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Merge branch 'python-style' into 'development' 

Python style

See merge request damask/DAMASK!132
This commit is contained in:
Karo 2020-03-06 00:42:48 +01:00
parent c06ef00fe2 7a0c20b6de
commit 31136100c6
11 changed files with 2220 additions and 2157 deletions
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2
python/damask/Lambert.py
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@ -131,12 +131,12 @@ def BallToCube(ball):
# inverse M_1 # inverse M_1
cube = np.array([ Tinv[0], Tinv[1], (-1.0 if xyz3[2] < 0.0 else 1.0) * rs / np.sqrt(6.0/np.pi) ]) /sc cube = np.array([ Tinv[0], Tinv[1], (-1.0 if xyz3[2] < 0.0 else 1.0) * rs / np.sqrt(6.0/np.pi) ]) /sc
# reverse the coordinates back to the regular order according to the original pyramid number # reverse the coordinates back to the regular order according to the original pyramid number
cube = cube[p] cube = cube[p]
return cube return cube
def get_order(xyz): def get_order(xyz):
""" """
Get order of the coordinates. Get order of the coordinates.

4
python/damask/__init__.py
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@ -13,7 +13,9 @@ from .asciitable import ASCIItable # noqa
from .config import Material # noqa from .config import Material # noqa
from .colormaps import Colormap, Color # noqa from .colormaps import Colormap, Color # noqa
from .orientation import Symmetry, Lattice, Rotation, Orientation # noqa from .rotation import Rotation # noqa
from .lattice import Symmetry, Lattice# noqa
from .orientation import Orientation # noqa
from .result import Result # noqa from .result import Result # noqa
from .result import Result as DADF5 # noqa from .result import Result as DADF5 # noqa

20
python/damask/colormaps.py
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@ -10,7 +10,6 @@ class Color():
] ]
# ------------------------------------------------------------------
def __init__(self, def __init__(self,
model = 'RGB', model = 'RGB',
color = np.zeros(3,'d')): color = np.zeros(3,'d')):
@ -49,20 +48,17 @@ class Color():
self.color = np.array(color,'d') self.color = np.array(color,'d')
# ------------------------------------------------------------------
def __repr__(self): def __repr__(self):
"""Color model and values.""" """Color model and values."""
return 'Model: %s Color: %s'%(self.model,str(self.color)) return 'Model: %s Color: %s'%(self.model,str(self.color))
# ------------------------------------------------------------------
def __str__(self): def __str__(self):
"""Color model and values.""" """Color model and values."""
return self.__repr__() return self.__repr__()
# ------------------------------------------------------------------ def convert_to(self,toModel = 'RGB'):
def convertTo(self,toModel = 'RGB'):
""" """
Change the color model permanently. Change the color model permanently.
@ -88,8 +84,7 @@ class Color():
return self return self
# ------------------------------------------------------------------ def express_as(self,asModel = 'RGB'):
def expressAs(self,asModel = 'RGB'):
""" """
Return the color in a different model. Return the color in a different model.
@ -99,7 +94,7 @@ class Color():
color model color model
""" """
return self.__class__(self.model,self.color).convertTo(asModel) return self.__class__(self.model,self.color).convert_to(asModel)
@ -293,6 +288,7 @@ class Color():
self.model = converted.model self.model = converted.model
self.color = converted.color self.color = converted.color
def _XYZ2CIELAB(self): def _XYZ2CIELAB(self):
""" """
Convert CIE XYZ to CIE Lab. Convert CIE XYZ to CIE Lab.
@ -498,13 +494,13 @@ class Colormap():
def interpolate_linear(lo, hi, frac): def interpolate_linear(lo, hi, frac):
"""Linear interpolation between lo and hi color at given fraction; output in model of lo color.""" """Linear interpolation between lo and hi color at given fraction; output in model of lo color."""
interpolation = (1.0 - frac) * np.array(lo.color[:]) \ interpolation = (1.0 - frac) * np.array(lo.color[:]) \
+ frac * np.array(hi.expressAs(lo.model).color[:]) + frac * np.array(hi.express_as(lo.model).color[:])
return Color(lo.model,interpolation) return Color(lo.model,interpolation)
if self.interpolate == 'perceptualuniform': if self.interpolate == 'perceptualuniform':
return interpolate_Msh(self.left.expressAs('MSH').color, return interpolate_Msh(self.left.express_as('MSH').color,
self.right.expressAs('MSH').color,fraction) self.right.express_as('MSH').color,fraction)
elif self.interpolate == 'linear': elif self.interpolate == 'linear':
return interpolate_linear(self.left, return interpolate_linear(self.left,
self.right,fraction) self.right,fraction)
@ -528,7 +524,7 @@ class Colormap():
""" """
format = format.lower() # consistent comparison basis format = format.lower() # consistent comparison basis
frac = 0.5*(np.array(crop) + 1.0) # rescale crop range to fractions frac = 0.5*(np.array(crop) + 1.0) # rescale crop range to fractions
colors = [self.color(float(i)/(steps-1)*(frac[1]-frac[0])+frac[0]).expressAs(model).color for i in range(steps)] colors = [self.color(float(i)/(steps-1)*(frac[1]-frac[0])+frac[0]).express_as(model).color for i in range(steps)]
if format == 'paraview': if format == 'paraview':
colormap = ['[\n {{\n "ColorSpace": "RGB", "Name": "{}", "DefaultMap": true,\n "RGBPoints" : ['.format(name)] \ colormap = ['[\n {{\n "ColorSpace": "RGB", "Name": "{}", "DefaultMap": true,\n "RGBPoints" : ['.format(name)] \
+ [' {:4d},{:8.6f},{:8.6f},{:8.6f},'.format(i,color[0],color[1],color[2],) \ + [' {:4d},{:8.6f},{:8.6f},{:8.6f},'.format(i,color[0],color[1],color[2],) \

2
python/damask/geom.py
View File

@ -269,7 +269,7 @@ class Geom():
comments = [] comments = []
for i,line in enumerate(content[:header_length]): for i,line in enumerate(content[:header_length]):
items = line.lower().strip().split() items = line.lower().strip().split()
key = items[0] if len(items) > 0 else '' key = items[0] if items else ''
if key == 'grid': if key == 'grid':
grid = np.array([ int(dict(zip(items[1::2],items[2::2]))[i]) for i in ['a','b','c']]) grid = np.array([ int(dict(zip(items[1::2],items[2::2]))[i]) for i in ['a','b','c']])
elif key == 'size': elif key == 'size':

24
python/damask/grid_filters.py
View File

@ -1,7 +1,7 @@
from scipy import spatial from scipy import spatial
import numpy as np import numpy as np
def __ks(size,grid,first_order=False): def _ks(size,grid,first_order=False):
""" """
Get wave numbers operator. Get wave numbers operator.
@ -34,7 +34,7 @@ def curl(size,field):
""" """
n = np.prod(field.shape[3:]) n = np.prod(field.shape[3:])
k_s = __ks(size,field.shape[:3],True) k_s = _ks(size,field.shape[:3],True)
e = np.zeros((3, 3, 3)) e = np.zeros((3, 3, 3))
e[0, 1, 2] = e[1, 2, 0] = e[2, 0, 1] = +1.0 # Levi-Civita symbol e[0, 1, 2] = e[1, 2, 0] = e[2, 0, 1] = +1.0 # Levi-Civita symbol
@ -58,7 +58,7 @@ def divergence(size,field):
""" """
n = np.prod(field.shape[3:]) n = np.prod(field.shape[3:])
k_s = __ks(size,field.shape[:3],True) k_s = _ks(size,field.shape[:3],True)
field_fourier = np.fft.rfftn(field,axes=(0,1,2)) field_fourier = np.fft.rfftn(field,axes=(0,1,2))
divergence = (np.einsum('ijkl,ijkl ->ijk', k_s,field_fourier)*2.0j*np.pi if n == 3 else # vector, 3 -> 1 divergence = (np.einsum('ijkl,ijkl ->ijk', k_s,field_fourier)*2.0j*np.pi if n == 3 else # vector, 3 -> 1
@ -78,7 +78,7 @@ def gradient(size,field):
""" """
n = np.prod(field.shape[3:]) n = np.prod(field.shape[3:])
k_s = __ks(size,field.shape[:3],True) k_s = _ks(size,field.shape[:3],True)
field_fourier = np.fft.rfftn(field,axes=(0,1,2)) field_fourier = np.fft.rfftn(field,axes=(0,1,2))
gradient = (np.einsum('ijkl,ijkm->ijkm', field_fourier,k_s)*2.0j*np.pi if n == 1 else # scalar, 1 -> 3 gradient = (np.einsum('ijkl,ijkm->ijkm', field_fourier,k_s)*2.0j*np.pi if n == 1 else # scalar, 1 -> 3
@ -110,6 +110,7 @@ def cell_coord0(grid,size,origin=np.zeros(3)):
return np.concatenate((z[:,:,:,None],y[:,:,:,None],x[:,:,:,None]),axis = 3) return np.concatenate((z[:,:,:,None],y[:,:,:,None],x[:,:,:,None]),axis = 3)
def cell_displacement_fluct(size,F): def cell_displacement_fluct(size,F):
""" """
Cell center displacement field from fluctuation part of the deformation gradient field. Cell center displacement field from fluctuation part of the deformation gradient field.
@ -124,7 +125,7 @@ def cell_displacement_fluct(size,F):
""" """
integrator = 0.5j*size/np.pi integrator = 0.5j*size/np.pi
k_s = __ks(size,F.shape[:3],False) k_s = _ks(size,F.shape[:3],False)
k_s_squared = np.einsum('...l,...l',k_s,k_s) k_s_squared = np.einsum('...l,...l',k_s,k_s)
k_s_squared[0,0,0] = 1.0 k_s_squared[0,0,0] = 1.0
@ -136,6 +137,7 @@ def cell_displacement_fluct(size,F):
return np.fft.irfftn(displacement,axes=(0,1,2),s=F.shape[:3]) return np.fft.irfftn(displacement,axes=(0,1,2),s=F.shape[:3])
def cell_displacement_avg(size,F): def cell_displacement_avg(size,F):
""" """
Cell center displacement field from average part of the deformation gradient field. Cell center displacement field from average part of the deformation gradient field.
@ -151,6 +153,7 @@ def cell_displacement_avg(size,F):
F_avg = np.average(F,axis=(0,1,2)) F_avg = np.average(F,axis=(0,1,2))
return np.einsum('ml,ijkl->ijkm',F_avg-np.eye(3),cell_coord0(F.shape[:3][::-1],size)) return np.einsum('ml,ijkl->ijkm',F_avg-np.eye(3),cell_coord0(F.shape[:3][::-1],size))
def cell_displacement(size,F): def cell_displacement(size,F):
""" """
Cell center displacement field from deformation gradient field. Cell center displacement field from deformation gradient field.
@ -165,6 +168,7 @@ def cell_displacement(size,F):
""" """
return cell_displacement_avg(size,F) + cell_displacement_fluct(size,F) return cell_displacement_avg(size,F) + cell_displacement_fluct(size,F)
def cell_coord(size,F,origin=np.zeros(3)): def cell_coord(size,F,origin=np.zeros(3)):
""" """
Cell center positions. Cell center positions.
@ -181,6 +185,7 @@ def cell_coord(size,F,origin=np.zeros(3)):
""" """
return cell_coord0(F.shape[:3][::-1],size,origin) + cell_displacement(size,F) return cell_coord0(F.shape[:3][::-1],size,origin) + cell_displacement(size,F)
def cell_coord0_gridSizeOrigin(coord0,ordered=True): def cell_coord0_gridSizeOrigin(coord0,ordered=True):
""" """
Return grid 'DNA', i.e. grid, size, and origin from array of cell positions. Return grid 'DNA', i.e. grid, size, and origin from array of cell positions.
@ -221,6 +226,7 @@ def cell_coord0_gridSizeOrigin(coord0,ordered=True):
return (grid,size,origin) return (grid,size,origin)
def coord0_check(coord0): def coord0_check(coord0):
""" """
Check whether coordinates lie on a regular grid. Check whether coordinates lie on a regular grid.
@ -234,7 +240,6 @@ def coord0_check(coord0):
cell_coord0_gridSizeOrigin(coord0,ordered=True) cell_coord0_gridSizeOrigin(coord0,ordered=True)
def node_coord0(grid,size,origin=np.zeros(3)): def node_coord0(grid,size,origin=np.zeros(3)):
""" """
Nodal positions (undeformed). Nodal positions (undeformed).
@ -256,6 +261,7 @@ def node_coord0(grid,size,origin=np.zeros(3)):
return np.concatenate((z[:,:,:,None],y[:,:,:,None],x[:,:,:,None]),axis = 3) return np.concatenate((z[:,:,:,None],y[:,:,:,None],x[:,:,:,None]),axis = 3)
def node_displacement_fluct(size,F): def node_displacement_fluct(size,F):
""" """
Nodal displacement field from fluctuation part of the deformation gradient field. Nodal displacement field from fluctuation part of the deformation gradient field.
@ -270,6 +276,7 @@ def node_displacement_fluct(size,F):
""" """
return cell_2_node(cell_displacement_fluct(size,F)) return cell_2_node(cell_displacement_fluct(size,F))
def node_displacement_avg(size,F): def node_displacement_avg(size,F):
""" """
Nodal displacement field from average part of the deformation gradient field. Nodal displacement field from average part of the deformation gradient field.
@ -285,6 +292,7 @@ def node_displacement_avg(size,F):
F_avg = np.average(F,axis=(0,1,2)) F_avg = np.average(F,axis=(0,1,2))
return np.einsum('ml,ijkl->ijkm',F_avg-np.eye(3),node_coord0(F.shape[:3][::-1],size)) return np.einsum('ml,ijkl->ijkm',F_avg-np.eye(3),node_coord0(F.shape[:3][::-1],size))
def node_displacement(size,F): def node_displacement(size,F):
""" """
Nodal displacement field from deformation gradient field. Nodal displacement field from deformation gradient field.
@ -299,6 +307,7 @@ def node_displacement(size,F):
""" """
return node_displacement_avg(size,F) + node_displacement_fluct(size,F) return node_displacement_avg(size,F) + node_displacement_fluct(size,F)
def node_coord(size,F,origin=np.zeros(3)): def node_coord(size,F,origin=np.zeros(3)):
""" """
Nodal positions. Nodal positions.
@ -315,6 +324,7 @@ def node_coord(size,F,origin=np.zeros(3)):
""" """
return node_coord0(F.shape[:3][::-1],size,origin) + node_displacement(size,F) return node_coord0(F.shape[:3][::-1],size,origin) + node_displacement(size,F)
def cell_2_node(cell_data): def cell_2_node(cell_data):
"""Interpolate periodic cell data to nodal data.""" """Interpolate periodic cell data to nodal data."""
n = ( cell_data + np.roll(cell_data,1,(0,1,2)) n = ( cell_data + np.roll(cell_data,1,(0,1,2))
@ -323,6 +333,7 @@ def cell_2_node(cell_data):
return np.pad(n,((0,1),(0,1),(0,1))+((0,0),)*len(cell_data.shape[3:]),mode='wrap') return np.pad(n,((0,1),(0,1),(0,1))+((0,0),)*len(cell_data.shape[3:]),mode='wrap')
def node_2_cell(node_data): def node_2_cell(node_data):
"""Interpolate periodic nodal data to cell data.""" """Interpolate periodic nodal data to cell data."""
c = ( node_data + np.roll(node_data,1,(0,1,2)) c = ( node_data + np.roll(node_data,1,(0,1,2))
@ -331,6 +342,7 @@ def node_2_cell(node_data):
return c[:-1,:-1,:-1] return c[:-1,:-1,:-1]
def node_coord0_gridSizeOrigin(coord0,ordered=False): def node_coord0_gridSizeOrigin(coord0,ordered=False):
""" """
Return grid 'DNA', i.e. grid, size, and origin from array of nodal positions. Return grid 'DNA', i.e. grid, size, and origin from array of nodal positions.

641
python/damask/lattice.py Normal file
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@ -0,0 +1,641 @@
import numpy as np
from .rotation import Rotation
P = -1
# ******************************************************************************************
class Symmetry:
"""
Symmetry operations for lattice systems.
References
----------
https://en.wikipedia.org/wiki/Crystal_system
"""
lattices = [None,'orthorhombic','tetragonal','hexagonal','cubic',]
def __init__(self, symmetry = None):
"""
Symmetry Definition.
Parameters
----------
symmetry : str, optional
label of the crystal system
"""
if symmetry is not None and symmetry.lower() not in Symmetry.lattices:
raise KeyError('Symmetry/crystal system "{}" is unknown'.format(symmetry))
self.lattice = symmetry.lower() if isinstance(symmetry,str) else symmetry
def __copy__(self):
"""Copy."""
return self.__class__(self.lattice)
copy = __copy__
def __repr__(self):
"""Readable string."""
return '{}'.format(self.lattice)
def __eq__(self, other):
"""
Equal to other.
Parameters
----------
other : Symmetry
Symmetry to check for equality.
"""
return self.lattice == other.lattice
def __neq__(self, other):
"""
Not Equal to other.
Parameters
----------
other : Symmetry
Symmetry to check for inequality.
"""
return not self.__eq__(other)
def __cmp__(self,other):
"""
Linear ordering.
Parameters
----------
other : Symmetry
Symmetry to check for for order.
"""
myOrder = Symmetry.lattices.index(self.lattice)
otherOrder = Symmetry.lattices.index(other.lattice)
return (myOrder > otherOrder) - (myOrder < otherOrder)
def symmetryOperations(self,members=[]):
"""List (or single element) of symmetry operations as rotations."""
if self.lattice == 'cubic':
symQuats = [
[ 1.0, 0.0, 0.0, 0.0 ],
[ 0.0, 1.0, 0.0, 0.0 ],
[ 0.0, 0.0, 1.0, 0.0 ],
[ 0.0, 0.0, 0.0, 1.0 ],
[ 0.0, 0.0, 0.5*np.sqrt(2), 0.5*np.sqrt(2) ],
[ 0.0, 0.0, 0.5*np.sqrt(2),-0.5*np.sqrt(2) ],
[ 0.0, 0.5*np.sqrt(2), 0.0, 0.5*np.sqrt(2) ],
[ 0.0, 0.5*np.sqrt(2), 0.0, -0.5*np.sqrt(2) ],
[ 0.0, 0.5*np.sqrt(2),-0.5*np.sqrt(2), 0.0 ],
[ 0.0, -0.5*np.sqrt(2),-0.5*np.sqrt(2), 0.0 ],
[ 0.5, 0.5, 0.5, 0.5 ],
[-0.5, 0.5, 0.5, 0.5 ],
[-0.5, 0.5, 0.5, -0.5 ],
[-0.5, 0.5, -0.5, 0.5 ],
[-0.5, -0.5, 0.5, 0.5 ],
[-0.5, -0.5, 0.5, -0.5 ],
[-0.5, -0.5, -0.5, 0.5 ],
[-0.5, 0.5, -0.5, -0.5 ],
[-0.5*np.sqrt(2), 0.0, 0.0, 0.5*np.sqrt(2) ],
[ 0.5*np.sqrt(2), 0.0, 0.0, 0.5*np.sqrt(2) ],
[-0.5*np.sqrt(2), 0.0, 0.5*np.sqrt(2), 0.0 ],
[-0.5*np.sqrt(2), 0.0, -0.5*np.sqrt(2), 0.0 ],
[-0.5*np.sqrt(2), 0.5*np.sqrt(2), 0.0, 0.0 ],
[-0.5*np.sqrt(2),-0.5*np.sqrt(2), 0.0, 0.0 ],
]
elif self.lattice == 'hexagonal':
symQuats = [
[ 1.0, 0.0, 0.0, 0.0 ],
[-0.5*np.sqrt(3), 0.0, 0.0, -0.5 ],
[ 0.5, 0.0, 0.0, 0.5*np.sqrt(3) ],
[ 0.0, 0.0, 0.0, 1.0 ],
[-0.5, 0.0, 0.0, 0.5*np.sqrt(3) ],
[-0.5*np.sqrt(3), 0.0, 0.0, 0.5 ],
[ 0.0, 1.0, 0.0, 0.0 ],
[ 0.0, -0.5*np.sqrt(3), 0.5, 0.0 ],
[ 0.0, 0.5, -0.5*np.sqrt(3), 0.0 ],
[ 0.0, 0.0, 1.0, 0.0 ],
[ 0.0, -0.5, -0.5*np.sqrt(3), 0.0 ],
[ 0.0, 0.5*np.sqrt(3), 0.5, 0.0 ],
]
elif self.lattice == 'tetragonal':
symQuats = [
[ 1.0, 0.0, 0.0, 0.0 ],
[ 0.0, 1.0, 0.0, 0.0 ],
[ 0.0, 0.0, 1.0, 0.0 ],
[ 0.0, 0.0, 0.0, 1.0 ],
[ 0.0, 0.5*np.sqrt(2), 0.5*np.sqrt(2), 0.0 ],
[ 0.0, -0.5*np.sqrt(2), 0.5*np.sqrt(2), 0.0 ],
[ 0.5*np.sqrt(2), 0.0, 0.0, 0.5*np.sqrt(2) ],
[-0.5*np.sqrt(2), 0.0, 0.0, 0.5*np.sqrt(2) ],
]
elif self.lattice == 'orthorhombic':
symQuats = [
[ 1.0,0.0,0.0,0.0 ],
[ 0.0,1.0,0.0,0.0 ],
[ 0.0,0.0,1.0,0.0 ],
[ 0.0,0.0,0.0,1.0 ],
]
else:
symQuats = [
[ 1.0,0.0,0.0,0.0 ],
]
symOps = list(map(Rotation,
np.array(symQuats)[np.atleast_1d(members) if members != [] else range(len(symQuats))]))
try:
iter(members) # asking for (even empty) list of members?
except TypeError:
return symOps[0] # no, return rotation object
else:
return symOps # yes, return list of rotations
def inFZ(self,rodrigues):
"""
Check whether given Rodriques-Frank vector falls into fundamental zone of own symmetry.
Fundamental zone in Rodrigues space is point symmetric around origin.
"""
if (len(rodrigues) != 3):
raise ValueError('Input is not a Rodriques-Frank vector.\n')
if np.any(rodrigues == np.inf): return False
Rabs = abs(rodrigues)
if self.lattice == 'cubic':
return np.sqrt(2.0)-1.0 >= Rabs[0] \
and np.sqrt(2.0)-1.0 >= Rabs[1] \
and np.sqrt(2.0)-1.0 >= Rabs[2] \
and 1.0 >= Rabs[0] + Rabs[1] + Rabs[2]
elif self.lattice == 'hexagonal':
return 1.0 >= Rabs[0] and 1.0 >= Rabs[1] and 1.0 >= Rabs[2] \
and 2.0 >= np.sqrt(3)*Rabs[0] + Rabs[1] \
and 2.0 >= np.sqrt(3)*Rabs[1] + Rabs[0] \
and 2.0 >= np.sqrt(3) + Rabs[2]
elif self.lattice == 'tetragonal':
return 1.0 >= Rabs[0] and 1.0 >= Rabs[1] \
and np.sqrt(2.0) >= Rabs[0] + Rabs[1] \
and np.sqrt(2.0) >= Rabs[2] + 1.0
elif self.lattice == 'orthorhombic':
return 1.0 >= Rabs[0] and 1.0 >= Rabs[1] and 1.0 >= Rabs[2]
else:
return True
def inDisorientationSST(self,rodrigues):
"""
Check whether given Rodriques-Frank vector (of misorientation) falls into standard stereographic triangle of own symmetry.
References
----------
A. Heinz and P. Neumann, Acta Crystallographica Section A 47:780-789, 1991
https://doi.org/10.1107/S0108767391006864
"""
if (len(rodrigues) != 3):
raise ValueError('Input is not a Rodriques-Frank vector.\n')
R = rodrigues
epsilon = 0.0
if self.lattice == 'cubic':
return R[0] >= R[1]+epsilon and R[1] >= R[2]+epsilon and R[2] >= epsilon
elif self.lattice == 'hexagonal':
return R[0] >= np.sqrt(3)*(R[1]-epsilon) and R[1] >= epsilon and R[2] >= epsilon
elif self.lattice == 'tetragonal':
return R[0] >= R[1]-epsilon and R[1] >= epsilon and R[2] >= epsilon
elif self.lattice == 'orthorhombic':
return R[0] >= epsilon and R[1] >= epsilon and R[2] >= epsilon
else:
return True
def inSST(self,
vector,
proper = False,
color = False):
"""
Check whether given vector falls into standard stereographic triangle of own symmetry.
proper considers only vectors with z >= 0, hence uses two neighboring SSTs.
Return inverse pole figure color if requested.
Bases are computed from
basis = {'cubic' : np.linalg.inv(np.array([[0.,0.,1.], # direction of red
[1.,0.,1.]/np.sqrt(2.), # direction of green
[1.,1.,1.]/np.sqrt(3.)]).T), # direction of blue
'hexagonal' : np.linalg.inv(np.array([[0.,0.,1.], # direction of red
[1.,0.,0.], # direction of green
[np.sqrt(3.),1.,0.]/np.sqrt(4.)]).T), # direction of blue
'tetragonal' : np.linalg.inv(np.array([[0.,0.,1.], # direction of red
[1.,0.,0.], # direction of green
[1.,1.,0.]/np.sqrt(2.)]).T), # direction of blue
'orthorhombic' : np.linalg.inv(np.array([[0.,0.,1.], # direction of red
[1.,0.,0.], # direction of green
[0.,1.,0.]]).T), # direction of blue
}
"""
if self.lattice == '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 self.lattice == '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 self.lattice == '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 self.lattice == '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: # direct exit for unspecified symmetry
if color:
return (True,np.zeros(3,'d'))
else:
return True
v = np.array(vector,dtype=float)
if proper: # check both improper ...
theComponents = np.around(np.dot(basis['improper'],v),12)
inSST = np.all(theComponents >= 0.0)
if not inSST: # ... and proper SST
theComponents = np.around(np.dot(basis['proper'],v),12)
inSST = np.all(theComponents >= 0.0)
else:
v[2] = abs(v[2]) # z component projects identical
theComponents = np.around(np.dot(basis['improper'],v),12) # for positive and negative values
inSST = np.all(theComponents >= 0.0)
if color: # have to return color array
if inSST:
rgb = np.power(theComponents/np.linalg.norm(theComponents),0.5) # smoothen color ramps
rgb = np.minimum(np.ones(3,dtype=float),rgb) # limit to maximum intensity
rgb /= max(rgb) # normalize to (HS)V = 1
else:
rgb = np.zeros(3,dtype=float)
return (inSST,rgb)
else:
return inSST
# code derived from https://github.com/ezag/pyeuclid
# suggested reading: http://web.mit.edu/2.998/www/QuaternionReport1.pdf
# ******************************************************************************************
class Lattice:
"""
Lattice system.
Currently, this contains only a mapping from Bravais lattice to symmetry
and orientation relationships. It could include twin and slip systems.
References
----------
https://en.wikipedia.org/wiki/Bravais_lattice
"""
lattices = {
'triclinic':{'symmetry':None},
'bct':{'symmetry':'tetragonal'},
'hex':{'symmetry':'hexagonal'},
'fcc':{'symmetry':'cubic','c/a':1.0},
'bcc':{'symmetry':'cubic','c/a':1.0},
}
def __init__(self, lattice):
"""
New lattice of given type.
Parameters
----------
lattice : str
Bravais lattice.
"""
self.lattice = lattice
self.symmetry = Symmetry(self.lattices[lattice]['symmetry'])
def __repr__(self):
"""Report basic lattice information."""
return 'Bravais lattice {} ({} symmetry)'.format(self.lattice,self.symmetry)
# 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
KS = {'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]],
[[ -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 relationOperations(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('Orientation relationship "{}" is unknown'.format(model))
if self.lattice not in relationship['mapping']:
raise ValueError('Relationship "{}" not supported for lattice "{}"'.format(model,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(Rotation.fromMatrix(np.dot(otherMatrix.T,myMatrix)))
return r

1497
python/damask/orientation.py
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python/damask/rotation.py Normal file
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import numpy as np
from . import Lambert
P = -1
def iszero(a):
return np.isclose(a,0.0,atol=1.0e-12,rtol=0.0)
class Rotation:
u"""
Orientation stored with functionality for conversion to different representations.
References
----------
D. Rowenhorst et al., Modelling and Simulation in Materials Science and Engineering 23:083501, 2015
https://doi.org/10.1088/0965-0393/23/8/083501
Conventions
-----------
Convention 1: Coordinate frames are right-handed.
Convention 2: 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.
Convention 3: Rotations will be interpreted in the passive sense.
Convention 4: Euler angle triplets are implemented using the Bunge convention,
with the angular ranges as [0, 2π],[0, π],[0, 2π].
Convention 5: The rotation angle ω is limited to the interval [0, π].
Convention 6: the real part of a quaternion is positive, Re(q) > 0
Convention 7: P = -1 (as default).
Usage
-----
Vector "a" (defined in coordinate system "A") is passively rotated
resulting in new coordinates "b" when expressed in system "B".
b = Q * a
b = np.dot(Q.asMatrix(),a)
"""
__slots__ = ['quaternion']
def __init__(self,quaternion = np.array([1.0,0.0,0.0,0.0])):
"""
Initializes to identity unless specified.
Parameters
----------
quaternion : numpy.ndarray, optional
Unit quaternion that follows the conventions. Use .fromQuaternion to perform a sanity check.
"""
self.quaternion = quaternion.copy()
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."""
return '\n'.join([
'Quaternion: (real={:.3f}, imag=<{:+.3f}, {:+.3f}, {:+.3f}>)'.format(*(self.quaternion)),
'Matrix:\n{}'.format(self.asMatrix()),
'Bunge Eulers / deg: ({:3.2f}, {:3.2f}, {:3.2f})'.format(*self.asEulers(degrees=True)),
])
def __mul__(self, other):
"""
Multiplication.
Parameters
----------
other : numpy.ndarray or Rotation
Vector, second or fourth order tensor, or rotation object that is rotated.
Todo
----
Document details active/passive)
considere rotation of (3,3,3,3)-matrix
"""
if isinstance(other, Rotation): # rotate a rotation
self_q = self.quaternion[0]
self_p = self.quaternion[1:]
other_q = other.quaternion[0]
other_p = other.quaternion[1:]
R = self.__class__(np.append(self_q*other_q - np.dot(self_p,other_p),
self_q*other_p + other_q*self_p + P * np.cross(self_p,other_p)))
return R.standardize()
elif isinstance(other, (tuple,np.ndarray)):
if isinstance(other,tuple) or other.shape == (3,): # rotate a single (3)-vector or meshgrid
A = self.quaternion[0]**2.0 - np.dot(self.quaternion[1:],self.quaternion[1:])
B = 2.0 * ( self.quaternion[1]*other[0]
+ self.quaternion[2]*other[1]
+ self.quaternion[3]*other[2])
C = 2.0 * P*self.quaternion[0]
return np.array([
A*other[0] + B*self.quaternion[1] + C*(self.quaternion[2]*other[2] - self.quaternion[3]*other[1]),
A*other[1] + B*self.quaternion[2] + C*(self.quaternion[3]*other[0] - self.quaternion[1]*other[2]),
A*other[2] + B*self.quaternion[3] + C*(self.quaternion[1]*other[1] - self.quaternion[2]*other[0]),
])
elif other.shape == (3,3,): # rotate a single (3x3)-matrix
return np.dot(self.asMatrix(),np.dot(other,self.asMatrix().T))
elif other.shape == (3,3,3,3,):
raise NotImplementedError
else:
return NotImplemented
else:
return NotImplemented
def inverse(self):
"""In-place inverse rotation/backward rotation."""
self.quaternion[1:] *= -1
return self
def inversed(self):
"""Inverse rotation/backward rotation."""
return self.copy().inverse()
def standardize(self):
"""In-place quaternion representation with positive q."""
if self.quaternion[0] < 0.0: self.quaternion*=-1
return self
def standardized(self):
"""Quaternion representation with positive q."""
return self.copy().standardize()
def misorientation(self,other):
"""
Get Misorientation.
Parameters
----------
other : Rotation
Rotation to which the misorientation is computed.
"""
return other*self.inversed()
def average(self,other):
"""
Calculate the average rotation.
Parameters
----------
other : Rotation
Rotation from which the average is rotated.
"""
return Rotation.fromAverage([self,other])
################################################################################################
# convert to different orientation representations (numpy arrays)
def asQuaternion(self):
"""
Unit quaternion [q, p_1, p_2, p_3] unless quaternion == True: damask.quaternion object.
Parameters
----------
quaternion : bool, optional
return quaternion as DAMASK object.
"""
return self.quaternion
def asEulers(self,
degrees = False):
"""
Bunge-Euler angles: (φ_1, ϕ, φ_2).
Parameters
----------
degrees : bool, optional
return angles in degrees.
"""
eu = Rotation.qu2eu(self.quaternion)
if degrees: eu = np.degrees(eu)
return eu
def asAxisAngle(self,
degrees = False,
pair = False):
"""
Axis angle representation [n_1, n_2, n_3, ω] unless pair == True: ([n_1, n_2, n_3], ω).
Parameters
----------
degrees : bool, optional
return rotation angle in degrees.
pair : bool, optional
return tuple of axis and angle.
"""
ax = Rotation.qu2ax(self.quaternion)
if degrees: ax[3] = np.degrees(ax[3])
return (ax[:3],np.degrees(ax[3])) if pair else ax
def asMatrix(self):
"""Rotation matrix."""
return Rotation.qu2om(self.quaternion)
def asRodrigues(self,
vector = False):
"""
Rodrigues-Frank vector representation [n_1, n_2, n_3, tan(ω/2)] unless vector == True: [n_1, n_2, n_3] * tan(ω/2).
Parameters
----------
vector : bool, optional
return as actual Rodrigues--Frank vector, i.e. rotation axis scaled by tan(ω/2).
"""
ro = Rotation.qu2ro(self.quaternion)
return ro[:3]*ro[3] if vector else ro
def asHomochoric(self):
"""Homochoric vector: (h_1, h_2, h_3)."""
return Rotation.qu2ho(self.quaternion)
def asCubochoric(self):
"""Cubochoric vector: (c_1, c_2, c_3)."""
return Rotation.qu2cu(self.quaternion)
def asM(self):
"""
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.outer(self.quaternion,self.quaternion)
################################################################################################
# static constructors. The input data needs to follow the convention, options allow to
# relax these convections
@staticmethod
def fromQuaternion(quaternion,
acceptHomomorph = False,
P = -1):
qu = quaternion if isinstance(quaternion,np.ndarray) and quaternion.dtype == np.dtype(float) \
else np.array(quaternion,dtype=float)
if P > 0: qu[1:4] *= -1 # convert from P=1 to P=-1
if qu[0] < 0.0:
if acceptHomomorph:
qu *= -1.
else:
raise ValueError('Quaternion has negative first component.\n{}'.format(qu[0]))
if not np.isclose(np.linalg.norm(qu), 1.0):
raise ValueError('Quaternion is not of unit length.\n{} {} {} {}'.format(*qu))
return Rotation(qu)
@staticmethod
def fromEulers(eulers,
degrees = False):
eu = eulers if isinstance(eulers, np.ndarray) and eulers.dtype == np.dtype(float) \
else np.array(eulers,dtype=float)
eu = np.radians(eu) if degrees else eu
if np.any(eu < 0.0) or np.any(eu > 2.0*np.pi) or eu[1] > np.pi:
raise ValueError('Euler angles outside of [0..2π],[0..π],[0..2π].\n{} {} {}.'.format(*eu))
return Rotation(Rotation.eu2qu(eu))
@staticmethod
def fromAxisAngle(angleAxis,
degrees = False,
normalise = False,
P = -1):
ax = angleAxis if isinstance(angleAxis, np.ndarray) and angleAxis.dtype == np.dtype(float) \
else np.array(angleAxis,dtype=float)
if P > 0: ax[0:3] *= -1 # convert from P=1 to P=-1
if degrees: ax[ 3] = np.radians(ax[3])
if normalise: ax[0:3] /= np.linalg.norm(ax[0:3])
if ax[3] < 0.0 or ax[3] > np.pi:
raise ValueError('Axis angle rotation angle outside of [0..π].\n'.format(ax[3]))
if not np.isclose(np.linalg.norm(ax[0:3]), 1.0):
raise ValueError('Axis angle rotation axis is not of unit length.\n{} {} {}'.format(*ax[0:3]))
return Rotation(Rotation.ax2qu(ax))
@staticmethod
def fromBasis(basis,
orthonormal = True,
reciprocal = False,
):
om = basis if isinstance(basis, np.ndarray) else np.array(basis).reshape((3,3))
if reciprocal:
om = np.linalg.inv(om.T/np.pi) # transform reciprocal basis set
orthonormal = False # contains stretch
if not orthonormal:
(U,S,Vh) = np.linalg.svd(om) # singular value decomposition
om = np.dot(U,Vh)
if not np.isclose(np.linalg.det(om),1.0):
raise ValueError('matrix is not a proper rotation.\n{}'.format(om))
if not np.isclose(np.dot(om[0],om[1]), 0.0) \
or not np.isclose(np.dot(om[1],om[2]), 0.0) \
or not np.isclose(np.dot(om[2],om[0]), 0.0):
raise ValueError('matrix is not orthogonal.\n{}'.format(om))
return Rotation(Rotation.om2qu(om))
@staticmethod
def fromMatrix(om,
):
return Rotation.fromBasis(om)
@staticmethod
def fromRodrigues(rodrigues,
normalise = False,
P = -1):
ro = rodrigues if isinstance(rodrigues, np.ndarray) and rodrigues.dtype == np.dtype(float) \
else np.array(rodrigues,dtype=float)
if P > 0: ro[0:3] *= -1 # convert from P=1 to P=-1
if normalise: ro[0:3] /= np.linalg.norm(ro[0:3])
if not np.isclose(np.linalg.norm(ro[0:3]), 1.0):
raise ValueError('Rodrigues rotation axis is not of unit length.\n{} {} {}'.format(*ro[0:3]))
if ro[3] < 0.0:
raise ValueError('Rodriques rotation angle not positive.\n'.format(ro[3]))
return Rotation(Rotation.ro2qu(ro))
@staticmethod
def fromHomochoric(homochoric,
P = -1):
ho = homochoric if isinstance(homochoric, np.ndarray) and homochoric.dtype == np.dtype(float) \
else np.array(homochoric,dtype=float)
if P > 0: ho *= -1 # convert from P=1 to P=-1
return Rotation(Rotation.ho2qu(ho))
@staticmethod
def fromCubochoric(cubochoric,
P = -1):
cu = cubochoric if isinstance(cubochoric, np.ndarray) and cubochoric.dtype == np.dtype(float) \
else np.array(cubochoric,dtype=float)
ho = Rotation.cu2ho(cu)
if P > 0: ho *= -1 # convert from P=1 to P=-1
return Rotation(Rotation.ho2qu(ho))
@staticmethod
def fromAverage(rotations,
weights = []):
"""
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 weights == [] or not weights:
weights = np.ones(N,dtype='i')
for i,(r,n) in enumerate(zip(rotations,weights)):
M = r.asM() * n if i == 0 \
else M + r.asM() * n # noqa add (multiples) of this rotation to average noqa
eig, vec = np.linalg.eig(M/N)
return Rotation.fromQuaternion(np.real(vec.T[eig.argmax()]),acceptHomomorph = True)
@staticmethod
def fromRandom():
r = np.random.random(3)
A = np.sqrt(r[2])
B = np.sqrt(1.0-r[2])
return Rotation(np.array([np.cos(2.0*np.pi*r[0])*A,
np.sin(2.0*np.pi*r[1])*B,
np.cos(2.0*np.pi*r[1])*B,
np.sin(2.0*np.pi*r[0])*A])).standardize()
####################################################################################################
# Code below available according to the following conditions on https://github.com/MarDiehl/3Drotations
####################################################################################################
# Copyright (c) 2017-2019, Martin Diehl/Max-Planck-Institut für Eisenforschung GmbH
# Copyright (c) 2013-2014, Marc De Graef/Carnegie Mellon University
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without modification, are
# permitted provided that the following conditions are met:
#
# - Redistributions of source code must retain the above copyright notice, this list
# of conditions and the following disclaimer.
# - Redistributions in binary form must reproduce the above copyright notice, this
# list of conditions and the following disclaimer in the documentation and/or
# other materials provided with the distribution.
# - Neither the names of Marc De Graef, Carnegie Mellon University nor the names
# of its contributors may be used to endorse or promote products derived from
# this software without specific prior written permission.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
# ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
# LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
# DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
# SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
# CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
# OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
# USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
####################################################################################################
#---------- Quaternion ----------
@staticmethod
def qu2om(qu):
"""Quaternion to rotation matrix."""
qq = qu[0]**2-(qu[1]**2 + qu[2]**2 + qu[3]**2)
om = np.diag(qq + 2.0*np.array([qu[1],qu[2],qu[3]])**2)
om[1,0] = 2.0*(qu[2]*qu[1]+qu[0]*qu[3])
om[0,1] = 2.0*(qu[1]*qu[2]-qu[0]*qu[3])
om[2,1] = 2.0*(qu[3]*qu[2]+qu[0]*qu[1])
om[1,2] = 2.0*(qu[2]*qu[3]-qu[0]*qu[1])
om[0,2] = 2.0*(qu[1]*qu[3]+qu[0]*qu[2])
om[2,0] = 2.0*(qu[3]*qu[1]-qu[0]*qu[2])
return om if P > 0.0 else om.T
@staticmethod
def qu2eu(qu):
"""Quaternion to Bunge-Euler angles."""
q03 = qu[0]**2+qu[3]**2
q12 = qu[1]**2+qu[2]**2
chi = np.sqrt(q03*q12)
if iszero(chi):
eu = np.array([np.arctan2(-P*2.0*qu[0]*qu[3],qu[0]**2-qu[3]**2), 0.0, 0.0]) if iszero(q12) else \
np.array([np.arctan2(2.0*qu[1]*qu[2],qu[1]**2-qu[2]**2), np.pi, 0.0])
else:
eu = np.array([np.arctan2((-P*qu[0]*qu[2]+qu[1]*qu[3])*chi, (-P*qu[0]*qu[1]-qu[2]*qu[3])*chi ),
np.arctan2( 2.0*chi, q03-q12 ),
np.arctan2(( P*qu[0]*qu[2]+qu[1]*qu[3])*chi, (-P*qu[0]*qu[1]+qu[2]*qu[3])*chi )])
# reduce Euler angles to definition range, i.e a lower limit of 0.0
eu = np.where(eu<0, (eu+2.0*np.pi)%np.array([2.0*np.pi,np.pi,2.0*np.pi]),eu)
return eu
@staticmethod
def qu2ax(qu):
"""
Quaternion to axis angle pair.
Modified version of the original formulation, should be numerically more stable
"""
if iszero(qu[1]**2+qu[2]**2+qu[3]**2): # set axis to [001] if the angle is 0/360
ax = [ 0.0, 0.0, 1.0, 0.0 ]
elif not iszero(qu[0]):
s = np.sign(qu[0])/np.sqrt(qu[1]**2+qu[2]**2+qu[3]**2)
omega = 2.0 * np.arccos(np.clip(qu[0],-1.0,1.0))
ax = [ qu[1]*s, qu[2]*s, qu[3]*s, omega ]
else:
ax = [ qu[1], qu[2], qu[3], np.pi]
return np.array(ax)
@staticmethod
def qu2ro(qu):
"""Quaternion to Rodriques-Frank vector."""
if iszero(qu[0]):
ro = [qu[1], qu[2], qu[3], np.inf]
else:
s = np.linalg.norm([qu[1],qu[2],qu[3]])
ro = [0.0,0.0,P,0.0] if iszero(s) else \
[ qu[1]/s, qu[2]/s, qu[3]/s, np.tan(np.arccos(np.clip(qu[0],-1.0,1.0)))]
return np.array(ro)
@staticmethod
def qu2ho(qu):
"""Quaternion to homochoric vector."""
omega = 2.0 * np.arccos(np.clip(qu[0],-1.0,1.0))
if iszero(omega):
ho = np.array([ 0.0, 0.0, 0.0 ])
else:
ho = np.array([qu[1], qu[2], qu[3]])
f = 0.75 * ( omega - np.sin(omega) )
ho = ho/np.linalg.norm(ho) * f**(1./3.)
return ho
@staticmethod
def qu2cu(qu):
"""Quaternion to cubochoric vector."""
return Rotation.ho2cu(Rotation.qu2ho(qu))
#---------- Rotation matrix ----------
@staticmethod
def om2qu(om):
"""
Rotation matrix to quaternion.
The original formulation (direct conversion) had (numerical?) issues
"""
return Rotation.eu2qu(Rotation.om2eu(om))
@staticmethod
def om2eu(om):
"""Rotation matrix to Bunge-Euler angles."""
if abs(om[2,2]) < 1.0:
zeta = 1.0/np.sqrt(1.0-om[2,2]**2)
eu = np.array([np.arctan2(om[2,0]*zeta,-om[2,1]*zeta),
np.arccos(om[2,2]),
np.arctan2(om[0,2]*zeta, om[1,2]*zeta)])
else:
eu = np.array([np.arctan2( om[0,1],om[0,0]), np.pi*0.5*(1-om[2,2]),0.0]) # following the paper, not the reference implementation
# reduce Euler angles to definition range, i.e a lower limit of 0.0
eu = np.where(eu<0, (eu+2.0*np.pi)%np.array([2.0*np.pi,np.pi,2.0*np.pi]),eu)
return eu
@staticmethod
def om2ax(om):
"""Rotation matrix to axis angle pair."""
ax=np.empty(4)
# first get the rotation angle
t = 0.5*(om.trace() -1.0)
ax[3] = np.arccos(np.clip(t,-1.0,1.0))
if iszero(ax[3]):
ax = [ 0.0, 0.0, 1.0, 0.0]
else:
w,vr = np.linalg.eig(om)
# next, find the eigenvalue (1,0j)
i = np.where(np.isclose(w,1.0+0.0j))[0][0]
ax[0:3] = np.real(vr[0:3,i])
diagDelta = np.array([om[1,2]-om[2,1],om[2,0]-om[0,2],om[0,1]-om[1,0]])
ax[0:3] = np.where(iszero(diagDelta), ax[0:3],np.abs(ax[0:3])*np.sign(-P*diagDelta))
return np.array(ax)
@staticmethod
def om2ro(om):
"""Rotation matrix to Rodriques-Frank vector."""
return Rotation.eu2ro(Rotation.om2eu(om))
@staticmethod
def om2ho(om):
"""Rotation matrix to homochoric vector."""
return Rotation.ax2ho(Rotation.om2ax(om))
@staticmethod
def om2cu(om):
"""Rotation matrix to cubochoric vector."""
return Rotation.ho2cu(Rotation.om2ho(om))
#---------- Bunge-Euler angles ----------
@staticmethod
def eu2qu(eu):
"""Bunge-Euler angles to quaternion."""
ee = 0.5*eu
cPhi = np.cos(ee[1])
sPhi = np.sin(ee[1])
qu = np.array([ cPhi*np.cos(ee[0]+ee[2]),
-P*sPhi*np.cos(ee[0]-ee[2]),
-P*sPhi*np.sin(ee[0]-ee[2]),
-P*cPhi*np.sin(ee[0]+ee[2]) ])
if qu[0] < 0.0: qu*=-1
return qu
@staticmethod
def eu2om(eu):
"""Bunge-Euler angles to rotation matrix."""
c = np.cos(eu)
s = np.sin(eu)
om = np.array([[+c[0]*c[2]-s[0]*s[2]*c[1], +s[0]*c[2]+c[0]*s[2]*c[1], +s[2]*s[1]],
[-c[0]*s[2]-s[0]*c[2]*c[1], -s[0]*s[2]+c[0]*c[2]*c[1], +c[2]*s[1]],
[+s[0]*s[1], -c[0]*s[1], +c[1] ]])
om[np.where(iszero(om))] = 0.0
return om
@staticmethod
def eu2ax(eu):
"""Bunge-Euler angles to axis angle pair."""
t = np.tan(eu[1]*0.5)
sigma = 0.5*(eu[0]+eu[2])
delta = 0.5*(eu[0]-eu[2])
tau = np.linalg.norm([t,np.sin(sigma)])
alpha = np.pi if iszero(np.cos(sigma)) else \
2.0*np.arctan(tau/np.cos(sigma))
if iszero(alpha):
ax = np.array([ 0.0, 0.0, 1.0, 0.0 ])
else:
ax = -P/tau * np.array([ t*np.cos(delta), t*np.sin(delta), np.sin(sigma) ]) # passive axis angle pair so a minus sign in front
ax = np.append(ax,alpha)
if alpha < 0.0: ax *= -1.0 # ensure alpha is positive
return ax
@staticmethod
def eu2ro(eu):
"""Bunge-Euler angles to Rodriques-Frank vector."""
ro = Rotation.eu2ax(eu) # convert to axis angle pair representation
if ro[3] >= np.pi: # Differs from original implementation. check convention 5
ro[3] = np.inf
elif iszero(ro[3]):
ro = np.array([ 0.0, 0.0, P, 0.0 ])
else:
ro[3] = np.tan(ro[3]*0.5)
return ro
@staticmethod
def eu2ho(eu):
"""Bunge-Euler angles to homochoric vector."""
return Rotation.ax2ho(Rotation.eu2ax(eu))
@staticmethod
def eu2cu(eu):
"""Bunge-Euler angles to cubochoric vector."""
return Rotation.ho2cu(Rotation.eu2ho(eu))
#---------- Axis angle pair ----------
@staticmethod
def ax2qu(ax):
"""Axis angle pair to quaternion."""
if iszero(ax[3]):
qu = np.array([ 1.0, 0.0, 0.0, 0.0 ])
else:
c = np.cos(ax[3]*0.5)
s = np.sin(ax[3]*0.5)
qu = np.array([ c, ax[0]*s, ax[1]*s, ax[2]*s ])
return qu
@staticmethod
def ax2om(ax):
"""Axis angle pair to rotation matrix."""
c = np.cos(ax[3])
s = np.sin(ax[3])
omc = 1.0-c
om=np.diag(ax[0:3]**2*omc + c)
for idx in [[0,1,2],[1,2,0],[2,0,1]]:
q = omc*ax[idx[0]] * ax[idx[1]]
om[idx[0],idx[1]] = q + s*ax[idx[2]]
om[idx[1],idx[0]] = q - s*ax[idx[2]]
return om if P < 0.0 else om.T
@staticmethod
def ax2eu(ax):
"""Rotation matrix to Bunge Euler angles."""
return Rotation.om2eu(Rotation.ax2om(ax))
@staticmethod
def ax2ro(ax):
"""Axis angle pair to Rodriques-Frank vector."""
if iszero(ax[3]):
ro = [ 0.0, 0.0, P, 0.0 ]
else:
ro = [ax[0], ax[1], ax[2]]
# 180 degree case
ro += [np.inf] if np.isclose(ax[3],np.pi,atol=1.0e-15,rtol=0.0) else \
[np.tan(ax[3]*0.5)]
return np.array(ro)
@staticmethod
def ax2ho(ax):
"""Axis angle pair to homochoric vector."""
f = (0.75 * ( ax[3] - np.sin(ax[3]) ))**(1.0/3.0)
ho = ax[0:3] * f
return ho
@staticmethod
def ax2cu(ax):
"""Axis angle pair to cubochoric vector."""
return Rotation.ho2cu(Rotation.ax2ho(ax))
#---------- Rodrigues-Frank vector ----------
@staticmethod
def ro2qu(ro):
"""Rodriques-Frank vector to quaternion."""
return Rotation.ax2qu(Rotation.ro2ax(ro))
@staticmethod
def ro2om(ro):
"""Rodgrigues-Frank vector to rotation matrix."""
return Rotation.ax2om(Rotation.ro2ax(ro))
@staticmethod
def ro2eu(ro):
"""Rodriques-Frank vector to Bunge-Euler angles."""
return Rotation.om2eu(Rotation.ro2om(ro))
@staticmethod
def ro2ax(ro):
"""Rodriques-Frank vector to axis angle pair."""
ta = ro[3]
if iszero(ta):
ax = [ 0.0, 0.0, 1.0, 0.0 ]
elif not np.isfinite(ta):
ax = [ ro[0], ro[1], ro[2], np.pi ]
else:
angle = 2.0*np.arctan(ta)
ta = 1.0/np.linalg.norm(ro[0:3])
ax = [ ro[0]/ta, ro[1]/ta, ro[2]/ta, angle ]
return np.array(ax)
@staticmethod
def ro2ho(ro):
"""Rodriques-Frank vector to homochoric vector."""
if iszero(np.sum(ro[0:3]**2.0)):
ho = [ 0.0, 0.0, 0.0 ]
else:
f = 2.0*np.arctan(ro[3]) -np.sin(2.0*np.arctan(ro[3])) if np.isfinite(ro[3]) else np.pi
ho = ro[0:3] * (0.75*f)**(1.0/3.0)
return np.array(ho)
@staticmethod
def ro2cu(ro):
"""Rodriques-Frank vector to cubochoric vector."""
return Rotation.ho2cu(Rotation.ro2ho(ro))
#---------- Homochoric vector----------
@staticmethod
def ho2qu(ho):
"""Homochoric vector to quaternion."""
return Rotation.ax2qu(Rotation.ho2ax(ho))
@staticmethod
def ho2om(ho):
"""Homochoric vector to rotation matrix."""
return Rotation.ax2om(Rotation.ho2ax(ho))
@staticmethod
def ho2eu(ho):
"""Homochoric vector to Bunge-Euler angles."""
return Rotation.ax2eu(Rotation.ho2ax(ho))
@staticmethod
def ho2ax(ho):
"""Homochoric vector to axis angle pair."""
tfit = np.array([+1.0000000000018852, -0.5000000002194847,
-0.024999992127593126, -0.003928701544781374,
-0.0008152701535450438, -0.0002009500426119712,
-0.00002397986776071756, -0.00008202868926605841,
+0.00012448715042090092, -0.0001749114214822577,
+0.0001703481934140054, -0.00012062065004116828,
+0.000059719705868660826, -0.00001980756723965647,
+0.000003953714684212874, -0.00000036555001439719544])
# normalize h and store the magnitude
hmag_squared = np.sum(ho**2.)
if iszero(hmag_squared):
ax = np.array([ 0.0, 0.0, 1.0, 0.0 ])
else:
hm = hmag_squared
# convert the magnitude to the rotation angle
s = tfit[0] + tfit[1] * hmag_squared
for i in range(2,16):
hm *= hmag_squared
s += tfit[i] * hm
ax = np.append(ho/np.sqrt(hmag_squared),2.0*np.arccos(np.clip(s,-1.0,1.0)))
return ax
@staticmethod
def ho2ro(ho):
"""Axis angle pair to Rodriques-Frank vector."""
return Rotation.ax2ro(Rotation.ho2ax(ho))
@staticmethod
def ho2cu(ho):
"""Homochoric vector to cubochoric vector."""
return Lambert.BallToCube(ho)
#---------- Cubochoric ----------
@staticmethod
def cu2qu(cu):
"""Cubochoric vector to quaternion."""
return Rotation.ho2qu(Rotation.cu2ho(cu))
@staticmethod
def cu2om(cu):
"""Cubochoric vector to rotation matrix."""
return Rotation.ho2om(Rotation.cu2ho(cu))
@staticmethod
def cu2eu(cu):
"""Cubochoric vector to Bunge-Euler angles."""
return Rotation.ho2eu(Rotation.cu2ho(cu))
@staticmethod
def cu2ax(cu):
"""Cubochoric vector to axis angle pair."""
return Rotation.ho2ax(Rotation.cu2ho(cu))
@staticmethod
def cu2ro(cu):
"""Cubochoric vector to Rodriques-Frank vector."""
return Rotation.ho2ro(Rotation.cu2ho(cu))
@staticmethod
def cu2ho(cu):
"""Cubochoric vector to homochoric vector."""
return Lambert.CubeToBall(cu)

94
python/damask/util.py
View File

@ -40,55 +40,92 @@ class bcolors:
self.CROSSOUT = '' self.CROSSOUT = ''
# -----------------------------
def srepr(arg,glue = '\n'): def srepr(arg,glue = '\n'):
"""Joins arguments as individual lines.""" r"""
Join arguments as individual lines.
Parameters
----------
arg : iterable
Items to join.
glue : str, optional
Defaults to \n.
"""
if (not hasattr(arg, "strip") and if (not hasattr(arg, "strip") and
(hasattr(arg, "__getitem__") or (hasattr(arg, "__getitem__") or
hasattr(arg, "__iter__"))): hasattr(arg, "__iter__"))):
return glue.join(str(x) for x in arg) return glue.join(str(x) for x in arg)
return arg if isinstance(arg,str) else repr(arg) return arg if isinstance(arg,str) else repr(arg)
# -----------------------------
def croak(what, newline = True): def croak(what, newline = True):
"""Writes formated to stderr.""" """
if what is not None: Write formated to stderr.
Parameters
----------
what : str or iterable
Content to be displayed
newline : bool, optional
Separate items of what by newline. Defaults to True.
"""
if not what:
sys.stderr.write(srepr(what,glue = '\n') + ('\n' if newline else '')) sys.stderr.write(srepr(what,glue = '\n') + ('\n' if newline else ''))
sys.stderr.flush() sys.stderr.flush()
# -----------------------------
def report(who = None, def report(who = None,
what = None): what = None):
"""Reports script and file name.""" """
Reports script and file name.
DEPRECATED
"""
croak( (emph(who)+': ' if who is not None else '') + (what if what is not None else '') + '\n' ) croak( (emph(who)+': ' if who is not None else '') + (what if what is not None else '') + '\n' )
# -----------------------------
def emph(what): def emph(what):
"""Formats string with emphasis.""" """Formats string with emphasis."""
return bcolors.BOLD+srepr(what)+bcolors.ENDC return bcolors.BOLD+srepr(what)+bcolors.ENDC
# -----------------------------
def deemph(what): def deemph(what):
"""Formats string with deemphasis.""" """Formats string with deemphasis."""
return bcolors.DIM+srepr(what)+bcolors.ENDC return bcolors.DIM+srepr(what)+bcolors.ENDC
# -----------------------------
def delete(what): def delete(what):
"""Formats string as deleted.""" """Formats string as deleted."""
return bcolors.DIM+srepr(what)+bcolors.ENDC return bcolors.DIM+srepr(what)+bcolors.ENDC
# -----------------------------
def strikeout(what): def strikeout(what):
"""Formats string as strikeout.""" """Formats string as strikeout."""
return bcolors.CROSSOUT+srepr(what)+bcolors.ENDC return bcolors.CROSSOUT+srepr(what)+bcolors.ENDC
# -----------------------------
def execute(cmd, def execute(cmd,
streamIn = None, streamIn = None,
wd = './', wd = './',
env = None): env = None):
"""Executes a command in given directory and returns stdout and stderr for optional stdin.""" """
Execute command.
Parameters
----------
cmd : str
Command to be executed.
streanIn :, optional
Input (via pipe) for executed process.
wd : str, optional
Working directory of process. Defaults to ./ .
env :
Environment
"""
initialPath = os.getcwd() initialPath = os.getcwd()
os.chdir(wd) os.chdir(wd)
myEnv = os.environ if env is None else env myEnv = os.environ if env is None else env
@ -102,15 +139,17 @@ def execute(cmd,
out = out.decode('utf-8').replace('\x08','') out = out.decode('utf-8').replace('\x08','')
error = error.decode('utf-8').replace('\x08','') error = error.decode('utf-8').replace('\x08','')
os.chdir(initialPath) os.chdir(initialPath)
if process.returncode != 0: raise RuntimeError('{} failed with returncode {}'.format(cmd,process.returncode)) if process.returncode != 0:
raise RuntimeError('{} failed with returncode {}'.format(cmd,process.returncode))
return out,error return out,error
# -----------------------------
class extendableOption(Option): class extendableOption(Option):
""" """
Used for definition of new option parser action 'extend', which enables to take multiple option arguments. Used for definition of new option parser action 'extend', which enables to take multiple option arguments.
Adopted from online tutorial http://docs.python.org/library/optparse.html Adopted from online tutorial http://docs.python.org/library/optparse.html
DEPRECATED
""" """
ACTIONS = Option.ACTIONS + ("extend",) ACTIONS = Option.ACTIONS + ("extend",)
@ -125,17 +164,24 @@ class extendableOption(Option):
else: else:
Option.take_action(self, action, dest, opt, value, values, parser) Option.take_action(self, action, dest, opt, value, values, parser)
# Print iterations progress
# from https://gist.github.com/aubricus/f91fb55dc6ba5557fbab06119420dd6a
def progressBar(iteration, total, prefix='', bar_length=50): def progressBar(iteration, total, prefix='', bar_length=50):
""" """
Call in a loop to create terminal progress bar. Call in a loop to create terminal progress bar.
@params: From https://gist.github.com/aubricus/f91fb55dc6ba5557fbab06119420dd6a
iteration - Required : current iteration (Int)
total - Required : total iterations (Int) Parameters
prefix - Optional : prefix string (Str) ----------
bar_length - Optional : character length of bar (Int) iteration : int
Current iteration.
total : int
Total iterations.
prefix : str, optional
Prefix string.
bar_length : int, optional
Character length of bar. Defaults to 50.
""" """
fraction = iteration / float(total) fraction = iteration / float(total)
if not hasattr(progressBar, "last_fraction"): # first call to function if not hasattr(progressBar, "last_fraction"): # first call to function
@ -159,7 +205,8 @@ def progressBar(iteration, total, prefix='', bar_length=50):
sys.stderr.write('\r{} {} {}'.format(prefix, bar, remaining_time)), sys.stderr.write('\r{} {} {}'.format(prefix, bar, remaining_time)),
if iteration == total: sys.stderr.write('\n') if iteration == total:
sys.stderr.write('\n')
sys.stderr.flush() sys.stderr.flush()
@ -199,3 +246,4 @@ class return_message():
def __repr__(self): def __repr__(self):
"""Return message suitable for interactive shells.""" """Return message suitable for interactive shells."""
return srepr(self.message) return srepr(self.message)

65
python/tests/test_Orientation.py Normal file
View File

@ -0,0 +1,65 @@
import os
from itertools import permutations
import pytest
import numpy as np
import damask
from damask import Rotation
from damask import Orientation
from damask import Lattice
n = 1000
@pytest.fixture
def default():
"""A set of n random rotations."""
return [Rotation.fromRandom() for r in range(n)]
@pytest.fixture
def reference_dir(reference_dir_base):
"""Directory containing reference results."""
return os.path.join(reference_dir_base,'Rotation')
class TestOrientation:
@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,default,color,lattice):
cube = damask.Orientation(damask.Rotation(),lattice)
for direction in set(permutations(np.array(color['direction']))):
assert np.allclose(cube.IPFcolor(direction),np.array(color['RGB']))
@pytest.mark.parametrize('lattice',Lattice.lattices)
def test_IPF(self,lattice):
direction = np.random.random(3)*2.0-1
for rot in [Rotation.fromRandom() for r in range(n//100)]:
R = damask.Orientation(rot,lattice)
color = R.IPFcolor(direction)
for equivalent in R.equivalentOrientations():
assert np.allclose(color,R.IPFcolor(direction))
@pytest.mark.parametrize('model',['Bain','KS','GT','GT_prime','NW','Pitsch'])
@pytest.mark.parametrize('lattice',['fcc','bcc'])
def test_relationship_forward_backward(self,model,lattice):
ori = Orientation(Rotation.fromRandom(),lattice)
for i,r in enumerate(ori.relatedOrientations(model)):
ori2 = r.relatedOrientations(model)[i]
misorientation = ori.rotation.misorientation(ori2.rotation)
assert misorientation.asAxisAngle(degrees=True)[3]<1.0e-5
@pytest.mark.parametrize('model',['Bain','KS','GT','GT_prime','NW','Pitsch'])
@pytest.mark.parametrize('lattice',['fcc','bcc'])
def test_relationship_reference(self,update,reference_dir,model,lattice):
reference = os.path.join(reference_dir,'{}_{}.txt'.format(lattice,model))
ori = Orientation(Rotation(),lattice)
eu = np.array([o.rotation.asEulers(degrees=True) for o in ori.relatedOrientations(model)])
if update:
coords = np.array([(1,i+1) for i,x in enumerate(eu)])
table = damask.Table(eu,{'Eulers':(3,)})
table.add('pos',coords)
table.to_ASCII(reference)
assert np.allclose(eu,damask.Table.from_ASCII(reference).get('Eulers'))

45
python/tests/test_Rotation.py
View File

@ -1,13 +1,9 @@
import os import os
from itertools import permutations
import pytest import pytest
import numpy as np import numpy as np
import damask
from damask import Rotation from damask import Rotation
from damask import Orientation
from damask import Lattice
n = 1000 n = 1000
@ -58,44 +54,3 @@ class TestRotation:
for rot in default: for rot in default:
assert np.allclose(rot.asCubochoric(), assert np.allclose(rot.asCubochoric(),
Rotation.fromQuaternion(rot.asQuaternion()).asCubochoric()) Rotation.fromQuaternion(rot.asQuaternion()).asCubochoric())
@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,default,color,lattice):
cube = damask.Orientation(damask.Rotation(),lattice)
for direction in set(permutations(np.array(color['direction']))):
assert np.allclose(cube.IPFcolor(direction),np.array(color['RGB']))
@pytest.mark.parametrize('lattice',Lattice.lattices)
def test_IPF(self,lattice):
direction = np.random.random(3)*2.0-1
for rot in [Rotation.fromRandom() for r in range(n//100)]:
R = damask.Orientation(rot,lattice)
color = R.IPFcolor(direction)
for equivalent in R.equivalentOrientations():
assert np.allclose(color,R.IPFcolor(direction))
@pytest.mark.parametrize('model',['Bain','KS','GT','GT_prime','NW','Pitsch'])
@pytest.mark.parametrize('lattice',['fcc','bcc'])
def test_relationship_forward_backward(self,model,lattice):
ori = Orientation(Rotation.fromRandom(),lattice)
for i,r in enumerate(ori.relatedOrientations(model)):
ori2 = r.relatedOrientations(model)[i]
misorientation = ori.rotation.misorientation(ori2.rotation)
assert misorientation.asAxisAngle(degrees=True)[3]<1.0e-5
@pytest.mark.parametrize('model',['Bain','KS','GT','GT_prime','NW','Pitsch'])
@pytest.mark.parametrize('lattice',['fcc','bcc'])
def test_relationship_reference(self,update,reference_dir,model,lattice):
reference = os.path.join(reference_dir,'{}_{}.txt'.format(lattice,model))
ori = Orientation(Rotation(),lattice)
eu = np.array([o.rotation.asEulers(degrees=True) for o in ori.relatedOrientations(model)])
if update:
coords = np.array([(1,i+1) for i,x in enumerate(eu)])
table = damask.Table(eu,{'Eulers':(3,)})
table.add('pos',coords)
table.to_ASCII(reference)
assert np.allclose(eu,damask.Table.from_ASCII(reference).get('Eulers'))