Use a local buffer in unique_writer for better write to disk performance

[SteveBronder]

Summary:

Just a note on two optimizations we could do when writing parameters.

Description:

When sampling with nuts the mcmc_writer generates the parameters it needs to write and then sends the parameters as a std::vector to a writer. For cmdstan the writer is the unique_stream_writer that writes to disk.

We call this function decently often and I think we could do a few things to both speed it up while being a little nicer to the system so we can write faster.

1. unique_stream_writer for a std::vector calls its write_vector member function. This function takes each value in the vector and one at a time write them to disk. Instead of many small calls for writing to disk we should have a string buffer inside of the unique_stream_writer that we write all of the values to first. Then we just write one large buffer to disk once instead of many times.

2. Inside of mcmc_writer::write_sample_params we keep making the std::vector<double> values for each call. Instead we can put those vectors directly in the mcmc_writer class. That would make mcmc_writer stateful in terms of memory, but to my knowledge we never call an mcmc_writer instance from multiple threads and idt it would make sense to. If we did not want to add state to mcmc_writer we could also pass mcmc_writer::write_sample_params a local allocator to reuse memory.

These optimizations would not really matter for small problems. But once we start getting to 100K+ parameter models reading and writing to disk can be an issue.

Current Version:

v2.36.0