Isn't it very unintuitive that `cholesky()` stores data in the *upper* triangular part?

A cholesky factor for a symmetric matrix A is usually described as a lower triangular matrix L such that A = LL'. But in Julia, the actual numerical value of L is stored in the upper triangular portion of cholesky(A).factors, that is, it is transposed.


This makes it awkward to actually access L. For example, how do I write an efficient half-vectorization routine? It feels like I need to throw around a bunch of transposes and UpperTriangular calls, and even then it’s still not clear how to access data in column major form.

You can ask for cholesky(A).L. More generally, Cholesky supports storing its factors either way — see the uplo field.


Thank you, but cholesky(A).L seems to be copying data internally, which is something I want to avoid.

I now see the uplo field, but have no idea how to actually change that. For example,

using LinearAlgebra
x = randn(5, 5);
sigma = x'*x;
L = cholesky(Symmetric(sigma));
L.uplo # returns 'U'

I guess L.uplo == 'U' means the data is actually stored in UpperTriangular(L.factors), but the documentation does not mention how to create a Cholesky type with L.uplo == 'L'.

The cholesky.jl file just seems a bit too complicated for me to just manually call the constructor of Cholesky <: Factorization directly.

julia> C = cholesky(Hermitian([2 1; 1 2], :L))
Cholesky{Float64, Matrix{Float64}}
L factor:
2×2 LowerTriangular{Float64, Matrix{Float64}}:
 1.41421    ⋅ 
 0.707107  1.22474

julia> C.uplo
'L': ASCII/Unicode U+004C (category Lu: Letter, uppercase)