Add wrapper for LAPACK _trexc methods (reordering of the Schur form)

[mfasi]

I need this wrapper to implement some of the points of #5840 (I'm sure I need it for funm and unwm). I'd be glad to add a few tests, but I have no idea how to test such an operation. Suggestions are welcome.

[andreasnoack]

Usually, we don't restrict the options supported by LAPACK so I'd prefer a version with a compq argument. I'd be fine with having a second method without the compq argument that calls the first with compq=='V'.

[mfasi]

I didn't know that, I simply used the trsen wrapper as a template. I can fix that one as well. Thank you for having a look at the commit, I'll correct what you suggested and add a few tests shortly.

[andreasnoack]

Oh. I see. It would be great if you could change that in trsen as well and preferably in a separate commit.

[andreasnoack]

Maybe try one or two reorderings and check that the eigenvalues are unaffected. The main point is to check that the wrapper is working. The two errors I've mentioned would probably have been found with such tests.

[andreasnoack]

I think it is fine to add these wrappers, but we should probably not add new functionality to 0.4 so please be patient.

[mfasi]

@andreasnoack I added the tests you suggested, but some of the checks fail for some reason I cannot understand. For instance, I get a MethodError for Linux x86_64, but not for Linux i686. Moreover, the lapack.jl test file works on my machine (Linux x86_64). Is there something I am grossly overlooking?
[I attach the stack trace for reference.]

The command "/tmp/julia/bin/julia -e 'versioninfo()'" exited with 0.

127.62s$ export JULIA_CPU_CORES=4 && cd /tmp/julia/share/julia/test && /tmp/julia/bin/julia --check-bounds=yes runtests.jl all && /tmp/julia/bin/julia --check-bounds=yes runtests.jl pkg

    From worker 5:       * linalg/matmul         in  10.61 seconds

    From worker 5:       * linalg/schur          in  15.55 seconds

    From worker 5:       * linalg/special        in   4.40 seconds

    From worker 5:       * linalg/eigen          in  10.10 seconds

    From worker 5:       * linalg/bunchkaufman   in   5.24 seconds

    From worker 5:       * linalg/svd            in   8.56 seconds

    From worker 3:       * linalg/qr             in  57.18 seconds

    From worker 4:       * linalg/dense          in  58.58 seconds

    From worker 3:       * linalg/tridiag        in  14.93 seconds

    From worker 4:       * linalg/bidiag         in  14.80 seconds

    From worker 2:       * linalg/triangular     in 120.64 seconds

ERROR: LoadError: On worker 5:

LoadError("/tmp/julia/share/julia/test/linalg/lapack.jl",431,MethodError(trexc!,(1,2,

Float32[11.416281 -1.1872973 1.902823 -2.0817497

        0.0 6.4523597 -0.34416994 2.085003

        0.0 0.0 3.5656812 1.325061

        0.0 0.0 -0.1481058 3.5656812],

Float32[-0.5339776 -0.78375375 0.20146918 -0.24496534

        -0.3179281 0.021552414 -0.9365313 -0.14617346

        -0.75296825 0.5962653 0.27554345 -0.039776057

        -0.21639903 -0.17243204 -0.07997203 0.9576237])))

 in anonymous at no file:435

 in include_string at loading.jl:233

 in include_from_node1 at ./loading.jl:274

 in runtests at /tmp/julia/share/julia/test/testdefs.jl:179

 in anonymous at multi.jl:889

 in run_work_thunk at multi.jl:642

 in anonymous at task.jl:889

while loading /tmp/julia/share/julia/test/runtests.jl, in expression starting on line 13

    From worker 5:       * linalg/lapack        

The command "export JULIA_CPU_CORES=4 && cd /tmp/julia/share/julia/test && /tmp/julia/bin/julia --check-bounds=yes runtests.jl all && /tmp/julia/bin/julia --check-bounds=yes runtests.jl pkg" exited with 1.

[mfasi]

Just to record that I solved the problem above. I'll just relax and wait for the end of the feature freeze.

[kshyatt]

@mfasi the feature freeze is done since we've branched and this looks possible to merge. Is it ready to go?

[mfasi]

@kshyatt I think so, feel free to merge.

[mfasi]

@jakebolewski Great, thanks.