lapack/netlib: require Gonum v0.13 and add missing methods

[vladimir-ch]

Let's give some TLC to the netlib packages. Let's start by requiring Gonum v0.13 and adding missing methods which are Dlapmr and Dpstrf. The editor reformatted comments on save and I also removed two unreachable returns that somehow sneaked in in the past.

Unfortunately, there are two failing tests: one in BLAS Drotg (new one) and one in LAPACK Dlarfb. I should probably identify the root cause before merging this.

Fixes #91

Please take a look.

[kortschak]

I should bump the Go versions for CI. We don't have any required version, so this is not needed, but it should be bumped in the CI config.

[vladimir-ch]

Ok, I'll bump the Go version too.

About Drotg, OpenBLAS seems to use their own C implementation in interface/rotg.c which is based on the previous reference version that doesn't handle extreme values well. I'll create an issue for them.

I'll check Dlarfb next.

[vladimir-ch]

The failure of Dlarfb test turns out to be a bug in LAPACKE: Reference-LAPACK/lapack#877

[kortschak]

After running go generate ./... to bring the errors and doc synchronisation up to date the only failure locally is the known drotg issue.

[vladimir-ch]

I've run go generate. I think OpenBLAS will pick up the fix for the Dlarfb issue but the Drotg issue will likely persist. Should I add a flag to skip testing huge numbers from this repo?

[kortschak]

Yeah, I think so.

[vladimir-ch]

I missed there's one more failure in Drotmg:

=== RUN   TestDrotmg
    level1double.go:2206: drotm y_0 mismatch RD1_Med_RD2_Big_Flag_0: expected 0, found 5.1194107541670215e-11
--- FAIL: TestDrotmg (0.00s)

[vladimir-ch]

The root cause is again the difference between using and not using FMA. The detection of the FMA instruction in the CI pipeline gives different results from running locally. It'd be nice to know how to get the same (or at least in terms of FMA) build in both environments. Anyway, I'll see if I can either improve the test or relax the tolerance.

[codecov-commenter]

Codecov Report

Patch coverage: 47.82% and project coverage change: -1.34% ⚠️

Comparison is base (ede9441) 30.46% compared to head (ac94acc) 29.12%.
Report is 4 commits behind head on master.

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Additional details and impacted files

@@            Coverage Diff             @@
##           master      #92      +/-   ##
==========================================
- Coverage   30.46%   29.12%   -1.34%     
==========================================
  Files           3        3              
  Lines        6513     6321     -192     
==========================================
- Hits         1984     1841     -143     
+ Misses       4096     4046      -50     
- Partials      433      434       +1     

Files Changed	Coverage Δ
blas/netlib/blas.go	28.51% <ø> (-0.66%)	⬇️
lapack/netlib/lapack.go	30.24% <47.82%> (-2.79%)	⬇️

... and 1 file with indirect coverage changes

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[vladimir-ch]

"All checks have passed" 🎉