httk.atomistic.data =================== .. py:module:: httk.atomistic.data .. autoapi-nested-parse:: Provide lazy access to five vendored crystallographic symmetry datasets. All five datasets ship as canonical upstream ``.json.gz`` artifacts, copied verbatim, read through :class:`~httk.core.DatasetLoader`, and licensed CC BY 4.0 (see the adjacent ``LICENSE`` and ``README.md``). The canonical per-concern split happened upstream. ``symmetry_basics.json.gz`` One record per space-group **setting** — 527 of them, of which 230 are flagged ``is_reference_setting`` (the International Tables standard setting for their IT number). Each record is self-contained *in its own setting*: its symmetry operations, its Wyckoff table, and its asymmetric-unit region are all expressed in that setting's coordinates. So SG 15 Wyckoff letter ``e`` reads ``0,y,1/4`` in the reference setting ``15:b1`` but ``1/4,0,z`` in ``15:c1``. ``spacegroup_setting_transforms.json.gz`` The change-of-basis operation taking each setting to its IT standard setting, keyed on Hall entry, covering all 527 settings. See :func:`setting_transform` for the direction convention, which is easy to get backwards. ``baernighausen_std.json.gz`` Per-IT-number Bärnighausen subgroup transformations. ``continuous_euclidean_normalizer_std.json.gz`` Per-IT-number continuous-normalizer bases. ``affine_normalizer_cosets.json.gz`` Affine-normalizer cosets for all 527 Hall entries. Nothing here is read at import time. The first lookup parses the whole document: about 0.4 s and 12 MB resident for ``symmetry_basics``, with the other datasets much smaller. Upstream also publishes ``.sqlar`` twins for lazy access to large datasets; they are readable by the same :class:`~httk.core.DatasetLoader`. Two field-choice traps worth stating once, because both fail silently: * Use ``symops`` and ``orbit``, not ``symops_mod_centering`` and ``orbit_mod_centering``. The former are the full sets with centering translations folded in, so ``len(orbit) == multiplicity`` holds; the ``_mod_centering`` variants are the factored forms and mixing the two in a set comparison misreports every centred group. * ``orbit[0]`` follows the record's ``first_orbit``, which differs from ``first_orbit_ita`` in 180 of the 3440 Wyckoff entries. Both describe the same orbit, but only the latter matches what International Tables prints. Functions --------- .. autoapisummary:: httk.atomistic.data.spacegroup_settings httk.atomistic.data.point_groups httk.atomistic.data.spacegroup_setting httk.atomistic.data.spacegroup_setting_by_symop_key httk.atomistic.data.standard_spacegroup_setting httk.atomistic.data.spglib_default_spacegroup_setting httk.atomistic.data.standard_setting_it_numbers httk.atomistic.data.setting_transform httk.atomistic.data.spacegroup_subgroup_record httk.atomistic.data.isomorphic_subgroup_record httk.atomistic.data.affine_normalizer_coset_record Package Contents ---------------- .. py:function:: spacegroup_settings() Return every tabulated space-group setting, one record each. The symmetry-basics dataset is loaded lazily on the first lookup. :return: All tabulated space-group setting records. .. py:function:: point_groups() Return the crystallographic point groups with their operations and character tables. The symmetry-basics dataset is loaded lazily on the first lookup. :return: All tabulated point-group records. .. py:function:: spacegroup_setting(*, hall_entry = None, setting_it_nc = None, hm_entry = None) The setting record identified by exactly one of the given keys. ``hall_entry`` is the normalized Hall symbol (``"-c_2yc"``), ``setting_it_nc`` the IT number with coordinate-system code (``"15:c1"``), and ``hm_entry`` the Hermann-Mauguin entry name (``"C 1 2/c 1"``). A Hall entry names a setting unambiguously — symbol, axes and origin — which is why it is the key the transform dataset uses. Raises :class:`KeyError` if the key is unknown, and :class:`TypeError` unless exactly one key is given. :param hall_entry: The normalized Hall symbol identifying the setting. :param setting_it_nc: The IT number and coordinate-system code identifying the setting. :param hm_entry: The Hermann-Mauguin entry name identifying the setting. :return: The matching space-group setting record. :raises KeyError: If the selected key is unknown. :raises TypeError: If zero or multiple keys are supplied. .. py:function:: spacegroup_setting_by_symop_key(key) Return the setting indexed by a canonical complete-operation-set key. :param key: The v1 key from :func:`httk.atomistic.symmetry.symop_key.symop_key_v1`. :return: The matching space-group setting record. :raises KeyError: If the operations key is not tabulated. .. py:function:: standard_spacegroup_setting(it_number) The IT standard (reference) setting for a space-group number, ``1 <= it_number <= 230``. This is the setting flagged ``is_reference_setting`` and is the one :func:`setting_transform` transforms to. Note it is **not** always spglib's default setting: the two differ for the 24 space groups with two origin choices (48, 50, 59, 68, 70, 85, 86, 88, 125, 126, 129, 130, 133, 134, 137, 138, 141, 142, 201, 203, 222, 224, 227, 228) and agree for the other 206. Any interoperation with spglib must go through an explicit transform rather than assuming the two coincide. :param it_number: The International Tables space-group number. :return: The reference setting record for the number. :raises KeyError: If no reference setting has the requested number. .. py:function:: spglib_default_spacegroup_setting(it_number) The setting spglib treats as its default for a space-group number. This differs from :func:`standard_spacegroup_setting` for the 24 space groups with two origin choices and coincides with it for the other 206, which is exactly why any code that hands coordinates to or takes them from spglib must transform explicitly rather than assume the two agree — the failure mode is a structure displaced by a fraction of a cell that still passes a symmetry check. :param it_number: The International Tables space-group number. :return: The setting record selected by spglib for the number. :raises KeyError: If spglib has no setting for the requested number. .. py:function:: standard_setting_it_numbers() Return the IT numbers that have a tabulated standard setting. :return: The available International Tables space-group numbers in ascending order. .. py:function:: setting_transform(hall_entry) The change-of-basis operation between a setting and its IT standard setting. The returned record's ``affine_transformation`` holds an exact rational ``matrix`` ``M`` and ``vector`` ``v``. **Direction matters and the field name is misleading**: despite deriving from a table called ``hall_to_it_std_transform``, the pair maps standard-setting coordinates *into* this setting, as column vectors:: x_own = M @ x_std + v Under httk's row-vector convention that is ``f_own = f_std @ M.T + v``, with the reverse ``f_std = (f_own - v) @ inv(M).T`` and cell basis rows transforming as ``B_own = inv(M).T @ B_std``. Applying it backwards yields a structurally valid but systematically wrong crystal. ``M`` is unimodular for 520 of the 527 settings. The exceptions are the seven rhombohedral-axes settings (IT numbers 146, 148, 155, 160, 161, 166, 167), where ``det M == 3`` because the standard hexagonal cell has three times the volume of the rhombohedral one — and correspondingly ``inv(M)`` has thirds, so nothing may assume the reverse transform is integral. :param hall_entry: The normalized Hall symbol identifying the setting. :return: The setting-transform record mapping standard-setting coordinates into the named setting. :raises KeyError: If no transform is tabulated for ``hall_entry``. .. py:function:: spacegroup_subgroup_record(it_number) Return the subgroup record for an IT number. :param it_number: The International Tables space-group number. :return: The Bärnighausen and continuous-normalizer record. :raises KeyError: If no record is tabulated for the IT number. .. py:function:: isomorphic_subgroup_record(it_number) Return the standard-setting same-setting isomorphic subgroup record for an IT number. The record's ``isomorphic_subgroups["items"]`` list holds one entry per tabulated isomorphic (same IT number) subgroup transform up to index 9, each with the same ``index``/``wyckoff_splitting``/``affine_transformation`` field shapes as the Bärnighausen entries; index 1 items are identity-cell re-descriptions. :param it_number: The International Tables space-group number. :return: The isomorphic subgroup record. :raises KeyError: If no record is tabulated for the IT number. .. py:function:: affine_normalizer_coset_record(hall_entry) Return the affine-normalizer coset record for a Hall entry. :param hall_entry: The normalized Hall symbol identifying the setting. :return: The affine-normalizer coset record. :raises KeyError: If no record is tabulated for the Hall entry.