Cleanup compiler warnings: unused variables/typedefs, uninitialised vars, etc.

[andrjohns]

Summary

Cleans up the following compiler warnings:

• Uninitalised variables
• Unused variables
• Unused typedefs
• Inconsistent class/struct typing
• Constructor initialiser ordering

Tests

No new tests, existing tests should pass

Side Effects

N/A

Release notes

Cleans up several compiler warnings throughout Math library and tests

Checklist

• Math issue #(issue number)

• Copyright holder: Andrew Johnson

  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]

This and the similar change in set_zero_all_adjoints_nested seem like they're different from the rest of the changes here - why do these functions become inline?

[andrjohns]

Static functions that aren't used in a given translation unit give an 'unused-function' warning, but this is suppressed if the static function is declared inline: https://sourceware.org/legacy-ml/gdb/2015-02/msg00064.html

These are small enough functions that I think inlining is fine imo

[WardBrian]

The latest set of changes seem good to me, I'd appreciate someone like @SteveBronder or @syclik giving it a once over before merging to make sure I'm not missing anything

[SteveBronder]

lgtm!

[syclik]

@andrjohns THANK YOU!!!

@WardBrian, thanks for reviewing!