Selecting specific elements from a matrix all at once

Indexing can be done with 2 column matrices. After converting those row and column numbers to a valid R object (rather than Matlab-style expressions):

> idxs <- gsub("\\]",")", gsub("\\[", "c(",  "[1,2], [2,3], [3,4], [4,5] ,[5,6]") )
# I edited the string value that idxs returned:
> midx <- rbind( c(1,2), c(2,3), c(3,4), c(4,5) ,c(5,6) )
> mat <-  matrix(scan(), nrow=6)  
1:  0.000000  3.772139  6.367721 8.978718 12.197210 13.401126
7:   3.772139  0.000000  3.755554 5.935946  9.592700 11.664533
13:   6.367721  3.755554  0.000000 5.999409  9.324764 11.991269
19:   8.978718  5.935946  5.999409 0.000000  3.810169  6.762802
25:  12.197210  9.592700  9.324764 3.810169  0.000000  3.796884
31:  13.401126 11.664533 11.991269 6.762802  3.796884  0.000000
37: 
Read 36 items
> mat[midx]
[1] 3.772139 3.755554 5.999409 3.810169 3.796884

If your goal were to index the super-diagonal that could be accomplished more generally:

> mat[col(mat)==row(mat)+1]
[1] 3.772139 3.755554 5.999409 3.810169 3.796884

A similar solution to that posted above, but one that deals with the situation of having a vector for the rows and a vector for the columns (which was my question when I came upon this thread) is as follows:

> rows <- c(1,2,3,4,5)
> cols <- c(2,3,4,5,6)
> call <- cbind(rows,cols)
> 
> mat[call]
[1] 3.772139 3.755554 5.999409 3.810169 3.796884

A solution to your specific situation would be to select the sub-matrix and use the diag function:

R> diag(x[-ncol(x),-1])
[1] 3.772139 3.755554 5.999409 3.810169 3.796884