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845 lines
28 KiB
Fortran
845 lines
28 KiB
Fortran
!!$
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!!$ Parallel Sparse BLAS version 3.0
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!!$ (C) Copyright 2006, 2007, 2008, 2009, 2010, 2012
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!!$ Salvatore Filippone University of Rome Tor Vergata
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!!$ Alfredo Buttari CNRS-IRIT, Toulouse
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!!$
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!!$ Contributions to this routine:
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!!$ Daniela di Serafino Second University of Naples
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!!$ Pasqua D'Ambra ICAR-CNR
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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_zrgmres.f90
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!
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! Subroutine: psb_zrgmres
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! This subroutine implements the restarted GMRES method with right
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! preconditioning.
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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,dimension(:) Input: vector containing the
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! right hand side B
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! x - complex,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|/(|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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! irst - integer(optional) Input: restart parameter
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!
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!!$Subroutine psb_zrgmres(a,prec,b,x,eps,desc_a,info,itmax,iter,err,itrace,irst,istop)
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!!$ use psb_base_mod
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!!$ use psb_prec_mod
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!!$ use psb_z_krylov_conv_mod
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!!$ use psb_krylov_mod
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!!$ implicit none
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!!$
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!!$! = Parameters
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!!$ Type(psb_zspmat_type), Intent(in) :: a
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!!$ class(psb_zprec_type), Intent(in) :: prec
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!!$ Type(psb_desc_type), Intent(in) :: desc_a
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!!$ complex(psb_dpk_), Intent(in) :: b(:)
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!!$ complex(psb_dpk_), 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(:),w(:),w1(:), v(:,:)
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!!$ complex(psb_dpk_), allocatable :: c(:),s(:), h(:,:), rs(:),rst(:),xt(:)
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!!$ Real(psb_dpk_) :: tmp
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!!$ complex(psb_dpk_) :: rti, rti1, scal
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!!$ integer(psb_ipk_) ::litmax, naux, mglob, it,k, itrace_,&
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!!$ & np,me, n_row, n_col, nl, int_err(5)
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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, isvch, ictxt,istop_, err_act
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!!$ integer(psb_ipk_) :: debug_level, debug_unit
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!!$ Real(psb_dpk_) :: rni, xni, bni, ani,bn2
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!!$ real(psb_dpk_) :: errnum, errden, deps, derr
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!!$ character(len=20) :: name
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!!$ character(len=*), parameter :: methdname='RGMRES'
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!!$
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!!$ info = psb_success_
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!!$ name = 'psb_zgmres'
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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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!!$
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!!$ ictxt = desc_a%get_context()
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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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!!$
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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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!!$
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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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!!$ !
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!!$ ! ISTOP_ = 1: Normwise backward error, infinity norm
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!!$ ! ISTOP_ = 2: ||r||/||b||, 2-norm
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!!$ !
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!!$
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!!$ if ((istop_ < 1 ).or.(istop_ > 2 ) ) then
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!!$ info=psb_err_invalid_istop_
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!!$ int_err(1)=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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!!$
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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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!!$
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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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!!$
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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 = 10
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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_istop_
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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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!!$
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!!$ call psb_chkvect(mglob,ione,size(x,1),ione,ione,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')
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!!$ goto 9999
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!!$ end if
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!!$ call psb_chkvect(mglob,ione,size(b,ione),ione,ione,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 B')
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!!$ goto 9999
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!!$ end if
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!!$
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!!$
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!!$ naux=4*n_col
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!!$ allocate(aux(naux),h(nl+1,nl+1),&
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!!$ &c(nl+1),s(nl+1),rs(nl+1), rst(nl+1),stat=info)
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!!$
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!!$ if (info == psb_success_) Call psb_geall(v,desc_a,info,n=nl+1)
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!!$ if (info == psb_success_) Call psb_geall(w,desc_a,info)
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!!$ if (info == psb_success_) Call psb_geall(w1,desc_a,info)
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!!$ if (info == psb_success_) Call psb_geall(xt,desc_a,info)
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!!$ if (info == psb_success_) Call psb_geasb(v,desc_a,info)
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!!$ if (info == psb_success_) Call psb_geasb(w,desc_a,info)
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!!$ if (info == psb_success_) Call psb_geasb(w1,desc_a,info)
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!!$ if (info == psb_success_) Call psb_geasb(xt,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 (debug_level >= psb_debug_ext_) &
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!!$ & write(debug_unit,*) me,' ',trim(name),&
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!!$ & ' Size of V,W,W1 ',size(v),size(v,1),&
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!!$ & size(w),size(w,1),size(w1),size(w1,1), size(v(:,1))
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!!$
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!!$
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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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!!$ errnum = dzero
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!!$ errden = done
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!!$ deps = eps
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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 ((itrace_ > 0).and.(me == 0)) call log_header(methdname)
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!!$
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!!$ itx = 0
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!!$ restart: do
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!!$
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!!$ ! compute r0 = b-ax0
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!!$ ! check convergence
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!!$ ! compute v1 = r0/||r0||_2
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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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!!$ & ' restart: ',itx,it
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!!$ it = 0
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!!$ call psb_geaxpby(zone,b,zzero,v(:,1),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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!!$
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!!$ call psb_spmm(-zone,a,x,zone,v(:,1),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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!!$
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!!$ rs(1) = psb_genrm2(v(:,1),desc_a,info)
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!!$ rs(2:) = zzero
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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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!!$ scal=done/rs(1) ! rs(1) MIGHT BE VERY SMALL - USE DSCAL TO DEAL WITH IT?
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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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!!$ & ' on entry to amax: b: ',Size(b),rs(1),scal
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!!$
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!!$ !
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!!$ ! check convergence
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!!$ !
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!!$ if (istop_ == 1) then
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!!$ rni = psb_geamax(v(:,1),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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!!$ else if (istop_ == 2) then
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!!$ rni = psb_genrm2(v(:,1),desc_a,info)
|
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!!$ errnum = rni
|
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!!$ errden = bn2
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!!$ endif
|
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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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!!$
|
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!!$ if (errnum <= deps*errden) exit restart
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!!$
|
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!!$ if (itrace_ > 0) &
|
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!!$ & call log_conv(methdname,me,itx,itrace_,errnum,errden,deps)
|
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!!$
|
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!!$ v(:,1) = v(:,1) * scal
|
|
!!$
|
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!!$ if (itx >= litmax) exit restart
|
|
!!$
|
|
!!$ !
|
|
!!$ ! inner iterations
|
|
!!$ !
|
|
!!$
|
|
!!$ inner: Do i=1,nl
|
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!!$ itx = itx + 1
|
|
!!$
|
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!!$ call prec%apply(v(:,i),w1,desc_a,info)
|
|
!!$ Call psb_spmm(zone,a,w1,zzero,w,desc_a,info,work=aux)
|
|
!!$ !
|
|
!!$
|
|
!!$ do k = 1, i
|
|
!!$ h(k,i) = psb_gedot(v(:,k),w,desc_a,info)
|
|
!!$ call psb_geaxpby(-h(k,i),v(:,k),zone,w,desc_a,info)
|
|
!!$ end do
|
|
!!$ h(i+1,i) = psb_genrm2(w,desc_a,info)
|
|
!!$ scal=done/h(i+1,i)
|
|
!!$ call psb_geaxpby(scal,w,zzero,v(:,i+1),desc_a,info)
|
|
!!$ do k=2,i
|
|
!!$ call zrot(1,h(k-1,i),1,h(k,i),1,real(c(k-1)),s(k-1))
|
|
!!$ enddo
|
|
!!$
|
|
!!$ rti = h(i,i)
|
|
!!$ rti1 = h(i+1,i)
|
|
!!$ call zrotg(rti,rti1,tmp,s(i))
|
|
!!$ c(i) = cmplx(tmp,szero)
|
|
!!$ call zrot(1,h(i,i),1,h(i+1,i),1,real(c(i)),s(i))
|
|
!!$ h(i+1,i) = zzero
|
|
!!$ call zrot(1,rs(i),1,rs(i+1),1,real(c(i)),s(i))
|
|
!!$
|
|
!!$ if (istop_ == 1) then
|
|
!!$ !
|
|
!!$ ! build x and then compute the residual and its infinity norm
|
|
!!$ !
|
|
!!$ rst = rs
|
|
!!$ xt = zzero
|
|
!!$ call ztrsm('l','u','n','n',i,1,zone,h,size(h,1),rst,size(rst,1))
|
|
!!$ if (debug_level >= psb_debug_ext_) &
|
|
!!$ & write(debug_unit,*) me,' ',trim(name),&
|
|
!!$ & ' Rebuild x-> RS:',rst(1:nl)
|
|
!!$ do k=1, i
|
|
!!$ call psb_geaxpby(rst(k),v(:,k),zone,xt,desc_a,info)
|
|
!!$ end do
|
|
!!$ call prec%apply(xt,desc_a,info)
|
|
!!$ call psb_geaxpby(zone,x,zone,xt,desc_a,info)
|
|
!!$ call psb_geaxpby(zone,b,zzero,w1,desc_a,info)
|
|
!!$ call psb_spmm(-zone,a,xt,zone,w1,desc_a,info,work=aux)
|
|
!!$ rni = psb_geamax(w1,desc_a,info)
|
|
!!$ xni = psb_geamax(xt,desc_a,info)
|
|
!!$ errnum = rni
|
|
!!$ errden = (ani*xni+bni)
|
|
!!$ !
|
|
!!$
|
|
!!$ else if (istop_ == 2) then
|
|
!!$ !
|
|
!!$ ! compute the residual 2-norm as byproduct of the solution
|
|
!!$ ! procedure of the least-squares problem
|
|
!!$ !
|
|
!!$ rni = abs(rs(i+1))
|
|
!!$ errnum = rni
|
|
!!$ errden = bn2
|
|
!!$ endif
|
|
!!$
|
|
!!$ If (errnum <= deps*errden) Then
|
|
!!$
|
|
!!$ if (istop_ == 1) then
|
|
!!$ x = xt
|
|
!!$ else if (istop_ == 2) then
|
|
!!$ !
|
|
!!$ ! build x
|
|
!!$ !
|
|
!!$ call ztrsm('l','u','n','n',i,1,zone,h,size(h,1),rs,size(rs,1))
|
|
!!$ if (debug_level >= psb_debug_ext_) &
|
|
!!$ & write(debug_unit,*) me,' ',trim(name),&
|
|
!!$ & ' Rebuild x-> RS:',rs(1:nl)
|
|
!!$ w1 = zzero
|
|
!!$ do k=1, i
|
|
!!$ call psb_geaxpby(rs(k),v(:,k),zone,w1,desc_a,info)
|
|
!!$ end do
|
|
!!$ call prec%apply(w1,w,desc_a,info)
|
|
!!$ call psb_geaxpby(zone,w,zone,x,desc_a,info)
|
|
!!$ end if
|
|
!!$
|
|
!!$ exit restart
|
|
!!$
|
|
!!$ end if
|
|
!!$
|
|
!!$ if (itrace_ > 0) &
|
|
!!$ & call log_conv(methdname,me,itx,itrace_,errnum,errden,deps)
|
|
!!$
|
|
!!$ end do inner
|
|
!!$
|
|
!!$ if (istop_ == 1) then
|
|
!!$ x = xt
|
|
!!$ else if (istop_ == 2) then
|
|
!!$ !
|
|
!!$ ! build x
|
|
!!$ !
|
|
!!$ call ztrsm('l','u','n','n',nl,1,zone,h,size(h,1),rs,size(rs,1))
|
|
!!$ if (debug_level >= psb_debug_ext_) &
|
|
!!$ & write(debug_unit,*) me,' ',trim(name),&
|
|
!!$ & ' Rebuild x-> RS:',rs(1:nl)
|
|
!!$ w1 = zzero
|
|
!!$ do k=1, nl
|
|
!!$ call psb_geaxpby(rs(k),v(:,k),zone,w1,desc_a,info)
|
|
!!$ end do
|
|
!!$ call prec%apply(w1,w,desc_a,info)
|
|
!!$ call psb_geaxpby(zone,w,zone,x,desc_a,info)
|
|
!!$ end if
|
|
!!$
|
|
!!$ end do restart
|
|
!!$ if (itrace_ > 0) &
|
|
!!$ & call log_conv(methdname,me,itx,ione,errnum,errden,deps)
|
|
!!$
|
|
!!$ call log_end(methdname,me,itx,errnum,errden,deps,err=derr,iter=iter)
|
|
!!$
|
|
!!$ if (present(err)) then
|
|
!!$ err = derr
|
|
!!$ end if
|
|
!!$
|
|
!!$
|
|
!!$ deallocate(aux,h,c,s,rs,rst, stat=info)
|
|
!!$ if (info == psb_success_) call psb_gefree(v,desc_a,info)
|
|
!!$ if (info == psb_success_) call psb_gefree(w,desc_a,info)
|
|
!!$ if (info == psb_success_) call psb_gefree(w1,desc_a,info)
|
|
!!$ if (info == psb_success_) call psb_gefree(xt,desc_a,info)
|
|
!!$ if (info /= psb_success_) then
|
|
!!$ info=psb_err_from_subroutine_non_
|
|
!!$ call psb_errpush(info,name)
|
|
!!$ goto 9999
|
|
!!$ end if
|
|
!!$
|
|
!!$ 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_zrgmres
|
|
|
|
|
|
|
|
subroutine psb_zrgmres_vect(a,prec,b,x,eps,desc_a,info,&
|
|
& itmax,iter,err,itrace,irst,istop)
|
|
use psb_base_mod
|
|
use psb_prec_mod
|
|
use psb_z_krylov_conv_mod
|
|
use psb_krylov_mod
|
|
implicit none
|
|
type(psb_zspmat_type), intent(in) :: a
|
|
Type(psb_desc_type), Intent(in) :: desc_a
|
|
class(psb_zprec_type), intent(inout) :: prec
|
|
type(psb_z_vect_type), Intent(inout) :: b
|
|
type(psb_z_vect_type), Intent(inout) :: x
|
|
Real(psb_dpk_), Intent(in) :: eps
|
|
integer(psb_ipk_), intent(out) :: info
|
|
integer(psb_ipk_), Optional, Intent(in) :: itmax, itrace, irst,istop
|
|
integer(psb_ipk_), Optional, Intent(out) :: iter
|
|
Real(psb_dpk_), Optional, Intent(out) :: err
|
|
! = local data
|
|
complex(psb_dpk_), allocatable :: aux(:)
|
|
complex(psb_dpk_), allocatable :: c(:), s(:), h(:,:), rs(:), rst(:)
|
|
type(psb_z_vect_type), allocatable :: v(:)
|
|
type(psb_z_vect_type) :: w, w1, xt
|
|
real(psb_dpk_) :: tmp
|
|
complex(psb_dpk_) :: scal, gm, rti, rti1
|
|
integer(psb_ipk_) ::litmax, naux, mglob, it,k, itrace_,&
|
|
& n_row, n_col, nl, int_err(5)
|
|
Logical, Parameter :: exchange=.True., noexchange=.False., use_srot=.true.
|
|
integer(psb_ipk_), Parameter :: irmax = 8
|
|
integer(psb_ipk_) :: itx, i, istop_, err_act
|
|
integer(psb_ipk_) :: debug_level, debug_unit
|
|
integer(psb_ipk_) :: ictxt, np, me
|
|
Real(psb_dpk_) :: rni, xni, bni, ani,bn2, dt
|
|
real(psb_dpk_) :: errnum, errden, deps, derr
|
|
character(len=20) :: name
|
|
character(len=*), parameter :: methdname='RGMRES'
|
|
|
|
info = psb_success_
|
|
name = 'psb_sgmres'
|
|
call psb_erractionsave(err_act)
|
|
debug_unit = psb_get_debug_unit()
|
|
debug_level = psb_get_debug_level()
|
|
|
|
ictxt = desc_a%get_context()
|
|
Call psb_info(ictxt, me, np)
|
|
if (debug_level >= psb_debug_ext_)&
|
|
& write(debug_unit,*) me,' ',trim(name),': from psb_info',np
|
|
if (.not.allocated(b%v)) then
|
|
info = psb_err_invalid_vect_state_
|
|
call psb_errpush(info,name)
|
|
goto 9999
|
|
endif
|
|
if (.not.allocated(x%v)) then
|
|
info = psb_err_invalid_vect_state_
|
|
call psb_errpush(info,name)
|
|
goto 9999
|
|
endif
|
|
|
|
mglob = desc_a%get_global_rows()
|
|
n_row = desc_a%get_local_rows()
|
|
n_col = desc_a%get_local_cols()
|
|
|
|
if (present(istop)) then
|
|
istop_ = istop
|
|
else
|
|
istop_ = 2
|
|
endif
|
|
!
|
|
! ISTOP_ = 1: Normwise backward error, infinity norm
|
|
! ISTOP_ = 2: ||r||/||b||, 2-norm
|
|
!
|
|
|
|
if ((istop_ < 1 ).or.(istop_ > 2 ) ) then
|
|
info=psb_err_invalid_istop_
|
|
int_err(1)=istop_
|
|
err=info
|
|
call psb_errpush(info,name,i_err=int_err)
|
|
goto 9999
|
|
endif
|
|
|
|
if (present(itmax)) then
|
|
litmax = itmax
|
|
else
|
|
litmax = 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 = 10
|
|
if (debug_level >= psb_debug_ext_) &
|
|
& write(debug_unit,*) me,' ',trim(name),&
|
|
& ' not present: irst: ',irst,nl
|
|
endif
|
|
if (nl <=0 ) then
|
|
info=psb_err_invalid_istop_
|
|
int_err(1)=nl
|
|
err=info
|
|
call psb_errpush(info,name,i_err=int_err)
|
|
goto 9999
|
|
endif
|
|
|
|
call psb_chkvect(mglob,ione,x%get_nrows(),ione,ione,desc_a,info)
|
|
if(info /= psb_success_) then
|
|
info=psb_err_from_subroutine_
|
|
call psb_errpush(info,name,a_err='psb_chkvect on X')
|
|
goto 9999
|
|
end if
|
|
call psb_chkvect(mglob,ione,b%get_nrows(),ione,ione,desc_a,info)
|
|
if(info /= psb_success_) then
|
|
info=psb_err_from_subroutine_
|
|
call psb_errpush(info,name,a_err='psb_chkvect on B')
|
|
goto 9999
|
|
end if
|
|
|
|
|
|
naux=4*n_col
|
|
allocate(aux(naux),h(nl+1,nl+1),&
|
|
&c(nl+1),s(nl+1),rs(nl+1), rst(nl+1),stat=info)
|
|
|
|
if (info == psb_success_) call psb_geall(v,desc_a,info,n=nl+1)
|
|
if (info == psb_success_) call psb_geall(w,desc_a,info)
|
|
if (info == psb_success_) call psb_geall(w1,desc_a,info)
|
|
if (info == psb_success_) call psb_geall(xt,desc_a,info)
|
|
if (info == psb_success_) call psb_geasb(v,desc_a,info,mold=x%v)
|
|
if (info == psb_success_) call psb_geasb(w,desc_a,info,mold=x%v)
|
|
if (info == psb_success_) call psb_geasb(w1,desc_a,info,mold=x%v)
|
|
if (info == psb_success_) call psb_geasb(xt,desc_a,info,mold=x%v)
|
|
if (info /= psb_success_) then
|
|
info=psb_err_from_subroutine_non_
|
|
call psb_errpush(info,name)
|
|
goto 9999
|
|
end if
|
|
if (debug_level >= psb_debug_ext_) &
|
|
& write(debug_unit,*) me,' ',trim(name),&
|
|
& ' Size of V,W,W1 ',v(1)%get_nrows(),size(v),&
|
|
& w%get_nrows(),w1%get_nrows()
|
|
|
|
|
|
if (istop_ == 1) then
|
|
ani = psb_spnrmi(a,desc_a,info)
|
|
bni = psb_geamax(b,desc_a,info)
|
|
else if (istop_ == 2) then
|
|
bn2 = psb_genrm2(b,desc_a,info)
|
|
endif
|
|
errnum = zzero
|
|
errden = zone
|
|
deps = eps
|
|
if (info /= psb_success_) then
|
|
info=psb_err_from_subroutine_non_
|
|
call psb_errpush(info,name)
|
|
goto 9999
|
|
end if
|
|
if ((itrace_ > 0).and.(me == 0)) call log_header(methdname)
|
|
|
|
itx = 0
|
|
restart: do
|
|
|
|
! compute r0 = b-ax0
|
|
! check convergence
|
|
! compute v1 = r0/||r0||_2
|
|
|
|
if (debug_level >= psb_debug_ext_) &
|
|
& write(debug_unit,*) me,' ',trim(name),&
|
|
& ' restart: ',itx,it
|
|
it = 0
|
|
call psb_geaxpby(zone,b,zzero,v(1),desc_a,info)
|
|
if (info /= psb_success_) then
|
|
info=psb_err_from_subroutine_non_
|
|
call psb_errpush(info,name)
|
|
goto 9999
|
|
end if
|
|
|
|
call psb_spmm(-zone,a,x,zone,v(1),desc_a,info,work=aux)
|
|
if (info /= psb_success_) then
|
|
info=psb_err_from_subroutine_non_
|
|
call psb_errpush(info,name)
|
|
goto 9999
|
|
end if
|
|
|
|
rs(1) = psb_genrm2(v(1),desc_a,info)
|
|
rs(2:) = zzero
|
|
if (info /= psb_success_) then
|
|
info=psb_err_from_subroutine_non_
|
|
call psb_errpush(info,name)
|
|
goto 9999
|
|
end if
|
|
scal=zone/rs(1) ! rs(1) MIGHT BE VERY SMALL - USE DSCAL TO DEAL WITH IT?
|
|
|
|
if (debug_level >= psb_debug_ext_) &
|
|
& write(debug_unit,*) me,' ',trim(name),&
|
|
& ' on entry to amax: b: ',b%get_nrows(),rs(1),scal
|
|
|
|
!
|
|
! check convergence
|
|
!
|
|
if (istop_ == 1) then
|
|
rni = psb_geamax(v(1),desc_a,info)
|
|
xni = psb_geamax(x,desc_a,info)
|
|
errnum = rni
|
|
errden = (ani*xni+bni)
|
|
else if (istop_ == 2) then
|
|
rni = psb_genrm2(v(1),desc_a,info)
|
|
errnum = rni
|
|
errden = bn2
|
|
endif
|
|
if (info /= psb_success_) then
|
|
info=psb_err_from_subroutine_non_
|
|
call psb_errpush(info,name)
|
|
goto 9999
|
|
end if
|
|
|
|
if (errnum <= eps*errden) exit restart
|
|
|
|
if (itrace_ > 0) &
|
|
& call log_conv(methdname,me,itx,itrace_,errnum,errden,deps)
|
|
|
|
call v(1)%scal(scal) !v(1) = v(1) * scal
|
|
|
|
if (itx >= litmax) exit restart
|
|
|
|
!
|
|
! inner iterations
|
|
!
|
|
|
|
inner: Do i=1,nl
|
|
itx = itx + 1
|
|
|
|
call prec%apply(v(i),w1,desc_a,info)
|
|
call psb_spmm(zone,a,w1,zzero,w,desc_a,info,work=aux)
|
|
!
|
|
|
|
do k = 1, i
|
|
h(k,i) = psb_gedot(v(k),w,desc_a,info)
|
|
call psb_geaxpby(-h(k,i),v(k),zone,w,desc_a,info)
|
|
end do
|
|
h(i+1,i) = psb_genrm2(w,desc_a,info)
|
|
scal=zone/h(i+1,i)
|
|
call psb_geaxpby(scal,w,zzero,v(i+1),desc_a,info)
|
|
do k=2,i
|
|
call zrot(1,h(k-1,i),1,h(k,i),1,real(c(k-1)),s(k-1))
|
|
enddo
|
|
|
|
|
|
rti = h(i,i)
|
|
rti1 = h(i+1,i)
|
|
call zrotg(rti,rti1,tmp,s(i))
|
|
c(i) = cmplx(tmp,szero)
|
|
call zrot(1,h(i,i),1,h(i+1,i),1,real(c(i)),s(i))
|
|
h(i+1,i) = zzero
|
|
call zrot(1,rs(i),1,rs(i+1),1,real(c(i)),s(i))
|
|
|
|
if (istop_ == 1) then
|
|
!
|
|
! build x and then compute the residual and its infinity norm
|
|
!
|
|
rst = rs
|
|
call w1%set(zzero)
|
|
call ztrsm('l','u','n','n',i,1,zone,h,size(h,1),rst,size(rst,1))
|
|
if (debug_level >= psb_debug_ext_) &
|
|
& write(debug_unit,*) me,' ',trim(name),&
|
|
& ' Rebuild x-> RS:',rst(1:nl)
|
|
do k=1, i
|
|
call psb_geaxpby(rst(k),v(k),zone,xt,desc_a,info)
|
|
end do
|
|
call prec%apply(xt,desc_a,info)
|
|
call psb_geaxpby(zone,x,zone,xt,desc_a,info)
|
|
call psb_geaxpby(zone,b,zzero,w1,desc_a,info)
|
|
call psb_spmm(-zone,a,xt,zone,w1,desc_a,info,work=aux)
|
|
rni = psb_geamax(w1,desc_a,info)
|
|
xni = psb_geamax(xt,desc_a,info)
|
|
errnum = rni
|
|
errden = (ani*xni+bni)
|
|
!
|
|
|
|
else if (istop_ == 2) then
|
|
!
|
|
! compute the residual 2-norm as byproduct of the solution
|
|
! procedure of the least-squares problem
|
|
!
|
|
rni = abs(rs(i+1))
|
|
errnum = rni
|
|
errden = bn2
|
|
endif
|
|
|
|
if (errnum <= eps*errden) then
|
|
|
|
if (istop_ == 1) then
|
|
call psb_geaxpby(zone,xt,zzero,x,desc_a,info)
|
|
! = x = xt
|
|
else if (istop_ == 2) then
|
|
!
|
|
! build x
|
|
!
|
|
call ztrsm('l','u','n','n',i,1,zone,h,size(h,1),rs,size(rs,1))
|
|
if (debug_level >= psb_debug_ext_) &
|
|
& write(debug_unit,*) me,' ',trim(name),&
|
|
& ' Rebuild x-> RS:',rs(1:nl)
|
|
call w1%set(zzero)
|
|
do k=1, i
|
|
call psb_geaxpby(rs(k),v(k),zone,w1,desc_a,info)
|
|
end do
|
|
call prec%apply(w1,w,desc_a,info)
|
|
call psb_geaxpby(zone,w,zone,x,desc_a,info)
|
|
end if
|
|
|
|
exit restart
|
|
|
|
end if
|
|
|
|
if (itrace_ > 0) &
|
|
& call log_conv(methdname,me,itx,itrace_,errnum,errden,deps)
|
|
|
|
end do inner
|
|
|
|
if (istop_ == 1) then
|
|
call psb_geaxpby(zone,xt,zzero,x,desc_a,info)! x = xt
|
|
else if (istop_ == 2) then
|
|
!
|
|
! build x
|
|
!
|
|
call ztrsm('l','u','n','n',nl,1,zone,h,size(h,1),rs,size(rs,1))
|
|
if (debug_level >= psb_debug_ext_) &
|
|
& write(debug_unit,*) me,' ',trim(name),&
|
|
& ' Rebuild x-> RS:',rs(1:nl)
|
|
call w1%set(zzero)
|
|
do k=1, nl
|
|
call psb_geaxpby(rs(k),v(k),zone,w1,desc_a,info)
|
|
end do
|
|
call prec%apply(w1,w,desc_a,info)
|
|
call psb_geaxpby(zone,w,zone,x,desc_a,info)
|
|
end if
|
|
|
|
end do restart
|
|
if (itrace_ > 0) &
|
|
& call log_conv(methdname,me,itx,ione,errnum,errden,deps)
|
|
|
|
call log_end(methdname,me,itx,errnum,errden,deps,err=derr,iter=iter)
|
|
if (present(err)) err = derr
|
|
|
|
|
|
if (info == psb_success_) call psb_gefree(v,desc_a,info)
|
|
if (info == psb_success_) call psb_gefree(w,desc_a,info)
|
|
if (info == psb_success_) call psb_gefree(w1,desc_a,info)
|
|
if (info == psb_success_) call psb_gefree(xt,desc_a,info)
|
|
if (info == psb_success_) deallocate(aux,h,c,s,rs,rst, stat=info)
|
|
if (info /= psb_success_) then
|
|
info=psb_err_from_subroutine_non_
|
|
call psb_errpush(info,name)
|
|
goto 9999
|
|
end if
|
|
|
|
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
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end subroutine psb_zrgmres_vect
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