valeriepieris

Find valeriepieris circles. There are the smallest circles containing at least a fraction f of the data. See the paper for much more details on how this works and what you can do with a valeriepieris circle.

The code expects 2d-numpy arrays from e.g. SEDAC.

Basic use

import numpy as np
input_data = np.loadtxt("gpw_v4_population_count_rev11_2020_1_deg.asc", skiprows=6 )
input_data[ input_data < 0] = 0

Then call

from valeriepieris import valeriepieris
data_bounds = [ -90,90, -180,180 ] ##[lowest lat, highest lat, lowest lon, highest lon]
target_fracs = [0.25, 0.5, 1]
rmin, smin, best_latlon, data, new_bounds  = valeriepieris(input_data,  data_bounds, target_fracs)		

This computes the centre and radius for all the target fractions

for i,f in enumerate(target_fracs):
	print("At f={}, radius={}, population={}, centre={}".format( f, rmin[i], smin[i], best_latlon[i] ) )

gives

At f=0.25, radius=1880.446017450536, population=1997830287.9875035, centre=[(25.5, 88.5)]
At f=0.5, radius=3376.532684670633, population=3985134876.8947124, centre=[(28.5, 100.5)]
At f=1, radius=14979.863821630814, population=7969444594.980903, centre=[(75.5, -112.5)]

note that each centre is a list, usually of one element, but for very small f there can be multiple centres.

Focussing on a specific area

europe_bounds = [ 34.1,80, -25,34.9 ] 
target_fracs = [0.5]
rmin, smin, best_latlon, europe_data, europe_data_bounds  = valeriepieris(input_data,  data_bounds, 0.5, target_bounds=europe_bounds)		

for i,f in enumerate(target_fracs):
  print("At f={}, radius={}, population={}, centre={}".format( f, rmin[i], smin[i], best_latlon[i] ) )
print("data in ", europe_data_bounds, "has shape", europe_data.shape)

At f=0.5, radius=946.0320718882176, population=371822374.10794944, centre=[(49.5, 9.5)]
data in  [34.1, 80, -25, 34.9] has shape (47, 61)

If the target_bounds argument is given, only data within that area will be considered. The data that was used in the calculation and its boundary (snapped to the input grid) is returned.

Focussing the search

If you think you know where the centre is, or you want the smallest circle containing a fraction f of the data, centered within a certain area do the following

data_bounds = [ -90,90, -180,180 ] ##[lowest lat, highest lat, lowest lon, highest lon]
target_fracs = [0.5]
search_bounds = [ 24,50, -125, -66 ] #~continental US
rmin, smin, best_latlon, data, new_bounds  = valeriepieris(input_data,  data_bounds, target_fracs, search_bounds=search_bounds)		

for i,f in enumerate(target_fracs):
	print("At f={}, radius={}, population={}, centre={}".format( f, rmin[i], smin[i], best_latlon[i] ) )

At f=0.5, radius=10344.885492078058, population=3987443544.209256, centre=[(50.5, -66.5)]

Plotting the circles

Remember the earth is round, so don't just draw a circle on a flat map! See test.py for code to make the plot at the top