QR Decomposition

[jwaldrop107]

NWX is currently stepping out of TA to eigen to handle QR decomposition, and it would be preferable to not have to do that. @wavefunction91 says he should be able to hook it up with the other linalg pieces.

[wavefunction91]

@evaleev I'll try to add this before the weekend

[wavefunction91]

@evaleev After briefly discussing @jwaldrop107's needs, it seems that NWX only needs explicit Q formation, i.e. not manipulation of the reflectors individually. So I have a few questions regarding what you'd like to see in TA

1. Do you want API's to manipulate block householder reflectors in addition to explicit formation of Q? It gets kind of fuzzy since TA doesn't really treat compact matrices straight forwardly (reflectors are generally stored SLT with the UT being the R + an extra array for the reflector coefficients). This might take some work is all I'm saying - and we could probably add APIs for e.g. QR LLSQ, etc without exposing that kind of functionality.
2. Formation of Q via Householder QR is not the most scalable procedure (mostly BLAS-2 with some BLAS-3 sprinkled in, communication heavy), would you be OK with me adding a cholesky_qr API? That would reduce communication and enable a BLAS-3-only implementation + would limit the number of times we need to convert between TA <-> block cyclic formats. Unless you're trying to do rank-revealing QR, Cholesky QR is more than stable

[wavefunction91]

Closed by #316