import pytest import numpy as np from itertools import permutations from damask import Rotation from damask import Orientation from damask import Table from damask import util from damask import grid_filters from damask import _crystal crystal_families = set(_crystal.lattice_symmetries.values()) @pytest.fixture def ref_path(ref_path_base): """Directory containing reference results.""" return ref_path_base/'Orientation' @pytest.fixture def set_of_rodrigues(set_of_quaternions): return Rotation(set_of_quaternions).as_Rodrigues_vector() class TestOrientation: @pytest.mark.parametrize('family',crystal_families) @pytest.mark.parametrize('shape',[None,5,(4,6)]) def test_equal(self,family,shape): R = Rotation.from_random(shape) assert Orientation(R,family=family) == Orientation(R,family=family) if shape is None else \ (Orientation(R,family=family) == Orientation(R,family=family)).all() @pytest.mark.parametrize('family',crystal_families) @pytest.mark.parametrize('shape',[None,5,(4,6)]) def test_unequal(self,family,shape): R = Rotation.from_random(shape) assert not ( Orientation(R,family=family) != Orientation(R,family=family) if shape is None else \ (Orientation(R,family=family) != Orientation(R,family=family)).any()) @pytest.mark.parametrize('family',crystal_families) @pytest.mark.parametrize('shape',[None,5,(4,6)]) def test_close(self,family,shape): R = Orientation.from_random(family=family,shape=shape) assert R.isclose(R.reduced).all() and R.allclose(R.reduced) @pytest.mark.parametrize('a,b',[ (dict(rotation=[1,0,0,0],family='triclinic'), dict(rotation=[0.5,0.5,0.5,0.5],family='triclinic')), (dict(rotation=[1,0,0,0],family='cubic'), dict(rotation=[1,0,0,0],family='hexagonal')), ]) def test_unequal_family(self,a,b): assert Orientation(**a) != Orientation(**b) @pytest.mark.parametrize('a,b',[ (dict(rotation=[1,0,0,0],lattice='cF',a=1), dict(rotation=[1,0,0,0],lattice='cF',a=2)), ]) def test_unequal_lattice(self,a,b): assert Orientation(**a) != Orientation(**b) @pytest.mark.parametrize('kwargs',[ dict(lattice='aP', alpha=np.pi/4,beta=np.pi/3, ), dict(lattice='mP', c=1.2,alpha=np.pi/4, gamma=np.pi/2), dict(lattice='oP', c=1.2,alpha=np.pi/4, ), dict(lattice='oS',a=1.0, c=2.0,alpha=np.pi/2,beta=np.pi/3, ), dict(lattice='tP',a=1.0,b=1.2, ), dict(lattice='tI', alpha=np.pi/3, ), dict(lattice='hP', gamma=np.pi/2), dict(lattice='cI',a=1.0, c=2.0,alpha=np.pi/2,beta=np.pi/2, ), dict(lattice='cF', beta=np.pi/3, ), ]) def test_invalid_init(self,kwargs): with pytest.raises(ValueError): Orientation(**kwargs) @pytest.mark.parametrize('invalid_family',[None,'fcc','bcc','hello']) def test_invalid_family_init(self,invalid_family): with pytest.raises(KeyError): Orientation(family=invalid_family) @pytest.mark.parametrize('invalid_lattice',[None,'fcc','bcc','hello']) def test_invalid_lattice_init(self,invalid_lattice): with pytest.raises(KeyError): Orientation(lattice=invalid_lattice) @pytest.mark.parametrize('kwargs',[ dict(lattice='aP',a=1.0,b=1.1,c=1.2,alpha=np.pi/4,beta=np.pi/3,gamma=np.pi/2), dict(lattice='mP',a=1.0,b=1.1,c=1.2, beta=np.pi/3 ), dict(lattice='oS',a=1.0,b=1.1,c=1.2, ), dict(lattice='tI',a=1.0, c=1.2, ), dict(lattice='hP',a=1.0 ), dict(lattice='cI',a=1.0, ), ]) def test_repr(self,kwargs): o = Orientation.from_random(**kwargs) assert isinstance(o.__repr__(),str) @pytest.mark.parametrize('kwargs',[ dict(lattice='aP',a=1.0,b=1.1,c=1.2,alpha=np.pi/4,beta=np.pi/3,gamma=np.pi/2), dict(lattice='mP',a=1.0,b=1.1,c=1.2, beta=np.pi/3 ), dict(lattice='oS',a=1.0,b=1.1,c=1.2, ), dict(lattice='tI',a=1.0, c=1.2, ), dict(lattice='hP',a=1.0 ), dict(lattice='cI',a=1.0, ), ]) def test_copy(self,kwargs): o = Orientation.from_random(**kwargs) p = o.copy(rotation=Rotation.from_random()) assert o != p def test_from_quaternion(self): assert np.all(Orientation.from_quaternion(q=np.array([1,0,0,0]),family='triclinic').as_matrix() == np.eye(3)) def test_from_Euler_angles(self): assert np.all(Orientation.from_Euler_angles(phi=np.zeros(3),family='triclinic').as_matrix() == np.eye(3)) def test_from_axis_angle(self): assert np.all(Orientation.from_axis_angle(n_omega=[1,0,0,0],family='triclinic').as_matrix() == np.eye(3)) def test_from_basis(self): assert np.all(Orientation.from_basis(basis=np.eye(3),family='triclinic').as_matrix() == np.eye(3)) def test_from_matrix(self): assert np.all(Orientation.from_matrix(R=np.eye(3),family='triclinic').as_matrix() == np.eye(3)) def test_from_Rodrigues_vector(self): assert np.all(Orientation.from_Rodrigues_vector(rho=np.array([0,0,1,0]),family='triclinic').as_matrix() == np.eye(3)) def test_from_homochoric(self): assert np.all(Orientation.from_homochoric(h=np.zeros(3),family='triclinic').as_matrix() == np.eye(3)) def test_from_cubochoric(self): assert np.all(Orientation.from_cubochoric(x=np.zeros(3),family='triclinic').as_matrix() == np.eye(3)) def test_from_spherical_component(self): assert np.all(Orientation.from_spherical_component(center=Rotation(), sigma=0.0,shape=1,family='triclinic').as_matrix() == np.eye(3)) def test_from_fiber_component(self): crystal = np.random.rand(2) * [180,360] sample = np.random.rand(2) * [180,360] r = Rotation.from_fiber_component(crystal=crystal,sample=sample, sigma=0.0,shape=1,rng_seed=0) assert np.all(Orientation.from_fiber_component(crystal=crystal,sample=sample, sigma=0.0,shape=None,rng_seed=0,lattice='cI').quaternion == r.quaternion) @pytest.mark.parametrize('crystal,sample,direction,color',[([np.pi/4,0],[np.pi/2,0],[1,0,0],[0,1,0]), ([np.arccos(3**(-.5)),np.pi/4,0],[0,0],[0,0,1],[0,0,1])]) def test_fiber_IPF(self,crystal,sample,direction,color): fiber = Orientation.from_fiber_component(crystal=crystal,sample=sample,family='cubic',shape=200) print(np.allclose(fiber.IPF_color(direction),color)) @pytest.mark.parametrize('kwargs',[ dict(lattice='aP',a=1.0,b=1.1,c=1.2,alpha=np.pi/4.5,beta=np.pi/3.5,gamma=np.pi/2.5), dict(lattice='mP',a=1.0,b=1.1,c=1.2, beta=np.pi/3.5), dict(lattice='oS',a=1.0,b=1.1,c=1.2,), dict(lattice='tI',a=1.0, c=1.2,), dict(lattice='hP',a=1.0 ), dict(lattice='cI',a=1.0, ), ]) def test_from_directions(self,kwargs): for a,b in np.random.random((10,2,3)): c = np.cross(b,a) if np.allclose(c,0): continue o = Orientation.from_directions(uvw=a,hkl=c,**kwargs) x = o.to_pole(uvw=a) z = o.to_pole(hkl=c) assert np.isclose(np.dot(x,np.array([1,0,0])),1) \ and np.isclose(np.dot(z,np.array([0,0,1])),1) @pytest.mark.parametrize('function',[Orientation.from_random, Orientation.from_quaternion, Orientation.from_Euler_angles, Orientation.from_axis_angle, Orientation.from_basis, Orientation.from_matrix, Orientation.from_Rodrigues_vector, Orientation.from_homochoric, Orientation.from_cubochoric, Orientation.from_spherical_component, Orientation.from_fiber_component, Orientation.from_directions]) def test_invalid_from(self,function): with pytest.raises(TypeError): function(c=.1,degrees=True,invalid=66) def test_negative_angle(self): with pytest.raises(ValueError): Orientation(lattice='aP',a=1,b=2,c=3,alpha=45,beta=45,gamma=-45,degrees=True) # noqa def test_excess_angle(self): with pytest.raises(ValueError): Orientation(lattice='aP',a=1,b=2,c=3,alpha=45,beta=45,gamma=90.0001,degrees=True) # noqa @pytest.mark.parametrize('family',crystal_families) @pytest.mark.parametrize('angle',[10,20,30,40]) def test_average(self,angle,family): o = Orientation.from_axis_angle(family=family,n_omega=[[0,0,1,10],[0,0,1,angle]],degrees=True) avg_angle = o.average().as_axis_angle(degrees=True,pair=True)[1] assert np.isclose(avg_angle,10+(angle-10)/2.) @pytest.mark.parametrize('family',crystal_families) def test_reduced_equivalent(self,family): i = Orientation(family=family) o = Orientation.from_random(family=family) eq = o.equivalent FZ = np.argmin(abs(eq.misorientation(i.broadcast_to(len(eq))).as_axis_angle(pair=True)[1])) assert o.reduced == eq[FZ] @pytest.mark.parametrize('family',crystal_families) def test_reduced_corner_cases(self,family): # test whether there is always exactly one sym-eq rotation that falls into the FZ N = np.random.randint(10,40) size = np.ones(3)*np.pi**(2./3.) grid = grid_filters.coordinates0_node([N+1,N+1,N+1],size,-size*.5) evenly_distributed = Orientation.from_cubochoric(x=grid,family=family) assert evenly_distributed.shape == evenly_distributed.reduced.shape @pytest.mark.parametrize('family',crystal_families) @pytest.mark.parametrize('N',[1,8,32]) def test_disorientation(self,family,N): o = Orientation.from_random(family=family,shape=N) p = Orientation.from_random(family=family,shape=N) d,ops = o.disorientation(p,return_operators=True) for n in range(N): assert np.allclose(d[n].as_quaternion(), o[n].equivalent[ops[n][0]] .misorientation(p[n].equivalent[ops[n][1]]) .as_quaternion()) \ or np.allclose((~d)[n].as_quaternion(), o[n].equivalent[ops[n][0]] .misorientation(p[n].equivalent[ops[n][1]]) .as_quaternion()) @pytest.mark.parametrize('family',crystal_families) def test_disorientation360(self,family): o_1 = Orientation(Rotation(),family=family) o_2 = Orientation.from_Euler_angles(family=family,phi=[360,0,0],degrees=True) assert np.allclose((o_1.disorientation(o_2)).as_matrix(),np.eye(3)) @pytest.mark.parametrize('color',[{'label':'red', 'RGB':[1,0,0],'direction':[0,0,1]}, {'label':'green','RGB':[0,1,0],'direction':[0,1,1]}, {'label':'blue', 'RGB':[0,0,1],'direction':[1,1,1]}]) @pytest.mark.parametrize('proper',[True,False]) def test_IPF_cubic(self,color,proper): cube = Orientation(family='cubic') for direction in set(permutations(np.array(color['direction']))): assert np.allclose(np.array(color['RGB']), cube.IPF_color(vector=np.array(direction),proper=proper)) @pytest.mark.parametrize('family',crystal_families) @pytest.mark.parametrize('proper',[True,False]) def test_IPF_equivalent(self,set_of_quaternions,family,proper): direction = np.random.random(3)*2.0-1.0 o = Orientation(rotation=set_of_quaternions,family=family).equivalent color = o.IPF_color(vector=direction,proper=proper) assert np.allclose(np.broadcast_to(color[0,...],color.shape),color) @pytest.mark.parametrize('relation',[None,'Peter','Paul']) def test_unknown_relation(self,relation): with pytest.raises(KeyError): Orientation(lattice='cF').related(relation) # noqa @pytest.mark.parametrize('relation,lattice,a,b,c,alpha,beta,gamma', [ ('Bain', 'aP',0.5,2.0,3.0,0.8,0.5,1.2), ('KS', 'mP',1.0,2.0,3.0,np.pi/2,0.5,np.pi/2), ('Pitsch', 'oI',0.5,1.5,3.0,np.pi/2,np.pi/2,np.pi/2), ('Burgers','tP',0.5,0.5,3.0,np.pi/2,np.pi/2,np.pi/2), ('GT', 'hP',1.0,None,1.6,np.pi/2,np.pi/2,2*np.pi/3), ('Burgers','cF',1.0,1.0,None,np.pi/2,np.pi/2,np.pi/2), ]) def test_unknown_relation_lattice(self,relation,lattice,a,b,c,alpha,beta,gamma): with pytest.raises(KeyError): Orientation(lattice=lattice, a=a,b=b,c=c, alpha=alpha,beta=beta,gamma=gamma).related(relation) # noqa @pytest.mark.parametrize('family',crystal_families) @pytest.mark.parametrize('proper',[True,False]) def test_in_SST(self,family,proper): assert Orientation(family=family).in_SST(np.zeros(3),proper) @pytest.mark.parametrize('function',['in_SST','IPF_color']) def test_invalid_argument(self,function): o = Orientation(family='cubic') # noqa with pytest.raises(ValueError): eval(f'o.{function}(np.ones(4))') @pytest.mark.parametrize('model',['Bain','KS','GT','GT_prime','NW','Pitsch']) @pytest.mark.parametrize('lattice',['cF','cI']) def test_relationship_forward_backward(self,model,lattice): o = Orientation.from_random(lattice=lattice) for i,r in enumerate(o.related(model)): assert o.disorientation(r.related(model)[i]).as_axis_angle(degrees=True,pair=True)[1]<1.0e-5 @pytest.mark.parametrize('model',['Bain','KS','GT','GT_prime','NW','Pitsch']) @pytest.mark.parametrize('lattice',['cF','cI']) def test_relationship_reference(self,update,ref_path,model,lattice): reference = ref_path/f'{lattice}_{model}.txt' o = Orientation(lattice=lattice) eu = o.related(model).as_Euler_angles(degrees=True) if update: coords = np.array([(1,i+1) for i,x in enumerate(eu)]) Table(eu,{'Eulers':(3,)})\ .add('pos',coords)\ .save(reference) assert np.allclose(eu,Table.load(reference).get('Eulers')) def test_basis_real(self): for gamma in np.random.random(2**8)*np.pi: basis = np.tril(np.random.random((3,3))+1e-6) basis[1,:2] = basis[1,1]*np.array([np.cos(gamma),np.sin(gamma)]) basis[2,:2] = basis[2,:2]*2-1 lengths = np.linalg.norm(basis,axis=-1) cosines = np.roll(np.einsum('ij,ij->i',basis,np.roll(basis,1,axis=0))/lengths/np.roll(lengths,1),1) o = Orientation.from_random(lattice='aP', **dict(zip(['a','b','c'],lengths)), **dict(zip(['alpha','beta','gamma'],np.arccos(cosines))), ) assert np.allclose(o.to_frame(uvw=np.eye(3)),basis), 'Lattice basis disagrees with initialization' @pytest.mark.parametrize('lattice,a,b,c,alpha,beta,gamma', [ ('aP',0.5,2.0,3.0,0.8,0.5,1.2), ('mP',1.0,2.0,3.0,np.pi/2,0.5,np.pi/2), ('oI',0.5,1.5,3.0,np.pi/2,np.pi/2,np.pi/2), ('tP',0.5,0.5,3.0,np.pi/2,np.pi/2,np.pi/2), ('hP',1.0,1.0,1.6,np.pi/2,np.pi/2,2*np.pi/3), ('cF',1.0,1.0,1.0,np.pi/2,np.pi/2,np.pi/2), ]) @pytest.mark.parametrize('kw',['uvw','hkl']) @pytest.mark.parametrize('with_symmetry',[False,True]) @pytest.mark.parametrize('shape',[None,1,(12,24)]) @pytest.mark.parametrize('vector',[ np.random.random( 3 ), np.random.random( (4,3)), np.random.random((4,8,3)), ]) def test_to_pole(self,shape,lattice,a,b,c,alpha,beta,gamma,vector,kw,with_symmetry): o = Orientation.from_random(shape=shape, lattice=lattice, a=a,b=b,c=c, alpha=alpha,beta=beta,gamma=gamma) assert o.to_pole(**{kw:vector,'with_symmetry':with_symmetry}).shape \ == o.shape + vector.shape[:-1] + (o.symmetry_operations.shape if with_symmetry else ()) + vector.shape[-1:] @pytest.mark.parametrize('lattice',['hP','cI','cF']) #tI not included yet def test_Schmid(self,update,ref_path,lattice): O = Orientation(lattice=lattice) # noqa for mode in ['slip','twin']: reference = ref_path/f'{lattice}_{mode}.txt' P = O.Schmid(N_slip='*') if mode == 'slip' else O.Schmid(N_twin='*') if update: table = Table(P.reshape(-1,9),{'Schmid':(3,3,)}) table.save(reference) assert np.allclose(P,Table.load(reference).get('Schmid')) def test_Schmid_invalid(self): with pytest.raises(KeyError): Orientation(lattice='fcc').Schmid() ### vectorization tests ### @pytest.mark.parametrize('lattice',['hP','cI','cF']) # tI not included yet def test_Schmid_vectorization(self,lattice): O = Orientation.from_random(shape=4,lattice=lattice) # noqa for mode in ['slip','twin']: Ps = O.Schmid(N_slip='*') if mode == 'slip' else O.Schmid(N_twin='*') for i in range(4): P = O[i].Schmid(N_slip='*') if mode == 'slip' else O[i].Schmid(N_twin='*') assert np.allclose(P,Ps[:,i]) @pytest.mark.parametrize('family',crystal_families) @pytest.mark.parametrize('shape',[(1),(2,3),(4,3,2)]) def test_reduced_vectorization(self,family,shape): o = Orientation.from_random(family=family,shape=shape) for r, theO in zip(o.reduced.flatten(),o.flatten()): assert r == theO.reduced @pytest.mark.parametrize('family',crystal_families) @pytest.mark.parametrize('shape',[(1),(2,3),(4,3,2)]) @pytest.mark.parametrize('vector',np.array([[1,0,0],[1,2,3],[-1,1,-1]])) @pytest.mark.parametrize('proper',[True,False]) def test_to_SST_vectorization(self,family,shape,vector,proper): o = Orientation.from_random(family=family,shape=shape) for r, theO in zip(o.to_SST(vector=vector,proper=proper).reshape((-1,3)),o.flatten()): assert np.allclose(r,theO.to_SST(vector=vector,proper=proper)) @pytest.mark.parametrize('proper',[True,False]) @pytest.mark.parametrize('family',crystal_families) def test_in_SST_vectorization(self,family,proper): vecs = np.random.rand(20,4,3) result = Orientation(family=family).in_SST(vecs,proper).flatten() for r,v in zip(result,vecs.reshape((-1,3))): assert np.all(r == Orientation(family=family).in_SST(v,proper)) @pytest.mark.parametrize('family',crystal_families) @pytest.mark.parametrize('shape',[(1),(2,3),(4,3,2)]) @pytest.mark.parametrize('vector',np.array([[1,0,0],[1,2,3],[-1,1,-1]])) @pytest.mark.parametrize('proper',[True,False]) @pytest.mark.parametrize('in_SST',[True,False]) def test_IPF_color_vectorization(self,family,shape,vector,proper,in_SST): o = Orientation.from_random(family=family,shape=shape) for r, theO in zip(o.IPF_color(vector,in_SST=in_SST,proper=proper).reshape((-1,3)),o.flatten()): assert np.allclose(r,theO.IPF_color(vector,in_SST=in_SST,proper=proper)) @pytest.mark.parametrize('family',crystal_families) def test_in_FZ_vectorization(self,set_of_rodrigues,family): result = Orientation.from_Rodrigues_vector(rho=set_of_rodrigues.reshape((-1,4,4)),family=family).in_FZ.reshape(-1) for r,rho in zip(result,set_of_rodrigues[:len(result)]): assert r == Orientation.from_Rodrigues_vector(rho=rho,family=family).in_FZ @pytest.mark.parametrize('family',crystal_families) def test_in_disorientation_FZ_vectorization(self,set_of_rodrigues,family): result = Orientation.from_Rodrigues_vector(rho=set_of_rodrigues.reshape((-1,4,4)), family=family).in_disorientation_FZ.reshape(-1) for r,rho in zip(result,set_of_rodrigues[:len(result)]): assert r == Orientation.from_Rodrigues_vector(rho=rho,family=family).in_disorientation_FZ @pytest.mark.parametrize('model',['Bain','KS','GT','GT_prime','NW','Pitsch']) @pytest.mark.parametrize('lattice',['cF','cI']) def test_relationship_vectorization(self,set_of_quaternions,lattice,model): r = Orientation(rotation=set_of_quaternions[:200].reshape((50,4,4)),lattice=lattice).related(model) for i in range(200): assert (r.reshape((-1,200))[:,i] == Orientation(set_of_quaternions[i],lattice=lattice).related(model)).all() ### blending tests ### @pytest.mark.parametrize('family',crystal_families) @pytest.mark.parametrize('left,right',[ ((2,3,2),(2,3,2)), ((2,2),(4,4)), ((3,1),(1,3)), (None,None), ]) def test_disorientation_blending(self,family,left,right): o = Orientation.from_random(family=family,shape=left) p = Orientation.from_random(family=family,shape=right) blend = util.shapeblender(o.shape,p.shape) for loc in np.random.randint(0,blend,(10,len(blend))): # print(f'{a}/{b} @ {loc}') # print(o[tuple(loc[:len(o.shape)])].disorientation(p[tuple(loc[-len(p.shape):])])) # print(o.disorientation(p)[tuple(loc)]) assert o[tuple(loc[:len(o.shape)])].disorientation(p[tuple(loc[-len(p.shape):])]) \ .isclose(o.disorientation(p)[tuple(loc)]) @pytest.mark.parametrize('family',crystal_families) @pytest.mark.parametrize('left,right',[ ((2,3,2),(2,3,2)), ((2,2),(4,4)), ((3,1),(1,3)), (None,(3,)), ]) def test_IPF_color_blending(self,family,left,right): o = Orientation.from_random(family=family,shape=left) v = np.random.random(right+(3,)) blend = util.shapeblender(o.shape,v.shape[:-1]) for loc in np.random.randint(0,blend,(10,len(blend))): assert np.allclose(o[tuple(loc[:len(o.shape)])].IPF_color(v[tuple(loc[-len(v.shape[:-1]):])]), o.IPF_color(v)[tuple(loc)]) @pytest.mark.parametrize('family',crystal_families) @pytest.mark.parametrize('left,right',[ ((2,3,2),(2,3,2)), ((2,2),(4,4)), ((3,1),(1,3)), (None,(3,)), ]) def test_to_SST_blending(self,family,left,right): o = Orientation.from_random(family=family,shape=left) v = np.random.random(right+(3,)) blend = util.shapeblender(o.shape,v.shape[:-1]) for loc in np.random.randint(0,blend,(10,len(blend))): assert np.allclose(o[tuple(loc[:len(o.shape)])].to_SST(v[tuple(loc[-len(v.shape[:-1]):])]), o.to_SST(v)[tuple(loc)]) @pytest.mark.parametrize('lattice,a,b,c,alpha,beta,gamma', [ ('aP',0.5,2.0,3.0,0.8,0.5,1.2), ('mP',1.0,2.0,3.0,np.pi/2,0.5,np.pi/2), ('oI',0.5,1.5,3.0,np.pi/2,np.pi/2,np.pi/2), ('tP',0.5,0.5,3.0,np.pi/2,np.pi/2,np.pi/2), ('hP',1.0,1.0,1.6,np.pi/2,np.pi/2,2*np.pi/3), ('cF',1.0,1.0,1.0,np.pi/2,np.pi/2,np.pi/2), ]) @pytest.mark.parametrize('left,right',[ ((2,3,2),(2,3,2)), ((2,2),(4,4)), ((3,1),(1,3)), (None,(3,)), ]) def test_to_pole_blending(self,lattice,a,b,c,alpha,beta,gamma,left,right): o = Orientation.from_random(shape=left, lattice=lattice, a=a,b=b,c=c, alpha=alpha,beta=beta,gamma=gamma) v = np.random.random(right+(3,)) blend = util.shapeblender(o.shape,v.shape[:-1]) for loc in np.random.randint(0,blend,(10,len(blend))): assert np.allclose(o[tuple(loc[:len(o.shape)])].to_pole(uvw=v[tuple(loc[-len(v.shape[:-1]):])]), o.to_pole(uvw=v)[tuple(loc)]) def test_mul_invalid(self): with pytest.raises(TypeError): Orientation.from_random(lattice='cF')*np.ones(3)