!!$ !!$ 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_dcgstab.f90 ! ! Subroutine: psb_dcgstab ! This subroutine implements the BiCG Stabilized method. ! ! ! Arguments: ! ! a - type() Input: sparse matrix containing A. ! prec - 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(). 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_dcgstab(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_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, istop Integer, Optional, Intent(out) :: iter Real(Kind(1.d0)), Optional, Intent(out) :: err !!$ Local data Real(Kind(1.d0)), allocatable, target :: aux(:),wwrk(:,:) Real(Kind(1.d0)), Pointer :: q(:),& & r(:), p(:), v(:), s(:), t(:), z(:), f(:) Real(Kind(1.d0)) :: rerr Integer :: litmax, naux, mglob, it,itrace_,& & np,me, n_row, n_col Logical, Parameter :: debug = .false. Logical, Parameter :: exchange=.True., noexchange=.False., debug1 = .False. Integer, Parameter :: irmax = 8 Integer :: itx, isvch, ictxt, err_act, int_err(5) Integer :: istop_ Real(Kind(1.d0)) :: alpha, beta, rho, rho_old, rni, xni, bni, ani,& & sigma, omega, tau, rn0, bn2 #ifdef MPE_KRYLOV Integer istpb, istpe, ifctb, ifcte, imerr, irank, icomm,immb,imme Integer mpe_log_get_event_number,mpe_Describe_state,mpe_log_event #endif character(len=20) :: name info = 0 name = 'psb_dcgstab' call psb_erractionsave(err_act) If (debug) Write(*,*) 'Entering PSB_DCGSTAB',present(istop) ictxt = psb_cd_get_context(desc_a) call psb_info(ictxt, me, np) if (debug) write(*,*) 'PSB_DCGSTAB: From GRIDINFO',np,me #ifdef MPE_KRYLOV call psb_get_mpicomm(ictxt,icomm) call psb_get_rank(irank,ictxt,me) istpb = mpe_log_get_event_number() istpe = mpe_log_get_event_number() ifctb = mpe_log_get_event_number() ifcte = mpe_log_get_event_number() immb = mpe_log_get_event_number() imme = mpe_log_get_event_number() if (irank==0) then info = mpe_describe_state(istpb,istpe,"Solver","WhiteSmoke") info = mpe_describe_state(ifctb,ifcte,"PREC","SteelBlue") info = mpe_describe_state(immb,imme,"SPMM","DarkOrange") endif #endif 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 ! #ifdef MPE_KRYLOV imerr = MPE_Log_event( istpb, 0, "st CGSTAB" ) #endif if ((istop_ < 1 ).or.(istop_ > 2 ) ) then write(0,*) 'psb_bicgstab: invalid istop',istop_ info=5001 int_err(1)=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=6*n_col allocate(aux(naux),stat=info) if (info == 0) call psb_geall(wwrk,desc_a,info,n=8) 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) R => WWRK(:,2) P => WWRK(:,3) V => WWRK(:,4) F => WWRK(:,5) S => WWRK(:,6) T => WWRK(:,7) Z => WWRK(:,8) 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 >= litmax) Exit restart it = 0 Call psb_geaxpby(done,b,dzero,r,desc_a,info) #ifdef MPE_KRYLOV imerr = MPE_Log_event( immb, 0, "st SPMM" ) #endif Call psb_spmm(-done,a,x,done,r,desc_a,info,work=aux) #ifdef MPE_KRYLOV imerr = MPE_Log_event( imme, 0, "ed SPMM" ) #endif Call psb_geaxpby(done,r,dzero,q,desc_a,info) if (info /= 0) Then info=4011 call psb_errpush(info,name) goto 9999 End If rho = dzero If (debug) Write(*,*) 'On entry to AMAX: B: ',Size(b) ! ! Must always provide norm of R into RNI below for first check on ! residual ! If (istop_ == 1) Then rni = psb_geamax(r,desc_a,info) xni = psb_geamax(x,desc_a,info) Else If (istop_ == 2) Then rni = psb_genrm2(r,desc_a,info) Endif if (info /= 0) Then info=4011 call psb_errpush(info,name) goto 9999 End If If (itx == 0) Then rn0 = rni End If If (rn0 == 0.d0 ) Then If (itrace_ > 0 ) Then If (me == 0) Write(*,*) 'BiCGSTAB: ',itx,rn0 Endif Exit restart End If If (istop_ == 1) Then xni = psb_geamax(x,desc_a,info) rerr = rni/(ani*xni+bni) Else If (istop_ == 2) Then 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 (((itx==0).or.(mod(itx,itrace_)==0)).and.(me == 0)) & & write(*,'(a,i4,3(2x,es10.4))') 'bicgstab: ',itx,rerr Endif iteration: Do it = it + 1 itx = itx + 1 If (debug) Write(*,*) 'Iteration: ',itx rho_old = rho rho = psb_gedot(q,r,desc_a,info) !!$ write(0,'(i2," rho old ",2(f,2x))')me,rho,rho_old If (debug) Write(0,*) 'Bi-CGSTAB RHO:',rho If (rho==dzero) Then If (debug) Write(0,*) 'Bi-CGSTAB Itxation breakdown R',rho Exit iteration Endif If (it==1) Then Call psb_geaxpby(done,r,dzero,p,desc_a,info) Else beta = (rho/rho_old)*(alpha/omega) Call psb_geaxpby(-omega,v,done,p,desc_a,info) Call psb_geaxpby(done,r,beta,p,desc_a,info) End If #ifdef MPE_KRYLOV imerr = MPE_Log_event( ifctb, 0, "st PREC" ) #endif Call psb_precaply(prec,p,f,desc_a,info,work=aux) #ifdef MPE_KRYLOV imerr = MPE_Log_event( ifcte, 0, "ed PREC" ) imerr = MPE_Log_event( immb, 0, "st SPMM" ) #endif Call psb_spmm(done,a,f,dzero,v,desc_a,info,& & work=aux) #ifdef MPE_KRYLOV imerr = MPE_Log_event( imme, 0, "ed SPMM" ) #endif sigma = psb_gedot(q,v,desc_a,info) If (sigma==dzero) Then If (debug) Write(0,*) 'Bi-CGSTAB Iteration breakdown S1', sigma Exit iteration Endif If (debug) Write(0,*) 'Bi-CGSTAB SIGMA:',sigma alpha = rho/sigma Call psb_geaxpby(done,r,dzero,s,desc_a,info) if(info /= 0) then call psb_errpush(4010,name,a_err='psb_geaxpby') goto 9999 end if Call psb_geaxpby(-alpha,v,done,s,desc_a,info) if(info /= 0) then call psb_errpush(4010,name,a_err='psb_geaxpby') goto 9999 end if #ifdef MPE_KRYLOV imerr = MPE_Log_event( ifctb, 0, "st PREC" ) #endif Call psb_precaply(prec,s,z,desc_a,info,work=aux) #ifdef MPE_KRYLOV imerr = MPE_Log_event( ifcte, 0, "ed PREC" ) #endif if(info /= 0) then call psb_errpush(4010,name,a_err='psb_precaply') goto 9999 end if #ifdef MPE_KRYLOV imerr = MPE_Log_event( immb, 0, "st SPMM" ) #endif Call psb_spmm(done,a,z,dzero,t,desc_a,info,& & work=aux) #ifdef MPE_KRYLOV imerr = MPE_Log_event( imme, 0, "ed SPMM" ) #endif if(info /= 0) then call psb_errpush(4010,name,a_err='psb_spmm') goto 9999 end if sigma = psb_gedot(t,t,desc_a,info) If (sigma==dzero) Then If (debug) Write(0,*) 'BI-CGSTAB ITERATION BREAKDOWN S2', sigma Exit iteration Endif tau = psb_gedot(t,s,desc_a,info) omega = tau/sigma If (debug) Write(0,*) 'Bi-CGSTAB OMEGA:',omega If (omega==dzero) Then If (debug) Write(0,*) 'BI-CGSTAB ITERATION BREAKDOWN O',omega Exit iteration Endif Call psb_geaxpby(alpha,f,done,x,desc_a,info) Call psb_geaxpby(omega,z,done,x,desc_a,info) Call psb_geaxpby(done,s,dzero,r,desc_a,info) Call psb_geaxpby(-omega,t,done,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))') & & 'bicgstab: ',itx,rerr Endif End Do iteration End Do restart If (itrace_ > 0) then if (me == 0) write(*,'(a,i4,3(2x,es10.4))') 'bicgstab: ',itx,rerr Endif If (Present(err)) err=rerr If (Present(iter)) iter = itx If (rerr>eps) Then Write(0,*) 'BI-CGSTAB 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) #ifdef MPE_KRYLOV imerr = MPE_Log_event( istpe, 0, "ed CGSTAB" ) #endif 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(ictxt) return end if return End Subroutine psb_dcgstab