Implement trace_dot

[jachymb]

Summary

Implements the trace_dot function that computes Tr(A * B) efficiently. This can be used to simplify code on some places.

I requested this in #3161 and decided to try it myself.

Tests

Tests for the new functions, inspired by tests for related functions.

Side Effects

Should not have.

Release notes

Implement trace_dot(A, B).

Checklist

• Copyright holder: Me, jachymb@gmail.com
  - 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

AI use disclosure*

I made this with help of claude code Opus 4.6

[jachymb]

Not sure what does the "Upstream CmdStan tests" failure indicate. Can anyone help? Is it maybe just a transient issue and simply rerunning the tests would be enough?

[WardBrian]

It looks like the tests tried to run during a GitHub outage, which caused the failure. I've triggered a re-run

[SteveBronder]

Thanks! I made a few little changes that were easier to show then tell. Once this passes the tests I'll merge!