relative_trial_numerator Function

    function relative_trial_numerator(tt_numerator, tt_denom, replica_pairs) &
        result(rel_tot_trial_numerator)
        implicit none
        HElement_t(dp), intent(in) :: tt_numerator(inum_runs), tt_denom(inum_runs)
        logical, intent(in) :: replica_pairs
        HElement_t(dp) :: rel_tot_trial_numerator(inum_runs)
        integer :: run

        if (.not. qmc_trial_wf) then
            ! Becuase tot_trial_numerator/tot_trial_denom is the energy
            ! relative to the the trial energy, add on this contribution to
            ! make it relative to the HF energy.
            if (ntrial_excits == 1) then
                rel_tot_trial_numerator = tt_numerator + (tt_denom * trial_energies(1))
            else
                if (replica_pairs) then
                    do run = 2, inum_runs, 2
                        rel_tot_trial_numerator(run - 1:run) = tt_numerator(run - 1:run) + &
                                                               tt_denom(run - 1:run) * trial_energies(run / 2)
                    end do
                else
                    rel_tot_trial_numerator = tt_numerator + (tt_denom * trial_energies)
                end if
            end if
        else
            rel_tot_trial_numerator = tt_numerator
        end if

    end function relative_trial_numerator