How to create non-square block diagonal matrices?-CodePudding

I want to expedite my code and, therefore, I am trying to avoid for loop. Also, I want to use the fact that the inverse of BD matrices is the inverse of each block. I am just trying to create a BD matrix.

Consider the following r code

x = matrix(1:12, 4)

# Now, I want each of the repeated x to be in a block diagonal matrix
# The final result should look like the following

res = matrix(c(1,2,0,0,
               5,6,0,0,
               9,10,0,0,
               0,0,3,4,
               0,0,7,8,
               0,0,11,12), ncol = 6)

I was suggested using the split function, but it seems that it drops a row and messes up the elements' order.

I can create a sparse identity matrix and extract each block then combine them together; however, the main goal is to expedite my code performance. Thus, a one-shot built-in optimized function is preferred.

The example I put here is for a square matrix, yet what I am dealing with is usually the number of rows is much larger than the number of columns.

CodePudding user response：

We can use bdiag from Matrix. Note that the Matrix package comes with R and does not have to be installed, just loaded with a library statement. Try any of these:

library(Matrix)

# 1
as.matrix(bdiag(x[1:2,], x[3:4, ]))

# 2
as.matrix(bdiag(lapply(split(as.data.frame(x), rep(1:2, each = 2)), as.matrix)))

# 3
x |>
 as.data.frame() |>
 split(rep(1:2, each = 2)) |>
 lapply(as.matrix) |>
 bdiag() |>
 as.matrix()

CodePudding user response：

Successively setting a part of the matrix to zero and cbind.

Map(\(x, y) {m[-(x*y), ] <- 0; m}, list(1:(nrow(m)/2)), c(1, -1)) |> do.call(what=cbind)
#      [,1] [,2] [,3] [,4] [,5] [,6]
# [1,]    1    5    9    0    0    0
# [2,]    2    6   10    0    0    0
# [3,]    0    0    0    3    7   11
# [4,]    0    0    0    4    8   12