ENH: Improve polynomial equations and analytical eigendecompositions
Summary
Analytical eigendecomposition routines show irregular numerical instabilities particularly for cases wherein off-diagonal elements of a tensor involve noise. The issue revealed to be caused by the polynomialEqn containers, particularly cubicEqn.
In addition, the analytical eigendecomposition routines seem to be mathematically inconsistent since tensors are not allowed to return complex types, which is nevertheless the norm for asymmetric matrices.
Accordingly, this set of commits aims to improve the numerical stability of analytical eigendecompositions, and to provide a group of verification tests to prevent future breaks in the workflow.
unit-test-notebooks-17-Feb-20.zip
Resolved bugs
#1311 (closed) #1312 (closed) #1527 #1575 #1596
Risks
Low.
polynomialEqns and analytical eigendecomposition routines were considerably isolated from the rest of the code.