cond(F) is not implemented for lufact return type

[garrison]

The documentation for lufact claims the returned factorization type implements cond(), but it does not:

julia> cond(lufact([1 0; 0 -1]))
ERROR: MethodError: no method matching cond(::Base.LinAlg.LU{Float64,Array{Float64,2}})

A similar issue exists in base/sparse/umfpack.jl.

I believe these methods should be implemented (otherwise the doc should be changed).

[garrison]

Actually, this seems to be implemented; I'm not sure why https://github.com/JuliaLang/julia/blob/8b2ee7126cc293893aae9acceb102fa766ccc6bf/base/linalg/lu.jl#L312-L314 is not being called.

EDIT: OK, the real reason is that this call does not have the default p=2, as the documentation suggests. The following works:

cond(lufact([1 0; 0 -1]), 2)

I would also expect cond(A, 2) to give the same result as cond(lufact(A), 2), but it does not:

julia> cond([1 0.2; 0 -1], 2)
1.220997512422418

julia> cond(lufact([1 0.2; 0 -1]), 2)
1.1786533995862283

Let me know if I am missing something here.

[andreasnoack]

I think the documentation is right since cond is implemented. I'm not sure how the table in the documentation could be improved and I don't think it makes sense to implement the p=2 version for LU since such a method would have to recreate the original matrix. Right now, p=2 is wrong and returns p=Inf. Do you think the table can be improved?

[garrison]

Right now, p=2 is wrong and returns p=Inf.

To clarify: I think p=2 is wrong (not sure what it returns, but it is not the same result as p=Inf). On the other hand, passing p=Inf does indeed give the correct result.

Do you think the table can be improved?

I think the table is fine as it is, but I think it would make sense to add a docstring for a second form of cond(), which takes an LU object as the first argument and which does not list a default p for the second argument. (The first form is here.)

[andreasnoack]

On the other hand, passing p=Inf does indeed give the correct result.

This line is pretty broken. It asks LAPACK for the Inf norm condition number estimate but it passes the two norm of the input. This is why 1, 2, and Inf give different results. We should error if p != 1 && p != Inf.

but I think it would make sense to add a docstring for a second form

Sounds like the right solution.

[garrison]

And actually, I think inv() should be added to the table as well. It is mentioned in the docstrings for bkfact, cholfact, and eigfact. But lufact, ldltfact, and qrfact currently neglect to mention it.

[andreasnoack]

I decided to take a different approach. See JuliaLang/julia#21577. @garrison It would be great if you could open a PR with the doc changes.