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Merge branch 'vectorize_rotation' into 'development' 

Vectorize rotation

See merge request damask/DAMASK!162
This commit is contained in:
Karo 2020-04-27 15:26:44 +02:00
parent 40fd0040a9 97438713cc
commit 6be1b63944
7 changed files with 188 additions and 117 deletions
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2
processing/post/addOrientations.py
View File

@ -172,7 +172,7 @@ for name in filenames:
elif inputtype == 'matrix': elif inputtype == 'matrix':
d = representations['matrix'][1] d = representations['matrix'][1]
o = damask.Rotation.fromMatrix(list(map(float,table.data[column:column+d]))) o = damask.Rotation.fromMatrix(np.array(list(map(float,table.data[column:column+d]))).reshape(3,3))
elif inputtype == 'frame': elif inputtype == 'frame':
M = np.array(list(map(float,table.data[column[0]:column[0]+3] + \ M = np.array(list(map(float,table.data[column[0]:column[0]+3] + \

2
processing/post/addSchmidfactors.py
View File

@ -214,7 +214,7 @@ for name in filenames:
outputAlive = True outputAlive = True
while outputAlive and table.data_read(): # read next data line of ASCII table while outputAlive and table.data_read(): # read next data line of ASCII table
o = damask.Rotation(list(map(float,table.data[column:column+4]))) o = damask.Rotation(np.array(list(map(float,table.data[column:column+4]))))
table.data_append( np.abs( np.sum(slip_direction * (o * force) ,axis=1) \ table.data_append( np.abs( np.sum(slip_direction * (o * force) ,axis=1) \
* np.sum(slip_normal * (o * normal),axis=1))) * np.sum(slip_normal * (o * normal),axis=1)))

3
python/.coveragerc
View File

@ -1,2 +1,5 @@
[run] [run]
omit = tests/* omit = tests/*
damask/_asciitable.py
damask/_test.py
damask/config/*

3
python/damask/_orientation.py
View File

@ -38,6 +38,9 @@ class Orientation:
else: else:
self.rotation = Rotation.fromQuaternion(rotation) # assume quaternion self.rotation = Rotation.fromQuaternion(rotation) # assume quaternion
if self.rotation.quaternion.shape != (4,):
raise NotImplementedError('Support for multiple rotations missing')
def disorientation(self, def disorientation(self,
other, other,
SST = True, SST = True,

259
python/damask/_rotation.py
View File

@ -1,6 +1,7 @@
import numpy as np import numpy as np
from ._Lambert import ball_to_cube, cube_to_ball from ._Lambert import ball_to_cube, cube_to_ball
from . import mechanics
_P = -1 _P = -1
@ -61,6 +62,8 @@ class Rotation:
def __repr__(self): def __repr__(self):
"""Orientation displayed as unit quaternion, rotation matrix, and Bunge-Euler angles.""" """Orientation displayed as unit quaternion, rotation matrix, and Bunge-Euler angles."""
if self.quaternion.shape != (4,):
raise NotImplementedError('Support for multiple rotations missing')
return '\n'.join([ return '\n'.join([
'Quaternion: (real={:.3f}, imag=<{:+.3f}, {:+.3f}, {:+.3f}>)'.format(*(self.quaternion)), 'Quaternion: (real={:.3f}, imag=<{:+.3f}, {:+.3f}, {:+.3f}>)'.format(*(self.quaternion)),
'Matrix:\n{}'.format(self.asMatrix()), 'Matrix:\n{}'.format(self.asMatrix()),
@ -83,6 +86,8 @@ class Rotation:
considere rotation of (3,3,3,3)-matrix considere rotation of (3,3,3,3)-matrix
""" """
if self.quaternion.shape != (4,):
raise NotImplementedError('Support for multiple rotations missing')
if isinstance(other, Rotation): # rotate a rotation if isinstance(other, Rotation): # rotate a rotation
self_q = self.quaternion[0] self_q = self.quaternion[0]
self_p = self.quaternion[1:] self_p = self.quaternion[1:]
@ -107,7 +112,7 @@ class Rotation:
elif other.shape == (3,3,): # rotate a single (3x3)-matrix elif other.shape == (3,3,): # rotate a single (3x3)-matrix
return np.dot(self.asMatrix(),np.dot(other,self.asMatrix().T)) return np.dot(self.asMatrix(),np.dot(other,self.asMatrix().T))
elif other.shape == (3,3,3,3,): elif other.shape == (3,3,3,3,):
raise NotImplementedError raise NotImplementedError('Support for rotation of 4th order tensors missing')
else: else:
return NotImplemented return NotImplemented
else: else:
@ -116,7 +121,7 @@ class Rotation:
def inverse(self): def inverse(self):
"""In-place inverse rotation/backward rotation.""" """In-place inverse rotation/backward rotation."""
self.quaternion[1:] *= -1 self.quaternion[...,1:] *= -1
return self return self
def inversed(self): def inversed(self):
@ -125,12 +130,12 @@ class Rotation:
def standardize(self): def standardize(self):
"""In-place quaternion representation with positive q.""" """In-place quaternion representation with positive real part."""
if self.quaternion[0] < 0.0: self.quaternion*=-1 self.quaternion[self.quaternion[...,0] < 0.0] *= -1
return self return self
def standardized(self): def standardized(self):
"""Quaternion representation with positive q.""" """Quaternion representation with positive real part."""
return self.copy().standardize() return self.copy().standardize()
@ -157,15 +162,17 @@ class Rotation:
Rotation from which the average is rotated. 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.fromAverage([self,other]) return Rotation.fromAverage([self,other])
################################################################################################ ################################################################################################
# convert to different orientation representations (numpy arrays) # convert to different orientation representations (numpy arrays)
def asQuaternion(self): def as_quaternion(self):
""" """
Unit quaternion [q, p_1, p_2, p_3] unless quaternion == True: damask.quaternion object. Unit quaternion [q, p_1, p_2, p_3].
Parameters Parameters
---------- ----------
@ -175,8 +182,8 @@ class Rotation:
""" """
return self.quaternion return self.quaternion
def asEulers(self, def as_Eulers(self,
degrees = False): degrees = False):
""" """
Bunge-Euler angles: (φ_1, ϕ, φ_2). Bunge-Euler angles: (φ_1, ϕ, φ_2).
@ -190,9 +197,9 @@ class Rotation:
if degrees: eu = np.degrees(eu) if degrees: eu = np.degrees(eu)
return eu return eu
def asAxisAngle(self, def as_axis_angle(self,
degrees = False, degrees = False,
pair = False): pair = False):
""" """
Axis angle representation [n_1, n_2, n_3, ω] unless pair == True: ([n_1, n_2, n_3], ω). Axis angle representation [n_1, n_2, n_3, ω] unless pair == True: ([n_1, n_2, n_3], ω).
@ -205,15 +212,15 @@ class Rotation:
""" """
ax = Rotation.qu2ax(self.quaternion) ax = Rotation.qu2ax(self.quaternion)
if degrees: ax[3] = np.degrees(ax[3]) if degrees: ax[...,3] = np.degrees(ax[...,3])
return (ax[:3],ax[3]) if pair else ax return (ax[...,:3],ax[...,3]) if pair else ax
def asMatrix(self): def as_matrix(self):
"""Rotation matrix.""" """Rotation matrix."""
return Rotation.qu2om(self.quaternion) return Rotation.qu2om(self.quaternion)
def asRodrigues(self, def as_Rodrigues(self,
vector = False): 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). 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).
@ -224,9 +231,9 @@ class Rotation:
""" """
ro = Rotation.qu2ro(self.quaternion) ro = Rotation.qu2ro(self.quaternion)
return ro[:3]*ro[3] if vector else ro return ro[...,:3]*ro[...,3] if vector else ro
def asHomochoric(self): def as_homochoric(self):
"""Homochoric vector: (h_1, h_2, h_3).""" """Homochoric vector: (h_1, h_2, h_3)."""
return Rotation.qu2ho(self.quaternion) return Rotation.qu2ho(self.quaternion)
@ -234,7 +241,7 @@ class Rotation:
"""Cubochoric vector: (c_1, c_2, c_3).""" """Cubochoric vector: (c_1, c_2, c_3)."""
return Rotation.qu2cu(self.quaternion) return Rotation.qu2cu(self.quaternion)
def asM(self): 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. Intermediate representation supporting quaternion averaging.
@ -244,114 +251,133 @@ class Rotation:
https://doi.org/10.2514/1.28949 https://doi.org/10.2514/1.28949
""" """
return np.outer(self.quaternion,self.quaternion) return np.einsum('...i,...j',self.quaternion,self.quaternion)
# for compatibility (old names do not follow convention)
asM = M
asQuaternion = as_quaternion
asEulers = as_Eulers
asAxisAngle = as_axis_angle
asMatrix = as_matrix
asRodrigues = as_Rodrigues
asHomochoric = as_homochoric
################################################################################################ ################################################################################################
# static constructors. The input data needs to follow the convention, options allow to # Static constructors. The input data needs to follow the conventions, options allow to
# relax these convections # relax the conventions.
@staticmethod @staticmethod
def fromQuaternion(quaternion, def from_quaternion(quaternion,
acceptHomomorph = False, acceptHomomorph = False,
P = -1): P = -1):
qu = quaternion if isinstance(quaternion,np.ndarray) and quaternion.dtype == np.dtype(float) \ qu = np.array(quaternion,dtype=float)
else np.array(quaternion,dtype=float) if qu.shape[:-2:-1] != (4,):
if P > 0: qu[1:4] *= -1 # convert from P=1 to P=-1 raise ValueError('Invalid shape.')
if qu[0] < 0.0:
if acceptHomomorph: if P > 0: qu[...,1:4] *= -1 # convert from P=1 to P=-1
qu *= -1. if acceptHomomorph:
else: qu[qu[...,0] < 0.0] *= -1
raise ValueError('Quaternion has negative first component: {}.'.format(qu[0])) else:
if not np.isclose(np.linalg.norm(qu), 1.0): if np.any(qu[...,0] < 0.0):
raise ValueError('Quaternion is not of unit length: {} {} {} {}.'.format(*qu)) raise ValueError('Quaternion with negative first (real) component.')
if not np.all(np.isclose(np.linalg.norm(qu,axis=-1), 1.0)):
raise ValueError('Quaternion is not of unit length.')
return Rotation(qu) return Rotation(qu)
@staticmethod @staticmethod
def fromEulers(eulers, def from_Eulers(eulers,
degrees = False): degrees = False):
eu = np.array(eulers,dtype=float)
if eu.shape[:-2:-1] != (3,):
raise ValueError('Invalid shape.')
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 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: if np.any(eu < 0.0) or np.any(eu > 2.0*np.pi) or np.any(eu[...,1] > np.pi): # ToDo: No separate check for PHI
raise ValueError('Euler angles outside of [0..2π],[0..π],[0..2π]: {} {} {}.'.format(*eu)) raise ValueError('Euler angles outside of [0..2π],[0..π],[0..2π].')
return Rotation(Rotation.eu2qu(eu)) return Rotation(Rotation.eu2qu(eu))
@staticmethod @staticmethod
def fromAxisAngle(angleAxis, def from_axis_angle(axis_angle,
degrees = False, degrees = False,
normalise = False, normalise = False,
P = -1): P = -1):
ax = angleAxis if isinstance(angleAxis, np.ndarray) and angleAxis.dtype == np.dtype(float) \ ax = np.array(axis_angle,dtype=float)
else np.array(angleAxis,dtype=float) if ax.shape[:-2:-1] != (4,):
if P > 0: ax[0:3] *= -1 # convert from P=1 to P=-1 raise ValueError('Invalid shape.')
if degrees: ax[ 3] = np.radians(ax[3])
if normalise: ax[0:3] /= np.linalg.norm(ax[0:3]) if P > 0: ax[...,0:3] *= -1 # convert from P=1 to P=-1
if ax[3] < 0.0 or ax[3] > np.pi: if degrees: ax[..., 3] = np.radians(ax[...,3])
raise ValueError('Axis angle rotation angle outside of [0..π]: {}.'.format(ax[3])) if normalise: ax[...,0:3] /= np.linalg.norm(ax[...,0:3],axis=-1)
if not np.isclose(np.linalg.norm(ax[0:3]), 1.0): if np.any(ax[...,3] < 0.0) or np.any(ax[...,3] > np.pi):
raise ValueError('Axis angle rotation axis is not of unit length: {} {} {}.'.format(*ax[0:3])) raise ValueError('Axis angle rotation angle outside of [0..π].')
if not np.all(np.isclose(np.linalg.norm(ax[...,0:3],axis=-1), 1.0)):
raise ValueError('Axis angle rotation axis is not of unit length.')
return Rotation(Rotation.ax2qu(ax)) return Rotation(Rotation.ax2qu(ax))
@staticmethod @staticmethod
def fromBasis(basis, def from_basis(basis,
orthonormal = True, orthonormal = True,
reciprocal = False, reciprocal = False):
):
om = np.array(basis,dtype=float)
if om.shape[:-3:-1] != (3,3):
raise ValueError('Invalid shape.')
om = basis if isinstance(basis, np.ndarray) else np.array(basis).reshape(3,3)
if reciprocal: if reciprocal:
om = np.linalg.inv(om.T/np.pi) # transform reciprocal basis set om = np.linalg.inv(mechanics.transpose(om)/np.pi) # transform reciprocal basis set
orthonormal = False # contains stretch orthonormal = False # contains stretch
if not orthonormal: if not orthonormal:
(U,S,Vh) = np.linalg.svd(om) # singular value decomposition (U,S,Vh) = np.linalg.svd(om) # singular value decomposition
om = np.dot(U,Vh) om = np.einsum('...ij,...jl->...il',U,Vh)
if not np.isclose(np.linalg.det(om),1.0): if not np.all(np.isclose(np.linalg.det(om),1.0)):
raise ValueError('matrix is not a proper rotation: {}.'.format(om)) raise ValueError('Orientation matrix has determinant ≠ 1.')
if not np.isclose(np.dot(om[0],om[1]), 0.0) \ if not np.all(np.isclose(np.einsum('...i,...i',om[...,0],om[...,1]), 0.0)) \
or not np.isclose(np.dot(om[1],om[2]), 0.0) \ or not np.all(np.isclose(np.einsum('...i,...i',om[...,1],om[...,2]), 0.0)) \
or not np.isclose(np.dot(om[2],om[0]), 0.0): or not np.all(np.isclose(np.einsum('...i,...i',om[...,2],om[...,0]), 0.0)):
raise ValueError('matrix is not orthogonal: {}.'.format(om)) raise ValueError('Orientation matrix is not orthogonal.')
return Rotation(Rotation.om2qu(om)) return Rotation(Rotation.om2qu(om))
@staticmethod @staticmethod
def fromMatrix(om, def from_matrix(om):
):
return Rotation.fromBasis(om) return Rotation.from_basis(om)
@staticmethod @staticmethod
def fromRodrigues(rodrigues, def from_Rodrigues(rodrigues,
normalise = False, normalise = False,
P = -1): P = -1):
ro = rodrigues if isinstance(rodrigues, np.ndarray) and rodrigues.dtype == np.dtype(float) \ ro = np.array(rodrigues,dtype=float)
else np.array(rodrigues,dtype=float) if ro.shape[:-2:-1] != (4,):
if P > 0: ro[0:3] *= -1 # convert from P=1 to P=-1 raise ValueError('Invalid shape.')
if normalise: ro[0:3] /= np.linalg.norm(ro[0:3])
if not np.isclose(np.linalg.norm(ro[0:3]), 1.0): if P > 0: ro[...,0:3] *= -1 # convert from P=1 to P=-1
raise ValueError('Rodrigues rotation axis is not of unit length: {} {} {}.'.format(*ro[0:3])) if normalise: ro[...,0:3] /= np.linalg.norm(ro[...,0:3],axis=-1)
if ro[3] < 0.0: if np.any(ro[...,3] < 0.0):
raise ValueError('Rodrigues rotation angle not positive: {}.'.format(ro[3])) raise ValueError('Rodrigues vector rotation angle not positive.')
if not np.all(np.isclose(np.linalg.norm(ro[...,0:3],axis=-1), 1.0)):
raise ValueError('Rodrigues vector rotation axis is not of unit length.')
return Rotation(Rotation.ro2qu(ro)) return Rotation(Rotation.ro2qu(ro))
@staticmethod @staticmethod
def fromHomochoric(homochoric, def from_homochoric(homochoric,
P = -1): P = -1):
ho = np.array(homochoric,dtype=float)
if ho.shape[:-2:-1] != (3,):
raise ValueError('Invalid shape.')
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 if P > 0: ho *= -1 # convert from P=1 to P=-1
if np.linalg.norm(ho) > (3.*np.pi/4.)**(1./3.)+1e-9: if np.any(np.linalg.norm(ho,axis=-1) > (3.*np.pi/4.)**(1./3.)+1e-9):
raise ValueError('Coordinate outside of the sphere: {} {} {}.'.format(ho)) raise ValueError('Homochoric coordinate outside of the sphere.')
return Rotation(Rotation.ho2qu(ho)) return Rotation(Rotation.ho2qu(ho))
@ -359,11 +385,12 @@ class Rotation:
def fromCubochoric(cubochoric, def fromCubochoric(cubochoric,
P = -1): P = -1):
cu = cubochoric if isinstance(cubochoric, np.ndarray) and cubochoric.dtype == np.dtype(float) \ cu = np.array(cubochoric,dtype=float)
else np.array(cubochoric,dtype=float) if cu.shape[:-2:-1] != (3,):
raise ValueError('Invalid shape.')
if np.abs(np.max(cu))>np.pi**(2./3.) * 0.5+1e-9: if np.abs(np.max(cu))>np.pi**(2./3.) * 0.5+1e-9:
raise ValueError('Coordinate outside of the cube: {} {} {}.'.format(*cu)) raise ValueError('Cubochoric coordinate outside of the cube: {} {} {}.'.format(*cu))
ho = Rotation.cu2ho(cu) ho = Rotation.cu2ho(cu)
if P > 0: ho *= -1 # convert from P=1 to P=-1 if P > 0: ho *= -1 # convert from P=1 to P=-1
@ -403,17 +430,34 @@ class Rotation:
return Rotation.fromQuaternion(np.real(vec.T[eig.argmax()]),acceptHomomorph = True) return Rotation.fromQuaternion(np.real(vec.T[eig.argmax()]),acceptHomomorph = True)
@staticmethod @staticmethod
def fromRandom(): def from_random(shape=None):
r = np.random.random(3) if shape is None:
A = np.sqrt(r[2]) r = np.random.random(3)
B = np.sqrt(1.0-r[2]) elif hasattr(shape, '__iter__'):
return Rotation(np.array([np.cos(2.0*np.pi*r[0])*A, r = np.random.random(tuple(shape)+(3,))
np.sin(2.0*np.pi*r[1])*B, else:
np.cos(2.0*np.pi*r[1])*B, r = np.random.random((shape,3))
np.sin(2.0*np.pi*r[0])*A])).standardize()
A = np.sqrt(r[...,2])
B = np.sqrt(1.0-r[...,2])
q = np.stack([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],axis=-1)
return Rotation(q.reshape(r.shape[:-1]+(4,)) if shape is not None else q).standardize()
# for compatibility (old names do not follow convention)
fromQuaternion = from_quaternion
fromEulers = from_Eulers
fromAxisAngle = from_axis_angle
fromBasis = from_basis
fromMatrix = from_matrix
fromRodrigues = from_Rodrigues
fromHomochoric = from_homochoric
fromRandom = from_random
#################################################################################################### ####################################################################################################
# Code below available according to the following conditions on https://github.com/MarDiehl/3Drotations # Code below available according to the following conditions on https://github.com/MarDiehl/3Drotations
@ -808,12 +852,11 @@ class Rotation:
c = np.cos(ax[3]*0.5) c = np.cos(ax[3]*0.5)
s = np.sin(ax[3]*0.5) s = np.sin(ax[3]*0.5)
qu = np.array([ c, ax[0]*s, ax[1]*s, ax[2]*s ]) qu = np.array([ c, ax[0]*s, ax[1]*s, ax[2]*s ])
return qu
else: else:
c = np.cos(ax[...,3:4]*.5) c = np.cos(ax[...,3:4]*.5)
s = np.sin(ax[...,3:4]*.5) s = np.sin(ax[...,3:4]*.5)
qu = np.where(np.abs(ax[...,3:4])<1.e-6,[1.0, 0.0, 0.0, 0.0],np.block([c, ax[...,:3]*s])) qu = np.where(np.abs(ax[...,3:4])<1.e-6,[1.0, 0.0, 0.0, 0.0],np.block([c, ax[...,:3]*s]))
return qu return qu
@staticmethod @staticmethod
def ax2om(ax): def ax2om(ax):
@ -859,7 +902,7 @@ class Rotation:
# 180 degree case # 180 degree case
ro += [np.inf] if np.isclose(ax[3],np.pi,atol=1.0e-15,rtol=0.0) else \ ro += [np.inf] if np.isclose(ax[3],np.pi,atol=1.0e-15,rtol=0.0) else \
[np.tan(ax[3]*0.5)] [np.tan(ax[3]*0.5)]
return np.array(ro) ro = np.array(ro)
else: else:
ro = np.block([ax[...,:3], ro = np.block([ax[...,:3],
np.where(np.isclose(ax[...,3:4],np.pi,atol=1.e-15,rtol=.0), np.where(np.isclose(ax[...,3:4],np.pi,atol=1.e-15,rtol=.0),
@ -867,7 +910,7 @@ class Rotation:
np.tan(ax[...,3:4]*0.5)) np.tan(ax[...,3:4]*0.5))
]) ])
ro[np.abs(ax[...,3])<1.e-6] = [.0,.0,_P,.0] ro[np.abs(ax[...,3])<1.e-6] = [.0,.0,_P,.0]
return ro return ro
@staticmethod @staticmethod
def ax2ho(ax): def ax2ho(ax):
@ -875,11 +918,10 @@ class Rotation:
if len(ax.shape) == 1: if len(ax.shape) == 1:
f = (0.75 * ( ax[3] - np.sin(ax[3]) ))**(1.0/3.0) f = (0.75 * ( ax[3] - np.sin(ax[3]) ))**(1.0/3.0)
ho = ax[0:3] * f ho = ax[0:3] * f
return ho
else: else:
f = (0.75 * ( ax[...,3:4] - np.sin(ax[...,3:4]) ))**(1.0/3.0) f = (0.75 * ( ax[...,3:4] - np.sin(ax[...,3:4]) ))**(1.0/3.0)
ho = ax[...,:3] * f ho = ax[...,:3] * f
return ho return ho
@staticmethod @staticmethod
def ax2cu(ax): def ax2cu(ax):
@ -936,7 +978,6 @@ class Rotation:
f = np.where(np.isfinite(ro[...,3:4]),2.0*np.arctan(ro[...,3:4]) -np.sin(2.0*np.arctan(ro[...,3:4])),np.pi) f = np.where(np.isfinite(ro[...,3:4]),2.0*np.arctan(ro[...,3:4]) -np.sin(2.0*np.arctan(ro[...,3:4])),np.pi)
ho = np.where(np.broadcast_to(np.sum(ro[...,0:3]**2.0,axis=-1,keepdims=True) < 1.e-6,ro[...,0:3].shape), ho = np.where(np.broadcast_to(np.sum(ro[...,0:3]**2.0,axis=-1,keepdims=True) < 1.e-6,ro[...,0:3].shape),
np.zeros(3), ro[...,0:3]* (0.75*f)**(1.0/3.0)) np.zeros(3), ro[...,0:3]* (0.75*f)**(1.0/3.0))
return ho return ho
@staticmethod @staticmethod
@ -1010,7 +1051,7 @@ class Rotation:
if len(ho.shape) == 1: if len(ho.shape) == 1:
return ball_to_cube(ho) return ball_to_cube(ho)
else: else:
raise NotImplementedError raise NotImplementedError('Support for multiple rotations missing')
#---------- Cubochoric ---------- #---------- Cubochoric ----------
@ -1045,4 +1086,4 @@ class Rotation:
if len(cu.shape) == 1: if len(cu.shape) == 1:
return cube_to_ball(cu) return cube_to_ball(cu)
else: else:
raise NotImplementedError raise NotImplementedError('Support for multiple rotations missing')

12
python/damask/mechanics.py
View File

@ -135,16 +135,16 @@ def PK2(P,F):
Parameters Parameters
---------- ----------
P : numpy.ndarray of shape (:,3,3) or (3,3) P : numpy.ndarray of shape (...,3,3) or (3,3)
First Piola-Kirchhoff stress. First Piola-Kirchhoff stress.
F : numpy.ndarray of shape (:,3,3) or (3,3) F : numpy.ndarray of shape (...,3,3) or (3,3)
Deformation gradient. Deformation gradient.
""" """
if _np.shape(F) == _np.shape(P) == (3,3): if _np.shape(F) == _np.shape(P) == (3,3):
S = _np.dot(_np.linalg.inv(F),P) S = _np.dot(_np.linalg.inv(F),P)
else: else:
S = _np.einsum('ijk,ikl->ijl',_np.linalg.inv(F),P) S = _np.einsum('...jk,...kl->...jl',_np.linalg.inv(F),P)
return symmetric(S) return symmetric(S)
@ -241,7 +241,7 @@ def symmetric(T):
Parameters Parameters
---------- ----------
T : numpy.ndarray of shape (:,3,3) or (3,3) T : numpy.ndarray of shape (...,3,3) or (3,3)
Tensor of which the symmetrized values are computed. Tensor of which the symmetrized values are computed.
""" """
@ -254,12 +254,12 @@ def transpose(T):
Parameters Parameters
---------- ----------
T : numpy.ndarray of shape (:,3,3) or (3,3) T : numpy.ndarray of shape (...,3,3) or (3,3)
Tensor of which the transpose is computed. Tensor of which the transpose is computed.
""" """
return T.T if _np.shape(T) == (3,3) else \ return T.T if _np.shape(T) == (3,3) else \
_np.transpose(T,(0,2,1)) _np.swapaxes(T,axis2=-2,axis1=-1)
def _polar_decomposition(T,requested): def _polar_decomposition(T,requested):

24
python/tests/test_Rotation.py
View File

@ -157,6 +157,30 @@ class TestRotation:
print(m,o,rot.asQuaternion()) print(m,o,rot.asQuaternion())
assert ok and o.max() < np.pi**(2./3.)*0.5+1.e-9 assert ok and o.max() < np.pi**(2./3.)*0.5+1.e-9
@pytest.mark.parametrize('function',[Rotation.from_quaternion,
Rotation.from_Eulers,
Rotation.from_axis_angle,
Rotation.from_matrix,
Rotation.from_Rodrigues,
Rotation.from_homochoric])
def test_invalid_shape(self,function):
invalid_shape = np.random.random(np.random.randint(8,32,(3)))
with pytest.raises(ValueError):
function(invalid_shape)
@pytest.mark.parametrize('function,invalid',[(Rotation.from_quaternion, np.array([-1,0,0,0])),
(Rotation.from_quaternion, np.array([1,1,1,0])),
(Rotation.from_Eulers, np.array([1,4,0])),
(Rotation.from_axis_angle, np.array([1,0,0,4])),
(Rotation.from_axis_angle, np.array([1,1,0,1])),
(Rotation.from_matrix, np.random.rand(3,3)),
(Rotation.from_Rodrigues, np.array([1,0,0,-1])),
(Rotation.from_Rodrigues, np.array([1,1,0,1])),
(Rotation.from_homochoric, np.array([2,2,2])) ])
def test_invalid(self,function,invalid):
with pytest.raises(ValueError):
function(invalid)
@pytest.mark.parametrize('conversion',[Rotation.qu2om, @pytest.mark.parametrize('conversion',[Rotation.qu2om,
Rotation.qu2eu, Rotation.qu2eu,
Rotation.qu2ax, Rotation.qu2ax,