1 function envelope = envelope(A)
2 ## Compute the envelope of the matrix ``A``. The envelope of a matrix
3 ## is defined as the set of indices,
4 ##
5 ## E = { (i,j) : i < j, A(k,j) != 0 for some k <= i }
6 ##
7 if (!issymmetric(A) && !is_upper_triangular(A))
8 ## The envelope of a matrix is only defined for U-T or symmetric
9 ## matrices.
10 envelope = {NA};
11 return;
12 end
14 ## Start with an empty result, and append to it as we find
15 ## satisfactory indices.
16 envelope = {};
18 for j = [ 1 : columns(A) ]
19 ## Everything below the first non-zero element in a column will be
20 ## part of the envelope. Since we're moving from top to bottom, we
21 ## can simply set a flag indicating that we've found the first
22 ## non-zero element. Thereafter, everything we encounter should be
23 ## added to the envelope.
24 found_nonzero = false;
26 for i = [ 1 : j-1 ]
27 if (A(i,j) != 0)
28 found_nonzero = true;
29 end
31 if (found_nonzero)
32 envelope{end+1} = [i,j];
33 end
34 end
36 end
38 end