From cef885cfde9b3673f5241ad480558c38bb48273b Mon Sep 17 00:00:00 2001
From: Daniel Otto de Mentock <daniel.mentock@mpie.de>
Date: Tue, 14 Dec 2021 17:05:00 +0100
Subject: [PATCH 01/72] added first typehints for rotation and orientation
 modules

---
 python/damask/_orientation.py | 136 ++++++++++--------
 python/damask/_rotation.py    | 251 ++++++++++++++++++----------------
 2 files changed, 211 insertions(+), 176 deletions(-)

diff --git a/python/damask/_orientation.py b/python/damask/_orientation.py
index e727c54ae..6c0dd2fa3 100644
--- a/python/damask/_orientation.py
+++ b/python/damask/_orientation.py
@@ -1,5 +1,6 @@
 import inspect
 import copy
+from typing import Union, Callable, Sequence, Dict, Any, Tuple, List
 
 import numpy as np
 
@@ -93,12 +94,12 @@ class Orientation(Rotation,Crystal):
 
     @util.extend_docstring(_parameter_doc)
     def __init__(self,
-                 rotation = np.array([1.0,0.0,0.0,0.0]), *,
-                 family = None,
-                 lattice = None,
-                 a = None,b = None,c = None,
-                 alpha = None,beta = None,gamma = None,
-                 degrees = False):
+                 rotation: Union[Sequence[float], np.ndarray, Rotation] = np.array([1.,0.,0.,0.]), *,
+                 family: str = None,
+                 lattice: str = None,
+                 a: float = None, b: float = None, c: float = None,
+                 alpha: float = None, beta: float = None, gamma: float = None,
+                 degrees: bool = False):
         """
         New orientation.
 
@@ -115,13 +116,12 @@ class Orientation(Rotation,Crystal):
                               a=a,b=b,c=c, alpha=alpha,beta=beta,gamma=gamma, degrees=degrees)
 
 
-    def __repr__(self):
+    def __repr__(self) -> str:
         """Represent."""
         return '\n'.join([Crystal.__repr__(self),
                           Rotation.__repr__(self)])
 
-
-    def __copy__(self,rotation=None):
+    def __copy__(self,rotation: Union[Sequence[float], np.ndarray, Rotation] = None) -> "Orientation":
         """Create deep copy."""
         dup = copy.deepcopy(self)
         if rotation is not None:
@@ -131,7 +131,8 @@ class Orientation(Rotation,Crystal):
     copy = __copy__
 
 
-    def __eq__(self,other):
+
+    def __eq__(self, other: object) -> bool:
         """
         Equal to other.
 
@@ -141,12 +142,14 @@ class Orientation(Rotation,Crystal):
             Orientation to check for equality.
 
         """
+        if not isinstance(other, Orientation):
+            raise TypeError
         matching_type = self.family == other.family and \
                         self.lattice == other.lattice and \
                         self.parameters == other.parameters
         return np.logical_and(matching_type,super(self.__class__,self.reduced).__eq__(other.reduced))
 
-    def __ne__(self,other):
+    def __ne__(self, other: object) -> bool:
         """
         Not equal to other.
 
@@ -156,10 +159,16 @@ class Orientation(Rotation,Crystal):
             Orientation to check for equality.
 
         """
+        if not isinstance(other, Orientation):
+            raise TypeError
         return np.logical_not(self==other)
 
 
-    def isclose(self,other,rtol=1e-5,atol=1e-8,equal_nan=True):
+    def isclose(self,
+                other: object,
+                rtol: float = 1e-5,
+                atol: float = 1e-8,
+                equal_nan: bool = True) -> bool:
         """
         Report where values are approximately equal to corresponding ones of other Orientation.
 
@@ -180,6 +189,8 @@ class Orientation(Rotation,Crystal):
             Mask indicating where corresponding orientations are close.
 
         """
+        if not isinstance(other, Orientation):
+            raise TypeError
         matching_type = self.family == other.family and \
                         self.lattice == other.lattice and \
                         self.parameters == other.parameters
@@ -187,7 +198,11 @@ class Orientation(Rotation,Crystal):
 
 
 
-    def allclose(self,other,rtol=1e-5,atol=1e-8,equal_nan=True):
+    def allclose(self,
+                 other: object,
+                 rtol: float = 1e-5,
+                 atol: float = 1e-8,
+                 equal_nan: bool = True) -> Union[bool, np.bool_]:
         """
         Test whether all values are approximately equal to corresponding ones of other Orientation.
 
@@ -208,10 +223,12 @@ class Orientation(Rotation,Crystal):
             Whether all values are close between both orientations.
 
         """
+        if not isinstance(other, Orientation):
+            raise TypeError
         return np.all(self.isclose(other,rtol,atol,equal_nan))
 
 
-    def __mul__(self,other):
+    def __mul__(self, other: Union[Rotation, "Orientation"]) -> "Orientation":
         """
         Compose this orientation with other.
 
@@ -233,7 +250,7 @@ class Orientation(Rotation,Crystal):
 
 
     @staticmethod
-    def _split_kwargs(kwargs,target):
+    def _split_kwargs(kwargs: Dict[str, Any], target: Callable) -> Tuple[Dict[str, Any], ...]:
         """
         Separate keyword arguments in 'kwargs' targeted at 'target' from general keyword arguments of Orientation objects.
 
@@ -252,7 +269,7 @@ class Orientation(Rotation,Crystal):
             Valid keyword arguments of Orientation object.
 
         """
-        kws = ()
+        kws: Tuple[Dict[str, Any], ...] = ()
         for t in (target,Orientation.__init__):
             kws += ({key: kwargs[key] for key in set(inspect.signature(t).parameters) & set(kwargs)},)
 
@@ -264,85 +281,88 @@ class Orientation(Rotation,Crystal):
 
 
     @classmethod
-    @util.extended_docstring(Rotation.from_random,_parameter_doc)
-    def from_random(cls,**kwargs):
+    @util.extended_docstring(Rotation.from_random, _parameter_doc)
+    def from_random(cls, **kwargs) -> "Orientation":
         kwargs_rot,kwargs_ori = Orientation._split_kwargs(kwargs,Rotation.from_random)
         return cls(rotation=Rotation.from_random(**kwargs_rot),**kwargs_ori)
 
 
     @classmethod
     @util.extended_docstring(Rotation.from_quaternion,_parameter_doc)
-    def from_quaternion(cls,**kwargs):
+    def from_quaternion(cls, **kwargs) -> "Orientation":
         kwargs_rot,kwargs_ori = Orientation._split_kwargs(kwargs,Rotation.from_quaternion)
         return cls(rotation=Rotation.from_quaternion(**kwargs_rot),**kwargs_ori)
 
 
     @classmethod
     @util.extended_docstring(Rotation.from_Euler_angles,_parameter_doc)
-    def from_Euler_angles(cls,**kwargs):
+    def from_Euler_angles(cls, **kwargs) -> "Orientation":
         kwargs_rot,kwargs_ori = Orientation._split_kwargs(kwargs,Rotation.from_Euler_angles)
         return cls(rotation=Rotation.from_Euler_angles(**kwargs_rot),**kwargs_ori)
 
 
     @classmethod
     @util.extended_docstring(Rotation.from_axis_angle,_parameter_doc)
-    def from_axis_angle(cls,**kwargs):
+    def from_axis_angle(cls, **kwargs) -> "Orientation":
         kwargs_rot,kwargs_ori = Orientation._split_kwargs(kwargs,Rotation.from_axis_angle)
         return cls(rotation=Rotation.from_axis_angle(**kwargs_rot),**kwargs_ori)
 
 
     @classmethod
     @util.extended_docstring(Rotation.from_basis,_parameter_doc)
-    def from_basis(cls,**kwargs):
+    def from_basis(cls, **kwargs) -> "Orientation":
         kwargs_rot,kwargs_ori = Orientation._split_kwargs(kwargs,Rotation.from_basis)
         return cls(rotation=Rotation.from_basis(**kwargs_rot),**kwargs_ori)
 
 
     @classmethod
     @util.extended_docstring(Rotation.from_matrix,_parameter_doc)
-    def from_matrix(cls,**kwargs):
+    def from_matrix(cls, **kwargs) -> "Orientation":
         kwargs_rot,kwargs_ori = Orientation._split_kwargs(kwargs,Rotation.from_matrix)
         return cls(rotation=Rotation.from_matrix(**kwargs_rot),**kwargs_ori)
 
 
     @classmethod
     @util.extended_docstring(Rotation.from_Rodrigues_vector,_parameter_doc)
-    def from_Rodrigues_vector(cls,**kwargs):
+    def from_Rodrigues_vector(cls, **kwargs) -> "Orientation":
         kwargs_rot,kwargs_ori = Orientation._split_kwargs(kwargs,Rotation.from_Rodrigues_vector)
         return cls(rotation=Rotation.from_Rodrigues_vector(**kwargs_rot),**kwargs_ori)
 
 
     @classmethod
     @util.extended_docstring(Rotation.from_homochoric,_parameter_doc)
-    def from_homochoric(cls,**kwargs):
+    def from_homochoric(cls, **kwargs) -> "Orientation":
         kwargs_rot,kwargs_ori = Orientation._split_kwargs(kwargs,Rotation.from_homochoric)
         return cls(rotation=Rotation.from_homochoric(**kwargs_rot),**kwargs_ori)
 
 
     @classmethod
     @util.extended_docstring(Rotation.from_cubochoric,_parameter_doc)
-    def from_cubochoric(cls,**kwargs):
+    def from_cubochoric(cls, **kwargs) -> "Orientation":
         kwargs_rot,kwargs_ori = Orientation._split_kwargs(kwargs,Rotation.from_cubochoric)
         return cls(rotation=Rotation.from_cubochoric(**kwargs_rot),**kwargs_ori)
 
 
     @classmethod
     @util.extended_docstring(Rotation.from_spherical_component,_parameter_doc)
-    def from_spherical_component(cls,**kwargs):
+    def from_spherical_component(cls, **kwargs) -> "Orientation":
         kwargs_rot,kwargs_ori = Orientation._split_kwargs(kwargs,Rotation.from_spherical_component)
         return cls(rotation=Rotation.from_spherical_component(**kwargs_rot),**kwargs_ori)
 
 
     @classmethod
     @util.extended_docstring(Rotation.from_fiber_component,_parameter_doc)
-    def from_fiber_component(cls,**kwargs):
+    def from_fiber_component(cls, **kwargs) -> "Orientation":
         kwargs_rot,kwargs_ori = Orientation._split_kwargs(kwargs,Rotation.from_fiber_component)
         return cls(rotation=Rotation.from_fiber_component(**kwargs_rot),**kwargs_ori)
 
 
     @classmethod
     @util.extend_docstring(_parameter_doc)
-    def from_directions(cls,uvw,hkl,**kwargs):
+    def from_directions(cls,
+                        uvw: Union[Sequence[float], np.ndarray],
+                        hkl: Union[Sequence[float], np.ndarray],
+                        **kwargs) -> "Orientation":
         """
         Initialize orientation object from two crystallographic directions.
 
@@ -362,7 +382,7 @@ class Orientation(Rotation,Crystal):
 
 
     @property
-    def equivalent(self):
+    def equivalent(self) -> "Orientation":
         """
         Orientations that are symmetrically equivalent.
 
@@ -376,7 +396,7 @@ class Orientation(Rotation,Crystal):
 
 
     @property
-    def reduced(self):
+    def reduced(self) -> "Orientation":
         """Select symmetrically equivalent orientation that falls into fundamental zone according to symmetry."""
         eq   = self.equivalent
         ok   = eq.in_FZ
@@ -385,9 +405,8 @@ class Orientation(Rotation,Crystal):
         sort = 0 if len(loc) == 1 else np.lexsort(loc[:0:-1])
         return eq[ok][sort].reshape(self.shape)
 
-
     @property
-    def in_FZ(self):
+    def in_FZ(self) -> Union[np.bool_, np.ndarray]:
         """
         Check whether orientation falls into fundamental zone of own symmetry.
 
@@ -431,7 +450,7 @@ class Orientation(Rotation,Crystal):
 
 
     @property
-    def in_disorientation_FZ(self):
+    def in_disorientation_FZ(self) -> np.ndarray:
         """
         Check whether orientation falls into fundamental zone of disorientations.
 
@@ -471,8 +490,7 @@ class Orientation(Rotation,Crystal):
             else:
                 return np.ones_like(rho[...,0],dtype=bool)
 
-
-    def disorientation(self,other,return_operators=False):
+    def disorientation(self, other, return_operators = False):
         """
         Calculate disorientation between myself and given other orientation.
 
@@ -518,8 +536,8 @@ class Orientation(Rotation,Crystal):
         if self.family != other.family:
             raise NotImplementedError('disorientation between different crystal families')
 
-        blend = util.shapeblender(self.shape,other.shape)
-        s =  self.equivalent
+        blend: Tuple[int, ...] = util.shapeblender(self.shape,other.shape)
+        s = self.equivalent
         o = other.equivalent
 
         s_ = s.reshape((s.shape[0],1)+ self.shape).broadcast_to((s.shape[0],o.shape[0])+blend,mode='right')
@@ -534,10 +552,9 @@ class Orientation(Rotation,Crystal):
         r = np.where(np.any(forward[...,np.newaxis],axis=(0,1),keepdims=True),
                      r_.quaternion,
                      _r.quaternion)
-        loc  = np.where(ok)
-        sort = 0 if len(loc) == 2 else np.lexsort(loc[:1:-1])
-        quat = r[ok][sort].reshape(blend+(4,))
-
+        loc: Tuple[float]  = np.where(ok)
+        sort: np.ndarray = 0 if len(loc) == 2 else np.lexsort(loc[:1:-1])
+        quat: np.ndarray = r[ok][sort].reshape(blend+(4,))
         return (
                 (self.copy(rotation=quat),
                  (np.vstack(loc[:2]).T)[sort].reshape(blend+(2,)))
@@ -546,7 +563,7 @@ class Orientation(Rotation,Crystal):
                )
 
 
-    def average(self,weights=None,return_cloud=False):
+    def average(self, weights = None, return_cloud = False):
         """
         Return orientation average over last dimension.
 
@@ -587,7 +604,10 @@ class Orientation(Rotation,Crystal):
                )
 
 
-    def to_SST(self,vector,proper=False,return_operators=False):
+    def to_SST(self,
+               vector: np.ndarray,
+               proper: bool = False,
+               return_operators: bool = False) -> np.ndarray:
         """
         Rotate vector to ensure it falls into (improper or proper) standard stereographic triangle of crystal symmetry.
 
@@ -626,7 +646,7 @@ class Orientation(Rotation,Crystal):
                )
 
 
-    def in_SST(self,vector,proper=False):
+    def in_SST(self, vector: np.ndarray, proper: bool = False) -> Union[np.bool_, np.ndarray]:
         """
         Check whether given crystal frame vector falls into standard stereographic triangle of own symmetry.
 
@@ -667,7 +687,7 @@ class Orientation(Rotation,Crystal):
             return np.all(components >= 0.0,axis=-1)
 
 
-    def IPF_color(self,vector,in_SST=True,proper=False):
+    def IPF_color(self, vector: np.ndarray, in_SST: bool = True, proper: bool = False) -> np.ndarray:
         """
         Map vector to RGB color within standard stereographic triangle of own symmetry.
 
@@ -715,30 +735,30 @@ class Orientation(Rotation,Crystal):
             components_improper = np.around(np.einsum('...ji,...i',
                                                       np.broadcast_to(self.standard_triangle['improper'], vector_.shape+(3,)),
                                                       vector_), 12)
-            in_SST = np.all(components_proper   >= 0.0,axis=-1) \
+            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 = 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 .standard_triangle['improper'], vector_.shape+(3,)),
                                              np.block([vector_[...,:2],np.abs(vector_[...,2:3])])), 12)
 
-            in_SST = np.all(components >= 0.0,axis=-1)
+            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
+        rgb[np.broadcast_to(~in_SST_[...,np.newaxis],rgb.shape)] = 0.0
 
         return rgb
 
 
     @property
-    def symmetry_operations(self):
+    def symmetry_operations(self) -> Rotation:
         """Symmetry operations as Rotations."""
-        _symmetry_operations = {
+        _symmetry_operations: Dict[str, List[List]] = {
             'cubic':         [
                               [ 1.0,            0.0,            0.0,            0.0            ],
                               [ 0.0,            1.0,            0.0,            0.0            ],
@@ -808,7 +828,10 @@ class Orientation(Rotation,Crystal):
 ####################################################################################################
     # functions that require lattice, not just family
 
-    def to_pole(self,*,uvw=None,hkl=None,with_symmetry=False):
+    def to_pole(self, *,
+                uvw: np.ndarray = None,
+                hkl: np.ndarray = None,
+                with_symmetry: bool = False) -> np.ndarray:
         """
         Calculate lab frame vector along lattice direction [uvw] or plane normal (hkl).
 
@@ -839,7 +862,9 @@ class Orientation(Rotation,Crystal):
                @ np.broadcast_to(v,blend+(3,))
 
 
-    def Schmid(self,*,N_slip=None,N_twin=None):
+    def Schmid(self, *,
+               N_slip: Sequence[int] = None,
+               N_twin: Sequence[int] = None) -> np.ndarray:
         u"""
         Calculate Schmid matrix P = d ⨂ n in the lab frame for selected deformation systems.
 
@@ -876,6 +901,7 @@ class Orientation(Rotation,Crystal):
                             (self.kinematics('twin'),N_twin)
         if active == '*': active = [len(a) for a in kinematics['direction']]
 
+        assert active
         d = self.to_frame(uvw=np.vstack([kinematics['direction'][i][:n] for i,n in enumerate(active)]))
         p = self.to_frame(hkl=np.vstack([kinematics['plane'][i][:n] for i,n in enumerate(active)]))
         P = np.einsum('...i,...j',d/np.linalg.norm(d,axis=1,keepdims=True),
@@ -886,7 +912,7 @@ class Orientation(Rotation,Crystal):
                @ np.broadcast_to(P.reshape(util.shapeshifter(P.shape,shape)),shape)
 
 
-    def related(self,model):
+    def related(self, model: str) -> "Orientation":
         """
         Orientations derived from the given relationship.
 
diff --git a/python/damask/_rotation.py b/python/damask/_rotation.py
index ac921d70a..0a4421090 100644
--- a/python/damask/_rotation.py
+++ b/python/damask/_rotation.py
@@ -6,6 +6,8 @@ from . import tensor
 from . import util
 from . import grid_filters
 
+from typing import Union, Sequence, Tuple, Literal, List
+
 _P = -1
 
 # parameters for conversion from/to cubochoric
@@ -61,7 +63,7 @@ class Rotation:
 
     __slots__ = ['quaternion']
 
-    def __init__(self,rotation = np.array([1.0,0.0,0.0,0.0])):
+    def __init__(self, rotation: Union[Sequence[float], np.ndarray, "Rotation"] = np.array([1.0,0.0,0.0,0.0])):
         """
         New rotation.
 
@@ -73,6 +75,7 @@ class Rotation:
             Defaults to no rotation.
 
         """
+        self.quaternion: np.ndarray
         if isinstance(rotation,Rotation):
             self.quaternion = rotation.quaternion.copy()
         elif np.array(rotation).shape[-1] == 4:
@@ -81,13 +84,13 @@ class Rotation:
             raise TypeError('"rotation" is neither a Rotation nor a quaternion')
 
 
-    def __repr__(self):
+    def __repr__(self) -> str:
         """Represent rotation as unit quaternion(s)."""
         return f'Quaternion{" " if self.quaternion.shape == (4,) else "s of shape "+str(self.quaternion.shape[:-1])+chr(10)}'\
                + str(self.quaternion)
 
 
-    def __copy__(self,rotation=None):
+    def __copy__(self, rotation: Union[Sequence[float], np.ndarray, "Rotation"] = None) -> "Rotation":
         """Create deep copy."""
         dup = copy.deepcopy(self)
         if rotation is not None:
@@ -97,14 +100,14 @@ class Rotation:
     copy = __copy__
 
 
-    def __getitem__(self,item):
+    def __getitem__(self, item: Union[Tuple[int], int, bool, np.bool_, np.ndarray]):
         """Return slice according to item."""
         return self.copy() \
                if self.shape == () else \
                self.copy(rotation=self.quaternion[item+(slice(None),)] if isinstance(item,tuple) else self.quaternion[item])
 
 
-    def __eq__(self,other):
+    def __eq__(self, other: object) -> bool:
         """
         Equal to other.
 
@@ -114,11 +117,13 @@ class Rotation:
             Rotation to check for equality.
 
         """
+        if not isinstance(other, Rotation):
+            raise TypeError
         return np.logical_or(np.all(self.quaternion ==      other.quaternion,axis=-1),
                              np.all(self.quaternion == -1.0*other.quaternion,axis=-1))
 
 
-    def __ne__(self,other):
+    def __ne__(self, other: object) -> bool:
         """
         Not equal to other.
 
@@ -128,10 +133,12 @@ class Rotation:
             Rotation to check for inequality.
 
         """
+        if not isinstance(other, Rotation):
+            raise TypeError
         return np.logical_not(self==other)
 
 
-    def isclose(self,other,rtol=1e-5,atol=1e-8,equal_nan=True):
+    def isclose(self, other: "Rotation", rtol: float = 1e-5, atol: float = 1e-8, equal_nan: bool = True) -> bool:
         """
         Report where values are approximately equal to corresponding ones of other Rotation.
 
@@ -158,7 +165,7 @@ class Rotation:
                              np.all(np.isclose(s,-1.0*o,rtol,atol,equal_nan),axis=-1))
 
 
-    def allclose(self,other,rtol=1e-5,atol=1e-8,equal_nan=True):
+    def allclose(self, other: "Rotation", rtol: float = 1e-5, atol: float = 1e-8, equal_nan: bool = True) -> Union[np.bool_, bool]:
         """
         Test whether all values are approximately equal to corresponding ones of other Rotation.
 
@@ -188,27 +195,27 @@ class Rotation:
 
 
     @property
-    def size(self):
+    def size(self) -> int:
         return self.quaternion[...,0].size
 
     @property
-    def shape(self):
+    def shape(self) -> Tuple[int, ...]:
         return self.quaternion[...,0].shape
 
 
-    def __len__(self):
+    def __len__(self) -> int:
         """Length of leading/leftmost dimension of array."""
         return 0 if self.shape == () else self.shape[0]
 
 
-    def __invert__(self):
+    def __invert__(self) -> "Rotation":
         """Inverse rotation (backward rotation)."""
         dup = self.copy()
         dup.quaternion[...,1:] *= -1
         return dup
 
 
-    def __pow__(self,exp):
+    def __pow__(self, exp: int) -> "Rotation":
         """
         Perform the rotation 'exp' times.
 
@@ -222,7 +229,7 @@ class Rotation:
         p = self.quaternion[...,1:]/np.linalg.norm(self.quaternion[...,1:],axis=-1,keepdims=True)
         return self.copy(rotation=Rotation(np.block([np.cos(exp*phi),np.sin(exp*phi)*p]))._standardize())
 
-    def __ipow__(self,exp):
+    def __ipow__(self, exp: int) -> "Rotation":
         """
         Perform the rotation 'exp' times (in-place).
 
@@ -235,7 +242,7 @@ class Rotation:
         return self**exp
 
 
-    def __mul__(self,other):
+    def __mul__(self, other: "Rotation") -> "Rotation":
         """
         Compose with other.
 
@@ -261,7 +268,7 @@ class Rotation:
         else:
             raise TypeError('Use "R@b", i.e. matmul, to apply rotation "R" to object "b"')
 
-    def __imul__(self,other):
+    def __imul__(self, other: "Rotation") -> "Rotation":
         """
         Compose with other (in-place).
 
@@ -274,7 +281,7 @@ class Rotation:
         return self*other
 
 
-    def __truediv__(self,other):
+    def __truediv__(self, other: "Rotation") -> "Rotation":
         """
         Compose with inverse of other.
 
@@ -294,7 +301,7 @@ class Rotation:
         else:
             raise TypeError('Use "R@b", i.e. matmul, to apply rotation "R" to object "b"')
 
-    def __itruediv__(self,other):
+    def __itruediv__(self, other: "Rotation") -> "Rotation":
         """
         Compose with inverse of other (in-place).
 
@@ -307,7 +314,7 @@ class Rotation:
         return self/other
 
 
-    def __matmul__(self,other):
+    def __matmul__(self, other: np.ndarray) -> np.ndarray:
         """
         Rotate vector, second order tensor, or fourth order tensor.
 
@@ -350,13 +357,13 @@ class Rotation:
     apply = __matmul__
 
 
-    def _standardize(self):
+    def _standardize(self) -> "Rotation":
         """Standardize quaternion (ensure positive real hemisphere)."""
         self.quaternion[self.quaternion[...,0] < 0.0] *= -1
         return self
 
 
-    def append(self,other):
+    def append(self, other: Union["Rotation", List["Rotation"]]) -> "Rotation":
         """
         Extend array along first dimension with other array(s).
 
@@ -369,7 +376,7 @@ class Rotation:
                                                       [self]+other if isinstance(other,list) else [self,other]))))
 
 
-    def flatten(self,order = 'C'):
+    def flatten(self, order: Literal['C','F','A'] = 'C') -> "Rotation":
         """
         Flatten array.
 
@@ -382,7 +389,7 @@ class Rotation:
         return self.copy(rotation=self.quaternion.reshape((-1,4),order=order))
 
 
-    def reshape(self,shape,order = 'C'):
+    def reshape(self,shape: Union[int, Tuple[int, ...]], order: Literal['C','F','A'] = 'C') -> "Rotation":
         """
         Reshape array.
 
@@ -396,7 +403,7 @@ class Rotation:
         return self.copy(rotation=self.quaternion.reshape(tuple(shape)+(4,),order=order))
 
 
-    def broadcast_to(self,shape,mode = 'right'):
+    def broadcast_to(self, shape: Union[int, Tuple[int, ...]], mode: Literal["left", "right"] = 'right') -> "Rotation":
         """
         Broadcast array.
 
@@ -458,7 +465,7 @@ class Rotation:
                                         accept_homomorph = True)
 
 
-    def misorientation(self,other):
+    def misorientation(self, other: "Rotation") -> "Rotation":
         """
         Calculate misorientation to other Rotation.
 
@@ -479,7 +486,7 @@ class Rotation:
     ################################################################################################
     # convert to different orientation representations (numpy arrays)
 
-    def as_quaternion(self):
+    def as_quaternion(self) -> np.ndarray:
         """
         Represent as unit quaternion.
 
@@ -492,7 +499,7 @@ class Rotation:
         return self.quaternion.copy()
 
     def as_Euler_angles(self,
-                        degrees = False):
+                        degrees: bool = False) -> np.ndarray:
         """
         Represent as Bunge Euler angles.
 
@@ -526,8 +533,8 @@ class Rotation:
         return eu
 
     def as_axis_angle(self,
-                      degrees = False,
-                      pair = False):
+                      degrees: bool = False,
+                      pair: bool = False) -> Union[Tuple[float, ...], np.ndarray]:
         """
         Represent as axis–angle pair.
 
@@ -554,11 +561,11 @@ class Rotation:
         (array([0., 0., 1.]), array(0.))
 
         """
-        ax = Rotation._qu2ax(self.quaternion)
+        ax: np.ndarray = Rotation._qu2ax(self.quaternion)
         if degrees: ax[...,3] = np.degrees(ax[...,3])
         return (ax[...,:3],ax[...,3]) if pair else ax
 
-    def as_matrix(self):
+    def as_matrix(self) -> np.ndarray:
         """
         Represent as rotation matrix.
 
@@ -582,7 +589,7 @@ class Rotation:
         return Rotation._qu2om(self.quaternion)
 
     def as_Rodrigues_vector(self,
-                            compact = False):
+                            compact: bool = False) -> np.ndarray:
         """
         Represent as Rodrigues–Frank vector with separate axis and angle argument.
 
@@ -615,7 +622,7 @@ class Rotation:
         else:
             return ro
 
-    def as_homochoric(self):
+    def as_homochoric(self) -> np.ndarray:
         """
         Represent as homochoric vector.
 
@@ -636,7 +643,7 @@ class Rotation:
         """
         return Rotation._qu2ho(self.quaternion)
 
-    def as_cubochoric(self):
+    def as_cubochoric(self) -> np.ndarray:
         """
         Represent as cubochoric vector.
 
@@ -661,9 +668,9 @@ class Rotation:
     # Static constructors. The input data needs to follow the conventions, options allow to
     # relax the conventions.
     @staticmethod
-    def from_quaternion(q,
-                        accept_homomorph = False,
-                        P = -1):
+    def from_quaternion(q: Union[Sequence[Sequence[float]], np.ndarray],
+                        accept_homomorph: bool = False,
+                        P: Literal[1, -1] = -1) -> "Rotation":
         """
         Initialize from quaternion.
 
@@ -678,7 +685,7 @@ class Rotation:
             Sign convention. Defaults to -1.
 
         """
-        qu = np.array(q,dtype=float)
+        qu: np.ndarray = np.array(q,dtype=float)
         if qu.shape[:-2:-1] != (4,):
             raise ValueError('Invalid shape.')
         if abs(P) != 1:
@@ -696,8 +703,8 @@ class Rotation:
         return Rotation(qu)
 
     @staticmethod
-    def from_Euler_angles(phi,
-                          degrees = False):
+    def from_Euler_angles(phi: np.ndarray,
+                          degrees: bool = False) -> "Rotation":
         """
         Initialize from Bunge Euler angles.
 
@@ -725,10 +732,10 @@ class Rotation:
         return Rotation(Rotation._eu2qu(eu))
 
     @staticmethod
-    def from_axis_angle(axis_angle,
-                        degrees = False,
-                        normalize = False,
-                        P = -1):
+    def from_axis_angle(axis_angle: np.ndarray,
+                        degrees:bool = False,
+                        normalize: bool = False,
+                        P: Literal[1, -1] = -1) -> "Rotation":
         """
         Initialize from Axis angle pair.
 
@@ -763,9 +770,9 @@ class Rotation:
         return Rotation(Rotation._ax2qu(ax))
 
     @staticmethod
-    def from_basis(basis,
-                   orthonormal = True,
-                   reciprocal = False):
+    def from_basis(basis: np.ndarray,
+                   orthonormal: bool = True,
+                   reciprocal: bool = False) -> "Rotation":
         """
         Initialize from lattice basis vectors.
 
@@ -799,7 +806,7 @@ class Rotation:
         return Rotation(Rotation._om2qu(om))
 
     @staticmethod
-    def from_matrix(R):
+    def from_matrix(R: np.ndarray) -> "Rotation":
         """
         Initialize from rotation matrix.
 
@@ -812,8 +819,9 @@ class Rotation:
         return Rotation.from_basis(R)
 
     @staticmethod
-    def from_parallel(a,b,
-                      **kwargs):
+    def from_parallel(a: np.ndarray,
+                      b: np.ndarray,
+                      **kwargs) -> "Rotation":
         """
         Initialize from pairs of two orthogonal lattice basis vectors.
 
@@ -841,9 +849,9 @@ class Rotation:
 
 
     @staticmethod
-    def from_Rodrigues_vector(rho,
-                              normalize = False,
-                              P = -1):
+    def from_Rodrigues_vector(rho: np.ndarray,
+                              normalize: bool = False,
+                              P: Literal[1, -1] = -1) -> "Rotation":
         """
         Initialize from Rodrigues–Frank vector (angle separated from axis).
 
@@ -873,8 +881,8 @@ class Rotation:
         return Rotation(Rotation._ro2qu(ro))
 
     @staticmethod
-    def from_homochoric(h,
-                        P = -1):
+    def from_homochoric(h: np.ndarray,
+                        P: Literal[1, -1] = -1) -> "Rotation":
         """
         Initialize from homochoric vector.
 
@@ -900,8 +908,8 @@ class Rotation:
         return Rotation(Rotation._ho2qu(ho))
 
     @staticmethod
-    def from_cubochoric(x,
-                        P = -1):
+    def from_cubochoric(x: np.ndarray,
+                        P: Literal[1, -1] = -1) -> "Rotation":
         """
         Initialize from cubochoric vector.
 
@@ -928,8 +936,8 @@ class Rotation:
 
 
     @staticmethod
-    def from_random(shape = None,
-                    rng_seed = None):
+    def from_random(shape: Tuple[int, ...] = None,
+                    rng_seed: Union[None, int, Sequence[int], np.ndarray] = None) -> "Rotation":
         """
         Initialize with random rotation.
 
@@ -958,13 +966,13 @@ class Rotation:
 
 
     @staticmethod
-    def from_ODF(weights,
-                 phi,
-                 N = 500,
-                 degrees = True,
-                 fractions = True,
-                 rng_seed = None,
-                 **kwargs):
+    def from_ODF(weights: np.ndarray,
+                 phi: np.ndarray,
+                 N: int = 500,
+                 degrees: bool = True,
+                 fractions: bool = True,
+                 rng_seed: Union[None, int, Sequence[int], np.ndarray] = None,
+                 **kwargs) -> "Rotation":
         """
         Sample discrete values from a binned orientation distribution function (ODF).
 
@@ -1017,11 +1025,11 @@ class Rotation:
 
 
     @staticmethod
-    def from_spherical_component(center,
-                                 sigma,
-                                 N = 500,
-                                 degrees = True,
-                                 rng_seed = None):
+    def from_spherical_component(center: "Rotation",
+                                 sigma: float,
+                                 N: int = 500,
+                                 degrees: bool = True,
+                                 rng_seed: Union[None, int, Sequence[float], np.ndarray] = None) -> "Rotation":
         """
         Calculate set of rotations with Gaussian distribution around center.
 
@@ -1052,12 +1060,12 @@ class Rotation:
 
 
     @staticmethod
-    def from_fiber_component(alpha,
-                             beta,
-                             sigma = 0.0,
-                             N = 500,
-                             degrees = True,
-                             rng_seed = None):
+    def from_fiber_component(alpha: np.ndarray,
+                             beta: np.ndarray,
+                             sigma: float = 0.0,
+                             N: int = 500,
+                             degrees: bool = True,
+                             rng_seed: bool = None):
         """
         Calculate set of rotations with Gaussian distribution around direction.
 
@@ -1080,7 +1088,8 @@ class Rotation:
 
         """
         rng = np.random.default_rng(rng_seed)
-        sigma_,alpha_,beta_ = map(np.radians,(sigma,alpha,beta)) if degrees else (sigma,alpha,beta)
+        sigma_: np.ndarray; alpha_: np.ndarray; beta_: np.ndarray
+        sigma_,alpha_,beta_ = map(np.radians,(sigma,alpha,beta)) if degrees else (sigma,alpha,beta) # type: ignore
 
         d_cr  = np.array([np.sin(alpha_[0])*np.cos(alpha_[1]), np.sin(alpha_[0])*np.sin(alpha_[1]), np.cos(alpha_[0])])
         d_lab = np.array([np.sin( beta_[0])*np.cos( beta_[1]), np.sin( beta_[0])*np.sin( beta_[1]), np.cos( beta_[0])])
@@ -1134,7 +1143,7 @@ class Rotation:
 ####################################################################################################
     #---------- Quaternion ----------
     @staticmethod
-    def _qu2om(qu):
+    def _qu2om(qu: np.ndarray) -> np.ndarray:
         qq = qu[...,0:1]**2-(qu[...,1:2]**2 + qu[...,2:3]**2 + qu[...,3:4]**2)
         om = np.block([qq + 2.0*qu[...,1:2]**2,
                        2.0*(qu[...,2:3]*qu[...,1:2]-_P*qu[...,0:1]*qu[...,3:4]),
@@ -1149,7 +1158,7 @@ class Rotation:
         return om
 
     @staticmethod
-    def _qu2eu(qu):
+    def _qu2eu(qu: np.ndarray) -> np.ndarray:
         """Quaternion to Bunge Euler angles."""
         q02   = qu[...,0:1]*qu[...,2:3]
         q13   = qu[...,1:2]*qu[...,3:4]
@@ -1177,7 +1186,7 @@ class Rotation:
         return eu
 
     @staticmethod
-    def _qu2ax(qu):
+    def _qu2ax(qu: np.ndarray) -> np.ndarray:
         """
         Quaternion to axis–angle pair.
 
@@ -1193,7 +1202,7 @@ class Rotation:
         return ax
 
     @staticmethod
-    def _qu2ro(qu):
+    def _qu2ro(qu: np.ndarray) -> np.ndarray:
         """Quaternion to Rodrigues–Frank vector."""
         with np.errstate(invalid='ignore',divide='ignore'):
             s  = np.linalg.norm(qu[...,1:4],axis=-1,keepdims=True)
@@ -1207,7 +1216,7 @@ class Rotation:
         return ro
 
     @staticmethod
-    def _qu2ho(qu):
+    def _qu2ho(qu: np.ndarray) -> np.ndarray:
         """Quaternion to homochoric vector."""
         with np.errstate(invalid='ignore'):
             omega = 2.0 * np.arccos(np.clip(qu[...,0:1],-1.0,1.0))
@@ -1218,14 +1227,14 @@ class Rotation:
         return ho
 
     @staticmethod
-    def _qu2cu(qu):
+    def _qu2cu(qu: np.ndarray) -> np.ndarray:
         """Quaternion to cubochoric vector."""
         return Rotation._ho2cu(Rotation._qu2ho(qu))
 
 
     #---------- Rotation matrix ----------
     @staticmethod
-    def _om2qu(om):
+    def _om2qu(om: np.ndarray) -> np.ndarray:
         """
         Rotation matrix to quaternion.
 
@@ -1267,7 +1276,7 @@ class Rotation:
         return qu
 
     @staticmethod
-    def _om2eu(om):
+    def _om2eu(om: np.ndarray) -> np.ndarray:
         """Rotation matrix to Bunge Euler angles."""
         with np.errstate(invalid='ignore',divide='ignore'):
             zeta = 1.0/np.sqrt(1.0-om[...,2,2:3]**2)
@@ -1286,7 +1295,7 @@ class Rotation:
         return eu
 
     @staticmethod
-    def _om2ax(om):
+    def _om2ax(om: np.ndarray) -> np.ndarray:
         """Rotation matrix to axis–angle pair."""
         diag_delta = -_P*np.block([om[...,1,2:3]-om[...,2,1:2],
                                    om[...,2,0:1]-om[...,0,2:3],
@@ -1307,24 +1316,24 @@ class Rotation:
         return ax
 
     @staticmethod
-    def _om2ro(om):
+    def _om2ro(om: np.ndarray) -> np.ndarray:
         """Rotation matrix to Rodrigues–Frank vector."""
         return Rotation._eu2ro(Rotation._om2eu(om))
 
     @staticmethod
-    def _om2ho(om):
+    def _om2ho(om: np.ndarray) -> np.ndarray:
         """Rotation matrix to homochoric vector."""
         return Rotation._ax2ho(Rotation._om2ax(om))
 
     @staticmethod
-    def _om2cu(om):
+    def _om2cu(om: np.ndarray) -> np.ndarray:
         """Rotation matrix to cubochoric vector."""
         return Rotation._ho2cu(Rotation._om2ho(om))
 
 
     #---------- Bunge Euler angles ----------
     @staticmethod
-    def _eu2qu(eu):
+    def _eu2qu(eu: np.ndarray) -> np.ndarray:
         """Bunge Euler angles to quaternion."""
         ee = 0.5*eu
         cPhi = np.cos(ee[...,1:2])
@@ -1337,7 +1346,7 @@ class Rotation:
         return qu
 
     @staticmethod
-    def _eu2om(eu):
+    def _eu2om(eu: np.ndarray) -> np.ndarray:
         """Bunge Euler angles to rotation matrix."""
         c = np.cos(eu)
         s = np.sin(eu)
@@ -1355,7 +1364,7 @@ class Rotation:
         return om
 
     @staticmethod
-    def _eu2ax(eu):
+    def _eu2ax(eu: np.ndarray) -> np.ndarray:
         """Bunge Euler angles to axis–angle pair."""
         t = np.tan(eu[...,1:2]*0.5)
         sigma = 0.5*(eu[...,0:1]+eu[...,2:3])
@@ -1374,7 +1383,7 @@ class Rotation:
         return ax
 
     @staticmethod
-    def _eu2ro(eu):
+    def _eu2ro(eu: np.ndarray) -> np.ndarray:
         """Bunge Euler angles to Rodrigues–Frank vector."""
         ax = Rotation._eu2ax(eu)
         ro = np.block([ax[...,:3],np.tan(ax[...,3:4]*.5)])
@@ -1383,19 +1392,19 @@ class Rotation:
         return ro
 
     @staticmethod
-    def _eu2ho(eu):
+    def _eu2ho(eu: np.ndarray) -> np.ndarray:
         """Bunge Euler angles to homochoric vector."""
         return Rotation._ax2ho(Rotation._eu2ax(eu))
 
     @staticmethod
-    def _eu2cu(eu):
+    def _eu2cu(eu: np.ndarray) -> np.ndarray:
         """Bunge Euler angles to cubochoric vector."""
         return Rotation._ho2cu(Rotation._eu2ho(eu))
 
 
     #---------- Axis angle pair ----------
     @staticmethod
-    def _ax2qu(ax):
+    def _ax2qu(ax: np.ndarray) -> np.ndarray:
         """Axis–angle pair to quaternion."""
         c = np.cos(ax[...,3:4]*.5)
         s = np.sin(ax[...,3:4]*.5)
@@ -1403,7 +1412,7 @@ class Rotation:
         return qu
 
     @staticmethod
-    def _ax2om(ax):
+    def _ax2om(ax: np.ndarray) -> np.ndarray:
         """Axis-angle pair to rotation matrix."""
         c = np.cos(ax[...,3:4])
         s = np.sin(ax[...,3:4])
@@ -1420,12 +1429,12 @@ class Rotation:
         return om if _P < 0.0 else np.swapaxes(om,-1,-2)
 
     @staticmethod
-    def _ax2eu(ax):
+    def _ax2eu(ax: np.ndarray) -> np.ndarray:
         """Rotation matrix to Bunge Euler angles."""
         return Rotation._om2eu(Rotation._ax2om(ax))
 
     @staticmethod
-    def _ax2ro(ax):
+    def _ax2ro(ax: np.ndarray) -> np.ndarray:
         """Axis–angle pair to Rodrigues–Frank vector."""
         ro = np.block([ax[...,:3],
                        np.where(np.isclose(ax[...,3:4],np.pi,atol=1.e-15,rtol=.0),
@@ -1436,36 +1445,36 @@ class Rotation:
         return ro
 
     @staticmethod
-    def _ax2ho(ax):
+    def _ax2ho(ax: np.ndarray) -> np.ndarray:
         """Axis–angle pair to homochoric vector."""
         f = (0.75 * ( ax[...,3:4] - np.sin(ax[...,3:4]) ))**(1.0/3.0)
         ho = ax[...,:3] * f
         return ho
 
     @staticmethod
-    def _ax2cu(ax):
+    def _ax2cu(ax: np.ndarray) -> np.ndarray:
         """Axis–angle pair to cubochoric vector."""
         return Rotation._ho2cu(Rotation._ax2ho(ax))
 
 
     #---------- Rodrigues-Frank vector ----------
     @staticmethod
-    def _ro2qu(ro):
+    def _ro2qu(ro: np.ndarray) -> np.ndarray:
         """Rodrigues–Frank vector to quaternion."""
         return Rotation._ax2qu(Rotation._ro2ax(ro))
 
     @staticmethod
-    def _ro2om(ro):
+    def _ro2om(ro: np.ndarray) -> np.ndarray:
         """Rodgrigues–Frank vector to rotation matrix."""
         return Rotation._ax2om(Rotation._ro2ax(ro))
 
     @staticmethod
-    def _ro2eu(ro):
+    def _ro2eu(ro: np.ndarray) -> np.ndarray:
         """Rodrigues–Frank vector to Bunge Euler angles."""
         return Rotation._om2eu(Rotation._ro2om(ro))
 
     @staticmethod
-    def _ro2ax(ro):
+    def _ro2ax(ro: np.ndarray) -> np.ndarray:
         """Rodrigues–Frank vector to axis–angle pair."""
         with np.errstate(invalid='ignore',divide='ignore'):
             ax = np.where(np.isfinite(ro[...,3:4]),
@@ -1475,7 +1484,7 @@ class Rotation:
         return ax
 
     @staticmethod
-    def _ro2ho(ro):
+    def _ro2ho(ro: np.ndarray) -> np.ndarray:
         """Rodrigues–Frank vector to homochoric vector."""
         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-8,ro[...,0:3].shape),
@@ -1483,29 +1492,29 @@ class Rotation:
         return ho
 
     @staticmethod
-    def _ro2cu(ro):
+    def _ro2cu(ro: np.ndarray) -> np.ndarray:
         """Rodrigues–Frank vector to cubochoric vector."""
         return Rotation._ho2cu(Rotation._ro2ho(ro))
 
 
     #---------- Homochoric vector----------
     @staticmethod
-    def _ho2qu(ho):
+    def _ho2qu(ho: np.ndarray) -> np.ndarray:
         """Homochoric vector to quaternion."""
         return Rotation._ax2qu(Rotation._ho2ax(ho))
 
     @staticmethod
-    def _ho2om(ho):
+    def _ho2om(ho: np.ndarray) -> np.ndarray:
         """Homochoric vector to rotation matrix."""
         return Rotation._ax2om(Rotation._ho2ax(ho))
 
     @staticmethod
-    def _ho2eu(ho):
+    def _ho2eu(ho: np.ndarray) -> np.ndarray:
         """Homochoric vector to Bunge Euler angles."""
         return Rotation._ax2eu(Rotation._ho2ax(ho))
 
     @staticmethod
-    def _ho2ax(ho):
+    def _ho2ax(ho: np.ndarray) -> np.ndarray:
         """Homochoric vector to axis–angle pair."""
         tfit = np.array([+1.0000000000018852,      -0.5000000002194847,
                          -0.024999992127593126,    -0.003928701544781374,
@@ -1528,12 +1537,12 @@ class Rotation:
         return ax
 
     @staticmethod
-    def _ho2ro(ho):
+    def _ho2ro(ho: np.ndarray) -> np.ndarray:
         """Axis–angle pair to Rodrigues–Frank vector."""
         return Rotation._ax2ro(Rotation._ho2ax(ho))
 
     @staticmethod
-    def _ho2cu(ho):
+    def _ho2cu(ho: np.ndarray) -> np.ndarray:
         """
         Homochoric vector to cubochoric vector.
 
@@ -1573,32 +1582,32 @@ class Rotation:
 
     #---------- Cubochoric ----------
     @staticmethod
-    def _cu2qu(cu):
+    def _cu2qu(cu: np.ndarray) -> np.ndarray:
         """Cubochoric vector to quaternion."""
         return Rotation._ho2qu(Rotation._cu2ho(cu))
 
     @staticmethod
-    def _cu2om(cu):
+    def _cu2om(cu: np.ndarray) -> np.ndarray:
         """Cubochoric vector to rotation matrix."""
         return Rotation._ho2om(Rotation._cu2ho(cu))
 
     @staticmethod
-    def _cu2eu(cu):
+    def _cu2eu(cu: np.ndarray) -> np.ndarray:
         """Cubochoric vector to Bunge Euler angles."""
         return Rotation._ho2eu(Rotation._cu2ho(cu))
 
     @staticmethod
-    def _cu2ax(cu):
+    def _cu2ax(cu: np.ndarray) -> np.ndarray:
         """Cubochoric vector to axis–angle pair."""
         return Rotation._ho2ax(Rotation._cu2ho(cu))
 
     @staticmethod
-    def _cu2ro(cu):
+    def _cu2ro(cu: np.ndarray) -> np.ndarray:
         """Cubochoric vector to Rodrigues–Frank vector."""
         return Rotation._ho2ro(Rotation._cu2ho(cu))
 
     @staticmethod
-    def _cu2ho(cu):
+    def _cu2ho(cu: np.ndarray) -> np.ndarray:
         """
         Cubochoric vector to homochoric vector.
 
@@ -1641,7 +1650,7 @@ class Rotation:
 
 
     @staticmethod
-    def _get_pyramid_order(xyz,direction=None):
+    def _get_pyramid_order(xyz: np.ndarray, direction: Literal['forward', 'backward']) -> np.ndarray:
         """
         Get order of the coordinates.
 

From 65633ee6b1f807d5d6b298ed188023eefea88590 Mon Sep 17 00:00:00 2001
From: Daniel Otto de Mentock <daniel.mentock@mpie.de>
Date: Tue, 14 Dec 2021 17:19:00 +0100
Subject: [PATCH 02/72] added typehints for rotation.average function [skip ci]

---
 python/damask/_rotation.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/python/damask/_rotation.py b/python/damask/_rotation.py
index 0a4421090..bf210a852 100644
--- a/python/damask/_rotation.py
+++ b/python/damask/_rotation.py
@@ -426,7 +426,7 @@ class Rotation:
                                                   shape+(4,)))
 
 
-    def average(self,weights = None):
+    def average(self, weights: np.ndarray = None) -> "Rotation":
         """
         Average along last array dimension.
 

From 5702614c4fdc8125dafe064407a774d2281d24ab Mon Sep 17 00:00:00 2001
From: Daniel Otto de Mentock <daniel.mentock@mpie.de>
Date: Mon, 3 Jan 2022 15:35:28 +0100
Subject: [PATCH 03/72] expanded rng_seed typehint to array_like type adjusted
 alpha and beta types for from_fiber_component to also accept lists removed
 superfluous kwargs argument in from_ODF and from_parallel functions

---
 python/damask/_rotation.py | 14 ++++++--------
 1 file changed, 6 insertions(+), 8 deletions(-)

diff --git a/python/damask/_rotation.py b/python/damask/_rotation.py
index bf210a852..aeac3c3e3 100644
--- a/python/damask/_rotation.py
+++ b/python/damask/_rotation.py
@@ -820,8 +820,7 @@ class Rotation:
 
     @staticmethod
     def from_parallel(a: np.ndarray,
-                      b: np.ndarray,
-                      **kwargs) -> "Rotation":
+                      b: np.ndarray ) -> "Rotation":
         """
         Initialize from pairs of two orthogonal lattice basis vectors.
 
@@ -971,8 +970,7 @@ class Rotation:
                  N: int = 500,
                  degrees: bool = True,
                  fractions: bool = True,
-                 rng_seed: Union[None, int, Sequence[int], np.ndarray] = None,
-                 **kwargs) -> "Rotation":
+                 rng_seed: Union[None, int, Sequence[int], np.ndarray] = None) -> "Rotation":
         """
         Sample discrete values from a binned orientation distribution function (ODF).
 
@@ -1029,7 +1027,7 @@ class Rotation:
                                  sigma: float,
                                  N: int = 500,
                                  degrees: bool = True,
-                                 rng_seed: Union[None, int, Sequence[float], np.ndarray] = None) -> "Rotation":
+                                 rng_seed: Union[None, int, Sequence[int], np.ndarray] = None) -> "Rotation":
         """
         Calculate set of rotations with Gaussian distribution around center.
 
@@ -1060,12 +1058,12 @@ class Rotation:
 
 
     @staticmethod
-    def from_fiber_component(alpha: np.ndarray,
-                             beta: np.ndarray,
+    def from_fiber_component(alpha: Union[Sequence[int], np.ndarray],
+                             beta: Union[Sequence[int], np.ndarray],
                              sigma: float = 0.0,
                              N: int = 500,
                              degrees: bool = True,
-                             rng_seed: bool = None):
+                             rng_seed: Union[None, int, Sequence[int], np.ndarray] = None):
         """
         Calculate set of rotations with Gaussian distribution around direction.
 

From 9a9ec11c29e681cd94f264e7e2a59c73f8bfe5d5 Mon Sep 17 00:00:00 2001
From: Daniel Otto de Mentock <daniel.mentock@mpie.de>
Date: Mon, 3 Jan 2022 16:44:27 +0100
Subject: [PATCH 04/72] added generator typehint to from_random function

---
 python/damask/_rotation.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/python/damask/_rotation.py b/python/damask/_rotation.py
index aeac3c3e3..448917488 100644
--- a/python/damask/_rotation.py
+++ b/python/damask/_rotation.py
@@ -951,7 +951,7 @@ class Rotation:
             Defaults to None, i.e. unpredictable entropy will be pulled from the OS.
 
         """
-        rng = np.random.default_rng(rng_seed)
+        rng: np.random.Generator = np.random.default_rng(rng_seed)
         r = rng.random(3 if shape is None else tuple(shape)+(3,) if hasattr(shape, '__iter__') else (shape,3))
 
         A = np.sqrt(r[...,2])

From 0a31ff098050b08f4eb854a228913f1e2c5d0ba5 Mon Sep 17 00:00:00 2001
From: Daniel Otto de Mentock <daniel.mentock@mpie.de>
Date: Thu, 6 Jan 2022 14:33:41 +0100
Subject: [PATCH 05/72] added type:ignore statement to broken line

---
 python/damask/_rotation.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/python/damask/_rotation.py b/python/damask/_rotation.py
index 448917488..d50b25c54 100644
--- a/python/damask/_rotation.py
+++ b/python/damask/_rotation.py
@@ -952,7 +952,7 @@ class Rotation:
 
         """
         rng: np.random.Generator = np.random.default_rng(rng_seed)
-        r = rng.random(3 if shape is None else tuple(shape)+(3,) if hasattr(shape, '__iter__') else (shape,3))
+        r = rng.random(3 if shape is None else tuple(shape)+(3,) if hasattr(shape, '__iter__') else (shape,3)) #type: ignore
 
         A = np.sqrt(r[...,2])
         B = np.sqrt(1.0-r[...,2])

From aabeee9de1aa38ccfe85c3c86c2df778a27f9e2c Mon Sep 17 00:00:00 2001
From: Daniel Otto de Mentock <d.mentock@mpie.de>
Date: Fri, 14 Jan 2022 14:37:48 +0100
Subject: [PATCH 06/72] Replaced relevant Sequences with FloatSequence and
 IntSequence types

---
 python/damask/_orientation.py | 16 +++++++++-------
 python/damask/_rotation.py    | 19 ++++++++++---------
 2 files changed, 19 insertions(+), 16 deletions(-)

diff --git a/python/damask/_orientation.py b/python/damask/_orientation.py
index afe4e605d..61c63ed66 100644
--- a/python/damask/_orientation.py
+++ b/python/damask/_orientation.py
@@ -1,6 +1,5 @@
 import inspect
 import copy
-from typing import Union, Callable, Sequence, Dict, Any, Tuple, List
 
 import numpy as np
 
@@ -9,6 +8,9 @@ from . import Crystal
 from . import util
 from . import tensor
 
+from typing import Union, Callable, Sequence, Dict, Any, Tuple, List
+from ._typehints import FloatSequence, IntSequence
+
 
 _parameter_doc = \
        """
@@ -94,7 +96,7 @@ class Orientation(Rotation,Crystal):
 
     @util.extend_docstring(_parameter_doc)
     def __init__(self,
-                 rotation: Union[Sequence[float], np.ndarray, Rotation] = np.array([1.,0.,0.,0.]), *,
+                 rotation: Union[FloatSequence, Rotation] = np.array([1.,0.,0.,0.]), *,
                  family: str = None,
                  lattice: str = None,
                  a: float = None, b: float = None, c: float = None,
@@ -121,7 +123,7 @@ class Orientation(Rotation,Crystal):
         return '\n'.join([Crystal.__repr__(self),
                           Rotation.__repr__(self)])
 
-    def __copy__(self,rotation: Union[Sequence[float], np.ndarray, Rotation] = None) -> "Orientation":
+    def __copy__(self,rotation: Union[FloatSequence, Rotation] = None) -> "Orientation":
         """Create deep copy."""
         dup = copy.deepcopy(self)
         if rotation is not None:
@@ -360,8 +362,8 @@ class Orientation(Rotation,Crystal):
     @classmethod
     @util.extend_docstring(_parameter_doc)
     def from_directions(cls,
-                        uvw: Union[Sequence[float], np.ndarray],
-                        hkl: Union[Sequence[float], np.ndarray],
+                        uvw: FloatSequence,
+                        hkl: FloatSequence,
                         **kwargs) -> "Orientation":
         """
         Initialize orientation object from two crystallographic directions.
@@ -874,8 +876,8 @@ class Orientation(Rotation,Crystal):
 
 
     def Schmid(self, *,
-               N_slip: Sequence[int] = None,
-               N_twin: Sequence[int] = None) -> np.ndarray:
+               N_slip: IntSequence = None,
+               N_twin: IntSequence = None) -> np.ndarray:
         u"""
         Calculate Schmid matrix P = d ⨂ n in the lab frame for selected deformation systems.
 
diff --git a/python/damask/_rotation.py b/python/damask/_rotation.py
index a0bf15e88..fa4f2ec14 100644
--- a/python/damask/_rotation.py
+++ b/python/damask/_rotation.py
@@ -7,6 +7,7 @@ from . import util
 from . import grid_filters
 
 from typing import Union, Sequence, Tuple, Literal, List
+from ._typehints import FloatSequence, IntSequence
 
 _P = -1
 
@@ -63,7 +64,7 @@ class Rotation:
 
     __slots__ = ['quaternion']
 
-    def __init__(self, rotation: Union[Sequence[float], np.ndarray, "Rotation"] = np.array([1.0,0.0,0.0,0.0])):
+    def __init__(self, rotation: Union[FloatSequence, "Rotation"] = np.array([1.0,0.0,0.0,0.0])):
         """
         New rotation.
 
@@ -90,7 +91,7 @@ class Rotation:
                + str(self.quaternion)
 
 
-    def __copy__(self, rotation: Union[Sequence[float], np.ndarray, "Rotation"] = None) -> "Rotation":
+    def __copy__(self, rotation: Union[FloatSequence, "Rotation"] = None) -> "Rotation":
         """Create deep copy."""
         dup = copy.deepcopy(self)
         if rotation is not None:
@@ -668,7 +669,7 @@ class Rotation:
     # Static constructors. The input data needs to follow the conventions, options allow to
     # relax the conventions.
     @staticmethod
-    def from_quaternion(q: Union[Sequence[Sequence[float]], np.ndarray],
+    def from_quaternion(q: Union[Sequence[FloatSequence], np.ndarray],
                         accept_homomorph: bool = False,
                         P: Literal[1, -1] = -1) -> "Rotation":
         """
@@ -936,7 +937,7 @@ class Rotation:
 
     @staticmethod
     def from_random(shape: Tuple[int, ...] = None,
-                    rng_seed: Union[None, int, Sequence[int], np.ndarray] = None) -> "Rotation":
+                    rng_seed: Union[int, IntSequence] = None) -> "Rotation":
         """
         Initialize with random rotation.
 
@@ -970,7 +971,7 @@ class Rotation:
                  N: int = 500,
                  degrees: bool = True,
                  fractions: bool = True,
-                 rng_seed: Union[None, int, Sequence[int], np.ndarray] = None) -> "Rotation":
+                 rng_seed: Union[None, int, IntSequence] = None) -> "Rotation":
         """
         Sample discrete values from a binned orientation distribution function (ODF).
 
@@ -1027,7 +1028,7 @@ class Rotation:
                                  sigma: float,
                                  N: int = 500,
                                  degrees: bool = True,
-                                 rng_seed: Union[None, int, Sequence[int], np.ndarray] = None) -> "Rotation":
+                                 rng_seed: Union[None, int, IntSequence] = None) -> "Rotation":
         """
         Calculate set of rotations with Gaussian distribution around center.
 
@@ -1058,12 +1059,12 @@ class Rotation:
 
 
     @staticmethod
-    def from_fiber_component(alpha: Union[Sequence[int], np.ndarray],
-                             beta: Union[Sequence[int], np.ndarray],
+    def from_fiber_component(alpha: IntSequence,
+                             beta: IntSequence,
                              sigma: float = 0.0,
                              N: int = 500,
                              degrees: bool = True,
-                             rng_seed: Union[None, int, Sequence[int], np.ndarray] = None):
+                             rng_seed: Union[int, IntSequence] = None):
         """
         Calculate set of rotations with Gaussian distribution around direction.
 

From 25513d572bacc2d65073e0199a917f6769ccf99a Mon Sep 17 00:00:00 2001
From: Daniel Otto de Mentock <d.mentock@mpie.de>
Date: Fri, 14 Jan 2022 14:55:08 +0100
Subject: [PATCH 07/72] minor type adjustment to rotation module removed
 superfluous Sequence type from orientation module

---
 python/damask/_orientation.py | 2 +-
 python/damask/_rotation.py    | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/python/damask/_orientation.py b/python/damask/_orientation.py
index 61c63ed66..3a1154a64 100644
--- a/python/damask/_orientation.py
+++ b/python/damask/_orientation.py
@@ -8,7 +8,7 @@ from . import Crystal
 from . import util
 from . import tensor
 
-from typing import Union, Callable, Sequence, Dict, Any, Tuple, List
+from typing import Union, Callable, Dict, Any, Tuple, List
 from ._typehints import FloatSequence, IntSequence
 
 
diff --git a/python/damask/_rotation.py b/python/damask/_rotation.py
index fa4f2ec14..17369c36a 100644
--- a/python/damask/_rotation.py
+++ b/python/damask/_rotation.py
@@ -535,7 +535,7 @@ class Rotation:
 
     def as_axis_angle(self,
                       degrees: bool = False,
-                      pair: bool = False) -> Union[Tuple[float, ...], np.ndarray]:
+                      pair: bool = False) -> Union[Tuple[np.ndarray, np.ndarray], np.ndarray]:
         """
         Represent as axis–angle pair.
 

From 0fe51f58a8686e6ab56d4297eda5a7e64971f229 Mon Sep 17 00:00:00 2001
From: Daniel Otto de Mentock <d.mentock@mpie.de>
Date: Wed, 26 Jan 2022 15:09:09 +0100
Subject: [PATCH 08/72] [skip ci] changed almost all function definition lines
 to multiline

---
 python/damask/_orientation.py | 35 ++++++++++++++++++-------
 python/damask/_rotation.py    | 49 +++++++++++++++++++++++++----------
 2 files changed, 60 insertions(+), 24 deletions(-)

diff --git a/python/damask/_orientation.py b/python/damask/_orientation.py
index 3a1154a64..35de041f8 100644
--- a/python/damask/_orientation.py
+++ b/python/damask/_orientation.py
@@ -123,7 +123,8 @@ class Orientation(Rotation,Crystal):
         return '\n'.join([Crystal.__repr__(self),
                           Rotation.__repr__(self)])
 
-    def __copy__(self,rotation: Union[FloatSequence, Rotation] = None) -> "Orientation":
+    def __copy__(self,
+                 rotation: Union[FloatSequence, Rotation] = None) -> "Orientation":
         """Create deep copy."""
         dup = copy.deepcopy(self)
         if rotation is not None:
@@ -134,7 +135,8 @@ class Orientation(Rotation,Crystal):
 
 
 
-    def __eq__(self, other: object) -> bool:
+    def __eq__(self,
+               other: object) -> bool:
         """
         Equal to other.
 
@@ -151,7 +153,8 @@ class Orientation(Rotation,Crystal):
                         self.parameters == other.parameters
         return np.logical_and(matching_type,super(self.__class__,self.reduced).__eq__(other.reduced))
 
-    def __ne__(self, other: object) -> bool:
+    def __ne__(self,
+               other: object) -> bool:
         """
         Not equal to other.
 
@@ -230,7 +233,8 @@ class Orientation(Rotation,Crystal):
         return np.all(self.isclose(other,rtol,atol,equal_nan))
 
 
-    def __mul__(self, other: Union[Rotation, "Orientation"]) -> "Orientation":
+    def __mul__(self,
+                other: Union[Rotation, "Orientation"]) -> "Orientation":
         """
         Compose this orientation with other.
 
@@ -252,7 +256,8 @@ class Orientation(Rotation,Crystal):
 
 
     @staticmethod
-    def _split_kwargs(kwargs: Dict[str, Any], target: Callable) -> Tuple[Dict[str, Any], ...]:
+    def _split_kwargs(kwargs: Dict[str, Any],
+                      target: Callable) -> Tuple[Dict[str, Any], ...]:
         """
         Separate keyword arguments in 'kwargs' targeted at 'target' from general keyword arguments of Orientation objects.
 
@@ -492,7 +497,9 @@ class Orientation(Rotation,Crystal):
             else:
                 return np.ones_like(rho[...,0],dtype=bool)
 
-    def disorientation(self, other, return_operators = False):
+    def disorientation(self,
+                       other,
+                       return_operators = False):
         """
         Calculate disorientation between myself and given other orientation.
 
@@ -576,7 +583,9 @@ class Orientation(Rotation,Crystal):
                )
 
 
-    def average(self, weights = None, return_cloud = False):
+    def average(self,
+                weights = None,
+                return_cloud = False):
         """
         Return orientation average over last dimension.
 
@@ -659,7 +668,9 @@ class Orientation(Rotation,Crystal):
                )
 
 
-    def in_SST(self, vector: np.ndarray, proper: bool = False) -> Union[np.bool_, np.ndarray]:
+    def in_SST(self,
+               vector: np.ndarray,
+               proper: bool = False) -> Union[np.bool_, np.ndarray]:
         """
         Check whether given crystal frame vector falls into standard stereographic triangle of own symmetry.
 
@@ -700,7 +711,10 @@ class Orientation(Rotation,Crystal):
             return np.all(components >= 0.0,axis=-1)
 
 
-    def IPF_color(self, vector: np.ndarray, in_SST: bool = True, proper: bool = False) -> np.ndarray:
+    def IPF_color(self,
+                  vector: np.ndarray,
+                  in_SST: bool = True,
+                  proper: bool = False) -> np.ndarray:
         """
         Map vector to RGB color within standard stereographic triangle of own symmetry.
 
@@ -925,7 +939,8 @@ class Orientation(Rotation,Crystal):
                @ np.broadcast_to(P.reshape(util.shapeshifter(P.shape,shape)),shape)
 
 
-    def related(self, model: str) -> "Orientation":
+    def related(self,
+                model: str) -> "Orientation":
         """
         Orientations derived from the given relationship.
 
diff --git a/python/damask/_rotation.py b/python/damask/_rotation.py
index 17369c36a..3266f4f41 100644
--- a/python/damask/_rotation.py
+++ b/python/damask/_rotation.py
@@ -64,7 +64,8 @@ class Rotation:
 
     __slots__ = ['quaternion']
 
-    def __init__(self, rotation: Union[FloatSequence, "Rotation"] = np.array([1.0,0.0,0.0,0.0])):
+    def __init__(self,
+                 rotation: Union[FloatSequence, "Rotation"] = np.array([1.0,0.0,0.0,0.0])):
         """
         New rotation.
 
@@ -91,7 +92,8 @@ class Rotation:
                + str(self.quaternion)
 
 
-    def __copy__(self, rotation: Union[FloatSequence, "Rotation"] = None) -> "Rotation":
+    def __copy__(self,
+                 rotation: Union[FloatSequence, "Rotation"] = None) -> "Rotation":
         """Create deep copy."""
         dup = copy.deepcopy(self)
         if rotation is not None:
@@ -101,7 +103,8 @@ class Rotation:
     copy = __copy__
 
 
-    def __getitem__(self, item: Union[Tuple[int], int, bool, np.bool_, np.ndarray]):
+    def __getitem__(self,
+                    item: Union[Tuple[int], int, bool, np.bool_, np.ndarray]):
         """Return slice according to item."""
         return self.copy() \
                if self.shape == () else \
@@ -139,7 +142,11 @@ class Rotation:
         return np.logical_not(self==other)
 
 
-    def isclose(self, other: "Rotation", rtol: float = 1e-5, atol: float = 1e-8, equal_nan: bool = True) -> bool:
+    def isclose(self,
+                other: "Rotation",
+                rtol: float = 1e-5,
+                atol: float = 1e-8,
+                equal_nan: bool = True) -> bool:
         """
         Report where values are approximately equal to corresponding ones of other Rotation.
 
@@ -166,7 +173,11 @@ class Rotation:
                              np.all(np.isclose(s,-1.0*o,rtol,atol,equal_nan),axis=-1))
 
 
-    def allclose(self, other: "Rotation", rtol: float = 1e-5, atol: float = 1e-8, equal_nan: bool = True) -> Union[np.bool_, bool]:
+    def allclose(self,
+                 other: "Rotation",
+                 rtol: float = 1e-5,
+                 atol: float = 1e-8,
+                 equal_nan: bool = True) -> Union[np.bool_, bool]:
         """
         Test whether all values are approximately equal to corresponding ones of other Rotation.
 
@@ -330,7 +341,7 @@ class Rotation:
             Rotated vector or tensor, i.e. transformed to frame defined by rotation.
 
         """
-        if isinstance(other,np.ndarray):
+        if isinstance(other, np.ndarray):
             if self.shape + (3,) == other.shape:
                 q_m = self.quaternion[...,0]
                 p_m = self.quaternion[...,1:]
@@ -350,7 +361,7 @@ class Rotation:
                 return np.einsum('...im,...jn,...ko,...lp,...mnop',R,R,R,R,other)
             else:
                 raise ValueError('Can only rotate vectors, 2nd order tensors, and 4th order tensors')
-        elif isinstance(other,Rotation):
+        elif isinstance(other, Rotation):
             raise TypeError('Use "R1*R2", i.e. multiplication, to compose rotations "R1" and "R2"')
         else:
             raise TypeError(f'Cannot rotate {type(other)}')
@@ -364,7 +375,9 @@ class Rotation:
         return self
 
 
-    def append(self, other: Union["Rotation", List["Rotation"]]) -> "Rotation":
+    def append(self,
+               other: Union["Rotation",
+               List["Rotation"]]) -> "Rotation":
         """
         Extend array along first dimension with other array(s).
 
@@ -377,7 +390,8 @@ class Rotation:
                                                       [self]+other if isinstance(other,list) else [self,other]))))
 
 
-    def flatten(self, order: Literal['C','F','A'] = 'C') -> "Rotation":
+    def flatten(self,
+                order: Literal['C','F','A'] = 'C') -> "Rotation":
         """
         Flatten array.
 
@@ -390,7 +404,9 @@ class Rotation:
         return self.copy(rotation=self.quaternion.reshape((-1,4),order=order))
 
 
-    def reshape(self,shape: Union[int, Tuple[int, ...]], order: Literal['C','F','A'] = 'C') -> "Rotation":
+    def reshape(self,
+                shape: Union[int, Tuple[int, ...]],
+                order: Literal['C','F','A'] = 'C') -> "Rotation":
         """
         Reshape array.
 
@@ -404,7 +420,9 @@ class Rotation:
         return self.copy(rotation=self.quaternion.reshape(tuple(shape)+(4,),order=order))
 
 
-    def broadcast_to(self, shape: Union[int, Tuple[int, ...]], mode: Literal["left", "right"] = 'right') -> "Rotation":
+    def broadcast_to(self,
+                     shape: Union[int, Tuple[int, ...]],
+                     mode: Literal["left", "right"] = 'right') -> "Rotation":
         """
         Broadcast array.
 
@@ -427,7 +445,8 @@ class Rotation:
                                                   shape+(4,)))
 
 
-    def average(self, weights: np.ndarray = None) -> "Rotation":
+    def average(self,
+                weights: np.ndarray = None) -> "Rotation":
         """
         Average along last array dimension.
 
@@ -466,7 +485,8 @@ class Rotation:
                                         accept_homomorph = True)
 
 
-    def misorientation(self, other: "Rotation") -> "Rotation":
+    def misorientation(self,
+                       other: "Rotation") -> "Rotation":
         """
         Calculate misorientation to other Rotation.
 
@@ -1649,7 +1669,8 @@ class Rotation:
 
 
     @staticmethod
-    def _get_pyramid_order(xyz: np.ndarray, direction: Literal['forward', 'backward']) -> np.ndarray:
+    def _get_pyramid_order(xyz: np.ndarray,
+                           direction: Literal['forward', 'backward']) -> np.ndarray:
         """
         Get order of the coordinates.
 

From 81ef865525f12c57c3f8ec3e92cf67ef1d55b56a Mon Sep 17 00:00:00 2001
From: Daniel Otto de Mentock <d.mentock@mpie.de>
Date: Fri, 28 Jan 2022 10:11:34 +0100
Subject: [PATCH 09/72] [skip ci] moved asterisk to seperate line

---
 python/damask/_orientation.py | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/python/damask/_orientation.py b/python/damask/_orientation.py
index 35de041f8..f84ca9952 100644
--- a/python/damask/_orientation.py
+++ b/python/damask/_orientation.py
@@ -96,7 +96,8 @@ class Orientation(Rotation,Crystal):
 
     @util.extend_docstring(_parameter_doc)
     def __init__(self,
-                 rotation: Union[FloatSequence, Rotation] = np.array([1.,0.,0.,0.]), *,
+                 rotation: Union[FloatSequence, Rotation] = np.array([1.,0.,0.,0.]),
+                 *,
                  family: str = None,
                  lattice: str = None,
                  a: float = None, b: float = None, c: float = None,

From 92ac01848614450d80a1d0d8e8b262cdb5e96c99 Mon Sep 17 00:00:00 2001
From: Daniel Otto de Mentock <d.mentock@mpie.de>
Date: Fri, 28 Jan 2022 13:34:42 +0100
Subject: [PATCH 10/72] removed superfluous break in function definition in
 rotation

---
 python/damask/_rotation.py | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/python/damask/_rotation.py b/python/damask/_rotation.py
index 3266f4f41..676df5c03 100644
--- a/python/damask/_rotation.py
+++ b/python/damask/_rotation.py
@@ -376,8 +376,7 @@ class Rotation:
 
 
     def append(self,
-               other: Union["Rotation",
-               List["Rotation"]]) -> "Rotation":
+           other: Union["Rotation", List["Rotation"]]) -> "Rotation":
         """
         Extend array along first dimension with other array(s).
 

From 53a0de2271c2ea33618aa733b64e0118de4fc83c Mon Sep 17 00:00:00 2001
From: Daniel Otto de Mentock <d.mentock@mpie.de>
Date: Fri, 28 Jan 2022 13:40:37 +0100
Subject: [PATCH 11/72] Adjusted docstrings in rotation

rewrote map(np.radians()) line to one line tuple
---
 python/damask/_rotation.py | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/python/damask/_rotation.py b/python/damask/_rotation.py
index 676df5c03..468fef2c5 100644
--- a/python/damask/_rotation.py
+++ b/python/damask/_rotation.py
@@ -382,7 +382,7 @@ class Rotation:
 
         Parameters
         ----------
-        other : damask.Rotation
+        other : (list of) damask.Rotation
 
         """
         return self.copy(rotation=np.vstack(tuple(map(lambda x:x.quaternion,
@@ -427,7 +427,7 @@ class Rotation:
 
         Parameters
         ----------
-        shape : tuple
+        shape : int, tuple
             Shape of broadcasted array.
         mode : str, optional
             Where to preferentially locate missing dimensions.
@@ -451,7 +451,7 @@ class Rotation:
 
         Parameters
         ----------
-        weights : list of floats, optional
+        weights : numpy.ndarray, optional
             Relative weight of each rotation.
 
         Returns
@@ -1107,7 +1107,7 @@ class Rotation:
         """
         rng = np.random.default_rng(rng_seed)
         sigma_: np.ndarray; alpha_: np.ndarray; beta_: np.ndarray
-        sigma_,alpha_,beta_ = map(np.radians,(sigma,alpha,beta)) if degrees else (sigma,alpha,beta) # type: ignore
+        sigma_,alpha_,beta_ = (np.radians(coordinate for coordinate in (sigma,alpha,beta))) if degrees else (sigma,alpha,beta) #type: ignore
 
         d_cr  = np.array([np.sin(alpha_[0])*np.cos(alpha_[1]), np.sin(alpha_[0])*np.sin(alpha_[1]), np.cos(alpha_[0])])
         d_lab = np.array([np.sin( beta_[0])*np.cos( beta_[1]), np.sin( beta_[0])*np.sin( beta_[1]), np.cos( beta_[0])])

From 33731e4948078e79f6710bdbc979730ecb3a7997 Mon Sep 17 00:00:00 2001
From: Daniel Otto de Mentock <d.mentock@mpie.de>
Date: Fri, 28 Jan 2022 15:15:20 +0100
Subject: [PATCH 12/72] adjusted bracket error in from_fiber_component

---
 python/damask/_rotation.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/python/damask/_rotation.py b/python/damask/_rotation.py
index 468fef2c5..b55f178f7 100644
--- a/python/damask/_rotation.py
+++ b/python/damask/_rotation.py
@@ -1107,7 +1107,7 @@ class Rotation:
         """
         rng = np.random.default_rng(rng_seed)
         sigma_: np.ndarray; alpha_: np.ndarray; beta_: np.ndarray
-        sigma_,alpha_,beta_ = (np.radians(coordinate for coordinate in (sigma,alpha,beta))) if degrees else (sigma,alpha,beta) #type: ignore
+        sigma_,alpha_,beta_ = (np.radians(coordinate) for coordinate in (sigma,alpha,beta)) if degrees else (sigma,alpha,beta) #type: ignore
 
         d_cr  = np.array([np.sin(alpha_[0])*np.cos(alpha_[1]), np.sin(alpha_[0])*np.sin(alpha_[1]), np.cos(alpha_[0])])
         d_lab = np.array([np.sin( beta_[0])*np.cos( beta_[1]), np.sin( beta_[0])*np.sin( beta_[1]), np.cos( beta_[0])])

From cb1143a47215d8327085cd975e45135b42fd9e57 Mon Sep 17 00:00:00 2001
From: Daniel Otto de Mentock <d.mentock@mpie.de>
Date: Tue, 1 Feb 2022 18:38:49 +0100
Subject: [PATCH 13/72] changed return type of util.shapeblender and
 util.shapeshifter from Sequence[SupportsIndex] to  Tuple[SupportsIndex, ...]

ignored lines in orientation module that attempt to pass objects of type
Tuple[SupportsIndex, ...] to np.broadcast_to()
---
 python/damask/_orientation.py | 5 ++---
 python/damask/util.py         | 6 +++---
 2 files changed, 5 insertions(+), 6 deletions(-)

diff --git a/python/damask/_orientation.py b/python/damask/_orientation.py
index f84ca9952..d1488c14e 100644
--- a/python/damask/_orientation.py
+++ b/python/damask/_orientation.py
@@ -657,7 +657,7 @@ class Orientation(Rotation,Crystal):
         """
         eq  = self.equivalent
         blend = util.shapeblender(eq.shape,np.array(vector).shape[:-1])
-        poles = eq.broadcast_to(blend,mode='right') @ np.broadcast_to(np.array(vector),blend+(3,))
+        poles = eq.broadcast_to(blend,mode='right') @ np.broadcast_to(np.array(vector),blend+(3,)) #type: ignore
         ok    = self.in_SST(poles,proper=proper)
         ok   &= np.cumsum(ok,axis=0) == 1
         loc   = np.where(ok)
@@ -886,8 +886,7 @@ class Orientation(Rotation,Crystal):
             blend += sym_ops.shape
             v = sym_ops.broadcast_to(shape) \
               @ np.broadcast_to(v.reshape(util.shapeshifter(v.shape,shape+(3,))),shape+(3,))
-        return ~(self.broadcast_to(blend)) \
-               @ np.broadcast_to(v,blend+(3,))
+        return ~(self.broadcast_to(blend))@ np.broadcast_to(v,blend+(3,)) #type: ignore
 
 
     def Schmid(self, *,
diff --git a/python/damask/util.py b/python/damask/util.py
index b4c287884..3b0af7177 100644
--- a/python/damask/util.py
+++ b/python/damask/util.py
@@ -9,7 +9,7 @@ import re
 import fractions
 from collections import abc
 from functools import reduce
-from typing import Union, Tuple, Iterable, Callable, Dict, List, Any, Literal, SupportsIndex, Sequence
+from typing import Union, Tuple, Iterable, Callable, Dict, List, Any, Literal, SupportsIndex
 from pathlib import Path
 
 import numpy as np
@@ -427,7 +427,7 @@ def hybrid_IA(dist: np.ndarray,
 def shapeshifter(fro: Tuple[int, ...],
                  to: Tuple[int, ...],
                  mode: Literal['left','right'] = 'left',
-                 keep_ones: bool = False) -> Sequence[SupportsIndex]:
+                 keep_ones: bool = False) -> Tuple[SupportsIndex, ...]:
     """
     Return dimensions that reshape 'fro' to become broadcastable to 'to'.
 
@@ -490,7 +490,7 @@ def shapeshifter(fro: Tuple[int, ...],
 
 
 def shapeblender(a: Tuple[int, ...],
-                 b: Tuple[int, ...]) -> Sequence[SupportsIndex]:
+                 b: Tuple[int, ...]) -> Tuple[SupportsIndex, ...]:
     """
     Return a shape that overlaps the rightmost entries of 'a' with the leftmost of 'b'.
 

From 71bc92fed054539fde49c6dee208f72a0d2bd0dc Mon Sep 17 00:00:00 2001
From: Daniel Otto de Mentock <d.mentock@mpie.de>
Date: Wed, 2 Feb 2022 11:11:59 +0100
Subject: [PATCH 14/72] changed quote layout to single quote Added
 NotImplemented returnvalue to __eq__ functions

---
 python/damask/_orientation.py | 36 +++++++++----------
 python/damask/_rotation.py    | 66 +++++++++++++++++------------------
 2 files changed, 51 insertions(+), 51 deletions(-)

diff --git a/python/damask/_orientation.py b/python/damask/_orientation.py
index d1488c14e..8a560e756 100644
--- a/python/damask/_orientation.py
+++ b/python/damask/_orientation.py
@@ -125,7 +125,7 @@ class Orientation(Rotation,Crystal):
                           Rotation.__repr__(self)])
 
     def __copy__(self,
-                 rotation: Union[FloatSequence, Rotation] = None) -> "Orientation":
+                 rotation: Union[FloatSequence, Rotation] = None) -> 'Orientation':
         """Create deep copy."""
         dup = copy.deepcopy(self)
         if rotation is not None:
@@ -148,7 +148,7 @@ class Orientation(Rotation,Crystal):
 
         """
         if not isinstance(other, Orientation):
-            raise TypeError
+            raise NotImplemented
         matching_type = self.family == other.family and \
                         self.lattice == other.lattice and \
                         self.parameters == other.parameters
@@ -235,7 +235,7 @@ class Orientation(Rotation,Crystal):
 
 
     def __mul__(self,
-                other: Union[Rotation, "Orientation"]) -> "Orientation":
+                other: Union[Rotation, 'Orientation']) -> 'Orientation':
         """
         Compose this orientation with other.
 
@@ -290,77 +290,77 @@ class Orientation(Rotation,Crystal):
 
     @classmethod
     @util.extended_docstring(Rotation.from_random, _parameter_doc)
-    def from_random(cls, **kwargs) -> "Orientation":
+    def from_random(cls, **kwargs) -> 'Orientation':
         kwargs_rot,kwargs_ori = Orientation._split_kwargs(kwargs,Rotation.from_random)
         return cls(rotation=Rotation.from_random(**kwargs_rot),**kwargs_ori)
 
 
     @classmethod
     @util.extended_docstring(Rotation.from_quaternion,_parameter_doc)
-    def from_quaternion(cls, **kwargs) -> "Orientation":
+    def from_quaternion(cls, **kwargs) -> 'Orientation':
         kwargs_rot,kwargs_ori = Orientation._split_kwargs(kwargs,Rotation.from_quaternion)
         return cls(rotation=Rotation.from_quaternion(**kwargs_rot),**kwargs_ori)
 
 
     @classmethod
     @util.extended_docstring(Rotation.from_Euler_angles,_parameter_doc)
-    def from_Euler_angles(cls, **kwargs) -> "Orientation":
+    def from_Euler_angles(cls, **kwargs) -> 'Orientation':
         kwargs_rot,kwargs_ori = Orientation._split_kwargs(kwargs,Rotation.from_Euler_angles)
         return cls(rotation=Rotation.from_Euler_angles(**kwargs_rot),**kwargs_ori)
 
 
     @classmethod
     @util.extended_docstring(Rotation.from_axis_angle,_parameter_doc)
-    def from_axis_angle(cls, **kwargs) -> "Orientation":
+    def from_axis_angle(cls, **kwargs) -> 'Orientation':
         kwargs_rot,kwargs_ori = Orientation._split_kwargs(kwargs,Rotation.from_axis_angle)
         return cls(rotation=Rotation.from_axis_angle(**kwargs_rot),**kwargs_ori)
 
 
     @classmethod
     @util.extended_docstring(Rotation.from_basis,_parameter_doc)
-    def from_basis(cls, **kwargs) -> "Orientation":
+    def from_basis(cls, **kwargs) -> 'Orientation':
         kwargs_rot,kwargs_ori = Orientation._split_kwargs(kwargs,Rotation.from_basis)
         return cls(rotation=Rotation.from_basis(**kwargs_rot),**kwargs_ori)
 
 
     @classmethod
     @util.extended_docstring(Rotation.from_matrix,_parameter_doc)
-    def from_matrix(cls, **kwargs) -> "Orientation":
+    def from_matrix(cls, **kwargs) -> 'Orientation':
         kwargs_rot,kwargs_ori = Orientation._split_kwargs(kwargs,Rotation.from_matrix)
         return cls(rotation=Rotation.from_matrix(**kwargs_rot),**kwargs_ori)
 
 
     @classmethod
     @util.extended_docstring(Rotation.from_Rodrigues_vector,_parameter_doc)
-    def from_Rodrigues_vector(cls, **kwargs) -> "Orientation":
+    def from_Rodrigues_vector(cls, **kwargs) -> 'Orientation':
         kwargs_rot,kwargs_ori = Orientation._split_kwargs(kwargs,Rotation.from_Rodrigues_vector)
         return cls(rotation=Rotation.from_Rodrigues_vector(**kwargs_rot),**kwargs_ori)
 
 
     @classmethod
     @util.extended_docstring(Rotation.from_homochoric,_parameter_doc)
-    def from_homochoric(cls, **kwargs) -> "Orientation":
+    def from_homochoric(cls, **kwargs) -> 'Orientation':
         kwargs_rot,kwargs_ori = Orientation._split_kwargs(kwargs,Rotation.from_homochoric)
         return cls(rotation=Rotation.from_homochoric(**kwargs_rot),**kwargs_ori)
 
 
     @classmethod
     @util.extended_docstring(Rotation.from_cubochoric,_parameter_doc)
-    def from_cubochoric(cls, **kwargs) -> "Orientation":
+    def from_cubochoric(cls, **kwargs) -> 'Orientation':
         kwargs_rot,kwargs_ori = Orientation._split_kwargs(kwargs,Rotation.from_cubochoric)
         return cls(rotation=Rotation.from_cubochoric(**kwargs_rot),**kwargs_ori)
 
 
     @classmethod
     @util.extended_docstring(Rotation.from_spherical_component,_parameter_doc)
-    def from_spherical_component(cls, **kwargs) -> "Orientation":
+    def from_spherical_component(cls, **kwargs) -> 'Orientation':
         kwargs_rot,kwargs_ori = Orientation._split_kwargs(kwargs,Rotation.from_spherical_component)
         return cls(rotation=Rotation.from_spherical_component(**kwargs_rot),**kwargs_ori)
 
 
     @classmethod
     @util.extended_docstring(Rotation.from_fiber_component,_parameter_doc)
-    def from_fiber_component(cls, **kwargs) -> "Orientation":
+    def from_fiber_component(cls, **kwargs) -> 'Orientation':
         kwargs_rot,kwargs_ori = Orientation._split_kwargs(kwargs,Rotation.from_fiber_component)
         return cls(rotation=Rotation.from_fiber_component(**kwargs_rot),**kwargs_ori)
 
@@ -370,7 +370,7 @@ class Orientation(Rotation,Crystal):
     def from_directions(cls,
                         uvw: FloatSequence,
                         hkl: FloatSequence,
-                        **kwargs) -> "Orientation":
+                        **kwargs) -> 'Orientation':
         """
         Initialize orientation object from two crystallographic directions.
 
@@ -390,7 +390,7 @@ class Orientation(Rotation,Crystal):
 
 
     @property
-    def equivalent(self) -> "Orientation":
+    def equivalent(self) -> 'Orientation':
         """
         Orientations that are symmetrically equivalent.
 
@@ -404,7 +404,7 @@ class Orientation(Rotation,Crystal):
 
 
     @property
-    def reduced(self) -> "Orientation":
+    def reduced(self) -> 'Orientation':
         """Select symmetrically equivalent orientation that falls into fundamental zone according to symmetry."""
         eq   = self.equivalent
         ok   = eq.in_FZ
@@ -940,7 +940,7 @@ class Orientation(Rotation,Crystal):
 
 
     def related(self,
-                model: str) -> "Orientation":
+                model: str) -> 'Orientation':
         """
         Orientations derived from the given relationship.
 
diff --git a/python/damask/_rotation.py b/python/damask/_rotation.py
index b55f178f7..6e01cae65 100644
--- a/python/damask/_rotation.py
+++ b/python/damask/_rotation.py
@@ -65,7 +65,7 @@ class Rotation:
     __slots__ = ['quaternion']
 
     def __init__(self,
-                 rotation: Union[FloatSequence, "Rotation"] = np.array([1.0,0.0,0.0,0.0])):
+                 rotation: Union[FloatSequence, 'Rotation'] = np.array([1.0,0.0,0.0,0.0])):
         """
         New rotation.
 
@@ -83,7 +83,7 @@ class Rotation:
         elif np.array(rotation).shape[-1] == 4:
             self.quaternion = np.array(rotation)
         else:
-            raise TypeError('"rotation" is neither a Rotation nor a quaternion')
+            raise TypeError('Rotation is neither a Rotation nor a quaternion')
 
 
     def __repr__(self) -> str:
@@ -93,7 +93,7 @@ class Rotation:
 
 
     def __copy__(self,
-                 rotation: Union[FloatSequence, "Rotation"] = None) -> "Rotation":
+                 rotation: Union[FloatSequence, 'Rotation'] = None) -> 'Rotation':
         """Create deep copy."""
         dup = copy.deepcopy(self)
         if rotation is not None:
@@ -122,7 +122,7 @@ class Rotation:
 
         """
         if not isinstance(other, Rotation):
-            raise TypeError
+            return NotImplemented
         return np.logical_or(np.all(self.quaternion ==      other.quaternion,axis=-1),
                              np.all(self.quaternion == -1.0*other.quaternion,axis=-1))
 
@@ -143,7 +143,7 @@ class Rotation:
 
 
     def isclose(self,
-                other: "Rotation",
+                other: 'Rotation',
                 rtol: float = 1e-5,
                 atol: float = 1e-8,
                 equal_nan: bool = True) -> bool:
@@ -174,7 +174,7 @@ class Rotation:
 
 
     def allclose(self,
-                 other: "Rotation",
+                 other: 'Rotation',
                  rtol: float = 1e-5,
                  atol: float = 1e-8,
                  equal_nan: bool = True) -> Union[np.bool_, bool]:
@@ -220,14 +220,14 @@ class Rotation:
         return 0 if self.shape == () else self.shape[0]
 
 
-    def __invert__(self) -> "Rotation":
+    def __invert__(self) -> 'Rotation':
         """Inverse rotation (backward rotation)."""
         dup = self.copy()
         dup.quaternion[...,1:] *= -1
         return dup
 
 
-    def __pow__(self, exp: int) -> "Rotation":
+    def __pow__(self, exp: int) -> 'Rotation':
         """
         Perform the rotation 'exp' times.
 
@@ -241,7 +241,7 @@ class Rotation:
         p = self.quaternion[...,1:]/np.linalg.norm(self.quaternion[...,1:],axis=-1,keepdims=True)
         return self.copy(rotation=Rotation(np.block([np.cos(exp*phi),np.sin(exp*phi)*p]))._standardize())
 
-    def __ipow__(self, exp: int) -> "Rotation":
+    def __ipow__(self, exp: int) -> 'Rotation':
         """
         Perform the rotation 'exp' times (in-place).
 
@@ -254,7 +254,7 @@ class Rotation:
         return self**exp
 
 
-    def __mul__(self, other: "Rotation") -> "Rotation":
+    def __mul__(self, other: 'Rotation') -> 'Rotation':
         """
         Compose with other.
 
@@ -280,7 +280,7 @@ class Rotation:
         else:
             raise TypeError('Use "R@b", i.e. matmul, to apply rotation "R" to object "b"')
 
-    def __imul__(self, other: "Rotation") -> "Rotation":
+    def __imul__(self, other: 'Rotation') -> 'Rotation':
         """
         Compose with other (in-place).
 
@@ -293,7 +293,7 @@ class Rotation:
         return self*other
 
 
-    def __truediv__(self, other: "Rotation") -> "Rotation":
+    def __truediv__(self, other: 'Rotation') -> 'Rotation':
         """
         Compose with inverse of other.
 
@@ -313,7 +313,7 @@ class Rotation:
         else:
             raise TypeError('Use "R@b", i.e. matmul, to apply rotation "R" to object "b"')
 
-    def __itruediv__(self, other: "Rotation") -> "Rotation":
+    def __itruediv__(self, other: 'Rotation') -> 'Rotation':
         """
         Compose with inverse of other (in-place).
 
@@ -369,14 +369,14 @@ class Rotation:
     apply = __matmul__
 
 
-    def _standardize(self) -> "Rotation":
+    def _standardize(self) -> 'Rotation':
         """Standardize quaternion (ensure positive real hemisphere)."""
         self.quaternion[self.quaternion[...,0] < 0.0] *= -1
         return self
 
 
     def append(self,
-           other: Union["Rotation", List["Rotation"]]) -> "Rotation":
+           other: Union['Rotation', List['Rotation']]) -> 'Rotation':
         """
         Extend array along first dimension with other array(s).
 
@@ -390,7 +390,7 @@ class Rotation:
 
 
     def flatten(self,
-                order: Literal['C','F','A'] = 'C') -> "Rotation":
+                order: Literal['C','F','A'] = 'C') -> 'Rotation':
         """
         Flatten array.
 
@@ -405,7 +405,7 @@ class Rotation:
 
     def reshape(self,
                 shape: Union[int, Tuple[int, ...]],
-                order: Literal['C','F','A'] = 'C') -> "Rotation":
+                order: Literal['C','F','A'] = 'C') -> 'Rotation':
         """
         Reshape array.
 
@@ -421,7 +421,7 @@ class Rotation:
 
     def broadcast_to(self,
                      shape: Union[int, Tuple[int, ...]],
-                     mode: Literal["left", "right"] = 'right') -> "Rotation":
+                     mode: Literal['left', 'right'] = 'right') -> 'Rotation':
         """
         Broadcast array.
 
@@ -445,7 +445,7 @@ class Rotation:
 
 
     def average(self,
-                weights: np.ndarray = None) -> "Rotation":
+                weights: np.ndarray = None) -> 'Rotation':
         """
         Average along last array dimension.
 
@@ -485,7 +485,7 @@ class Rotation:
 
 
     def misorientation(self,
-                       other: "Rotation") -> "Rotation":
+                       other: 'Rotation') -> 'Rotation':
         """
         Calculate misorientation to other Rotation.
 
@@ -690,7 +690,7 @@ class Rotation:
     @staticmethod
     def from_quaternion(q: Union[Sequence[FloatSequence], np.ndarray],
                         accept_homomorph: bool = False,
-                        P: Literal[1, -1] = -1) -> "Rotation":
+                        P: Literal[1, -1] = -1) -> 'Rotation':
         """
         Initialize from quaternion.
 
@@ -724,7 +724,7 @@ class Rotation:
 
     @staticmethod
     def from_Euler_angles(phi: np.ndarray,
-                          degrees: bool = False) -> "Rotation":
+                          degrees: bool = False) -> 'Rotation':
         """
         Initialize from Bunge Euler angles.
 
@@ -755,7 +755,7 @@ class Rotation:
     def from_axis_angle(axis_angle: np.ndarray,
                         degrees:bool = False,
                         normalize: bool = False,
-                        P: Literal[1, -1] = -1) -> "Rotation":
+                        P: Literal[1, -1] = -1) -> 'Rotation':
         """
         Initialize from Axis angle pair.
 
@@ -792,7 +792,7 @@ class Rotation:
     @staticmethod
     def from_basis(basis: np.ndarray,
                    orthonormal: bool = True,
-                   reciprocal: bool = False) -> "Rotation":
+                   reciprocal: bool = False) -> 'Rotation':
         """
         Initialize from lattice basis vectors.
 
@@ -826,7 +826,7 @@ class Rotation:
         return Rotation(Rotation._om2qu(om))
 
     @staticmethod
-    def from_matrix(R: np.ndarray) -> "Rotation":
+    def from_matrix(R: np.ndarray) -> 'Rotation':
         """
         Initialize from rotation matrix.
 
@@ -840,7 +840,7 @@ class Rotation:
 
     @staticmethod
     def from_parallel(a: np.ndarray,
-                      b: np.ndarray ) -> "Rotation":
+                      b: np.ndarray ) -> 'Rotation':
         """
         Initialize from pairs of two orthogonal lattice basis vectors.
 
@@ -870,7 +870,7 @@ class Rotation:
     @staticmethod
     def from_Rodrigues_vector(rho: np.ndarray,
                               normalize: bool = False,
-                              P: Literal[1, -1] = -1) -> "Rotation":
+                              P: Literal[1, -1] = -1) -> 'Rotation':
         """
         Initialize from Rodrigues–Frank vector (angle separated from axis).
 
@@ -901,7 +901,7 @@ class Rotation:
 
     @staticmethod
     def from_homochoric(h: np.ndarray,
-                        P: Literal[1, -1] = -1) -> "Rotation":
+                        P: Literal[1, -1] = -1) -> 'Rotation':
         """
         Initialize from homochoric vector.
 
@@ -928,7 +928,7 @@ class Rotation:
 
     @staticmethod
     def from_cubochoric(x: np.ndarray,
-                        P: Literal[1, -1] = -1) -> "Rotation":
+                        P: Literal[1, -1] = -1) -> 'Rotation':
         """
         Initialize from cubochoric vector.
 
@@ -956,7 +956,7 @@ class Rotation:
 
     @staticmethod
     def from_random(shape: Tuple[int, ...] = None,
-                    rng_seed: Union[int, IntSequence] = None) -> "Rotation":
+                    rng_seed: Union[int, IntSequence] = None) -> 'Rotation':
         """
         Initialize with random rotation.
 
@@ -990,7 +990,7 @@ class Rotation:
                  N: int = 500,
                  degrees: bool = True,
                  fractions: bool = True,
-                 rng_seed: Union[None, int, IntSequence] = None) -> "Rotation":
+                 rng_seed: Union[None, int, IntSequence] = None) -> 'Rotation':
         """
         Sample discrete values from a binned orientation distribution function (ODF).
 
@@ -1043,11 +1043,11 @@ class Rotation:
 
 
     @staticmethod
-    def from_spherical_component(center: "Rotation",
+    def from_spherical_component(center: 'Rotation',
                                  sigma: float,
                                  N: int = 500,
                                  degrees: bool = True,
-                                 rng_seed: Union[None, int, IntSequence] = None) -> "Rotation":
+                                 rng_seed: Union[None, int, IntSequence] = None) -> 'Rotation':
         """
         Calculate set of rotations with Gaussian distribution around center.
 

From 3df411469b5cf2a68a845e54bfa6affa1d45f7fb Mon Sep 17 00:00:00 2001
From: Daniel Otto de Mentock <d.mentock@mpie.de>
Date: Wed, 2 Feb 2022 12:14:00 +0100
Subject: [PATCH 15/72] Added generic type to rotation functions not
 overwritten by orientation

---
 python/damask/_rotation.py | 43 ++++++++++++++++++++++----------------
 1 file changed, 25 insertions(+), 18 deletions(-)

diff --git a/python/damask/_rotation.py b/python/damask/_rotation.py
index 6e01cae65..a04b20e62 100644
--- a/python/damask/_rotation.py
+++ b/python/damask/_rotation.py
@@ -6,7 +6,7 @@ from . import tensor
 from . import util
 from . import grid_filters
 
-from typing import Union, Sequence, Tuple, Literal, List
+from typing import Union, Sequence, Tuple, Literal, List, TypeVar
 from ._typehints import FloatSequence, IntSequence
 
 _P = -1
@@ -16,6 +16,8 @@ _sc   = np.pi**(1./6.)/6.**(1./6.)
 _beta = np.pi**(5./6.)/6.**(1./6.)/2.
 _R1   = (3.*np.pi/4.)**(1./3.)
 
+MyType = TypeVar('MyType', bound='Rotation')
+
 class Rotation:
     u"""
     Rotation with functionality for conversion between different representations.
@@ -92,8 +94,8 @@ class Rotation:
                + str(self.quaternion)
 
 
-    def __copy__(self,
-                 rotation: Union[FloatSequence, 'Rotation'] = None) -> 'Rotation':
+    def __copy__(self: MyType,
+                 rotation: Union[FloatSequence, 'Rotation'] = None) -> MyType:
         """Create deep copy."""
         dup = copy.deepcopy(self)
         if rotation is not None:
@@ -220,14 +222,15 @@ class Rotation:
         return 0 if self.shape == () else self.shape[0]
 
 
-    def __invert__(self) -> 'Rotation':
+    def __invert__(self: MyType) -> MyType:
         """Inverse rotation (backward rotation)."""
         dup = self.copy()
         dup.quaternion[...,1:] *= -1
         return dup
 
 
-    def __pow__(self, exp: int) -> 'Rotation':
+    def __pow__(self: MyType,
+                exp: int) -> MyType:
         """
         Perform the rotation 'exp' times.
 
@@ -241,7 +244,8 @@ class Rotation:
         p = self.quaternion[...,1:]/np.linalg.norm(self.quaternion[...,1:],axis=-1,keepdims=True)
         return self.copy(rotation=Rotation(np.block([np.cos(exp*phi),np.sin(exp*phi)*p]))._standardize())
 
-    def __ipow__(self, exp: int) -> 'Rotation':
+    def __ipow__(self: MyType,
+                 exp: int) -> MyType:
         """
         Perform the rotation 'exp' times (in-place).
 
@@ -280,7 +284,8 @@ class Rotation:
         else:
             raise TypeError('Use "R@b", i.e. matmul, to apply rotation "R" to object "b"')
 
-    def __imul__(self, other: 'Rotation') -> 'Rotation':
+    def __imul__(self,
+                 other: 'Rotation') -> 'Rotation':
         """
         Compose with other (in-place).
 
@@ -293,7 +298,8 @@ class Rotation:
         return self*other
 
 
-    def __truediv__(self, other: 'Rotation') -> 'Rotation':
+    def __truediv__(self: 'Rotation',
+                    other: 'Rotation') -> 'Rotation':
         """
         Compose with inverse of other.
 
@@ -313,7 +319,8 @@ class Rotation:
         else:
             raise TypeError('Use "R@b", i.e. matmul, to apply rotation "R" to object "b"')
 
-    def __itruediv__(self, other: 'Rotation') -> 'Rotation':
+    def __itruediv__(self: 'Rotation',
+                     other: 'Rotation') -> 'Rotation':
         """
         Compose with inverse of other (in-place).
 
@@ -369,14 +376,14 @@ class Rotation:
     apply = __matmul__
 
 
-    def _standardize(self) -> 'Rotation':
+    def _standardize(self: MyType) -> MyType:
         """Standardize quaternion (ensure positive real hemisphere)."""
         self.quaternion[self.quaternion[...,0] < 0.0] *= -1
         return self
 
 
-    def append(self,
-           other: Union['Rotation', List['Rotation']]) -> 'Rotation':
+    def append(self: MyType,
+               other: Union[MyType, List[MyType]]) -> MyType:
         """
         Extend array along first dimension with other array(s).
 
@@ -389,8 +396,8 @@ class Rotation:
                                                       [self]+other if isinstance(other,list) else [self,other]))))
 
 
-    def flatten(self,
-                order: Literal['C','F','A'] = 'C') -> 'Rotation':
+    def flatten(self: MyType,
+                order: Literal['C','F','A'] = 'C') -> MyType:
         """
         Flatten array.
 
@@ -403,9 +410,9 @@ class Rotation:
         return self.copy(rotation=self.quaternion.reshape((-1,4),order=order))
 
 
-    def reshape(self,
+    def reshape(self: MyType,
                 shape: Union[int, Tuple[int, ...]],
-                order: Literal['C','F','A'] = 'C') -> 'Rotation':
+                order: Literal['C','F','A'] = 'C') -> MyType:
         """
         Reshape array.
 
@@ -419,9 +426,9 @@ class Rotation:
         return self.copy(rotation=self.quaternion.reshape(tuple(shape)+(4,),order=order))
 
 
-    def broadcast_to(self,
+    def broadcast_to(self: MyType,
                      shape: Union[int, Tuple[int, ...]],
-                     mode: Literal['left', 'right'] = 'right') -> 'Rotation':
+                     mode: Literal['left', 'right'] = 'right') -> MyType:
         """
         Broadcast array.
 

From fc8cd6322c52eebc13c1485aea64e79328e1b8e6 Mon Sep 17 00:00:00 2001
From: Daniel Otto de Mentock <d.mentock@mpie.de>
Date: Wed, 2 Feb 2022 12:16:57 +0100
Subject: [PATCH 16/72] adjusted rng_seed type in rotation adjusted
 NotImplemented error return in orientation

---
 python/damask/_orientation.py | 2 +-
 python/damask/_rotation.py    | 4 ++--
 2 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/python/damask/_orientation.py b/python/damask/_orientation.py
index 8a560e756..dff380dcf 100644
--- a/python/damask/_orientation.py
+++ b/python/damask/_orientation.py
@@ -148,7 +148,7 @@ class Orientation(Rotation,Crystal):
 
         """
         if not isinstance(other, Orientation):
-            raise NotImplemented
+            return NotImplemented
         matching_type = self.family == other.family and \
                         self.lattice == other.lattice and \
                         self.parameters == other.parameters
diff --git a/python/damask/_rotation.py b/python/damask/_rotation.py
index a04b20e62..361dba7c1 100644
--- a/python/damask/_rotation.py
+++ b/python/damask/_rotation.py
@@ -997,7 +997,7 @@ class Rotation:
                  N: int = 500,
                  degrees: bool = True,
                  fractions: bool = True,
-                 rng_seed: Union[None, int, IntSequence] = None) -> 'Rotation':
+                 rng_seed: Union[int, IntSequence] = None) -> 'Rotation':
         """
         Sample discrete values from a binned orientation distribution function (ODF).
 
@@ -1054,7 +1054,7 @@ class Rotation:
                                  sigma: float,
                                  N: int = 500,
                                  degrees: bool = True,
-                                 rng_seed: Union[None, int, IntSequence] = None) -> 'Rotation':
+                                 rng_seed: Union[int, IntSequence] = None) -> 'Rotation':
         """
         Calculate set of rotations with Gaussian distribution around center.
 

From f80de7d0b36b8dcd63e876a43763e4a897fdd01e Mon Sep 17 00:00:00 2001
From: Daniel Otto de Mentock <d.mentock@mpie.de>
Date: Thu, 3 Feb 2022 12:04:31 +0100
Subject: [PATCH 17/72] added NumpyRngSeed type to rotation rng_seed objects

---
 python/damask/_rotation.py | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/python/damask/_rotation.py b/python/damask/_rotation.py
index 361dba7c1..d919c9029 100644
--- a/python/damask/_rotation.py
+++ b/python/damask/_rotation.py
@@ -7,7 +7,7 @@ from . import util
 from . import grid_filters
 
 from typing import Union, Sequence, Tuple, Literal, List, TypeVar
-from ._typehints import FloatSequence, IntSequence
+from ._typehints import FloatSequence, IntSequence, NumpyRngSeed
 
 _P = -1
 
@@ -963,7 +963,7 @@ class Rotation:
 
     @staticmethod
     def from_random(shape: Tuple[int, ...] = None,
-                    rng_seed: Union[int, IntSequence] = None) -> 'Rotation':
+                    rng_seed: NumpyRngSeed = None) -> 'Rotation':
         """
         Initialize with random rotation.
 
@@ -997,7 +997,7 @@ class Rotation:
                  N: int = 500,
                  degrees: bool = True,
                  fractions: bool = True,
-                 rng_seed: Union[int, IntSequence] = None) -> 'Rotation':
+                 rng_seed: NumpyRngSeed = None) -> 'Rotation':
         """
         Sample discrete values from a binned orientation distribution function (ODF).
 
@@ -1054,7 +1054,7 @@ class Rotation:
                                  sigma: float,
                                  N: int = 500,
                                  degrees: bool = True,
-                                 rng_seed: Union[int, IntSequence] = None) -> 'Rotation':
+                                 rng_seed: NumpyRngSeed = None) -> 'Rotation':
         """
         Calculate set of rotations with Gaussian distribution around center.
 
@@ -1090,7 +1090,7 @@ class Rotation:
                              sigma: float = 0.0,
                              N: int = 500,
                              degrees: bool = True,
-                             rng_seed: Union[int, IntSequence] = None):
+                             rng_seed: NumpyRngSeed = None):
         """
         Calculate set of rotations with Gaussian distribution around direction.
 

From d1f9e98e3ce071c9e24488675bc6ed9b579fb524 Mon Sep 17 00:00:00 2001
From: Daniel Otto de Mentock <d.mentock@mpie.de>
Date: Thu, 3 Feb 2022 16:11:09 +0100
Subject: [PATCH 18/72] moved typecheck of __ne__ functions to __eq__

added initial empty runtimeerror to Schmid function

minor corrections
---
 python/damask/_orientation.py | 13 ++++++++-----
 python/damask/_rotation.py    |  7 ++++---
 2 files changed, 12 insertions(+), 8 deletions(-)

diff --git a/python/damask/_orientation.py b/python/damask/_orientation.py
index dff380dcf..780a5929e 100644
--- a/python/damask/_orientation.py
+++ b/python/damask/_orientation.py
@@ -165,8 +165,10 @@ class Orientation(Rotation,Crystal):
             Orientation to check for equality.
 
         """
-        if not isinstance(other, Orientation):
-            raise TypeError
+
+        eq = self.__eq__(other)
+        if not isinstance(eq, bool):
+            return eq
         return np.logical_not(self==other)
 
 
@@ -557,7 +559,7 @@ class Orientation(Rotation,Crystal):
         if self.family != other.family:
             raise NotImplementedError('disorientation between different crystal families')
 
-        blend: Tuple[int, ...] = util.shapeblender(self.shape,other.shape)
+        blend = util.shapeblender(self.shape,other.shape)
         s = self.equivalent
         o = other.equivalent
 
@@ -764,7 +766,7 @@ class Orientation(Rotation,Crystal):
                                                       np.broadcast_to(self.standard_triangle['improper'], vector_.shape+(3,)),
                                                       vector_), 12)
             in_SST_ = np.all(components_proper   >= 0.0,axis=-1) \
-                   | np.all(components_improper >= 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:
@@ -928,7 +930,8 @@ class Orientation(Rotation,Crystal):
                             (self.kinematics('twin'),N_twin)
         if active == '*': active = [len(a) for a in kinematics['direction']]
 
-        assert active
+        if not active:
+            raise RuntimeError
         d = self.to_frame(uvw=np.vstack([kinematics['direction'][i][:n] for i,n in enumerate(active)]))
         p = self.to_frame(hkl=np.vstack([kinematics['plane'][i][:n] for i,n in enumerate(active)]))
         P = np.einsum('...i,...j',d/np.linalg.norm(d,axis=1,keepdims=True),
diff --git a/python/damask/_rotation.py b/python/damask/_rotation.py
index d919c9029..c3f6407f2 100644
--- a/python/damask/_rotation.py
+++ b/python/damask/_rotation.py
@@ -85,7 +85,7 @@ class Rotation:
         elif np.array(rotation).shape[-1] == 4:
             self.quaternion = np.array(rotation)
         else:
-            raise TypeError('Rotation is neither a Rotation nor a quaternion')
+            raise TypeError('"rotation" is neither a Rotation nor a quaternion')
 
 
     def __repr__(self) -> str:
@@ -139,8 +139,9 @@ class Rotation:
             Rotation to check for inequality.
 
         """
-        if not isinstance(other, Rotation):
-            raise TypeError
+        eq = self.__eq__(other)
+        if not isinstance(eq, bool):
+            return eq
         return np.logical_not(self==other)
 
 

From c70e535da83d876d52b636149503a5d5f3365871 Mon Sep 17 00:00:00 2001
From: Martin Diehl <mail@martin-diehl.net>
Date: Fri, 4 Feb 2022 00:11:08 +0100
Subject: [PATCH 19/72] avoid access by el/ip

---
 src/phase_mechanical_plastic_nonlocal.f90 | 36 ++++++++++++-----------
 1 file changed, 19 insertions(+), 17 deletions(-)

diff --git a/src/phase_mechanical_plastic_nonlocal.f90 b/src/phase_mechanical_plastic_nonlocal.f90
index a8f56b5c5..81ce4d08e 100644
--- a/src/phase_mechanical_plastic_nonlocal.f90
+++ b/src/phase_mechanical_plastic_nonlocal.f90
@@ -123,8 +123,10 @@ submodule(phase:plastic) nonlocal
 
   type :: tNonlocalDependentState
     real(pReal), allocatable, dimension(:,:) :: &
-     tau_pass, &
-     tau_Back
+      tau_pass, &
+      tau_Back
+    real(pReal), allocatable, dimension(:,:,:,:,:) :: &
+      compatibility
   end type tNonlocalDependentState
 
   type :: tNonlocalState
@@ -160,7 +162,6 @@ submodule(phase:plastic) nonlocal
     state0
 
   type(tParameters), dimension(:), allocatable :: param                                             !< containers of constitutive parameters
-
   type(tNonlocalDependentState), dimension(:), allocatable :: dependentState
 
 contains
@@ -489,6 +490,7 @@ module function plastic_nonlocal_init() result(myPlasticity)
 
     allocate(dst%tau_pass(prm%sum_N_sl,Nmembers),source=0.0_pReal)
     allocate(dst%tau_back(prm%sum_N_sl,Nmembers),source=0.0_pReal)
+    allocate(dst%compatibility(2,maxval(param%sum_N_sl),maxval(param%sum_N_sl),nIPneighbors,Nmembers),source=0.0_pReal)
     end associate
 
     if (Nmembers > 0) call stateInit(ini,ph,Nmembers)
@@ -669,7 +671,7 @@ module subroutine nonlocal_dependentState(ph, en, ip, el)
                                           - discretization_IPcoords(1:3,el+neighbor_ip-1))
             normal_latticeConf = matmul(transpose(invFp), IPareaNormal(1:3,n,ip,el))
             if (math_inner(normal_latticeConf,connection_latticeConf(1:3,n)) < 0.0_pReal) &         ! neighboring connection points in opposite direction to face normal: must be periodic image
-              connection_latticeConf(1:3,n) = normal_latticeConf * IPvolume(ip,el)/IParea(n,ip,el)  ! instead take the surface normal scaled with the diameter of the cell
+              connection_latticeConf(1:3,n) = normal_latticeConf * geom(ph)%V_0(en)/IParea(n,ip,el)  ! instead take the surface normal scaled with the diameter of the cell
         else
           ! local neighbor or different lattice structure or different constitution instance -> use central values instead
           connection_latticeConf(1:3,n) = 0.0_pReal
@@ -1110,7 +1112,7 @@ module subroutine nonlocal_dotState(Mp,timestep, &
      .or. any(rho(:,dip) + rhoDot(:,9:10) * timestep < -prm%atol_rho)) then
 #ifdef DEBUG
     if (debugConstitutive%extensive) then
-      print'(a,i5,a,i2)', '<< CONST >> evolution rate leads to negative density at el ',el,' ip ',ip
+      print'(a,i5,a,i2)', '<< CONST >> evolution rate leads to negative density at ph ',ph,' en ',en
       print'(a)', '<< CONST >> enforcing cutback !!!'
     end if
 #endif
@@ -1215,14 +1217,14 @@ function rhoDotFlux(timestep,ph,en,ip,el)
     !*** check CFL (Courant-Friedrichs-Lewy) condition for flux
     if (any( abs(dot_gamma) > 0.0_pReal &                                                           ! any active slip system ...
             .and. prm%C_CFL * abs(v0) * timestep &
-                > IPvolume(ip,el) / maxval(IParea(:,ip,el)))) then                                  ! ...with velocity above critical value (we use the reference volume and area for simplicity here)
+                > geom(ph)%V_0(en)/ maxval(IParea(:,ip,el)))) then                                  ! ...with velocity above critical value (we use the reference volume and area for simplicity here)
 #ifdef DEBUG
     if (debugConstitutive%extensive) then
-      print'(a,i5,a,i2)', '<< CONST >> CFL condition not fullfilled at el ',el,' ip ',ip
+      print'(a,i5,a,i2)', '<< CONST >> CFL condition not fullfilled at ph ',ph,' en ',en
       print'(a,e10.3,a,e10.3)', '<< CONST >> velocity is at  ', &
         maxval(abs(v0), abs(dot_gamma) > 0.0_pReal &
                        .and.  prm%C_CFL * abs(v0) * timestep &
-                             > IPvolume(ip,el) / maxval(IParea(:,ip,el))), &
+                             > geom(ph)%V_0(en) / maxval(IParea(:,ip,el))), &
         ' at a timestep of ',timestep
       print*, '<< CONST >> enforcing cutback !!!'
     end if
@@ -1277,7 +1279,7 @@ function rhoDotFlux(timestep,ph,en,ip,el)
       !* compatibility
       if (neighbor_n > 0) then
       if (phase_plasticity(material_phaseAt(1,neighbor_el)) == PLASTIC_NONLOCAL_ID .and. &
-          any(compatibility(:,:,:,n,ip,el) > 0.0_pReal)) then
+          any(dependentState(ph)%compatibility(:,:,:,n,en) > 0.0_pReal)) then
 
         forall (s = 1:ns, t = 1:4)
           neighbor_v0(s,t) =          plasticState(np)%state0(iV   (s,t,neighbor_ph),no)
@@ -1301,12 +1303,12 @@ function rhoDotFlux(timestep,ph,en,ip,el)
                 .and. v0(s,t) * neighbor_v0(s,t) >= 0.0_pReal ) then                                ! ... only if no sign change in flux density
               lineLength = neighbor_rhoSgl0(s,t) * neighbor_v0(s,t) &
                          * math_inner(m(1:3,s,t), normal_neighbor2me) * area                        ! positive line length that wants to enter through this interface
-              where (compatibility(c,:,s,n,ip,el) > 0.0_pReal) &
+              where (dependentState(ph)%compatibility(c,:,s,n,en) > 0.0_pReal) &
                 rhoDotFlux(:,t) = rhoDotFlux(1:ns,t) &
-                                + lineLength/IPvolume(ip,el)*compatibility(c,:,s,n,ip,el)**2        ! transferring to equally signed mobile dislocation type
-              where (compatibility(c,:,s,n,ip,el) < 0.0_pReal) &
+                                + lineLength/geom(ph)%V_0(en)*dependentState(ph)%compatibility(c,:,s,n,en)**2        ! transferring to equally signed mobile dislocation type
+              where (dependentState(ph)%compatibility(c,:,s,n,en) < 0.0_pReal) &
                 rhoDotFlux(:,topp) = rhoDotFlux(:,topp) &
-                                   + lineLength/IPvolume(ip,el)*compatibility(c,:,s,n,ip,el)**2     ! transferring to opposite signed mobile dislocation type
+                                   + lineLength/geom(ph)%V_0(en)*dependentState(ph)%compatibility(c,:,s,n,en)**2     ! transferring to opposite signed mobile dislocation type
 
             end if
           end do
@@ -1335,15 +1337,15 @@ function rhoDotFlux(timestep,ph,en,ip,el)
             c = (t + 1) / 2
             if (v0(s,t) * math_inner(m(1:3,s,t), normal_me2neighbor) > 0.0_pReal ) then             ! flux from en to my neighbor == leaving flux for en (might also be a pure flux from my mobile density to dead density if interface not at all transmissive)
               if (v0(s,t) * neighbor_v0(s,t) >= 0.0_pReal) then                                     ! no sign change in flux density
-                transmissivity = sum(compatibility(c,:,s,n,ip,el)**2)                               ! overall transmissivity from this slip system to my neighbor
+                transmissivity = sum(dependentState(ph)%compatibility(c,:,s,n,en)**2)               ! overall transmissivity from this slip system to my neighbor
               else                                                                                  ! sign change in flux density means sign change in stress which does not allow for dislocations to arive at the neighbor
                 transmissivity = 0.0_pReal
               end if
               lineLength = my_rhoSgl0(s,t) * v0(s,t) &
                          * math_inner(m(1:3,s,t), normal_me2neighbor) * area                        ! positive line length of mobiles that wants to leave through this interface
-              rhoDotFlux(s,t) = rhoDotFlux(s,t) - lineLength / IPvolume(ip,el)                      ! subtract dislocation flux from current type
+              rhoDotFlux(s,t) = rhoDotFlux(s,t) - lineLength / geom(ph)%V_0(en)                     ! subtract dislocation flux from current type
               rhoDotFlux(s,t+4) = rhoDotFlux(s,t+4) &
-                                + lineLength / IPvolume(ip,el) * (1.0_pReal - transmissivity) &
+                                + lineLength / geom(ph)%V_0(en) * (1.0_pReal - transmissivity) &
                                 * sign(1.0_pReal, v0(s,t))                                          ! dislocation flux that is not able to leave through interface (because of low transmissivity) will remain as immobile single density at the material point
             end if
           end do
@@ -1465,7 +1467,7 @@ module subroutine plastic_nonlocal_updateCompatibility(orientation,ph,i,e)
 
     end do neighbors
 
-    compatibility(:,:,:,:,i,e) = my_compatibility
+    dependentState(ph)%compatibility(:,:,:,:,material_phaseEntry(1,(e-1)*discretization_nIPs + i)) = my_compatibility
 
   end associate
 

From 8b12814eec5678221d7b0e2535a9d5f53a105266 Mon Sep 17 00:00:00 2001
From: Martin Diehl <mail@martin-diehl.net>
Date: Fri, 4 Feb 2022 06:42:14 +0100
Subject: [PATCH 20/72] common variable names

---
 src/phase.f90                             |  6 +++---
 src/phase_mechanical_plastic_nonlocal.f90 | 14 +++++++-------
 2 files changed, 10 insertions(+), 10 deletions(-)

diff --git a/src/phase.f90 b/src/phase.f90
index b7bace81a..82bc44bfd 100644
--- a/src/phase.f90
+++ b/src/phase.f90
@@ -264,11 +264,11 @@ module phase
       real(pReal) :: f
     end function phase_f_T
 
-    module subroutine plastic_nonlocal_updateCompatibility(orientation,ph,i,e)
+    module subroutine plastic_nonlocal_updateCompatibility(orientation,ph,ip,el)
       integer, intent(in) :: &
         ph, &
-        i, &
-        e
+        ip, &
+        el
         type(tRotationContainer), dimension(:), intent(in) :: orientation
     end subroutine plastic_nonlocal_updateCompatibility
 
diff --git a/src/phase_mechanical_plastic_nonlocal.f90 b/src/phase_mechanical_plastic_nonlocal.f90
index 81ce4d08e..bb36aee06 100644
--- a/src/phase_mechanical_plastic_nonlocal.f90
+++ b/src/phase_mechanical_plastic_nonlocal.f90
@@ -1366,14 +1366,14 @@ end function rhoDotFlux
 ! plane normals and signed cosine of the angle between the slip directions. Only the largest values
 ! that sum up to a total of 1 are considered, all others are set to zero.
 !--------------------------------------------------------------------------------------------------
-module subroutine plastic_nonlocal_updateCompatibility(orientation,ph,i,e)
+module subroutine plastic_nonlocal_updateCompatibility(orientation,ph,ip,el)
 
   type(tRotationContainer), dimension(:), intent(in) :: &
     orientation                                                                                     ! crystal orientation
   integer, intent(in) :: &
     ph, &
-    i, &
-    e
+    ip, &
+    el
 
   integer :: &
     n, &                                                                                            ! neighbor index
@@ -1399,14 +1399,14 @@ module subroutine plastic_nonlocal_updateCompatibility(orientation,ph,i,e)
   associate(prm => param(ph))
     ns = prm%sum_N_sl
 
-    en = material_phaseMemberAt(1,i,e)
+    en = material_phaseMemberAt(1,ip,el)
     !*** start out fully compatible
     my_compatibility = 0.0_pReal
     forall(s1 = 1:ns) my_compatibility(:,s1,s1,:) = 1.0_pReal
 
     neighbors: do n = 1,nIPneighbors
-      neighbor_e = IPneighborhood(1,n,i,e)
-      neighbor_i = IPneighborhood(2,n,i,e)
+      neighbor_e = IPneighborhood(1,n,ip,el)
+      neighbor_i = IPneighborhood(2,n,ip,el)
       neighbor_me = material_phaseMemberAt(1,neighbor_i,neighbor_e)
       neighbor_phase = material_phaseAt(1,neighbor_e)
 
@@ -1467,7 +1467,7 @@ module subroutine plastic_nonlocal_updateCompatibility(orientation,ph,i,e)
 
     end do neighbors
 
-    dependentState(ph)%compatibility(:,:,:,:,material_phaseEntry(1,(e-1)*discretization_nIPs + i)) = my_compatibility
+    dependentState(ph)%compatibility(:,:,:,:,material_phaseEntry(1,(el-1)*discretization_nIPs + ip)) = my_compatibility
 
   end associate
 

From 900ef0a2c96544d5d72246e86f0f00e3ee6ad93f Mon Sep 17 00:00:00 2001
From: Martin Diehl <mail@martin-diehl.net>
Date: Fri, 4 Feb 2022 07:33:12 +0100
Subject: [PATCH 21/72] store IP neighborhood for ph/en access

---
 src/phase_mechanical_plastic_nonlocal.f90 | 63 ++++++++++++++---------
 1 file changed, 40 insertions(+), 23 deletions(-)

diff --git a/src/phase_mechanical_plastic_nonlocal.f90 b/src/phase_mechanical_plastic_nonlocal.f90
index bb36aee06..78271b92f 100644
--- a/src/phase_mechanical_plastic_nonlocal.f90
+++ b/src/phase_mechanical_plastic_nonlocal.f90
@@ -15,6 +15,9 @@ submodule(phase:plastic) nonlocal
 
   type :: tGeometry
     real(pReal), dimension(:), allocatable :: V_0
+    integer, dimension(:,:,:), allocatable :: IPneighborhood
+    real(pReal), dimension(:,:), allocatable :: IParea
+    real(pReal), dimension(:,:,:), allocatable :: IPareaNormal
   end type tGeometry
 
   type(tGeometry), dimension(:), allocatable :: geom
@@ -407,6 +410,9 @@ module function plastic_nonlocal_init() result(myPlasticity)
     call phase_allocateState(plasticState(ph),Nmembers,sizeState,sizeDotState,sizeDeltaState,0)     ! ToDo: state structure does not follow convention
 
     allocate(geom(ph)%V_0(Nmembers))
+    allocate(geom(ph)%IPneighborhood(3,nIPneighbors,Nmembers))
+    allocate(geom(ph)%IPareaNormal(3,nIPneighbors,Nmembers))
+    allocate(geom(ph)%IParea(nIPneighbors,Nmembers))
     call storeGeometry(ph)
 
     if(plasticState(ph)%nonlocal .and. .not. allocated(IPneighborhood)) &
@@ -652,8 +658,8 @@ module subroutine nonlocal_dependentState(ph, en, ip, el)
     nRealNeighbors = 0.0_pReal
     neighbor_rhoTotal = 0.0_pReal
     do n = 1,nIPneighbors
-      neighbor_el = IPneighborhood(1,n,ip,el)
-      neighbor_ip = IPneighborhood(2,n,ip,el)
+      neighbor_el = geom(ph)%IPneighborhood(1,n,en)
+      neighbor_ip = geom(ph)%IPneighborhood(2,n,en)
       no = material_phasememberAt(1,neighbor_ip,neighbor_el)
       if (neighbor_el > 0 .and. neighbor_ip > 0) then
         if (material_phaseAt(1,neighbor_el) == ph) then
@@ -669,9 +675,9 @@ module subroutine nonlocal_dependentState(ph, en, ip, el)
 
             connection_latticeConf(1:3,n) = matmul(invFe, discretization_IPcoords(1:3,neighbor_el+neighbor_ip-1) &
                                           - discretization_IPcoords(1:3,el+neighbor_ip-1))
-            normal_latticeConf = matmul(transpose(invFp), IPareaNormal(1:3,n,ip,el))
+            normal_latticeConf = matmul(transpose(invFp), geom(ph)%IPareaNormal(1:3,n,en))
             if (math_inner(normal_latticeConf,connection_latticeConf(1:3,n)) < 0.0_pReal) &         ! neighboring connection points in opposite direction to face normal: must be periodic image
-              connection_latticeConf(1:3,n) = normal_latticeConf * geom(ph)%V_0(en)/IParea(n,ip,el)  ! instead take the surface normal scaled with the diameter of the cell
+              connection_latticeConf(1:3,n) = normal_latticeConf * geom(ph)%V_0(en)/geom(ph)%IParea(n,en)  ! instead take the surface normal scaled with the diameter of the cell
         else
           ! local neighbor or different lattice structure or different constitution instance -> use central values instead
           connection_latticeConf(1:3,n) = 0.0_pReal
@@ -1101,7 +1107,7 @@ module subroutine nonlocal_dotState(Mp,timestep, &
                                          - rhoDip(s,1) / timestep - rhoDotAthermalAnnihilation(s,9) &
                                                                   - rhoDotSingle2DipoleGlide(s,9))  ! make sure that we do not annihilate more dipoles than we have
 
-  rhoDot = rhoDotFlux(timestep, ph,en,ip,el) &
+  rhoDot = rhoDotFlux(timestep, ph,en) &
          + rhoDotMultiplication &
          + rhoDotSingle2DipoleGlide &
          + rhoDotAthermalAnnihilation &
@@ -1131,17 +1137,15 @@ end subroutine nonlocal_dotState
 !> @brief calculates the rate of change of microstructure
 !---------------------------------------------------------------------------------------------------
 #if __INTEL_COMPILER >= 2020
-non_recursive function rhoDotFlux(timestep,ph,en,ip,el)
+non_recursive function rhoDotFlux(timestep,ph,en)
 #else
-function rhoDotFlux(timestep,ph,en,ip,el)
+function rhoDotFlux(timestep,ph,en)
 #endif
   real(pReal), intent(in) :: &
     timestep                                                                                        !< substepped crystallite time increment
   integer, intent(in) :: &
     ph, &
-    en, &
-    ip, &                                                                                           !< current integration point
-    el                                                                                              !< current element number
+    en
 
   integer ::  &
     neighbor_ph, &                                                                                  !< phase of my neighbor's plasticity
@@ -1217,14 +1221,14 @@ function rhoDotFlux(timestep,ph,en,ip,el)
     !*** check CFL (Courant-Friedrichs-Lewy) condition for flux
     if (any( abs(dot_gamma) > 0.0_pReal &                                                           ! any active slip system ...
             .and. prm%C_CFL * abs(v0) * timestep &
-                > geom(ph)%V_0(en)/ maxval(IParea(:,ip,el)))) then                                  ! ...with velocity above critical value (we use the reference volume and area for simplicity here)
+                > geom(ph)%V_0(en)/ maxval(geom(ph)%IParea(:,en)))) then                            ! ...with velocity above critical value (we use the reference volume and area for simplicity here)
 #ifdef DEBUG
     if (debugConstitutive%extensive) then
       print'(a,i5,a,i2)', '<< CONST >> CFL condition not fullfilled at ph ',ph,' en ',en
       print'(a,e10.3,a,e10.3)', '<< CONST >> velocity is at  ', &
         maxval(abs(v0), abs(dot_gamma) > 0.0_pReal &
                        .and.  prm%C_CFL * abs(v0) * timestep &
-                             > geom(ph)%V_0(en) / maxval(IParea(:,ip,el))), &
+                             > geom(ph)%V_0(en) / maxval(geom(ph)%IParea(:,en))), &
         ' at a timestep of ',timestep
       print*, '<< CONST >> enforcing cutback !!!'
     end if
@@ -1247,16 +1251,16 @@ function rhoDotFlux(timestep,ph,en,ip,el)
 
     neighbors: do n = 1,nIPneighbors
 
-      neighbor_el = IPneighborhood(1,n,ip,el)
-      neighbor_ip = IPneighborhood(2,n,ip,el)
-      neighbor_n  = IPneighborhood(3,n,ip,el)
+      neighbor_el = geom(ph)%IPneighborhood(1,n,en)
+      neighbor_ip = geom(ph)%IPneighborhood(2,n,en)
+      neighbor_n  = geom(ph)%IPneighborhood(3,n,en)
       np = material_phaseAt(1,neighbor_el)
       no = material_phasememberAt(1,neighbor_ip,neighbor_el)
 
       opposite_neighbor = n + mod(n,2) - mod(n+1,2)
-      opposite_el = IPneighborhood(1,opposite_neighbor,ip,el)
-      opposite_ip = IPneighborhood(2,opposite_neighbor,ip,el)
-      opposite_n  = IPneighborhood(3,opposite_neighbor,ip,el)
+      opposite_el = geom(ph)%IPneighborhood(1,opposite_neighbor,en)
+      opposite_ip = geom(ph)%IPneighborhood(2,opposite_neighbor,en)
+      opposite_n  = geom(ph)%IPneighborhood(3,opposite_neighbor,en)
 
       if (neighbor_n > 0) then                                                                      ! if neighbor exists, average deformation gradient
         neighbor_ph = material_phaseAt(1,neighbor_el)
@@ -1327,10 +1331,10 @@ function rhoDotFlux(timestep,ph,en,ip,el)
       if (phase_plasticity(material_phaseAt(1,opposite_el)) == PLASTIC_NONLOCAL_ID) then
 
         normal_me2neighbor_defConf = math_det33(Favg) &
-                                   * matmul(math_inv33(transpose(Favg)),IPareaNormal(1:3,n,ip,el))  ! normal of the interface in (average) deformed configuration (pointing en => neighbor)
+                                   * matmul(math_inv33(transpose(Favg)),geom(ph)%IPareaNormal(1:3,n,en))  ! normal of the interface in (average) deformed configuration (pointing en => neighbor)
         normal_me2neighbor = matmul(transpose(my_Fe), normal_me2neighbor_defConf) &
                            / math_det33(my_Fe)                                                      ! interface normal in my lattice configuration
-        area = IParea(n,ip,el) * norm2(normal_me2neighbor)
+        area = geom(ph)%IParea(n,en) * norm2(normal_me2neighbor)
         normal_me2neighbor = normal_me2neighbor / norm2(normal_me2neighbor)                         ! normalize the surface normal to unit length
         do s = 1,ns
           do t = 1,4
@@ -1758,14 +1762,27 @@ subroutine storeGeometry(ph)
 
   integer, intent(in) :: ph
 
-  integer :: ce, co
+  integer :: ce, co, nCell
   real(pReal), dimension(:), allocatable :: V
+  integer, dimension(:,:,:), allocatable :: neighborhood
+  real(pReal), dimension(:,:), allocatable :: area
+  real(pReal), dimension(:,:,:), allocatable :: areaNormal
 
+  nCell = product(shape(IPvolume))
+
+  V = reshape(IPvolume,[nCell])
+  neighborhood = reshape(IPneighborhood,[3,nIPneighbors,nCell])
+  area = reshape(IParea,[nIPneighbors,nCell])
+  areaNormal = reshape(IPareaNormal,[3,nIPneighbors,nCell])
 
-  V = reshape(IPvolume,[product(shape(IPvolume))])
   do ce = 1, size(material_homogenizationEntry,1)
     do co = 1, homogenization_maxNconstituents
-      if (material_phaseID(co,ce) == ph) geom(ph)%V_0(material_phaseEntry(co,ce)) = V(ce)
+      if (material_phaseID(co,ce) == ph) then
+        geom(ph)%V_0(material_phaseEntry(co,ce)) = V(ce)
+        geom(ph)%IPneighborhood(:,:,material_phaseEntry(co,ce)) = neighborhood(:,:,ce)
+        geom(ph)%IParea(:,material_phaseEntry(co,ce)) = area(:,ce)
+        geom(ph)%IPareaNormal(:,:,material_phaseEntry(co,ce)) = areaNormal(:,:,ce)
+      end if
     end do
   end do
 

From 2bd10a126178a540b7c85e8f72e08fe80c674537 Mon Sep 17 00:00:00 2001
From: Martin Diehl <mail@martin-diehl.net>
Date: Fri, 4 Feb 2022 08:25:51 +0100
Subject: [PATCH 22/72] avoid use of IP/el

---
 src/phase_mechanical_plastic.f90          | 16 ++++++----------
 src/phase_mechanical_plastic_nonlocal.f90 | 23 +++++++++++------------
 2 files changed, 17 insertions(+), 22 deletions(-)

diff --git a/src/phase_mechanical_plastic.f90 b/src/phase_mechanical_plastic.f90
index 912aadc03..9378edfdc 100644
--- a/src/phase_mechanical_plastic.f90
+++ b/src/phase_mechanical_plastic.f90
@@ -154,16 +154,14 @@ submodule(phase:mechanical) plastic
         en
     end subroutine dislotungsten_dotState
 
-    module subroutine nonlocal_dotState(Mp,timestep,ph,en,ip,el)
+    module subroutine nonlocal_dotState(Mp,timestep,ph,en)
       real(pReal), dimension(3,3), intent(in) :: &
         Mp                                                                                          !< MandelStress
       real(pReal), intent(in) :: &
         timestep                                                                                    !< substepped crystallite time increment
       integer, intent(in) :: &
         ph, &
-        en, &
-        ip, &                                                                                       !< current integration point
-        el                                                                                          !< current element number
+        en
     end subroutine nonlocal_dotState
 
     module subroutine dislotwin_dependentState(T,ph,en)
@@ -180,12 +178,10 @@ submodule(phase:mechanical) plastic
         en
     end subroutine dislotungsten_dependentState
 
-    module subroutine nonlocal_dependentState(ph, en, ip, el)
+    module subroutine nonlocal_dependentState(ph, en)
       integer, intent(in) :: &
         ph, &
-        en, &
-        ip, &                                                                                       !< current integration point
-        el                                                                                          !< current element number
+        en
     end subroutine nonlocal_dependentState
 
     module subroutine plastic_kinehardening_deltaState(Mp,ph,en)
@@ -333,7 +329,7 @@ module function plastic_dotState(subdt,co,ip,el,ph,en) result(dotState)
         call dislotungsten_dotState(Mp,thermal_T(ph,en),ph,en)
 
       case (PLASTIC_NONLOCAL_ID) plasticType
-        call nonlocal_dotState(Mp,subdt,ph,en,ip,el)
+        call nonlocal_dotState(Mp,subdt,ph,en)
     end select plasticType
   end if
 
@@ -369,7 +365,7 @@ module subroutine plastic_dependentState(co, ip, el)
       call dislotungsten_dependentState(ph,en)
 
     case (PLASTIC_NONLOCAL_ID) plasticType
-      call nonlocal_dependentState(ph,en,ip,el)
+      call nonlocal_dependentState(ph,en)
 
   end select plasticType
 
diff --git a/src/phase_mechanical_plastic_nonlocal.f90 b/src/phase_mechanical_plastic_nonlocal.f90
index 78271b92f..9c901f6b0 100644
--- a/src/phase_mechanical_plastic_nonlocal.f90
+++ b/src/phase_mechanical_plastic_nonlocal.f90
@@ -16,7 +16,7 @@ submodule(phase:plastic) nonlocal
   type :: tGeometry
     real(pReal), dimension(:), allocatable :: V_0
     integer, dimension(:,:,:), allocatable :: IPneighborhood
-    real(pReal), dimension(:,:), allocatable :: IParea
+    real(pReal), dimension(:,:), allocatable :: IParea, IPcoordinates
     real(pReal), dimension(:,:,:), allocatable :: IPareaNormal
   end type tGeometry
 
@@ -413,6 +413,7 @@ module function plastic_nonlocal_init() result(myPlasticity)
     allocate(geom(ph)%IPneighborhood(3,nIPneighbors,Nmembers))
     allocate(geom(ph)%IPareaNormal(3,nIPneighbors,Nmembers))
     allocate(geom(ph)%IParea(nIPneighbors,Nmembers))
+    allocate(geom(ph)%IPcoordinates(3,Nmembers))
     call storeGeometry(ph)
 
     if(plasticState(ph)%nonlocal .and. .not. allocated(IPneighborhood)) &
@@ -551,13 +552,11 @@ end function plastic_nonlocal_init
 !--------------------------------------------------------------------------------------------------
 !> @brief calculates quantities characterizing the microstructure
 !--------------------------------------------------------------------------------------------------
-module subroutine nonlocal_dependentState(ph, en, ip, el)
+module subroutine nonlocal_dependentState(ph, en)
 
   integer, intent(in) :: &
     ph, &
-    en, &
-    ip, &
-    el
+    en
 
   integer :: &
     no, &                                                                                           !< neighbor offset
@@ -673,8 +672,8 @@ module subroutine nonlocal_dependentState(ph, en, ip, el)
             neighbor_rhoTotal(1,:,n) = sum(abs(rho_neighbor0(:,edg)),2)
             neighbor_rhoTotal(2,:,n) = sum(abs(rho_neighbor0(:,scr)),2)
 
-            connection_latticeConf(1:3,n) = matmul(invFe, discretization_IPcoords(1:3,neighbor_el+neighbor_ip-1) &
-                                          - discretization_IPcoords(1:3,el+neighbor_ip-1))
+            connection_latticeConf(1:3,n) = matmul(invFe, geom(ph)%IPcoordinates(1:3,en) &
+                                          - geom(ph)%IPcoordinates(1:3,en-1))                       ! ToDo: broken for different materials
             normal_latticeConf = matmul(transpose(invFp), geom(ph)%IPareaNormal(1:3,n,en))
             if (math_inner(normal_latticeConf,connection_latticeConf(1:3,n)) < 0.0_pReal) &         ! neighboring connection points in opposite direction to face normal: must be periodic image
               connection_latticeConf(1:3,n) = normal_latticeConf * geom(ph)%V_0(en)/geom(ph)%IParea(n,en)  ! instead take the surface normal scaled with the diameter of the cell
@@ -947,7 +946,7 @@ end subroutine plastic_nonlocal_deltaState
 !> @brief calculates the rate of change of microstructure
 !---------------------------------------------------------------------------------------------------
 module subroutine nonlocal_dotState(Mp,timestep, &
-                                    ph,en,ip,el)
+                                    ph,en)
 
   real(pReal), dimension(3,3), intent(in) :: &
     Mp                                                                                              !< MandelStress
@@ -955,9 +954,7 @@ module subroutine nonlocal_dotState(Mp,timestep, &
     timestep                                                                                        !< substepped crystallite time increment
   integer, intent(in) :: &
     ph, &
-    en, &
-    ip, &                                                                                           !< current integration point
-    el                                                                                              !< current element number
+    en
 
   integer ::  &
     c, &                                                                                            !< character of dislocation
@@ -1765,7 +1762,7 @@ subroutine storeGeometry(ph)
   integer :: ce, co, nCell
   real(pReal), dimension(:), allocatable :: V
   integer, dimension(:,:,:), allocatable :: neighborhood
-  real(pReal), dimension(:,:), allocatable :: area
+  real(pReal), dimension(:,:), allocatable :: area, coords
   real(pReal), dimension(:,:,:), allocatable :: areaNormal
 
   nCell = product(shape(IPvolume))
@@ -1774,6 +1771,7 @@ subroutine storeGeometry(ph)
   neighborhood = reshape(IPneighborhood,[3,nIPneighbors,nCell])
   area = reshape(IParea,[nIPneighbors,nCell])
   areaNormal = reshape(IPareaNormal,[3,nIPneighbors,nCell])
+  coords = reshape(discretization_IPcoords,[3,nCell])
 
   do ce = 1, size(material_homogenizationEntry,1)
     do co = 1, homogenization_maxNconstituents
@@ -1782,6 +1780,7 @@ subroutine storeGeometry(ph)
         geom(ph)%IPneighborhood(:,:,material_phaseEntry(co,ce)) = neighborhood(:,:,ce)
         geom(ph)%IParea(:,material_phaseEntry(co,ce)) = area(:,ce)
         geom(ph)%IPareaNormal(:,:,material_phaseEntry(co,ce)) = areaNormal(:,:,ce)
+        geom(ph)%IPcoordinates(:,material_phaseEntry(co,ce)) = coords(:,ce)
       end if
     end do
   end do

From 3a0596a274f673a3bf93b308c6b4cf2b41c4835f Mon Sep 17 00:00:00 2001
From: Martin Diehl <mail@martin-diehl.net>
Date: Fri, 4 Feb 2022 08:49:00 +0100
Subject: [PATCH 23/72] use en/ph access

---
 src/phase.f90                             | 15 ++++++++-------
 src/phase_mechanical.f90                  |  2 +-
 src/phase_mechanical_plastic.f90          | 14 +++-----------
 src/phase_mechanical_plastic_nonlocal.f90 |  4 ++--
 4 files changed, 14 insertions(+), 21 deletions(-)

diff --git a/src/phase.f90 b/src/phase.f90
index 82bc44bfd..4d180d439 100644
--- a/src/phase.f90
+++ b/src/phase.f90
@@ -272,14 +272,12 @@ module phase
         type(tRotationContainer), dimension(:), intent(in) :: orientation
     end subroutine plastic_nonlocal_updateCompatibility
 
-    module subroutine plastic_dependentState(co,ip,el)
+    module subroutine plastic_dependentState(en,ph)
       integer, intent(in) :: &
-        co, &                                                                                       !< component-ID of integration point
-        ip, &                                                                                       !< integration point
-        el                                                                                          !< element
+        en, &
+        ph
     end subroutine plastic_dependentState
 
-
     module subroutine damage_anisobrittle_LiAndItsTangent(Ld, dLd_dTstar, S, ph,en)
       integer, intent(in) :: ph, en
       real(pReal),   intent(in),  dimension(3,3) :: &
@@ -503,7 +501,8 @@ subroutine crystallite_init()
     el, &                                                                                           !< counter in element loop
     cMax, &                                                                                         !< maximum number of  integration point components
     iMax, &                                                                                         !< maximum number of integration points
-    eMax                                                                                            !< maximum number of elements
+    eMax, &                                                                                         !< maximum number of elements
+    en, ph
 
   class(tNode), pointer :: &
     num_crystallite, &
@@ -560,8 +559,10 @@ subroutine crystallite_init()
     do ip = 1, iMax
       ce = (el-1)*discretization_nIPs + ip
       do co = 1,homogenization_Nconstituents(material_homogenizationID(ce))
+        en = material_phaseEntry(co,ce)
+        ph = material_phaseID(co,ce)
         call crystallite_orientations(co,ip,el)
-        call plastic_dependentState(co,ip,el)                                                       ! update dependent state variables to be consistent with basic states
+        call plastic_dependentState(en,ph)                                                          ! update dependent state variables to be consistent with basic states
      end do
     end do
   end do
diff --git a/src/phase_mechanical.f90 b/src/phase_mechanical.f90
index 04cc4b946..c97e4a13b 100644
--- a/src/phase_mechanical.f90
+++ b/src/phase_mechanical.f90
@@ -431,7 +431,7 @@ function integrateStress(F,subFp0,subFi0,Delta_t,co,ip,el) result(broken)
   ph = material_phaseID(co,(el-1)*discretization_nIPs + ip)
   en = material_phaseEntry(co,(el-1)*discretization_nIPs + ip)
 
-  call plastic_dependentState(co,ip,el)
+  call plastic_dependentState(en,ph)
 
   Lpguess = phase_mechanical_Lp(ph)%data(1:3,1:3,en)                                              ! take as first guess
   Liguess = phase_mechanical_Li(ph)%data(1:3,1:3,en)                                              ! take as first guess
diff --git a/src/phase_mechanical_plastic.f90 b/src/phase_mechanical_plastic.f90
index 9378edfdc..a5f40a2df 100644
--- a/src/phase_mechanical_plastic.f90
+++ b/src/phase_mechanical_plastic.f90
@@ -341,20 +341,12 @@ end function plastic_dotState
 !--------------------------------------------------------------------------------------------------
 !> @brief calls microstructure function of the different plasticity constitutive models
 !--------------------------------------------------------------------------------------------------
-module subroutine plastic_dependentState(co, ip, el)
+module subroutine plastic_dependentState(en,ph)
 
   integer, intent(in) :: &
-    co, &                                                                                           !< component-ID of integration point
-    ip, &                                                                                           !< integration point
-    el                                                                                              !< element
+    en, &
+    ph
 
-  integer :: &
-    ph, &
-    en
-
-
-  ph = material_phaseID(co,(el-1)*discretization_nIPs + ip)
-  en = material_phaseEntry(co,(el-1)*discretization_nIPs + ip)
 
   plasticType: select case (phase_plasticity(ph))
 
diff --git a/src/phase_mechanical_plastic_nonlocal.f90 b/src/phase_mechanical_plastic_nonlocal.f90
index 9c901f6b0..dec7ea8e7 100644
--- a/src/phase_mechanical_plastic_nonlocal.f90
+++ b/src/phase_mechanical_plastic_nonlocal.f90
@@ -672,8 +672,8 @@ module subroutine nonlocal_dependentState(ph, en)
             neighbor_rhoTotal(1,:,n) = sum(abs(rho_neighbor0(:,edg)),2)
             neighbor_rhoTotal(2,:,n) = sum(abs(rho_neighbor0(:,scr)),2)
 
-            connection_latticeConf(1:3,n) = matmul(invFe, geom(ph)%IPcoordinates(1:3,en) &
-                                          - geom(ph)%IPcoordinates(1:3,en-1))                       ! ToDo: broken for different materials
+            connection_latticeConf(1:3,n) = matmul(invFe, geom(ph)%IPcoordinates(1:3,no) &
+                                          - geom(ph)%IPcoordinates(1:3,en))
             normal_latticeConf = matmul(transpose(invFp), geom(ph)%IPareaNormal(1:3,n,en))
             if (math_inner(normal_latticeConf,connection_latticeConf(1:3,n)) < 0.0_pReal) &         ! neighboring connection points in opposite direction to face normal: must be periodic image
               connection_latticeConf(1:3,n) = normal_latticeConf * geom(ph)%V_0(en)/geom(ph)%IParea(n,en)  ! instead take the surface normal scaled with the diameter of the cell

From 9dad54304c8886596bd84bac5722466d5c923eb8 Mon Sep 17 00:00:00 2001
From: Daniel Otto de Mentock <d.mentock@mpie.de>
Date: Fri, 4 Feb 2022 09:57:42 +0100
Subject: [PATCH 24/72] added generic types to remaining non-overwritten
 rotation functions (exception __mul__)

---
 python/damask/_orientation.py | 11 +++++------
 python/damask/_rotation.py    | 20 ++++++++++----------
 2 files changed, 15 insertions(+), 16 deletions(-)

diff --git a/python/damask/_orientation.py b/python/damask/_orientation.py
index 780a5929e..2dedc13e4 100644
--- a/python/damask/_orientation.py
+++ b/python/damask/_orientation.py
@@ -165,7 +165,6 @@ class Orientation(Rotation,Crystal):
             Orientation to check for equality.
 
         """
-
         eq = self.__eq__(other)
         if not isinstance(eq, bool):
             return eq
@@ -501,8 +500,8 @@ class Orientation(Rotation,Crystal):
                 return np.ones_like(rho[...,0],dtype=bool)
 
     def disorientation(self,
-                       other,
-                       return_operators = False):
+                       other: "Orientation",
+                       return_operators: bool = False) -> object:
         """
         Calculate disorientation between myself and given other orientation.
 
@@ -575,9 +574,9 @@ class Orientation(Rotation,Crystal):
         r = np.where(np.any(forward[...,np.newaxis],axis=(0,1),keepdims=True),
                      r_.quaternion,
                      _r.quaternion)
-        loc: Tuple[float]  = np.where(ok)
-        sort: np.ndarray = 0 if len(loc) == 2 else np.lexsort(loc[:1:-1])
-        quat: np.ndarray = r[ok][sort].reshape(blend+(4,))
+        loc  = np.where(ok)
+        sort = 0 if len(loc) == 2 else np.lexsort(loc[:1:-1])
+        quat = r[ok][sort].reshape(blend+(4,))
         return (
                 (self.copy(rotation=quat),
                  (np.vstack(loc[:2]).T)[sort].reshape(blend+(2,)))
diff --git a/python/damask/_rotation.py b/python/damask/_rotation.py
index c3f6407f2..d40b48669 100644
--- a/python/damask/_rotation.py
+++ b/python/damask/_rotation.py
@@ -259,7 +259,7 @@ class Rotation:
         return self**exp
 
 
-    def __mul__(self, other: 'Rotation') -> 'Rotation':
+    def __mul__(self: MyType, other: MyType) -> MyType:
         """
         Compose with other.
 
@@ -281,12 +281,12 @@ class Rotation:
             p_o = other.quaternion[...,1:]
             q = (q_m*q_o - np.einsum('...i,...i',p_m,p_o).reshape(self.shape+(1,)))
             p = q_m*p_o + q_o*p_m + _P * np.cross(p_m,p_o)
-            return Rotation(np.block([q,p]))._standardize()
+            return Rotation(np.block([q,p]))._standardize() #type: ignore
         else:
             raise TypeError('Use "R@b", i.e. matmul, to apply rotation "R" to object "b"')
 
-    def __imul__(self,
-                 other: 'Rotation') -> 'Rotation':
+    def __imul__(self: MyType,
+                 other: MyType) -> MyType:
         """
         Compose with other (in-place).
 
@@ -299,8 +299,8 @@ class Rotation:
         return self*other
 
 
-    def __truediv__(self: 'Rotation',
-                    other: 'Rotation') -> 'Rotation':
+    def __truediv__(self: MyType,
+                    other: MyType) -> MyType:
         """
         Compose with inverse of other.
 
@@ -320,8 +320,8 @@ class Rotation:
         else:
             raise TypeError('Use "R@b", i.e. matmul, to apply rotation "R" to object "b"')
 
-    def __itruediv__(self: 'Rotation',
-                     other: 'Rotation') -> 'Rotation':
+    def __itruediv__(self: MyType,
+                     other: MyType) -> MyType:
         """
         Compose with inverse of other (in-place).
 
@@ -492,8 +492,8 @@ class Rotation:
                                         accept_homomorph = True)
 
 
-    def misorientation(self,
-                       other: 'Rotation') -> 'Rotation':
+    def misorientation(self: MyType,
+                       other: MyType) -> MyType:
         """
         Calculate misorientation to other Rotation.
 

From 7a405125daa7f29b3b9d13d7b5c1fdb59d435bfd Mon Sep 17 00:00:00 2001
From: Daniel Otto de Mentock <d.mentock@mpie.de>
Date: Fri, 4 Feb 2022 10:57:24 +0100
Subject: [PATCH 25/72] added type:ignore statements to Tuple Supportsindex
 addition in  Orientation.disorientation function

---
 python/damask/_orientation.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/python/damask/_orientation.py b/python/damask/_orientation.py
index 2dedc13e4..4817ddb6f 100644
--- a/python/damask/_orientation.py
+++ b/python/damask/_orientation.py
@@ -562,8 +562,8 @@ class Orientation(Rotation,Crystal):
         s = self.equivalent
         o = other.equivalent
 
-        s_ = s.reshape((s.shape[0],1)+ self.shape).broadcast_to((s.shape[0],o.shape[0])+blend,mode='right')
-        o_ = o.reshape((1,o.shape[0])+other.shape).broadcast_to((s.shape[0],o.shape[0])+blend,mode='right')
+        s_ = s.reshape((s.shape[0],1)+ self.shape).broadcast_to((s.shape[0],o.shape[0])+blend,mode='right') #type: ignore
+        o_ = o.reshape((1,o.shape[0])+other.shape).broadcast_to((s.shape[0],o.shape[0])+blend,mode='right') #type: ignore
         r_ = s_.misorientation(o_)
         _r = ~r_
 

From 8aed927989ee5edec91f03479bb110e660c3d4c6 Mon Sep 17 00:00:00 2001
From: Martin Diehl <mail@martin-diehl.net>
Date: Fri, 4 Feb 2022 11:28:54 +0100
Subject: [PATCH 26/72] avoid use of co/ip/el at the phase level

---
 src/phase_mechanical.f90         | 105 ++++++++++++-------------------
 src/phase_mechanical_plastic.f90 |   5 +-
 2 files changed, 42 insertions(+), 68 deletions(-)

diff --git a/src/phase_mechanical.f90 b/src/phase_mechanical.f90
index c97e4a13b..88e98cc2e 100644
--- a/src/phase_mechanical.f90
+++ b/src/phase_mechanical.f90
@@ -79,15 +79,12 @@ submodule(phase) mechanical
         en
     end subroutine plastic_isotropic_LiAndItsTangent
 
-    module function plastic_dotState(subdt,co,ip,el,ph,en) result(dotState)
+    module function plastic_dotState(subdt,ph,en) result(dotState)
       integer, intent(in) :: &
-        co, &                                                                                           !< component-ID of integration point
-        ip, &                                                                                           !< integration point
-        el, &                                                                                           !< element
         ph, &
         en
       real(pReal),  intent(in) :: &
-        subdt                                                                                           !< timestep
+        subdt                                                                                       !< timestep
       real(pReal), dimension(plasticState(ph)%sizeDotState) :: &
         dotState
     end function plastic_dotState
@@ -365,13 +362,11 @@ end subroutine mechanical_results
 !> @brief calculation of stress (P) with time integration based on a residuum in Lp and
 !> intermediate acceleration of the Newton-Raphson correction
 !--------------------------------------------------------------------------------------------------
-function integrateStress(F,subFp0,subFi0,Delta_t,co,ip,el) result(broken)
+function integrateStress(F,subFp0,subFi0,Delta_t,en,ph) result(broken)
 
   real(pReal), dimension(3,3), intent(in) :: F,subFp0,subFi0
   real(pReal),                 intent(in) :: Delta_t
-  integer, intent(in)::         el, &                                                               ! element index
-                                      ip, &                                                         ! integration point index
-                                      co                                                            ! grain index
+  integer, intent(in) :: en, ph
 
   real(pReal), dimension(3,3)::       Fp_new, &                                                     ! plastic deformation gradient at end of timestep
                                       invFp_new, &                                                  ! inverse of Fp_new
@@ -427,10 +422,6 @@ function integrateStress(F,subFp0,subFi0,Delta_t,co,ip,el) result(broken)
 
 
   broken = .true.
-
-  ph = material_phaseID(co,(el-1)*discretization_nIPs + ip)
-  en = material_phaseEntry(co,(el-1)*discretization_nIPs + ip)
-
   call plastic_dependentState(en,ph)
 
   Lpguess = phase_mechanical_Lp(ph)%data(1:3,1:3,en)                                              ! take as first guess
@@ -579,15 +570,14 @@ end function integrateStress
 !> @brief integrate stress, state with adaptive 1st order explicit Euler method
 !> using Fixed Point Iteration to adapt the stepsize
 !--------------------------------------------------------------------------------------------------
-function integrateStateFPI(F_0,F,subFp0,subFi0,subState0,Delta_t,co,ip,el) result(broken)
+function integrateStateFPI(F_0,F,subFp0,subFi0,subState0,Delta_t,en,ph) result(broken)
 
   real(pReal), intent(in),dimension(3,3) :: F_0,F,subFp0,subFi0
   real(pReal), intent(in),dimension(:)   :: subState0
   real(pReal), intent(in) :: Delta_t
   integer, intent(in) :: &
-    el, &                                                                                           !< element index in element loop
-    ip, &                                                                                           !< integration point index in ip loop
-    co                                                                                              !< grain index in grain loop
+    en, &
+    ph
   logical :: &
     broken
 
@@ -598,18 +588,16 @@ function integrateStateFPI(F_0,F,subFp0,subFi0,subState0,Delta_t,co,ip,el) resul
     sizeDotState
   real(pReal) :: &
     zeta
-  real(pReal), dimension(plasticState(material_phaseID(co,(el-1)*discretization_nIPs+ip))%sizeDotState) :: &
+  real(pReal), dimension(plasticState(ph)%sizeDotState) :: &
     r, &                                                                                            ! state residuum
     dotState
-  real(pReal), dimension(plasticState(material_phaseID(co,(el-1)*discretization_nIPs+ip))%sizeDotState,2) :: &
+  real(pReal), dimension(plasticState(ph)%sizeDotState,2) :: &
     dotState_last
 
 
-  ph = material_phaseID(co,(el-1)*discretization_nIPs + ip)
-  en = material_phaseEntry(co,(el-1)*discretization_nIPs + ip)
   broken = .true.
 
-  dotState = plastic_dotState(Delta_t, co,ip,el,ph,en)
+  dotState = plastic_dotState(Delta_t,ph,en)
   if (any(IEEE_is_NaN(dotState))) return
 
   sizeDotState = plasticState(ph)%sizeDotState
@@ -620,10 +608,10 @@ function integrateStateFPI(F_0,F,subFp0,subFi0,subState0,Delta_t,co,ip,el) resul
     dotState_last(1:sizeDotState,2) = merge(dotState_last(1:sizeDotState,1),0.0, nIterationState > 1)
     dotState_last(1:sizeDotState,1) = dotState
 
-    broken = integrateStress(F,subFp0,subFi0,Delta_t,co,ip,el)
+    broken = integrateStress(F,subFp0,subFi0,Delta_t,en,ph)
     if(broken) exit iteration
 
-    dotState = plastic_dotState(Delta_t, co,ip,el,ph,en)
+    dotState = plastic_dotState(Delta_t,ph,en)
     if (any(IEEE_is_NaN(dotState))) exit iteration
 
     zeta = damper(dotState,dotState_last(1:sizeDotState,1),dotState_last(1:sizeDotState,2))
@@ -672,19 +660,18 @@ end function integrateStateFPI
 !--------------------------------------------------------------------------------------------------
 !> @brief integrate state with 1st order explicit Euler method
 !--------------------------------------------------------------------------------------------------
-function integrateStateEuler(F_0,F,subFp0,subFi0,subState0,Delta_t,co,ip,el) result(broken)
+function integrateStateEuler(F_0,F,subFp0,subFi0,subState0,Delta_t,en,ph) result(broken)
 
   real(pReal), intent(in),dimension(3,3) :: F_0,F,subFp0,subFi0
   real(pReal), intent(in),dimension(:)   :: subState0
   real(pReal), intent(in) :: Delta_t
   integer, intent(in) :: &
-    el, &                                                                                            !< element index in element loop
-    ip, &                                                                                            !< integration point index in ip loop
-    co                                                                                               !< grain index in grain loop
+    en, &
+    ph                                                                                               !< grain index in grain loop
   logical :: &
     broken
 
-  real(pReal), dimension(plasticState(material_phaseID(co,(el-1)*discretization_nIPs+ip))%sizeDotState) :: &
+  real(pReal), dimension(plasticState(ph)%sizeDotState) :: &
     dotState
   integer :: &
     ph, &
@@ -692,11 +679,9 @@ function integrateStateEuler(F_0,F,subFp0,subFi0,subState0,Delta_t,co,ip,el) res
     sizeDotState
 
 
-  ph = material_phaseID(co,(el-1)*discretization_nIPs + ip)
-  en = material_phaseEntry(co,(el-1)*discretization_nIPs + ip)
   broken = .true.
 
-  dotState = plastic_dotState(Delta_t, co,ip,el,ph,en)
+  dotState = plastic_dotState(Delta_t,ph,en)
   if (any(IEEE_is_NaN(dotState))) return
 
   sizeDotState = plasticState(ph)%sizeDotState
@@ -706,7 +691,7 @@ function integrateStateEuler(F_0,F,subFp0,subFi0,subState0,Delta_t,co,ip,el) res
   broken = plastic_deltaState(ph,en)
   if(broken) return
 
-  broken = integrateStress(F,subFp0,subFi0,Delta_t,co,ip,el)
+  broken = integrateStress(F,subFp0,subFi0,Delta_t,en,ph)
 
 end function integrateStateEuler
 
@@ -714,15 +699,14 @@ end function integrateStateEuler
 !--------------------------------------------------------------------------------------------------
 !> @brief integrate stress, state with 1st order Euler method with adaptive step size
 !--------------------------------------------------------------------------------------------------
-function integrateStateAdaptiveEuler(F_0,F,subFp0,subFi0,subState0,Delta_t,co,ip,el) result(broken)
+function integrateStateAdaptiveEuler(F_0,F,subFp0,subFi0,subState0,Delta_t,en,ph) result(broken)
 
   real(pReal), intent(in),dimension(3,3) :: F_0,F,subFp0,subFi0
   real(pReal), intent(in),dimension(:)   :: subState0
   real(pReal), intent(in) :: Delta_t
   integer, intent(in) :: &
-    el, &                                                                                            !< element index in element loop
-    ip, &                                                                                            !< integration point index in ip loop
-    co                                                                                               !< grain index in grain loop
+    en, &
+    ph
   logical :: &
     broken
 
@@ -730,16 +714,14 @@ function integrateStateAdaptiveEuler(F_0,F,subFp0,subFi0,subState0,Delta_t,co,ip
     ph, &
     en, &
     sizeDotState
-  real(pReal), dimension(plasticState(material_phaseID(co,(el-1)*discretization_nIPs+ip))%sizeDotState) :: &
+  real(pReal), dimension(plasticState(ph)%sizeDotState) :: &
     r, &
     dotState
 
 
-  ph = material_phaseID(co,(el-1)*discretization_nIPs + ip)
-  en = material_phaseEntry(co,(el-1)*discretization_nIPs + ip)
   broken = .true.
 
-  dotState = plastic_dotState(Delta_t, co,ip,el,ph,en)
+  dotState = plastic_dotState(Delta_t,ph,en)
   if (any(IEEE_is_NaN(dotState))) return
 
   sizeDotState = plasticState(ph)%sizeDotState
@@ -751,10 +733,10 @@ function integrateStateAdaptiveEuler(F_0,F,subFp0,subFi0,subState0,Delta_t,co,ip
   broken = plastic_deltaState(ph,en)
   if(broken) return
 
-  broken = integrateStress(F,subFp0,subFi0,Delta_t,co,ip,el)
+  broken = integrateStress(F,subFp0,subFi0,Delta_t,en,ph)
   if(broken) return
 
-  dotState = plastic_dotState(Delta_t, co,ip,el,ph,en)
+  dotState = plastic_dotState(Delta_t,ph,en)
   if (any(IEEE_is_NaN(dotState))) return
 
   broken = .not. converged(r + 0.5_pReal * dotState * Delta_t, &
@@ -767,12 +749,12 @@ end function integrateStateAdaptiveEuler
 !---------------------------------------------------------------------------------------------------
 !> @brief Integrate state (including stress integration) with the classic Runge Kutta method
 !---------------------------------------------------------------------------------------------------
-function integrateStateRK4(F_0,F,subFp0,subFi0,subState0,Delta_t,co,ip,el) result(broken)
+function integrateStateRK4(F_0,F,subFp0,subFi0,subState0,Delta_t,en,ph) result(broken)
 
   real(pReal), intent(in),dimension(3,3) :: F_0,F,subFp0,subFi0
   real(pReal), intent(in),dimension(:)   :: subState0
   real(pReal), intent(in) :: Delta_t
-  integer, intent(in) :: co,ip,el
+  integer, intent(in) :: en, ph
   logical :: broken
 
   real(pReal), dimension(3,3), parameter :: &
@@ -787,7 +769,7 @@ function integrateStateRK4(F_0,F,subFp0,subFi0,subState0,Delta_t,co,ip,el) resul
     B = [1.0_pReal/6.0_pReal, 1.0_pReal/3.0_pReal, 1.0_pReal/3.0_pReal, 1.0_pReal/6.0_pReal]
 
 
-  broken = integrateStateRK(F_0,F,subFp0,subFi0,subState0,Delta_t,co,ip,el,A,B,C)
+  broken = integrateStateRK(F_0,F,subFp0,subFi0,subState0,Delta_t,en,ph,A,B,C)
 
 end function integrateStateRK4
 
@@ -795,12 +777,12 @@ end function integrateStateRK4
 !---------------------------------------------------------------------------------------------------
 !> @brief Integrate state (including stress integration) with the Cash-Carp method
 !---------------------------------------------------------------------------------------------------
-function integrateStateRKCK45(F_0,F,subFp0,subFi0,subState0,Delta_t,co,ip,el) result(broken)
+function integrateStateRKCK45(F_0,F,subFp0,subFi0,subState0,Delta_t,en,ph) result(broken)
 
   real(pReal), intent(in),dimension(3,3) :: F_0,F,subFp0,subFi0
   real(pReal), intent(in),dimension(:)   :: subState0
   real(pReal), intent(in) :: Delta_t
-  integer, intent(in) :: co,ip,el
+  integer, intent(in) :: en, ph
   logical :: broken
 
   real(pReal), dimension(5,5), parameter :: &
@@ -822,7 +804,7 @@ function integrateStateRKCK45(F_0,F,subFp0,subFi0,subState0,Delta_t,co,ip,el) re
       13525.0_pReal/55296.0_pReal, 277.0_pReal/14336.0_pReal,  1._pReal/4._pReal]
 
 
-  broken = integrateStateRK(F_0,F,subFp0,subFi0,subState0,Delta_t,co,ip,el,A,B,C,DB)
+  broken = integrateStateRK(F_0,F,subFp0,subFi0,subState0,Delta_t,en,ph,A,B,C,DB)
 
 end function integrateStateRKCK45
 
@@ -831,7 +813,7 @@ end function integrateStateRKCK45
 !> @brief Integrate state (including stress integration) with an explicit Runge-Kutta method or an
 !! embedded explicit Runge-Kutta method
 !--------------------------------------------------------------------------------------------------
-function integrateStateRK(F_0,F,subFp0,subFi0,subState0,Delta_t,co,ip,el,A,B,C,DB) result(broken)
+function integrateStateRK(F_0,F,subFp0,subFi0,subState0,Delta_t,en,ph,A,B,C,DB) result(broken)
 
   real(pReal), intent(in),dimension(3,3) :: F_0,F,subFp0,subFi0
   real(pReal), intent(in),dimension(:)   :: subState0
@@ -840,9 +822,8 @@ function integrateStateRK(F_0,F,subFp0,subFi0,subState0,Delta_t,co,ip,el,A,B,C,D
   real(pReal), dimension(:),   intent(in) :: B, C
   real(pReal), dimension(:),   intent(in), optional :: DB
   integer, intent(in) :: &
-    el, &                                                                                            !< element index in element loop
-    ip, &                                                                                            !< integration point index in ip loop
-    co                                                                                               !< grain index in grain loop
+    en, &
+    ph
   logical :: broken
 
   integer :: &
@@ -851,17 +832,15 @@ function integrateStateRK(F_0,F,subFp0,subFi0,subState0,Delta_t,co,ip,el,A,B,C,D
     ph, &
     en, &
     sizeDotState
-  real(pReal), dimension(plasticState(material_phaseID(co,(el-1)*discretization_nIPs+ip))%sizeDotState) :: &
+  real(pReal), dimension(plasticState(ph)%sizeDotState) :: &
     dotState
-  real(pReal), dimension(plasticState(material_phaseID(co,(el-1)*discretization_nIPs+ip))%sizeDotState,size(B)) :: &
+  real(pReal), dimension(plasticState(ph)%sizeDotState,size(B)) :: &
     plastic_RKdotState
 
 
-  ph = material_phaseID(co,(el-1)*discretization_nIPs + ip)
-  en = material_phaseEntry(co,(el-1)*discretization_nIPs + ip)
   broken = .true.
 
-  dotState = plastic_dotState(Delta_t, co,ip,el,ph,en)
+  dotState = plastic_dotState(Delta_t,ph,en)
   if (any(IEEE_is_NaN(dotState))) return
 
   sizeDotState = plasticState(ph)%sizeDotState
@@ -879,10 +858,10 @@ function integrateStateRK(F_0,F,subFp0,subFi0,subState0,Delta_t,co,ip,el,A,B,C,D
     plasticState(ph)%state(1:sizeDotState,en) = subState0 &
                                               + dotState * Delta_t
 
-    broken = integrateStress(F_0 + (F - F_0) * Delta_t * C(stage),subFp0,subFi0,Delta_t * C(stage),co,ip,el)
+    broken = integrateStress(F_0 + (F - F_0) * Delta_t * C(stage),subFp0,subFi0,Delta_t * C(stage),en,ph)
     if(broken) exit
 
-    dotState = plastic_dotState(Delta_t, co,ip,el,ph,en)
+    dotState = plastic_dotState(Delta_t,ph,en)
     if (any(IEEE_is_NaN(dotState))) exit
 
   enddo
@@ -904,7 +883,7 @@ function integrateStateRK(F_0,F,subFp0,subFi0,subState0,Delta_t,co,ip,el,A,B,C,D
   broken = plastic_deltaState(ph,en)
   if(broken) return
 
-  broken = integrateStress(F,subFp0,subFi0,Delta_t,co,ip,el)
+  broken = integrateStress(F,subFp0,subFi0,Delta_t,en,ph)
 
 end function integrateStateRK
 
@@ -1031,8 +1010,6 @@ module function phase_mechanical_constitutive(Delta_t,co,ip,el) result(converged
   real(pReal), dimension(:), allocatable :: subState0
 
 
-  ph = material_phaseID(co,(el-1)*discretization_nIPs + ip)
-  en = material_phaseEntry(co,(el-1)*discretization_nIPs + ip)
   sizeDotState = plasticState(ph)%sizeDotState
 
   subLi0 = phase_mechanical_Li0(ph)%data(1:3,1:3,en)
@@ -1084,7 +1061,7 @@ module function phase_mechanical_constitutive(Delta_t,co,ip,el) result(converged
     if (todo) then
       subF = subF0 &
            + subStep * (phase_mechanical_F(ph)%data(1:3,1:3,en) - phase_mechanical_F0(ph)%data(1:3,1:3,en))
-      converged_ = .not. integrateState(subF0,subF,subFp0,subFi0,subState0(1:sizeDotState),subStep * Delta_t,co,ip,el)
+      converged_ = .not. integrateState(subF0,subF,subFp0,subFi0,subState0(1:sizeDotState),subStep * Delta_t,en,ph)
     endif
 
   enddo cutbackLooping
diff --git a/src/phase_mechanical_plastic.f90 b/src/phase_mechanical_plastic.f90
index a5f40a2df..13f14717e 100644
--- a/src/phase_mechanical_plastic.f90
+++ b/src/phase_mechanical_plastic.f90
@@ -291,12 +291,9 @@ end subroutine plastic_LpAndItsTangents
 !--------------------------------------------------------------------------------------------------
 !> @brief contains the constitutive equation for calculating the rate of change of microstructure
 !--------------------------------------------------------------------------------------------------
-module function plastic_dotState(subdt,co,ip,el,ph,en) result(dotState)
+module function plastic_dotState(subdt,ph,en) result(dotState)
 
   integer, intent(in) :: &
-    co, &                                                                                           !< component-ID of integration point
-    ip, &                                                                                           !< integration point
-    el, &                                                                                           !< element
     ph, &
     en
   real(pReal),  intent(in) :: &

From 019ae1c536c26c5ed6662dbddad4d12736c7f5be Mon Sep 17 00:00:00 2001
From: Daniel Otto de Mentock <d.mentock@mpie.de>
Date: Fri, 4 Feb 2022 11:43:35 +0100
Subject: [PATCH 27/72] adjusted typecheck in __eq__ and __ne__ functions

---
 python/damask/_orientation.py | 6 ++----
 python/damask/_rotation.py    | 6 ++----
 2 files changed, 4 insertions(+), 8 deletions(-)

diff --git a/python/damask/_orientation.py b/python/damask/_orientation.py
index 4817ddb6f..2221af8a4 100644
--- a/python/damask/_orientation.py
+++ b/python/damask/_orientation.py
@@ -148,7 +148,7 @@ class Orientation(Rotation,Crystal):
 
         """
         if not isinstance(other, Orientation):
-            return NotImplemented
+            raise NotImplementedError
         matching_type = self.family == other.family and \
                         self.lattice == other.lattice and \
                         self.parameters == other.parameters
@@ -165,9 +165,7 @@ class Orientation(Rotation,Crystal):
             Orientation to check for equality.
 
         """
-        eq = self.__eq__(other)
-        if not isinstance(eq, bool):
-            return eq
+        self.__eq__(other)
         return np.logical_not(self==other)
 
 
diff --git a/python/damask/_rotation.py b/python/damask/_rotation.py
index d40b48669..5efaf9d9e 100644
--- a/python/damask/_rotation.py
+++ b/python/damask/_rotation.py
@@ -124,7 +124,7 @@ class Rotation:
 
         """
         if not isinstance(other, Rotation):
-            return NotImplemented
+            raise NotImplementedError
         return np.logical_or(np.all(self.quaternion ==      other.quaternion,axis=-1),
                              np.all(self.quaternion == -1.0*other.quaternion,axis=-1))
 
@@ -139,9 +139,7 @@ class Rotation:
             Rotation to check for inequality.
 
         """
-        eq = self.__eq__(other)
-        if not isinstance(eq, bool):
-            return eq
+        self.__eq__(other)
         return np.logical_not(self==other)
 
 

From afed13e2ca5d6c33bc5b85e339512b99e29eca03 Mon Sep 17 00:00:00 2001
From: Martin Diehl <mail@martin-diehl.net>
Date: Fri, 4 Feb 2022 12:25:11 +0100
Subject: [PATCH 28/72] ip/el not of interest

---
 src/homogenization.f90   |  4 ++--
 src/phase.f90            |  8 ++++----
 src/phase_damage.f90     |  9 ++++-----
 src/phase_mechanical.f90 | 17 ++++-------------
 4 files changed, 14 insertions(+), 24 deletions(-)

diff --git a/src/homogenization.f90 b/src/homogenization.f90
index 3d96b007f..1f9fb2221 100644
--- a/src/homogenization.f90
+++ b/src/homogenization.f90
@@ -259,7 +259,7 @@ subroutine homogenization_mechanical_response(Delta_t,FEsolving_execIP,FEsolving
         NiterationMPstate = NiterationMPstate + 1
 
         call mechanical_partition(homogenization_F(1:3,1:3,ce),ce)
-        converged = all([(phase_mechanical_constitutive(Delta_t,co,ip,el),co=1,homogenization_Nconstituents(ho))])
+        converged = all([(phase_mechanical_constitutive(Delta_t,co,ce),co=1,homogenization_Nconstituents(ho))])
         if (converged) then
           doneAndHappy = mechanical_updateState(Delta_t,homogenization_F(1:3,1:3,ce),ce)
           converged = all(doneAndHappy)
@@ -268,7 +268,7 @@ subroutine homogenization_mechanical_response(Delta_t,FEsolving_execIP,FEsolving
         endif
       enddo convergenceLooping
 
-      converged = converged .and. all([(phase_damage_constitutive(Delta_t,co,ip,el),co=1,homogenization_Nconstituents(ho))])
+      converged = converged .and. all([(phase_damage_constitutive(Delta_t,co,ce),co=1,homogenization_Nconstituents(ho))])
 
       if (.not. converged) then
         if (.not. terminallyIll) print*, ' Cell ', ce, ' terminally ill'
diff --git a/src/phase.f90 b/src/phase.f90
index 4d180d439..8bc797e85 100644
--- a/src/phase.f90
+++ b/src/phase.f90
@@ -228,15 +228,15 @@ module phase
 
     end function phase_thermal_constitutive
 
-    module function phase_damage_constitutive(Delta_t,co,ip,el) result(converged_)
+    module function phase_damage_constitutive(Delta_t,co,ce) result(converged_)
       real(pReal), intent(in) :: Delta_t
-      integer, intent(in) :: co, ip, el
+      integer, intent(in) :: co, ce
       logical :: converged_
     end function phase_damage_constitutive
 
-    module function phase_mechanical_constitutive(Delta_t,co,ip,el) result(converged_)
+    module function phase_mechanical_constitutive(Delta_t,co,ce) result(converged_)
       real(pReal), intent(in) :: Delta_t
-      integer, intent(in) :: co, ip, el
+      integer, intent(in) :: co, ce
       logical :: converged_
     end function phase_mechanical_constitutive
 
diff --git a/src/phase_damage.f90 b/src/phase_damage.f90
index 2fa5ab9ea..e4700938f 100644
--- a/src/phase_damage.f90
+++ b/src/phase_damage.f90
@@ -127,21 +127,20 @@ end subroutine damage_init
 !--------------------------------------------------------------------------------------------------
 !> @brief calculate stress (P)
 !--------------------------------------------------------------------------------------------------
-module function phase_damage_constitutive(Delta_t,co,ip,el) result(converged_)
+module function phase_damage_constitutive(Delta_t,co,ce) result(converged_)
 
   real(pReal), intent(in) :: Delta_t
   integer, intent(in) :: &
     co, &
-    ip, &
-    el
+    ce
   logical :: converged_
 
   integer :: &
     ph, en
 
 
-  ph = material_phaseID(co,(el-1)*discretization_nIPs + ip)
-  en = material_phaseEntry(co,(el-1)*discretization_nIPs + ip)
+  ph = material_phaseID(co,ce)
+  en = material_phaseEntry(co,ce)
 
   converged_ = .not. integrateDamageState(Delta_t,ph,en)
 
diff --git a/src/phase_mechanical.f90 b/src/phase_mechanical.f90
index 88e98cc2e..655f53ad8 100644
--- a/src/phase_mechanical.f90
+++ b/src/phase_mechanical.f90
@@ -414,8 +414,6 @@ function integrateStress(F,subFp0,subFi0,Delta_t,en,ph) result(broken)
                                       ierr, &                                                       ! error indicator for LAPACK
                                       o, &
                                       p, &
-                                      ph, &
-                                      en, &
                                       jacoCounterLp, &
                                       jacoCounterLi                                                 ! counters to check for Jacobian update
   logical :: error,broken
@@ -583,8 +581,6 @@ function integrateStateFPI(F_0,F,subFp0,subFi0,subState0,Delta_t,en,ph) result(b
 
   integer :: &
     NiterationState, &                                                                              !< number of iterations in state loop
-    ph, &
-    en, &
     sizeDotState
   real(pReal) :: &
     zeta
@@ -674,8 +670,6 @@ function integrateStateEuler(F_0,F,subFp0,subFi0,subState0,Delta_t,en,ph) result
   real(pReal), dimension(plasticState(ph)%sizeDotState) :: &
     dotState
   integer :: &
-    ph, &
-    en, &
     sizeDotState
 
 
@@ -711,8 +705,6 @@ function integrateStateAdaptiveEuler(F_0,F,subFp0,subFi0,subState0,Delta_t,en,ph
     broken
 
   integer :: &
-    ph, &
-    en, &
     sizeDotState
   real(pReal), dimension(plasticState(ph)%sizeDotState) :: &
     r, &
@@ -829,8 +821,6 @@ function integrateStateRK(F_0,F,subFp0,subFi0,subState0,Delta_t,en,ph,A,B,C,DB)
   integer :: &
     stage, &                                                                                        ! stage index in integration stage loop
     n, &
-    ph, &
-    en, &
     sizeDotState
   real(pReal), dimension(plasticState(ph)%sizeDotState) :: &
     dotState
@@ -985,13 +975,12 @@ end subroutine mechanical_forward
 !--------------------------------------------------------------------------------------------------
 !> @brief calculate stress (P)
 !--------------------------------------------------------------------------------------------------
-module function phase_mechanical_constitutive(Delta_t,co,ip,el) result(converged_)
+module function phase_mechanical_constitutive(Delta_t,co,ce) result(converged_)
 
   real(pReal), intent(in) :: Delta_t
   integer, intent(in) :: &
     co, &
-    ip, &
-    el
+    ce
   logical :: converged_
 
   real(pReal) :: &
@@ -1010,6 +999,8 @@ module function phase_mechanical_constitutive(Delta_t,co,ip,el) result(converged
   real(pReal), dimension(:), allocatable :: subState0
 
 
+  ph = material_phaseID(co,ce)
+  en = material_phaseEntry(co,ce)
   sizeDotState = plasticState(ph)%sizeDotState
 
   subLi0 = phase_mechanical_Li0(ph)%data(1:3,1:3,en)

From c1c23366383f96182fee8ff8411d83ab58b94b79 Mon Sep 17 00:00:00 2001
From: Daniel Otto de Mentock <d.mentock@mpie.de>
Date: Fri, 4 Feb 2022 16:57:25 +0100
Subject: [PATCH 29/72] reverted __eq__ and __ne type verification to return
 NotImplemented constant

changed rotation.average input type to FloatSequence

minor adjustments
---
 python/damask/_orientation.py | 10 ++++------
 python/damask/_rotation.py    | 24 ++++++++++++------------
 2 files changed, 16 insertions(+), 18 deletions(-)

diff --git a/python/damask/_orientation.py b/python/damask/_orientation.py
index 2221af8a4..d90cc70e6 100644
--- a/python/damask/_orientation.py
+++ b/python/damask/_orientation.py
@@ -148,7 +148,7 @@ class Orientation(Rotation,Crystal):
 
         """
         if not isinstance(other, Orientation):
-            raise NotImplementedError
+            return NotImplemented
         matching_type = self.family == other.family and \
                         self.lattice == other.lattice and \
                         self.parameters == other.parameters
@@ -165,8 +165,7 @@ class Orientation(Rotation,Crystal):
             Orientation to check for equality.
 
         """
-        self.__eq__(other)
-        return np.logical_not(self==other)
+        return np.logical_not(self==other) if isinstance(other, Orientation) else NotImplemented
 
 
     def isclose(self,
@@ -498,7 +497,7 @@ class Orientation(Rotation,Crystal):
                 return np.ones_like(rho[...,0],dtype=bool)
 
     def disorientation(self,
-                       other: "Orientation",
+                       other: 'Orientation',
                        return_operators: bool = False) -> object:
         """
         Calculate disorientation between myself and given other orientation.
@@ -612,8 +611,7 @@ class Orientation(Rotation,Crystal):
         """
         eq = self.equivalent
         m  = eq.misorientation(self[...,0].reshape((1,)+self.shape[:-1]+(1,))
-                                          .broadcast_to(eq.shape))\
-               .as_axis_angle()[...,3]
+                                          .broadcast_to(eq.shape)).as_axis_angle()[...,3]
         r = Rotation(np.squeeze(np.take_along_axis(eq.quaternion,
                                                    np.argmin(m,axis=0)[np.newaxis,...,np.newaxis],
                                                    axis=0),
diff --git a/python/damask/_rotation.py b/python/damask/_rotation.py
index 5efaf9d9e..53902def7 100644
--- a/python/damask/_rotation.py
+++ b/python/damask/_rotation.py
@@ -124,12 +124,13 @@ class Rotation:
 
         """
         if not isinstance(other, Rotation):
-            raise NotImplementedError
+            return NotImplemented
         return np.logical_or(np.all(self.quaternion ==      other.quaternion,axis=-1),
                              np.all(self.quaternion == -1.0*other.quaternion,axis=-1))
 
 
-    def __ne__(self, other: object) -> bool:
+    def __ne__(self,
+               other: object) -> bool:
         """
         Not equal to other.
 
@@ -139,9 +140,7 @@ class Rotation:
             Rotation to check for inequality.
 
         """
-        self.__eq__(other)
-        return np.logical_not(self==other)
-
+        return np.logical_not(self==other) if isinstance(other, Rotation) else NotImplemented
 
     def isclose(self,
                 other: 'Rotation',
@@ -257,7 +256,8 @@ class Rotation:
         return self**exp
 
 
-    def __mul__(self: MyType, other: MyType) -> MyType:
+    def __mul__(self: MyType,
+                other: MyType) -> MyType:
         """
         Compose with other.
 
@@ -332,7 +332,8 @@ class Rotation:
         return self/other
 
 
-    def __matmul__(self, other: np.ndarray) -> np.ndarray:
+    def __matmul__(self,
+                   other: np.ndarray) -> np.ndarray:
         """
         Rotate vector, second order tensor, or fourth order tensor.
 
@@ -451,7 +452,7 @@ class Rotation:
 
 
     def average(self,
-                weights: np.ndarray = None) -> 'Rotation':
+                weights: FloatSequence = None) -> 'Rotation':
         """
         Average along last array dimension.
 
@@ -475,11 +476,10 @@ class Rotation:
             """Intermediate representation supporting quaternion averaging."""
             return np.einsum('...i,...j',quat,quat)
 
-        if weights is None:
-            weights = np.ones(self.shape,dtype=float)
+        weights_ = np.ones(self.shape,dtype=float) if weights is None else np.array(weights,float)
 
-        eig, vec = np.linalg.eig(np.sum(_M(self.quaternion) * weights[...,np.newaxis,np.newaxis],axis=-3) \
-                                /np.sum(                      weights[...,np.newaxis,np.newaxis],axis=-3))
+        eig, vec = np.linalg.eig(np.sum(_M(self.quaternion) * weights_[...,np.newaxis,np.newaxis],axis=-3) \
+                                /np.sum(                      weights_[...,np.newaxis,np.newaxis],axis=-3))
 
         return Rotation.from_quaternion(np.real(
                                         np.squeeze(

From 72978df099a7c86958d4c315facbfe1c90c91e69 Mon Sep 17 00:00:00 2001
From: Daniel Otto de Mentock <d.mentock@mpie.de>
Date: Fri, 4 Feb 2022 17:41:29 +0100
Subject: [PATCH 30/72] minor correction

---
 python/damask/_rotation.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/python/damask/_rotation.py b/python/damask/_rotation.py
index 53902def7..226d66f69 100644
--- a/python/damask/_rotation.py
+++ b/python/damask/_rotation.py
@@ -458,7 +458,7 @@ class Rotation:
 
         Parameters
         ----------
-        weights : numpy.ndarray, optional
+        weights : FloatSequence, optional
             Relative weight of each rotation.
 
         Returns

From 3990536f1ca90d6e2f9709bd8b9b2f54732819e8 Mon Sep 17 00:00:00 2001
From: Martin Diehl <mail@martin-diehl.net>
Date: Fri, 4 Feb 2022 17:42:05 +0100
Subject: [PATCH 31/72] consistent order of arguments

---
 src/phase.f90                    |  8 ++---
 src/phase_mechanical.f90         | 54 ++++++++++++++++----------------
 src/phase_mechanical_plastic.f90 |  8 ++---
 3 files changed, 35 insertions(+), 35 deletions(-)

diff --git a/src/phase.f90 b/src/phase.f90
index 8bc797e85..c4e7142f8 100644
--- a/src/phase.f90
+++ b/src/phase.f90
@@ -272,10 +272,10 @@ module phase
         type(tRotationContainer), dimension(:), intent(in) :: orientation
     end subroutine plastic_nonlocal_updateCompatibility
 
-    module subroutine plastic_dependentState(en,ph)
+    module subroutine plastic_dependentState(ph,en)
       integer, intent(in) :: &
-        en, &
-        ph
+        ph, &
+        en
     end subroutine plastic_dependentState
 
     module subroutine damage_anisobrittle_LiAndItsTangent(Ld, dLd_dTstar, S, ph,en)
@@ -562,7 +562,7 @@ subroutine crystallite_init()
         en = material_phaseEntry(co,ce)
         ph = material_phaseID(co,ce)
         call crystallite_orientations(co,ip,el)
-        call plastic_dependentState(en,ph)                                                          ! update dependent state variables to be consistent with basic states
+        call plastic_dependentState(ph,en)                                                          ! update dependent state variables to be consistent with basic states
      end do
     end do
   end do
diff --git a/src/phase_mechanical.f90 b/src/phase_mechanical.f90
index 655f53ad8..de9c2bea2 100644
--- a/src/phase_mechanical.f90
+++ b/src/phase_mechanical.f90
@@ -362,11 +362,11 @@ end subroutine mechanical_results
 !> @brief calculation of stress (P) with time integration based on a residuum in Lp and
 !> intermediate acceleration of the Newton-Raphson correction
 !--------------------------------------------------------------------------------------------------
-function integrateStress(F,subFp0,subFi0,Delta_t,en,ph) result(broken)
+function integrateStress(F,subFp0,subFi0,Delta_t,ph,en) result(broken)
 
   real(pReal), dimension(3,3), intent(in) :: F,subFp0,subFi0
   real(pReal),                 intent(in) :: Delta_t
-  integer, intent(in) :: en, ph
+  integer, intent(in) :: ph, en
 
   real(pReal), dimension(3,3)::       Fp_new, &                                                     ! plastic deformation gradient at end of timestep
                                       invFp_new, &                                                  ! inverse of Fp_new
@@ -420,7 +420,7 @@ function integrateStress(F,subFp0,subFi0,Delta_t,en,ph) result(broken)
 
 
   broken = .true.
-  call plastic_dependentState(en,ph)
+  call plastic_dependentState(ph,en)
 
   Lpguess = phase_mechanical_Lp(ph)%data(1:3,1:3,en)                                              ! take as first guess
   Liguess = phase_mechanical_Li(ph)%data(1:3,1:3,en)                                              ! take as first guess
@@ -568,14 +568,14 @@ end function integrateStress
 !> @brief integrate stress, state with adaptive 1st order explicit Euler method
 !> using Fixed Point Iteration to adapt the stepsize
 !--------------------------------------------------------------------------------------------------
-function integrateStateFPI(F_0,F,subFp0,subFi0,subState0,Delta_t,en,ph) result(broken)
+function integrateStateFPI(F_0,F,subFp0,subFi0,subState0,Delta_t,ph,en) result(broken)
 
   real(pReal), intent(in),dimension(3,3) :: F_0,F,subFp0,subFi0
   real(pReal), intent(in),dimension(:)   :: subState0
   real(pReal), intent(in) :: Delta_t
   integer, intent(in) :: &
-    en, &
-    ph
+    ph, &
+    en
   logical :: &
     broken
 
@@ -604,7 +604,7 @@ function integrateStateFPI(F_0,F,subFp0,subFi0,subState0,Delta_t,en,ph) result(b
     dotState_last(1:sizeDotState,2) = merge(dotState_last(1:sizeDotState,1),0.0, nIterationState > 1)
     dotState_last(1:sizeDotState,1) = dotState
 
-    broken = integrateStress(F,subFp0,subFi0,Delta_t,en,ph)
+    broken = integrateStress(F,subFp0,subFi0,Delta_t,ph,en)
     if(broken) exit iteration
 
     dotState = plastic_dotState(Delta_t,ph,en)
@@ -656,14 +656,14 @@ end function integrateStateFPI
 !--------------------------------------------------------------------------------------------------
 !> @brief integrate state with 1st order explicit Euler method
 !--------------------------------------------------------------------------------------------------
-function integrateStateEuler(F_0,F,subFp0,subFi0,subState0,Delta_t,en,ph) result(broken)
+function integrateStateEuler(F_0,F,subFp0,subFi0,subState0,Delta_t,ph,en) result(broken)
 
   real(pReal), intent(in),dimension(3,3) :: F_0,F,subFp0,subFi0
   real(pReal), intent(in),dimension(:)   :: subState0
   real(pReal), intent(in) :: Delta_t
   integer, intent(in) :: &
-    en, &
-    ph                                                                                               !< grain index in grain loop
+    ph, &
+    en                                                                                               !< grain index in grain loop
   logical :: &
     broken
 
@@ -685,7 +685,7 @@ function integrateStateEuler(F_0,F,subFp0,subFi0,subState0,Delta_t,en,ph) result
   broken = plastic_deltaState(ph,en)
   if(broken) return
 
-  broken = integrateStress(F,subFp0,subFi0,Delta_t,en,ph)
+  broken = integrateStress(F,subFp0,subFi0,Delta_t,ph,en)
 
 end function integrateStateEuler
 
@@ -693,14 +693,14 @@ end function integrateStateEuler
 !--------------------------------------------------------------------------------------------------
 !> @brief integrate stress, state with 1st order Euler method with adaptive step size
 !--------------------------------------------------------------------------------------------------
-function integrateStateAdaptiveEuler(F_0,F,subFp0,subFi0,subState0,Delta_t,en,ph) result(broken)
+function integrateStateAdaptiveEuler(F_0,F,subFp0,subFi0,subState0,Delta_t,ph,en) result(broken)
 
   real(pReal), intent(in),dimension(3,3) :: F_0,F,subFp0,subFi0
   real(pReal), intent(in),dimension(:)   :: subState0
   real(pReal), intent(in) :: Delta_t
   integer, intent(in) :: &
-    en, &
-    ph
+    ph, &
+    en
   logical :: &
     broken
 
@@ -725,7 +725,7 @@ function integrateStateAdaptiveEuler(F_0,F,subFp0,subFi0,subState0,Delta_t,en,ph
   broken = plastic_deltaState(ph,en)
   if(broken) return
 
-  broken = integrateStress(F,subFp0,subFi0,Delta_t,en,ph)
+  broken = integrateStress(F,subFp0,subFi0,Delta_t,ph,en)
   if(broken) return
 
   dotState = plastic_dotState(Delta_t,ph,en)
@@ -741,12 +741,12 @@ end function integrateStateAdaptiveEuler
 !---------------------------------------------------------------------------------------------------
 !> @brief Integrate state (including stress integration) with the classic Runge Kutta method
 !---------------------------------------------------------------------------------------------------
-function integrateStateRK4(F_0,F,subFp0,subFi0,subState0,Delta_t,en,ph) result(broken)
+function integrateStateRK4(F_0,F,subFp0,subFi0,subState0,Delta_t,ph,en) result(broken)
 
   real(pReal), intent(in),dimension(3,3) :: F_0,F,subFp0,subFi0
   real(pReal), intent(in),dimension(:)   :: subState0
   real(pReal), intent(in) :: Delta_t
-  integer, intent(in) :: en, ph
+  integer, intent(in) :: ph, en
   logical :: broken
 
   real(pReal), dimension(3,3), parameter :: &
@@ -761,7 +761,7 @@ function integrateStateRK4(F_0,F,subFp0,subFi0,subState0,Delta_t,en,ph) result(b
     B = [1.0_pReal/6.0_pReal, 1.0_pReal/3.0_pReal, 1.0_pReal/3.0_pReal, 1.0_pReal/6.0_pReal]
 
 
-  broken = integrateStateRK(F_0,F,subFp0,subFi0,subState0,Delta_t,en,ph,A,B,C)
+  broken = integrateStateRK(F_0,F,subFp0,subFi0,subState0,Delta_t,ph,en,A,B,C)
 
 end function integrateStateRK4
 
@@ -769,12 +769,12 @@ end function integrateStateRK4
 !---------------------------------------------------------------------------------------------------
 !> @brief Integrate state (including stress integration) with the Cash-Carp method
 !---------------------------------------------------------------------------------------------------
-function integrateStateRKCK45(F_0,F,subFp0,subFi0,subState0,Delta_t,en,ph) result(broken)
+function integrateStateRKCK45(F_0,F,subFp0,subFi0,subState0,Delta_t,ph,en) result(broken)
 
   real(pReal), intent(in),dimension(3,3) :: F_0,F,subFp0,subFi0
   real(pReal), intent(in),dimension(:)   :: subState0
   real(pReal), intent(in) :: Delta_t
-  integer, intent(in) :: en, ph
+  integer, intent(in) :: ph, en
   logical :: broken
 
   real(pReal), dimension(5,5), parameter :: &
@@ -796,7 +796,7 @@ function integrateStateRKCK45(F_0,F,subFp0,subFi0,subState0,Delta_t,en,ph) resul
       13525.0_pReal/55296.0_pReal, 277.0_pReal/14336.0_pReal,  1._pReal/4._pReal]
 
 
-  broken = integrateStateRK(F_0,F,subFp0,subFi0,subState0,Delta_t,en,ph,A,B,C,DB)
+  broken = integrateStateRK(F_0,F,subFp0,subFi0,subState0,Delta_t,ph,en,A,B,C,DB)
 
 end function integrateStateRKCK45
 
@@ -805,7 +805,7 @@ end function integrateStateRKCK45
 !> @brief Integrate state (including stress integration) with an explicit Runge-Kutta method or an
 !! embedded explicit Runge-Kutta method
 !--------------------------------------------------------------------------------------------------
-function integrateStateRK(F_0,F,subFp0,subFi0,subState0,Delta_t,en,ph,A,B,C,DB) result(broken)
+function integrateStateRK(F_0,F,subFp0,subFi0,subState0,Delta_t,ph,en,A,B,C,DB) result(broken)
 
   real(pReal), intent(in),dimension(3,3) :: F_0,F,subFp0,subFi0
   real(pReal), intent(in),dimension(:)   :: subState0
@@ -814,8 +814,8 @@ function integrateStateRK(F_0,F,subFp0,subFi0,subState0,Delta_t,en,ph,A,B,C,DB)
   real(pReal), dimension(:),   intent(in) :: B, C
   real(pReal), dimension(:),   intent(in), optional :: DB
   integer, intent(in) :: &
-    en, &
-    ph
+    ph, &
+    en
   logical :: broken
 
   integer :: &
@@ -848,7 +848,7 @@ function integrateStateRK(F_0,F,subFp0,subFi0,subState0,Delta_t,en,ph,A,B,C,DB)
     plasticState(ph)%state(1:sizeDotState,en) = subState0 &
                                               + dotState * Delta_t
 
-    broken = integrateStress(F_0 + (F - F_0) * Delta_t * C(stage),subFp0,subFi0,Delta_t * C(stage),en,ph)
+    broken = integrateStress(F_0 + (F - F_0) * Delta_t * C(stage),subFp0,subFi0,Delta_t * C(stage),ph,en)
     if(broken) exit
 
     dotState = plastic_dotState(Delta_t,ph,en)
@@ -873,7 +873,7 @@ function integrateStateRK(F_0,F,subFp0,subFi0,subState0,Delta_t,en,ph,A,B,C,DB)
   broken = plastic_deltaState(ph,en)
   if(broken) return
 
-  broken = integrateStress(F,subFp0,subFi0,Delta_t,en,ph)
+  broken = integrateStress(F,subFp0,subFi0,Delta_t,ph,en)
 
 end function integrateStateRK
 
@@ -1052,7 +1052,7 @@ module function phase_mechanical_constitutive(Delta_t,co,ce) result(converged_)
     if (todo) then
       subF = subF0 &
            + subStep * (phase_mechanical_F(ph)%data(1:3,1:3,en) - phase_mechanical_F0(ph)%data(1:3,1:3,en))
-      converged_ = .not. integrateState(subF0,subF,subFp0,subFi0,subState0(1:sizeDotState),subStep * Delta_t,en,ph)
+      converged_ = .not. integrateState(subF0,subF,subFp0,subFi0,subState0(1:sizeDotState),subStep * Delta_t,ph,en)
     endif
 
   enddo cutbackLooping
diff --git a/src/phase_mechanical_plastic.f90 b/src/phase_mechanical_plastic.f90
index 13f14717e..973f0ddbf 100644
--- a/src/phase_mechanical_plastic.f90
+++ b/src/phase_mechanical_plastic.f90
@@ -178,7 +178,7 @@ submodule(phase:mechanical) plastic
         en
     end subroutine dislotungsten_dependentState
 
-    module subroutine nonlocal_dependentState(ph, en)
+    module subroutine nonlocal_dependentState(ph,en)
       integer, intent(in) :: &
         ph, &
         en
@@ -338,11 +338,11 @@ end function plastic_dotState
 !--------------------------------------------------------------------------------------------------
 !> @brief calls microstructure function of the different plasticity constitutive models
 !--------------------------------------------------------------------------------------------------
-module subroutine plastic_dependentState(en,ph)
+module subroutine plastic_dependentState(ph,en)
 
   integer, intent(in) :: &
-    en, &
-    ph
+    ph, &
+    en
 
 
   plasticType: select case (phase_plasticity(ph))

From 3c148b5b0e0e4229cafe97adea42d5731ab9056d Mon Sep 17 00:00:00 2001
From: Martin Diehl <mail@martin-diehl.net>
Date: Fri, 4 Feb 2022 18:55:59 +0100
Subject: [PATCH 32/72] bugfix: openMP variable was not protected

---
 src/homogenization.f90 | 2 +-
 src/phase.f90          | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/homogenization.f90 b/src/homogenization.f90
index 1f9fb2221..8c9ecaecb 100644
--- a/src/homogenization.f90
+++ b/src/homogenization.f90
@@ -237,7 +237,7 @@ subroutine homogenization_mechanical_response(Delta_t,FEsolving_execIP,FEsolving
     doneAndHappy
 
 
-  !$OMP PARALLEL DO PRIVATE(ce,en,ho,NiterationMPstate,converged,doneAndHappy)
+  !$OMP PARALLEL DO PRIVATE(ce,co,en,ho,NiterationMPstate,converged,doneAndHappy)
   do el = FEsolving_execElem(1),FEsolving_execElem(2)
 
     do ip = FEsolving_execIP(1),FEsolving_execIP(2)
diff --git a/src/phase.f90 b/src/phase.f90
index c4e7142f8..9943c777a 100644
--- a/src/phase.f90
+++ b/src/phase.f90
@@ -554,7 +554,7 @@ subroutine crystallite_init()
   flush(IO_STDOUT)
 
 
-  !$OMP PARALLEL DO PRIVATE(ce)
+  !$OMP PARALLEL DO PRIVATE(ce,ph,en)
   do el = 1, eMax
     do ip = 1, iMax
       ce = (el-1)*discretization_nIPs + ip

From 6d78400f875b7642baf9d3ad5ad86111c403ea5e Mon Sep 17 00:00:00 2001
From: Martin Diehl <mail@martin-diehl.net>
Date: Sat, 5 Feb 2022 07:29:00 +0100
Subject: [PATCH 33/72] the concept of IP/element_ID should not be used at the
 DAMASK core

---
 src/CPFEM.f90                   |   3 +-
 src/grid/spectral_utilities.f90 |   4 +-
 src/homogenization.f90          | 106 +++++++++++++++-----------------
 src/mesh/FEM_utilities.f90      |   2 +-
 4 files changed, 53 insertions(+), 62 deletions(-)

diff --git a/src/CPFEM.f90 b/src/CPFEM.f90
index 0f7590782..8f10d39b2 100644
--- a/src/CPFEM.f90
+++ b/src/CPFEM.f90
@@ -193,11 +193,10 @@ subroutine CPFEM_general(mode, ffn, ffn1, temperature_inp, dt, elFE, ip, cauchyS
 
     else validCalculation
       if (debugCPFEM%extensive)  print'(a,i8,1x,i2)', '<< CPFEM >> calculation for elFE ip ',elFE,ip
-      call homogenization_mechanical_response(dt,[ip,ip],[elCP,elCP])
+      call homogenization_mechanical_response(dt,(elCP-1)*discretization_nIPs + ip,(elCP-1)*discretization_nIPs + ip)
       if (.not. terminallyIll) &
         call homogenization_mechanical_response2(dt,[ip,ip],[elCP,elCP])
 
-
       terminalIllness: if (terminallyIll) then
 
         call random_number(rnd)
diff --git a/src/grid/spectral_utilities.f90 b/src/grid/spectral_utilities.f90
index d95580145..34a976644 100644
--- a/src/grid/spectral_utilities.f90
+++ b/src/grid/spectral_utilities.f90
@@ -812,9 +812,9 @@ subroutine utilities_constitutiveResponse(P,P_av,C_volAvg,C_minmaxAvg,&
 
   homogenization_F  = reshape(F,[3,3,product(cells(1:2))*cells3])                                   ! set materialpoint target F to estimated field
 
-  call homogenization_mechanical_response(Delta_t,[1,1],[1,product(cells(1:2))*cells3])             ! calculate P field
+  call homogenization_mechanical_response(Delta_t,1,product(cells(1:2))*cells3)                     ! calculate P field
   if (.not. terminallyIll) &
-    call homogenization_thermal_response(Delta_t,[1,1],[1,product(cells(1:2))*cells3])
+    call homogenization_thermal_response(Delta_t,1,product(cells(1:2))*cells3)
   if (.not. terminallyIll) &
     call homogenization_mechanical_response2(Delta_t,[1,1],[1,product(cells(1:2))*cells3])
 
diff --git a/src/homogenization.f90 b/src/homogenization.f90
index 8c9ecaecb..8539df994 100644
--- a/src/homogenization.f90
+++ b/src/homogenization.f90
@@ -222,14 +222,13 @@ end subroutine homogenization_init
 !--------------------------------------------------------------------------------------------------
 !> @brief
 !--------------------------------------------------------------------------------------------------
-subroutine homogenization_mechanical_response(Delta_t,FEsolving_execIP,FEsolving_execElem)
+subroutine homogenization_mechanical_response(Delta_t,cell_start,cell_end)
 
   real(pReal), intent(in) :: Delta_t                                                                !< time increment
-  integer, dimension(2), intent(in) :: FEsolving_execElem, FEsolving_execIP
+  integer, intent(in) :: &
+    cell_start, cell_end
   integer :: &
     NiterationMPstate, &
-    ip, &                                                                                            !< integration point number
-    el, &                                                                                            !< element number
     co, ce, ho, en
   logical :: &
     converged
@@ -237,45 +236,42 @@ subroutine homogenization_mechanical_response(Delta_t,FEsolving_execIP,FEsolving
     doneAndHappy
 
 
-  !$OMP PARALLEL DO PRIVATE(ce,co,en,ho,NiterationMPstate,converged,doneAndHappy)
-  do el = FEsolving_execElem(1),FEsolving_execElem(2)
+  !$OMP PARALLEL DO PRIVATE(en,ho,co,NiterationMPstate,converged,doneAndHappy)
+  do ce = cell_start, cell_end
 
-    do ip = FEsolving_execIP(1),FEsolving_execIP(2)
-      ce = (el-1)*discretization_nIPs + ip
-      en = material_homogenizationEntry(ce)
-      ho = material_homogenizationID(ce)
+    en = material_homogenizationEntry(ce)
+    ho = material_homogenizationID(ce)
 
-      call phase_restore(ce,.false.) ! wrong name (is more a forward function)
+    call phase_restore(ce,.false.) ! wrong name (is more a forward function)
 
-      if(homogState(ho)%sizeState > 0)  homogState(ho)%state(:,en) = homogState(ho)%state0(:,en)
-      if(damageState_h(ho)%sizeState > 0) damageState_h(ho)%state(:,en) = damageState_h(ho)%state0(:,en)
-      call damage_partition(ce)
+    if(homogState(ho)%sizeState > 0)  homogState(ho)%state(:,en) = homogState(ho)%state0(:,en)
+    if(damageState_h(ho)%sizeState > 0) damageState_h(ho)%state(:,en) = damageState_h(ho)%state0(:,en)
+    call damage_partition(ce)
 
-      doneAndHappy = [.false.,.true.]
+    doneAndHappy = [.false.,.true.]
 
-      NiterationMPstate = 0
-      convergenceLooping: do while (.not. (terminallyIll .or. doneAndHappy(1)) &
-                                    .and. NiterationMPstate < num%nMPstate)
-        NiterationMPstate = NiterationMPstate + 1
+    NiterationMPstate = 0
+    convergenceLooping: do while (.not. (terminallyIll .or. doneAndHappy(1)) &
+                                  .and. NiterationMPstate < num%nMPstate)
+      NiterationMPstate = NiterationMPstate + 1
 
-        call mechanical_partition(homogenization_F(1:3,1:3,ce),ce)
-        converged = all([(phase_mechanical_constitutive(Delta_t,co,ce),co=1,homogenization_Nconstituents(ho))])
-        if (converged) then
-          doneAndHappy = mechanical_updateState(Delta_t,homogenization_F(1:3,1:3,ce),ce)
-          converged = all(doneAndHappy)
-        else
-          doneAndHappy = [.true.,.false.]
-        endif
-      enddo convergenceLooping
+      call mechanical_partition(homogenization_F(1:3,1:3,ce),ce)
+      converged = all([(phase_mechanical_constitutive(Delta_t,co,ce),co=1,homogenization_Nconstituents(ho))])
+      if (converged) then
+        doneAndHappy = mechanical_updateState(Delta_t,homogenization_F(1:3,1:3,ce),ce)
+        converged = all(doneAndHappy)
+      else
+        doneAndHappy = [.true.,.false.]
+      end if
+    end do convergenceLooping
 
-      converged = converged .and. all([(phase_damage_constitutive(Delta_t,co,ce),co=1,homogenization_Nconstituents(ho))])
+    converged = converged .and. all([(phase_damage_constitutive(Delta_t,co,ce),co=1,homogenization_Nconstituents(ho))])
 
-      if (.not. converged) then
-        if (.not. terminallyIll) print*, ' Cell ', ce, ' terminally ill'
-        terminallyIll = .true.
-      endif
-    enddo
-  enddo
+    if (.not. converged) then
+      if (.not. terminallyIll) print*, ' Cell ', ce, ' terminally ill'
+      terminallyIll = .true.
+    end if
+  end do
   !$OMP END PARALLEL DO
 
 end subroutine homogenization_mechanical_response
@@ -284,31 +280,27 @@ end subroutine homogenization_mechanical_response
 !--------------------------------------------------------------------------------------------------
 !> @brief
 !--------------------------------------------------------------------------------------------------
-subroutine homogenization_thermal_response(Delta_t,FEsolving_execIP,FEsolving_execElem)
+subroutine homogenization_thermal_response(Delta_t,cell_start,cell_end)
 
   real(pReal), intent(in) :: Delta_t                                                                !< time increment
-  integer, dimension(2), intent(in) :: FEsolving_execElem, FEsolving_execIP
+  integer, intent(in) :: &
+    cell_start, cell_end
   integer :: &
-    ip, &                                                                                           !< integration point number
-    el, &                                                                                           !< element number
     co, ce, ho
 
 
-  !$OMP PARALLEL DO PRIVATE(ho,ce)
-  do el = FEsolving_execElem(1),FEsolving_execElem(2)
+  !$OMP PARALLEL DO PRIVATE(ho)
+  do ce = cell_start, cell_end
     if (terminallyIll) continue
-    do ip = FEsolving_execIP(1),FEsolving_execIP(2)
-      ce = (el-1)*discretization_nIPs + ip
-      ho = material_homogenizationID(ce)
-      call thermal_partition(ce)
-      do co = 1, homogenization_Nconstituents(ho)
-        if (.not. phase_thermal_constitutive(Delta_t,material_phaseID(co,ce),material_phaseEntry(co,ce))) then
-          if (.not. terminallyIll) print*, ' Cell ', ce, ' terminally ill'
-          terminallyIll = .true.
-        endif
-      enddo
-    enddo
-  enddo
+    ho = material_homogenizationID(ce)
+    call thermal_partition(ce)
+    do co = 1, homogenization_Nconstituents(ho)
+      if (.not. phase_thermal_constitutive(Delta_t,material_phaseID(co,ce),material_phaseEntry(co,ce))) then
+        if (.not. terminallyIll) print*, ' Cell ', ce, ' terminally ill'
+        terminallyIll = .true.
+      end if
+    end do
+  end do
   !$OMP END PARALLEL DO
 
 end subroutine homogenization_thermal_response
@@ -331,11 +323,11 @@ subroutine homogenization_mechanical_response2(Delta_t,FEsolving_execIP,FEsolvin
   elementLooping3: do el = FEsolving_execElem(1),FEsolving_execElem(2)
     IpLooping3: do ip = FEsolving_execIP(1),FEsolving_execIP(2)
       ce = (el-1)*discretization_nIPs + ip
-      ho = material_homogenizationID(ce)
-      do co = 1, homogenization_Nconstituents(ho)
-        call crystallite_orientations(co,ip,el)
+    ho = material_homogenizationID(ce)
+    do co = 1, homogenization_Nconstituents(ho)
+      call crystallite_orientations(co,ip,el)
       enddo
-      call mechanical_homogenize(Delta_t,ce)
+    call mechanical_homogenize(Delta_t,ce)
     enddo IpLooping3
   enddo elementLooping3
   !$OMP END PARALLEL DO
diff --git a/src/mesh/FEM_utilities.f90 b/src/mesh/FEM_utilities.f90
index 703c6c818..4e31a0475 100644
--- a/src/mesh/FEM_utilities.f90
+++ b/src/mesh/FEM_utilities.f90
@@ -150,7 +150,7 @@ subroutine utilities_constitutiveResponse(timeinc,P_av,forwardData)
 
   print'(/,1x,a)', '... evaluating constitutive response ......................................'
 
-  call homogenization_mechanical_response(timeinc,[1,mesh_maxNips],[1,mesh_NcpElems])                ! calculate P field
+  call homogenization_mechanical_response(timeinc,1,mesh_maxNips*mesh_NcpElems)                     ! calculate P field
   if (.not. terminallyIll) &
     call homogenization_mechanical_response2(timeinc,[1,mesh_maxNips],[1,mesh_NcpElems])
   cutBack = .false.

From 5f0a630fa6000a236bb359c83603cd74966b6d52 Mon Sep 17 00:00:00 2001
From: Martin Diehl <mail@martin-diehl.net>
Date: Sat, 5 Feb 2022 08:12:35 +0100
Subject: [PATCH 34/72] remove deprecated phaseAt/phaseMemberAt

---
 src/phase_mechanical_plastic_nonlocal.f90 | 26 +++++++++++------------
 1 file changed, 12 insertions(+), 14 deletions(-)

diff --git a/src/phase_mechanical_plastic_nonlocal.f90 b/src/phase_mechanical_plastic_nonlocal.f90
index dec7ea8e7..9d809e0dc 100644
--- a/src/phase_mechanical_plastic_nonlocal.f90
+++ b/src/phase_mechanical_plastic_nonlocal.f90
@@ -659,10 +659,10 @@ module subroutine nonlocal_dependentState(ph, en)
     do n = 1,nIPneighbors
       neighbor_el = geom(ph)%IPneighborhood(1,n,en)
       neighbor_ip = geom(ph)%IPneighborhood(2,n,en)
-      no = material_phasememberAt(1,neighbor_ip,neighbor_el)
-      if (neighbor_el > 0 .and. neighbor_ip > 0) then
-        if (material_phaseAt(1,neighbor_el) == ph) then
 
+      if (neighbor_el > 0 .and. neighbor_ip > 0) then
+        if (material_phaseID(1,(neighbor_el-1)*discretization_nIPs + neighbor_ip) == ph) then
+            no = material_phaseEntry(1,(neighbor_el-1)*discretization_nIPs + neighbor_ip)
             nRealNeighbors = nRealNeighbors + 1.0_pReal
             rho_neighbor0 = getRho0(ph,no)
 
@@ -1145,7 +1145,6 @@ function rhoDotFlux(timestep,ph,en)
     en
 
   integer ::  &
-    neighbor_ph, &                                                                                  !< phase of my neighbor's plasticity
     ns, &                                                                                           !< short notation for the total number of active slip systems
     c, &                                                                                            !< character of dislocation
     n, &                                                                                            !< index of my current neighbor
@@ -1251,8 +1250,8 @@ function rhoDotFlux(timestep,ph,en)
       neighbor_el = geom(ph)%IPneighborhood(1,n,en)
       neighbor_ip = geom(ph)%IPneighborhood(2,n,en)
       neighbor_n  = geom(ph)%IPneighborhood(3,n,en)
-      np = material_phaseAt(1,neighbor_el)
-      no = material_phasememberAt(1,neighbor_ip,neighbor_el)
+      np = material_phaseID(1,(neighbor_el-1)*discretization_nIPs + neighbor_ip)
+      no = material_phaseEntry(1,(neighbor_el-1)*discretization_nIPs + neighbor_ip)
 
       opposite_neighbor = n + mod(n,2) - mod(n+1,2)
       opposite_el = geom(ph)%IPneighborhood(1,opposite_neighbor,en)
@@ -1260,7 +1259,6 @@ function rhoDotFlux(timestep,ph,en)
       opposite_n  = geom(ph)%IPneighborhood(3,opposite_neighbor,en)
 
       if (neighbor_n > 0) then                                                                      ! if neighbor exists, average deformation gradient
-        neighbor_ph = material_phaseAt(1,neighbor_el)
         neighbor_F = phase_mechanical_F(np)%data(1:3,1:3,no)
         neighbor_Fe = matmul(neighbor_F, math_inv33(phase_mechanical_Fp(np)%data(1:3,1:3,no)))
         Favg = 0.5_pReal * (my_F + neighbor_F)
@@ -1279,12 +1277,12 @@ function rhoDotFlux(timestep,ph,en)
       !* The entering flux from my neighbor will be distributed on my slip systems according to the
       !* compatibility
       if (neighbor_n > 0) then
-      if (phase_plasticity(material_phaseAt(1,neighbor_el)) == PLASTIC_NONLOCAL_ID .and. &
+      if (phase_plasticity(np) == PLASTIC_NONLOCAL_ID .and. &
           any(dependentState(ph)%compatibility(:,:,:,n,en) > 0.0_pReal)) then
 
         forall (s = 1:ns, t = 1:4)
-          neighbor_v0(s,t) =          plasticState(np)%state0(iV   (s,t,neighbor_ph),no)
-          neighbor_rhoSgl0(s,t) = max(plasticState(np)%state0(iRhoU(s,t,neighbor_ph),no),0.0_pReal)
+          neighbor_v0(s,t) =          plasticState(np)%state0(iV   (s,t,np),no)
+          neighbor_rhoSgl0(s,t) = max(plasticState(np)%state0(iRhoU(s,t,np),no),0.0_pReal)
         endforall
 
         where (neighbor_rhoSgl0 * IPvolume(neighbor_ip,neighbor_el) ** 0.667_pReal < prm%rho_min &
@@ -1325,7 +1323,7 @@ function rhoDotFlux(timestep,ph,en)
       !* In case of reduced transmissivity, part of the leaving flux is stored as dead dislocation density.
       !* That means for an interface of zero transmissivity the leaving flux is fully converted to dead dislocations.
       if (opposite_n > 0) then
-      if (phase_plasticity(material_phaseAt(1,opposite_el)) == PLASTIC_NONLOCAL_ID) then
+      if (phase_plasticity(np) == PLASTIC_NONLOCAL_ID) then
 
         normal_me2neighbor_defConf = math_det33(Favg) &
                                    * matmul(math_inv33(transpose(Favg)),geom(ph)%IPareaNormal(1:3,n,en))  ! normal of the interface in (average) deformed configuration (pointing en => neighbor)
@@ -1400,7 +1398,7 @@ module subroutine plastic_nonlocal_updateCompatibility(orientation,ph,ip,el)
   associate(prm => param(ph))
     ns = prm%sum_N_sl
 
-    en = material_phaseMemberAt(1,ip,el)
+    en = material_phaseEntry(1,(el-1)*discretization_nIPs + ip)
     !*** start out fully compatible
     my_compatibility = 0.0_pReal
     forall(s1 = 1:ns) my_compatibility(:,s1,s1,:) = 1.0_pReal
@@ -1408,8 +1406,8 @@ module subroutine plastic_nonlocal_updateCompatibility(orientation,ph,ip,el)
     neighbors: do n = 1,nIPneighbors
       neighbor_e = IPneighborhood(1,n,ip,el)
       neighbor_i = IPneighborhood(2,n,ip,el)
-      neighbor_me = material_phaseMemberAt(1,neighbor_i,neighbor_e)
-      neighbor_phase = material_phaseAt(1,neighbor_e)
+      neighbor_me = material_phaseEntry(1,(neighbor_e-1)*discretization_nIPs + neighbor_i)
+      neighbor_phase = material_phaseID(1,(neighbor_e-1)*discretization_nIPs + neighbor_i)
 
       if (neighbor_e <= 0 .or. neighbor_i <= 0) then
         !* FREE SURFACE

From 6c032e3ce6f01f93d15c7a643b17c117ca54bebf Mon Sep 17 00:00:00 2001
From: Martin Diehl <mail@martin-diehl.net>
Date: Sat, 5 Feb 2022 09:03:10 +0100
Subject: [PATCH 35/72] remove deprecated mappings

almost done with having a consistent access pattern

solver
======
grid: x,y,z; mesh: el,ip

homogenization
==============
interface to solver: ce
internal: ho,en

phase
=====
interface to homogenization: co,ce
internal: ph,en
---
 src/material.f90 | 81 ++++++++++++++++++++++--------------------------
 src/phase.f90    |  4 +--
 2 files changed, 39 insertions(+), 46 deletions(-)

diff --git a/src/material.f90 b/src/material.f90
index fd1531964..bf78a77a6 100644
--- a/src/material.f90
+++ b/src/material.f90
@@ -17,16 +17,17 @@ module material
   implicit none
   private
 
-  type :: tRotationContainer
-    type(tRotation), dimension(:),  allocatable :: data
-  end type
-  type :: tTensorContainer
+  type, public :: tRotationContainer
+    type(tRotation), dimension(:), allocatable :: data
+  end type tRotationContainer
+
+  type, public :: tTensorContainer
     real(pReal), dimension(:,:,:), allocatable :: data
-  end type
+  end type tTensorContainer
 
 
-  type(tRotationContainer), dimension(:), allocatable :: material_O_0
-  type(tTensorContainer),   dimension(:), allocatable :: material_F_i_0
+  type(tRotationContainer), dimension(:), allocatable, public, protected :: material_O_0
+  type(tTensorContainer),   dimension(:), allocatable, public, protected :: material_F_i_0
 
   integer, dimension(:), allocatable, public, protected :: &
     homogenization_Nconstituents                                                                    !< number of grains in each homogenization
@@ -37,20 +38,14 @@ module material
     material_name_phase, &                                                                          !< name of each phase
     material_name_homogenization                                                                    !< name of each homogenization
 
-  integer, dimension(:),     allocatable, public, protected :: &                                    ! (elem)
-    material_homogenizationID, &                                                                    !< per cell TODO: material_ID_homogenization
-    material_homogenizationEntry                                                                    !< per cell TODO: material_entry_homogenization
-  integer, dimension(:,:),   allocatable, public, protected :: &                                    ! (constituent,elem)
-    material_phaseAt, &                                                                             !< phase ID of each element TODO: remove
-    material_phaseID, &                                                                             !< per (constituent,cell) TODO: material_ID_phase
-    material_phaseEntry                                                                             !< per (constituent,cell) TODO: material_entry_phase
-  integer, dimension(:,:,:), allocatable, public, protected :: &                                    ! (constituent,IP,elem)
-    material_phaseMemberAt                                                                          !TODO: remove
+  integer, dimension(:),   allocatable, public, protected :: &                                      ! (cell)
+    material_homogenizationID, &                                                                    ! TODO: rename to material_ID_homogenization
+    material_homogenizationEntry                                                                    ! TODO: rename to material_entry_homogenization
+  integer, dimension(:,:), allocatable, public, protected :: &                                      ! (constituent,cell)
+    material_phaseID, &                                                                             ! TODO: rename to material_ID_phase
+    material_phaseEntry                                                                             ! TODO: rename to material_entry_phase
+
   public :: &
-    tTensorContainer, &
-    tRotationContainer, &
-    material_F_i_0, &
-    material_O_0, &
     material_init
 
 contains
@@ -97,11 +92,12 @@ subroutine parse()
     counterPhase, &
     counterHomogenization
 
-  real(pReal) :: &
-    frac
+  real(pReal) :: v
   integer :: &
-    el, ip, co, ma, &
-    h, ce
+    el, ip, &
+    ho, ph, &
+    co, ce, &
+    ma
 
   materials       => config_material%get('material')
   phases          => config_material%get('phase')
@@ -118,51 +114,48 @@ subroutine parse()
 #endif
 
   allocate(homogenization_Nconstituents(homogenizations%length))
-  do h=1, homogenizations%length
-    homogenization => homogenizations%get(h)
-    homogenization_Nconstituents(h) = homogenization%get_asInt('N_constituents')
+  do ho=1, homogenizations%length
+    homogenization => homogenizations%get(ho)
+    homogenization_Nconstituents(ho) = homogenization%get_asInt('N_constituents')
   end do
   homogenization_maxNconstituents = maxval(homogenization_Nconstituents)
 
   allocate(counterPhase(phases%length),source=0)
   allocate(counterHomogenization(homogenizations%length),source=0)
 
-  allocate(material_phaseAt(homogenization_maxNconstituents,discretization_Nelems),source=0)
-  allocate(material_phaseMemberAt(homogenization_maxNconstituents,discretization_nIPs,discretization_Nelems),source=0)
-
-
   allocate(material_homogenizationID(discretization_nIPs*discretization_Nelems),source=0)
   allocate(material_homogenizationEntry(discretization_nIPs*discretization_Nelems),source=0)
+
   allocate(material_phaseID(homogenization_maxNconstituents,discretization_nIPs*discretization_Nelems),source=0)
   allocate(material_phaseEntry(homogenization_maxNconstituents,discretization_nIPs*discretization_Nelems),source=0)
 
   do el = 1, discretization_Nelems
-    material     => materials%get(discretization_materialAt(el))
-    constituents => material%get('constituents')
+    material => materials%get(discretization_materialAt(el))
 
+    ho = homogenizations%getIndex(material%get_asString('homogenization'))
     do ip = 1, discretization_nIPs
       ce = (el-1)*discretization_nIPs + ip
-      material_homogenizationID(ce) = homogenizations%getIndex(material%get_asString('homogenization'))
-      counterHomogenization(material_homogenizationID(ce)) = counterHomogenization(material_homogenizationID(ce)) + 1
-      material_homogenizationEntry(ce) = counterHomogenization(material_homogenizationID(ce))
+      material_homogenizationID(ce) = ho
+      counterHomogenization(ho) = counterHomogenization(ho) + 1
+      material_homogenizationEntry(ce) = counterHomogenization(ho)
     end do
 
-    frac = 0.0_pReal
+    v = 0.0_pReal
+    constituents => material%get('constituents')
     do co = 1, constituents%length
       constituent => constituents%get(co)
-      frac = frac + constituent%get_asFloat('v')
+      v = v + constituent%get_asFloat('v')
 
-      material_phaseAt(co,el) = phases%getIndex(constituent%get_asString('phase'))
+      ph = phases%getIndex(constituent%get_asString('phase'))
       do ip = 1, discretization_nIPs
         ce = (el-1)*discretization_nIPs + ip
-        counterPhase(material_phaseAt(co,el)) = counterPhase(material_phaseAt(co,el)) + 1
-        material_phaseMemberAt(co,ip,el)      = counterPhase(material_phaseAt(co,el))
-        material_phaseEntry(co,ce) = counterPhase(material_phaseAt(co,el))
-        material_phaseID(co,ce) = material_phaseAt(co,el)
+        material_phaseID(co,ce) = ph
+        counterPhase(ph) = counterPhase(ph) + 1
+        material_phaseEntry(co,ce) = counterPhase(ph)
       end do
 
     end do
-    if (dNeq(frac,1.0_pReal,1.e-12_pReal)) call IO_error(153,ext_msg='constituent')
+    if (dNeq(v,1.0_pReal,1.e-12_pReal)) call IO_error(153,ext_msg='constituent')
 
   end do
 
diff --git a/src/phase.f90 b/src/phase.f90
index 9943c777a..354c738f1 100644
--- a/src/phase.f90
+++ b/src/phase.f90
@@ -590,8 +590,8 @@ subroutine crystallite_orientations(co,ip,el)
 
   call phase_O(ph)%data(en)%fromMatrix(transpose(math_rotationalPart(mechanical_F_e(ph,en))))
 
-  if (plasticState(material_phaseAt(1,el))%nonlocal) &
-    call plastic_nonlocal_updateCompatibility(phase_O,material_phaseAt(1,el),ip,el)
+  if (plasticState(material_phaseID(1,(el-1)*discretization_nIPs + ip))%nonlocal) &
+    call plastic_nonlocal_updateCompatibility(phase_O,material_phaseID(1,(el-1)*discretization_nIPs + ip),ip,el)
 
 
 end subroutine crystallite_orientations

From 9386ba5ef5a453e338d4f1f5c189025bee042f64 Mon Sep 17 00:00:00 2001
From: Martin Diehl <mail@martin-diehl.net>
Date: Sun, 6 Feb 2022 12:59:41 +0100
Subject: [PATCH 36/72] allocate not needed

---
 src/phase_mechanical.f90 | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/src/phase_mechanical.f90 b/src/phase_mechanical.f90
index de9c2bea2..fe62e16f5 100644
--- a/src/phase_mechanical.f90
+++ b/src/phase_mechanical.f90
@@ -996,16 +996,15 @@ module function phase_mechanical_constitutive(Delta_t,co,ce) result(converged_)
     subLi0, &
     subF0, &
     subF
-  real(pReal), dimension(:), allocatable :: subState0
+  real(pReal), dimension(plasticState(material_phaseID(co,ce))%sizeState) :: subState0
 
 
   ph = material_phaseID(co,ce)
   en = material_phaseEntry(co,ce)
-  sizeDotState = plasticState(ph)%sizeDotState
 
+  subState0 = plasticState(ph)%state0(:,en)
   subLi0 = phase_mechanical_Li0(ph)%data(1:3,1:3,en)
   subLp0 = phase_mechanical_Lp0(ph)%data(1:3,1:3,en)
-  allocate(subState0,source=plasticState(ph)%State0(:,en))
   subFp0 = phase_mechanical_Fp0(ph)%data(1:3,1:3,en)
   subFi0 = phase_mechanical_Fi0(ph)%data(1:3,1:3,en)
   subF0  = phase_mechanical_F0(ph)%data(1:3,1:3,en)
@@ -1038,7 +1037,7 @@ module function phase_mechanical_constitutive(Delta_t,co,ce) result(converged_)
       subStep       = num%subStepSizeCryst * subStep
       phase_mechanical_Fp(ph)%data(1:3,1:3,en) = subFp0
       phase_mechanical_Fi(ph)%data(1:3,1:3,en) = subFi0
-      phase_mechanical_S(ph)%data(1:3,1:3,en) = phase_mechanical_S0(ph)%data(1:3,1:3,en)            ! why no subS0 ? is S0 of any use?
+      phase_mechanical_S(ph)%data(1:3,1:3,en) = phase_mechanical_S0(ph)%data(1:3,1:3,en)
       if (subStep < 1.0_pReal) then                                                                 ! actual (not initial) cutback
         phase_mechanical_Lp(ph)%data(1:3,1:3,en) = subLp0
         phase_mechanical_Li(ph)%data(1:3,1:3,en) = subLi0
@@ -1050,6 +1049,7 @@ module function phase_mechanical_constitutive(Delta_t,co,ce) result(converged_)
 !--------------------------------------------------------------------------------------------------
 !  prepare for integration
     if (todo) then
+      sizeDotState = plasticState(ph)%sizeDotState
       subF = subF0 &
            + subStep * (phase_mechanical_F(ph)%data(1:3,1:3,en) - phase_mechanical_F0(ph)%data(1:3,1:3,en))
       converged_ = .not. integrateState(subF0,subF,subFp0,subFi0,subState0(1:sizeDotState),subStep * Delta_t,ph,en)

From a6e83c70ece1de13e989b49419daa62c6459d075 Mon Sep 17 00:00:00 2001
From: Martin Diehl <mail@martin-diehl.net>
Date: Sun, 6 Feb 2022 17:11:18 +0100
Subject: [PATCH 37/72] adjustments to follow de-facto standard in other parts
 of the python library

---
 python/damask/_crystal.py     |  5 +++--
 python/damask/_orientation.py | 22 +++++++++++-----------
 2 files changed, 14 insertions(+), 13 deletions(-)

diff --git a/python/damask/_crystal.py b/python/damask/_crystal.py
index 0b1c00458..ad5b9ed31 100644
--- a/python/damask/_crystal.py
+++ b/python/damask/_crystal.py
@@ -2,6 +2,7 @@ from typing import Union, Dict, List, Tuple
 
 import numpy as np
 
+from ._typehints import FloatSequence
 from . import util
 from . import Rotation
 
@@ -341,8 +342,8 @@ class Crystal():
 
 
     def to_frame(self, *,
-                 uvw: np.ndarray = None,
-                 hkl: np.ndarray = None) -> np.ndarray:
+                 uvw: FloatSequence = None,
+                 hkl: FloatSequence = None) -> np.ndarray:
         """
         Calculate crystal frame vector along lattice direction [uvw] or plane normal (hkl).
 
diff --git a/python/damask/_orientation.py b/python/damask/_orientation.py
index d90cc70e6..c28332012 100644
--- a/python/damask/_orientation.py
+++ b/python/damask/_orientation.py
@@ -1,15 +1,15 @@
 import inspect
 import copy
+from typing import Union, Callable, Dict, Any, Tuple
 
 import numpy as np
 
+from ._typehints import FloatSequence, IntSequence
 from . import Rotation
 from . import Crystal
 from . import util
 from . import tensor
 
-from typing import Union, Callable, Dict, Any, Tuple, List
-from ._typehints import FloatSequence, IntSequence
 
 
 _parameter_doc = \
@@ -165,7 +165,7 @@ class Orientation(Rotation,Crystal):
             Orientation to check for equality.
 
         """
-        return np.logical_not(self==other) if isinstance(other, Orientation) else NotImplemented
+        return np.logical_not(self==other)
 
 
     def isclose(self,
@@ -206,7 +206,7 @@ class Orientation(Rotation,Crystal):
                  other: object,
                  rtol: float = 1e-5,
                  atol: float = 1e-8,
-                 equal_nan: bool = True) -> Union[bool, np.bool_]:
+                 equal_nan: bool = True) -> bool:
         """
         Test whether all values are approximately equal to corresponding ones of other Orientation.
 
@@ -227,9 +227,7 @@ class Orientation(Rotation,Crystal):
             Whether all values are close between both orientations.
 
         """
-        if not isinstance(other, Orientation):
-            raise TypeError
-        return np.all(self.isclose(other,rtol,atol,equal_nan))
+        return bool(np.all(self.isclose(other,rtol,atol,equal_nan)))
 
 
     def __mul__(self,
@@ -411,6 +409,7 @@ class Orientation(Rotation,Crystal):
         sort = 0 if len(loc) == 1 else np.lexsort(loc[:0:-1])
         return eq[ok][sort].reshape(self.shape)
 
+
     @property
     def in_FZ(self) -> Union[np.bool_, np.ndarray]:
         """
@@ -574,6 +573,7 @@ class Orientation(Rotation,Crystal):
         loc  = np.where(ok)
         sort = 0 if len(loc) == 2 else np.lexsort(loc[:1:-1])
         quat = r[ok][sort].reshape(blend+(4,))
+
         return (
                 (self.copy(rotation=quat),
                  (np.vstack(loc[:2]).T)[sort].reshape(blend+(2,)))
@@ -783,7 +783,7 @@ class Orientation(Rotation,Crystal):
     @property
     def symmetry_operations(self) -> Rotation:
         """Symmetry operations as Rotations."""
-        _symmetry_operations: Dict[str, List[List]] = {
+        _symmetry_operations  = {
             'cubic':         [
                               [ 1.0,            0.0,            0.0,            0.0            ],
                               [ 0.0,            1.0,            0.0,            0.0            ],
@@ -854,8 +854,8 @@ class Orientation(Rotation,Crystal):
     # functions that require lattice, not just family
 
     def to_pole(self, *,
-                uvw: np.ndarray = None,
-                hkl: np.ndarray = None,
+                uvw: FloatSequence = None,
+                hkl: FloatSequence = None,
                 with_symmetry: bool = False) -> np.ndarray:
         """
         Calculate lab frame vector along lattice direction [uvw] or plane normal (hkl).
@@ -926,7 +926,7 @@ class Orientation(Rotation,Crystal):
         if active == '*': active = [len(a) for a in kinematics['direction']]
 
         if not active:
-            raise RuntimeError
+            raise RuntimeError # ToDo
         d = self.to_frame(uvw=np.vstack([kinematics['direction'][i][:n] for i,n in enumerate(active)]))
         p = self.to_frame(hkl=np.vstack([kinematics['plane'][i][:n] for i,n in enumerate(active)]))
         P = np.einsum('...i,...j',d/np.linalg.norm(d,axis=1,keepdims=True),

From 739a4b7a26022c1a0d5c40d561a54d1a83917d79 Mon Sep 17 00:00:00 2001
From: Martin Diehl <mail@martin-diehl.net>
Date: Mon, 7 Feb 2022 14:25:03 +0100
Subject: [PATCH 38/72] need to store fraction for proper homogenization

---
 src/discretization.f90 |  4 +++-
 src/material.f90       | 17 ++++++++++++-----
 2 files changed, 15 insertions(+), 6 deletions(-)

diff --git a/src/discretization.f90 b/src/discretization.f90
index c79c72b5e..5f4d1c5a6 100644
--- a/src/discretization.f90
+++ b/src/discretization.f90
@@ -12,7 +12,8 @@ module discretization
 
   integer,     public, protected :: &
     discretization_nIPs, &
-    discretization_Nelems
+    discretization_Nelems, &
+    discretization_Ncells
 
   integer,     public, protected, dimension(:),   allocatable :: &
     discretization_materialAt                                                                       !ToDo: discretization_ID_material
@@ -53,6 +54,7 @@ subroutine discretization_init(materialAt,&
 
   discretization_Nelems = size(materialAt,1)
   discretization_nIPs   = size(IPcoords0,2)/discretization_Nelems
+  discretization_Ncells = discretization_Nelems*discretization_nIPs
 
   discretization_materialAt = materialAt
 
diff --git a/src/material.f90 b/src/material.f90
index bf78a77a6..10cf2aa7e 100644
--- a/src/material.f90
+++ b/src/material.f90
@@ -45,6 +45,9 @@ module material
     material_phaseID, &                                                                             ! TODO: rename to material_ID_phase
     material_phaseEntry                                                                             ! TODO: rename to material_entry_phase
 
+  real(pReal), dimension(:,:), allocatable, public, protected :: &
+    material_v                                                                                      ! fraction
+
   public :: &
     material_init
 
@@ -123,11 +126,13 @@ subroutine parse()
   allocate(counterPhase(phases%length),source=0)
   allocate(counterHomogenization(homogenizations%length),source=0)
 
-  allocate(material_homogenizationID(discretization_nIPs*discretization_Nelems),source=0)
-  allocate(material_homogenizationEntry(discretization_nIPs*discretization_Nelems),source=0)
+  allocate(material_homogenizationID(discretization_Ncells),source=0)
+  allocate(material_homogenizationEntry(discretization_Ncells),source=0)
 
-  allocate(material_phaseID(homogenization_maxNconstituents,discretization_nIPs*discretization_Nelems),source=0)
-  allocate(material_phaseEntry(homogenization_maxNconstituents,discretization_nIPs*discretization_Nelems),source=0)
+  allocate(material_phaseID(homogenization_maxNconstituents,discretization_Ncells),source=0)
+  allocate(material_phaseEntry(homogenization_maxNconstituents,discretization_Ncells),source=0)
+
+  allocate(material_v(homogenization_maxNconstituents,discretization_Ncells),source=0.0_pReal)
 
   do el = 1, discretization_Nelems
     material => materials%get(discretization_materialAt(el))
@@ -144,7 +149,9 @@ subroutine parse()
     constituents => material%get('constituents')
     do co = 1, constituents%length
       constituent => constituents%get(co)
-      v = v + constituent%get_asFloat('v')
+
+      material_v(co,ce) = constituent%get_asFloat('v')
+      v = v + material_v(co,ce)
 
       ph = phases%getIndex(constituent%get_asString('phase'))
       do ip = 1, discretization_nIPs

From 28eda648937b287435df9b2a7aa75b58d3302032 Mon Sep 17 00:00:00 2001
From: Martin Diehl <mail@martin-diehl.net>
Date: Mon, 7 Feb 2022 14:43:32 +0100
Subject: [PATCH 39/72] bugfix: change of behavior

fraction needed for calculation of homogenized response
---
 src/homogenization_mechanical.f90 | 13 ++++---------
 src/homogenization_thermal.f90    | 18 ++++++------------
 src/material.f90                  |  8 ++++----
 3 files changed, 14 insertions(+), 25 deletions(-)

diff --git a/src/homogenization_mechanical.f90 b/src/homogenization_mechanical.f90
index d2ec08394..1280a9cf3 100644
--- a/src/homogenization_mechanical.f90
+++ b/src/homogenization_mechanical.f90
@@ -131,20 +131,15 @@ module subroutine mechanical_homogenize(Delta_t,ce)
   integer :: co
 
 
-  homogenization_P(1:3,1:3,ce)            = phase_P(1,ce)
-  homogenization_dPdF(1:3,1:3,1:3,1:3,ce) = phase_mechanical_dPdF(Delta_t,1,ce)
+  homogenization_P(1:3,1:3,ce)            = phase_P(1,ce)*material_v(1,ce)
+  homogenization_dPdF(1:3,1:3,1:3,1:3,ce) = phase_mechanical_dPdF(Delta_t,1,ce)*material_v(1,ce)
   do co = 2, homogenization_Nconstituents(material_homogenizationID(ce))
     homogenization_P(1:3,1:3,ce)            = homogenization_P(1:3,1:3,ce) &
-                                            + phase_P(co,ce)
+                                            + phase_P(co,ce)*material_v(co,ce)
     homogenization_dPdF(1:3,1:3,1:3,1:3,ce) = homogenization_dPdF(1:3,1:3,1:3,1:3,ce) &
-                                            + phase_mechanical_dPdF(Delta_t,co,ce)
+                                            + phase_mechanical_dPdF(Delta_t,co,ce)*material_v(co,ce)
   end do
 
-  homogenization_P(1:3,1:3,ce)            = homogenization_P(1:3,1:3,ce) &
-                                          / real(homogenization_Nconstituents(material_homogenizationID(ce)),pReal)
-  homogenization_dPdF(1:3,1:3,1:3,1:3,ce) = homogenization_dPdF(1:3,1:3,1:3,1:3,ce) &
-                                          / real(homogenization_Nconstituents(material_homogenizationID(ce)),pReal)
-
 end subroutine mechanical_homogenize
 
 
diff --git a/src/homogenization_thermal.f90 b/src/homogenization_thermal.f90
index c5490d869..9aa727041 100644
--- a/src/homogenization_thermal.f90
+++ b/src/homogenization_thermal.f90
@@ -105,13 +105,11 @@ module function homogenization_mu_T(ce) result(mu)
   integer :: co
 
 
-  mu = phase_mu_T(1,ce)
+  mu = phase_mu_T(1,ce)*material_v(1,ce)
   do co = 2, homogenization_Nconstituents(material_homogenizationID(ce))
-    mu = mu + phase_mu_T(co,ce)
+    mu = mu + phase_mu_T(co,ce)*material_v(co,ce)
   end do
 
-  mu = mu / real(homogenization_Nconstituents(material_homogenizationID(ce)),pReal)
-
 end function homogenization_mu_T
 
 
@@ -126,13 +124,11 @@ module function homogenization_K_T(ce) result(K)
   integer :: co
 
 
-  K = phase_K_T(1,ce)
+  K = phase_K_T(1,ce)*material_v(1,ce)
   do co = 2, homogenization_Nconstituents(material_homogenizationID(ce))
-    K = K + phase_K_T(co,ce)
+    K = K + phase_K_T(co,ce)*material_v(co,ce)
   end do
 
-  K = K / real(homogenization_Nconstituents(material_homogenizationID(ce)),pReal)
-
 end function homogenization_K_T
 
 
@@ -147,13 +143,11 @@ module function homogenization_f_T(ce) result(f)
   integer :: co
 
 
-  f = phase_f_T(material_phaseID(1,ce),material_phaseEntry(1,ce))
+  f = phase_f_T(material_phaseID(1,ce),material_phaseEntry(1,ce))*material_v(1,ce)
   do co = 2, homogenization_Nconstituents(material_homogenizationID(ce))
-    f = f + phase_f_T(material_phaseID(co,ce),material_phaseEntry(co,ce))
+    f = f + phase_f_T(material_phaseID(co,ce),material_phaseEntry(co,ce))*material_v(co,ce)
   end do
 
-  f = f/real(homogenization_Nconstituents(material_homogenizationID(ce)),pReal)
-
 end function homogenization_f_T
 
 
diff --git a/src/material.f90 b/src/material.f90
index 10cf2aa7e..3ff280b0d 100644
--- a/src/material.f90
+++ b/src/material.f90
@@ -145,13 +145,11 @@ subroutine parse()
       material_homogenizationEntry(ce) = counterHomogenization(ho)
     end do
 
-    v = 0.0_pReal
     constituents => material%get('constituents')
     do co = 1, constituents%length
       constituent => constituents%get(co)
 
-      material_v(co,ce) = constituent%get_asFloat('v')
-      v = v + material_v(co,ce)
+      v = constituent%get_asFloat('v')
 
       ph = phases%getIndex(constituent%get_asString('phase'))
       do ip = 1, discretization_nIPs
@@ -159,10 +157,12 @@ subroutine parse()
         material_phaseID(co,ce) = ph
         counterPhase(ph) = counterPhase(ph) + 1
         material_phaseEntry(co,ce) = counterPhase(ph)
+        material_v(co,ce) = v
       end do
 
     end do
-    if (dNeq(v,1.0_pReal,1.e-12_pReal)) call IO_error(153,ext_msg='constituent')
+    if (dNeq(sum(material_v(1:constituents%length,ce)),1.0_pReal,1.e-9_pReal)) &
+      call IO_error(153,ext_msg='constituent')
 
   end do
 

From 8c6225794d3953a22f7828c9354b6a8489e73de3 Mon Sep 17 00:00:00 2001
From: Daniel Otto de Mentock <d.mentock@mpie.de>
Date: Tue, 8 Feb 2022 14:47:23 +0100
Subject: [PATCH 40/72] adjusted return of Orientation.__ne__ function to
 return NotImplemented in case of wrong input type

---
 python/damask/_orientation.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/python/damask/_orientation.py b/python/damask/_orientation.py
index c28332012..06caf9b4c 100644
--- a/python/damask/_orientation.py
+++ b/python/damask/_orientation.py
@@ -165,7 +165,7 @@ class Orientation(Rotation,Crystal):
             Orientation to check for equality.
 
         """
-        return np.logical_not(self==other)
+        return np.logical_not(self==other) if isinstance(other, Orientation) else NotImplemented
 
 
     def isclose(self,

From 0a52ae3b6f3e338ffedff35deaff4bab578f115b Mon Sep 17 00:00:00 2001
From: Philip Eisenlohr <eisenlohr@egr.msu.edu>
Date: Fri, 11 Feb 2022 12:10:29 -0500
Subject: [PATCH 41/72] polishing of help and style; relax to FloatSequence
 type where appropriate but keep doc at np.ndarray

---
 python/damask/_crystal.py     |   9 ++-
 python/damask/_orientation.py |  84 +++++++++++++-------------
 python/damask/_rotation.py    | 109 ++++++++++++++++++++--------------
 python/damask/_table.py       |   2 +-
 4 files changed, 113 insertions(+), 91 deletions(-)

diff --git a/python/damask/_crystal.py b/python/damask/_crystal.py
index ad5b9ed31..a63cb0c81 100644
--- a/python/damask/_crystal.py
+++ b/python/damask/_crystal.py
@@ -131,9 +131,8 @@ class Crystal():
             Crystal to check for equality.
 
         """
-        if not isinstance(other, Crystal):
-            return NotImplemented
-        return self.lattice == other.lattice and \
+        return NotImplemented if not isinstance(other, Crystal) else \
+               self.lattice == other.lattice and \
                self.parameters == other.parameters and \
                self.family == other.family
 
@@ -316,8 +315,8 @@ class Crystal():
                                               self.lattice[-1],None),dtype=float)
 
     def to_lattice(self, *,
-                   direction: np.ndarray = None,
-                   plane: np.ndarray = None) -> np.ndarray:
+                   direction: FloatSequence = None,
+                   plane: FloatSequence = None) -> np.ndarray:
         """
         Calculate lattice vector corresponding to crystal frame direction or plane normal.
 
diff --git a/python/damask/_orientation.py b/python/damask/_orientation.py
index 06caf9b4c..5a9b7b141 100644
--- a/python/damask/_orientation.py
+++ b/python/damask/_orientation.py
@@ -189,7 +189,7 @@ class Orientation(Rotation,Crystal):
 
         Returns
         -------
-        mask : numpy.ndarray bool
+        mask : numpy.ndarray of bool
             Mask indicating where corresponding orientations are close.
 
         """
@@ -372,10 +372,10 @@ class Orientation(Rotation,Crystal):
 
         Parameters
         ----------
-        uvw : list, numpy.ndarray of shape (...,3)
-            lattice direction aligned with lab frame x-direction.
-        hkl : list, numpy.ndarray of shape (...,3)
-            lattice plane normal aligned with lab frame z-direction.
+        uvw : numpy.ndarray, shape (...,3)
+            Lattice direction aligned with lab frame x-direction.
+        hkl : numpy.ndarray, shape (...,3)
+            Lattice plane normal aligned with lab frame z-direction.
 
         """
         o = cls(**kwargs)
@@ -417,7 +417,7 @@ class Orientation(Rotation,Crystal):
 
         Returns
         -------
-        in : numpy.ndarray of bool, quaternion.shape
+        in : numpy.ndarray of bool, shape (self.shape)
             Whether Rodrigues-Frank vector falls into fundamental zone.
 
         Notes
@@ -461,7 +461,7 @@ class Orientation(Rotation,Crystal):
 
         Returns
         -------
-        in : numpy.ndarray of bool, quaternion.shape
+        in : numpy.ndarray of bool, shape (self.shape)
             Whether Rodrigues-Frank vector falls into disorientation FZ.
 
         References
@@ -515,7 +515,7 @@ class Orientation(Rotation,Crystal):
         -------
         disorientation : Orientation
             Disorientation between self and other.
-        operators : numpy.ndarray int of shape (...,2), conditional
+        operators : numpy.ndarray of int, shape (...,2), conditional
             Index of symmetrically equivalent orientation that rotated vector to the SST.
 
         Notes
@@ -583,14 +583,14 @@ class Orientation(Rotation,Crystal):
 
 
     def average(self,
-                weights = None,
-                return_cloud = False):
+                weights: FloatSequence = None,
+                return_cloud: bool = False):
         """
         Return orientation average over last dimension.
 
         Parameters
         ----------
-        weights : numpy.ndarray, optional
+        weights : numpy.ndarray, shape (self.shape), optional
             Relative weights of orientations.
         return_cloud : bool, optional
             Return the set of symmetrically equivalent orientations that was used in averaging.
@@ -610,8 +610,8 @@ class Orientation(Rotation,Crystal):
 
         """
         eq = self.equivalent
-        m  = eq.misorientation(self[...,0].reshape((1,)+self.shape[:-1]+(1,))
-                                          .broadcast_to(eq.shape)).as_axis_angle()[...,3]
+        m  = eq.misorientation(self[...,0].reshape((1,)+self.shape[:-1]+(1,))             # type: ignore
+                                          .broadcast_to(eq.shape)).as_axis_angle()[...,3] # type: ignore
         r = Rotation(np.squeeze(np.take_along_axis(eq.quaternion,
                                                    np.argmin(m,axis=0)[np.newaxis,...,np.newaxis],
                                                    axis=0),
@@ -625,7 +625,7 @@ class Orientation(Rotation,Crystal):
 
 
     def to_SST(self,
-               vector: np.ndarray,
+               vector: FloatSequence,
                proper: bool = False,
                return_operators: bool = False) -> np.ndarray:
         """
@@ -633,10 +633,10 @@ class Orientation(Rotation,Crystal):
 
         Parameters
         ----------
-        vector : numpy.ndarray of shape (...,3)
+        vector : numpy.ndarray, shape (...,3)
             Lab frame vector to align with crystal frame direction.
             Shape of vector blends with shape of own rotation array.
-            For example, a rotation array of shape (3,2) and a (2,4) vector array result in (3,2,4) outputs.
+            For example, a rotation array of shape (3,2) and a vector array of shape (2,4) result in (3,2,4) outputs.
         proper : bool, optional
             Consider only vectors with z >= 0, hence combine two neighboring SSTs.
             Defaults to False.
@@ -646,15 +646,18 @@ class Orientation(Rotation,Crystal):
 
         Returns
         -------
-        vector_SST : numpy.ndarray of shape (...,3)
+        vector_SST : numpy.ndarray, shape (...,3)
             Rotated vector falling into SST.
-        operators : numpy.ndarray int of shape (...), conditional
+        operators : numpy.ndarray of int, shape (...), conditional
             Index of symmetrically equivalent orientation that rotated vector to SST.
 
         """
+        vector_ = np.array(vector,float)
+        if vector_.shape[-1] != 3:
+            raise ValueError('input is not a field of three-dimensional vectors')
         eq  = self.equivalent
-        blend = util.shapeblender(eq.shape,np.array(vector).shape[:-1])
-        poles = eq.broadcast_to(blend,mode='right') @ np.broadcast_to(np.array(vector),blend+(3,)) #type: ignore
+        blend = util.shapeblender(eq.shape,vector_.shape[:-1])
+        poles = eq.broadcast_to(blend,mode='right') @ np.broadcast_to(vector_,blend+(3,)) #type: ignore
         ok    = self.in_SST(poles,proper=proper)
         ok   &= np.cumsum(ok,axis=0) == 1
         loc   = np.where(ok)
@@ -667,14 +670,14 @@ class Orientation(Rotation,Crystal):
 
 
     def in_SST(self,
-               vector: np.ndarray,
+               vector: FloatSequence,
                proper: bool = False) -> Union[np.bool_, np.ndarray]:
         """
         Check whether given crystal frame vector falls into standard stereographic triangle of own symmetry.
 
         Parameters
         ----------
-        vector : numpy.ndarray of shape (...,3)
+        vector : numpy.ndarray, shape (...,3)
             Vector to check.
         proper : bool, optional
             Consider only vectors with z >= 0, hence combine two neighboring SSTs.
@@ -686,31 +689,32 @@ class Orientation(Rotation,Crystal):
             Whether vector falls into SST.
 
         """
-        if not isinstance(vector,np.ndarray) or vector.shape[-1] != 3:
+        vector_ = np.array(vector,float)
+        if vector_.shape[-1] != 3:
             raise ValueError('input is not a field of three-dimensional vectors')
 
         if self.standard_triangle is None:                                                          # direct exit for no symmetry
-            return  np.ones_like(vector[...,0],bool)
+            return np.ones_like(vector_[...,0],bool)
 
         if proper:
             components_proper   = np.around(np.einsum('...ji,...i',
-                                                      np.broadcast_to(self.standard_triangle['proper'], vector.shape+(3,)),
-                                                      vector), 12)
+                                                      np.broadcast_to(self.standard_triangle['proper'],   vector_.shape+(3,)),
+                                                      vector_), 12)
             components_improper = np.around(np.einsum('...ji,...i',
-                                                      np.broadcast_to(self.standard_triangle['improper'], vector.shape+(3,)),
-                                                      vector), 12)
+                                                      np.broadcast_to(self.standard_triangle['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.standard_triangle['improper'], vector.shape+(3,)),
-                                             np.block([vector[...,:2],np.abs(vector[...,2:3])])), 12)
+                                             np.broadcast_to(self.standard_triangle['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: np.ndarray,
+                  vector: FloatSequence,
                   in_SST: bool = True,
                   proper: bool = False) -> np.ndarray:
         """
@@ -718,10 +722,10 @@ class Orientation(Rotation,Crystal):
 
         Parameters
         ----------
-        vector : numpy.ndarray of shape (...,3)
+        vector : numpy.ndarray, shape (...,3)
             Vector to colorize.
             Shape of vector blends with shape of own rotation array.
-            For example, a rotation array of shape (3,2) and a (2,4) vector array result in (3,2,4) outputs.
+            For example, a rotation array of shape (3,2) and a vector array of shape (2,4) result in (3,2,4) outputs.
         in_SST : bool, optional
             Consider symmetrically equivalent orientations such that poles are located in SST.
             Defaults to True.
@@ -731,7 +735,7 @@ class Orientation(Rotation,Crystal):
 
         Returns
         -------
-        rgb : numpy.ndarray of shape (...,3)
+        rgb : numpy.ndarray, shape (...,3)
            RGB array of IPF colors.
 
         Examples
@@ -755,7 +759,7 @@ class Orientation(Rotation,Crystal):
 
         if proper:
             components_proper   = np.around(np.einsum('...ji,...i',
-                                                      np.broadcast_to(self.standard_triangle['proper'], vector_.shape+(3,)),
+                                                      np.broadcast_to(self.standard_triangle['proper'],   vector_.shape+(3,)),
                                                       vector_), 12)
             components_improper = np.around(np.einsum('...ji,...i',
                                                       np.broadcast_to(self.standard_triangle['improper'], vector_.shape+(3,)),
@@ -862,16 +866,16 @@ class Orientation(Rotation,Crystal):
 
         Parameters
         ----------
-        uvw|hkl : numpy.ndarray of shape (...,3)
+        uvw|hkl : numpy.ndarray, shape (...,3)
             Miller indices of crystallographic direction or plane normal.
             Shape of vector blends with shape of own rotation array.
-            For example, a rotation array of shape (3,2) and a (2,4) vector array result in (3,2,4) outputs.
+            For example, a rotation array, shape (3,2) and a vector array of shape (2,4) result in (3,2,4) outputs.
         with_symmetry : bool, optional
             Calculate all N symmetrically equivalent vectors.
 
         Returns
         -------
-        vector : numpy.ndarray of shape (...,3) or (...,N,3)
+        vector : numpy.ndarray, shape (...,3) or (...,N,3)
             Lab frame vector (or vectors if with_symmetry) along [uvw] direction or (hkl) plane normal.
 
         """
@@ -894,13 +898,13 @@ class Orientation(Rotation,Crystal):
 
         Parameters
         ----------
-        N_slip|N_twin : iterable of int
+        N_slip|N_twin : '*' or iterable of int
             Number of deformation systems per family of the deformation system.
             Use '*' to select all.
 
         Returns
         -------
-        P : numpy.ndarray of shape (N,...,3,3)
+        P : numpy.ndarray, shape (N,...,3,3)
             Schmid matrix for each of the N deformation systems.
 
         Examples
diff --git a/python/damask/_rotation.py b/python/damask/_rotation.py
index 226d66f69..273cf8e92 100644
--- a/python/damask/_rotation.py
+++ b/python/damask/_rotation.py
@@ -108,12 +108,12 @@ class Rotation:
     def __getitem__(self,
                     item: Union[Tuple[int], int, bool, np.bool_, np.ndarray]):
         """Return slice according to item."""
-        return self.copy() \
-               if self.shape == () else \
+        return self.copy() if self.shape == () else \
                self.copy(rotation=self.quaternion[item+(slice(None),)] if isinstance(item,tuple) else self.quaternion[item])
 
 
-    def __eq__(self, other: object) -> bool:
+    def __eq__(self,
+               other: object) -> bool:
         """
         Equal to other.
 
@@ -123,9 +123,8 @@ class Rotation:
             Rotation to check for equality.
 
         """
-        if not isinstance(other, Rotation):
-            return NotImplemented
-        return np.logical_or(np.all(self.quaternion ==      other.quaternion,axis=-1),
+        return NotImplemented if not isinstance(other, Rotation) else \
+               np.logical_or(np.all(self.quaternion ==      other.quaternion,axis=-1),
                              np.all(self.quaternion == -1.0*other.quaternion,axis=-1))
 
 
@@ -163,7 +162,7 @@ class Rotation:
 
         Returns
         -------
-        mask : numpy.ndarray bool
+        mask : numpy.ndarray of bool
             Mask indicating where corresponding rotations are close.
 
         """
@@ -228,13 +227,13 @@ class Rotation:
 
 
     def __pow__(self: MyType,
-                exp: int) -> MyType:
+                exp: Union[float, int]) -> MyType:
         """
         Perform the rotation 'exp' times.
 
         Parameters
         ----------
-        exp : float
+        exp : scalar
             Exponent.
 
         """
@@ -243,13 +242,13 @@ class Rotation:
         return self.copy(rotation=Rotation(np.block([np.cos(exp*phi),np.sin(exp*phi)*p]))._standardize())
 
     def __ipow__(self: MyType,
-                 exp: int) -> MyType:
+                 exp: Union[float, int]) -> MyType:
         """
         Perform the rotation 'exp' times (in-place).
 
         Parameters
         ----------
-        exp : float
+        exp : scalar
             Exponent.
 
         """
@@ -263,7 +262,7 @@ class Rotation:
 
         Parameters
         ----------
-        other : Rotation of shape (self.shape)
+        other : Rotation, shape (self.shape)
             Rotation for composition.
 
         Returns
@@ -290,7 +289,7 @@ class Rotation:
 
         Parameters
         ----------
-        other : Rotation of shape (self.shape)
+        other : Rotation, shape (self.shape)
             Rotation for composition.
 
         """
@@ -304,7 +303,7 @@ class Rotation:
 
         Parameters
         ----------
-        other : damask.Rotation of shape (self.shape)
+        other : damask.Rotation, shape (self.shape)
             Rotation to invert for composition.
 
         Returns
@@ -325,7 +324,7 @@ class Rotation:
 
         Parameters
         ----------
-        other : Rotation of shape (self.shape)
+        other : Rotation, shape (self.shape)
             Rotation to invert for composition.
 
         """
@@ -339,12 +338,12 @@ class Rotation:
 
         Parameters
         ----------
-        other : numpy.ndarray of shape (...,3), (...,3,3), or (...,3,3,3,3)
+        other : numpy.ndarray, shape (...,3), (...,3,3), or (...,3,3,3,3)
             Vector or tensor on which to apply the rotation.
 
         Returns
         -------
-        rotated : numpy.ndarray of shape (...,3), (...,3,3), or (...,3,3,3,3)
+        rotated : numpy.ndarray, shape (...,3), (...,3,3), or (...,3,3,3,3)
             Rotated vector or tensor, i.e. transformed to frame defined by rotation.
 
         """
@@ -401,6 +400,15 @@ class Rotation:
         """
         Flatten array.
 
+        Parameters
+        ----------
+        order : {'C', 'F', 'A'}, optional
+            'C' flattens in row-major (C-style) order.
+            'F' flattens in column-major (Fortran-style) order.
+            'A' flattens in column-major order if object is Fortran contiguous in memory,
+            row-major order otherwise.
+            Defaults to 'C'.
+
         Returns
         -------
         flattened : damask.Rotation
@@ -416,6 +424,18 @@ class Rotation:
         """
         Reshape array.
 
+        Parameters
+        ----------
+        shape : int or tuple of ints
+            The new shape should be compatible with the original shape.
+            If an integer is supplied, then the result will be a 1-D array of that length.
+        order : {'C', 'F', 'A'}, optional
+            'C' flattens in row-major (C-style) order.
+            'F' flattens in column-major (Fortran-style) order.
+            'A' flattens in column-major order if object is Fortran contiguous in memory,
+            row-major order otherwise.
+            Defaults to 'C'.
+
         Returns
         -------
         reshaped : damask.Rotation
@@ -434,7 +454,7 @@ class Rotation:
 
         Parameters
         ----------
-        shape : int, tuple
+        shape : int or tuple of ints
             Shape of broadcasted array.
         mode : str, optional
             Where to preferentially locate missing dimensions.
@@ -458,7 +478,7 @@ class Rotation:
 
         Parameters
         ----------
-        weights : FloatSequence, optional
+        weights : numpy.ndarray, optional
             Relative weight of each rotation.
 
         Returns
@@ -518,7 +538,7 @@ class Rotation:
 
         Returns
         -------
-        q : numpy.ndarray of shape (...,4)
+        q : numpy.ndarray, shape (...,4)
             Unit quaternion (q_0, q_1, q_2, q_3) in positive real hemisphere, i.e. ǀqǀ = 1, q_0 ≥ 0.
 
         """
@@ -536,7 +556,7 @@ class Rotation:
 
         Returns
         -------
-        phi : numpy.ndarray of shape (...,3)
+        phi : numpy.ndarray, shape (...,3)
             Bunge Euler angles (φ_1 ∈ [0,2π], ϕ ∈ [0,π], φ_2 ∈ [0,2π])
             or (φ_1 ∈ [0,360], ϕ ∈ [0,180], φ_2 ∈ [0,360]) if degrees == True.
 
@@ -555,8 +575,7 @@ class Rotation:
 
         """
         eu = Rotation._qu2eu(self.quaternion)
-        if degrees: eu = np.degrees(eu)
-        return eu
+        return np.degrees(eu) if degrees else eu
 
     def as_axis_angle(self,
                       degrees: bool = False,
@@ -573,7 +592,7 @@ class Rotation:
 
         Returns
         -------
-        axis_angle : numpy.ndarray of shape (...,4) or tuple ((...,3), (...)) if pair == True
+        axis_angle : numpy.ndarray, shape (...,4) or tuple ((...,3), (...)) if pair == True
             Axis and angle [n_1, n_2, n_3, ω] with ǀnǀ = 1 and ω ∈ [0,π]
             or ω ∈ [0,180] if degrees == True.
 
@@ -597,7 +616,7 @@ class Rotation:
 
         Returns
         -------
-        R : numpy.ndarray of shape (...,3,3)
+        R : numpy.ndarray, shape (...,3,3)
             Rotation matrix R with det(R) = 1, R.T ∙ R = I.
 
         Examples
@@ -627,7 +646,7 @@ class Rotation:
 
         Returns
         -------
-        rho : numpy.ndarray of shape (...,4) or (...,3) if compact == True
+        rho : numpy.ndarray, shape (...,4) or (...,3) if compact == True
             Rodrigues–Frank vector [n_1, n_2, n_3, tan(ω/2)] with ǀnǀ = 1 and ω ∈ [0,π]
             or [n_1, n_2, n_3] with ǀnǀ = tan(ω/2) and ω ∈ [0,π] if compact == True.
 
@@ -654,7 +673,7 @@ class Rotation:
 
         Returns
         -------
-        h : numpy.ndarray of shape (...,3)
+        h : numpy.ndarray, shape (...,3)
             Homochoric vector (h_1, h_2, h_3) with ǀhǀ < (3/4*π)^(1/3).
 
         Examples
@@ -675,7 +694,7 @@ class Rotation:
 
         Returns
         -------
-        x : numpy.ndarray of shape (...,3)
+        x : numpy.ndarray, shape (...,3)
               Cubochoric vector (x_1, x_2, x_3) with max(x_i) < 1/2*π^(2/3).
 
         Examples
@@ -702,7 +721,7 @@ class Rotation:
 
         Parameters
         ----------
-        q : numpy.ndarray of shape (...,4)
+        q : numpy.ndarray, shape (...,4)
             Unit quaternion (q_0, q_1, q_2, q_3) in positive real hemisphere, i.e. ǀqǀ = 1, q_0 ≥ 0.
         accept_homomorph : bool, optional
             Allow homomorphic variants, i.e. q_0 < 0 (negative real hemisphere).
@@ -736,7 +755,7 @@ class Rotation:
 
         Parameters
         ----------
-        phi : numpy.ndarray of shape (...,3)
+        phi : numpy.ndarray, shape (...,3)
             Euler angles (φ_1 ∈ [0,2π], ϕ ∈ [0,π], φ_2 ∈ [0,2π])
             or (φ_1 ∈ [0,360], ϕ ∈ [0,180], φ_2 ∈ [0,360]) if degrees == True.
         degrees : bool, optional
@@ -767,7 +786,7 @@ class Rotation:
 
         Parameters
         ----------
-        axis_angle : numpy.ndarray of shape (...,4)
+        axis_angle : numpy.ndarray, shape (...,4)
             Axis and angle (n_1, n_2, n_3, ω) with ǀnǀ = 1 and ω ∈ [0,π]
             or ω ∈ [0,180] if degrees == True.
         degrees : bool, optional
@@ -804,7 +823,7 @@ class Rotation:
 
         Parameters
         ----------
-        basis : numpy.ndarray of shape (...,3,3)
+        basis : numpy.ndarray, shape (...,3,3)
             Three three-dimensional lattice basis vectors.
         orthonormal : bool, optional
             Basis is strictly orthonormal, i.e. is free of stretch components. Defaults to True.
@@ -838,7 +857,7 @@ class Rotation:
 
         Parameters
         ----------
-        R : numpy.ndarray of shape (...,3,3)
+        R : numpy.ndarray, shape (...,3,3)
             Rotation matrix with det(R) = 1, R.T ∙ R = I.
 
         """
@@ -852,9 +871,9 @@ class Rotation:
 
         Parameters
         ----------
-        a : numpy.ndarray of shape (...,2,3)
+        a : numpy.ndarray, shape (...,2,3)
             Two three-dimensional lattice vectors of first orthogonal basis.
-        b : numpy.ndarray of shape (...,2,3)
+        b : numpy.ndarray, shape (...,2,3)
             Corresponding three-dimensional lattice vectors of second basis.
 
         """
@@ -882,7 +901,7 @@ class Rotation:
 
         Parameters
         ----------
-        rho : numpy.ndarray of shape (...,4)
+        rho : numpy.ndarray, shape (...,4)
             Rodrigues–Frank vector (n_1, n_2, n_3, tan(ω/2)) with ǀnǀ = 1  and ω ∈ [0,π].
         normalize : bool, optional
             Allow ǀnǀ ≠ 1. Defaults to False.
@@ -913,7 +932,7 @@ class Rotation:
 
         Parameters
         ----------
-        h : numpy.ndarray of shape (...,3)
+        h : numpy.ndarray, shape (...,3)
             Homochoric vector (h_1, h_2, h_3) with ǀhǀ < (3/4*π)^(1/3).
         P : int ∈ {-1,1}, optional
             Sign convention. Defaults to -1.
@@ -940,7 +959,7 @@ class Rotation:
 
         Parameters
         ----------
-        x : numpy.ndarray of shape (...,3)
+        x : numpy.ndarray, shape (...,3)
             Cubochoric vector (x_1, x_2, x_3) with max(x_i) < 1/2*π^(2/3).
         P : int ∈ {-1,1}, optional
             Sign convention. Defaults to -1.
@@ -1002,9 +1021,9 @@ class Rotation:
 
         Parameters
         ----------
-        weights : numpy.ndarray of shape (n)
+        weights : numpy.ndarray, shape (n)
             Texture intensity values (probability density or volume fraction) at Euler space grid points.
-        phi : numpy.ndarray of shape (n,3)
+        phi : numpy.ndarray, shape (n,3)
             Grid coordinates in Euler space at which weights are defined.
         N : integer, optional
             Number of discrete orientations to be sampled from the given ODF.
@@ -1020,14 +1039,14 @@ class Rotation:
 
         Returns
         -------
-        samples : damask.Rotation of shape (N)
-            Array of sampled rotations closely representing the input ODF.
+        samples : damask.Rotation, shape (N)
+            Array of sampled rotations that approximate the input ODF.
 
         Notes
         -----
         Due to the distortion of Euler space in the vicinity of ϕ = 0, probability densities, p, defined on
         grid points with ϕ = 0 will never result in reconstructed orientations as their dV/V = p dγ = p × 0.
-        Hence, it is recommended to transform any such dataset to cell centers that avoid grid points at ϕ = 0.
+        Hence, it is recommended to transform any such dataset to a cell-centered version, which avoids grid points at ϕ = 0.
 
         References
         ----------
@@ -1095,9 +1114,9 @@ class Rotation:
 
         Parameters
         ----------
-        alpha : numpy.ndarray of shape (2)
+        alpha : numpy.ndarray, shape (2)
             Polar coordinates (phi from x, theta from z) of fiber direction in crystal frame.
-        beta : numpy.ndarray of shape (2)
+        beta : numpy.ndarray, shape (2)
             Polar coordinates (phi from x, theta from z) of fiber direction in sample frame.
         sigma : float, optional
             Standard deviation of (Gaussian) misorientation distribution.
diff --git a/python/damask/_table.py b/python/damask/_table.py
index 1572c4f76..189f46d6b 100644
--- a/python/damask/_table.py
+++ b/python/damask/_table.py
@@ -185,7 +185,7 @@ class Table:
 
         Returns
         -------
-        mask : numpy.ndarray bool
+        mask : numpy.ndarray of bool
             Mask indicating where corresponding table values are close.
 
         """

From c6a188a1fe1b96da102afbf714c1472f3be9b876 Mon Sep 17 00:00:00 2001
From: Philip Eisenlohr <eisenlohr@egr.msu.edu>
Date: Fri, 11 Feb 2022 15:40:14 -0500
Subject: [PATCH 42/72] added CrystalFamily, CrystalLattice, CrystalKinematics
 typehints

---
 python/damask/_crystal.py     | 26 +++++++++++++-------------
 python/damask/_orientation.py | 10 +++++-----
 python/damask/_typehints.py   |  6 +++++-
 3 files changed, 23 insertions(+), 19 deletions(-)

diff --git a/python/damask/_crystal.py b/python/damask/_crystal.py
index a63cb0c81..6da13f679 100644
--- a/python/damask/_crystal.py
+++ b/python/damask/_crystal.py
@@ -2,11 +2,11 @@ from typing import Union, Dict, List, Tuple
 
 import numpy as np
 
-from ._typehints import FloatSequence
+from ._typehints import FloatSequence, CrystalFamily, CrystalLattice, CrystalKinematics
 from . import util
 from . import Rotation
 
-lattice_symmetries = {
+lattice_symmetries: Dict[CrystalLattice, CrystalFamily] = {
                 'aP': 'triclinic',
 
                 'mP': 'monoclinic',
@@ -32,8 +32,8 @@ class Crystal():
     """Crystal lattice."""
 
     def __init__(self,*,
-                 family = None,
-                 lattice = None,
+                 family: CrystalFamily = None,
+                 lattice: CrystalLattice = None,
                  a: float = None, b: float = None, c: float = None,
                  alpha: float = None, beta: float = None, gamma: float = None,
                  degrees: bool = False):
@@ -208,7 +208,7 @@ class Crystal():
         ...    }
 
         """
-        _basis  = {
+        _basis: Dict[CrystalFamily, Dict[str, np.ndarray]]  = {
             'cubic':    {'improper':np.array([ [-1.            ,  0.            ,  1. ],
                                                [ np.sqrt(2.)   , -np.sqrt(2.)   ,  0. ],
                                                [ 0.            ,  np.sqrt(3.)   ,  0. ] ]),
@@ -322,12 +322,12 @@ class Crystal():
 
         Parameters
         ----------
-        direction|plane : numpy.ndarray of shape (...,3)
+        direction|plane : numpy.ndarray, shape (...,3)
             Vector along direction or plane normal.
 
         Returns
         -------
-        Miller : numpy.ndarray of shape (...,3)
+        Miller : numpy.ndarray, shape (...,3)
             Lattice vector of direction or plane.
             Use util.scale_to_coprime to convert to (integer) Miller indices.
 
@@ -348,12 +348,12 @@ class Crystal():
 
         Parameters
         ----------
-        uvw|hkl : numpy.ndarray of shape (...,3)
+        uvw|hkl : numpy.ndarray, shape (...,3)
             Miller indices of crystallographic direction or plane normal.
 
         Returns
         -------
-        vector : numpy.ndarray of shape (...,3)
+        vector : numpy.ndarray, shape (...,3)
             Crystal frame vector along [uvw] direction or (hkl) plane normal.
 
         """
@@ -366,7 +366,7 @@ class Crystal():
 
 
     def kinematics(self,
-                   mode: str) -> Dict[str, List[np.ndarray]]:
+                   mode: CrystalKinematics) -> Dict[str, List[np.ndarray]]:
         """
         Return crystal kinematics systems.
 
@@ -381,7 +381,7 @@ class Crystal():
             Directions and planes of deformation mode families.
 
         """
-        _kinematics = {
+        _kinematics: Dict[CrystalLattice, Dict[CrystalKinematics, List[np.ndarray]]] = {
             'cF': {
                 'slip': [np.array([
                            [+0,+1,-1, +1,+1,+1],
@@ -626,7 +626,7 @@ class Crystal():
 
 
     def relation_operations(self,
-                            model: str) -> Tuple[str, Rotation]:
+                            model: str) -> Tuple[CrystalLattice, Rotation]:
         """
         Crystallographic orientation relationships for phase transformations.
 
@@ -658,7 +658,7 @@ class Crystal():
         https://doi.org/10.1016/j.actamat.2004.11.021
 
         """
-        _orientation_relationships = {
+        _orientation_relationships: Dict[str, Dict[CrystalLattice,np.ndarray]] = {
           'KS': {
             'cF' : np.array([
                 [[-1, 0, 1],[ 1, 1, 1]],
diff --git a/python/damask/_orientation.py b/python/damask/_orientation.py
index 5a9b7b141..54ffb6728 100644
--- a/python/damask/_orientation.py
+++ b/python/damask/_orientation.py
@@ -1,10 +1,10 @@
 import inspect
 import copy
-from typing import Union, Callable, Dict, Any, Tuple
+from typing import Union, Callable, List, Dict, Any, Tuple
 
 import numpy as np
 
-from ._typehints import FloatSequence, IntSequence
+from ._typehints import FloatSequence, IntSequence, CrystalFamily, CrystalLattice
 from . import Rotation
 from . import Crystal
 from . import util
@@ -98,8 +98,8 @@ class Orientation(Rotation,Crystal):
     def __init__(self,
                  rotation: Union[FloatSequence, Rotation] = np.array([1.,0.,0.,0.]),
                  *,
-                 family: str = None,
-                 lattice: str = None,
+                 family: CrystalFamily = None,
+                 lattice: CrystalLattice = None,
                  a: float = None, b: float = None, c: float = None,
                  alpha: float = None, beta: float = None, gamma: float = None,
                  degrees: bool = False):
@@ -787,7 +787,7 @@ class Orientation(Rotation,Crystal):
     @property
     def symmetry_operations(self) -> Rotation:
         """Symmetry operations as Rotations."""
-        _symmetry_operations  = {
+        _symmetry_operations: Dict[CrystalFamily, List]  = {
             'cubic':         [
                               [ 1.0,            0.0,            0.0,            0.0            ],
                               [ 0.0,            1.0,            0.0,            0.0            ],
diff --git a/python/damask/_typehints.py b/python/damask/_typehints.py
index 0b4a56a69..674f54721 100644
--- a/python/damask/_typehints.py
+++ b/python/damask/_typehints.py
@@ -1,6 +1,6 @@
 """Functionality for typehints."""
 
-from typing import Sequence, Union, TextIO
+from typing import Sequence, Union, Literal, TextIO
 from pathlib import Path
 
 import numpy as np
@@ -10,5 +10,9 @@ FloatSequence = Union[np.ndarray,Sequence[float]]
 IntSequence = Union[np.ndarray,Sequence[int]]
 FileHandle = Union[TextIO, str, Path]
 NumpyRngSeed = Union[int, IntSequence, np.random.SeedSequence, np.random.Generator]
+CrystalFamily = Union[None,Literal['triclinic', 'monoclinic', 'orthorhombic', 'tetragonal', 'hexagonal', 'cubic']]
+CrystalLattice = Union[None,Literal['aP', 'mP', 'mS', 'oP', 'oS', 'oI', 'oF', 'tP', 'tI', 'hP', 'cP', 'cI', 'cF']]
+CrystalKinematics = Literal['slip', 'twin']
+
 # BitGenerator does not exists in older numpy versions
 #NumpyRngSeed = Union[int, IntSequence, np.random.SeedSequence, np.random.BitGenerator, np.random.Generator]

From eb0fca922247543990e36ba2a73812f4a1defe98 Mon Sep 17 00:00:00 2001
From: Martin Diehl <mail@martin-diehl.net>
Date: Sat, 12 Feb 2022 09:08:38 +0100
Subject: [PATCH 43/72] generic examples

might help some users to make the connection between old an new names,
good to have examples anyways
---
 examples/config/phase/bct.yaml | 2 ++
 examples/config/phase/hcp.yaml | 2 ++
 2 files changed, 4 insertions(+)
 create mode 100644 examples/config/phase/bct.yaml
 create mode 100644 examples/config/phase/hcp.yaml

diff --git a/examples/config/phase/bct.yaml b/examples/config/phase/bct.yaml
new file mode 100644
index 000000000..a840e6ede
--- /dev/null
+++ b/examples/config/phase/bct.yaml
@@ -0,0 +1,2 @@
+lattice: tI
+c/a: 0.55
diff --git a/examples/config/phase/hcp.yaml b/examples/config/phase/hcp.yaml
new file mode 100644
index 000000000..e9bf6b85c
--- /dev/null
+++ b/examples/config/phase/hcp.yaml
@@ -0,0 +1,2 @@
+lattice: hP
+c/a: 1.6333

From 3bdfc29fb2a685613409f02838b5396c363082ff Mon Sep 17 00:00:00 2001
From: Martin Diehl <mail@martin-diehl.net>
Date: Sat, 12 Feb 2022 11:40:30 +0100
Subject: [PATCH 44/72] Parameter set for beta-Sn

---
 examples/config/phase/Sn-beta.yaml            |  8 +++++
 .../eigen/thermalexpansion_Sn-beta.yaml       | 13 +++++++++
 .../mechanical/elastic/Hooke_Sn-beta.yaml     | 25 ++++++++++++++++
 .../plastic/phenopowerlaw_Sn-beta.yaml        | 29 +++++++++++++++++++
 4 files changed, 75 insertions(+)
 create mode 100644 examples/config/phase/Sn-beta.yaml
 create mode 100644 examples/config/phase/mechanical/eigen/thermalexpansion_Sn-beta.yaml
 create mode 100644 examples/config/phase/mechanical/elastic/Hooke_Sn-beta.yaml
 create mode 100644 examples/config/phase/mechanical/plastic/phenopowerlaw_Sn-beta.yaml

diff --git a/examples/config/phase/Sn-beta.yaml b/examples/config/phase/Sn-beta.yaml
new file mode 100644
index 000000000..fbf885fb8
--- /dev/null
+++ b/examples/config/phase/Sn-beta.yaml
@@ -0,0 +1,8 @@
+references:
+  - J.A. Rayne and B.S. Chandrasekhar,
+    Physical Review 120(5):1658-1663, 1960,
+    https://doi.org/10.1103/PhysRev.120.1658
+  - https://en.wikipedia.org/wiki/Tin
+lattice: tI
+c/a: 0.5458 # T=300K (c=31.83nm, a=5.832nm)
+rho: 7265.0
diff --git a/examples/config/phase/mechanical/eigen/thermalexpansion_Sn-beta.yaml b/examples/config/phase/mechanical/eigen/thermalexpansion_Sn-beta.yaml
new file mode 100644
index 000000000..7da58b246
--- /dev/null
+++ b/examples/config/phase/mechanical/eigen/thermalexpansion_Sn-beta.yaml
@@ -0,0 +1,13 @@
+type: thermalexpansion
+references:
+  - V.T. Deshpande and D.B. Sirdeshmukh,
+    Acta Crystallographica 15:294-295, 1962,
+    https://doi.org/10.1107/S0365110X62000742,
+    fitted from Tab. 2
+A_11: 1.639e-05
+A_11,T: 1.799e-08
+A_11,T^2: 1.734e-10
+A_33: 3.263e-05
+A_33,T: 1.387e-08
+A_33,T^2: 5.794e-10
+T_ref: 293.15
diff --git a/examples/config/phase/mechanical/elastic/Hooke_Sn-beta.yaml b/examples/config/phase/mechanical/elastic/Hooke_Sn-beta.yaml
new file mode 100644
index 000000000..c6a77729e
--- /dev/null
+++ b/examples/config/phase/mechanical/elastic/Hooke_Sn-beta.yaml
@@ -0,0 +1,25 @@
+type: Hooke
+references:
+  - J.A. Rayne and B.S. Chandrasekhar,
+    Physical Review 120(5):1658-1663, 1960,
+    https://doi.org/10.1103/PhysRev.120.1658,
+    fitted from Fig. 2 and Tab. IV (C_13)
+C_11: 72.89e+9
+C_11,T: -4.479e+7
+C_11,T^2: -3.149e+4
+C_12: 59.27e+9
+C_12,T: 1.110e+7
+C_12,T^2: 1.300e+4
+C_13: 35.97e+9
+C_13,T: -2.638e+7
+C_13,T^2: -1.123e+5
+C_33: 88.77e+10
+C_33,T: -5.361e+7
+C_33,T^2: -2.770e+3
+C_44: 22.26e+9
+C_44,T: -1.994e+7
+C_44,T^2: -9.519e+3
+C_66: 24.17e+9
+C_66,T: -1.919e+7
+C_66,T^2: -1.161e+4
+T_ref: 293.15
diff --git a/examples/config/phase/mechanical/plastic/phenopowerlaw_Sn-beta.yaml b/examples/config/phase/mechanical/plastic/phenopowerlaw_Sn-beta.yaml
new file mode 100644
index 000000000..2f7871cf5
--- /dev/null
+++ b/examples/config/phase/mechanical/plastic/phenopowerlaw_Sn-beta.yaml
@@ -0,0 +1,29 @@
+type: phenopowerlaw
+references:
+  - A. Chakraborty and P. Eisenlohr,
+    Journal of Applied Physics 124:025302, 2018,
+    https://doi.org/10.1063/1.5029933
+output: [xi_sl, gamma_sl]
+N_sl: [2, 2, 2, 4, 2, 4, 2, 2, 4, 0, 0, 8]
+n_sl: 6.0
+a_sl: 2.0
+h_0_sl-sl: 20.0e+6
+xi_0_sl:   [8.5e+6,  4.3e+6, 10.4e+6, 4.5e+6,  5.6e+6,  5.1e+6,  7.4e+6, 15.0e+6, 6.6e+6, 0.0, 0.0, 12.0e+6]
+xi_inf_sl: [11.0e+6, 9.0e+6, 11.0e+6, 9.0e+6, 10.0e+6, 10.0e+6, 10.0e+6, 10.0e+6, 9.0e+6, 0.0, 0.0, 13.0e+6]
+h_sl-sl: [+1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,
+          +1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,
+          +1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,
+          +1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,
+          +1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0, # 50
+          +1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,
+          +1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,
+          +1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,
+          +1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,
+          -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, # 100
+          -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0,
+          -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0,
+          -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0,
+          -1.0, -1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,
+          +1.0, -1.0, -1.0,  1.0,  1.0, -1.0, -1.0,  1.0,  1.0,  1.0, # 150
+          +1.0,  1.0,  1.0,  1.0,  1.0,  1.0]  # unused entries are indicated by -1.0
+dot_gamma_0_sl: 2.6e-8

From cdabdb98829395ac3433591d1c2302f7a1a23992 Mon Sep 17 00:00:00 2001
From: Martin Diehl <mail@martin-diehl.net>
Date: Sat, 12 Feb 2022 16:11:09 +0100
Subject: [PATCH 45/72] temperature-dependent thermal conductivity

---
 examples/config/phase/thermal/Al.yaml | 10 ++++++++--
 examples/config/phase/thermal/Cu.yaml |  9 ++++++++-
 examples/config/phase/thermal/Fe.yaml | 11 +++++++++++
 examples/config/phase/thermal/W.yaml  |  9 ++++++++-
 4 files changed, 35 insertions(+), 4 deletions(-)
 create mode 100644 examples/config/phase/thermal/Fe.yaml

diff --git a/examples/config/phase/thermal/Al.yaml b/examples/config/phase/thermal/Al.yaml
index 50273fde3..6e9705e82 100644
--- a/examples/config/phase/thermal/Al.yaml
+++ b/examples/config/phase/thermal/Al.yaml
@@ -1,5 +1,11 @@
 references:
-  - https://www.engineeringtoolbox.com/thermal-conductivity-metals-d_858.html
+  - J.G. Hust and A.B. Lankford,
+    Thermal Conductivity of Aluminum, Copper, Iron, and Tungsten from 1K to the Melting Point,
+    US Department of Commerce, Boulder, Colorado, 1984,
+    fitted to Tab. 3.4.1 (RRR=1000, T_min=200K, T_max=900K)
   - https://www.engineeringtoolbox.com/specific-heat-metals-d_152.html
+K_11: 2.380e+02
+K_11,T: 2.068e-03
+K_11,T^2: -7.765e-05
+T_ref: 293.15
 C_p: 910.0
-K_11: 236.0
diff --git a/examples/config/phase/thermal/Cu.yaml b/examples/config/phase/thermal/Cu.yaml
index c171d3245..cd4df2d74 100644
--- a/examples/config/phase/thermal/Cu.yaml
+++ b/examples/config/phase/thermal/Cu.yaml
@@ -1,4 +1,11 @@
 references:
+  - J.G. Hust and A.B. Lankford,
+    Thermal Conductivity of Aluminum, Copper, Iron, and Tungsten from 1K to the Melting Point,
+    US Department of Commerce, Boulder, Colorado, 1984,
+    fitted to Tab. 2.4.1 (RRR=1000, T_min=200K, T_max=1000K)
   - https://www.mit.edu/~6.777/matprops/copper.htm
+K_11: 4.039e+02
+K_11,T: -8.119e-02
+K_11,T^2: 1.454e-05
+T_ref: 293.15
 C_p: 385.0
-K_11: 401.0
diff --git a/examples/config/phase/thermal/Fe.yaml b/examples/config/phase/thermal/Fe.yaml
new file mode 100644
index 000000000..49d397599
--- /dev/null
+++ b/examples/config/phase/thermal/Fe.yaml
@@ -0,0 +1,11 @@
+references:
+  - J.G. Hust and A.B. Lankford,
+    Thermal Conductivity of Aluminum, Copper, Iron, and Tungsten from 1K to the Melting Point,
+    US Department of Commerce, Boulder, Colorado, 1984,
+    fitted to Tab. 4.4.1 (RRR=300, T_min=200K, T_max=1000K)
+  - https://www.engineeringtoolbox.com/specific-heat-metals-d_152.html
+K_11: 8.055e+01
+K_11,T: -1.051e-01
+K_11,T^2: 5.464e-05
+T_ref: 293.15
+C_p: 450.0
diff --git a/examples/config/phase/thermal/W.yaml b/examples/config/phase/thermal/W.yaml
index 95918303f..af4a164c8 100644
--- a/examples/config/phase/thermal/W.yaml
+++ b/examples/config/phase/thermal/W.yaml
@@ -1,4 +1,11 @@
 references:
+  - J.G. Hust and A.B. Lankford,
+    Thermal Conductivity of Aluminum, Copper, Iron, and Tungsten from 1K to the Melting Point,
+    US Department of Commerce, Boulder, Colorado, 1984,
+    fitted to Tab. 5.4.1 (RRR=300, T_min=200K, T_max=1000K)
   - https://www.mit.edu/~6.777/matprops/tungsten.htm
+K_11: 1.758e+02
+K_11,T: -1.605e-01
+K_11,T^2: 1.160e-04
+T_ref: 293.15
 C_p: 132.51
-K_11: 178.0

From 4d808335de2ced0792eed8a59948f4490f3e17af Mon Sep 17 00:00:00 2001
From: Martin Diehl <mail@martin-diehl.net>
Date: Sat, 12 Feb 2022 18:41:59 +0100
Subject: [PATCH 46/72] polishing

---
 examples/config/phase/AISI304.yaml                    |  5 +++--
 examples/config/phase/Ag.yaml                         |  1 +
 examples/config/phase/Al.yaml                         |  1 +
 examples/config/phase/Au.yaml                         |  1 +
 examples/config/phase/Cu.yaml                         |  1 +
 examples/config/phase/Fe.yaml                         |  1 +
 examples/config/phase/Mg.yaml                         |  1 +
 examples/config/phase/Ni.yaml                         |  1 +
 examples/config/phase/Sn-beta.yaml                    |  1 +
 examples/config/phase/Ti.yaml                         |  1 +
 examples/config/phase/W.yaml                          |  1 +
 examples/config/phase/damage/anisobrittle_cubic.yaml  |  6 ++++--
 examples/config/phase/damage/isobrittle_generic.yaml  |  2 +-
 .../mechanical/eigen/thermalexpansion_AISI304.yaml    |  6 ++++--
 .../phase/mechanical/eigen/thermalexpansion_Al.yaml   |  2 ++
 .../phase/mechanical/eigen/thermalexpansion_Au.yaml   |  2 ++
 .../phase/mechanical/eigen/thermalexpansion_C35E.yaml |  5 ++++-
 .../phase/mechanical/eigen/thermalexpansion_Cu.yaml   |  2 ++
 .../phase/mechanical/eigen/thermalexpansion_Fe.yaml   |  2 ++
 .../mechanical/eigen/thermalexpansion_Sn-beta.yaml    |  6 +++++-
 .../phase/mechanical/eigen/thermalexpansion_W.yaml    |  2 ++
 .../mechanical/eigen/thermalexpansion_X20Cr13.yaml    |  7 +++++--
 .../phase/mechanical/elastic/Hooke_AISI304.yaml       |  6 ++++--
 .../config/phase/mechanical/elastic/Hooke_Ag.yaml     |  5 +++--
 .../config/phase/mechanical/elastic/Hooke_Al.yaml     |  5 +++--
 .../config/phase/mechanical/elastic/Hooke_Au.yaml     |  2 ++
 .../config/phase/mechanical/elastic/Hooke_Cu.yaml     |  2 ++
 .../config/phase/mechanical/elastic/Hooke_Fe.yaml     |  5 +++--
 .../config/phase/mechanical/elastic/Hooke_Mg.yaml     |  2 ++
 .../config/phase/mechanical/elastic/Hooke_Ni.yaml     |  2 ++
 .../mechanical/elastic/Hooke_SAE1050-martensite.yaml  |  2 ++
 .../phase/mechanical/elastic/Hooke_Sn-beta.yaml       | 10 +++++++++-
 .../phase/mechanical/elastic/Hooke_TWIP-steel.yaml    |  2 ++
 .../config/phase/mechanical/elastic/Hooke_Ti.yaml     |  2 ++
 examples/config/phase/mechanical/elastic/Hooke_W.yaml |  2 ++
 .../elastic/Hooke_vanishing-Poisson-ratio.yaml        |  2 ++
 .../phase/mechanical/plastic/dislotungsten_W.yaml     |  4 ++++
 .../phase/mechanical/plastic/dislotwin_IF-steel.yaml  |  4 ++++
 .../mechanical/plastic/isotropic_free-surface.yaml    |  3 +++
 .../config/phase/mechanical/plastic/nonlocal_Al.yaml  | 11 +++++++----
 .../config/phase/mechanical/plastic/nonlocal_Ni.yaml  | 11 +++++++----
 .../phase/mechanical/plastic/phenopowerlaw_Al.yaml    |  4 ++++
 .../phase/mechanical/plastic/phenopowerlaw_Au.yaml    |  4 ++++
 .../phase/mechanical/plastic/phenopowerlaw_Cu.yaml    |  4 ++++
 .../plastic/phenopowerlaw_DP-steel-ferrite.yaml       |  4 ++++
 .../phase/mechanical/plastic/phenopowerlaw_Mg.yaml    |  1 +
 .../mechanical/plastic/phenopowerlaw_Sn-beta.yaml     |  4 ++++
 .../phase/mechanical/plastic/phenopowerlaw_Ti.yaml    |  3 +++
 examples/config/phase/thermal/AISI304.yaml            |  1 +
 examples/config/phase/thermal/Al.yaml                 |  5 ++++-
 examples/config/phase/thermal/Au.yaml                 |  1 +
 examples/config/phase/thermal/Cu.yaml                 |  5 ++++-
 examples/config/phase/thermal/Fe.yaml                 |  5 ++++-
 examples/config/phase/thermal/W.yaml                  |  5 ++++-
 .../phase/thermal/source/dissipation_generic.yaml     |  1 +
 .../thermal/source/externalheat_ramp-and-hold.yaml    |  1 +
 examples/config/phase/thermal/steel-0.5C.yaml         |  1 +
 57 files changed, 156 insertions(+), 32 deletions(-)

diff --git a/examples/config/phase/AISI304.yaml b/examples/config/phase/AISI304.yaml
index 0ca55635b..4d83ad8b5 100644
--- a/examples/config/phase/AISI304.yaml
+++ b/examples/config/phase/AISI304.yaml
@@ -1,6 +1,7 @@
 references:
-  - H.M. Ledbetter
-    physica status solidi (a) 85(1):89-96, 1984
+  - H.M. Ledbetter,
+    physica status solidi (a) 85(1):89-96, 1984,
     https://doi.org/10.1002/pssa.2210850111
+
 lattice: cF
 rho: 7937.0
diff --git a/examples/config/phase/Ag.yaml b/examples/config/phase/Ag.yaml
index ebcd21082..1d870d4bf 100644
--- a/examples/config/phase/Ag.yaml
+++ b/examples/config/phase/Ag.yaml
@@ -1,4 +1,5 @@
 references:
   - https://en.wikipedia.org/wiki/Silver
+
 lattice: cF
 rho: 10490.0
diff --git a/examples/config/phase/Al.yaml b/examples/config/phase/Al.yaml
index f3c19924b..ae48a06b4 100644
--- a/examples/config/phase/Al.yaml
+++ b/examples/config/phase/Al.yaml
@@ -1,4 +1,5 @@
 references:
   - https://en.wikipedia.org/wiki/Aluminium
+
 lattice: cF
 rho: 2700.0
diff --git a/examples/config/phase/Au.yaml b/examples/config/phase/Au.yaml
index fab05ad99..5dd3ff6f2 100644
--- a/examples/config/phase/Au.yaml
+++ b/examples/config/phase/Au.yaml
@@ -1,4 +1,5 @@
 references:
   - https://en.wikipedia.org/wiki/Gold
+
 lattice: cF
 rho: 19300.0
diff --git a/examples/config/phase/Cu.yaml b/examples/config/phase/Cu.yaml
index f1e1e9e36..3d742fd25 100644
--- a/examples/config/phase/Cu.yaml
+++ b/examples/config/phase/Cu.yaml
@@ -1,4 +1,5 @@
 references:
   - https://en.wikipedia.org/wiki/Copper
+
 lattice: cF
 rho: 8960.0
diff --git a/examples/config/phase/Fe.yaml b/examples/config/phase/Fe.yaml
index 271ff8661..2189957c9 100644
--- a/examples/config/phase/Fe.yaml
+++ b/examples/config/phase/Fe.yaml
@@ -1,4 +1,5 @@
 references:
   - https://en.wikipedia.org/wiki/Iron
+
 lattice: cI
 rho: 7874.0
diff --git a/examples/config/phase/Mg.yaml b/examples/config/phase/Mg.yaml
index 96eb6ad78..39e878b68 100644
--- a/examples/config/phase/Mg.yaml
+++ b/examples/config/phase/Mg.yaml
@@ -2,6 +2,7 @@ references:
   - D. Tromans,
     International Journal of Recent Research and Applied Studies 6(4):462-483, 2011,
     https://www.arpapress.com/Volumes/Vol6Issue4/IJRRAS_6_4_14.pdf
+
 lattice: hP
 c/a: 1.62350
 rho: 1740.0
diff --git a/examples/config/phase/Ni.yaml b/examples/config/phase/Ni.yaml
index 575984583..149889302 100644
--- a/examples/config/phase/Ni.yaml
+++ b/examples/config/phase/Ni.yaml
@@ -1,4 +1,5 @@
 references:
   - https://en.wikipedia.org/wiki/Nickel
+
 lattice: cF
 rho: 8908.0
diff --git a/examples/config/phase/Sn-beta.yaml b/examples/config/phase/Sn-beta.yaml
index fbf885fb8..833995f30 100644
--- a/examples/config/phase/Sn-beta.yaml
+++ b/examples/config/phase/Sn-beta.yaml
@@ -3,6 +3,7 @@ references:
     Physical Review 120(5):1658-1663, 1960,
     https://doi.org/10.1103/PhysRev.120.1658
   - https://en.wikipedia.org/wiki/Tin
+
 lattice: tI
 c/a: 0.5458 # T=300K (c=31.83nm, a=5.832nm)
 rho: 7265.0
diff --git a/examples/config/phase/Ti.yaml b/examples/config/phase/Ti.yaml
index 48eae3949..886830194 100644
--- a/examples/config/phase/Ti.yaml
+++ b/examples/config/phase/Ti.yaml
@@ -1,6 +1,7 @@
 references:
   - https://www.totalmateria.com/page.aspx?ID=CheckArticle&site=ktn&NM=221
   - https://en.wikipedia.org/wiki/Titanium
+
 lattice: hP
 c/a: 1.587
 rho: 4506.0
diff --git a/examples/config/phase/W.yaml b/examples/config/phase/W.yaml
index 740fe0992..7b4d7d4d3 100644
--- a/examples/config/phase/W.yaml
+++ b/examples/config/phase/W.yaml
@@ -1,4 +1,5 @@
 references:
   - https://en.wikipedia.org/wiki/Tungsten
+
 lattice: cI
 rho: 19300.0
diff --git a/examples/config/phase/damage/anisobrittle_cubic.yaml b/examples/config/phase/damage/anisobrittle_cubic.yaml
index 41f64efcf..372fdc6d0 100644
--- a/examples/config/phase/damage/anisobrittle_cubic.yaml
+++ b/examples/config/phase/damage/anisobrittle_cubic.yaml
@@ -1,11 +1,13 @@
 type: anisobrittle
+
+output: [f_phi]
+
 N_cl: [3]
+
 g_crit: [0.5e+7]
 s_crit: [0.006666]
 dot_o: 1.e-3
 q: 20
 
-output: [f_phi]
-
 D_11: 1.0
 mu: 0.001
diff --git a/examples/config/phase/damage/isobrittle_generic.yaml b/examples/config/phase/damage/isobrittle_generic.yaml
index 95c0e8b61..851302a49 100644
--- a/examples/config/phase/damage/isobrittle_generic.yaml
+++ b/examples/config/phase/damage/isobrittle_generic.yaml
@@ -1,7 +1,7 @@
 type: isobrittle
-W_crit: 1400000.0
 
 output: [f_phi]
 
+W_crit: 1400000.0
 D_11: 1.0
 mu: 0.001
diff --git a/examples/config/phase/mechanical/eigen/thermalexpansion_AISI304.yaml b/examples/config/phase/mechanical/eigen/thermalexpansion_AISI304.yaml
index 6a3b339bb..f3605e1d9 100644
--- a/examples/config/phase/mechanical/eigen/thermalexpansion_AISI304.yaml
+++ b/examples/config/phase/mechanical/eigen/thermalexpansion_AISI304.yaml
@@ -1,7 +1,9 @@
 type: thermalexpansion
+
 references:
-  - R.H. Bogaard et al.
-    Thermochimica Acta 218:373-393, 1993
+  - R.H. Bogaard et al.,
+    Thermochimica Acta 218:373-393, 1993,
     https://doi.org/10.1016/0040-6031(93)80437-F
+
 A_11: 15.0e-6
 T_ref: 300.0
diff --git a/examples/config/phase/mechanical/eigen/thermalexpansion_Al.yaml b/examples/config/phase/mechanical/eigen/thermalexpansion_Al.yaml
index b0db392e1..ccd8b347b 100644
--- a/examples/config/phase/mechanical/eigen/thermalexpansion_Al.yaml
+++ b/examples/config/phase/mechanical/eigen/thermalexpansion_Al.yaml
@@ -1,5 +1,7 @@
 type: thermalexpansion
+
 references:
   - https://en.wikipedia.org/wiki/Thermal_expansion
+
 A_11: 23.1e-6
 T_ref: 293.15
diff --git a/examples/config/phase/mechanical/eigen/thermalexpansion_Au.yaml b/examples/config/phase/mechanical/eigen/thermalexpansion_Au.yaml
index 934b4f721..8211516de 100644
--- a/examples/config/phase/mechanical/eigen/thermalexpansion_Au.yaml
+++ b/examples/config/phase/mechanical/eigen/thermalexpansion_Au.yaml
@@ -1,5 +1,7 @@
 type: thermalexpansion
+
 references:
   - https://en.wikipedia.org/wiki/Thermal_expansion
+
 A_11: 14.e-6
 T_ref: 293.15
diff --git a/examples/config/phase/mechanical/eigen/thermalexpansion_C35E.yaml b/examples/config/phase/mechanical/eigen/thermalexpansion_C35E.yaml
index 13d99b0ed..08e9d6894 100644
--- a/examples/config/phase/mechanical/eigen/thermalexpansion_C35E.yaml
+++ b/examples/config/phase/mechanical/eigen/thermalexpansion_C35E.yaml
@@ -1,8 +1,11 @@
 type: thermalexpansion
+
 references:
   - https://commons.wikimedia.org/wiki/File:Coefficient_dilatation_lineique_aciers.svg,
-    fitted from image description (Scilab code)
+    fit to image description (Scilab code)
+
 A_11: 12.70371e-6
 A_11,T: 7.54e-9
 A_11,T^2: -1.0e-11
+
 T_ref: 273.0
diff --git a/examples/config/phase/mechanical/eigen/thermalexpansion_Cu.yaml b/examples/config/phase/mechanical/eigen/thermalexpansion_Cu.yaml
index 4c82421f3..d7c71931b 100644
--- a/examples/config/phase/mechanical/eigen/thermalexpansion_Cu.yaml
+++ b/examples/config/phase/mechanical/eigen/thermalexpansion_Cu.yaml
@@ -1,5 +1,7 @@
 type: thermalexpansion
+
 references:
   - https://en.wikipedia.org/wiki/Thermal_expansion
+
 A_11: 17.e-6
 T_ref: 293.15
diff --git a/examples/config/phase/mechanical/eigen/thermalexpansion_Fe.yaml b/examples/config/phase/mechanical/eigen/thermalexpansion_Fe.yaml
index c0891ea6a..9798fb8a0 100644
--- a/examples/config/phase/mechanical/eigen/thermalexpansion_Fe.yaml
+++ b/examples/config/phase/mechanical/eigen/thermalexpansion_Fe.yaml
@@ -1,5 +1,7 @@
 type: thermalexpansion
+
 references:
   - https://en.wikipedia.org/wiki/Thermal_expansion
+
 A_11: 11.8e-6
 T_ref: 293.15
diff --git a/examples/config/phase/mechanical/eigen/thermalexpansion_Sn-beta.yaml b/examples/config/phase/mechanical/eigen/thermalexpansion_Sn-beta.yaml
index 7da58b246..16e78f82c 100644
--- a/examples/config/phase/mechanical/eigen/thermalexpansion_Sn-beta.yaml
+++ b/examples/config/phase/mechanical/eigen/thermalexpansion_Sn-beta.yaml
@@ -1,13 +1,17 @@
 type: thermalexpansion
+
 references:
   - V.T. Deshpande and D.B. Sirdeshmukh,
     Acta Crystallographica 15:294-295, 1962,
     https://doi.org/10.1107/S0365110X62000742,
-    fitted from Tab. 2
+    fit to Tab. 2
+
 A_11: 1.639e-05
 A_11,T: 1.799e-08
 A_11,T^2: 1.734e-10
+
 A_33: 3.263e-05
 A_33,T: 1.387e-08
 A_33,T^2: 5.794e-10
+
 T_ref: 293.15
diff --git a/examples/config/phase/mechanical/eigen/thermalexpansion_W.yaml b/examples/config/phase/mechanical/eigen/thermalexpansion_W.yaml
index 427731186..338f60fe2 100644
--- a/examples/config/phase/mechanical/eigen/thermalexpansion_W.yaml
+++ b/examples/config/phase/mechanical/eigen/thermalexpansion_W.yaml
@@ -1,5 +1,7 @@
 type: thermalexpansion
+
 references:
   - https://en.wikipedia.org/wiki/Thermal_expansion
+
 A_11: 4.5e-6
 T_ref: 293.15
diff --git a/examples/config/phase/mechanical/eigen/thermalexpansion_X20Cr13.yaml b/examples/config/phase/mechanical/eigen/thermalexpansion_X20Cr13.yaml
index 19b4cb485..1b8f1545b 100644
--- a/examples/config/phase/mechanical/eigen/thermalexpansion_X20Cr13.yaml
+++ b/examples/config/phase/mechanical/eigen/thermalexpansion_X20Cr13.yaml
@@ -1,7 +1,10 @@
 type: thermalexpansion
+
 references:
-  - https://commons.wikimedia.org/wiki/File:Coefficient_dilatation_lineique_aciers.svg
-    fitted from image description (Scilab code)
+  - https://commons.wikimedia.org/wiki/File:Coefficient_dilatation_lineique_aciers.svg,
+    fit to image description (Scilab code)
+
 A_11: 11.365e-6
 A_11,T: 5.0e-9
+
 T_ref: 273.0
diff --git a/examples/config/phase/mechanical/elastic/Hooke_AISI304.yaml b/examples/config/phase/mechanical/elastic/Hooke_AISI304.yaml
index 70fbd25c7..898702455 100644
--- a/examples/config/phase/mechanical/elastic/Hooke_AISI304.yaml
+++ b/examples/config/phase/mechanical/elastic/Hooke_AISI304.yaml
@@ -1,8 +1,10 @@
 type: Hooke
+
 references:
-  - H.M. Ledbetter
-    physica status solidi (a) 85(1):89-96, 1984
+  - H.M. Ledbetter,
+    physica status solidi (a) 85(1):89-96, 1984,
     https://doi.org/10.1002/pssa.2210850111
+
 C_11: 204.6e+9
 C_12: 137.7e+9
 C_44: 126.2e+9
diff --git a/examples/config/phase/mechanical/elastic/Hooke_Ag.yaml b/examples/config/phase/mechanical/elastic/Hooke_Ag.yaml
index 9485a4bb2..3b136a5c2 100644
--- a/examples/config/phase/mechanical/elastic/Hooke_Ag.yaml
+++ b/examples/config/phase/mechanical/elastic/Hooke_Ag.yaml
@@ -1,4 +1,5 @@
 type: Hooke
+
 references:
   - J.R. Neighbours and G.A. Alers,
     Physical Review 111:707-712, 1958,
@@ -7,8 +8,6 @@ references:
     Journal of Applied Physics 37:3567-3572, 1966,
     https://doi.org/10.1063/1.1708903
 
-T_ref: 300
-
 C_11: 122.9e+9
 C_11,T: -313.5e+5
 C_11,T^2: -107.3e+2
@@ -20,3 +19,5 @@ C_12,T^2: -681.6e+1
 C_44: 42.63e+9
 C_44,T: -180.5e+5
 C_44,T^2: -353.8e+1
+
+T_ref: 300
diff --git a/examples/config/phase/mechanical/elastic/Hooke_Al.yaml b/examples/config/phase/mechanical/elastic/Hooke_Al.yaml
index f4c266d54..97d45e62f 100644
--- a/examples/config/phase/mechanical/elastic/Hooke_Al.yaml
+++ b/examples/config/phase/mechanical/elastic/Hooke_Al.yaml
@@ -1,4 +1,5 @@
 type: Hooke
+
 references:
   - G.N. Kamm and G.A. Alers,
     Journal of Applied Physics 35:327-330, 1964,
@@ -7,8 +8,6 @@ references:
     Journal of Physics and Chemistry of Solids 30:1197-1205, 1969
     https://doi.org/10.1016/0022-3697(69)90377-1
 
-T_ref: 300
-
 C_11: 106.1e+9
 C_11,T: -359.3e+5
 C_11,T^2: -152.7e+2
@@ -20,3 +19,5 @@ C_12,T^2: -551.3e+1
 C_44: 24.31e+9
 C_44,T: -142.9e+5
 C_44,T^2: -404.6e+1
+
+T_ref: 300
diff --git a/examples/config/phase/mechanical/elastic/Hooke_Au.yaml b/examples/config/phase/mechanical/elastic/Hooke_Au.yaml
index 452807a6e..47afd262b 100644
--- a/examples/config/phase/mechanical/elastic/Hooke_Au.yaml
+++ b/examples/config/phase/mechanical/elastic/Hooke_Au.yaml
@@ -1,9 +1,11 @@
 type: Hooke
+
 references:
   - J.P. Hirth and J. Lothe,
     Theory of Dislocations, 1982,
     John Wiley & Sons,
     page 837
+
 C_11: 186.e+9
 C_12: 157.e+9
 C_44: 42.e+9
diff --git a/examples/config/phase/mechanical/elastic/Hooke_Cu.yaml b/examples/config/phase/mechanical/elastic/Hooke_Cu.yaml
index 7b458a421..90a0bd269 100644
--- a/examples/config/phase/mechanical/elastic/Hooke_Cu.yaml
+++ b/examples/config/phase/mechanical/elastic/Hooke_Cu.yaml
@@ -1,7 +1,9 @@
 type: Hooke
+
 references:
   - https://www.mit.edu/~6.777/matprops/copper.htm,
     fixed typo
+
 C_11: 168.3e+9
 C_12: 122.1e+9
 C_44: 75.7e+9
diff --git a/examples/config/phase/mechanical/elastic/Hooke_Fe.yaml b/examples/config/phase/mechanical/elastic/Hooke_Fe.yaml
index 94e761aaf..a6d7d1868 100644
--- a/examples/config/phase/mechanical/elastic/Hooke_Fe.yaml
+++ b/examples/config/phase/mechanical/elastic/Hooke_Fe.yaml
@@ -1,11 +1,10 @@
 type: Hooke
+
 references:
   - D.J. Dever,
     Journal of Applied Physics 43(8):3293-3301, 1972,
     https://doi.org/10.1063/1.1661710
 
-T_ref: 300
-
 C_11: 231.7e+9
 C_11,T: -47.6e+6
 C_11,T^2: -54.4e+3
@@ -17,3 +16,5 @@ C_12,T^2: -7.3e+3
 C_44: 116.8e+9
 C_44,T: -19.4e+6
 C_44,T^2: -2.5e+3
+
+T_ref: 300
diff --git a/examples/config/phase/mechanical/elastic/Hooke_Mg.yaml b/examples/config/phase/mechanical/elastic/Hooke_Mg.yaml
index 1e08a94a9..aa089d4b4 100644
--- a/examples/config/phase/mechanical/elastic/Hooke_Mg.yaml
+++ b/examples/config/phase/mechanical/elastic/Hooke_Mg.yaml
@@ -1,8 +1,10 @@
 type: Hooke
+
 references:
   - D. Tromans,
     International Journal of Recent Research and Applied Studies 6(4):462-483, 2011,
     https://www.arpapress.com/Volumes/Vol6Issue4/IJRRAS_6_4_14.pdf
+
 C_11: 59.3e+9
 C_33: 61.5e+9
 C_44: 16.4e+9
diff --git a/examples/config/phase/mechanical/elastic/Hooke_Ni.yaml b/examples/config/phase/mechanical/elastic/Hooke_Ni.yaml
index c11f664d3..6bba784fb 100644
--- a/examples/config/phase/mechanical/elastic/Hooke_Ni.yaml
+++ b/examples/config/phase/mechanical/elastic/Hooke_Ni.yaml
@@ -1,9 +1,11 @@
 type: Hooke
+
 references:
   - J.P. Hirth and J. Lothe,
     Theory of Dislocations, 1982,
     John Wiley & Sons,
     page 837
+
 C_11: 246.5e+9
 C_12: 147.3e+9
 C_44: 124.7e+9
diff --git a/examples/config/phase/mechanical/elastic/Hooke_SAE1050-martensite.yaml b/examples/config/phase/mechanical/elastic/Hooke_SAE1050-martensite.yaml
index 7ba941066..191756cc7 100644
--- a/examples/config/phase/mechanical/elastic/Hooke_SAE1050-martensite.yaml
+++ b/examples/config/phase/mechanical/elastic/Hooke_SAE1050-martensite.yaml
@@ -1,8 +1,10 @@
 type: Hooke
+
 references:
   - S.A. Kim and W.L. Johnson,
     Materials Science & Engineering A 452-453:633-639, 2007,
     https://doi.org/10.1016/j.msea.2006.11.147
+
 C_11: 268.1e+9
 C_12: 111.2e+9
 C_44: 79.06e+9
diff --git a/examples/config/phase/mechanical/elastic/Hooke_Sn-beta.yaml b/examples/config/phase/mechanical/elastic/Hooke_Sn-beta.yaml
index c6a77729e..a49c246f9 100644
--- a/examples/config/phase/mechanical/elastic/Hooke_Sn-beta.yaml
+++ b/examples/config/phase/mechanical/elastic/Hooke_Sn-beta.yaml
@@ -1,25 +1,33 @@
 type: Hooke
+
 references:
   - J.A. Rayne and B.S. Chandrasekhar,
     Physical Review 120(5):1658-1663, 1960,
     https://doi.org/10.1103/PhysRev.120.1658,
-    fitted from Fig. 2 and Tab. IV (C_13)
+    fit to Fig. 2 and Tab. IV (C_13)
+
 C_11: 72.89e+9
 C_11,T: -4.479e+7
 C_11,T^2: -3.149e+4
+
 C_12: 59.27e+9
 C_12,T: 1.110e+7
 C_12,T^2: 1.300e+4
+
 C_13: 35.97e+9
 C_13,T: -2.638e+7
 C_13,T^2: -1.123e+5
+
 C_33: 88.77e+10
 C_33,T: -5.361e+7
 C_33,T^2: -2.770e+3
+
 C_44: 22.26e+9
 C_44,T: -1.994e+7
 C_44,T^2: -9.519e+3
+
 C_66: 24.17e+9
 C_66,T: -1.919e+7
 C_66,T^2: -1.161e+4
+
 T_ref: 293.15
diff --git a/examples/config/phase/mechanical/elastic/Hooke_TWIP-steel.yaml b/examples/config/phase/mechanical/elastic/Hooke_TWIP-steel.yaml
index c31589955..d4f5b684a 100644
--- a/examples/config/phase/mechanical/elastic/Hooke_TWIP-steel.yaml
+++ b/examples/config/phase/mechanical/elastic/Hooke_TWIP-steel.yaml
@@ -1,4 +1,5 @@
 type: Hooke
+
 references:
   - D. Music et al.,
     Applied Physics Letters 99(19):191904, 2007,
@@ -6,6 +7,7 @@ references:
   - S.L. Wong et al.,
     Acta Materialia 118:140-151, 2016,
     https://doi.org/10.1016/j.actamat.2016.07.032
+
 C_11: 175.0e+9
 C_12: 115.0e+9
 C_44: 135.0e+9
diff --git a/examples/config/phase/mechanical/elastic/Hooke_Ti.yaml b/examples/config/phase/mechanical/elastic/Hooke_Ti.yaml
index ee8cae0ad..79b7c04f7 100644
--- a/examples/config/phase/mechanical/elastic/Hooke_Ti.yaml
+++ b/examples/config/phase/mechanical/elastic/Hooke_Ti.yaml
@@ -1,8 +1,10 @@
 type: Hooke
+
 references:
   - L. Wang et al.,
     Acta Materialia 132:598-610, 2017,
     https://doi.org/10.1016/j.actamat.2017.05.015
+
 C_11: 162.4e+9
 C_33: 181.6e+9
 C_44: 47.2e+9
diff --git a/examples/config/phase/mechanical/elastic/Hooke_W.yaml b/examples/config/phase/mechanical/elastic/Hooke_W.yaml
index 49bb7858a..a1191f8c7 100644
--- a/examples/config/phase/mechanical/elastic/Hooke_W.yaml
+++ b/examples/config/phase/mechanical/elastic/Hooke_W.yaml
@@ -1,8 +1,10 @@
 type: Hooke
+
 references:
   - D. Cereceda et al.,
     International Journal of Plasticity 78:242-265, 2016,
     https://doi.org/10.1016/j.ijplas.2015.09.002
+
 C_11: 523.e+9
 C_12: 202.e+9
 C_44: 161.e+9
diff --git a/examples/config/phase/mechanical/elastic/Hooke_vanishing-Poisson-ratio.yaml b/examples/config/phase/mechanical/elastic/Hooke_vanishing-Poisson-ratio.yaml
index 9a69dda4e..04045c0c4 100644
--- a/examples/config/phase/mechanical/elastic/Hooke_vanishing-Poisson-ratio.yaml
+++ b/examples/config/phase/mechanical/elastic/Hooke_vanishing-Poisson-ratio.yaml
@@ -1,8 +1,10 @@
 type: Hooke
+
 references:
   - T. Maiti and P. Eisenlohr,
     Scripta Materialia 145:37-40, 2018,
     https://doi.org/10.1016/j.scriptamat.2017.09.047
+
 C_11: 1.e+8
 C_12: 1.e+6
 C_44: 4.95e+7
diff --git a/examples/config/phase/mechanical/plastic/dislotungsten_W.yaml b/examples/config/phase/mechanical/plastic/dislotungsten_W.yaml
index 55814c3f8..a1332acc9 100644
--- a/examples/config/phase/mechanical/plastic/dislotungsten_W.yaml
+++ b/examples/config/phase/mechanical/plastic/dislotungsten_W.yaml
@@ -1,4 +1,5 @@
 type: dislotungsten
+
 references:
   - D. Cereceda et al.,
     International Journal of Plasticity 78:242-265, 2016,
@@ -6,8 +7,11 @@ references:
   - R. Gröger et al.,
     Acta Materialia 56(19):5412-5425, 2008,
     https://doi.org/10.1016/j.actamat.2008.07.037
+
 output: [Lambda_sl]
+
 N_sl: [12]
+
 b_sl: [2.72e-10]
 rho_mob_0: [1.0e+9]  # estimated from section 3.2
 rho_dip_0: [1.0]     # not given
diff --git a/examples/config/phase/mechanical/plastic/dislotwin_IF-steel.yaml b/examples/config/phase/mechanical/plastic/dislotwin_IF-steel.yaml
index 4e4ff1a9f..62801414f 100644
--- a/examples/config/phase/mechanical/plastic/dislotwin_IF-steel.yaml
+++ b/examples/config/phase/mechanical/plastic/dislotwin_IF-steel.yaml
@@ -1,4 +1,5 @@
 type: dislotwin
+
 references:
   - K. Sedighiani et al.,
     International Journal of Plasticity 134:102779, 2020,
@@ -6,8 +7,11 @@ references:
   - K. Sedighiani et al.,
     Mechanics of Materials, 164:104117, 2022,
     https://doi.org/10.1016/j.mechmat.2021.104117
+
 output: [rho_dip, rho_mob]
+
 N_sl: [12, 12]
+
 b_sl: [2.49e-10, 2.49e-10]
 rho_mob_0: [2.81e12, 2.8e+12]
 rho_dip_0: [1.0, 1.0] # not given
diff --git a/examples/config/phase/mechanical/plastic/isotropic_free-surface.yaml b/examples/config/phase/mechanical/plastic/isotropic_free-surface.yaml
index fba7effa8..c58dc24fc 100644
--- a/examples/config/phase/mechanical/plastic/isotropic_free-surface.yaml
+++ b/examples/config/phase/mechanical/plastic/isotropic_free-surface.yaml
@@ -1,9 +1,12 @@
 type: isotropic
+
 references:
   - T. Maiti and P. Eisenlohr,
     Scripta Materialia 145:37-40, 2018,
     https://doi.org/10.1016/j.scriptamat.2017.09.047
+
 output: [xi]
+
 dot_gamma_0: 0.001
 n: 20.
 xi_0: 0.3e+6
diff --git a/examples/config/phase/mechanical/plastic/nonlocal_Al.yaml b/examples/config/phase/mechanical/plastic/nonlocal_Al.yaml
index 7ee79f9e5..451ce53db 100644
--- a/examples/config/phase/mechanical/plastic/nonlocal_Al.yaml
+++ b/examples/config/phase/mechanical/plastic/nonlocal_Al.yaml
@@ -1,10 +1,13 @@
 type: nonlocal
+
 references:
-  C. Kords,
-  On the role of dislocation transport in the constitutive description of crystal plasticity,
-  RWTH Aachen 2013,
-  http://publications.rwth-aachen.de/record/229993/files/4862.pdf
+  - C. Kords,
+    On the role of dislocation transport in the constitutive description of crystal plasticity,
+    RWTH Aachen 2013,
+    http://publications.rwth-aachen.de/record/229993/files/4862.pdf
+
 output: [rho_u_ed_pos, rho_b_ed_pos, rho_u_ed_neg, rho_b_ed_neg, rho_u_sc_pos, rho_b_sc_pos, rho_u_sc_neg, rho_b_sc_neg, rho_d_ed, rho_d_sc]
+
 N_sl: [12]
 
 b_sl: [2.86e-10]
diff --git a/examples/config/phase/mechanical/plastic/nonlocal_Ni.yaml b/examples/config/phase/mechanical/plastic/nonlocal_Ni.yaml
index c14b912b1..68cf48f3c 100644
--- a/examples/config/phase/mechanical/plastic/nonlocal_Ni.yaml
+++ b/examples/config/phase/mechanical/plastic/nonlocal_Ni.yaml
@@ -1,10 +1,13 @@
 type: nonlocal
+
 references:
-  C. Kords,
-  On the role of dislocation transport in the constitutive description of crystal plasticity,
-  RWTH Aachen 2013,
-  http://publications.rwth-aachen.de/record/229993/files/4862.pdf
+  - C. Kords,
+    On the role of dislocation transport in the constitutive description of crystal plasticity,
+    RWTH Aachen 2013,
+    http://publications.rwth-aachen.de/record/229993/files/4862.pdf
+
 output: [rho_u_ed_pos, rho_b_ed_pos, rho_u_ed_neg, rho_b_ed_neg, rho_u_sc_pos, rho_b_sc_pos, rho_u_sc_neg, rho_b_sc_neg, rho_d_ed, rho_d_sc]
+
 N_sl: [12]
 
 b_sl: [2.48e-10]
diff --git a/examples/config/phase/mechanical/plastic/phenopowerlaw_Al.yaml b/examples/config/phase/mechanical/plastic/phenopowerlaw_Al.yaml
index cc4b56eb6..68c51cdea 100644
--- a/examples/config/phase/mechanical/plastic/phenopowerlaw_Al.yaml
+++ b/examples/config/phase/mechanical/plastic/phenopowerlaw_Al.yaml
@@ -1,4 +1,5 @@
 type: phenopowerlaw
+
 references:
   - W.F. Hosford et al.,
     Acta Metallurgica 8(3):187-199, 1960,
@@ -7,8 +8,11 @@ references:
   - U.F. Kocks,
     Metallurgical and Materials Transactions B 1:1121–1143, 1970,
     https://doi.org/10.1007/BF02900224
+
 output: [xi_sl, gamma_sl]
+
 N_sl: [12]
+
 n_sl: 20
 a_sl: 3.1
 h_0_sl-sl: 1.7e+8
diff --git a/examples/config/phase/mechanical/plastic/phenopowerlaw_Au.yaml b/examples/config/phase/mechanical/plastic/phenopowerlaw_Au.yaml
index ac9c93ccf..3eaed00c4 100644
--- a/examples/config/phase/mechanical/plastic/phenopowerlaw_Au.yaml
+++ b/examples/config/phase/mechanical/plastic/phenopowerlaw_Au.yaml
@@ -1,4 +1,5 @@
 type: phenopowerlaw
+
 references:
   - D. Ma et al.,
     Acta Materialia 103:796-808, 2016,
@@ -9,8 +10,11 @@ references:
   - U.F. Kocks,
     Metallurgical and Materials Transactions B 1:1121–1143, 1970,
     https://doi.org/10.1007/BF02900224
+
 output: [xi_sl, gamma_sl]
+
 N_sl: [12]
+
 n_sl: 83.3
 a_sl: 1.0
 h_0_sl-sl: 75.0e+6
diff --git a/examples/config/phase/mechanical/plastic/phenopowerlaw_Cu.yaml b/examples/config/phase/mechanical/plastic/phenopowerlaw_Cu.yaml
index 4047703cb..223495d26 100644
--- a/examples/config/phase/mechanical/plastic/phenopowerlaw_Cu.yaml
+++ b/examples/config/phase/mechanical/plastic/phenopowerlaw_Cu.yaml
@@ -1,4 +1,5 @@
 type: phenopowerlaw
+
 references:
   - T Takeuchi,
     Transactions of the Japan Institute of Metals 16(10):629-640, 1975,
@@ -7,8 +8,11 @@ references:
   - U.F. Kocks,
     Metallurgical and Materials Transactions B 1:1121–1143, 1970,
     https://doi.org/10.1007/BF02900224
+
 output: [xi_sl, gamma_sl]
+
 N_sl: [12]
+
 n_sl: 20
 a_sl: 1.0
 h_0_sl-sl: 2.4e+8
diff --git a/examples/config/phase/mechanical/plastic/phenopowerlaw_DP-steel-ferrite.yaml b/examples/config/phase/mechanical/plastic/phenopowerlaw_DP-steel-ferrite.yaml
index 5218e42a8..023159bb2 100644
--- a/examples/config/phase/mechanical/plastic/phenopowerlaw_DP-steel-ferrite.yaml
+++ b/examples/config/phase/mechanical/plastic/phenopowerlaw_DP-steel-ferrite.yaml
@@ -1,4 +1,5 @@
 type: phenopowerlaw
+
 references:
   - C.C. Tasan et al.,
     Acta Materialia 81:386-400, 2014,
@@ -6,8 +7,11 @@ references:
   - U.F. Kocks,
     Metallurgical and Materials Transactions B 1:1121–1143, 1970,
     https://doi.org/10.1007/BF02900224
+
 output: [xi_sl, gamma_sl]
+
 N_sl: [12, 12]
+
 n_sl: 20
 a_sl: 2.25
 h_0_sl-sl: 1.0e+9
diff --git a/examples/config/phase/mechanical/plastic/phenopowerlaw_Mg.yaml b/examples/config/phase/mechanical/plastic/phenopowerlaw_Mg.yaml
index 8a3147604..9ccc0ab3c 100644
--- a/examples/config/phase/mechanical/plastic/phenopowerlaw_Mg.yaml
+++ b/examples/config/phase/mechanical/plastic/phenopowerlaw_Mg.yaml
@@ -1,4 +1,5 @@
 type: phenopowerlaw
+
 references:
   - F. Wang et al.,
     Acta Materialia 80:77-93, 2014,
diff --git a/examples/config/phase/mechanical/plastic/phenopowerlaw_Sn-beta.yaml b/examples/config/phase/mechanical/plastic/phenopowerlaw_Sn-beta.yaml
index 2f7871cf5..6877fe229 100644
--- a/examples/config/phase/mechanical/plastic/phenopowerlaw_Sn-beta.yaml
+++ b/examples/config/phase/mechanical/plastic/phenopowerlaw_Sn-beta.yaml
@@ -1,10 +1,14 @@
 type: phenopowerlaw
+
 references:
   - A. Chakraborty and P. Eisenlohr,
     Journal of Applied Physics 124:025302, 2018,
     https://doi.org/10.1063/1.5029933
+
 output: [xi_sl, gamma_sl]
+
 N_sl: [2, 2, 2, 4, 2, 4, 2, 2, 4, 0, 0, 8]
+
 n_sl: 6.0
 a_sl: 2.0
 h_0_sl-sl: 20.0e+6
diff --git a/examples/config/phase/mechanical/plastic/phenopowerlaw_Ti.yaml b/examples/config/phase/mechanical/plastic/phenopowerlaw_Ti.yaml
index 890f580cc..2dbf81ddc 100644
--- a/examples/config/phase/mechanical/plastic/phenopowerlaw_Ti.yaml
+++ b/examples/config/phase/mechanical/plastic/phenopowerlaw_Ti.yaml
@@ -1,4 +1,5 @@
 type: phenopowerlaw
+
 references:
   - C. Zambaldi et al.,
     Journal of Materials Research 27(1):356-367, 2021,
@@ -6,9 +7,11 @@ references:
   - L. Wang et al.,
     Acta Materialia 132:598-610, 2017,
     https://doi.org/10.1016/j.actamat.2017.05.015
+
 output: [gamma_sl]
 
 N_sl: [3, 3, 0, 12]   # basal, prism, -, 1. pyr<c+a>
+
 n_sl: 20
 a_sl: 2.0
 dot_gamma_0_sl: 0.001
diff --git a/examples/config/phase/thermal/AISI304.yaml b/examples/config/phase/thermal/AISI304.yaml
index ef09fd850..7d7cbd40c 100644
--- a/examples/config/phase/thermal/AISI304.yaml
+++ b/examples/config/phase/thermal/AISI304.yaml
@@ -5,5 +5,6 @@ references:
   - R.H. Bogaard et al.
     Thermochimica Acta 218:373-393, 1993
     https://doi.org/10.1016/0040-6031(93)80437-F
+
 C_p: 470.0
 K_11: 14.34
diff --git a/examples/config/phase/thermal/Al.yaml b/examples/config/phase/thermal/Al.yaml
index 6e9705e82..485cc5a31 100644
--- a/examples/config/phase/thermal/Al.yaml
+++ b/examples/config/phase/thermal/Al.yaml
@@ -2,10 +2,13 @@ references:
   - J.G. Hust and A.B. Lankford,
     Thermal Conductivity of Aluminum, Copper, Iron, and Tungsten from 1K to the Melting Point,
     US Department of Commerce, Boulder, Colorado, 1984,
-    fitted to Tab. 3.4.1 (RRR=1000, T_min=200K, T_max=900K)
+    fit to Tab. 3.4.1 (RRR=1000, T_min=200K, T_max=900K)
   - https://www.engineeringtoolbox.com/specific-heat-metals-d_152.html
+
 K_11: 2.380e+02
 K_11,T: 2.068e-03
 K_11,T^2: -7.765e-05
+
 T_ref: 293.15
+
 C_p: 910.0
diff --git a/examples/config/phase/thermal/Au.yaml b/examples/config/phase/thermal/Au.yaml
index 43fe9558e..7ff814d53 100644
--- a/examples/config/phase/thermal/Au.yaml
+++ b/examples/config/phase/thermal/Au.yaml
@@ -1,4 +1,5 @@
 references:
   - https://de.wikipedia.org/wiki/Gold
+
 C_p: 128.0
 K_11: 320.0
diff --git a/examples/config/phase/thermal/Cu.yaml b/examples/config/phase/thermal/Cu.yaml
index cd4df2d74..50e3fdc23 100644
--- a/examples/config/phase/thermal/Cu.yaml
+++ b/examples/config/phase/thermal/Cu.yaml
@@ -2,10 +2,13 @@ references:
   - J.G. Hust and A.B. Lankford,
     Thermal Conductivity of Aluminum, Copper, Iron, and Tungsten from 1K to the Melting Point,
     US Department of Commerce, Boulder, Colorado, 1984,
-    fitted to Tab. 2.4.1 (RRR=1000, T_min=200K, T_max=1000K)
+    fit to Tab. 2.4.1 (RRR=1000, T_min=200K, T_max=1000K)
   - https://www.mit.edu/~6.777/matprops/copper.htm
+
 K_11: 4.039e+02
 K_11,T: -8.119e-02
 K_11,T^2: 1.454e-05
+
 T_ref: 293.15
+
 C_p: 385.0
diff --git a/examples/config/phase/thermal/Fe.yaml b/examples/config/phase/thermal/Fe.yaml
index 49d397599..7fa8902bb 100644
--- a/examples/config/phase/thermal/Fe.yaml
+++ b/examples/config/phase/thermal/Fe.yaml
@@ -2,10 +2,13 @@ references:
   - J.G. Hust and A.B. Lankford,
     Thermal Conductivity of Aluminum, Copper, Iron, and Tungsten from 1K to the Melting Point,
     US Department of Commerce, Boulder, Colorado, 1984,
-    fitted to Tab. 4.4.1 (RRR=300, T_min=200K, T_max=1000K)
+    fit to Tab. 4.4.1 (RRR=300, T_min=200K, T_max=1000K)
   - https://www.engineeringtoolbox.com/specific-heat-metals-d_152.html
+
 K_11: 8.055e+01
 K_11,T: -1.051e-01
 K_11,T^2: 5.464e-05
+
 T_ref: 293.15
+
 C_p: 450.0
diff --git a/examples/config/phase/thermal/W.yaml b/examples/config/phase/thermal/W.yaml
index af4a164c8..2f9ef56e8 100644
--- a/examples/config/phase/thermal/W.yaml
+++ b/examples/config/phase/thermal/W.yaml
@@ -2,10 +2,13 @@ references:
   - J.G. Hust and A.B. Lankford,
     Thermal Conductivity of Aluminum, Copper, Iron, and Tungsten from 1K to the Melting Point,
     US Department of Commerce, Boulder, Colorado, 1984,
-    fitted to Tab. 5.4.1 (RRR=300, T_min=200K, T_max=1000K)
+    fit to Tab. 5.4.1 (RRR=300, T_min=200K, T_max=1000K)
   - https://www.mit.edu/~6.777/matprops/tungsten.htm
+
 K_11: 1.758e+02
 K_11,T: -1.605e-01
 K_11,T^2: 1.160e-04
+
 T_ref: 293.15
+
 C_p: 132.51
diff --git a/examples/config/phase/thermal/source/dissipation_generic.yaml b/examples/config/phase/thermal/source/dissipation_generic.yaml
index af5214582..87bed84af 100644
--- a/examples/config/phase/thermal/source/dissipation_generic.yaml
+++ b/examples/config/phase/thermal/source/dissipation_generic.yaml
@@ -1,2 +1,3 @@
 type: dissipation
+
 kappa: .9
diff --git a/examples/config/phase/thermal/source/externalheat_ramp-and-hold.yaml b/examples/config/phase/thermal/source/externalheat_ramp-and-hold.yaml
index 333ece989..3567f55cf 100644
--- a/examples/config/phase/thermal/source/externalheat_ramp-and-hold.yaml
+++ b/examples/config/phase/thermal/source/externalheat_ramp-and-hold.yaml
@@ -1,3 +1,4 @@
 type: externalheat
+
 f_T: [1, 1, 0, 0]
 t_n: [0, 500, 500.001, 1000]
diff --git a/examples/config/phase/thermal/steel-0.5C.yaml b/examples/config/phase/thermal/steel-0.5C.yaml
index 1b1d8995a..e810a811d 100644
--- a/examples/config/phase/thermal/steel-0.5C.yaml
+++ b/examples/config/phase/thermal/steel-0.5C.yaml
@@ -1,5 +1,6 @@
 references:
   - https://www.engineeringtoolbox.com/thermal-conductivity-metals-d_858.html
   - https://www.engineeringtoolbox.com/specific-heat-metals-d_152.html
+
 C_p: 490.0
 K_11: 54.0

From 80f5496ef2862ef2c6b8c63247a408667056b3e1 Mon Sep 17 00:00:00 2001
From: Martin Diehl <mail@martin-diehl.net>
Date: Sat, 12 Feb 2022 21:26:42 +0100
Subject: [PATCH 47/72] adjustments and improved documentation

---
 .../eigen/thermalexpansion_AISI304.yaml       | 10 ++++++---
 .../mechanical/eigen/thermalexpansion_Al.yaml |  4 ++--
 .../mechanical/eigen/thermalexpansion_Au.yaml |  4 ++--
 .../mechanical/eigen/thermalexpansion_Cu.yaml |  4 ++--
 .../mechanical/eigen/thermalexpansion_Fe.yaml |  4 ++--
 .../eigen/thermalexpansion_Sn-beta.yaml       |  2 +-
 .../mechanical/eigen/thermalexpansion_W.yaml  |  4 ++--
 .../phase/mechanical/elastic/Hooke_Fe.yaml    | 21 ++++++++++---------
 8 files changed, 29 insertions(+), 24 deletions(-)

diff --git a/examples/config/phase/mechanical/eigen/thermalexpansion_AISI304.yaml b/examples/config/phase/mechanical/eigen/thermalexpansion_AISI304.yaml
index f3605e1d9..bc0db5c5e 100644
--- a/examples/config/phase/mechanical/eigen/thermalexpansion_AISI304.yaml
+++ b/examples/config/phase/mechanical/eigen/thermalexpansion_AISI304.yaml
@@ -3,7 +3,11 @@ type: thermalexpansion
 references:
   - R.H. Bogaard et al.,
     Thermochimica Acta 218:373-393, 1993,
-    https://doi.org/10.1016/0040-6031(93)80437-F
+    https://doi.org/10.1016/0040-6031(93)80437-F,
+    fit to Fig. 6 (T_min=100K, T_max=1400K)
 
-A_11: 15.0e-6
-T_ref: 300.0
+A_11: 2.068e-08
+A_11,T: 1.579e-09
+A_11,T^2: 3.449e-13
+
+T_ref: 293.15
diff --git a/examples/config/phase/mechanical/eigen/thermalexpansion_Al.yaml b/examples/config/phase/mechanical/eigen/thermalexpansion_Al.yaml
index ccd8b347b..495680b4e 100644
--- a/examples/config/phase/mechanical/eigen/thermalexpansion_Al.yaml
+++ b/examples/config/phase/mechanical/eigen/thermalexpansion_Al.yaml
@@ -1,7 +1,7 @@
 type: thermalexpansion
 
 references:
-  - https://en.wikipedia.org/wiki/Thermal_expansion
+  - https://en.wikipedia.org/wiki/Thermal_expansion,
+    293.15K
 
 A_11: 23.1e-6
-T_ref: 293.15
diff --git a/examples/config/phase/mechanical/eigen/thermalexpansion_Au.yaml b/examples/config/phase/mechanical/eigen/thermalexpansion_Au.yaml
index 8211516de..a14ac6b0f 100644
--- a/examples/config/phase/mechanical/eigen/thermalexpansion_Au.yaml
+++ b/examples/config/phase/mechanical/eigen/thermalexpansion_Au.yaml
@@ -1,7 +1,7 @@
 type: thermalexpansion
 
 references:
-  - https://en.wikipedia.org/wiki/Thermal_expansion
+  - https://en.wikipedia.org/wiki/Thermal_expansion,
+    293.15K
 
 A_11: 14.e-6
-T_ref: 293.15
diff --git a/examples/config/phase/mechanical/eigen/thermalexpansion_Cu.yaml b/examples/config/phase/mechanical/eigen/thermalexpansion_Cu.yaml
index d7c71931b..a0a35c955 100644
--- a/examples/config/phase/mechanical/eigen/thermalexpansion_Cu.yaml
+++ b/examples/config/phase/mechanical/eigen/thermalexpansion_Cu.yaml
@@ -1,7 +1,7 @@
 type: thermalexpansion
 
 references:
-  - https://en.wikipedia.org/wiki/Thermal_expansion
+  - https://en.wikipedia.org/wiki/Thermal_expansion,
+    293.15K
 
 A_11: 17.e-6
-T_ref: 293.15
diff --git a/examples/config/phase/mechanical/eigen/thermalexpansion_Fe.yaml b/examples/config/phase/mechanical/eigen/thermalexpansion_Fe.yaml
index 9798fb8a0..da8ead4c1 100644
--- a/examples/config/phase/mechanical/eigen/thermalexpansion_Fe.yaml
+++ b/examples/config/phase/mechanical/eigen/thermalexpansion_Fe.yaml
@@ -1,7 +1,7 @@
 type: thermalexpansion
 
 references:
-  - https://en.wikipedia.org/wiki/Thermal_expansion
+  - https://en.wikipedia.org/wiki/Thermal_expansion,
+    293.15K
 
 A_11: 11.8e-6
-T_ref: 293.15
diff --git a/examples/config/phase/mechanical/eigen/thermalexpansion_Sn-beta.yaml b/examples/config/phase/mechanical/eigen/thermalexpansion_Sn-beta.yaml
index 16e78f82c..f77f79bba 100644
--- a/examples/config/phase/mechanical/eigen/thermalexpansion_Sn-beta.yaml
+++ b/examples/config/phase/mechanical/eigen/thermalexpansion_Sn-beta.yaml
@@ -4,7 +4,7 @@ references:
   - V.T. Deshpande and D.B. Sirdeshmukh,
     Acta Crystallographica 15:294-295, 1962,
     https://doi.org/10.1107/S0365110X62000742,
-    fit to Tab. 2
+    fit to Tab. 2 (T_min=30ºC, T_max=210ºC)
 
 A_11: 1.639e-05
 A_11,T: 1.799e-08
diff --git a/examples/config/phase/mechanical/eigen/thermalexpansion_W.yaml b/examples/config/phase/mechanical/eigen/thermalexpansion_W.yaml
index 338f60fe2..cb29ab270 100644
--- a/examples/config/phase/mechanical/eigen/thermalexpansion_W.yaml
+++ b/examples/config/phase/mechanical/eigen/thermalexpansion_W.yaml
@@ -1,7 +1,7 @@
 type: thermalexpansion
 
 references:
-  - https://en.wikipedia.org/wiki/Thermal_expansion
+  - https://en.wikipedia.org/wiki/Thermal_expansion,
+    293.15K
 
 A_11: 4.5e-6
-T_ref: 293.15
diff --git a/examples/config/phase/mechanical/elastic/Hooke_Fe.yaml b/examples/config/phase/mechanical/elastic/Hooke_Fe.yaml
index a6d7d1868..198a2b4d3 100644
--- a/examples/config/phase/mechanical/elastic/Hooke_Fe.yaml
+++ b/examples/config/phase/mechanical/elastic/Hooke_Fe.yaml
@@ -4,17 +4,18 @@ references:
   - D.J. Dever,
     Journal of Applied Physics 43(8):3293-3301, 1972,
     https://doi.org/10.1063/1.1661710
+    fit to Tab. II (T_min=25ºC, T_max=880ºC)
 
-C_11: 231.7e+9
-C_11,T: -47.6e+6
-C_11,T^2: -54.4e+3
+C_11: 232.1e+9
+C_11,T: -4.678e+7
+C_11,T^2: -5.762e+4
 
-C_12: 135.8e+9
-C_12,T: -12.9e+6
-C_12,T^2: -7.3e+3
+C_12: 135.9e+9
+C_12,T: -1.695e+7
+C_12,T^2: 1.555e+3
 
-C_44: 116.8e+9
-C_44,T: -19.4e+6
-C_44,T^2: -2.5e+3
+C_44: 117.0e+9
+C_44,T: -2.047e+7
+C_44,T^2: -2.814e+2
 
-T_ref: 300
+T_ref: 293.15

From 663b84641e20521896ca15cd0473680fd5349ac6 Mon Sep 17 00:00:00 2001
From: Martin Diehl <mail@martin-diehl.net>
Date: Sat, 12 Feb 2022 22:29:56 +0100
Subject: [PATCH 48/72] needed for a complete set for Sn-beta

---
 examples/config/phase/thermal/Sn-beta.yaml | 18 ++++++++++++++++++
 1 file changed, 18 insertions(+)
 create mode 100644 examples/config/phase/thermal/Sn-beta.yaml

diff --git a/examples/config/phase/thermal/Sn-beta.yaml b/examples/config/phase/thermal/Sn-beta.yaml
new file mode 100644
index 000000000..a4d16cd98
--- /dev/null
+++ b/examples/config/phase/thermal/Sn-beta.yaml
@@ -0,0 +1,18 @@
+references:
+  - Y.S. Touloukian et al.,
+    TPRC Data Series Volume 1. Thermal conductivity - metallic elements and alloys,
+    IFI/Plenum, 1970,
+    fit to Tab. 61R (T_min=100K, T_max=400K)
+  - https://www.engineeringtoolbox.com/specific-heat-metals-d_152.html
+
+K_11: 7.414e+1
+K_11,T: -6.465e-2
+K_11,T^2: 2.066e-4
+
+K_33: 5.147e+1
+K_33,T: -4.506e-2
+K_33,T^2: 1.435e-4
+
+T_ref: 293.15
+
+C_p: 210.0

From 2c05395b88c4b0b6e693e87db2ad0845b4de1556 Mon Sep 17 00:00:00 2001
From: Martin Diehl <mail@martin-diehl.net>
Date: Sat, 12 Feb 2022 22:30:46 +0100
Subject: [PATCH 49/72] including test for new data

---
 PRIVATE | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/PRIVATE b/PRIVATE
index 5774122bf..19a2a62de 160000
--- a/PRIVATE
+++ b/PRIVATE
@@ -1 +1 @@
-Subproject commit 5774122bf48d637704bb4afb10b87c34a4dbcaba
+Subproject commit 19a2a62ded818e4843cf8a248ec6189ff9e4359b

From 99c2f5855332885a2bf8ead476f1824ed9748fd8 Mon Sep 17 00:00:00 2001
From: Martin Diehl <mail@martin-diehl.net>
Date: Sat, 12 Feb 2022 22:38:58 +0100
Subject: [PATCH 50/72] ensure that data is read

---
 src/phase_mechanical_elastic.f90 |  2 +-
 src/phase_thermal.f90            | 21 ++++++++++++++-------
 2 files changed, 15 insertions(+), 8 deletions(-)

diff --git a/src/phase_mechanical_elastic.f90 b/src/phase_mechanical_elastic.f90
index 7f30c8165..84ad7a20e 100644
--- a/src/phase_mechanical_elastic.f90
+++ b/src/phase_mechanical_elastic.f90
@@ -48,7 +48,7 @@ module subroutine elastic_init(phases)
       prm%C_11 = polynomial(elastic%asDict(),'C_11','T')
       prm%C_12 = polynomial(elastic%asDict(),'C_12','T')
       prm%C_44 = polynomial(elastic%asDict(),'C_44','T')
- 
+
       if (any(phase_lattice(ph) == ['hP','tI'])) then
         prm%C_13 = polynomial(elastic%asDict(),'C_13','T')
         prm%C_33 = polynomial(elastic%asDict(),'C_33','T')
diff --git a/src/phase_thermal.f90 b/src/phase_thermal.f90
index bc464d35a..11314531e 100644
--- a/src/phase_thermal.f90
+++ b/src/phase_thermal.f90
@@ -96,17 +96,24 @@ module subroutine thermal_init(phases)
 
   do ph = 1, phases%length
     Nmembers = count(material_phaseID == ph)
-    allocate(current(ph)%T(Nmembers),source=300.0_pReal)
+    allocate(current(ph)%T(Nmembers),source=T_ROOM)
     allocate(current(ph)%dot_T(Nmembers),source=0.0_pReal)
     phase => phases%get(ph)
     thermal => phase%get('thermal',defaultVal=emptyDict)
-    param(ph)%C_p = thermal%get_asFloat('C_p',defaultVal=0.0_pReal)                                 ! ToDo: make mandatory?
-    param(ph)%K(1,1) = thermal%get_asFloat('K_11',defaultVal=0.0_pReal)                             ! ToDo: make mandatory?
-    param(ph)%K(3,3) = thermal%get_asFloat('K_33',defaultVal=0.0_pReal)                             ! ToDo: depends on symmtery
-    param(ph)%K = lattice_symmetrize_33(param(ph)%K,phase_lattice(ph))
 
-    sources => thermal%get('source',defaultVal=emptyList)
-    thermal_Nsources(ph) = sources%length
+    ! ToDo: temperature dependency of K and C_p
+    if (thermal%length > 0) then
+      param(ph)%C_p = thermal%get_asFloat('C_p')
+      param(ph)%K(1,1) = thermal%get_asFloat('K_11')
+      if (any(phase_lattice(ph) == ['hP','tI'])) param(ph)%K(3,3) = thermal%get_asFloat('K_33')
+      param(ph)%K = lattice_symmetrize_33(param(ph)%K,phase_lattice(ph))
+
+      sources => thermal%get('source',defaultVal=emptyList)
+      thermal_Nsources(ph) = sources%length
+    else
+      thermal_Nsources(ph) = 0
+    end if
+
     allocate(thermalstate(ph)%p(thermal_Nsources(ph)))
 
   enddo

From 2907facfd34c4ad79b3f89fb7609c536c892d63a Mon Sep 17 00:00:00 2001
From: Martin Diehl <mail@martin-diehl.net>
Date: Sun, 13 Feb 2022 01:24:02 +0100
Subject: [PATCH 51/72] polishing

classes should return 'MyType' for inheritance without hassle
---
 python/damask/_crystal.py     |  2 +-
 python/damask/_orientation.py | 39 ++++++++++++-------------
 python/damask/_rotation.py    | 55 +++++++++++++++++------------------
 python/damask/_typehints.py   |  3 +-
 4 files changed, 47 insertions(+), 52 deletions(-)

diff --git a/python/damask/_crystal.py b/python/damask/_crystal.py
index 6da13f679..077d2e13a 100644
--- a/python/damask/_crystal.py
+++ b/python/damask/_crystal.py
@@ -31,7 +31,7 @@ lattice_symmetries: Dict[CrystalLattice, CrystalFamily] = {
 class Crystal():
     """Crystal lattice."""
 
-    def __init__(self,*,
+    def __init__(self, *,
                  family: CrystalFamily = None,
                  lattice: CrystalLattice = None,
                  a: float = None, b: float = None, c: float = None,
diff --git a/python/damask/_orientation.py b/python/damask/_orientation.py
index 54ffb6728..16df11984 100644
--- a/python/damask/_orientation.py
+++ b/python/damask/_orientation.py
@@ -1,6 +1,6 @@
 import inspect
 import copy
-from typing import Union, Callable, List, Dict, Any, Tuple
+from typing import Union, Callable, List, Dict, Any, Tuple, TypeVar
 
 import numpy as np
 
@@ -11,7 +11,6 @@ from . import util
 from . import tensor
 
 
-
 _parameter_doc = \
        """
         family : {'triclinic', 'monoclinic', 'orthorhombic', 'tetragonal', 'hexagonal', 'cubic'}, optional.
@@ -36,6 +35,7 @@ _parameter_doc = \
 
        """
 
+MyType = TypeVar('MyType', bound='Orientation')
 
 class Orientation(Rotation,Crystal):
     """
@@ -124,8 +124,8 @@ class Orientation(Rotation,Crystal):
         return '\n'.join([Crystal.__repr__(self),
                           Rotation.__repr__(self)])
 
-    def __copy__(self,
-                 rotation: Union[FloatSequence, Rotation] = None) -> 'Orientation':
+    def __copy__(self: MyType,
+                 rotation: Union[FloatSequence, Rotation] = None) -> MyType:
         """Create deep copy."""
         dup = copy.deepcopy(self)
         if rotation is not None:
@@ -189,7 +189,7 @@ class Orientation(Rotation,Crystal):
 
         Returns
         -------
-        mask : numpy.ndarray of bool
+        mask : numpy.ndarray of bool, shape (self.shape)
             Mask indicating where corresponding orientations are close.
 
         """
@@ -230,8 +230,8 @@ class Orientation(Rotation,Crystal):
         return bool(np.all(self.isclose(other,rtol,atol,equal_nan)))
 
 
-    def __mul__(self,
-                other: Union[Rotation, 'Orientation']) -> 'Orientation':
+    def __mul__(self: MyType,
+                other: Union[Rotation, 'Orientation']) -> MyType:
         """
         Compose this orientation with other.
 
@@ -246,8 +246,8 @@ class Orientation(Rotation,Crystal):
             Compound rotation self*other, i.e. first other then self rotation.
 
         """
-        if isinstance(other,Orientation) or isinstance(other,Rotation):
-            return self.copy(rotation=Rotation.__mul__(self,Rotation(other.quaternion)))
+        if isinstance(other, (Orientation,Rotation)):
+            return self.copy(Rotation(self.quaternion)*Rotation(other.quaternion))
         else:
             raise TypeError('use "O@b", i.e. matmul, to apply Orientation "O" to object "b"')
 
@@ -382,11 +382,11 @@ class Orientation(Rotation,Crystal):
         x = o.to_frame(uvw=uvw)
         z = o.to_frame(hkl=hkl)
         om = np.stack([x,np.cross(z,x),z],axis=-2)
-        return o.copy(rotation=Rotation.from_matrix(tensor.transpose(om/np.linalg.norm(om,axis=-1,keepdims=True))))
+        return o.copy(Rotation.from_matrix(tensor.transpose(om/np.linalg.norm(om,axis=-1,keepdims=True))))
 
 
     @property
-    def equivalent(self) -> 'Orientation':
+    def equivalent(self: MyType) -> MyType:
         """
         Orientations that are symmetrically equivalent.
 
@@ -396,11 +396,11 @@ class Orientation(Rotation,Crystal):
         """
         sym_ops = self.symmetry_operations
         o = sym_ops.broadcast_to(sym_ops.shape+self.shape,mode='right')
-        return self.copy(rotation=o*Rotation(self.quaternion).broadcast_to(o.shape,mode='left'))
+        return self.copy(o*Rotation(self.quaternion).broadcast_to(o.shape,mode='left'))
 
 
     @property
-    def reduced(self) -> 'Orientation':
+    def reduced(self: MyType) -> MyType:
         """Select symmetrically equivalent orientation that falls into fundamental zone according to symmetry."""
         eq   = self.equivalent
         ok   = eq.in_FZ
@@ -616,11 +616,8 @@ class Orientation(Rotation,Crystal):
                                                    np.argmin(m,axis=0)[np.newaxis,...,np.newaxis],
                                                    axis=0),
                                 axis=0))
-        return (
-                (self.copy(rotation=Rotation(r).average(weights)),
-                 self.copy(rotation=Rotation(r)))
-                if return_cloud else
-                self.copy(rotation=Rotation(r).average(weights))
+        return ((self.copy(Rotation(r).average(weights)),self.copy(Rotation(r))) if return_cloud else
+                self.copy(Rotation(r).average(weights))
                )
 
 
@@ -930,7 +927,7 @@ class Orientation(Rotation,Crystal):
         if active == '*': active = [len(a) for a in kinematics['direction']]
 
         if not active:
-            raise RuntimeError # ToDo
+            raise ValueError('Schmid matrix not defined')
         d = self.to_frame(uvw=np.vstack([kinematics['direction'][i][:n] for i,n in enumerate(active)]))
         p = self.to_frame(hkl=np.vstack([kinematics['plane'][i][:n] for i,n in enumerate(active)]))
         P = np.einsum('...i,...j',d/np.linalg.norm(d,axis=1,keepdims=True),
@@ -941,8 +938,8 @@ class Orientation(Rotation,Crystal):
                @ np.broadcast_to(P.reshape(util.shapeshifter(P.shape,shape)),shape)
 
 
-    def related(self,
-                model: str) -> 'Orientation':
+    def related(self: MyType,
+                model: str) -> MyType:
         """
         Orientations derived from the given relationship.
 
diff --git a/python/damask/_rotation.py b/python/damask/_rotation.py
index 273cf8e92..b11147482 100644
--- a/python/damask/_rotation.py
+++ b/python/damask/_rotation.py
@@ -1,14 +1,13 @@
 import copy
+from typing import Union, Sequence, Tuple, Literal, List, TypeVar
 
 import numpy as np
 
+from ._typehints import FloatSequence, IntSequence, NumpyRngSeed
 from . import tensor
 from . import util
 from . import grid_filters
 
-from typing import Union, Sequence, Tuple, Literal, List, TypeVar
-from ._typehints import FloatSequence, IntSequence, NumpyRngSeed
-
 _P = -1
 
 # parameters for conversion from/to cubochoric
@@ -109,7 +108,7 @@ class Rotation:
                     item: Union[Tuple[int], int, bool, np.bool_, np.ndarray]):
         """Return slice according to item."""
         return self.copy() if self.shape == () else \
-               self.copy(rotation=self.quaternion[item+(slice(None),)] if isinstance(item,tuple) else self.quaternion[item])
+               self.copy(self.quaternion[item+(slice(None),)] if isinstance(item,tuple) else self.quaternion[item])
 
 
     def __eq__(self,
@@ -162,7 +161,7 @@ class Rotation:
 
         Returns
         -------
-        mask : numpy.ndarray of bool
+        mask : numpy.ndarray of bool, shape (self.shape)
             Mask indicating where corresponding rotations are close.
 
         """
@@ -233,13 +232,13 @@ class Rotation:
 
         Parameters
         ----------
-        exp : scalar
+        exp : float
             Exponent.
 
         """
         phi = np.arccos(self.quaternion[...,0:1])
         p = self.quaternion[...,1:]/np.linalg.norm(self.quaternion[...,1:],axis=-1,keepdims=True)
-        return self.copy(rotation=Rotation(np.block([np.cos(exp*phi),np.sin(exp*phi)*p]))._standardize())
+        return self.copy(Rotation(np.block([np.cos(exp*phi),np.sin(exp*phi)*p]))._standardize())
 
     def __ipow__(self: MyType,
                  exp: Union[float, int]) -> MyType:
@@ -248,7 +247,7 @@ class Rotation:
 
         Parameters
         ----------
-        exp : scalar
+        exp : float
             Exponent.
 
         """
@@ -278,7 +277,7 @@ class Rotation:
             p_o = other.quaternion[...,1:]
             q = (q_m*q_o - np.einsum('...i,...i',p_m,p_o).reshape(self.shape+(1,)))
             p = q_m*p_o + q_o*p_m + _P * np.cross(p_m,p_o)
-            return Rotation(np.block([q,p]))._standardize() #type: ignore
+            return self.copy(Rotation(np.block([q,p]))._standardize())
         else:
             raise TypeError('Use "R@b", i.e. matmul, to apply rotation "R" to object "b"')
 
@@ -391,8 +390,8 @@ class Rotation:
         other : (list of) damask.Rotation
 
         """
-        return self.copy(rotation=np.vstack(tuple(map(lambda x:x.quaternion,
-                                                      [self]+other if isinstance(other,list) else [self,other]))))
+        return self.copy(np.vstack(tuple(map(lambda x:x.quaternion,
+                                             [self]+other if isinstance(other,list) else [self,other]))))
 
 
     def flatten(self: MyType,
@@ -415,7 +414,7 @@ class Rotation:
             Rotation flattened to single dimension.
 
         """
-        return self.copy(rotation=self.quaternion.reshape((-1,4),order=order))
+        return self.copy(self.quaternion.reshape((-1,4),order=order))
 
 
     def reshape(self: MyType,
@@ -443,7 +442,7 @@ class Rotation:
 
         """
         if isinstance(shape,(int,np.integer)): shape = (shape,)
-        return self.copy(rotation=self.quaternion.reshape(tuple(shape)+(4,),order=order))
+        return self.copy(self.quaternion.reshape(tuple(shape)+(4,),order=order))
 
 
     def broadcast_to(self: MyType,
@@ -467,18 +466,18 @@ class Rotation:
 
         """
         if isinstance(shape,(int,np.integer)): shape = (shape,)
-        return self.copy(rotation=np.broadcast_to(self.quaternion.reshape(util.shapeshifter(self.shape,shape,mode)+(4,)),
+        return self.copy(np.broadcast_to(self.quaternion.reshape(util.shapeshifter(self.shape,shape,mode)+(4,)),
                                                   shape+(4,)))
 
 
-    def average(self,
-                weights: FloatSequence = None) -> 'Rotation':
+    def average(self: MyType,
+                weights: FloatSequence = None) -> MyType:
         """
         Average along last array dimension.
 
         Parameters
         ----------
-        weights : numpy.ndarray, optional
+        weights : numpy.ndarray, shape (self.shape), optional
             Relative weight of each rotation.
 
         Returns
@@ -501,13 +500,13 @@ class Rotation:
         eig, vec = np.linalg.eig(np.sum(_M(self.quaternion) * weights_[...,np.newaxis,np.newaxis],axis=-3) \
                                 /np.sum(                      weights_[...,np.newaxis,np.newaxis],axis=-3))
 
-        return Rotation.from_quaternion(np.real(
-                                        np.squeeze(
-                                        np.take_along_axis(vec,
-                                                           eig.argmax(axis=-1)[...,np.newaxis,np.newaxis],
-                                                           axis=-1),
-                                        axis=-1)),
-                                        accept_homomorph = True)
+        return self.copy(Rotation.from_quaternion(np.real(
+                                                  np.squeeze(
+                                                  np.take_along_axis(vec,
+                                                                     eig.argmax(axis=-1)[...,np.newaxis,np.newaxis],
+                                                                     axis=-1),
+                                                  axis=-1)),
+                                                  accept_homomorph = True))
 
 
     def misorientation(self: MyType,
@@ -730,7 +729,7 @@ class Rotation:
             Sign convention. Defaults to -1.
 
         """
-        qu: np.ndarray = np.array(q,dtype=float)
+        qu = np.array(q,dtype=float)
         if qu.shape[:-2:-1] != (4,):
             raise ValueError('Invalid shape.')
         if abs(P) != 1:
@@ -996,7 +995,7 @@ class Rotation:
             Defaults to None, i.e. unpredictable entropy will be pulled from the OS.
 
         """
-        rng: np.random.Generator = np.random.default_rng(rng_seed)
+        rng = np.random.default_rng(rng_seed)
         r = rng.random(3 if shape is None else tuple(shape)+(3,) if hasattr(shape, '__iter__') else (shape,3)) #type: ignore
 
         A = np.sqrt(r[...,2])
@@ -1131,8 +1130,8 @@ class Rotation:
 
         """
         rng = np.random.default_rng(rng_seed)
-        sigma_: np.ndarray; alpha_: np.ndarray; beta_: np.ndarray
-        sigma_,alpha_,beta_ = (np.radians(coordinate) for coordinate in (sigma,alpha,beta)) if degrees else (sigma,alpha,beta) #type: ignore
+        sigma_,alpha_,beta_ = (np.radians(coordinate) for coordinate in (sigma,alpha,beta)) if degrees else \
+                              map(np.array, (sigma,alpha,beta))
 
         d_cr  = np.array([np.sin(alpha_[0])*np.cos(alpha_[1]), np.sin(alpha_[0])*np.sin(alpha_[1]), np.cos(alpha_[0])])
         d_lab = np.array([np.sin( beta_[0])*np.cos( beta_[1]), np.sin( beta_[0])*np.sin( beta_[1]), np.cos( beta_[0])])
diff --git a/python/damask/_typehints.py b/python/damask/_typehints.py
index 674f54721..5fcf39a41 100644
--- a/python/damask/_typehints.py
+++ b/python/damask/_typehints.py
@@ -9,10 +9,9 @@ import numpy as np
 FloatSequence = Union[np.ndarray,Sequence[float]]
 IntSequence = Union[np.ndarray,Sequence[int]]
 FileHandle = Union[TextIO, str, Path]
-NumpyRngSeed = Union[int, IntSequence, np.random.SeedSequence, np.random.Generator]
 CrystalFamily = Union[None,Literal['triclinic', 'monoclinic', 'orthorhombic', 'tetragonal', 'hexagonal', 'cubic']]
 CrystalLattice = Union[None,Literal['aP', 'mP', 'mS', 'oP', 'oS', 'oI', 'oF', 'tP', 'tI', 'hP', 'cP', 'cI', 'cF']]
 CrystalKinematics = Literal['slip', 'twin']
-
+NumpyRngSeed = Union[int, IntSequence, np.random.SeedSequence, np.random.Generator]
 # BitGenerator does not exists in older numpy versions
 #NumpyRngSeed = Union[int, IntSequence, np.random.SeedSequence, np.random.BitGenerator, np.random.Generator]

From b1922c9fc03c295446b320281c44da0eda212225 Mon Sep 17 00:00:00 2001
From: Martin Diehl <mail@martin-diehl.net>
Date: Sun, 13 Feb 2022 10:41:10 +0100
Subject: [PATCH 52/72] return most specific type

---
 python/damask/_orientation.py | 8 ++++----
 python/damask/util.py         | 6 +++---
 2 files changed, 7 insertions(+), 7 deletions(-)

diff --git a/python/damask/_orientation.py b/python/damask/_orientation.py
index 16df11984..c3afd0bed 100644
--- a/python/damask/_orientation.py
+++ b/python/damask/_orientation.py
@@ -558,8 +558,8 @@ class Orientation(Rotation,Crystal):
         s = self.equivalent
         o = other.equivalent
 
-        s_ = s.reshape((s.shape[0],1)+ self.shape).broadcast_to((s.shape[0],o.shape[0])+blend,mode='right') #type: ignore
-        o_ = o.reshape((1,o.shape[0])+other.shape).broadcast_to((s.shape[0],o.shape[0])+blend,mode='right') #type: ignore
+        s_ = s.reshape((s.shape[0],1)+ self.shape).broadcast_to((s.shape[0],o.shape[0])+blend,mode='right')
+        o_ = o.reshape((1,o.shape[0])+other.shape).broadcast_to((s.shape[0],o.shape[0])+blend,mode='right')
         r_ = s_.misorientation(o_)
         _r = ~r_
 
@@ -654,7 +654,7 @@ class Orientation(Rotation,Crystal):
             raise ValueError('input is not a field of three-dimensional vectors')
         eq  = self.equivalent
         blend = util.shapeblender(eq.shape,vector_.shape[:-1])
-        poles = eq.broadcast_to(blend,mode='right') @ np.broadcast_to(vector_,blend+(3,)) #type: ignore
+        poles = eq.broadcast_to(blend,mode='right') @ np.broadcast_to(vector_,blend+(3,))
         ok    = self.in_SST(poles,proper=proper)
         ok   &= np.cumsum(ok,axis=0) == 1
         loc   = np.where(ok)
@@ -884,7 +884,7 @@ class Orientation(Rotation,Crystal):
             blend += sym_ops.shape
             v = sym_ops.broadcast_to(shape) \
               @ np.broadcast_to(v.reshape(util.shapeshifter(v.shape,shape+(3,))),shape+(3,))
-        return ~(self.broadcast_to(blend))@ np.broadcast_to(v,blend+(3,)) #type: ignore
+        return ~(self.broadcast_to(blend))@ np.broadcast_to(v,blend+(3,))
 
 
     def Schmid(self, *,
diff --git a/python/damask/util.py b/python/damask/util.py
index cc5b8906e..ab34df7c0 100644
--- a/python/damask/util.py
+++ b/python/damask/util.py
@@ -9,7 +9,7 @@ import re
 import fractions
 from collections import abc
 from functools import reduce
-from typing import Union, Tuple, Iterable, Callable, Dict, List, Any, Literal, SupportsIndex
+from typing import Union, Tuple, Iterable, Callable, Dict, List, Any, Literal
 from pathlib import Path
 
 import numpy as np
@@ -427,7 +427,7 @@ def hybrid_IA(dist: np.ndarray,
 def shapeshifter(fro: Tuple[int, ...],
                  to: Tuple[int, ...],
                  mode: Literal['left','right'] = 'left',
-                 keep_ones: bool = False) -> Tuple[SupportsIndex, ...]:
+                 keep_ones: bool = False) -> Tuple[int, ...]:
     """
     Return dimensions that reshape 'fro' to become broadcastable to 'to'.
 
@@ -490,7 +490,7 @@ def shapeshifter(fro: Tuple[int, ...],
 
 
 def shapeblender(a: Tuple[int, ...],
-                 b: Tuple[int, ...]) -> Tuple[SupportsIndex, ...]:
+                 b: Tuple[int, ...]) -> Tuple[int, ...]:
     """
     Return a shape that overlaps the rightmost entries of 'a' with the leftmost of 'b'.
 

From bb6a62c475a34c6f764d6d647c04316089b16277 Mon Sep 17 00:00:00 2001
From: Martin Diehl <mail@martin-diehl.net>
Date: Sun, 13 Feb 2022 01:49:07 +0100
Subject: [PATCH 53/72] more temperature dependent data

---
 PRIVATE                                       |  2 +-
 .../phase/mechanical/elastic/Hooke_Cu.yaml    | 22 ++++++++---
 .../phase/mechanical/elastic/Hooke_Mg.yaml    | 33 +++++++++++++----
 .../phase/mechanical/elastic/Hooke_Ni.yaml    | 24 ++++++++----
 .../phase/mechanical/elastic/Hooke_Ti.yaml    | 37 +++++++++++++++----
 .../phase/mechanical/elastic/Hooke_W.yaml     | 22 ++++++++---
 examples/config/phase/thermal/Al.yaml         |  6 +--
 examples/config/phase/thermal/Cu.yaml         |  6 +--
 examples/config/phase/thermal/Fe.yaml         |  6 +--
 examples/config/phase/thermal/Ni.yaml         | 14 +++++++
 examples/config/phase/thermal/W.yaml          |  6 +--
 11 files changed, 131 insertions(+), 47 deletions(-)
 create mode 100644 examples/config/phase/thermal/Ni.yaml

diff --git a/PRIVATE b/PRIVATE
index 19a2a62de..0d639a9ba 160000
--- a/PRIVATE
+++ b/PRIVATE
@@ -1 +1 @@
-Subproject commit 19a2a62ded818e4843cf8a248ec6189ff9e4359b
+Subproject commit 0d639a9ba41db279b0d2825c8e8eddf0ccd91326
diff --git a/examples/config/phase/mechanical/elastic/Hooke_Cu.yaml b/examples/config/phase/mechanical/elastic/Hooke_Cu.yaml
index 90a0bd269..d21324084 100644
--- a/examples/config/phase/mechanical/elastic/Hooke_Cu.yaml
+++ b/examples/config/phase/mechanical/elastic/Hooke_Cu.yaml
@@ -1,9 +1,21 @@
 type: Hooke
 
 references:
-  - https://www.mit.edu/~6.777/matprops/copper.htm,
-    fixed typo
+  - W.C. Overton, Jr. and J. Gaffney,
+    Physical Review 98(4):969-977, 1955,
+    https://doi.org/10.1103/PhysRev.98.969,
+    fit to Tab. I (T_min=100K, T_max=300K)
 
-C_11: 168.3e+9
-C_12: 122.1e+9
-C_44: 75.7e+9
+C_11: 168.6e+9
+C_11,T: -3.779e+7
+C_11,T^2: -2.536e+4
+
+C_12: 121.5e+9
+C_12,T: -1.632e+7
+C_12,T^2: -1.116e+4
+
+C_44: 75.59e+9
+C_44,T: -2.912e+7
+C_44,T^2: -1.669e+4
+
+T_ref: 293.15
diff --git a/examples/config/phase/mechanical/elastic/Hooke_Mg.yaml b/examples/config/phase/mechanical/elastic/Hooke_Mg.yaml
index aa089d4b4..06a6cfb62 100644
--- a/examples/config/phase/mechanical/elastic/Hooke_Mg.yaml
+++ b/examples/config/phase/mechanical/elastic/Hooke_Mg.yaml
@@ -1,12 +1,29 @@
 type: Hooke
 
 references:
-  - D. Tromans,
-    International Journal of Recent Research and Applied Studies 6(4):462-483, 2011,
-    https://www.arpapress.com/Volumes/Vol6Issue4/IJRRAS_6_4_14.pdf
+  - L.J. Slutsky and C.W. Garland,
+    Physical Review 107(4):972-976, 1957,
+    https://doi.org/10.1103/PhysRev.107.972,
+    fit to Tab. I (T_min=100K, T_max=300K)
 
-C_11: 59.3e+9
-C_33: 61.5e+9
-C_44: 16.4e+9
-C_12: 25.7e+9
-C_13: 21.4e+9
+C_11: 59.50e+9
+C_11,T: -1.930e+7
+C_11,T^2: -1.215e+4
+
+C_33: 61.72e+9
+C_33,T: -2.175e+7
+C_33,T^2: -5.624e+3
+
+C_44: 16.46e+9
+C_44,T: -1.006e+7
+C_44,T^2: -7.692e+3
+
+C_12: 25.62e+9
+C_12,T: -2.216e+6
+C_12,T^2: -4.138e+3
+
+C_13: 21.46e+9
+C_13,T: -1.921e+6
+C_13,T^2: -4.283e+3
+
+T_ref: 293.15
diff --git a/examples/config/phase/mechanical/elastic/Hooke_Ni.yaml b/examples/config/phase/mechanical/elastic/Hooke_Ni.yaml
index 6bba784fb..bf63ae047 100644
--- a/examples/config/phase/mechanical/elastic/Hooke_Ni.yaml
+++ b/examples/config/phase/mechanical/elastic/Hooke_Ni.yaml
@@ -1,11 +1,21 @@
 type: Hooke
 
 references:
-  - J.P. Hirth and J. Lothe,
-    Theory of Dislocations, 1982,
-    John Wiley & Sons,
-    page 837
+  - G.A. Alers,
+    Journal of Physics and Chemistry of Solids 13(1-2):40-55, 1960,
+    https://doi.org/10.1016/0022-3697(60)90125-6,
+    fit to Tab. 2 (T_min=100K, T_max=700K)
 
-C_11: 246.5e+9
-C_12: 147.3e+9
-C_44: 124.7e+9
+C_11: 251.0e+9
+C_11,T: -4.998e+7
+C_11,T^2: -2.952e+4
+
+C_12: 150.0e+9
+C_12,T: -4.269e+6
+C_12,T^2: -6.429e+3
+
+C_44: 123.7e+9
+C_44,T: -3.618e+7
+C_44,T^2: -7.024e+3
+
+T_ref: 293.15
diff --git a/examples/config/phase/mechanical/elastic/Hooke_Ti.yaml b/examples/config/phase/mechanical/elastic/Hooke_Ti.yaml
index 79b7c04f7..983452cd9 100644
--- a/examples/config/phase/mechanical/elastic/Hooke_Ti.yaml
+++ b/examples/config/phase/mechanical/elastic/Hooke_Ti.yaml
@@ -1,12 +1,33 @@
 type: Hooke
 
 references:
-  - L. Wang et al.,
-    Acta Materialia 132:598-610, 2017,
-    https://doi.org/10.1016/j.actamat.2017.05.015
+  - E.S. Fisher and C.J. Renken,
+    Physical Review 135(2A):A482-A494, 1964,
+    https://doi.org/10.1103/PhysRev.135.A482,
+    fit to Tab. IV (T_min=150K, T_max=250K)
+  - H. Ogi et al.,
+    Acta Materialia 52(7):2075-2080, 2004,
+    https://doi.org/10.1016/j.actamat.2004.01.002,
+    fit to Fig. 3 (T_min=300K, T_max=900K)
 
-C_11: 162.4e+9
-C_33: 181.6e+9
-C_44: 47.2e+9
-C_12: 92.e+9
-C_13: 69.e+9
+C_11: 162.6e+9
+C_11,T: -6.150e+7
+C_11,T^2: -5.557e+2
+
+C_33: 183.3e+9
+C_33,T: -1.655e+07
+C_33,T^2: -1.022e+04
+
+C_44: 45.80e+9
+C_44,T: -2.936e+07
+C_44,T^2: 7.120e+02
+
+C_12: 89.97e+9
+C_12,T: 2.776e+6
+C_12,T^2: -2.389e+4
+
+C_13: 69.53e+9
+C_13,T: 1.057e+7
+C_13,T^2: -2.966e+3
+
+T_ref: 293.15
diff --git a/examples/config/phase/mechanical/elastic/Hooke_W.yaml b/examples/config/phase/mechanical/elastic/Hooke_W.yaml
index a1191f8c7..bb333d6af 100644
--- a/examples/config/phase/mechanical/elastic/Hooke_W.yaml
+++ b/examples/config/phase/mechanical/elastic/Hooke_W.yaml
@@ -1,10 +1,20 @@
 type: Hooke
 
 references:
-  - D. Cereceda et al.,
-    International Journal of Plasticity 78:242-265, 2016,
-    https://doi.org/10.1016/j.ijplas.2015.09.002
+  - F.H. Featherston and J.R. Nieghbours,
+    Physical Review 130(4):1324-1333,
+    https://doi.org/10.1103/PhysRev.130.1324,
+    fit to Tab. III (T_min=100K, T_max=300K)
 
-C_11: 523.e+9
-C_12: 202.e+9
-C_44: 161.e+9
+C_11: 523.6e+9
+C_11,T: -7.607e+7
+C_11,T^2: -1.551e+5
+
+C_12: 205.1e+9
+C_12,T: -2.843e+6
+
+C_44: 160.8e+9
+C_44,T: -1.057e+7
+C_44,T^2: 9.933e+3
+
+T_ref: 293.15
diff --git a/examples/config/phase/thermal/Al.yaml b/examples/config/phase/thermal/Al.yaml
index 485cc5a31..d2015a5b2 100644
--- a/examples/config/phase/thermal/Al.yaml
+++ b/examples/config/phase/thermal/Al.yaml
@@ -5,9 +5,9 @@ references:
     fit to Tab. 3.4.1 (RRR=1000, T_min=200K, T_max=900K)
   - https://www.engineeringtoolbox.com/specific-heat-metals-d_152.html
 
-K_11: 2.380e+02
-K_11,T: 2.068e-03
-K_11,T^2: -7.765e-05
+K_11: 2.380e+2
+K_11,T: 2.068e-3
+K_11,T^2: -7.765e-5
 
 T_ref: 293.15
 
diff --git a/examples/config/phase/thermal/Cu.yaml b/examples/config/phase/thermal/Cu.yaml
index 50e3fdc23..332ef7cc0 100644
--- a/examples/config/phase/thermal/Cu.yaml
+++ b/examples/config/phase/thermal/Cu.yaml
@@ -5,9 +5,9 @@ references:
     fit to Tab. 2.4.1 (RRR=1000, T_min=200K, T_max=1000K)
   - https://www.mit.edu/~6.777/matprops/copper.htm
 
-K_11: 4.039e+02
-K_11,T: -8.119e-02
-K_11,T^2: 1.454e-05
+K_11: 4.039e+2
+K_11,T: -8.119e-2
+K_11,T^2: 1.454e-5
 
 T_ref: 293.15
 
diff --git a/examples/config/phase/thermal/Fe.yaml b/examples/config/phase/thermal/Fe.yaml
index 7fa8902bb..a8e06ed04 100644
--- a/examples/config/phase/thermal/Fe.yaml
+++ b/examples/config/phase/thermal/Fe.yaml
@@ -5,9 +5,9 @@ references:
     fit to Tab. 4.4.1 (RRR=300, T_min=200K, T_max=1000K)
   - https://www.engineeringtoolbox.com/specific-heat-metals-d_152.html
 
-K_11: 8.055e+01
-K_11,T: -1.051e-01
-K_11,T^2: 5.464e-05
+K_11: 8.055e+1
+K_11,T: -1.051e-1
+K_11,T^2: 5.464e-5
 
 T_ref: 293.15
 
diff --git a/examples/config/phase/thermal/Ni.yaml b/examples/config/phase/thermal/Ni.yaml
new file mode 100644
index 000000000..d71c15a3f
--- /dev/null
+++ b/examples/config/phase/thermal/Ni.yaml
@@ -0,0 +1,14 @@
+references:
+  - Y.S. Touloukian et al.,
+    TPRC Data Series Volume 1. Thermal conductivity - metallic elements and alloys,
+    IFI/Plenum, 1970,
+    fit to Tab. 35R (T_min=150K, T_max=500K)
+  - https://www.engineeringtoolbox.com/specific-heat-metals-d_152.html
+
+K_11: 9.132e+1
+K_11,T: -1.525e-1
+K_11,T^2: 3.053e-4
+
+T_ref: 293.15
+
+C_p: 440.0
diff --git a/examples/config/phase/thermal/W.yaml b/examples/config/phase/thermal/W.yaml
index 2f9ef56e8..fb01c285a 100644
--- a/examples/config/phase/thermal/W.yaml
+++ b/examples/config/phase/thermal/W.yaml
@@ -5,9 +5,9 @@ references:
     fit to Tab. 5.4.1 (RRR=300, T_min=200K, T_max=1000K)
   - https://www.mit.edu/~6.777/matprops/tungsten.htm
 
-K_11: 1.758e+02
-K_11,T: -1.605e-01
-K_11,T^2: 1.160e-04
+K_11: 1.758e+2
+K_11,T: -1.605e-1
+K_11,T^2: 1.160e-4
 
 T_ref: 293.15
 

From ba16ea21a0a6d133fcaa7581afd417e4f47fd8c2 Mon Sep 17 00:00:00 2001
From: Martin Diehl <mail@martin-diehl.net>
Date: Sun, 13 Feb 2022 14:48:15 +0100
Subject: [PATCH 54/72] avoid overfitting

there are only 3 data points for C_13, with one close to 0K. Leave this
point out and fit only a 1st order polynomial
---
 .../config/phase/mechanical/elastic/Hooke_Sn-beta.yaml     | 7 +++----
 1 file changed, 3 insertions(+), 4 deletions(-)

diff --git a/examples/config/phase/mechanical/elastic/Hooke_Sn-beta.yaml b/examples/config/phase/mechanical/elastic/Hooke_Sn-beta.yaml
index a49c246f9..57cd2913c 100644
--- a/examples/config/phase/mechanical/elastic/Hooke_Sn-beta.yaml
+++ b/examples/config/phase/mechanical/elastic/Hooke_Sn-beta.yaml
@@ -4,7 +4,7 @@ references:
   - J.A. Rayne and B.S. Chandrasekhar,
     Physical Review 120(5):1658-1663, 1960,
     https://doi.org/10.1103/PhysRev.120.1658,
-    fit to Fig. 2 and Tab. IV (C_13)
+    fit to Fig. 2 (T_min=40K, T_max=300K) and Tab. IV (C_13, T_min=77K, T_max=300K)
 
 C_11: 72.89e+9
 C_11,T: -4.479e+7
@@ -14,9 +14,8 @@ C_12: 59.27e+9
 C_12,T: 1.110e+7
 C_12,T^2: 1.300e+4
 
-C_13: 35.97e+9
-C_13,T: -2.638e+7
-C_13,T^2: -1.123e+5
+C_13: 35.80e+9
+C_13,T: -2.870e+6
 
 C_33: 88.77e+10
 C_33,T: -5.361e+7

From e3a64ae4ff33867827611a3bd481db82aa583e4b Mon Sep 17 00:00:00 2001
From: Martin Diehl <mail@martin-diehl.net>
Date: Sun, 13 Feb 2022 14:57:01 +0100
Subject: [PATCH 55/72] don't fit close to 0K

cryogenic temperatures are normally not of interest, avoid considering
the strongly curved region below 80K in the fit gives probably better
extrapolation properties for T>300K
---
 .../mechanical/elastic/Hooke_Sn-beta.yaml     | 28 +++++++++----------
 1 file changed, 14 insertions(+), 14 deletions(-)

diff --git a/examples/config/phase/mechanical/elastic/Hooke_Sn-beta.yaml b/examples/config/phase/mechanical/elastic/Hooke_Sn-beta.yaml
index 57cd2913c..a208c3aec 100644
--- a/examples/config/phase/mechanical/elastic/Hooke_Sn-beta.yaml
+++ b/examples/config/phase/mechanical/elastic/Hooke_Sn-beta.yaml
@@ -4,29 +4,29 @@ references:
   - J.A. Rayne and B.S. Chandrasekhar,
     Physical Review 120(5):1658-1663, 1960,
     https://doi.org/10.1103/PhysRev.120.1658,
-    fit to Fig. 2 (T_min=40K, T_max=300K) and Tab. IV (C_13, T_min=77K, T_max=300K)
+    fit to Fig. 2 (T_min=100K, T_max=300K) and Tab. IV (C_13, T_min=77K, T_max=300K)
 
-C_11: 72.89e+9
-C_11,T: -4.479e+7
-C_11,T^2: -3.149e+4
+C_11: 72.90e+9
+C_11,T: -4.399e+7
+C_11,T^2: -2.645e+4
 
 C_12: 59.27e+9
-C_12,T: 1.110e+7
-C_12,T^2: 1.300e+4
+C_12,T: 1.058e+7
+C_12,T^2: 1.002e+4
 
 C_13: 35.80e+9
 C_13,T: -2.870e+6
 
-C_33: 88.77e+10
-C_33,T: -5.361e+7
-C_33,T^2: -2.770e+3
+C_33: 88.78e+9
+C_33,T: -5.250e+7
+C_33,T^2: 3.546e+3
 
 C_44: 22.26e+9
-C_44,T: -1.994e+7
-C_44,T^2: -9.519e+3
+C_44,T: -1.982e+7
+C_44,T^2: -8.711e+3
 
-C_66: 24.17e+9
-C_66,T: -1.919e+7
-C_66,T^2: -1.161e+4
+C_66: 24.18e+9
+C_66,T: -1.806e+7
+C_66,T^2: -4.112e+3
 
 T_ref: 293.15

From bba105c2a824aae9133e3809fa129405d6f99549 Mon Sep 17 00:00:00 2001
From: Martin Diehl <mail@martin-diehl.net>
Date: Sun, 13 Feb 2022 17:58:51 +0100
Subject: [PATCH 56/72] re-fit, documented details

---
 .../phase/mechanical/elastic/Hooke_Al.yaml    | 26 ++++++++++---------
 1 file changed, 14 insertions(+), 12 deletions(-)

diff --git a/examples/config/phase/mechanical/elastic/Hooke_Al.yaml b/examples/config/phase/mechanical/elastic/Hooke_Al.yaml
index 97d45e62f..3550449a3 100644
--- a/examples/config/phase/mechanical/elastic/Hooke_Al.yaml
+++ b/examples/config/phase/mechanical/elastic/Hooke_Al.yaml
@@ -3,21 +3,23 @@ type: Hooke
 references:
   - G.N. Kamm and G.A. Alers,
     Journal of Applied Physics 35:327-330, 1964,
-    https://doi.org/10.1063/1.1713309
+    https://doi.org/10.1063/1.1713309,
+    fit to Tab. I (T_min=100K, T_max=300K)
   - D. Gerlich and E.S. Fisher,
     Journal of Physics and Chemistry of Solids 30:1197-1205, 1969
-    https://doi.org/10.1016/0022-3697(69)90377-1
+    https://doi.org/10.1016/0022-3697(69)90377-1,
+    fit to Tab. 2 (T_min=293K, T_max=900K)
 
-C_11: 106.1e+9
-C_11,T: -359.3e+5
-C_11,T^2: -152.7e+2
+C_11: 106.9e+9
+C_11,T: -3.685e+7
+C_11,T^2: -1.016e+4
 
-C_12: 57.83e+9
-C_12,T: -781.6e+4
-C_12,T^2: -551.3e+1
+C_12: 60.55e+9
+C_12,T: -8.307e+6
+C_12,T^2: -4.353e+3
 
-C_44: 24.31e+9
-C_44,T: -142.9e+5
-C_44,T^2: -404.6e+1
+C_44: 28.37e+9
+C_44,T: -1.418e+7
+C_44,T^2: -3.253e+3
 
-T_ref: 300
+T_ref: 293.15

From e210a9873d33783289a33349164e689f49a20ff6 Mon Sep 17 00:00:00 2001
From: Test User <damask_user@mpie.de>
Date: Mon, 14 Feb 2022 02:21:46 +0100
Subject: [PATCH 57/72] [skip ci] updated version information after successful
 test of v3.0.0-alpha5-624-g26979da58

---
 python/damask/VERSION | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/python/damask/VERSION b/python/damask/VERSION
index 00113e2f3..90c1162f3 100644
--- a/python/damask/VERSION
+++ b/python/damask/VERSION
@@ -1 +1 @@
-v3.0.0-alpha5-608-g3e8d1a60d
+v3.0.0-alpha5-624-g26979da58

From 0300912b3032eb7c1a309e620de01c0efecb4b3a Mon Sep 17 00:00:00 2001
From: Philip Eisenlohr <eisenlohr@egr.msu.edu>
Date: Sun, 13 Feb 2022 22:00:48 -0500
Subject: [PATCH 58/72] Table.__eq__ for proper comparison; logical masks for
 slicing now work

---
 python/damask/_table.py    | 27 ++++++++++++++++++---------
 python/tests/test_Table.py |  6 +++++-
 2 files changed, 23 insertions(+), 10 deletions(-)

diff --git a/python/damask/_table.py b/python/damask/_table.py
index 1572c4f76..81c23e73b 100644
--- a/python/damask/_table.py
+++ b/python/damask/_table.py
@@ -44,6 +44,13 @@ class Table:
         return '\n'.join(['# '+c for c in self.comments])+'\n'+data_repr
 
 
+    def __eq__(self,
+               other: object) -> bool:
+        """Compare to other Table."""
+        return NotImplemented if not isinstance(other,Table) else \
+               self.shapes == other.shapes and self.data.equals(other.data)
+
+
     def __getitem__(self,
                     item: Union[slice, Tuple[slice, ...]]) -> 'Table':
         """
@@ -75,20 +82,22 @@ class Table:
            colB  colA
         0     1     0
         2     7     6
-        >>> tbl[1:2,'colB']
+        >>> tbl[[True,False,False,True],'colB']
            colB
-        1     4
-        2     7
+        0     1
+        3    10
 
         """
-        item = (item,slice(None,None,None)) if isinstance(item,slice) else \
-               item if isinstance(item[0],slice) else \
-               (slice(None,None,None),item)
-        sliced = self.data.loc[item]
-        cols = np.array(sliced.columns if isinstance(sliced,pd.core.frame.DataFrame) else [item[1]])
+        item_ = (item,slice(None,None,None)) if isinstance(item,(slice,np.ndarray)) else \
+                (np.array(item),slice(None,None,None)) if isinstance(item,list) and np.array(item).dtype == np.bool_ else \
+                (np.array(item[0]),item[1]) if isinstance(item[0],list) else \
+                item if isinstance(item[0],(slice,np.ndarray)) else \
+                (slice(None,None,None),item)
+        sliced = self.data.loc[item_]
+        cols = np.array(sliced.columns if isinstance(sliced,pd.core.frame.DataFrame) else [item_[1]])
         _,idx = np.unique(cols,return_index=True)
         return self.__class__(data=sliced,
-                              shapes = {k:self.shapes[k] for k in cols[np.sort(idx)]},
+                              shapes={k:self.shapes[k] for k in cols[np.sort(idx)]},
                               comments=self.comments)
 
 
diff --git a/python/tests/test_Table.py b/python/tests/test_Table.py
index 62eb6d63b..1f89026a3 100644
--- a/python/tests/test_Table.py
+++ b/python/tests/test_Table.py
@@ -59,10 +59,14 @@ class TestTable:
 
     @pytest.mark.parametrize('N',[1,3,4])
     def test_slice(self,default,N):
+        mask = np.random.choice([True,False],len(default))
         assert len(default[:N]) == 1+N
         assert len(default[:N,['F','s']]) == 1+N
+        assert len(default[mask,['F','s']]) == np.count_nonzero(mask)
+        assert default[mask,['F','s']] == default[mask][['F','s']] == default[['F','s']][mask]
+        assert default[np.logical_not(mask),['F','s']] != default[mask][['F','s']]
         assert default[N:].get('F').shape == (len(default)-N,3,3)
-        assert (default[:N,['v','s']].data == default['v','s'][:N].data).all().all()
+        assert default[:N,['v','s']].data.equals(default['v','s'][:N].data)
 
     @pytest.mark.parametrize('mode',['str','path'])
     def test_write_read(self,default,tmp_path,mode):

From ac4beea14b718b5c86ebc59356e614dbba0c1a42 Mon Sep 17 00:00:00 2001
From: Martin Diehl <mail@martin-diehl.net>
Date: Sun, 13 Feb 2022 21:00:21 +0100
Subject: [PATCH 59/72] use precalculated dyad

---
 src/grid/spectral_utilities.f90 | 22 ++++++++++------------
 1 file changed, 10 insertions(+), 12 deletions(-)

diff --git a/src/grid/spectral_utilities.f90 b/src/grid/spectral_utilities.f90
index 34a976644..28ff0f8b3 100644
--- a/src/grid/spectral_utilities.f90
+++ b/src/grid/spectral_utilities.f90
@@ -372,7 +372,7 @@ subroutine utilities_updateGamma(C)
   C_ref = C
 
   if (.not. num%memory_efficient) then
-    gamma_hat =  cmplx(0.0_pReal,0.0_pReal,pReal)                                                   ! for the singular point and any non invertible A
+    gamma_hat = cmplx(0.0_pReal,0.0_pReal,pReal)                                                    ! for the singular point and any non invertible A
     do k = cells3Offset+1, cells3Offset+cells3; do j = 1, cells(2); do i = 1, grid1Red
       if (any([i,j,k] /= 1)) then                                                                   ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
         do concurrent (l = 1:3, m = 1:3)
@@ -387,8 +387,7 @@ subroutine utilities_updateGamma(C)
           call math_invert(A_inv, err, A)
           temp33_complex = cmplx(A_inv(1:3,1:3),A_inv(1:3,4:6),pReal)
           do concurrent(l=1:3, m=1:3, n=1:3, o=1:3)
-            gamma_hat(l,m,n,o,i,j,k-cells3Offset) = temp33_complex(l,n)* &
-                                                    conjg(-xi1st(o,i,j,k-cells3Offset))*xi1st(m,i,j,k-cells3Offset)
+            gamma_hat(l,m,n,o,i,j,k-cells3Offset) = temp33_complex(l,n) * xiDyad_cmplx(o,m)
           end do
         end if
       end if
@@ -507,7 +506,7 @@ subroutine utilities_fourierGammaConvolution(fieldAim)
           call math_invert(A_inv, err, A)
           temp33_complex = cmplx(A_inv(1:3,1:3),A_inv(1:3,4:6),pReal)
           do concurrent(l=1:3, m=1:3, n=1:3, o=1:3)
-            gamma_hat(l,m,n,o,1,1,1) =  temp33_complex(l,n)*conjg(-xi1st(o,i,j,k))*xi1st(m,i,j,k)
+            gamma_hat(l,m,n,o,1,1,1) = temp33_complex(l,n)*xiDyad_cmplx(o,m)
           end do
         else
           gamma_hat(1:3,1:3,1:3,1:3,1,1,1) = cmplx(0.0_pReal,0.0_pReal,pReal)
@@ -521,7 +520,7 @@ subroutine utilities_fourierGammaConvolution(fieldAim)
   else memoryEfficient
     do k = 1, cells3;  do j = 1, cells(2);  do i = 1,grid1Red
       do concurrent(l = 1:3, m = 1:3)
-        temp33_Complex(l,m) = sum(gamma_hat(l,m,1:3,1:3,i,j,k) * tensorField_fourier(1:3,1:3,i,j,k))
+        temp33_Complex(l,m) = sum(gamma_hat(l,m,1:3,1:3,i,j,k)*tensorField_fourier(1:3,1:3,i,j,k))
       end do
       tensorField_fourier(1:3,1:3,i,j,k) = temp33_Complex
     end do; end do; end do
@@ -884,11 +883,10 @@ pure function utilities_calculateRate(heterogeneous,field0,field,dt,avRate)
   real(pReal),             dimension(3,3,cells(1),cells(2),cells3) :: &
     utilities_calculateRate
 
-  if (heterogeneous) then
-    utilities_calculateRate = (field-field0) / dt
-  else
-    utilities_calculateRate = spread(spread(spread(avRate,3,cells(1)),4,cells(2)),5,cells3)
-  endif
+
+  utilities_calculateRate = merge((field-field0) / dt, &
+                                  spread(spread(spread(avRate,3,cells(1)),4,cells(2)),5,cells3), &
+                                  heterogeneous)
 
 end function utilities_calculateRate
 
@@ -1041,7 +1039,7 @@ subroutine utilities_updateCoords(F)
   rank_b = modulo(worldrank-1_MPI_INTEGER_KIND,worldsize)
 
   ! send bottom layer to process below
-  call MPI_Isend(IPfluct_padded(:,:,:,2),      c,MPI_DOUBLE,rank_b,0_MPI_INTEGER_KIND,MPI_COMM_WORLD,request(1),err_MPI)
+  call MPI_Isend(IPfluct_padded(:,:,:,2),       c,MPI_DOUBLE,rank_b,0_MPI_INTEGER_KIND,MPI_COMM_WORLD,request(1),err_MPI)
   if (err_MPI /= 0_MPI_INTEGER_KIND) error stop 'MPI error'
   call MPI_Irecv(IPfluct_padded(:,:,:,cells3+2),c,MPI_DOUBLE,rank_t,0_MPI_INTEGER_KIND,MPI_COMM_WORLD,request(2),err_MPI)
   if (err_MPI /= 0_MPI_INTEGER_KIND) error stop 'MPI error'
@@ -1049,7 +1047,7 @@ subroutine utilities_updateCoords(F)
   ! send top layer to process above
   call MPI_Isend(IPfluct_padded(:,:,:,cells3+1),c,MPI_DOUBLE,rank_t,1_MPI_INTEGER_KIND,MPI_COMM_WORLD,request(3),err_MPI)
   if (err_MPI /= 0_MPI_INTEGER_KIND) error stop 'MPI error'
-  call MPI_Irecv(IPfluct_padded(:,:,:,1),      c,MPI_DOUBLE,rank_b,1_MPI_INTEGER_KIND,MPI_COMM_WORLD,request(4),err_MPI)
+  call MPI_Irecv(IPfluct_padded(:,:,:,1),       c,MPI_DOUBLE,rank_b,1_MPI_INTEGER_KIND,MPI_COMM_WORLD,request(4),err_MPI)
   if (err_MPI /= 0_MPI_INTEGER_KIND) error stop 'MPI error'
 
   call MPI_Waitall(4,request,status,err_MPI)

From 1b08f90d6c8911e1b2f171ff0319c687b7ca820a Mon Sep 17 00:00:00 2001
From: Philip Eisenlohr <eisenlohr@egr.msu.edu>
Date: Sun, 13 Feb 2022 23:54:16 -0500
Subject: [PATCH 60/72] allow constant (non-label) value in cm.from_table()
 keys

---
 python/damask/_configmaterial.py    | 22 +++++++++++++++++++---
 python/tests/test_ConfigMaterial.py | 12 ++++++++++++
 2 files changed, 31 insertions(+), 3 deletions(-)

diff --git a/python/damask/_configmaterial.py b/python/damask/_configmaterial.py
index 01d85f6a4..250b52e7e 100644
--- a/python/damask/_configmaterial.py
+++ b/python/damask/_configmaterial.py
@@ -178,8 +178,9 @@ class ConfigMaterial(Config):
         table : damask.Table
             Table that contains material information.
         **kwargs
-            Keyword arguments where the key is the name and the value specifies
-            the label of the data column in the table.
+            Keyword arguments where the key is the property name and
+            the value specifies either the label of the data column in the table
+            or a constant value.
 
         Returns
         -------
@@ -211,8 +212,23 @@ class ConfigMaterial(Config):
         homogenization: {}
         phase: {}
 
+        >>> cm.from_table(t,O='qu',phase='phase',homogenization='SX')
+        material:
+          - constituents:
+              - O: [0.19, 0.8, 0.24, -0.51]
+                v: 1.0
+                phase: Aluminum
+            homogenization: SX
+          - constituents:
+              - O: [0.8, 0.19, 0.24, -0.51]
+                v: 1.0
+                phase: Steel
+            homogenization: SX
+        homogenization: {}
+        phase: {}
+
         """
-        kwargs_ = {k:table.get(v) for k,v in kwargs.items()}
+        kwargs_ = {k:table.get(v) if v in table.labels else np.atleast_2d([v]*len(table)).T for k,v in kwargs.items()}
 
         _,idx = np.unique(np.hstack(list(kwargs_.values())),return_index=True,axis=0)
         idx = np.sort(idx)
diff --git a/python/tests/test_ConfigMaterial.py b/python/tests/test_ConfigMaterial.py
index a713b636f..b8b5df52a 100644
--- a/python/tests/test_ConfigMaterial.py
+++ b/python/tests/test_ConfigMaterial.py
@@ -96,6 +96,18 @@ class TestConfigMaterial:
         for i,m in enumerate(c['material']):
             assert m['homogenization'] == 1 and (m['constituents'][0]['O'] == [1,0,1,1]).all()
 
+    def test_from_table_with_constant(self):
+        N = np.random.randint(3,10)
+        a = np.vstack((np.hstack((np.arange(N),np.arange(N)[::-1])),
+                       np.ones(N*2),np.zeros(N*2),np.ones(N*2),np.ones(N*2),
+                       np.ones(N*2),
+                      )).T
+        t = Table(a,{'varying':1,'constant':4,'ones':1})
+        c = ConfigMaterial.from_table(t,**{'phase':'varying','O':'constant','homogenization':1})
+        assert len(c['material']) == N
+        for i,m in enumerate(c['material']):
+            assert m['homogenization'] == 1 and (m['constituents'][0]['O'] == [1,0,1,1]).all()
+
     @pytest.mark.parametrize('N,n,kw',[
                                         (1,1,{'phase':'Gold',
                                               'O':[1,0,0,0],

From 0008ad1bf8fe7eea6728ab742bd2480b8072a33e Mon Sep 17 00:00:00 2001
From: Martin Diehl <mail@martin-diehl.net>
Date: Mon, 14 Feb 2022 05:57:48 +0100
Subject: [PATCH 61/72] easier to understand

---
 src/grid/spectral_utilities.f90 | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/src/grid/spectral_utilities.f90 b/src/grid/spectral_utilities.f90
index 28ff0f8b3..08d983c8a 100644
--- a/src/grid/spectral_utilities.f90
+++ b/src/grid/spectral_utilities.f90
@@ -508,13 +508,13 @@ subroutine utilities_fourierGammaConvolution(fieldAim)
           do concurrent(l=1:3, m=1:3, n=1:3, o=1:3)
             gamma_hat(l,m,n,o,1,1,1) = temp33_complex(l,n)*xiDyad_cmplx(o,m)
           end do
+          do concurrent(l = 1:3, m = 1:3)
+            temp33_Complex(l,m) = sum(gamma_hat(l,m,1:3,1:3,1,1,1)*tensorField_fourier(1:3,1:3,i,j,k))
+          end do
+          tensorField_fourier(1:3,1:3,i,j,k) = temp33_Complex
         else
-          gamma_hat(1:3,1:3,1:3,1:3,1,1,1) = cmplx(0.0_pReal,0.0_pReal,pReal)
+          tensorField_fourier(1:3,1:3,i,j,k) = cmplx(0.0_pReal,0.0_pReal,pReal)
         end if
-        do concurrent(l = 1:3, m = 1:3)
-          temp33_Complex(l,m) = sum(gamma_hat(l,m,1:3,1:3,1,1,1)*tensorField_fourier(1:3,1:3,i,j,k))
-        end do
-        tensorField_fourier(1:3,1:3,i,j,k) = temp33_Complex
       end if
     end do; end do; end do
   else memoryEfficient

From 61e11a0529f8f192b411304a8d382feb59532e71 Mon Sep 17 00:00:00 2001
From: Martin Diehl <mail@martin-diehl.net>
Date: Mon, 14 Feb 2022 07:58:15 +0100
Subject: [PATCH 62/72] use openMP for operations in Fourier space

---
 src/grid/spectral_utilities.f90 | 65 ++++++++++++++++++++-------------
 1 file changed, 39 insertions(+), 26 deletions(-)

diff --git a/src/grid/spectral_utilities.f90 b/src/grid/spectral_utilities.f90
index 08d983c8a..418f83b05 100644
--- a/src/grid/spectral_utilities.f90
+++ b/src/grid/spectral_utilities.f90
@@ -362,7 +362,7 @@ end subroutine spectral_utilities_init
 subroutine utilities_updateGamma(C)
 
   real(pReal), intent(in), dimension(3,3,3,3) :: C                                                  !< input stiffness to store as reference stiffness
-  complex(pReal),              dimension(3,3) :: temp33_complex, xiDyad_cmplx
+  complex(pReal),              dimension(3,3) :: temp33_cmplx, xiDyad_cmplx
   real(pReal),                 dimension(6,6) :: A, A_inv
   integer :: &
     i, j, k, &
@@ -373,25 +373,27 @@ subroutine utilities_updateGamma(C)
 
   if (.not. num%memory_efficient) then
     gamma_hat = cmplx(0.0_pReal,0.0_pReal,pReal)                                                    ! for the singular point and any non invertible A
+    !$OMP PARALLEL DO PRIVATE(l,m,n,o,temp33_cmplx,xiDyad_cmplx,A,A_inv,err)
     do k = cells3Offset+1, cells3Offset+cells3; do j = 1, cells(2); do i = 1, grid1Red
       if (any([i,j,k] /= 1)) then                                                                   ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
         do concurrent (l = 1:3, m = 1:3)
           xiDyad_cmplx(l,m) = conjg(-xi1st(l,i,j,k-cells3Offset))*xi1st(m,i,j,k-cells3Offset)
         end do
         do concurrent(l = 1:3, m = 1:3)
-          temp33_complex(l,m) = sum(cmplx(C_ref(l,1:3,m,1:3),0.0_pReal)*xiDyad_cmplx)
+          temp33_cmplx(l,m) = sum(cmplx(C_ref(l,1:3,m,1:3),0.0_pReal)*xiDyad_cmplx)
         end do
-        A(1:3,1:3) = temp33_complex%re; A(4:6,4:6) =  temp33_complex%re
-        A(1:3,4:6) = temp33_complex%im; A(4:6,1:3) = -temp33_complex%im
+        A(1:3,1:3) = temp33_cmplx%re; A(4:6,4:6) =  temp33_cmplx%re
+        A(1:3,4:6) = temp33_cmplx%im; A(4:6,1:3) = -temp33_cmplx%im
         if (abs(math_det33(A(1:3,1:3))) > 1e-16) then
           call math_invert(A_inv, err, A)
-          temp33_complex = cmplx(A_inv(1:3,1:3),A_inv(1:3,4:6),pReal)
+          temp33_cmplx = cmplx(A_inv(1:3,1:3),A_inv(1:3,4:6),pReal)
           do concurrent(l=1:3, m=1:3, n=1:3, o=1:3)
-            gamma_hat(l,m,n,o,i,j,k-cells3Offset) = temp33_complex(l,n) * xiDyad_cmplx(o,m)
+            gamma_hat(l,m,n,o,i,j,k-cells3Offset) = temp33_cmplx(l,n) * xiDyad_cmplx(o,m)
           end do
         end if
       end if
     end do; end do; end do
+    !$OMP END PARALLEL DO
   endif
 
 end subroutine utilities_updateGamma
@@ -477,7 +479,7 @@ end subroutine utilities_FFTvectorBackward
 subroutine utilities_fourierGammaConvolution(fieldAim)
 
   real(pReal), intent(in), dimension(3,3) :: fieldAim                                               !< desired average value of the field after convolution
-  complex(pReal),          dimension(3,3) :: temp33_complex, xiDyad_cmplx
+  complex(pReal),          dimension(3,3) :: temp33_cmplx, xiDyad_cmplx
   real(pReal),             dimension(6,6) :: A, A_inv
 
   integer :: &
@@ -492,38 +494,42 @@ subroutine utilities_fourierGammaConvolution(fieldAim)
 !--------------------------------------------------------------------------------------------------
 ! do the actual spectral method calculation (mechanical equilibrium)
   memoryEfficient: if (num%memory_efficient) then
+    !$OMP PARALLEL DO PRIVATE(l,m,n,o,temp33_cmplx,xiDyad_cmplx,A,A_inv,err,gamma_hat)
     do k = 1, cells3; do j = 1, cells(2); do i = 1, grid1Red
       if (any([i,j,k+cells3Offset] /= 1)) then                                                      ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
         do concurrent(l = 1:3, m = 1:3)
           xiDyad_cmplx(l,m) = conjg(-xi1st(l,i,j,k))*xi1st(m,i,j,k)
         end do
         do concurrent(l = 1:3, m = 1:3)
-          temp33_complex(l,m) = sum(cmplx(C_ref(l,1:3,m,1:3),0.0_pReal)*xiDyad_cmplx)
+          temp33_cmplx(l,m) = sum(cmplx(C_ref(l,1:3,m,1:3),0.0_pReal)*xiDyad_cmplx)
         end do
-        A(1:3,1:3) = temp33_complex%re; A(4:6,4:6) =  temp33_complex%re
-        A(1:3,4:6) = temp33_complex%im; A(4:6,1:3) = -temp33_complex%im
+        A(1:3,1:3) = temp33_cmplx%re; A(4:6,4:6) =  temp33_cmplx%re
+        A(1:3,4:6) = temp33_cmplx%im; A(4:6,1:3) = -temp33_cmplx%im
         if (abs(math_det33(A(1:3,1:3))) > 1e-16) then
           call math_invert(A_inv, err, A)
-          temp33_complex = cmplx(A_inv(1:3,1:3),A_inv(1:3,4:6),pReal)
+          temp33_cmplx = cmplx(A_inv(1:3,1:3),A_inv(1:3,4:6),pReal)
           do concurrent(l=1:3, m=1:3, n=1:3, o=1:3)
-            gamma_hat(l,m,n,o,1,1,1) = temp33_complex(l,n)*xiDyad_cmplx(o,m)
+            gamma_hat(l,m,n,o,1,1,1) = temp33_cmplx(l,n)*xiDyad_cmplx(o,m)
           end do
           do concurrent(l = 1:3, m = 1:3)
-            temp33_Complex(l,m) = sum(gamma_hat(l,m,1:3,1:3,1,1,1)*tensorField_fourier(1:3,1:3,i,j,k))
+            temp33_cmplx(l,m) = sum(gamma_hat(l,m,1:3,1:3,1,1,1)*tensorField_fourier(1:3,1:3,i,j,k))
           end do
-          tensorField_fourier(1:3,1:3,i,j,k) = temp33_Complex
+          tensorField_fourier(1:3,1:3,i,j,k) = temp33_cmplx
         else
           tensorField_fourier(1:3,1:3,i,j,k) = cmplx(0.0_pReal,0.0_pReal,pReal)
         end if
       end if
     end do; end do; end do
+    !$OMP END PARALLEL DO
   else memoryEfficient
+    !$OMP PARALLEL DO PRIVATE(l,m,temp33_cmplx)
     do k = 1, cells3;  do j = 1, cells(2);  do i = 1,grid1Red
       do concurrent(l = 1:3, m = 1:3)
-        temp33_Complex(l,m) = sum(gamma_hat(l,m,1:3,1:3,i,j,k)*tensorField_fourier(1:3,1:3,i,j,k))
+        temp33_cmplx(l,m) = sum(gamma_hat(l,m,1:3,1:3,i,j,k)*tensorField_fourier(1:3,1:3,i,j,k))
       end do
-      tensorField_fourier(1:3,1:3,i,j,k) = temp33_Complex
+      tensorField_fourier(1:3,1:3,i,j,k) = temp33_cmplx
     end do; end do; end do
+    !$OMP END PARALLEL DO
   end if memoryEfficient
 
   if (cells3Offset == 0) tensorField_fourier(1:3,1:3,1,1,1) = cmplx(fieldAim/wgt,0.0_pReal,pReal)
@@ -543,12 +549,14 @@ subroutine utilities_fourierGreenConvolution(D_ref, mu_ref, Delta_t)
 
 !--------------------------------------------------------------------------------------------------
 ! do the actual spectral method calculation
+  !$OMP PARALLEL DO PRIVATE(GreenOp_hat)
   do k = 1, cells3; do j = 1, cells(2) ;do i = 1, grid1Red
     GreenOp_hat = cmplx(1.0_pReal,0.0_pReal,pReal) &
                 / (cmplx(mu_ref,0.0_pReal,pReal) + cmplx(Delta_t,0.0_pReal) &
                    * sum(conjg(xi1st(1:3,i,j,k))* matmul(cmplx(D_ref,0.0_pReal),xi1st(1:3,i,j,k))))
     scalarField_fourier(i,j,k) = scalarField_fourier(i,j,k)*GreenOp_hat
   enddo; enddo; enddo
+  !$OMP END PARALLEL DO
 
 end subroutine utilities_fourierGreenConvolution
 
@@ -735,9 +743,10 @@ subroutine utilities_fourierScalarGradient()
 
   integer :: i, j, k
 
+
   do k = 1, cells3;  do j = 1, cells(2);  do i = 1,grid1Red
     vectorField_fourier(1:3,i,j,k) = scalarField_fourier(i,j,k)*xi1st(1:3,i,j,k)                    ! ToDo: no -conjg?
-  enddo; enddo; enddo
+  end do; end do; end do
 
 end subroutine utilities_fourierScalarGradient
 
@@ -747,11 +756,9 @@ end subroutine utilities_fourierScalarGradient
 !--------------------------------------------------------------------------------------------------
 subroutine utilities_fourierVectorDivergence()
 
-  integer :: i, j, k
 
-  do k = 1, cells3;  do j = 1, cells(2);  do i = 1,grid1Red
-    scalarField_fourier(i,j,k) = sum(vectorField_fourier(1:3,i,j,k)*conjg(-xi1st(1:3,i,j,k)))
-  enddo; enddo; enddo
+  scalarField_fourier(1:grid1Red,1:cells(2),1:cells3) = sum(vectorField_fourier(1:3,1:grid1Red,1:cells(2),1:cells3) &
+                                                            *conjg(-xi1st))
 
 end subroutine utilities_fourierVectorDivergence
 
@@ -763,11 +770,12 @@ subroutine utilities_fourierVectorGradient()
 
   integer :: i, j, k, m, n
 
+
   do k = 1, cells3;  do j = 1, cells(2);  do i = 1,grid1Red
     do m = 1, 3; do n = 1, 3
       tensorField_fourier(m,n,i,j,k) = vectorField_fourier(m,i,j,k)*xi1st(n,i,j,k)
-    enddo; enddo
-  enddo; enddo; enddo
+    end do; end do
+  end do; end do; end do
 
 end subroutine utilities_fourierVectorGradient
 
@@ -779,9 +787,10 @@ subroutine utilities_fourierTensorDivergence()
 
   integer :: i, j, k
 
+
   do k = 1, cells3;  do j = 1, cells(2);  do i = 1,grid1Red
     vectorField_fourier(:,i,j,k) = matmul(tensorField_fourier(:,:,i,j,k),conjg(-xi1st(:,i,j,k)))
-  enddo; enddo; enddo
+  end do; end do; end do
 
 end subroutine utilities_fourierTensorDivergence
 
@@ -978,6 +987,7 @@ end function utilities_getFreqDerivative
 subroutine utilities_updateCoords(F)
 
   real(pReal),   dimension(3,3,cells(1),cells(2),cells3), intent(in) :: F
+
   real(pReal),   dimension(3,  cells(1),cells(2),cells3)             :: IPcoords
   real(pReal),   dimension(3,  cells(1),cells(2),cells3+2)           :: IPfluct_padded              ! Fluctuations of cell center displacement (padded along z for MPI)
   real(pReal),   dimension(3,  cells(1)+1,cells(2)+1,cells3+1)       :: nodeCoords
@@ -1008,20 +1018,23 @@ subroutine utilities_updateCoords(F)
                         1, 1, 1, &
                         0, 1, 1  ], [3,8])
 
+
   step = geomSize/real(cells, pReal)
  !--------------------------------------------------------------------------------------------------
  ! integration in Fourier space to get fluctuations of cell center discplacements
   tensorField_real(1:3,1:3,1:cells(1),1:cells(2),1:cells3) = F
   call utilities_FFTtensorForward()
 
+  !$OMP PARALLEL DO
   do k = 1, cells3; do j = 1, cells(2); do i = 1, grid1Red
     if (any([i,j,k+cells3Offset] /= 1)) then
       vectorField_fourier(1:3,i,j,k) = matmul(tensorField_fourier(1:3,1:3,i,j,k),xi2nd(1:3,i,j,k)) &
                                      / sum(conjg(-xi2nd(1:3,i,j,k))*xi2nd(1:3,i,j,k)) * cmplx(wgt,0.0,pReal)
     else
       vectorField_fourier(1:3,i,j,k) = cmplx(0.0,0.0,pReal)
-    endif
-  enddo; enddo; enddo
+    end if
+  end do; end do; end do
+  !$OMP END PARALLEL DO
 
   call fftw_mpi_execute_dft_c2r(planVectorBack,vectorField_fourier,vectorField_real)
 

From 466682e9787453fa28dd47c3794c036913c0e2da Mon Sep 17 00:00:00 2001
From: Martin Diehl <mail@martin-diehl.net>
Date: Mon, 14 Feb 2022 08:32:48 +0100
Subject: [PATCH 63/72] missing rename grid -> cells

---
 src/grid/spectral_utilities.f90 | 62 ++++++++++++++++-----------------
 1 file changed, 31 insertions(+), 31 deletions(-)

diff --git a/src/grid/spectral_utilities.f90 b/src/grid/spectral_utilities.f90
index 418f83b05..f89485c7a 100644
--- a/src/grid/spectral_utilities.f90
+++ b/src/grid/spectral_utilities.f90
@@ -31,7 +31,7 @@ module spectral_utilities
 !--------------------------------------------------------------------------------------------------
 ! grid related information
   real(pReal), protected,  public                :: wgt                                             !< weighting factor 1/Nelems
-  integer,     protected,  public                :: grid1Red                                        !< cells(1)/2
+  integer,     protected,  public                :: cells1Red                                       !< cells(1)/2
   real(pReal), protected,  public,  dimension(3) :: scaledGeomSize                                  !< scaled geometry size for calculation of divergence
 
 !--------------------------------------------------------------------------------------------------
@@ -201,7 +201,7 @@ subroutine spectral_utilities_init
                                 num_grid%get_asString('PETSc_options',defaultVal=''),err_PETSc)
   CHKERRQ(err_PETSc)
 
-  grid1Red = cells(1)/2 + 1
+  cells1Red = cells(1)/2 + 1
   wgt = 1.0/real(product(cells),pReal)
 
   num%memory_efficient      = num_grid%get_asInt('memory_efficient',      defaultVal=1) > 0         ! ToDo: should be logical in YAML file
@@ -265,8 +265,8 @@ subroutine spectral_utilities_init
   gridFFTW = int(cells,C_INTPTR_T)
   alloc_local = fftw_mpi_local_size_3d(gridFFTW(3), gridFFTW(2), gridFFTW(1)/2 +1, &
                                        PETSC_COMM_WORLD, local_K, local_K_offset)
-  allocate (xi1st (3,grid1Red,cells(2),cells3),source = cmplx(0.0_pReal,0.0_pReal,pReal))           ! frequencies for first derivatives, only half the size for first dimension
-  allocate (xi2nd (3,grid1Red,cells(2),cells3),source = cmplx(0.0_pReal,0.0_pReal,pReal))           ! frequencies for second derivatives, only half the size for first dimension
+  allocate (xi1st (3,cells1Red,cells(2),cells3),source = cmplx(0.0_pReal,0.0_pReal,pReal))          ! frequencies for first derivatives, only half the size for first dimension
+  allocate (xi2nd (3,cells1Red,cells(2),cells3),source = cmplx(0.0_pReal,0.0_pReal,pReal))          ! frequencies for second derivatives, only half the size for first dimension
 
   tensorField = fftw_alloc_complex(tensorSize*alloc_local)
   call c_f_pointer(tensorField, tensorField_real,    [3_C_INTPTR_T,3_C_INTPTR_T, &
@@ -333,7 +333,7 @@ subroutine spectral_utilities_init
       do j = 1, cells(2)
         k_s(2) = j - 1
         if (j > cells(2)/2 + 1) k_s(2) = k_s(2) - cells(2)                                          ! running from 0,1,...,N/2,N/2+1,-N/2,-N/2+1,...,-1
-          do i = 1, grid1Red
+          do i = 1, cells1Red
             k_s(1) = i - 1                                                                          ! symmetry, junst running from 0,1,...,N/2,N/2+1
             xi2nd(1:3,i,j,k-cells3Offset) = utilities_getFreqDerivative(k_s)
             where(mod(cells,2)==0 .and. [i,j,k] == cells/2+1 .and. &
@@ -347,7 +347,7 @@ subroutine spectral_utilities_init
   if (num%memory_efficient) then                                                                    ! allocate just single fourth order tensor
     allocate (gamma_hat(3,3,3,3,1,1,1), source = cmplx(0.0_pReal,0.0_pReal,pReal))
   else                                                                                              ! precalculation of gamma_hat field
-    allocate (gamma_hat(3,3,3,3,grid1Red,cells(2),cells3), source = cmplx(0.0_pReal,0.0_pReal,pReal))
+    allocate (gamma_hat(3,3,3,3,cells1Red,cells(2),cells3), source = cmplx(0.0_pReal,0.0_pReal,pReal))
   endif
 
 end subroutine spectral_utilities_init
@@ -374,7 +374,7 @@ subroutine utilities_updateGamma(C)
   if (.not. num%memory_efficient) then
     gamma_hat = cmplx(0.0_pReal,0.0_pReal,pReal)                                                    ! for the singular point and any non invertible A
     !$OMP PARALLEL DO PRIVATE(l,m,n,o,temp33_cmplx,xiDyad_cmplx,A,A_inv,err)
-    do k = cells3Offset+1, cells3Offset+cells3; do j = 1, cells(2); do i = 1, grid1Red
+    do k = cells3Offset+1, cells3Offset+cells3; do j = 1, cells(2); do i = 1, cells1Red
       if (any([i,j,k] /= 1)) then                                                                   ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
         do concurrent (l = 1:3, m = 1:3)
           xiDyad_cmplx(l,m) = conjg(-xi1st(l,i,j,k-cells3Offset))*xi1st(m,i,j,k-cells3Offset)
@@ -406,7 +406,7 @@ end subroutine utilities_updateGamma
 !--------------------------------------------------------------------------------------------------
 subroutine utilities_FFTtensorForward
 
-  tensorField_real(1:3,1:3,cells(1)+1:grid1Red*2,:,:) = 0.0_pReal
+  tensorField_real(1:3,1:3,cells(1)+1:cells1Red*2,:,:) = 0.0_pReal
   call fftw_mpi_execute_dft_r2c(planTensorForth,tensorField_real,tensorField_fourier)
 
 end subroutine utilities_FFTtensorForward
@@ -430,7 +430,7 @@ end subroutine utilities_FFTtensorBackward
 !--------------------------------------------------------------------------------------------------
 subroutine utilities_FFTscalarForward
 
-  scalarField_real(cells(1)+1:grid1Red*2,:,:) = 0.0_pReal
+  scalarField_real(cells(1)+1:cells1Red*2,:,:) = 0.0_pReal
   call fftw_mpi_execute_dft_r2c(planScalarForth,scalarField_real,scalarField_fourier)
 
 end subroutine utilities_FFTscalarForward
@@ -455,7 +455,7 @@ end subroutine utilities_FFTscalarBackward
 !--------------------------------------------------------------------------------------------------
 subroutine utilities_FFTvectorForward
 
-  vectorField_real(1:3,cells(1)+1:grid1Red*2,:,:) = 0.0_pReal
+  vectorField_real(1:3,cells(1)+1:cells1Red*2,:,:) = 0.0_pReal
   call fftw_mpi_execute_dft_r2c(planVectorForth,vectorField_real,vectorField_fourier)
 
 end subroutine utilities_FFTvectorForward
@@ -495,7 +495,7 @@ subroutine utilities_fourierGammaConvolution(fieldAim)
 ! do the actual spectral method calculation (mechanical equilibrium)
   memoryEfficient: if (num%memory_efficient) then
     !$OMP PARALLEL DO PRIVATE(l,m,n,o,temp33_cmplx,xiDyad_cmplx,A,A_inv,err,gamma_hat)
-    do k = 1, cells3; do j = 1, cells(2); do i = 1, grid1Red
+    do k = 1, cells3; do j = 1, cells(2); do i = 1, cells1Red
       if (any([i,j,k+cells3Offset] /= 1)) then                                                      ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
         do concurrent(l = 1:3, m = 1:3)
           xiDyad_cmplx(l,m) = conjg(-xi1st(l,i,j,k))*xi1st(m,i,j,k)
@@ -523,7 +523,7 @@ subroutine utilities_fourierGammaConvolution(fieldAim)
     !$OMP END PARALLEL DO
   else memoryEfficient
     !$OMP PARALLEL DO PRIVATE(l,m,temp33_cmplx)
-    do k = 1, cells3;  do j = 1, cells(2);  do i = 1,grid1Red
+    do k = 1, cells3;  do j = 1, cells(2);  do i = 1,cells1Red
       do concurrent(l = 1:3, m = 1:3)
         temp33_cmplx(l,m) = sum(gamma_hat(l,m,1:3,1:3,i,j,k)*tensorField_fourier(1:3,1:3,i,j,k))
       end do
@@ -550,7 +550,7 @@ subroutine utilities_fourierGreenConvolution(D_ref, mu_ref, Delta_t)
 !--------------------------------------------------------------------------------------------------
 ! do the actual spectral method calculation
   !$OMP PARALLEL DO PRIVATE(GreenOp_hat)
-  do k = 1, cells3; do j = 1, cells(2) ;do i = 1, grid1Red
+  do k = 1, cells3; do j = 1, cells(2) ;do i = 1, cells1Red
     GreenOp_hat = cmplx(1.0_pReal,0.0_pReal,pReal) &
                 / (cmplx(mu_ref,0.0_pReal,pReal) + cmplx(Delta_t,0.0_pReal) &
                    * sum(conjg(xi1st(1:3,i,j,k))* matmul(cmplx(D_ref,0.0_pReal),xi1st(1:3,i,j,k))))
@@ -579,7 +579,7 @@ real(pReal) function utilities_divergenceRMS()
 ! calculating RMS divergence criterion in Fourier space
   utilities_divergenceRMS = 0.0_pReal
   do k = 1, cells3; do j = 1, cells(2)
-    do i = 2, grid1Red -1                                                                           ! Has somewhere a conj. complex counterpart. Therefore count it twice.
+    do i = 2, cells1Red -1                                                                          ! Has somewhere a conj. complex counterpart. Therefore count it twice.
       utilities_divergenceRMS = utilities_divergenceRMS &
             + 2.0_pReal*(sum (real(matmul(tensorField_fourier(1:3,1:3,i,j,k), &                     ! (sqrt(real(a)**2 + aimag(a)**2))**2 = real(a)**2 + aimag(a)**2, i.e. do not take square root and square again
                                           conjg(-xi1st(1:3,i,j,k))*rescaledGeom))**2) &             ! --> sum squared L_2 norm of vector
@@ -591,10 +591,10 @@ real(pReal) function utilities_divergenceRMS()
                                   conjg(-xi1st(1:3,1,j,k))*rescaledGeom))**2) &
                + sum(aimag(matmul(tensorField_fourier(1:3,1:3,1       ,j,k), &
                                   conjg(-xi1st(1:3,1,j,k))*rescaledGeom))**2) &
-               + sum( real(matmul(tensorField_fourier(1:3,1:3,grid1Red,j,k), &
-                                  conjg(-xi1st(1:3,grid1Red,j,k))*rescaledGeom))**2) &
-               + sum(aimag(matmul(tensorField_fourier(1:3,1:3,grid1Red,j,k), &
-                                  conjg(-xi1st(1:3,grid1Red,j,k))*rescaledGeom))**2)
+               + sum( real(matmul(tensorField_fourier(1:3,1:3,cells1Red,j,k), &
+                                  conjg(-xi1st(1:3,cells1Red,j,k))*rescaledGeom))**2) &
+               + sum(aimag(matmul(tensorField_fourier(1:3,1:3,cells1Red,j,k), &
+                                  conjg(-xi1st(1:3,cells1Red,j,k))*rescaledGeom))**2)
   enddo; enddo
   if (cells(1) == 1) utilities_divergenceRMS = utilities_divergenceRMS * 0.5_pReal                   ! counted twice in case of cells(1) == 1
   call MPI_Allreduce(MPI_IN_PLACE,utilities_divergenceRMS,1_MPI_INTEGER_KIND,MPI_DOUBLE,MPI_SUM,MPI_COMM_WORLD,err_MPI)
@@ -624,7 +624,7 @@ real(pReal) function utilities_curlRMS()
   utilities_curlRMS = 0.0_pReal
 
   do k = 1, cells3; do j = 1, cells(2);
-    do i = 2, grid1Red - 1
+    do i = 2, cells1Red - 1
       do l = 1, 3
         curl_fourier(l,1) = (+tensorField_fourier(l,3,i,j,k)*xi1st(2,i,j,k)*rescaledGeom(2) &
                              -tensorField_fourier(l,2,i,j,k)*xi1st(3,i,j,k)*rescaledGeom(3))
@@ -647,12 +647,12 @@ real(pReal) function utilities_curlRMS()
     utilities_curlRMS = utilities_curlRMS &
                       + sum(curl_fourier%re**2 + curl_fourier%im**2)                                ! this layer (DC) does not have a conjugate complex counterpart (if cells(1) /= 1)
     do l = 1, 3
-      curl_fourier = (+tensorField_fourier(l,3,grid1Red,j,k)*xi1st(2,grid1Red,j,k)*rescaledGeom(2) &
-                      -tensorField_fourier(l,2,grid1Red,j,k)*xi1st(3,grid1Red,j,k)*rescaledGeom(3))
-      curl_fourier = (+tensorField_fourier(l,1,grid1Red,j,k)*xi1st(3,grid1Red,j,k)*rescaledGeom(3) &
-                      -tensorField_fourier(l,3,grid1Red,j,k)*xi1st(1,grid1Red,j,k)*rescaledGeom(1))
-      curl_fourier = (+tensorField_fourier(l,2,grid1Red,j,k)*xi1st(1,grid1Red,j,k)*rescaledGeom(1) &
-                      -tensorField_fourier(l,1,grid1Red,j,k)*xi1st(2,grid1Red,j,k)*rescaledGeom(2))
+      curl_fourier = (+tensorField_fourier(l,3,cells1Red,j,k)*xi1st(2,cells1Red,j,k)*rescaledGeom(2) &
+                      -tensorField_fourier(l,2,cells1Red,j,k)*xi1st(3,cells1Red,j,k)*rescaledGeom(3))
+      curl_fourier = (+tensorField_fourier(l,1,cells1Red,j,k)*xi1st(3,cells1Red,j,k)*rescaledGeom(3) &
+                      -tensorField_fourier(l,3,cells1Red,j,k)*xi1st(1,cells1Red,j,k)*rescaledGeom(1))
+      curl_fourier = (+tensorField_fourier(l,2,cells1Red,j,k)*xi1st(1,cells1Red,j,k)*rescaledGeom(1) &
+                      -tensorField_fourier(l,1,cells1Red,j,k)*xi1st(2,cells1Red,j,k)*rescaledGeom(2))
     enddo
     utilities_curlRMS = utilities_curlRMS &
                       + sum(curl_fourier%re**2 + curl_fourier%im**2)                                ! this layer (Nyquist) does not have a conjugate complex counterpart (if cells(1) /= 1)
@@ -744,7 +744,7 @@ subroutine utilities_fourierScalarGradient()
   integer :: i, j, k
 
 
-  do k = 1, cells3;  do j = 1, cells(2);  do i = 1,grid1Red
+  do k = 1, cells3;  do j = 1, cells(2);  do i = 1,cells1Red
     vectorField_fourier(1:3,i,j,k) = scalarField_fourier(i,j,k)*xi1st(1:3,i,j,k)                    ! ToDo: no -conjg?
   end do; end do; end do
 
@@ -757,8 +757,8 @@ end subroutine utilities_fourierScalarGradient
 subroutine utilities_fourierVectorDivergence()
 
 
-  scalarField_fourier(1:grid1Red,1:cells(2),1:cells3) = sum(vectorField_fourier(1:3,1:grid1Red,1:cells(2),1:cells3) &
-                                                            *conjg(-xi1st))
+  scalarField_fourier(1:cells1Red,1:cells(2),1:cells3) = sum(vectorField_fourier(1:3,1:cells1Red,1:cells(2),1:cells3) &
+                                                             *conjg(-xi1st))
 
 end subroutine utilities_fourierVectorDivergence
 
@@ -771,7 +771,7 @@ subroutine utilities_fourierVectorGradient()
   integer :: i, j, k, m, n
 
 
-  do k = 1, cells3;  do j = 1, cells(2);  do i = 1,grid1Red
+  do k = 1, cells3;  do j = 1, cells(2);  do i = 1,cells1Red
     do m = 1, 3; do n = 1, 3
       tensorField_fourier(m,n,i,j,k) = vectorField_fourier(m,i,j,k)*xi1st(n,i,j,k)
     end do; end do
@@ -788,7 +788,7 @@ subroutine utilities_fourierTensorDivergence()
   integer :: i, j, k
 
 
-  do k = 1, cells3;  do j = 1, cells(2);  do i = 1,grid1Red
+  do k = 1, cells3;  do j = 1, cells(2);  do i = 1,cells1Red
     vectorField_fourier(:,i,j,k) = matmul(tensorField_fourier(:,:,i,j,k),conjg(-xi1st(:,i,j,k)))
   end do; end do; end do
 
@@ -1026,7 +1026,7 @@ subroutine utilities_updateCoords(F)
   call utilities_FFTtensorForward()
 
   !$OMP PARALLEL DO
-  do k = 1, cells3; do j = 1, cells(2); do i = 1, grid1Red
+  do k = 1, cells3; do j = 1, cells(2); do i = 1, cells1Red
     if (any([i,j,k+cells3Offset] /= 1)) then
       vectorField_fourier(1:3,i,j,k) = matmul(tensorField_fourier(1:3,1:3,i,j,k),xi2nd(1:3,i,j,k)) &
                                      / sum(conjg(-xi2nd(1:3,i,j,k))*xi2nd(1:3,i,j,k)) * cmplx(wgt,0.0,pReal)

From 1d5abc206aa630596ca82b6d6349865bc018a3f3 Mon Sep 17 00:00:00 2001
From: Test User <damask_user@mpie.de>
Date: Mon, 14 Feb 2022 11:23:42 +0100
Subject: [PATCH 64/72] [skip ci] updated version information after successful
 test of v3.0.0-alpha5-638-g1ecbeb692

---
 python/damask/VERSION | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/python/damask/VERSION b/python/damask/VERSION
index 90c1162f3..5041b8cde 100644
--- a/python/damask/VERSION
+++ b/python/damask/VERSION
@@ -1 +1 @@
-v3.0.0-alpha5-624-g26979da58
+v3.0.0-alpha5-638-g1ecbeb692

From c66e2336c25d704a36a60ea121c837c34210a388 Mon Sep 17 00:00:00 2001
From: Martin Diehl <mail@martin-diehl.net>
Date: Mon, 14 Feb 2022 08:58:40 +0100
Subject: [PATCH 65/72] some versions of ifort have problems with 'do
 concurrent'

---
 src/grid/spectral_utilities.f90  | 35 ++++++++++++++++++++++++++++++--
 src/math.f90                     | 31 ++++++++--------------------
 src/phase_mechanical_plastic.f90 |  3 +--
 3 files changed, 42 insertions(+), 27 deletions(-)

diff --git a/src/grid/spectral_utilities.f90 b/src/grid/spectral_utilities.f90
index f89485c7a..2a675c9b6 100644
--- a/src/grid/spectral_utilities.f90
+++ b/src/grid/spectral_utilities.f90
@@ -376,20 +376,32 @@ subroutine utilities_updateGamma(C)
     !$OMP PARALLEL DO PRIVATE(l,m,n,o,temp33_cmplx,xiDyad_cmplx,A,A_inv,err)
     do k = cells3Offset+1, cells3Offset+cells3; do j = 1, cells(2); do i = 1, cells1Red
       if (any([i,j,k] /= 1)) then                                                                   ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
-        do concurrent (l = 1:3, m = 1:3)
+#ifndef __INTEL_COMPILER
+        do concurrent(l = 1:3, m = 1:3)
           xiDyad_cmplx(l,m) = conjg(-xi1st(l,i,j,k-cells3Offset))*xi1st(m,i,j,k-cells3Offset)
         end do
         do concurrent(l = 1:3, m = 1:3)
           temp33_cmplx(l,m) = sum(cmplx(C_ref(l,1:3,m,1:3),0.0_pReal)*xiDyad_cmplx)
         end do
+#else
+        forall(l = 1:3, m = 1:3) &
+          xiDyad_cmplx(l,m) = conjg(-xi1st(l,i,j,k-cells3Offset))*xi1st(m,i,j,k-cells3Offset)
+        forall(l = 1:3, m = 1:3) &
+          temp33_cmplx(l,m) = sum(cmplx(C_ref(l,1:3,m,1:3),0.0_pReal)*xiDyad_cmplx)
+#endif
         A(1:3,1:3) = temp33_cmplx%re; A(4:6,4:6) =  temp33_cmplx%re
         A(1:3,4:6) = temp33_cmplx%im; A(4:6,1:3) = -temp33_cmplx%im
         if (abs(math_det33(A(1:3,1:3))) > 1e-16) then
           call math_invert(A_inv, err, A)
           temp33_cmplx = cmplx(A_inv(1:3,1:3),A_inv(1:3,4:6),pReal)
+#ifndef __INTEL_COMPILER
           do concurrent(l=1:3, m=1:3, n=1:3, o=1:3)
             gamma_hat(l,m,n,o,i,j,k-cells3Offset) = temp33_cmplx(l,n) * xiDyad_cmplx(o,m)
           end do
+#else
+          forall(l=1:3, m=1:3, n=1:3, o=1:3) &
+            gamma_hat(l,m,n,o,i,j,k-cells3Offset) = temp33_cmplx(l,n) * xiDyad_cmplx(o,m)
+#endif
         end if
       end if
     end do; end do; end do
@@ -497,23 +509,37 @@ subroutine utilities_fourierGammaConvolution(fieldAim)
     !$OMP PARALLEL DO PRIVATE(l,m,n,o,temp33_cmplx,xiDyad_cmplx,A,A_inv,err,gamma_hat)
     do k = 1, cells3; do j = 1, cells(2); do i = 1, cells1Red
       if (any([i,j,k+cells3Offset] /= 1)) then                                                      ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
+#ifndef __INTEL_COMPILER
         do concurrent(l = 1:3, m = 1:3)
           xiDyad_cmplx(l,m) = conjg(-xi1st(l,i,j,k))*xi1st(m,i,j,k)
         end do
         do concurrent(l = 1:3, m = 1:3)
           temp33_cmplx(l,m) = sum(cmplx(C_ref(l,1:3,m,1:3),0.0_pReal)*xiDyad_cmplx)
         end do
+#else
+        forall(l = 1:3, m = 1:3) &
+          xiDyad_cmplx(l,m) = conjg(-xi1st(l,i,j,k))*xi1st(m,i,j,k)
+        forall(l = 1:3, m = 1:3) &
+          temp33_cmplx(l,m) = sum(cmplx(C_ref(l,1:3,m,1:3),0.0_pReal)*xiDyad_cmplx)
+#endif
         A(1:3,1:3) = temp33_cmplx%re; A(4:6,4:6) =  temp33_cmplx%re
         A(1:3,4:6) = temp33_cmplx%im; A(4:6,1:3) = -temp33_cmplx%im
         if (abs(math_det33(A(1:3,1:3))) > 1e-16) then
           call math_invert(A_inv, err, A)
           temp33_cmplx = cmplx(A_inv(1:3,1:3),A_inv(1:3,4:6),pReal)
+#ifndef __INTEL_COMPILER
           do concurrent(l=1:3, m=1:3, n=1:3, o=1:3)
             gamma_hat(l,m,n,o,1,1,1) = temp33_cmplx(l,n)*xiDyad_cmplx(o,m)
           end do
           do concurrent(l = 1:3, m = 1:3)
             temp33_cmplx(l,m) = sum(gamma_hat(l,m,1:3,1:3,1,1,1)*tensorField_fourier(1:3,1:3,i,j,k))
           end do
+#else
+          forall(l=1:3, m=1:3, n=1:3, o=1:3) &
+            gamma_hat(l,m,n,o,1,1,1) = temp33_cmplx(l,n)*xiDyad_cmplx(o,m)
+          forall(l = 1:3, m = 1:3) &
+            temp33_cmplx(l,m) = sum(gamma_hat(l,m,1:3,1:3,1,1,1)*tensorField_fourier(1:3,1:3,i,j,k))
+#endif
           tensorField_fourier(1:3,1:3,i,j,k) = temp33_cmplx
         else
           tensorField_fourier(1:3,1:3,i,j,k) = cmplx(0.0_pReal,0.0_pReal,pReal)
@@ -524,9 +550,14 @@ subroutine utilities_fourierGammaConvolution(fieldAim)
   else memoryEfficient
     !$OMP PARALLEL DO PRIVATE(l,m,temp33_cmplx)
     do k = 1, cells3;  do j = 1, cells(2);  do i = 1,cells1Red
+#ifndef __INTEL_COMPILER
       do concurrent(l = 1:3, m = 1:3)
         temp33_cmplx(l,m) = sum(gamma_hat(l,m,1:3,1:3,i,j,k)*tensorField_fourier(1:3,1:3,i,j,k))
       end do
+#else
+      forall(l = 1:3, m = 1:3) &
+        temp33_cmplx(l,m) = sum(gamma_hat(l,m,1:3,1:3,i,j,k)*tensorField_fourier(1:3,1:3,i,j,k))
+#endif
       tensorField_fourier(1:3,1:3,i,j,k) = temp33_cmplx
     end do; end do; end do
     !$OMP END PARALLEL DO
@@ -758,7 +789,7 @@ subroutine utilities_fourierVectorDivergence()
 
 
   scalarField_fourier(1:cells1Red,1:cells(2),1:cells3) = sum(vectorField_fourier(1:3,1:cells1Red,1:cells(2),1:cells3) &
-                                                             *conjg(-xi1st))
+                                                             *conjg(-xi1st),1)
 
 end subroutine utilities_fourierVectorDivergence
 
diff --git a/src/math.f90 b/src/math.f90
index dd4690672..75b9ddea2 100644
--- a/src/math.f90
+++ b/src/math.f90
@@ -262,9 +262,8 @@ pure function math_identity4th()
     math_identity4th(i,j,k,l) = 0.5_pReal*(math_I3(i,k)*math_I3(j,l)+math_I3(i,l)*math_I3(j,k))
   enddo
 #else
-  do i=1,3; do j=1,3; do k=1,3; do l=1,3
+  forall(i=1:3, j=1:3, k=1:3, l=1:3) &
     math_identity4th(i,j,k,l) = 0.5_pReal*(math_I3(i,k)*math_I3(j,l)+math_I3(i,l)*math_I3(j,k))
-  enddo; enddo; enddo; enddo
 #endif
 
 end function math_identity4th
@@ -338,9 +337,7 @@ pure function math_outer(A,B)
     math_outer(i,j) = A(i)*B(j)
   enddo
 #else
-  do i=1,size(A,1); do j=1,size(B,1)
-    math_outer(i,j) = A(i)*B(j)
-  enddo; enddo
+  forall(i=1:size(A,1), j=1:size(B,1)) math_outer(i,j) = A(i)*B(j)
 #endif
 
 end function math_outer
@@ -387,9 +384,7 @@ pure function math_mul3333xx33(A,B)
     math_mul3333xx33(i,j) = sum(A(i,j,1:3,1:3)*B(1:3,1:3))
   enddo
 #else
-  do i=1,3; do j=1,3
-    math_mul3333xx33(i,j) = sum(A(i,j,1:3,1:3)*B(1:3,1:3))
-  enddo; enddo
+  forall (i=1:3, j=1:3) math_mul3333xx33(i,j) = sum(A(i,j,1:3,1:3)*B(1:3,1:3))
 #endif
 
 end function math_mul3333xx33
@@ -411,9 +406,7 @@ pure function math_mul3333xx3333(A,B)
     math_mul3333xx3333(i,j,k,l) = sum(A(i,j,1:3,1:3)*B(1:3,1:3,k,l))
   enddo
 #else
-  do i=1,3; do j=1,3; do k=1,3; do l=1,3
-    math_mul3333xx3333(i,j,k,l) = sum(A(i,j,1:3,1:3)*B(1:3,1:3,k,l))
-  enddo; enddo; enddo; enddo
+  forall(i=1:3, j=1:3, k=1:3, l=1:3) math_mul3333xx3333(i,j,k,l) = sum(A(i,j,1:3,1:3)*B(1:3,1:3,k,l))
 #endif
 
 end function math_mul3333xx3333
@@ -752,9 +745,7 @@ pure function math_3333to99(m3333)
     math_3333to99(i,j) = m3333(MAPPLAIN(1,i),MAPPLAIN(2,i),MAPPLAIN(1,j),MAPPLAIN(2,j))
   enddo
 #else
-  do i=1,9; do j=1,9
-    math_3333to99(i,j) = m3333(MAPPLAIN(1,i),MAPPLAIN(2,i),MAPPLAIN(1,j),MAPPLAIN(2,j))
-  enddo; enddo
+  forall(i=1:9, j=1:9) math_3333to99(i,j) = m3333(MAPPLAIN(1,i),MAPPLAIN(2,i),MAPPLAIN(1,j),MAPPLAIN(2,j))
 #endif
 
 end function math_3333to99
@@ -775,9 +766,7 @@ pure function math_99to3333(m99)
     math_99to3333(MAPPLAIN(1,i),MAPPLAIN(2,i),MAPPLAIN(1,j),MAPPLAIN(2,j)) = m99(i,j)
   enddo
 #else
-  do i=1,9; do j=1,9
-    math_99to3333(MAPPLAIN(1,i),MAPPLAIN(2,i),MAPPLAIN(1,j),MAPPLAIN(2,j)) = m99(i,j)
-  enddo; enddo
+  forall(i=1:9, j=1:9) math_99to3333(MAPPLAIN(1,i),MAPPLAIN(2,i),MAPPLAIN(1,j),MAPPLAIN(2,j)) = m99(i,j)
 #endif
 
 end function math_99to3333
@@ -810,9 +799,7 @@ pure function math_sym3333to66(m3333,weighted)
     math_sym3333to66(i,j) = w(i)*w(j)*m3333(MAPNYE(1,i),MAPNYE(2,i),MAPNYE(1,j),MAPNYE(2,j))
   enddo
 #else
-  do i=1,6; do j=1,6
-    math_sym3333to66(i,j) = w(i)*w(j)*m3333(MAPNYE(1,i),MAPNYE(2,i),MAPNYE(1,j),MAPNYE(2,j))
-  enddo; enddo
+  forall(i=1:6, j=1:6) math_sym3333to66(i,j) = w(i)*w(j)*m3333(MAPNYE(1,i),MAPNYE(2,i),MAPNYE(1,j),MAPNYE(2,j))
 #endif
 
 end function math_sym3333to66
@@ -950,9 +937,7 @@ pure function math_3333toVoigt66_stiffness(C) result(C_tilde)
     C_tilde(i,j) = C(MAPVOIGT(1,i),MAPVOIGT(2,i),MAPVOIGT(1,j),MAPVOIGT(2,j))
   end do
 #else
-  do i=1,6; do j=1,6
-    C_tilde(i,j) = C(MAPVOIGT(1,i),MAPVOIGT(2,i),MAPVOIGT(1,j),MAPVOIGT(2,j))
-  end do; end do
+  forall(i=1:6, j=1:6) C_tilde(i,j) = C(MAPVOIGT(1,i),MAPVOIGT(2,i),MAPVOIGT(1,j),MAPVOIGT(2,j))
 #endif
 
 end function math_3333toVoigt66_stiffness
diff --git a/src/phase_mechanical_plastic.f90 b/src/phase_mechanical_plastic.f90
index 72b67ef64..3915c3b2d 100644
--- a/src/phase_mechanical_plastic.f90
+++ b/src/phase_mechanical_plastic.f90
@@ -379,10 +379,9 @@ module function plastic_deltaState(ph, en) result(broken)
     en
   logical :: broken
 
-  real(pReal),               dimension(3,3) :: &
+  real(pReal), dimension(3,3) :: &
     Mp
   integer :: &
-    myOffset, &
     mySize
 
 

From 7d015fbdc518a2a4081054b4ad0a44495ca63d2a Mon Sep 17 00:00:00 2001
From: Martin Diehl <mail@martin-diehl.net>
Date: Mon, 14 Feb 2022 14:32:02 +0000
Subject: [PATCH 66/72] avoid confusion with existing table entry

---
 python/damask/_configmaterial.py | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/python/damask/_configmaterial.py b/python/damask/_configmaterial.py
index 250b52e7e..725567b7f 100644
--- a/python/damask/_configmaterial.py
+++ b/python/damask/_configmaterial.py
@@ -212,18 +212,18 @@ class ConfigMaterial(Config):
         homogenization: {}
         phase: {}
 
-        >>> cm.from_table(t,O='qu',phase='phase',homogenization='SX')
+        >>> cm.from_table(t,O='qu',phase='phase',homogenization='single_crystal')
         material:
           - constituents:
               - O: [0.19, 0.8, 0.24, -0.51]
                 v: 1.0
                 phase: Aluminum
-            homogenization: SX
+            homogenization: single_crystal
           - constituents:
               - O: [0.8, 0.19, 0.24, -0.51]
                 v: 1.0
                 phase: Steel
-            homogenization: SX
+            homogenization: single_crystal
         homogenization: {}
         phase: {}
 

From bdeb3e042ea09bd1723d74ceb6fb619782acbfda Mon Sep 17 00:00:00 2001
From: Test User <damask_user@mpie.de>
Date: Tue, 15 Feb 2022 01:20:38 +0100
Subject: [PATCH 67/72] [skip ci] updated version information after successful
 test of v3.0.0-alpha5-642-ge38786515

---
 python/damask/VERSION | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/python/damask/VERSION b/python/damask/VERSION
index 5041b8cde..c1421b337 100644
--- a/python/damask/VERSION
+++ b/python/damask/VERSION
@@ -1 +1 @@
-v3.0.0-alpha5-638-g1ecbeb692
+v3.0.0-alpha5-642-ge38786515

From 00f44c9ed6b9ff79b1b4b45d88e780cefd01deeb Mon Sep 17 00:00:00 2001
From: Test User <damask_user@mpie.de>
Date: Tue, 15 Feb 2022 17:06:48 +0100
Subject: [PATCH 68/72] [skip ci] updated version information after successful
 test of v3.0.0-alpha5-651-gd4f711416

---
 python/damask/VERSION | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/python/damask/VERSION b/python/damask/VERSION
index c1421b337..6de98cde2 100644
--- a/python/damask/VERSION
+++ b/python/damask/VERSION
@@ -1 +1 @@
-v3.0.0-alpha5-642-ge38786515
+v3.0.0-alpha5-651-gd4f711416

From 35caed305fce4f0c049a01370ad29d0a8ae8d0ca Mon Sep 17 00:00:00 2001
From: Martin Diehl <mail@martin-diehl.net>
Date: Tue, 15 Feb 2022 22:08:12 +0100
Subject: [PATCH 69/72] consistently define allclose for own type only

---
 python/damask/_orientation.py | 10 ++++------
 python/damask/_rotation.py    |  8 ++++----
 2 files changed, 8 insertions(+), 10 deletions(-)

diff --git a/python/damask/_orientation.py b/python/damask/_orientation.py
index c3afd0bed..c7fbbbb85 100644
--- a/python/damask/_orientation.py
+++ b/python/damask/_orientation.py
@@ -168,8 +168,8 @@ class Orientation(Rotation,Crystal):
         return np.logical_not(self==other) if isinstance(other, Orientation) else NotImplemented
 
 
-    def isclose(self,
-                other: object,
+    def isclose(self: MyType,
+                other: MyType,
                 rtol: float = 1e-5,
                 atol: float = 1e-8,
                 equal_nan: bool = True) -> bool:
@@ -193,8 +193,6 @@ class Orientation(Rotation,Crystal):
             Mask indicating where corresponding orientations are close.
 
         """
-        if not isinstance(other, Orientation):
-            raise TypeError
         matching_type = self.family == other.family and \
                         self.lattice == other.lattice and \
                         self.parameters == other.parameters
@@ -202,8 +200,8 @@ class Orientation(Rotation,Crystal):
 
 
 
-    def allclose(self,
-                 other: object,
+    def allclose(self: MyType,
+                 other: MyType,
                  rtol: float = 1e-5,
                  atol: float = 1e-8,
                  equal_nan: bool = True) -> bool:
diff --git a/python/damask/_rotation.py b/python/damask/_rotation.py
index b11147482..9c6bde2dc 100644
--- a/python/damask/_rotation.py
+++ b/python/damask/_rotation.py
@@ -140,8 +140,8 @@ class Rotation:
         """
         return np.logical_not(self==other) if isinstance(other, Rotation) else NotImplemented
 
-    def isclose(self,
-                other: 'Rotation',
+    def isclose(self: MyType,
+                other: MyType,
                 rtol: float = 1e-5,
                 atol: float = 1e-8,
                 equal_nan: bool = True) -> bool:
@@ -171,8 +171,8 @@ class Rotation:
                              np.all(np.isclose(s,-1.0*o,rtol,atol,equal_nan),axis=-1))
 
 
-    def allclose(self,
-                 other: 'Rotation',
+    def allclose(self: MyType,
+                 other: MyType,
                  rtol: float = 1e-5,
                  atol: float = 1e-8,
                  equal_nan: bool = True) -> Union[np.bool_, bool]:

From 96133c68e90741f7e962aad8b9fb19dfa983bfcd Mon Sep 17 00:00:00 2001
From: Philip Eisenlohr <eisenlohr@egr.msu.edu>
Date: Tue, 15 Feb 2022 22:53:08 +0000
Subject: [PATCH 70/72] Corrected documentation for Table.set/add/sort_by

---
 python/damask/_table.py | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/python/damask/_table.py b/python/damask/_table.py
index 81c23e73b..df364d46e 100644
--- a/python/damask/_table.py
+++ b/python/damask/_table.py
@@ -372,9 +372,9 @@ class Table:
         label : str
             Column label.
         data : numpy.ndarray
-            New data.
+            Replacement data.
         info : str, optional
-            Human-readable information about the new data.
+            Human-readable information about the modified data.
 
         Returns
         -------
@@ -407,9 +407,9 @@ class Table:
         label : str
             Column label.
         data : numpy.ndarray
-            Modified data.
+            New data.
         info : str, optional
-            Human-readable information about the modified data.
+            Human-readable information about the new data.
 
         Returns
         -------
@@ -485,7 +485,7 @@ class Table:
                 labels: Union[str, List[str]],
                 ascending: Union[bool, List[bool]] = True) -> 'Table':
         """
-        Sort table by values of given labels.
+        Sort table by data of given columns.
 
         Parameters
         ----------

From 0f579e44ab1ad31a77cbb1929fe0720e63c9768a Mon Sep 17 00:00:00 2001
From: Test User <damask_user@mpie.de>
Date: Wed, 16 Feb 2022 07:51:02 +0100
Subject: [PATCH 71/72] [skip ci] updated version information after successful
 test of v3.0.0-alpha5-691-gfe0ff7cab

---
 python/damask/VERSION | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/python/damask/VERSION b/python/damask/VERSION
index 6de98cde2..d0eea3ce8 100644
--- a/python/damask/VERSION
+++ b/python/damask/VERSION
@@ -1 +1 @@
-v3.0.0-alpha5-651-gd4f711416
+v3.0.0-alpha5-691-gfe0ff7cab

From 138b0e03f2b98151e4a3e933e0e7201c15ebe01e Mon Sep 17 00:00:00 2001
From: Test User <damask_user@mpie.de>
Date: Wed, 16 Feb 2022 19:11:10 +0100
Subject: [PATCH 72/72] [skip ci] updated version information after successful
 test of v3.0.0-alpha5-696-g6fce27dee

---
 python/damask/VERSION | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/python/damask/VERSION b/python/damask/VERSION
index d0eea3ce8..a275a6f55 100644
--- a/python/damask/VERSION
+++ b/python/damask/VERSION
@@ -1 +1 @@
-v3.0.0-alpha5-691-gfe0ff7cab
+v3.0.0-alpha5-696-g6fce27dee