LinearAlgebra.normalize(x) should work for scalars

[stevengj]

Currently, this is defined only for arrays, but it seems like we should have

normalize(x::Number) = x / abs(x)

(I just came across this when trying to implement this algorithm for random unitary matrices, which is basically Q * Diagonal(normalize.(diag(R)), but I discovered that normalize didn't work.)

[Seelengrab]

Is this the same as sign(x) for numbers?

[oscardssmith]

it's very similar, but has different behavior for zero.

[Seelengrab]

Does that matter for this case? If I'm reading the paper right, R should be invertible, so no zeros on the main diagonal 🤔

[stevengj]

Yes, in this particular case, you're right that I could have used sign.

However, it still doesn't make sense to me that the normalize function isn't defined for scalars; it seems like it should be defined for any normed vector space.

Indeed, we could just define the fallback:

normalize(x) = x / norm(x)
normalize(x, p) = x / norm(x, p)

(where norm falls back to abs for scalars).

[mikerouleau]

I've been meaning to get more involved and this looks like a good first issue. I should have a PR ready later today.