For certain inputs, the real schur decomposition might get stuck in a cycle.
Exceptional shifts are supposed to knock us out of that - but previously
they were only ever applied at iteration 10 and 30, which doesn't help if
the cycle starts after cycle 30. Modified to apply a shift every 16 iterations
(for reference, LAPACK seems to do it every 6 iterations).
Also added an assert in polynomial solver to verify that the schur decomposition
was successful.
Fixes#2633.
This provide several advantages:
- more flexibility in designing unit tests
- unit tests can be glued to speed up compilation
- unit tests are compiled with same predefined macros, which is a requirement for zapcc
- Updated unit tests to check above constructor.
- In the compute() method of decompositions: Made temporary matrices/vectors class members to avoid heap allocations during compute() (when dynamic matrices are used, of course).
These changes can speed up decomposition computation time when a solver instance is used to solve multiple same-sized problems. An added benefit is that the compute() method can now be invoked in contexts were heap allocations are forbidden, such as in real-time control loops.
CAVEAT: Not all of the decompositions in the Eigenvalues module have a heap-allocation-free compute() method. A future patch may address this issue, but some required API changes need to be incorporated first.
