I am trying to find an efficient way to retrieve a list / vector / array of the non-zero upper triangular elements of a sparse matrix in R. For example:
library(igraph)
Gmini <- as.directed(graph.lattice(c(3,5)))
GminiMat <- sparseMatrix(i=get.edgelist(Gmini)[,1],j=get.edgelist(Gmini)[,2],x=1:length(E(Gmini)))
GminiMat
15 x 15 sparse Matrix of class "dgCMatrix"
[1,] . 1 . 2 . . . . . . . . . . .
[2,] 23 . 3 . 4 . . . . . . . . . .
[3,] . 25 . . . 5 . . . . . . . . .
[4,] 24 . . . 6 . 7 . . . . . . . .
[5,] . 26 . 28 . 8 . 9 . . . . . . .
[6,] . . 27 . 30 . . . 10 . . . . . .
[7,] . . . 29 . . . 11 . 12 . . . . .
[8,] . . . . 31 . 33 . 13 . 14 . . . .
[9,] . . . . . 32 . 35 . . . 15 . . .
[10,] . . . . . . 34 . . . 16 . 17 . .
[11,] . . . . . . . 36 . 38 . 18 . 19 .
[12,] . . . . . . . . 37 . 40 . . . 20
[13,] . . . . . . . . . 39 . . . 21 .
[14,] . . . . . . . . . . 41 . 43 . 22
[15,] . . . . . . . . . . . 42 . 44 .
So ideally i would like to make a function getUpper(mat) such that getUpper(GminiMat) would yield the vector of 1:22 (the upper triangular non-zero entries of GminiMat)
Ideally, I need a fairly memory and speed efficient approach since I may need to apply it to large systems (e.g. the matrix could come from a multi-dimensional lattice with a several hundred nodes in each dimension).
There is a method triu in package Matrix that will return the upper triangle while preserving sparseness:
triu(GminiMat)
15 x 15 sparse Matrix of class "dtCMatrix"
[1,] . 1 . 2 . . . . . . . . . . .
[2,] . . 3 . 4 . . . . . . . . . .
[3,] . . . . . 5 . . . . . . . . .
[4,] . . . . 6 . 7 . . . . . . . .
[5,] . . . . . 8 . 9 . . . . . . .
[6,] . . . . . . . . 10 . . . . . .
[7,] . . . . . . . 11 . 12 . . . . .
[8,] . . . . . . . . 13 . 14 . . . .
[9,] . . . . . . . . . . . 15 . . .
[10,] . . . . . . . . . . 16 . 17 . .
[11,] . . . . . . . . . . . 18 . 19 .
[12,] . . . . . . . . . . . . . . 20
[13,] . . . . . . . . . . . . . 21 .
[14,] . . . . . . . . . . . . . . 22
[15,] . . . . . . . . . . . . . . .