!!$ !!$ Parallel Sparse BLAS version 3.0 !!$ (C) Copyright 2006, 2007, 2008, 2009, 2010 !!$ Salvatore Filippone University of Rome Tor Vergata !!$ Alfredo Buttari CNRS-IRIT, Toulouse !!$ !!$ Redistribution and use in source and binary forms, with or without !!$ modification, are permitted provided that the following conditions !!$ are met: !!$ 1. Redistributions of source code must retain the above copyright !!$ notice, this list of conditions and the following disclaimer. !!$ 2. Redistributions in binary form must reproduce the above copyright !!$ notice, this list of conditions, and the following disclaimer in the !!$ documentation and/or other materials provided with the distribution. !!$ 3. The name of the PSBLAS group or the names of its contributors may !!$ not be used to endorse or promote products derived from this !!$ software without specific written permission. !!$ !!$ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS !!$ ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED !!$ TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR !!$ PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE PSBLAS GROUP OR ITS CONTRIBUTORS !!$ BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR !!$ CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF !!$ SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS !!$ INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN !!$ CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) !!$ ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE !!$ POSSIBILITY OF SUCH DAMAGE. !!$ !!$ ! File: psb_dcg.f90 !!$ CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC !!$ C C !!$ C References: C !!$ C [1] Duff, I., Marrone, M., Radicati, G., and Vittoli, C. C !!$ C Level 3 basic linear algebra subprograms for sparse C !!$ C matrices: a user level interface C !!$ C ACM Trans. Math. Softw., 23(3), 379-401, 1997. C !!$ C C !!$ C C !!$ C [2] S. Filippone, M. Colajanni C !!$ C PSBLAS: A library for parallel linear algebra C !!$ C computation on sparse matrices C !!$ C ACM Trans. on Math. Softw., 26(4), 527-550, Dec. 2000. C !!$ C C !!$ C [3] M. Arioli, I. Duff, M. Ruiz C !!$ C Stopping criteria for iterative solvers C !!$ C SIAM J. Matrix Anal. Appl., Vol. 13, pp. 138-144, 1992 C !!$ C C !!$ C C !!$ C [4] R. Barrett et al C !!$ C Templates for the solution of linear systems C !!$ C SIAM, 1993 !!$ C C !!$ C C !!$ CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC ! File: psb_dcg.f90 ! ! Subroutine: psb_dcg ! This subroutine implements the Conjugate Gradient method. ! ! ! Arguments: ! ! a - type(psb_dspmat_type) Input: sparse matrix containing A. ! prec - class(psb_dprec_type) Input: preconditioner ! b - real,dimension(:) Input: vector containing the ! right hand side B ! x - real,dimension(:) Input/Output: vector containing the ! initial guess and final solution X. ! eps - real Input: Stopping tolerance; the iteration is ! stopped when the error estimate |err| <= eps ! desc_a - type(psb_desc_type). Input: The communication descriptor. ! info - integer. Output: Return code ! ! itmax - integer(optional) Input: maximum number of iterations to be ! performed. ! iter - integer(optional) Output: how many iterations have been ! performed. ! performed. ! err - real (optional) Output: error estimate on exit. If the ! denominator of the estimate is exactly ! 0, it is changed into 1. ! itrace - integer(optional) Input: print an informational message ! with the error estimate every itrace ! iterations ! istop - integer(optional) Input: stopping criterion, or how ! to estimate the error. ! 1: err = |r|/(|a||x|+|b|); here the iteration is ! stopped when |r| <= eps * (|a||x|+|b|) ! 2: err = |r|/|b|; here the iteration is ! stopped when |r| <= eps * |b| ! where r is the (preconditioned, recursive ! estimate of) residual. ! ! subroutine psb_dcg(a,prec,b,x,eps,desc_a,info,itmax,iter,err,itrace,istop,cond) use psb_base_mod use psb_prec_mod use psb_inner_krylov_mod use psb_krylov_mod implicit none type(psb_dspmat_type), intent(in) :: a class(psb_dprec_type), Intent(in) :: prec Type(psb_desc_type), Intent(in) :: desc_a Real(psb_dpk_), Intent(in) :: b(:) Real(psb_dpk_), Intent(inout) :: x(:) Real(psb_dpk_), Intent(in) :: eps integer, intent(out) :: info Integer, Optional, Intent(in) :: itmax, itrace, istop Integer, Optional, Intent(out) :: iter Real(psb_dpk_), Optional, Intent(out) :: err,cond !!$ Local data real(psb_dpk_), allocatable, target :: aux(:), wwrk(:,:), td(:),tu(:),eig(:),ewrk(:) integer, allocatable :: ibl(:), ispl(:), iwrk(:) real(psb_dpk_), pointer :: q(:), p(:), r(:), z(:), w(:) real(psb_dpk_) :: alpha, beta, rho, rho_old, sigma,alpha_old,beta_old integer :: itmax_, istop_, naux, mglob, it, itx, itrace_,& & np,me, n_col, isvch, ictxt, n_row,err_act, int_err(5), ieg,nspl, istebz integer :: debug_level, debug_unit type(psb_itconv_type) :: stopdat logical :: do_cond character(len=20) :: name character(len=*), parameter :: methdname='CG' info = psb_success_ name = 'psb_dcg' 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) 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 call psb_chkvect(mglob,1,size(x,1),1,1,desc_a,info) if (info == psb_success_) call psb_chkvect(mglob,1,size(b,1),1,1,desc_a,info) if(info /= psb_success_) then info=psb_err_from_subroutine_ call psb_errpush(info,name,a_err='psb_chkvect on X/B') goto 9999 end if naux=4*n_col allocate(aux(naux), stat=info) if (info == psb_success_) call psb_geall(wwrk,desc_a,info,n=psb_err_invalid_input_) if (info == psb_success_) call psb_geasb(wwrk,desc_a,info) if (info /= psb_success_) then info=psb_err_from_subroutine_non_ call psb_errpush(info,name) goto 9999 end if p => wwrk(:,1) q => wwrk(:,2) r => wwrk(:,3) z => wwrk(:,4) w => wwrk(:,5) if (present(itmax)) then itmax_ = itmax else itmax_ = 1000 endif if (present(itrace)) then itrace_ = itrace else itrace_ = 0 end if do_cond=present(cond) if (do_cond) then istebz = 0 allocate(td(itmax_),tu(itmax_), eig(itmax_),& & ibl(itmax_),ispl(itmax_),iwrk(3*itmax_),ewrk(4*itmax_),& & stat=info) if (info /= psb_success_) then info=psb_err_from_subroutine_non_ call psb_errpush(info,name) goto 9999 end if end if itx=0 ! Ensure global coherence for convergence checks. call psb_set_coher(ictxt,isvch) restart: do !!$ !!$ r0 = b-Ax0 !!$ if (itx>= itmax_) exit restart it = 0 call psb_geaxpby(done,b,dzero,r,desc_a,info) if (info == psb_success_) call psb_spmm(-done,a,x,done,r,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 rho = dzero call psb_init_conv(methdname,istop_,itrace_,itmax_,a,b,eps,desc_a,stopdat,info) if (info /= psb_success_) Then call psb_errpush(psb_err_from_subroutine_non_,name) goto 9999 End If iteration: do it = it + 1 itx = itx + 1 call prec%apply(r,z,desc_a,info,work=aux) rho_old = rho rho = psb_gedot(r,z,desc_a,info) if (it == 1) then call psb_geaxpby(done,z,dzero,p,desc_a,info) else if (rho_old == dzero) then if (debug_level >= psb_debug_ext_)& & write(debug_unit,*) me,' ',trim(name),& & ': CG Iteration breakdown rho' exit iteration endif beta = rho/rho_old call psb_geaxpby(done,z,beta,p,desc_a,info) end if call psb_spmm(done,a,p,dzero,q,desc_a,info,work=aux) sigma = psb_gedot(p,q,desc_a,info) if (sigma == dzero) then if (debug_level >= psb_debug_ext_)& & write(debug_unit,*) me,' ',trim(name),& & ': CG Iteration breakdown sigma' exit iteration endif alpha_old = alpha alpha = rho/sigma if (do_cond) then istebz = istebz + 1 if (istebz == 1) then td(istebz) = done/alpha else td(istebz) = done/alpha + beta/alpha_old tu(istebz-1) = sqrt(beta)/alpha_old end if end if call psb_geaxpby(alpha,p,done,x,desc_a,info) call psb_geaxpby(-alpha,q,done,r,desc_a,info) if (psb_check_conv(methdname,itx,x,r,desc_a,stopdat,info)) exit restart if (info /= psb_success_) Then call psb_errpush(psb_err_from_subroutine_non_,name) goto 9999 End If end do iteration end do restart if (do_cond) then if (me == 0) then #if defined(HAVE_LAPACK) call dstebz('A','E',istebz,dzero,dzero,0,0,-done,td,tu,& & ieg,nspl,eig,ibl,ispl,ewrk,iwrk,info) if (info < 0) then call psb_errpush(psb_err_from_subroutine_ai_,name,a_err='dstebz',i_err=(/info,0,0,0,0/)) info = psb_err_from_subroutine_ai_ goto 9999 end if cond = eig(ieg)/eig(1) #else cond = -1.0 #endif info = psb_success_ end if call psb_bcast(ictxt,cond,root=0) end if call psb_end_conv(methdname,itx,desc_a,stopdat,info,err,iter) call psb_gefree(wwrk,desc_a,info) if (info /= psb_success_) then call psb_errpush(info,name) goto 9999 end if ! restore external global coherence behaviour call psb_restore_coher(ictxt,isvch) call psb_erractionrestore(err_act) return 9999 continue call psb_erractionrestore(err_act) if (err_act == psb_act_abort_) then call psb_error() return end if return end subroutine psb_dcg