R 用偏移量i将矩阵拆分为大小为n的块(矢量化方法)
我想将大小为R 用偏移量i将矩阵拆分为大小为n的块(矢量化方法),r,matrix,vectorization,R,Matrix,Vectorization,我想将大小为kxl的矩阵拆分为大小为nxn的块,考虑一组o(就像Mathematica的函数那样) 例如,给定一个矩阵a类似 A <- matrix(seq(1:16), nrow = 4, ncol = 4) [,1] [,2] [,3] [,4] [1,] 1 5 9 13 [2,] 2 6 10 14 [3,] 3 7 11 15 [4,] 4 8 12 16 如果offset等于2或3,
kxl
的矩阵拆分为大小为nxn
的块,考虑一组o
(就像Mathematica的函数那样)
例如,给定一个矩阵a
类似
A <- matrix(seq(1:16), nrow = 4, ncol = 4)
[,1] [,2] [,3] [,4]
[1,] 1 5 9 13
[2,] 2 6 10 14
[3,] 3 7 11 15
[4,] 4 8 12 16
如果offset等于2或3,那么本例的输出应该只是我从中得到的子矩阵
A[1:3, 1:3]
如何将其矢量化?可能有一种更优雅的方法。下面是通过编写一个模拟mathematica
Partition
函数的myPartition
函数来实现的。首先使用Map
沿行轴和列轴构建可能的索引,其中使用seq
考虑offset
,然后使用cross2
frompurrr
构建子集索引的所有可能组合的列表。最后使用lappy
对矩阵进行子集,并返回子集矩阵列表
偏移量1
、2
和3
的测试结果如下所示,其表现似乎与预期相符:
library(purrr)
ind <- function(k, n, o) Map(`:`, seq(1, k-n+1, by = o), seq(n, k, by = o))
# this is a little helper function that generates subset index according to dimension of the
# matrix, the first sequence construct the starting point of the subset index with an interval
# of o which is the offset while the second sequence construct the ending point of the subset index
# use Map to construct vector from start to end which in OP's case will be 1:3 and 2:4.
myPartition <- function(mat, n, o) {
lapply(cross2(ind(nrow(mat),n,o), ind(ncol(mat),n,o)), function(i) mat[i[[1]], i[[2]]])
}
# This is basically an lapply. we use cross2 to construct combinations of all subset index
# which will be 1:3 and 1:3, 1:3 and 2:4, 2:4 and 1:3 and 2:4 and 2:4 in OP's case. Use lapply
# to loop through the index and subset.
# Testing case for offset = 1
myPartition(A, 3, 1)
# [[1]]
# [,1] [,2] [,3]
# [1,] 1 5 9
# [2,] 2 6 10
# [3,] 3 7 11
# [[2]]
# [,1] [,2] [,3]
# [1,] 2 6 10
# [2,] 3 7 11
# [3,] 4 8 12
# [[3]]
# [,1] [,2] [,3]
# [1,] 5 9 13
# [2,] 6 10 14
# [3,] 7 11 15
# [[4]]
# [,1] [,2] [,3]
# [1,] 6 10 14
# [2,] 7 11 15
# [3,] 8 12 16
# Testing case for offset = 2
myPartition(A, 3, 2)
# [[1]]
# [,1] [,2] [,3]
# [1,] 1 5 9
# [2,] 2 6 10
# [3,] 3 7 11
# Testing case for offset = 3
myPartition(A, 3, 3)
# [[1]]
# [,1] [,2] [,3]
# [1,] 1 5 9
# [2,] 2 6 10
# [3,] 3 7 11
库(purrr)
ind如何使用base
R,其思想是在考虑偏移量的同时,生成大小为n*n
的所有可能窗口(即风
)。然后在矩阵A
中打印winds
元素的所有可能排列(即perms
)。它适用于大小为k*l
的任何A
A <- matrix(seq(1:16), nrow = 4, ncol = 4)
c <- ncol(A); r <- nrow(A)
offset <- 1; size <- 3
sq <- seq(1, max(r,c), offset)
winds <- t(sapply(sq, function(x) c(x,(x+size-1))))
winds <- winds[winds[,2]<=max(r, c),] # check the range
if (is.vector(winds)) dim(winds) <- c(1,2) # vector to matrix
perms <- expand.grid(list(1:nrow(winds), 1:nrow(winds)))
out=apply(perms, 1, function(x) {
a11 <- winds[x[1],1];a12 <- winds[x[1],2];a21 <- winds[x[2],1];a22 <- winds[x[2],2]
if (ifelse(r<c, a12<=r, a22<=c)) { # check the range
cat("A[", a11, ":", a12, ", ", a21, ":", a22, "]", sep="", "\n")
print(A[a11:a12, a21:a22])
}
})
# A[1:3, 1:3]
# [,1] [,2] [,3]
# [1,] 1 5 9
# [2,] 2 6 10
# [3,] 3 7 11
# A[2:4, 1:3]
# [,1] [,2] [,3]
# [1,] 2 6 10
# [2,] 3 7 11
# [3,] 4 8 12
# A[1:3, 2:4]
# [,1] [,2] [,3]
# [1,] 5 9 13
# [2,] 6 10 14
# [3,] 7 11 15
# A[2:4, 2:4]
# [,1] [,2] [,3]
# [1,] 6 10 14
# [2,] 7 11 15
# [3,] 8 12 16
对于offset=2
和size=2
:
# A[1:2, 1:2]
# [,1] [,2]
# [1,] 1 5
# [2,] 2 6
# A[3:4, 1:2]
# [,1] [,2]
# [1,] 3 7
# [2,] 4 8
# A[1:2, 3:4]
# [,1] [,2]
# [1,] 9 13
# [2,] 10 14
# A[3:4, 3:4]
# [,1] [,2]
# [1,] 11 15
# [2,] 12 16
您可以使用负索引,尽管这可能是特定于大小写的:apply(combn(c(-1,-1,-4,-4),2),2,function(x){list(A[x[1],x[2]])
如果offset==2
,我们应该有什么?@Psidom,一个两行两列的偏移量。在上述示例的4 x 4矩阵中,偏移量2和偏移量3都给出了子矩阵A[1:3,1:3]
,这可能是类似的-特别是如果删除了对阵列部分的简化
# A[1:3, 1:3]
# [,1] [,2] [,3]
# [1,] 1 5 9
# [2,] 2 6 10
# [3,] 3 7 11
# A[1:2, 1:2]
# [,1] [,2]
# [1,] 1 5
# [2,] 2 6
# A[3:4, 1:2]
# [,1] [,2]
# [1,] 3 7
# [2,] 4 8
# A[1:2, 3:4]
# [,1] [,2]
# [1,] 9 13
# [2,] 10 14
# A[3:4, 3:4]
# [,1] [,2]
# [1,] 11 15
# [2,] 12 16