WIP: refactoring Orientation=Symmetry+Rotation, Lattice=subclass of Sym, and Crystal=Lattice+Rotation
This commit is contained in:
Martin Diehl
parent
5aad1d6c21
commit
5926f84851
2
PRIVATE
2
PRIVATE
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@ -1 +1 @@
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Subproject commit 92b7b1314a9c576a20f073a230e2aaf811cb932a
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Subproject commit f529a16d100434c736476944a3a696d8f95ac770
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@ -15,12 +15,12 @@ from . import seeds # noqa
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from . import mechanics # noqa
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from . import solver # noqa
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from . import grid_filters # noqa
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from ._lattice import Symmetry, Lattice# noqa
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from ._table import Table # noqa
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from . import lattice # noqa
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from ._rotation import Rotation # noqa
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from ._orientation import Orientation # noqa
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from ._table import Table # noqa
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from ._vtk import VTK # noqa
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from ._colormap import Colormap # noqa
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from ._orientation import Orientation # noqa
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from ._config import Config # noqa
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from ._configmaterial import ConfigMaterial # noqa
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from ._geom import Geom # noqa
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@ -3,8 +3,8 @@ import copy
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import numpy as np
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from . import Config
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from . import Lattice
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from . import Rotation
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from . import Orientation
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class ConfigMaterial(Config):
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"""Material configuration."""
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@ -152,7 +152,7 @@ class ConfigMaterial(Config):
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for k,v in self['phase'].items():
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if 'lattice' in v:
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try:
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Lattice(v['lattice'])
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Orientation(lattice=v['lattice'])
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except KeyError:
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s = v['lattice']
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print(f"Invalid lattice: '{s}' in phase '{k}'")
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@ -1,646 +0,0 @@
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import numpy as np
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class Symmetry:
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"""
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Symmetry-related operations for crystal systems.
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References
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----------
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https://en.wikipedia.org/wiki/Crystal_system
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"""
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crystal_systems = [None,'orthorhombic','tetragonal','hexagonal','cubic']
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def __init__(self, system = None):
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"""
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Symmetry Definition.
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Parameters
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----------
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system : {None,'orthorhombic','tetragonal','hexagonal','cubic'}, optional
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Name of the crystal system. Defaults to 'None'.
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"""
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if system is not None and system.lower() not in self.crystal_systems:
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raise KeyError(f'Crystal system "{system}" is unknown')
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self.system = system.lower() if isinstance(system,str) else system
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def __copy__(self):
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"""Copy."""
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return self.__class__(self.system)
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copy = __copy__
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def __repr__(self):
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"""Readable string."""
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return f'{self.system}'
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def __eq__(self, other):
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"""
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Equal to other.
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Parameters
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----------
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other : Symmetry
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Symmetry to check for equality.
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"""
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return self.system == other.system
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def __neq__(self, other):
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"""
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Not Equal to other.
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Parameters
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----------
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other : Symmetry
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Symmetry to check for inequality.
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"""
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return not self.__eq__(other)
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def __cmp__(self,other):
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"""
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Linear ordering.
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Parameters
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----------
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other : Symmetry
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Symmetry to check for for order.
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"""
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myOrder = self.crystal_systems.index(self.system)
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otherOrder = self.crystal_systems.index(other.system)
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return (myOrder > otherOrder) - (myOrder < otherOrder)
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@property
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def symmetry_operations(self):
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"""Symmetry operations as quaternions."""
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if self.system == 'cubic':
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sym_quats = [
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[ 1.0, 0.0, 0.0, 0.0 ],
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[ 0.0, 1.0, 0.0, 0.0 ],
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[ 0.0, 0.0, 1.0, 0.0 ],
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[ 0.0, 0.0, 0.0, 1.0 ],
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[ 0.0, 0.0, 0.5*np.sqrt(2), 0.5*np.sqrt(2) ],
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[ 0.0, 0.0, 0.5*np.sqrt(2),-0.5*np.sqrt(2) ],
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[ 0.0, 0.5*np.sqrt(2), 0.0, 0.5*np.sqrt(2) ],
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[ 0.0, 0.5*np.sqrt(2), 0.0, -0.5*np.sqrt(2) ],
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[ 0.0, 0.5*np.sqrt(2),-0.5*np.sqrt(2), 0.0 ],
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[ 0.0, -0.5*np.sqrt(2),-0.5*np.sqrt(2), 0.0 ],
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[ 0.5, 0.5, 0.5, 0.5 ],
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[-0.5, 0.5, 0.5, 0.5 ],
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[-0.5, 0.5, 0.5, -0.5 ],
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[-0.5, 0.5, -0.5, 0.5 ],
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[-0.5, -0.5, 0.5, 0.5 ],
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[-0.5, -0.5, 0.5, -0.5 ],
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[-0.5, -0.5, -0.5, 0.5 ],
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[-0.5, 0.5, -0.5, -0.5 ],
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[-0.5*np.sqrt(2), 0.0, 0.0, 0.5*np.sqrt(2) ],
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[ 0.5*np.sqrt(2), 0.0, 0.0, 0.5*np.sqrt(2) ],
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[-0.5*np.sqrt(2), 0.0, 0.5*np.sqrt(2), 0.0 ],
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[-0.5*np.sqrt(2), 0.0, -0.5*np.sqrt(2), 0.0 ],
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[-0.5*np.sqrt(2), 0.5*np.sqrt(2), 0.0, 0.0 ],
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[-0.5*np.sqrt(2),-0.5*np.sqrt(2), 0.0, 0.0 ],
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]
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elif self.system == 'hexagonal':
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sym_quats = [
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[ 1.0, 0.0, 0.0, 0.0 ],
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[-0.5*np.sqrt(3), 0.0, 0.0, -0.5 ],
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[ 0.5, 0.0, 0.0, 0.5*np.sqrt(3) ],
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[ 0.0, 0.0, 0.0, 1.0 ],
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[-0.5, 0.0, 0.0, 0.5*np.sqrt(3) ],
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[-0.5*np.sqrt(3), 0.0, 0.0, 0.5 ],
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[ 0.0, 1.0, 0.0, 0.0 ],
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[ 0.0, -0.5*np.sqrt(3), 0.5, 0.0 ],
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[ 0.0, 0.5, -0.5*np.sqrt(3), 0.0 ],
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[ 0.0, 0.0, 1.0, 0.0 ],
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[ 0.0, -0.5, -0.5*np.sqrt(3), 0.0 ],
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[ 0.0, 0.5*np.sqrt(3), 0.5, 0.0 ],
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]
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elif self.system == 'tetragonal':
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sym_quats = [
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[ 1.0, 0.0, 0.0, 0.0 ],
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[ 0.0, 1.0, 0.0, 0.0 ],
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[ 0.0, 0.0, 1.0, 0.0 ],
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[ 0.0, 0.0, 0.0, 1.0 ],
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[ 0.0, 0.5*np.sqrt(2), 0.5*np.sqrt(2), 0.0 ],
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[ 0.0, -0.5*np.sqrt(2), 0.5*np.sqrt(2), 0.0 ],
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[ 0.5*np.sqrt(2), 0.0, 0.0, 0.5*np.sqrt(2) ],
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[-0.5*np.sqrt(2), 0.0, 0.0, 0.5*np.sqrt(2) ],
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]
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elif self.system == 'orthorhombic':
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sym_quats = [
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[ 1.0,0.0,0.0,0.0 ],
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[ 0.0,1.0,0.0,0.0 ],
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[ 0.0,0.0,1.0,0.0 ],
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[ 0.0,0.0,0.0,1.0 ],
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]
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else:
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sym_quats = [
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[ 1.0,0.0,0.0,0.0 ],
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]
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return np.array(sym_quats)
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def in_FZ(self,rho):
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"""
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Check whether given Rodrigues-Frank vector falls into fundamental zone.
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Fundamental zone in Rodrigues space is point symmetric around origin.
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"""
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if(rho.shape[-1] != 3):
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raise ValueError('Input is not a Rodrigues-Frank vector field.')
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rho_abs = np.abs(rho)
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with np.errstate(invalid='ignore'):
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# using '*'/prod for 'and'
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if self.system == 'cubic':
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return np.where(np.prod(np.sqrt(2)-1. >= rho_abs,axis=-1) *
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(1. >= np.sum(rho_abs,axis=-1)),True,False)
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elif self.system == 'hexagonal':
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return np.where(np.prod(1. >= rho_abs,axis=-1) *
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(2. >= np.sqrt(3)*rho_abs[...,0] + rho_abs[...,1]) *
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(2. >= np.sqrt(3)*rho_abs[...,1] + rho_abs[...,0]) *
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(2. >= np.sqrt(3) + rho_abs[...,2]),True,False)
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elif self.system == 'tetragonal':
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return np.where(np.prod(1. >= rho_abs[...,:2],axis=-1) *
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(np.sqrt(2) >= rho_abs[...,0] + rho_abs[...,1]) *
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(np.sqrt(2) >= rho_abs[...,2] + 1.),True,False)
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elif self.system == 'orthorhombic':
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return np.where(np.prod(1. >= rho_abs,axis=-1),True,False)
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else:
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return np.where(np.all(np.isfinite(rho_abs),axis=-1),True,False)
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def in_disorientation_SST(self,rho):
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"""
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Check whether given Rodrigues-Frank vector (of misorientation) falls into standard stereographic triangle.
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References
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----------
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A. Heinz and P. Neumann, Acta Crystallographica Section A 47:780-789, 1991
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https://doi.org/10.1107/S0108767391006864
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"""
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if(rho.shape[-1] != 3):
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raise ValueError('Input is not a Rodrigues-Frank vector field.')
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with np.errstate(invalid='ignore'):
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# using '*' for 'and'
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if self.system == 'cubic':
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return np.where((rho[...,0] >= rho[...,1]) * \
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(rho[...,1] >= rho[...,2]) * \
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(rho[...,2] >= 0),True,False)
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elif self.system == 'hexagonal':
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return np.where((rho[...,0] >= rho[...,1]*np.sqrt(3)) * \
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(rho[...,1] >= 0) * \
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(rho[...,2] >= 0),True,False)
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elif self.system == 'tetragonal':
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return np.where((rho[...,0] >= rho[...,1]) * \
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(rho[...,1] >= 0) * \
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(rho[...,2] >= 0),True,False)
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elif self.system == 'orthorhombic':
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return np.where((rho[...,0] >= 0) * \
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(rho[...,1] >= 0) * \
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(rho[...,2] >= 0),True,False)
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else:
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return np.ones_like(rho[...,0],dtype=bool)
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#ToDo: IPF color in separate function
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def in_SST(self,vector,proper=False,color=False):
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"""
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Check whether given vector falls into standard stereographic triangle of own symmetry.
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proper considers only vectors with z >= 0, hence uses two neighboring SSTs.
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Return inverse pole figure color if requested.
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Bases are computed from
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>>> basis = {'cubic' : np.linalg.inv(np.array([[0.,0.,1.], # direction of red
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... [1.,0.,1.]/np.sqrt(2.), # direction of green
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... [1.,1.,1.]/np.sqrt(3.)]).T), # direction of blue
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... 'hexagonal' : np.linalg.inv(np.array([[0.,0.,1.], # direction of red
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... [1.,0.,0.], # direction of green
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... [np.sqrt(3.),1.,0.]/np.sqrt(4.)]).T), # direction of blue
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... 'tetragonal' : np.linalg.inv(np.array([[0.,0.,1.], # direction of red
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... [1.,0.,0.], # direction of green
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... [1.,1.,0.]/np.sqrt(2.)]).T), # direction of blue
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... 'orthorhombic': np.linalg.inv(np.array([[0.,0.,1.], # direction of red
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... [1.,0.,0.], # direction of green
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... [0.,1.,0.]]).T), # direction of blue
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... }
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"""
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if(vector.shape[-1] != 3):
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raise ValueError('Input is not a 3D vector field.')
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if self.system == 'cubic':
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basis = {'improper':np.array([ [-1. , 0. , 1. ],
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[ np.sqrt(2.) , -np.sqrt(2.) , 0. ],
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[ 0. , np.sqrt(3.) , 0. ] ]),
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'proper':np.array([ [ 0. , -1. , 1. ],
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[-np.sqrt(2.) , np.sqrt(2.) , 0. ],
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[ np.sqrt(3.) , 0. , 0. ] ]),
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}
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elif self.system == 'hexagonal':
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basis = {'improper':np.array([ [ 0. , 0. , 1. ],
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[ 1. , -np.sqrt(3.) , 0. ],
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[ 0. , 2. , 0. ] ]),
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'proper':np.array([ [ 0. , 0. , 1. ],
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[-1. , np.sqrt(3.) , 0. ],
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[ np.sqrt(3.) , -1. , 0. ] ]),
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}
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elif self.system == 'tetragonal':
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basis = {'improper':np.array([ [ 0. , 0. , 1. ],
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[ 1. , -1. , 0. ],
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[ 0. , np.sqrt(2.) , 0. ] ]),
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'proper':np.array([ [ 0. , 0. , 1. ],
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[-1. , 1. , 0. ],
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[ np.sqrt(2.) , 0. , 0. ] ]),
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}
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elif self.system == 'orthorhombic':
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basis = {'improper':np.array([ [ 0., 0., 1.],
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[ 1., 0., 0.],
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[ 0., 1., 0.] ]),
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'proper':np.array([ [ 0., 0., 1.],
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[-1., 0., 0.],
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[ 0., 1., 0.] ]),
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}
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else: # direct exit for unspecified symmetry
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if color:
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return (np.ones_like(vector[...,0],bool),np.zeros_like(vector))
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else:
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return np.ones_like(vector[...,0],bool)
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b_i = np.broadcast_to(basis['improper'],vector.shape+(3,))
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if proper:
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b_p = np.broadcast_to(basis['proper'], vector.shape+(3,))
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improper = np.all(np.around(np.einsum('...ji,...i',b_i,vector),12)>=0.0,axis=-1,keepdims=True)
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theComponents = np.where(np.broadcast_to(improper,vector.shape),
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np.around(np.einsum('...ji,...i',b_i,vector),12),
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np.around(np.einsum('...ji,...i',b_p,vector),12))
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else:
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vector_ = np.block([vector[...,0:2],np.abs(vector[...,2:3])]) # z component projects identical
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theComponents = np.around(np.einsum('...ji,...i',b_i,vector_),12)
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in_SST = np.all(theComponents >= 0.0,axis=-1)
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if color: # have to return color array
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with np.errstate(invalid='ignore',divide='ignore'):
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rgb = (theComponents/np.linalg.norm(theComponents,axis=-1,keepdims=True))**0.5 # smoothen color ramps
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rgb = np.minimum(1.,rgb) # limit to maximum intensity
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rgb /= np.max(rgb,axis=-1,keepdims=True) # normalize to (HS)V = 1
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rgb[np.broadcast_to(~in_SST.reshape(vector[...,0].shape+(1,)),vector.shape)] = 0.0
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return (in_SST,rgb)
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else:
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return in_SST
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# ******************************************************************************************
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class Lattice: # ToDo: Make a subclass of Symmetry!
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"""
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Bravais lattice.
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This contains only a mapping from Bravais lattice to symmetry
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and orientation relationships. It could include twin and slip systems.
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References
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----------
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https://en.wikipedia.org/wiki/Bravais_lattice
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"""
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lattices = {
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'iso': {'system':None},
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'triclinic':{'system':None},
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'bct': {'system':'tetragonal'},
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'hex': {'system':'hexagonal'},
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'fcc': {'system':'cubic','c/a':1.0},
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'bcc': {'system':'cubic','c/a':1.0},
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}
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def __init__(self,lattice,c_over_a=None):
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"""
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New lattice of given type.
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Parameters
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----------
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lattice : str
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Bravais lattice.
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"""
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self.lattice = lattice
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self.symmetry = Symmetry(self.lattices[lattice]['system'])
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# transition to subclass
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self.system = self.symmetry.system
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self.in_SST = self.symmetry.in_SST
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self.in_FZ = self.symmetry.in_FZ
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self.in_disorientation_SST = self.symmetry.in_disorientation_SST
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def __repr__(self):
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"""Report basic lattice information."""
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return f'Bravais lattice {self.lattice} ({self.symmetry} crystal system)'
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# Kurdjomov--Sachs orientation relationship for fcc <-> bcc transformation
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# from S. Morito et al., Journal of Alloys and Compounds 577:s587-s592, 2013
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# also see K. Kitahara et al., Acta Materialia 54:1279-1288, 2006
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_KS = {'mapping':{'fcc':0,'bcc':1},
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'planes': np.array([
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[[ 1, 1, 1],[ 0, 1, 1]],
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[[ 1, 1, 1],[ 0, 1, 1]],
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[[ 1, 1, 1],[ 0, 1, 1]],
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[[ 1, 1, 1],[ 0, 1, 1]],
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[[ 1, 1, 1],[ 0, 1, 1]],
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[[ 1, 1, 1],[ 0, 1, 1]],
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[[ 1, -1, 1],[ 0, 1, 1]],
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[[ 1, -1, 1],[ 0, 1, 1]],
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[[ 1, -1, 1],[ 0, 1, 1]],
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[[ 1, -1, 1],[ 0, 1, 1]],
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[[ 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'),
|
||||
'directions': 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')}
|
||||
|
||||
# Greninger--Troiano orientation relationship for fcc <-> bcc transformation
|
||||
# from Y. He et al., Journal of Applied Crystallography 39:72-81, 2006
|
||||
_GT = {'mapping':{'fcc':0,'bcc':1},
|
||||
'planes': np.array([
|
||||
[[ 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],[ 0, -1, 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],[ 0, -1, 1]],
|
||||
[[ 1, -1, 1],[ 1, 0, 1]]],dtype='float'),
|
||||
'directions': np.array([
|
||||
[[ -5,-12, 17],[-17, -7, 17]],
|
||||
[[ 17, -5,-12],[ 17,-17, -7]],
|
||||
[[-12, 17, -5],[ -7, 17,-17]],
|
||||
[[ 5, 12, 17],[ 17, 7, 17]],
|
||||
[[-17, 5,-12],[-17, 17, -7]],
|
||||
[[ 12,-17, -5],[ 7,-17,-17]],
|
||||
[[ -5, 12,-17],[-17, 7,-17]],
|
||||
[[ 17, 5, 12],[ 17, 17, 7]],
|
||||
[[-12,-17, 5],[ -7,-17, 17]],
|
||||
[[ 5,-12,-17],[ 17, -7,-17]],
|
||||
[[-17, -5, 12],[-17,-17, 7]],
|
||||
[[ 12, 17, 5],[ 7, 17, 17]],
|
||||
[[ -5, 17,-12],[-17, 17, -7]],
|
||||
[[-12, -5, 17],[ -7,-17, 17]],
|
||||
[[ 17,-12, -5],[ 17, -7,-17]],
|
||||
[[ 5,-17,-12],[ 17,-17, -7]],
|
||||
[[ 12, 5, 17],[ 7, 17, 17]],
|
||||
[[-17, 12, -5],[-17, 7,-17]],
|
||||
[[ -5,-17, 12],[-17,-17, 7]],
|
||||
[[-12, 5,-17],[ -7, 17,-17]],
|
||||
[[ 17, 12, 5],[ 17, 7, 17]],
|
||||
[[ 5, 17, 12],[ 17, 17, 7]],
|
||||
[[ 12, -5,-17],[ 7,-17,-17]],
|
||||
[[-17,-12, 5],[-17,-7, 17]]],dtype='float')}
|
||||
|
||||
# Greninger--Troiano' orientation relationship for fcc <-> bcc transformation
|
||||
# from Y. He et al., Journal of Applied Crystallography 39:72-81, 2006
|
||||
_GTprime = {'mapping':{'fcc':0,'bcc':1},
|
||||
'planes': np.array([
|
||||
[[ 7, 17, 17],[ 12, 5, 17]],
|
||||
[[ 17, 7, 17],[ 17, 12, 5]],
|
||||
[[ 17, 17, 7],[ 5, 17, 12]],
|
||||
[[ -7,-17, 17],[-12, -5, 17]],
|
||||
[[-17, -7, 17],[-17,-12, 5]],
|
||||
[[-17,-17, 7],[ -5,-17, 12]],
|
||||
[[ 7,-17,-17],[ 12, -5,-17]],
|
||||
[[ 17, -7,-17],[ 17,-12, -5]],
|
||||
[[ 17,-17, -7],[ 5,-17,-12]],
|
||||
[[ -7, 17,-17],[-12, 5,-17]],
|
||||
[[-17, 7,-17],[-17, 12, -5]],
|
||||
[[-17, 17, -7],[ -5, 17,-12]],
|
||||
[[ 7, 17, 17],[ 12, 17, 5]],
|
||||
[[ 17, 7, 17],[ 5, 12, 17]],
|
||||
[[ 17, 17, 7],[ 17, 5, 12]],
|
||||
[[ -7,-17, 17],[-12,-17, 5]],
|
||||
[[-17, -7, 17],[ -5,-12, 17]],
|
||||
[[-17,-17, 7],[-17, -5, 12]],
|
||||
[[ 7,-17,-17],[ 12,-17, -5]],
|
||||
[[ 17, -7,-17],[ 5, -12,-17]],
|
||||
[[ 17,-17, -7],[ 17, -5,-12]],
|
||||
[[ -7, 17,-17],[-12, 17, -5]],
|
||||
[[-17, 7,-17],[ -5, 12,-17]],
|
||||
[[-17, 17, -7],[-17, 5,-12]]],dtype='float'),
|
||||
'directions': 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]],
|
||||
[[ 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]]],dtype='float')}
|
||||
|
||||
# Nishiyama--Wassermann orientation relationship for fcc <-> bcc transformation
|
||||
# from H. Kitahara et al., Materials Characterization 54:378-386, 2005
|
||||
_NW = {'mapping':{'fcc':0,'bcc':1},
|
||||
'planes': 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]]],dtype='float'),
|
||||
'directions': np.array([
|
||||
[[ 2, -1, -1],[ 0, -1, 1]],
|
||||
[[ -1, 2, -1],[ 0, -1, 1]],
|
||||
[[ -1, -1, 2],[ 0, -1, 1]],
|
||||
[[ -2, -1, -1],[ 0, -1, 1]],
|
||||
[[ 1, 2, -1],[ 0, -1, 1]],
|
||||
[[ 1, -1, 2],[ 0, -1, 1]],
|
||||
[[ 2, 1, -1],[ 0, -1, 1]],
|
||||
[[ -1, -2, -1],[ 0, -1, 1]],
|
||||
[[ -1, 1, 2],[ 0, -1, 1]],
|
||||
[[ 2, -1, 1],[ 0, -1, 1]], #It is wrong in the paper, but matrix is correct
|
||||
[[ -1, 2, 1],[ 0, -1, 1]],
|
||||
[[ -1, -1, -2],[ 0, -1, 1]]],dtype='float')}
|
||||
|
||||
# Pitsch orientation relationship for fcc <-> bcc transformation
|
||||
# from Y. He et al., Acta Materialia 53:1179-1190, 2005
|
||||
_Pitsch = {'mapping':{'fcc':0,'bcc':1},
|
||||
'planes': np.array([
|
||||
[[ 0, 1, 0],[ -1, 0, 1]],
|
||||
[[ 0, 0, 1],[ 1, -1, 0]],
|
||||
[[ 1, 0, 0],[ 0, 1, -1]],
|
||||
[[ 1, 0, 0],[ 0, -1, -1]],
|
||||
[[ 0, 1, 0],[ -1, 0, -1]],
|
||||
[[ 0, 0, 1],[ -1, -1, 0]],
|
||||
[[ 0, 1, 0],[ -1, 0, -1]],
|
||||
[[ 0, 0, 1],[ -1, -1, 0]],
|
||||
[[ 1, 0, 0],[ 0, -1, -1]],
|
||||
[[ 1, 0, 0],[ 0, -1, 1]],
|
||||
[[ 0, 1, 0],[ 1, 0, -1]],
|
||||
[[ 0, 0, 1],[ -1, 1, 0]]],dtype='float'),
|
||||
'directions': np.array([
|
||||
[[ 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],[ 1, 1, -1]]],dtype='float')}
|
||||
|
||||
# Bain orientation relationship for fcc <-> bcc transformation
|
||||
# from Y. He et al., Journal of Applied Crystallography 39:72-81, 2006
|
||||
_Bain = {'mapping':{'fcc':0,'bcc':1},
|
||||
'planes': np.array([
|
||||
[[ 1, 0, 0],[ 1, 0, 0]],
|
||||
[[ 0, 1, 0],[ 0, 1, 0]],
|
||||
[[ 0, 0, 1],[ 0, 0, 1]]],dtype='float'),
|
||||
'directions': np.array([
|
||||
[[ 0, 1, 0],[ 0, 1, 1]],
|
||||
[[ 0, 0, 1],[ 1, 0, 1]],
|
||||
[[ 1, 0, 0],[ 1, 1, 0]]],dtype='float')}
|
||||
|
||||
|
||||
def relation_operations(self,model):
|
||||
"""
|
||||
Crystallographic orientation relationships for phase transformations.
|
||||
|
||||
References
|
||||
----------
|
||||
S. Morito et al., Journal of Alloys and Compounds 577:s587-s592, 2013
|
||||
https://doi.org/10.1016/j.jallcom.2012.02.004
|
||||
|
||||
K. Kitahara et al., Acta Materialia 54(5):1279-1288, 2006
|
||||
https://doi.org/10.1016/j.actamat.2005.11.001
|
||||
|
||||
Y. He et al., Journal of Applied Crystallography 39:72-81, 2006
|
||||
https://doi.org/10.1107/S0021889805038276
|
||||
|
||||
H. Kitahara et al., Materials Characterization 54(4-5):378-386, 2005
|
||||
https://doi.org/10.1016/j.matchar.2004.12.015
|
||||
|
||||
Y. He et al., Acta Materialia 53(4):1179-1190, 2005
|
||||
https://doi.org/10.1016/j.actamat.2004.11.021
|
||||
|
||||
"""
|
||||
models={'KS':self._KS, 'GT':self._GT, 'GT_prime':self._GTprime,
|
||||
'NW':self._NW, 'Pitsch': self._Pitsch, 'Bain':self._Bain}
|
||||
try:
|
||||
relationship = models[model]
|
||||
except KeyError :
|
||||
raise KeyError(f'Orientation relationship "{model}" is unknown')
|
||||
|
||||
if self.lattice not in relationship['mapping']:
|
||||
raise ValueError(f'Relationship "{model}" not supported for lattice "{self.lattice}"')
|
||||
|
||||
r = {'lattice':Lattice((set(relationship['mapping'])-{self.lattice}).pop()), # target lattice
|
||||
'rotations':[] }
|
||||
|
||||
myPlane_id = relationship['mapping'][self.lattice]
|
||||
otherPlane_id = (myPlane_id+1)%2
|
||||
myDir_id = myPlane_id +2
|
||||
otherDir_id = otherPlane_id +2
|
||||
|
||||
for miller in np.hstack((relationship['planes'],relationship['directions'])):
|
||||
myPlane = miller[myPlane_id]/ np.linalg.norm(miller[myPlane_id])
|
||||
myDir = miller[myDir_id]/ np.linalg.norm(miller[myDir_id])
|
||||
myMatrix = np.array([myDir,np.cross(myPlane,myDir),myPlane])
|
||||
|
||||
otherPlane = miller[otherPlane_id]/ np.linalg.norm(miller[otherPlane_id])
|
||||
otherDir = miller[otherDir_id]/ np.linalg.norm(miller[otherDir_id])
|
||||
otherMatrix = np.array([otherDir,np.cross(otherPlane,otherDir),otherPlane])
|
||||
|
||||
r['rotations'].append(np.dot(otherMatrix.T,myMatrix))
|
||||
|
||||
r['rotations'] = np.array(r['rotations'])
|
||||
|
||||
return r
|
||||
File diff suppressed because it is too large
Load Diff
|
|
@ -15,7 +15,6 @@ from numpy.lib import recfunctions as rfn
|
|||
import damask
|
||||
from . import VTK
|
||||
from . import Table
|
||||
from . import Rotation
|
||||
from . import Orientation
|
||||
from . import grid_filters
|
||||
from . import mechanics
|
||||
|
|
@ -743,11 +742,13 @@ class Result:
|
|||
def _add_IPF_color(q,l):
|
||||
m = util.scale_to_coprime(np.array(l))
|
||||
|
||||
o = Orientation(Rotation(rfn.structured_to_unstructured(q['data'])),
|
||||
lattice = q['meta']['Lattice'])
|
||||
o = Orientation(rotation = (rfn.structured_to_unstructured(q['data'])),
|
||||
lattice = {'fcc':'cF',
|
||||
'bcc':'cI',
|
||||
'hex':'hP'}[q['meta']['Lattice']])
|
||||
|
||||
return {
|
||||
'data': np.uint8(o.IPF_color(l)*255),
|
||||
'data': np.uint8(o.IPF_color(o.to_SST(l))*255),
|
||||
'label': 'IPFcolor_[{} {} {}]'.format(*m),
|
||||
'meta' : {
|
||||
'Unit': '8-bit RGB',
|
||||
|
|
@ -897,42 +898,47 @@ class Result:
|
|||
self._add_generic_pointwise(self._add_PK2,{'P':P,'F':F})
|
||||
|
||||
|
||||
@staticmethod
|
||||
def _add_pole(q,p,polar):
|
||||
pole = np.array(p)
|
||||
unit_pole = pole/np.linalg.norm(pole)
|
||||
m = util.scale_to_coprime(pole)
|
||||
rot = Rotation(q['data'].view(np.double).reshape(-1,4))
|
||||
# The add_pole functionality needs discussion.
|
||||
# The new Crystal object can perform such a calculation but the outcome depends on the lattice parameters
|
||||
# as well as on whether a direction or plane is concerned (see the DAMASK_examples/pole_figure notebook).
|
||||
# Below code appears to be too simplistic.
|
||||
|
||||
rotatedPole = rot @ np.broadcast_to(unit_pole,rot.shape+(3,)) # rotate pole according to crystal orientation
|
||||
xy = rotatedPole[:,0:2]/(1.+abs(unit_pole[2])) # stereographic projection
|
||||
coords = xy if not polar else \
|
||||
np.block([np.sqrt(xy[:,0:1]*xy[:,0:1]+xy[:,1:2]*xy[:,1:2]),np.arctan2(xy[:,1:2],xy[:,0:1])])
|
||||
return {
|
||||
'data': coords,
|
||||
'label': 'p^{}_[{} {} {})'.format(u'rφ' if polar else 'xy',*m),
|
||||
'meta' : {
|
||||
'Unit': '1',
|
||||
'Description': '{} coordinates of stereographic projection of pole (direction/plane) in crystal frame'\
|
||||
.format('Polar' if polar else 'Cartesian'),
|
||||
'Creator': 'add_pole'
|
||||
}
|
||||
}
|
||||
def add_pole(self,q,p,polar=False):
|
||||
"""
|
||||
Add coordinates of stereographic projection of given pole in crystal frame.
|
||||
|
||||
Parameters
|
||||
----------
|
||||
q : str
|
||||
Label of the dataset containing the crystallographic orientation as quaternions.
|
||||
p : numpy.array of shape (3)
|
||||
Crystallographic direction or plane.
|
||||
polar : bool, optional
|
||||
Give pole in polar coordinates. Defaults to False.
|
||||
|
||||
"""
|
||||
self._add_generic_pointwise(self._add_pole,{'q':q},{'p':p,'polar':polar})
|
||||
# @staticmethod
|
||||
# def _add_pole(q,p,polar):
|
||||
# pole = np.array(p)
|
||||
# unit_pole = pole/np.linalg.norm(pole)
|
||||
# m = util.scale_to_coprime(pole)
|
||||
# rot = Rotation(q['data'].view(np.double).reshape(-1,4))
|
||||
#
|
||||
# rotatedPole = rot @ np.broadcast_to(unit_pole,rot.shape+(3,)) # rotate pole according to crystal orientation
|
||||
# xy = rotatedPole[:,0:2]/(1.+abs(unit_pole[2])) # stereographic projection
|
||||
# coords = xy if not polar else \
|
||||
# np.block([np.sqrt(xy[:,0:1]*xy[:,0:1]+xy[:,1:2]*xy[:,1:2]),np.arctan2(xy[:,1:2],xy[:,0:1])])
|
||||
# return {
|
||||
# 'data': coords,
|
||||
# 'label': 'p^{}_[{} {} {})'.format(u'rφ' if polar else 'xy',*m),
|
||||
# 'meta' : {
|
||||
# 'Unit': '1',
|
||||
# 'Description': '{} coordinates of stereographic projection of pole (direction/plane) in crystal frame'\
|
||||
# .format('Polar' if polar else 'Cartesian'),
|
||||
# 'Creator': 'add_pole'
|
||||
# }
|
||||
# }
|
||||
# def add_pole(self,q,p,polar=False):
|
||||
# """
|
||||
# Add coordinates of stereographic projection of given pole in crystal frame.
|
||||
#
|
||||
# Parameters
|
||||
# ----------
|
||||
# q : str
|
||||
# Label of the dataset containing the crystallographic orientation as quaternions.
|
||||
# p : numpy.array of shape (3)
|
||||
# Crystallographic direction or plane.
|
||||
# polar : bool, optional
|
||||
# Give pole in polar coordinates. Defaults to False.
|
||||
#
|
||||
# """
|
||||
# self._add_generic_pointwise(self._add_pole,{'q':q},{'p':p,'polar':polar})
|
||||
|
||||
|
||||
@staticmethod
|
||||
|
|
|
|||
|
|
@ -13,18 +13,18 @@ _R1 = (3.*np.pi/4.)**(1./3.)
|
|||
|
||||
class Rotation:
|
||||
u"""
|
||||
Orientation stored with functionality for conversion to different representations.
|
||||
Rotation with functionality for conversion between different representations.
|
||||
|
||||
The following conventions apply:
|
||||
|
||||
- coordinate frames are right-handed.
|
||||
- a rotation angle ω is taken to be positive for a counterclockwise rotation
|
||||
- Coordinate frames are right-handed.
|
||||
- A rotation angle ω is taken to be positive for a counterclockwise rotation
|
||||
when viewing from the end point of the rotation axis towards the origin.
|
||||
- rotations will be interpreted in the passive sense.
|
||||
- Rotations will be interpreted in the passive sense.
|
||||
- Euler angle triplets are implemented using the Bunge convention,
|
||||
with the angular ranges as [0,2π], [0,π], [0,2π].
|
||||
- the rotation angle ω is limited to the interval [0,π].
|
||||
- the real part of a quaternion is positive, Re(q) > 0
|
||||
with angular ranges of [0,2π], [0,π], [0,2π].
|
||||
- The rotation angle ω is limited to the interval [0,π].
|
||||
- The real part of a quaternion is positive, Re(q) > 0
|
||||
- P = -1 (as default).
|
||||
|
||||
Examples
|
||||
|
|
@ -33,7 +33,7 @@ class Rotation:
|
|||
coordinates "b" expressed in system "B":
|
||||
|
||||
- b = Q @ a
|
||||
- b = np.dot(Q.asMatrix(),a)
|
||||
- b = np.dot(Q.as_matrix(),a)
|
||||
|
||||
References
|
||||
----------
|
||||
|
|
@ -44,20 +44,83 @@ class Rotation:
|
|||
|
||||
__slots__ = ['quaternion']
|
||||
|
||||
def __init__(self,quaternion = np.array([1.0,0.0,0.0,0.0])):
|
||||
def __init__(self,rotation = np.array([1.0,0.0,0.0,0.0])):
|
||||
"""
|
||||
Initializes to identity unless specified.
|
||||
Initialize rotation object.
|
||||
|
||||
Parameters
|
||||
----------
|
||||
quaternion : numpy.ndarray, optional
|
||||
rotation : list, numpy.ndarray, Rotation, optional
|
||||
Unit quaternion in positive real hemisphere.
|
||||
Use .from_quaternion to perform a sanity check.
|
||||
Defaults to no rotation.
|
||||
|
||||
"""
|
||||
if quaternion.shape[-1] != 4:
|
||||
raise ValueError('Not a quaternion')
|
||||
self.quaternion = quaternion.copy()
|
||||
if isinstance(rotation,Rotation):
|
||||
self.quaternion = rotation.quaternion.copy()
|
||||
elif np.array(rotation).shape[-1] == 4:
|
||||
self.quaternion = np.array(rotation)
|
||||
else:
|
||||
raise ValueError('"rotation" is neither a Rotation nor a quaternion')
|
||||
|
||||
|
||||
def __repr__(self):
|
||||
"""Represent rotation as unit quaternion, rotation matrix, and Bunge-Euler angles."""
|
||||
return 'Quaternions:\n'+str(self.quaternion) \
|
||||
if self.quaternion.shape != (4,) else \
|
||||
'\n'.join([
|
||||
'Quaternion: (real={:.3f}, imag=<{:+.3f}, {:+.3f}, {:+.3f}>)'.format(*(self.quaternion)),
|
||||
'Matrix:\n{}'.format(np.round(self.as_matrix(),8)),
|
||||
'Bunge Eulers / deg: ({:3.2f}, {:3.2f}, {:3.2f})'.format(*self.as_Eulers(degrees=True)),
|
||||
])
|
||||
|
||||
|
||||
# ToDo: Check difference __copy__ vs __deepcopy__
|
||||
def __copy__(self,**kwargs):
|
||||
"""Copy."""
|
||||
return self.__class__(rotation=kwargs['rotation'] if 'rotation' in kwargs else self.quaternion)
|
||||
|
||||
copy = __copy__
|
||||
|
||||
|
||||
def __getitem__(self,item):
|
||||
"""Return slice according to item."""
|
||||
return self.copy() \
|
||||
if self.shape == () else \
|
||||
self.copy(rotation=self.quaternion[item+(slice(None),)] if isinstance(item,tuple) else self.quaternion[item])
|
||||
|
||||
|
||||
def __eq__(self,other):
|
||||
"""
|
||||
Equal to other.
|
||||
|
||||
Equality is determined taking limited floating point precision into
|
||||
account. See numpy.allclose for details.
|
||||
|
||||
Parameters
|
||||
----------
|
||||
other : Rotation
|
||||
Rotation to check for equality.
|
||||
|
||||
"""
|
||||
return np.prod(self.shape,dtype=int) == np.prod(other.shape,dtype=int) \
|
||||
and np.allclose(self.quaternion,other.quaternion)
|
||||
|
||||
|
||||
def __neq__(self,other):
|
||||
"""
|
||||
Not Equal to other.
|
||||
|
||||
Equality is determined taking limited floating point precision into
|
||||
account. See numpy.allclose for details.
|
||||
|
||||
Parameters
|
||||
----------
|
||||
other : Rotation
|
||||
Rotation to check for inequality.
|
||||
|
||||
"""
|
||||
return not self.__eq__(other)
|
||||
|
||||
|
||||
@property
|
||||
|
|
@ -65,38 +128,35 @@ class Rotation:
|
|||
return self.quaternion.shape[:-1]
|
||||
|
||||
|
||||
# ToDo: Check difference __copy__ vs __deepcopy__
|
||||
def __copy__(self):
|
||||
"""Copy."""
|
||||
return self.__class__(self.quaternion)
|
||||
|
||||
copy = __copy__
|
||||
|
||||
|
||||
def __repr__(self):
|
||||
"""Orientation displayed as unit quaternion, rotation matrix, and Bunge-Euler angles."""
|
||||
if self.quaternion.shape != (4,):
|
||||
return 'Quaternions:\n'+str(self.quaternion) # ToDo: could be nicer ...
|
||||
return '\n'.join([
|
||||
'Quaternion: (real={:.3f}, imag=<{:+.3f}, {:+.3f}, {:+.3f}>)'.format(*(self.quaternion)),
|
||||
'Matrix:\n{}'.format(np.round(self.as_matrix(),8)),
|
||||
'Bunge Eulers / deg: ({:3.2f}, {:3.2f}, {:3.2f})'.format(*self.as_Eulers(degrees=True)),
|
||||
])
|
||||
|
||||
|
||||
def __getitem__(self,item):
|
||||
"""Iterate over leading/leftmost dimension of Rotation array."""
|
||||
if self.shape == (): return self.copy()
|
||||
if isinstance(item,tuple) and len(item) >= len(self):
|
||||
raise IndexError('Too many indices')
|
||||
return self.__class__(self.quaternion[item])
|
||||
|
||||
|
||||
def __len__(self):
|
||||
"""Length of leading/leftmost dimension of Rotation array."""
|
||||
return 0 if self.shape == () else self.shape[0]
|
||||
|
||||
|
||||
def __invert__(self):
|
||||
"""Inverse rotation (backward rotation)."""
|
||||
dup = self.copy()
|
||||
dup.quaternion[...,1:] *= -1
|
||||
return dup
|
||||
|
||||
|
||||
def __pow__(self,pwr):
|
||||
"""
|
||||
Raise quaternion to power.
|
||||
|
||||
Equivalent to performing the rotation 'pwr' times.
|
||||
|
||||
Parameters
|
||||
----------
|
||||
pwr : float
|
||||
Power to raise quaternion to.
|
||||
|
||||
"""
|
||||
phi = np.arccos(self.quaternion[...,0:1])
|
||||
p = self.quaternion[...,1:]/np.linalg.norm(self.quaternion[...,1:],axis=-1,keepdims=True)
|
||||
return self.copy(rotation=Rotation(np.block([np.cos(pwr*phi),np.sin(pwr*phi)*p]))._standardize())
|
||||
|
||||
|
||||
def __matmul__(self,other):
|
||||
"""
|
||||
Rotation of vector, second or fourth order tensor, or rotation object.
|
||||
|
|
@ -119,7 +179,7 @@ class Rotation:
|
|||
p_o = other.quaternion[...,1:]
|
||||
q = (q_m*q_o - np.einsum('...i,...i',p_m,p_o).reshape(self.shape+(1,)))
|
||||
p = q_m*p_o + q_o*p_m + _P * np.cross(p_m,p_o)
|
||||
return self.__class__(np.block([q,p]))._standardize()
|
||||
return Rotation(np.block([q,p]))._standardize()
|
||||
|
||||
elif isinstance(other,np.ndarray):
|
||||
if self.shape + (3,) == other.shape:
|
||||
|
|
@ -146,27 +206,89 @@ class Rotation:
|
|||
|
||||
|
||||
def _standardize(self):
|
||||
"""Standardize (ensure positive real hemisphere)."""
|
||||
"""Standardize quaternion (ensure positive real hemisphere)."""
|
||||
self.quaternion[self.quaternion[...,0] < 0.0] *= -1
|
||||
return self
|
||||
|
||||
def inverse(self):
|
||||
"""In-place inverse rotation (backward rotation)."""
|
||||
self.quaternion[...,1:] *= -1
|
||||
return self
|
||||
|
||||
def __invert__(self):
|
||||
"""Inverse rotation (backward rotation)."""
|
||||
return self.copy().inverse()
|
||||
def append(self,other):
|
||||
"""Extend rotation array along first dimension with other array."""
|
||||
return self.copy(rotation=np.vstack((self.quaternion,other.quaternion)))
|
||||
|
||||
def inversed(self):
|
||||
"""Inverse rotation (backward rotation)."""
|
||||
return ~ self
|
||||
|
||||
def flatten(self,order = 'C'):
|
||||
"""Flatten quaternion array."""
|
||||
return self.copy(rotation=self.quaternion.reshape((-1,4),order=order))
|
||||
|
||||
|
||||
def reshape(self,shape,order = 'C'):
|
||||
"""Reshape quaternion array."""
|
||||
if isinstance(shape,(int,np.integer)): shape = (shape,)
|
||||
return self.copy(rotation=self.quaternion.reshape(tuple(shape)+(4,),order=order))
|
||||
|
||||
|
||||
def broadcast_to(self,shape,mode = 'right'):
|
||||
"""
|
||||
Broadcast quaternion array to shape.
|
||||
|
||||
Parameters
|
||||
----------
|
||||
shape : tuple
|
||||
Shape of broadcasted array.
|
||||
mode : str, optional
|
||||
Where to preferentially locate missing dimensions.
|
||||
Either 'left' or 'right' (default).
|
||||
|
||||
"""
|
||||
if isinstance(shape,(int,np.integer)): shape = (shape,)
|
||||
return self.copy(rotation=np.broadcast_to(self.quaternion.reshape(util.shapeshifter(self.shape,shape,mode)+(4,)),
|
||||
shape+(4,)))
|
||||
|
||||
|
||||
def average(self,weights = None):
|
||||
"""
|
||||
Average rotations along last dimension.
|
||||
|
||||
Parameters
|
||||
----------
|
||||
weights : list of floats, optional
|
||||
Relative weight of each rotation.
|
||||
|
||||
Returns
|
||||
-------
|
||||
average : Rotation
|
||||
Weighted average of original Rotation field.
|
||||
|
||||
References
|
||||
----------
|
||||
Quaternion averaging
|
||||
F. Landis Markley, Yang Cheng, John L. Crassidis, Yaakov Oshman
|
||||
Journal of Guidance, Control, and Dynamics 30(4):1193-1197, 2007
|
||||
10.2514/1.28949
|
||||
|
||||
"""
|
||||
def _M(quat):
|
||||
"""Intermediate representation supporting quaternion averaging."""
|
||||
return np.einsum('...i,...j',quat,quat)
|
||||
|
||||
if not weights:
|
||||
weights = np.ones(self.shape,dtype=float)
|
||||
|
||||
eig, vec = np.linalg.eig(np.sum(_M(self.quaternion) * weights[...,np.newaxis,np.newaxis],axis=-3) \
|
||||
/np.sum( weights[...,np.newaxis,np.newaxis],axis=-3))
|
||||
|
||||
return Rotation.from_quaternion(np.real(
|
||||
np.squeeze(
|
||||
np.take_along_axis(vec,
|
||||
eig.argmax(axis=-1)[...,np.newaxis,np.newaxis],
|
||||
axis=-1),
|
||||
axis=-1)),
|
||||
accept_homomorph = True)
|
||||
|
||||
|
||||
def misorientation(self,other):
|
||||
"""
|
||||
Get Misorientation.
|
||||
Calculate misorientation from self to other Rotation.
|
||||
|
||||
Parameters
|
||||
----------
|
||||
|
|
@ -177,33 +299,6 @@ class Rotation:
|
|||
return other@~self
|
||||
|
||||
|
||||
def broadcast_to(self,shape):
|
||||
if isinstance(shape,(int,np.integer)): shape = (shape,)
|
||||
if self.shape == ():
|
||||
q = np.broadcast_to(self.quaternion,shape+(4,))
|
||||
else:
|
||||
q = np.block([np.broadcast_to(self.quaternion[...,0:1],shape).reshape(shape+(1,)),
|
||||
np.broadcast_to(self.quaternion[...,1:2],shape).reshape(shape+(1,)),
|
||||
np.broadcast_to(self.quaternion[...,2:3],shape).reshape(shape+(1,)),
|
||||
np.broadcast_to(self.quaternion[...,3:4],shape).reshape(shape+(1,))])
|
||||
return self.__class__(q)
|
||||
|
||||
|
||||
def average(self,other): #ToDo: discuss calling for vectors
|
||||
"""
|
||||
Calculate the average rotation.
|
||||
|
||||
Parameters
|
||||
----------
|
||||
other : Rotation
|
||||
Rotation from which the average is rotated.
|
||||
|
||||
"""
|
||||
if self.quaternion.shape != (4,) or other.quaternion.shape != (4,):
|
||||
raise NotImplementedError('Support for multiple rotations missing')
|
||||
return Rotation.from_average([self,other])
|
||||
|
||||
|
||||
################################################################################################
|
||||
# convert to different orientation representations (numpy arrays)
|
||||
|
||||
|
|
@ -326,20 +421,6 @@ class Rotation:
|
|||
"""
|
||||
return Rotation._qu2cu(self.quaternion)
|
||||
|
||||
@property
|
||||
def M(self): # ToDo not sure about the name: as_M or M? we do not have a from_M
|
||||
"""
|
||||
Intermediate representation supporting quaternion averaging.
|
||||
|
||||
References
|
||||
----------
|
||||
F. Landis Markley et al., Journal of Guidance, Control, and Dynamics 30(4):1193-1197, 2007
|
||||
https://doi.org/10.2514/1.28949
|
||||
|
||||
"""
|
||||
return np.einsum('...i,...j',self.quaternion,self.quaternion)
|
||||
|
||||
|
||||
################################################################################################
|
||||
# Static constructors. The input data needs to follow the conventions, options allow to
|
||||
# relax the conventions.
|
||||
|
|
@ -347,7 +428,7 @@ class Rotation:
|
|||
def from_quaternion(q,
|
||||
accept_homomorph = False,
|
||||
P = -1,
|
||||
acceptHomomorph = None): # old name (for compatibility)
|
||||
**kwargs):
|
||||
"""
|
||||
Initialize from quaternion.
|
||||
|
||||
|
|
@ -363,15 +444,13 @@ class Rotation:
|
|||
Convention used. Defaults to -1.
|
||||
|
||||
"""
|
||||
if acceptHomomorph is not None:
|
||||
accept_homomorph = acceptHomomorph # for compatibility
|
||||
qu = np.array(q,dtype=float)
|
||||
if qu.shape[:-2:-1] != (4,):
|
||||
raise ValueError('Invalid shape.')
|
||||
if abs(P) != 1:
|
||||
raise ValueError('P ∉ {-1,1}')
|
||||
|
||||
if P == 1: qu[...,1:4] *= -1
|
||||
qu[...,1:4] *= -P
|
||||
if accept_homomorph:
|
||||
qu[qu[...,0] < 0.0] *= -1
|
||||
else:
|
||||
|
|
@ -384,7 +463,8 @@ class Rotation:
|
|||
|
||||
@staticmethod
|
||||
def from_Eulers(phi,
|
||||
degrees = False):
|
||||
degrees = False,
|
||||
**kwargs):
|
||||
"""
|
||||
Initialize from Bunge-Euler angles.
|
||||
|
||||
|
|
@ -411,7 +491,8 @@ class Rotation:
|
|||
def from_axis_angle(axis_angle,
|
||||
degrees = False,
|
||||
normalize = False,
|
||||
P = -1):
|
||||
P = -1,
|
||||
**kwargs):
|
||||
"""
|
||||
Initialize from Axis angle pair.
|
||||
|
||||
|
|
@ -434,7 +515,7 @@ class Rotation:
|
|||
if abs(P) != 1:
|
||||
raise ValueError('P ∉ {-1,1}')
|
||||
|
||||
if P == 1: ax[...,0:3] *= -1
|
||||
ax[...,0:3] *= -P
|
||||
if degrees: ax[..., 3] = np.radians(ax[...,3])
|
||||
if normalize: ax[...,0:3] /= np.linalg.norm(ax[...,0:3],axis=-1,keepdims=True)
|
||||
if np.any(ax[...,3] < 0.0) or np.any(ax[...,3] > np.pi):
|
||||
|
|
@ -448,14 +529,15 @@ class Rotation:
|
|||
@staticmethod
|
||||
def from_basis(basis,
|
||||
orthonormal = True,
|
||||
reciprocal = False):
|
||||
reciprocal = False,
|
||||
**kwargs):
|
||||
"""
|
||||
Initialize from lattice basis vectors.
|
||||
|
||||
Parameters
|
||||
----------
|
||||
basis : numpy.ndarray of shape (...,3,3)
|
||||
Three lattice basis vectors in three dimensions.
|
||||
Three three-dimensional lattice basis vectors.
|
||||
orthonormal : boolean, optional
|
||||
Basis is strictly orthonormal, i.e. is free of stretch components. Defaults to True.
|
||||
reciprocal : boolean, optional
|
||||
|
|
@ -463,7 +545,7 @@ class Rotation:
|
|||
|
||||
"""
|
||||
om = np.array(basis,dtype=float)
|
||||
if om.shape[:-3:-1] != (3,3):
|
||||
if om.shape[-2:] != (3,3):
|
||||
raise ValueError('Invalid shape.')
|
||||
|
||||
if reciprocal:
|
||||
|
|
@ -482,7 +564,7 @@ class Rotation:
|
|||
return Rotation(Rotation._om2qu(om))
|
||||
|
||||
@staticmethod
|
||||
def from_matrix(R):
|
||||
def from_matrix(R,**kwargs):
|
||||
"""
|
||||
Initialize from rotation matrix.
|
||||
|
||||
|
|
@ -494,10 +576,40 @@ class Rotation:
|
|||
"""
|
||||
return Rotation.from_basis(R)
|
||||
|
||||
@staticmethod
|
||||
def from_parallel(a,b,
|
||||
**kwargs):
|
||||
"""
|
||||
Initialize from pairs of two orthogonal lattice basis vectors.
|
||||
|
||||
Parameters
|
||||
----------
|
||||
a : numpy.ndarray of shape (...,2,3)
|
||||
Two three-dimensional lattice vectors of first orthogonal basis.
|
||||
b : numpy.ndarray of shape (...,2,3)
|
||||
Corresponding three-dimensional lattice vectors of second basis.
|
||||
|
||||
"""
|
||||
a_ = np.array(a)
|
||||
b_ = np.array(b)
|
||||
if a_.shape[-2:] != (2,3) or b_.shape[-2:] != (2,3) or a_.shape != b_.shape:
|
||||
raise ValueError('Invalid shape.')
|
||||
am = np.stack([ a_[...,0,:],
|
||||
a_[...,1,:],
|
||||
np.cross(a_[...,0,:],a_[...,1,:]) ],axis=-2)
|
||||
bm = np.stack([ b_[...,0,:],
|
||||
b_[...,1,:],
|
||||
np.cross(b_[...,0,:],b_[...,1,:]) ],axis=-2)
|
||||
|
||||
return Rotation.from_basis(np.swapaxes(am/np.linalg.norm(am,axis=-1,keepdims=True),-1,-2))\
|
||||
.misorientation(Rotation.from_basis(np.swapaxes(bm/np.linalg.norm(bm,axis=-1,keepdims=True),-1,-2)))
|
||||
|
||||
|
||||
@staticmethod
|
||||
def from_Rodrigues(rho,
|
||||
normalize = False,
|
||||
P = -1):
|
||||
P = -1,
|
||||
**kwargs):
|
||||
"""
|
||||
Initialize from Rodrigues-Frank vector.
|
||||
|
||||
|
|
@ -518,7 +630,7 @@ class Rotation:
|
|||
if abs(P) != 1:
|
||||
raise ValueError('P ∉ {-1,1}')
|
||||
|
||||
if P == 1: ro[...,0:3] *= -1
|
||||
ro[...,0:3] *= -P
|
||||
if normalize: ro[...,0:3] /= np.linalg.norm(ro[...,0:3],axis=-1,keepdims=True)
|
||||
if np.any(ro[...,3] < 0.0):
|
||||
raise ValueError('Rodrigues vector rotation angle not positive.')
|
||||
|
|
@ -529,7 +641,8 @@ class Rotation:
|
|||
|
||||
@staticmethod
|
||||
def from_homochoric(h,
|
||||
P = -1):
|
||||
P = -1,
|
||||
**kwargs):
|
||||
"""
|
||||
Initialize from homochoric vector.
|
||||
|
||||
|
|
@ -547,7 +660,7 @@ class Rotation:
|
|||
if abs(P) != 1:
|
||||
raise ValueError('P ∉ {-1,1}')
|
||||
|
||||
if P == 1: ho *= -1
|
||||
ho *= -P
|
||||
|
||||
if np.any(np.linalg.norm(ho,axis=-1) >_R1+1e-9):
|
||||
raise ValueError('Homochoric coordinate outside of the sphere.')
|
||||
|
|
@ -556,7 +669,8 @@ class Rotation:
|
|||
|
||||
@staticmethod
|
||||
def from_cubochoric(c,
|
||||
P = -1):
|
||||
P = -1,
|
||||
**kwargs):
|
||||
"""
|
||||
Initialize from cubochoric vector.
|
||||
|
||||
|
|
@ -577,46 +691,15 @@ class Rotation:
|
|||
if np.abs(np.max(cu)) > np.pi**(2./3.) * 0.5+1e-9:
|
||||
raise ValueError('Cubochoric coordinate outside of the cube.')
|
||||
|
||||
ho = Rotation._cu2ho(cu)
|
||||
if P == 1: ho *= -1
|
||||
ho = -P * Rotation._cu2ho(cu)
|
||||
|
||||
return Rotation(Rotation._ho2qu(ho))
|
||||
|
||||
|
||||
@staticmethod
|
||||
def from_average(rotations,weights = None):
|
||||
"""
|
||||
Average rotation.
|
||||
|
||||
References
|
||||
----------
|
||||
F. Landis Markley et al., Journal of Guidance, Control, and Dynamics 30(4):1193-1197, 2007
|
||||
https://doi.org/10.2514/1.28949
|
||||
|
||||
Parameters
|
||||
----------
|
||||
rotations : list of Rotations
|
||||
Rotations to average from
|
||||
weights : list of floats, optional
|
||||
Weights for each rotation used for averaging
|
||||
|
||||
"""
|
||||
if not all(isinstance(item, Rotation) for item in rotations):
|
||||
raise TypeError('Only instances of Rotation can be averaged.')
|
||||
|
||||
N = len(rotations)
|
||||
if not weights:
|
||||
weights = np.ones(N,dtype='i')
|
||||
|
||||
for i,(r,n) in enumerate(zip(rotations,weights)):
|
||||
M = r.M * n if i == 0 \
|
||||
else M + r.M * n # noqa add (multiples) of this rotation to average noqa
|
||||
eig, vec = np.linalg.eig(M/N)
|
||||
|
||||
return Rotation.from_quaternion(np.real(vec.T[eig.argmax()]),accept_homomorph = True)
|
||||
|
||||
@staticmethod
|
||||
def from_random(shape=None,seed=None):
|
||||
def from_random(shape = None,
|
||||
seed = None,
|
||||
**kwargs):
|
||||
"""
|
||||
Draw random rotation.
|
||||
|
||||
|
|
@ -633,12 +716,7 @@ class Rotation:
|
|||
|
||||
"""
|
||||
rng = np.random.default_rng(seed)
|
||||
if shape is None:
|
||||
r = rng.random(3)
|
||||
elif hasattr(shape, '__iter__'):
|
||||
r = rng.random(tuple(shape)+(3,))
|
||||
else:
|
||||
r = rng.random((shape,3))
|
||||
r = rng.random(3 if shape is None else tuple(shape)+(3,) if hasattr(shape, '__iter__') else (shape,3))
|
||||
|
||||
A = np.sqrt(r[...,2])
|
||||
B = np.sqrt(1.0-r[...,2])
|
||||
|
|
@ -647,14 +725,17 @@ class Rotation:
|
|||
np.cos(2.0*np.pi*r[...,1])*B,
|
||||
np.sin(2.0*np.pi*r[...,0])*A],axis=-1)
|
||||
|
||||
return Rotation(q.reshape(r.shape[:-1]+(4,)) if shape is not None else q)._standardize()
|
||||
|
||||
# for compatibility
|
||||
__mul__ = __matmul__
|
||||
return Rotation(q if shape is None else q.reshape(r.shape[:-1]+(4,)))._standardize()
|
||||
|
||||
|
||||
@staticmethod
|
||||
def from_ODF(weights,Eulers,N=500,degrees=True,fractions=True,seed=None):
|
||||
def from_ODF(weights,
|
||||
Eulers,
|
||||
N = 500,
|
||||
degrees = True,
|
||||
fractions = True,
|
||||
seed = None,
|
||||
**kwargs):
|
||||
"""
|
||||
Sample discrete values from a binned ODF.
|
||||
|
||||
|
|
@ -707,7 +788,12 @@ class Rotation:
|
|||
|
||||
|
||||
@staticmethod
|
||||
def from_spherical_component(center,sigma,N=500,degrees=True,seed=None):
|
||||
def from_spherical_component(center,
|
||||
sigma,
|
||||
N = 500,
|
||||
degrees = True,
|
||||
seed = None,
|
||||
**kwargs):
|
||||
"""
|
||||
Calculate set of rotations with Gaussian distribution around center.
|
||||
|
||||
|
|
@ -738,7 +824,13 @@ class Rotation:
|
|||
|
||||
|
||||
@staticmethod
|
||||
def from_fiber_component(alpha,beta,sigma=0.0,N=500,degrees=True,seed=None):
|
||||
def from_fiber_component(alpha,
|
||||
beta,
|
||||
sigma = 0.0,
|
||||
N = 500,
|
||||
degrees = True,
|
||||
seed = None,
|
||||
**kwargs):
|
||||
"""
|
||||
Calculate set of rotations with Gaussian distribution around direction.
|
||||
|
||||
|
|
|
|||
|
|
@ -175,7 +175,7 @@ class Table:
|
|||
|
||||
@property
|
||||
def labels(self):
|
||||
return list(self.shapes.keys())
|
||||
return list(self.shapes)
|
||||
|
||||
|
||||
def get(self,label):
|
||||
|
|
|
|||
|
|
@ -0,0 +1,420 @@
|
|||
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],
|
||||
],'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),
|
||||
},
|
||||
}
|
||||
|
|
@ -3,6 +3,7 @@ import datetime
|
|||
import os
|
||||
import subprocess
|
||||
import shlex
|
||||
import re
|
||||
import fractions
|
||||
from functools import reduce
|
||||
from optparse import Option
|
||||
|
|
@ -20,10 +21,13 @@ __all__=[
|
|||
'execute',
|
||||
'show_progress',
|
||||
'scale_to_coprime',
|
||||
'project_stereographic',
|
||||
'hybrid_IA',
|
||||
'return_message',
|
||||
'extendableOption',
|
||||
'execution_stamp'
|
||||
'execution_stamp',
|
||||
'shapeshifter',
|
||||
'shapeblender',
|
||||
]
|
||||
|
||||
####################################################################################################
|
||||
|
|
@ -182,6 +186,28 @@ def scale_to_coprime(v):
|
|||
return m
|
||||
|
||||
|
||||
def project_stereographic(vector,normalize=False):
|
||||
"""
|
||||
Apply stereographic projection to vector.
|
||||
|
||||
Parameters
|
||||
----------
|
||||
vector : numpy.ndarray of shape (...,3)
|
||||
Vector coordinates to be projected.
|
||||
normalize : bool
|
||||
Ensure unit length for vector. Defaults to False.
|
||||
|
||||
Returns
|
||||
-------
|
||||
coordinates : numpy.ndarray of shape (...,2)
|
||||
Projected coordinates.
|
||||
|
||||
"""
|
||||
v_ = vector/np.linalg.norm(vector,axis=-1,keepdims=True) if normalize else vector
|
||||
return np.block([v_[...,:2]/(1+np.abs(v_[...,2:3])),
|
||||
np.zeros_like(v_[...,2:3])])
|
||||
|
||||
|
||||
def execution_stamp(class_name,function_name=None):
|
||||
"""Timestamp the execution of a (function within a) class."""
|
||||
now = datetime.datetime.now().astimezone().strftime('%Y-%m-%d %H:%M:%S%z')
|
||||
|
|
@ -203,6 +229,77 @@ def hybrid_IA(dist,N,seed=None):
|
|||
return np.repeat(np.arange(len(dist)),repeats)[np.random.default_rng(seed).permutation(N_inv_samples)[:N]]
|
||||
|
||||
|
||||
def shapeshifter(fro,to,mode='left',keep_ones=False):
|
||||
"""
|
||||
Return a tuple that reshapes 'fro' to become broadcastable to 'to'.
|
||||
|
||||
Parameters
|
||||
----------
|
||||
fro : tuple
|
||||
Original shape of array.
|
||||
to : tuple
|
||||
Target shape of array after broadcasting.
|
||||
len(to) cannot be less than len(fro).
|
||||
mode : str, optional
|
||||
Indicates whether new axes are preferably added to
|
||||
either 'left' or 'right' of the original shape.
|
||||
Defaults to 'left'.
|
||||
keep_ones : bool, optional
|
||||
Treat '1' in fro as literal value instead of dimensional placeholder.
|
||||
Defaults to False.
|
||||
|
||||
"""
|
||||
beg = dict(left ='(^.*\\b)',
|
||||
right='(^.*?\\b)')
|
||||
sep = dict(left ='(.*\\b)',
|
||||
right='(.*?\\b)')
|
||||
end = dict(left ='(.*?$)',
|
||||
right='(.*$)')
|
||||
fro = (1,) if not len(fro) else fro
|
||||
to = (1,) if not len(to) else to
|
||||
try:
|
||||
grp = re.match(beg[mode]
|
||||
+f',{sep[mode]}'.join(map(lambda x: f'{x}'
|
||||
if x>1 or (keep_ones and len(fro)>1) else
|
||||
'\\d+',fro))
|
||||
+f',{end[mode]}',
|
||||
','.join(map(str,to))+',').groups()
|
||||
except AttributeError:
|
||||
raise ValueError(f'Shapes can not be shifted {fro} --> {to}')
|
||||
fill = ()
|
||||
for g,d in zip(grp,fro+(None,)):
|
||||
fill += (1,)*g.count(',')+(d,)
|
||||
return fill[:-1]
|
||||
|
||||
|
||||
def shapeblender(a,b):
|
||||
"""
|
||||
Return a shape that overlaps the rightmost entries of 'a' with the leftmost of 'b'.
|
||||
|
||||
Parameters
|
||||
----------
|
||||
a : tuple
|
||||
Shape of first array.
|
||||
b : tuple
|
||||
Shape of second array.
|
||||
|
||||
Examples
|
||||
--------
|
||||
>>> shapeblender((4,4,3),(3,2,1))
|
||||
(4,4,3,2,1)
|
||||
>>> shapeblender((1,2),(1,2,3))
|
||||
(1,2,3)
|
||||
>>> shapeblender((1,),(2,2,1))
|
||||
(1,2,2,1)
|
||||
>>> shapeblender((3,2),(3,2))
|
||||
(3,2)
|
||||
|
||||
"""
|
||||
i = min(len(a),len(b))
|
||||
while i > 0 and a[-i:] != b[:i]: i -= 1
|
||||
return a + b[i:]
|
||||
|
||||
|
||||
####################################################################################################
|
||||
# Classes
|
||||
####################################################################################################
|
||||
|
|
|
|||
|
|
@ -36,9 +36,9 @@ phase:
|
|||
elasticity: {C_11: 106.75e9, C_12: 60.41e9, C_44: 28.34e9, type: hooke}
|
||||
generic:
|
||||
output: [F, P, Fe, Fp, Lp]
|
||||
lattice: fcc
|
||||
lattice: cF
|
||||
Steel:
|
||||
elasticity: {C_11: 233.3e9, C_12: 135.5e9, C_44: 118.0e9, type: hooke}
|
||||
generic:
|
||||
output: [F, P, Fe, Fp, Lp]
|
||||
lattice: bcc
|
||||
lattice: cI
|
||||
|
|
|
|||
|
|
@ -0,0 +1,5 @@
|
|||
1 header
|
||||
1_Eulers 2_Eulers 3_Eulers 1_pos 2_pos
|
||||
180.0 45.00000000000001 180.0 1 1
|
||||
270.0 45.00000000000001 90.0 1 2
|
||||
315.0 0.0 0.0 1 3
|
||||
|
|
@ -0,0 +1,26 @@
|
|||
1 header
|
||||
1_Eulers 2_Eulers 3_Eulers 1_pos 2_pos
|
||||
146.75362934444064 9.976439066337804 256.395594327347 1 1
|
||||
356.59977719102034 43.39784965440254 12.173896584899929 1 2
|
||||
75.92521636876346 43.82007387041961 277.8843642946069 1 3
|
||||
326.75362934444064 9.976439066337806 76.39559432734703 1 4
|
||||
176.59977719102034 43.397849654402556 192.17389658489986 1 5
|
||||
255.92521636876344 43.82007387041961 97.88436429460687 1 6
|
||||
213.24637065555936 9.976439066337804 103.604405672653 1 7
|
||||
3.400222808979685 43.39784965440255 347.8261034151001 1 8
|
||||
284.0747836312365 43.82007387041961 82.11563570539313 1 9
|
||||
33.24637065555936 9.976439066337804 283.60440567265294 1 10
|
||||
183.40022280897963 43.397849654402556 167.8261034151001 1 11
|
||||
104.07478363123654 43.82007387041961 262.1156357053931 1 12
|
||||
273.4002228089796 43.397849654402556 77.82610341510008 1 13
|
||||
123.24637065555939 9.976439066337806 193.60440567265297 1 14
|
||||
194.07478363123653 43.82007387041961 172.11563570539317 1 15
|
||||
93.40022280897969 43.39784965440255 257.8261034151001 1 16
|
||||
303.24637065555936 9.976439066337804 13.604405672652977 1 17
|
||||
14.074783631236542 43.82007387041961 352.1156357053931 1 18
|
||||
86.59977719102032 43.39784965440254 282.17389658489986 1 19
|
||||
236.75362934444058 9.976439066337804 166.39559432734703 1 20
|
||||
165.92521636876344 43.82007387041961 187.88436429460683 1 21
|
||||
266.59977719102034 43.39784965440254 102.17389658489992 1 22
|
||||
56.75362934444064 9.976439066337804 346.395594327347 1 23
|
||||
345.9252163687635 43.82007387041961 7.884364294606862 1 24
|
||||
|
|
@ -0,0 +1,26 @@
|
|||
1 header
|
||||
1_Eulers 2_Eulers 3_Eulers 1_pos 2_pos
|
||||
166.39559432734697 9.976439066337804 236.75362934444058 1 1
|
||||
352.1156357053931 43.82007387041961 14.074783631236542 1 2
|
||||
77.82610341510008 43.397849654402556 273.4002228089796 1 3
|
||||
346.395594327347 9.976439066337804 56.75362934444064 1 4
|
||||
172.11563570539317 43.82007387041961 194.07478363123653 1 5
|
||||
257.8261034151001 43.39784965440255 93.40022280897969 1 6
|
||||
193.604405672653 9.976439066337804 123.24637065555939 1 7
|
||||
7.884364294606862 43.82007387041961 345.9252163687635 1 8
|
||||
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|
||||
13.604405672652977 9.976439066337804 303.24637065555936 1 10
|
||||
187.88436429460683 43.82007387041961 165.92521636876344 1 11
|
||||
102.17389658489992 43.39784965440254 266.59977719102034 1 12
|
||||
277.8843642946069 43.82007387041961 75.92521636876346 1 13
|
||||
103.604405672653 9.976439066337804 213.24637065555936 1 14
|
||||
192.17389658489986 43.397849654402556 176.59977719102034 1 15
|
||||
97.88436429460687 43.82007387041961 255.92521636876344 1 16
|
||||
283.60440567265294 9.976439066337804 33.24637065555936 1 17
|
||||
12.173896584899929 43.39784965440254 356.59977719102034 1 18
|
||||
82.11563570539313 43.82007387041961 284.0747836312365 1 19
|
||||
256.395594327347 9.976439066337804 146.75362934444064 1 20
|
||||
167.8261034151001 43.397849654402556 183.40022280897963 1 21
|
||||
262.1156357053931 43.82007387041961 104.07478363123654 1 22
|
||||
76.39559432734703 9.976439066337806 326.75362934444064 1 23
|
||||
347.8261034151001 43.39784965440255 3.400222808979685 1 24
|
||||
|
|
@ -0,0 +1,26 @@
|
|||
1 header
|
||||
1_Eulers 2_Eulers 3_Eulers 1_pos 2_pos
|
||||
114.20342833932975 10.52877936550932 204.20342833932972 1 1
|
||||
94.3573968784815 80.40593177313954 311.22729452432543 1 2
|
||||
175.6426031215185 80.40593177313954 48.77270547567447 1 3
|
||||
155.79657166067025 10.52877936550932 155.79657166067025 1 4
|
||||
99.62136089109411 85.70366403943004 318.04510841542015 1 5
|
||||
170.37863910890587 85.70366403943002 41.954891584579855 1 6
|
||||
85.64260312151852 80.40593177313954 48.77270547567448 1 7
|
||||
65.79657166067024 10.52877936550932 155.79657166067025 1 8
|
||||
9.621360891094124 85.70366403943004 318.04510841542015 1 9
|
||||
80.37863910890587 85.70366403943004 41.95489158457987 1 10
|
||||
24.203428339329758 10.52877936550932 204.20342833932975 1 11
|
||||
4.357396878481486 80.40593177313954 311.2272945243255 1 12
|
||||
204.20342833932972 10.52877936550932 204.20342833932972 1 13
|
||||
184.35739687848147 80.40593177313954 311.2272945243255 1 14
|
||||
265.64260312151845 80.40593177313953 48.77270547567449 1 15
|
||||
245.79657166067025 10.528779365509317 155.79657166067025 1 16
|
||||
189.62136089109413 85.70366403943004 318.04510841542015 1 17
|
||||
260.3786391089059 85.70366403943002 41.954891584579855 1 18
|
||||
170.37863910890587 94.29633596056996 138.04510841542015 1 19
|
||||
99.62136089109411 94.29633596056998 221.95489158457983 1 20
|
||||
155.79657166067025 169.4712206344907 24.203428339329754 1 21
|
||||
175.64260312151848 99.59406822686046 131.22729452432552 1 22
|
||||
94.35739687848151 99.59406822686046 228.77270547567446 1 23
|
||||
114.20342833932975 169.4712206344907 335.7965716606702 1 24
|
||||
|
|
@ -0,0 +1,14 @@
|
|||
1 header
|
||||
1_Eulers 2_Eulers 3_Eulers 1_pos 2_pos
|
||||
96.91733794010702 83.13253115922213 314.5844440567886 1 1
|
||||
173.082662059893 83.13253115922211 45.41555594321143 1 2
|
||||
135.0 9.735610317245317 180.0 1 3
|
||||
263.082662059893 83.13253115922213 45.415555943211444 1 4
|
||||
186.91733794010702 83.13253115922211 314.5844440567886 1 5
|
||||
224.99999999999997 9.735610317245317 180.0 1 6
|
||||
83.082662059893 83.13253115922213 45.415555943211444 1 7
|
||||
6.917337940106983 83.13253115922211 314.5844440567886 1 8
|
||||
45.0 9.73561031724532 180.0 1 9
|
||||
13.638707279476469 45.81931182053557 80.40196970123216 1 10
|
||||
256.36129272052347 45.81931182053556 279.59803029876775 1 11
|
||||
315.0 99.73561031724536 0.0 1 12
|
||||
|
|
@ -0,0 +1,14 @@
|
|||
1 header
|
||||
1_Eulers 2_Eulers 3_Eulers 1_pos 2_pos
|
||||
135.41555594321144 83.13253115922213 173.082662059893 1 1
|
||||
260.26438968275465 90.0 135.0 1 2
|
||||
260.40196970123213 45.81931182053557 13.638707279476478 1 3
|
||||
314.5844440567886 83.13253115922213 96.91733794010702 1 4
|
||||
350.40196970123213 45.81931182053557 283.6387072794765 1 5
|
||||
170.26438968275465 90.0 224.99999999999997 1 6
|
||||
315.4155559432114 83.13253115922213 353.08266205989304 1 7
|
||||
99.73561031724536 90.0 225.0 1 8
|
||||
279.59803029876787 45.819311820535574 166.36129272052352 1 9
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||||
134.58444405678856 83.13253115922213 276.91733794010696 1 10
|
||||
9.598030298767851 45.819311820535574 76.36129272052355 1 11
|
||||
9.735610317245369 90.0 315.0 1 12
|
||||
|
|
@ -0,0 +1,19 @@
|
|||
3x3:1_Schmid 3x3:2_Schmid 3x3:3_Schmid 3x3:4_Schmid 3x3:5_Schmid 3x3:6_Schmid 3x3:7_Schmid 3x3:8_Schmid 3x3:9_Schmid
|
||||
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||||
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|
||||
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||||
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||||
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||||
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||||
0.0 0.0 0.0 -0.408248290463863 0.408248290463863 0.408248290463863 0.4082482904638631 -0.4082482904638631 -0.4082482904638631
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||||
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|
||||
0.408248290463863 -0.408248290463863 -0.408248290463863 0.408248290463863 -0.408248290463863 -0.408248290463863 0.0 0.0 0.0
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||||
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|
||||
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|
||||
0.408248290463863 -0.408248290463863 0.40824829046386296 0.408248290463863 -0.408248290463863 0.40824829046386296 0.0 0.0 0.0
|
||||
0.4999999999999999 -0.4999999999999999 0.0 0.4999999999999999 -0.4999999999999999 0.0 0.0 0.0 0.0
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||||
0.5 0.4999999999999999 -6.123233995736766e-17 -0.5000000000000001 -0.5 6.123233995736767e-17 0.0 0.0 0.0
|
||||
0.4999999999999999 -3.0616169978683824e-17 -0.4999999999999999 3.0616169978683824e-17 -1.874699728327322e-33 -3.0616169978683824e-17 0.4999999999999999 -3.0616169978683824e-17 -0.4999999999999999
|
||||
0.5 -3.061616997868383e-17 0.4999999999999999 -3.0616169978683836e-17 1.8746997283273227e-33 -3.061616997868383e-17 -0.5000000000000001 3.0616169978683836e-17 -0.5
|
||||
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|
||||
0.0 0.0 0.0 0.0 0.5 0.4999999999999999 0.0 -0.5000000000000001 -0.5
|
||||
|
|
@ -0,0 +1,13 @@
|
|||
3x3:1_Schmid 3x3:2_Schmid 3x3:3_Schmid 3x3:4_Schmid 3x3:5_Schmid 3x3:6_Schmid 3x3:7_Schmid 3x3:8_Schmid 3x3:9_Schmid
|
||||
-0.4714045207910318 -0.4714045207910318 -0.47140452079103173 0.2357022603955159 0.2357022603955159 0.23570226039551587 0.2357022603955159 0.2357022603955159 0.23570226039551587
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
0.2357022603955159 0.23570226039551587 -0.2357022603955159 0.2357022603955159 0.23570226039551587 -0.2357022603955159 0.4714045207910317 0.47140452079103157 -0.4714045207910317
|
||||
-0.4714045207910318 0.4714045207910318 0.4714045207910318 -0.2357022603955159 0.2357022603955159 0.2357022603955159 -0.2357022603955159 0.2357022603955159 0.2357022603955159
|
||||
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|
||||
0.2357022603955159 -0.2357022603955159 -0.2357022603955159 -0.23570226039551587 0.23570226039551587 0.23570226039551587 0.4714045207910318 -0.4714045207910318 -0.4714045207910318
|
||||
-0.4714045207910318 0.4714045207910318 -0.47140452079103173 -0.23570226039551587 0.23570226039551587 -0.23570226039551584 0.2357022603955159 -0.2357022603955159 0.23570226039551587
|
||||
0.23570226039551595 -0.23570226039551595 0.2357022603955159 0.4714045207910318 -0.4714045207910318 0.47140452079103173 0.2357022603955159 -0.2357022603955159 0.23570226039551587
|
||||
0.23570226039551584 -0.23570226039551584 0.23570226039551578 -0.23570226039551595 0.23570226039551595 -0.2357022603955159 -0.4714045207910318 0.4714045207910318 -0.47140452079103173
|
||||
|
|
@ -0,0 +1,5 @@
|
|||
1 header
|
||||
1_Eulers 2_Eulers 3_Eulers 1_pos 2_pos
|
||||
0.0 45.00000000000001 0.0 1 1
|
||||
90.0 45.00000000000001 270.0 1 2
|
||||
45.00000000000001 0.0 0.0 1 3
|
||||
|
|
@ -0,0 +1,26 @@
|
|||
1 header
|
||||
1_Eulers 2_Eulers 3_Eulers 1_pos 2_pos
|
||||
283.60440567265294 9.976439066337804 33.24637065555936 1 1
|
||||
167.8261034151001 43.397849654402556 183.40022280897963 1 2
|
||||
262.1156357053931 43.82007387041961 104.07478363123654 1 3
|
||||
103.604405672653 9.976439066337804 213.24637065555936 1 4
|
||||
347.8261034151001 43.39784965440255 3.400222808979685 1 5
|
||||
82.11563570539313 43.82007387041961 284.0747836312365 1 6
|
||||
76.39559432734703 9.976439066337806 326.75362934444064 1 7
|
||||
192.17389658489986 43.397849654402556 176.59977719102034 1 8
|
||||
97.88436429460687 43.82007387041961 255.92521636876344 1 9
|
||||
256.395594327347 9.976439066337804 146.75362934444064 1 10
|
||||
12.173896584899929 43.39784965440254 356.59977719102034 1 11
|
||||
277.8843642946069 43.82007387041961 75.92521636876346 1 12
|
||||
102.17389658489992 43.39784965440254 266.59977719102034 1 13
|
||||
346.395594327347 9.976439066337804 56.75362934444064 1 14
|
||||
7.884364294606862 43.82007387041961 345.9252163687635 1 15
|
||||
282.17389658489986 43.39784965440254 86.59977719102032 1 16
|
||||
166.39559432734703 9.976439066337804 236.75362934444058 1 17
|
||||
187.88436429460683 43.82007387041961 165.92521636876344 1 18
|
||||
257.8261034151001 43.39784965440255 93.40022280897969 1 19
|
||||
13.604405672652977 9.976439066337804 303.24637065555936 1 20
|
||||
352.1156357053931 43.82007387041961 14.074783631236542 1 21
|
||||
77.82610341510008 43.397849654402556 273.4002228089796 1 22
|
||||
193.60440567265297 9.976439066337806 123.24637065555939 1 23
|
||||
172.11563570539317 43.82007387041961 194.07478363123653 1 24
|
||||
|
|
@ -0,0 +1,26 @@
|
|||
1 header
|
||||
1_Eulers 2_Eulers 3_Eulers 1_pos 2_pos
|
||||
303.24637065555936 9.976439066337804 13.604405672652977 1 1
|
||||
165.92521636876344 43.82007387041961 187.88436429460683 1 2
|
||||
266.59977719102034 43.39784965440254 102.17389658489992 1 3
|
||||
123.24637065555939 9.976439066337804 193.604405672653 1 4
|
||||
345.9252163687635 43.82007387041961 7.884364294606862 1 5
|
||||
86.59977719102032 43.39784965440254 282.17389658489986 1 6
|
||||
56.75362934444064 9.976439066337804 346.395594327347 1 7
|
||||
194.07478363123653 43.82007387041961 172.11563570539317 1 8
|
||||
93.40022280897969 43.39784965440255 257.8261034151001 1 9
|
||||
236.75362934444058 9.976439066337804 166.39559432734697 1 10
|
||||
14.074783631236542 43.82007387041961 352.1156357053931 1 11
|
||||
273.4002228089796 43.397849654402556 77.82610341510008 1 12
|
||||
104.07478363123654 43.82007387041961 262.1156357053931 1 13
|
||||
326.75362934444064 9.976439066337806 76.39559432734703 1 14
|
||||
3.400222808979685 43.39784965440255 347.8261034151001 1 15
|
||||
284.0747836312365 43.82007387041961 82.11563570539313 1 16
|
||||
146.75362934444064 9.976439066337804 256.395594327347 1 17
|
||||
183.40022280897963 43.397849654402556 167.8261034151001 1 18
|
||||
255.92521636876344 43.82007387041961 97.88436429460687 1 19
|
||||
33.24637065555936 9.976439066337804 283.60440567265294 1 20
|
||||
356.59977719102034 43.39784965440254 12.173896584899929 1 21
|
||||
75.92521636876346 43.82007387041961 277.8843642946069 1 22
|
||||
213.24637065555936 9.976439066337804 103.604405672653 1 23
|
||||
176.59977719102034 43.397849654402556 192.17389658489986 1 24
|
||||
|
|
@ -0,0 +1,26 @@
|
|||
1 header
|
||||
1_Eulers 2_Eulers 3_Eulers 1_pos 2_pos
|
||||
335.7965716606702 10.528779365509317 65.79657166067024 1 1
|
||||
228.77270547567446 80.40593177313953 85.64260312151849 1 2
|
||||
131.22729452432552 80.40593177313954 4.357396878481506 1 3
|
||||
24.20342833932977 10.52877936550932 24.20342833932976 1 4
|
||||
221.95489158457983 85.70366403943002 80.37863910890589 1 5
|
||||
138.04510841542015 85.70366403943004 9.621360891094124 1 6
|
||||
131.22729452432552 80.40593177313953 94.35739687848151 1 7
|
||||
24.203428339329765 10.52877936550932 114.20342833932976 1 8
|
||||
221.95489158457983 85.70366403943004 170.37863910890587 1 9
|
||||
138.04510841542015 85.70366403943004 99.62136089109411 1 10
|
||||
335.7965716606702 10.52877936550932 155.79657166067025 1 11
|
||||
228.77270547567448 80.40593177313954 175.6426031215185 1 12
|
||||
335.7965716606702 10.52877936550932 335.7965716606702 1 13
|
||||
228.77270547567448 80.40593177313954 355.6426031215185 1 14
|
||||
131.2272945243255 80.40593177313954 274.35739687848144 1 15
|
||||
24.203428339329747 10.52877936550932 294.2034283393298 1 16
|
||||
221.95489158457985 85.70366403943004 350.3786391089059 1 17
|
||||
138.04510841542015 85.70366403943004 279.6213608910941 1 18
|
||||
41.95489158457986 94.29633596056998 9.621360891094133 1 19
|
||||
318.04510841542015 94.29633596056996 80.37863910890589 1 20
|
||||
155.79657166067025 169.4712206344907 24.203428339329754 1 21
|
||||
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|
||||
311.2272945243255 99.59406822686046 85.64260312151852 1 23
|
||||
204.20342833932975 169.4712206344907 65.79657166067024 1 24
|
||||
|
|
@ -0,0 +1,14 @@
|
|||
1 header
|
||||
1_Eulers 2_Eulers 3_Eulers 1_pos 2_pos
|
||||
225.41555594321144 83.13253115922213 83.08266205989301 1 1
|
||||
134.58444405678856 83.13253115922211 6.917337940107012 1 2
|
||||
4.702125169424418e-15 9.735610317245317 45.0 1 3
|
||||
134.58444405678856 83.13253115922213 276.91733794010696 1 4
|
||||
225.4155559432114 83.13253115922213 353.082662059893 1 5
|
||||
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|
||||
134.58444405678858 83.13253115922213 96.91733794010702 1 7
|
||||
225.41555594321142 83.13253115922213 173.082662059893 1 8
|
||||
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|
||||
99.59803029876785 45.81931182053557 166.36129272052355 1 10
|
||||
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||||
180.0 99.73561031724535 225.0 1 12
|
||||
|
|
@ -0,0 +1,14 @@
|
|||
1 header
|
||||
1_Eulers 2_Eulers 3_Eulers 1_pos 2_pos
|
||||
6.9173379401070045 83.13253115922213 44.58444405678856 1 1
|
||||
45.0 89.99999999999999 279.7356103172453 1 2
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||||
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||||
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||||
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||||
315.0 90.0 9.735610317245369 1 6
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||||
186.917337940107 83.13253115922213 224.58444405678856 1 7
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||||
315.0 90.0 80.26438968275463 1 8
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||||
13.638707279476478 45.81931182053557 260.40196970123213 1 9
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||||
263.082662059893 83.13253115922213 45.415555943211444 1 10
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||||
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|
||||
224.99999999999997 90.0 170.26438968275465 1 12
|
||||
|
|
@ -0,0 +1,25 @@
|
|||
3x3:1_Schmid 3x3:2_Schmid 3x3:3_Schmid 3x3:4_Schmid 3x3:5_Schmid 3x3:6_Schmid 3x3:7_Schmid 3x3:8_Schmid 3x3:9_Schmid
|
||||
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||||
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||||
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||||
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|
||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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|
||||
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||||
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||||
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||||
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|
||||
|
|
@ -0,0 +1,13 @@
|
|||
3x3:1_Schmid 3x3:2_Schmid 3x3:3_Schmid 3x3:4_Schmid 3x3:5_Schmid 3x3:6_Schmid 3x3:7_Schmid 3x3:8_Schmid 3x3:9_Schmid
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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||||
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||||
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||||
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|
||||
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|
||||
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|
||||
|
|
@ -0,0 +1,34 @@
|
|||
3x3:1_Schmid 3x3:2_Schmid 3x3:3_Schmid 3x3:4_Schmid 3x3:5_Schmid 3x3:6_Schmid 3x3:7_Schmid 3x3:8_Schmid 3x3:9_Schmid
|
||||
0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0
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||||
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|
||||
0.0 0.0 -0.5000000000000001 0.0 0.0 -0.8660254037844386 0.0 0.0 0.0
|
||||
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|
||||
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||||
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||||
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||||
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|
||||
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||||
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||||
0.0 -0.8834522085987724 0.46852128566581835 0.0 0.0 0.0 0.0 0.0 0.0
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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|
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||||
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|
||||
|
|
@ -0,0 +1,25 @@
|
|||
3x3:1_Schmid 3x3:2_Schmid 3x3:3_Schmid 3x3:4_Schmid 3x3:5_Schmid 3x3:6_Schmid 3x3:7_Schmid 3x3:8_Schmid 3x3:9_Schmid
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||||
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||||
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||||
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||||
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||||
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||||
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|
||||
-0.27994168488950616 6.2159540823338e-17 0.08571428571428573 -5.407625012016776e-17 1.2007339593759827e-32 1.6557402499691063e-17 -0.9142857142857143 2.0301221021717148e-16 0.27994168488950605
|
||||
-0.0699854212223766 -0.12121830534626538 0.04285714285714291 -0.12121830534626538 -0.20995626366712963 0.07423074889580909 -0.45714285714285724 -0.7917946548886295 0.2799416848895062
|
||||
-0.06998542122237648 0.12121830534626521 -0.04285714285714283 0.12121830534626538 -0.20995626366712966 0.07423074889580906 0.45714285714285724 -0.7917946548886297 0.2799416848895061
|
||||
-0.27994168488950605 6.215954082333798e-17 -0.08571428571428569 5.407625012016776e-17 -1.2007339593759827e-32 1.6557402499691063e-17 0.9142857142857143 -2.0301221021717148e-16 0.27994168488950605
|
||||
0.3104371234477526 0.17923095678901296 0.19010313741609627 0.17923095678901305 0.1034790411492508 0.1097560975609756 -0.6759222663683424 -0.39024390243902424 -0.41391616459700337
|
||||
0.0 7.68600963028337e-17 4.07612214737886e-17 0.0 0.4139161645970035 0.21951219512195125 0.0 -0.7804878048780488 -0.4139161645970034
|
||||
0.31043712344775254 -0.17923095678901305 -0.19010313741609627 -0.17923095678901302 0.10347904114925086 0.1097560975609756 0.6759222663683423 -0.3902439024390244 -0.41391616459700337
|
||||
0.3104371234477527 0.179230956789013 -0.19010313741609638 0.17923095678901313 0.10347904114925086 -0.10975609756097568 0.6759222663683424 0.3902439024390242 -0.4139161645970035
|
||||
0.0 1.3539199431344235e-16 -7.180244797305419e-17 0.0 0.4139161645970036 -0.21951219512195136 0.0 0.7804878048780487 -0.41391616459700353
|
||||
0.3104371234477525 -0.179230956789013 0.19010313741609622 -0.17923095678901313 0.10347904114925092 -0.10975609756097565 -0.6759222663683423 0.3902439024390244 -0.41391616459700337
|
||||
0.11134044285378089 0.19284730395996755 0.1363636363636364 0.19284730395996755 0.3340213285613424 0.23618874648666507 -0.36363636363636365 -0.6298366572977734 -0.44536177141512323
|
||||
0.11134044285378081 -0.1928473039599675 -0.13636363636363633 -0.19284730395996758 0.3340213285613426 0.2361887464866651 0.3636363636363637 -0.6298366572977737 -0.4453617714151233
|
||||
0.44536177141512323 -9.889017858258314e-17 -0.2727272727272727 4.301519895922435e-17 -9.551292858672588e-33 -2.634132215859942e-17 0.7272727272727272 -1.6148698540002275e-16 -0.44536177141512323
|
||||
0.1113404428537809 0.1928473039599676 -0.13636363636363644 0.1928473039599676 0.33402132856134253 -0.23618874648666516 0.36363636363636365 0.6298366572977734 -0.44536177141512323
|
||||
0.11134044285378074 -0.19284730395996735 0.13636363636363627 -0.19284730395996758 0.33402132856134253 -0.23618874648666516 -0.3636363636363636 0.6298366572977734 -0.44536177141512323
|
||||
0.44536177141512334 -9.889017858258316e-17 0.2727272727272727 -4.3015198959224354e-17 9.55129285867259e-33 -2.634132215859942e-17 -0.7272727272727273 1.6148698540002277e-16 -0.44536177141512323
|
||||
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|
|
@ -1,157 +0,0 @@
|
|||
import random
|
||||
|
||||
import pytest
|
||||
import numpy as np
|
||||
|
||||
from damask import Rotation
|
||||
from damask import Symmetry
|
||||
|
||||
def in_FZ(system,rho):
|
||||
"""Non-vectorized version of 'in_FZ'."""
|
||||
rho_abs = abs(rho)
|
||||
|
||||
if system == 'cubic':
|
||||
return np.sqrt(2.0)-1.0 >= rho_abs[0] \
|
||||
and np.sqrt(2.0)-1.0 >= rho_abs[1] \
|
||||
and np.sqrt(2.0)-1.0 >= rho_abs[2] \
|
||||
and 1.0 >= rho_abs[0] + rho_abs[1] + rho_abs[2]
|
||||
elif system == 'hexagonal':
|
||||
return 1.0 >= rho_abs[0] and 1.0 >= rho_abs[1] and 1.0 >= rho_abs[2] \
|
||||
and 2.0 >= np.sqrt(3)*rho_abs[0] + rho_abs[1] \
|
||||
and 2.0 >= np.sqrt(3)*rho_abs[1] + rho_abs[0] \
|
||||
and 2.0 >= np.sqrt(3) + rho_abs[2]
|
||||
elif system == 'tetragonal':
|
||||
return 1.0 >= rho_abs[0] and 1.0 >= rho_abs[1] \
|
||||
and np.sqrt(2.0) >= rho_abs[0] + rho_abs[1] \
|
||||
and np.sqrt(2.0) >= rho_abs[2] + 1.0
|
||||
elif system == 'orthorhombic':
|
||||
return 1.0 >= rho_abs[0] and 1.0 >= rho_abs[1] and 1.0 >= rho_abs[2]
|
||||
else:
|
||||
return np.all(np.isfinite(rho_abs))
|
||||
|
||||
|
||||
def in_disorientation_SST(system,rho):
|
||||
"""Non-vectorized version of 'in_Disorientation_SST'."""
|
||||
epsilon = 0.0
|
||||
if system == 'cubic':
|
||||
return rho[0] >= rho[1]+epsilon and rho[1] >= rho[2]+epsilon and rho[2] >= epsilon
|
||||
elif system == 'hexagonal':
|
||||
return rho[0] >= np.sqrt(3)*(rho[1]-epsilon) and rho[1] >= epsilon and rho[2] >= epsilon
|
||||
elif system == 'tetragonal':
|
||||
return rho[0] >= rho[1]-epsilon and rho[1] >= epsilon and rho[2] >= epsilon
|
||||
elif system == 'orthorhombic':
|
||||
return rho[0] >= epsilon and rho[1] >= epsilon and rho[2] >= epsilon
|
||||
else:
|
||||
return True
|
||||
|
||||
|
||||
def in_SST(system,vector,proper = False):
|
||||
"""Non-vectorized version of 'in_SST'."""
|
||||
if system == 'cubic':
|
||||
basis = {'improper':np.array([ [-1. , 0. , 1. ],
|
||||
[ np.sqrt(2.) , -np.sqrt(2.) , 0. ],
|
||||
[ 0. , np.sqrt(3.) , 0. ] ]),
|
||||
'proper':np.array([ [ 0. , -1. , 1. ],
|
||||
[-np.sqrt(2.) , np.sqrt(2.) , 0. ],
|
||||
[ np.sqrt(3.) , 0. , 0. ] ]),
|
||||
}
|
||||
elif system == 'hexagonal':
|
||||
basis = {'improper':np.array([ [ 0. , 0. , 1. ],
|
||||
[ 1. , -np.sqrt(3.) , 0. ],
|
||||
[ 0. , 2. , 0. ] ]),
|
||||
'proper':np.array([ [ 0. , 0. , 1. ],
|
||||
[-1. , np.sqrt(3.) , 0. ],
|
||||
[ np.sqrt(3.) , -1. , 0. ] ]),
|
||||
}
|
||||
elif system == 'tetragonal':
|
||||
basis = {'improper':np.array([ [ 0. , 0. , 1. ],
|
||||
[ 1. , -1. , 0. ],
|
||||
[ 0. , np.sqrt(2.) , 0. ] ]),
|
||||
'proper':np.array([ [ 0. , 0. , 1. ],
|
||||
[-1. , 1. , 0. ],
|
||||
[ np.sqrt(2.) , 0. , 0. ] ]),
|
||||
}
|
||||
elif system == 'orthorhombic':
|
||||
basis = {'improper':np.array([ [ 0., 0., 1.],
|
||||
[ 1., 0., 0.],
|
||||
[ 0., 1., 0.] ]),
|
||||
'proper':np.array([ [ 0., 0., 1.],
|
||||
[-1., 0., 0.],
|
||||
[ 0., 1., 0.] ]),
|
||||
}
|
||||
else:
|
||||
return True
|
||||
|
||||
v = np.array(vector,dtype=float)
|
||||
if proper:
|
||||
theComponents = np.around(np.dot(basis['improper'],v),12)
|
||||
inSST = np.all(theComponents >= 0.0)
|
||||
if not inSST:
|
||||
theComponents = np.around(np.dot(basis['proper'],v),12)
|
||||
inSST = np.all(theComponents >= 0.0)
|
||||
else:
|
||||
v[2] = abs(v[2])
|
||||
theComponents = np.around(np.dot(basis['improper'],v),12)
|
||||
inSST = np.all(theComponents >= 0.0)
|
||||
|
||||
return inSST
|
||||
|
||||
|
||||
@pytest.fixture
|
||||
def set_of_rodrigues(set_of_quaternions):
|
||||
return Rotation(set_of_quaternions).as_Rodrigues(vector=True)[:200]
|
||||
|
||||
class TestSymmetry:
|
||||
|
||||
@pytest.mark.parametrize('system',Symmetry.crystal_systems)
|
||||
def test_in_FZ_vectorize(self,set_of_rodrigues,system):
|
||||
result = Symmetry(system).in_FZ(set_of_rodrigues.reshape(50,4,3)).reshape(200)
|
||||
for i,r in enumerate(result):
|
||||
assert r == in_FZ(system,set_of_rodrigues[i])
|
||||
|
||||
@pytest.mark.parametrize('system',Symmetry.crystal_systems)
|
||||
def test_in_disorientation_SST_vectorize(self,set_of_rodrigues,system):
|
||||
result = Symmetry(system).in_disorientation_SST(set_of_rodrigues.reshape(50,4,3)).reshape(200)
|
||||
for i,r in enumerate(result):
|
||||
assert r == in_disorientation_SST(system,set_of_rodrigues[i])
|
||||
|
||||
@pytest.mark.parametrize('proper',[True,False])
|
||||
@pytest.mark.parametrize('system',Symmetry.crystal_systems)
|
||||
def test_in_SST_vectorize(self,system,proper):
|
||||
vecs = np.random.rand(20,4,3)
|
||||
result = Symmetry(system).in_SST(vecs,proper).reshape(20*4)
|
||||
for i,r in enumerate(result):
|
||||
assert r == in_SST(system,vecs.reshape(20*4,3)[i],proper)
|
||||
|
||||
@pytest.mark.parametrize('invalid_symmetry',['fcc','bcc','hello'])
|
||||
def test_invalid_symmetry(self,invalid_symmetry):
|
||||
with pytest.raises(KeyError):
|
||||
s = Symmetry(invalid_symmetry) # noqa
|
||||
|
||||
def test_equal(self):
|
||||
symmetry = random.choice(Symmetry.crystal_systems)
|
||||
print(symmetry)
|
||||
assert Symmetry(symmetry) == Symmetry(symmetry)
|
||||
|
||||
def test_not_equal(self):
|
||||
symmetries = random.sample(Symmetry.crystal_systems,k=2)
|
||||
assert Symmetry(symmetries[0]) != Symmetry(symmetries[1])
|
||||
|
||||
@pytest.mark.parametrize('system',Symmetry.crystal_systems)
|
||||
def test_in_FZ(self,system):
|
||||
assert Symmetry(system).in_FZ(np.zeros(3))
|
||||
|
||||
@pytest.mark.parametrize('system',Symmetry.crystal_systems)
|
||||
def test_in_disorientation_SST(self,system):
|
||||
assert Symmetry(system).in_disorientation_SST(np.zeros(3))
|
||||
|
||||
@pytest.mark.parametrize('system',Symmetry.crystal_systems)
|
||||
@pytest.mark.parametrize('proper',[True,False])
|
||||
def test_in_SST(self,system,proper):
|
||||
assert Symmetry(system).in_SST(np.zeros(3),proper)
|
||||
|
||||
@pytest.mark.parametrize('function',['in_FZ','in_disorientation_SST','in_SST'])
|
||||
def test_invalid_argument(self,function):
|
||||
s = Symmetry() # noqa
|
||||
with pytest.raises(ValueError):
|
||||
eval(f's.{function}(np.ones(4))')
|
||||
|
|
@ -1,131 +1,536 @@
|
|||
import os
|
||||
from itertools import permutations
|
||||
|
||||
import pytest
|
||||
import numpy as np
|
||||
from itertools import permutations
|
||||
|
||||
from damask import Table
|
||||
from damask import Rotation
|
||||
from damask import Orientation
|
||||
from damask import Lattice
|
||||
|
||||
n = 1000
|
||||
|
||||
def IPF_color(orientation,direction):
|
||||
"""TSL color of inverse pole figure for given axis (non-vectorized)."""
|
||||
for o in orientation.equivalent:
|
||||
pole = o.rotation@direction
|
||||
inSST,color = orientation.lattice.in_SST(pole,color=True)
|
||||
if inSST: break
|
||||
|
||||
return color
|
||||
|
||||
def inverse_pole(orientation,axis,proper=False,SST=True):
|
||||
if SST:
|
||||
for eq in orientation.equivalent:
|
||||
pole = eq.rotation @ axis/np.linalg.norm(axis)
|
||||
if orientation.lattice.in_SST(pole,proper=proper):
|
||||
return pole
|
||||
else:
|
||||
return orientation.rotation @ axis/np.linalg.norm(axis)
|
||||
from damask import Table
|
||||
from damask import lattice
|
||||
from damask import util
|
||||
|
||||
|
||||
@pytest.fixture
|
||||
def reference_dir(reference_dir_base):
|
||||
"""Directory containing reference results."""
|
||||
return reference_dir_base/'Rotation'
|
||||
return reference_dir_base/'Orientation'
|
||||
|
||||
@pytest.fixture
|
||||
def set_of_rodrigues(set_of_quaternions):
|
||||
return Rotation(set_of_quaternions).as_Rodrigues()[:200]
|
||||
|
||||
|
||||
class TestOrientation:
|
||||
|
||||
@pytest.mark.parametrize('model',['Bain','KS','GT','GT_prime','NW','Pitsch'])
|
||||
@pytest.mark.parametrize('lattice',['fcc','bcc'])
|
||||
def test_relationship_vectorize(self,set_of_quaternions,lattice,model):
|
||||
result = Orientation(set_of_quaternions[:200].reshape(50,4,4),lattice).related(model)
|
||||
ref_qu = result.rotation.quaternion.reshape(-1,200,4)
|
||||
for i in range(200):
|
||||
single = Orientation(set_of_quaternions[i],lattice).related(model).rotation.quaternion
|
||||
assert np.allclose(ref_qu[:,i,:],single)
|
||||
@pytest.mark.parametrize('lattice',Orientation.crystal_families)
|
||||
@pytest.mark.parametrize('shape',[None,5,(4,6)])
|
||||
def test_equal(self,lattice,shape):
|
||||
R = Rotation.from_random(shape)
|
||||
assert Orientation(R,lattice) == Orientation(R,lattice)
|
||||
|
||||
@pytest.mark.parametrize('lattice',Lattice.lattices)
|
||||
def test_IPF_vectorize(self,set_of_quaternions,lattice):
|
||||
direction = np.random.random(3)*2.0-1
|
||||
oris = Orientation(Rotation(set_of_quaternions),lattice)[:200]
|
||||
for i,color in enumerate(oris.IPF_color(direction)):
|
||||
assert np.allclose(color,IPF_color(oris[i],direction))
|
||||
@pytest.mark.parametrize('lattice',Orientation.crystal_families)
|
||||
@pytest.mark.parametrize('shape',[None,5,(4,6)])
|
||||
def test_unequal(self,lattice,shape):
|
||||
R = Rotation.from_random(shape)
|
||||
assert not(Orientation(R,lattice) != Orientation(R,lattice))
|
||||
|
||||
@pytest.mark.parametrize('SST',[False,True])
|
||||
@pytest.mark.parametrize('a,b',[
|
||||
(dict(rotation=[1,0,0,0]),
|
||||
dict(rotation=[0.5,0.5,0.5,0.5])),
|
||||
|
||||
(dict(rotation=[1,0,0,0],lattice='cubic'),
|
||||
dict(rotation=[1,0,0,0],lattice='hexagonal')),
|
||||
|
||||
(dict(rotation=[1,0,0,0],lattice='cF',a=1),
|
||||
dict(rotation=[1,0,0,0],lattice='cF',a=2)),
|
||||
])
|
||||
def test_nonequal(self,a,b):
|
||||
assert Orientation(**a) != Orientation(**b)
|
||||
|
||||
@pytest.mark.parametrize('kwargs',[
|
||||
dict(lattice='aP', alpha=np.pi/4,beta=np.pi/3, ),
|
||||
dict(lattice='mP', c=1.2,alpha=np.pi/4, gamma=np.pi/2),
|
||||
dict(lattice='oP', c=1.2,alpha=np.pi/4, ),
|
||||
dict(lattice='oS',a=1.0, c=2.0,alpha=np.pi/2,beta=np.pi/3, ),
|
||||
dict(lattice='tP',a=1.0,b=1.2, ),
|
||||
dict(lattice='tI', alpha=np.pi/3, ),
|
||||
dict(lattice='hP', gamma=np.pi/2),
|
||||
dict(lattice='cI',a=1.0, c=2.0,alpha=np.pi/2,beta=np.pi/2, ),
|
||||
dict(lattice='cF', beta=np.pi/3, ),
|
||||
])
|
||||
def test_invalid_init(self,kwargs):
|
||||
with pytest.raises(ValueError):
|
||||
Orientation(**kwargs).parameters # noqa
|
||||
|
||||
@pytest.mark.parametrize('kwargs',[
|
||||
dict(lattice='aP',a=1.0,b=1.1,c=1.2,alpha=np.pi/4,beta=np.pi/3,gamma=np.pi/2),
|
||||
dict(lattice='mP',a=1.0,b=1.1,c=1.2, beta=np.pi/3 ),
|
||||
dict(lattice='oS',a=1.0,b=1.1,c=1.2, ),
|
||||
dict(lattice='tI',a=1.0, c=1.2, ),
|
||||
dict(lattice='hP',a=1.0 ),
|
||||
dict(lattice='cI',a=1.0, ),
|
||||
])
|
||||
def test_repr(self,kwargs):
|
||||
o = Orientation.from_random(**kwargs)
|
||||
assert isinstance(o.__repr__(),str)
|
||||
|
||||
@pytest.mark.parametrize('kwargs',[
|
||||
dict(lattice='aP',a=1.0,b=1.1,c=1.2,alpha=np.pi/4,beta=np.pi/3,gamma=np.pi/2),
|
||||
dict(lattice='mP',a=1.0,b=1.1,c=1.2, beta=np.pi/3 ),
|
||||
dict(lattice='oS',a=1.0,b=1.1,c=1.2, ),
|
||||
dict(lattice='tI',a=1.0, c=1.2, ),
|
||||
dict(lattice='hP',a=1.0 ),
|
||||
dict(lattice='cI',a=1.0, ),
|
||||
])
|
||||
def test_copy(self,kwargs):
|
||||
o = Orientation.from_random(**kwargs)
|
||||
p = o.copy(rotation=Rotation.from_random())
|
||||
assert o != p
|
||||
|
||||
def test_from_quaternion(self):
|
||||
assert np.all(Orientation.from_quaternion(q=np.array([1,0,0,0]),lattice='triclinic').as_matrix()
|
||||
== np.eye(3))
|
||||
|
||||
def test_from_Eulers(self):
|
||||
assert np.all(Orientation.from_Eulers(phi=np.zeros(3),lattice='triclinic').as_matrix()
|
||||
== np.eye(3))
|
||||
|
||||
def test_from_axis_angle(self):
|
||||
assert np.all(Orientation.from_axis_angle(axis_angle=[1,0,0,0],lattice='triclinic').as_matrix()
|
||||
== np.eye(3))
|
||||
|
||||
def test_from_basis(self):
|
||||
assert np.all(Orientation.from_basis(basis=np.eye(3),lattice='triclinic').as_matrix()
|
||||
== np.eye(3))
|
||||
|
||||
def test_from_matrix(self):
|
||||
assert np.all(Orientation.from_matrix(R=np.eye(3),lattice='triclinic').as_matrix()
|
||||
== np.eye(3))
|
||||
|
||||
def test_from_Rodrigues(self):
|
||||
assert np.all(Orientation.from_Rodrigues(rho=np.array([0,0,1,0]),lattice='triclinic').as_matrix()
|
||||
== np.eye(3))
|
||||
|
||||
def test_from_homochoric(self):
|
||||
assert np.all(Orientation.from_homochoric(h=np.zeros(3),lattice='triclinic').as_matrix()
|
||||
== np.eye(3))
|
||||
|
||||
def test_from_cubochoric(self):
|
||||
assert np.all(Orientation.from_cubochoric(c=np.zeros(3),lattice='triclinic').as_matrix()
|
||||
== np.eye(3))
|
||||
|
||||
def test_from_spherical_component(self):
|
||||
assert np.all(Orientation.from_spherical_component(center=Rotation(),
|
||||
sigma=0.0,N=1,lattice='triclinic').as_matrix()
|
||||
== np.eye(3))
|
||||
|
||||
def test_from_fiber_component(self):
|
||||
r = Rotation.from_fiber_component(alpha=np.zeros(2),beta=np.zeros(2),
|
||||
sigma=0.0,N=1,seed=0)
|
||||
assert np.all(Orientation.from_fiber_component(alpha=np.zeros(2),beta=np.zeros(2),
|
||||
sigma=0.0,N=1,seed=0,lattice='triclinic').quaternion
|
||||
== r.quaternion)
|
||||
|
||||
@pytest.mark.parametrize('kwargs',[
|
||||
dict(lattice='aP',a=1.0,b=1.1,c=1.2,alpha=np.pi/4.5,beta=np.pi/3.5,gamma=np.pi/2.5),
|
||||
dict(lattice='mP',a=1.0,b=1.1,c=1.2, beta=np.pi/3.5),
|
||||
dict(lattice='oS',a=1.0,b=1.1,c=1.2,),
|
||||
dict(lattice='tI',a=1.0, c=1.2,),
|
||||
dict(lattice='hP',a=1.0 ),
|
||||
dict(lattice='cI',a=1.0, ),
|
||||
])
|
||||
def test_from_direction(self,kwargs):
|
||||
for a,b in np.random.random((10,2,3)):
|
||||
c = np.cross(b,a)
|
||||
if np.all(np.isclose(c,0)): continue
|
||||
o = Orientation.from_directions(uvw=a,hkl=c,**kwargs)
|
||||
x = o.to_pole(uvw=a)
|
||||
z = o.to_pole(hkl=c)
|
||||
assert np.isclose(np.dot(x/np.linalg.norm(x),np.array([1,0,0])),1) \
|
||||
and np.isclose(np.dot(z/np.linalg.norm(z),np.array([0,0,1])),1)
|
||||
|
||||
|
||||
def test_negative_angle(self):
|
||||
with pytest.raises(ValueError):
|
||||
Orientation(lattice='aP',a=1,b=2,c=3,alpha=45,beta=45,gamma=-45,degrees=True) # noqa
|
||||
|
||||
def test_excess_angle(self):
|
||||
with pytest.raises(ValueError):
|
||||
Orientation(lattice='aP',a=1,b=2,c=3,alpha=45,beta=45,gamma=90.0001,degrees=True) # noqa
|
||||
|
||||
@pytest.mark.parametrize('lattice',Orientation.crystal_families)
|
||||
@pytest.mark.parametrize('angle',[10,20,30,40])
|
||||
def test_average(self,angle,lattice):
|
||||
o = Orientation.from_axis_angle(lattice=lattice,axis_angle=[[0,0,1,10],[0,0,1,angle]],degrees=True)
|
||||
avg_angle = o.average().as_axis_angle(degrees=True,pair=True)[1]
|
||||
assert np.isclose(avg_angle,10+(angle-10)/2.)
|
||||
|
||||
@pytest.mark.parametrize('lattice',Orientation.crystal_families)
|
||||
def test_reduced_equivalent(self,lattice):
|
||||
i = Orientation(lattice=lattice)
|
||||
o = Orientation.from_random(lattice=lattice)
|
||||
eq = o.equivalent
|
||||
FZ = np.argmin(abs(eq.misorientation(i.broadcast_to(len(eq))).as_axis_angle(pair=True)[1]))
|
||||
assert o.reduced == eq[FZ]
|
||||
|
||||
@pytest.mark.parametrize('lattice',Orientation.crystal_families)
|
||||
@pytest.mark.parametrize('N',[1,8,32])
|
||||
def test_disorientation(self,lattice,N):
|
||||
o = Orientation.from_random(lattice=lattice,shape=N,seed=0)
|
||||
p = Orientation.from_random(lattice=lattice,shape=N,seed=1)
|
||||
|
||||
d,ops = o.disorientation(p,return_operators=True)
|
||||
|
||||
for n in range(N):
|
||||
assert np.allclose(d[n].as_quaternion(),
|
||||
o[n].equivalent[ops[n][0]]
|
||||
.misorientation(p[n].equivalent[ops[n][1]])
|
||||
.as_quaternion()) \
|
||||
or np.allclose((~d)[n].as_quaternion(),
|
||||
o[n].equivalent[ops[n][0]]
|
||||
.misorientation(p[n].equivalent[ops[n][1]])
|
||||
.as_quaternion())
|
||||
|
||||
@pytest.mark.parametrize('lattice',Orientation.crystal_families)
|
||||
@pytest.mark.parametrize('a,b',[
|
||||
((2,3,2),(2,3,2)),
|
||||
((2,2),(4,4)),
|
||||
((3,1),(1,3)),
|
||||
(None,None),
|
||||
])
|
||||
def test_disorientation_blending(self,lattice,a,b):
|
||||
o = Orientation.from_random(lattice=lattice,shape=a,seed=0)
|
||||
p = Orientation.from_random(lattice=lattice,shape=b,seed=1)
|
||||
blend = util.shapeblender(o.shape,p.shape)
|
||||
for loc in np.random.randint(0,blend,(10,len(blend))):
|
||||
assert o[tuple(loc[:len(o.shape)])].disorientation(p[tuple(loc[-len(p.shape):])]) \
|
||||
== o.disorientation(p)[tuple(loc)]
|
||||
|
||||
@pytest.mark.parametrize('lattice',Orientation.crystal_families)
|
||||
def test_disorientation360(self,lattice):
|
||||
o_1 = Orientation(Rotation(),lattice)
|
||||
o_2 = Orientation.from_Eulers(lattice=lattice,phi=[360,0,0],degrees=True)
|
||||
assert np.allclose((o_1.disorientation(o_2)).as_matrix(),np.eye(3))
|
||||
|
||||
@pytest.mark.parametrize('lattice',Orientation.crystal_families)
|
||||
@pytest.mark.parametrize('shape',[(1),(2,3),(4,3,2)])
|
||||
def test_reduced_vectorization(self,lattice,shape):
|
||||
o = Orientation.from_random(lattice=lattice,shape=shape,seed=0)
|
||||
for r, theO in zip(o.reduced.flatten(),o.flatten()):
|
||||
assert r == theO.reduced
|
||||
|
||||
@pytest.mark.parametrize('lattice',Orientation.crystal_families)
|
||||
@pytest.mark.parametrize('shape',[(1),(2,3),(4,3,2)])
|
||||
@pytest.mark.parametrize('vector',np.array([[1,0,0],[1,2,3],[-1,1,-1]]))
|
||||
@pytest.mark.parametrize('proper',[True,False])
|
||||
@pytest.mark.parametrize('lattice',Lattice.lattices)
|
||||
def test_inverse_pole_vectorize(self,set_of_quaternions,lattice,SST,proper):
|
||||
axis = np.random.random(3)*2.0-1
|
||||
oris = Orientation(Rotation(set_of_quaternions),lattice)[:200]
|
||||
for i,pole in enumerate(oris.inverse_pole(axis,SST=SST)):
|
||||
assert np.allclose(pole,inverse_pole(oris[i],axis,SST=SST))
|
||||
def test_to_SST_vectorization(self,lattice,shape,vector,proper):
|
||||
o = Orientation.from_random(lattice=lattice,shape=shape,seed=0)
|
||||
for r, theO in zip(o.to_SST(vector=vector,proper=proper).reshape((-1,3)),o.flatten()):
|
||||
assert np.allclose(r,theO.to_SST(vector=vector,proper=proper))
|
||||
|
||||
@pytest.mark.parametrize('lattice',Orientation.crystal_families)
|
||||
@pytest.mark.parametrize('shape',[(1),(2,3),(4,3,2)])
|
||||
@pytest.mark.parametrize('vector',np.array([[1,0,0],[1,2,3],[-1,1,-1]]))
|
||||
@pytest.mark.parametrize('proper',[True,False])
|
||||
def test_IPF_color_vectorization(self,lattice,shape,vector,proper):
|
||||
o = Orientation.from_random(lattice=lattice,shape=shape,seed=0)
|
||||
poles = o.to_SST(vector=vector,proper=proper)
|
||||
for r, theO in zip(o.IPF_color(poles,proper=proper).reshape((-1,3)),o.flatten()):
|
||||
assert np.allclose(r,theO.IPF_color(theO.to_SST(vector=vector,proper=proper),proper=proper))
|
||||
|
||||
@pytest.mark.parametrize('lattice',Orientation.crystal_families)
|
||||
@pytest.mark.parametrize('a,b',[
|
||||
((2,3,2),(2,3,2)),
|
||||
((2,2),(4,4)),
|
||||
((3,1),(1,3)),
|
||||
(None,(3,)),
|
||||
])
|
||||
def test_to_SST_blending(self,lattice,a,b):
|
||||
o = Orientation.from_random(lattice=lattice,shape=a,seed=0)
|
||||
v = np.random.random(b+(3,))
|
||||
blend = util.shapeblender(o.shape,b)
|
||||
for loc in np.random.randint(0,blend,(10,len(blend))):
|
||||
print(f'{a}/{b} @ {loc}')
|
||||
print(o[tuple(loc[:len(o.shape)])].to_SST(v[tuple(loc[-len(b):])]))
|
||||
print(o.to_SST(v)[tuple(loc)])
|
||||
assert np.allclose(o[tuple(loc[:len(o.shape)])].to_SST(v[tuple(loc[-len(b):])]),
|
||||
o.to_SST(v)[tuple(loc)])
|
||||
|
||||
@pytest.mark.parametrize('color',[{'label':'red', 'RGB':[1,0,0],'direction':[0,0,1]},
|
||||
{'label':'green','RGB':[0,1,0],'direction':[0,1,1]},
|
||||
{'label':'blue', 'RGB':[0,0,1],'direction':[1,1,1]}])
|
||||
@pytest.mark.parametrize('lattice',['fcc','bcc'])
|
||||
def test_IPF_cubic(self,color,lattice):
|
||||
cube = Orientation(Rotation(),lattice)
|
||||
@pytest.mark.parametrize('proper',[True,False])
|
||||
def test_IPF_cubic(self,color,proper):
|
||||
cube = Orientation(lattice='cubic')
|
||||
for direction in set(permutations(np.array(color['direction']))):
|
||||
assert np.allclose(cube.IPF_color(np.array(direction)),np.array(color['RGB']))
|
||||
assert np.allclose(np.array(color['RGB']),
|
||||
cube.IPF_color(cube.to_SST(vector=np.array(direction),proper=proper),proper=proper))
|
||||
|
||||
@pytest.mark.parametrize('lattice',Lattice.lattices)
|
||||
def test_IPF_equivalent(self,set_of_quaternions,lattice):
|
||||
direction = np.random.random(3)*2.0-1
|
||||
for ori in Orientation(Rotation(set_of_quaternions),lattice)[:200]:
|
||||
color = ori.IPF_color(direction)
|
||||
for equivalent in ori.equivalent:
|
||||
assert np.allclose(color,equivalent.IPF_color(direction))
|
||||
@pytest.mark.parametrize('lattice',Orientation.crystal_families)
|
||||
@pytest.mark.parametrize('proper',[True,False])
|
||||
def test_IPF_equivalent(self,set_of_quaternions,lattice,proper):
|
||||
direction = np.random.random(3)*2.0-1.0
|
||||
o = Orientation(rotation=set_of_quaternions,lattice=lattice).equivalent
|
||||
color = o.IPF_color(o.to_SST(vector=direction,proper=proper),proper=proper)
|
||||
assert np.allclose(np.broadcast_to(color[0,...],color.shape),color)
|
||||
|
||||
@pytest.mark.parametrize('lattice',Lattice.lattices)
|
||||
def test_reduced(self,set_of_quaternions,lattice):
|
||||
oris = Orientation(Rotation(set_of_quaternions),lattice)
|
||||
reduced = oris.reduced
|
||||
assert np.all(reduced.in_FZ) and oris.rotation.shape == reduced.rotation.shape
|
||||
@pytest.mark.parametrize('lattice',Orientation.crystal_families)
|
||||
def test_in_FZ_vectorization(self,set_of_rodrigues,lattice):
|
||||
result = Orientation.from_Rodrigues(rho=set_of_rodrigues.reshape((50,4,-1)),lattice=lattice).in_FZ.reshape(-1)
|
||||
for r,rho in zip(result,set_of_rodrigues[:len(result)]):
|
||||
assert r == Orientation.from_Rodrigues(rho=rho,lattice=lattice).in_FZ
|
||||
|
||||
@pytest.mark.parametrize('lattice',Orientation.crystal_families)
|
||||
def test_in_disorientation_FZ_vectorization(self,set_of_rodrigues,lattice):
|
||||
result = Orientation.from_Rodrigues(rho=set_of_rodrigues.reshape((50,4,-1)),
|
||||
lattice=lattice).in_disorientation_FZ.reshape(-1)
|
||||
for r,rho in zip(result,set_of_rodrigues[:len(result)]):
|
||||
assert r == Orientation.from_Rodrigues(rho=rho,lattice=lattice).in_disorientation_FZ
|
||||
|
||||
@pytest.mark.parametrize('proper',[True,False])
|
||||
@pytest.mark.parametrize('lattice',Orientation.crystal_families)
|
||||
def test_in_SST_vectorization(self,lattice,proper):
|
||||
vecs = np.random.rand(20,4,3)
|
||||
result = Orientation(lattice=lattice).in_SST(vecs,proper).flatten()
|
||||
for r,v in zip(result,vecs.reshape((-1,3))):
|
||||
assert np.all(r == Orientation(lattice=lattice).in_SST(v,proper))
|
||||
|
||||
@pytest.mark.parametrize('invalid_lattice',['fcc','bcc','hello'])
|
||||
def test_invalid_lattice_init(self,invalid_lattice):
|
||||
with pytest.raises(KeyError):
|
||||
Orientation(lattice=invalid_lattice) # noqa
|
||||
|
||||
@pytest.mark.parametrize('invalid_family',[None,'fcc','bcc','hello'])
|
||||
def test_invalid_symmetry_family(self,invalid_family):
|
||||
with pytest.raises(KeyError):
|
||||
o = Orientation(lattice='cubic')
|
||||
o.family = invalid_family
|
||||
o.symmetry_operations # noqa
|
||||
|
||||
def test_missing_symmetry_equivalent(self):
|
||||
with pytest.raises(ValueError):
|
||||
Orientation(lattice=None).equivalent # noqa
|
||||
|
||||
def test_missing_symmetry_reduced(self):
|
||||
with pytest.raises(ValueError):
|
||||
Orientation(lattice=None).reduced # noqa
|
||||
|
||||
def test_missing_symmetry_in_FZ(self):
|
||||
with pytest.raises(ValueError):
|
||||
Orientation(lattice=None).in_FZ # noqa
|
||||
|
||||
def test_missing_symmetry_in_disorientation_FZ(self):
|
||||
with pytest.raises(ValueError):
|
||||
Orientation(lattice=None).in_disorientation_FZ # noqa
|
||||
|
||||
def test_missing_symmetry_disorientation(self):
|
||||
with pytest.raises(ValueError):
|
||||
Orientation(lattice=None).disorientation(Orientation(lattice=None)) # noqa
|
||||
|
||||
def test_missing_symmetry_average(self):
|
||||
with pytest.raises(ValueError):
|
||||
Orientation(lattice=None).average() # noqa
|
||||
|
||||
def test_missing_symmetry_to_SST(self):
|
||||
with pytest.raises(ValueError):
|
||||
Orientation(lattice=None).to_SST(np.zeros(3)) # noqa
|
||||
|
||||
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_Bravais_to_Miller(self):
|
||||
with pytest.raises(KeyError):
|
||||
Orientation.Bravais_to_Miller(uvtw=np.ones(4),hkil=np.ones(4)) # noqa
|
||||
|
||||
def test_double_Miller_to_Bravais(self):
|
||||
with pytest.raises(KeyError):
|
||||
Orientation.Miller_to_Bravais(uvw=np.ones(4),hkl=np.ones(4)) # 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'])
|
||||
def test_unknown_relation(self,relation):
|
||||
with pytest.raises(KeyError):
|
||||
Orientation(lattice='cF').related(relation) # noqa
|
||||
|
||||
@pytest.mark.parametrize('relation,lattice,a,b,c,alpha,beta,gamma',
|
||||
[
|
||||
('Bain', 'aP',0.5,2.0,3.0,0.8,0.5,1.2),
|
||||
('KS', 'mP',1.0,2.0,3.0,np.pi/2,0.5,np.pi/2),
|
||||
('Pitsch', 'oI',0.5,1.5,3.0,np.pi/2,np.pi/2,np.pi/2),
|
||||
('Burgers','tP',0.5,0.5,3.0,np.pi/2,np.pi/2,np.pi/2),
|
||||
('GT', 'hP',1.0,None,1.6,np.pi/2,np.pi/2,2*np.pi/3),
|
||||
('Burgers','cF',1.0,1.0,None,np.pi/2,np.pi/2,np.pi/2),
|
||||
])
|
||||
def test_unknown_relation_lattice(self,relation,lattice,a,b,c,alpha,beta,gamma):
|
||||
with pytest.raises(KeyError):
|
||||
Orientation(lattice=lattice,
|
||||
a=a,b=b,c=c,
|
||||
alpha=alpha,beta=beta,gamma=gamma).related(relation) # noqa
|
||||
|
||||
@pytest.mark.parametrize('lattice',Orientation.crystal_families)
|
||||
@pytest.mark.parametrize('proper',[True,False])
|
||||
def test_in_SST(self,lattice,proper):
|
||||
assert Orientation(lattice=lattice).in_SST(np.zeros(3),proper)
|
||||
|
||||
@pytest.mark.parametrize('function',['in_SST','IPF_color'])
|
||||
def test_invalid_argument(self,function):
|
||||
o = Orientation(lattice='cubic') # noqa
|
||||
with pytest.raises(ValueError):
|
||||
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('lattice',['fcc','bcc'])
|
||||
@pytest.mark.parametrize('lattice',['cF','cI'])
|
||||
def test_relationship_vectorize(self,set_of_quaternions,lattice,model):
|
||||
r = Orientation(rotation=set_of_quaternions[:200].reshape((50,4,4)),lattice=lattice).related(model)
|
||||
for i in range(200):
|
||||
assert r.reshape((-1,200))[:,i] == Orientation(set_of_quaternions[i],lattice).related(model)
|
||||
|
||||
@pytest.mark.parametrize('model',['Bain','KS','GT','GT_prime','NW','Pitsch'])
|
||||
@pytest.mark.parametrize('lattice',['cF','cI'])
|
||||
def test_relationship_forward_backward(self,model,lattice):
|
||||
ori = Orientation(Rotation.from_random(),lattice)
|
||||
for i,r in enumerate(ori.related(model)):
|
||||
ori2 = r.related(model)[i]
|
||||
misorientation = ori.rotation.misorientation(ori2.rotation)
|
||||
assert misorientation.as_axis_angle(degrees=True)[3]<1.0e-5
|
||||
o = Orientation.from_random(lattice=lattice)
|
||||
for i,r in enumerate(o.related(model)):
|
||||
assert o.disorientation(r.related(model)[i]).as_axis_angle(degrees=True,pair=True)[1]<1.0e-5
|
||||
|
||||
@pytest.mark.parametrize('model',['Bain','KS','GT','GT_prime','NW','Pitsch'])
|
||||
@pytest.mark.parametrize('lattice',['fcc','bcc'])
|
||||
@pytest.mark.parametrize('lattice',['cF','cI'])
|
||||
def test_relationship_reference(self,update,reference_dir,model,lattice):
|
||||
reference = os.path.join(reference_dir,f'{lattice}_{model}.txt')
|
||||
ori = Orientation(Rotation(),lattice)
|
||||
eu = np.array([o.rotation.as_Eulers(degrees=True) for o in ori.related(model)])
|
||||
reference = reference_dir/f'{lattice}_{model}.txt'
|
||||
o = Orientation(lattice=lattice)
|
||||
eu = o.related(model).as_Eulers(degrees=True)
|
||||
if update:
|
||||
coords = np.array([(1,i+1) for i,x in enumerate(eu)])
|
||||
table = Table(eu,{'Eulers':(3,)})
|
||||
table = table.add('pos',coords)
|
||||
table.save(reference)
|
||||
Table(eu,{'Eulers':(3,)})\
|
||||
.add('pos',coords)\
|
||||
.save(reference)
|
||||
assert np.allclose(eu,Table.load(reference).get('Eulers'))
|
||||
|
||||
@pytest.mark.parametrize('lattice',Lattice.lattices)
|
||||
def test_disorientation360(self,lattice):
|
||||
R_1 = Orientation(Rotation(),lattice)
|
||||
R_2 = Orientation(Rotation.from_Eulers([360,0,0],degrees=True),lattice)
|
||||
assert np.allclose(R_1.disorientation(R_2).as_matrix(),np.eye(3))
|
||||
def test_basis_real(self):
|
||||
for gamma in np.random.random(2**8)*np.pi:
|
||||
basis = np.tril(np.random.random((3,3))+1e-6)
|
||||
basis[1,:2] = basis[1,1]*np.array([np.cos(gamma),np.sin(gamma)])
|
||||
basis[2,:2] = basis[2,:2]*2-1
|
||||
lengths = np.linalg.norm(basis,axis=-1)
|
||||
cosines = np.roll(np.einsum('ij,ij->i',basis,np.roll(basis,1,axis=0))/lengths/np.roll(lengths,1),1)
|
||||
o = Orientation.from_random(lattice='aP',
|
||||
**dict(zip(['a','b','c'],lengths)),
|
||||
**dict(zip(['alpha','beta','gamma'],np.arccos(cosines))),
|
||||
)
|
||||
assert np.allclose(o.to_frame(uvw=np.eye(3)),basis), 'Lattice basis disagrees with initialization'
|
||||
|
||||
@pytest.mark.parametrize('lattice',Lattice.lattices)
|
||||
@pytest.mark.parametrize('angle',[10,20,30,40])
|
||||
def test_average(self,angle,lattice):
|
||||
R_1 = Orientation(Rotation.from_axis_angle([0,0,1,10],degrees=True),lattice)
|
||||
R_2 = Orientation(Rotation.from_axis_angle([0,0,1,angle],degrees=True),lattice)
|
||||
avg_angle = R_1.average(R_2).rotation.as_axis_angle(degrees=True,pair=True)[1]
|
||||
assert np.isclose(avg_angle,10+(angle-10)/2.)
|
||||
@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('lattice',Lattice.lattices)
|
||||
def test_from_average(self,lattice):
|
||||
R_1 = Orientation(Rotation.from_random(),lattice)
|
||||
eqs = [r for r in R_1.equivalent]
|
||||
R_2 = Orientation.from_average(eqs)
|
||||
assert np.allclose(R_1.rotation.quaternion,R_2.rotation.quaternion)
|
||||
@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('vector',np.array([
|
||||
[1,0,0],
|
||||
[1,1,0],
|
||||
[1,1,1],
|
||||
[1,0,-2],
|
||||
]))
|
||||
@pytest.mark.parametrize('kw_Miller,kw_Bravais',[('uvw','uvtw'),('hkl','hkil')])
|
||||
def test_Miller_Bravais_Miller(self,vector,kw_Miller,kw_Bravais):
|
||||
assert np.all(vector == Orientation.Bravais_to_Miller(**{kw_Bravais:Orientation.Miller_to_Bravais(**{kw_Miller:vector})}))
|
||||
|
||||
@pytest.mark.parametrize('vector',np.array([
|
||||
[1,0,-1,2],
|
||||
[1,-1,0,3],
|
||||
[1,1,-2,-3],
|
||||
[0,0,0,1],
|
||||
]))
|
||||
@pytest.mark.parametrize('kw_Miller,kw_Bravais',[('uvw','uvtw'),('hkl','hkil')])
|
||||
def test_Bravais_Miller_Bravais(self,vector,kw_Miller,kw_Bravais):
|
||||
assert np.all(vector == Orientation.Miller_to_Bravais(**{kw_Miller:Orientation.Bravais_to_Miller(**{kw_Bravais:vector})}))
|
||||
|
||||
@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),
|
||||
])
|
||||
|
||||
@pytest.mark.parametrize('kw',['uvw','hkl'])
|
||||
@pytest.mark.parametrize('with_symmetry',[False,True])
|
||||
@pytest.mark.parametrize('shape',[None,1,(12,24)])
|
||||
@pytest.mark.parametrize('vector',[
|
||||
np.random.random( 3 ),
|
||||
np.random.random( (4,3)),
|
||||
np.random.random((4,8,3)),
|
||||
])
|
||||
def test_to_pole(self,shape,lattice,a,b,c,alpha,beta,gamma,vector,kw,with_symmetry):
|
||||
o = Orientation.from_random(shape=shape,
|
||||
lattice=lattice,
|
||||
a=a,b=b,c=c,
|
||||
alpha=alpha,beta=beta,gamma=gamma)
|
||||
assert o.to_pole(**{kw:vector,'with_symmetry':with_symmetry}).shape \
|
||||
== o.shape + (o.symmetry_operations.shape if with_symmetry else ()) + vector.shape
|
||||
|
||||
@pytest.mark.parametrize('lattice',['hP','cI','cF'])
|
||||
def test_Schmid(self,update,reference_dir,lattice):
|
||||
L = Orientation(lattice=lattice)
|
||||
for mode in L.kinematics:
|
||||
reference = reference_dir/f'{lattice}_{mode}.txt'
|
||||
P = L.Schmid(mode)
|
||||
if update:
|
||||
table = Table(P.reshape(-1,9),{'Schmid':(3,3,)})
|
||||
table.save(reference)
|
||||
assert np.allclose(P,Table.load(reference).get('Schmid'))
|
||||
|
|
|
|||
|
|
@ -168,15 +168,16 @@ class TestResult:
|
|||
|
||||
@pytest.mark.parametrize('d',[[1,0,0],[0,1,0],[0,0,1]])
|
||||
def test_add_IPF_color(self,default,d):
|
||||
default.add_IPF_color('O',d)
|
||||
loc = {'orientation': default.get_dataset_location('O'),
|
||||
default.add_IPF_color('O',np.array(d))
|
||||
loc = {'O': default.get_dataset_location('O'),
|
||||
'color': default.get_dataset_location('IPFcolor_[{} {} {}]'.format(*d))}
|
||||
qu = default.read_dataset(loc['orientation']).view(np.double).reshape(-1,4)
|
||||
qu = default.read_dataset(loc['O']).view(np.double).squeeze()
|
||||
crystal_structure = default.get_crystal_structure()
|
||||
in_memory = np.empty((qu.shape[0],3),np.uint8)
|
||||
for i,q in enumerate(qu):
|
||||
o = Orientation(q,crystal_structure).reduced
|
||||
in_memory[i] = np.uint8(o.IPF_color(np.array(d))*255)
|
||||
c = Orientation(rotation=qu,
|
||||
lattice={'fcc':'cF',
|
||||
'bcc':'cI',
|
||||
'hex':'hP'}[crystal_structure])
|
||||
in_memory = np.uint8(c.IPF_color(c.to_SST(np.array(d)))*255)
|
||||
in_file = default.read_dataset(loc['color'])
|
||||
assert np.allclose(in_memory,in_file)
|
||||
|
||||
|
|
@ -244,13 +245,14 @@ class TestResult:
|
|||
in_file = default.read_dataset(loc['S'],0)
|
||||
assert np.allclose(in_memory,in_file)
|
||||
|
||||
@pytest.mark.skip(reason='requires rework of lattice.f90')
|
||||
@pytest.mark.parametrize('polar',[True,False])
|
||||
def test_add_pole(self,default,polar):
|
||||
pole = np.array([1.,0.,0.])
|
||||
default.add_pole('O',pole,polar)
|
||||
loc = {'orientation': default.get_dataset_location('O'),
|
||||
loc = {'O': default.get_dataset_location('O'),
|
||||
'pole': default.get_dataset_location('p^{}_[1 0 0)'.format(u'rφ' if polar else 'xy'))}
|
||||
rot = Rotation(default.read_dataset(loc['orientation']).view(np.double))
|
||||
rot = Rotation(default.read_dataset(loc['O']).view(np.double))
|
||||
rotated_pole = rot * np.broadcast_to(pole,rot.shape+(3,))
|
||||
xy = rotated_pole[:,0:2]/(1.+abs(pole[2]))
|
||||
in_memory = xy if not polar else \
|
||||
|
|
|
|||
|
|
@ -771,6 +771,53 @@ class TestRotation:
|
|||
def test_random(self,shape):
|
||||
Rotation.from_random(shape)
|
||||
|
||||
def test_equal(self):
|
||||
r = Rotation.from_random(seed=0)
|
||||
assert r == r
|
||||
|
||||
def test_unequal(self):
|
||||
r = Rotation.from_random(seed=0)
|
||||
assert not (r != r)
|
||||
|
||||
def test_inversion(self):
|
||||
r = Rotation.from_random(seed=0)
|
||||
assert r == ~~r
|
||||
|
||||
@pytest.mark.parametrize('shape',[None,1,(1,),(4,2),(1,1,1)])
|
||||
def test_shape(self,shape):
|
||||
r = Rotation.from_random(shape=shape)
|
||||
assert r.shape == (shape if isinstance(shape,tuple) else (shape,) if shape else ())
|
||||
|
||||
@pytest.mark.parametrize('shape',[None,1,(1,),(4,2),(3,3,2)])
|
||||
def test_append(self,shape):
|
||||
r = Rotation.from_random(shape=shape)
|
||||
p = Rotation.from_random(shape=shape)
|
||||
s = r.append(p)
|
||||
print(f'append 2x {shape} --> {s.shape}')
|
||||
assert s[0,...] == r[0,...] and s[-1,...] == p[-1,...]
|
||||
|
||||
@pytest.mark.parametrize('quat,standardized',[
|
||||
([-1,0,0,0],[1,0,0,0]),
|
||||
([-0.5,-0.5,-0.5,-0.5],[0.5,0.5,0.5,0.5]),
|
||||
])
|
||||
def test_standardization(self,quat,standardized):
|
||||
assert Rotation(quat)._standardize() == Rotation(standardized)
|
||||
|
||||
@pytest.mark.parametrize('shape,length',[
|
||||
((2,3,4),2),
|
||||
(4,4),
|
||||
((),0)
|
||||
])
|
||||
def test_len(self,shape,length):
|
||||
r = Rotation.from_random(shape=shape)
|
||||
assert len(r) == length
|
||||
|
||||
@pytest.mark.parametrize('shape',[(4,6),(2,3,4),(3,3,3)])
|
||||
@pytest.mark.parametrize('order',['C','F'])
|
||||
def test_flatten_reshape(self,shape,order):
|
||||
r = Rotation.from_random(shape=shape)
|
||||
assert r == r.flatten(order).reshape(shape,order)
|
||||
|
||||
@pytest.mark.parametrize('function',[Rotation.from_quaternion,
|
||||
Rotation.from_Eulers,
|
||||
Rotation.from_axis_angle,
|
||||
|
|
@ -848,7 +895,8 @@ class TestRotation:
|
|||
np.random.rand(3,3,3,3)])
|
||||
def test_rotate_identity(self,data):
|
||||
R = Rotation()
|
||||
assert np.allclose(data,R*data)
|
||||
print(R,data)
|
||||
assert np.allclose(data,R@data)
|
||||
|
||||
@pytest.mark.parametrize('data',[np.random.rand(3),
|
||||
np.random.rand(3,3),
|
||||
|
|
@ -860,6 +908,16 @@ class TestRotation:
|
|||
R_2 = Rotation.from_Eulers(np.array([0.,0.,phi_2]))
|
||||
assert np.allclose(data,R_2@(R_1@data))
|
||||
|
||||
@pytest.mark.parametrize('pwr',[-10,0,1,2.5,np.pi,np.random.random()])
|
||||
def test_rotate_power(self,pwr):
|
||||
R = Rotation.from_random()
|
||||
axis_angle = R.as_axis_angle()
|
||||
axis_angle[ 3] = (pwr*axis_angle[-1])%(2.*np.pi)
|
||||
if axis_angle[3] > np.pi:
|
||||
axis_angle[3] -= 2.*np.pi
|
||||
axis_angle *= -1
|
||||
assert R**pwr == Rotation.from_axis_angle(axis_angle)
|
||||
|
||||
def test_rotate_inverse(self):
|
||||
R = Rotation.from_random()
|
||||
assert np.allclose(np.eye(3),(~R@R).as_matrix())
|
||||
|
|
@ -877,7 +935,7 @@ class TestRotation:
|
|||
def test_rotate_invalid_shape(self,data):
|
||||
R = Rotation.from_random()
|
||||
with pytest.raises(ValueError):
|
||||
R*data
|
||||
R@data
|
||||
|
||||
@pytest.mark.parametrize('data',['does_not_work',
|
||||
(1,2),
|
||||
|
|
@ -885,7 +943,7 @@ class TestRotation:
|
|||
def test_rotate_invalid_type(self,data):
|
||||
R = Rotation.from_random()
|
||||
with pytest.raises(TypeError):
|
||||
R*data
|
||||
R@data
|
||||
|
||||
def test_misorientation(self):
|
||||
R = Rotation.from_random()
|
||||
|
|
@ -898,9 +956,8 @@ class TestRotation:
|
|||
|
||||
@pytest.mark.parametrize('angle',[10,20,30,40,50,60,70,80,90,100,120])
|
||||
def test_average(self,angle):
|
||||
R_1 = Rotation.from_axis_angle([0,0,1,10],degrees=True)
|
||||
R_2 = Rotation.from_axis_angle([0,0,1,angle],degrees=True)
|
||||
avg_angle = R_1.average(R_2).as_axis_angle(degrees=True,pair=True)[1]
|
||||
R = Rotation.from_axis_angle([[0,0,1,10],[0,0,1,angle]],degrees=True)
|
||||
avg_angle = R.average().as_axis_angle(degrees=True,pair=True)[1]
|
||||
assert np.isclose(avg_angle,10+(angle-10)/2.)
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -44,3 +44,52 @@ class TestUtil:
|
|||
selected = util.hybrid_IA(dist,N_samples)
|
||||
dist_sampled = np.histogram(centers[selected],bins)[0]/N_samples*np.sum(dist)
|
||||
assert np.sqrt(((dist - dist_sampled) ** 2).mean()) < .025 and selected.shape[0]==N_samples
|
||||
|
||||
@pytest.mark.parametrize('point,normalize,answer',
|
||||
[
|
||||
([1,0,0],False,[1,0,0]),
|
||||
([1,0,0],True, [1,0,0]),
|
||||
([0,1,1],False,[0,0.5,0]),
|
||||
([0,1,1],True, [0,0.41421356,0]),
|
||||
([1,1,1],False,[0.5,0.5,0]),
|
||||
([1,1,1],True, [0.3660254, 0.3660254, 0]),
|
||||
])
|
||||
def test_project_stereographic(self,point,normalize,answer):
|
||||
assert np.allclose(util.project_stereographic(np.array(point),normalize=normalize),answer)
|
||||
|
||||
@pytest.mark.parametrize('fro,to,mode,answer',
|
||||
[
|
||||
((),(1,),'left',(1,)),
|
||||
((1,),(7,),'right',(1,)),
|
||||
((1,2),(1,1,2,2),'right',(1,1,2,1)),
|
||||
((1,2),(1,1,2,2),'left',(1,1,1,2)),
|
||||
((1,2,3),(1,1,2,3,4),'right',(1,1,2,3,1)),
|
||||
((10,2),(10,3,2,2,),'right',(10,1,2,1)),
|
||||
((10,2),(10,3,2,2,),'left',(10,1,1,2)),
|
||||
((2,2,3),(2,2,2,3,4),'left',(1,2,2,3,1)),
|
||||
((2,2,3),(2,2,2,3,4),'right',(2,2,1,3,1)),
|
||||
])
|
||||
def test_shapeshifter(self,fro,to,mode,answer):
|
||||
assert util.shapeshifter(fro,to,mode) == answer
|
||||
|
||||
@pytest.mark.parametrize('fro,to,mode',
|
||||
[
|
||||
((10,3,4),(10,3,2,2),'left'),
|
||||
((2,3),(10,3,2,2),'right'),
|
||||
])
|
||||
def test_invalid_shapeshifter(self,fro,to,mode):
|
||||
with pytest.raises(ValueError):
|
||||
util.shapeshifter(fro,to,mode)
|
||||
|
||||
@pytest.mark.parametrize('a,b,answer',
|
||||
[
|
||||
((),(1,),(1,)),
|
||||
((1,),(),(1,)),
|
||||
((1,),(7,),(1,7)),
|
||||
((2,),(2,2),(2,2)),
|
||||
((1,2),(2,2),(1,2,2)),
|
||||
((1,2,3),(2,3,4),(1,2,3,4)),
|
||||
((1,2,3),(1,2,3),(1,2,3)),
|
||||
])
|
||||
def test_shapeblender(self,a,b,answer):
|
||||
assert util.shapeblender(a,b) == answer
|
||||
|
|
|
|||
|
|
@ -93,7 +93,8 @@ subroutine prec_init
|
|||
print'(a,i19)', ' Maximum value: ',huge(0)
|
||||
print'(/,a,i3)', ' Size of float in bit: ',storage_size(0.0_pReal)
|
||||
print'(a,e10.3)', ' Maximum value: ',huge(0.0_pReal)
|
||||
print'(a,e10.3)', ' Minimum value: ',tiny(0.0_pReal)
|
||||
print'(a,e10.3)', ' Minimum value: ',PREAL_MIN
|
||||
print'(a,e10.3)', ' Epsilon value: ',PREAL_EPSILON
|
||||
print'(a,i3)', ' Decimal precision: ',precision(0.0_pReal)
|
||||
|
||||
call selfTest
|
||||
|
|
|
|||
Loading…
Reference in New Issue