How to extract the upper/lower triangular matrix values except the diagonal?

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1

Consider the following matrix:

julia> c = rand(2, 2)
2×2 Matrix{Float64}:
 0.0443768  0.515352
 0.531426   0.967584

Expected output:

1-element Vector{Float64}:
0.531426

I can do:

julia> using LinearAlgebra: LowerTriangular

julia> LowerTriangular(c)
2×2 LowerTriangular{Float64, Matrix{Float64}}:
 0.0443768   ⋅
 0.531426   0.967584

Collecting the previous lower triangular includes the diagonal of the matrix too. I want to omit the diagonal. How to do it?

2

You can use the tril function:

julia> c = rand(4,4)
4×4 Matrix{Float64}:
 0.508891  0.659778  0.639252  0.569137
 0.212345  0.834971  0.233612  0.564073
 0.812287  0.760213  0.224285  0.466787
 0.872574  0.516204  0.701075  0.359622

julia> LowerTriangular(tril(c, -1))
4×4 LowerTriangular{Float64, Matrix{Float64}}:
 0.0        ⋅         ⋅         ⋅ 
 0.212345  0.0        ⋅         ⋅ 
 0.812287  0.760213  0.0        ⋅ 
 0.872574  0.516204  0.701075  0.0

It’s not clear how useful the LowerTriangular type is here, however, rather than simply tril(c, -1) stored as a Matrix. The main utility of the LowerTriangular type is to support fast methods for solving Lx =b lower-triangular systems, but with a zero diagonal the problem is singular so those methods aren’t applicable.

(Another application of LowerTriangular is to have an in-place lower-triangular view of a matrix where you are storing something else in the upper triangle, as sometimes happens with in-place matrix factorizations, but that’s not the case if you use tril.)

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3

Isn’t tril(c, -1) enough?

Thank you so much!

4

Yes, depends on what matrix type you want to use. See also the comments at the bottom of my revised post (I was editing it while you responded).

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5

If you wanted the vector of entries, maybe this will do:

julia> A = rand(3,3)
3×3 Matrix{Float64}:
 0.212689  0.222497  0.34268
 0.376084  0.004906  0.706805
 0.395929  0.334694  0.883166

julia> [v for (k,v) in pairs(A) if k[1]>k[2]]
3-element Vector{Float64}:
 0.37608410776838963
 0.3959294893831178
 0.33469399665884414
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