import os import pytest import numpy as np 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( [np.array([ 1.0, 0.0, 0.0, 0.0]), #----------------------------------------------- np.array([0.0, 1.0, 0.0, 0.0]), np.array([0.0, 0.0, 1.0, 0.0]), np.array([0.0, 0.0, 0.0, 1.0]), np.array([0.0,-1.0, 0.0, 0.0]), np.array([0.0, 0.0,-1.0, 0.0]), np.array([0.0, 0.0, 0.0,-1.0]), #----------------------------------------------- np.array([1.0, 1.0, 0.0, 0.0])/np.sqrt(2.), np.array([1.0, 0.0, 1.0, 0.0])/np.sqrt(2.), np.array([1.0, 0.0, 0.0, 1.0])/np.sqrt(2.), np.array([0.0, 1.0, 1.0, 0.0])/np.sqrt(2.), np.array([0.0, 1.0, 0.0, 1.0])/np.sqrt(2.), np.array([0.0, 0.0, 1.0, 1.0])/np.sqrt(2.), #----------------------------------------------- np.array([1.0,-1.0, 0.0, 0.0])/np.sqrt(2.), np.array([1.0, 0.0,-1.0, 0.0])/np.sqrt(2.), np.array([1.0, 0.0, 0.0,-1.0])/np.sqrt(2.), np.array([0.0, 1.0,-1.0, 0.0])/np.sqrt(2.), np.array([0.0, 1.0, 0.0,-1.0])/np.sqrt(2.), np.array([0.0, 0.0, 1.0,-1.0])/np.sqrt(2.), #----------------------------------------------- np.array([0.0, 1.0,-1.0, 0.0])/np.sqrt(2.), np.array([0.0, 1.0, 0.0,-1.0])/np.sqrt(2.), np.array([0.0, 0.0, 1.0,-1.0])/np.sqrt(2.), #----------------------------------------------- np.array([0.0,-1.0,-1.0, 0.0])/np.sqrt(2.), np.array([0.0,-1.0, 0.0,-1.0])/np.sqrt(2.), np.array([0.0, 0.0,-1.0,-1.0])/np.sqrt(2.), #----------------------------------------------- np.array([1.0, 1.0, 1.0, 0.0])/np.sqrt(3.), np.array([1.0, 1.0, 0.0, 1.0])/np.sqrt(3.), np.array([1.0, 0.0, 1.0, 1.0])/np.sqrt(3.), np.array([1.0,-1.0, 1.0, 0.0])/np.sqrt(3.), np.array([1.0,-1.0, 0.0, 1.0])/np.sqrt(3.), np.array([1.0, 0.0,-1.0, 1.0])/np.sqrt(3.), np.array([1.0, 1.0,-1.0, 0.0])/np.sqrt(3.), np.array([1.0, 1.0, 0.0,-1.0])/np.sqrt(3.), np.array([1.0, 0.0, 1.0,-1.0])/np.sqrt(3.), np.array([1.0,-1.0,-1.0, 0.0])/np.sqrt(3.), np.array([1.0,-1.0, 0.0,-1.0])/np.sqrt(3.), np.array([1.0, 0.0,-1.0,-1.0])/np.sqrt(3.), #----------------------------------------------- np.array([0.0, 1.0, 1.0, 1.0])/np.sqrt(3.), np.array([0.0, 1.0,-1.0, 1.0])/np.sqrt(3.), np.array([0.0, 1.0, 1.0,-1.0])/np.sqrt(3.), np.array([0.0,-1.0, 1.0, 1.0])/np.sqrt(3.), np.array([0.0,-1.0,-1.0, 1.0])/np.sqrt(3.), np.array([0.0,-1.0, 1.0,-1.0])/np.sqrt(3.), np.array([0.0,-1.0,-1.0,-1.0])/np.sqrt(3.), #----------------------------------------------- np.array([1.0, 1.0, 1.0, 1.0])/2., np.array([1.0,-1.0, 1.0, 1.0])/2., np.array([1.0, 1.0,-1.0, 1.0])/2., np.array([1.0, 1.0, 1.0,-1.0])/2., np.array([1.0,-1.0,-1.0, 1.0])/2., np.array([1.0,-1.0, 1.0,-1.0])/2., np.array([1.0, 1.0,-1.0,-1.0])/2., np.array([1.0,-1.0,-1.0,-1.0])/2., ]) 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.fromQuaternion(s) for s in specials] + \ [Rotation.fromQuaternion(s) for s in specials_scatter] + \ [Rotation.fromRandom() 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') class TestRotation: def test_Eulers(self,default): for rot in default: m = rot.asQuaternion() o = Rotation.fromEulers(rot.asEulers()).asQuaternion() ok = np.allclose(m,o,atol=atol) if np.isclose(rot.asQuaternion()[0],0.0,atol=atol): ok = ok or np.allclose(m*-1.,o,atol=atol) print(m,o,rot.asQuaternion()) assert ok and np.isclose(np.linalg.norm(o),1.0) def test_AxisAngle(self,default): for rot in default: m = rot.asEulers() o = Rotation.fromAxisAngle(rot.asAxisAngle()).asEulers() 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.asQuaternion()) 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.asAxisAngle() o = Rotation.fromAxisAngle(rot.asAxisAngle()).asAxisAngle() 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.asQuaternion()) assert ok and np.isclose(np.linalg.norm(o[:3]),1.0) and o[3]<=np.pi++1.e-9 def test_Rodrigues(self,default): for rot in default: m = rot.asMatrix() o = Rotation.fromRodrigues(rot.asRodrigues()).asMatrix() ok = np.allclose(m,o,atol=atol) print(m,o) assert ok and np.isclose(np.linalg.det(o),1.0) def test_Homochoric(self,default): cutoff = np.tan(np.pi*.5*(1.-1e-4)) for rot in default: m = rot.asRodrigues() o = Rotation.fromHomochoric(rot.asHomochoric()).asRodrigues() 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.asQuaternion()) assert ok and np.isclose(np.linalg.norm(o[:3]),1.0) def test_Cubochoric(self,default): for rot in default: m = rot.asHomochoric() o = Rotation.fromCubochoric(rot.asCubochoric()).asHomochoric() ok = np.allclose(m,o,atol=atol) print(m,o,rot.asQuaternion()) assert ok and np.linalg.norm(o) < (3.*np.pi/4.)**(1./3.) + 1.e-9 def test_Quaternion(self,default): for rot in default: m = rot.asCubochoric() o = Rotation.fromQuaternion(rot.asQuaternion()).asCubochoric() ok = np.allclose(m,o,atol=atol) print(m,o,rot.asQuaternion()) assert ok and o.max() < np.pi**(2./3.)*0.5+1.e-9 @pytest.mark.parametrize('function',[Rotation.from_quaternion, Rotation.from_Eulers, Rotation.from_axis_angle, Rotation.from_matrix, Rotation.from_Rodrigues, Rotation.from_homochoric]) 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('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_Rodrigues, np.array([1,0,0,-1])), (Rotation.from_Rodrigues, np.array([1,1,0,1])), (Rotation.from_homochoric, np.array([2,2,2])) ]) def test_invalid(self,function,invalid): with pytest.raises(ValueError): function(invalid) @pytest.mark.parametrize('conversion',[Rotation.qu2om, Rotation.qu2eu, Rotation.qu2ax, Rotation.qu2ro, Rotation.qu2ho]) def test_quaternion_vectorization(self,default,conversion): qu = np.array([rot.asQuaternion() for rot in default]) conversion(qu.reshape(qu.shape[0]//2,-1,4)) co = conversion(qu) for q,c in zip(qu,co): print(q,c) assert np.allclose(conversion(q),c) @pytest.mark.parametrize('conversion',[Rotation.om2qu, Rotation.om2eu, Rotation.om2ax, Rotation.om2ro, Rotation.om2ho, ]) def test_matrix_vectorization(self,default,conversion): om = np.array([rot.asMatrix() for rot in default]) conversion(om.reshape(om.shape[0]//2,-1,3,3)) co = conversion(om) for o,c in zip(om,co): print(o,c) assert np.allclose(conversion(o),c) @pytest.mark.parametrize('conversion',[Rotation.eu2qu, Rotation.eu2om, Rotation.eu2ax, Rotation.eu2ro, Rotation.eu2ho, ]) def test_Euler_vectorization(self,default,conversion): eu = np.array([rot.asEulers() for rot in default]) conversion(eu.reshape(eu.shape[0]//2,-1,3)) co = conversion(eu) for e,c in zip(eu,co): print(e,c) assert np.allclose(conversion(e),c) @pytest.mark.parametrize('conversion',[Rotation.ax2qu, Rotation.ax2om, Rotation.ax2eu, Rotation.ax2ro, Rotation.ax2ho, ]) def test_axisAngle_vectorization(self,default,conversion): ax = np.array([rot.asAxisAngle() for rot in default]) conversion(ax.reshape(ax.shape[0]//2,-1,4)) co = conversion(ax) for a,c in zip(ax,co): print(a,c) assert np.allclose(conversion(a),c) @pytest.mark.parametrize('conversion',[Rotation.ro2qu, Rotation.ro2om, Rotation.ro2eu, Rotation.ro2ax, Rotation.ro2ho, ]) def test_Rodrigues_vectorization(self,default,conversion): ro = np.array([rot.asRodrigues() for rot in default]) conversion(ro.reshape(ro.shape[0]//2,-1,4)) co = conversion(ro) for r,c in zip(ro,co): print(r,c) assert np.allclose(conversion(r),c) @pytest.mark.parametrize('conversion',[Rotation.ho2qu, Rotation.ho2om, Rotation.ho2eu, Rotation.ho2ax, Rotation.ho2ro, ]) def test_homochoric_vectorization(self,default,conversion): ho = np.array([rot.asHomochoric() for rot in default]) conversion(ho.reshape(ho.shape[0]//2,-1,3)) co = conversion(ho) for h,c in zip(ho,co): print(h,c) assert np.allclose(conversion(h),c) @pytest.mark.parametrize('direction',['forward', 'backward']) def test_pyramid_vectorization(self,direction): p = np.random.rand(n,3) o = Rotation._get_order(p,direction) for i,o_i in enumerate(o): assert np.allclose(o_i,Rotation._get_order(p[i],direction)) def test_pyramid_invariant(self): a = np.random.rand(n,3) f = damask.Rotation._get_order(a,'forward') b = damask.Rotation._get_order(a,'backward') assert np.all(np.take_along_axis(np.take_along_axis(a,f,-1),b,-1) == a)