program FSVD_trunc
  implicit none
  BEGIN_DOC
  ! study precision variation with truncated SVD
  END_DOC
  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(:,:,:)

  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 --- '

  !lrank_min = 100
  !lrank_max = nn
  !do low_rank = lrank_min, lrank_max, 1
  !  err_verif = 0.d0
  !  do j = 1, nn
  !    do i = 1, mm
  !      err_tmp = 0.d0
  !      do l = 1, low_rank
  !        err_tmp = err_tmp + D_FSVD(l) * U_FSVD(i,l) * Vt_FSVD(l,j)
  !      enddo
  !      err_verif = err_verif + (A_FSVD(i,j)-err_tmp) * (A_FSVD(i,j)-err_tmp) 
  !    enddo
  !  enddo
  !  print*, ' low rank      = ', low_rank
  !  print*, ' err verif (%) = ', 100.d0 * dsqrt(err_verif/norm_psi)
  !enddo

  ! ------------------------------------------------------------------------------------------------
  !                           set to EZFIO for a fixed low rank

  low_rank = min(mm,nn)
  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

  !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_alpha(Uezfio)
  call ezfio_set_spindeterminants_psi_svd_beta(Vezfio )
  call ezfio_set_spindeterminants_psi_svd_coefs(Dezfio)

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

  deallocate( Uezfio, Dezfio, Vezfio )
  deallocate( U_FSVD, D_FSVD, Vt_FSVD )

end