Add a fast method for diag of Cholesky matrices

[dev10110]

Normally diag(C::Cholesky) throws an error, and I was forced to do diag(Array(C)).

But its faster to just compute the diagonal elements of the matrix directly, so I thought I would contribute this code.

[longemen3000]

is the docstring necessary? i would say that it isn't. otherwise, seems pretty good

[dev10110]

Does anyone know why the tests are failing? It seems to be failing for unrelated reasons

https://buildkite.com/julialang/julia-master/builds/34771#018e51df-687f-4c40-b2b2-a44e7ab4b249

[jishnub]

You can ignore this failure.

[jishnub]

Should tr be defined as well if diag is defined? Perhaps there could be a generic fallback tr(A) = sum(diag(A))?

[dev10110]

Actually, it seems its already defined in

julia/stdlib/LinearAlgebra/src/generic.jl

Lines 1021 to 1025 in 4ee1022

	function tr(A::AbstractMatrix)
	checksquare(A)
	sum(diag(A))
	end
	tr(x::Number) = x

Do you think it helps to define it the way I have done it?

[dev10110]

Can the reviewers check if this is ready?

[jishnub]

The tr method seems to be defined for AbstractMatrix types, but a Cholesky would be a Factorization, and not an AbstractMatrix. We may probably just relax the type signature of the tr method to

-function tr(A::AbstractMatrix) 
+function tr(A) 

so that any type that defines diag would get tr for free.

[dkarrasch]

@dev10110 Would you be willing and able to incorporate the comments? Afterwards, this nice contribution would be ready to go.