!--------------------------------------------------------------------------------
! Copyright (c) 2016 Peter Grünberg Institut, Forschungszentrum Jülich, Germany
! This file is part of FLEUR and available as free software under the conditions
! of the MIT license as expressed in the LICENSE file in more detail.
!--------------------------------------------------------------------------------
!<@brief
!<The eigen routine sets up and solves the generalized eigenvalue problem
!More description at end of file
MODULE m_eigen
  USE m_juDFT
  IMPLICIT NONE
CONTAINS
  !>The eigenvalue problem is constructed and solved in this routine. The following steps are performed:
  !> 1. Preparation: generate energy parameters, open eig-file
  !> 2. CALL to mt_setup() : this constructs the local Hamiltonian (i.e. the Hamiltonian in the \f$ u,\dot u, u_{lo} \f$ basis) LDA+U is also added here
  !> 3. within the (collinear)spin and k-point loop: CALL to eigen_hssetup() to generate the matrices, CALL to eigen_diag() to perform diagonalization 
  !> 4. writing (saving) of eigenvectors
  !>
  !> The matrices generated and diagonalized here are of type m_mat as defined in m_types_mat. 
  !>@author D. Wortmann
  SUBROUTINE eigen(mpi,stars,sphhar,atoms,obsolete,xcpot,sym,kpts,DIMENSION,vacuum,input,&
                   cell,enpara,banddos,noco,oneD,hybrid,iter,eig_id,results,inden,v,vx)

#include"cpp_double.h"
    USE m_constants, ONLY : pi_const,sfp_const
    USE m_types
    USE m_apws
    USE m_eigen_hssetup
    USE m_pot_io
    USE m_eigen_diag
    USE m_add_vnonlocal
    USE m_subvxc
    !USE m_hsefunctional
    USE m_mt_setup
    USE m_util
    USE m_io_hybrid
    !USE m_icorrkeys
    USE m_eig66_io, ONLY : open_eig, write_eig, close_eig,read_eig
    USE m_xmlOutput
#ifdef CPP_MPI
    USE m_mpi_bc_potden
#endif
    USE m_symmetrize_matrix
    USE m_unfold_band_kpts !used for unfolding bands
    USE m_types_mpimat

    
    IMPLICIT NONE
    TYPE(t_results),INTENT(INOUT):: results
    CLASS(t_xcpot),INTENT(IN)    :: xcpot
    TYPE(t_mpi),INTENT(IN)       :: mpi
    TYPE(t_dimension),INTENT(IN) :: DIMENSION
    TYPE(t_oneD),INTENT(IN)      :: oneD
    TYPE(t_hybrid),INTENT(INOUT) :: hybrid
    TYPE(t_enpara),INTENT(INOUT) :: enpara
    TYPE(t_obsolete),INTENT(IN)  :: obsolete
    TYPE(t_input),INTENT(IN)     :: input
    TYPE(t_vacuum),INTENT(IN)    :: vacuum
    TYPE(t_noco),INTENT(IN)      :: noco
    TYPE(t_banddos),INTENT(IN)   :: banddos
    TYPE(t_sym),INTENT(IN)       :: sym  
    TYPE(t_stars),INTENT(IN)     :: stars
    TYPE(t_cell),INTENT(IN)      :: cell
    TYPE(t_kpts),INTENT(INOUT)   :: kpts
    TYPE(t_sphhar),INTENT(IN)    :: sphhar
    TYPE(t_atoms),INTENT(IN)     :: atoms
    TYPE(t_potden),INTENT(IN)    :: inden,vx
    TYPE(t_potden),INTENT(INOUT) :: v    !u_setup will modify the potential matrix
   
#ifdef CPP_MPI
    INCLUDE 'mpif.h'
#endif

!    EXTERNAL MPI_BCAST    !only used by band_unfolding to broadcast the gvec

    ! Scalar Arguments
    INTEGER,INTENT(IN)    :: iter
    INTEGER,INTENT(IN)    :: eig_id

    ! Local Scalars
    INTEGER jsp,nk,nred,ne_all,ne_found
    INTEGER ne,lh0
    INTEGER isp,i,j,err
    LOGICAL l_wu,l_file,l_real,l_zref

    ! Local Arrays
    INTEGER              :: ierr(3)
    INTEGER              :: neigBuffer(kpts%nkpt,input%jspins)

    COMPLEX              :: unfoldingBuffer(SIZE(results%unfolding_weights,1),kpts%nkpt,input%jspins) ! needed for unfolding bandstructure mpi case

    INTEGER, PARAMETER   :: lmaxb = 3
    REAL,    ALLOCATABLE :: bkpt(:)
    REAL,    ALLOCATABLE :: eig(:)
    COMPLEX, ALLOCATABLE :: vs_mmp(:,:,:,:)

	INTEGER                   :: jsp_m, i_kpt_m, i_m

    TYPE(t_tlmplm)            :: td
    TYPE(t_usdus)             :: ud
    TYPE(t_lapw)              :: lapw
    CLASS(t_mat), ALLOCATABLE :: zMat
    CLASS(t_mat), ALLOCATABLE :: hmat,smat
    CLASS(t_mat), ALLOCATABLE :: smat_unfold !used for unfolding bandstructure

    ! Variables for HF or hybrid functional calculation
    INTEGER                   :: comm(kpts%nkpt),irank2(kpts%nkpt),isize2(kpts%nkpt), dealloc_stat
    character(len=300)        :: errmsg
    
    call ud%init(atoms,DIMENSION%jspd)
    ALLOCATE (eig(DIMENSION%neigd),bkpt(3))
    
    l_real=sym%invs.AND..NOT.noco%l_noco

    ! check if z-reflection trick can be used
    l_zref=(sym%zrfs.AND.(SUM(ABS(kpts%bk(3,:kpts%nkpt))).LT.1e-9).AND..NOT.noco%l_noco) 
    IF (mpi%n_size > 1) l_zref = .FALSE.
 
#ifdef CPP_MPI
    CALL mpi_bc_potden(mpi,stars,sphhar,atoms,input,vacuum,oneD,noco,v)
#endif

    !IF (mpi%irank.EQ.0) CALL openXMLElementFormPoly('iteration',(/'numberForCurrentRun','overallNumber      '/),(/iter,v%iter/),&
    !                                                RESHAPE((/19,13,5,5/),(/2,2/)))
    
    ! Set up and solve the eigenvalue problem
    !   loop over spins
    !     set up k-point independent t(l'm',lm) matrices
    CALL mt_setup(atoms,sym,sphhar,input,noco,enpara,inden,v,mpi,results,DIMENSION,td,ud)

    neigBuffer = 0
    results%neig = 0
    results%eig = 1.0e300
    unfoldingBuffer = CMPLX(0.0,0.0)

    DO jsp = 1,MERGE(1,input%jspins,noco%l_noco)
       k_loop:DO nk = mpi%n_start,kpts%nkpt,mpi%n_stride

          ! Set up lapw list        
          CALL lapw%init(input,noco, kpts,atoms,sym,nk,cell,l_zref, mpi)
          call timestart("Setup of H&S matrices")
          CALL eigen_hssetup(jsp,mpi,DIMENSION,hybrid,enpara,input,vacuum,noco,sym,&
                             stars,cell,sphhar,atoms,ud,td,v,lapw,l_real,smat,hmat)
          CALL timestop("Setup of H&S matrices")

          IF(hybrid%l_hybrid) THEN

      DO i = 1, hmat%matsize1
	 DO j = 1, i
	    IF (hmat%l_real) THEN
	       IF ((i.LE.5).AND.(j.LE.5)) THEN
		  WRITE(1233,'(2i7,2f15.8)') i, j, hmat%data_r(i,j), hmat%data_r(j,i)
	       END IF
	    ELSE
	    ENDIF
	 END DO
      END DO

             ! Write overlap matrix smat to direct access file olap
             print *,"Wrong overlap matrix used, fix this later"
             CALL write_olap(smat,(jsp-1)*kpts%nkpt+nk) ! Note: At this moment this only works without MPI parallelization
             PRINT *,"TODO"
!             STOP "TODO"
             PRINT *,"BASIS:", lapw%nv(jsp), atoms%nlotot
             IF (hybrid%l_addhf) CALL add_Vnonlocal(nk,lapw,atoms,hybrid,dimension,kpts,jsp,results,xcpot,noco,hmat)

             IF(hybrid%l_subvxc) THEN
                CALL subvxc(lapw,kpts%bk(:,nk),DIMENSION,input,jsp,v%mt(:,0,:,:),atoms,ud,hybrid,enpara%el0,enpara%ello0,&
                            sym,cell,sphhar,stars,xcpot,mpi,oneD,hmat,vx)
             END IF
          END IF ! hybrid%l_hybrid

          l_wu=.FALSE.
          ne_all=DIMENSION%neigd
          if (allocated(zmat)) then
             deallocate(zmat, stat=dealloc_stat, errmsg=errmsg)
             if(dealloc_stat /= 0) call juDFT_error("deallocate failed for zmat",&
                                                hint=errmsg, calledby="eigen.F90")
          endif

          !Try to symmetrize matrix
          CALL symmetrize_matrix(mpi,noco,kpts,nk,hmat,smat)
          
          IF (banddos%unfoldband) THEN
		select type(smat)
		type is (t_mat)
			allocate(t_mat::smat_unfold)
			select type(smat_unfold)
		             type is (t_mat)
			     smat_unfold=smat
			end select
		type is (t_mpimat)
			allocate(t_mpimat::smat_unfold)
			select type(smat_unfold)
		             type is (t_mpimat)
			     smat_unfold=smat
			end select
		end select
          END IF

          CALL eigen_diag(mpi,hmat,smat,nk,jsp,iter,ne_all,eig,zMat)
          CALL smat%free()
          DEALLOCATE(hmat,smat, stat=dealloc_stat, errmsg=errmsg)
          if(dealloc_stat /= 0) call juDFT_error("deallocate failed for hmat or smat",&
                                             hint=errmsg, calledby="eigen.F90")

          ! Output results
          CALL timestart("EV output")
#if defined(CPP_MPI)
          ! Collect number of all eigenvalues
          ne_found=ne_all
          CALL MPI_ALLREDUCE(ne_found,ne_all,1,MPI_INTEGER,MPI_SUM, mpi%sub_comm,ierr)
          ne_all=MIN(DIMENSION%neigd,ne_all)
#else
          ne_found=ne_all
#endif          
          IF (.NOT.zmat%l_real) THEN
             zMat%data_c(:lapw%nmat,:ne_found) = CONJG(zMat%data_c(:lapw%nmat,:ne_found))
          END IF
          CALL write_eig(eig_id, nk,jsp,ne_found,ne_all,&
                         eig(:ne_found),n_start=mpi%n_size,n_end=mpi%n_rank,zmat=zMat)
          neigBuffer(nk,jsp) = ne_found
#if defined(CPP_MPI)
          ! RMA synchronization
          CALL MPI_BARRIER(mpi%MPI_COMM,ierr)
#endif
          CALL timestop("EV output")

          IF (banddos%unfoldband) THEN
               CALL calculate_plot_w_n(banddos,cell,kpts,smat_unfold,zMat,lapw,nk,jsp,eig,results,input,atoms,unfoldingBuffer,mpi)
	       DEALLOCATE(smat_unfold, stat=dealloc_stat, errmsg=errmsg)
          if(dealloc_stat /= 0) call juDFT_error("deallocate failed for smat_unfold",&
                                             hint=errmsg, calledby="eigen.F90")
          END IF

       END DO  k_loop
    END DO ! spin loop ends

#ifdef CPP_MPI
    IF (banddos%unfoldband) THEN
       write(1230+mpi%irank,*) SHAPE(results%unfolding_weights)
       write(1230+mpi%irank,*) SHAPE(unfoldingBuffer)
       DO jsp_m = 1, SIZE(unfoldingBuffer,3)
		DO i_kpt_m = 1, SIZE(unfoldingBuffer,2)
			DO i_m = 1, SIZE(unfoldingBuffer,1)
             write(1230+mpi%irank,'(2f15.8)') unfoldingBuffer(i_m, i_kpt_m,jsp_m)
			END DO
		END DO
	END DO
        write(*,*) SHAPE(results%unfolding_weights)
!       FLUSH(1230+mpi%irank)
       results%unfolding_weights = CMPLX(0.0,0.0)
       CALL MPI_ALLREDUCE(unfoldingBuffer,results%unfolding_weights,SIZE(results%unfolding_weights,1)*SIZE(results%unfolding_weights,2)*SIZE(results%unfolding_weights,3),CPP_MPI_COMPLEX,MPI_SUM,mpi%mpi_comm,ierr)
	       write(1240+mpi%irank,*) SHAPE(results%unfolding_weights)       
	DO jsp_m = 1, SIZE(results%unfolding_weights,3)
		DO i_kpt_m = 1, SIZE(results%unfolding_weights,2)
			DO i_m = 1, SIZE(results%unfolding_weights,1)
             write(1240+mpi%irank,'(2f15.8)') results%unfolding_weights(i_m, i_kpt_m,jsp_m)
			END DO
		END DO
	END DO
    END IF
    CALL MPI_ALLREDUCE(neigBuffer,results%neig,kpts%nkpt*input%jspins,MPI_INTEGER,MPI_SUM,mpi%sub_comm,ierr)
    CALL MPI_BARRIER(mpi%MPI_COMM,ierr)
#else
    results%neig(:,:) = neigBuffer(:,:)
    results%unfolding_weights(:,:,:) = unfoldingBuffer(:,:,:)
#endif

    ! Sorry for the following strange workaround to fill the results%eig array.
    ! At some point someone should have a closer look at how the eigenvalues are
    ! distributed and fill the array without using the eigenvalue-IO.
    DO jsp = 1,MERGE(1,input%jspins,noco%l_noco)
       DO nk = 1,kpts%nkpt
          CALL read_eig(eig_id,nk,jsp,results%neig(nk,jsp),results%eig(:,nk,jsp))
#ifdef CPP_MPI
          CALL MPI_BARRIER(mpi%MPI_COMM,ierr)
#endif
       END DO
    END DO

    !IF (hybrid%l_hybrid.OR.hybrid%l_calhf) CALL close_eig(eig_id)

    IF( input%jspins .EQ. 1 .AND. hybrid%l_hybrid ) THEN
       results%te_hfex%valence = 2*results%te_hfex%valence
       IF(hybrid%l_calhf) results%te_hfex%core = 2*results%te_hfex%core
    END IF
    enpara%epara_min = MINVAL(enpara%el0)
    enpara%epara_min = MIN(MINVAL(enpara%ello0),enpara%epara_min)
  END SUBROUTINE eigen
END MODULE m_eigen