void fit()
        {

            std::cerr << "\nbefore the fit, thickness is set to be " << thickness << "\n";

            assert( ug_size );
            assert( ar_dim );
            assert( column_index < ar_dim );
            assert( std::abs(std::real(thickness)) < 1.0e-10 );
            assert( std::imag(thickness) > 1.0e-10 );
            assert( diag_matrix.col() == ar_dim );
            assert( diag_matrix.row() == intensity_matrix.row() );
            assert( intensity_matrix.col() == ar_dim );
            assert( initial_ug.row() == ug_size );
            assert( initial_ug.col() == 1 );
            assert( ar.row() == ar.col() );
            assert( ar_dim == ar.row() );
            assert( progress_ratio >= value_type{0} );
            assert( progress_ratio <= value_type{1} );
            assert( alpha );
            assert( beta );
            assert( gamma );

            new_residual = iterate( initial_ug, new_ug );

            matrix_type second_ug{ initial_ug };

            size_type current_iteration = 0;

            matrix_vector_type  vm;
            vector_type         vr;

            vm.push_back( new_ug );
            vr.push_back( new_residual );

            value_type best_residual_so_far = new_residual;

            while ( true )
            {
                value_type const second_residual = iterate( new_ug, second_ug );

                bool break_flag = false;

                //??
                if ( best_residual_so_far > max_iteration * second_residual ) break_flag = true;

                best_residual_so_far = std::min( second_residual, best_residual_so_far );

                if( ++current_iteration  > max_iteration ) break_flag = true;

                new_ug.swap( second_ug );
                new_residual = second_residual;

                vm.push_back( new_ug );
                vr.push_back( new_residual );

                if ( break_flag ) break;
            }

            size_type const elite_index = std::distance( vr.begin(), std::min_element( vr.begin(), vr.end() ) );
            std::copy( vm[elite_index].begin(), vm[elite_index].end(), new_ug.begin() );
            
            //std::cout << "\ncurrent elite residual is " << vr[elite_index] << ", at iteration " << current_iteration <<  std::endl;
        }