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!!$
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!!$ Parallel Sparse BLAS version 2.2
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!!$ (C) Copyright 2006/2007/2008
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!!$ 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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! Implements the BICGSTAB(L) method
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!
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!
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! Arguments:
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!
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! a - type(psb_dspmat_type) Input: sparse matrix containing A.
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! prec - type(psb_dprec_type) Input: preconditioner
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! b - real,dimension(:) Input: vector containing the
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! right hand side B
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! x - real,dimension(:) Input/Output: vector containing the
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! initial guess and final solution X.
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! eps - real Input: Stopping tolerance; the iteration is
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! stopped when the error estimate |err| <= eps
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! desc_a - type(psb_desc_type). Input: The communication descriptor.
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! info - integer. Output: Return code
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!
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! itmax - integer(optional) Input: maximum number of iterations to be
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! performed.
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! iter - integer(optional) Output: how many iterations have been
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! performed.
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! performed.
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! err - real (optional) Output: error estimate on exit. If the
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! denominator of the estimate is exactly
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! 0, it is changed into 1.
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|
! itrace - integer(optional) Input: print an informational message
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|
! with the error estimate every itrace
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|
! iterations
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|
! istop - integer(optional) Input: stopping criterion, or how
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|
! to estimate the error.
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|
! 1: err = |r|/|b|; here the iteration is
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|
! stopped when |r| <= eps * |b|
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|
! 2: err = |r|/(|a||x|+|b|); here the iteration is
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|
! stopped when |r| <= eps * (|a||x|+|b|)
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|
|
! where r is the (preconditioned, recursive
|
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|
|
! estimate of) residual.
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|
! irst - integer(optional) Input: restart parameter L
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|
!
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|
!
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|
!
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|
|
Subroutine psb_dcgstabl(a,prec,b,x,eps,desc_a,info,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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|
|
use psb_krylov_mod, psb_protect_name => psb_dcgstabl
|
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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(psb_dpk_), Intent(in) :: b(:)
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|
|
Real(psb_dpk_), Intent(inout) :: x(:)
|
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|
|
Real(psb_dpk_), Intent(in) :: eps
|
|
|
|
|
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(psb_dpk_), Optional, Intent(out) :: err
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|
|
!!$ local data
|
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|
|
Real(psb_dpk_), allocatable, target :: aux(:),wwrk(:,:),uh(:,:), rh(:,:)
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|
|
Real(psb_dpk_), Pointer :: ww(:), q(:), r(:), rt0(:), p(:), v(:), &
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|
|
& s(:), t(:), z(:), f(:), gamma(:), gamma1(:), gamma2(:), taum(:,:), sigma(:)
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|
|
Integer :: itmax_, naux, mglob, it, itrace_,&
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|
|
& np,me, n_row, n_col, nl, err_act
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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, ictxt,istop_,j, int_err(5)
|
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|
|
integer :: debug_level, debug_unit
|
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|
|
Real(psb_dpk_) :: alpha, beta, rho, rho_old, rni, xni, bni, ani,bn2,&
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|
|
& omega
|
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|
|
type(psb_itconv_type) :: stopdat
|
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|
|
character(len=20) :: name
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|
|
character(len=*), parameter :: methdname='BiCGStab(L)'
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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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|
|
debug_unit = psb_get_debug_unit()
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|
|
debug_level = psb_get_debug_level()
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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_level >= psb_debug_ext_)&
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|
|
& write(debug_unit,*) me,' ',trim(name),': from psb_info',np
|
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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)
|
|
|
|
|
n_col = psb_cd_get_local_cols(desc_a)
|
|
|
|
|
|
|
|
|
|
if (present(istop)) then
|
|
|
|
|
istop_ = istop
|
|
|
|
|
else
|
|
|
|
|
istop_ = 1
|
|
|
|
|
endif
|
|
|
|
|
|
|
|
|
|
if (present(itmax)) then
|
|
|
|
|
itmax_ = itmax
|
|
|
|
|
else
|
|
|
|
|
itmax_ = 1000
|
|
|
|
|
endif
|
|
|
|
|
|
|
|
|
|
if (present(itrace)) then
|
|
|
|
|
itrace_ = itrace
|
|
|
|
|
else
|
|
|
|
|
itrace_ = 0
|
|
|
|
|
end if
|
|
|
|
|
|
|
|
|
|
if (present(irst)) then
|
|
|
|
|
nl = irst
|
|
|
|
|
if (debug_level >= psb_debug_ext_) &
|
|
|
|
|
& write(debug_unit,*) me,' ',trim(name),&
|
|
|
|
|
& 'present: irst: ',irst,nl
|
|
|
|
|
else
|
|
|
|
|
nl = 1
|
|
|
|
|
if (debug_level >= psb_debug_ext_) &
|
|
|
|
|
& write(debug_unit,*) me,' ',trim(name),&
|
|
|
|
|
& ' not present: irst: ',irst,nl
|
|
|
|
|
endif
|
|
|
|
|
if (nl <=0 ) then
|
|
|
|
|
info=5001
|
|
|
|
|
int_err(1)=nl
|
|
|
|
|
err=info
|
|
|
|
|
call psb_errpush(info,name,i_err=int_err)
|
|
|
|
|
goto 9999
|
|
|
|
|
endif
|
|
|
|
|
|
|
|
|
|
call psb_chkvect(mglob,1,size(x,1),1,1,desc_a,info)
|
|
|
|
|
if (info == 0) call psb_chkvect(mglob,1,size(b,1),1,1,desc_a,info)
|
|
|
|
|
if (info /= 0) then
|
|
|
|
|
info=4010
|
|
|
|
|
call psb_errpush(info,name,a_err='psb_chkvect on X/B')
|
|
|
|
|
goto 9999
|
|
|
|
|
end if
|
|
|
|
|
|
|
|
|
|
naux=4*n_col
|
|
|
|
|
allocate(aux(naux),gamma(0:nl),gamma1(nl),&
|
|
|
|
|
&gamma2(nl),taum(nl,nl),sigma(nl), stat=info)
|
|
|
|
|
|
|
|
|
|
if (info /= 0) then
|
|
|
|
|
info=4000
|
|
|
|
|
call psb_errpush(info,name)
|
|
|
|
|
goto 9999
|
|
|
|
|
end if
|
|
|
|
|
if (info == 0) Call psb_geall(wwrk,desc_a,info,n=10)
|
|
|
|
|
if (info == 0) Call psb_geall(uh,desc_a,info,n=nl+1,lb=0)
|
|
|
|
|
if (info == 0) Call psb_geall(rh,desc_a,info,n=nl+1,lb=0)
|
|
|
|
|
if (info == 0) Call psb_geasb(wwrk,desc_a,info)
|
|
|
|
|
if (info == 0) Call psb_geasb(uh,desc_a,info)
|
|
|
|
|
if (info == 0) Call psb_geasb(rh,desc_a,info)
|
|
|
|
|
if (info /= 0) then
|
|
|
|
|
info=4011
|
|
|
|
|
call psb_errpush(info,name)
|
|
|
|
|
goto 9999
|
|
|
|
|
end if
|
|
|
|
|
|
|
|
|
|
q => wwrk(:,1)
|
|
|
|
|
r => wwrk(:,2)
|
|
|
|
|
p => wwrk(:,3)
|
|
|
|
|
v => wwrk(:,4)
|
|
|
|
|
f => wwrk(:,5)
|
|
|
|
|
s => wwrk(:,6)
|
|
|
|
|
t => wwrk(:,7)
|
|
|
|
|
z => wwrk(:,8)
|
|
|
|
|
ww => wwrk(:,9)
|
|
|
|
|
rt0 => wwrk(:,10)
|
|
|
|
|
|
|
|
|
|
! Ensure global coherence for convergence checks.
|
|
|
|
|
call psb_set_coher(ictxt,isvch)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
call psb_init_conv(methdname,istop_,itrace_,itmax_,a,b,eps,desc_a,stopdat,info)
|
|
|
|
|
if (info /= 0) Then
|
|
|
|
|
call psb_errpush(4011,name)
|
|
|
|
|
goto 9999
|
|
|
|
|
End If
|
|
|
|
|
|
|
|
|
|
itx = 0
|
|
|
|
|
restart: do
|
|
|
|
|
!!$
|
|
|
|
|
!!$ r0 = b-ax0
|
|
|
|
|
!!$
|
|
|
|
|
if (debug_level >= psb_debug_ext_) &
|
|
|
|
|
& write(debug_unit,*) me,' ',trim(name),' restart: ',itx,it
|
|
|
|
|
if (itx >= itmax_) exit restart
|
|
|
|
|
|
|
|
|
|
it = 0
|
|
|
|
|
call psb_geaxpby(done,b,dzero,r,desc_a,info)
|
|
|
|
|
if (info == 0) call psb_spmm(-done,a,x,done,r,desc_a,info,work=aux)
|
|
|
|
|
|
|
|
|
|
if (info == 0) call psb_precaply(prec,r,desc_a,info)
|
|
|
|
|
|
|
|
|
|
if (info == 0) call psb_geaxpby(done,r,dzero,rt0,desc_a,info)
|
|
|
|
|
if (info == 0) call psb_geaxpby(done,r,dzero,rh(:,0),desc_a,info)
|
|
|
|
|
if (info == 0) call psb_geaxpby(dzero,r,dzero,uh(:,0),desc_a,info)
|
|
|
|
|
if (info /= 0) then
|
|
|
|
|
info=4011
|
|
|
|
|
call psb_errpush(info,name)
|
|
|
|
|
goto 9999
|
|
|
|
|
end if
|
|
|
|
|
|
|
|
|
|
rho = done
|
|
|
|
|
alpha = dzero
|
|
|
|
|
omega = done
|
|
|
|
|
|
|
|
|
|
if (debug_level >= psb_debug_ext_) &
|
|
|
|
|
& write(debug_unit,*) me,' ',trim(name),&
|
|
|
|
|
& ' on entry to amax: b: ',Size(b)
|
|
|
|
|
|
|
|
|
|
if (psb_check_conv(methdname,itx,x,r,desc_a,stopdat,info)) exit restart
|
|
|
|
|
if (info /= 0) Then
|
|
|
|
|
call psb_errpush(4011,name)
|
|
|
|
|
goto 9999
|
|
|
|
|
End If
|
|
|
|
|
|
|
|
|
|
iteration: do
|
|
|
|
|
it = it + nl
|
|
|
|
|
itx = itx + nl
|
|
|
|
|
rho = -omega*rho
|
|
|
|
|
|
|
|
|
|
if (debug_level >= psb_debug_ext_) &
|
|
|
|
|
& write(debug_unit,*) me,' ',trim(name),&
|
|
|
|
|
& ' iteration: ',itx, rho,rh(1,0)
|
|
|
|
|
|
|
|
|
|
do j = 0, nl -1
|
|
|
|
|
If (debug_level >= psb_debug_ext_) &
|
|
|
|
|
& write(debug_unit,*) me,' ',trim(name),'bicg part: ',j, nl
|
|
|
|
|
|
|
|
|
|
rho_old = rho
|
|
|
|
|
rho = psb_gedot(rh(:,j),rt0,desc_a,info)
|
|
|
|
|
if (rho==dzero) then
|
|
|
|
|
if (debug_level >= psb_debug_ext_) &
|
|
|
|
|
& write(debug_unit,*) me,' ',trim(name),&
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|
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& ' 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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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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|
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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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|
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if (debug_level >= psb_debug_ext_) &
|
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& write(debug_unit,*) me,' ',trim(name),&
|
|
|
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& ' bi-cgstab iteration breakdown s2',gamma(j)
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|
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exit iteration
|
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|
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endif
|
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alpha = rho/gamma(j)
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|
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if (debug_level >= psb_debug_ext_) &
|
|
|
|
|
& write(debug_unit,*) me,' ',trim(name),&
|
|
|
|
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& ' 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)
|
|
|
|
|
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)
|
|
|
|
|
|
|
|
|
|
call psb_precaply(prec,rh(:,j+1),desc_a,info)
|
|
|
|
|
|
|
|
|
|
enddo
|
|
|
|
|
|
|
|
|
|
do j=1, nl
|
|
|
|
|
if (debug_level >= psb_debug_ext_) &
|
|
|
|
|
& write(debug_unit,*) me,' ',trim(name),&
|
|
|
|
|
& ' mod g-s part: ',j, nl,rh(1,0)
|
|
|
|
|
|
|
|
|
|
do i=1, j-1
|
|
|
|
|
taum(i,j) = psb_gedot(rh(:,i),rh(:,j),desc_a,info)
|
|
|
|
|
taum(i,j) = taum(i,j)/sigma(i)
|
|
|
|
|
call psb_geaxpby(-taum(i,j),rh(:,i),done,rh(:,j),desc_a,info)
|
|
|
|
|
enddo
|
|
|
|
|
sigma(j) = psb_gedot(rh(:,j),rh(:,j),desc_a,info)
|
|
|
|
|
gamma1(j) = psb_gedot(rh(:,0),rh(:,j),desc_a,info)
|
|
|
|
|
gamma1(j) = gamma1(j)/sigma(j)
|
|
|
|
|
enddo
|
|
|
|
|
|
|
|
|
|
gamma(nl) = gamma1(nl)
|
|
|
|
|
omega = gamma(nl)
|
|
|
|
|
|
|
|
|
|
do j=nl-1,1,-1
|
|
|
|
|
gamma(j) = gamma1(j)
|
|
|
|
|
do i=j+1,nl
|
|
|
|
|
gamma(j) = gamma(j) - taum(j,i) * gamma(i)
|
|
|
|
|
enddo
|
|
|
|
|
enddo
|
|
|
|
|
|
|
|
|
|
do j=1,nl-1
|
|
|
|
|
gamma2(j) = gamma(j+1)
|
|
|
|
|
do i=j+1,nl-1
|
|
|
|
|
gamma2(j) = gamma2(j) + taum(j,i) * gamma(i+1)
|
|
|
|
|
enddo
|
|
|
|
|
enddo
|
|
|
|
|
|
|
|
|
|
call psb_geaxpby(gamma(1),rh(:,0),done,x,desc_a,info)
|
|
|
|
|
call psb_geaxpby(-gamma1(nl),rh(:,nl),done,rh(:,0),desc_a,info)
|
|
|
|
|
call psb_geaxpby(-gamma(nl),uh(:,nl),done,uh(:,0),desc_a,info)
|
|
|
|
|
|
|
|
|
|
do j=1, nl-1
|
|
|
|
|
call psb_geaxpby(-gamma(j),uh(:,j),done,uh(:,0),desc_a,info)
|
|
|
|
|
call psb_geaxpby(gamma2(j),rh(:,j),done,x,desc_a,info)
|
|
|
|
|
call psb_geaxpby(-gamma1(j),rh(:,j),done,rh(:,0),desc_a,info)
|
|
|
|
|
enddo
|
|
|
|
|
|
|
|
|
|
if (psb_check_conv(methdname,itx,x,rh(:,0),desc_a,stopdat,info)) exit restart
|
|
|
|
|
if (info /= 0) Then
|
|
|
|
|
call psb_errpush(4011,name)
|
|
|
|
|
goto 9999
|
|
|
|
|
End If
|
|
|
|
|
|
|
|
|
|
end do iteration
|
|
|
|
|
end do restart
|
|
|
|
|
|
|
|
|
|
call psb_end_conv(methdname,itx,desc_a,stopdat,info,err,iter)
|
|
|
|
|
|
|
|
|
|
deallocate(aux,stat=info)
|
|
|
|
|
if (info == 0) call psb_gefree(wwrk,desc_a,info)
|
|
|
|
|
if (info == 0) call psb_gefree(uh,desc_a,info)
|
|
|
|
|
if (info == 0) call psb_gefree(rh,desc_a,info)
|
|
|
|
|
if (info/=0) then
|
|
|
|
|
call psb_errpush(info,name)
|
|
|
|
|
goto 9999
|
|
|
|
|
end if
|
|
|
|
|
|
|
|
|
|
! restore external global coherence behaviour
|
|
|
|
|
call psb_restore_coher(ictxt,isvch)
|
|
|
|
|
call psb_erractionrestore(err_act)
|
|
|
|
|
return
|
|
|
|
|
|
|
|
|
|
9999 continue
|
|
|
|
|
call psb_erractionrestore(err_act)
|
|
|
|
|
if (err_act == psb_act_abort_) then
|
|
|
|
|
call psb_error()
|
|
|
|
|
return
|
|
|
|
|
end if
|
|
|
|
|
return
|
|
|
|
|
|
|
|
|
|
End Subroutine psb_dcgstabl
|
|
|
|
|
|
|
|
|
|
|
