!!$ !!$ 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: ! ! 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 ! irst - integer(optional) Input: restart parameter ! ! 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_zgmresr(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_zspmat_type), Intent(in) :: a Type(psb_zprec_type), Intent(in) :: prec Type(psb_desc_type), Intent(in) :: desc_a 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, irst,istop Integer, Optional, Intent(out) :: iter Real(Kind(1.d0)), Optional, Intent(out) :: err !!$ local data complex(Kind(1.d0)), allocatable, target :: aux(:),w(:),w1(:), v(:,:) complex(Kind(1.d0)), allocatable :: c(:),s(:), h(:,:), rs(:),rst(:),xt(:) Real(Kind(1.d0)) :: rerr, tmp complex(kind(1.d0)) :: rti, rti1, scal Integer ::litmax, naux, mglob, it,k, itrace_,& & np,me, n_row, n_col, nl, int_err(5) Logical, Parameter :: exchange=.True., noexchange=.False. 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 real(kind(1.d0)), external :: dznrm2 character(len=20) :: name info = 0 name = 'psb_zgmres' call psb_erractionsave(err_act) If (debug) Write(0,*) 'entering psb_zgmres' 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(zone,b,zzero,v(:,1),desc_a,info) if (info.ne.0) Then info=4011 call psb_errpush(info,name) goto 9999 End If Call psb_spmm(-zone,a,x,zone,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:) = zzero 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(zone,a,w1,zzero,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),zone,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,zzero,v(:,i+1),desc_a,info) do k=2,i call zrot(1,h(k-1,i),1,h(k,i),1,real(c(k-1)),s(k-1)) enddo rti = h(i,i) rti1 = h(i+1,i) call zrotg(rti,rti1,tmp,s(i)) c(i) = cmplx(tmp,dzero) call zrot(1,h(i,i),1,h(i+1,i),1,real(c(i)),s(i)) h(i+1,i) = zzero call zrot(1,rs(i),1,rs(i+1),1,real(c(i)),s(i)) if (istop_ == 1) then ! ! build x and then compute the residual and its infinity norm ! rst = rs xt = zzero call ztrsm('l','u','n','n',i,1,zone,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),zone,xt,desc_a,info) end do call psb_precaply(prec,xt,desc_a,info) call psb_geaxpby(zone,x,zone,xt,desc_a,info) call psb_geaxpby(zone,b,zzero,w1,desc_a,info) call psb_spmm(-zone,a,xt,zone,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 ztrsm('l','u','n','n',i,1,zone,h,size(h,1),rs,size(rs,1)) if (debug) write(0,*) 'Rebuild x-> RS:',rs(21:nl) w1 = zzero do k=1, i call psb_geaxpby(rs(k),v(:,k),zone,w1,desc_a,info) end do call psb_precaply(prec,w1,w,desc_a,info) call psb_geaxpby(zone,w,zone,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 ztrsm('l','u','n','n',nl,1,zone,h,size(h,1),rs,size(rs,1)) if (debug) write(0,*) 'Rebuild x-> RS:',rs(21:nl) w1 = zzero do k=1, nl call psb_geaxpby(rs(k),v(:,k),zone,w1,desc_a,info) end do call psb_precaply(prec,w1,w,desc_a,info) call psb_geaxpby(zone,w,zone,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 subroutine zrot( n, cx, incx, cy, incy, c, s ) ! ! -- lapack auxiliary routine (version 3.0) -- ! univ. of tennessee, univ. of california berkeley, nag ltd., ! courant institute, argonne national lab, and rice university ! october 31, 1992 ! ! .. scalar arguments .. integer incx, incy, n real(kind(1.d0)) c complex(kind(1.d0)) s ! .. ! .. array arguments .. complex(kind(1.d0)) cx( * ), cy( * ) ! .. ! ! purpose ! ======= ! ! zrot applies a plane rotation, where the cos (c) is real and the ! sin (s) is complex, and the vectors cx and cy are complex. ! ! arguments ! ========= ! ! n (input) integer ! the number of elements in the vectors cx and cy. ! ! cx (input/output) complex*16 array, dimension (n) ! on input, the vector x. ! on output, cx is overwritten with c*x + s*y. ! ! incx (input) integer ! the increment between successive values of cy. incx <> 0. ! ! cy (input/output) complex*16 array, dimension (n) ! on input, the vector y. ! on output, cy is overwritten with -conjg(s)*x + c*y. ! ! incy (input) integer ! the increment between successive values of cy. incx <> 0. ! ! c (input) double precision ! s (input) complex*16 ! c and s define a rotation ! [ c s ] ! [ -conjg(s) c ] ! where c*c + s*conjg(s) = 1.0. ! ! ===================================================================== ! ! .. local scalars .. integer i, ix, iy complex(kind(1.d0)) stemp ! .. ! .. intrinsic functions .. intrinsic dconjg ! .. ! .. executable statements .. ! if( n.le.0 ) return if( incx.eq.1 .and. incy.eq.1 ) then ! ! code for both increments equal to 1 ! do i = 1, n stemp = c*cx(i) + s*cy(i) cy(i) = c*cy(i) - dconjg(s)*cx(i) cx(i) = stemp end do else ! ! code for unequal increments or equal increments not equal to 1 ! ix = 1 iy = 1 if( incx.lt.0 )ix = ( -n+1 )*incx + 1 if( incy.lt.0 )iy = ( -n+1 )*incy + 1 do i = 1, n stemp = c*cx(ix) + s*cy(iy) cy(iy) = c*cy(iy) - dconjg(s)*cx(ix) cx(ix) = stemp ix = ix + incx iy = iy + incy end do end if return return end subroutine zrot ! ! subroutine zrotg(ca,cb,c,s) complex(kind(1.d0)) ca,cb,s real(kind(1.d0)) c real(kind(1.d0)) norm,scale complex(kind(1.d0)) alpha ! if (cdabs(ca) == 0.0d0) then ! c = 0.0d0 s = (1.0d0,0.0d0) ca = cb return end if ! scale = cdabs(ca) + cdabs(cb) norm = scale*dsqrt((cdabs(ca/dcmplx(scale,0.0d0)))**2 +& & (cdabs(cb/dcmplx(scale,0.0d0)))**2) alpha = ca /cdabs(ca) c = cdabs(ca) / norm s = alpha * dconjg(cb) / norm ca = alpha * norm ! return end subroutine zrotg End Subroutine psb_zgmresr