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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def intersect_index_quadrats(gdf, geometry, quadrat_width=0.05, min_num=3, buffer_amount=1e-9):
 """ Intersect points with a polygon, using an r-tree spatial index and cutting the polygon up into smaller sub-polygons for r-tree acceleration. Parameters gdf : GeoDataFrame the set of points to intersect geometry : shapely Polygon or MultiPolygon the geometry to intersect with the points quadrat_width : numeric the linear length (in degrees) of the quadrats with which to cut up the geometry (default = 0.05, approx 4km at NYC's latitude) min_num : int the minimum number of linear quadrat lines (e.g., min_num=3 would produce a quadrat grid of 4 squares) buffer_amount : numeric buffer the quadrat grid lines by quadrat_width times buffer_amount Returns ------- GeoDataFrame """


    # create an empty dataframe to append matches to
    points_within_geometry = pd.DataFrame()

    # cut the geometry into chunks for r-tree spatial index intersecting
    multipoly = quadrat_cut_geometry(geometry, quadrat_width=quadrat_width, buffer_amount=buffer_amount, min_num=min_num)

    # create an r-tree spatial index for the nodes (ie, points)
    start_time = time.time()
    sindex = gdf['geometry'].sindex
    log('Created r-tree spatial index for {:,} points in {:,.2f} seconds'.format(len(gdf), time.time()-start_time))

    # loop through each chunk of the geometry to find approximate and then
    # precisely intersecting points
    start_time = time.time()
    for poly in multipoly:

        # buffer by the tiny distance to account for any space lost in the
        # quadrat cutting, otherwise may miss point(s) that lay directly on
        # quadrat line
        buffer_size = quadrat_width * buffer_amount
        poly = poly.buffer(buffer_size).buffer(0)

        # find approximate matches with r-tree, then precise matches from those
        # approximate ones
        if poly.is_valid and poly.area > 0:
            possible_matches_index = list(sindex.intersection(poly.bounds))
            possible_matches = gdf.iloc[possible_matches_index]
            precise_matches = possible_matches[possible_matches.intersects(poly)]
            points_within_geometry = points_within_geometry.append(precise_matches)

    if len(points_within_geometry) > 0:
        # drop duplicate points, if buffered poly caused an overlap on point(s)
        # that lay directly on a quadrat line
        points_within_geometry = points_within_geometry.drop_duplicates(subset='node')
    else:
        # after simplifying the graph, and given the requested network type,
        # there are no nodes inside the polygon - can't create graph from that
        # so throw error
        raise Exception('There are no nodes within the requested geometry')

    log('Identified {:,} nodes inside polygon in {:,.2f} seconds'.format(len(points_within_geometry), time.time()-start_time))
    return points_within_geometry