有效计算两个数据集之间的成对haversine距离 - NumPy / Python

Question

我想计算经纬度之间的地理距离。

我已经检查过这个线程Vectorizing Haversine distance calculation in Python 但是当我将它用于两组不同的坐标时，我得到了一个错误。

df1 的大小可以以百万计，如果有任何其他方法可以在更短的时间内计算出准确的地理距离，那将非常有帮助。

length1 = 1000
d1 = np.random.uniform(-90, 90, length1)
d2 = np.random.uniform(-180, 180, length1)
length2 = 100
d3 = np.random.uniform(-90, 90, length2)
d4 = np.random.uniform(-180, 180, length2)
coords = tuple(zip(d1, d2))
df1 = pd.DataFrame({'coordinates':coords})
coords = tuple(zip(d3, d4))
df2 = pd.DataFrame({'coordinates':coords})

def get_diff(df1, df2):
    data1 = np.array(df1['coordinates'].tolist())
    data2 = np.array(df2['coordinates'].tolist())
    lat1 = data1[:,0]                     
    lng1 = data1[:,1]
    lat2 = data2[:,0]                     
    lng2 = data2[:,1]
    #print(lat1.shape)
    #print(lng1.shape)
    #print(lat2.shape)
    #print(lng2.shape)
    diff_lat = lat1[:,None] - lat2

    diff_lng = lng1[:,None] - lng2
    #print(diff_lat.shape)
    #print(diff_lng.shape)
    d = np.sin(diff_lat/2)**2 + np.cos(lat1[:,None])*np.cos(lat1) * np.sin(diff_lng/2)**2
    return 2 * 6371 * np.arcsin(np.sqrt(d))

get_diff(df1, df2)

ValueError                                Traceback (most recent call last)
<ipython-input-58-df06c7cff72c> in <module>
----> 1 get_diff(df1, df2)

<ipython-input-57-9bd8f10189e6> in get_diff(df1, df2)
     26     print(diff_lat.shape)
     27     print(diff_lng.shape)
---> 28     d = np.sin(diff_lat/2)**2 + np.cos(lat1[:,None])*np.cos(lat1) * np.sin(diff_lng/2)**2
     29     return 2 * 6371 * np.arcsin(np.sqrt(d))

ValueError: operands could not be broadcast together with shapes (1000,1000) (1000,100) 

Answer 1

成对半正弦距离

这是基于this post 的broadcasting 的矢量化方式-

def convert_to_arrays(df1, df2):
    d1 = np.array(df1['coordinates'].tolist())
    d2 = np.array(df2['coordinates'].tolist())
    return d1,d2

def broadcasting_based_lng_lat(data1, data2):
    # data1, data2 are the data arrays with 2 cols and they hold
    # lat., lng. values in those cols respectively
    data1 = np.deg2rad(data1)                     
    data2 = np.deg2rad(data2)                     

    lat1 = data1[:,0]                     
    lng1 = data1[:,1]         

    lat2 = data2[:,0]                     
    lng2 = data2[:,1]         

    diff_lat = lat1[:,None] - lat2
    diff_lng = lng1[:,None] - lng2
    d = np.sin(diff_lat/2)**2 + np.cos(lat1[:,None])*np.cos(lat2) * np.sin(diff_lng/2)**2
    return 2 * 6371 * np.arcsin(np.sqrt(d))

因此，要解决您的情况以获得所有成对的haversine距离，它将是 -

broadcasting_based_lng_lat(*convert_to_arrays(df1,df2))

---

元素的半正弦距离

对于两个数据之间的元素级正弦距离计算，例如每个数据在两列中保存纬度和经度，或者每个包含两个元素的列表，我们将跳过对2D 的一些扩展并最终得到类似这-

def broadcasting_based_lng_lat_elementwise(data1, data2):
    # data1, data2 are the data arrays with 2 cols and they hold
    # lat., lng. values in those cols respectively
    data1 = np.deg2rad(data1)                     
    data2 = np.deg2rad(data2)                     

    lat1 = data1[:,0]                     
    lng1 = data1[:,1]         

    lat2 = data2[:,0]                     
    lng2 = data2[:,1]         

    diff_lat = lat1 - lat2
    diff_lng = lng1 - lng2
    d = np.sin(diff_lat/2)**2 + np.cos(lat1)*np.cos(lat2) * np.sin(diff_lng/2)**2
    return 2 * 6371 * np.arcsin(np.sqrt(d))

使用数据框在两列中保存两个数据的示例运行 -

In [42]: np.random.seed(0)
    ...: a = np.random.randint(10,100,(5,2)).tolist()
    ...: b = np.random.randint(10,100,(5,2)).tolist()
    ...: df = pd.DataFrame({'A':a,'B':b})

In [43]: df
Out[43]: 
          A         B
0  [54, 57]  [80, 98]
1  [74, 77]  [98, 22]
2  [77, 19]  [68, 75]
3  [93, 31]  [49, 97]
4  [46, 97]  [56, 98]

In [44]: from haversine import haversine

In [45]: [haversine(i,j) for (i,j) in zip(df.A,df.B)]
Out[45]: 
[3235.9659882513424,
 2399.6124657290075,
 2012.0851666001824,
 4702.8069773315865,
 1114.1193334220534]

In [46]: broadcasting_based_lng_lat_elementwise(np.vstack(df.A), np.vstack(df.B))
Out[46]: 
array([3235.96151855, 2399.60915125, 2012.08238739, 4702.80048155,
       1114.11779454])

这些细微的差别主要是因为haversine library 假设6371.0088 为地球半径，而我们在这里将其视为6371。

Answer 2

使用简单的print 语句来显示方程的参数。 sin 表达式中的一些操作长度不同——底层的broadcast 操作（类似于zip 的矢量化等效项）需要相同的长度。