Discussed in #3202 (comment), counterpart to stan-dev/stanc3#1521

Summary

Theta0 is now a tolerance parameter rather than required. When not provided, we assume a vector of 0s is sufficient.

This required a bit of re-organization to get the size right, but otherwise wasn't too bad because we call the covariance function pretty early and can get the size from the return of that function.

Tests

Existing tests updated

Side Effects

Release notes

Checklist

• Copyright holder: (fill in copyright holder information)

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  - 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