add minus_path_weights to path weights

[dz24]

Currently get_path_weights does not print the weights for the paths sampled in the [0-] ensemble.

We now do this, according to the simplified version under eq 19. in https://arxiv.org/abs/2602.05793

Note that the the minus paths are not sorted according to sampling.. maybe we should do that ..

[lukasbaldauf]

Maybe we could save it to another file instead, e.g., by adding a -minus outfile option and only calculate these if that is given. Because we can't know whether it's a minus or a plus path from this, and most scripts that use the path_weights.txt file do not need minus paths.

[dz24]

What about just making it a bool option? and save it in the same file if -minus?

[lukasbaldauf]

Then one would need to add another column as either ones or zeros to specify if the path is a minus path or not, which is maybe a bit redundant

[lukasbaldauf]

Also, many of the scripts use the path_weights.txt file, so it might cause unexpected issues when they do not check if something is a minus or plus path (among other inf-init), which is why another text file might be preferred.

But I guess if the flag -minus is not given the files looks as previously, so nvm this comment.

[dz24]

Right, maybe you were more thinking about the following two averages

while I was thinking of

where I want the curly A average (which includes both 0- and i+ ensembles)

I guess either way works, but yeah I was thinking that just having a default -minus=False would not break stuff.

[lukasbaldauf]

Right, yes I was thinking on that line. In that regard, we do not actually need to care about whether it's a minus or a plus path. And if its False by default all should be fine.
LGTM!