Merge branch 'vectorize_rotation' into 'development'
Vectorize rotation See merge request damask/DAMASK!162
This commit is contained in:
Karo
commit
6be1b63944
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@ -172,7 +172,7 @@ for name in filenames:
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elif inputtype == 'matrix':
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d = representations['matrix'][1]
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o = damask.Rotation.fromMatrix(list(map(float,table.data[column:column+d])))
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o = damask.Rotation.fromMatrix(np.array(list(map(float,table.data[column:column+d]))).reshape(3,3))
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elif inputtype == 'frame':
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M = np.array(list(map(float,table.data[column[0]:column[0]+3] + \
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@ -214,7 +214,7 @@ for name in filenames:
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outputAlive = True
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while outputAlive and table.data_read(): # read next data line of ASCII table
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o = damask.Rotation(list(map(float,table.data[column:column+4])))
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o = damask.Rotation(np.array(list(map(float,table.data[column:column+4]))))
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table.data_append( np.abs( np.sum(slip_direction * (o * force) ,axis=1) \
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* np.sum(slip_normal * (o * normal),axis=1)))
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@ -1,2 +1,5 @@
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[run]
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omit = tests/*
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damask/_asciitable.py
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damask/_test.py
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damask/config/*
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@ -38,6 +38,9 @@ class Orientation:
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else:
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self.rotation = Rotation.fromQuaternion(rotation) # assume quaternion
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if self.rotation.quaternion.shape != (4,):
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raise NotImplementedError('Support for multiple rotations missing')
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def disorientation(self,
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other,
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SST = True,
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@ -1,6 +1,7 @@
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import numpy as np
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from ._Lambert import ball_to_cube, cube_to_ball
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from . import mechanics
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_P = -1
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@ -61,6 +62,8 @@ class Rotation:
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def __repr__(self):
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"""Orientation displayed as unit quaternion, rotation matrix, and Bunge-Euler angles."""
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if self.quaternion.shape != (4,):
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raise NotImplementedError('Support for multiple rotations missing')
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return '\n'.join([
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'Quaternion: (real={:.3f}, imag=<{:+.3f}, {:+.3f}, {:+.3f}>)'.format(*(self.quaternion)),
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'Matrix:\n{}'.format(self.asMatrix()),
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@ -83,6 +86,8 @@ class Rotation:
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considere rotation of (3,3,3,3)-matrix
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"""
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if self.quaternion.shape != (4,):
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raise NotImplementedError('Support for multiple rotations missing')
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if isinstance(other, Rotation): # rotate a rotation
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self_q = self.quaternion[0]
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self_p = self.quaternion[1:]
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@ -107,7 +112,7 @@ class Rotation:
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elif other.shape == (3,3,): # rotate a single (3x3)-matrix
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return np.dot(self.asMatrix(),np.dot(other,self.asMatrix().T))
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elif other.shape == (3,3,3,3,):
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raise NotImplementedError
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raise NotImplementedError('Support for rotation of 4th order tensors missing')
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else:
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return NotImplemented
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else:
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@ -116,7 +121,7 @@ class Rotation:
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def inverse(self):
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"""In-place inverse rotation/backward rotation."""
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self.quaternion[1:] *= -1
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self.quaternion[...,1:] *= -1
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return self
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def inversed(self):
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@ -125,12 +130,12 @@ class Rotation:
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def standardize(self):
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"""In-place quaternion representation with positive q."""
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if self.quaternion[0] < 0.0: self.quaternion*=-1
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"""In-place quaternion representation with positive real part."""
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self.quaternion[self.quaternion[...,0] < 0.0] *= -1
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return self
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def standardized(self):
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"""Quaternion representation with positive q."""
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"""Quaternion representation with positive real part."""
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return self.copy().standardize()
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@ -157,15 +162,17 @@ class Rotation:
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Rotation from which the average is rotated.
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"""
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if self.quaternion.shape != (4,) or other.quaternion.shape != (4,):
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raise NotImplementedError('Support for multiple rotations missing')
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return Rotation.fromAverage([self,other])
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################################################################################################
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# convert to different orientation representations (numpy arrays)
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def asQuaternion(self):
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def as_quaternion(self):
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"""
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Unit quaternion [q, p_1, p_2, p_3] unless quaternion == True: damask.quaternion object.
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Unit quaternion [q, p_1, p_2, p_3].
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Parameters
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----------
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@ -175,7 +182,7 @@ class Rotation:
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"""
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return self.quaternion
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def asEulers(self,
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def as_Eulers(self,
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degrees = False):
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"""
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Bunge-Euler angles: (φ_1, ϕ, φ_2).
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@ -190,7 +197,7 @@ class Rotation:
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if degrees: eu = np.degrees(eu)
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return eu
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def asAxisAngle(self,
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def as_axis_angle(self,
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degrees = False,
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pair = False):
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"""
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@ -205,14 +212,14 @@ class Rotation:
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"""
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ax = Rotation.qu2ax(self.quaternion)
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if degrees: ax[3] = np.degrees(ax[3])
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return (ax[:3],ax[3]) if pair else ax
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if degrees: ax[...,3] = np.degrees(ax[...,3])
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return (ax[...,:3],ax[...,3]) if pair else ax
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def asMatrix(self):
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def as_matrix(self):
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"""Rotation matrix."""
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return Rotation.qu2om(self.quaternion)
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def asRodrigues(self,
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def as_Rodrigues(self,
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vector = False):
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"""
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Rodrigues-Frank vector representation [n_1, n_2, n_3, tan(ω/2)] unless vector == True: [n_1, n_2, n_3] * tan(ω/2).
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@ -224,9 +231,9 @@ class Rotation:
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"""
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ro = Rotation.qu2ro(self.quaternion)
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return ro[:3]*ro[3] if vector else ro
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return ro[...,:3]*ro[...,3] if vector else ro
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def asHomochoric(self):
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def as_homochoric(self):
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"""Homochoric vector: (h_1, h_2, h_3)."""
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return Rotation.qu2ho(self.quaternion)
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@ -234,7 +241,7 @@ class Rotation:
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"""Cubochoric vector: (c_1, c_2, c_3)."""
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return Rotation.qu2cu(self.quaternion)
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def asM(self):
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def M(self): # ToDo not sure about the name: as_M or M? we do not have a from_M
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"""
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Intermediate representation supporting quaternion averaging.
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@ -244,114 +251,133 @@ class Rotation:
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https://doi.org/10.2514/1.28949
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"""
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return np.outer(self.quaternion,self.quaternion)
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return np.einsum('...i,...j',self.quaternion,self.quaternion)
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# for compatibility (old names do not follow convention)
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asM = M
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asQuaternion = as_quaternion
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asEulers = as_Eulers
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asAxisAngle = as_axis_angle
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asMatrix = as_matrix
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asRodrigues = as_Rodrigues
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asHomochoric = as_homochoric
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################################################################################################
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# static constructors. The input data needs to follow the convention, options allow to
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# relax these convections
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# Static constructors. The input data needs to follow the conventions, options allow to
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# relax the conventions.
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@staticmethod
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def fromQuaternion(quaternion,
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def from_quaternion(quaternion,
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acceptHomomorph = False,
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P = -1):
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qu = quaternion if isinstance(quaternion,np.ndarray) and quaternion.dtype == np.dtype(float) \
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else np.array(quaternion,dtype=float)
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if P > 0: qu[1:4] *= -1 # convert from P=1 to P=-1
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if qu[0] < 0.0:
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qu = np.array(quaternion,dtype=float)
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if qu.shape[:-2:-1] != (4,):
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raise ValueError('Invalid shape.')
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if P > 0: qu[...,1:4] *= -1 # convert from P=1 to P=-1
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if acceptHomomorph:
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qu *= -1.
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qu[qu[...,0] < 0.0] *= -1
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else:
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raise ValueError('Quaternion has negative first component: {}.'.format(qu[0]))
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if not np.isclose(np.linalg.norm(qu), 1.0):
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raise ValueError('Quaternion is not of unit length: {} {} {} {}.'.format(*qu))
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if np.any(qu[...,0] < 0.0):
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raise ValueError('Quaternion with negative first (real) component.')
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if not np.all(np.isclose(np.linalg.norm(qu,axis=-1), 1.0)):
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raise ValueError('Quaternion is not of unit length.')
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return Rotation(qu)
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@staticmethod
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def fromEulers(eulers,
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def from_Eulers(eulers,
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degrees = False):
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eu = eulers if isinstance(eulers, np.ndarray) and eulers.dtype == np.dtype(float) \
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else np.array(eulers,dtype=float)
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eu = np.array(eulers,dtype=float)
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if eu.shape[:-2:-1] != (3,):
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raise ValueError('Invalid shape.')
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eu = np.radians(eu) if degrees else eu
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if np.any(eu < 0.0) or np.any(eu > 2.0*np.pi) or eu[1] > np.pi:
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raise ValueError('Euler angles outside of [0..2π],[0..π],[0..2π]: {} {} {}.'.format(*eu))
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if np.any(eu < 0.0) or np.any(eu > 2.0*np.pi) or np.any(eu[...,1] > np.pi): # ToDo: No separate check for PHI
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raise ValueError('Euler angles outside of [0..2π],[0..π],[0..2π].')
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return Rotation(Rotation.eu2qu(eu))
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@staticmethod
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def fromAxisAngle(angleAxis,
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def from_axis_angle(axis_angle,
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degrees = False,
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normalise = False,
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P = -1):
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ax = angleAxis if isinstance(angleAxis, np.ndarray) and angleAxis.dtype == np.dtype(float) \
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else np.array(angleAxis,dtype=float)
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if P > 0: ax[0:3] *= -1 # convert from P=1 to P=-1
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if degrees: ax[ 3] = np.radians(ax[3])
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if normalise: ax[0:3] /= np.linalg.norm(ax[0:3])
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if ax[3] < 0.0 or ax[3] > np.pi:
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raise ValueError('Axis angle rotation angle outside of [0..π]: {}.'.format(ax[3]))
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if not np.isclose(np.linalg.norm(ax[0:3]), 1.0):
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raise ValueError('Axis angle rotation axis is not of unit length: {} {} {}.'.format(*ax[0:3]))
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ax = np.array(axis_angle,dtype=float)
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if ax.shape[:-2:-1] != (4,):
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raise ValueError('Invalid shape.')
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if P > 0: ax[...,0:3] *= -1 # convert from P=1 to P=-1
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if degrees: ax[..., 3] = np.radians(ax[...,3])
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if normalise: ax[...,0:3] /= np.linalg.norm(ax[...,0:3],axis=-1)
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if np.any(ax[...,3] < 0.0) or np.any(ax[...,3] > np.pi):
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raise ValueError('Axis angle rotation angle outside of [0..π].')
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if not np.all(np.isclose(np.linalg.norm(ax[...,0:3],axis=-1), 1.0)):
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raise ValueError('Axis angle rotation axis is not of unit length.')
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return Rotation(Rotation.ax2qu(ax))
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@staticmethod
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def fromBasis(basis,
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def from_basis(basis,
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orthonormal = True,
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reciprocal = False,
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):
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reciprocal = False):
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om = np.array(basis,dtype=float)
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if om.shape[:-3:-1] != (3,3):
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raise ValueError('Invalid shape.')
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om = basis if isinstance(basis, np.ndarray) else np.array(basis).reshape(3,3)
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if reciprocal:
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om = np.linalg.inv(om.T/np.pi) # transform reciprocal basis set
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om = np.linalg.inv(mechanics.transpose(om)/np.pi) # transform reciprocal basis set
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orthonormal = False # contains stretch
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if not orthonormal:
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(U,S,Vh) = np.linalg.svd(om) # singular value decomposition
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om = np.dot(U,Vh)
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if not np.isclose(np.linalg.det(om),1.0):
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raise ValueError('matrix is not a proper rotation: {}.'.format(om))
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if not np.isclose(np.dot(om[0],om[1]), 0.0) \
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or not np.isclose(np.dot(om[1],om[2]), 0.0) \
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or not np.isclose(np.dot(om[2],om[0]), 0.0):
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raise ValueError('matrix is not orthogonal: {}.'.format(om))
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om = np.einsum('...ij,...jl->...il',U,Vh)
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if not np.all(np.isclose(np.linalg.det(om),1.0)):
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raise ValueError('Orientation matrix has determinant ≠ 1.')
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if not np.all(np.isclose(np.einsum('...i,...i',om[...,0],om[...,1]), 0.0)) \
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or not np.all(np.isclose(np.einsum('...i,...i',om[...,1],om[...,2]), 0.0)) \
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or not np.all(np.isclose(np.einsum('...i,...i',om[...,2],om[...,0]), 0.0)):
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raise ValueError('Orientation matrix is not orthogonal.')
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return Rotation(Rotation.om2qu(om))
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@staticmethod
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def fromMatrix(om,
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):
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def from_matrix(om):
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return Rotation.fromBasis(om)
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return Rotation.from_basis(om)
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@staticmethod
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def fromRodrigues(rodrigues,
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def from_Rodrigues(rodrigues,
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normalise = False,
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P = -1):
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ro = rodrigues if isinstance(rodrigues, np.ndarray) and rodrigues.dtype == np.dtype(float) \
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else np.array(rodrigues,dtype=float)
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if P > 0: ro[0:3] *= -1 # convert from P=1 to P=-1
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if normalise: ro[0:3] /= np.linalg.norm(ro[0:3])
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if not np.isclose(np.linalg.norm(ro[0:3]), 1.0):
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raise ValueError('Rodrigues rotation axis is not of unit length: {} {} {}.'.format(*ro[0:3]))
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if ro[3] < 0.0:
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raise ValueError('Rodrigues rotation angle not positive: {}.'.format(ro[3]))
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ro = np.array(rodrigues,dtype=float)
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if ro.shape[:-2:-1] != (4,):
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raise ValueError('Invalid shape.')
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if P > 0: ro[...,0:3] *= -1 # convert from P=1 to P=-1
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if normalise: ro[...,0:3] /= np.linalg.norm(ro[...,0:3],axis=-1)
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if np.any(ro[...,3] < 0.0):
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raise ValueError('Rodrigues vector rotation angle not positive.')
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if not np.all(np.isclose(np.linalg.norm(ro[...,0:3],axis=-1), 1.0)):
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raise ValueError('Rodrigues vector rotation axis is not of unit length.')
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return Rotation(Rotation.ro2qu(ro))
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@staticmethod
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def fromHomochoric(homochoric,
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def from_homochoric(homochoric,
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P = -1):
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ho = homochoric if isinstance(homochoric, np.ndarray) and homochoric.dtype == np.dtype(float) \
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else np.array(homochoric,dtype=float)
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ho = np.array(homochoric,dtype=float)
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if ho.shape[:-2:-1] != (3,):
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raise ValueError('Invalid shape.')
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if P > 0: ho *= -1 # convert from P=1 to P=-1
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if np.linalg.norm(ho) > (3.*np.pi/4.)**(1./3.)+1e-9:
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raise ValueError('Coordinate outside of the sphere: {} {} {}.'.format(ho))
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if np.any(np.linalg.norm(ho,axis=-1) > (3.*np.pi/4.)**(1./3.)+1e-9):
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raise ValueError('Homochoric coordinate outside of the sphere.')
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return Rotation(Rotation.ho2qu(ho))
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||||
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|
@ -359,11 +385,12 @@ class Rotation:
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|||
def fromCubochoric(cubochoric,
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P = -1):
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cu = cubochoric if isinstance(cubochoric, np.ndarray) and cubochoric.dtype == np.dtype(float) \
|
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else np.array(cubochoric,dtype=float)
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cu = np.array(cubochoric,dtype=float)
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if cu.shape[:-2:-1] != (3,):
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raise ValueError('Invalid shape.')
|
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if np.abs(np.max(cu))>np.pi**(2./3.) * 0.5+1e-9:
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raise ValueError('Coordinate outside of the cube: {} {} {}.'.format(*cu))
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raise ValueError('Cubochoric coordinate outside of the cube: {} {} {}.'.format(*cu))
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ho = Rotation.cu2ho(cu)
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if P > 0: ho *= -1 # convert from P=1 to P=-1
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|
|
@ -403,17 +430,34 @@ class Rotation:
|
|||
|
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return Rotation.fromQuaternion(np.real(vec.T[eig.argmax()]),acceptHomomorph = True)
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||||
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||||
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@staticmethod
|
||||
def fromRandom():
|
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def from_random(shape=None):
|
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if shape is None:
|
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r = np.random.random(3)
|
||||
A = np.sqrt(r[2])
|
||||
B = np.sqrt(1.0-r[2])
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return Rotation(np.array([np.cos(2.0*np.pi*r[0])*A,
|
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np.sin(2.0*np.pi*r[1])*B,
|
||||
np.cos(2.0*np.pi*r[1])*B,
|
||||
np.sin(2.0*np.pi*r[0])*A])).standardize()
|
||||
elif hasattr(shape, '__iter__'):
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||||
r = np.random.random(tuple(shape)+(3,))
|
||||
else:
|
||||
r = np.random.random((shape,3))
|
||||
|
||||
A = np.sqrt(r[...,2])
|
||||
B = np.sqrt(1.0-r[...,2])
|
||||
q = np.stack([np.cos(2.0*np.pi*r[...,0])*A,
|
||||
np.sin(2.0*np.pi*r[...,1])*B,
|
||||
np.cos(2.0*np.pi*r[...,1])*B,
|
||||
np.sin(2.0*np.pi*r[...,0])*A],axis=-1)
|
||||
|
||||
return Rotation(q.reshape(r.shape[:-1]+(4,)) if shape is not None else q).standardize()
|
||||
|
||||
|
||||
# for compatibility (old names do not follow convention)
|
||||
fromQuaternion = from_quaternion
|
||||
fromEulers = from_Eulers
|
||||
fromAxisAngle = from_axis_angle
|
||||
fromBasis = from_basis
|
||||
fromMatrix = from_matrix
|
||||
fromRodrigues = from_Rodrigues
|
||||
fromHomochoric = from_homochoric
|
||||
fromRandom = from_random
|
||||
|
||||
####################################################################################################
|
||||
# Code below available according to the following conditions on https://github.com/MarDiehl/3Drotations
|
||||
|
|
@ -808,7 +852,6 @@ class Rotation:
|
|||
c = np.cos(ax[3]*0.5)
|
||||
s = np.sin(ax[3]*0.5)
|
||||
qu = np.array([ c, ax[0]*s, ax[1]*s, ax[2]*s ])
|
||||
return qu
|
||||
else:
|
||||
c = np.cos(ax[...,3:4]*.5)
|
||||
s = np.sin(ax[...,3:4]*.5)
|
||||
|
|
@ -859,7 +902,7 @@ class Rotation:
|
|||
# 180 degree case
|
||||
ro += [np.inf] if np.isclose(ax[3],np.pi,atol=1.0e-15,rtol=0.0) else \
|
||||
[np.tan(ax[3]*0.5)]
|
||||
return np.array(ro)
|
||||
ro = np.array(ro)
|
||||
else:
|
||||
ro = np.block([ax[...,:3],
|
||||
np.where(np.isclose(ax[...,3:4],np.pi,atol=1.e-15,rtol=.0),
|
||||
|
|
@ -875,7 +918,6 @@ class Rotation:
|
|||
if len(ax.shape) == 1:
|
||||
f = (0.75 * ( ax[3] - np.sin(ax[3]) ))**(1.0/3.0)
|
||||
ho = ax[0:3] * f
|
||||
return ho
|
||||
else:
|
||||
f = (0.75 * ( ax[...,3:4] - np.sin(ax[...,3:4]) ))**(1.0/3.0)
|
||||
ho = ax[...,:3] * f
|
||||
|
|
@ -936,7 +978,6 @@ class Rotation:
|
|||
f = np.where(np.isfinite(ro[...,3:4]),2.0*np.arctan(ro[...,3:4]) -np.sin(2.0*np.arctan(ro[...,3:4])),np.pi)
|
||||
ho = np.where(np.broadcast_to(np.sum(ro[...,0:3]**2.0,axis=-1,keepdims=True) < 1.e-6,ro[...,0:3].shape),
|
||||
np.zeros(3), ro[...,0:3]* (0.75*f)**(1.0/3.0))
|
||||
|
||||
return ho
|
||||
|
||||
@staticmethod
|
||||
|
|
@ -1010,7 +1051,7 @@ class Rotation:
|
|||
if len(ho.shape) == 1:
|
||||
return ball_to_cube(ho)
|
||||
else:
|
||||
raise NotImplementedError
|
||||
raise NotImplementedError('Support for multiple rotations missing')
|
||||
|
||||
|
||||
#---------- Cubochoric ----------
|
||||
|
|
@ -1045,4 +1086,4 @@ class Rotation:
|
|||
if len(cu.shape) == 1:
|
||||
return cube_to_ball(cu)
|
||||
else:
|
||||
raise NotImplementedError
|
||||
raise NotImplementedError('Support for multiple rotations missing')
|
||||
|
|
|
|||
|
|
@ -135,16 +135,16 @@ def PK2(P,F):
|
|||
|
||||
Parameters
|
||||
----------
|
||||
P : numpy.ndarray of shape (:,3,3) or (3,3)
|
||||
P : numpy.ndarray of shape (...,3,3) or (3,3)
|
||||
First Piola-Kirchhoff stress.
|
||||
F : numpy.ndarray of shape (:,3,3) or (3,3)
|
||||
F : numpy.ndarray of shape (...,3,3) or (3,3)
|
||||
Deformation gradient.
|
||||
|
||||
"""
|
||||
if _np.shape(F) == _np.shape(P) == (3,3):
|
||||
S = _np.dot(_np.linalg.inv(F),P)
|
||||
else:
|
||||
S = _np.einsum('ijk,ikl->ijl',_np.linalg.inv(F),P)
|
||||
S = _np.einsum('...jk,...kl->...jl',_np.linalg.inv(F),P)
|
||||
return symmetric(S)
|
||||
|
||||
|
||||
|
|
@ -241,7 +241,7 @@ def symmetric(T):
|
|||
|
||||
Parameters
|
||||
----------
|
||||
T : numpy.ndarray of shape (:,3,3) or (3,3)
|
||||
T : numpy.ndarray of shape (...,3,3) or (3,3)
|
||||
Tensor of which the symmetrized values are computed.
|
||||
|
||||
"""
|
||||
|
|
@ -254,12 +254,12 @@ def transpose(T):
|
|||
|
||||
Parameters
|
||||
----------
|
||||
T : numpy.ndarray of shape (:,3,3) or (3,3)
|
||||
T : numpy.ndarray of shape (...,3,3) or (3,3)
|
||||
Tensor of which the transpose is computed.
|
||||
|
||||
"""
|
||||
return T.T if _np.shape(T) == (3,3) else \
|
||||
_np.transpose(T,(0,2,1))
|
||||
_np.swapaxes(T,axis2=-2,axis1=-1)
|
||||
|
||||
|
||||
def _polar_decomposition(T,requested):
|
||||
|
|
|
|||
|
|
@ -157,6 +157,30 @@ class TestRotation:
|
|||
print(m,o,rot.asQuaternion())
|
||||
assert ok and o.max() < np.pi**(2./3.)*0.5+1.e-9
|
||||
|
||||
@pytest.mark.parametrize('function',[Rotation.from_quaternion,
|
||||
Rotation.from_Eulers,
|
||||
Rotation.from_axis_angle,
|
||||
Rotation.from_matrix,
|
||||
Rotation.from_Rodrigues,
|
||||
Rotation.from_homochoric])
|
||||
def test_invalid_shape(self,function):
|
||||
invalid_shape = np.random.random(np.random.randint(8,32,(3)))
|
||||
with pytest.raises(ValueError):
|
||||
function(invalid_shape)
|
||||
|
||||
@pytest.mark.parametrize('function,invalid',[(Rotation.from_quaternion, np.array([-1,0,0,0])),
|
||||
(Rotation.from_quaternion, np.array([1,1,1,0])),
|
||||
(Rotation.from_Eulers, np.array([1,4,0])),
|
||||
(Rotation.from_axis_angle, np.array([1,0,0,4])),
|
||||
(Rotation.from_axis_angle, np.array([1,1,0,1])),
|
||||
(Rotation.from_matrix, np.random.rand(3,3)),
|
||||
(Rotation.from_Rodrigues, np.array([1,0,0,-1])),
|
||||
(Rotation.from_Rodrigues, np.array([1,1,0,1])),
|
||||
(Rotation.from_homochoric, np.array([2,2,2])) ])
|
||||
def test_invalid(self,function,invalid):
|
||||
with pytest.raises(ValueError):
|
||||
function(invalid)
|
||||
|
||||
@pytest.mark.parametrize('conversion',[Rotation.qu2om,
|
||||
Rotation.qu2eu,
|
||||
Rotation.qu2ax,
|
||||
|
|
|
|||
Loading…
Reference in New Issue