fixedpoint improvements

[pbrehmer]

As suggested by @leburgel in #336, here we improve a couple of things about the fixedpoint optimization routine:

• We add a check_input(::typeof(fixedpoint), args...) method that verifies that the chosen inputs are compatible with the PEPS optimization algorithm
• For any boundary contraction algorithm, its leading_boundary call should return an info named tuple which contains a contraction_metrics field that carries boundary-algorithm-specific information such as the truncation error, condition number, etc.
• I added a boundary algorithm type parameter to PEPSOptimize and also loosened type restrictions of fixedpoint such that it is compatible with different environment types.

I'm not so sure yet about the name contraction_metrics, so let me know what you think. After the first round of reviews I will update the examples such that they match the new fixedpoint.

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[codecov]

Codecov Report

❌ Patch coverage is 93.93939% with 2 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
...rithms/optimization/fixed_point_differentiation.jl	80.00%	2 Missing ⚠️

Files with missing lines	Coverage Δ
src/algorithms/ctmrg/c4v.jl	90.29% <100.00%> (+0.19%)	⬆️
src/algorithms/ctmrg/ctmrg.jl	90.27% <100.00%> (ø)
src/algorithms/ctmrg/sequential.jl	100.00% <100.00%> (ø)
src/algorithms/ctmrg/simultaneous.jl	100.00% <100.00%> (ø)
src/algorithms/optimization/peps_optimization.jl	98.66% <100.00%> (+0.01%)	⬆️
src/algorithms/select_algorithm.jl	78.57% <100.00%> (+2.57%)	⬆️
...rithms/optimization/fixed_point_differentiation.jl	94.65% <80.00%> (-0.86%)	⬇️

... and 7 files with indirect coverage changes

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[leburgel]

Overall looks good, I'm happy losing any restrictions on the contraction algorithm where possible. I don't know if contraction_metrics is the best name and whether this change will break things for many users, but I can't think of a better name and it shouldn't be too big of a change I guess.

Aside from the minor comments, can you update the changelog to record the fact that the truncation_error and condition_number have moved to a different place? We've been forgetting about that a bit, but I think this should definitely go in there at least.

[pbrehmer]

Alright, the PEPSOptimize constructor now errors when the user uses anything else than symmetrization = RotateReflect(). Still, when calling fixedpoint and specifying alg = :c4v as the boundary algorithm, the symmetrization defaults to RotateReflect since that is the only sensible default. This would be good to go for me now!