Square to "diagonal" matrix in R - r

Question

I have a set of vectors, and would like to stack them on top of each other to create diagonal entries to a matrix.
What would be an easy way to create the example_out matrix from c1 and c2?
c1 <- seq(1, 4)
c2 <- seq(5, 8)
example_out <- matrix(c(1,0,0,0,5,2,0,0,0,6,3,0,0,0,7,4,0,0,0,8), nrow=5, byrow=T)
example_out

Answer 1

Create a matrix out of 0s, then fill main diagonal with c1 and sub diagonal with c2.
example_out <- matrix(rep(0, 20), 5, 4)
diag(example_out) <- c1
diag(example_out[-1, ]) <- c2
Yielding
> example_out
[,1] [,2] [,3] [,4]
[1,] 1 0 0 0
[2,] 5 2 0 0
[3,] 0 6 3 0
[4,] 0 0 7 4
[5,] 0 0 0 8
Data
c1 <- seq(1, 4)
c2 <- seq(5, 8)

Answer 2

Another simple approach, augmenting two diagonal matrices with 0 rows and adding them:
rbind(diag(c1), 0) + rbind(0, diag(c2))
# [,1] [,2] [,3] [,4]
# [1,] 1 0 0 0
# [2,] 5 2 0 0
# [3,] 0 6 3 0
# [4,] 0 0 7 4
# [5,] 0 0 0 8

Answer 3

Here is an alternative approach replaceing entries in a numeric vector before casting as matrix
matrix(unlist(sapply(seq_along(c1), function(i)
replace(rep(0, length(c1) + 1), i:(i+1), c(c1[i], c2[i])))),
ncol = length(c1))
# [,1] [,2] [,3] [,4]
#[1,] 1 0 0 0
#[2,] 5 2 0 0
#[3,] 0 6 3 0
#[4,] 0 0 7 4
#[5,] 0 0 0 8
Update
I was curious to see how the different methods compared in terms of performance/runtime. Here is a short microbenchmark analysis using two larger vectors c1 and c2.
set.seed(2017)
c1 <- sample(1000)
c2 <- sample(1000)
library(microbenchmark)
library(Matrix)
res <- microbenchmark(
method_jaySF = {
example_out <- matrix(0, length(c1) + 1, length(c2))
diag(example_out) <- c1
diag(example_out[-1, ]) <- c2
},
method_Roland = {
bandSparse(length(c1) + 1, length(c2), 0:-1, list(c1, c2))
},
method_Onyambu = {
a = matrix(0,length(c1)+1,length(c2))
a[row(a)==col(a)]=c1
a[row(a)==col(a)+1]=c2
},
method_Gregor = {
rbind(diag(c1), 0) + rbind(0, diag(c2))
},
method_Maurits = {
matrix(unlist(sapply(seq_along(c1), function(i)
replace(rep(0, length(c1) + 1), i:(i+1), c(c1[i], c2[i])))),
ncol = length(c1))
}
)
res;
#Unit: microseconds
# expr min lq mean median uq max
# method_jaySF 31894.439 37850.81 58452.41 40560.992 46224.579 208862.631
# method_Roland 940.535 1342.32 1675.29 1457.928 1869.621 8228.287
# method_Onyambu 55033.797 66083.67 124364.44 73143.798 195886.534 274383.132
# method_Gregor 37784.977 44049.87 69918.85 47539.793 53122.162 243774.715
# method_Maurits 14961.924 21378.77 42834.89 23536.966 27270.953 186088.146
autoplot(res)

Answer 4

You should create a sparse matrix. Use the Matrix package:
c1 <- seq(1, 4)
c2 <- seq(5, 8)
library(Matrix)
bandSparse(5, 4, 0:-1, list(c1, c2))
#5 x 4 sparse Matrix of class "dgCMatrix"
#
#[1,] 1 . . .
#[2,] 5 2 . .
#[3,] . 6 3 .
#[4,] . . 7 4
#[5,] . . . 8

Answer 5

a = matrix(0,length(c1)+1,length(c2))
a[row(a)==col(a)]=c1
a[row(a)==col(a)+1]=c2
a
[,1] [,2] [,3] [,4]
[1,] 1 0 0 0
[2,] 5 2 0 0
[3,] 0 6 3 0
[4,] 0 0 7 4
[5,] 0 0 0 8