New larft branches - #1399
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jprhyne wants to merge 5 commits into
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… the character flag parsing, and added error messages for unimplemented cases. TODO: add LVL2 and failing tests
Codecov Report❌ Patch coverage is
Additional details and impacted files@@ Coverage Diff @@
## master #1399 +/- ##
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- Coverage 69.36% 69.33% -0.03%
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Files 6122 6122
Lines 486337 486647 +310
Branches 23268 23268
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+ Hits 337330 337426 +96
- Misses 148569 148783 +214
Partials 438 438
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Description
As discussed in PR #1373 this is the proposed changes to just larft. I propose adding computing the conjugate transpose of the T factor associated with the LQ and RQ factorizations. (I also took another look at the documentation and fixed the mistakes I made from #1373. Thanks all!)
The key difference between the larft implementation in this PR and #1373 is that I am no longer using larft_ut as the terminating case and thus need to add the new branches to the level 2 implementation.
The current implementation requires us to apply the conjugate transpose of this T factor, so we are effectively always doing I - VT**H V. This allows for a more obvious connection between (QR,LQ) and (QL,RQ), but prevents us from using the space the R or L matrix as a workspace to hold T. This becomes a problem for an algorithm I want to submit to LAPACK where we compute a panel factorization as follows:
where we store V and T where Q will be on output. I have a write-up associated with this algorithm I made for my Master's project that I can add if further justification is needed.
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