Add power trace optimization conforming to c++14

[trevor-vincent]

Context:

The power trace computation in eigenvalue_hafnian uses Eigen's diagonalization routine. This can be made potentially faster by computing the characteristic polynomial first. Eigen also doesn't support long double.

Description of the Change:

Use the Labudde algorithm and optimization in Appendix B of Nico's paper to compute the power trace faster than Eigen for most sizes. Labudde is faster and more stable than Fadeev-Leverrier, see more here: https://arxiv.org/abs/1104.3769. With this change it will be easier to optimize the eigenvalue hafnian algorithm even further if needed.

Benefits:

Speed-up Removes Eigen from the hafnian calculation Long double support

Possible Drawbacks:

• None

Related GitHub Issues: Fadeev-Leverrier algorithm for power traces #36

[trevor-vincent]

Sorry for the large delay on this, I went down the tensor network rabbit hole and didn't come out. Won't happen again! Everything is now conforming to C++11. I have improved the code a bit more as well. I have taken into account all of Josh's/Nico's suggestions from the previous pull request (which I closed because it's been so long... might as well start again).

[nquesada]

It seems like there are a lot of diffs that are just formatting. @josh146 can correct me if I am wrong, but It would be nice to pass astyle on the code http://astyle.sourceforge.net/ (or whichever other formatter we have used in the past) so that the diff is reduced and is easier to parse what the changes are.

[josh146]

Yep, astyle is the one we have been using!

[trevor-vincent]

Yes good catch, I will fix that!

[nquesada]

Funnily enough, after this the eigenvalue algorithm will not be using eigenvalues.

[codecov[bot]]

Codecov Report

Merging #199 into master will not change coverage. The diff coverage is n/a.

@@            Coverage Diff            @@
##            master      #199   +/-   ##
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  Coverage   100.00%   100.00%           
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  Files           20        20           
  Lines         1131      1131           
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  Hits          1131      1131           

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