成对haversine距离计算

Question

我有两个带 lat 和 long 的数组。我想计算数组中每对纬度和经度与其他每对经度和经度之间的距离。 这是我的两个数组。

lat_array

array([ 0.33356456,  0.33355585,  0.33355585,  0.33401788,  0.33370132,
        0.33370132,  0.33370132,  0.33371075,  0.33371075,  0.33370132,
        0.33370132,  0.33370132,  0.33356488,  0.33356488,  0.33370132,
        0.33370132,  0.33370132,  0.33401788,  0.33362632,  0.33362632,
        0.33364007,  0.33370132,  0.33401788,  0.33401788,  0.33358399,
        0.33358399,  0.33358399,  0.33370132,  0.33370132,  0.33362632,
        0.33370132,  0.33370132,  0.33370132,  0.33370132,  0.33370132,
        0.33356488,  0.33356456,  0.33391071,  0.33370132,  0.33356488,
        0.33356488,  0.33356456,  0.33356456,  0.33356456,  0.33362632,
        0.33364804,  0.3336314 ,  0.33370132,  0.33370132,  0.33370132,
        0.33364034,  0.33359921,  0.33370132,  0.33360397,  0.33348863,
        0.33370132])
long_array

array([ 1.27253229,  1.27249141,  1.27249141,  1.27259085,  1.2724337 ,
        1.2724337 ,  1.2724337 ,  1.27246931,  1.27246931,  1.2724337 ,
        1.2724337 ,  1.2724337 ,  1.27254305,  1.27254305,  1.2724337 ,
        1.2724337 ,  1.2724337 ,  1.27259085,  1.27250461,  1.27250461,
        1.27251211,  1.2724337 ,  1.27259085,  1.27259085,  1.27252134,
        1.27252134,  1.27252134,  1.2724337 ,  1.2724337 ,  1.27250461,
        1.2724337 ,  1.2724337 ,  1.2724337 ,  1.2724337 ,  1.2724337 ,
        1.27254305,  1.27253229,  1.27266808,  1.2724337 ,  1.27254305,
        1.27254305,  1.27253229,  1.27253229,  1.27253229,  1.27250461,
        1.27250534,  1.27250184,  1.2724337 ,  1.2724337 ,  1.2724337 ,
        1.27251339,  1.27223739,  1.2724337 ,  1.2722575 ,  1.27237575,
        1.2724337 ])

转换为弧度后。现在我想要第一对lat和long之间的距离，剩下的lat和long对等等。并想打印对和对应的距离。

这就是我在 python 中所做的。

distance = []
R = 6371.0

for i in range(len(lat_array)):
   for j in (i+1,len(lat_array)):
      dlon = long_array[j]-long_array[i]
      dlat = lat_array[j]-lat_array[i]
      a = sin(dlat / 2)**2 + cos(lat_array[i]) * cos(lat_array[j]) *     
          sin(dlon / 2)**2
      c = 2 * atan2(sqrt(a), sqrt(1 - a))

      distance.append(R * c)

它给了我一个错误IndexError: index 56 is out of bounds for axis 0 with size 56 我在哪里做错了？如果数组很大，如何使计算更快？请帮忙。

Answer 1

由于这是目前 Google 的“成对半正弦距离”的最高结果，我将加两分钱：如果您可以访问 scikit-learn，这个问题可以很快得到解决。查看sklearn.metrics.pairwise_distances 时，您会注意到不支持“haversine”指标，但它在sklearn.neighbors.DistanceMetric 中实现。

这意味着您可以执行以下操作：

from sklearn.neighbors import DistanceMetric

def sklearn_haversine(lat, lon):
    haversine = DistanceMetric.get_metric('haversine')
    latlon = np.hstack((lat[:, np.newaxis], lon[:, np.newaxis]))
    dists = haversine.pairwise(latlon)
    return 6371 * dists

请注意，lat 和 lon 的串联只是必要的，因为它们是单独的数组。如果您将它们作为形状(n_samples, 2) 的组合数组传递，您可以直接在它们上调用haversine.pairwise。此外，仅当您需要以公里为单位的距离时，才需要乘以 6371。例如。如果您只想找到最近的一对点，则无需执行此步骤。

验证：

In [87]: lat = np.array([ 0.33356456,  0.33355585,  0.33355585,  0.33401788,  0.33370132])

In [88]: lng = np.array([ 1.27253229,  1.27249141,  1.27249141,  1.27259085,  1.2724337 ])

In [89]: sklearn_haversine(lat, lng)
Out[89]:
array([[ 0.        ,  0.25227021,  0.25227021,  2.90953323,  1.05422047],
       [ 0.25227021,  0.        ,  0.        ,  3.00383463,  0.98975923],
       [ 0.25227021,  0.        ,  0.        ,  3.00383463,  0.98975923],
       [ 2.90953323,  3.00383463,  3.00383463,  0.        ,  2.2276139 ],
       [ 1.05422047,  0.98975923,  0.98975923,  2.2276139 ,  0.        ]])

性能：

In [91]: lat = np.random.randn(1000)

In [92]: lng = np.random.randn(1000)

In [93]: %timeit original_app(lat,lng)
1 loops, best of 3: 1.46 s per loop

In [94]: %timeit vectorized_app1(lat,lng)
10 loops, best of 3: 86.7 ms per loop

In [95]: %timeit vectorized_app2(lat,lng)
10 loops, best of 3: 75.7 ms per loop

In [96]: %timeit sklearn_haversine(lat,lng)
10 loops, best of 3: 76 ms per loop

总之，您可以用更短更简单的代码以vectorized_app2 的速度获得 Divakar 的vectorized_app1 的输出。

Answer 2

假设lat 和lng 是纬度和经度数组，并且它们的数据以弧度为单位，这是一个基于this other solution 的矢量化解决方案-

# Elementwise differentiations for lattitudes & longitudes
dflat = lat[:,None] - lat
dflng = lng[:,None] - lng

# Finally Calculate haversine using its distance formula
d = np.sin(dflat/2)**2 + np.cos(lat[:,None])*np.cos(lat) * np.sin(dflng/2)**2
hav_dists = 2 * 6371 * np.arcsin(np.sqrt(d))

现在，上述方法将为我们提供所有对的输出，而不管它们的顺序如何。因此，即使距离相同，我们也会为两对 :(point1,point2) 和 (point2,point1) 提供两个距离输出。因此，为了节省内存并希望获得更好的性能，您可以使用 np.triu_indices 创建唯一的配对 ID，并修改前面列出的方法，如下所示 -

# Elementwise differentiations for lattitudes & longitudes, 
# but not repeat for the same paired elements
N = lat.size
idx1,idx2 = np.triu_indices(N,1)
dflat = lat[idx2] - lat[idx1]
dflng = lng[idx2] - lng[idx1]

# Finally Calculate haversine using its distance formula
d = np.sin(dflat/2)**2 + np.cos(lat[idx2])*np.cos(lat[idx1]) * np.sin(dflng/2)**2
hav_dists = 2 * 6371 * np.arcsin(np.sqrt(d))

---

函数定义-

def original_app(lat,lng):
    distance = []
    R = 6371.0
    for i in range(len(lat)):
       for j in range(i+1,len(lat)):
          dlon = lng[j]-lng[i]
          dlat = lat[j]-lat[i]
          a = sin(dlat / 2)**2 + cos(lat[i]) * cos(lat[j]) * sin(dlon / 2)**2
          c = 2 * atan2(sqrt(a), sqrt(1 - a))
          distance.append(R * c)
    return distance

def vectorized_app1(lat,lng):                               
    dflat = lat[:,None] - lat
    dflng = lng[:,None] - lng
    d = np.sin(dflat/2)**2 + np.cos(lat[:,None])*np.cos(lat) * np.sin(dflng/2)**2
    return 2 * 6371 * np.arcsin(np.sqrt(d))

def vectorized_app2(lat,lng):                               
    N = lat.size
    idx1,idx2 = np.triu_indices(N,1)
    dflat = lat[idx2] - lat[idx1]
    dflng = lng[idx2] - lng[idx1]
    d =np.sin(dflat/2)**2+np.cos(lat[idx2])*np.cos(lat[idx1])*np.sin(dflng/2)**2
    return  2 * 6371 * np.arcsin(np.sqrt(d))

验证输出 -

In [78]: lat
Out[78]: array([ 0.33356456,  0.33355585,  0.33355585,  0.33401788,  0.33370132])

In [79]: lng
Out[79]: array([ 1.27253229,  1.27249141,  1.27249141,  1.27259085,  1.2724337 ])

In [80]: original_app(lat,lng)
Out[80]: 
[0.2522702110418014,
 0.2522702110418014,
 2.909533226553249,
 1.0542204712876762,
 0.0,
 3.003834632906676,
 0.9897592295963831,
 3.003834632906676,
 0.9897592295963831,
 2.2276138997714474]

In [81]: vectorized_app1(lat,lng)
Out[81]: 
array([[ 0.        ,  0.25227021,  0.25227021,  2.90953323,  1.05422047],
       [ 0.25227021,  0.        ,  0.        ,  3.00383463,  0.98975923],
       [ 0.25227021,  0.        ,  0.        ,  3.00383463,  0.98975923],
       [ 2.90953323,  3.00383463,  3.00383463,  0.        ,  2.2276139 ],
       [ 1.05422047,  0.98975923,  0.98975923,  2.2276139 ,  0.        ]])

In [82]: vectorized_app2(lat,lng)
Out[82]: 
array([ 0.25227021,  0.25227021,  2.90953323,  1.05422047,  0.        ,
        3.00383463,  0.98975923,  3.00383463,  0.98975923,  2.2276139 ])

运行时测试-

In [83]: lat = np.random.randn(1000)

In [84]: lng = np.random.randn(1000)

In [85]: %timeit original_app(lat,lng)
1 loops, best of 3: 2.11 s per loop

In [86]: %timeit vectorized_app1(lat,lng)
1 loops, best of 3: 263 ms per loop

In [87]: %timeit vectorized_app2(lat,lng)
1 loops, best of 3: 224 ms per loop

因此，就性能而言，vectorized_app2 可能是要走的路！

Answer 3

您的代码中有错字。改变

for j in (i+1,len(lat_array)):

到

for j in range(i+1,len(lat_array)):

否则，您将迭代一个由两个元素 i+1 和 len(lat_array) 组成的元组。第二个导致错误。

Answer 4

scikit-learn 0.21.0（2019-05 发布）中引入的 hasrsine_distances 函数可用于此目的。示例命令：

 % ipython     
Python 3.8.5 (default, Sep  4 2020, 07:30:14) 
Type 'copyright', 'credits' or 'license' for more information
IPython 7.18.1 -- An enhanced Interactive Python. Type '?' for help.

In [1]: 
import numpy as np
lat = np.array([ 0.33356456,  0.33355585,  0.33355585,  0.33401788,  0.33370132])
lon = np.array([ 1.27253229,  1.27249141,  1.27249141,  1.27259085,  1.2724337 ])
position = np.column_stack((lat, lon))
position
Out[1]: 
array([[0.33356456, 1.27253229],
       [0.33355585, 1.27249141],
       [0.33355585, 1.27249141],
       [0.33401788, 1.27259085],
       [0.33370132, 1.2724337 ]])

In [2]: 
from sklearn.metrics.pairwise import haversine_distances
R = 6371.0
D1 = R * haversine_distances(position)
D1
Out[2]: 
array([[0.        , 0.25227021, 0.25227021, 2.90953323, 1.05422047],
       [0.25227021, 0.        , 0.        , 3.00383463, 0.98975923],
       [0.25227021, 0.        , 0.        , 3.00383463, 0.98975923],
       [2.90953323, 3.00383463, 3.00383463, 0.        , 2.2276139 ],
       [1.05422047, 0.98975923, 0.98975923, 2.2276139 , 0.        ]])

参考：-

• https://scikit-learn.org/dev/whats_new/v0.21.html#id16 - 更新日志 进入
• https://scikit-learn.org/dev/whats_new/v0.21.html#version-0-21-0 - 显示发布日期