Feature/issue 512 speedup ode

[wds15]

Submission Checklist

• Run unit tests: ./runTests.py test/unit
• Run cpplint: make cpplint
• Declare copyright holder and open-source license: see below

Summary:

Internal changes to the non-stiff ODE solver which speedup ODE integration whenever the ODE RHS side is costly to evaluate. This is the case whenever complicated forcing functions are involved. For example, a dosing schedule in PK/PD models.

Intended Effect:

Make non-stiff ODE integration faster. This is realized by avoiding duplicate evaluation of the ODE RHS whenever the ODE integrator calls the () operator of the coupled_ode_system.

How to Verify:

Look at code changes and run tests

• test/unit/math/rev/arr/functor/coupled_ode_system_test.cpp
• test/unit/math/prim/arr/functor/coupled_ode_system_test.cpp

To observe the speedup I have run a benchmark which involves a costly ODE RHS and the execution time goes down from 3.51h (2.14.0) to 2.38h (this branch) which is a ~50% speed increase.

The tests required a minor adjustment. The old test code passed a dy_dt into the coupled_ode_system () operator which had the size of the base system. However, odeint will always pass in a vector as dy_dt into the coupled ode system () operator which is as large as the coupled system and expect that this vector is updated. Hence, we can do the update in-place instead of doing a reallocation which was done before. Therefore, tests need to pass a vector into the () operator which corresponds in size to the coupled ode system, i.e. the vector must be as large as the initial_state vector.

Side Effects:

None.

Documentation:

Reviewer Suggestions:

Anyone.

Copyright and Licensing

Please list the copyright holder for the work you are submitting (this will be you or your assignee, such as a university or company): Sebastian Weber

By submitting this pull request, the copyright holder is requiring to 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/)

[bob-carpenter]

I can review this early next week after the ONR grant gets done. Or someone else might do it sooner. @syclik or @betanalpha perhaps?

[wds15]

Sooner is always better, but early next week would be great, Bob. Then it should be available with 2.15.

Thanks.

[bob-carpenter]

2.15 is still a ways off, but we want to start finishing off issues for it now.

[bob-carpenter]

Looks good. There was only a comment, not a change request---I'm just curious how boost::ref helps where you used it. I'm going to approve and merge, but I'd still like to know!

[bob-carpenter]

Not a change request, just a question: Is this boost::ref because you're calling boost::numeric::odeint::integrate_times on the coupled system and don't want to make a copy (I see that integrate_times just takes the system, not a system reference)? Does it actually prevent copying?

[wds15]

Hi!

odeint does lots of copy-constructions of the ode RHS functor. The author of odeint claims that with compiler optimizations this will make sure that code being generated is faster. However, I have observed the reverse. That is, since we have some instances as copies inside the ode rhs functor, lots of copies are being made of these during the ode integration. I noticed a few % speedup when using boost::ref. So I am not saving a single, but many copies.

Sebastian