[WIP] Laplace Approximation

[SteveBronder]

Summary

This is a very WIP PR, mostly for @charlesm93 and I to debug some things

Tests

Side Effects

Release notes

Checklist

• [ ] Math issue #(issue number)

• [x] Copyright holder: Charles Margossian and Steve Bronder

  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

[SteveBronder]

Also should we be using the BlockSparseMatrix type from Eigen?

https://eigen.tuxfamily.org/dox/unsupported/classEigen_1_1BlockSparseMatrix.html

[syclik]

Changed status to draft; looks like a bunch of work left to do here.