[wien2k] rotate the symmetry matrices into the local solver frame (dft_tools#148)

[krystophny]

Fixes the local-frame symmetry error documented in TRIQS/dft_tools#148. This PR is independent of the dmftproj generator stack.

case.symqmc and case.sympar describe operations in the global frame, while Symmetry.symmetrize acts on quantities in the rot_mat-equalized solver frame. Conversion now stores R_j^dag M_ji R_i, with the source rotation conjugated for antiunitary operations, using rot_mat for correlated shells and rot_mat_all for partial shells.

The shell mapping includes atom, sort, angular momentum, and dimension. This prevents a symmetry operation from pairing the wrong shell when one atom contains multiple angular momenta; duplicate or missing identities fail explicitly. The two affected converter reference archives are regenerated for the corrected mat datasets, with all unrelated datasets and attributes verified unchanged.

Validation: a NumPy-only regression covers unitary and antiunitary operations while swapping two atoms that each contain two shells. The documented full-BZ tellurium oracle reduces local-Hamiltonian eigenvalue drift from 1.302e-1 to 2.483e-8; centrosymmetric CaOs2 remains at numerical noise. The focused local test passes, and the existing scalar-relativistic and SOC converter archive comparisons cover the stored frame transformation in CI.

Chris&AI

[krystophny]

GPT Sol rebased this onto current unstable and completed the remaining review fixes. Extracted the frame transform into a tested helper, made shell mapping include l and dimension, and added explicit failures for ambiguous or missing targets. The focused unitary/antiunitary regression passes locally; CI is running.

Chris&AI

[krystophny]

GPT Sol followed the first CI run through to the archive comparisons. The corrected frame transformation changed the expected dft_symmcorr_input/mat and dft_symmpar_input/mat values, so I regenerated both affected HDF5 references from their stored rotations and verified that every other dataset and attribute remained identical. The focused unitary/antiunitary frame test still passes; CI is rerunning with the corrected references.

Chris&AI

[krystophny]

GPT Sol strengthened the solver-frame test with an independent density-matrix covariance oracle, covering noncommuting symmetry matrices, unitary/antiunitary actions, exchanged atoms and multiple angular momenta. It passes. This converter fix remains independent of the generator stack and is ready for review. Latest-head CI is running/queued.

Chris&AI