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482 lines
17 KiB
Fortran
482 lines
17 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_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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Type(psb_desc_type), Intent(in) :: desc_a
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class(psb_zprec_type), intent(inout) :: prec
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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 :: aux(:)
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complex(psb_dpk_), allocatable :: c(:), s(:), h(:,:), rs(:), rst(:)
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type(psb_z_vect_type), allocatable :: v(:)
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type(psb_z_vect_type) :: w, w1, xt
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real(psb_dpk_) :: tmp
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complex(psb_dpk_) :: scal, gm, rti, rti1
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integer(psb_ipk_) ::litmax, naux, mglob, it,k, itrace_,&
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& n_row, n_col, nl, int_err(5)
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Logical, Parameter :: exchange=.True., noexchange=.False., use_srot=.true.
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integer(psb_ipk_), Parameter :: irmax = 8
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integer(psb_ipk_) :: itx, i, istop_, err_act
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integer(psb_ipk_) :: debug_level, debug_unit
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integer(psb_ipk_) :: ictxt, np, me
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Real(psb_dpk_) :: rni, xni, bni, ani,bn2, dt
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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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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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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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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_ = 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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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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if (present(itmax)) then
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litmax = itmax
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else
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litmax = 1000
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endif
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if (present(itrace)) then
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itrace_ = itrace
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else
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itrace_ = 0
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end if
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if (present(irst)) then
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nl = irst
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if (debug_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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call psb_chkvect(mglob,ione,x%get_nrows(),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,b%get_nrows(),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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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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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,mold=x%v)
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if (info == psb_success_) call psb_geasb(w,desc_a,info,mold=x%v)
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if (info == psb_success_) call psb_geasb(w1,desc_a,info,mold=x%v)
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if (info == psb_success_) call psb_geasb(xt,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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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 ',v(1)%get_nrows(),size(v),&
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& w%get_nrows(),w1%get_nrows()
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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 = zzero
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errden = zone
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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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itx = 0
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restart: do
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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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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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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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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=zone/rs(1) ! rs(1) MIGHT BE VERY SMALL - USE DSCAL TO DEAL WITH IT?
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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(),rs(1),scal
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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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if (errnum <= eps*errden) exit restart
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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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call v(1)%scal(scal) !v(1) = v(1) * scal
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if (itx >= litmax) exit restart
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!
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! inner iterations
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!
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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)
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call psb_spmm(zone,a,w1,zzero,w,desc_a,info,work=aux)
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!
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do k = 1, i
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h(k,i) = psb_gedot(v(k),w,desc_a,info)
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call psb_geaxpby(-h(k,i),v(k),zone,w,desc_a,info)
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end do
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h(i+1,i) = psb_genrm2(w,desc_a,info)
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scal=zone/h(i+1,i)
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call psb_geaxpby(scal,w,zzero,v(i+1),desc_a,info)
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do k=2,i
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call zrot(1,h(k-1,i),1,h(k,i),1,real(c(k-1),kind=psb_dpk_),s(k-1))
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enddo
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rti = h(i,i)
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rti1 = h(i+1,i)
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call zrotg(rti,rti1,tmp,s(i))
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c(i) = cmplx(tmp,dzero)
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call zrot(1,h(i,i),1,h(i+1,i),1,real(c(i),kind=psb_dpk_),s(i))
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h(i+1,i) = zzero
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call zrot(1,rs(i),1,rs(i+1),1,real(c(i),kind=psb_dpk_),s(i))
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if (istop_ == 1) then
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!
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! build x and then compute the residual and its infinity norm
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!
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rst = rs
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call w1%set(zzero)
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call ztrsm('l','u','n','n',i,1,zone,h,size(h,1),rst,size(rst,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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& ' Rebuild x-> RS:',rst(1:i)
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do k=1, i
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call psb_geaxpby(rst(k),v(k),zone,xt,desc_a,info)
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end do
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call prec%apply(xt,desc_a,info)
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call psb_geaxpby(zone,x,zone,xt,desc_a,info)
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call psb_geaxpby(zone,b,zzero,w1,desc_a,info)
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call psb_spmm(-zone,a,xt,zone,w1,desc_a,info,work=aux)
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rni = psb_geamax(w1,desc_a,info)
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xni = psb_geamax(xt,desc_a,info)
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errnum = rni
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errden = (ani*xni+bni)
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!
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else if (istop_ == 2) then
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!
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! compute the residual 2-norm as byproduct of the solution
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! procedure of the least-squares problem
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!
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rni = abs(rs(i+1))
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errnum = rni
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errden = bn2
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endif
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if (errnum <= eps*errden) then
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if (istop_ == 1) then
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call psb_geaxpby(zone,xt,zzero,x,desc_a,info)
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! = x = xt
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else if (istop_ == 2) then
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!
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! build x
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!
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call ztrsm('l','u','n','n',i,1,zone,h,size(h,1),rs,size(rs,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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& ' Rebuild x-> RS:',rs(1:i)
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call w1%set(zzero)
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do k=1, i
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call psb_geaxpby(rs(k),v(k),zone,w1,desc_a,info)
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end do
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call prec%apply(w1,w,desc_a,info)
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call psb_geaxpby(zone,w,zone,x,desc_a,info)
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end if
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exit restart
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end if
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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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end do inner
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if (istop_ == 1) then
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call psb_geaxpby(zone,xt,zzero,x,desc_a,info)! x = xt
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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
|
|
|
|
end subroutine psb_zrgmres_vect
|
|
|