Add @system macro

[ueliwechsler]

Closes #76.

[schillic]

Does this close #76?

[ueliwechsler]

Yes, once it is done.

[ueliwechsler]

Similar to the noise default value, I added a default value for input u which can be changed by adding input: u1 to the system definition.

[schillic]

another try on making doctests work

You can let Documenter fix the doctests for you 😉

[ueliwechsler]

another try on making doctests work

You can let Documenter fix the doctests for you 😉

😂🙈 the more you know

[schillic]

There are still some unresolved discussions here. Can you check if they can be closed?

[ueliwechsler]

I tried to address the comments from @schillic as well as possible and updated the todo list #125 (comment).

I found some more "loopholes" in the definition and the documentation is not yet where it should be, but I think the behavior of the macro, in general, is as it is supposed to be. The requested or intended changes are either bug fixes or additional feature, but not breaking.

The remaining design decision that comes to my mind is if we want to have dim=1 as default case for affine systems with only one term such as x'=0 or x'=2x.

[mforets]

The remaining design decision that comes to my mind is if we want to have dim=1 as default case for affine systems with only one term such as x'=0 or x'=2x.

If the scalar differential equation x' = 2x can be written as @system x' = 2x, that's simple and intuitive. If we require to additionally write , dim=1, this adds one (small but) unnecessary level of verbosity. The argument dim allows one to specify a non-default value of the state-space dimension.

[ueliwechsler]

If the scalar differential equation x' = 2x can be written as @system x' = 2x, that's simple and intuitive

I agree with you. The question came up in a review comment.

The argument dim allows one to specify a non-default value of the state-space dimension.

Another point as part of a comment is having similar default value for black-box sytems, i.e. dim=(1,1,1) as default (see #125 (comment)). What is your opinion on that?

[schillic]

Looks good from my side.

[mforets]

Another point as part of a comment is having similar default value for black-box sytems, i.e. dim=(1,1,1) as default (see #125 (comment)). What is your opinion on that?

In such systems, the dimension is part of the struct so providing that information seems reasonable. Moreover, how can one tell the dimension from x ' = f(x)? I can't think of an example where there could be an ambiguity. In x' = 2x, if x is a vector we can pass dim = n otherwise it is interpreted as a scalar.

[ueliwechsler]

I agree. So we keep the implementation as it is now, right?
Is there anything else to address for this PR?

[schillic]

Is there anything else to address for this PR?

There are two one unresolved discussions here and here.

[mforets]

LGTM, great job!!! 🎉

Regarding the other tasks listed before, I opened #133.