Update/eigen 5.0.1

[SteveBronder]

Summary

This moves Stan math up to Eigen 5.0.1. I broke this up by commit so that the changes would be more legible

14cbe65 removes the old Eigen
3d74c35 adds new eigen
4607907 adds the patch as discussed in RcppCore/RcppEigen#143 (comment)
7164bb2 for stan specific changes

The biggest stan changes are the we have to use val_op() instead of plain val() more often. Then we had some type deduction issues with mdivide_lower_tri. Besides that it was not too bad!

Note that this is just for Stan Math, I still need to run all of the tests with the stan repo. I'm guessing we will have some issues up there since we use a few weird views

Tests

No new tests

Release notes

Update to Eigen 5.0.1

Checklist

• Copyright holder: Simons Foundation

  The copyright holder is typically you or your assignee, such as a university or company. By submitting this pull request, the copyright holder is agreeing to the license the submitted work under the following licenses:
  - Code: BSD 3-clause (https://opensource.org/licenses/BSD-3-Clause)
  - Documentation: CC-BY 4.0 (https://creativecommons.org/licenses/by/4.0/)

• the basic tests are passing

  • unit tests pass (to run, use: ./runTests.py test/unit)
  • header checks pass, (make test-headers)
  • dependencies checks pass, (make test-math-dependencies)
  • docs build, (make doxygen)
  • code passes the built in C++ standards checks (make cpplint)

• the code is written in idiomatic C++ and changes are documented in the doxygen

• the new changes are tested

[WardBrian]

4607907 should probably lead to a STAN_CHANGES file like we do for tbb, just for documentation: https://github.com/stan-dev/math/blob/develop/lib/tbb_2020.3/STAN_CHANGES

[SteveBronder]

Yes. Also I tried to rebase / squash some commits right before I pushed and that has made a few tests break. But I can fix that stuff and repush.