Make qr type stable

[andreasnoack]

For now, it requires some type asserts to achieve this. Hopefully, they'll be unnecessary at some point.

[andreasnoack]

As discussed in #11240

[timholy]

LGTM. Since the type of F[:X] depends on the value of X, I don't think there is any way to make this type stable without the asserts (unless we use Val for this, too).

[andreasnoack]

That's right, but we never know what the future will bring to Julia.

[tkelman]

Some of the type asserts are failing on the integer type https://travis-ci.org/JuliaLang/julia/jobs/62418292, and there are some other scary-looking failures that have recently started showing up in a few other builds too...

[daviddelaat]

I'm sure this has been discussed somewhere (and maybe its off-topic here), but do you know why indexing with symbols is used instead of functions to get the factors? I would think that something like qfactor(F), rfactor(F), pivotvector(F), and pivotmatrix(F) looks fine and is easier to implement efficiently.

[andreasnoack]

Initially, we underestimated the importance of type stability in the factorization methods, e.g. we moved from qrpfact to using a keyword argument which has recently changed to using Val to regain type stability. Another problem is that it is not satisfactory to have so many different extractor functions. It is not really generic or dispatchy enough for Julia.

I believe that we'll be able to make the extraction of factors type stable with an approach very similar to what we are doing now. I'm very interested in this and eventually we'll find some type stable solution to this.

[andreasnoack]

@tkelman Thanks for pointing out the integer type error. It was 32 bit related and is now fixed. The other error was unrelated so I'll merge.

[daviddelaat]

Thanks for the explanation Andreas!