R:是否有一种简单有效的方法来取回 block 对角矩阵的构建 block 矩阵列表？

Question

我正在寻找一个(内置)函数，它通过以下方式有效地返回 block 对角矩阵的构建 block 列表(而不是遍历插槽以手动获取列表):

#construct bdiag-matrix
library("Matrix")
listElems <- list(matrix(1:4,ncol=2,nrow=2),matrix(5:8,ncol=2,nrow=2))
mat <- bdiag(listElems)

#get back the list
res <- theFunctionImLookingFor(mat)

结果 res 产生构建 block :

[[1]]
      [,1] [,2]
[1,]    1    3
[2,]    2    4

[[2]]
      [,1] [,2]
[1,]    5    7
[2,]    6    8

编辑:关于我的用例，listElems 中的列表元素是方阵和对称矩阵。如果 block 是对角矩阵，theFunctionImLookingFor 应该为每个对角元素返回一个列表元素。

但是，该函数应该能够处理像这样的构建 block 矩阵

       [,1] [,2] [,3]
[1,]    1    1    0
[2,]    1    1    1
[3,]    0    1    1

或

       [,1] [,2] [,3]
[1,]    1    0    1
[2,]    0    1    1
[3,]    1    1    1

即处理不是对角矩阵的 block 中的零。

Answer 1

我希望这对您的所有情况都有效，底部的测试包括一个包含零的 block 。

theFunctionImLookingFor <- function(mat, plot.graph = FALSE) {
   stopifnot(nrow(mat) == ncol(mat))
   x <- mat
   diag(x) <- 1
   edges <- as.matrix(summary(x)[c("i", "j")])
   library(igraph)
   g <- graph.edgelist(edges, directed = FALSE)
   if (plot.graph) plot(g)
   groups <- unique(Map(sort, neighborhood(g, nrow(mat))))
   sub.Mat <- Map(`[`, list(mat), groups, groups, drop = FALSE)
   sub.mat <- Map(as.matrix, sub.Mat)
   return(sub.mat)
}

listElems <- list(matrix(1:4,ncol=2,nrow=2),
                  matrix(5:8,ncol=2,nrow=2),
                  matrix(c(0, 1, 0, 0, 0, 1, 0, 0, 1),ncol=3,nrow=3),
                  matrix(1:1,ncol=1, nrow=1))

mat <- bdiag(listElems)

theFunctionImLookingFor(mat, plot.graph = TRUE)
# [[1]]
#      [,1] [,2]
# [1,]    1    3
# [2,]    2    4

# [[2]]
#      [,1] [,2]
# [1,]    5    7
# [2,]    6    8

# [[3]]
#      [,1] [,2] [,3]
# [1,]    0    0    0
# [2,]    1    0    0
# [3,]    0    1    1

# [[4]]
#      [,1]
# [1,]    1