Evaluate state (Kin) quantities exploiting CasADi code-generation

[FabioBergonti]

This PR decreases the computational time for evaluating jacobian, ...

[FabioBergonti]

I compared 4s of a kinematic simulation of an 8x8 mesh W/O codegen.
Using codegen the computational time is lower.

If we increase the length of the simulation 10s the gap increase even more

This PR could be beneficial also for #2

[gabrielenava]

interesting! so the mex file is generated every time you run a new simulation and then deleted at the end? Do you think it may be convenient to keep also the generated mex files somewhere or not?

[Giulero]

Left a couple of comments for curiosity ;)
It looks fine to me btw!

[Giulero]

For curiosity :)
Once the function mystica_stateKin is generated, does it live in the workspace and be called in every part of the code?

[Giulero]

Also, is it computationally expensive to generate it?
I might understand why you don't check if the function already exists.
To check if the content of the function changed, you have to generate it again :D

[FabioBergonti]

I generate the MEX files in the current folder. So, until you do not change the current directory, they can be called everywhere

[Giulero]

Does it also work without parenthesis?

[FabioBergonti]

In matlab yes :)

[Giulero]

Also, is it computationally expensive to generate it?
I might understand why you don't check if the function already exists.
To check if the content of the function changed, you have to generate it again :D

[FabioBergonti]

@gabrielenava

interesting! so the mex file is generated every time you run a new simulation and then deleted at the end?

Exactly!

Do you think it may be convenient to keep also the generated mex files somewhere or not?

The generated MEX files are model dependent. If I want to keep them I have to add a check to verify that the model is not changed.
For the moment I decided to regenerate them every time also because it requires only ~10s

[FabioBergonti]

@Giulero @gabrielenava

Also, is it computationally expensive to generate it?

~10s but it depends on the dimension of the problem

I might understand why you don't check if the function already exists.
To check if the content of the function changed, you have to generate it again :D

The time-demanding operation is the generation of the MEX files
Theoretically, I can compare the mystica_stateKin.c file and if they are different I can generate the MEX file

[FabioBergonti]

Thanks @gabrielenava and @Giulero
Merging!

[traversaro]

If you are using mex, probably you need to also add in your dependencies a supported C compiler for mex (see https://it.mathworks.com/support/requirements/supported-compilers.html). It is kind of obvious having that on Linux/macOS, but it may be not obvious to have it on Windows.