diff --git a/python/damask/_rotation.py b/python/damask/_rotation.py index 166863e70..cd3164db4 100644 --- a/python/damask/_rotation.py +++ b/python/damask/_rotation.py @@ -1324,28 +1324,41 @@ class Rotation: @staticmethod def _qu2eu(qu: np.ndarray) -> np.ndarray: - """Quaternion to Bunge Euler angles.""" - q02 = qu[...,0:1]*qu[...,2:3] - q13 = qu[...,1:2]*qu[...,3:4] - q01 = qu[...,0:1]*qu[...,1:2] - q23 = qu[...,2:3]*qu[...,3:4] - q03_s = qu[...,0:1]**2+qu[...,3:4]**2 - q12_s = qu[...,1:2]**2+qu[...,2:3]**2 - chi = np.sqrt(q03_s*q12_s) + """ + Quaternion to Bunge Euler angles. - 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.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.*chi, q03_s-q12_s ), - np.arctan2(( _P*q02+q13)*chi, (-_P*q01+q23)*chi)]) - ) - ) - eu[np.abs(eu) < 1.e-6] = 0. + References + ---------- + E. Bernardes and S. Viollet, PLoS ONE 17(11):e0276302, 2022 + https://doi.org/10.1371/journal.pone.0276302 + + """ + a = qu[...,0:1] + b = -_P*qu[...,3:4] + c = -_P*qu[...,1:2] + d = -_P*qu[...,2:3] + + eu = np.block([ + np.arctan2(b,a), + np.arccos(2*(a**2+b**2)/(a**2+b**2+c**2+d**2)-1), + np.arctan2(-d,c), + ]) + + eu_sum = eu[...,0] + eu[...,2] + eu_diff = eu[...,0] - eu[...,2] + + is_zero = np.isclose(eu[...,1],0.0) + is_pi = np.isclose(eu[...,1],np.pi) + is_ok = ~np.logical_or(is_zero,is_pi) + + eu[...,0][is_zero] = 2*eu[...,0][is_zero] + eu[...,0][is_pi] = -2*eu[...,2][is_pi] + eu[...,2][~is_ok] = 0.0 + eu[...,0][is_ok] = eu_diff[is_ok] + eu[...,2][is_ok] = eu_sum [is_ok] + + eu[np.logical_or(np.abs(eu) < 1.e-6, + np.abs(eu-2*np.pi) < 1.e-6)] = 0. return np.where(eu < 0., eu%(np.pi*np.array([2.,1.,2.])),eu) @staticmethod