amg4psblas/mlprec/mld_zmlprec_aply.f90

!!$
!!$ 
!!$                                MLD2P4
!!$  MultiLevel Domain Decomposition Parallel Preconditioners Package
!!$             based on PSBLAS (Parallel Sparse BLAS v.2.0)
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!!$  (C) Copyright 2007  Alfredo Buttari      University of Rome Tor Vergata
!!$                      Pasqua D'Ambra       ICAR-CNR, Naples
!!$                      Daniela di Serafino  Second University of Naples
!!$                      Salvatore Filippone  University of Rome Tor Vergata
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! File: mld_zmlprec_aply.f90
!
! Subroutine: mld_zmlprec_aply
! Version:    complex
!
!  This routine computes
!  
!                        Y = beta*Y + alpha*op(M^(-1))*X,
!  where 
!  - M is a multilevel domain decomposition (Schwarz) preconditioner associated
!    to a certain matrix A and stored in the array baseprecv,
!  - op(M^(-1)) is M^(-1) or its transpose, according to the value of trans,
!  - X and Y are vectors,
!  - alpha and beta are scalars.
!
!  For each level we have as many submatrices as processes (except for the coarsest
!  level where we might have a replicated index space) and each process takes care
!  of one submatrix.
!
!  The multilevel preconditioner M is regarded as an array of 'base preconditioners',
!  each representing the part of the preconditioner associated to a certain level.
!  For each level ilev, the base preconditioner K(ilev) is stored in baseprecv(ilev)
!  and is associated to a matrix A(ilev), obtained by 'tranferring' the original
!  matrix A (i.e. the matrix to be preconditioned) to the level ilev, through smoothed
!  aggregation.
!
!  The levels are numbered in increasing order starting from the finest one, i.e.
!  level 1 is the finest level and A(1) is the matrix A.
!
!  For a general description of (parallel) multilevel preconditioners see
!    -  B.F. Smith, P.E. Bjorstad & W.D. Gropp,
!       Domain decomposition: parallel multilevel methods for elliptic partial
!       differential equations,
!       Cambridge University Press, 1996.
!    -  K. Stuben,
!       Algebraic Multigrid (AMG): An Introduction with Applications,
!       GMD Report N. 70, 1999.
!
!
! Arguments:
!  alpha       -   complex(kind(0.d0)), input.
!                  The scalar alpha.
!   baseprecv  -   type(mld_zbaseprc_type), dimension(:), input.
!                  The array of base preconditioner data structures containing the
!                  local parts of the preconditioners to be applied at each level.
!      Note that nlev = size(baseprecv) = number of levels.
!      baseprecv(ilev)%av  -  type(psb_zspmat_type), dimension(:), allocatable(:).
!                             The sparse matrices needed to apply the preconditioner 
!                             at level ilev. 
!        baseprecv(ilev)%av(mld_l_pr_)    -  The L factor of the ILU factorization of the 
!                                            local diagonal block of A(ilev).
!        baseprecv(ilev)%av(mld_u_pr_)    -  The U factor of the ILU factorization of the
!                                            local diagonal block of A(ilev), except its
!                                            diagonal entries (stored in baseprecv(ilev)%d).
!        baseprecv(ilev)%av(mld_ap_nd_)   -  The entries of the local part of A(ilev)
!                                            outside the diagonal block, for block-Jacobi
!                                            sweeps.
!        baseprecv(ilev)%av(mld_ac_)      -  The local part of the matrix A(ilev).
!        baseprecv(ilev)%av(mld_sm_pr_)   -  The smoother prolongator.   
!                                            It maps vectors (ilev) ---> (ilev-1).
!        baseprecv(ilev)%av(mld_sm_pr_t_) -  The smoother prolongator transpose.   
!                                            It maps vectors (ilev-1) ---> (ilev).
!      baseprecv(ilev)%d         -  complex(kind(1.d0)), dimension(:), allocatable.
!                                   The diagonal entries of the U factor in the ILU
!                                   factorization of A(ilev).
!      baseprecv(ilev)%desc_data -  type(psb_desc_type).
!                                   The communication descriptor associated to the base
!                                   preconditioner, i.e. to the sparse matrices needed
!                                   to apply the base preconditioner at the current level.
!      baseprecv(ilev)%desc_ac   -  type(psb_desc_type).
!                                   The communication descriptor associated to the sparse
!                                   matrix A(ilev), stored in baseprecv(ilev)%av(mld_ac_).
!      baseprecv(ilev)%iprcparm  -  integer, dimension(:), allocatable.
!                                   The integer parameters defining the base
!                                   preconditioner K(ilev).
!      baseprecv(ilev)%dprcparm  -  complex(kind(1.d0)), dimension(:), allocatable.
!                                   The real parameters defining the base preconditioner
!                                   K(ilev).
!      baseprecv(ilev)%perm      -  integer, dimension(:), allocatable.
!                                   The row and column permutations applied to the local
!                                   part of A(ilev) (defined only if baseprecv(ilev)%
!                                   iprcparm(mld_sub_ren_)>0). 
!      baseprecv(ilev)%invperm   -  integer, dimension(:), allocatable.
!                                   The inverse of the permutation stored in
!                                   baseprecv(ilev)%perm.
!      baseprecv(ilev)%mlia      -  integer, dimension(:), allocatable.
!                                   The aggregation map (ilev-1) --> (ilev).
!                                   In case of non-smoothed aggregation, it is used
!                                   instead of mld_sm_pr_.
!      baseprecv(ilev)%nlaggr    -  integer, dimension(:), allocatable.
!                                   The number of aggregates (rows of A(ilev)) on the
!                                   various processes. 
!      baseprecv(ilev)%base_a    -  type(psb_zspmat_type), pointer.
!                                   Pointer (really a pointer!) to the base matrix of
!                                   the current level, i.e. the local part of A(ilev);
!                                   so we have a unified treatment of residuals. We
!                                   need this to avoid passing explicitly the matrix
!                                   A(ilev) to the routine which applies the
!                                   preconditioner.
!      baseprecv(ilev)%base_desc -  type(psb_desc_type), pointer.
!                                   Pointer to the communication descriptor associated
!                                   to the sparse matrix pointed by base_a.  
!      baseprecv(ilev)%dorig     -  complex(kind(1.d0)), dimension(:), allocatable.
!                                   Diagonal entries of the matrix pointed by base_a.
!                  
!   x          -  complex(kind(0.d0)), dimension(:), input.
!                 The local part of the vector X.
!   beta       -  complex(kind(0.d0)), input.
!                 The scalar beta.
!   y          -  complex(kind(0.d0)), dimension(:), input/output.
!                 The local part of the vector Y.
!   desc_data  -  type(psb_desc_type), input.
!                 The communication descriptor associated to the matrix to be
!                 preconditioned.
!   trans      -  character, optional.
!                 If trans='N','n' then op(M^(-1)) = M^(-1);
!                 if trans='T','t' then op(M^(-1)) = M^(-T) (transpose of M^(-1)).
!   work       -  complex(kind(0.d0)), dimension (:), optional, target.
!                 Workspace. Its size must be at least 4*psb_cd_get_local_cols(desc_data).
!   info       -  integer, output.
!                 Error code.
!
!   Note that when the LU factorization of the matrix A(ilev) is computed instead of
!   the ILU one, by using UMFPACK or SuperLU, the corresponding L and U factors
!   are stored in data structures provided by UMFPACK or SuperLU and pointed by
!   baseprecv(ilev)%iprcparm(mld_umf_ptr) or baseprecv(ilev)%iprcparm(mld_slu_ptr),
!   respectively.
!  
subroutine mld_zmlprec_aply(alpha,baseprecv,x,beta,y,desc_data,trans,work,info)

  use psb_base_mod
  use mld_inner_mod, mld_protect_name => mld_zmlprec_aply

  implicit none

  ! Arguments
  type(psb_desc_type),intent(in)      :: desc_data
  type(mld_zbaseprc_type), intent(in) :: baseprecv(:)
  complex(kind(1.d0)),intent(in)      :: alpha,beta
  complex(kind(1.d0)),intent(in)      :: x(:)
  complex(kind(1.d0)),intent(inout)   :: y(:)
  character, intent(in)               :: trans
  complex(kind(1.d0)),target          :: work(:)
  integer, intent(out)                :: info

  ! Local variables
  integer           :: ictxt, np, me, err_act
  integer           :: debug_level, debug_unit
  character(len=20) :: name
  character         :: trans_

  name = 'mld_zmlprec_aply'
  info = 0
  call psb_erractionsave(err_act)
  debug_unit  = psb_get_debug_unit()
  debug_level = psb_get_debug_level()

  ictxt = psb_cd_get_context(desc_data)
  call psb_info(ictxt, me, np)

  if (debug_level >= psb_debug_inner_) &
       & write(debug_unit,*) me,' ',trim(name),&
       & ' Entry  ', size(baseprecv)

  trans_ = toupper(trans)

  select case(baseprecv(2)%iprcparm(mld_ml_type_)) 

  case(mld_no_ml_)
    !
    ! No preconditioning, should not really get here
    ! 
    call psb_errpush(4001,name,a_err='mld_no_ml_ in mlprc_aply?')
    goto 9999      


  case(mld_add_ml_)

    call add_ml_aply(alpha,baseprecv,x,beta,y,desc_data,trans_,work,info)

  case(mld_mult_ml_)

    ! 
    !  Multiplicative multilevel (multiplicative among the levels, additive inside
    !  each level)
    !
    !  Pre/post-smoothing versions.
    !  Note that the transpose switches pre <-> post.
    !

    select case(baseprecv(2)%iprcparm(mld_smooth_pos_))

    case(mld_post_smooth_)
      
      select case (trans_) 
      case('N')
        call mlt_post_ml_aply(alpha,baseprecv,x,beta,y,desc_data,trans_,work,info)
      case('T','C')
        call mlt_pre_ml_aply(alpha,baseprecv,x,beta,y,desc_data,trans_,work,info)
      case default
        info = 4001
        call psb_errpush(info,name,a_err='invalid trans')
        goto 9999      
      end select

      
    case(mld_pre_smooth_)

      select case (trans_) 
      case('N')
        call mlt_pre_ml_aply(alpha,baseprecv,x,beta,y,desc_data,trans_,work,info)
      case('T','C')
        call mlt_post_ml_aply(alpha,baseprecv,x,beta,y,desc_data,trans_,work,info)
      case default
        info = 4001
        call psb_errpush(info,name,a_err='invalid trans')
        goto 9999      
      end select

    case(mld_twoside_smooth_)

      call mlt_twoside_ml_aply(alpha,baseprecv,x,beta,y,desc_data,trans_,work,info)

    case default
      info = 4013
      call psb_errpush(info,name,a_err='invalid smooth_pos',&
           &  i_Err=(/baseprecv(2)%iprcparm(mld_smooth_pos_),0,0,0,0/))
      goto 9999      

    end select

  case default
    info = 4013
    call psb_errpush(info,name,a_err='invalid mltype',&
         &  i_Err=(/baseprecv(2)%iprcparm(mld_ml_type_),0,0,0,0/))
    goto 9999      

  end select

  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: add_ml_aply
  ! Version:    complex
  ! Note: internal subroutine of mld_dmlprec_aply.
  ! This routine computes
  !  
  !                        Y = beta*Y + alpha*op(M^(-1))*X,
  !  where 
  !  - M is a multilevel domain decomposition (Schwarz) preconditioner associated
  !    to a certain matrix A and stored in the array baseprecv,
  !  - op(M^(-1)) is M^(-1) or its (conjugate) transpose, according to
  !    the value of trans,
  !  - X and Y are vectors,
  !  - alpha and beta are scalars.
  !
  !  For each level we have as many submatrices as processes (except for the coarsest
  !  level where we might have a replicated index space) and each process takes care
  !  of one submatrix. 
  !
  !  The multilevel preconditioner M is regarded as an array of 'base preconditioners',
  !  each representing the part of the preconditioner associated to a certain level.
  !  For each level ilev, the base preconditioner K(ilev) is stored in baseprecv(ilev)
  !  and is associated to a matrix A(ilev), obtained by 'tranferring' the original
  !  matrix A (i.e. the matrix to be preconditioned) to the level ilev, through smoothed
  !  aggregation.
  !
  !  The levels are numbered in increasing order starting from the finest one, i.e.
  !  level 1 is the finest level and A(1) is the matrix A. 
  !  This routine applies the multilevel preconditioner in an additive
  !  way (additive through the levels and additive on the same level).
  !  For details on the additive multilevel Schwarz preconditioner see
  !  the Algorithm 3.1.1 in the book:
  !    -  B.F. Smith, P.E. Bjorstad & W.D. Gropp,
  !       Domain decomposition: parallel multilevel methods for elliptic partial
  !       differential equations, Cambridge University Press, 1996.
  !
  !  For a detailed description of the arguments, see mld_dmlprec_aply.
  !
  subroutine add_ml_aply(alpha,baseprecv,x,beta,y,desc_data,trans,work,info)
    implicit none 
    ! Arguments
    type(psb_desc_type),intent(in)      :: desc_data
    type(mld_zbaseprc_type), intent(in) :: baseprecv(:)
    complex(kind(1.d0)),intent(in)      :: alpha,beta
    complex(kind(1.d0)),intent(in)      :: x(:)
    complex(kind(1.d0)),intent(inout)   :: y(:)
    character, intent(in)               :: trans
    complex(kind(1.d0)),target          :: work(:)
    integer, intent(out)                :: info

    ! Local variables
    integer            :: n_row,n_col
    integer            :: ictxt,np,me,i, nr2l,nc2l,err_act
    integer            :: debug_level, debug_unit
    integer            :: ismth, nlev, ilev, icm
    character(len=20)  :: name

    type psb_mlprec_wrk_type
      complex(kind(1.d0)), allocatable  :: tx(:),ty(:),x2l(:),y2l(:)
    end type psb_mlprec_wrk_type
    type(psb_mlprec_wrk_type), allocatable :: mlprec_wrk(:)

    name = 'add_ml_aply'
    info = 0
    call psb_erractionsave(err_act)
    debug_unit  = psb_get_debug_unit()
    debug_level = psb_get_debug_level()

    ictxt = psb_cd_get_context(desc_data)
    call psb_info(ictxt, me, np)

    if (debug_level >= psb_debug_inner_) &
         & write(debug_unit,*) me,' ',trim(name),&
         & ' Entry  ', size(baseprecv)

    nlev = size(baseprecv)
    allocate(mlprec_wrk(nlev),stat=info) 
    if (info /= 0) then 
      call psb_errpush(4010,name,a_err='Allocate')
      goto 9999      
    end if
    !
    ! STEP 1
    !
    ! Apply the base preconditioner at the finest level
    !
    allocate(mlprec_wrk(1)%x2l(size(x)),mlprec_wrk(1)%y2l(size(y)), stat=info)
    if (info /= 0) then 
      info=4025
      call psb_errpush(info,name,i_err=(/size(x)+size(y),0,0,0,0/),&
           & a_err='real(kind(1.d0))')
      goto 9999      
    end if

    mlprec_wrk(1)%x2l(:) = x(:) 
    mlprec_wrk(1)%y2l(:) = zzero 


    call mld_baseprec_aply(alpha,baseprecv(1),x,beta,y,&
         & baseprecv(1)%base_desc,trans,work,info)
    if (info /=0) then 
      call psb_errpush(4010,name,a_err='baseprec_aply')
      goto 9999
    end if
    !
    ! STEP 2
    !
    !
    !      For each level except the finest one ...
    !
    do ilev = 2, nlev
      n_row = psb_cd_get_local_rows(baseprecv(ilev-1)%base_desc)
      n_col = psb_cd_get_local_cols(baseprecv(ilev-1)%desc_data)
      nc2l  = psb_cd_get_local_cols(baseprecv(ilev)%desc_data)
      nr2l  = psb_cd_get_local_rows(baseprecv(ilev)%desc_data)
      allocate(mlprec_wrk(ilev)%x2l(nc2l),mlprec_wrk(ilev)%y2l(nc2l),&
           & mlprec_wrk(ilev)%tx(max(n_row,n_col)),&
           & mlprec_wrk(ilev)%ty(max(n_row,n_col)), stat=info)
      if (info /= 0) then 
        info=4025
        call psb_errpush(info,name,i_err=(/2*(nc2l+max(n_row,n_col)),0,0,0,0/),&
             & a_err='real(kind(1.d0))')
        goto 9999      
      end if

      mlprec_wrk(ilev)%x2l(:) = zzero
      mlprec_wrk(ilev)%y2l(:) = zzero
      mlprec_wrk(ilev)%tx(1:n_row) = mlprec_wrk(ilev-1)%x2l(1:n_row) 
      mlprec_wrk(ilev)%tx(n_row+1:max(n_row,n_col)) = zzero
      mlprec_wrk(ilev)%ty(:) = zzero

      ismth = baseprecv(ilev)%iprcparm(mld_aggr_kind_)
      icm   = baseprecv(ilev)%iprcparm(mld_coarse_mat_)
      if (ismth  /= mld_no_smooth_) then 
        !
        ! Apply the smoothed prolongator transpose
        !
        call psb_halo(mlprec_wrk(ilev-1)%x2l,baseprecv(ilev-1)%base_desc,&
             &  info,work=work) 
        if (info == 0)  call psb_csmm(zone,baseprecv(ilev)%av(mld_sm_pr_t_),&
             & mlprec_wrk(ilev-1)%x2l,zzero,mlprec_wrk(ilev)%x2l,info)
      else
        !
        ! Apply the raw aggregation map transpose (take a shortcut)
        !
        do i=1,n_row
          mlprec_wrk(ilev)%x2l(baseprecv(ilev)%mlia(i)) = &
               &  mlprec_wrk(ilev)%x2l(baseprecv(ilev)%mlia(i)) + &
               &  mlprec_wrk(ilev-1)%x2l(i)
        end do

      end if
      if (info /=0) then
        call psb_errpush(4001,name,a_err='Error during restriction')
        goto 9999
      end if


      if (icm == mld_repl_mat_) then 
        call psb_sum(ictxt,mlprec_wrk(ilev)%x2l(1:nr2l))
      else if (icm /= mld_distr_mat_) then 
        info = 4013
        call psb_errpush(info,name,a_err='invalid mld_coarse_mat_',&
             &  i_Err=(/icm,0,0,0,0/))
        goto 9999
      endif

      !
      ! Apply the base preconditioner
      !
      call mld_baseprec_aply(zone,baseprecv(ilev),&
           & mlprec_wrk(ilev)%x2l,zzero,mlprec_wrk(ilev)%y2l,&
           & baseprecv(ilev)%desc_data,trans,work,info)

    enddo

    !
    ! STEP 3
    !
    !
    !      For each level except the finest one ...
    !
    do ilev =nlev,2,-1

      n_row = psb_cd_get_local_rows(baseprecv(ilev-1)%base_desc)
      n_col = psb_cd_get_local_cols(baseprecv(ilev-1)%desc_data)
      nc2l  = psb_cd_get_local_cols(baseprecv(ilev)%desc_data)
      nr2l  = psb_cd_get_local_rows(baseprecv(ilev)%desc_data)
      ismth = baseprecv(ilev)%iprcparm(mld_aggr_kind_)
      icm   = baseprecv(ilev)%iprcparm(mld_coarse_mat_)

      if (ismth  /= mld_no_smooth_) then 
        !
        ! Apply the smoothed prolongator
        !
        call psb_csmm(zone,baseprecv(ilev)%av(mld_sm_pr_),mlprec_wrk(ilev)%y2l,&
             & zone,mlprec_wrk(ilev-1)%y2l,info)
      else
        !
        ! Apply the raw aggregation map (take a shortcut)
        !
        do i=1, n_row
          mlprec_wrk(ilev-1)%y2l(i) = mlprec_wrk(ilev-1)%y2l(i) + &
               &   mlprec_wrk(ilev)%y2l(baseprecv(ilev)%mlia(i))
        enddo

      end if
      if (info /=0) then
        call psb_errpush(4001,name,a_err='Error during prolongation')
        goto 9999
      end if
    end do

    !
    ! STEP 4
    !
    ! Compute the output vector Y
    !
    call psb_geaxpby(alpha,mlprec_wrk(1)%y2l,zone,y,baseprecv(1)%base_desc,info)
    if (info /= 0) then
      call psb_errpush(4001,name,a_err='Error on final update')
      goto 9999
    end if

    deallocate(mlprec_wrk,stat=info)
    if (info /= 0) then 
      call psb_errpush(4000,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 add_ml_aply
  !
  ! Subroutine: mlt_pre_ml_aply
  ! Version:    complex
  ! Note: internal subroutine of mld_dmlprec_aply.
  ! This routine computes
  !  
  !                        Y = beta*Y + alpha*op(M^(-1))*X,
  !  where 
  !  - M is a multilevel domain decomposition (Schwarz) preconditioner associated
  !    to a certain matrix A and stored in the array baseprecv,
  !  - op(M^(-1)) is M^(-1) or its (conjugate) transpose, according to
  !    the value of trans,
  !  - X and Y are vectors,
  !  - alpha and beta are scalars.
  !
  !  For each level we have as many submatrices as processes (except for the coarsest
  !  level where we might have a replicated index space) and each process takes care
  !  of one submatrix. 
  !
  !  The multilevel preconditioner M is regarded as an array of 'base preconditioners',
  !  each representing the part of the preconditioner associated to a certain level.
  !  For each level ilev, the base preconditioner K(ilev) is stored in baseprecv(ilev)
  !  and is associated to a matrix A(ilev), obtained by 'tranferring' the original
  !  matrix A (i.e. the matrix to be preconditioned) to the level ilev, through smoothed
  !  aggregation.
  !
  !  The levels are numbered in increasing order starting from the finest one, i.e.
  !  level 1 is the finest level and A(1) is the matrix A. 
  !
  !  This routine applies the multilevel preconditioner in a hybrid way
  !  (multiplicative through the levels and additive on the same level)
  !  and pre-smoothing.
  !  For details on pre-smoothed hybrid multiplicative multilevel Schwarz preconditioner,
  !  see the Algorithm 3.2.1 in the book:
  !    -  B.F. Smith, P.E. Bjorstad & W.D. Gropp,
  !       Domain decomposition: parallel multilevel methods for elliptic partial
  !       differential equations, Cambridge University Press, 1996.
  !
  !  For a detailed description of the arguments, see mld_dmlprec_aply.
  subroutine mlt_pre_ml_aply(alpha,baseprecv,x,beta,y,desc_data,trans,work,info)
    !
    implicit none 
    ! Arguments
    type(psb_desc_type),intent(in)      :: desc_data
    type(mld_zbaseprc_type), intent(in) :: baseprecv(:)
    complex(kind(1.d0)),intent(in)      :: alpha,beta
    complex(kind(1.d0)),intent(in)      :: x(:)
    complex(kind(1.d0)),intent(inout)   :: y(:)
    character, intent(in)               :: trans
    complex(kind(1.d0)),target          :: work(:)
    integer, intent(out)                :: info

    ! Local variables
    integer            :: n_row,n_col
    integer            :: ictxt,np,me,i, nr2l,nc2l,err_act
    integer            :: debug_level, debug_unit
    integer            :: ismth, nlev, ilev, icm
    character(len=20)  :: name

    type psb_mlprec_wrk_type
      complex(kind(1.d0)), allocatable  :: tx(:),ty(:),x2l(:),y2l(:)
    end type psb_mlprec_wrk_type
    type(psb_mlprec_wrk_type), allocatable :: mlprec_wrk(:)

    name = 'mlt_pre_ml_aply'
    info = 0
    call psb_erractionsave(err_act)
    debug_unit  = psb_get_debug_unit()
    debug_level = psb_get_debug_level()

    ictxt = psb_cd_get_context(desc_data)
    call psb_info(ictxt, me, np)

    if (debug_level >= psb_debug_inner_) &
         & write(debug_unit,*) me,' ',trim(name),&
         & ' Entry  ', size(baseprecv)

    nlev = size(baseprecv)
    allocate(mlprec_wrk(nlev),stat=info) 
    if (info /= 0) then 
      call psb_errpush(4010,name,a_err='Allocate')
      goto 9999      
    end if


    !
    ! STEP 1
    !
    ! Copy the input vector X
    !
    n_col = psb_cd_get_local_cols(desc_data)
    nc2l  = psb_cd_get_local_cols(baseprecv(1)%desc_data)

    allocate(mlprec_wrk(1)%x2l(nc2l),mlprec_wrk(1)%y2l(nc2l), &
         & mlprec_wrk(1)%tx(nc2l), stat=info)
    if (info /= 0) then 
      info=4025
      call psb_errpush(info,name,i_err=(/4*nc2l,0,0,0,0/),&
           & a_err='real(kind(1.d0))')
      goto 9999
    end if

    mlprec_wrk(1)%y2l(:) = zzero
    mlprec_wrk(1)%x2l(:) = x

    !
    ! STEP 2
    !
    ! Apply the base preconditioner at the finest level
    !
    call mld_baseprec_aply(zone,baseprecv(1),mlprec_wrk(1)%x2l,&
         &  zzero,mlprec_wrk(1)%y2l,baseprecv(1)%base_desc,&
         &  trans,work,info)
    if (info /=0) then
      call psb_errpush(4010,name,a_err=' baseprec_aply')
      goto 9999
    end if

    !
    ! STEP 3
    !
    ! Compute the residual at the finest level
    !
    mlprec_wrk(1)%tx = mlprec_wrk(1)%x2l

    call psb_spmm(-zone,baseprecv(1)%base_a,mlprec_wrk(1)%y2l,&
         & zone,mlprec_wrk(1)%tx,baseprecv(1)%base_desc,info,&
         & work=work,trans=trans)
    if (info /=0) then
      call psb_errpush(4001,name,a_err=' fine level residual')
      goto 9999
    end if

    !
    ! STEP 4
    !
    ! For each level but the finest one ...
    !
    do ilev = 2, nlev

      n_row = psb_cd_get_local_rows(baseprecv(ilev-1)%base_desc)
      n_col = psb_cd_get_local_cols(baseprecv(ilev-1)%desc_data)
      nc2l  = psb_cd_get_local_cols(baseprecv(ilev)%desc_data)
      nr2l  = psb_cd_get_local_rows(baseprecv(ilev)%desc_data)
      ismth = baseprecv(ilev)%iprcparm(mld_aggr_kind_)
      icm   = baseprecv(ilev)%iprcparm(mld_coarse_mat_)

      allocate(mlprec_wrk(ilev)%tx(nc2l),mlprec_wrk(ilev)%y2l(nc2l),&
           &   mlprec_wrk(ilev)%x2l(nc2l), stat=info)
      if (info /= 0) then 
        info=4025
        call psb_errpush(info,name,i_err=(/4*nc2l,0,0,0,0/),&
             & a_err='real(kind(1.d0))')
        goto 9999      
      end if

      mlprec_wrk(ilev)%x2l(:) = zzero
      mlprec_wrk(ilev)%y2l(:) = zzero
      mlprec_wrk(ilev)%tx(:)  = zzero

      if (ismth  /= mld_no_smooth_) then 
        !
        ! Apply the smoothed prolongator transpose
        !
        call psb_halo(mlprec_wrk(ilev-1)%tx,baseprecv(ilev-1)%base_desc,&
             & info,work=work) 
        if (info == 0) call psb_csmm(zone,baseprecv(ilev)%av(mld_sm_pr_t_),&
             & mlprec_wrk(ilev-1)%tx,zzero,mlprec_wrk(ilev)%x2l,info)
      else
        !
        ! Apply the raw aggregation map transpose (take a shortcut)
        !
        mlprec_wrk(ilev)%x2l = zzero
        do i=1,n_row
          mlprec_wrk(ilev)%x2l(baseprecv(ilev)%mlia(i)) = &
               & mlprec_wrk(ilev)%x2l(baseprecv(ilev)%mlia(i)) + &
               &  mlprec_wrk(ilev-1)%tx(i)
        end do
      end if
      if (info /=0) then
        call psb_errpush(4001,name,a_err='Error during restriction')
        goto 9999
      end if

      if (icm ==mld_repl_mat_) then 
        call psb_sum(ictxt,mlprec_wrk(ilev)%x2l(1:nr2l))
      else if (icm  /= mld_distr_mat_) then 
        info = 4013
        call psb_errpush(info,name,a_err='invalid mld_coarse_mat_',&
             &  i_Err=(/icm,0,0,0,0/))
        goto 9999
      endif

      !
      ! Apply the base preconditioner
      !
      call mld_baseprec_aply(zone,baseprecv(ilev),mlprec_wrk(ilev)%x2l,&
           & zzero,mlprec_wrk(ilev)%y2l,baseprecv(ilev)%desc_data,trans,work,info)

      !
      ! Compute the residual (at all levels but the coarsest one)
      !
      if (ilev < nlev) then
        mlprec_wrk(ilev)%tx = mlprec_wrk(ilev)%x2l
        if (info == 0) call psb_spmm(-zone,baseprecv(ilev)%base_a,&
             & mlprec_wrk(ilev)%y2l,zone,mlprec_wrk(ilev)%tx,&
             & baseprecv(ilev)%base_desc,info,work=work,trans=trans)
      endif
      if (info /=0) then
        call psb_errpush(4001,name,a_err='Error on up sweep residual')
        goto 9999
      end if
    enddo

    !
    ! STEP 5
    !
    ! For each level but the coarsest one ...
    !
    do ilev = nlev-1, 1, -1

      ismth = baseprecv(ilev+1)%iprcparm(mld_aggr_kind_)
      n_row = psb_cd_get_local_rows(baseprecv(ilev)%base_desc)

      if (ismth  /= mld_no_smooth_) then 
        !
        ! Apply the smoothed prolongator
        !
        if (ismth == mld_smooth_prol_) &
             & call psb_halo(mlprec_wrk(ilev+1)%y2l,&
             & baseprecv(ilev+1)%desc_data,info,work=work) 
        if (info == 0) call psb_csmm(zone,baseprecv(ilev+1)%av(mld_sm_pr_),&
             & mlprec_wrk(ilev+1)%y2l,zone,mlprec_wrk(ilev)%y2l,info)
      else
        !
        ! Apply the raw aggregation map (take a shortcut)
        !
        do i=1, n_row
          mlprec_wrk(ilev)%y2l(i) = mlprec_wrk(ilev)%y2l(i) + &
               & mlprec_wrk(ilev+1)%y2l(baseprecv(ilev+1)%mlia(i))
        enddo
      end if
      if (info /=0) then
        call psb_errpush(4001,name,a_err='Error during prolongation')
        goto 9999
      end if
    enddo

    !
    ! STEP 6
    !
    ! Compute the output vector Y
    !
    call psb_geaxpby(alpha,mlprec_wrk(1)%y2l,beta,y,&
         &  baseprecv(1)%base_desc,info)
    if (info /=0) then
      call psb_errpush(4001,name,a_err='Error on final update')
      goto 9999
    end if

    deallocate(mlprec_wrk,stat=info)
    if (info /= 0) then 
      call psb_errpush(4000,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 mlt_pre_ml_aply
  !
  ! Subroutine: mlt_post_ml_aply
  ! Version:    complex
  ! Note: internal subroutine of mld_dmlprec_aply.
  ! This routine computes
  !  
  !                        Y = beta*Y + alpha*op(M^(-1))*X,
  !  where 
  !  - M is a multilevel domain decomposition (Schwarz) preconditioner associated
  !    to a certain matrix A and stored in the array baseprecv,
  !  - op(M^(-1)) is M^(-1) or its (conjugate) transpose, according to
  !    the value of trans,
  !  - X and Y are vectors,
  !  - alpha and beta are scalars.
  !
  !  For each level we have as many submatrices as processes (except for the coarsest
  !  level where we might have a replicated index space) and each process takes care
  !  of one submatrix. 
  !
  !  The multilevel preconditioner M is regarded as an array of 'base preconditioners',
  !  each representing the part of the preconditioner associated to a certain level.
  !  For each level ilev, the base preconditioner K(ilev) is stored in baseprecv(ilev)
  !  and is associated to a matrix A(ilev), obtained by 'tranferring' the original
  !  matrix A (i.e. the matrix to be preconditioned) to the level ilev, through smoothed
  !  aggregation.
  !
  !  The levels are numbered in increasing order starting from the finest one, i.e.
  !  level 1 is the finest level and A(1) is the matrix A. 
  !
  !  This routine applies the multilevel preconditioner in a hybrid way
  !  (multiplicative through the levels and additive on the same level)
  !  and post-smoothing.
  !  For details on hybrid multiplicative multilevel Schwarz preconditioners, see
  !    -  B.F. Smith, P.E. Bjorstad & W.D. Gropp,
  !       Domain decomposition: parallel multilevel methods for elliptic partial
  !       differential equations, Cambridge University Press, 1996.
  !
  !  For a detailed description of the arguments, see mld_dmlprec_aply.
  subroutine mlt_post_ml_aply(alpha,baseprecv,x,beta,y,desc_data,trans,work,info)
    !
    implicit none 
    ! Arguments
    type(psb_desc_type),intent(in)      :: desc_data
    type(mld_zbaseprc_type), intent(in) :: baseprecv(:)
    complex(kind(1.d0)),intent(in)      :: alpha,beta
    complex(kind(1.d0)),intent(in)      :: x(:)
    complex(kind(1.d0)),intent(inout)   :: y(:)
    character, intent(in)               :: trans
    complex(kind(1.d0)),target          :: work(:)
    integer, intent(out)                :: info

    ! Local variables
    integer            :: n_row,n_col
    integer            :: ictxt,np,me,i, nr2l,nc2l,err_act
    integer            :: debug_level, debug_unit
    integer            :: ismth, nlev, ilev, icm
    character(len=20)  :: name

    type psb_mlprec_wrk_type
      complex(kind(1.d0)), allocatable  :: tx(:),ty(:),x2l(:),y2l(:)
    end type psb_mlprec_wrk_type
    type(psb_mlprec_wrk_type), allocatable :: mlprec_wrk(:)

    name = 'mlt_post_ml_aply'
    info = 0
    call psb_erractionsave(err_act)
    debug_unit  = psb_get_debug_unit()
    debug_level = psb_get_debug_level()

    ictxt = psb_cd_get_context(desc_data)
    call psb_info(ictxt, me, np)

    if (debug_level >= psb_debug_inner_) &
         & write(debug_unit,*) me,' ',trim(name),&
         & ' Entry  ', size(baseprecv)

    nlev = size(baseprecv)
    allocate(mlprec_wrk(nlev),stat=info) 
    if (info /= 0) then 
      call psb_errpush(4010,name,a_err='Allocate')
      goto 9999      
    end if
    !
    ! STEP 1
    !
    ! Copy the input vector X
    !
    if (debug_level >= psb_debug_inner_) &
         & write(debug_unit,*) me,' ',trim(name),&
         & ' desc_data status',allocated(desc_data%matrix_data)    

    n_col = psb_cd_get_local_cols(desc_data)
    nc2l  = psb_cd_get_local_cols(baseprecv(1)%desc_data)

    allocate(mlprec_wrk(1)%x2l(nc2l),mlprec_wrk(1)%y2l(nc2l), &
         & mlprec_wrk(1)%tx(nc2l), stat=info)
    mlprec_wrk(1)%x2l(:) = zzero
    mlprec_wrk(1)%y2l(:) = zzero
    mlprec_wrk(1)%tx(:)  = zzero

    call psb_geaxpby(zone,x,zzero,mlprec_wrk(1)%tx,&
         & baseprecv(1)%base_desc,info)
    call psb_geaxpby(zone,x,zzero,mlprec_wrk(1)%x2l,&
         & baseprecv(1)%base_desc,info)

    !
    ! STEP 2
    !
    ! For each level but the finest one ...
    !
    do ilev=2, nlev

      n_row = psb_cd_get_local_rows(baseprecv(ilev-1)%base_desc)
      n_col = psb_cd_get_local_cols(baseprecv(ilev-1)%desc_data)
      nc2l  = psb_cd_get_local_cols(baseprecv(ilev)%desc_data)
      nr2l  = psb_cd_get_local_rows(baseprecv(ilev)%desc_data)
      ismth = baseprecv(ilev)%iprcparm(mld_aggr_kind_)
      icm   = baseprecv(ilev)%iprcparm(mld_coarse_mat_)

      if (debug_level >= psb_debug_inner_) &
           & write(debug_unit,*) me,' ',trim(name), &
           & ' starting up sweep ',&
           & ilev,allocated(baseprecv(ilev)%iprcparm),n_row,n_col,&
           & nc2l, nr2l,ismth

      allocate(mlprec_wrk(ilev)%tx(nc2l),mlprec_wrk(ilev)%y2l(nc2l),&
           &   mlprec_wrk(ilev)%x2l(nc2l), stat=info)

      if (info /= 0) then 
        info=4025
        call psb_errpush(info,name,i_err=(/4*nc2l,0,0,0,0/),&
             & a_err='real(kind(1.d0))')
        goto 9999      
      end if

      mlprec_wrk(ilev)%x2l(:) = zzero
      mlprec_wrk(ilev)%y2l(:) = zzero
      mlprec_wrk(ilev)%tx(:)  = zzero
      if (ismth  /= mld_no_smooth_) then 
        !
        ! Apply the smoothed prolongator transpose
        !
        if (debug_level >= psb_debug_inner_) &
             & write(debug_unit,*) me,' ',trim(name), ' up sweep ', ilev

        call psb_halo(mlprec_wrk(ilev-1)%x2l,&
             &  baseprecv(ilev-1)%base_desc,info,work=work) 
        if (info == 0) call psb_csmm(zone,baseprecv(ilev)%av(mld_sm_pr_t_),&
             & mlprec_wrk(ilev-1)%x2l,zzero,mlprec_wrk(ilev)%x2l,info)
      else
        !
        ! Apply the raw aggregation map transpose (take a shortcut)
        !
        do i=1,n_row
          mlprec_wrk(ilev)%x2l(baseprecv(ilev)%mlia(i)) = &
               & mlprec_wrk(ilev)%x2l(baseprecv(ilev)%mlia(i)) + &
               & mlprec_wrk(ilev-1)%x2l(i)
        end do

      end if
      if (info /=0) then
        call psb_errpush(4001,name,a_err='Error during restriction')
        goto 9999
      end if

      if (icm == mld_repl_mat_) Then 
        call psb_sum(ictxt,mlprec_wrk(ilev)%x2l(1:nr2l))
      else if (icm  /= mld_distr_mat_) Then 
        info = 4013
        call psb_errpush(info,name,a_err='invalid mld_coarse_mat_',&
             &  i_Err=(/icm,0,0,0,0/))
        goto 9999
      endif

      !
      ! update x2l
      !
      call psb_geaxpby(zone,mlprec_wrk(ilev)%x2l,zzero,mlprec_wrk(ilev)%tx,&
           & baseprecv(ilev)%base_desc,info)
      if (info /= 0) then
        call psb_errpush(4001,name,a_err='Error in update')
        goto 9999
      end if

      if (debug_level >= psb_debug_inner_) &
           & write(debug_unit,*) me,' ',trim(name),&
           & ' done up sweep ', ilev

    enddo

    !
    ! STEP 3
    !
    ! Apply the base preconditioner at the coarsest level
    !
    call mld_baseprec_aply(zone,baseprecv(nlev),mlprec_wrk(nlev)%x2l, &
         & zzero, mlprec_wrk(nlev)%y2l,baseprecv(nlev)%desc_data,trans,work,info)
    if (info /=0) then
      call psb_errpush(4010,name,a_err='baseprec_aply')
      goto 9999
    end if

    if (debug_level >= psb_debug_inner_) write(debug_unit,*) &
         & me,' ',trim(name), ' done baseprec_aply ', nlev

    !
    ! STEP 4
    !
    ! For each level but the coarsest one ...
    !
    do ilev=nlev-1, 1, -1

      if (debug_level >= psb_debug_inner_) &
           & write(debug_unit,*) me,' ',trim(name),&
           & ' starting down sweep',ilev

      ismth = baseprecv(ilev+1)%iprcparm(mld_aggr_kind_)
      n_row = psb_cd_get_local_rows(baseprecv(ilev)%base_desc)

      if (ismth  /= mld_no_smooth_) then
        !
        ! Apply the smoothed prolongator
        !  
        if (ismth == mld_smooth_prol_) &
             & call psb_halo(mlprec_wrk(ilev+1)%y2l,baseprecv(ilev+1)%desc_data,&
             &  info,work=work) 
        if (info == 0) call psb_csmm(zone,baseprecv(ilev+1)%av(mld_sm_pr_),&
             & mlprec_wrk(ilev+1)%y2l, zzero,mlprec_wrk(ilev)%y2l,info)
      else
        !
        ! Apply the raw aggregation map (take a shortcut)
        !
        mlprec_wrk(ilev)%y2l(:) = zzero
        do i=1, n_row
          mlprec_wrk(ilev)%y2l(i) = mlprec_wrk(ilev)%y2l(i) + &
               & mlprec_wrk(ilev+1)%y2l(baseprecv(ilev+1)%mlia(i))
        enddo
      end if
      if (info /=0) then
        call psb_errpush(4001,name,a_err='Error during prolongation')
        goto 9999
      end if

      !
      ! Compute the residual
      !
      call psb_spmm(-zone,baseprecv(ilev)%base_a,mlprec_wrk(ilev)%y2l,&
           & zone,mlprec_wrk(ilev)%tx,baseprecv(ilev)%base_desc,info,&
           & work=work,trans=trans)

      !
      ! Apply the base preconditioner
      !
      if (info == 0) call mld_baseprec_aply(zone,baseprecv(ilev),mlprec_wrk(ilev)%tx,&
           & zone,mlprec_wrk(ilev)%y2l,baseprecv(ilev)%base_desc,trans,work,info)
      if (info /=0) then
        call psb_errpush(4001,name,a_err=' spmm/baseprec_aply')
        goto 9999
      end if

      if (debug_level >= psb_debug_inner_) &
           & write(debug_unit,*) me,' ',trim(name),&
           & ' done down sweep',ilev
    enddo

    !
    ! STEP 5
    !
    ! Compute the output vector Y
    !
    call psb_geaxpby(alpha,mlprec_wrk(1)%y2l,beta,y,baseprecv(1)%base_desc,info)

    if (info /=0) then
      call psb_errpush(4001,name,a_err=' Final update')
      goto 9999
    end if



    deallocate(mlprec_wrk,stat=info)
    if (info /= 0) then 
      call psb_errpush(4000,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 mlt_post_ml_aply
  !
  ! Subroutine: mlt_twoside_ml_aply
  ! Version:    complex
  ! Note: internal subroutine of mld_dmlprec_aply.
  ! This routine computes
  !  
  !                        Y = beta*Y + alpha*op(M^(-1))*X,
  !  where 
  !  - M is a multilevel domain decomposition (Schwarz) preconditioner associated
  !    to a certain matrix A and stored in the array baseprecv,
  !  - op(M^(-1)) is M^(-1) or its (conjugate) transpose, according to
  !    the value of trans,
  !  - X and Y are vectors,               
  !  - alpha and beta are scalars.
  !
  !  For each level we have as many submatrices as processes (except for the coarsest
  !  level where we might have a replicated index space) and each process takes care
  !  of one submatrix.   
  !
  !  The multilevel preconditioner M is regarded as an array of 'base preconditioners',
  !  each representing the part of the preconditioner associated to a certain level.
  !  For each level ilev, the base preconditioner K(ilev) is stored in baseprecv(ilev)
  !  and is associated to a matrix A(ilev), obtained by 'tranferring' the original
  !  matrix A (i.e. the matrix to be preconditioned) to the level ilev, through smoothed
  !  aggregation.
  !
  !  The levels are numbered in increasing order starting from the finest one, i.e.
  !  level 1 is the finest level and A(1) is the matrix A. 
  !
  !  This routine applies the multilevel preconditioner in a symmetrized hybrid way
  !  (multiplicative through the levels and additive on the same level, with pre and 
  !  post-smoothing).
  !  For details on the symmetrized hybrid multiplicative multilevel Schwarz
  !  preconditioners, see the Algorithm 3.2.2 of the book:
  !    -  B.F. Smith, P.E. Bjorstad & W.D. Gropp,
  !       Domain decomposition: parallel multilevel methods for elliptic partial
  !       differential equations, Cambridge University Press, 1996.
  !
  !  For a detailed description of the arguments, see mld_dmlprec_aply.
  !
  subroutine mlt_twoside_ml_aply(alpha,baseprecv,x,beta,y,desc_data,trans,work,info)
    !
    implicit none 
    ! Arguments
    type(psb_desc_type),intent(in)      :: desc_data
    type(mld_zbaseprc_type), intent(in) :: baseprecv(:)
    complex(kind(1.d0)),intent(in)      :: alpha,beta
    complex(kind(1.d0)),intent(in)      :: x(:)
    complex(kind(1.d0)),intent(inout)   :: y(:)
    character, intent(in)               :: trans
    complex(kind(1.d0)),target          :: work(:)
    integer, intent(out)                :: info

    ! Local variables
    integer            :: n_row,n_col
    integer            :: ictxt,np,me,i, nr2l,nc2l,err_act
    integer            :: debug_level, debug_unit
    integer            :: ismth, nlev, ilev, icm
    character(len=20)  :: name

    type psb_mlprec_wrk_type
      complex(kind(1.d0)), allocatable  :: tx(:),ty(:),x2l(:),y2l(:)
    end type psb_mlprec_wrk_type
    type(psb_mlprec_wrk_type), allocatable :: mlprec_wrk(:)

    name = 'mlt_twoside_ml_aply'
    info = 0
    call psb_erractionsave(err_act)
    debug_unit  = psb_get_debug_unit()
    debug_level = psb_get_debug_level()

    ictxt = psb_cd_get_context(desc_data)
    call psb_info(ictxt, me, np)

    if (debug_level >= psb_debug_inner_) &
         & write(debug_unit,*) me,' ',trim(name),&
         & ' Entry  ', size(baseprecv)

    nlev = size(baseprecv)
    allocate(mlprec_wrk(nlev),stat=info) 
    if (info /= 0) then 
      call psb_errpush(4010,name,a_err='Allocate')
      goto 9999      
    end if
    ! STEP 1
    !
    ! Copy the input vector X
    !
    n_col = psb_cd_get_local_cols(desc_data)
    nc2l  = psb_cd_get_local_cols(baseprecv(1)%desc_data)

    allocate(mlprec_wrk(1)%x2l(nc2l),mlprec_wrk(1)%y2l(nc2l), &
         & mlprec_wrk(1)%ty(nc2l), mlprec_wrk(1)%tx(nc2l), stat=info)

    if (info /= 0) then 
      info=4025
      call psb_errpush(info,name,i_err=(/4*nc2l,0,0,0,0/),&
           & a_err='real(kind(1.d0))')
      goto 9999
    end if
    mlprec_wrk(1)%x2l(:) = zzero
    mlprec_wrk(1)%y2l(:) = zzero
    mlprec_wrk(1)%tx(:)  = zzero
    mlprec_wrk(1)%ty(:)  = zzero


    call psb_geaxpby(zone,x,zzero,mlprec_wrk(1)%x2l,&
         & baseprecv(1)%base_desc,info)
    call psb_geaxpby(zone,x,zzero,mlprec_wrk(1)%tx,&
         & baseprecv(1)%base_desc,info)

    !
    ! STEP 2
    !
    ! Apply the base preconditioner at the finest level
    !
    call mld_baseprec_aply(zone,baseprecv(1),mlprec_wrk(1)%x2l,&
         &  zzero,mlprec_wrk(1)%y2l,baseprecv(1)%base_desc,&
         &  trans,work,info)
    !
    ! STEP 3
    !
    ! Compute the residual at the finest level
    !
    mlprec_wrk(1)%ty = mlprec_wrk(1)%x2l
    if (info == 0) call psb_spmm(-zone,baseprecv(1)%base_a,mlprec_wrk(1)%y2l,&
         & zone,mlprec_wrk(1)%ty,baseprecv(1)%base_desc,info,&
         & work=work,trans=trans)
    if (info /=0) then
      call psb_errpush(4010,name,a_err='Fine level baseprec/residual')
      goto 9999
    end if

    !
    ! STEP 4
    !
    ! For each level but the finest one ...
    !
    do ilev = 2, nlev

      n_row = psb_cd_get_local_rows(baseprecv(ilev-1)%base_desc)
      n_col = psb_cd_get_local_cols(baseprecv(ilev-1)%desc_data)
      nc2l  = psb_cd_get_local_cols(baseprecv(ilev)%desc_data)
      nr2l  = psb_cd_get_local_rows(baseprecv(ilev)%desc_data)
      ismth = baseprecv(ilev)%iprcparm(mld_aggr_kind_)
      icm   = baseprecv(ilev)%iprcparm(mld_coarse_mat_)
      allocate(mlprec_wrk(ilev)%ty(nc2l),mlprec_wrk(ilev)%y2l(nc2l),&
           &   mlprec_wrk(ilev)%x2l(nc2l), stat=info)

      if (info /= 0) then 
        info=4025
        call psb_errpush(info,name,i_err=(/4*nc2l,0,0,0,0/),&
             & a_err='real(kind(1.d0))')
        goto 9999      
      end if

      mlprec_wrk(ilev)%x2l(:) = zzero
      mlprec_wrk(ilev)%y2l(:) = zzero
      mlprec_wrk(ilev)%tx(:)  = zzero
      mlprec_wrk(ilev)%ty(:)  = zzero


      if (ismth  /= mld_no_smooth_) then 
        !
        ! Apply the smoothed prolongator transpose
        !
        call psb_halo(mlprec_wrk(ilev-1)%ty,baseprecv(ilev-1)%base_desc,&
             & info,work=work) 
        if (info == 0) call psb_csmm(zone,baseprecv(ilev)%av(mld_sm_pr_t_),&
             & mlprec_wrk(ilev-1)%ty,zzero,mlprec_wrk(ilev)%x2l,info)
      else
        !
        ! Apply the raw aggregation map transpose (take a shortcut)
        !
        mlprec_wrk(ilev)%x2l = zzero
        do i=1,n_row
          mlprec_wrk(ilev)%x2l(baseprecv(ilev)%mlia(i)) = &
               & mlprec_wrk(ilev)%x2l(baseprecv(ilev)%mlia(i)) + &
               &  mlprec_wrk(ilev-1)%ty(i)
        end do
      end if
      if (info /=0) then
        call psb_errpush(4001,name,a_err='Error during restriction')
        goto 9999
      end if

      if (icm == mld_repl_mat_) then 
        call psb_sum(ictxt,mlprec_wrk(ilev)%x2l(1:nr2l))
      else if (icm /= mld_distr_mat_) then 
        info = 4013
        call psb_errpush(info,name,a_err='invalid mld_coarse_mat_',&
             &  i_Err=(/icm,0,0,0,0/))
        goto 9999
      endif

      call psb_geaxpby(zone,mlprec_wrk(ilev)%x2l,zzero,mlprec_wrk(ilev)%tx,&
           & baseprecv(ilev)%base_desc,info)
      !
      ! Apply the base preconditioner
      !
      if (info == 0) call mld_baseprec_aply(zone,baseprecv(ilev),&
           & mlprec_wrk(ilev)%x2l,zzero,mlprec_wrk(ilev)%y2l,&
           &baseprecv(ilev)%desc_data,trans,work,info)
      !
      ! Compute the residual (at all levels but the coarsest one)
      !
      if(ilev < nlev) then
        mlprec_wrk(ilev)%ty = mlprec_wrk(ilev)%x2l
        if (info == 0) call psb_spmm(-zone,baseprecv(ilev)%base_a,&
             & mlprec_wrk(ilev)%y2l,zone,mlprec_wrk(ilev)%ty,&
             & baseprecv(ilev)%base_desc,info,work=work,trans=trans)
      endif
      if (info /=0) then
        call psb_errpush(4001,name,a_err='baseprec_aply/residual')
        goto 9999
      end if

    enddo

    !
    ! STEP 5
    !
    ! For each level but the coarsest one ...
    !
    do ilev=nlev-1, 1, -1

      ismth = baseprecv(ilev+1)%iprcparm(mld_aggr_kind_)
      n_row = psb_cd_get_local_rows(baseprecv(ilev)%base_desc)

      if (ismth  /= mld_no_smooth_) then
        !
        ! Apply the smoothed prolongator
        ! 
        if (ismth == mld_smooth_prol_) &
             & call psb_halo(mlprec_wrk(ilev+1)%y2l,baseprecv(ilev+1)%desc_data,&
             &  info,work=work) 
        if (info == 0) call psb_csmm(zone,baseprecv(ilev+1)%av(mld_sm_pr_),&
             & mlprec_wrk(ilev+1)%y2l,zone,mlprec_wrk(ilev)%y2l,info)
      else
        !
        ! Apply the raw aggregation map (take a shortcut)
        !
        do i=1, n_row
          mlprec_wrk(ilev)%y2l(i) = mlprec_wrk(ilev)%y2l(i) + &
               & mlprec_wrk(ilev+1)%y2l(baseprecv(ilev+1)%mlia(i))
        enddo
      end if
      if (info /=0 ) then
        call psb_errpush(4001,name,a_err='Error during restriction')
        goto 9999
      end if

      !
      ! Compute the residual
      !
      call psb_spmm(-zone,baseprecv(ilev)%base_a,mlprec_wrk(ilev)%y2l,&
           & zone,mlprec_wrk(ilev)%tx,baseprecv(ilev)%base_desc,info,&
           & work=work,trans=trans)
      !
      ! Apply the base preconditioner
      !
      if (info == 0) call mld_baseprec_aply(zone,baseprecv(ilev),mlprec_wrk(ilev)%tx,&
           & zone,mlprec_wrk(ilev)%y2l,baseprecv(ilev)%base_desc, trans, work,info)
      if (info /= 0) then
        call psb_errpush(4001,name,a_err='Error: residual/baseprec_aply')
        goto 9999
      end if
    enddo

    !
    ! STEP 6
    !
    ! Compute the output vector Y
    !
    call psb_geaxpby(alpha,mlprec_wrk(1)%y2l,beta,y,&
         &   baseprecv(1)%base_desc,info)

    if (info /= 0) then
      call psb_errpush(4001,name,a_err='Error final update')
      goto 9999
    end if



    deallocate(mlprec_wrk,stat=info)
    if (info /= 0) then 
      call psb_errpush(4000,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 mlt_twoside_ml_aply

end subroutine mld_zmlprec_aply