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!
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! Parallel Sparse BLAS version 3.5
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! (C) Copyright 2006-2018
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! Salvatore Filippone
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! Alfredo Buttari
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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_zcgstabl.f90
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!
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! Subroutine: psb_zcgstabl
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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_zspmat_type) Input: sparse matrix containing A.
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! prec - class(psb_zprec_type) Input: preconditioner
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! b(:) - complex Input: vector containing the
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! right hand side B
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! x(:) - complex 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|/(|a||x|+|b|); here the iteration
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! is stopped when |r| <= eps * (|a||x|+|b|)
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! 2: err = |r|/|b|; here the iteration is
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! stopped when |r| <= eps * |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_zcgstabl_vect(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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use psb_z_krylov_conv_mod
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use psb_krylov_mod
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implicit none
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type(psb_zspmat_type), intent(in) :: a
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class(psb_zprec_type), Intent(inout) :: prec
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Type(psb_desc_type), Intent(in) :: desc_a
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type(psb_z_vect_type), Intent(inout) :: b
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type(psb_z_vect_type), Intent(inout) :: x
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Real(psb_dpk_), Intent(in) :: eps
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integer(psb_ipk_), intent(out) :: info
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integer(psb_ipk_), Optional, Intent(in) :: itmax, itrace, irst,istop
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integer(psb_ipk_), 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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complex(psb_dpk_), allocatable, target :: aux(:), gamma(:),&
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& gamma1(:), gamma2(:), taum(:,:), sigma(:)
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type(psb_z_vect_type), allocatable, target :: wwrk(:),uh(:), rh(:)
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type(psb_z_vect_type), Pointer :: ww, q, r, rt0, p, v, &
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& s, t, z, f
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integer(psb_ipk_) :: itmax_, naux, it, itrace_,&
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& n_row, n_col, nl, err_act
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integer(psb_lpk_) :: mglob
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Logical, Parameter :: exchange=.True., noexchange=.False.
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integer(psb_ipk_), Parameter :: irmax = 8
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integer(psb_ipk_) :: itx, i, istop_,j, k
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integer(psb_ipk_) :: debug_level, debug_unit
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type(psb_ctxt_type) :: ctxt
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integer(psb_ipk_) :: np, me
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complex(psb_dpk_) :: alpha, beta, rho, rho_old, rni, xni, bni, ani,bn2,&
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& omega
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real(psb_dpk_) :: derr
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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 = psb_success_
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name = 'psb_zcgstabl'
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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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ctxt = desc_a%get_context()
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Call psb_info(ctxt, 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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if (.not.allocated(x%v)) then
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info = psb_err_invalid_vect_state_
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call psb_errpush(info,name)
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goto 9999
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endif
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if (.not.allocated(b%v)) then
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info = psb_err_invalid_vect_state_
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call psb_errpush(info,name)
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goto 9999
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endif
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mglob = desc_a%get_global_rows()
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n_row = desc_a%get_local_rows()
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n_col = desc_a%get_local_cols()
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if (present(istop)) then
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istop_ = istop
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else
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istop_ = 2
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endif
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if (present(itmax)) then
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itmax_ = itmax
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else
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itmax_ = 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_level >= psb_debug_ext_) &
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& write(debug_unit,*) me,' ',trim(name),&
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& 'present: irst: ',irst,nl
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else
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nl = 1
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if (debug_level >= psb_debug_ext_) &
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& write(debug_unit,*) me,' ',trim(name),&
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& ' not present: irst: ',irst,nl
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endif
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if (nl <=0 ) then
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info=psb_err_invalid_irst_
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err=info
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call psb_errpush(info,name,i_err=(/nl/))
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goto 9999
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endif
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call psb_chkvect(mglob,lone,x%get_nrows(),lone,lone,desc_a,info)
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if (info == psb_success_) call psb_chkvect(mglob,lone,b%get_nrows(),lone,lone,desc_a,info)
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if (info /= psb_success_) then
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info=psb_err_from_subroutine_
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call psb_errpush(info,name,a_err='psb_chkvect on X/B')
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goto 9999
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end if
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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 /= psb_success_) then
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info=psb_err_alloc_dealloc_
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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 == psb_success_) Call psb_geall(wwrk,desc_a,info,n=10_psb_ipk_)
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if (info == psb_success_) Call psb_geall(uh,desc_a,info,n=nl+1,lb=izero)
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if (info == psb_success_) Call psb_geall(rh,desc_a,info,n=nl+1,lb=izero)
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if (info == psb_success_) Call psb_geasb(wwrk,desc_a,info,mold=x%v)
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if (info == psb_success_) Call psb_geasb(uh,desc_a,info,mold=x%v)
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if (info == psb_success_) Call psb_geasb(rh,desc_a,info,mold=x%v)
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if (info /= psb_success_) then
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info=psb_err_from_subroutine_non_
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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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call psb_init_conv(methdname,istop_,itrace_,itmax_,a,x,b,eps,desc_a,stopdat,info)
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if (info /= psb_success_) Then
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call psb_errpush(psb_err_from_subroutine_non_,name)
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goto 9999
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End If
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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_level >= psb_debug_ext_) &
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& write(debug_unit,*) me,' ',trim(name),' restart: ',itx,it
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if (itx >= itmax_) exit restart
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it = 0
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call psb_geaxpby(zone,b,zzero,r,desc_a,info)
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if (info == psb_success_) call psb_spmm(-zone,a,x,zone,r,desc_a,info,work=aux)
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if (info == psb_success_) call prec%apply(r,desc_a,info)
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if (info == psb_success_) call psb_geaxpby(zone,r,zzero,rt0,desc_a,info)
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if (info == psb_success_) call psb_geaxpby(zone,r,zzero,rh(0),desc_a,info)
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if (info == psb_success_) call psb_geaxpby(zzero,r,zzero,uh(0),desc_a,info)
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if (info /= psb_success_) then
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info=psb_err_from_subroutine_non_
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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 = zone
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alpha = zzero
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omega = zone
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if (debug_level >= psb_debug_ext_) &
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& write(debug_unit,*) me,' ',trim(name),&
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& ' on entry to amax: b: ',b%get_nrows()
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if (psb_check_conv(methdname,itx,x,r,desc_a,stopdat,info)) exit restart
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if (info /= psb_success_) Then
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call psb_errpush(psb_err_from_subroutine_non_,name)
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goto 9999
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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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|
|
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|
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if (debug_level >= psb_debug_ext_) &
|
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|
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|
& write(debug_unit,*) me,' ',trim(name),&
|
|
|
|
|
& ' iteration: ',itx, rho
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do j = 0, nl -1
|
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|
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If (debug_level >= psb_debug_ext_) &
|
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|
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& write(debug_unit,*) me,' ',trim(name),'bicg part: ',j, nl
|
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|
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|
rho_old = rho
|
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|
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rho = psb_gedot(rh(j),rt0,desc_a,info)
|
|
|
|
|
if (rho == zzero) then
|
|
|
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|
if (debug_level >= psb_debug_ext_) &
|
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|
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|
& write(debug_unit,*) me,' ',trim(name),&
|
|
|
|
|
& ' bi-cgstab iteration breakdown r',rho
|
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|
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exit iteration
|
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endif
|
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|
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beta = alpha*rho/rho_old
|
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|
|
|
rho_old = rho
|
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|
|
|
do k=0, j
|
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|
|
|
! = call psb_geaxpby(zone,rh(:,0:j),-beta,uh(:,0:j),desc_a,info)
|
|
|
|
|
call psb_geaxpby(zone,rh(k),-beta,uh(k),desc_a,info)
|
|
|
|
|
end do
|
|
|
|
|
call psb_spmm(zone,a,uh(j),zzero,uh(j+1),desc_a,info,work=aux)
|
|
|
|
|
|
|
|
|
|
call prec%apply(uh(j+1),desc_a,info)
|
|
|
|
|
|
|
|
|
|
gamma(j) = psb_gedot(uh(j+1),rt0,desc_a,info)
|
|
|
|
|
|
|
|
|
|
if (gamma(j) == zzero) then
|
|
|
|
|
if (debug_level >= psb_debug_ext_) &
|
|
|
|
|
& write(debug_unit,*) me,' ',trim(name),&
|
|
|
|
|
& ' bi-cgstab iteration breakdown s2',gamma(j)
|
|
|
|
|
exit iteration
|
|
|
|
|
endif
|
|
|
|
|
alpha = rho/gamma(j)
|
|
|
|
|
if (debug_level >= psb_debug_ext_) &
|
|
|
|
|
& write(debug_unit,*) me,' ',trim(name),&
|
|
|
|
|
& ' bicg part: alpha=r/g ',alpha,rho,gamma(j)
|
|
|
|
|
|
|
|
|
|
do k=0,j
|
|
|
|
|
! = call psb_geaxpby(-alpha,uh(:,1:j+1),zone,rh(:,0:j),desc_a,info)
|
|
|
|
|
call psb_geaxpby(-alpha,uh(k+1),zone,rh(k),desc_a,info)
|
|
|
|
|
end do
|
|
|
|
|
call psb_geaxpby(alpha,uh(0),zone,x,desc_a,info)
|
|
|
|
|
call psb_spmm(zone,a,rh(j),zzero,rh(j+1),desc_a,info,work=aux)
|
|
|
|
|
|
|
|
|
|
call prec%apply(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
|
|
|
|
|
|
|
|
|
|
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),zone,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),zone,x,desc_a,info)
|
|
|
|
|
call psb_geaxpby(-gamma1(nl),rh(nl),zone,rh(0),desc_a,info)
|
|
|
|
|
call psb_geaxpby(-gamma(nl),uh(nl),zone,uh(0),desc_a,info)
|
|
|
|
|
|
|
|
|
|
do j=1, nl-1
|
|
|
|
|
call psb_geaxpby(-gamma(j),uh(j),zone,uh(0),desc_a,info)
|
|
|
|
|
call psb_geaxpby(gamma2(j),rh(j),zone,x,desc_a,info)
|
|
|
|
|
call psb_geaxpby(-gamma1(j),rh(j),zone,rh(0),desc_a,info)
|
|
|
|
|
enddo
|
|
|
|
|
|
|
|
|
|
if (psb_check_conv(methdname,itx,x,rh(0),desc_a,stopdat,info)) exit restart
|
|
|
|
|
if (info /= psb_success_) Then
|
|
|
|
|
call psb_errpush(psb_err_from_subroutine_non_,name)
|
|
|
|
|
goto 9999
|
|
|
|
|
End If
|
|
|
|
|
|
|
|
|
|
end do iteration
|
|
|
|
|
end do restart
|
|
|
|
|
|
|
|
|
|
call psb_end_conv(methdname,itx,desc_a,stopdat,info,derr,iter)
|
|
|
|
|
if (present(err)) err = derr
|
|
|
|
|
|
|
|
|
|
if (info == psb_success_) call psb_gefree(uh,desc_a,info)
|
|
|
|
|
if (info == psb_success_) call psb_gefree(rh,desc_a,info)
|
|
|
|
|
if (info == psb_success_) call psb_gefree(wwrk,desc_a,info)
|
|
|
|
|
if (info == psb_success_) deallocate(aux,stat=info)
|
|
|
|
|
if (info /= psb_success_) then
|
|
|
|
|
call psb_errpush(info,name)
|
|
|
|
|
goto 9999
|
|
|
|
|
end if
|
|
|
|
|
|
|
|
|
|
call psb_erractionrestore(err_act)
|
|
|
|
|
return
|
|
|
|
|
|
|
|
|
|
9999 call psb_error_handler(err_act)
|
|
|
|
|
return
|
|
|
|
|
|
|
|
|
|
End Subroutine psb_zcgstabl_vect
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
