averaging possible for rotations and orientations; Rodrigues 3Dvector output only at top-level; code reordering
This commit is contained in:
Philip Eisenlohr
parent
3d6eb76da3
commit
3a7408a213
|
|
@ -260,6 +260,63 @@ class Rotation:
|
|||
'Bunge Eulers / deg: {}'.format('\t'.join(list(map(str,self.asEulers(degrees=True)))) ),
|
||||
])
|
||||
|
||||
def __mul__(self, other):
|
||||
"""
|
||||
Multiplication
|
||||
|
||||
Rotation: Details needed (active/passive), rotation of (3,3,3,3)-matrix should be considered
|
||||
"""
|
||||
if isinstance(other, Rotation): # rotate a rotation
|
||||
return self.__class__((self.quaternion * other.quaternion).asArray())
|
||||
elif isinstance(other, np.ndarray):
|
||||
if other.shape == (3,): # rotate a single (3)-vector
|
||||
( x, y, z) = self.quaternion.p
|
||||
(Vx,Vy,Vz) = other[0:3]
|
||||
A = self.quaternion.q*self.quaternion.q - np.dot(self.quaternion.p,self.quaternion.p)
|
||||
B = 2.0 * (x*Vx + y*Vy + z*Vz)
|
||||
C = 2.0 * P*self.quaternion.q
|
||||
|
||||
return np.array([
|
||||
A*Vx + B*x + C*(y*Vz - z*Vy),
|
||||
A*Vy + B*y + C*(z*Vx - x*Vz),
|
||||
A*Vz + B*z + C*(x*Vy - y*Vx),
|
||||
])
|
||||
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
|
||||
elif isinstance(other, tuple): # used to rotate a meshgrid-tuple
|
||||
( x, y, z) = self.quaternion.p
|
||||
(Vx,Vy,Vz) = other[0:3]
|
||||
A = self.quaternion.q*self.quaternion.q - np.dot(self.quaternion.p,self.quaternion.p)
|
||||
B = 2.0 * (x*Vx + y*Vy + z*Vz)
|
||||
C = 2.0 * P*self.quaternion.q
|
||||
|
||||
return np.array([
|
||||
A*Vx + B*x + C*(y*Vz - z*Vy),
|
||||
A*Vy + B*y + C*(z*Vx - x*Vz),
|
||||
A*Vz + B*z + C*(x*Vy - y*Vx),
|
||||
])
|
||||
else:
|
||||
return NotImplemented
|
||||
|
||||
|
||||
def inverse(self):
|
||||
"""In-place inverse rotation/backward rotation"""
|
||||
self.quaternion.conjugate()
|
||||
return self
|
||||
|
||||
def inversed(self):
|
||||
"""Inverse rotation/backward rotation"""
|
||||
return self.__class__(self.quaternion.conjugated())
|
||||
|
||||
|
||||
def misorientation(self,other):
|
||||
"""Misorientation"""
|
||||
return self.__class__(other.quaternion*self.quaternion.conjugated())
|
||||
|
||||
|
||||
################################################################################################
|
||||
# convert to different orientation representations (numpy arrays)
|
||||
|
|
@ -288,7 +345,8 @@ class Rotation:
|
|||
|
||||
def asRodrigues(self,vector=False):
|
||||
"""Rodrigues-Frank vector: ([n_1, n_2, n_3], tan(ω/2))"""
|
||||
return qu2ro(self.quaternion.asArray(),vector)
|
||||
ro = qu2ro(self.quaternion.asArray())
|
||||
return ro[:3]*ro[3] if vector else ro
|
||||
|
||||
def asHomochoric(self):
|
||||
"""Homochoric vector: (h_1, h_2, h_3)"""
|
||||
|
|
@ -298,7 +356,7 @@ class Rotation:
|
|||
return qu2cu(self.quaternion.asArray())
|
||||
|
||||
def asM(self):
|
||||
"""Intermediate representation useful fro quaternion averaging (see F. Landis Markley et al.)"""
|
||||
"""Intermediate representation supporting quaternion averaging (see F. Landis Markley et al.)"""
|
||||
return self.quaternion.asM()
|
||||
|
||||
|
||||
|
|
@ -409,62 +467,31 @@ class Rotation:
|
|||
return cls(ho2qu(ho))
|
||||
|
||||
|
||||
def __mul__(self, other):
|
||||
@classmethod
|
||||
def average(cls,
|
||||
rotations,
|
||||
weights = []):
|
||||
"""
|
||||
Multiplication
|
||||
Average rotation
|
||||
|
||||
Rotation: Details needed (active/passive), rotation of (3,3,3,3)-matrix should be considered
|
||||
ref: F. Landis Markley, Yang Cheng, John Lucas Crassidis, and Yaakov Oshman.
|
||||
Averaging Quaternions,
|
||||
Journal of Guidance, Control, and Dynamics, Vol. 30, No. 4 (2007), pp. 1193-1197.
|
||||
doi: 10.2514/1.28949
|
||||
"""
|
||||
if isinstance(other, Rotation): # rotate a rotation
|
||||
return self.__class__((self.quaternion * other.quaternion).asArray())
|
||||
elif isinstance(other, np.ndarray):
|
||||
if other.shape == (3,): # rotate a single (3)-vector
|
||||
( x, y, z) = self.quaternion.p
|
||||
(Vx,Vy,Vz) = other[0:3]
|
||||
A = self.quaternion.q*self.quaternion.q - np.dot(self.quaternion.p,self.quaternion.p)
|
||||
B = 2.0 * (x*Vx + y*Vy + z*Vz)
|
||||
C = 2.0 * P*self.quaternion.q
|
||||
if not all(isinstance(item, Rotation) for item in rotations):
|
||||
raise TypeError("Only instances of Rotation can be averaged.")
|
||||
|
||||
return np.array([
|
||||
A*Vx + B*x + C*(y*Vz - z*Vy),
|
||||
A*Vy + B*y + C*(z*Vx - x*Vz),
|
||||
A*Vz + B*z + C*(x*Vy - y*Vx),
|
||||
])
|
||||
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
|
||||
elif isinstance(other, tuple): # used to rotate a meshgrid-tuple
|
||||
( x, y, z) = self.quaternion.p
|
||||
(Vx,Vy,Vz) = other[0:3]
|
||||
A = self.quaternion.q*self.quaternion.q - np.dot(self.quaternion.p,self.quaternion.p)
|
||||
B = 2.0 * (x*Vx + y*Vy + z*Vz)
|
||||
C = 2.0 * P*self.quaternion.q
|
||||
N = len(rotations)
|
||||
if weights == [] or not weights:
|
||||
weights = np.ones(N,dtype='i')
|
||||
|
||||
return np.array([
|
||||
A*Vx + B*x + C*(y*Vz - z*Vy),
|
||||
A*Vy + B*y + C*(z*Vx - x*Vz),
|
||||
A*Vz + B*z + C*(x*Vy - y*Vx),
|
||||
])
|
||||
else:
|
||||
return NotImplemented
|
||||
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)
|
||||
|
||||
|
||||
def inverse(self):
|
||||
"""Inverse rotation/backward rotation"""
|
||||
self.quaternion.conjugate()
|
||||
return self
|
||||
|
||||
def inversed(self):
|
||||
"""In-place inverse rotation/backward rotation"""
|
||||
return self.__class__(self.quaternion.conjugated())
|
||||
|
||||
|
||||
def misorientation(self,other):
|
||||
"""Misorientation"""
|
||||
return self.__class__(other.quaternion*self.quaternion.conjugated())
|
||||
return Rotation.fromQuaternion(np.real(vec.T[eig.argmax()]),acceptHomomorph = True)
|
||||
|
||||
|
||||
# ******************************************************************************************
|
||||
|
|
@ -511,7 +538,7 @@ class Symmetry:
|
|||
return (myOrder > otherOrder) - (myOrder < otherOrder)
|
||||
|
||||
def symmetryOperations(self,members=[]):
|
||||
"""List of symmetry operations as quaternions."""
|
||||
"""List (or single element) of symmetry operations as rotations."""
|
||||
if self.lattice == 'cubic':
|
||||
symQuats = [
|
||||
[ 1.0, 0.0, 0.0, 0.0 ],
|
||||
|
|
@ -880,7 +907,7 @@ class Lattice:
|
|||
|
||||
# Greninger--Troiano' orientation relationship for fcc <-> bcc transformation
|
||||
# from Y. He et al./Journal of Applied Crystallography (2006). 39, 72-81
|
||||
GTdash = {'mapping':{'fcc':0,'bcc':1},
|
||||
GTprime = {'mapping':{'fcc':0,'bcc':1},
|
||||
'planes': np.array([
|
||||
[[ 7, 17, 17],[ 12, 5, 17]],
|
||||
[[ 17, 7, 17],[ 17, 12, 5]],
|
||||
|
|
@ -1006,7 +1033,7 @@ class Lattice:
|
|||
|
||||
def relationOperations(self,model):
|
||||
|
||||
models={'KS':self.KS, 'GT':self.GT, "GT'":self.GTdash,
|
||||
models={'KS':self.KS, 'GT':self.GT, "GT'":self.GTprime,
|
||||
'NW':self.NW, 'Pitsch': self.Pitsch, 'Bain':self.Bain}
|
||||
try:
|
||||
relationship = models[model]
|
||||
|
|
@ -1154,7 +1181,7 @@ class Orientation:
|
|||
@classmethod
|
||||
def average(cls,
|
||||
orientations,
|
||||
multiplicity = []):
|
||||
weights = []):
|
||||
"""
|
||||
Average orientation
|
||||
|
||||
|
|
@ -1168,22 +1195,17 @@ class Orientation:
|
|||
avg = Orientation.average([a,b])
|
||||
"""
|
||||
if not all(isinstance(item, Orientation) for item in orientations):
|
||||
print('got a list of {}'.format(orientations))
|
||||
raise TypeError("Only instances of Orientation can be averaged.")
|
||||
|
||||
N = len(orientations)
|
||||
if multiplicity == [] or not multiplicity:
|
||||
multiplicity = np.ones(N,dtype='i')
|
||||
closest = []
|
||||
ref = orientations[0]
|
||||
for o in orientations:
|
||||
closest.append(o.equivalentOrientations(
|
||||
ref.disorientation(o,
|
||||
SST = False, # select (o[ther]'s) sym orientation
|
||||
symmetries = True)[2]).rotation) # with lowest misorientation
|
||||
|
||||
ref = orientations[0] # take first as reference
|
||||
for i,(o,n) in enumerate(zip(orientations,multiplicity)):
|
||||
closest = o.equivalentOrientations(ref.disorientation(o,SST=False,symmetries=True)[2])[0] # select sym orientation with lowest misorientation
|
||||
M = closest.rotation.asM() * n if i == 0 \
|
||||
else M + closest.rotation.asM() * n # noqa add (multiples) of this orientation to average noqa
|
||||
eig, vec = np.linalg.eig(M/N)
|
||||
|
||||
return Orientation(Rotation.fromQuaternion(np.real(vec.T[eig.argmax()]),acceptHomomorph = True),
|
||||
ref.lattice)
|
||||
return Orientation(Rotation.average(closest,weights),ref.lattice)
|
||||
|
||||
|
||||
####################################################################################################
|
||||
|
|
@ -1275,7 +1297,7 @@ def qu2ax(qu):
|
|||
return np.array(ax)
|
||||
|
||||
|
||||
def qu2ro(qu,vector=False):
|
||||
def qu2ro(qu):
|
||||
"""Quaternion to Rodrigues vector"""
|
||||
if iszero(qu[0]):
|
||||
ro = [qu[1], qu[2], qu[3], np.inf]
|
||||
|
|
@ -1284,7 +1306,7 @@ def qu2ro(qu,vector=False):
|
|||
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)))] # avoid numerical difficulties
|
||||
|
||||
return np.array(ro[:3])*ro[3] if vector else np.array(ro)
|
||||
return np.array(ro)
|
||||
|
||||
|
||||
def qu2ho(qu):
|
||||
|
|
@ -1354,9 +1376,9 @@ def om2qu(om):
|
|||
return ax2qu(om2ax(om))
|
||||
|
||||
|
||||
def om2ro(om,vector=False):
|
||||
def om2ro(om):
|
||||
"""Orientation matrix to Rodriques vector"""
|
||||
return eu2ro(om2eu(om,vector))
|
||||
return eu2ro(om2eu(om))
|
||||
|
||||
|
||||
def om2cu(om):
|
||||
|
|
@ -1404,7 +1426,7 @@ def eu2ax(eu):
|
|||
return ax
|
||||
|
||||
|
||||
def eu2ro(eu,vector=False):
|
||||
def eu2ro(eu):
|
||||
"""Euler angles to Rodrigues vector"""
|
||||
ro = eu2ax(eu) # convert to axis angle representation
|
||||
if ro[3] >= np.pi: # Differs from original implementation. check convention 5
|
||||
|
|
@ -1414,7 +1436,7 @@ def eu2ro(eu,vector=False):
|
|||
else:
|
||||
ro[3] = np.tan(ro[3]*0.5)
|
||||
|
||||
return ro[:3] * ro[3] if vector else ro
|
||||
return ro
|
||||
|
||||
|
||||
def eu2ho(eu):
|
||||
|
|
@ -1463,7 +1485,7 @@ def ax2om(ax):
|
|||
return om if P < 0.0 else om.T
|
||||
|
||||
|
||||
def ax2ro(ax,vector=False):
|
||||
def ax2ro(ax):
|
||||
"""Axis angle to Rodrigues vector"""
|
||||
if iszero(ax[3]):
|
||||
ro = [ 0.0, 0.0, P, 0.0 ]
|
||||
|
|
@ -1473,7 +1495,7 @@ def ax2ro(ax,vector=False):
|
|||
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[:3])*ro[3] if vector else np.array(ro)
|
||||
return np.array(ro)
|
||||
|
||||
|
||||
def ax2qu(ax):
|
||||
|
|
@ -1594,9 +1616,9 @@ def ho2om(ho):
|
|||
return ax2om(ho2ax(ho))
|
||||
|
||||
|
||||
def ho2ro(ho,vector=False):
|
||||
def ho2ro(ho):
|
||||
"""Axis angle to Rodriques vector"""
|
||||
return ax2ro(ho2ax(ho,vector))
|
||||
return ax2ro(ho2ax(ho))
|
||||
|
||||
|
||||
def ho2qu(ho):
|
||||
|
|
@ -1619,9 +1641,9 @@ def cu2ax(cu):
|
|||
return ho2ax(cu2ho(cu))
|
||||
|
||||
|
||||
def cu2ro(cu,vector=False):
|
||||
def cu2ro(cu):
|
||||
"""Cubochoric to Rodrigues vector"""
|
||||
return ho2ro(cu2ho(cu,vector))
|
||||
return ho2ro(cu2ho(cu))
|
||||
|
||||
|
||||
def cu2qu(cu):
|
||||
|
|
|
|||
Loading…
Reference in New Issue