extensive style polish; no functional changes
This commit is contained in:
Philip Eisenlohr
parent
1f947245bb
commit
87579dff11
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@ -66,7 +66,7 @@ class Rotation:
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__slots__ = ['quaternion']
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def __init__(self,
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rotation: Union[FloatSequence, 'Rotation'] = np.array([1.0,0.0,0.0,0.0])):
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rotation: Union[FloatSequence, 'Rotation'] = np.array([1.,0.,0.,0.])):
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"""
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New rotation.
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@ -82,7 +82,7 @@ class Rotation:
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if isinstance(rotation,Rotation):
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self.quaternion = rotation.quaternion.copy()
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elif np.array(rotation).shape[-1] == 4:
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self.quaternion = np.array(rotation)
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self.quaternion = np.array(rotation,dtype=float)
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else:
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raise TypeError('"rotation" is neither a Rotation nor a quaternion')
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@ -141,7 +141,7 @@ class Rotation:
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"""
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return NotImplemented if not isinstance(other, Rotation) else \
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np.logical_or(np.all(self.quaternion == other.quaternion,axis=-1),
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np.all(self.quaternion == -1.0*other.quaternion,axis=-1))
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np.all(self.quaternion == -1.*other.quaternion,axis=-1))
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def __ne__(self,
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@ -161,8 +161,8 @@ class Rotation:
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def isclose(self: MyType,
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other: MyType,
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rtol: float = 1e-5,
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atol: float = 1e-8,
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rtol: float = 1.e-5,
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atol: float = 1.e-8,
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equal_nan: bool = True) -> bool:
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"""
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Report where values are approximately equal to corresponding ones of other Rotation.
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@ -187,13 +187,13 @@ class Rotation:
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s = self.quaternion
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o = other.quaternion
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return np.logical_or(np.all(np.isclose(s, o,rtol,atol,equal_nan),axis=-1),
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np.all(np.isclose(s,-1.0*o,rtol,atol,equal_nan),axis=-1))
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np.all(np.isclose(s,-1.*o,rtol,atol,equal_nan),axis=-1))
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def allclose(self: MyType,
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other: MyType,
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rtol: float = 1e-5,
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atol: float = 1e-8,
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rtol: float = 1.e-5,
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atol: float = 1.e-8,
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equal_nan: bool = True) -> Union[np.bool_, bool]:
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"""
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Test whether all values are approximately equal to corresponding ones of other Rotation.
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@ -250,7 +250,7 @@ class Rotation:
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"""
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dup = self.copy()
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dup.quaternion[...,1:] *= -1
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dup.quaternion[...,1:] *= -1.
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return dup
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@ -393,9 +393,9 @@ class Rotation:
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if self.shape + (3,) == other.shape:
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q_m = self.quaternion[...,0]
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p_m = self.quaternion[...,1:]
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A = q_m**2.0 - np.einsum('...i,...i',p_m,p_m)
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B = 2.0 * np.einsum('...i,...i',p_m,other)
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C = 2.0 * _P * q_m
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A = q_m**2 - np.einsum('...i,...i',p_m,p_m)
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B = 2. * np.einsum('...i,...i',p_m,other)
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C = 2. * _P * q_m
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return np.block([(A * other[...,i]).reshape(self.shape+(1,)) +
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(B * p_m[...,i]).reshape(self.shape+(1,)) +
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(C * ( p_m[...,(i+1)%3]*other[...,(i+2)%3]\
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@ -419,7 +419,7 @@ class Rotation:
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def _standardize(self: MyType) -> MyType:
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"""Standardize quaternion (ensure positive real hemisphere)."""
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self.quaternion[self.quaternion[...,0] < 0.0] *= -1
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self.quaternion[self.quaternion[...,0] < 0.] *= -1.
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return self
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@ -540,7 +540,7 @@ class Rotation:
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weights_ = np.ones(self.shape,dtype=float) if weights is None else np.array(weights,float)
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eig, vec = np.linalg.eig(np.sum(_M(self.quaternion) * weights_[...,np.newaxis,np.newaxis],axis=-3) \
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eig, vec = np.linalg.eig(np.sum(_M(self.quaternion) * weights_[...,np.newaxis,np.newaxis],axis=-3)
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/np.sum( weights_[...,np.newaxis,np.newaxis],axis=-3))
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return self.copy(Rotation.from_quaternion(np.real(
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@ -770,20 +770,18 @@ class Rotation:
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"""
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qu = np.array(q,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 abs(P) != 1:
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raise ValueError('P ∉ {-1,1}')
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if qu.shape[:-2:-1] != (4,): raise ValueError('invalid shape')
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if abs(P) != 1: raise ValueError('P ∉ {-1,1}')
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qu[...,1:4] *= -P
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if accept_homomorph:
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qu[qu[...,0] < 0.0] *= -1
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elif np.any(qu[...,0] < 0.0):
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qu[qu[...,0]<0.] *= -1.
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elif np.any(qu[...,0] < 0.):
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raise ValueError('quaternion with negative first (real) component')
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if normalize:
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qu /= np.linalg.norm(qu,axis=-1,keepdims=True)
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elif not np.all(np.isclose(np.linalg.norm(qu,axis=-1), 1.0,rtol=1e-8)):
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elif not np.allclose(np.linalg.norm(qu,axis=-1),1.,rtol=1.e-8):
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raise ValueError('quaternion is not of unit length')
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return Rotation(qu)
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@ -808,11 +806,10 @@ class Rotation:
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"""
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eu = np.array(phi,dtype=float)
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if eu.shape[:-2:-1] != (3,):
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raise ValueError('invalid shape')
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if eu.shape[:-2:-1] != (3,): 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 np.any(eu[...,1] > np.pi): # ToDo: No separate check for PHI
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if np.any(eu < 0.) or np.any(eu > np.pi*np.array([2.,1.,2.])):
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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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@ -839,18 +836,17 @@ class Rotation:
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"""
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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 abs(P) != 1:
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raise ValueError('P ∉ {-1,1}')
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if ax.shape[:-2:-1] != (4,): raise ValueError('invalid shape')
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if abs(P) != 1: raise ValueError('P ∉ {-1,1}')
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ax[...,0:3] *= -P
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if degrees: ax[..., 3] = np.radians(ax[...,3])
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if normalize: ax[...,0:3] /= np.linalg.norm(ax[...,0:3],axis=-1,keepdims=True)
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if np.any(ax[...,3] < 0.0) or np.any(ax[...,3] > np.pi):
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if np.any(ax[...,3] < 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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print(np.linalg.norm(ax[...,0:3],axis=-1))
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if normalize:
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ax[...,0:3] /= np.linalg.norm(ax[...,0:3],axis=-1,keepdims=True)
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elif not np.allclose(np.linalg.norm(ax[...,0:3],axis=-1),1.):
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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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@ -873,22 +869,23 @@ class Rotation:
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"""
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om = np.array(basis,dtype=float)
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if om.shape[-2:] != (3,3):
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raise ValueError('invalid shape')
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if om.shape[-2:] != (3,3): raise ValueError('invalid shape')
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if reciprocal:
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om = np.linalg.inv(tensor.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.einsum('...ij,...jl',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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elif not np.allclose(np.einsum('...i,...i',om[...,0],om[...,1]),0.) \
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or not np.allclose(np.einsum('...i,...i',om[...,1],om[...,2]),0.) \
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or not np.allclose(np.einsum('...i,...i',om[...,2],om[...,0]),0.):
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raise ValueError('orientation matrix is not orthogonal')
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if not np.allclose(np.linalg.det(om),1.):
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raise ValueError('orientation matrix has determinant ≠ 1')
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return Rotation(Rotation._om2qu(om))
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@staticmethod
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@ -918,8 +915,8 @@ class Rotation:
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Corresponding three-dimensional vectors of second basis.
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"""
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a_ = np.array(a)
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b_ = np.array(b)
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a_ = np.array(a,dtype=float)
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b_ = np.array(b,dtype=float)
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if a_.shape[-2:] != (2,3) or b_.shape[-2:] != (2,3) or a_.shape != b_.shape:
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raise ValueError('invalid shape')
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am = np.stack([ a_[...,0,:],
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@ -951,16 +948,15 @@ class Rotation:
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"""
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ro = np.array(rho,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 abs(P) != 1:
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raise ValueError('P ∉ {-1,1}')
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if ro.shape[:-2:-1] != (4,): raise ValueError('invalid shape')
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if abs(P) != 1: raise ValueError('P ∉ {-1,1}')
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ro[...,0:3] *= -P
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if normalize: ro[...,0:3] /= np.linalg.norm(ro[...,0:3],axis=-1,keepdims=True)
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if np.any(ro[...,3] < 0.0):
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raise ValueError('Rodrigues vector rotation angle is negative')
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if not np.all(np.isclose(np.linalg.norm(ro[...,0:3],axis=-1), 1.0)):
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if np.any(ro[...,3] < 0.): raise ValueError('Rodrigues vector rotation angle is negative')
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if normalize:
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ro[...,0:3] /= np.linalg.norm(ro[...,0:3],axis=-1,keepdims=True)
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elif not np.allclose(np.linalg.norm(ro[...,0:3],axis=-1),1.):
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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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@ -980,14 +976,12 @@ class Rotation:
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"""
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ho = np.array(h,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 abs(P) != 1:
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raise ValueError('P ∉ {-1,1}')
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if ho.shape[:-2:-1] != (3,): raise ValueError('invalid shape')
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if abs(P) != 1: raise ValueError('P ∉ {-1,1}')
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ho *= -P
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if np.any(np.linalg.norm(ho,axis=-1) >_R1+1e-9):
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if np.any(np.linalg.norm(ho,axis=-1) > _R1+1.e-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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@ -1007,12 +1001,9 @@ class Rotation:
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"""
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cu = np.array(x,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 abs(P) != 1:
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raise ValueError('P ∉ {-1,1}')
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if np.abs(np.max(cu)) > np.pi**(2./3.) * 0.5+1e-9:
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if cu.shape[:-2:-1] != (3,): raise ValueError('invalid shape')
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if abs(P) != 1: raise ValueError('P ∉ {-1,1}')
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if np.abs(np.max(cu)) > np.pi**(2./3.) * 0.5+1.e-9:
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raise ValueError('cubochoric coordinate outside of the cube')
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ho = -P * Rotation._cu2ho(cu)
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@ -1039,11 +1030,11 @@ class Rotation:
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r = rng.random(3 if shape is None else tuple(shape)+(3,) if hasattr(shape, '__iter__') else (shape,3)) # type: ignore
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A = np.sqrt(r[...,2])
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B = np.sqrt(1.0-r[...,2])
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q = np.stack([np.cos(2.0*np.pi*r[...,0])*A,
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np.sin(2.0*np.pi*r[...,1])*B,
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np.cos(2.0*np.pi*r[...,1])*B,
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np.sin(2.0*np.pi*r[...,0])*A],axis=-1)
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B = np.sqrt(1.-r[...,2])
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q = np.stack([np.cos(2.*np.pi*r[...,0])*A,
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np.sin(2.*np.pi*r[...,1])*B,
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np.cos(2.*np.pi*r[...,1])*B,
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np.sin(2.*np.pi*r[...,0])*A],axis=-1)
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return Rotation(q if shape is None else q.reshape(r.shape[:-1]+(4,)))._standardize()
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@ -1092,10 +1083,10 @@ class Rotation:
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phi_sorted = eu[np.lexsort((eu[:,0],eu[:,1],eu[:,2]))]
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steps,size,_ = grid_filters.cellsSizeOrigin_coordinates0_point(phi_sorted)
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delta = np.radians(size/steps) if deg else size/steps
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return delta[0]*2.0*np.sin(delta[1]/2.0)*delta[2] / 8.0 / np.pi**2 * np.sin(np.radians(eu[:,1]) if deg else eu[:,1])
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return delta[0]*2.*np.sin(delta[1]/2.)*delta[2] / 8. / np.pi**2 * np.sin(np.radians(eu[:,1]) if deg else eu[:,1])
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dg = 1.0 if fractions else _dg(phi,degrees)
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dV_V = dg * np.maximum(0.0,weights.squeeze())
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dg = 1. if fractions else _dg(phi,degrees)
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dV_V = dg * np.maximum(0.,weights.squeeze())
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N = 1 if shape is None else np.prod(shape)
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return Rotation.from_Euler_angles(phi[util.hybrid_IA(dV_V,N,rng_seed)],degrees).reshape(() if shape is None else shape)
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@ -1130,24 +1121,24 @@ class Rotation:
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200 orientations:
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>>> import damask
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>>> center = damask.Rotation.from_Euler_angles([35.0,45.0,0.0],degrees=True)
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>>> brass = damask.Rotation.from_spherical_component(center=center,sigma=3.0,shape=200,degrees=True)
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>>> center = damask.Rotation.from_Euler_angles([35.,45.,0.],degrees=True)
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>>> brass = damask.Rotation.from_spherical_component(center=center,sigma=3.,shape=200,degrees=True)
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Create a Goss texture consisting of
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100 orientations:
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>>> import damask
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>>> center = damask.Rotation.from_Euler_angles([0.0,45.0,0.0],degrees=True)
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>>> goss = damask.Rotation.from_spherical_component(center=center,sigma=3.0,shape=100,degrees=True)
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>>> center = damask.Rotation.from_Euler_angles([0.,45.,0.],degrees=True)
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>>> goss = damask.Rotation.from_spherical_component(center=center,sigma=3.,shape=100,degrees=True)
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"""
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rng = np.random.default_rng(rng_seed)
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sigma = np.radians(sigma) if degrees else sigma
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N = 1 if shape is None else np.prod(shape)
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u,Theta = (rng.random((N,2)) * 2.0 * np.array([1,np.pi]) - np.array([1.0, 0])).T
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u,Theta = (rng.random((N,2)) * 2. * np.array([1.,np.pi]) - np.array([1.,0.])).T
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omega = abs(rng.normal(scale=sigma,size=N))
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p = np.column_stack([np.sqrt(1-u**2)*np.cos(Theta),
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np.sqrt(1-u**2)*np.sin(Theta),
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p = np.column_stack([np.sqrt(1.-u**2)*np.cos(Theta),
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np.sqrt(1.-u**2)*np.sin(Theta),
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u, omega])
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return Rotation.from_axis_angle(p).reshape(() if shape is None else shape) * center
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@ -1156,7 +1147,7 @@ class Rotation:
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@staticmethod
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def from_fiber_component(crystal: IntSequence,
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sample: IntSequence,
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sigma: float = 0.0,
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sigma: float = 0.,
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shape: Union[int, IntSequence] = None,
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degrees: bool = False,
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rng_seed: NumpyRngSeed = None):
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@ -1206,7 +1197,7 @@ class Rotation:
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100 orientations:
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>>> import damask
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>>> gamma = damask.Rotation.from_fiber_component([54.7,45.0],[0.,0.],shape=100,degrees=True)
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>>> gamma = damask.Rotation.from_fiber_component([54.7,45.],[0.,0.],shape=100,degrees=True)
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"""
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rng = np.random.default_rng(rng_seed)
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@ -1216,18 +1207,18 @@ class Rotation:
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d_cr = np.array([np.sin(alpha[0])*np.cos(alpha[1]), np.sin(alpha[0])*np.sin(alpha[1]), np.cos(alpha[0])])
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d_lab = np.array([np.sin( beta[0])*np.cos( beta[1]), np.sin( beta[0])*np.sin( beta[1]), np.cos( beta[0])])
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ax_align = np.append(np.cross(d_lab,d_cr), np.arccos(np.dot(d_lab,d_cr)))
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if np.isclose(ax_align[3],0.0): ax_align[:3] = np.array([1,0,0])
|
||||
R_align = Rotation.from_axis_angle(ax_align if ax_align[3] > 0.0 else -ax_align,normalize=True) # rotate fiber axis from sample to crystal frame
|
||||
if np.isclose(ax_align[3],0.): ax_align[:3] = np.array([1.,0.,0.])
|
||||
R_align = Rotation.from_axis_angle(ax_align if ax_align[3] > 0. else -ax_align,normalize=True) # rotate fiber axis from sample to crystal frame
|
||||
|
||||
N = 1 if shape is None else np.prod(shape)
|
||||
u,Theta = (rng.random((N,2)) * 2.0 * np.array([1,np.pi]) - np.array([1.0, 0])).T
|
||||
u,Theta = (rng.random((N,2)) * 2. * np.array([1.,np.pi]) - np.array([1.,0.])).T
|
||||
omega = abs(rng.normal(scale=sigma_,size=N))
|
||||
p = np.column_stack([np.sqrt(1-u**2)*np.cos(Theta),
|
||||
np.sqrt(1-u**2)*np.sin(Theta),
|
||||
u, omega])
|
||||
p[:,:3] = np.einsum('ij,...j',np.eye(3)-np.outer(d_lab,d_lab),p[:,:3]) # remove component along fiber axis
|
||||
f = np.column_stack((np.broadcast_to(d_lab,(N,3)),rng.random(N)*np.pi))
|
||||
f[::2,:3] *= -1 # flip half the rotation axes to negative sense
|
||||
f[::2,:3] *= -1. # flip half the rotation axes to negative sense
|
||||
|
||||
return (R_align.broadcast_to(N)
|
||||
* Rotation.from_axis_angle(p,normalize=True)
|
||||
|
|
@ -1268,15 +1259,15 @@ class Rotation:
|
|||
@staticmethod
|
||||
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]),
|
||||
2.0*(qu[...,3:4]*qu[...,1:2]+_P*qu[...,0:1]*qu[...,2:3]),
|
||||
2.0*(qu[...,1:2]*qu[...,2:3]+_P*qu[...,0:1]*qu[...,3:4]),
|
||||
qq + 2.0*qu[...,2:3]**2,
|
||||
2.0*(qu[...,3:4]*qu[...,2:3]-_P*qu[...,0:1]*qu[...,1:2]),
|
||||
2.0*(qu[...,1:2]*qu[...,3:4]-_P*qu[...,0:1]*qu[...,2:3]),
|
||||
2.0*(qu[...,2:3]*qu[...,3:4]+_P*qu[...,0:1]*qu[...,1:2]),
|
||||
qq + 2.0*qu[...,3:4]**2,
|
||||
om = np.block([qq + 2.*qu[...,1:2]**2,
|
||||
2.*(qu[...,2:3]*qu[...,1:2]-_P*qu[...,0:1]*qu[...,3:4]),
|
||||
2.*(qu[...,3:4]*qu[...,1:2]+_P*qu[...,0:1]*qu[...,2:3]),
|
||||
2.*(qu[...,1:2]*qu[...,2:3]+_P*qu[...,0:1]*qu[...,3:4]),
|
||||
qq + 2.*qu[...,2:3]**2,
|
||||
2.*(qu[...,3:4]*qu[...,2:3]-_P*qu[...,0:1]*qu[...,1:2]),
|
||||
2.*(qu[...,1:2]*qu[...,3:4]-_P*qu[...,0:1]*qu[...,2:3]),
|
||||
2.*(qu[...,2:3]*qu[...,3:4]+_P*qu[...,0:1]*qu[...,1:2]),
|
||||
qq + 2.*qu[...,3:4]**2,
|
||||
]).reshape(qu.shape[:-1]+(3,3))
|
||||
return om
|
||||
|
||||
|
|
@ -1291,22 +1282,20 @@ class Rotation:
|
|||
q12_s = qu[...,1:2]**2+qu[...,2:3]**2
|
||||
chi = np.sqrt(q03_s*q12_s)
|
||||
|
||||
eu = np.where(np.abs(q12_s) < 1.0e-8,
|
||||
np.block([np.arctan2(-_P*2.0*qu[...,0:1]*qu[...,3:4],qu[...,0:1]**2-qu[...,3:4]**2),
|
||||
eu = np.where(np.abs(q12_s) < 1.e-8,
|
||||
np.block([np.arctan2(-_P*2.*qu[...,0:1]*qu[...,3:4],qu[...,0:1]**2-qu[...,3:4]**2),
|
||||
np.zeros(qu.shape[:-1]+(2,))]),
|
||||
np.where(np.abs(q03_s) < 1.0e-8,
|
||||
np.block([np.arctan2( 2.0*qu[...,1:2]*qu[...,2:3],qu[...,1:2]**2-qu[...,2:3]**2),
|
||||
np.where(np.abs(q03_s) < 1.e-8,
|
||||
np.block([np.arctan2( 2.*qu[...,1:2]*qu[...,2:3],qu[...,1:2]**2-qu[...,2:3]**2),
|
||||
np.broadcast_to(np.pi,qu[...,0:1].shape),
|
||||
np.zeros(qu.shape[:-1]+(1,))]),
|
||||
np.block([np.arctan2((-_P*q02+q13)*chi, (-_P*q01-q23)*chi),
|
||||
np.arctan2( 2.0*chi, q03_s-q12_s ),
|
||||
np.arctan2( 2.*chi, q03_s-q12_s ),
|
||||
np.arctan2(( _P*q02+q13)*chi, (-_P*q01+q23)*chi)])
|
||||
)
|
||||
)
|
||||
# reduce Euler angles to definition range
|
||||
eu[np.abs(eu)<1.e-6] = 0.0
|
||||
eu = np.where(eu<0, (eu+2.0*np.pi)%np.array([2.0*np.pi,np.pi,2.0*np.pi]),eu) # needed?
|
||||
return eu
|
||||
eu[np.abs(eu) < 1.e-6] = 0.
|
||||
return np.where(eu < 0., eu%(np.pi*np.array([2.,1.,2.])),eu)
|
||||
|
||||
@staticmethod
|
||||
def _qu2ax(qu: np.ndarray) -> np.ndarray:
|
||||
|
|
@ -1317,11 +1306,11 @@ class Rotation:
|
|||
"""
|
||||
with np.errstate(invalid='ignore',divide='ignore'):
|
||||
s = np.sign(qu[...,0:1])/np.sqrt(qu[...,1:2]**2+qu[...,2:3]**2+qu[...,3:4]**2)
|
||||
omega = 2.0 * np.arccos(np.clip(qu[...,0:1],-1.0,1.0))
|
||||
ax = np.where(np.broadcast_to(qu[...,0:1] < 1.0e-8,qu.shape),
|
||||
omega = 2. * np.arccos(np.clip(qu[...,0:1],-1.,1.))
|
||||
ax = np.where(np.broadcast_to(qu[...,0:1] < 1.e-8,qu.shape),
|
||||
np.block([qu[...,1:4],np.broadcast_to(np.pi,qu[...,0:1].shape)]),
|
||||
np.block([qu[...,1:4]*s,omega]))
|
||||
ax[np.isclose(qu[...,0],1.,rtol=0.0)] = [0.0, 0.0, 1.0, 0.0]
|
||||
ax[np.isclose(qu[...,0],1.,rtol=0.)] = np.array([0.,0.,1.,0.])
|
||||
return ax
|
||||
|
||||
@staticmethod
|
||||
|
|
@ -1329,23 +1318,23 @@ class Rotation:
|
|||
"""Quaternion to Rodrigues–Frank vector."""
|
||||
with np.errstate(invalid='ignore',divide='ignore'):
|
||||
s = np.linalg.norm(qu[...,1:4],axis=-1,keepdims=True)
|
||||
ro = np.where(np.broadcast_to(np.abs(qu[...,0:1]) < 1.0e-12,qu.shape),
|
||||
ro = np.where(np.broadcast_to(np.abs(qu[...,0:1]) < 1.e-12,qu.shape),
|
||||
np.block([qu[...,1:2], qu[...,2:3], qu[...,3:4], np.broadcast_to(np.inf,qu[...,0:1].shape)]),
|
||||
np.block([qu[...,1:2]/s,qu[...,2:3]/s,qu[...,3:4]/s,
|
||||
np.tan(np.arccos(np.clip(qu[...,0:1],-1.0,1.0)))
|
||||
np.tan(np.arccos(np.clip(qu[...,0:1],-1.,1.)))
|
||||
])
|
||||
)
|
||||
ro[np.abs(s).squeeze(-1) < 1.0e-12] = [0.0,0.0,_P,0.0]
|
||||
ro[np.abs(s).squeeze(-1) < 1.e-12] = np.array([0.,0.,_P,0.])
|
||||
return ro
|
||||
|
||||
@staticmethod
|
||||
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))
|
||||
ho = np.where(np.abs(omega) < 1.0e-12,
|
||||
omega = 2. * np.arccos(np.clip(qu[...,0:1],-1.,1.))
|
||||
ho = np.where(np.abs(omega) < 1.e-12,
|
||||
np.zeros(3),
|
||||
qu[...,1:4]/np.linalg.norm(qu[...,1:4],axis=-1,keepdims=True) \
|
||||
qu[...,1:4]/np.linalg.norm(qu[...,1:4],axis=-1,keepdims=True)
|
||||
* (0.75*(omega - np.sin(omega)))**(1./3.))
|
||||
return ho
|
||||
|
||||
|
|
@ -1367,12 +1356,12 @@ class Rotation:
|
|||
trace = om[...,0,0:1] + om[...,1,1:2] + om[...,2,2:3]
|
||||
|
||||
with np.errstate(invalid='ignore',divide='ignore'):
|
||||
s = [
|
||||
0.5 / np.sqrt( 1.0 + trace),
|
||||
2.0 * np.sqrt( 1.0 + om[...,0,0:1] - om[...,1,1:2] - om[...,2,2:3]),
|
||||
2.0 * np.sqrt( 1.0 + om[...,1,1:2] - om[...,2,2:3] - om[...,0,0:1]),
|
||||
2.0 * np.sqrt( 1.0 + om[...,2,2:3] - om[...,0,0:1] - om[...,1,1:2] )
|
||||
]
|
||||
s = np.array([
|
||||
0.5 / np.sqrt( 1. + trace),
|
||||
2. * np.sqrt( 1. + om[...,0,0:1] - om[...,1,1:2] - om[...,2,2:3]),
|
||||
2. * np.sqrt( 1. + om[...,1,1:2] - om[...,2,2:3] - om[...,0,0:1]),
|
||||
2. * np.sqrt( 1. + om[...,2,2:3] - om[...,0,0:1] - om[...,1,1:2] )
|
||||
])
|
||||
qu = np.where(trace>0,
|
||||
np.block([0.25 / s[0],
|
||||
(om[...,2,1:2] - om[...,1,2:3] ) * s[0],
|
||||
|
|
@ -1394,16 +1383,16 @@ class Rotation:
|
|||
0.25 * s[3]]),
|
||||
)
|
||||
)
|
||||
)*np.array([1,_P,_P,_P])
|
||||
qu[qu[...,0]<0] *=-1
|
||||
)*np.array([1.,_P,_P,_P])
|
||||
qu[qu[...,0] < 0.] *= -1.
|
||||
return qu
|
||||
|
||||
@staticmethod
|
||||
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)
|
||||
eu = np.where(np.isclose(np.abs(om[...,2,2:3]),1.0,0.0),
|
||||
zeta = 1./np.sqrt(1.-om[...,2,2:3]**2)
|
||||
eu = np.where(np.isclose(np.abs(om[...,2,2:3]),1.,0.),
|
||||
np.block([np.arctan2(om[...,0,1:2],om[...,0,0:1]),
|
||||
np.pi*0.5*(1-om[...,2,2:3]),
|
||||
np.zeros(om.shape[:-2]+(1,)),
|
||||
|
|
@ -1414,8 +1403,7 @@ class Rotation:
|
|||
])
|
||||
)
|
||||
eu[np.abs(eu) < 1.e-8] = 0.0
|
||||
eu = np.where(eu<0, (eu+2.0*np.pi)%np.array([2.0*np.pi,np.pi,2.0*np.pi]),eu)
|
||||
return eu
|
||||
return np.where(eu < 0., eu%(np.pi*np.array([2.,1.,2.])),eu)
|
||||
|
||||
@staticmethod
|
||||
def _om2ax(om: np.ndarray) -> np.ndarray:
|
||||
|
|
@ -1424,18 +1412,18 @@ class Rotation:
|
|||
om[...,2,0:1]-om[...,0,2:3],
|
||||
om[...,0,1:2]-om[...,1,0:1]
|
||||
])
|
||||
t = 0.5*(om.trace(axis2=-2,axis1=-1) -1.0).reshape(om.shape[:-2]+(1,))
|
||||
t = 0.5*(om.trace(axis2=-2,axis1=-1) -1.).reshape(om.shape[:-2]+(1,))
|
||||
w,vr = np.linalg.eig(om)
|
||||
# mask duplicated real eigenvalues
|
||||
w[np.isclose(w[...,0],1.0+0.0j),1:] = 0.
|
||||
w[np.isclose(w[...,1],1.0+0.0j),2:] = 0.
|
||||
w[np.isclose(w[...,0],1.+0.j),1:] = 0.
|
||||
w[np.isclose(w[...,1],1.+0.j),2:] = 0.
|
||||
vr = np.swapaxes(vr,-1,-2)
|
||||
ax = np.where(np.abs(diag_delta)<1e-13,
|
||||
np.real(vr[np.isclose(w,1.0+0.0j)]).reshape(om.shape[:-2]+(3,)),
|
||||
np.abs(np.real(vr[np.isclose(w,1.0+0.0j)]).reshape(om.shape[:-2]+(3,))) \
|
||||
ax = np.where(np.abs(diag_delta)<1.e-13,
|
||||
np.real(vr[np.isclose(w,1.+0.j)]).reshape(om.shape[:-2]+(3,)),
|
||||
np.abs(np.real(vr[np.isclose(w,1.+0.j)]).reshape(om.shape[:-2]+(3,)))
|
||||
*np.sign(diag_delta))
|
||||
ax = np.block([ax,np.arccos(np.clip(t,-1.0,1.0))])
|
||||
ax[np.abs(ax[...,3])<1.e-8] = [ 0.0, 0.0, 1.0, 0.0]
|
||||
ax = np.block([ax,np.arccos(np.clip(t,-1.,1.))])
|
||||
ax[np.abs(ax[...,3]) < 1.e-8] = np.array([0.,0.,1.,0.])
|
||||
return ax
|
||||
|
||||
@staticmethod
|
||||
|
|
@ -1465,7 +1453,7 @@ class Rotation:
|
|||
-_P*sPhi*np.cos(ee[...,0:1]-ee[...,2:3]),
|
||||
-_P*sPhi*np.sin(ee[...,0:1]-ee[...,2:3]),
|
||||
-_P*cPhi*np.sin(ee[...,0:1]+ee[...,2:3])])
|
||||
qu[qu[...,0]<0.0]*=-1
|
||||
qu[qu[...,0] < 0.] *= -1.
|
||||
return qu
|
||||
|
||||
@staticmethod
|
||||
|
|
@ -1483,7 +1471,7 @@ class Rotation:
|
|||
-c[...,0:1]*s[...,1:2],
|
||||
+c[...,1:2]
|
||||
]).reshape(eu.shape[:-1]+(3,3))
|
||||
om[np.abs(om)<1.e-12] = 0.0
|
||||
om[np.abs(om) < 1.e-12] = 0.
|
||||
return om
|
||||
|
||||
@staticmethod
|
||||
|
|
@ -1493,16 +1481,16 @@ class Rotation:
|
|||
sigma = 0.5*(eu[...,0:1]+eu[...,2:3])
|
||||
delta = 0.5*(eu[...,0:1]-eu[...,2:3])
|
||||
tau = np.linalg.norm(np.block([t,np.sin(sigma)]),axis=-1,keepdims=True)
|
||||
alpha = np.where(np.abs(np.cos(sigma))<1.e-12,np.pi,2.0*np.arctan(tau/np.cos(sigma)))
|
||||
alpha = np.where(np.abs(np.cos(sigma))<1.e-12,np.pi,2.*np.arctan(tau/np.cos(sigma)))
|
||||
with np.errstate(invalid='ignore',divide='ignore'):
|
||||
ax = np.where(np.broadcast_to(np.abs(alpha)<1.0e-12,eu.shape[:-1]+(4,)),
|
||||
[0.0,0.0,1.0,0.0],
|
||||
ax = np.where(np.broadcast_to(np.abs(alpha)<1.e-12,eu.shape[:-1]+(4,)),
|
||||
[0.,0.,1.,0.],
|
||||
np.block([-_P/tau*t*np.cos(delta),
|
||||
-_P/tau*t*np.sin(delta),
|
||||
-_P/tau* np.sin(sigma),
|
||||
alpha
|
||||
]))
|
||||
ax[(alpha<0.0).squeeze()] *=-1
|
||||
ax[(alpha<0.).squeeze()] *= -1.
|
||||
return ax
|
||||
|
||||
@staticmethod
|
||||
|
|
@ -1511,7 +1499,7 @@ class Rotation:
|
|||
ax = Rotation._eu2ax(eu)
|
||||
ro = np.block([ax[...,:3],np.tan(ax[...,3:4]*.5)])
|
||||
ro[ax[...,3] >= np.pi,3] = np.inf
|
||||
ro[np.abs(ax[...,3])<1.e-16] = [ 0.0, 0.0, _P, 0.0 ]
|
||||
ro[np.abs(ax[...,3])<1.e-16] = np.array([0.,0.,_P,0.])
|
||||
return ro
|
||||
|
||||
@staticmethod
|
||||
|
|
@ -1531,7 +1519,7 @@ class Rotation:
|
|||
"""Axis–angle pair to quaternion."""
|
||||
c = np.cos(ax[...,3:4]*.5)
|
||||
s = np.sin(ax[...,3:4]*.5)
|
||||
qu = np.where(np.abs(ax[...,3:4])<1.e-6,[1.0, 0.0, 0.0, 0.0],np.block([c, ax[...,:3]*s]))
|
||||
qu = np.where(np.abs(ax[...,3:4]) < 1.e-6,[1.,0.,0.,0.],np.block([c,ax[...,:3]*s]))
|
||||
return qu
|
||||
|
||||
@staticmethod
|
||||
|
|
@ -1549,7 +1537,7 @@ class Rotation:
|
|||
omc*ax[...,0:1]*ax[...,2:3] + s*ax[...,1:2],
|
||||
omc*ax[...,1:2]*ax[...,2:3] - s*ax[...,0:1],
|
||||
c+omc*ax[...,2:3]**2]).reshape(ax.shape[:-1]+(3,3))
|
||||
return om if _P < 0.0 else np.swapaxes(om,-1,-2)
|
||||
return om if _P < 0. else np.swapaxes(om,-1,-2)
|
||||
|
||||
@staticmethod
|
||||
def _ax2eu(ax: np.ndarray) -> np.ndarray:
|
||||
|
|
@ -1564,15 +1552,14 @@ class Rotation:
|
|||
np.inf,
|
||||
np.tan(ax[...,3:4]*0.5))
|
||||
])
|
||||
ro[np.abs(ax[...,3])<1.e-6] = [.0,.0,_P,.0]
|
||||
ro[np.abs(ax[...,3]) < 1.e-6] = np.array([.0,.0,_P,.0])
|
||||
return ro
|
||||
|
||||
@staticmethod
|
||||
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
|
||||
f = (0.75 * ( ax[...,3:4] - np.sin(ax[...,3:4]) ))**(1./3.)
|
||||
return ax[...,:3] * f
|
||||
|
||||
@staticmethod
|
||||
def _ax2cu(ax: np.ndarray) -> np.ndarray:
|
||||
|
|
@ -1603,16 +1590,15 @@ class Rotation:
|
|||
ax = np.where(np.isfinite(ro[...,3:4]),
|
||||
np.block([ro[...,0:3]*np.linalg.norm(ro[...,0:3],axis=-1,keepdims=True),2.*np.arctan(ro[...,3:4])]),
|
||||
np.block([ro[...,0:3],np.broadcast_to(np.pi,ro[...,3:4].shape)]))
|
||||
ax[np.abs(ro[...,3]) < 1.e-8] = np.array([ 0.0, 0.0, 1.0, 0.0 ])
|
||||
ax[np.abs(ro[...,3]) < 1.e-8] = np.array([0.,0.,1.,0.])
|
||||
return ax
|
||||
|
||||
@staticmethod
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def _ro2ho(ro: np.ndarray) -> np.ndarray:
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"""Rodrigues–Frank vector to homochoric vector."""
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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)
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ho = np.where(np.broadcast_to(np.sum(ro[...,0:3]**2.0,axis=-1,keepdims=True) < 1.e-8,ro[...,0:3].shape),
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np.zeros(3), ro[...,0:3]* (0.75*f)**(1.0/3.0))
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return ho
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f = np.where(np.isfinite(ro[...,3:4]),2.*np.arctan(ro[...,3:4]) -np.sin(2.*np.arctan(ro[...,3:4])),np.pi)
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return np.where(np.broadcast_to(np.sum(ro[...,0:3]**2,axis=-1,keepdims=True) < 1.e-8,ro[...,0:3].shape),
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np.zeros(3), ro[...,0:3]* (0.75*f)**(1./3.))
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@staticmethod
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def _ro2cu(ro: np.ndarray) -> np.ndarray:
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|
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@ -1646,13 +1632,12 @@ class Rotation:
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+9.528014229335313e-6, -5.660288876265125e-6, +1.2844901692764126e-6,
|
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+1.1255185726258763e-6, -1.3834391419956455e-6, +7.513691751164847e-7,
|
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-2.401996891720091e-7, +4.386887017466388e-8, -3.5917775353564864e-9])
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hmag_squared = np.sum(ho**2.,axis=-1,keepdims=True)
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hmag_squared = np.sum(ho**2,axis=-1,keepdims=True)
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s = np.sum(tfit*hmag_squared**np.arange(len(tfit)),axis=-1,keepdims=True)
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with np.errstate(invalid='ignore'):
|
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ax = np.where(np.broadcast_to(np.abs(hmag_squared)<1.e-8,ho.shape[:-1]+(4,)),
|
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[ 0.0, 0.0, 1.0, 0.0 ],
|
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np.block([ho/np.sqrt(hmag_squared),2.0*np.arccos(np.clip(s,-1.0,1.0))]))
|
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return ax
|
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return np.where(np.broadcast_to(np.abs(hmag_squared)<1.e-8,ho.shape[:-1]+(4,)),
|
||||
[0.,0.,1.,0.],
|
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np.block([ho/np.sqrt(hmag_squared),2.*np.arccos(np.clip(s,-1.,1.))]))
|
||||
|
||||
@staticmethod
|
||||
def _ho2ro(ho: np.ndarray) -> np.ndarray:
|
||||
|
|
@ -1676,27 +1661,25 @@ class Rotation:
|
|||
|
||||
with np.errstate(invalid='ignore',divide='ignore'):
|
||||
# inverse M_3
|
||||
xyz2 = xyz3[...,0:2] * np.sqrt( 2.0*rs/(rs+np.abs(xyz3[...,2:3])) )
|
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xyz2 = xyz3[...,0:2] * np.sqrt( 2.*rs/(rs+np.abs(xyz3[...,2:3])) )
|
||||
qxy = np.sum(xyz2**2,axis=-1,keepdims=True)
|
||||
|
||||
q2 = qxy + np.max(np.abs(xyz2),axis=-1,keepdims=True)**2
|
||||
sq2 = np.sqrt(q2)
|
||||
q = (_beta/np.sqrt(2.0)/_R1) * np.sqrt(q2*qxy/(q2-np.max(np.abs(xyz2),axis=-1,keepdims=True)*sq2))
|
||||
q = (_beta/np.sqrt(2.)/_R1) * np.sqrt(q2*qxy/(q2-np.max(np.abs(xyz2),axis=-1,keepdims=True)*sq2))
|
||||
tt = np.clip((np.min(np.abs(xyz2),axis=-1,keepdims=True)**2\
|
||||
+np.max(np.abs(xyz2),axis=-1,keepdims=True)*sq2)/np.sqrt(2.0)/qxy,-1.0,1.0)
|
||||
+np.max(np.abs(xyz2),axis=-1,keepdims=True)*sq2)/np.sqrt(2.)/qxy,-1.,1.)
|
||||
T_inv = np.where(np.abs(xyz2[...,1:2]) <= np.abs(xyz2[...,0:1]),
|
||||
np.block([np.ones_like(tt),np.arccos(tt)/np.pi*12.0]),
|
||||
np.block([np.arccos(tt)/np.pi*12.0,np.ones_like(tt)]))*q
|
||||
T_inv[xyz2<0.0] *= -1.0
|
||||
T_inv[np.broadcast_to(np.isclose(qxy,0.0,rtol=0.0,atol=1.0e-12),T_inv.shape)] = 0.0
|
||||
cu = np.block([T_inv, np.where(xyz3[...,2:3]<0.0,-np.ones_like(xyz3[...,2:3]),np.ones_like(xyz3[...,2:3])) \
|
||||
* rs/np.sqrt(6.0/np.pi),
|
||||
np.block([np.ones_like(tt),np.arccos(tt)/np.pi*12.]),
|
||||
np.block([np.arccos(tt)/np.pi*12.,np.ones_like(tt)]))*q
|
||||
T_inv[xyz2<0.] *= -1.
|
||||
T_inv[np.broadcast_to(np.isclose(qxy,0.,rtol=0.,atol=1.e-12),T_inv.shape)] = 0.
|
||||
cu = np.block([T_inv, np.where(xyz3[...,2:3]<0.,-np.ones_like(xyz3[...,2:3]),np.ones_like(xyz3[...,2:3])) \
|
||||
* rs/np.sqrt(6./np.pi),
|
||||
])/ _sc
|
||||
|
||||
cu[np.isclose(np.sum(np.abs(ho),axis=-1),0.0,rtol=0.0,atol=1.0e-16)] = 0.0
|
||||
cu = np.take_along_axis(cu,Rotation._get_pyramid_order(ho,'backward'),-1)
|
||||
|
||||
return cu
|
||||
cu[np.isclose(np.sum(np.abs(ho),axis=-1),0.,rtol=0.,atol=1.e-16)] = 0.
|
||||
return np.take_along_axis(cu,Rotation._get_pyramid_order(ho,'backward'),-1)
|
||||
|
||||
#---------- Cubochoric ----------
|
||||
@staticmethod
|
||||
|
|
@ -1739,32 +1722,30 @@ class Rotation:
|
|||
# get pyramid and scale by grid parameter ratio
|
||||
XYZ = np.take_along_axis(cu,Rotation._get_pyramid_order(cu,'forward'),-1) * _sc
|
||||
order = np.abs(XYZ[...,1:2]) <= np.abs(XYZ[...,0:1])
|
||||
q = np.pi/12.0 * np.where(order,XYZ[...,1:2],XYZ[...,0:1]) \
|
||||
q = np.pi/12. * np.where(order,XYZ[...,1:2],XYZ[...,0:1]) \
|
||||
/ np.where(order,XYZ[...,0:1],XYZ[...,1:2])
|
||||
c = np.cos(q)
|
||||
s = np.sin(q)
|
||||
q = _R1*2.0**0.25/_beta/ np.sqrt(np.sqrt(2.0)-c) \
|
||||
q = _R1*2.**0.25/_beta/ np.sqrt(np.sqrt(2.)-c) \
|
||||
* np.where(order,XYZ[...,0:1],XYZ[...,1:2])
|
||||
|
||||
T = np.block([ (np.sqrt(2.0)*c - 1.0), np.sqrt(2.0) * s]) * q
|
||||
T = np.block([(np.sqrt(2.)*c - 1.), np.sqrt(2.) * s]) * q
|
||||
|
||||
# transform to sphere grid (inverse Lambert)
|
||||
c = np.sum(T**2,axis=-1,keepdims=True)
|
||||
s = c * np.pi/24.0 /XYZ[...,2:3]**2
|
||||
c = c * np.sqrt(np.pi/24.0)/XYZ[...,2:3]
|
||||
q = np.sqrt( 1.0 - s)
|
||||
s = c * np.pi/24. /XYZ[...,2:3]**2
|
||||
c = c * np.sqrt(np.pi/24.)/XYZ[...,2:3]
|
||||
q = np.sqrt( 1. - s)
|
||||
|
||||
ho = np.where(np.isclose(np.sum(np.abs(XYZ[...,0:2]),axis=-1,keepdims=True),0.0,rtol=0.0,atol=1.0e-16),
|
||||
np.block([np.zeros_like(XYZ[...,0:2]),np.sqrt(6.0/np.pi) *XYZ[...,2:3]]),
|
||||
ho = np.where(np.isclose(np.sum(np.abs(XYZ[...,0:2]),axis=-1,keepdims=True),0.,rtol=0.,atol=1.e-16),
|
||||
np.block([np.zeros_like(XYZ[...,0:2]),np.sqrt(6./np.pi)*XYZ[...,2:3]]),
|
||||
np.block([np.where(order,T[...,0:1],T[...,1:2])*q,
|
||||
np.where(order,T[...,1:2],T[...,0:1])*q,
|
||||
np.sqrt(6.0/np.pi) * XYZ[...,2:3] - c])
|
||||
np.sqrt(6./np.pi) * XYZ[...,2:3] - c])
|
||||
)
|
||||
|
||||
ho[np.isclose(np.sum(np.abs(cu),axis=-1),0.0,rtol=0.0,atol=1.0e-16)] = 0.0
|
||||
ho = np.take_along_axis(ho,Rotation._get_pyramid_order(cu,'backward'),-1)
|
||||
|
||||
return ho
|
||||
ho[np.isclose(np.sum(np.abs(cu),axis=-1),0.,rtol=0.,atol=1.e-16)] = 0.
|
||||
return np.take_along_axis(ho,Rotation._get_pyramid_order(cu,'backward'),-1)
|
||||
|
||||
|
||||
@staticmethod
|
||||
|
|
|
|||
Loading…
Reference in New Issue