Performance aspects

[PierreMartinon]

General notes: scripts for benchmarking / profiling are in benchmark folder:

• Benchmarking solves a collection of problems for a given set of options (NLP and linear solvers, solve options), and returns times.
• Profiling focuses more about speed and allocations for a single solve or the NLP objective and constraints functions. Uses tools such as timev, btime, code_warntype, JET

Summary:

• most type instabilities have been resolved
• efforts to reduce allocations have had mixed results, either for the variables getters or the OCP function calls

Concerning the getters for the state/control variables at each time step:

• views are not necessarily better than the very small vectors we often have. A Julia view is indeed an object with some fields, not a C-like basic pointer.
• static vectors from StaticArrays do not seem compatible with AD, raising a setindex error even when using the supposedly mutable MVector...
• the use of inplace getters is possible with the proper type (cf similar), however this does not seem to reduce allocations. This may due to the 'smart update' in the trapeze method where we copy some values from one time step to another to avoid recomputing the same dynamics twice. In particular some formulations compile and execute without errors, but with obviously wrong derivatives. Things may be easier to figure out a more standard scheme such as midpoint.

Concerning the OCP functions calls:

• using inplace versions of the OCP functions will hopefully help.
• the handling of possible scalar variables (x, u or v) is still annoying as there doesn't seem to be an automatic (eg without requiring a test) conversion from a 1-size vector to a scalar. For instance x[] does not work on a vector of size greater than 1. Current version returns scalar variables at the getters level. Using multiple dispatch with 8 methods (all possible scalar/vector cases) for the OCP functions was not better. Maybe reworking the OCP functions so that they take references (if feasible at all) could be an improvement ?