这是一个很好的例子。我做了 4x4 所以我们可以很容易地看到它,但它都是可以调整的n
。它也是完全矢量化的,因此应该具有良好的速度。
n = 4
mat = matrix(1:n^2, nrow = n)
mat.pad = rbind(NA, cbind(NA, mat, NA), NA)
对于填充矩阵,邻居只是 n × n 子矩阵,四处移动。使用罗盘方向作为标签:
ind = 2:(n + 1) # row/column indices of the "middle"
neigh = rbind(N = as.vector(mat.pad[ind - 1, ind ]),
NE = as.vector(mat.pad[ind - 1, ind + 1]),
E = as.vector(mat.pad[ind , ind + 1]),
SE = as.vector(mat.pad[ind + 1, ind + 1]),
S = as.vector(mat.pad[ind + 1, ind ]),
SW = as.vector(mat.pad[ind + 1, ind - 1]),
W = as.vector(mat.pad[ind , ind - 1]),
NW = as.vector(mat.pad[ind - 1, ind - 1]))
mat
# [,1] [,2] [,3] [,4]
# [1,] 1 5 9 13
# [2,] 2 6 10 14
# [3,] 3 7 11 15
# [4,] 4 8 12 16
neigh[, 1:6]
# [,1] [,2] [,3] [,4] [,5] [,6]
# N NA 1 2 3 NA 5
# NE NA 5 6 7 NA 9
# E 5 6 7 8 9 10
# SE 6 7 8 NA 10 11
# S 2 3 4 NA 6 7
# SW NA NA NA NA 2 3
# W NA NA NA NA 1 2
# NW NA NA NA NA NA 1
所以你可以看到第一个元素mat[1,1]
,从北开始,顺时针方向,邻居是第一列neigh
。下一个元素是mat[2,1]
,依此类推mat
。 (您还可以与 @mrip 的答案进行比较,看到我们的列具有相同的元素,只是顺序不同。)
标杆管理
小矩阵
mat = matrix(1:16, nrow = 4)
mbm(gregor(mat), mrip(mat), marat(mat), u20650(mat), times = 100)
# Unit: microseconds
# expr min lq mean median uq max neval cld
# gregor(mat) 25.054 30.0345 34.04585 31.9960 34.7130 61.879 100 a
# mrip(mat) 420.167 443.7120 482.44136 466.1995 483.4045 1820.121 100 c
# marat(mat) 746.462 784.0410 812.10347 808.1880 832.4870 911.570 100 d
# u20650(mat) 186.843 206.4620 220.07242 217.3285 230.7605 269.850 100 b
在更大的矩阵上,我不得不取出 user20650 的函数,因为它试图分配 232.8 Gb 向量,并且在等待大约 10 分钟后我还取出了 Marat 的答案。
mat = matrix(1:500^2, nrow = 500)
mbm(gregor(mat), mrip(mat), times = 100)
# Unit: milliseconds
# expr min lq mean median uq max neval cld
# gregor(mat) 19.583951 21.127883 30.674130 21.656866 22.433661 127.2279 100 b
# mrip(mat) 2.213725 2.368421 8.957648 2.758102 2.958677 104.9983 100 a
所以看起来在任何时间很重要的情况下,@mrip 的解决方案都是迄今为止最快的。
使用的函数:
gregor = function(mat) {
n = nrow(mat)
mat.pad = rbind(NA, cbind(NA, mat, NA), NA)
ind = 2:(n + 1) # row/column indices of the "middle"
neigh = rbind(N = as.vector(mat.pad[ind - 1, ind ]),
NE = as.vector(mat.pad[ind - 1, ind + 1]),
E = as.vector(mat.pad[ind , ind + 1]),
SE = as.vector(mat.pad[ind + 1, ind + 1]),
S = as.vector(mat.pad[ind + 1, ind ]),
SW = as.vector(mat.pad[ind + 1, ind - 1]),
W = as.vector(mat.pad[ind , ind - 1]),
NW = as.vector(mat.pad[ind - 1, ind - 1]))
return(neigh)
}
mrip = function(mat) {
m2<-cbind(NA,rbind(NA,mat,NA),NA)
addresses <- expand.grid(x = 1:4, y = 1:4)
ret <- c()
for(i in 1:-1)
for(j in 1:-1)
if(i!=0 || j !=0)
ret <- rbind(ret,m2[addresses$x+i+1+nrow(m2)*(addresses$y+j)])
return(ret)
}
get.neighbors <- function(rw, z, mat) {
# Convert to absolute addresses
z2 <- t(z + unlist(rw))
# Choose those with indices within mat
b.good <- rowSums(z2 > 0)==2 & z2[,1] <= nrow(mat) & z2[,2] <= ncol(mat)
mat[z2[b.good,]]
}
marat = function(mat) {
n.row = n.col = nrow(mat)
addresses <- expand.grid(x = 1:n.row, y = 1:n.col)
# Relative addresses
z <- rbind(c(-1,0,1,-1,1,-1,0,1), c(-1,-1,-1,0,0,1,1,1))
apply(addresses, 1,
get.neighbors, z = z, mat = mat) # Returns a list with neighbors
}
u20650 = function(mat) {
w <- which(mat==mat, arr.ind=TRUE)
d <- as.matrix(dist(w, "maximum", diag=TRUE, upper=TRUE))
# extract neighbouring values for each element
# extract where max distance is one
a <- apply(d, 1, function(i) mat[i == 1] )
names(a) <- mat
return(a)
}