距离倒数python

### 实现距离倒数计算

在 Python 中实现距离倒数计算主要依赖于先计算两点之间的欧几里得距离或其他形式的距离，之后取该距离的倒数。对于两个点 \(P_1\) 和 \(P_2\) 的欧几里得距离可以表示为：

\[d(P_1,P_2)=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\]

其对应的倒数则简单地写作 \(\frac{1}{d(P_1,P_2)}\)。

下面给出一段基于上述公式的代码来说明如何具体操作这一过程[^3]：

import numpy as np

def euclidean_distance(point_a, point_b):
    """Calculate the Euclidean distance between two points."""
    return np.sqrt(np.sum((point_a - point_b)**2))

def inverse_euclidean_distance(point_a, point_b):
    """Calculate the inverse of the Euclidean distance between two points.
       If the points are identical (distance is zero), returns a large number to avoid division by zero."""
    dist = euclidean_distance(point_a, point_b)
    if dist == 0:
        # Avoid division by zero; set to infinity or another suitable value
        return float('inf')
    else:
        return 1 / dist

# Example usage with random data points
points = np.random.rand(5, 2)  # Generate five 2D points randomly
for i in range(len(points)):
    for j in range(i+1, len(points)):
        inv_dist = inverse_euclidean_distance(points[i], points[j])
        print(f"Inverse distance between point {i} and point {j}: {inv_dist}")

这段程序首先定义了一个函数 `euclidean_distance` 来计算两给定点间的欧氏距离；接着定义了另一个名为 `inverse_euclidean_distance` 函数用来返回这两个点之间距离的倒数。当遇到相同的位置（即零距离）时，为了避免除以零错误，这里选择了返回无穷大作为处理方式。最后部分展示了如何利用这些函数对一组随机生成的数据点进行成对的距离倒数运算并打印结果。