fixed and finalized BdG spin configuration

[zerothi]

This brought about lots of restructuring because
it was a nightmare to test.

• tests have added more functionality Now a sisl_allclose returns a dictionary with an appropriate partial(allclose, ...) with suitable defaults for rtol/atol. The keys are numpy data-types

• Changed the argument for transpose(hermitian=) to transpose(conjugate=). This is much more intuitive.

• The Cython files got an overhaul. Now the addition of NC/SOC/Nambu spin configuration is off-loaded into a separate routine. This means that if something needs to change down the line, there is only a single place to do so. And then it will work for all the variants, phase, phase_sc and phase3.

  Much simpler, and less error-prone!

  The benchmarks/optimizations/hamiltonian.ipynb was used to assert this did not introduce a performance regression! Same perf as before the commit.

  I still wonder why the dtype=float k=Gamma for <=polarized calculations shows such bad performance, 10 times slower than when using dtype=complex?

• added more tests to assert that complex-conjugation actually works.

This fixes #873.

• Closes Support for SIESTA-BdG in sisl #873
• Added tests for new/changed functions?
• Documentation for functionality in docs/
• Changes documented in changes/<pr-num>.<type>.rst

[zerothi]

@ahkole could you please try this branch? I think (hope it should work).

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 86.87%. Comparing base (ad56e5a) to head (7afbefb).
Report is 11 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #896      +/-   ##
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+ Coverage   86.82%   86.87%   +0.04%     
==========================================
  Files         405      405              
  Lines       53308    53369      +61     
==========================================
+ Hits        46286    46365      +79     
+ Misses       7022     7004      -18     

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[ahkole]

Hi, I ran the test I did before in #873 and on first inspection the results are positive!

Here the black line is the SIESTA-BdG bands and the red dots are the bands computed with sisl from the HSX file of the same calculation. I also read the k-points that SIESTA-BdG used to make sure those were the same. (On a sidenote, is there a way with sisl.viz to label the lines and add a legend to the plot? I wasn't able to figure out how to do this).

Which functionality should now be supported with BdG? Then I will try to test most of that.

[zerothi]

Hi, I ran the test I did before in #873 and on first inspection the results are positive!

Great, this indeed looks awesome!

Here the black line is the SIESTA-BdG bands and the red dots are the bands computed with sisl from the HSX file of the same calculation. I also read the k-points that SIESTA-BdG used to make sure those were the same. (On a sidenote, is there a way with sisl.viz to label the lines and add a legend to the plot? I wasn't able to figure out how to do this).

Which functionality should now be supported with BdG? Then I will try to test most of that.

Basically everything should be covered now. Pdos, velocity etc. Try it all. ;) and transport things would also be nice to check, I.e. Self energies etc.

[zerothi]

I think the most pressing thing is to do PDOS, velocity, and perhaps some berry-curvature calculations.

I just did the velocity, and it seems to still fulfill the mirror symmetry around the states. Which kind of makes sense since the BS is symmetric.

Well, perhaps I should just merge this, it is tedious as it stands to have this development waiting (quite a bit of fixes elsewhere as well).

So if you don't mind, I'll merge this start of next week, then you can just give feedback once it is there.

[ahkole]

Well, perhaps I should just merge this, it is tedious as it stands to have this development waiting (quite a bit of fixes elsewhere as well).

So if you don't mind, I'll merge this start of next week, then you can just give feedback once it is there.

This sounds fine to me. Some of the features you mention I also wouldn't be sure how to verify since we haven't looked at those with siesta-bdg before, like the Berry curvature. So most I could do for those would be test if doesn't throw errors or give very weird results. PDOS I can compare directly with siesta-bdg so will test that soon.

[zerothi]

Agreed, pdos would be the most useful just now!