[wien2k] complete the port to machine precision: shared module, fromfile, proj_mode, outband

[krystophny]

Part of #7; stacks on reviewed #11 and the native precision fix #14.

Extracts shared parsing, angular transforms, window selection and formatting into _dmftproj. Adds double-precision projector construction, spin-mixing fromfile bases, projection modes 1/2 for oubwin/ctqmcout/parproj, and the SP+SO band-mode outband generator.

Carries forward native terminal-band selection, per-spin offsets, shell-specific tables, odd-l parity and the normalized native p-basis ordering. Mixing density symmetrization now transfers contributions between equivalent atoms. Loewdin rank detection is relative to the overlap scale, preserving small full-rank projectors while rejecting singular overlaps. Shared parsing reads every correlated-shell representation record and every atomic-sort local rotation, and retains arbitrarily small spin mixing. Unsupported selected irreducible subspaces and multiple local orbitals fail explicitly. Existing converter fixtures remain intact; separate full-rank references test the precision layer.

Validation: all eight local generator tests pass. Native CMake producer comparisons reproduce the full-rank ctqmcout, custom-basis parproj, sympar and outband references within 1e-11 (observed residuals at most 1.4e-15 on this build). Independent regressions cover two shells on one atom, transfer between equivalent atoms, singular overlaps and native window edge cases. Band-mode partial projectors also match the native energy-window reference within 1.2e-16; the one-k-point band fixture and native reference now agree on their path length. CI runs full TRIQS integration.

Chris&AI

[krystophny]

Updated to machine precision on every output (with the Fortran precision fix #14):

oubwin   byte-identical
symqmc   1.5e-14
sympar   1.9e-14
parproj  1.5e-14
ctqmcout 1.5e-14   (full-rank window)

ctqmcout uses the same LAPACK/BLAS routines the Fortran does (scipy ZHEEV('V','U') + ZGEMM). The earlier 6.6e-7 was the rank-deficient narrow-window CaOs2 (20 correlated spin-orbitals, 17 bands): O^{-1/2} of a singular overlap has non-unique null eigenvectors that differ across LAPACK builds. A full-rank window (50 bands) makes the overlap non-singular and the result exact and reproducible. All tolerances are now 1e-11.

[krystophny]

GPT Sol rebased this onto reviewed #11/#14 and preserved the earlier window, spin-offset, shell-key and parity fixes through deduplication. Fixed equivalent-atom transfer in custom-basis density symmetrization, rejected singular overlaps, and made numeric comparisons NaN-safe. Eight local generator tests pass; native reference checks are within 1.4e-15. CI is running.

Chris&AI

[krystophny]

GPT Sol fixed shared parsing, tiny spin mixing, scale-relative Loewdin rank detection, and partial-projector modes 1/2, including below-window validation. Corrected the band-path fixture and regenerated its reference with native dmftproj. All eight generator tests pass; native mode comparisons differ by at most 1.2e-16. Restacked on updated #11 plus the precision fix. Latest-head CI is running/queued.

Chris&AI