I want to apply two functions one function on the block diagonal and the second function on the off-diagonal elements in the data frame

Question

df<- data.frame(a=c(1:10), b=c(21:30),c=c(1:10), d=c(14:23),e=c(11:20),f=c(-6:-15),g=c(11:20),h=c(-14:-23),i=c(4:13),j=c(1:10))

In this data frame, I have three block-diagonal matrices which are as shown in the image below

I want to apply two functions, one is the sine function for block diagonal and the second is cosine function for the other elements and generates the same structure of the data frame.

sin(df[1:2,1:2])
sin(df[3:5,3:5])
sin(df[6:10,6:10])
cos(the rest of the elements)

Answer 1

1) outer/arithmetic Create a logical block diagonal matrix indicating whether the current cell is on the block diagonal or not and then use that to take a convex combination of the sin and cos values giving a data.frame as follows:

v <- rep(1:3, c(2, 3, 5))
ind <- outer(v, v, `==`)
ind * sin(df) + (!ind) * cos(df)

2) ifelse Alternately, this gives a matrix result (or use as.matrix on the above). ind is from above.

m <- as.matrix(df)
ifelse(ind, sin(m), cos(m))

3) Matrix::bdiag Another approach is to use bdiag in the Matrix package (which comes with R -- no need to install it).

library(Matrix)

ones <- function(n) matrix(1, n, n)
ind <- bdiag(ones(2), ones(3), ones(5)) == 1

Now proceed as in the last line of (1) or as in (2).