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DAMASK_EICMD
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most functions require only lattice family, functions that require full
lattice details are at the end
This commit is contained in:
Martin Diehl 2021-06-02 17:25:24 +02:00
parent 302da1f76a
commit 87e94b6cf4
1 changed files with 189 additions and 188 deletions
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377
python/damask/_orientation.py
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@ -132,7 +132,7 @@ class Orientation(Rotation):
"""
super().__init__(rotation)
if family in set(lattice_symmetries.values()) and lattice is None:
if family in set(lattice_symmetries.values()) and lattice is None:
self.family = family
self.lattice = None
@ -178,6 +178,11 @@ class Orientation(Rotation):
+ ([f'Crystal family {self.family}'])
+ [super().__repr__()])
@property
def parameters(self):
"""Return lattice parameters a, b, c, alpha, beta, gamma."""
return (self.a,self.b,self.c,self.alpha,self.beta,self.gamma)
def __copy__(self,**kwargs):
"""Create deep copy."""
@ -533,193 +538,6 @@ class Orientation(Rotation):
return np.ones_like(rho[...,0],dtype=bool)
def relation_operations(self,model,return_lattice=False):
"""
Crystallographic orientation relationships for phase transformations.
Parameters
----------
model : str
Name of orientation relationship.
return_lattice : bool, optional
Return the target lattice in addition.
Returns
-------
operations : Rotations
Rotations characterizing the orientation relationship.
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
"""
if model not in self.orientation_relationships:
raise KeyError(f'unknown orientation relationship "{model}"')
r = self.orientation_relationships[model]
sl = self.lattice
ol = (set(r)-{sl}).pop()
m = r[sl]
o = r[ol]
p_,_p = np.zeros(m.shape[:-1]+(3,)),np.zeros(o.shape[:-1]+(3,))
p_[...,0,:] = m[...,0,:] if m.shape[-1] == 3 else util.Bravais_to_Miller(uvtw=m[...,0,0:4])
p_[...,1,:] = m[...,1,:] if m.shape[-1] == 3 else util.Bravais_to_Miller(hkil=m[...,1,0:4])
_p[...,0,:] = o[...,0,:] if o.shape[-1] == 3 else util.Bravais_to_Miller(uvtw=o[...,0,0:4])
_p[...,1,:] = o[...,1,:] if o.shape[-1] == 3 else util.Bravais_to_Miller(hkil=o[...,1,0:4])
return (Rotation.from_parallel(p_,_p),ol) \
if return_lattice else \
Rotation.from_parallel(p_,_p)
def related(self,model):
"""
Orientations derived from the given relationship.
One dimension (length according to number of related orientations)
is added to the left of the Rotation array.
"""
o,lattice = self.relation_operations(model,return_lattice=True)
target = Orientation(lattice=lattice)
o = o.broadcast_to(o.shape+self.shape,mode='right')
return self.copy(rotation=o*Rotation(self.quaternion).broadcast_to(o.shape,mode='left'),
lattice=lattice,
b = self.b if target.ratio['b'] is None else self.a*target.ratio['b'],
c = self.c if target.ratio['c'] is None else self.a*target.ratio['c'],
alpha = None if 'alpha' in target.immutable else self.alpha,
beta = None if 'beta' in target.immutable else self.beta,
gamma = None if 'gamma' in target.immutable else self.gamma,
)
@property
def parameters(self):
"""Return lattice parameters a, b, c, alpha, beta, gamma."""
return (self.a,self.b,self.c,self.alpha,self.beta,self.gamma)
def in_SST(self,vector,proper=False):
"""
Check whether given crystal frame vector falls into standard stereographic triangle of own symmetry.
Parameters
----------
vector : numpy.ndarray of shape (...,3)
Vector to check.
proper : bool, optional
Consider only vectors with z >= 0, hence combine two neighboring SSTs.
Defaults to False.
Returns
-------
in : numpy.ndarray of shape (...)
Boolean array indicating whether vector falls into SST.
"""
if not isinstance(vector,np.ndarray) or vector.shape[-1] != 3:
raise ValueError('input is not a field of three-dimensional vectors')
if self.basis is None: # direct exit for no symmetry
return np.ones_like(vector[...,0],bool)
if proper:
components_proper = np.around(np.einsum('...ji,...i',
np.broadcast_to(self.basis['proper'], vector.shape+(3,)),
vector), 12)
components_improper = np.around(np.einsum('...ji,...i',
np.broadcast_to(self.basis['improper'], vector.shape+(3,)),
vector), 12)
return np.all(components_proper >= 0.0,axis=-1) \
| np.all(components_improper >= 0.0,axis=-1)
else:
components = np.around(np.einsum('...ji,...i',
np.broadcast_to(self.basis['improper'], vector.shape+(3,)),
np.block([vector[...,:2],np.abs(vector[...,2:3])])), 12)
return np.all(components >= 0.0,axis=-1)
def IPF_color(self,vector,in_SST=True,proper=False):
"""
Map vector to RGB color within standard stereographic triangle of own symmetry.
Parameters
----------
vector : numpy.ndarray of shape (...,3)
Vector to colorize.
in_SST : bool, optional
Consider symmetrically equivalent orientations such that poles are located in SST.
Defaults to True.
proper : bool, optional
Consider only vectors with z >= 0, hence combine two neighboring SSTs (with mirrored colors).
Defaults to False.
Returns
-------
rgb : numpy.ndarray of shape (...,3)
RGB array of IPF colors.
Examples
--------
Inverse pole figure color of the e_3 direction for a crystal in "Cube" orientation with cubic symmetry:
>>> o = damask.Orientation(lattice='cubic')
>>> o.IPF_color([0,0,1])
array([1., 0., 0.])
"""
if np.array(vector).shape[-1] != 3:
raise ValueError('input is not a field of three-dimensional vectors')
vector_ = self.to_SST(vector,proper) if in_SST else \
self @ np.broadcast_to(vector,self.shape+(3,))
if self.basis is None: # direct exit for no symmetry
return np.zeros_like(vector_)
if proper:
components_proper = np.around(np.einsum('...ji,...i',
np.broadcast_to(self.basis['proper'], vector_.shape+(3,)),
vector_), 12)
components_improper = np.around(np.einsum('...ji,...i',
np.broadcast_to(self.basis['improper'], vector_.shape+(3,)),
vector_), 12)
in_SST = np.all(components_proper >= 0.0,axis=-1) \
| np.all(components_improper >= 0.0,axis=-1)
components = np.where((in_SST & np.all(components_proper >= 0.0,axis=-1))[...,np.newaxis],
components_proper,components_improper)
else:
components = np.around(np.einsum('...ji,...i',
np.broadcast_to(self.basis['improper'], vector_.shape+(3,)),
np.block([vector_[...,:2],np.abs(vector_[...,2:3])])), 12)
in_SST = np.all(components >= 0.0,axis=-1)
with np.errstate(invalid='ignore',divide='ignore'):
rgb = (components/np.linalg.norm(components,axis=-1,keepdims=True))**0.5 # smoothen color ramps
rgb = np.clip(rgb,0.,1.) # clip intensity
rgb /= np.max(rgb,axis=-1,keepdims=True) # normalize to (HS)V = 1
rgb[np.broadcast_to(~in_SST[...,np.newaxis],rgb.shape)] = 0.0
return rgb
def disorientation(self,other,return_operators=False):
"""
Calculate disorientation between myself and given other orientation.
@ -874,6 +692,114 @@ class Orientation(Rotation):
)
def in_SST(self,vector,proper=False):
"""
Check whether given crystal frame vector falls into standard stereographic triangle of own symmetry.
Parameters
----------
vector : numpy.ndarray of shape (...,3)
Vector to check.
proper : bool, optional
Consider only vectors with z >= 0, hence combine two neighboring SSTs.
Defaults to False.
Returns
-------
in : numpy.ndarray of shape (...)
Boolean array indicating whether vector falls into SST.
"""
if not isinstance(vector,np.ndarray) or vector.shape[-1] != 3:
raise ValueError('input is not a field of three-dimensional vectors')
if self.basis is None: # direct exit for no symmetry
return np.ones_like(vector[...,0],bool)
if proper:
components_proper = np.around(np.einsum('...ji,...i',
np.broadcast_to(self.basis['proper'], vector.shape+(3,)),
vector), 12)
components_improper = np.around(np.einsum('...ji,...i',
np.broadcast_to(self.basis['improper'], vector.shape+(3,)),
vector), 12)
return np.all(components_proper >= 0.0,axis=-1) \
| np.all(components_improper >= 0.0,axis=-1)
else:
components = np.around(np.einsum('...ji,...i',
np.broadcast_to(self.basis['improper'], vector.shape+(3,)),
np.block([vector[...,:2],np.abs(vector[...,2:3])])), 12)
return np.all(components >= 0.0,axis=-1)
def IPF_color(self,vector,in_SST=True,proper=False):
"""
Map vector to RGB color within standard stereographic triangle of own symmetry.
Parameters
----------
vector : numpy.ndarray of shape (...,3)
Vector to colorize.
in_SST : bool, optional
Consider symmetrically equivalent orientations such that poles are located in SST.
Defaults to True.
proper : bool, optional
Consider only vectors with z >= 0, hence combine two neighboring SSTs (with mirrored colors).
Defaults to False.
Returns
-------
rgb : numpy.ndarray of shape (...,3)
RGB array of IPF colors.
Examples
--------
Inverse pole figure color of the e_3 direction for a crystal in "Cube" orientation with cubic symmetry:
>>> o = damask.Orientation(lattice='cubic')
>>> o.IPF_color([0,0,1])
array([1., 0., 0.])
"""
if np.array(vector).shape[-1] != 3:
raise ValueError('input is not a field of three-dimensional vectors')
vector_ = self.to_SST(vector,proper) if in_SST else \
self @ np.broadcast_to(vector,self.shape+(3,))
if self.basis is None: # direct exit for no symmetry
return np.zeros_like(vector_)
if proper:
components_proper = np.around(np.einsum('...ji,...i',
np.broadcast_to(self.basis['proper'], vector_.shape+(3,)),
vector_), 12)
components_improper = np.around(np.einsum('...ji,...i',
np.broadcast_to(self.basis['improper'], vector_.shape+(3,)),
vector_), 12)
in_SST = np.all(components_proper >= 0.0,axis=-1) \
| np.all(components_improper >= 0.0,axis=-1)
components = np.where((in_SST & np.all(components_proper >= 0.0,axis=-1))[...,np.newaxis],
components_proper,components_improper)
else:
components = np.around(np.einsum('...ji,...i',
np.broadcast_to(self.basis['improper'], vector_.shape+(3,)),
np.block([vector_[...,:2],np.abs(vector_[...,2:3])])), 12)
in_SST = np.all(components >= 0.0,axis=-1)
with np.errstate(invalid='ignore',divide='ignore'):
rgb = (components/np.linalg.norm(components,axis=-1,keepdims=True))**0.5 # smoothen color ramps
rgb = np.clip(rgb,0.,1.) # clip intensity
rgb /= np.max(rgb,axis=-1,keepdims=True) # normalize to (HS)V = 1
rgb[np.broadcast_to(~in_SST[...,np.newaxis],rgb.shape)] = 0.0
return rgb
# functions that require lattice, not just family
def to_pole(self,*,uvw=None,hkl=None,with_symmetry=False):
"""
Calculate lab frame vector along lattice direction [uvw] or plane normal (hkl).
@ -938,3 +864,78 @@ class Orientation(Rotation):
return ~self.broadcast_to( self.shape+P.shape[:-2],mode='right') \
@ np.broadcast_to(P,self.shape+P.shape)
def relation_operations(self,model,return_lattice=False):
"""
Crystallographic orientation relationships for phase transformations.
Parameters
----------
model : str
Name of orientation relationship.
return_lattice : bool, optional
Return the target lattice in addition.
Returns
-------
operations : Rotations
Rotations characterizing the orientation relationship.
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
"""
if model not in self.orientation_relationships:
raise KeyError(f'unknown orientation relationship "{model}"')
r = self.orientation_relationships[model]
sl = self.lattice
ol = (set(r)-{sl}).pop()
m = r[sl]
o = r[ol]
p_,_p = np.zeros(m.shape[:-1]+(3,)),np.zeros(o.shape[:-1]+(3,))
p_[...,0,:] = m[...,0,:] if m.shape[-1] == 3 else util.Bravais_to_Miller(uvtw=m[...,0,0:4])
p_[...,1,:] = m[...,1,:] if m.shape[-1] == 3 else util.Bravais_to_Miller(hkil=m[...,1,0:4])
_p[...,0,:] = o[...,0,:] if o.shape[-1] == 3 else util.Bravais_to_Miller(uvtw=o[...,0,0:4])
_p[...,1,:] = o[...,1,:] if o.shape[-1] == 3 else util.Bravais_to_Miller(hkil=o[...,1,0:4])
return (Rotation.from_parallel(p_,_p),ol) \
if return_lattice else \
Rotation.from_parallel(p_,_p)
def related(self,model):
"""
Orientations derived from the given relationship.
One dimension (length according to number of related orientations)
is added to the left of the Rotation array.
"""
o,lattice = self.relation_operations(model,return_lattice=True)
target = Orientation(lattice=lattice)
o = o.broadcast_to(o.shape+self.shape,mode='right')
return self.copy(rotation=o*Rotation(self.quaternion).broadcast_to(o.shape,mode='left'),
lattice=lattice,
b = self.b if target.ratio['b'] is None else self.a*target.ratio['b'],
c = self.c if target.ratio['c'] is None else self.a*target.ratio['c'],
alpha = None if 'alpha' in target.immutable else self.alpha,
beta = None if 'beta' in target.immutable else self.beta,
gamma = None if 'gamma' in target.immutable else self.gamma,
)