Units and tolerances¶
Units¶
AngleUnit(value: int)
The units of a number representing an angle.
from brille import AngleUnit r = AngleUnit.radian
Members:
not_provided : unknown, will be inferred
radian : radian
degree : degree
pi : radian divided by pi
Attributes:
LengthUnit(value: int)
The units of a number representing a length.
from brille import LengthUnit a = LengthUnit.angstrom
Members:
none : A default value, the used value may be inferred
angstrom : 10\ :sup:-10 meter
inverse_angstrom : 1 / angstrom
real_lattice : fractional coordinates of real lattice
reciprocal_lattice : fractional coordinates of reciprocal lattice
Attributes:
-
angstrom(LengthUnit) – -
inverse_angstrom(LengthUnit) – -
none(LengthUnit) – -
real_lattice(LengthUnit) – -
reciprocal_lattice(LengthUnit) – -
name(str) – -
value(int) –
NodeType(value: int)
An enumeration to differentiate between Node types of the brille._brille.BZTrellisQdd,
brille._brille.BZTrellisQdc, and brille._brille.BZTrellisQcc, classes.
The return type of the methods, e.g.,
node_at_type,
node_containing_type, and
all_node_types.
from brill import NodeType nt = NodeType.polygon
Members:
assumed_null : Indicates a node which should be null but no explicit check was performed
found_null : A node which an explicit check found to be null
null : A null node
cube : A cube shaped node
polygon : A convex polygon shaped node
Attributes:
Floating point tolerance¶
brille decides the zone and mesh geometry with exact predicates (Shewchuk's robust predicates and exact expansion arithmetic), but compares user-provided lattices, symmetry operations and points with a floating point tolerance, to allow for rounding in the input and in calculations. Two numbers \(a\) and \(b\) are equal if \(|a - b| \le t + \epsilon\,|a + b|\), with \(t\) an absolute tolerance and \(\epsilon\) machine epsilon.
No one absolute tolerance suits all input: atom positions written as 32-bit floats, for example, are far less precise than the lattice vectors beside them. So real-space and reciprocal-space comparisons have separate tolerances.
The absolute tolerances are \(10^{-12}\) Å in real space and \(10^{-12}\) Å⁻¹ in reciprocal space. They can be changed for the whole module,
import brille
brille.real_space_tolerance(1e-10)
brille.reciprocal_space_tolerance(1e-14)
or for one call, with an ApproxConfig:
config = brille.ApproxConfig()
config.real_space_tolerance = 1e-10
config.reciprocal_space_tolerance = 1e-14
Note
Typical input should not need either. Changing them can cause surprising errors elsewhere.
ApproxConfig(digits: int = 1000, real_space_tolerance: float = 1e-10, reciprocal_space_tolerance: float = 1e-10)
A local set of approximate floating point comparison values
Attributes:
-
digits(int) –A multiplier on the machine epsilon, below which two floating point numbers are approximately the same.
-
real_space_tolerance(float) –An absolute real space floating point tolerance in angstrom
-
reciprocal_space_tolerance(float) –An absolute reciprocal space floating point tolerance in inverse angstrom
property
writable
¶
digits: int
A multiplier on the machine epsilon, below which two floating point numbers are approximately the same.
property
writable
¶
real_space_tolerance: float
An absolute real space floating point tolerance in angstrom
property
writable
¶
reciprocal_space_tolerance: float
An absolute reciprocal space floating point tolerance in inverse angstrom
real_space_tolerance() -> float
real_space_tolerance(tolerance: float) -> None
real_space_tolerance() -> float
Return the module-global real space floating point tolerance in angstrom.
reciprocal_space_tolerance() -> float
reciprocal_space_tolerance(tolerance: float) -> None
reciprocal_space_tolerance() -> float
Return the module-global reciprocal space floating point tolerance in inverse angstrom.