!!$ !!$ 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 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_dcgstabl.f90 ! ! Subroutine: psb_dcgstabl ! ! 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. ! istop - integer(optional). The stopping criterium. ! Subroutine psb_dcgstabl(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(:),wwrk(:,:),uh(:,:), rh(:,:) Real(Kind(1.d0)), Pointer :: ww(:), q(:), r(:), rt0(:), p(:), v(:), & & s(:), t(:), z(:), f(:), gamma(:), gamma1(:), gamma2(:), taum(:,:), sigma(:) Real(Kind(1.d0)) :: rerr Integer :: litmax, naux, mglob, it, itrace_,& & np,me, n_row, n_col, nl, err_act Logical, Parameter :: exchange=.True., noexchange=.False. Integer, Parameter :: irmax = 8 Integer :: itx, i, isvch, ictxt,istop_,j, int_err(5) Logical, Parameter :: debug = .False. Real(Kind(1.d0)) :: alpha, beta, rho, rho_old, rni, xni, bni, ani,bn2,& & omega character(len=20) :: name info = 0 name = 'psb_dcgstabl' call psb_erractionsave(err_act) If (debug) Write(0,*) 'entering psb_dbicgstabl' ictxt = psb_cd_get_context(desc_a) Call psb_info(ictxt, me, np) If (debug) Write(0,*) 'psb_dbicgstabl: 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 ((istop_ < 1 ).or.(istop_ > 2 ) ) then write(0,*) 'psb_bicgstabl: invalid istop',istop_ info=5001 int_err=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 = 1 If (debug) Write(0,*) 'not present: irst: ',irst,nl Endif if (nl <=0 ) then write(0,*) 'psb_bicgstabl: 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),gamma(0:nl),gamma1(nl),& &gamma2(nl),taum(nl,nl),sigma(nl), stat=info) If (info.Ne.0) Then info=4000 call psb_errpush(info,name) goto 9999 End If if (info == 0) Call psb_geall(wwrk,desc_a,info,n=10) if (info == 0) Call psb_geall(uh,desc_a,info,n=nl+1) if (info == 0) Call psb_geall(rh,desc_a,info,n=nl+1) if (info == 0) Call psb_geasb(wwrk,desc_a,info) if (info == 0) Call psb_geasb(uh,desc_a,info) if (info == 0) Call psb_geasb(rh,desc_a,info) if (info.ne.0) Then info=4011 call psb_errpush(info,name) goto 9999 End If q => wwrk(:,1) r => wwrk(:,2) p => wwrk(:,3) v => wwrk(:,4) f => wwrk(:,5) s => wwrk(:,6) t => wwrk(:,7) z => wwrk(:,8) ww => wwrk(:,9) rt0 => wwrk(:,10) ! 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 !!$ !!$ r0 = b-ax0 !!$ If (debug) Write(0,*) 'restart: ',itx,it If (itx.Ge.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) call psb_precaply(prec,r,desc_a,info) Call psb_geaxpby(done,r,dzero,rt0,desc_a,info) Call psb_geaxpby(done,r,dzero,rh(:,0),desc_a,info) Call psb_geaxpby(dzero,r,dzero,uh(:,0),desc_a,info) if (info.ne.0) Then info=4011 call psb_errpush(info,name) goto 9999 End If rho = done alpha = dzero omega = done If (debug) Write(0,*) '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.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))') 'bicgstab(l): ',itx,rerr end If iteration: Do it = it + nl itx = itx + nl rho = -omega*rho If (debug) Write(0,*) 'iteration: ',itx, rho,rh(1,0) Do j = 0, nl -1 If (debug) Write(0,*) 'bicg part: ',j, nl rho_old = rho rho = psb_gedot(rh(:,j),rt0,desc_a,info) If (rho==dzero) Then If (debug) Write(0,*) 'bi-cgstab iteration breakdown r',rho Exit iteration Endif beta = alpha*rho/rho_old If (debug) Write(0,*) 'bicg part: ',alpha,beta,rho,rho_old rho_old = rho Call psb_geaxpby(done,rh(:,0:j),-beta,uh(:,0:j),desc_a,info) If (debug) Write(0,*) 'bicg part: ',rh(1,0),beta Call psb_spmm(done,a,uh(:,j),dzero,uh(:,j+1),desc_a,info,work=aux) call psb_precaply(prec,uh(:,j+1),desc_a,info) gamma(j) = psb_gedot(uh(:,j+1),rt0,desc_a,info) If (gamma(j)==dzero) Then If (debug) Write(0,*) 'bi-cgstab iteration breakdown s2',gamma(j) Exit iteration Endif alpha = rho/gamma(j) If (debug) Write(0,*) 'bicg part: alpha=r/g ',alpha,rho,gamma(j) Call psb_geaxpby(-alpha,uh(:,1:j+1),done,rh(:,0:j),desc_a,info) Call psb_geaxpby(alpha,uh(:,0),done,x,desc_a,info) Call psb_spmm(done,a,rh(:,j),dzero,rh(:,j+1),desc_a,info,work=aux) call psb_precaply(prec,rh(:,j+1),desc_a,info) Enddo Do j=1, nl If (debug) Write(0,*) 'mod g-s part: ',j, nl,rh(1,0) Do i=1, j-1 taum(i,j) = psb_gedot(rh(:,i),rh(:,j),desc_a,info) taum(i,j) = taum(i,j)/sigma(i) Call psb_geaxpby(-taum(i,j),rh(:,i),done,rh(:,j),desc_a,info) Enddo If (debug) Write(0,*) 'mod g-s part: dot prod ' sigma(j) = psb_gedot(rh(:,j),rh(:,j),desc_a,info) gamma1(j) = psb_gedot(rh(:,0),rh(:,j),desc_a,info) If (debug) Write(0,*) 'mod g-s part: gamma1 ', & &gamma1(j), sigma(j) gamma1(j) = gamma1(j)/sigma(j) Enddo gamma(nl) = gamma1(nl) omega = gamma(nl) Do j=nl-1,1,-1 gamma(j) = gamma1(j) Do i=j+1,nl gamma(j) = gamma(j) - taum(j,i) * gamma(i) Enddo Enddo If (debug) Write(0,*) 'first solve: ', gamma(:) Do j=1,nl-1 gamma2(j) = gamma(j+1) Do i=j+1,nl-1 gamma2(j) = gamma2(j) + taum(j,i) * gamma(i+1) Enddo Enddo If (debug) Write(0,*) 'second solve: ', gamma(:) Call psb_geaxpby(gamma(1),rh(:,0),done,x,desc_a,info) Call psb_geaxpby(-gamma1(nl),rh(:,nl),done,rh(:,0),desc_a,info) Call psb_geaxpby(-gamma(nl),uh(:,nl),done,uh(:,0),desc_a,info) Do j=1, nl-1 Call psb_geaxpby(-gamma(j),uh(:,j),done,uh(:,0),desc_a,info) Call psb_geaxpby(gamma2(j),rh(:,j),done,x,desc_a,info) Call psb_geaxpby(-gamma1(j),rh(:,j),done,rh(:,0),desc_a,info) Enddo if (istop_ == 1) then rni = psb_geamax(rh(:,0),desc_a,info) xni = psb_geamax(x,desc_a,info) rerr = rni/(ani*xni+bni) else if (istop_ == 2) then rni = psb_genrm2(rh(:,0),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))') 'bicgstab(l): ',itx,rerr end If End Do iteration End Do restart If (itrace_ > 0) then if (me == 0) write(*,'(a,i4,3(2x,es10.4))') 'bicgstab(l): ',itx,rerr end If If (Present(err)) err=rerr If (Present(iter)) iter = itx If (rerr>eps) Then Write(0,*) 'bi-cgstabl failed to converge to ',eps,& & ' in ',itx,' iterations ' End If Deallocate(aux) Call psb_gefree(wwrk,desc_a,info) Call psb_gefree(uh,desc_a,info) Call psb_gefree(rh,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_dcgstabl