@nanosoldier runbenchmarks("linalg"; vs=":master")

In a manual 1000x1000 test, I see slight to no improvement, but certainly no regression.

It turns out that the LAPACK function is calling the BLAS function internally (https://netlib.org/lapack/explore-html/d4/dc1/group__trtrs_gab0b6a7438a7eb98fe2ab28e6c4d84b21.html), but checks for exact singularity upfront, nothing else. It seems we could rather switch to the "augmented" LAPACK functions throughout instead?

@jishnub @andreasnoack @amontoison

Nevermind, there is no triangular right-solve in LAPACK.

@dkarrasch I was thinking of LBT if we switch the backend, like BLIS. Sometimes, we only have the BLAS routine available.

Ok, we can of course switch, but then we should perhaps add the exact singularity check?

Yes, and we can do that for both trsv! and trsm! such that it is consistent.
Using trsv! for one right-hand and trtrs! for multiple ones have a different behaviour if the triangular matrix is singular.

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 91.86%. Comparing base (e7da19f) to head (f8850f0).

@@            Coverage Diff             @@
##           master    #1194      +/-   ##
==========================================
- Coverage   91.89%   91.86%   -0.03%     
==========================================
  Files          34       34              
  Lines       15360    15371      +11     
==========================================
+ Hits        14115    14121       +6     
- Misses       1245     1250       +5     

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This appears to have introduced a bug into the benchmarking tests (I cannot vouch for their quality, only that this commit seems to have introduced a regression in them): JuliaLang/julia@c8ed17f#commitcomment-153581870