Question

我需要一种有效的方法来计算一系列点之间的距离矩阵。问题是，你只能从点“我”到达。指出＆＃39; k＆＃39;通过所有点＆＃39; j＆＃39;之间。例如，想象一个拥有5个海滩的岛屿，您想要计算沿海岸线所有海滩之间的距离，因为您无法穿越岛屿（包括两个方向：顺时针或逆时针）。

以下是一些示例数据。 （注意：您需要安装包＆＃39; geosphere＆＃39;才能使用＆＃39; distm＆＃39;功能，它计算沿地球表面的GPS坐标之间的距离）

library("geosphere")

longitude = c(-119.003, -119.067, -119.121, -119.089, -119.003)
latitude = c(33.503, 33.539, 33.485, 33.413, 33.440)
long.lat.mat = as.matrix(cbind(longitude, latitude))

# Use "distm" to calculate Euclidean (straight-line) distances between sites (in km)
euclid.dist.mat = distm(long.lat.mat) / 1000

# Create an empty matrix of alongshore distances (from "rows" to "columns")
alongshore.dist.mat = matrix(ncol=dim(long.lat.mat)[1], nrow=dim(long.lat.mat)[1], data=NA)   

# Diagonal is zero. Adjacent sites are the same as Euclidean distance
diag(alongshore.dist.mat) = 0   
diag(alongshore.dist.mat[,-1]) = diag(euclid.dist.mat[,-1])
alongshore.dist.mat[1,dim(long.lat.mat)[1]] = euclid.dist.mat[1,dim(long.lat.mat)[1]]
alongshore.dist.mat[lower.tri(alongshore.dist.mat)] = t(alongshore.dist.mat)[lower.tri(t(alongshore.dist.mat))]

# > alongshore.dist.mat
#           [,1]      [,2]      [,3]      [,4]      [,5]
# [1,] 0.0000000 7.1650632        NA        NA 7.0131279
# [2,] 7.1650632 0.0000000 7.8265783        NA        NA
# [3,]        NA 7.8265783 0.0000000 8.5483605        NA
# [4,]        NA        NA 8.5483605 0.0000000 8.5365807
# [5,] 7.0131279        NA        NA 8.5365807 0.0000000

现在，如何填补剩余的细胞？举个例子：

alongshore.dist.mat[1,3] = 7.1650632 + 7.8265783 = 14.991642

...代表网站1 - ＆gt;网站2 - ＆gt; 3.相比之下：

alongshore.dist.mat[3,1] = 8.5483605 + 8.5365807 + 7.0131279 = 24.098069

...代表网站3 - ＆gt;网站4 - ＆gt;网站5 - ＆gt;网站1.

我怀疑＆＃34; cumsum＆＃34;功能可以有效使用，但不确定如何设置它。我希望有一个避免for循环的解决方案，因为我实际上正在处理包含几十个点的数据。

Answer 1

您可以先构建两个位置之间所有边的矩阵：

dists <- expand.grid(x=1:5, y=1:5)
dists$weight <- alongshore.dist.mat[as.matrix(dists)]
dists <- subset(dists, x != y & !is.na(weight))
dists
#    x y   weight
# 2  2 1 7.165063
# 5  5 1 7.013128
# 6  1 2 7.165063
# 8  3 2 7.826578
# 12 2 3 7.826578
# 14 4 3 8.548360
# 18 3 4 8.548360
# 20 5 4 8.536581
# 21 1 5 7.013128
# 24 4 5 8.536581

现在，您可以构建图形并计算所有对最短路径：

library(igraph)
g <- graph.data.frame(dists, vertices=data.frame(x=1:5))
shortest.paths(g)
#           1         2         3         4         5
# 1  0.000000  7.165063 14.991642 15.549709  7.013128
# 2  7.165063  0.000000  7.826578 16.374939 14.178191
# 3 14.991642  7.826578  0.000000  8.548360 17.084941
# 4 15.549709 16.374939  8.548360  0.000000  8.536581
# 5  7.013128 14.178191 17.084941  8.536581  0.000000

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