docs: approximate api and kwargs implementations

[VinceNeede]

Closes #461

This PR implements a keyword-based caller for approximate on the same line as find_groundstate. I've also updated the docstring to better reflect the real implementations, in particular which algorithm is able to process what (e.g. in place methods implemented or not, approximation of mpo*mps or also mps only)

[codecov]

Codecov Report

❌ Patch coverage is 0% with 14 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
src/algorithms/approximate/approximate.jl	0.00%	11 Missing ⚠️
src/algorithms/unionalg.jl	0.00%	3 Missing ⚠️

Files with missing lines	Coverage Δ
src/algorithms/unionalg.jl	31.25% <0.00%> (-7.22%)	⬇️
src/algorithms/approximate/approximate.jl	56.00% <0.00%> (-44.00%)	⬇️

... and 14 files with indirect coverage changes

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[lkdvos]

Thanks for this!
I think there's a minor typo , that should be ; for the keywords, but otherwise I really like the table.

For the default algorithms, I think it might be okay to not have IDMRG in that mix, to make it more in line with how find_groundstate works as well. Ultimately I think we expect VOMPS to converge as fast/faster, and IDMRG is mostly there for the purpose of handling non-injective states

[lkdvos]

Looks good to me, thanks again!

Did you try and locally run the formatter? The github actions are failing because of security issues, since you have not committed to this repository (yet), and it's a bit of a pain to bypass this.

[VinceNeede]

Yes, I have run it locally:

vince@fedora:~/MPSKit.jl$ git log --oneline -1
c044f7d (HEAD -> vb-approximate_api, origin/vb-approximate_api) converge with VOMPS directly, without using IDMRG
vince@fedora:~/MPSKit.jl$ git runic main
runic did not modify any files