!!$ !!$ Parallel Sparse BLAS v2.0 !!$ (C) Copyright 2006 Salvatore Filippone University of Rome Tor Vergata !!$ Alfredo Buttari University of Rome Tor Vergata !!$ !!$ 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 - type(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. ! err - real (optional) Output: error estimate on exit ! 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|/|b| ! 2: err = |r|/(|a||x|+|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) use psb_base_mod use psb_prec_mod implicit none !!$ Parameters Type(psb_dspmat_type), Intent(in) :: a Type(psb_dprec_type), Intent(in) :: prec Type(psb_desc_type), Intent(in) :: desc_a Real(Kind(1.d0)), Intent(in) :: b(:) Real(Kind(1.d0)), Intent(inout) :: x(:) Real(Kind(1.d0)), Intent(in) :: eps integer, intent(out) :: info Integer, Optional, Intent(in) :: itmax, itrace, istop Integer, Optional, Intent(out) :: iter Real(Kind(1.d0)), Optional, Intent(out) :: err !!$ Local data real(kind(1.d0)), allocatable, target :: aux(:), wwrk(:,:) real(kind(1.d0)), pointer :: q(:), p(:), r(:), z(:), w(:) real(kind(1.d0)) ::rerr real(kind(1.d0)) ::alpha, beta, rho, rho_old, rni, xni, bni, ani,bn2,& & sigma integer :: litmax, istop_, naux, mglob, it, itx, itrace_,& & np,me, n_col, isvch, ictxt, n_row,err_act, int_err(5) logical, parameter :: exchange=.true., noexchange=.false. character(len=20) :: name info = 0 name = 'psb_dcg' call psb_erractionsave(err_act) ictxt = psb_cd_get_context(desc_a) call psb_info(ictxt, me, np) mglob = psb_cd_get_global_rows(desc_a) n_row = psb_cd_get_local_rows(desc_a) n_col = psb_cd_get_local_cols(desc_a) if (present(istop)) then istop_ = istop else istop_ = 1 endif ! ! ISTOP_ = 1: Normwise backward error, infinity norm ! ISTOP_ = 2: ||r||/||b|| norm 2 ! if ((istop_ < 1 ).or.(istop_ > 2 ) ) then write(0,*) 'psb_cg: invalid istop',istop_ info=5001 int_err(1)=istop_ err=info call psb_errpush(info,name,i_err=int_err) goto 9999 endif call psb_chkvect(mglob,1,size(x,1),1,1,desc_a,info) if(info /= 0) then info=4010 call psb_errpush(info,name,a_err='psb_chkvect on X') goto 9999 end if call psb_chkvect(mglob,1,size(b,1),1,1,desc_a,info) if(info /= 0) then info=4010 call psb_errpush(info,name,a_err='psb_chkvect on B') goto 9999 end if naux=4*n_col allocate(aux(naux), stat=info) if (info == 0) call psb_geall(wwrk,desc_a,info,n=5) if (info == 0) call psb_geasb(wwrk,desc_a,info) if (info.ne.0) then info=4011 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 litmax = itmax else litmax = 1000 endif if (present(itrace)) then itrace_ = itrace else itrace_ = 0 end if itx=0 ! Ensure global coherence for convergence checks. call psb_set_coher(ictxt,isvch) restart: do !!$ !!$ r0 = b-Ax0 !!$ if (itx>= litmax) exit restart it = 0 call psb_geaxpby(done,b,dzero,r,desc_a,info) call psb_spmm(-done,a,x,done,r,desc_a,info,work=aux) if (info.ne.0) then info=4011 call psb_errpush(info,name) goto 9999 end if rho = dzero 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 if (info.ne.0) then info=4011 call psb_errpush(info,name) goto 9999 end if iteration: do it = it + 1 itx = itx + 1 Call psb_precaply(prec,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 write(0,*) 'CG Iteration breakdown' 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 write(0,*) 'CG Iteration breakdown' exit iteration endif alpha = rho/sigma call psb_geaxpby(alpha,p,done,x,desc_a,info) call psb_geaxpby(-alpha,q,done,r,desc_a,info) if (istop_ == 1) Then rni = psb_geamax(r,desc_a,info) xni = psb_geamax(x,desc_a,info) rerr = rni/(ani*xni+bni) Else If (istop_ == 2) Then rni = psb_genrm2(r,desc_a,info) rerr = rni/bn2 Endif if (rerr<=eps) exit restart if (itx>= litmax) exit restart If (itrace_ > 0) then if ((mod(itx,itrace_)==0).and.(me == 0))& & write(*,'(a,i4,3(2x,es10.4))') 'cg: ',itx,rerr end If end do iteration end do restart If (itrace_ > 0) then if (me == 0) write(*,'(a,i4,3(2x,es10.4))') 'cg: ',itx,rerr end If if (present(err)) err=rerr if (present(iter)) iter = itx if (rerr>eps) then write(0,*) 'CG Failed to converge to ',eps,& & ' in ',litmax,' iterations ' info=itx end if deallocate(aux) call psb_gefree(wwrk,desc_a,info) ! restore external global coherence behaviour call psb_restore_coher(ictxt,isvch) if (info.ne.0) then 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.eq.psb_act_abort_) then call psb_error() return end if return end subroutine psb_dcg