psblas3/krylov/psb_dcgstab.F90

!!$ 
!!$              Parallel Sparse BLAS  v2.0
!!$    (C) Copyright 2006 Salvatore Filippone    University of Rome Tor Vergata
!!$                       Alfredo Buttari        University of Rome Tor Vergata
!!$ 
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!!$ 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(psb_dspmat_type)      Input: sparse matrix containing A.
!    prec   -  type(psb_dprec_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(psb_desc_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
  integer            :: debug_level, debug_unit
  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)
  debug_unit  = psb_get_debug_unit()
  debug_level = psb_get_debug_level()
  ictxt = psb_cd_get_context(desc_a)
  call psb_info(ictxt, me, np)
  if (debug_level >= psb_debug_ext_)&
       & write(debug_unit,*) me,' ',trim(name),': from psb_info',np

#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
    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_level >= psb_debug_ext_) &
         & write(debug_unit,*) me,' ',trim(name),&
         & ' 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_level >= psb_debug_ext_)&
           & write(debug_unit,*) me,' ',trim(name),&
           & ' Iteration: ',itx
      rho_old = rho    
      rho = psb_gedot(q,r,desc_a,info)

      If (debug_level >= psb_debug_ext_) &
           & write(debug_unit,*) me,' ',trim(name),&
           & ' RHO:',rho
      If (rho==dzero) Then
         If (debug_level >= psb_debug_ext_) &
              & write(debug_unit,*) me,' ',trim(name),&
              & ' Iteration 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_level >= psb_debug_ext_) &
              & write(debug_unit,*) me,' ',trim(name),&
              & ' Iteration breakdown S1', sigma
         Exit iteration
      Endif
      If (debug_level >= psb_debug_ext_) &
           & write(debug_unit,*) me,' ',trim(name),&
           & ' 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_level >= psb_debug_ext_) &
              & write(debug_unit,*) me,' ',trim(name),&
              & ' Iteration breakdown S2', sigma
        Exit iteration
      Endif
      
      tau  = psb_gedot(t,s,desc_a,info)
      omega = tau/sigma
      If (debug_level >= psb_debug_ext_) &
           & write(debug_unit,*) me,' ',trim(name),&
           & ' Omega:',omega      
      If (omega==dzero) Then
         If (debug_level >= psb_debug_ext_) &
              & write(debug_unit,*) me,' ',trim(name),&
              & ' 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(debug_unit,*) '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