Given only the following vector:
v <- c(2, 4, 6, 8)
The following matrix is desired in which the row-wise directions are alternately right-to-left and left-to-right (by traversing the matrix from top to bottom) and the anti-diagonal is set to zero.
8 6 4 2 0
2 4 6 0 8
8 6 0 4 2
2 0 4 6 8
0 8 6 4 2
How this can be accomplished efficiently in R?
How about this?
v <- c(2, 4, 6, 8)
First create a matrix with alternating directions of v. Because matrices are filled column-wise we have to transpose in the end.
m <- matrix(0, length(v), length(v) + 1)
m[, c(FALSE, TRUE)] <- rev(v)
m[, c(TRUE, FALSE)] <- v
m <- t(m)
Now create the zero anti-diagonal by filling the upper and lower triangles and then reversing the columns:
m1 <- matrix(0, length(v) + 1, length(v) + 1)
m1[upper.tri(m1)] <- m[upper.tri(m, TRUE)]
m1[lower.tri(m1)] <- m[lower.tri(m)]
m1[, rev(seq_len(ncol(m1)))]
# [,1] [,2] [,3] [,4] [,5]
#[1,] 8 6 4 2 0
#[2,] 2 4 6 0 8
#[3,] 8 6 0 4 2
#[4,] 2 0 4 6 8
#[5,] 0 8 6 4 2
I expect this to be an efficient solution for vectors of a larger size. For small vectors loop-based solutions are possibly faster.