如何在Pandas中生成城市间欧氏距离交叉表

To generate the desired Euclidean distance cross table from your city coordinate data, follow these straightforward steps:

1. Set Up the Initial DataFrame #

First, create a Pandas DataFrame using your city longitude and latitude values, with city names as the index for easy labeling later:

import pandas as pd

# Create the coordinate DataFrame
city_data = {
    'City': ['A', 'B', 'C'],
    'Longitude': [2, 5, 8],
    'Latitude': [2, 6, 10]
}
df = pd.DataFrame(city_data).set_index('City')

2. Calculate Pairwise Euclidean Distances #

The Euclidean distance between two points ((x_1, y_1)) and ((x_2, y_2)) is defined by this formula:
[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} ]

You can compute the full distance matrix using either of these methods:

Method 1: Use SciPy's Built-in Distance Function #

This is the simplest approach, leveraging SciPy's optimized distance_matrix function:

from scipy.spatial import distance_matrix

# Compute the distance matrix and format as a DataFrame
distance_table = pd.DataFrame(
    distance_matrix(df.values, df.values),
    index=df.index,
    columns=df.index
).astype(int)  # Convert to integer to match your expected output

print(distance_table)

Method 2: Manual Formula Implementation #

If you want to directly apply the Euclidean formula without external libraries:

# Extract coordinates as a numpy array
coords = df.to_numpy()

# Calculate pairwise distances using the Euclidean formula
pairwise_distances = ((coords[:, None] - coords) ** 2).sum(axis=2) ** 0.5

# Convert to labeled DataFrame
distance_table = pd.DataFrame(pairwise_distances, index=df.index, columns=df.index).astype(int)

print(distance_table)

3. Final Output #

Both methods will produce your desired cross table:

A  B   C
City          
A     0  5  10
B     5  0   5
C    10  5   0

The .astype(int) step is optional but ensures integer values, which aligns with your example's whole-number distances.

内容的提问来源于stack exchange，提问作者Nabih Bawazir