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[wien2k] pure-Python case.sympar partial-shell symmetry matrices#10

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[wien2k] pure-Python case.sympar partial-shell symmetry matrices#10
krystophny wants to merge 5 commits into
TRIQS:unstablefrom
krystophny:port/dmftproj-sympar-python

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Part of #7. Stacks on #9 (net new: sympar.py + test + fixture).

case.sympar = the symmetry matrices for all included shells (correlated + partial), the partial-charge analog of symqmc. Validated against a CaOs2 variant with an added uncorrelated Ca d-shell (minted with the dmftproj container).

Verification

wien2k_sympar_python: ok    # max float diff 4.4e-8 vs dmftproj

…CaOs2)

dftkit's Wien2k converter is only covered by the non-SOC SrVO3 case. This adds a
SOC + spin-polarized golden test: CaOs2, a cubic fluorite cell with two
symmetry-equivalent correlated Os atoms whose magnetic point group has 16
operations, 8 of them time-reversal. It exercises the combined-spin 'ud' block
and the time-reversal symmetry path of dmftproj + the converter on a small
8-k-point fixture, validated by h5diff against a reference produced by this
converter.
triqs_dftkit.wien2k.symqmc.write_symqmc builds the correlated-shell spinor
symmetry matrices (case.symqmc) from case.dmftsym + case.indmftpr + case.struct,
reproducing the dmftproj Fortran construction (Wigner D, orbital and spinor
time-reversal operators, angular-harmonics basis transform, spin-1/2 phase
blocks). It is a full replacement of the symqmc-writing, covering every path:

- non-mixing spin-diagonal bases (complex, cubic): the up/up block scaled by
  the +-(a+g)/2 phase, with the orbital time-reversal operator on the magnetic
  operations;
- mixing fromfile bases that couple spin (the |j,m_j> basis): the full 2(2l+1)
  spinor representation P spinrot P^dag with the spinor time-reversal
  -i sigma_y (x) T on the magnetic operations;
- l=0 (s) shells: the 2x2 spin phase block.

Verified against the dmftproj Fortran output for all three paths on CaOs2 (16
operations, 8 time-reversal): the cubic converter HDF5 is identical (h5diff) and
every matrix matches to machine precision. The mixing fromfile path is the one
dft_tools #148 singles out; dmftproj reads that basis with a single-precision
CMPLX cast and a 250-column line cap (set_ang_trans.f), so its case.symqmc
carries a ~1e-7 error there while this generator is full double precision.

Tests: the cubic path reuses the SOC golden h5; the mixing and l=0 paths compare
to the dmftproj matrix data (single precision, ~26 kB) and assert unitarity.
Port the dmftproj almblm reader and case.oubwin writer to numpy. Given
case.almblm{up,dn} and the energy window in case.indmftpr, select the
contiguous band range per k-point and spin and write case.oubwin{up,dn}
in the dmftproj format. Proven byte-identical to the Fortran output on
CaOs2 (proj_mode 0; band-index modes raise NotImplementedError pending a
fixture). Part of TRIQS#7.
Port the dmftproj projector core to numpy: read the almblm Alm/Clm
coefficients, build the raw correlated projector over the in-window bands,
apply the local rotation and cubic basis transform, Loewdin-orthonormalize
the stacked shells (orthogonal_wannier_SO), and write case.ctqmcout. Matches
the dmftproj CaOs2 reference to 4.3e-7 (the single-precision basis-transform
floor); integer fields identical. cubic/complex bases; fromfile raises
NotImplementedError pending a fixture. almblm fixtures switched to gzip
(shared with the oubwin test). Part of TRIQS#7.
Port the dmftproj case.sympar writer to numpy: the symmetry matrices for all
included shells (correlated + partial), the partial-charge analog of symqmc.
Matches the dmftproj CaOs2_partial reference (an added uncorrelated Ca d-shell)
to 4.4e-8. cubic/complex bases; fromfile raises NotImplementedError. Part of TRIQS#7.
@krystophny

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Accuracy: reproduces the released dmftproj case.sympar to 4.4e-8; 1.9e-14 (machine precision) with the precision fix #14 + exact Python #12.

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