def compute(self):
        """Perform the smoothing operations."""
        self._compute_window_size()
        smooth = []
        residual = []

        x, y = self.x, self.y

        # step through x and y data with a window window_size wide.
        self._update_values_in_window()
        self._update_mean_in_window()
        self._update_variance_in_window()
        for i, (xi, yi) in enumerate(zip(x, y)):
            if ((i - self._neighbors_on_each_side) > 0.0 and
                    (i + self._neighbors_on_each_side) < len(x)):
                self._advance_window()
            smooth_here = self._compute_smooth_during_construction(xi)
            residual_here = self._compute_cross_validated_residual_here(xi, yi, smooth_here)
            smooth.append(smooth_here)
            residual.append(residual_here)

        self._store_unsorted_results(smooth, residual)
Perform the smoothing operations.