Fast Haversine Approximation (Python/Pandas)

Question

Each row in a Pandas dataframe contains lat/lng coordinates of 2 points. Using the Python code below, calculating the distances between these 2 points for many (millions) of rows takes a very long time!

Considering that the 2 points are under 50 miles apart and accuracy is not very important, is it possible to make the calculation faster?

from math import radians, cos, sin, asin, sqrt
def haversine(lon1, lat1, lon2, lat2):
    """
    Calculate the great circle distance between two points 
    on the earth (specified in decimal degrees)
    """
    # convert decimal degrees to radians 
    lon1, lat1, lon2, lat2 = map(radians, [lon1, lat1, lon2, lat2])
    # haversine formula 
    dlon = lon2 - lon1 
    dlat = lat2 - lat1 
    a = sin(dlat/2)**2 + cos(lat1) * cos(lat2) * sin(dlon/2)**2
    c = 2 * asin(sqrt(a)) 
    km = 6367 * c
    return km


for index, row in df.iterrows():
    df.loc[index, 'distance'] = haversine(row['a_longitude'], row['a_latitude'], row['b_longitude'], row['b_latitude'])

Answer 1

Here is a vectorized numpy version of the same function:

import numpy as np

def haversine_np(lon1, lat1, lon2, lat2):
    """
    Calculate the great circle distance between two points
    on the earth (specified in decimal degrees)

    All args must be of equal length.    

    """
    lon1, lat1, lon2, lat2 = map(np.radians, [lon1, lat1, lon2, lat2])

    dlon = lon2 - lon1
    dlat = lat2 - lat1

    a = np.sin(dlat/2.0)**2 + np.cos(lat1) * np.cos(lat2) * np.sin(dlon/2.0)**2

    c = 2 * np.arcsin(np.sqrt(a))
    km = 6367 * c
    return km

The inputs are all arrays of values, and it should be able to do millions of points instantly. The requirement is that the inputs are ndarrays but the columns of your pandas table will work.

For example, with randomly generated values:

>>> import numpy as np
>>> import pandas
>>> lon1, lon2, lat1, lat2 = np.random.randn(4, 1000000)
>>> df = pandas.DataFrame(data={'lon1':lon1,'lon2':lon2,'lat1':lat1,'lat2':lat2})
>>> km = haversine_np(df['lon1'],df['lat1'],df['lon2'],df['lat2'])

Or if you want to create another column:

>>> df['distance'] = haversine_np(df['lon1'],df['lat1'],df['lon2'],df['lat2'])

Looping through arrays of data is very slow in python. Numpy provides functions that operate on entire arrays of data, which lets you avoid looping and drastically improve performance.

This is an example of vectorization.