[eigen] problem with MKL bindings for dense Eigen

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Dear All,

the discussion on MKL and sparse Eigen routines reminded me,
that I used to have problems with the MKL bindings, so just tried it again.

I'm currently investigating a system, where a phase transition
including scaling laws is governed by the precision of the underlying
arithmetic. From a numerical point of view it is a nice testbed for the
precision of the libraries. In case you are curious, there's a preprint
on the arxiv server:  < https://arxiv.org/abs/1803.08480 > .

Taking the code for double precision and compiling with  -DEIGEN_USE_BLAS
I get similar results, as without MKL. Albeit I see small deviations already
in the stable regime. IN this regime, the MKL version appears to be more accurate
compared to plain Eigen. However, in the precision sensitive region, MKL is less accurate.

My real problem is, that compiling with  -DEIGEN_USE_BLAS -DEIGEN_USE_LAPACKE_STRICT
gives me a few iteration steps that are still correct and then complete nonsense.

The only LAPACK routine I'm aware of that could be called from the bindings should
be a diagonalization (yeah, the code is written by me, but some parts are a few years old):

Eigen::SelfAdjointEigenSolver<TpMatrix> eigensolverH;
eigensolverH.compute(  *itH->second );  ///< within a loop over matrices

Before I spend time in hunting the problem, I'd like to ask whether there's
more to do than the above defines and the correct linking options.
Note, I'm using a 2018 MKL and compiled with g++ 7.2 on Linux 4.15.13

CFLAGS = -std=c++11 -O3 -march=native -DNDEBUG

linking with MKL is done via
MKLLIBS = -L $(HOME)/intel/MKL2018/mkl/lib/intel64 -lmkl_intel_lp64 -lmkl_intel_thread -lmkl_core -liomp5 -lpthread -lm -ldl
MKLLIBS = -L $(HOME)/intel/MKL2018/mkl/lib/intel64 -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lpthread -lm -ldl

both versions show the same nonsense.

Thanks in advance,
best regards,

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