!!$ !!$ Parallel Sparse BLAS v2.0 !!$ (C) Copyright 2006 Salvatore Filippone University of Rome Tor Vergata !!$ Alfredo Buttari University of Rome Tor Vergata !!$ !!$ Contributions to this routine: !!$ Daniela di Serafino Second University of Naples !!$ Pasqua D'Ambra ICAR-CNR !!$ !!$ 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 C !!$ C [5] G. Sleijpen, D. Fokkema C !!$ C BICGSTAB(L) for linear equations involving unsymmetric C !!$ C matrices with complex spectrum C !!$ C Electronic Trans. on Numer. Analysis, Vol. 1, pp. 11-32, C !!$ C Sep. 1993 C !!$ C C !!$ C C !!$ CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC ! File: psb_dgmresr.f90 ! ! Subroutine: psb_dgmres ! This subroutine implements the restarted GMRES method with right ! preconditioning. ! ! Arguments: ! a - type(). The sparse matrix containing A. ! prec - type(). The data structure containing the preconditioner. ! b - real,dimension(:). The right hand side. ! x - real,dimension(:). The vector of unknowns. ! eps - real. The error tolerance. ! desc_a - type(). The communication descriptor. ! info - integer. Return code ! itmax - integer(optional). The maximum number of iterations. ! iter - integer(optional). The number of iterations performed. ! err - real(optional). The error on return. ! itrace - integer(optional). The unit to write messages onto. ! irst - integer(optional). The restart value. ! istop - integer(optional). The stopping criterium. ! Subroutine psb_dgmresr(a,prec,b,x,eps,desc_a,info,& &itmax,iter,err,itrace,irst,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, irst,istop Integer, Optional, Intent(out) :: iter Real(Kind(1.d0)), Optional, Intent(out) :: err !!$ local data Real(Kind(1.d0)), allocatable, target :: aux(:),w(:),w1(:), v(:,:) Real(Kind(1.d0)), allocatable :: c(:),s(:), h(:,:), rs(:),rst(:),xt(:) Real(Kind(1.d0)) :: rerr, scal, gm, rti, rti1 Integer ::litmax, naux, mglob, it,k, itrace_,& & np,me, n_row, n_col, nl, int_err(5) Logical, Parameter :: exchange=.True., noexchange=.False., use_drot=.true. Integer, Parameter :: irmax = 8 Integer :: itx, i, isvch, ictxt,istop_, err_act Logical, Parameter :: debug = .false. Real(Kind(1.d0)) :: rni, xni, bni, ani,bn2, dt real(kind(1.d0)), external :: dnrm2 character(len=20) :: name info = 0 name = 'psb_dgmres' call psb_erractionsave(err_act) If (debug) Write(0,*) 'entering psb_dgmres' ictxt = psb_cd_get_context(desc_a) Call psb_info(ictxt, me, np) If (debug) Write(0,*) 'psb_dgmres: 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||, 2-norm ! if ((istop_ < 1 ).or.(istop_ > 2 ) ) then write(0,*) 'psb_dgmres: invalid istop',istop_ info=5001 int_err(1)=istop_ err=info call psb_errpush(info,name,i_err=int_err) goto 9999 endif If (Present(itmax)) Then litmax = itmax Else litmax = 1000 Endif If (Present(itrace)) Then itrace_ = itrace Else itrace_ = 0 End If If (Present(irst)) Then nl = irst If (debug) Write(0,*) 'present: irst: ',irst,nl Else nl = 10 If (debug) Write(0,*) 'not present: irst: ',irst,nl Endif if (nl <=0 ) then write(0,*) 'psb_dgmres: invalid irst ',nl info=5001 int_err(1)=nl 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),h(nl+1,nl+1),& &c(nl+1),s(nl+1),rs(nl+1), rst(nl+1),stat=info) if (info == 0) Call psb_geall(v,desc_a,info,n=nl+1) if (info == 0) Call psb_geall(w,desc_a,info) if (info == 0) Call psb_geall(w1,desc_a,info) if (info == 0) Call psb_geall(xt,desc_a,info) if (info == 0) Call psb_geasb(v,desc_a,info) if (info == 0) Call psb_geasb(w,desc_a,info) if (info == 0) Call psb_geasb(w1,desc_a,info) if (info == 0) Call psb_geasb(xt,desc_a,info) if (info.ne.0) Then info=4011 call psb_errpush(info,name) goto 9999 End If if (debug) write(0,*) 'Size of V,W,W1 ',size(v),size(v,1),& &size(w),size(w,1),size(w1),size(w1,1), size(v(:,1)) ! Ensure global coherence for convergence checks. call psb_set_coher(ictxt,isvch) 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 itx = 0 restart: Do ! compute r0 = b-ax0 ! check convergence ! compute v1 = r0/||r0||_2 If (debug) Write(0,*) 'restart: ',itx,it it = 0 Call psb_geaxpby(done,b,dzero,v(:,1),desc_a,info) if (info.ne.0) Then info=4011 call psb_errpush(info,name) goto 9999 End If Call psb_spmm(-done,a,x,done,v(:,1),desc_a,info,work=aux) if (info.ne.0) Then info=4011 call psb_errpush(info,name) goto 9999 End If rs(1) = psb_genrm2(v(:,1),desc_a,info) rs(2:) = dzero if (info.ne.0) Then info=4011 call psb_errpush(info,name) goto 9999 End If scal=done/rs(1) ! rs(1) MIGHT BE VERY SMALL - USE DSCAL TO DEAL WITH IT? If (debug) Write(0,*) 'on entry to amax: b: ',Size(b),rs(1),scal ! ! check convergence ! if (istop_ == 1) then rni = psb_geamax(v(:,1),desc_a,info) xni = psb_geamax(x,desc_a,info) rerr = rni/(ani*xni+bni) else if (istop_ == 2) then rni = psb_genrm2(v(:,1),desc_a,info) rerr = rni/bn2 endif if (info.ne.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))') 'gmres(l): ',itx,rerr end If v(:,1) = v(:,1) * scal If (itx.Ge.litmax) Exit restart ! ! inner iterations ! inner: Do i=1,nl itx = itx + 1 call psb_precaply(prec,v(:,i),w1,desc_a,info) Call psb_spmm(done,a,w1,dzero,w,desc_a,info,work=aux) ! do k = 1, i h(k,i) = psb_gedot(v(:,k),w,desc_a,info) call psb_geaxpby(-h(k,i),v(:,k),done,w,desc_a,info) end do h(i+1,i) = psb_genrm2(w,desc_a,info) scal=done/h(i+1,i) call psb_geaxpby(scal,w,dzero,v(:,i+1),desc_a,info) if (use_drot) then do k=2,i call drot(1,h(k-1,i),1,h(k,i),1,c(k-1),s(k-1)) enddo rti = h(i,i) rti1 = h(i+1,i) call drotg(rti,rti1,c(i),s(i)) call drot(1,h(i,i),1,h(i+1,i),1,c(i),s(i)) h(i+1,i) = dzero call drot(1,rs(i),1,rs(i+1),1,c(i),s(i)) else do k=2,i dt = h(k-1,i) h(k-1,i) = c(k-1)*dt + s(k-1)*h(k,i) h(k,i) = -s(k-1)*dt + c(k-1)*h(k,i) enddo gm = safe_dn2(h(i,i),h(i+1,i)) if (debug) write(0,*) 'GM : ',gm gm = max(gm,epstol) c(i) = h(i,i)/gm s(i) = h(i+1,i)/gm rs(i+1) = -s(i)*rs(i) rs(i) = c(i)*rs(i) h(i,i) = c(i)*h(i,i)+s(i)*h(i+1,i) endif if (istop_ == 1) then ! ! build x and then compute the residual and its infinity norm ! rst = rs xt = dzero call dtrsm('l','u','n','n',i,1,done,h,size(h,1),rst,size(rst,1)) if (debug) write(0,*) 'Rebuild x-> RS:',rst(1:nl) do k=1, i call psb_geaxpby(rst(k),v(:,k),done,xt,desc_a,info) end do call psb_precaply(prec,xt,desc_a,info) call psb_geaxpby(done,x,done,xt,desc_a,info) call psb_geaxpby(done,b,dzero,w1,desc_a,info) call psb_spmm(-done,a,xt,done,w1,desc_a,info,work=aux) rni = psb_geamax(w1,desc_a,info) xni = psb_geamax(xt,desc_a,info) rerr = rni/(ani*xni+bni) ! else if (istop_ == 2) then ! ! compute the residual 2-norm as byproduct of the solution ! procedure of the least-squares problem ! rni = abs(rs(i+1)) rerr = rni/bn2 endif if (rerr < eps ) then if (istop_ == 1) then x = xt else if (istop_ == 2) then ! ! build x ! call dtrsm('l','u','n','n',i,1,done,h,size(h,1),rs,size(rs,1)) if (debug) write(0,*) 'Rebuild x-> RS:',rs(21:nl) w1 = dzero do k=1, i call psb_geaxpby(rs(k),v(:,k),done,w1,desc_a,info) end do call psb_precaply(prec,w1,w,desc_a,info) call psb_geaxpby(done,w,done,x,desc_a,info) end if exit restart end if If (itrace_ > 0) then if ((mod(itx,itrace_)==0).and.(me == 0))& & write(*,'(a,i4,3(2x,es10.4))') 'gmres(l): ',itx,rerr end If end Do inner if (istop_ == 1) then x = xt else if (istop_ == 2) then ! ! build x ! call dtrsm('l','u','n','n',nl,1,done,h,size(h,1),rs,size(rs,1)) if (debug) write(0,*) 'Rebuild x-> RS:',rs(21:nl) w1 = dzero do k=1, nl call psb_geaxpby(rs(k),v(:,k),done,w1,desc_a,info) end do call psb_precaply(prec,w1,w,desc_a,info) call psb_geaxpby(done,w,done,x,desc_a,info) end if End Do restart If (itrace_ > 0) then if (me == 0) write(*,'(a,i4,3(2x,es10.4))') 'gmres(l): ',itx,rerr end If If (Present(err)) err=rerr If (Present(iter)) iter = itx If ((rerr>eps).and. (me == 0)) Then Write(0,*) 'gmresr(l) failed to converge to ',eps,& & ' in ',itx,' iterations ' End If Deallocate(aux,h,c,s,rs,rst, stat=info) Call psb_gefree(v,desc_a,info) Call psb_gefree(w,desc_a,info) Call psb_gefree(w1,desc_a,info) Call psb_gefree(xt,desc_a,info) ! restore external global coherence behaviour call psb_restore_coher(ictxt,isvch) if (info /= 0) then info=4011 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 contains function safe_dn2(a,b) real(kind(1.d0)), intent(in) :: a, b real(kind(1.d0)) :: safe_dn2 real(kind(1.d0)) :: t t = max(abs(a),abs(b)) if (t==0.d0) then safe_dn2 = 0.d0 else safe_dn2 = t * sqrt(abs(a/t)**2 + abs(b/t)**2) endif return end function safe_dn2 End Subroutine psb_dgmresr