python – 沿坐标列表给出的路径向量化沿着距离计算
作者:互联网
我有一个坐标列表,可以使用haversine distance指标计算所有点之间的距离矩阵.
坐标是一个numpy.array形状(n,2)的(纬度,经度)对:
[[ 16.34576887 -107.90942116]
[ 12.49474931 -107.76030036]
[ 27.79461514 -107.98607881]
...
[ 12.90258404 -107.96786569]
[ -6.29109889 -107.88681145]
[ -2.68531605 -107.72796034]]
我也可以沿着坐标序列隐含的路径提取距离,如下所示:
coordinates = np.deg2rad(coordinates)
lat, lng = coordinates[:, 0], coordinates[:, 1]
diff_lat = lat[:, None] - lat
diff_lng = lng[:, None] - lng
d = np.sin(diff_lat / 2) ** 2 + np.cos(lat[:, None]) * np.cos(lat) * np.sin(diff_lng / 2) ** 2
dist_matrix = 2 * 6371 * np.arcsin(np.sqrt(d))
np.diagonal(dist_matrix, offset=1)
[ 428.51472359 1701.42935402 1849.52714339 12707.47743385
13723.9087041 4521.8250695 2134.258953 401.33113696
4571.69119707 73.82631307 6078.48898641 9870.17140175
...
2109.57319898 12959.56540448 16680.64546196 3050.96912506
3419.95053226 4209.71641445 9467.85523888 2805.65191129
4120.18701177]
我想只计算距离向量而不是整个矩阵,然后选择相关的对角线.
解决方法:
这是一种可以在不创建大矩阵的情况下对该计算进行矢量化的方法. coslat是纬度的余弦数组,coslat [: – 1] * coslat [1:]是Haversine公式中表达式cos(φ1)cos(φ2)的矢量化版本.
from __future__ import division, print_function
import numpy as np
def hav(theta):
return np.sin(theta/2)**2
coords = [[ 16.34576887, -107.90942116],
[ 12.49474931, -107.76030036],
[ 27.79461514, -107.98607881],
[ 12.90258404, -107.96786569],
[ -6.29109889, -107.88681145],
[ -2.68531605, -107.72796034]]
r = 6371
coordinates = np.deg2rad(coords)
lat = coordinates[:, 0]
lng = coordinates[:, 1]
coslat = np.cos(lat)
t = hav(np.diff(lat)) + coslat[:-1]*coslat[1:]*hav(np.diff(lng))
d = 2*r*np.arcsin(np.sqrt(t))
print(d)
输出:
[ 428.51472353 1701.42935412 1655.91938575 2134.25895299 401.33113696]
标签:python,vectorization,distance,numpy,haversine 来源: https://codeday.me/bug/20190611/1220815.html