!!$ !!$ 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. !!$ !!$ !!$ 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_zcgs.f90 ! ! Subroutine: psb_zcgs ! Implements the Conjugate Gradient Squared method. ! ! Arguments: ! ! methd - character The specific method; can take the values: ! CGS ! BICGSTAB ! RGMRES ! ! a - type() Input: sparse matrix containing A. ! prec - type() Input: preconditioner ! b - complex,dimension(:) Input: vector containing the ! right hand side B ! x - complex,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(). 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_zcgs(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_zspmat_type), Intent(in) :: a Type(psb_desc_type), Intent(in) :: desc_a Type(psb_zprec_type), Intent(in) :: prec Complex(Kind(1.d0)), Intent(in) :: b(:) Complex(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 Complex(Kind(1.d0)), allocatable, target :: aux(:),wwrk(:,:) Complex(Kind(1.d0)), Pointer :: ww(:), q(:),& & r(:), p(:), v(:), s(:), z(:), f(:), rt(:),qt(:),uv(:) Real(Kind(1.d0)) :: rerr Integer :: litmax, naux, mglob, it, itrace_,int_err(5),& & np,me, n_row, n_col,istop_, err_act Logical, Parameter :: exchange=.True., noexchange=.False. Integer, Parameter :: irmax = 8 Integer :: itx, isvch, ictxt Logical, Parameter :: debug = .false. Real(Kind(1.d0)) :: rni, xni, bni, ani,bn2 complex(Kind(1.d0)) :: alpha, beta, rho, rho_old, sigma character(len=20) :: name info = 0 name = 'psb_zcgs' call psb_erractionsave(err_act) If (debug) Write(*,*) 'entering psb_zcgs' ictxt = psb_cd_get_context(desc_a) Call psb_info(ictxt, me, np) If (debug) Write(*,*) 'psb_zcgs: from gridinfo',np,me 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 ((prec%prec < 0).Or.(prec%prec > 6) ) Then !!$ Write(0,*) 'f90_cgstab: invalid iprec',prec%prec !!$ If (Present(ierr)) ierr=-1 !!$ Return !!$ Endif if ((istop_ < 1 ).or.(istop_ > 2 ) ) then write(0,*) 'psb_cgs: invalid istop',istop_ info=5001 int_err=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=11) 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 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 litmax = itmax Else litmax = 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 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/=0)then info=4011 call psb_errpush(info,name) goto 9999 end if restart: Do !!$ !!$ r0 = b-ax0 !!$ If (itx.Ge.litmax) Exit restart it = 0 Call psb_geaxpby(zone,b,zzero,r,desc_a,info) Call psb_spmm(-zone,a,x,zone,r,desc_a,info,work=aux) Call psb_geaxpby(zone,r,zzero,rt,desc_a,info) if(info/=0)then info=4011 call psb_errpush(info,name) goto 9999 end if rho = zzero If (debug) Write(*,*) 'on entry to amax: b: ',Size(b) 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(info/=0)then info=4011 call psb_errpush(info,name) goto 9999 end if If (rerr<=eps) Then Exit restart End If If (itrace_ > 0) then if ((mod(itx,itrace_)==0).and.(me == 0))& & write(*,'(a,i4,3(2x,es10.4))') 'cgs: ',itx,rerr end If iteration: Do it = it + 1 itx = itx + 1 If (debug) Write(*,*) 'iteration: ',itx rho_old = rho rho = psb_gedot(rt,r,desc_a,info) If (rho==zzero) Then If (debug) Write(0,*) 'cgs iteration breakdown r',rho Exit iteration Endif If (it==1) Then Call psb_geaxpby(zone,r,zzero,uv,desc_a,info) Call psb_geaxpby(zone,r,zzero,p,desc_a,info) Else beta = (rho/rho_old) Call psb_geaxpby(zone,r,zzero,uv,desc_a,info) Call psb_geaxpby(beta,q,zone,uv,desc_a,info) Call psb_geaxpby(zone,q,beta,p,desc_a,info) Call psb_geaxpby(zone,uv,beta,p,desc_a,info) End If Call psb_precaply(prec,p,f,desc_a,info,work=aux) Call psb_spmm(zone,a,f,zzero,v,desc_a,info,& & work=aux) sigma = psb_gedot(rt,v,desc_a,info) If (sigma==zzero) Then If (debug) Write(0,*) 'cgs iteration breakdown s1', sigma Exit iteration Endif alpha = rho/sigma Call psb_geaxpby(zone,uv,zzero,q,desc_a,info) Call psb_geaxpby(-alpha,v,zone,q,desc_a,info) Call psb_geaxpby(zone,uv,zzero,s,desc_a,info) Call psb_geaxpby(zone,q,zone,s,desc_a,info) Call psb_precaply(prec,s,z,desc_a,info,work=aux) Call psb_geaxpby(alpha,z,zone,x,desc_a,info) Call psb_spmm(zone,a,z,zzero,qt,desc_a,info,& & work=aux) Call psb_geaxpby(-alpha,qt,zone,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) Then Exit restart End If If (itx.Ge.litmax) Exit restart If (itrace_ > 0) then if ((mod(itx,itrace_)==0).and.(me == 0))& & write(*,'(a,i4,3(2x,es10.4))') 'cgs: ',itx,rerr end If End Do iteration End Do restart If (itrace_ > 0) then if (me == 0) write(*,'(a,i4,3(2x,es10.4))') 'cgs: ',itx,rerr end If If (Present(err)) err=rerr If (Present(iter)) iter = itx If (rerr>eps) Then Write(0,*) 'cgs failed to converge to ',eps,& & ' in ',itx,' iterations ' End If Deallocate(aux) Call psb_gefree(wwrk,desc_a,info) ! restore external global coherence behaviour call psb_restore_coher(ictxt,isvch) if(info/=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_zcgs