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527 lines
18 KiB
Fortran
527 lines
18 KiB
Fortran
!
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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 prior 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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! File: psb_dminres.f90
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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
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! C C
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! C C
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! CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
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! File: psb_dminres.f90
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!
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! Subroutine: psb_dminres
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! This subroutine implements the MINRES 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 - class(psb_dprec_type) Input: preconditioner
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! b(:) - real Input: vector containing the
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! right hand side B
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! x(:) - real 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 is
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! 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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!
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!
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subroutine psb_dminres_vect(a,prec,b,x,eps,desc_a,info,&
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& itmax,iter,err,itrace,istop,cond)
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use psb_base_mod
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use psb_prec_mod
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use psb_d_linsolve_conv_mod
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use psb_linsolve_mod
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implicit none
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type(psb_dspmat_type), intent(in) :: a
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Type(psb_desc_type), Intent(in) :: desc_a
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class(psb_dprec_type), intent(inout) :: prec
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type(psb_d_vect_type), Intent(inout) :: b
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type(psb_d_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, istop
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integer(psb_ipk_), Optional, Intent(out) :: iter
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Real(psb_dpk_), Optional, Intent(out) :: err, cond
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! = Local data
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real(psb_dpk_), allocatable, target :: aux(:)
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type(psb_d_vect_type), allocatable, target :: wwrk(:)
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type(psb_d_vect_type), pointer :: y, r1, r2, v, w, w1, w2, wtmp, res
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real(psb_dpk_) :: alfa, beta, beta1, dbar, delta, denom
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real(psb_dpk_) :: epsln, gamma, gbar, oldb, oldeps, phi, phibar
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real(psb_dpk_) :: rhs1, rhs2, s, zeta, betatmp
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real(psb_dpk_) :: rotx(1), roty(1)
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real(psb_dpk_) :: cs
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real(psb_dpk_) :: sn
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integer(psb_ipk_) :: itmax_, istop_, naux, itx, itrace_, n_col, n_row, err_act
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integer(psb_lpk_) :: mglob
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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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real(psb_dpk_) :: derr, errnum, errden, deps
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logical :: do_cond
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logical :: converged
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real(psb_dpk_) :: epsmach
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real(psb_dpk_) :: gmax, gmin, tnorm2, ynorm2
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real(psb_dpk_) :: rni, xni, bni, ani, bn2, r0n2
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real(psb_dpk_) :: dotv
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character(len=20) :: name
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character(len=*), parameter :: methdname='MINRES'
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info = psb_success_
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name = 'psb_dminres'
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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 (.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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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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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_ = psb_get_istop_default()
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endif
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if (.not.psb_is_valid_istop(istop_)) then
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info=psb_err_invalid_istop_
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err=info
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call psb_errpush(info,name,i_err=(/istop_/))
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goto 9999
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end if
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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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select case(istop_)
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case(psb_istop_ani_,psb_istop_bn2_,&
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& psb_istop_rn2_abs_, psb_istop_rrn2_)
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! nothing needed
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case default
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! should never get here
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info=psb_err_internal_error_
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err=info
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call psb_errpush(info,name,a_err="invalid istop_")
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goto 9999
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end select
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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_)&
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& 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), stat=info)
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if (info == psb_success_) call psb_geall(wwrk,desc_a,info,n=9_psb_ipk_)
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if (info == psb_success_) call psb_geasb(wwrk,desc_a,info,mold=x%v,scratch=.true.)
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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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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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y => wwrk(1)
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r1 => wwrk(2)
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r2 => wwrk(3)
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v => wwrk(4)
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w => wwrk(5)
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w1 => wwrk(6)
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w2 => wwrk(7)
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wtmp => wwrk(8)
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res => wwrk(9)
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do_cond = present(cond)
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epsmach = epsilon(done)
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! res = b - A*x
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call psb_geaxpby(done,b,dzero,res,desc_a,info)
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if (info == psb_success_) call psb_spmm(-done,a,x,done,res,desc_a,info,work=aux)
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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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select case(istop_)
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case(psb_istop_ani_)
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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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case(psb_istop_bn2_)
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bn2 = psb_genrm2(b,desc_a,info)
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case(psb_istop_rn2_abs_)
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! nothing needed
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case(psb_istop_rrn2_)
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r0n2 = psb_genrm2(res,desc_a,info)
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end select
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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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errnum = dzero
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errden = done
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deps = eps
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converged = .false.
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if ((itrace_ > 0).and.(me == 0)) call log_header(methdname)
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! y = beta1 * P' * v1, with v1 the first Lanczos vector.
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call psb_geaxpby(done,res,dzero,y,desc_a,info)
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if (info == psb_success_) call psb_geaxpby(done,res,dzero,r1,desc_a,info)
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if (info == psb_success_) call prec%apply(res,y,desc_a,info,work=aux)
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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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dotv = psb_gedot(res,y,desc_a,info)
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if (dotv < -epsmach*max(done,abs(dotv))) then
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info=psb_err_pivot_too_small_
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call psb_errpush(info,name,a_err='MINRES breakdown: negative (r,z)')
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goto 9999
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end if
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if (dotv < dzero) dotv = dzero
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beta1 = sqrt(dotv)
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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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! If beta1 is numerically zero, x is already acceptable.
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if (abs(beta1) <= epsmach) then
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itx = 0
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converged = .true.
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if (do_cond) cond = dzero
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select case(istop_)
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case(psb_istop_ani_)
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rni = psb_geamax(res,desc_a,info)
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xni = psb_geamax(x,desc_a,info)
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errnum = rni
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errden = ani*xni + bni
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case(psb_istop_bn2_)
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errnum = abs(beta1)
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errden = bn2
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case(psb_istop_rn2_abs_)
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errnum = abs(beta1)
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errden = done
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case(psb_istop_rrn2_)
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errnum = abs(beta1)
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errden = r0n2
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end select
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if (errden == dzero) errden = done
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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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end if
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beta = beta1
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oldb = dzero
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dbar = dzero
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epsln = dzero
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phibar = beta1
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rhs1 = beta1
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rhs2 = dzero
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cs = -done
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sn = dzero
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itx = 0
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if (do_cond) then
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tnorm2 = 0.0_psb_dpk_
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ynorm2 = 0.0_psb_dpk_
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gmax = 0.0_psb_dpk_
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gmin = huge(done)
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end if
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call psb_geaxpby(done,r1,dzero,r2,desc_a,info)
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if (info == psb_success_) call psb_geaxpby(dzero,x,dzero,w,desc_a,info)
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if (info == psb_success_) call psb_geaxpby(dzero,x,dzero,w1,desc_a,info)
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if (info == psb_success_) call psb_geaxpby(dzero,x,dzero,w2,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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if (.not.converged) then
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do while (itx < itmax_)
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if (abs(beta) <= epsmach) exit
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itx = itx + 1
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s = done/beta
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call psb_geaxpby(s,y,dzero,v,desc_a,info)
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if (info == psb_success_) call psb_spmm(done,a,v,dzero,y,desc_a,info,work=aux)
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if (itx >= 2 .and. info == psb_success_) then
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call psb_geaxpby((-beta/oldb),r1,done,y,desc_a,info)
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end if
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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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alfa = psb_gedot(v,y,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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call psb_geaxpby((-alfa/beta),r2,done,y,desc_a,info)
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if (info == psb_success_) call psb_geaxpby(done,r2,dzero,r1,desc_a,info)
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if (info == psb_success_) call psb_geaxpby(done,y,dzero,r2,desc_a,info)
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if (info == psb_success_) call prec%apply(r2,y,desc_a,info,work=aux)
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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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oldb = beta
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dotv = psb_gedot(r2,y,desc_a,info)
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if (dotv < -epsmach*max(done,abs(dotv))) then
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info=psb_err_pivot_too_small_
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call psb_errpush(info,name,a_err='MINRES breakdown: negative (r2,z2)')
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goto 9999
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end if
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if (dotv < dzero) dotv = dzero
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beta = sqrt(dotv)
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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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if (do_cond) then
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tnorm2 = tnorm2 + abs(alfa)**2 + abs(oldb)**2 + abs(beta)**2
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if (itx == 1) then
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gmax = abs(alfa)
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gmin = gmax
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end if
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end if
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oldeps = epsln
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delta = dbar
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gbar = alfa
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rotx(1) = delta
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roty(1) = gbar
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call drot(1,rotx,1,roty,1,cs,sn)
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delta = rotx(1)
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gbar = -roty(1)
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epsln = dzero
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dbar = beta
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rotx(1) = epsln
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roty(1) = dbar
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call drot(1,rotx,1,roty,1,cs,sn)
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epsln = rotx(1)
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dbar = -roty(1)
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gamma = gbar
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betatmp = beta
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call drotg(gamma,betatmp,cs,sn)
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if (abs(gamma) <= epsmach) exit
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phi = phibar
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phibar = dzero
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rotx(1) = phi
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roty(1) = phibar
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call drot(1,rotx,1,roty,1,cs,-sn)
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phi = rotx(1)
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phibar = roty(1)
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denom = done/gamma
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call psb_geaxpby(done,w2,dzero,w1,desc_a,info)
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if (info == psb_success_) call psb_geaxpby(done,w,dzero,w2,desc_a,info)
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if (info == psb_success_) call psb_geaxpby(done,v,dzero,wtmp,desc_a,info)
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if (info == psb_success_) call psb_geaxpby(-oldeps,w1,done,wtmp,desc_a,info)
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if (info == psb_success_) call psb_geaxpby(-delta,w2,done,wtmp,desc_a,info)
|
|
if (info == psb_success_) call psb_geaxpby(denom,wtmp,dzero,w,desc_a,info)
|
|
if (info == psb_success_) call psb_geaxpby(phi,w,done,x,desc_a,info)
|
|
if (info /= psb_success_) then
|
|
info=psb_err_from_subroutine_non_
|
|
call psb_errpush(info,name)
|
|
goto 9999
|
|
end if
|
|
|
|
if (do_cond) then
|
|
gmax = max(gmax,abs(gamma))
|
|
gmin = min(gmin,abs(gamma))
|
|
zeta = rhs1/gamma
|
|
ynorm2 = ynorm2 + abs(zeta)**2
|
|
rhs1 = rhs2 - delta*zeta
|
|
rhs2 = -epsln*zeta
|
|
end if
|
|
|
|
select case(istop_)
|
|
case(psb_istop_ani_)
|
|
! Compute true residual only for the ANI stopping criterion.
|
|
call psb_geaxpby(done,b,dzero,res,desc_a,info)
|
|
if (info == psb_success_) call psb_spmm(-done,a,x,done,res,desc_a,info,work=aux)
|
|
if (info == psb_success_) rni = psb_geamax(res,desc_a,info)
|
|
if (info == psb_success_) xni = psb_geamax(x,desc_a,info)
|
|
errnum = rni
|
|
errden = ani*xni + bni
|
|
case(psb_istop_bn2_)
|
|
errnum = abs(phibar)
|
|
errden = bn2
|
|
case(psb_istop_rn2_abs_)
|
|
errnum = abs(phibar)
|
|
errden = done
|
|
case(psb_istop_rrn2_)
|
|
errnum = abs(phibar)
|
|
errden = r0n2
|
|
end select
|
|
if (errden == dzero) errden = done
|
|
if (info /= psb_success_) then
|
|
info=psb_err_from_subroutine_non_
|
|
call psb_errpush(info,name)
|
|
goto 9999
|
|
end if
|
|
|
|
if (itrace_ > 0) &
|
|
& call log_conv(methdname,me,itx,itrace_,errnum,errden,deps)
|
|
|
|
if (errnum <= eps*errden) then
|
|
converged = .true.
|
|
exit
|
|
end if
|
|
end do
|
|
end if
|
|
|
|
if ((.not.converged) .and. (itx >= itmax_)) then
|
|
if (debug_level >= psb_debug_ext_)&
|
|
& write(debug_unit,*) me,' ',trim(name),': MINRES reached iteration limit'
|
|
end if
|
|
|
|
if (do_cond) then
|
|
if (gmin > 0.0_psb_dpk_) then
|
|
cond = gmax/gmin
|
|
else
|
|
cond = huge(done)
|
|
end if
|
|
end if
|
|
|
|
call log_end(methdname,me,itx,itrace_,errnum,errden,deps,err=derr,iter=iter)
|
|
if (present(err)) err = derr
|
|
|
|
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_dminres_vect
|