documentation improvments + acceptance of lists
example code at respective function, no space in 'or' variable names (sphinx cannot handle this)
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Martin Diehl
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@ -69,18 +69,6 @@ class Orientation(Rotation):
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An array of 3 x 5 random orientations reduced to the fundamental zone of tetragonal symmetry:
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>>> damask.Orientation.from_random(shape=(3,5),lattice='tetragonal').reduced
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Disorientation between two specific orientations of hexagonal symmetry:
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>>> a = damask.Orientation.from_Eulers(phi=[123,32,21],degrees=True,lattice='hexagonal')
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>>> b = damask.Orientation.from_Eulers(phi=[104,11,87],degrees=True,lattice='hexagonal')
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>>> a.disorientation(b)
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Inverse pole figure color of the e_3 direction for a crystal in "Cube" orientation with cubic symmetry:
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>>> o = damask.Orientation(lattice='cubic')
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>>> o.IPF_color(o.to_SST(np.array([0,0,1])))
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Schmid matrix (in lab frame) of slip systems of a face-centered cubic crystal in "Goss" orientation:
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>>> damask.Orientation.from_Eulers(phi=[0,45,0],degrees=True,lattice='cF').Schmid('slip')
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"""
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crystal_families = ['triclinic',
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@ -831,6 +819,14 @@ class Orientation(Rotation):
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rgb : numpy.ndarray of shape (...,3)
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RGB array of IPF colors.
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Examples
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--------
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Inverse pole figure color of the e_3 direction for a crystal in "Cube" orientation with cubic symmetry:
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>>> o = damask.Orientation(lattice='cubic')
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>>> o.IPF_color(o.to_SST([0,0,1]))
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array([1., 0., 0.])
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References
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----------
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Bases are computed from
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@ -851,7 +847,8 @@ class Orientation(Rotation):
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... }
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"""
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if vector.shape[-1] != 3:
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vector_ = np.array(vector)
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if vector_.shape[-1] != 3:
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raise ValueError('Input is not a field of three-dimensional vectors.')
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if self.family == 'cubic':
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@ -887,23 +884,23 @@ class Orientation(Rotation):
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[ 0., 1., 0.] ]),
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}
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else: # direct exit for unspecified symmetry
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return np.zeros_like(vector)
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return np.zeros_like(vector_)
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if proper:
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components_proper = np.around(np.einsum('...ji,...i',
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np.broadcast_to(basis['proper'], vector.shape+(3,)),
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vector), 12)
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np.broadcast_to(basis['proper'], vector_.shape+(3,)),
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vector_), 12)
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components_improper = np.around(np.einsum('...ji,...i',
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np.broadcast_to(basis['improper'], vector.shape+(3,)),
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vector), 12)
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np.broadcast_to(basis['improper'], vector_.shape+(3,)),
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vector_), 12)
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in_SST = np.all(components_proper >= 0.0,axis=-1) \
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| np.all(components_improper >= 0.0,axis=-1)
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components = np.where((in_SST & np.all(components_proper >= 0.0,axis=-1))[...,np.newaxis],
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components_proper,components_improper)
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else:
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components = np.around(np.einsum('...ji,...i',
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np.broadcast_to(basis['improper'], vector.shape+(3,)),
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np.block([vector[...,:2],np.abs(vector[...,2:3])])), 12)
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np.broadcast_to(basis['improper'], vector_.shape+(3,)),
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np.block([vector_[...,:2],np.abs(vector_[...,2:3])])), 12)
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in_SST = np.all(components >= 0.0,axis=-1)
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@ -941,6 +938,22 @@ class Orientation(Rotation):
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Currently requires same crystal family for both orientations.
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For extension to cases with differing symmetry see A. Heinz and P. Neumann 1991 and 10.1107/S0021889808016373.
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Examples
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--------
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Disorientation between two specific orientations of hexagonal symmetry:
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>>> import damask
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>>> a = damask.Orientation.from_Eulers(phi=[123,32,21],degrees=True,lattice='hexagonal')
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>>> b = damask.Orientation.from_Eulers(phi=[104,11,87],degrees=True,lattice='hexagonal')
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>>> a.disorientation(b)
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Crystal family hexagonal
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Quaternion: (real=0.976, imag=<+0.189, +0.018, +0.103>)
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Matrix:
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[[ 0.97831006 0.20710935 0.00389135]
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[-0.19363288 0.90765544 0.37238141]
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[ 0.07359167 -0.36505797 0.92807163]]
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Bunge Eulers / deg: (11.40, 21.86, 0.60)
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"""
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if self.family is None or other.family is None:
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raise ValueError('Missing crystal symmetry')
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@ -1049,8 +1062,8 @@ class Orientation(Rotation):
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raise ValueError('Missing crystal symmetry')
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eq = self.equivalent
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blend = util.shapeblender(eq.shape,vector.shape[:-1])
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poles = eq.broadcast_to(blend,mode='right') @ np.broadcast_to(vector,blend+(3,))
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blend = util.shapeblender(eq.shape,np.array(vector).shape[:-1])
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poles = eq.broadcast_to(blend,mode='right') @ np.broadcast_to(np.array(vector),blend+(3,))
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ok = self.in_SST(poles,proper=proper)
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ok &= np.cumsum(ok,axis=0) == 1
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loc = np.where(ok)
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@ -1069,12 +1082,12 @@ class Orientation(Rotation):
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Parameters
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----------
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uvtw | hkil : numpy.ndarray of shape (...,4)
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uvtw|hkil : numpy.ndarray of shape (...,4)
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Miller–Bravais indices of crystallographic direction [uvtw] or plane normal (hkil).
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Returns
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-------
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uvw | hkl : numpy.ndarray of shape (...,3)
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uvw|hkl : numpy.ndarray of shape (...,3)
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Miller indices of [uvw] direction or (hkl) plane normal.
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"""
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@ -1097,12 +1110,12 @@ class Orientation(Rotation):
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Parameters
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----------
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uvw | hkl : numpy.ndarray of shape (...,3)
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uvw|hkl : numpy.ndarray of shape (...,3)
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Miller indices of crystallographic direction [uvw] or plane normal (hkl).
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Returns
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-------
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uvtw | hkil : numpy.ndarray of shape (...,4)
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uvtw|hkil : numpy.ndarray of shape (...,4)
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Miller–Bravais indices of [uvtw] direction or (hkil) plane normal.
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"""
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@ -1126,7 +1139,7 @@ class Orientation(Rotation):
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Parameters
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----------
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direction | normal : numpy.ndarray of shape (...,3)
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direction|normal : numpy.ndarray of shape (...,3)
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Vector along direction or plane normal.
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Returns
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@ -1150,7 +1163,7 @@ class Orientation(Rotation):
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Parameters
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----------
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uvw | hkl : numpy.ndarray of shape (...,3)
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uvw|hkl : numpy.ndarray of shape (...,3)
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Miller indices of crystallographic direction or plane normal.
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with_symmetry : bool, optional
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Calculate all N symmetrically equivalent vectors.
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@ -1178,7 +1191,7 @@ class Orientation(Rotation):
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Parameters
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----------
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uvw | hkl : numpy.ndarray of shape (...,3)
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uvw|hkl : numpy.ndarray of shape (...,3)
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Miller indices of crystallographic direction or plane normal.
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with_symmetry : bool, optional
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Calculate all N symmetrically equivalent vectors.
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@ -1201,13 +1214,25 @@ class Orientation(Rotation):
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Parameters
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----------
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mode : str
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Type of kinematics, e.g. 'slip' or 'twin'.
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Type of kinematics, i.e. 'slip' or 'twin'.
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Returns
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-------
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P : numpy.ndarray of shape (...,N,3,3)
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Schmid matrix for each of the N deformation systems.
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Examples
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--------
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Schmid matrix (in lab frame) of slip systems of a face-centered
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cubic crystal in "Goss" orientation.
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>>> import damask
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>>> import numpy as np
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>>> np.set_printoptions(3,suppress=True,floatmode='fixed')
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>>> damask.Orientation.from_Eulers(phi=[0,45,0],degrees=True,lattice='cF').Schmid('slip')[0]
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array([[ 0.000, 0.000, 0.000],
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[ 0.577, -0.000, 0.816],
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[ 0.000, 0.000, 0.000]])
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"""
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d = self.to_frame(uvw=self.kinematics[mode]['direction'],with_symmetry=False)
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p = self.to_frame(hkl=self.kinematics[mode]['plane'] ,with_symmetry=False)
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@ -404,7 +404,7 @@ class Rotation:
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Returns
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-------
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h : numpy.ndarray of shape (...,3)
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Homochoric vector: (h_1, h_2, h_3), ǀhǀ < 1/2*π^(2/3).
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Homochoric vector: (h_1, h_2, h_3), ǀhǀ < (3/4*π)^(1/3).
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"""
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return Rotation._qu2ho(self.quaternion)
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