Martin Diehl
parent
3f63a4fdbc
commit
15b43bcebf
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@ -325,13 +325,13 @@ class Rotation:
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Parameters
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----------
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q: numpy.ndarray of shape (...,4)
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q : numpy.ndarray of shape (...,4)
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Unit quaternion in positive real hemisphere: (q_0, q_1, q_2, q_3),
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|q|=1, q_0 ≥ 0.
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accept_homomorph: boolean, optional
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accept_homomorph : boolean, optional
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Allow homomorphic variants, i.e. q_0 < 0 (negative real hemisphere).
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Defaults to False.
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P: integer ∈ {-1,1}, optional
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P : integer ∈ {-1,1}, optional
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Convention used. Defaults to -1.
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"""
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@ -362,10 +362,10 @@ class Rotation:
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Parameters
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----------
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phi: numpy.ndarray of shape (...,3)
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phi : numpy.ndarray of shape (...,3)
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Bunge-Euler angles: (φ_1, ϕ, φ_2), φ_1 ∈ [0,2π], ϕ ∈ [0,π], φ_2 ∈ [0,2π]
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unless degrees == True: φ_1 ∈ [0,360], ϕ ∈ [0,180], φ_2 ∈ [0,360].
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degrees: boolean, optional
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degrees : boolean, optional
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Bunge-Euler angles are given in degrees. Defaults to False.
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"""
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@ -389,14 +389,14 @@ class Rotation:
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Parameters
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----------
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axis_angle: numpy.ndarray of shape (...,4)
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axis_angle : numpy.ndarray of shape (...,4)
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Axis angle pair: [n_1, n_2, n_3, ω], |n| = 1 and ω ∈ [0,π]
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unless degrees = True: ω ∈ [0,180].
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degrees: boolean, optional
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degrees : boolean, optional
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Angle ω is given in degrees. Defaults to False.
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normalize: boolean, optional
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Allow |n| ≠ 1. Defaults to False.
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P: integer ∈ {-1,1}, optional
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P : integer ∈ {-1,1}, optional
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Convention used. Defaults to -1.
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"""
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@ -421,16 +421,16 @@ class Rotation:
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orthonormal = True,
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reciprocal = False):
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"""
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Initialize from tbd.
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Initialize from lattice basis vectors.
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Parameters
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----------
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basis: numpy.ndarray of shape (...,3,3)
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tbd
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orthonormal: boolean, optional
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tbd. Defaults to True.
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reciprocal: boolean, optional
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tbd. Defaults to False.
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basis : numpy.ndarray of shape (...,3,3)
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Three lattice basis vectors in three dimensions.
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orthonormal : boolean, optional
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Basis is strictly orthonormal, i.e. is free of stretch components. Defaults to True.
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reciprocal : boolean, optional
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Basis vectors are given in reciprocal (instead of real) space. Defaults to False.
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"""
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om = np.array(basis,dtype=float)
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@ -452,27 +452,6 @@ class Rotation:
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return Rotation(Rotation._om2qu(om))
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@staticmethod
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def from_directions(hkl,uvw):
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"""
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Initialize from pair of directions/planes.
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Parameters
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----------
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hkl: numpy.ndarray of shape (...,3)
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Direction parallel to z direction, i.e. (h k l) || (0,0,1).
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uvw: numpy.ndarray of shape (...,3)
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Direction parallel to x direction, i.e. <u v w> || (1,0,0).
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"""
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hkl_ = hkl/np.linalg.norm(hkl,axis=-1,keepdims=True)
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uvw_ = uvw/np.linalg.norm(uvw,axis=-1,keepdims=True)
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v_1 = np.block([uvw_,np.cross(hkl_,uvw_),hkl_]).reshape(hkl_.shape+(3,))
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v_2 = np.block([uvw_,np.cross(uvw_,hkl_),hkl_]).reshape(hkl_.shape+(3,))
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R = np.where(np.broadcast_to(np.expand_dims(np.expand_dims(np.linalg.det(v_1)>0,-1),-1),v_1.shape),
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v_1,v_2)
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return Rotation.from_basis(np.swapaxes(R,axis2=-2,axis1=-1))
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@staticmethod
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def from_matrix(R):
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"""
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@ -480,7 +459,7 @@ class Rotation:
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Parameters
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----------
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R: numpy.ndarray of shape (...,3,3)
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R : numpy.ndarray of shape (...,3,3)
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Rotation matrix: det(R) = 1, R.T∙R=I.
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"""
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@ -495,12 +474,12 @@ class Rotation:
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Parameters
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----------
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rho: numpy.ndarray of shape (...,4)
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rho : numpy.ndarray of shape (...,4)
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Rodrigues-Frank vector (angle separated from axis).
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(n_1, n_2, n_3, tan(ω/2)), |n| = 1 and ω ∈ [0,π].
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normalize: boolean, optional
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normalize : boolean, optional
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Allow |n| ≠ 1. Defaults to False.
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P: integer ∈ {-1,1}, optional
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P : integer ∈ {-1,1}, optional
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Convention used. Defaults to -1.
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"""
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@ -527,9 +506,9 @@ class Rotation:
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Parameters
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----------
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h: numpy.ndarray of shape (...,3)
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h : numpy.ndarray of shape (...,3)
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Homochoric vector: (h_1, h_2, h_3), |h| < (3/4*π)^(1/3).
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P: integer ∈ {-1,1}, optional
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P : integer ∈ {-1,1}, optional
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Convention used. Defaults to -1.
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"""
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@ -554,9 +533,9 @@ class Rotation:
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Parameters
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----------
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c: numpy.ndarray of shape (...,3)
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c : numpy.ndarray of shape (...,3)
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Cubochoric vector: (c_1, c_2, c_3), max(c_i) < 1/2*π^(2/3).
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P: integer ∈ {-1,1}, optional
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P : integer ∈ {-1,1}, optional
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Convention used. Defaults to -1.
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"""
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@ -854,11 +854,6 @@ class TestRotation:
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rot = Rotation.from_basis(om,False,reciprocal=reciprocal)
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assert np.isclose(np.linalg.det(rot.as_matrix()),1.0)
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def test_directions(self):
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hkl = np.array([0.,0.,1.])
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uvw = np.array([1.,0.,0.])
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assert np.allclose(Rotation.from_directions(hkl,uvw).as_matrix(),np.eye(3))
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@pytest.mark.parametrize('shape',[None,1,(4,4)])
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def test_random(self,shape):
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Rotation.from_random(shape)
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