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:
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.