get_partial_lno_encode_input_val Subroutine

  pure subroutine get_partial_lno_encode_input_val( &
       this, upstream_grad, output)
    !! dL/du = E^T @ upstream  [n_in, batch]
    implicit none
    class(array_type), intent(in) :: this
    real(real32), dimension(:,:), intent(in)  :: upstream_grad
    real(real32), dimension(:,:), intent(out) :: output

    integer :: n_in, num_modes, mode_index, j, s, num_samples
    real(real32) :: t, mu_m
    real(real32), allocatable :: ET(:,:)  ! [n_in, num_modes]

    n_in = this%indices(1)
    num_modes = this%indices(2)
    num_samples = size(upstream_grad, 2)

    allocate(ET(n_in, num_modes))
    do mode_index = 1, num_modes
       mu_m = this%right_operand%val(mode_index, 1)
       do j = 1, n_in
          if(n_in .gt. 1)then
             t = real(j-1, real32) / real(n_in-1, real32)
          else
             t = 0.0_real32
          end if
          ET(j, mode_index) = exp(-mu_m * t)
       end do
    end do

    output = matmul(ET, upstream_grad)

    deallocate(ET)

  end subroutine get_partial_lno_encode_input_val