Introduce decorator to describe 1d spaces and regime ids. Fixes #192.

[hmgaudecker]

This gets rid of having to specify consecutive integers in describing 1d spaces manually.

Simple enough, but I am not perfectly sure about the naming yet.

[hmgaudecker]

Sorry for the mess...

[timmens]

Very nice. I have mainly two comments:

1. I think the naming style is very different compared to other parts of lcm. Maybe rather something like @lcm.space_dimension. Or we actually also differentiate between state and action here (just like in the type annotations) and do @lcm.state_space_dimension and @lcm.action_space_dimension.
2. I am not a fan of removing the explicit enumeration. I think a big advantage of the explicit enumeration was that users could debug more easily. Now users need to count, which is of course error prone, if they need to check which dimension of their Markov array corresponds to which category, or if they debug lcm.

[hmgaudecker]

1. Fair enough. I will try to come up with something better, currently working through the big pic.

   In the end, this is the grid description, maybe merging those is the way to go -- but not sure yet.

   In the docstring of DiscreteGrid, I find:

   Must be a dataclass with fields that have unique scalar int or float values.

   Can you remind me of a use case for floats? Or is this outdated?

2. I am not sure whether I agree yet -- in my mind this was one of the main points of ENH: Single action sets and state spaces #192 -- but I see your point.

[timmens]

1. This seems to be outdated. The dataclass should only allow ints. Also: The naming should not be a showstopper. We can always rename afterwards.
2. I remember that I actually proposed to use something similar to enum.auto() to generate the indices automatically. Since then I changed my mind, and think that the indices might be helpful after all. But also here, we could go ahead and merge, and if users miss the indices we revert that change.

[hmgaudecker]

Great. How about @categorical for the decorator?

This is explicitly similar to pandas' notion of categoricals since it is precisely the same idea.

A natural way of passing transition matrices would be a DataFrame with a MultiIndex of (typically) Age and the current states and actions / future states, each of which have CategoricalDtypes corresponding to the attributes of the dataclasses decorated with @categorical.

[hmgaudecker]

I remember that I actually proposed to use something similar to enum.auto() to generate the indices automatically. Since then I changed my mind, and think that the indices might be helpful after all. But also here, we could go ahead and merge, and if users miss the indices we revert that change.

I'd prefer that. We won't have too many outcomes, typically. And it is near-trivial to look at the actual DiscreteGrid or a dataclass like LaborSupply by just importing file or setting a breakpoint in the user entry code.

[timmens]

I like this!