pyextal.jaxJoint.link

Which structure factor is which, across datasets.

The engine names each refined structure factor by a representative it picks from the dataset’s own beam list: under SpaceGroup the first member of the symmetry group it meets (GroupSymmetry.uniqueBeams), under Friedel whichever of g and -g comes first. Two datasets – another zone axis, or just a different beam list – can therefore name the same U_g differently, and the values under the two names are not equal: a glide or screw translation t makes

U(R g) = U(g) exp(-2 pi i t.g)

– a sign change for a phase of pi, which on La4Ni3O10 (P2_1/a) is a third of all equivalent pairs – and U(-g) = U(g)* for the Friedel mate.

So every U_g has a canonical key, the largest (h, k, l) of its whole orbit, which no beam list influences; the shared parameter is U at the canonical key. Each dataset’s own label r reaches it through a fixed link map M, 4 x 4 on (xfre, xfim, afre, afim): U_local = M @ U_shared – a rotation by the translation phase, preceded by a conjugation when r lies in the orbit of -g. M is orthogonal, so U_shared = M.T @ U_local.

check_links verifies every map against the engine’s own structure factors (defaultsf) before anything is refined.

Attributes

CONJ

Functions

as_hkl(g)	Any triple (ints, floats, numpy scalars) -> a tuple of ints.
neg(g)
rotation(phi)	M multiplying U and U' by exp(i phi).
_symmetry_members(g)	[(member, translation)] of g's orbit under the engine's operations.
is_centro()
orbit(g, symmetry, centro)	Every reflection sharing g's refined structure factor.
canonical(g, symmetry, centro)	The canonical key of g's structure factor: the largest member of its orbit.
link_map(local, key, symmetry, centro)	M with U(local) = M @ U(key).
tabulated(g)	The engine's (xfre, xfim, afre, afim) for g, from the crystal structure.
check_links(links[, rtol, floor])	Verifies each link map against the engine's structure factors.
beam_differences(hkl)	Every g = h_i - h_j of a beam list, (000) excluded: the U_g its matrix holds.
sort_keys(keys)	Shortest index first, as the engine orders its reflections.

Module Contents

pyextal.jaxJoint.link.CONJ

pyextal.jaxJoint.link.as_hkl(g)

Any triple (ints, floats, numpy scalars) -> a tuple of ints.

pyextal.jaxJoint.link.neg(g)

pyextal.jaxJoint.link.rotation(phi)

M multiplying U and U’ by exp(i phi).

pyextal.jaxJoint.link._symmetry_members(g)

[(member, translation)] of g’s orbit under the engine’s operations.

pyextal.jaxJoint.link.is_centro()

pyextal.jaxJoint.link.orbit(g, symmetry, centro)

Every reflection sharing g’s refined structure factor.

Parameters:

• g (tuple) – A reflection.

• symmetry (str) – 'Friedel' – g and -g only – or 'SpaceGroup' – the orbit under the space group, with that of -g when the group is centrosymmetric (the engine keeps ops without the inversion and adds it itself, as GroupSymmetry does).

• centro (bool) – The group is centrosymmetric.

Returns:

set[tuple]

pyextal.jaxJoint.link.canonical(g, symmetry, centro)

The canonical key of g’s structure factor: the largest member of its orbit.

pyextal.jaxJoint.link.link_map(local, key, symmetry, centro)

M with U(local) = M @ U(key).

Parameters:

• local (tuple) – The dataset’s label.

• key (tuple) – The canonical key, in local’s orbit.

• symmetry (str) – 'Friedel' or 'SpaceGroup'.

• centro (bool) – The group is centrosymmetric.

Returns:

(4, 4).

Return type:

np.ndarray

Raises:

SetupError – If local is not in key’s orbit.

pyextal.jaxJoint.link.tabulated(g)

The engine’s (xfre, xfim, afre, afim) for g, from the crystal structure.

pyextal.jaxJoint.link.check_links(links, rtol=0.001, floor=1e-07)

Verifies each link map against the engine’s structure factors.

For every (local, key, M), M @ U(key) must equal U(local) as defaultsf computes them from the atom positions. This catches a wrong sign convention, which would otherwise quietly refine a sum of U_g that should be a difference.

Parameters:

• links (list) – (local, key, M) triples; the engine must hold the dataset they belong to.

• rtol (float) – Tolerance, relative to the larger of the two values.

• floor (float) – Pairs where both are below this are not tested (the sign of a zero cannot be checked).

Raises:

SetupError – Naming the pairs that disagree.

pyextal.jaxJoint.link.beam_differences(hkl)

Every g = h_i - h_j of a beam list, (000) excluded: the U_g its matrix holds.

pyextal.jaxJoint.link.sort_keys(keys)

Shortest index first, as the engine orders its reflections.