idklu solver for convert_to_casadi=True

[martinjrobins]

Summary

The current idklu solver goes back to python whenever it needs to calculate the rhs, algebraic or event equations. It also runs very slow when using convert_to_casadi=True. This issue aims to develop a new idklu solver that directly calls casadi functions from C++, with ideally no memory copying to/from casadi arrays

Motivation

We want to get the superior event handling capabilities of the ida solvers with efficient casadi evaluation of equations

[valentinsulzer]

A major addition here would be to look at the iterative solvers

Iterative solvers only start to outperform direct solvers at relatively large matrix sizes, right? (don't know how large)

[martinjrobins]

Yes, iterative solvers can give speed benefits at the very large matrix sizes, as long as you have a decent preconditioner (i.e. a good approximation to the jacobian that you can solve easily).

[martinjrobins]

This is largely finished, see pr #2002, here is my todo list for subsequent issues:

• we're allocating memory for return vectors in the solve, this could be done in solver setup
• we initialise ida_mem and everything every time, could do this once when solver is created, or only on the 1st solve etc
• create an options dict to pass to the solver, e.g. option to print solver stats, don't/do use jacobian
• add option to use iterative solvers
• add option to use other linear solvers in ida
• add option to use dense jacobian
• benchmarks for all of the above solver options
• investigate if we need to densify the rhs_algebraic casadi evaluation, could it return a sparse vector?
• investigate if constructing a new casadi function for the residual (rather than doing it manually in c++) is faster
• investigate if constructing a new casadi function for the sensitivity calculations (rather than doing it manually in c++) is faster
• we calculate consistent initial conditions at the start of the idklu solve, so we might not need to do it in the BaseSolver setup