk(:,8)
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ww => wwrk(:,9)
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rt0 => wwrk(:,10)
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! Ensure global coherence for convergence checks.
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call psb_set_coher(ictxt,isvch)
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if (istop_ == 1) then
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ani = psb_spnrmi(a,desc_a,info)
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bni = psb_geamax(b,desc_a,info)
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else if (istop_ == 2) then
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bn2 = psb_genrm2(b,desc_a,info)
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endif
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if (info.ne.0) Then
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info=4011
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call psb_errpush(info,name)
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goto 9999
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End If
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diagl = 'u'
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diagu = 'u'
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itx = 0
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restart: Do
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!!$
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!!$ r0 = b-ax0
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!!$
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If (debug) Write(0,*) 'restart: ',itx,it
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If (itx.Ge.litmax) Exit restart
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it = 0
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Call psb_geaxpby(done,b,dzero,r,desc_a,info)
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Call psb_spmm(-done,a,x,done,r,desc_a,info,work=aux)
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call psb_precaply(prec,r,desc_a,info)
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Call psb_geaxpby(done,r,dzero,rt0,desc_a,info)
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Call psb_geaxpby(done,r,dzero,rh(:,0),desc_a,info)
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Call psb_geaxpby(dzero,r,dzero,uh(:,0),desc_a,info)
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if (info.ne.0) Then
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info=4011
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call psb_errpush(info,name)
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goto 9999
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End If
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rho = done
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alpha = dzero
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omega = done
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If (debug) Write(0,*) 'on entry to amax: b: ',Size(b)
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if (istop_ == 1) then
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rni = psb_geamax(r,desc_a,info)
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xni = psb_geamax(x,desc_a,info)
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rerr = rni/(ani*xni+bni)
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else if (istop_ == 2) then
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rni = psb_genrm2(r,desc_a,info)
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rerr = rni/bn2
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endif
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if (info.ne.0) Then
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info=4011
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call psb_errpush(info,name)
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goto 9999
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End If
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If (rerr<=eps) Then
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Exit restart
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End If
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If (itrace_ > 0) then
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if ((mod(itx,itrace_)==0).and.(me == 0))&
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& write(*,'(a,i4,3(2x,es10.4))') 'bicgstab(l): ',itx,rerr
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end If
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iteration: Do
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it = it + nl
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itx = itx + nl
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rho = -omega*rho
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If (debug) Write(0,*) 'iteration: ',itx, rho,rh(1,0)
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Do j = 0, nl -1
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If (debug) Write(0,*) 'bicg part: ',j, nl
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rho_old = rho
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rho = psb_gedot(rh(:,j),rt0,desc_a,info)
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If (rho==dzero) Then
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If (debug) Write(0,*) 'bi-cgstab iteration breakdown r',rho
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Exit iteration
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Endif
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beta = alpha*rho/rho_old
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If (debug) Write(0,*) 'bicg part: ',alpha,beta,rho,rho_old
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rho_old = rho
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Call psb_geaxpby(done,rh(:,0:j),-beta,uh(:,0:j),desc_a,info)
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If (debug) Write(0,*) 'bicg part: ',rh(1,0),beta
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Call psb_spmm(done,a,uh(:,j),dzero,uh(:,j+1),desc_a,info,work=aux)
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call psb_precaply(prec,uh(:,j+1),desc_a,info)
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gamma(j) = psb_gedot(uh(:,j+1),rt0,desc_a,info)
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If (gamma(j)==dzero) Then
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If (debug) Write(0,*) 'bi-cgstab iteration breakdown s2',gamma(j)
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Exit iteration
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Endif
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alpha = rho/gamma(j)
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If (debug) Write(0,*) 'bicg part: alpha=r/g ',alpha,rho,gamma(j)
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Call psb_geaxpby(-alpha,uh(:,1:j+1),done,rh(:,0:j),desc_a,info)
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Call psb_geaxpby(alpha,uh(:,0),done,x,desc_a,info)
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Call psb_spmm(done,a,rh(:,j),dzero,rh(:,j+1),desc_a,info,work=aux)
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call psb_precaply(prec,rh(:,j+1),desc_a,info)
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Enddo
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Do j=1, nl
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If (debug) Write(0,*) 'mod g-s part: ',j, nl,rh(1,0)
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Do i=1, j-1
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taum(i,j) = psb_gedot(rh(:,i),rh(:,j),desc_a,info)
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taum(i,j) = taum(i,j)/sigma(i)
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Call psb_geaxpby(-taum(i,j),rh(:,i),done,rh(:,j),desc_a,info)
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Enddo
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If (debug) Write(0,*) 'mod g-s part: dot prod '
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sigma(j) = psb_gedot(rh(:,j),rh(:,j),desc_a,info)
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gamma1(j) = psb_gedot(rh(:,0),rh(:,j),desc_a,info)
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If (debug) Write(0,*) 'mod g-s part: gamma1 ', &
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&gamma1(j), sigma(j)
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gamma1(j) = gamma1(j)/sigma(j)
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Enddo
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gamma(nl) = gamma1(nl)
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omega = gamma(nl)
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Do j=nl-1,1,-1
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gamma(j) = gamma1(j)
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Do i=j+1,nl
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gamma(j) = gamma(j) - taum(j,i) * gamma(i)
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Enddo
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Enddo
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If (debug) Write(0,*) 'first solve: ', gamma(:)
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Do j=1,nl-1
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gamma2(j) = gamma(j+1)
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Do i=j+1,nl-1
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gamma2(j) = gamma2(j) + taum(j,i) * gamma(i+1)
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Enddo
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Enddo
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If (debug) Write(0,*) 'second solve: ', gamma(:)
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Call psb_geaxpby(gamma(1),rh(:,0),done,x,desc_a,info)
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Call psb_geaxpby(-gamma1(nl),rh(:,nl),done,rh(:,0),desc_a,info)
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Call psb_geaxpby(-gamma(nl),uh(:,nl),done,uh(:,0),desc_a,info)
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Do j=1, nl-1
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Call psb_geaxpby(-gamma(j),uh(:,j),done,uh(:,0),desc_a,info)
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Call psb_geaxpby(gamma2(j),rh(:,j),done,x,desc_a,info)
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Call psb_geaxpby(-gamma1(j),rh(:,j),done,rh(:,0),desc_a,info)
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Enddo
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if (istop_ == 1) then
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rni = psb_geamax(rh(:,0),desc_a,info)
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xni = psb_geamax(x,desc_a,info)
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rerr = rni/(ani*xni+bni)
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else if (istop_ == 2) then
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rni = psb_genrm2(rh(:,0),desc_a,info)
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rerr = rni/bn2
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endif
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If (rerr<=eps) Then
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Exit restart
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End If
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If (itx.Ge.litmax) Exit restart
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If (itrace_ > 0) then
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if ((mod(itx,itrace_)==0).and.(me == 0))&
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& write(*,'(a,i4,3(2x,es10.4))') 'bicgstab(l): ',itx,rerr
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end If
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End Do iteration
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End Do restart
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If (itrace_ > 0) then
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if (me == 0) write(*,'(a,i4,3(2x,es10.4))') 'bicgstab(l): ',itx,rerr
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end If
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If (Present(err)) err=rerr
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If (Present(iter)) iter = itx
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If (rerr>eps) Then
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Write(0,*) 'bi-cgstabl failed to converge to ',eps,&
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& ' in ',itx,' iterations '
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End If
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Deallocate(aux)
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Call psb_gefree(wwrk,desc_a,info)
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Call psb_gefree(uh,desc_a,info)
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Call psb_gefree(rh,desc_a,info)
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! restore external global coherence behaviour
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call psb_restore_coher(ictxt,isvch)
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if(info/=0) then
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call psb_errpush(info,name)
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goto 9999
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end if
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call psb_erractionrestore(err_act)
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return
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9999 continue
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call psb_erractionrestore(err_act)
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if (err_act.eq.psb_act_abort_) then
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call psb_error()
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return
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end if
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return
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End Subroutine psb_dcgstabl
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