Doing simple operations with itertools combinatorics?

Question

I have a python dataset that has the following structure:

cluster  pts   lon   lat

0        5      45    24
1        6      47    23
2        10     45    20

As you can see, I have a column that refers to a cluster, the number of points within a cluster, the representative latitude of the cluster and the representative longitude of the cluster. In the whole dataframe I have 140 clusters.

Now I would like to calculate for each cluster the following operation by means of a combinatorial:

 ℎ ( , )=− + / ( , )

where i refers to a cluster and j to another.
where n refers to the number of pts

On the one hand it does the sum of the points between cluster i and cluster j, and in the denominator it calculates by means of haversine the distance between the two clusters taking into account their representative coordinates.

I’ve started by coming up with a code that uses itertools, but I have problems to continue. Any idea?

from itertools import combinations

for c in combinations(df['cluster'],2):
    sum_pts=
    distance=
    weight=-(sum_pts/distance)
    print(c,weight)

Asked By: Stackoverflow Stackoverflow

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Source

Answer 1

As you mentioned, to do the combinations, you can use itertools.
To calculate the distance you can use geopy.distance.distance. Refer to the documentation for details: https://geopy.readthedocs.io/en/stable/#module-geopy.distance

This should work:

from itertools import combinations
from geopy.distance import distance

for p1, p2 in combinations(df['cluster'], 2):
    sum_pts = df['pts'][p1] + df['pts'][p2]
# distance in km
    dist = distance(df.loc[p1, ['lat', 'lon']], df.loc[p2, ['lat', 'lon']]).km
    weight = -sum_pts/dist
    print ((p1, p2), weight)

Edit: for a case when clusters don’t necessarily correspond to index

for c1, c2 in combinations(df['cluster'], 2):
    p1, p2 = df[df['cluster'] == c1].iloc[0], df[df['cluster'] == c2].iloc[0] 
    sum_pts = p1['pts'] + p2['pts']
    dist = distance((p1['lat'], p1['lon']), (p2['lat'], p2['lon'])).km
    weight = -sum_pts/dist
    print ((c1, c2), weight)

Output:

(0, 1) -0.04733881547464973
(0, 2) -0.033865977446857085
(1, 2) -0.04086856230889897

Answered By: D.Manasreh

Answer 2

If you care about performance you may want to use merge and vectorized operations.

import numpy as np
import pandas as pd


def haversine_distance(lat1, lon1, lat2, lon2):
    R = 6372800  # Earth radius in meters
    phi1, phi2 = np.radians(lat1), np.radians(lat2)
    dphi = np.radians(lat2 - lat1)
    dlambda = np.radians(lon2 - lon1)

    a = np.sin(dphi / 2) ** 2 + np.cos(phi1) * np.cos(phi2) * np.sin(dlambda / 2) ** 2

    return 2 * R * np.arctan2(np.sqrt(a), np.sqrt(1 - a))


df = pd.DataFrame({
    'cluster': [0, 1, 2],
    'pts': [5, 6, 10],
    'lat': [45, 47, 45],
    'lon': [24, 23, 20],
})

df = pd.merge(df, df, suffixes=('_1', '_2'), how="cross")
df = df[df['cluster_1'] != df['cluster_2']]
df["weight"] = -df['pts_1'] + df['pts_2'] / haversine_distance(df['lat_1'], df['lon_1'], df['lat_2'], df['lon_2'])

Answered By: Dimitrius

Doing simple operations with itertools combinatorics?

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