program saveSVD_asEZ

  BEGIN_DOC
  ! save SVD manually
  END_DOC

  implicit none
  read_wf = .True.
  TOUCH read_wf

  call run()

end


subroutine run

  implicit none

  integer                       :: mm, nn, i_state, low_rank, lrank_min, lrank_max
  integer                       :: i, j, k, l
  double precision              :: norm_psi, err_verif, err_tmp
  double precision, allocatable :: U_FSVD(:,:), D_FSVD(:), Vt_FSVD(:,:), A_FSVD(:,:)
  double precision, allocatable :: Uezfio(:,:,:), Dezfio(:,:), Vezfio(:,:,:)
  double precision, allocatable :: US(:,:), A_TSVD(:,:)
  double precision              :: t0, t1, t2
 
  call CPU_TIME(t0)

  i_state = 1
  mm      = n_det_alpha_unique
  nn      = n_det_beta_unique

  print *, ' matrix dimensions:', mm,'x',nn
  print *, ' N det:', N_det

  allocate( A_FSVD(mm,nn), U_FSVD(mm,mm), D_FSVD(min(mm,nn)), Vt_FSVD(nn,nn) )

  norm_psi    = 0.d0
  A_FSVD(:,:) = 0.d0
  do k = 1, N_det
    i           = psi_bilinear_matrix_rows(k)
    j           = psi_bilinear_matrix_columns(k)
    A_FSVD(i,j) = psi_bilinear_matrix_values(k,i_state)
    norm_psi   += psi_bilinear_matrix_values(k,i_state) * psi_bilinear_matrix_values(k,i_state)
  enddo

  call svd_s( A_FSVD, size(A_FSVD,1), U_FSVD, size(U_FSVD,1), D_FSVD, Vt_FSVD, size(Vt_FSVD,1), mm, nn)
  print *, ' --- Full SVD: ok --- '
  call CPU_TIME(t1)
  print *, (t1-t0)/60.d0, 'min'


  ! ------------------------------------------


  !low_rank = 24
  low_rank = min(mm,nn)

  ! US = U x SV :
  allocate( US(mm,low_rank) )
  US(:,:) = 0.d0
  do i = 1, mm
    do l = 1, low_rank
      US(i,l) = U_FSVD(i,l) * D_FSVD(l)
    enddo
  enddo

  ! A_TSVD = US x Vt_FSVD
  allocate( A_TSVD(mm,nn) )
  A_TSVD(:,:) = 0.d0
  call dgemm( 'N', 'N', mm, nn, low_rank, 1.d0 &
                , US     , size(US     ,1)     &
                , Vt_FSVD, size(Vt_FSVD,1)     &
                , 0.d0, A_TSVD, size(A_TSVD,1) )
  deallocatE(US)

  ! |A_FSVD-A_TSVD|
  err_verif = 0.d0
  do j = 1, nn
    do i = 1, mm
      err_tmp   = A_FSVD(i,j) - A_TSVD(i,j)
      err_verif = err_verif + err_tmp * err_tmp
    enddo
  enddo
  print*, ' rank          = ', low_rank
  print*, ' err verif (%) = ', 100.d0 * dsqrt(err_verif/norm_psi)

  deallocate( A_FSVD , A_TSVD )


  ! ------------------------------------------------------------------------------------------------
  !                           set to EZFIO for a fixed low rank
  allocate( Uezfio(mm,low_rank,1), Dezfio(low_rank,1), Vezfio(nn,low_rank,1))

  do l = 1, low_rank
    Dezfio(l,1) = D_FSVD(l)
    do j = 1, mm
      Uezfio(j,l,1) = U_FSVD(j,l)
    enddo
    do j = 1, nn
      Vezfio(j,l,1) = Vt_FSVD(l,j)
    enddo
  enddo

  deallocate( U_FSVD, D_FSVD, Vt_FSVD )

  !call ezfio_set_spindeterminants_n_det(N_det)
  !call ezfio_set_spindeterminants_n_states(N_states)
  !call ezfio_set_spindeterminants_n_det_alpha(n_det_alpha_unique)
  !call ezfio_set_spindeterminants_n_det_beta(n_det_beta_unique)
  !call ezfio_set_spindeterminants_psi_coef_matrix_rows(psi_bilinear_matrix_rows)
  !call ezfio_set_spindeterminants_psi_coef_matrix_columns(psi_bilinear_matrix_columns)
  !call ezfio_set_spindeterminants_psi_coef_matrix_values(psi_bilinear_matrix_values)

  call ezfio_set_spindeterminants_n_svd_coefs(low_rank)
  call ezfio_set_spindeterminants_psi_svd_coefs(Dezfio)
  deallocate( Dezfio)

  ! does not work for big matrices
  !call ezfio_set_spindeterminants_psi_svd_alpha(Uezfio)
  !call ezfio_set_spindeterminants_psi_svd_beta(Vezfio )

  open(unit=11, file="u_svd.txt", action='write')
    do l = 1, low_rank
      do i = 1, mm
        write(11,*) Uezfio(i,l,1) 
      enddo
    enddo
  close(11)
  deallocate( Uezfio )

  open(unit=11, file="v_svd.txt", action='write')
    do l = 1, low_rank
      do i = 1, nn
        write(11,*) Vezfio(i,l,1) 
      enddo
    enddo
  close(11)
  deallocate( Vezfio )

  ! ------------------------------------------------------------------------------------------------

  call CPU_TIME(t2)
  print *, ''
  print *, ' end after'
  print *, (t2-t0)/60.d0, 'min'

end