Newton solver now exposed to Stan language

Developers
1

The Newton solver, based on KINSOL, is now exposed to the Stan language and in the master branch of stanc3. Its signature is identical to the previous solver:

algebra_solver_newton(system, y_guess, theta, x_r, x_i, 
                      rel_tol, f_tol, max_num_steps)

You can still use the original solver, based on Powell’s dogleg method, via algebra_solver(). In my experience, the Newton method is better to much better than Powell, so I recommend using it as a default.

This update is long overdue, so sorry for the delay. I wasn’t sure there’d be much use for it (but folks have been requesting this feature) and was also holding off to add the below-described features, but it seems better to go at it step-by-step. Thank you, @rok_cesnovar for reviewing the PR!

Where we go next

We’ll use two signatures and deprecate the original signature, much like was done for the ode integrator:

  • algebra_solver_newton()
  • algebra_solver_powell()
  • algebra_solver() (deprecated)

Still following the example of the ODE integrators, the algebraic solver will take in variadic arguments (and/or closures). Using @bbbales2’s work on nested backward autodiff, we’ll also improve the differentiation, using an adjoint method.

@wds15 @yizhang

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Nice thanks!

3

stanc3 has a vey nice, but little know flag “–print-canonical” that in addition to other cleanups, replaces deprecated functions using non-deprecated ones. Any thoughts on what should we do here: replace with _powell so we remain numerically consistent or replace with _newton which you say is much better?

also tagging @nhuurre, the author of the “canonicalizer”, maybe there is already some precedent here that requires us to use _powell for consistency.

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I am not sure on this one specifically, but it sounds like you would even standardize integrate_ode calls… which one should not. So I think if a user requests Powell, then he should get that.

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No no, —print-canonical does not try to be smart about such stuff. Just replaces deprecated signatures. For example multiply_log is replaced by lmultiply, integrate_ode is replaced with the explicit call to integrate_ode_rk45, etc. So probably I answered myself and it should just use algebra_solver_powell explicitly.

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