I'm using 7 functions to create dot density maps in Python, Pandas, and GeoPandas. The functions read the US Census blockgroups and create random points that fall within the blockgroup polygon. The end result is a nice dot density map where each point represents 300 people of a certain ethnicity.

For some of the counties, this works totally fine. Here's Denver County Denver county dot density map

But for others I'm hitting list index out of range and I can't figure out why. I'm using the FIPS blockgroup as the index this is what the dataframe ends up looking like.


gen_count_dot_density_map('Yakima County, WA')

Error message:

IndexError                                Traceback (most recent call last)
<ipython-input-25-3174d4f9a7b7> in <module>()
----> 1 gen_count_dot_density_map('Yakima County, WA')

3 frames
/usr/local/lib/python3.7/dist-packages/pandas/core/reshape/reshape.py in stack(frame, level, dropna)
    520         # we concatenate instead.
    521         dtypes = list(frame.dtypes._values)
--> 522         dtype = dtypes[0]
    524         if is_extension_array_dtype(dtype):

IndexError: list index out of range

Here are the functions I'm using.

from urllib.request import urlopen
from zipfile import ZipFile
from io import BytesIO, StringIO
import shapefile
import geopandas as gpd
from shapely.geometry import shape  
import osr
import pandas as pd
import requests
from shapely.geometry import Point
from numpy.random import RandomState, uniform
import numpy as np

def gen_random_points_poly(poly, num_points, seed = None):
    Returns a list of N randomly generated points within a polygon. 
    min_x, min_y, max_x, max_y = poly.bounds
    points = []
    while len(points) < num_points:
        s=RandomState(seed+i) if seed else RandomState(seed)
        random_point = Point([s.uniform(min_x, max_x), s.uniform(min_y, max_y)])
        if random_point.within(poly):
    return points

def gen_points_in_gdf_polys(geometry, values, points_per_value = None, seed = None):
    Take a GeoSeries of Polygons along with a Series of values and returns randomly generated points within
    these polygons. Optionally takes a "points_per_value" integer which indicates the number of points that 
    should be generated for each 1 value.
    if points_per_value:
        new_values = (values/points_per_value).astype(int)
        new_values = values
    new_values = new_values[new_values>0]
    g = gpd.GeoDataFrame(data = {'vals':new_values}, geometry = geometry)
    a = g.apply(lambda row: tuple(gen_random_points_poly(row['geometry'], row['vals'], seed)),1)
    b = gpd.GeoSeries(a.apply(pd.Series).stack(), crs = geometry.crs)
    return b

def zip_shp_to_gdf(zip_file_name):
    Returns a GeoDataFrame from a URL for a zipped Shapefile
    zipfile = ZipFile(BytesIO(urlopen(zip_file_name).read()))
    filenames = [y for y in sorted(zipfile.namelist()) for ending in ['dbf', 'prj', 'shp', 'shx']\
                 if y.endswith(ending)] 
    dbf, prj, shp, shx = [BytesIO(zipfile.read(filename)) for filename in filenames]
    r = shapefile.Reader(shp=shp, shx=shx, dbf=dbf)
    attributes, geometry = [], []
    field_names = [field[0] for field in r.fields[1:]]  
    for row in r.shapeRecords():  
        attributes.append(dict(zip(field_names, row.record)))  
    proj4_string = osr.SpatialReference(prj.read().decode('UTF-8')).ExportToProj4()
    gdf = gpd.GeoDataFrame(data = attributes, geometry = geometry, crs = proj4_string)
    return gdf

def get_census_variables(year, dataset, geography, area, variables, variable_labels = None):
    """Wraps the Census API and returns a DataFrame of Census Data
    year : integer
        Year representing the dataset vintage 
    dataset : string
        the name of the dataset (https://api.census.gov/data.html)
    geography : string
        the census geography
    area : dictionary
        dictionary contains the FIPS codes at each nested geographic level. For example "{'county':'001', 'state':'06'}"
    variables : list
        list of the variables to be extracted
    variable_labels : list
        optional to relabel the variable names. Must be same length as "variables"
    base_url = 'https://api.census.gov/data/{}/acs/{}'.format(year, dataset)
    #define parameters
    get_parameter = ','.join(['NAME'] + variables)
    for_parameter = '{}:*'.format(geography)
    in_paramater = '+'.join([k+':'+v for (k,v) in area.items()])

    parameters = {'get' : get_parameter, 
                  'for' : for_parameter,
                  'in' : in_paramater}
    #make request specifiying url and parameters
    r = requests.get(base_url, params=parameters)
    #read json into pandas dataframe, specifying first row as column names
    data = r.json()
    df=pd.DataFrame(columns = data[0], data = data[1:])
    #identify geography fields - concatenate them into a fips code to be set as index and then delete them
    geo_fields = [x for x in df.columns if x not in ['NAME'] + variables]
    df.index = df[geo_fields].apply(lambda row: ''.join(map(str, row)), 1)
    df.index.name = 'FIPS'
    df = df.drop(geo_fields, 1)
    if variable_labels:
        df = df.rename(columns = dict(zip(variables, variable_labels)))
    #convert data numeric 
    df = df.applymap(lambda x:pd.to_numeric(x, errors='ignore'))
    return df

def gen_count_dot_density_map(county, pts_per_person = 300, 
                              epsg = 2163, seed=10,
                              dot_transparency=0.4, figsize=(12,12), 
                              ax=None, legend=False):
    Wraps previous functions and generates population dot density maps for a specified county by race
    #read in fips to county name relationship file
    fips = pd.read_csv('https://www2.census.gov/geo/docs/reference/codes/files/national_county.txt',
                   header=None, dtype={1:np.object, 2:np.object})
    fips['name']=fips[3]+', '+fips[0]
    #get name from fips if fips specified
    if county.isdigit():
        lookup = fips.set_index('fips')['name']
        county_fips = county
        name = lookup[county_fips]
    #get fips from name if name specified
        lookup = fips.set_index('name')['fips']
        name = county
        county_fips = lookup[name]
    #get geodataframe of block group shapefile
    bgfile_name = 'http://www2.census.gov/geo/tiger/GENZ2015/shp/cb_2015_{}_bg_500k.zip'.format(county_fips[:2])
    bg_geo = zip_shp_to_gdf(bgfile_name)
    #subset to those that are in the county and project it to the CRS
    #specify variable list and variable names for the census api function
    varlist = ['B03002_003E', 
    names = ['White',
             'Two Plus']
    #read in block group level census variables
    dems = get_census_variables(2015, 'acs5', 'block group', 
                                 'state':county_fips[:2]}, varlist, names)
    #Calculate other as sum of those not in the 4 most populated race categories
    dems['Other']=dems[['AI/AN', 'NH/PI','Other_', 'Two Plus']].sum(1)
    #Calculate county boundaries as the union of block groups 
    union = gpd.GeoSeries(bg_geo.unary_union)
    #if axes object is specified, plot to this axis, otherwise create a new one
    if ax:
        union.plot(color='white', figsize=figsize, ax=ax)
        ax = union.plot(color='white', figsize=figsize)
    #set aspect equal and add title if specified
    ax.set(aspect='equal', xticks=[], yticks=[])
    #set title as county name
    ax.set_title(name, size=15)
    #annotate the dot per person ratio
    # ax.annotate("1 dot = {} people".format(pts_per_person), 
                # xy=(.5, .97), xycoords='axes fraction', horizontalalignment='center',
                # fontsize = 12)
    #loop each race category and generate points for each within each block group 
    for field in ['White','Hispanic','Black','Asian','Other']:           
        ps=gpd.GeoDataFrame(gen_points_in_gdf_polys(geometry = bg_geo, values=dems[field],
                             points_per_value = pts_per_person, seed=seed))
    all_points.plot(ax=ax, markersize=2, alpha=dot_transparency, column='field', categorical=True, legend=legend)

    return ax
  • 5
    You've assumed that the list dtypes is not empty. You probably ought to test before appling a radix beyond length.
    – Vince
    Sep 13, 2021 at 23:06

1 Answer 1


This is a pure Python problem (not a geospatial problem) and is due to the value of pts_per_person in the function gen_points_in_gdf_polys(geometry, values, points_per_value = None, seed = None) (300 in your example)

 if points_per_value:
    new_values = (values/points_per_value).astype(int)

In your example, most of the values of dems['White'] (for example) are > 300, so:

values.min(), values.max()
(18, 2704)
new_values = (values/300).astype(int)
new_values = new_values[new_values>0]
new_values.min(), new_values.max()
(1, 9)

But this is not the case with dems['Asian']

values.min(), values.max()
(0, 241)
new_values = (values/300°.astype(int)
new_values = new_values[new_values>0]
new_values.min(), new_values.max()
(nan, nan)

Here all the values are null, and the result is the error indexError: list index out of range

Choosing a smaller value resolves the problem. With pts_per_person = 180 and your script, for example

enter image description here

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