separating functionality

This commit is contained in:
Martin Diehl 2021-06-02 09:28:27 +02:00
parent b55d51491d
commit 302da1f76a
7 changed files with 755 additions and 674 deletions

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@ -14,11 +14,11 @@ from . import tensor # noqa
from . import mechanics # noqa from . import mechanics # noqa
from . import solver # noqa from . import solver # noqa
from . import grid_filters # noqa from . import grid_filters # noqa
from . import lattice # noqa
#Modules that contain only one class (of the same name), are prefixed by a '_'. #Modules that contain only one class (of the same name), are prefixed by a '_'.
#For example, '_colormap' containsa class called 'Colormap' which is imported as 'damask.Colormap'. #For example, '_colormap' containsa class called 'Colormap' which is imported as 'damask.Colormap'.
from ._rotation import Rotation # noqa from ._rotation import Rotation # noqa
from ._lattice_family import LatticeFamily # noqa from ._lattice_family import LatticeFamily # noqa
from ._lattice import Lattice # noqa
from ._orientation import Orientation # noqa from ._orientation import Orientation # noqa
from ._table import Table # noqa from ._table import Table # noqa
from ._vtk import VTK # noqa from ._vtk import VTK # noqa

651
python/damask/_lattice.py Normal file
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@ -0,0 +1,651 @@
import numpy as np
from . import util
from . import LatticeFamily
lattice_symmetries = {
'aP': 'triclinic',
'mP': 'monoclinic',
'mS': 'monoclinic',
'oP': 'orthorhombic',
'oS': 'orthorhombic',
'oI': 'orthorhombic',
'oF': 'orthorhombic',
'tP': 'tetragonal',
'tI': 'tetragonal',
'hP': 'hexagonal',
'cP': 'cubic',
'cI': 'cubic',
'cF': 'cubic',
}
class Lattice(LatticeFamily):
"""Lattice."""
def __init__(self,
lattice = None,
a = None,b = None,c = None,
alpha = None,beta = None,gamma = None,
degrees = False):
"""
Lattice.
Parameters
----------
lattice : {'aP', 'mP', 'mS', 'oP', 'oS', 'oI', 'oF', 'tP', 'tI', 'hP', 'cP', 'cI', 'cF'}.
Name of the Bravais lattice in Pearson notation.
a : float, optional
Length of lattice parameter 'a'.
b : float, optional
Length of lattice parameter 'b'.
c : float, optional
Length of lattice parameter 'c'.
alpha : float, optional
Angle between b and c lattice basis.
beta : float, optional
Angle between c and a lattice basis.
gamma : float, optional
Angle between a and b lattice basis.
degrees : bool, optional
Angles are given in degrees. Defaults to False.
"""
super().__init__(lattice_symmetries[lattice])
self.lattice = lattice
self.a = 1 if a is None else a
self.b = b
self.c = c
self.a = float(self.a) if self.a is not None else \
(self.b / self.ratio['b'] if self.b is not None and self.ratio['b'] is not None else
self.c / self.ratio['c'] if self.c is not None and self.ratio['c'] is not None else None)
self.b = float(self.b) if self.b is not None else \
(self.a * self.ratio['b'] if self.a is not None and self.ratio['b'] is not None else
self.c / self.ratio['c'] * self.ratio['b']
if self.c is not None and self.ratio['b'] is not None and self.ratio['c'] is not None else None)
self.c = float(self.c) if self.c is not None else \
(self.a * self.ratio['c'] if self.a is not None and self.ratio['c'] is not None else
self.b / self.ratio['b'] * self.ratio['c']
if self.c is not None and self.ratio['b'] is not None and self.ratio['c'] is not None else None)
self.alpha = np.radians(alpha) if degrees and alpha is not None else alpha
self.beta = np.radians(beta) if degrees and beta is not None else beta
self.gamma = np.radians(gamma) if degrees and gamma is not None else gamma
if self.alpha is None and 'alpha' in self.immutable: self.alpha = self.immutable['alpha']
if self.beta is None and 'beta' in self.immutable: self.beta = self.immutable['beta']
if self.gamma is None and 'gamma' in self.immutable: self.gamma = self.immutable['gamma']
if \
(self.a is None) \
or (self.b is None or ('b' in self.immutable and self.b != self.immutable['b'] * self.a)) \
or (self.c is None or ('c' in self.immutable and self.c != self.immutable['c'] * self.b)) \
or (self.alpha is None or ('alpha' in self.immutable and self.alpha != self.immutable['alpha'])) \
or (self.beta is None or ( 'beta' in self.immutable and self.beta != self.immutable['beta'])) \
or (self.gamma is None or ('gamma' in self.immutable and self.gamma != self.immutable['gamma'])):
raise ValueError (f'Incompatible parameters {self.parameters} for crystal family {self.family}')
if np.any(np.array([self.alpha,self.beta,self.gamma]) <= 0):
raise ValueError ('Lattice angles must be positive')
if np.any([np.roll([self.alpha,self.beta,self.gamma],r)[0]
> np.sum(np.roll([self.alpha,self.beta,self.gamma],r)[1:]) for r in range(3)]):
raise ValueError ('Each lattice angle must be less than sum of others')
@property
def parameters(self):
"""Return lattice parameters a, b, c, alpha, beta, gamma."""
return (self.a,self.b,self.c,self.alpha,self.beta,self.gamma)
@property
def ratio(self):
"""Return axes ratios of own lattice."""
_ratio = { 'hexagonal': {'c': np.sqrt(8./3.)}}
return dict(b = self.immutable['b']
if 'b' in self.immutable else
_ratio[self.family]['b'] if self.family in _ratio and 'b' in _ratio[self.family] else None,
c = self.immutable['c']
if 'c' in self.immutable else
_ratio[self.family]['c'] if self.family in _ratio and 'c' in _ratio[self.family] else None,
)
@property
def basis_real(self):
"""
Calculate orthogonal real space crystal basis.
References
----------
C.T. Young and J.L. Lytton, Journal of Applied Physics 43:14081417, 1972
https://doi.org/10.1063/1.1661333
"""
if None in self.parameters:
raise KeyError('missing crystal lattice parameters')
return np.array([
[1,0,0],
[np.cos(self.gamma),np.sin(self.gamma),0],
[np.cos(self.beta),
(np.cos(self.alpha)-np.cos(self.beta)*np.cos(self.gamma)) /np.sin(self.gamma),
np.sqrt(1 - np.cos(self.alpha)**2 - np.cos(self.beta)**2 - np.cos(self.gamma)**2
+ 2 * np.cos(self.alpha) * np.cos(self.beta) * np.cos(self.gamma))/np.sin(self.gamma)],
],dtype=float).T \
* np.array([self.a,self.b,self.c])
@property
def basis_reciprocal(self):
"""Calculate reciprocal (dual) crystal basis."""
return np.linalg.inv(self.basis_real.T)
def to_lattice(self,*,direction=None,plane=None):
"""
Calculate lattice vector corresponding to crystal frame direction or plane normal.
Parameters
----------
direction|normal : numpy.ndarray of shape (...,3)
Vector along direction or plane normal.
Returns
-------
Miller : numpy.ndarray of shape (...,3)
lattice vector of direction or plane.
Use util.scale_to_coprime to convert to (integer) Miller indices.
"""
if (direction is not None) ^ (plane is None):
raise KeyError('Specify either "direction" or "plane"')
axis,basis = (np.array(direction),self.basis_reciprocal.T) \
if plane is None else \
(np.array(plane),self.basis_real.T)
return np.einsum('il,...l',basis,axis)
def to_frame(self,*,uvw=None,hkl=None):
"""
Calculate crystal frame vector along lattice direction [uvw] or plane normal (hkl).
Parameters
----------
uvw|hkl : numpy.ndarray of shape (...,3)
Miller indices of crystallographic direction or plane normal.
Returns
-------
vector : numpy.ndarray of shape (...,3) or (N,...,3)
Crystal frame vector (or vectors if with_symmetry) along [uvw] direction or (hkl) plane normal.
"""
if (uvw is not None) ^ (hkl is None):
raise KeyError('Specify either "uvw" or "hkl"')
axis,basis = (np.array(uvw),self.basis_real) \
if hkl is None else \
(np.array(hkl),self.basis_reciprocal)
return np.einsum('il,...l',basis,axis)
def kinematics(self,mode):
master = self._kinematics[self.lattice][mode]
if self.lattice == 'hP':
return {'direction':util.Bravais_to_Miller(uvtw=master[:,0:4]),
'plane': util.Bravais_to_Miller(hkil=master[:,4:8])}
else:
return {'direction':master[:,0:3],
'plane': master[:,3:6]}
@property
def orientation_relationships(self):
return {k:v for k,v in self._orientation_relationships.items() if self.lattice in v}
_kinematics = {
'cF': {
'slip' : np.array([
[+0,+1,-1, +1,+1,+1],
[-1,+0,+1, +1,+1,+1],
[+1,-1,+0, +1,+1,+1],
[+0,-1,-1, -1,-1,+1],
[+1,+0,+1, -1,-1,+1],
[-1,+1,+0, -1,-1,+1],
[+0,-1,+1, +1,-1,-1],
[-1,+0,-1, +1,-1,-1],
[+1,+1,+0, +1,-1,-1],
[+0,+1,+1, -1,+1,-1],
[+1,+0,-1, -1,+1,-1],
[-1,-1,+0, -1,+1,-1],
[+1,+1,+0, +1,-1,+0],
[+1,-1,+0, +1,+1,+0],
[+1,+0,+1, +1,+0,-1],
[+1,+0,-1, +1,+0,+1],
[+0,+1,+1, +0,+1,-1],
[+0,+1,-1, +0,+1,+1],
],'d'),
'twin' : np.array([
[-2, 1, 1, 1, 1, 1],
[ 1,-2, 1, 1, 1, 1],
[ 1, 1,-2, 1, 1, 1],
[ 2,-1, 1, -1,-1, 1],
[-1, 2, 1, -1,-1, 1],
[-1,-1,-2, -1,-1, 1],
[-2,-1,-1, 1,-1,-1],
[ 1, 2,-1, 1,-1,-1],
[ 1,-1, 2, 1,-1,-1],
[ 2, 1,-1, -1, 1,-1],
[-1,-2,-1, -1, 1,-1],
[-1, 1, 2, -1, 1,-1],
],dtype=float),
},
'cI': {
'slip' : np.array([
[+1,-1,+1, +0,+1,+1],
[-1,-1,+1, +0,+1,+1],
[+1,+1,+1, +0,-1,+1],
[-1,+1,+1, +0,-1,+1],
[-1,+1,+1, +1,+0,+1],
[-1,-1,+1, +1,+0,+1],
[+1,+1,+1, -1,+0,+1],
[+1,-1,+1, -1,+0,+1],
[-1,+1,+1, +1,+1,+0],
[-1,+1,-1, +1,+1,+0],
[+1,+1,+1, -1,+1,+0],
[+1,+1,-1, -1,+1,+0],
[-1,+1,+1, +2,+1,+1],
[+1,+1,+1, -2,+1,+1],
[+1,+1,-1, +2,-1,+1],
[+1,-1,+1, +2,+1,-1],
[+1,-1,+1, +1,+2,+1],
[+1,+1,-1, -1,+2,+1],
[+1,+1,+1, +1,-2,+1],
[-1,+1,+1, +1,+2,-1],
[+1,+1,-1, +1,+1,+2],
[+1,-1,+1, -1,+1,+2],
[-1,+1,+1, +1,-1,+2],
[+1,+1,+1, +1,+1,-2],
[+1,+1,-1, +1,+2,+3],
[+1,-1,+1, -1,+2,+3],
[-1,+1,+1, +1,-2,+3],
[+1,+1,+1, +1,+2,-3],
[+1,-1,+1, +1,+3,+2],
[+1,+1,-1, -1,+3,+2],
[+1,+1,+1, +1,-3,+2],
[-1,+1,+1, +1,+3,-2],
[+1,+1,-1, +2,+1,+3],
[+1,-1,+1, -2,+1,+3],
[-1,+1,+1, +2,-1,+3],
[+1,+1,+1, +2,+1,-3],
[+1,-1,+1, +2,+3,+1],
[+1,+1,-1, -2,+3,+1],
[+1,+1,+1, +2,-3,+1],
[-1,+1,+1, +2,+3,-1],
[-1,+1,+1, +3,+1,+2],
[+1,+1,+1, -3,+1,+2],
[+1,+1,-1, +3,-1,+2],
[+1,-1,+1, +3,+1,-2],
[-1,+1,+1, +3,+2,+1],
[+1,+1,+1, -3,+2,+1],
[+1,+1,-1, +3,-2,+1],
[+1,-1,+1, +3,+2,-1],
],'d'),
'twin' : np.array([
[-1, 1, 1, 2, 1, 1],
[ 1, 1, 1, -2, 1, 1],
[ 1, 1,-1, 2,-1, 1],
[ 1,-1, 1, 2, 1,-1],
[ 1,-1, 1, 1, 2, 1],
[ 1, 1,-1, -1, 2, 1],
[ 1, 1, 1, 1,-2, 1],
[-1, 1, 1, 1, 2,-1],
[ 1, 1,-1, 1, 1, 2],
[ 1,-1, 1, -1, 1, 2],
[-1, 1, 1, 1,-1, 2],
[ 1, 1, 1, 1, 1,-2],
],dtype=float),
},
'hP': {
'slip' : np.array([
[+2,-1,-1,+0, +0,+0,+0,+1],
[-1,+2,-1,+0, +0,+0,+0,+1],
[-1,-1,+2,+0, +0,+0,+0,+1],
[+2,-1,-1,+0, +0,+1,-1,+0],
[-1,+2,-1,+0, -1,+0,+1,+0],
[-1,-1,+2,+0, +1,-1,+0,+0],
[-1,+1,+0,+0, +1,+1,-2,+0],
[+0,-1,+1,+0, -2,+1,+1,+0],
[+1,+0,-1,+0, +1,-2,+1,+0],
[-1,+2,-1,+0, +1,+0,-1,+1],
[-2,+1,+1,+0, +0,+1,-1,+1],
[-1,-1,+2,+0, -1,+1,+0,+1],
[+1,-2,+1,+0, -1,+0,+1,+1],
[+2,-1,-1,+0, +0,-1,+1,+1],
[+1,+1,-2,+0, +1,-1,+0,+1],
[-2,+1,+1,+3, +1,+0,-1,+1],
[-1,-1,+2,+3, +1,+0,-1,+1],
[-1,-1,+2,+3, +0,+1,-1,+1],
[+1,-2,+1,+3, +0,+1,-1,+1],
[+1,-2,+1,+3, -1,+1,+0,+1],
[+2,-1,-1,+3, -1,+1,+0,+1],
[+2,-1,-1,+3, -1,+0,+1,+1],
[+1,+1,-2,+3, -1,+0,+1,+1],
[+1,+1,-2,+3, +0,-1,+1,+1],
[-1,+2,-1,+3, +0,-1,+1,+1],
[-1,+2,-1,+3, +1,-1,+0,+1],
[-2,+1,+1,+3, +1,-1,+0,+1],
[-1,-1,+2,+3, +1,+1,-2,+2],
[+1,-2,+1,+3, -1,+2,-1,+2],
[+2,-1,-1,+3, -2,+1,+1,+2],
[+1,+1,-2,+3, -1,-1,+2,+2],
[-1,+2,-1,+3, +1,-2,+1,+2],
[-2,+1,+1,+3, +2,-1,-1,+2],
],'d'),
'twin' : np.array([
[-1, 0, 1, 1, 1, 0,-1, 2], # shear = (3-(c/a)^2)/(sqrt(3) c/a) <-10.1>{10.2}
[ 0,-1, 1, 1, 0, 1,-1, 2],
[ 1,-1, 0, 1, -1, 1, 0, 2],
[ 1, 0,-1, 1, -1, 0, 1, 2],
[ 0, 1,-1, 1, 0,-1, 1, 2],
[-1, 1, 0, 1, 1,-1, 0, 2],
[-1,-1, 2, 6, 1, 1,-2, 1], # shear = 1/(c/a) <11.6>{-1-1.1}
[ 1,-2, 1, 6, -1, 2,-1, 1],
[ 2,-1,-1, 6, -2, 1, 1, 1],
[ 1, 1,-2, 6, -1,-1, 2, 1],
[-1, 2,-1, 6, 1,-2, 1, 1],
[-2, 1, 1, 6, 2,-1,-1, 1],
[ 1, 0,-1,-2, 1, 0,-1, 1], # shear = (4(c/a)^2-9)/(4 sqrt(3) c/a) <10.-2>{10.1}
[ 0, 1,-1,-2, 0, 1,-1, 1],
[-1, 1, 0,-2, -1, 1, 0, 1],
[-1, 0, 1,-2, -1, 0, 1, 1],
[ 0,-1, 1,-2, 0,-1, 1, 1],
[ 1,-1, 0,-2, 1,-1, 0, 1],
[ 1, 1,-2,-3, 1, 1,-2, 2], # shear = 2((c/a)^2-2)/(3 c/a) <11.-3>{11.2}
[-1, 2,-1,-3, -1, 2,-1, 2],
[-2, 1, 1,-3, -2, 1, 1, 2],
[-1,-1, 2,-3, -1,-1, 2, 2],
[ 1,-2, 1,-3, 1,-2, 1, 2],
[ 2,-1,-1,-3, 2,-1,-1, 2],
],dtype=float),
},
}
_orientation_relationships = {
'KS': {
'cF' : np.array([
[[-1, 0, 1],[ 1, 1, 1]],
[[-1, 0, 1],[ 1, 1, 1]],
[[ 0, 1,-1],[ 1, 1, 1]],
[[ 0, 1,-1],[ 1, 1, 1]],
[[ 1,-1, 0],[ 1, 1, 1]],
[[ 1,-1, 0],[ 1, 1, 1]],
[[ 1, 0,-1],[ 1,-1, 1]],
[[ 1, 0,-1],[ 1,-1, 1]],
[[-1,-1, 0],[ 1,-1, 1]],
[[-1,-1, 0],[ 1,-1, 1]],
[[ 0, 1, 1],[ 1,-1, 1]],
[[ 0, 1, 1],[ 1,-1, 1]],
[[ 0,-1, 1],[-1, 1, 1]],
[[ 0,-1, 1],[-1, 1, 1]],
[[-1, 0,-1],[-1, 1, 1]],
[[-1, 0,-1],[-1, 1, 1]],
[[ 1, 1, 0],[-1, 1, 1]],
[[ 1, 1, 0],[-1, 1, 1]],
[[-1, 1, 0],[ 1, 1,-1]],
[[-1, 1, 0],[ 1, 1,-1]],
[[ 0,-1,-1],[ 1, 1,-1]],
[[ 0,-1,-1],[ 1, 1,-1]],
[[ 1, 0, 1],[ 1, 1,-1]],
[[ 1, 0, 1],[ 1, 1,-1]],
],dtype=float),
'cI' : np.array([
[[-1,-1, 1],[ 0, 1, 1]],
[[-1, 1,-1],[ 0, 1, 1]],
[[-1,-1, 1],[ 0, 1, 1]],
[[-1, 1,-1],[ 0, 1, 1]],
[[-1,-1, 1],[ 0, 1, 1]],
[[-1, 1,-1],[ 0, 1, 1]],
[[-1,-1, 1],[ 0, 1, 1]],
[[-1, 1,-1],[ 0, 1, 1]],
[[-1,-1, 1],[ 0, 1, 1]],
[[-1, 1,-1],[ 0, 1, 1]],
[[-1,-1, 1],[ 0, 1, 1]],
[[-1, 1,-1],[ 0, 1, 1]],
[[-1,-1, 1],[ 0, 1, 1]],
[[-1, 1,-1],[ 0, 1, 1]],
[[-1,-1, 1],[ 0, 1, 1]],
[[-1, 1,-1],[ 0, 1, 1]],
[[-1,-1, 1],[ 0, 1, 1]],
[[-1, 1,-1],[ 0, 1, 1]],
[[-1,-1, 1],[ 0, 1, 1]],
[[-1, 1,-1],[ 0, 1, 1]],
[[-1,-1, 1],[ 0, 1, 1]],
[[-1, 1,-1],[ 0, 1, 1]],
[[-1,-1, 1],[ 0, 1, 1]],
[[-1, 1,-1],[ 0, 1, 1]],
],dtype=float),
},
'GT': {
'cF' : np.array([
[[ -5,-12, 17],[ 1, 1, 1]],
[[ 17, -5,-12],[ 1, 1, 1]],
[[-12, 17, -5],[ 1, 1, 1]],
[[ 5, 12, 17],[ -1, -1, 1]],
[[-17, 5,-12],[ -1, -1, 1]],
[[ 12,-17, -5],[ -1, -1, 1]],
[[ -5, 12,-17],[ -1, 1, 1]],
[[ 17, 5, 12],[ -1, 1, 1]],
[[-12,-17, 5],[ -1, 1, 1]],
[[ 5,-12,-17],[ 1, -1, 1]],
[[-17, -5, 12],[ 1, -1, 1]],
[[ 12, 17, 5],[ 1, -1, 1]],
[[ -5, 17,-12],[ 1, 1, 1]],
[[-12, -5, 17],[ 1, 1, 1]],
[[ 17,-12, -5],[ 1, 1, 1]],
[[ 5,-17,-12],[ -1, -1, 1]],
[[ 12, 5, 17],[ -1, -1, 1]],
[[-17, 12, -5],[ -1, -1, 1]],
[[ -5,-17, 12],[ -1, 1, 1]],
[[-12, 5,-17],[ -1, 1, 1]],
[[ 17, 12, 5],[ -1, 1, 1]],
[[ 5, 17, 12],[ 1, -1, 1]],
[[ 12, -5,-17],[ 1, -1, 1]],
[[-17,-12, 5],[ 1, -1, 1]],
],dtype=float),
'cI' : np.array([
[[-17, -7, 17],[ 1, 0, 1]],
[[ 17,-17, -7],[ 1, 1, 0]],
[[ -7, 17,-17],[ 0, 1, 1]],
[[ 17, 7, 17],[ -1, 0, 1]],
[[-17, 17, -7],[ -1, -1, 0]],
[[ 7,-17,-17],[ 0, -1, 1]],
[[-17, 7,-17],[ -1, 0, 1]],
[[ 17, 17, 7],[ -1, 1, 0]],
[[ -7,-17, 17],[ 0, 1, 1]],
[[ 17, -7,-17],[ 1, 0, 1]],
[[-17,-17, 7],[ 1, -1, 0]],
[[ 7, 17, 17],[ 0, -1, 1]],
[[-17, 17, -7],[ 1, 1, 0]],
[[ -7,-17, 17],[ 0, 1, 1]],
[[ 17, -7,-17],[ 1, 0, 1]],
[[ 17,-17, -7],[ -1, -1, 0]],
[[ 7, 17, 17],[ 0, -1, 1]],
[[-17, 7,-17],[ -1, 0, 1]],
[[-17,-17, 7],[ -1, 1, 0]],
[[ -7, 17,-17],[ 0, 1, 1]],
[[ 17, 7, 17],[ -1, 0, 1]],
[[ 17, 17, 7],[ 1, -1, 0]],
[[ 7,-17,-17],[ 0, -1, 1]],
[[-17, -7, 17],[ 1, 0, 1]],
],dtype=float),
},
'GT_prime': {
'cF' : np.array([
[[ 0, 1, -1],[ 7, 17, 17]],
[[ -1, 0, 1],[ 17, 7, 17]],
[[ 1, -1, 0],[ 17, 17, 7]],
[[ 0, -1, -1],[ -7,-17, 17]],
[[ 1, 0, 1],[-17, -7, 17]],
[[ 1, -1, 0],[-17,-17, 7]],
[[ 0, 1, -1],[ 7,-17,-17]],
[[ 1, 0, 1],[ 17, -7,-17]],
[[ -1, -1, 0],[ 17,-17, -7]],
[[ 0, -1, -1],[ -7, 17,-17]],
[[ -1, 0, 1],[-17, 7,-17]],
[[ -1, -1, 0],[-17, 17, -7]],
[[ 0, -1, 1],[ 7, 17, 17]],
[[ 1, 0, -1],[ 17, 7, 17]],
[[ -1, 1, 0],[ 17, 17, 7]],
[[ 0, 1, 1],[ -7,-17, 17]],
[[ -1, 0, -1],[-17, -7, 17]],
[[ -1, 1, 0],[-17,-17, 7]],
[[ 0, -1, 1],[ 7,-17,-17]],
[[ -1, 0, -1],[ 17, -7,-17]],
[[ 1, 1, 0],[ 17,-17, -7]],
[[ 0, 1, 1],[ -7, 17,-17]],
[[ 1, 0, -1],[-17, 7,-17]],
[[ 1, 1, 0],[-17, 17, -7]],
],dtype=float),
'cI' : np.array([
[[ 1, 1, -1],[ 12, 5, 17]],
[[ -1, 1, 1],[ 17, 12, 5]],
[[ 1, -1, 1],[ 5, 17, 12]],
[[ -1, -1, -1],[-12, -5, 17]],
[[ 1, -1, 1],[-17,-12, 5]],
[[ 1, -1, -1],[ -5,-17, 12]],
[[ -1, 1, -1],[ 12, -5,-17]],
[[ 1, 1, 1],[ 17,-12, -5]],
[[ -1, -1, 1],[ 5,-17,-12]],
[[ 1, -1, -1],[-12, 5,-17]],
[[ -1, -1, 1],[-17, 12, -5]],
[[ -1, -1, -1],[ -5, 17,-12]],
[[ 1, -1, 1],[ 12, 17, 5]],
[[ 1, 1, -1],[ 5, 12, 17]],
[[ -1, 1, 1],[ 17, 5, 12]],
[[ -1, 1, 1],[-12,-17, 5]],
[[ -1, -1, -1],[ -5,-12, 17]],
[[ -1, 1, -1],[-17, -5, 12]],
[[ -1, -1, 1],[ 12,-17, -5]],
[[ -1, 1, -1],[ 5,-12,-17]],
[[ 1, 1, 1],[ 17, -5,-12]],
[[ 1, 1, 1],[-12, 17, -5]],
[[ 1, -1, -1],[ -5, 12,-17]],
[[ 1, 1, -1],[-17, 5,-12]],
],dtype=float),
},
'NW': {
'cF' : np.array([
[[ 2, -1, -1],[ 1, 1, 1]],
[[ -1, 2, -1],[ 1, 1, 1]],
[[ -1, -1, 2],[ 1, 1, 1]],
[[ -2, -1, -1],[ -1, 1, 1]],
[[ 1, 2, -1],[ -1, 1, 1]],
[[ 1, -1, 2],[ -1, 1, 1]],
[[ 2, 1, -1],[ 1, -1, 1]],
[[ -1, -2, -1],[ 1, -1, 1]],
[[ -1, 1, 2],[ 1, -1, 1]],
[[ 2, -1, 1],[ -1, -1, 1]],
[[ -1, 2, 1],[ -1, -1, 1]],
[[ -1, -1, -2],[ -1, -1, 1]],
],dtype=float),
'cI' : np.array([
[[ 0, -1, 1],[ 0, 1, 1]],
[[ 0, -1, 1],[ 0, 1, 1]],
[[ 0, -1, 1],[ 0, 1, 1]],
[[ 0, -1, 1],[ 0, 1, 1]],
[[ 0, -1, 1],[ 0, 1, 1]],
[[ 0, -1, 1],[ 0, 1, 1]],
[[ 0, -1, 1],[ 0, 1, 1]],
[[ 0, -1, 1],[ 0, 1, 1]],
[[ 0, -1, 1],[ 0, 1, 1]],
[[ 0, -1, 1],[ 0, 1, 1]],
[[ 0, -1, 1],[ 0, 1, 1]],
[[ 0, -1, 1],[ 0, 1, 1]],
],dtype=float),
},
'Pitsch': {
'cF' : np.array([
[[ 1, 0, 1],[ 0, 1, 0]],
[[ 1, 1, 0],[ 0, 0, 1]],
[[ 0, 1, 1],[ 1, 0, 0]],
[[ 0, 1, -1],[ 1, 0, 0]],
[[ -1, 0, 1],[ 0, 1, 0]],
[[ 1, -1, 0],[ 0, 0, 1]],
[[ 1, 0, -1],[ 0, 1, 0]],
[[ -1, 1, 0],[ 0, 0, 1]],
[[ 0, -1, 1],[ 1, 0, 0]],
[[ 0, 1, 1],[ 1, 0, 0]],
[[ 1, 0, 1],[ 0, 1, 0]],
[[ 1, 1, 0],[ 0, 0, 1]],
],dtype=float),
'cI' : np.array([
[[ 1, -1, 1],[ -1, 0, 1]],
[[ 1, 1, -1],[ 1, -1, 0]],
[[ -1, 1, 1],[ 0, 1, -1]],
[[ -1, 1, -1],[ 0, -1, -1]],
[[ -1, -1, 1],[ -1, 0, -1]],
[[ 1, -1, -1],[ -1, -1, 0]],
[[ 1, -1, -1],[ -1, 0, -1]],
[[ -1, 1, -1],[ -1, -1, 0]],
[[ -1, -1, 1],[ 0, -1, -1]],
[[ -1, 1, 1],[ 0, -1, 1]],
[[ 1, -1, 1],[ 1, 0, -1]],
[[ 1, 1, -1],[ -1, 1, 0]],
],dtype=float),
},
'Bain': {
'cF' : np.array([
[[ 0, 1, 0],[ 1, 0, 0]],
[[ 0, 0, 1],[ 0, 1, 0]],
[[ 1, 0, 0],[ 0, 0, 1]],
],dtype=float),
'cI' : np.array([
[[ 0, 1, 1],[ 1, 0, 0]],
[[ 1, 0, 1],[ 0, 1, 0]],
[[ 1, 1, 0],[ 0, 0, 1]],
],dtype=float),
},
'Burgers' : {
'cI' : np.array([
[[ -1, 1, 1],[ 1, 1, 0]],
[[ -1, 1, -1],[ 1, 1, 0]],
[[ 1, 1, 1],[ 1, -1, 0]],
[[ 1, 1, -1],[ 1, -1, 0]],
[[ 1, 1, -1],[ 1, 0, 1]],
[[ -1, 1, 1],[ 1, 0, 1]],
[[ 1, 1, 1],[ -1, 0, 1]],
[[ 1, -1, 1],[ -1, 0, 1]],
[[ -1, 1, -1],[ 0, 1, 1]],
[[ 1, 1, -1],[ 0, 1, 1]],
[[ -1, 1, 1],[ 0, -1, 1]],
[[ 1, 1, 1],[ 0, -1, 1]],
],dtype=float),
'hP' : np.array([
[[ -1, 2, -1, 0],[ 0, 0, 0, 1]],
[[ -1, -1, 2, 0],[ 0, 0, 0, 1]],
[[ -1, 2, -1, 0],[ 0, 0, 0, 1]],
[[ -1, -1, 2, 0],[ 0, 0, 0, 1]],
[[ -1, 2, -1, 0],[ 0, 0, 0, 1]],
[[ -1, -1, 2, 0],[ 0, 0, 0, 1]],
[[ -1, 2, -1, 0],[ 0, 0, 0, 1]],
[[ -1, -1, 2, 0],[ 0, 0, 0, 1]],
[[ -1, 2, -1, 0],[ 0, 0, 0, 1]],
[[ -1, -1, 2, 0],[ 0, 0, 0, 1]],
[[ -1, 2, -1, 0],[ 0, 0, 0, 1]],
[[ -1, -1, 2, 0],[ 0, 0, 0, 1]],
],dtype=float),
},
}

View File

@ -5,7 +5,15 @@ from . import Rotation
class LatticeFamily(): class LatticeFamily():
def __init__(self,family): def __init__(self,family):
"""Symmetry-related operations for crystal families.""" """
Symmetry-related operations for crystal families.
Parameters
----------
family : {'triclinic', 'monoclinic', 'orthorhombic', 'tetragonal', 'hexagonal', 'cubic'}
Name of the crystal family.
"""
if family not in self._immutable.keys(): if family not in self._immutable.keys():
raise KeyError(f'invalid lattice family "{family}"') raise KeyError(f'invalid lattice family "{family}"')
self.family = family self.family = family
@ -121,41 +129,36 @@ class LatticeFamily():
_immutable = { _immutable = {
'cubic': 'cubic': {
{
'b': 1.0, 'b': 1.0,
'c': 1.0, 'c': 1.0,
'alpha': np.pi/2., 'alpha': np.pi/2.,
'beta': np.pi/2., 'beta': np.pi/2.,
'gamma': np.pi/2., 'gamma': np.pi/2.,
}, },
'hexagonal': 'hexagonal': {
{
'b': 1.0, 'b': 1.0,
'alpha': np.pi/2., 'alpha': np.pi/2.,
'beta': np.pi/2., 'beta': np.pi/2.,
'gamma': 2.*np.pi/3., 'gamma': 2.*np.pi/3.,
}, },
'tetragonal': 'tetragonal': {
{
'b': 1.0, 'b': 1.0,
'alpha': np.pi/2., 'alpha': np.pi/2.,
'beta': np.pi/2., 'beta': np.pi/2.,
'gamma': np.pi/2., 'gamma': np.pi/2.,
}, },
'orthorhombic': 'orthorhombic': {
{
'alpha': np.pi/2., 'alpha': np.pi/2.,
'beta': np.pi/2., 'beta': np.pi/2.,
'gamma': np.pi/2., 'gamma': np.pi/2.,
}, },
'monoclinic': 'monoclinic': {
{
'alpha': np.pi/2., 'alpha': np.pi/2.,
'gamma': np.pi/2., 'gamma': np.pi/2.,
}, },
'triclinic': {} 'triclinic': {}
} }
_basis = { _basis = {

View File

@ -4,9 +4,9 @@ import numpy as np
from . import Rotation from . import Rotation
from . import LatticeFamily from . import LatticeFamily
from . import Lattice
from . import util from . import util
from . import tensor from . import tensor
from . import lattice as lattice_
lattice_symmetries = { lattice_symmetries = {
@ -130,13 +130,13 @@ class Orientation(Rotation):
Defaults to no rotation. Defaults to no rotation.
""" """
Rotation.__init__(self,rotation=rotation) super().__init__(rotation)
if family in set(lattice_symmetries.values()) and lattice is None: if family in set(lattice_symmetries.values()) and lattice is None:
self.family = family self.family = family
self.lattice = None self.lattice = None
l = LatticeFamily(self.family) l = LatticeFamily(self.family) # noqa
self.immutable = l.immutable self.immutable = l.immutable
self.basis = l.basis self.basis = l.basis
self.symmetry_operations = l.symmetry_operations self.symmetry_operations = l.symmetry_operations
@ -149,48 +149,25 @@ class Orientation(Rotation):
self.family = lattice_symmetries[lattice] self.family = lattice_symmetries[lattice]
self.lattice = lattice self.lattice = lattice
l = LatticeFamily(self.family) l = Lattice(self.lattice, a,b,c, alpha,beta,gamma, degrees) # noqa
self.immutable = l.immutable self.immutable = l.immutable
self.basis = l.basis self.basis = l.basis
self.symmetry_operations = l.symmetry_operations self.symmetry_operations = l.symmetry_operations
self.a = 1 if a is None else a self.a = l.a
self.b = b self.b = l.b
self.c = c self.c = l.c
self.a = float(self.a) if self.a is not None else \
(self.b / self.ratio['b'] if self.b is not None and self.ratio['b'] is not None else
self.c / self.ratio['c'] if self.c is not None and self.ratio['c'] is not None else None)
self.b = float(self.b) if self.b is not None else \
(self.a * self.ratio['b'] if self.a is not None and self.ratio['b'] is not None else
self.c / self.ratio['c'] * self.ratio['b']
if self.c is not None and self.ratio['b'] is not None and self.ratio['c'] is not None else None)
self.c = float(self.c) if self.c is not None else \
(self.a * self.ratio['c'] if self.a is not None and self.ratio['c'] is not None else
self.b / self.ratio['b'] * self.ratio['c']
if self.c is not None and self.ratio['b'] is not None and self.ratio['c'] is not None else None)
self.alpha = np.radians(alpha) if degrees and alpha is not None else alpha self.alpha = l.alpha
self.beta = np.radians(beta) if degrees and beta is not None else beta self.beta = l.beta
self.gamma = np.radians(gamma) if degrees and gamma is not None else gamma self.gamma = l.gamma
if self.alpha is None and 'alpha' in self.immutable: self.alpha = self.immutable['alpha']
if self.beta is None and 'beta' in self.immutable: self.beta = self.immutable['beta']
if self.gamma is None and 'gamma' in self.immutable: self.gamma = self.immutable['gamma']
if \ self.ratio = l.ratio
(self.a is None) \
or (self.b is None or ('b' in self.immutable and self.b != self.immutable['b'] * self.a)) \
or (self.c is None or ('c' in self.immutable and self.c != self.immutable['c'] * self.b)) \
or (self.alpha is None or ('alpha' in self.immutable and self.alpha != self.immutable['alpha'])) \
or (self.beta is None or ( 'beta' in self.immutable and self.beta != self.immutable['beta'])) \
or (self.gamma is None or ('gamma' in self.immutable and self.gamma != self.immutable['gamma'])):
raise ValueError (f'Incompatible parameters {self.parameters} for crystal family {self.family}')
if np.any(np.array([self.alpha,self.beta,self.gamma]) <= 0): self.to_frame = l.to_frame
raise ValueError ('Lattice angles must be positive')
if np.any([np.roll([self.alpha,self.beta,self.gamma],r)[0]
> np.sum(np.roll([self.alpha,self.beta,self.gamma],r)[1:]) for r in range(3)]):
raise ValueError ('Each lattice angle must be less than sum of others')
self.kinematics = l.kinematics
self.orientation_relationships = l.orientation_relationships
else: else:
raise KeyError(f'no valid family or lattice') raise KeyError(f'no valid family or lattice')
@ -590,12 +567,9 @@ class Orientation(Rotation):
https://doi.org/10.1016/j.actamat.2004.11.021 https://doi.org/10.1016/j.actamat.2004.11.021
""" """
if model not in lattice_.relations: if model not in self.orientation_relationships:
raise KeyError(f'unknown orientation relationship "{model}"') raise KeyError(f'unknown orientation relationship "{model}"')
r = lattice_.relations[model] r = self.orientation_relationships[model]
if self.lattice not in r:
raise KeyError(f'relationship "{model}" not supported for lattice "{self.lattice}"')
sl = self.lattice sl = self.lattice
ol = (set(r)-{sl}).pop() ol = (set(r)-{sl}).pop()
@ -640,50 +614,6 @@ class Orientation(Rotation):
return (self.a,self.b,self.c,self.alpha,self.beta,self.gamma) return (self.a,self.b,self.c,self.alpha,self.beta,self.gamma)
@property
def ratio(self):
"""Return axes ratios of own lattice."""
_ratio = { 'hexagonal': {'c': np.sqrt(8./3.)}}
return dict(b = self.immutable['b']
if 'b' in self.immutable else
_ratio[self.family]['b'] if self.family in _ratio and 'b' in _ratio[self.family] else None,
c = self.immutable['c']
if 'c' in self.immutable else
_ratio[self.family]['c'] if self.family in _ratio and 'c' in _ratio[self.family] else None,
)
@property
def basis_real(self):
"""
Calculate orthogonal real space crystal basis.
References
----------
C.T. Young and J.L. Lytton, Journal of Applied Physics 43:14081417, 1972
https://doi.org/10.1063/1.1661333
"""
if None in self.parameters:
raise KeyError('missing crystal lattice parameters')
return np.array([
[1,0,0],
[np.cos(self.gamma),np.sin(self.gamma),0],
[np.cos(self.beta),
(np.cos(self.alpha)-np.cos(self.beta)*np.cos(self.gamma)) /np.sin(self.gamma),
np.sqrt(1 - np.cos(self.alpha)**2 - np.cos(self.beta)**2 - np.cos(self.gamma)**2
+ 2 * np.cos(self.alpha) * np.cos(self.beta) * np.cos(self.gamma))/np.sin(self.gamma)],
],dtype=float).T \
* np.array([self.a,self.b,self.c])
@property
def basis_reciprocal(self):
"""Calculate reciprocal (dual) crystal basis."""
return np.linalg.inv(self.basis_real.T)
def in_SST(self,vector,proper=False): def in_SST(self,vector,proper=False):
""" """
Check whether given crystal frame vector falls into standard stereographic triangle of own symmetry. Check whether given crystal frame vector falls into standard stereographic triangle of own symmetry.
@ -944,58 +874,6 @@ class Orientation(Rotation):
) )
def to_lattice(self,*,direction=None,plane=None):
"""
Calculate lattice vector corresponding to crystal frame direction or plane normal.
Parameters
----------
direction|normal : numpy.ndarray of shape (...,3)
Vector along direction or plane normal.
Returns
-------
Miller : numpy.ndarray of shape (...,3)
lattice vector of direction or plane.
Use util.scale_to_coprime to convert to (integer) Miller indices.
"""
if (direction is not None) ^ (plane is None):
raise KeyError('specify either "direction" or "plane"')
axis,basis = (np.array(direction),self.basis_reciprocal.T) \
if plane is None else \
(np.array(plane),self.basis_real.T)
return np.einsum('il,...l',basis,axis)
def to_frame(self,*,uvw=None,hkl=None,with_symmetry=False):
"""
Calculate crystal frame vector along lattice direction [uvw] or plane normal (hkl).
Parameters
----------
uvw|hkl : numpy.ndarray of shape (...,3)
Miller indices of crystallographic direction or plane normal.
with_symmetry : bool, optional
Calculate all N symmetrically equivalent vectors.
Returns
-------
vector : numpy.ndarray of shape (...,3) or (N,...,3)
Crystal frame vector (or vectors if with_symmetry) along [uvw] direction or (hkl) plane normal.
"""
if (uvw is not None) ^ (hkl is None):
raise KeyError('specify either "uvw" or "hkl"')
axis,basis = (np.array(uvw),self.basis_real) \
if hkl is None else \
(np.array(hkl),self.basis_reciprocal)
return (self.symmetry_operations.broadcast_to(self.symmetry_operations.shape+axis.shape[:-1],mode='right')
@ np.broadcast_to(np.einsum('il,...l',basis,axis),self.symmetry_operations.shape+axis.shape)
if with_symmetry else
np.einsum('il,...l',basis,axis))
def to_pole(self,*,uvw=None,hkl=None,with_symmetry=False): def to_pole(self,*,uvw=None,hkl=None,with_symmetry=False):
""" """
Calculate lab frame vector along lattice direction [uvw] or plane normal (hkl). Calculate lab frame vector along lattice direction [uvw] or plane normal (hkl).
@ -1013,7 +891,11 @@ class Orientation(Rotation):
Lab frame vector (or vectors if with_symmetry) along [uvw] direction or (hkl) plane normal. Lab frame vector (or vectors if with_symmetry) along [uvw] direction or (hkl) plane normal.
""" """
v = self.to_frame(uvw=uvw,hkl=hkl,with_symmetry=with_symmetry) # ToDo: simplify 'with_symmetry'
v = self.to_frame(uvw=uvw,hkl=hkl)
if with_symmetry:
v = self.symmetry_operations.broadcast_to(self.symmetry_operations.shape+v.shape[:-1],mode='right') \
@ np.broadcast_to(v,self.symmetry_operations.shape+v.shape)
return ~(self if self.shape+v.shape[:-1] == () else self.broadcast_to(self.shape+v.shape[:-1],mode='right')) \ return ~(self if self.shape+v.shape[:-1] == () else self.broadcast_to(self.shape+v.shape[:-1],mode='right')) \
@ np.broadcast_to(v,self.shape+v.shape) @ np.broadcast_to(v,self.shape+v.shape)
@ -1047,15 +929,10 @@ class Orientation(Rotation):
""" """
try: try:
master = lattice_.kinematics[self.lattice][mode] d = self.to_frame(uvw=self.kinematics(mode)['direction'])
kinematics = {'direction':master[:,0:3],'plane':master[:,3:6]} \ p = self.to_frame(hkl=self.kinematics(mode)['plane'])
if master.shape[-1] == 6 else \
{'direction':util.Bravais_to_Miller(uvtw=master[:,0:4]),
'plane': util.Bravais_to_Miller(hkil=master[:,4:8])}
except KeyError: except KeyError:
raise (f'"{mode}" not defined for lattice "{self.lattice}"') raise (f'"{mode}" not defined for lattice "{self.lattice}"')
d = self.to_frame(uvw=kinematics['direction'],with_symmetry=False)
p = self.to_frame(hkl=kinematics['plane'] ,with_symmetry=False)
P = np.einsum('...i,...j',d/np.linalg.norm(d,axis=-1,keepdims=True), P = np.einsum('...i,...j',d/np.linalg.norm(d,axis=-1,keepdims=True),
p/np.linalg.norm(p,axis=-1,keepdims=True)) p/np.linalg.norm(p,axis=-1,keepdims=True))

View File

@ -1,444 +0,0 @@
import numpy as _np
kinematics = {
'cF': {
'slip' : _np.array([
[+0,+1,-1 , +1,+1,+1],
[-1,+0,+1 , +1,+1,+1],
[+1,-1,+0 , +1,+1,+1],
[+0,-1,-1 , -1,-1,+1],
[+1,+0,+1 , -1,-1,+1],
[-1,+1,+0 , -1,-1,+1],
[+0,-1,+1 , +1,-1,-1],
[-1,+0,-1 , +1,-1,-1],
[+1,+1,+0 , +1,-1,-1],
[+0,+1,+1 , -1,+1,-1],
[+1,+0,-1 , -1,+1,-1],
[-1,-1,+0 , -1,+1,-1],
[+1,+1,+0 , +1,-1,+0],
[+1,-1,+0 , +1,+1,+0],
[+1,+0,+1 , +1,+0,-1],
[+1,+0,-1 , +1,+0,+1],
[+0,+1,+1 , +0,+1,-1],
[+0,+1,-1 , +0,+1,+1],
],'d'),
'twin' : _np.array([
[-2, 1, 1, 1, 1, 1],
[ 1,-2, 1, 1, 1, 1],
[ 1, 1,-2, 1, 1, 1],
[ 2,-1, 1, -1,-1, 1],
[-1, 2, 1, -1,-1, 1],
[-1,-1,-2, -1,-1, 1],
[-2,-1,-1, 1,-1,-1],
[ 1, 2,-1, 1,-1,-1],
[ 1,-1, 2, 1,-1,-1],
[ 2, 1,-1, -1, 1,-1],
[-1,-2,-1, -1, 1,-1],
[-1, 1, 2, -1, 1,-1],
],dtype=float),
},
'cI': {
'slip' : _np.array([
[+1,-1,+1 , +0,+1,+1],
[-1,-1,+1 , +0,+1,+1],
[+1,+1,+1 , +0,-1,+1],
[-1,+1,+1 , +0,-1,+1],
[-1,+1,+1 , +1,+0,+1],
[-1,-1,+1 , +1,+0,+1],
[+1,+1,+1 , -1,+0,+1],
[+1,-1,+1 , -1,+0,+1],
[-1,+1,+1 , +1,+1,+0],
[-1,+1,-1 , +1,+1,+0],
[+1,+1,+1 , -1,+1,+0],
[+1,+1,-1 , -1,+1,+0],
[-1,+1,+1 , +2,+1,+1],
[+1,+1,+1 , -2,+1,+1],
[+1,+1,-1 , +2,-1,+1],
[+1,-1,+1 , +2,+1,-1],
[+1,-1,+1 , +1,+2,+1],
[+1,+1,-1 , -1,+2,+1],
[+1,+1,+1 , +1,-2,+1],
[-1,+1,+1 , +1,+2,-1],
[+1,+1,-1 , +1,+1,+2],
[+1,-1,+1 , -1,+1,+2],
[-1,+1,+1 , +1,-1,+2],
[+1,+1,+1 , +1,+1,-2],
[+1,+1,-1 , +1,+2,+3],
[+1,-1,+1 , -1,+2,+3],
[-1,+1,+1 , +1,-2,+3],
[+1,+1,+1 , +1,+2,-3],
[+1,-1,+1 , +1,+3,+2],
[+1,+1,-1 , -1,+3,+2],
[+1,+1,+1 , +1,-3,+2],
[-1,+1,+1 , +1,+3,-2],
[+1,+1,-1 , +2,+1,+3],
[+1,-1,+1 , -2,+1,+3],
[-1,+1,+1 , +2,-1,+3],
[+1,+1,+1 , +2,+1,-3],
[+1,-1,+1 , +2,+3,+1],
[+1,+1,-1 , -2,+3,+1],
[+1,+1,+1 , +2,-3,+1],
[-1,+1,+1 , +2,+3,-1],
[-1,+1,+1 , +3,+1,+2],
[+1,+1,+1 , -3,+1,+2],
[+1,+1,-1 , +3,-1,+2],
[+1,-1,+1 , +3,+1,-2],
[-1,+1,+1 , +3,+2,+1],
[+1,+1,+1 , -3,+2,+1],
[+1,+1,-1 , +3,-2,+1],
[+1,-1,+1 , +3,+2,-1],
],'d'),
'twin' : _np.array([
[-1, 1, 1, 2, 1, 1],
[ 1, 1, 1, -2, 1, 1],
[ 1, 1,-1, 2,-1, 1],
[ 1,-1, 1, 2, 1,-1],
[ 1,-1, 1, 1, 2, 1],
[ 1, 1,-1, -1, 2, 1],
[ 1, 1, 1, 1,-2, 1],
[-1, 1, 1, 1, 2,-1],
[ 1, 1,-1, 1, 1, 2],
[ 1,-1, 1, -1, 1, 2],
[-1, 1, 1, 1,-1, 2],
[ 1, 1, 1, 1, 1,-2],
],dtype=float),
},
'hP': {
'slip' : _np.array([
[+2,-1,-1,+0 , +0,+0,+0,+1],
[-1,+2,-1,+0 , +0,+0,+0,+1],
[-1,-1,+2,+0 , +0,+0,+0,+1],
[+2,-1,-1,+0 , +0,+1,-1,+0],
[-1,+2,-1,+0 , -1,+0,+1,+0],
[-1,-1,+2,+0 , +1,-1,+0,+0],
[-1,+1,+0,+0 , +1,+1,-2,+0],
[+0,-1,+1,+0 , -2,+1,+1,+0],
[+1,+0,-1,+0 , +1,-2,+1,+0],
[-1,+2,-1,+0 , +1,+0,-1,+1],
[-2,+1,+1,+0 , +0,+1,-1,+1],
[-1,-1,+2,+0 , -1,+1,+0,+1],
[+1,-2,+1,+0 , -1,+0,+1,+1],
[+2,-1,-1,+0 , +0,-1,+1,+1],
[+1,+1,-2,+0 , +1,-1,+0,+1],
[-2,+1,+1,+3 , +1,+0,-1,+1],
[-1,-1,+2,+3 , +1,+0,-1,+1],
[-1,-1,+2,+3 , +0,+1,-1,+1],
[+1,-2,+1,+3 , +0,+1,-1,+1],
[+1,-2,+1,+3 , -1,+1,+0,+1],
[+2,-1,-1,+3 , -1,+1,+0,+1],
[+2,-1,-1,+3 , -1,+0,+1,+1],
[+1,+1,-2,+3 , -1,+0,+1,+1],
[+1,+1,-2,+3 , +0,-1,+1,+1],
[-1,+2,-1,+3 , +0,-1,+1,+1],
[-1,+2,-1,+3 , +1,-1,+0,+1],
[-2,+1,+1,+3 , +1,-1,+0,+1],
[-1,-1,+2,+3 , +1,+1,-2,+2],
[+1,-2,+1,+3 , -1,+2,-1,+2],
[+2,-1,-1,+3 , -2,+1,+1,+2],
[+1,+1,-2,+3 , -1,-1,+2,+2],
[-1,+2,-1,+3 , +1,-2,+1,+2],
[-2,+1,+1,+3 , +2,-1,-1,+2],
],'d'),
'twin' : _np.array([
[-1, 0, 1, 1, 1, 0, -1, 2], # shear = (3-(c/a)^2)/(sqrt(3) c/a) <-10.1>{10.2}
[ 0, -1, 1, 1, 0, 1, -1, 2],
[ 1, -1, 0, 1, -1, 1, 0, 2],
[ 1, 0, -1, 1, -1, 0, 1, 2],
[ 0, 1, -1, 1, 0, -1, 1, 2],
[-1, 1, 0, 1, 1, -1, 0, 2],
[-1, -1, 2, 6, 1, 1, -2, 1], # shear = 1/(c/a) <11.6>{-1-1.1}
[ 1, -2, 1, 6, -1, 2, -1, 1],
[ 2, -1, -1, 6, -2, 1, 1, 1],
[ 1, 1, -2, 6, -1, -1, 2, 1],
[-1, 2, -1, 6, 1, -2, 1, 1],
[-2, 1, 1, 6, 2, -1, -1, 1],
[ 1, 0, -1, -2, 1, 0, -1, 1], # shear = (4(c/a)^2-9)/(4 sqrt(3) c/a) <10.-2>{10.1}
[ 0, 1, -1, -2, 0, 1, -1, 1],
[-1, 1, 0, -2, -1, 1, 0, 1],
[-1, 0, 1, -2, -1, 0, 1, 1],
[ 0, -1, 1, -2, 0, -1, 1, 1],
[ 1, -1, 0, -2, 1, -1, 0, 1],
[ 1, 1, -2, -3, 1, 1, -2, 2], # shear = 2((c/a)^2-2)/(3 c/a) <11.-3>{11.2}
[-1, 2, -1, -3, -1, 2, -1, 2],
[-2, 1, 1, -3, -2, 1, 1, 2],
[-1, -1, 2, -3, -1, -1, 2, 2],
[ 1, -2, 1, -3, 1, -2, 1, 2],
[ 2, -1, -1, -3, 2, -1, -1, 2],
],dtype=float),
},
}
# Kurdjomov--Sachs orientation relationship for fcc <-> bcc transformation
# from S. Morito et al., Journal of Alloys and Compounds 577:s587-s592, 2013
# also see K. Kitahara et al., Acta Materialia 54:1279-1288, 2006
relations = {
'KS': {
'cF' : _np.array([
[[ -1, 0, 1],[ 1, 1, 1]],
[[ -1, 0, 1],[ 1, 1, 1]],
[[ 0, 1, -1],[ 1, 1, 1]],
[[ 0, 1, -1],[ 1, 1, 1]],
[[ 1, -1, 0],[ 1, 1, 1]],
[[ 1, -1, 0],[ 1, 1, 1]],
[[ 1, 0, -1],[ 1, -1, 1]],
[[ 1, 0, -1],[ 1, -1, 1]],
[[ -1, -1, 0],[ 1, -1, 1]],
[[ -1, -1, 0],[ 1, -1, 1]],
[[ 0, 1, 1],[ 1, -1, 1]],
[[ 0, 1, 1],[ 1, -1, 1]],
[[ 0, -1, 1],[ -1, 1, 1]],
[[ 0, -1, 1],[ -1, 1, 1]],
[[ -1, 0, -1],[ -1, 1, 1]],
[[ -1, 0, -1],[ -1, 1, 1]],
[[ 1, 1, 0],[ -1, 1, 1]],
[[ 1, 1, 0],[ -1, 1, 1]],
[[ -1, 1, 0],[ 1, 1, -1]],
[[ -1, 1, 0],[ 1, 1, -1]],
[[ 0, -1, -1],[ 1, 1, -1]],
[[ 0, -1, -1],[ 1, 1, -1]],
[[ 1, 0, 1],[ 1, 1, -1]],
[[ 1, 0, 1],[ 1, 1, -1]],
],dtype=float),
'cI' : _np.array([
[[ -1, -1, 1],[ 0, 1, 1]],
[[ -1, 1, -1],[ 0, 1, 1]],
[[ -1, -1, 1],[ 0, 1, 1]],
[[ -1, 1, -1],[ 0, 1, 1]],
[[ -1, -1, 1],[ 0, 1, 1]],
[[ -1, 1, -1],[ 0, 1, 1]],
[[ -1, -1, 1],[ 0, 1, 1]],
[[ -1, 1, -1],[ 0, 1, 1]],
[[ -1, -1, 1],[ 0, 1, 1]],
[[ -1, 1, -1],[ 0, 1, 1]],
[[ -1, -1, 1],[ 0, 1, 1]],
[[ -1, 1, -1],[ 0, 1, 1]],
[[ -1, -1, 1],[ 0, 1, 1]],
[[ -1, 1, -1],[ 0, 1, 1]],
[[ -1, -1, 1],[ 0, 1, 1]],
[[ -1, 1, -1],[ 0, 1, 1]],
[[ -1, -1, 1],[ 0, 1, 1]],
[[ -1, 1, -1],[ 0, 1, 1]],
[[ -1, -1, 1],[ 0, 1, 1]],
[[ -1, 1, -1],[ 0, 1, 1]],
[[ -1, -1, 1],[ 0, 1, 1]],
[[ -1, 1, -1],[ 0, 1, 1]],
[[ -1, -1, 1],[ 0, 1, 1]],
[[ -1, 1, -1],[ 0, 1, 1]],
],dtype=float),
},
'GT': {
'cF' : _np.array([
[[ -5,-12, 17],[ 1, 1, 1]],
[[ 17, -5,-12],[ 1, 1, 1]],
[[-12, 17, -5],[ 1, 1, 1]],
[[ 5, 12, 17],[ -1, -1, 1]],
[[-17, 5,-12],[ -1, -1, 1]],
[[ 12,-17, -5],[ -1, -1, 1]],
[[ -5, 12,-17],[ -1, 1, 1]],
[[ 17, 5, 12],[ -1, 1, 1]],
[[-12,-17, 5],[ -1, 1, 1]],
[[ 5,-12,-17],[ 1, -1, 1]],
[[-17, -5, 12],[ 1, -1, 1]],
[[ 12, 17, 5],[ 1, -1, 1]],
[[ -5, 17,-12],[ 1, 1, 1]],
[[-12, -5, 17],[ 1, 1, 1]],
[[ 17,-12, -5],[ 1, 1, 1]],
[[ 5,-17,-12],[ -1, -1, 1]],
[[ 12, 5, 17],[ -1, -1, 1]],
[[-17, 12, -5],[ -1, -1, 1]],
[[ -5,-17, 12],[ -1, 1, 1]],
[[-12, 5,-17],[ -1, 1, 1]],
[[ 17, 12, 5],[ -1, 1, 1]],
[[ 5, 17, 12],[ 1, -1, 1]],
[[ 12, -5,-17],[ 1, -1, 1]],
[[-17,-12, 5],[ 1, -1, 1]],
],dtype=float),
'cI' : _np.array([
[[-17, -7, 17],[ 1, 0, 1]],
[[ 17,-17, -7],[ 1, 1, 0]],
[[ -7, 17,-17],[ 0, 1, 1]],
[[ 17, 7, 17],[ -1, 0, 1]],
[[-17, 17, -7],[ -1, -1, 0]],
[[ 7,-17,-17],[ 0, -1, 1]],
[[-17, 7,-17],[ -1, 0, 1]],
[[ 17, 17, 7],[ -1, 1, 0]],
[[ -7,-17, 17],[ 0, 1, 1]],
[[ 17, -7,-17],[ 1, 0, 1]],
[[-17,-17, 7],[ 1, -1, 0]],
[[ 7, 17, 17],[ 0, -1, 1]],
[[-17, 17, -7],[ 1, 1, 0]],
[[ -7,-17, 17],[ 0, 1, 1]],
[[ 17, -7,-17],[ 1, 0, 1]],
[[ 17,-17, -7],[ -1, -1, 0]],
[[ 7, 17, 17],[ 0, -1, 1]],
[[-17, 7,-17],[ -1, 0, 1]],
[[-17,-17, 7],[ -1, 1, 0]],
[[ -7, 17,-17],[ 0, 1, 1]],
[[ 17, 7, 17],[ -1, 0, 1]],
[[ 17, 17, 7],[ 1, -1, 0]],
[[ 7,-17,-17],[ 0, -1, 1]],
[[-17, -7, 17],[ 1, 0, 1]],
],dtype=float),
},
'GT_prime': {
'cF' : _np.array([
[[ 0, 1, -1],[ 7, 17, 17]],
[[ -1, 0, 1],[ 17, 7, 17]],
[[ 1, -1, 0],[ 17, 17, 7]],
[[ 0, -1, -1],[ -7,-17, 17]],
[[ 1, 0, 1],[-17, -7, 17]],
[[ 1, -1, 0],[-17,-17, 7]],
[[ 0, 1, -1],[ 7,-17,-17]],
[[ 1, 0, 1],[ 17, -7,-17]],
[[ -1, -1, 0],[ 17,-17, -7]],
[[ 0, -1, -1],[ -7, 17,-17]],
[[ -1, 0, 1],[-17, 7,-17]],
[[ -1, -1, 0],[-17, 17, -7]],
[[ 0, -1, 1],[ 7, 17, 17]],
[[ 1, 0, -1],[ 17, 7, 17]],
[[ -1, 1, 0],[ 17, 17, 7]],
[[ 0, 1, 1],[ -7,-17, 17]],
[[ -1, 0, -1],[-17, -7, 17]],
[[ -1, 1, 0],[-17,-17, 7]],
[[ 0, -1, 1],[ 7,-17,-17]],
[[ -1, 0, -1],[ 17, -7,-17]],
[[ 1, 1, 0],[ 17,-17, -7]],
[[ 0, 1, 1],[ -7, 17,-17]],
[[ 1, 0, -1],[-17, 7,-17]],
[[ 1, 1, 0],[-17, 17, -7]],
],dtype=float),
'cI' : _np.array([
[[ 1, 1, -1],[ 12, 5, 17]],
[[ -1, 1, 1],[ 17, 12, 5]],
[[ 1, -1, 1],[ 5, 17, 12]],
[[ -1, -1, -1],[-12, -5, 17]],
[[ 1, -1, 1],[-17,-12, 5]],
[[ 1, -1, -1],[ -5,-17, 12]],
[[ -1, 1, -1],[ 12, -5,-17]],
[[ 1, 1, 1],[ 17,-12, -5]],
[[ -1, -1, 1],[ 5,-17,-12]],
[[ 1, -1, -1],[-12, 5,-17]],
[[ -1, -1, 1],[-17, 12, -5]],
[[ -1, -1, -1],[ -5, 17,-12]],
[[ 1, -1, 1],[ 12, 17, 5]],
[[ 1, 1, -1],[ 5, 12, 17]],
[[ -1, 1, 1],[ 17, 5, 12]],
[[ -1, 1, 1],[-12,-17, 5]],
[[ -1, -1, -1],[ -5,-12, 17]],
[[ -1, 1, -1],[-17, -5, 12]],
[[ -1, -1, 1],[ 12,-17, -5]],
[[ -1, 1, -1],[ 5,-12,-17]],
[[ 1, 1, 1],[ 17, -5,-12]],
[[ 1, 1, 1],[-12, 17, -5]],
[[ 1, -1, -1],[ -5, 12,-17]],
[[ 1, 1, -1],[-17, 5,-12]],
],dtype=float),
},
'NW': {
'cF' : _np.array([
[[ 2, -1, -1],[ 1, 1, 1]],
[[ -1, 2, -1],[ 1, 1, 1]],
[[ -1, -1, 2],[ 1, 1, 1]],
[[ -2, -1, -1],[ -1, 1, 1]],
[[ 1, 2, -1],[ -1, 1, 1]],
[[ 1, -1, 2],[ -1, 1, 1]],
[[ 2, 1, -1],[ 1, -1, 1]],
[[ -1, -2, -1],[ 1, -1, 1]],
[[ -1, 1, 2],[ 1, -1, 1]],
[[ 2, -1, 1],[ -1, -1, 1]],
[[ -1, 2, 1],[ -1, -1, 1]],
[[ -1, -1, -2],[ -1, -1, 1]],
],dtype=float),
'cI' : _np.array([
[[ 0, -1, 1],[ 0, 1, 1]],
[[ 0, -1, 1],[ 0, 1, 1]],
[[ 0, -1, 1],[ 0, 1, 1]],
[[ 0, -1, 1],[ 0, 1, 1]],
[[ 0, -1, 1],[ 0, 1, 1]],
[[ 0, -1, 1],[ 0, 1, 1]],
[[ 0, -1, 1],[ 0, 1, 1]],
[[ 0, -1, 1],[ 0, 1, 1]],
[[ 0, -1, 1],[ 0, 1, 1]],
[[ 0, -1, 1],[ 0, 1, 1]],
[[ 0, -1, 1],[ 0, 1, 1]],
[[ 0, -1, 1],[ 0, 1, 1]],
],dtype=float),
},
'Pitsch': {
'cF' : _np.array([
[[ 1, 0, 1],[ 0, 1, 0]],
[[ 1, 1, 0],[ 0, 0, 1]],
[[ 0, 1, 1],[ 1, 0, 0]],
[[ 0, 1, -1],[ 1, 0, 0]],
[[ -1, 0, 1],[ 0, 1, 0]],
[[ 1, -1, 0],[ 0, 0, 1]],
[[ 1, 0, -1],[ 0, 1, 0]],
[[ -1, 1, 0],[ 0, 0, 1]],
[[ 0, -1, 1],[ 1, 0, 0]],
[[ 0, 1, 1],[ 1, 0, 0]],
[[ 1, 0, 1],[ 0, 1, 0]],
[[ 1, 1, 0],[ 0, 0, 1]],
],dtype=float),
'cI' : _np.array([
[[ 1, -1, 1],[ -1, 0, 1]],
[[ 1, 1, -1],[ 1, -1, 0]],
[[ -1, 1, 1],[ 0, 1, -1]],
[[ -1, 1, -1],[ 0, -1, -1]],
[[ -1, -1, 1],[ -1, 0, -1]],
[[ 1, -1, -1],[ -1, -1, 0]],
[[ 1, -1, -1],[ -1, 0, -1]],
[[ -1, 1, -1],[ -1, -1, 0]],
[[ -1, -1, 1],[ 0, -1, -1]],
[[ -1, 1, 1],[ 0, -1, 1]],
[[ 1, -1, 1],[ 1, 0, -1]],
[[ 1, 1, -1],[ -1, 1, 0]],
],dtype=float),
},
'Bain': {
'cF' : _np.array([
[[ 0, 1, 0],[ 1, 0, 0]],
[[ 0, 0, 1],[ 0, 1, 0]],
[[ 1, 0, 0],[ 0, 0, 1]],
],dtype=float),
'cI' : _np.array([
[[ 0, 1, 1],[ 1, 0, 0]],
[[ 1, 0, 1],[ 0, 1, 0]],
[[ 1, 1, 0],[ 0, 0, 1]],
],dtype=float),
},
'Burgers' : {
'cI' : _np.array([
[[ -1, 1, 1],[ 1, 1, 0]],
[[ -1, 1, -1],[ 1, 1, 0]],
[[ 1, 1, 1],[ 1, -1, 0]],
[[ 1, 1, -1],[ 1, -1, 0]],
[[ 1, 1, -1],[ 1, 0, 1]],
[[ -1, 1, 1],[ 1, 0, 1]],
[[ 1, 1, 1],[ -1, 0, 1]],
[[ 1, -1, 1],[ -1, 0, 1]],
[[ -1, 1, -1],[ 0, 1, 1]],
[[ 1, 1, -1],[ 0, 1, 1]],
[[ -1, 1, 1],[ 0, -1, 1]],
[[ 1, 1, 1],[ 0, -1, 1]],
],dtype=float),
'hP' : _np.array([
[[ -1, 2, -1, 0],[ 0, 0, 0, 1]],
[[ -1, -1, 2, 0],[ 0, 0, 0, 1]],
[[ -1, 2, -1, 0],[ 0, 0, 0, 1]],
[[ -1, -1, 2, 0],[ 0, 0, 0, 1]],
[[ -1, 2, -1, 0],[ 0, 0, 0, 1]],
[[ -1, -1, 2, 0],[ 0, 0, 0, 1]],
[[ -1, 2, -1, 0],[ 0, 0, 0, 1]],
[[ -1, -1, 2, 0],[ 0, 0, 0, 1]],
[[ -1, 2, -1, 0],[ 0, 0, 0, 1]],
[[ -1, -1, 2, 0],[ 0, 0, 0, 1]],
[[ -1, 2, -1, 0],[ 0, 0, 0, 1]],
[[ -1, -1, 2, 0],[ 0, 0, 0, 1]],
],dtype=float),
},
}

View File

@ -0,0 +1,64 @@
import pytest
import numpy as np
from damask import Lattice
class TestLattice:
def test_double_to_lattice(self):
L = Lattice('cF')
with pytest.raises(KeyError):
L.to_lattice(direction=np.ones(3),plane=np.ones(3))
def test_double_to_frame(self):
L = Lattice('cF')
with pytest.raises(KeyError):
L.to_frame(uvw=np.ones(3),hkl=np.ones(3))
@pytest.mark.parametrize('lattice,a,b,c,alpha,beta,gamma',
[
('aP',0.5,2.0,3.0,0.8,0.5,1.2),
('mP',1.0,2.0,3.0,np.pi/2,0.5,np.pi/2),
('oI',0.5,1.5,3.0,np.pi/2,np.pi/2,np.pi/2),
('tP',0.5,0.5,3.0,np.pi/2,np.pi/2,np.pi/2),
('hP',1.0,None,1.6,np.pi/2,np.pi/2,2*np.pi/3),
('cF',1.0,1.0,None,np.pi/2,np.pi/2,np.pi/2),
])
def test_bases_contraction(self,lattice,a,b,c,alpha,beta,gamma):
L = Lattice(lattice=lattice,
a=a,b=b,c=c,
alpha=alpha,beta=beta,gamma=gamma)
assert np.allclose(np.eye(3),np.einsum('ik,jk',L.basis_real,L.basis_reciprocal))
@pytest.mark.parametrize('keyFrame,keyLattice',[('uvw','direction'),('hkl','plane'),])
@pytest.mark.parametrize('vector',np.array([
[1.,1.,1.],
[-2.,3.,0.5],
[0.,0.,1.],
[1.,1.,1.],
[2.,2.,2.],
[0.,1.,1.],
]))
@pytest.mark.parametrize('lattice,a,b,c,alpha,beta,gamma',
[
('aP',0.5,2.0,3.0,0.8,0.5,1.2),
('mP',1.0,2.0,3.0,np.pi/2,0.5,np.pi/2),
('oI',0.5,1.5,3.0,np.pi/2,np.pi/2,np.pi/2),
('tP',0.5,0.5,3.0,np.pi/2,np.pi/2,np.pi/2),
('hP',1.0,1.0,1.6,np.pi/2,np.pi/2,2*np.pi/3),
('cF',1.0,1.0,1.0,np.pi/2,np.pi/2,np.pi/2),
])
def test_to_frame_to_lattice(self,lattice,a,b,c,alpha,beta,gamma,vector,keyFrame,keyLattice):
L = Lattice(lattice=lattice,
a=a,b=b,c=c,
alpha=alpha,beta=beta,gamma=gamma)
assert np.allclose(vector,
L.to_frame(**{keyFrame:L.to_lattice(**{keyLattice:vector})}))
@pytest.mark.parametrize('model',['Bain','KS','GT','GT_prime','NW','Pitsch','Burgers'])
def test_relationship_definition(self,model):
m,o = list(Lattice._orientation_relationships[model])
assert Lattice._orientation_relationships[model][m].shape[:-1] == \
Lattice._orientation_relationships[model][o].shape[:-1]

View File

@ -7,7 +7,6 @@ from damask import Orientation
from damask import Table from damask import Table
from damask import util from damask import util
from damask import grid_filters from damask import grid_filters
from damask import lattice
from damask import _orientation from damask import _orientation
crystal_families = set(_orientation.lattice_symmetries.values()) crystal_families = set(_orientation.lattice_symmetries.values())
@ -341,29 +340,6 @@ class TestOrientation:
with pytest.raises(KeyError): with pytest.raises(KeyError):
Orientation(family=invalid_family) Orientation(family=invalid_family)
def test_invalid_rot(self):
with pytest.raises(TypeError):
Orientation.from_random(family='cubic') * np.ones(3)
def test_missing_symmetry_immutable(self):
with pytest.raises(KeyError):
Orientation(lattice=None).immutable # noqa
def test_missing_symmetry_basis_real(self):
with pytest.raises(KeyError):
Orientation(lattice=None).basis_real # noqa
def test_missing_symmetry_basis_reciprocal(self):
with pytest.raises(KeyError):
Orientation(lattice=None).basis_reciprocal # noqa
def test_double_to_lattice(self):
with pytest.raises(KeyError):
Orientation().to_lattice(direction=np.ones(3),plane=np.ones(3)) # noqa
def test_double_to_frame(self):
with pytest.raises(KeyError):
Orientation().to_frame(uvw=np.ones(3),hkl=np.ones(3)) # noqa
@pytest.mark.parametrize('relation',[None,'Peter','Paul']) @pytest.mark.parametrize('relation',[None,'Peter','Paul'])
def test_unknown_relation(self,relation): def test_unknown_relation(self,relation):
@ -395,12 +371,6 @@ class TestOrientation:
o = Orientation(family='cubic') # noqa o = Orientation(family='cubic') # noqa
with pytest.raises(ValueError): with pytest.raises(ValueError):
eval(f'o.{function}(np.ones(4))') eval(f'o.{function}(np.ones(4))')
@pytest.mark.parametrize('model',lattice.relations)
def test_relationship_definition(self,model):
m,o = list(lattice.relations[model])
assert lattice.relations[model][m].shape[:-1] == lattice.relations[model][o].shape[:-1]
@pytest.mark.parametrize('model',['Bain','KS','GT','GT_prime','NW','Pitsch']) @pytest.mark.parametrize('model',['Bain','KS','GT','GT_prime','NW','Pitsch'])
@pytest.mark.parametrize('lattice',['cF','cI']) @pytest.mark.parametrize('lattice',['cF','cI'])
def test_relationship_vectorize(self,set_of_quaternions,lattice,model): def test_relationship_vectorize(self,set_of_quaternions,lattice,model):
@ -441,46 +411,6 @@ class TestOrientation:
) )
assert np.allclose(o.to_frame(uvw=np.eye(3)),basis), 'Lattice basis disagrees with initialization' assert np.allclose(o.to_frame(uvw=np.eye(3)),basis), 'Lattice basis disagrees with initialization'
@pytest.mark.parametrize('lattice,a,b,c,alpha,beta,gamma',
[
('aP',0.5,2.0,3.0,0.8,0.5,1.2),
('mP',1.0,2.0,3.0,np.pi/2,0.5,np.pi/2),
('oI',0.5,1.5,3.0,np.pi/2,np.pi/2,np.pi/2),
('tP',0.5,0.5,3.0,np.pi/2,np.pi/2,np.pi/2),
('hP',1.0,None,1.6,np.pi/2,np.pi/2,2*np.pi/3),
('cF',1.0,1.0,None,np.pi/2,np.pi/2,np.pi/2),
])
def test_bases_contraction(self,lattice,a,b,c,alpha,beta,gamma):
L = Orientation(lattice=lattice,
a=a,b=b,c=c,
alpha=alpha,beta=beta,gamma=gamma)
assert np.allclose(np.eye(3),np.einsum('ik,jk',L.basis_real,L.basis_reciprocal))
@pytest.mark.parametrize('keyFrame,keyLattice',[('uvw','direction'),('hkl','plane'),])
@pytest.mark.parametrize('vector',np.array([
[1.,1.,1.],
[-2.,3.,0.5],
[0.,0.,1.],
[1.,1.,1.],
[2.,2.,2.],
[0.,1.,1.],
]))
@pytest.mark.parametrize('lattice,a,b,c,alpha,beta,gamma',
[
('aP',0.5,2.0,3.0,0.8,0.5,1.2),
('mP',1.0,2.0,3.0,np.pi/2,0.5,np.pi/2),
('oI',0.5,1.5,3.0,np.pi/2,np.pi/2,np.pi/2),
('tP',0.5,0.5,3.0,np.pi/2,np.pi/2,np.pi/2),
('hP',1.0,1.0,1.6,np.pi/2,np.pi/2,2*np.pi/3),
('cF',1.0,1.0,1.0,np.pi/2,np.pi/2,np.pi/2),
])
def test_to_frame_to_lattice(self,lattice,a,b,c,alpha,beta,gamma,vector,keyFrame,keyLattice):
L = Orientation(lattice=lattice,
a=a,b=b,c=c,
alpha=alpha,beta=beta,gamma=gamma)
assert np.allclose(vector,
L.to_frame(**{keyFrame:L.to_lattice(**{keyLattice:vector})}))
@pytest.mark.parametrize('lattice,a,b,c,alpha,beta,gamma', @pytest.mark.parametrize('lattice,a,b,c,alpha,beta,gamma',
[ [