more testing and related fixes
This commit is contained in:
Martin Diehl
parent
43e7639f77
commit
cbfde73a29
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@ -474,7 +474,7 @@ class Rotation:
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q03 = qu[0]**2+qu[3]**2
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q12 = qu[1]**2+qu[2]**2
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chi = np.sqrt(q03*q12)
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if np.abs(q03)< 1.e-6:
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if np.abs(chi)< 1.e-6:
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eu = np.array([np.arctan2(-P*2.0*qu[0]*qu[3],qu[0]**2-qu[3]**2), 0.0, 0.0])
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elif np.abs(q12)< 1.e-6:
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eu = np.array([np.arctan2( 2.0*qu[1]*qu[2],qu[1]**2-qu[2]**2), np.pi, 0.0])
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@ -491,14 +491,14 @@ class Rotation:
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q12_s = qu[...,1:2]**2+qu[...,2:3]**2
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chi = np.sqrt(q03_s*q12_s)
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eu = np.where(np.abs(q12_s) < 1.0e-6,
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eu = np.where(np.abs(chi) < 1.0e-6,
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np.block([np.arctan2(-P*2.0*qu[...,0:1]*qu[...,3:4],qu[...,0:1]**2-qu[...,3:4]**2),
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np.zeros(qu.shape[:-1]+(2,))]),
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np.block([np.arctan2((-P*q02+q13)*chi, (-P*q01-q23)*chi),
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np.arctan2( 2.0*chi, q03_s-q12_s ),
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np.arctan2(( P*q02+q13)*chi, (-P*q01+q23)*chi)])
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)
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eu = np.where(np.abs(q03_s) < 1.0e-6,
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eu = np.where(np.logical_and(np.abs(q03_s) < 1.0e-6, np.abs(chi) > 1.0e-6),
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np.block([np.arctan2( 2.0*qu[...,1:2]*qu[...,2:3],qu[...,1:2]**2-qu[...,2:3]**2),
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np.ones( qu.shape[:-1]+(1,))*np.pi,
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np.zeros(qu.shape[:-1]+(1,))]),
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@ -525,18 +525,15 @@ class Rotation:
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else:
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ax = ax = np.array([ qu[1], qu[2], qu[3], np.pi])
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else:
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with np.errstate(divide='ignore'):
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with np.errstate(invalid='ignore',divide='ignore'):
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s = np.sign(qu[...,0:1])/np.sqrt(qu[...,1:2]**2+qu[...,2:3]**2+qu[...,3:4]**2)
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omega = 2.0 * np.arccos(np.clip(qu[...,0:1],-1.0,1.0))
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omega = 2.0 * np.arccos(np.clip(qu[...,0:1],-1.0,1.0))
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ax = np.where(np.expand_dims(np.sum(np.abs(qu[:,1:4])**2,axis=-1) < 1.0e-6,-1),
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[0.0, 0.0, 1.0, 0.0], np.block([qu[...,1:4]*s,omega]))
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ax = np.where(qu[...,0:1] < 1.0e-6,
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np.block([qu[...,1:4],np.ones(qu.shape[:-1]+(1,))*np.pi]),
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np.block([qu[...,1:4]*s,omega]))
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ax = np.where(np.expand_dims(np.sum(np.abs(qu[:,1:4])**2,axis=-1) < 1.0e-6,-1),
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[0.0, 0.0, 1.0, 0.0], ax) # TODO: Where not needed
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np.block([qu[...,1:4],np.ones(qu.shape[:-1]+(1,))*np.pi]),ax) # TODO: Where not needed
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return ax
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@staticmethod
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def qu2ro(qu):
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"""Quaternion to Rodrigues-Frank vector."""
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@ -548,12 +545,13 @@ class Rotation:
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ro = np.array([0.0,0.0,P,0.0] if iszero(s) else \
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[ qu[1]/s, qu[2]/s, qu[3]/s, np.tan(np.arccos(np.clip(qu[0],-1.0,1.0)))])
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else:
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s = np.expand_dims(np.linalg.norm(qu[...,1:4],axis=1),-1)
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ro = np.where(np.abs(s) < 1.0e-12,
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[0.0,0.0,P,0.0],
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np.block([qu[...,1:2]/s,qu[...,2:3]/s,qu[...,3:4]/s,
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np.tan(np.arccos(np.clip(qu[:,0:1],-1.0,1.0)))
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])
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with np.errstate(invalid='ignore',divide='ignore'):
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s = np.expand_dims(np.linalg.norm(qu[...,1:4],axis=1),-1)
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ro = np.where(np.abs(s) < 1.0e-12,
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[0.0,0.0,P,0.0],
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np.block([qu[...,1:2]/s,qu[...,2:3]/s,qu[...,3:4]/s,
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np.tan(np.arccos(np.clip(qu[:,0:1],-1.0,1.0)))
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])
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)
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ro = np.where(np.abs(qu[...,0:1]) < 1.0e-12,
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np.block([qu[...,1:2], qu[...,2:3], qu[...,3:4], np.ones(qu.shape[:-1]+(1,))*np.inf]),ro) # TODO: Where not needed
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@ -571,10 +569,12 @@ class Rotation:
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f = 0.75 * ( omega - np.sin(omega) )
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ho = ho/np.linalg.norm(ho) * f**(1./3.)
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else:
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omega = 2.0 * np.arccos(np.clip(qu[...,0:1],-1.0,1.0))
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ho = np.where(np.abs(omega) < 1.0e-12,
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np.zeros(3),
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qu[...,1:4]/np.linalg.norm(qu[...,1:4],axis=1).reshape(qu.shape[:-1]+(1,)) * (0.75*(omega - np.sin(omega)))**(1./3.))
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with np.errstate(invalid='ignore'):
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omega = 2.0 * np.arccos(np.clip(qu[...,0:1],-1.0,1.0))
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ho = np.where(np.abs(omega) < 1.0e-12,
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np.zeros(3),
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qu[...,1:4]/np.linalg.norm(qu[...,1:4],axis=1).reshape(qu.shape[:-1]+(1,)) \
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* (0.75*(omega - np.sin(omega)))**(1./3.))
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return ho
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@staticmethod
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@ -605,13 +605,18 @@ class Rotation:
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else:
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eu = np.array([np.arctan2( om[0,1],om[0,0]), np.pi*0.5*(1-om[2,2]),0.0]) # following the paper, not the reference implementation
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else:
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with np.errstate(divide='ignore'):
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zeta = 1.0/np.sqrt(1.0-om[...,2,2:3]**2)
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eu = np.block([np.arctan2(om[...,2,0:1]*zeta,-om[...,2,1:2]*zeta),
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np.arccos(om[...,2,2:3]),
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np.arctan2(om[...,0,2:3]*zeta,+om[...,1,2:3]*zeta)
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])
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# TODO Special case not implemented!
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with np.errstate(invalid='ignore',divide='ignore'):
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zeta = 1.0/np.sqrt(1.0-om[...,2,2:3]**2)
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eu = np.where(np.isclose(np.abs(om[...,2,2:3]),1.0,1e-4),
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np.block([np.arctan2(om[...,0,1:2],om[...,0,0:1]),
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np.pi*0.5*(1-om[...,2,2:3]),
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np.zeros(om.shape[:-2]+(1,)),
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]),
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np.block([np.arctan2(om[...,2,0:1]*zeta,-om[...,2,1:2]*zeta),
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np.arccos(om[...,2,2:3]),
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np.arctan2(om[...,0,2:3]*zeta,+om[...,1,2:3]*zeta)
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])
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)
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eu[np.abs(eu)<1.e-6] = 0.0
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eu = np.where(eu<0, (eu+2.0*np.pi)%np.array([2.0*np.pi,np.pi,2.0*np.pi]),eu)
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return eu
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@ -620,22 +625,30 @@ class Rotation:
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@staticmethod
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def om2ax(om):
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"""Rotation matrix to axis angle pair."""
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ax=np.empty(4)
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if len(om.shape) == 2:
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ax=np.empty(4)
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# first get the rotation angle
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t = 0.5*(om.trace() -1.0)
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ax[3] = np.arccos(np.clip(t,-1.0,1.0))
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# first get the rotation angle
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t = 0.5*(om.trace() -1.0)
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ax[3] = np.arccos(np.clip(t,-1.0,1.0))
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if np.abs(ax[3])<1.e-6:
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ax = np.array([ 0.0, 0.0, 1.0, 0.0])
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if np.abs(ax[3])<1.e-6:
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ax = np.array([ 0.0, 0.0, 1.0, 0.0])
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else:
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w,vr = np.linalg.eig(om)
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# next, find the eigenvalue (1,0j)
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i = np.where(np.isclose(w,1.0+0.0j))[0][0]
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ax[0:3] = np.real(vr[0:3,i])
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diagDelta = np.array([om[1,2]-om[2,1],om[2,0]-om[0,2],om[0,1]-om[1,0]])
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ax[0:3] = np.where(np.abs(diagDelta)<1.e-6, ax[0:3],np.abs(ax[0:3])*np.sign(-P*diagDelta))
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return ax
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else:
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diag_delta = np.block([om[...,1,2:3]-om[...,2,1:2],
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om[...,2,0:1]-om[...,0,2:3],
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om[...,0,1:2]-om[...,1,0:1]
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])
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w,vr = np.linalg.eig(om)
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# next, find the eigenvalue (1,0j)
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i = np.where(np.isclose(w,1.0+0.0j))[0][0]
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ax[0:3] = np.real(vr[0:3,i])
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diagDelta = np.array([om[1,2]-om[2,1],om[2,0]-om[0,2],om[0,1]-om[1,0]])
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ax[0:3] = np.where(np.abs(diagDelta)<1.e-6, ax[0:3],np.abs(ax[0:3])*np.sign(-P*diagDelta))
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return ax
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# TODO ------------------
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@staticmethod
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def om2ro(om):
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@ -727,13 +740,14 @@ class Rotation:
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delta = 0.5*(eu[...,0:1]-eu[...,2:3])
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tau = np.linalg.norm(np.block([t,np.sin(sigma)]),axis=-1).reshape(-1,1)
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alpha = np.where(np.abs(np.cos(sigma))<1.e-12,np.pi,2.0*np.arctan(tau/np.cos(sigma)))
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ax = np.where(np.broadcast_to(np.abs(alpha)<1.0e-12,eu.shape[:-1]+(4,)),
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[0.0,0.0,1.0,0.0],
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np.block([-P/tau*t*np.cos(delta),
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-P/tau*t*np.sin(delta),
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-P/tau* np.sin(sigma),
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alpha
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]))
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with np.errstate(invalid='ignore',divide='ignore'):
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ax = np.where(np.broadcast_to(np.abs(alpha)<1.0e-12,eu.shape[:-1]+(4,)),
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[0.0,0.0,1.0,0.0],
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np.block([-P/tau*t*np.cos(delta),
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-P/tau*t*np.sin(delta),
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-P/tau* np.sin(sigma),
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alpha
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]))
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ax[(alpha<0.0).squeeze()] *=-1
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return ax
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@ -5,7 +5,7 @@ import numpy as np
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from damask import Rotation
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n = 1000
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n = 1100
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atol=1.e-4
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scatter=1.e-2
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@ -74,10 +74,12 @@ def default():
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np.array([1.0, 1.0,-1.0,-1.0])/2.,
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np.array([1.0,-1.0,-1.0,-1.0])/2.,
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])
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specials += np.broadcast_to(np.random.rand(4)*scatter,specials.shape)
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specials /= np.linalg.norm(specials,axis=1).reshape(-1,1)
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specials[specials[:,0]<0]*=-1
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specials_scatter = specials + np.broadcast_to(np.random.rand(4)*scatter,specials.shape)
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specials_scatter /= np.linalg.norm(specials_scatter,axis=1).reshape(-1,1)
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specials_scatter[specials_scatter[:,0]<0]*=-1
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return [Rotation.fromQuaternion(s) for s in specials] + \
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[Rotation.fromQuaternion(s) for s in specials_scatter] + \
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[Rotation.fromRandom() for _ in range(n-len(specials))]
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@pytest.fixture
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