!!$ !!$ Parallel Sparse BLAS version 2.2 !!$ (C) Copyright 2006/2007/2008 !!$ 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. !!$ !!$ !!$ 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_dcgs.f90 ! ! Subroutine: psb_dcgs ! Implements the Conjugate Gradient Squared 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. ! 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|/|b|; here the iteration is ! stopped when |r| <= eps * |b| ! 2: err = |r|/(|a||x|+|b|); here the iteration is ! stopped when |r| <= eps * (|a||x|+|b|) ! where r is the (preconditioned, recursive ! estimate of) residual. ! ! Subroutine psb_dcgs(a,prec,b,x,eps,desc_a,info,itmax,iter,err,itrace,istop) use psb_base_mod use psb_prec_mod use psb_krylov_mod, psb_protect_name => psb_dcgs use psb_d_mat_mod implicit none type(psb_d_sparse_mat), intent(in) :: a !!$ parameters !!$ Type(psb_dspmat_type), Intent(in) :: a Type(psb_desc_type), Intent(in) :: desc_a Type(psb_dprec_type), Intent(in) :: prec 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 !!$ local data Real(psb_dpk_), allocatable, target :: aux(:),wwrk(:,:) Real(psb_dpk_), Pointer :: ww(:), q(:),& & r(:), p(:), v(:), s(:), z(:), f(:), rt(:),qt(:),uv(:) Integer :: itmax_, naux, mglob, it, itrace_,int_err(5),& & np,me, n_row, n_col,istop_, err_act Integer :: itx, isvch, ictxt integer :: debug_level, debug_unit Real(psb_dpk_) :: alpha, beta, rho, rho_old, sigma type(psb_itconv_type) :: stopdat character(len=20) :: name character(len=*), parameter :: methdname='CGS' info = 0 name = 'psb_dcgs' call psb_erractionsave(err_act) debug_unit = psb_get_debug_unit() debug_level = psb_get_debug_level() ictxt = psb_cd_get_context(desc_a) Call psb_info(ictxt, me, np) if (debug_level >= psb_debug_ext_)& & write(debug_unit,*) me,' ',trim(name),': from psb_info',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_ = 2 Endif call psb_chkvect(mglob,1,size(x,1),1,1,desc_a,info) if (info == 0) 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 X/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=11) if (info == 0) Call psb_geasb(wwrk,desc_a,info) if (info /= 0) Then info=4011 call psb_errpush(info,name) goto 9999 End If q => wwrk(:,1) qt => wwrk(:,2) r => wwrk(:,3) rt => wwrk(:,4) p => wwrk(:,5) v => wwrk(:,6) uv => wwrk(:,7) z => wwrk(:,8) f => wwrk(:,9) s => wwrk(:,10) ww => wwrk(:,11) If (Present(itmax)) Then itmax_ = itmax Else itmax_ = 1000 Endif If (Present(itrace)) Then itrace_ = itrace Else itrace_ = 0 End If ! Ensure global coherence for convergence checks. call psb_set_coher(ictxt,isvch) itx = 0 call psb_init_conv(methdname,istop_,itrace_,itmax_,a,b,eps,desc_a,stopdat,info) if (info /= 0) Then call psb_errpush(4011,name) goto 9999 End If restart: Do !!$ !!$ r0 = b-ax0 !!$ if (itx >= itmax_) exit restart it = 0 call psb_geaxpby(done,b,dzero,r,desc_a,info) if (info == 0) call psb_spmm(-done,a,x,done,r,desc_a,info,work=aux) if (info == 0) call psb_geaxpby(done,r,dzero,rt,desc_a,info) if (info/=0) then info=4011 call psb_errpush(info,name) goto 9999 end if ! Perhaps we already satisfy the convergence criterion... if (psb_check_conv(methdname,itx,x,r,desc_a,stopdat,info)) exit restart if (info /= 0) Then call psb_errpush(4011,name) goto 9999 End If rho = dzero iteration: do it = it + 1 itx = itx + 1 if (debug_level >= psb_debug_ext_) & & write(debug_unit,*) me,' ',trim(name),'iteration: ',itx rho_old = rho rho = psb_gedot(rt,r,desc_a,info) if (rho==dzero) then if (debug_level >= psb_debug_ext_) & & write(debug_unit,*) me,' ',trim(name),& & ' iteration breakdown r',rho exit iteration endif if (it==1) then call psb_geaxpby(done,r,dzero,uv,desc_a,info) if (info == 0) call psb_geaxpby(done,r,dzero,p,desc_a,info) else beta = (rho/rho_old) call psb_geaxpby(done,r,dzero,uv,desc_a,info) if (info == 0) call psb_geaxpby(beta,q,done,uv,desc_a,info) if (info == 0) call psb_geaxpby(done,q,beta,p,desc_a,info) if (info == 0) call psb_geaxpby(done,uv,beta,p,desc_a,info) end if if (info == 0) call psb_precaply(prec,p,f,desc_a,info,work=aux) if (info == 0) call psb_spmm(done,a,f,dzero,v,desc_a,info,& & work=aux) if (info /= 0) then call psb_errpush(4010,name,a_err='First loop part ') goto 9999 end if sigma = psb_gedot(rt,v,desc_a,info) if (sigma==dzero) then if (debug_level >= psb_debug_ext_) & & write(debug_unit,*) me,' ',trim(name),& & ' iteration breakdown s1', sigma exit iteration endif alpha = rho/sigma if (info == 0) call psb_geaxpby(done,uv,dzero,q,desc_a,info) if (info == 0) call psb_geaxpby(-alpha,v,done,q,desc_a,info) if (info == 0) call psb_geaxpby(done,uv,dzero,s,desc_a,info) if (info == 0) call psb_geaxpby(done,q,done,s,desc_a,info) if (info == 0) call psb_precaply(prec,s,z,desc_a,info,work=aux) if (info == 0) call psb_geaxpby(alpha,z,done,x,desc_a,info) if (info == 0) call psb_spmm(done,a,z,dzero,qt,desc_a,info,& & work=aux) if (info == 0) call psb_geaxpby(-alpha,qt,done,r,desc_a,info) if (info /= 0) then call psb_errpush(4010,name,a_err='X update ') goto 9999 end if if (psb_check_conv(methdname,itx,x,r,desc_a,stopdat,info)) exit restart if (info /= 0) Then call psb_errpush(4011,name) goto 9999 End If end do iteration end do restart call psb_end_conv(methdname,itx,desc_a,stopdat,info,err,iter) deallocate(aux,stat=info) if (info == 0) call psb_gefree(wwrk,desc_a,info) if (info /= 0) 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_dcgs