Update LAPACK/LAPACKE to Reference-LAPACK 3.10.1

[martin-frbg]

fixes #3495 and fixes #2154

[h-vetinari]

Hey @martin-frbg, do you think it would make sense to include this PR in 0.3.21?

[martin-frbg]

I remember seeing a handful of new failures in the LAPACK testsuite with this, which is why it is not merged yet. Seems some of the new algorithms are a lot more sensitive to numerical accuracy of the underlying BLAS than before.

[martin-frbg]

Current state on Haswell for reference (used to be just 1 each in REAL/COMPLEX due to ?TFSM) - additional errors are in SGS/CGV/ZGV (with significant error values, in the 1.e6 and 1.e16 range). ARMV8 is clean but with a low test count.

                        -->   LAPACK TESTING SUMMARY  <--
SUMMARY                 nb test run     numerical error         other error  
================        ===========     =================       ================  
REAL                    1308531         2       (0.000%)        1       (0.000%)
DOUBLE PRECISION        1318689         0       (0.000%)        0       (0.000%)
COMPLEX                 768751          5       (0.001%)        0       (0.000%)
COMPLEX16               776246          21      (0.003%)        0       (0.000%)

--> ALL PRECISIONS      4172217         28      (0.001%)        1       (0.000%)

[brada4]

Well FMA and parallel accumulators almost guarantee different result. I suppose those tests impose exact result.

[martin-frbg]

Tests are not meant to impose exact results - in fact the input files define thresholds and the netlib faq explains that even further deviations in about the same order of magnitude can be expected to arise from harmless numerical differences. I guess there is a risk that more involved calculations, e.g. iterative ones, may be derailed to give a perturbed result. In any case, errors of 1e+16 will warrant a closer look.

[brada4]

It is to look at each test individually why rounding particularities do not cancel out correctly.