CODEWITHSUNDEEP
pythonloopsmathhaversine
Joehat
Joehat

Reputation: 1129

Python: Computing the distance between two point coordinates using two columns

I would like to compute the distance between two coordinates. I know I can compute the haversine distance between two points. However, I was wondering if there is an easier way of doing it instead of creating a loop using the formula iterating over the entire columns (also getting errors in the loop).

Here's some data for the example

# Random values for the duration from one point to another
random_values = random.sample(range(2,20), 8)
random_values

# Creating arrays for the coordinates
lat_coor = [11.923855, 11.923862, 11.923851, 11.923847, 11.923865, 11.923841, 11.923860, 11.923846]
lon_coor = [57.723843, 57.723831, 57.723839, 57.723831, 57.723827, 57.723831, 57.723835, 57.723827]

df = pd.DataFrame(
    {'duration': random_values,
     'latitude': lat_coor,
     'longitude': lon_coor
    })

df

    duration    latitude    longitude
0   5           11.923855   57.723843
1   2           11.923862   57.723831
2   10          11.923851   57.723839
3   19         11.923847    57.723831
4   16         11.923865    57.723827
5   4          11.923841    57.723831
6   13         11.923860    57.723835
7   3          11.923846    57.723827

To compute the distance this is what I've attempted:

# Looping over each row to compute the Haversine distance between two points
# Earth's radius (in m)
R = 6373.0 * 1000

lat = df["latitude"]
lon = df["longitude"]


for i in lat:
    lat1 = lat[i]
    lat2 = lat[i+1]
    
    for j in lon:
        lon1 = lon[i]
        lon2 = lon[i+1]
        
        dlon = lon2 - lon1
        dlat = lat2 - lat1
        
        # Haversine formula
        a = math.sin(dlat / 2)**2 + math.cos(lat1) * math.cos(lat2) * math.sin(dlon / 2)**2
        c = 2 * math.atan2(math.sqrt(a), math.sqrt(1 - a))
        distance = R * c
        
        print(distance) # in m

However, this is the error I get: enter image description here

The two points to compute the distance should be taken from the same column.

first distance value:

11.923855 57.723843 (point1/observation1)

11.923862 57.723831 (point2/observation2)

second distance value:

11.923862 57.723831 (point1/observation2)

11.923851 57.723839(point2/observation3)

third distance value:

11.923851 57.723839(point1/observation3)

11.923847 57.723831 (point1/observation4)

... (and so on)

Upvotes: 0

Views: 2343

Answers (3)

Hammurabi
Hammurabi

Reputation: 1179

You are confusing the index versus the values themselves, so you are getting a key error because there is no lat[i] (e.g., lat[11.923855]) in your example. After fixing i to be the index, your code would go beyond the last row of lat and lon with your [i+1]. Since you want to compare each row to the previous row, how about starting at index 1 and looking back by 1, then you won't go out of range. This edited version of your code does not crash:

for i in range(1, len(lat)):
    lat1 = lat[i - 1]
    lat2 = lat[i]

    for j in range(1, len(lon)):
        lon1 = lon[i - 1]
        lon2 = lon[i]

        dlon = lon2 - lon1
        dlat = lat2 - lat1

        # Haversine formula
        a = math.sin(dlat / 2) ** 2 + math.cos(lat1) * math.cos(lat2) * math.sin(dlon / 2) ** 2
        c = 2 * math.atan2(math.sqrt(a), math.sqrt(1 - a))
        distance = R * c

        print(distance)  # in m

Upvotes: 1

mozway
mozway

Reputation: 262294

OK, first you can create a dataframe that combine each measurement with the previous one:

df2 = pd.concat([df.add_suffix('_pre').shift(), df], axis=1)
df2

This outputs:

    duration_pre    latitude_pre    longitude_pre   duration    latitude    longitude
0   NaN     NaN     NaN     5   11.923855   57.723843
1   5.0     11.923855   57.723843   2   11.923862   57.723831
2   2.0     11.923862   57.723831   10  11.923851   57.723839
…

Then create a haversine function and apply it to the rows:

def haversine(lat1, lon1, lat2, lon2):
    import math
    R = 6373.0 * 1000
    dlon = lon2 - lon1
    dlat = lat2 - lat1
    a = math.sin(dlat / 2)**2 + math.cos(lat1) * math.cos(lat2) * math.sin(dlon / 2)**2
    return R *2 * math.atan2(math.sqrt(a), math.sqrt(1 - a))

df2.apply(lambda x: haversine(x['latitude_pre'], x['longitude_pre'], x['latitude'], x['longitude']), axis=1)

which computes for each row the distance with the previous row (first one is thus NaN).

0           NaN
1     75.754755
2     81.120210
3     48.123604
…

And, if you want to include a new column in the original dataframe in one line:

df['distance'] = pd.concat([df.add_suffix('_pre').shift(), df], axis=1).apply(lambda x: haversine(x['latitude_pre'], x['longitude_pre'], x['latitude'], x['longitude']), axis=1)

Output:

  duration  latitude    longitude   distance
0   5   11.923855   57.723843   NaN
1   2   11.923862   57.723831   75.754755
2   10  11.923851   57.723839   81.120210
3   19  11.923847   57.723831   48.123604
4   16  11.923865   57.723827   116.515304
5   4   11.923841   57.723831   154.307571
6   13  11.923860   57.723835   122.794838
7   3   11.923846   57.723827   98.115312

Upvotes: 1

Hagen
Hagen

Reputation: 56

I understood that you want to get the pairwise haversine distance between all points in your df. Here's how this could be done:

Be careful when using this approach with a lot of points as it generates a lot of columns quickly

Setup

import random 
random_values = random.sample(range(2,20), 8)
random_values

# Creating arrays for the coordinates
lat_coor = [11.923855, 11.923862, 11.923851, 11.923847, 11.923865, 11.923841, 11.923860, 11.923846]
lon_coor = [57.723843, 57.723831, 57.723839, 57.723831, 57.723827, 57.723831, 57.723835, 57.723827]

df = pd.DataFrame(
    {'duration': random_values,
     'latitude': lat_coor,
     'longitude': lon_coor
    })

Get radians

import math
df['lat_rad'] = df.latitude.apply(math.radians)
df['long_rad'] = df.latitude.apply(math.radians)

Calculate pairwise distances

from sklearn.metrics.pairwise import haversine_distances

for idx_from, from_point in df.iterrows():
    for idx_to, to_point in df.iterrows():
            column_name = f"Distance_to_point_{idx_from}"
            haversine_matrix = haversine_distances([[from_point.lat_rad, from_point.long_rad], [to_point.lat_rad, to_point.long_rad]])
            point_distance = haversine_matrix[0][1] * 6371000/1000
            df.loc[idx_to, column_name] = point_distance
df

    duration    latitude    longitude   lat_rad long_rad    Distance_to_point_0 Distance_to_point_1 Distance_to_point_2 Distance_to_point_3 Distance_to_point_4 Distance_to_point_5 Distance_to_point_6 Distance_to_point_7
0   3   11.923855   57.723843   0.20811052928038845 0.20811052928038845 0.0 0.0010889626934743966   0.0006222644021223135   0.001244528808978787    0.0015556609862946524   0.002177925427923575    0.000777830496776312    0.0014000949117650525
1   13  11.923862   57.723831   0.2081106514534361  0.2081106514534361  0.0010889626934743966   0.0 0.0017112270955967099   0.002333491502453183    0.0004666982928202561   0.00326688812139797 0.00031113219669808446  0.0024890576052394482
2   14  11.923851   57.723839   0.2081104594672184  0.2081104594672184  0.0006222644021223135   0.0017112270955967099   0.0 0.0006222644068564735   0.002177925388416966    0.0015556610258012616   0.0014000948988986254   0.0007778305096427389
3   4   11.923847   57.723831   0.20811038965404832 0.20811038965404832 0.001244528808978787    0.002333491502453183    0.0006222644068564735   0.0 0.0028001897952734385   0.0009333966189447881   0.002022359305755099    0.0001555661027862654
4   5   11.923865   57.723827   0.20811070381331365 0.20811070381331365 0.0015556609862946524   0.0004666982928202561   0.002177925388416966    0.0028001897952734385   0.0 0.003733586414218225    0.0007778304895183407   0.002955755898059704
5   7   11.923841   57.723831   0.20811028493429318 0.20811028493429318 0.002177925427923575    0.00326688812139797 0.0015556610258012616   0.0009333966189447881   0.003733586414218225    0.0 0.002955755924699886    0.0007778305161585227
6   9   11.92386    57.723835   0.20811061654685106 0.20811061654685106 0.000777830496776312    0.00031113219669808446  0.0014000948988986254   0.002022359305755099    0.0007778304895183407   0.002955755924699886    0.0 0.002177925408541364
7   8   11.923846   57.723827   0.20811037220075576 0.20811037220075576 0.0014000949117650525   0.0024890576052394482   0.0007778305096427389   0.0001555661027862654   0.002955755898059704    0.0007778305161585227   0.002177925408541364    0.0

Upvotes: 1

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