text: !   
  !   
  !                             AMG4PSBLAS version 1.0
  !    Algebraic Multigrid Package
  !               based on PSBLAS (Parallel Sparse BLAS version 3.7)
  !    
  !    (C) Copyright 2021 
  !  
  !        Salvatore Filippone  
  !        Pasqua D'Ambra   
  !        Fabio Durastante        
  !   
  !    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 AMG4PSBLAS 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 AMG4PSBLAS GROUP OR ITS CONTRIBUTORS
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  !    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.
  !   
  !  
  ! File: amg_zaggrmat_smth_bld.F90
  !
  ! Subroutine: amg_zaggrmat_smth_bld
  ! Version:    complex
  !
  !  This routine builds a coarse-level matrix A_C from a fine-level matrix A
  !  by using the Galerkin approach, i.e.
  !
  !                               A_C = P_C^T A P_C,
  !
  !  where P_C is a prolongator from the coarse level to the fine one.
  ! 
  !  The prolongator P_C is built according to a smoothed aggregation algorithm,
  !  i.e. it is obtained by applying a damped Jacobi smoother to the piecewise
  !  constant interpolation operator P corresponding to the fine-to-coarse level 
  !  mapping built by the amg_aggrmap_bld subroutine:
  !
  !                            P_C = (I - omega*D^(-1)A) * P,
  !
  !  where D is the diagonal matrix with main diagonal equal to the main diagonal
  !  of A, and omega is a suitable smoothing parameter. An estimate of the spectral
  !  radius of D^(-1)A, to be used in the computation of omega, is provided, 
  !  according to the value of p%parms%aggr_omega_alg, specified by the user
  !  through amg_zprecinit and amg_zprecset.
  !
  !  The coarse-level matrix A_C is distributed among the parallel processes or
  !  replicated on each of them, according to the value of p%parms%coarse_mat,
  !  specified by the user through amg_zprecinit and amg_zprecset.
  !  On output from this routine the entries of AC, op_prol, op_restr
  !  are still in "global numbering" mode; this is fixed in the calling routine
  !  aggregator%mat_bld.
  !
  !
  ! Arguments:
  !    a          -  type(psb_zspmat_type), input.     
  !                  The sparse matrix structure containing the local part of
  !                  the fine-level matrix.
  !    desc_a     -  type(psb_desc_type), input.
  !                  The communication descriptor of the fine-level matrix.
  !    p          -  type(amg_z_onelev_type), input/output.
  !                  The 'one-level' data structure that will contain the local
  !                  part of the matrix to be built as well as the information
  !                  concerning the prolongator and its transpose.
  !    parms      -   type(amg_dml_parms), input
  !                  Parameters controlling the choice of algorithm
  !    ac         -  type(psb_zspmat_type), output
  !                  The coarse matrix on output 
  !                  
  !    ilaggr     -  integer, dimension(:), input
  !                  The mapping between the row indices of the coarse-level
  !                  matrix and the row indices of the fine-level matrix.
  !                  ilaggr(i)=j means that node i in the adjacency graph
  !                  of the fine-level matrix is mapped onto node j in the
  !                  adjacency graph of the coarse-level matrix. Note that the indices
  !                  are assumed to be shifted so as to make sure the ranges on
  !                  the various processes do not   overlap.
  !    nlaggr     -  integer, dimension(:) input
  !                  nlaggr(i) contains the aggregates held by process i.
  !    op_prol    -  type(psb_zspmat_type), input/output
  !                  The tentative prolongator on input, the computed prolongator on output
  !               
  !    op_restr    -  type(psb_zspmat_type), output
  !                  The restrictor operator; normally, it is the transpose of the prolongator. 
  !               
  !    info       -  integer, output.
  !                  Error code.
  !
  subroutine amg_zaggrmat_smth_bld(a,desc_a,ilaggr,nlaggr,parms,&
       & ac,desc_ac,op_prol,op_restr,t_prol,info)
    use psb_base_mod
    use amg_base_prec_type
    use amg_z_inner_mod, amg_protect_name => amg_zaggrmat_smth_bld
    use amg_z_base_aggregator_mod
  
    implicit none
  
    ! Arguments
    type(psb_zspmat_type), intent(in)      :: a
    type(psb_desc_type), intent(inout)       :: desc_a
    integer(psb_lpk_), intent(inout)         :: ilaggr(:), nlaggr(:)
    type(amg_dml_parms), intent(inout)      :: parms 
    type(psb_zspmat_type), intent(inout)      :: op_prol,ac,op_restr
    type(psb_lzspmat_type), intent(inout)    :: t_prol
    type(psb_desc_type), intent(inout)       :: desc_ac
    integer(psb_ipk_), intent(out)           :: info
  
    ! Local variables
    integer(psb_lpk_) :: nrow, nglob, ncol, ntaggr, ip, &
         & naggr, nzl,naggrm1,naggrp1, i, j, k, jd, icolF, nrw
    integer(psb_ipk_) :: inaggr, nzlp
    type(psb_ctxt_type) :: ctxt
    integer(psb_ipk_) :: np, me
    character(len=20) :: name
    type(psb_lz_coo_sparse_mat) :: tmpcoo
    type(psb_z_coo_sparse_mat) :: coo_prol, coo_restr
    type(psb_z_csr_sparse_mat) :: acsr1,  acsrf, csr_prol, acsr
    complex(psb_dpk_), allocatable :: adiag(:)
    real(psb_dpk_), allocatable :: arwsum(:)
    integer(psb_ipk_)  :: ierr(5)
    logical            :: filter_mat
    integer(psb_ipk_)            :: debug_level, debug_unit, err_act
    integer(psb_ipk_), parameter :: ncmax=16
    real(psb_dpk_)     :: anorm, omega, tmp, dg, theta
    logical, parameter :: debug_new=.false.
    character(len=80) :: filename
  
    name='amg_aggrmat_smth_bld'
    info=psb_success_
    call psb_erractionsave(err_act)
    if (psb_errstatus_fatal()) then
      info = psb_err_internal_error_; goto 9999
    end if
    debug_unit  = psb_get_debug_unit()
    debug_level = psb_get_debug_level()
  
    ctxt = desc_a%get_context()
  
    call psb_info(ctxt, me, np)
  
    nglob = desc_a%get_global_rows()
    nrow  = desc_a%get_local_rows()
    ncol  = desc_a%get_local_cols()
  
    theta = parms%aggr_thresh
  
    naggr  = nlaggr(me+1)
    ntaggr = sum(nlaggr)
  
    naggrm1 = sum(nlaggr(1:me))
    naggrp1 = sum(nlaggr(1:me+1))
    filter_mat = (parms%aggr_filter == amg_filter_mat_)
  
    !
    ! naggr: number of local aggregates
    ! nrow: local rows. 
    ! 
  
    ! Get the diagonal D
    adiag = a%get_diag(info)
    if (info == psb_success_) &
         & call psb_realloc(ncol,adiag,info)
    if (info == psb_success_) &
         & call psb_halo(adiag,desc_a,info)
    if (info == psb_success_) call a%cp_to(acsr)
  
    if(info /= psb_success_) then
      call psb_errpush(psb_err_from_subroutine_,name,a_err='sp_getdiag')
      goto 9999
    end if
  
    if (debug_level >= psb_debug_outer_) &
         & write(debug_unit,*) me,' ',trim(name),&
         & ' Initial copies done.'
  
    call acsr%cp_to_fmt(acsrf,info)
  
  
    if (filter_mat) then
      !
      ! Build the filtered matrix Af from A
      ! 
  
      do i=1, nrow
        tmp = zzero
        jd  = -1 
        do j=acsrf%irp(i),acsrf%irp(i+1)-1
          if (acsrf%ja(j) == i) jd = j 
          if (abs(acsrf%val(j)) < theta*sqrt(abs(adiag(i)*adiag(acsrf%ja(j))))) then
            tmp=tmp+acsrf%val(j)
            acsrf%val(j)=zzero
          endif
  
        enddo
        if (jd == -1) then 
          write(0,*) 'Wrong input: we need the diagonal!!!!', i
        else
          acsrf%val(jd)=acsrf%val(jd)-tmp
        end if
      enddo
      ! Take out zeroed terms 
      call acsrf%clean_zeros(info)
    end if
  
  
    do i=1,size(adiag)
      if (adiag(i) /= zzero) then
        adiag(i) = zone / adiag(i)
      else
        adiag(i) = zone
      end if
    end do
  
    if (parms%aggr_omega_alg == amg_eig_est_) then 
  
      if (parms%aggr_eig == amg_max_norm_) then 
        allocate(arwsum(nrow))
        call acsr%arwsum(arwsum)      
        anorm = maxval(abs(adiag(1:nrow)*arwsum(1:nrow)))
        call psb_amx(ctxt,anorm)
        omega = 4.d0/(3.d0*anorm)
        parms%aggr_omega_val = omega 
  
      else 
        info = psb_err_internal_error_
        call psb_errpush(info,name,a_err='invalid amg_aggr_eig_')
        goto 9999
      end if
  
    else if (parms%aggr_omega_alg == amg_user_choice_) then 
  
      omega = parms%aggr_omega_val 
  
    else if (parms%aggr_omega_alg /= amg_user_choice_) then 
      info = psb_err_internal_error_
      call psb_errpush(info,name,a_err='invalid amg_aggr_omega_alg_')
      goto 9999
    end if
  
    
    call acsrf%scal(adiag,info)
    if (info /= psb_success_) goto 9999
  
    call t_prol%mv_to(tmpcoo)
    inaggr = naggr
    call psb_cdall(ctxt,desc_ac,info,nl=inaggr)
    nzlp = tmpcoo%get_nzeros()
    call desc_ac%indxmap%g2lip_ins(tmpcoo%ja(1:nzlp),info) 
    call tmpcoo%set_ncols(desc_ac%get_local_cols())
    call tmpcoo%mv_to_ifmt(csr_prol,info)
  
    call psb_cdasb(desc_ac,info)
    call psb_cd_reinit(desc_ac,info)
    !
    ! Build the smoothed prolongator using either A or Af
    !    acsr1 = (I-w*D*A) Prol      acsr1 = (I-w*D*Af) Prol 
    ! This is always done through the variable acsrf which
    ! is a bit less readable, but saves space and one matrix copy
    ! 
    call omega_smooth(omega,acsrf)
    call psb_par_spspmm(acsrf,desc_a,csr_prol,acsr1,desc_ac,info)
    if(info /= psb_success_) then
      call psb_errpush(psb_err_from_subroutine_,name,a_err='spspmm 1')
      goto 9999
    end if
  
  
    if (debug_level >= psb_debug_outer_) &
         & write(debug_unit,*) me,' ',trim(name),&
         & 'Done SPSPMM 1'
    nzl = acsr1%get_nzeros()
    call acsr1%mv_to_coo(coo_prol,info)
    
    call amg_ptap_bld(acsr,desc_a,nlaggr,parms,ac,&
         & coo_prol,desc_ac,coo_restr,info)
  
    call op_prol%mv_from(coo_prol)
    call op_restr%mv_from(coo_restr)
  
    if (debug_level >= psb_debug_outer_) &
         & write(debug_unit,*) me,' ',trim(name),&
         & 'Done smooth_aggregate '
    call psb_erractionrestore(err_act)
    return
  
  9999 continue
    call psb_errpush(info,name)
    call psb_error_handler(err_act)
    return
  
  contains
  
    subroutine omega_smooth(omega,acsr)
      implicit none 
      real(psb_dpk_),intent(in) :: omega
      type(psb_z_csr_sparse_mat), intent(inout) :: acsr
      !
      integer(psb_lpk_) :: i,j
      do i=1,acsr%get_nrows()
        do j=acsr%irp(i),acsr%irp(i+1)-1
          if (acsr%ja(j) == i) then 
            acsr%val(j) = zone - omega*acsr%val(j) 
          else
            acsr%val(j) = - omega*acsr%val(j) 
          end if
        end do
      end do
    end subroutine omega_smooth
  
  end subroutine amg_zaggrmat_smth_bld
  