def get_axes_ratio(ax):
    """Return height / width ratio of the given Axes object.
    
    The ratio is calculated in 'display coordinate',
    defined in matplotlib document on transformation.
    Thus, the calculated ratio is what one would feels when the Axes
    is displayed to the her/him.
    """
    ax_bbox_points_in_fig_coord = ax.get_position().get_points()
    ax_bbox_points_in_display_coord = [
            ax.figure.transFigure.transform(point) for point in ax_bbox_points_in_fig_coord ]
    lower_left_coord, upper_right_coord = ax_bbox_points_in_display_coord
    ax_bbox_dimension_in_display_coord = upper_right_coord - lower_left_coord
    width, height = ax_bbox_dimension_in_display_coord
    ratio = height / width
    return ratio