import os import pytest import numpy as np from damask import Rotation from damask import _rotation n = 1100 atol=1.e-4 scatter=1.e-2 @pytest.fixture def default(): """A set of n random rotations.""" specials = np.array([ [1.0, 0.0, 0.0, 0.0], #---------------------- [0.0, 1.0, 0.0, 0.0], [0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 0.0, 1.0], [0.0,-1.0, 0.0, 0.0], [0.0, 0.0,-1.0, 0.0], [0.0, 0.0, 0.0,-1.0], #---------------------- [1.0, 1.0, 0.0, 0.0], [1.0, 0.0, 1.0, 0.0], [1.0, 0.0, 0.0, 1.0], [0.0, 1.0, 1.0, 0.0], [0.0, 1.0, 0.0, 1.0], [0.0, 0.0, 1.0, 1.0], #---------------------- [1.0,-1.0, 0.0, 0.0], [1.0, 0.0,-1.0, 0.0], [1.0, 0.0, 0.0,-1.0], [0.0, 1.0,-1.0, 0.0], [0.0, 1.0, 0.0,-1.0], [0.0, 0.0, 1.0,-1.0], #---------------------- [0.0, 1.0,-1.0, 0.0], [0.0, 1.0, 0.0,-1.0], [0.0, 0.0, 1.0,-1.0], #---------------------- [0.0,-1.0,-1.0, 0.0], [0.0,-1.0, 0.0,-1.0], [0.0, 0.0,-1.0,-1.0], #---------------------- [1.0, 1.0, 1.0, 0.0], [1.0, 1.0, 0.0, 1.0], [1.0, 0.0, 1.0, 1.0], [1.0,-1.0, 1.0, 0.0], [1.0,-1.0, 0.0, 1.0], [1.0, 0.0,-1.0, 1.0], [1.0, 1.0,-1.0, 0.0], [1.0, 1.0, 0.0,-1.0], [1.0, 0.0, 1.0,-1.0], [1.0,-1.0,-1.0, 0.0], [1.0,-1.0, 0.0,-1.0], [1.0, 0.0,-1.0,-1.0], #---------------------- [0.0, 1.0, 1.0, 1.0], [0.0, 1.0,-1.0, 1.0], [0.0, 1.0, 1.0,-1.0], [0.0,-1.0, 1.0, 1.0], [0.0,-1.0,-1.0, 1.0], [0.0,-1.0, 1.0,-1.0], [0.0,-1.0,-1.0,-1.0], #---------------------- [1.0, 1.0, 1.0, 1.0], [1.0,-1.0, 1.0, 1.0], [1.0, 1.0,-1.0, 1.0], [1.0, 1.0, 1.0,-1.0], [1.0,-1.0,-1.0, 1.0], [1.0,-1.0, 1.0,-1.0], [1.0, 1.0,-1.0,-1.0], [1.0,-1.0,-1.0,-1.0], ]) specials /= np.linalg.norm(specials,axis=1).reshape(-1,1) specials_scatter = specials + np.broadcast_to(np.random.rand(4)*scatter,specials.shape) specials_scatter /= np.linalg.norm(specials_scatter,axis=1).reshape(-1,1) specials_scatter[specials_scatter[:,0]<0]*=-1 return [Rotation.from_quaternion(s) for s in specials] + \ [Rotation.from_quaternion(s) for s in specials_scatter] + \ [Rotation.from_random() for _ in range(n-len(specials)-len(specials_scatter))] @pytest.fixture def reference_dir(reference_dir_base): """Directory containing reference results.""" return os.path.join(reference_dir_base,'Rotation') #################################################################################################### # Code below available according to the following conditions on https://github.com/MarDiehl/3Drotations #################################################################################################### # Copyright (c) 2017-2019, Martin Diehl/Max-Planck-Institut für Eisenforschung GmbH # Copyright (c) 2013-2014, Marc De Graef/Carnegie Mellon University # All rights reserved. # # Redistribution and use in source and binary forms, with or without modification, are # permitted provided that the following conditions are met: # # - Redistributions of source code must retain the above copyright notice, this list # of conditions and the following disclaimer. # - Redistributions in binary form must reproduce the above copyright notice, this # list of conditions and the following disclaimer in the documentation and/or # other materials provided with the distribution. # - Neither the names of Marc De Graef, Carnegie Mellon University nor the names # of its contributors may be used to endorse or promote products derived from # this software without specific prior written permission. # # THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" # AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE # IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE # ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE # LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL # DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR # SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER # CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, # OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE # USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. #################################################################################################### _P = _rotation._P # parameters for conversion from/to cubochoric _sc = _rotation._sc _beta = _rotation._beta _R1 = _rotation._R1 def iszero(a): return np.isclose(a,0.0,atol=1.0e-12,rtol=0.0) #---------- Quaternion ---------- def qu2om(qu): """Quaternion to rotation matrix.""" qq = qu[0]**2-(qu[1]**2 + qu[2]**2 + qu[3]**2) om = np.diag(qq + 2.0*np.array([qu[1],qu[2],qu[3]])**2) om[0,1] = 2.0*(qu[2]*qu[1]+qu[0]*qu[3]) om[1,0] = 2.0*(qu[1]*qu[2]-qu[0]*qu[3]) om[1,2] = 2.0*(qu[3]*qu[2]+qu[0]*qu[1]) om[2,1] = 2.0*(qu[2]*qu[3]-qu[0]*qu[1]) om[2,0] = 2.0*(qu[1]*qu[3]+qu[0]*qu[2]) om[0,2] = 2.0*(qu[3]*qu[1]-qu[0]*qu[2]) return om if _P < 0.0 else np.swapaxes(om,-1,-2) def qu2eu(qu): """Quaternion to Bunge-Euler angles.""" q03 = qu[0]**2+qu[3]**2 q12 = qu[1]**2+qu[2]**2 chi = np.sqrt(q03*q12) if np.abs(q12) < 1.e-8: eu = np.array([np.arctan2(-_P*2.0*qu[0]*qu[3],qu[0]**2-qu[3]**2), 0.0, 0.0]) elif np.abs(q03) < 1.e-8: eu = np.array([np.arctan2( 2.0*qu[1]*qu[2],qu[1]**2-qu[2]**2), np.pi, 0.0]) else: eu = np.array([np.arctan2((-_P*qu[0]*qu[2]+qu[1]*qu[3])*chi, (-_P*qu[0]*qu[1]-qu[2]*qu[3])*chi ), np.arctan2( 2.0*chi, q03-q12 ), np.arctan2(( _P*qu[0]*qu[2]+qu[1]*qu[3])*chi, (-_P*qu[0]*qu[1]+qu[2]*qu[3])*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) return eu def qu2ax(qu): """ Quaternion to axis angle pair. Modified version of the original formulation, should be numerically more stable """ if np.isclose(qu[0],1.,rtol=0.0): # set axis to [001] if the angle is 0/360 ax = np.array([ 0.0, 0.0, 1.0, 0.0 ]) elif qu[0] > 1.e-8: s = np.sign(qu[0])/np.sqrt(qu[1]**2+qu[2]**2+qu[3]**2) omega = 2.0 * np.arccos(np.clip(qu[0],-1.0,1.0)) ax = ax = np.array([ qu[1]*s, qu[2]*s, qu[3]*s, omega ]) else: ax = ax = np.array([ qu[1], qu[2], qu[3], np.pi]) return ax def qu2ro(qu): """Quaternion to Rodrigues-Frank vector.""" if iszero(qu[0]): ro = np.array([qu[1], qu[2], qu[3], np.inf]) else: s = np.linalg.norm(qu[1:4]) ro = np.array([0.0,0.0,_P,0.0] if iszero(s) else \ [ qu[1]/s, qu[2]/s, qu[3]/s, np.tan(np.arccos(np.clip(qu[0],-1.0,1.0)))]) return ro def qu2ho(qu): """Quaternion to homochoric vector.""" omega = 2.0 * np.arccos(np.clip(qu[0],-1.0,1.0)) if np.abs(omega) < 1.0e-12: ho = np.zeros(3) else: ho = np.array([qu[1], qu[2], qu[3]]) f = 0.75 * ( omega - np.sin(omega) ) ho = ho/np.linalg.norm(ho) * f**(1./3.) return ho #---------- Rotation matrix ---------- def om2qu(a): trace = a[0,0] + a[1,1] + a[2,2] if trace > 0: s = 0.5 / np.sqrt(trace+ 1.0) qu = np.array([0.25 / s,( a[2,1] - a[1,2] ) * s,( a[0,2] - a[2,0] ) * s,( a[1,0] - a[0,1] ) * s]) else: if ( a[0,0] > a[1,1] and a[0,0] > a[2,2] ): s = 2.0 * np.sqrt( 1.0 + a[0,0] - a[1,1] - a[2,2]) qu = np.array([ (a[2,1] - a[1,2]) / s,0.25 * s,(a[0,1] + a[1,0]) / s,(a[0,2] + a[2,0]) / s]) elif (a[1,1] > a[2,2]): s = 2.0 * np.sqrt( 1.0 + a[1,1] - a[0,0] - a[2,2]) qu = np.array([ (a[0,2] - a[2,0]) / s,(a[0,1] + a[1,0]) / s,0.25 * s,(a[1,2] + a[2,1]) / s]) else: s = 2.0 * np.sqrt( 1.0 + a[2,2] - a[0,0] - a[1,1] ) qu = np.array([ (a[1,0] - a[0,1]) / s,(a[0,2] + a[2,0]) / s,(a[1,2] + a[2,1]) / s,0.25 * s]) if qu[0]<0: qu*=-1 return qu*np.array([1.,_P,_P,_P]) def om2eu(om): """Rotation matrix to Bunge-Euler angles.""" if not np.isclose(np.abs(om[2,2]),1.0,1.e-9): zeta = 1.0/np.sqrt(1.0-om[2,2]**2) eu = np.array([np.arctan2(om[2,0]*zeta,-om[2,1]*zeta), np.arccos(om[2,2]), np.arctan2(om[0,2]*zeta, om[1,2]*zeta)]) else: 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 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 def om2ax(om): """Rotation matrix to axis angle pair.""" #return qu2ax(om2qu(om)) # HOTFIX ax=np.empty(4) # first get the rotation angle t = 0.5*(om.trace() -1.0) ax[3] = np.arccos(np.clip(t,-1.0,1.0)) if np.abs(ax[3])<1.e-8: ax = np.array([ 0.0, 0.0, 1.0, 0.0]) else: w,vr = np.linalg.eig(om) # next, find the eigenvalue (1,0j) i = np.where(np.isclose(w,1.0+0.0j))[0][0] ax[0:3] = np.real(vr[0:3,i]) diagDelta = -_P*np.array([om[1,2]-om[2,1],om[2,0]-om[0,2],om[0,1]-om[1,0]]) ax[0:3] = np.where(np.abs(diagDelta)<1e-12, ax[0:3],np.abs(ax[0:3])*np.sign(diagDelta)) return ax #---------- Bunge-Euler angles ---------- def eu2qu(eu): """Bunge-Euler angles to quaternion.""" ee = 0.5*eu cPhi = np.cos(ee[1]) sPhi = np.sin(ee[1]) qu = np.array([ cPhi*np.cos(ee[0]+ee[2]), -_P*sPhi*np.cos(ee[0]-ee[2]), -_P*sPhi*np.sin(ee[0]-ee[2]), -_P*cPhi*np.sin(ee[0]+ee[2]) ]) if qu[0] < 0.0: qu*=-1 return qu def eu2om(eu): """Bunge-Euler angles to rotation matrix.""" c = np.cos(eu) s = np.sin(eu) om = np.array([[+c[0]*c[2]-s[0]*s[2]*c[1], +s[0]*c[2]+c[0]*s[2]*c[1], +s[2]*s[1]], [-c[0]*s[2]-s[0]*c[2]*c[1], -s[0]*s[2]+c[0]*c[2]*c[1], +c[2]*s[1]], [+s[0]*s[1], -c[0]*s[1], +c[1] ]]) om[np.abs(om)<1.e-12] = 0.0 return om def eu2ax(eu): """Bunge-Euler angles to axis angle pair.""" t = np.tan(eu[1]*0.5) sigma = 0.5*(eu[0]+eu[2]) delta = 0.5*(eu[0]-eu[2]) tau = np.linalg.norm([t,np.sin(sigma)]) alpha = np.pi if iszero(np.cos(sigma)) else \ 2.0*np.arctan(tau/np.cos(sigma)) if np.abs(alpha)<1.e-6: ax = np.array([ 0.0, 0.0, 1.0, 0.0 ]) else: ax = -_P/tau * np.array([ t*np.cos(delta), t*np.sin(delta), np.sin(sigma) ]) # passive axis angle pair so a minus sign in front ax = np.append(ax,alpha) if alpha < 0.0: ax *= -1.0 # ensure alpha is positive return ax def eu2ro(eu): """Bunge-Euler angles to Rodrigues-Frank vector.""" ro = eu2ax(eu) # convert to axis angle pair representation if ro[3] >= np.pi: # Differs from original implementation. check convention 5 ro[3] = np.inf elif iszero(ro[3]): ro = np.array([ 0.0, 0.0, _P, 0.0 ]) else: ro[3] = np.tan(ro[3]*0.5) return ro #---------- Axis angle pair ---------- def ax2qu(ax): """Axis angle pair to quaternion.""" if np.abs(ax[3])<1.e-6: qu = np.array([ 1.0, 0.0, 0.0, 0.0 ]) else: 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 def ax2om(ax): """Axis angle pair to rotation matrix.""" c = np.cos(ax[3]) s = np.sin(ax[3]) omc = 1.0-c om=np.diag(ax[0:3]**2*omc + c) for idx in [[0,1,2],[1,2,0],[2,0,1]]: q = omc*ax[idx[0]] * ax[idx[1]] om[idx[0],idx[1]] = q + s*ax[idx[2]] om[idx[1],idx[0]] = q - s*ax[idx[2]] return om if _P < 0.0 else om.T def ax2ro(ax): """Axis angle pair to Rodrigues-Frank vector.""" if np.abs(ax[3])<1.e-6: ro = [ 0.0, 0.0, _P, 0.0 ] else: ro = [ax[0], ax[1], ax[2]] # 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)] ro = np.array(ro) return ro def ax2ho(ax): """Axis angle pair to homochoric vector.""" f = (0.75 * ( ax[3] - np.sin(ax[3]) ))**(1.0/3.0) ho = ax[0:3] * f return ho #---------- Rodrigues-Frank vector ---------- def ro2ax(ro): """Rodrigues-Frank vector to axis angle pair.""" if np.abs(ro[3]) < 1.e-8: ax = np.array([ 0.0, 0.0, 1.0, 0.0 ]) elif not np.isfinite(ro[3]): ax = np.array([ ro[0], ro[1], ro[2], np.pi ]) else: angle = 2.0*np.arctan(ro[3]) ta = np.linalg.norm(ro[0:3]) ax = np.array([ ro[0]*ta, ro[1]*ta, ro[2]*ta, angle ]) return ax def ro2ho(ro): """Rodrigues-Frank vector to homochoric vector.""" if np.sum(ro[0:3]**2.0) < 1.e-8: ho = np.zeros(3) else: f = 2.0*np.arctan(ro[3]) -np.sin(2.0*np.arctan(ro[3])) if np.isfinite(ro[3]) else np.pi ho = ro[0:3] * (0.75*f)**(1.0/3.0) return ho #---------- Homochoric vector---------- def ho2ax(ho): """Homochoric vector to axis angle pair.""" tfit = np.array([+1.0000000000018852, -0.5000000002194847, -0.024999992127593126, -0.003928701544781374, -0.0008152701535450438, -0.0002009500426119712, -0.00002397986776071756, -0.00008202868926605841, +0.00012448715042090092, -0.0001749114214822577, +0.0001703481934140054, -0.00012062065004116828, +0.000059719705868660826, -0.00001980756723965647, +0.000003953714684212874, -0.00000036555001439719544]) # normalize h and store the magnitude hmag_squared = np.sum(ho**2.) if iszero(hmag_squared): ax = np.array([ 0.0, 0.0, 1.0, 0.0 ]) else: hm = hmag_squared # convert the magnitude to the rotation angle s = tfit[0] + tfit[1] * hmag_squared for i in range(2,16): hm *= hmag_squared s += tfit[i] * hm ax = np.append(ho/np.sqrt(hmag_squared),2.0*np.arccos(np.clip(s,-1.0,1.0))) return ax def ho2cu(ho): """ Homochoric vector to cubochoric vector. References ---------- D. Roşca et al., Modelling and Simulation in Materials Science and Engineering 22:075013, 2014 https://doi.org/10.1088/0965-0393/22/7/075013 """ rs = np.linalg.norm(ho) if np.allclose(ho,0.0,rtol=0.0,atol=1.0e-16): cu = np.zeros(3) else: xyz3 = ho[_get_pyramid_order(ho,'forward')] # inverse M_3 xyz2 = xyz3[0:2] * np.sqrt( 2.0*rs/(rs+np.abs(xyz3[2])) ) # inverse M_2 qxy = np.sum(xyz2**2) if np.isclose(qxy,0.0,rtol=0.0,atol=1.0e-16): Tinv = np.zeros(2) else: q2 = qxy + np.max(np.abs(xyz2))**2 sq2 = np.sqrt(q2) q = (_beta/np.sqrt(2.0)/_R1) * np.sqrt(q2*qxy/(q2-np.max(np.abs(xyz2))*sq2)) tt = np.clip((np.min(np.abs(xyz2))**2+np.max(np.abs(xyz2))*sq2)/np.sqrt(2.0)/qxy,-1.0,1.0) Tinv = np.array([1.0,np.arccos(tt)/np.pi*12.0]) if np.abs(xyz2[1]) <= np.abs(xyz2[0]) else \ np.array([np.arccos(tt)/np.pi*12.0,1.0]) Tinv = q * np.where(xyz2<0.0,-Tinv,Tinv) # inverse M_1 cu = np.array([ Tinv[0], Tinv[1], (-1.0 if xyz3[2] < 0.0 else 1.0) * rs / np.sqrt(6.0/np.pi) ]) /_sc cu = cu[_get_pyramid_order(ho,'backward')] return cu #---------- Cubochoric ---------- def cu2ho(cu): """ Cubochoric vector to homochoric vector. References ---------- D. Roşca et al., Modelling and Simulation in Materials Science and Engineering 22:075013, 2014 https://doi.org/10.1088/0965-0393/22/7/075013 """ # transform to the sphere grid via the curved square, and intercept the zero point if np.allclose(cu,0.0,rtol=0.0,atol=1.0e-16): ho = np.zeros(3) else: # get pyramide and scale by grid parameter ratio XYZ = cu[_get_pyramid_order(cu,'forward')] * _sc # intercept all the points along the z-axis if np.allclose(XYZ[0:2],0.0,rtol=0.0,atol=1.0e-16): ho = np.array([0.0, 0.0, np.sqrt(6.0/np.pi) * XYZ[2]]) else: order = [1,0] if np.abs(XYZ[1]) <= np.abs(XYZ[0]) else [0,1] q = np.pi/12.0 * XYZ[order[0]]/XYZ[order[1]] c = np.cos(q) s = np.sin(q) q = _R1*2.0**0.25/_beta * XYZ[order[1]] / np.sqrt(np.sqrt(2.0)-c) T = np.array([ (np.sqrt(2.0)*c - 1.0), np.sqrt(2.0) * s]) * q # transform to sphere grid (inverse Lambert) # note that there is no need to worry about dividing by zero, since XYZ[2] can not become zero c = np.sum(T**2) s = c * np.pi/24.0 /XYZ[2]**2 c = c * np.sqrt(np.pi/24.0)/XYZ[2] q = np.sqrt( 1.0 - s ) ho = np.array([ T[order[1]] * q, T[order[0]] * q, np.sqrt(6.0/np.pi) * XYZ[2] - c ]) ho = ho[_get_pyramid_order(cu,'backward')] return ho def _get_pyramid_order(xyz,direction=None): """ Get order of the coordinates. Depending on the pyramid in which the point is located, the order need to be adjusted. Parameters ---------- xyz : numpy.ndarray coordinates of a point on a uniform refinable grid on a ball or in a uniform refinable cubical grid. References ---------- D. Roşca et al., Modelling and Simulation in Materials Science and Engineering 22:075013, 2014 https://doi.org/10.1088/0965-0393/22/7/075013 """ order = {'forward':np.array([[0,1,2],[1,2,0],[2,0,1]]), 'backward':np.array([[0,1,2],[2,0,1],[1,2,0]])} if np.maximum(abs(xyz[0]),abs(xyz[1])) <= xyz[2] or \ np.maximum(abs(xyz[0]),abs(xyz[1])) <=-xyz[2]: p = 0 elif np.maximum(abs(xyz[1]),abs(xyz[2])) <= xyz[0] or \ np.maximum(abs(xyz[1]),abs(xyz[2])) <=-xyz[0]: p = 1 elif np.maximum(abs(xyz[2]),abs(xyz[0])) <= xyz[1] or \ np.maximum(abs(xyz[2]),abs(xyz[0])) <=-xyz[1]: p = 2 return order[direction][p] #################################################################################################### #################################################################################################### def mul(me, other): """ Multiplication. Parameters ---------- other : numpy.ndarray or Rotation Vector, second or fourth order tensor, or rotation object that is rotated. Todo ---- Document details active/passive) consider rotation of (3,3,3,3)-matrix """ if me.quaternion.shape != (4,): raise NotImplementedError('Support for multiple rotations missing') if isinstance(other, Rotation): me_q = me.quaternion[0] me_p = me.quaternion[1:] other_q = other.quaternion[0] other_p = other.quaternion[1:] R = me.__class__(np.append(me_q*other_q - np.dot(me_p,other_p), me_q*other_p + other_q*me_p + _P * np.cross(me_p,other_p))) return R.standardize() elif isinstance(other, np.ndarray): if other.shape == (3,): A = me.quaternion[0]**2.0 - np.dot(me.quaternion[1:],me.quaternion[1:]) B = 2.0 * np.dot(me.quaternion[1:],other) C = 2.0 * _P*me.quaternion[0] return A*other + B*me.quaternion[1:] + C * np.cross(me.quaternion[1:],other) elif other.shape == (3,3,): R = me.as_matrix() return np.dot(R,np.dot(other,R.T)) elif other.shape == (3,3,3,3,): R = me.as_matrix() return np.einsum('ia,jb,kc,ld,abcd->ijkl',R,R,R,R,other) RR = np.outer(R, R) RRRR = np.outer(RR, RR).reshape(4 * (3,3)) axes = ((0, 2, 4, 6), (0, 1, 2, 3)) return np.tensordot(RRRR, other, axes) else: raise ValueError('Can only rotate vectors, 2nd order ternsors, and 4th order tensors') else: raise TypeError('Cannot rotate {}'.format(type(other))) class TestRotation: @pytest.mark.parametrize('forward,backward',[(Rotation._qu2om,Rotation._om2qu), (Rotation._qu2eu,Rotation._eu2qu), (Rotation._qu2ax,Rotation._ax2qu), (Rotation._qu2ro,Rotation._ro2qu), (Rotation._qu2ho,Rotation._ho2qu), (Rotation._qu2cu,Rotation._cu2qu)]) def test_quaternion_internal(self,default,forward,backward): """Ensure invariance of conversion from quaternion and back.""" for rot in default: m = rot.as_quaternion() o = backward(forward(m)) ok = np.allclose(m,o,atol=atol) if np.isclose(rot.as_quaternion()[0],0.0,atol=atol): ok = ok or np.allclose(m*-1.,o,atol=atol) print(m,o,rot.as_quaternion()) assert ok and np.isclose(np.linalg.norm(o),1.0) @pytest.mark.parametrize('forward,backward',[(Rotation._om2qu,Rotation._qu2om), (Rotation._om2eu,Rotation._eu2om), (Rotation._om2ax,Rotation._ax2om), (Rotation._om2ro,Rotation._ro2om), (Rotation._om2ho,Rotation._ho2om), (Rotation._om2cu,Rotation._cu2om)]) def test_matrix_internal(self,default,forward,backward): """Ensure invariance of conversion from rotation matrix and back.""" for rot in default: m = rot.as_matrix() o = backward(forward(m)) ok = np.allclose(m,o,atol=atol) print(m,o,rot.as_quaternion()) assert ok and np.isclose(np.linalg.det(o),1.0) @pytest.mark.parametrize('forward,backward',[(Rotation._eu2qu,Rotation._qu2eu), (Rotation._eu2om,Rotation._om2eu), (Rotation._eu2ax,Rotation._ax2eu), (Rotation._eu2ro,Rotation._ro2eu), (Rotation._eu2ho,Rotation._ho2eu), (Rotation._eu2cu,Rotation._cu2eu)]) def test_Eulers_internal(self,default,forward,backward): """Ensure invariance of conversion from Euler angles and back.""" for rot in default: m = rot.as_Eulers() o = backward(forward(m)) u = np.array([np.pi*2,np.pi,np.pi*2]) ok = np.allclose(m,o,atol=atol) ok = ok or np.allclose(np.where(np.isclose(m,u),m-u,m),np.where(np.isclose(o,u),o-u,o),atol=atol) if np.isclose(m[1],0.0,atol=atol) or np.isclose(m[1],np.pi,atol=atol): sum_phi = np.unwrap([m[0]+m[2],o[0]+o[2]]) ok = ok or np.isclose(sum_phi[0],sum_phi[1],atol=atol) print(m,o,rot.as_quaternion()) assert ok and (np.zeros(3)-1.e-9 <= o).all() and (o <= np.array([np.pi*2.,np.pi,np.pi*2.])+1.e-9).all() @pytest.mark.parametrize('forward,backward',[(Rotation._ax2qu,Rotation._qu2ax), (Rotation._ax2om,Rotation._om2ax), (Rotation._ax2eu,Rotation._eu2ax), (Rotation._ax2ro,Rotation._ro2ax), (Rotation._ax2ho,Rotation._ho2ax), (Rotation._ax2cu,Rotation._cu2ax)]) def test_axis_angle_internal(self,default,forward,backward): """Ensure invariance of conversion from axis angle angles pair and back.""" for rot in default: m = rot.as_axis_angle() o = backward(forward(m)) ok = np.allclose(m,o,atol=atol) if np.isclose(m[3],np.pi,atol=atol): ok = ok or np.allclose(m*np.array([-1.,-1.,-1.,1.]),o,atol=atol) print(m,o,rot.as_quaternion()) assert ok and np.isclose(np.linalg.norm(o[:3]),1.0) and o[3]<=np.pi+1.e-9 @pytest.mark.parametrize('forward,backward',[(Rotation._ro2qu,Rotation._qu2ro), #(Rotation._ro2om,Rotation._om2ro), #(Rotation._ro2eu,Rotation._eu2ro), (Rotation._ro2ax,Rotation._ax2ro), (Rotation._ro2ho,Rotation._ho2ro), (Rotation._ro2cu,Rotation._cu2ro)]) def test_Rodrigues_internal(self,default,forward,backward): """Ensure invariance of conversion from Rodrigues-Frank vector and back.""" cutoff = np.tan(np.pi*.5*(1.-1e-4)) for rot in default: m = rot.as_Rodrigues() o = backward(forward(m)) ok = np.allclose(np.clip(m,None,cutoff),np.clip(o,None,cutoff),atol=atol) ok = ok or np.isclose(m[3],0.0,atol=atol) print(m,o,rot.as_quaternion()) assert ok and np.isclose(np.linalg.norm(o[:3]),1.0) @pytest.mark.parametrize('forward,backward',[(Rotation._ho2qu,Rotation._qu2ho), (Rotation._ho2om,Rotation._om2ho), #(Rotation._ho2eu,Rotation._eu2ho), (Rotation._ho2ax,Rotation._ax2ho), (Rotation._ho2ro,Rotation._ro2ho), (Rotation._ho2cu,Rotation._cu2ho)]) def test_homochoric_internal(self,default,forward,backward): """Ensure invariance of conversion from homochoric vector and back.""" for rot in default: m = rot.as_homochoric() o = backward(forward(m)) ok = np.allclose(m,o,atol=atol) print(m,o,rot.as_quaternion()) assert ok and np.linalg.norm(o) < _R1 + 1.e-9 @pytest.mark.parametrize('forward,backward',[(Rotation._cu2qu,Rotation._qu2cu), (Rotation._cu2om,Rotation._om2cu), (Rotation._cu2eu,Rotation._eu2cu), (Rotation._cu2ax,Rotation._ax2cu), (Rotation._cu2ro,Rotation._ro2cu), (Rotation._cu2ho,Rotation._ho2cu)]) def test_cubochoric_internal(self,default,forward,backward): """Ensure invariance of conversion from cubochoric vector and back.""" for rot in default: m = rot.as_cubochoric() o = backward(forward(m)) ok = np.allclose(m,o,atol=atol) if np.count_nonzero(np.isclose(np.abs(o),np.pi**(2./3.)*.5)): ok = ok or np.allclose(m*-1.,o,atol=atol) print(m,o,rot.as_quaternion()) assert ok and np.max(np.abs(o)) < np.pi**(2./3.) * 0.5 + 1.e-9 @pytest.mark.parametrize('vectorized, single',[(Rotation._qu2om,qu2om), (Rotation._qu2eu,qu2eu), (Rotation._qu2ax,qu2ax), (Rotation._qu2ro,qu2ro), (Rotation._qu2ho,qu2ho)]) def test_quaternion_vectorization(self,default,vectorized,single): """Check vectorized implementation for quaternion against single point calculation.""" qu = np.array([rot.as_quaternion() for rot in default]) vectorized(qu.reshape(qu.shape[0]//2,-1,4)) co = vectorized(qu) for q,c in zip(qu,co): print(q,c) assert np.allclose(single(q),c) and np.allclose(single(q),vectorized(q)) @pytest.mark.parametrize('vectorized, single',[(Rotation._om2qu,om2qu), (Rotation._om2eu,om2eu), (Rotation._om2ax,om2ax)]) def test_matrix_vectorization(self,default,vectorized,single): """Check vectorized implementation for rotation matrix against single point calculation.""" om = np.array([rot.as_matrix() for rot in default]) vectorized(om.reshape(om.shape[0]//2,-1,3,3)) co = vectorized(om) for o,c in zip(om,co): print(o,c) assert np.allclose(single(o),c) and np.allclose(single(o),vectorized(o)) @pytest.mark.parametrize('vectorized, single',[(Rotation._eu2qu,eu2qu), (Rotation._eu2om,eu2om), (Rotation._eu2ax,eu2ax), (Rotation._eu2ro,eu2ro)]) def test_Eulers_vectorization(self,default,vectorized,single): """Check vectorized implementation for Euler angles against single point calculation.""" eu = np.array([rot.as_Eulers() for rot in default]) vectorized(eu.reshape(eu.shape[0]//2,-1,3)) co = vectorized(eu) for e,c in zip(eu,co): print(e,c) assert np.allclose(single(e),c) and np.allclose(single(e),vectorized(e)) @pytest.mark.parametrize('vectorized, single',[(Rotation._ax2qu,ax2qu), (Rotation._ax2om,ax2om), (Rotation._ax2ro,ax2ro), (Rotation._ax2ho,ax2ho)]) def test_axis_angle_vectorization(self,default,vectorized,single): """Check vectorized implementation for axis angle pair against single point calculation.""" ax = np.array([rot.as_axis_angle() for rot in default]) vectorized(ax.reshape(ax.shape[0]//2,-1,4)) co = vectorized(ax) for a,c in zip(ax,co): print(a,c) assert np.allclose(single(a),c) and np.allclose(single(a),vectorized(a)) @pytest.mark.parametrize('vectorized, single',[(Rotation._ro2ax,ro2ax), (Rotation._ro2ho,ro2ho)]) def test_Rodrigues_vectorization(self,default,vectorized,single): """Check vectorized implementation for Rodrigues-Frank vector against single point calculation.""" ro = np.array([rot.as_Rodrigues() for rot in default]) vectorized(ro.reshape(ro.shape[0]//2,-1,4)) co = vectorized(ro) for r,c in zip(ro,co): print(r,c) assert np.allclose(single(r),c) and np.allclose(single(r),vectorized(r)) @pytest.mark.parametrize('vectorized, single',[(Rotation._ho2ax,ho2ax), (Rotation._ho2cu,ho2cu)]) def test_homochoric_vectorization(self,default,vectorized,single): """Check vectorized implementation for homochoric vector against single point calculation.""" ho = np.array([rot.as_homochoric() for rot in default]) vectorized(ho.reshape(ho.shape[0]//2,-1,3)) co = vectorized(ho) for h,c in zip(ho,co): print(h,c) assert np.allclose(single(h),c) and np.allclose(single(h),vectorized(h)) @pytest.mark.parametrize('vectorized, single',[(Rotation._cu2ho,cu2ho)]) def test_cubochoric_vectorization(self,default,vectorized,single): """Check vectorized implementation for cubochoric vector against single point calculation.""" cu = np.array([rot.as_cubochoric() for rot in default]) vectorized(cu.reshape(cu.shape[0]//2,-1,3)) co = vectorized(cu) for u,c in zip(cu,co): print(u,c) assert np.allclose(single(u),c) and np.allclose(single(u),vectorized(u)) @pytest.mark.parametrize('degrees',[True,False]) def test_Eulers(self,default,degrees): for rot in default: m = rot.as_quaternion() o = Rotation.from_Eulers(rot.as_Eulers(degrees),degrees).as_quaternion() ok = np.allclose(m,o,atol=atol) if np.isclose(rot.as_quaternion()[0],0.0,atol=atol): ok = ok or np.allclose(m*-1.,o,atol=atol) print(m,o,rot.as_quaternion()) assert ok and np.isclose(np.linalg.norm(o),1.0) @pytest.mark.parametrize('P',[1,-1]) @pytest.mark.parametrize('normalise',[True,False]) @pytest.mark.parametrize('degrees',[True,False]) def test_axis_angle(self,default,degrees,normalise,P): c = np.array([P*-1,P*-1,P*-1,1.]) for rot in default: m = rot.as_Eulers() o = Rotation.from_axis_angle(rot.as_axis_angle(degrees)*c,degrees,normalise,P).as_Eulers() u = np.array([np.pi*2,np.pi,np.pi*2]) ok = np.allclose(m,o,atol=atol) ok = ok or np.allclose(np.where(np.isclose(m,u),m-u,m),np.where(np.isclose(o,u),o-u,o),atol=atol) if np.isclose(m[1],0.0,atol=atol) or np.isclose(m[1],np.pi,atol=atol): sum_phi = np.unwrap([m[0]+m[2],o[0]+o[2]]) ok = ok or np.isclose(sum_phi[0],sum_phi[1],atol=atol) print(m,o,rot.as_quaternion()) assert ok and (np.zeros(3)-1.e-9 <= o).all() and (o <= np.array([np.pi*2.,np.pi,np.pi*2.])+1.e-9).all() def test_matrix(self,default): for rot in default: m = rot.as_axis_angle() o = Rotation.from_axis_angle(rot.as_axis_angle()).as_axis_angle() ok = np.allclose(m,o,atol=atol) if np.isclose(m[3],np.pi,atol=atol): ok = ok or np.allclose(m*np.array([-1.,-1.,-1.,1.]),o,atol=atol) print(m,o,rot.as_quaternion()) assert ok and np.isclose(np.linalg.norm(o[:3]),1.0) and o[3]<=np.pi+1.e-9 @pytest.mark.parametrize('P',[1,-1]) @pytest.mark.parametrize('normalise',[True,False]) def test_Rodrigues(self,default,normalise,P): c = np.array([P*-1,P*-1,P*-1,1.]) for rot in default: m = rot.as_matrix() o = Rotation.from_Rodrigues(rot.as_Rodrigues()*c,normalise,P).as_matrix() ok = np.allclose(m,o,atol=atol) print(m,o) assert ok and np.isclose(np.linalg.det(o),1.0) @pytest.mark.parametrize('P',[1,-1]) def test_homochoric(self,default,P): cutoff = np.tan(np.pi*.5*(1.-1e-4)) for rot in default: m = rot.as_Rodrigues() o = Rotation.from_homochoric(rot.as_homochoric()*P*-1,P).as_Rodrigues() ok = np.allclose(np.clip(m,None,cutoff),np.clip(o,None,cutoff),atol=atol) ok = ok or np.isclose(m[3],0.0,atol=atol) print(m,o,rot.as_quaternion()) assert ok and np.isclose(np.linalg.norm(o[:3]),1.0) @pytest.mark.parametrize('P',[1,-1]) def test_cubochoric(self,default,P): for rot in default: m = rot.as_homochoric() o = Rotation.from_cubochoric(rot.as_cubochoric()*P*-1,P).as_homochoric() ok = np.allclose(m,o,atol=atol) print(m,o,rot.as_quaternion()) assert ok and np.linalg.norm(o) < (3.*np.pi/4.)**(1./3.) + 1.e-9 @pytest.mark.parametrize('P',[1,-1]) @pytest.mark.parametrize('accept_homomorph',[True,False]) def test_quaternion(self,default,P,accept_homomorph): c = np.array([1,P*-1,P*-1,P*-1]) * (-1 if accept_homomorph else 1) for rot in default: m = rot.as_cubochoric() o = Rotation.from_quaternion(rot.as_quaternion()*c,accept_homomorph,P).as_cubochoric() ok = np.allclose(m,o,atol=atol) if np.count_nonzero(np.isclose(np.abs(o),np.pi**(2./3.)*.5)): ok = ok or np.allclose(m*-1.,o,atol=atol) print(m,o,rot.as_quaternion()) assert ok and o.max() < np.pi**(2./3.)*0.5+1.e-9 @pytest.mark.parametrize('reciprocal',[True,False]) def test_basis(self,default,reciprocal): for rot in default: om = rot.as_matrix() + 0.1*np.eye(3) rot = Rotation.from_basis(om,False,reciprocal=reciprocal) assert np.isclose(np.linalg.det(rot.as_matrix()),1.0) @pytest.mark.parametrize('function',[Rotation.from_quaternion, Rotation.from_Eulers, Rotation.from_axis_angle, Rotation.from_matrix, Rotation.from_Rodrigues, Rotation.from_homochoric, Rotation.from_cubochoric]) 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('shape',[None,(3,),(4,2)]) def test_broadcast(self,shape): rot = Rotation.from_random(shape) new_shape = tuple(np.random.randint(8,32,(3))) if shape is None else \ rot.shape + (np.random.randint(8,32),) rot_broadcast = rot.broadcast_to(tuple(new_shape)) for i in range(rot_broadcast.shape[-1]): assert (rot_broadcast.quaternion[...,i,:], rot.quaternion) @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_matrix, np.array([[1,1,0],[1,2,0],[0,0,1]])), (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])), (Rotation.from_cubochoric, np.array([1.1,0,0])) ]) def test_invalid_value(self,function,invalid): with pytest.raises(ValueError): function(invalid) @pytest.mark.parametrize('direction',['forward', 'backward']) def test_pyramid_vectorization(self,direction): p = np.random.rand(n,3) o = Rotation._get_pyramid_order(p,direction) for i,o_i in enumerate(o): assert np.all(o_i==Rotation._get_pyramid_order(p[i],direction)) def test_pyramid_invariant(self): a = np.random.rand(n,3) f = Rotation._get_pyramid_order(a,'forward') b = Rotation._get_pyramid_order(a,'backward') assert np.all(np.take_along_axis(np.take_along_axis(a,f,-1),b,-1) == a) @pytest.mark.parametrize('data',[np.random.rand(5,3), np.random.rand(5,3,3), np.random.rand(5,3,3,3,3)]) def test_rotate_vectorization(self,default,data): for rot in default: v = rot.broadcast_to((5,)) @ data for i in range(data.shape[0]): print(i-data[i]) assert np.allclose(mul(rot,data[i]),v[i]) @pytest.mark.parametrize('data',[np.random.rand(3), np.random.rand(3,3), np.random.rand(3,3,3,3)]) def test_rotate_identity(self,data): R = Rotation() assert np.allclose(data,R*data) @pytest.mark.parametrize('data',[np.random.rand(3), np.random.rand(3,3), np.random.rand(3,3,3,3)]) def test_rotate_360deg(self,data): phi_1 = np.random.random() * np.pi phi_2 = 2*np.pi - phi_1 R_1 = Rotation.from_Eulers(np.array([phi_1,0.,0.])) R_2 = Rotation.from_Eulers(np.array([0.,0.,phi_2])) assert np.allclose(data,R_2*(R_1*data)) @pytest.mark.parametrize('data',[np.random.rand(3), np.random.rand(3,3), np.random.rand(3,3,3,3)]) def test_rotate_inverse(self,data): R = Rotation.from_random() assert np.allclose(data,R.inversed()*(R*data)) @pytest.mark.parametrize('data',[np.random.rand(4), np.random.rand(3,2), np.random.rand(3,2,3,3)]) def test_rotate_invalid_shape(self,data): R = Rotation.from_random() with pytest.raises(ValueError): R*data @pytest.mark.parametrize('data',['does_not_work', (1,2), 5]) def test_rotate_invalid_type(self,data): R = Rotation.from_random() with pytest.raises(TypeError): R*data