DAMASK_EICMD/python/tests/test_Orientation.py

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 lattice
from damask import _orientation

crystal_families = set(_orientation.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('lattice',crystal_families)
    @pytest.mark.parametrize('shape',[None,5,(4,6)])
    def test_equal(self,lattice,shape):
        R = Rotation.from_random(shape)
        assert Orientation(R,lattice) == Orientation(R,lattice) if shape is None else \
              (Orientation(R,lattice) == Orientation(R,lattice)).all()


    @pytest.mark.parametrize('lattice',crystal_families)
    @pytest.mark.parametrize('shape',[None,5,(4,6)])
    def test_unequal(self,lattice,shape):
        R = Rotation.from_random(shape)
        assert not ( Orientation(R,lattice) != Orientation(R,lattice) if shape is None else \
                    (Orientation(R,lattice) != Orientation(R,lattice)).any())

    @pytest.mark.parametrize('lattice',crystal_families)
    @pytest.mark.parametrize('shape',[None,5,(4,6)])
    def test_close(self,lattice,shape):
        R = Orientation.from_random(lattice=lattice,shape=shape)
        assert R.isclose(R.reduced).all() and R.allclose(R.reduced)

    @pytest.mark.parametrize('a,b',[
                                    (dict(rotation=[1,0,0,0],lattice='triclinic'),
                                     dict(rotation=[0.5,0.5,0.5,0.5],lattice='triclinic')),

                                    (dict(rotation=[1,0,0,0],lattice='cubic'),
                                     dict(rotation=[1,0,0,0],lattice='hexagonal')),

                                    (dict(rotation=[1,0,0,0],lattice='cF',a=1),
                                     dict(rotation=[1,0,0,0],lattice='cF',a=2)),
                                    ])
    def test_nonequal(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).parameters                                                        # noqa

    @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]),lattice='triclinic').as_matrix()
                   == np.eye(3))

    def test_from_Euler_angles(self):
        assert np.all(Orientation.from_Euler_angles(phi=np.zeros(3),lattice='triclinic').as_matrix()
                   == np.eye(3))

    def test_from_axis_angle(self):
        assert np.all(Orientation.from_axis_angle(axis_angle=[1,0,0,0],lattice='triclinic').as_matrix()
                   == np.eye(3))

    def test_from_basis(self):
        assert np.all(Orientation.from_basis(basis=np.eye(3),lattice='triclinic').as_matrix()
                   == np.eye(3))

    def test_from_matrix(self):
        assert np.all(Orientation.from_matrix(R=np.eye(3),lattice='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]),lattice='triclinic').as_matrix()
                   == np.eye(3))

    def test_from_homochoric(self):
        assert np.all(Orientation.from_homochoric(h=np.zeros(3),lattice='triclinic').as_matrix()
                   == np.eye(3))

    def test_from_cubochoric(self):
        assert np.all(Orientation.from_cubochoric(x=np.zeros(3),lattice='triclinic').as_matrix()
                   == np.eye(3))

    def test_from_spherical_component(self):
        assert np.all(Orientation.from_spherical_component(center=Rotation(),
                                                           sigma=0.0,N=1,lattice='triclinic').as_matrix()
                   == np.eye(3))

    def test_from_fiber_component(self):
        r = Rotation.from_fiber_component(alpha=np.zeros(2),beta=np.zeros(2),
                                          sigma=0.0,N=1,rng_seed=0)
        assert np.all(Orientation.from_fiber_component(alpha=np.zeros(2),beta=np.zeros(2),
                                                       sigma=0.0,N=1,rng_seed=0,lattice='triclinic').quaternion
                   == r.quaternion)

    @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.all(np.isclose(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.linalg.norm(x),np.array([1,0,0])),1) \
               and np.isclose(np.dot(z/np.linalg.norm(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('lattice',crystal_families)
    @pytest.mark.parametrize('angle',[10,20,30,40])
    def test_average(self,angle,lattice):
        o = Orientation.from_axis_angle(lattice=lattice,axis_angle=[[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('lattice',crystal_families)
    def test_reduced_equivalent(self,lattice):
        i = Orientation(lattice=lattice)
        o = Orientation.from_random(lattice=lattice)
        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('lattice',crystal_families)
    @pytest.mark.parametrize('N',[1,8,32])
    def test_disorientation(self,lattice,N):
        o = Orientation.from_random(lattice=lattice,shape=N)
        p = Orientation.from_random(lattice=lattice,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('lattice',crystal_families)
    @pytest.mark.parametrize('a,b',[
                                    ((2,3,2),(2,3,2)),
                                    ((2,2),(4,4)),
                                    ((3,1),(1,3)),
                                    (None,None),
                                   ])
    def test_disorientation_blending(self,lattice,a,b):
        o = Orientation.from_random(lattice=lattice,shape=a)
        p = Orientation.from_random(lattice=lattice,shape=b)
        blend = util.shapeblender(o.shape,p.shape)
        for loc in np.random.randint(0,blend,(10,len(blend))):
            assert o[tuple(loc[:len(o.shape)])].disorientation(p[tuple(loc[-len(p.shape):])]) \
                   .isclose(o.disorientation(p)[tuple(loc)])

    @pytest.mark.parametrize('lattice',crystal_families)
    def test_disorientation360(self,lattice):
        o_1 = Orientation(Rotation(),lattice)
        o_2 = Orientation.from_Euler_angles(lattice=lattice,phi=[360,0,0],degrees=True)
        assert np.allclose((o_1.disorientation(o_2)).as_matrix(),np.eye(3))

    @pytest.mark.parametrize('lattice',crystal_families)
    @pytest.mark.parametrize('shape',[(1),(2,3),(4,3,2)])
    def test_reduced_vectorization(self,lattice,shape):
        o = Orientation.from_random(lattice=lattice,shape=shape)
        for r, theO in zip(o.reduced.flatten(),o.flatten()):
            assert r == theO.reduced

    @pytest.mark.parametrize('lattice',crystal_families)
    def test_reduced_corner_cases(self,lattice):
        # test whether there is always a 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[:-2,:-2,:-2],lattice=lattice)
        assert evenly_distributed.shape == evenly_distributed.reduced.shape


    @pytest.mark.parametrize('lattice',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,lattice,shape,vector,proper):
        o = Orientation.from_random(lattice=lattice,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('lattice',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,lattice,shape,vector,proper,in_SST):
        o = Orientation.from_random(lattice=lattice,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('lattice',crystal_families)
    @pytest.mark.parametrize('a,b',[
                                    ((2,3,2),(2,3,2)),
                                    ((2,2),(4,4)),
                                    ((3,1),(1,3)),
                                    (None,(3,)),
                                   ])
    def test_to_SST_blending(self,lattice,a,b):
        o = Orientation.from_random(lattice=lattice,shape=a)
        v = np.random.random(b+(3,))
        blend = util.shapeblender(o.shape,b)
        for loc in np.random.randint(0,blend,(10,len(blend))):
            print(f'{a}/{b} @ {loc}')
            print(o[tuple(loc[:len(o.shape)])].to_SST(v[tuple(loc[-len(b):])]))
            print(o.to_SST(v)[tuple(loc)])
            assert np.allclose(o[tuple(loc[:len(o.shape)])].to_SST(v[tuple(loc[-len(b):])]),
                               o.to_SST(v)[tuple(loc)])

    @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(lattice='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('lattice',crystal_families)
    @pytest.mark.parametrize('proper',[True,False])
    def test_IPF_equivalent(self,set_of_quaternions,lattice,proper):
        direction = np.random.random(3)*2.0-1.0
        o = Orientation(rotation=set_of_quaternions,lattice=lattice).equivalent
        color = o.IPF_color(vector=direction,proper=proper)
        assert np.allclose(np.broadcast_to(color[0,...],color.shape),color)

    @pytest.mark.parametrize('lattice',crystal_families)
    def test_in_FZ_vectorization(self,set_of_rodrigues,lattice):
        result = Orientation.from_Rodrigues_vector(rho=set_of_rodrigues.reshape((-1,4,4)),lattice=lattice).in_FZ.reshape(-1)
        for r,rho in zip(result,set_of_rodrigues[:len(result)]):
            assert r == Orientation.from_Rodrigues_vector(rho=rho,lattice=lattice).in_FZ

    @pytest.mark.parametrize('lattice',crystal_families)
    def test_in_disorientation_FZ_vectorization(self,set_of_rodrigues,lattice):
        result = Orientation.from_Rodrigues_vector(rho=set_of_rodrigues.reshape((-1,4,4)),
                                            lattice=lattice).in_disorientation_FZ.reshape(-1)
        for r,rho in zip(result,set_of_rodrigues[:len(result)]):
            assert r == Orientation.from_Rodrigues_vector(rho=rho,lattice=lattice).in_disorientation_FZ

    @pytest.mark.parametrize('proper',[True,False])
    @pytest.mark.parametrize('lattice',crystal_families)
    def test_in_SST_vectorization(self,lattice,proper):
        vecs = np.random.rand(20,4,3)
        result = Orientation(lattice=lattice).in_SST(vecs,proper).flatten()
        for r,v in zip(result,vecs.reshape((-1,3))):
            assert np.all(r == Orientation(lattice=lattice).in_SST(v,proper))

    @pytest.mark.parametrize('invalid_lattice',['fcc','bcc','hello'])
    def test_invalid_lattice_init(self,invalid_lattice):
        with pytest.raises(KeyError):
            Orientation(lattice=invalid_lattice)                                                    # noqa

    @pytest.mark.parametrize('invalid_family',[None,'fcc','bcc','hello'])
    def test_invalid_symmetry_family(self,invalid_family):
        with pytest.raises(KeyError):
            o = Orientation(lattice='cubic')
            o.family = invalid_family
            o.symmetry_operations                                                                   # noqa

    def test_invalid_rot(self):
        with pytest.raises(TypeError):
            Orientation.from_random(lattice='cubic') * np.ones(3)

    def test_missing_symmetry_immutable(self):
        with pytest.raises(KeyError):
            Orientation(lattice=None).immutable                                                     # noqa

    def test_missing_symmetry_basis_real(self):
        with pytest.raises(KeyError):
            Orientation(lattice=None).basis_real                                                    # noqa

    def test_missing_symmetry_basis_reciprocal(self):
        with pytest.raises(KeyError):
            Orientation(lattice=None).basis_reciprocal                                              # noqa

    def test_double_to_lattice(self):
        with pytest.raises(KeyError):
            Orientation().to_lattice(direction=np.ones(3),plane=np.ones(3))                         # noqa

    def test_double_to_frame(self):
        with pytest.raises(KeyError):
            Orientation().to_frame(uvw=np.ones(3),hkl=np.ones(3))                                   # noqa

    @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('lattice',crystal_families)
    @pytest.mark.parametrize('proper',[True,False])
    def test_in_SST(self,lattice,proper):
          assert Orientation(lattice=lattice).in_SST(np.zeros(3),proper)

    @pytest.mark.parametrize('function',['in_SST','IPF_color'])
    def test_invalid_argument(self,function):
        o = Orientation(lattice='cubic')                                                            # noqa
        with pytest.raises(ValueError):
            eval(f'o.{function}(np.ones(4))')

    @pytest.mark.parametrize('model',lattice.relations)
    def test_relationship_definition(self,model):
        m,o = list(lattice.relations[model])
        assert lattice.relations[model][m].shape[:-1] == lattice.relations[model][o].shape[:-1]

    @pytest.mark.parametrize('model',['Bain','KS','GT','GT_prime','NW','Pitsch'])
    @pytest.mark.parametrize('lattice',['cF','cI'])
    def test_relationship_vectorize(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).related(model)).all()

    @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,None,1.6,np.pi/2,np.pi/2,2*np.pi/3),
                             ('cF',1.0,1.0,None,np.pi/2,np.pi/2,np.pi/2),
                            ])
    def test_bases_contraction(self,lattice,a,b,c,alpha,beta,gamma):
        L = Orientation(lattice=lattice,
                        a=a,b=b,c=c,
                        alpha=alpha,beta=beta,gamma=gamma)
        assert np.allclose(np.eye(3),np.einsum('ik,jk',L.basis_real,L.basis_reciprocal))

    @pytest.mark.parametrize('keyFrame,keyLattice',[('uvw','direction'),('hkl','plane'),])
    @pytest.mark.parametrize('vector',np.array([
                                                [1.,1.,1.],
                                                [-2.,3.,0.5],
                                                [0.,0.,1.],
                                                [1.,1.,1.],
                                                [2.,2.,2.],
                                                [0.,1.,1.],
                                               ]))
    @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),
                            ])
    def test_to_frame_to_lattice(self,lattice,a,b,c,alpha,beta,gamma,vector,keyFrame,keyLattice):
        L = Orientation(lattice=lattice,
                        a=a,b=b,c=c,
                        alpha=alpha,beta=beta,gamma=gamma)
        assert np.allclose(vector,
                           L.to_frame(**{keyFrame:L.to_lattice(**{keyLattice:vector})}))

    @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 + (o.symmetry_operations.shape if with_symmetry else ()) + vector.shape

    @pytest.mark.parametrize('lattice',['hP','cI','cF'])
    @pytest.mark.parametrize('mode',['slip','twin'])
    def test_Schmid(self,update,ref_path,lattice,mode):
        L = Orientation(lattice=lattice)
        reference = ref_path/f'{lattice}_{mode}.txt'
        P = L.Schmid(mode)
        if update:
            table = Table(P.reshape(-1,9),{'Schmid':(3,3,)})
            table.save(reference)
        assert np.allclose(P,Table.load(reference).get('Schmid'))