396 lines
20 KiB
Python
396 lines
20 KiB
Python
import os
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import pytest
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import numpy as np
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from damask import Rotation
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import rotation_conversion
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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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@pytest.fixture
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def default():
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"""A set of n random rotations."""
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specials = np.array(
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[np.array([ 1.0, 0.0, 0.0, 0.0]),
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#-----------------------------------------------
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np.array([0.0, 1.0, 0.0, 0.0]),
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np.array([0.0, 0.0, 1.0, 0.0]),
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np.array([0.0, 0.0, 0.0, 1.0]),
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np.array([0.0,-1.0, 0.0, 0.0]),
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np.array([0.0, 0.0,-1.0, 0.0]),
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np.array([0.0, 0.0, 0.0,-1.0]),
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#-----------------------------------------------
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np.array([1.0, 1.0, 0.0, 0.0])/np.sqrt(2.),
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np.array([1.0, 0.0, 1.0, 0.0])/np.sqrt(2.),
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np.array([1.0, 0.0, 0.0, 1.0])/np.sqrt(2.),
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np.array([0.0, 1.0, 1.0, 0.0])/np.sqrt(2.),
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np.array([0.0, 1.0, 0.0, 1.0])/np.sqrt(2.),
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np.array([0.0, 0.0, 1.0, 1.0])/np.sqrt(2.),
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#-----------------------------------------------
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np.array([1.0,-1.0, 0.0, 0.0])/np.sqrt(2.),
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np.array([1.0, 0.0,-1.0, 0.0])/np.sqrt(2.),
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np.array([1.0, 0.0, 0.0,-1.0])/np.sqrt(2.),
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np.array([0.0, 1.0,-1.0, 0.0])/np.sqrt(2.),
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np.array([0.0, 1.0, 0.0,-1.0])/np.sqrt(2.),
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np.array([0.0, 0.0, 1.0,-1.0])/np.sqrt(2.),
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#-----------------------------------------------
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np.array([0.0, 1.0,-1.0, 0.0])/np.sqrt(2.),
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np.array([0.0, 1.0, 0.0,-1.0])/np.sqrt(2.),
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np.array([0.0, 0.0, 1.0,-1.0])/np.sqrt(2.),
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#-----------------------------------------------
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np.array([0.0,-1.0,-1.0, 0.0])/np.sqrt(2.),
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np.array([0.0,-1.0, 0.0,-1.0])/np.sqrt(2.),
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np.array([0.0, 0.0,-1.0,-1.0])/np.sqrt(2.),
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#-----------------------------------------------
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np.array([1.0, 1.0, 1.0, 0.0])/np.sqrt(3.),
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np.array([1.0, 1.0, 0.0, 1.0])/np.sqrt(3.),
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np.array([1.0, 0.0, 1.0, 1.0])/np.sqrt(3.),
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np.array([1.0,-1.0, 1.0, 0.0])/np.sqrt(3.),
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np.array([1.0,-1.0, 0.0, 1.0])/np.sqrt(3.),
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np.array([1.0, 0.0,-1.0, 1.0])/np.sqrt(3.),
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np.array([1.0, 1.0,-1.0, 0.0])/np.sqrt(3.),
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np.array([1.0, 1.0, 0.0,-1.0])/np.sqrt(3.),
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np.array([1.0, 0.0, 1.0,-1.0])/np.sqrt(3.),
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np.array([1.0,-1.0,-1.0, 0.0])/np.sqrt(3.),
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np.array([1.0,-1.0, 0.0,-1.0])/np.sqrt(3.),
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np.array([1.0, 0.0,-1.0,-1.0])/np.sqrt(3.),
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#-----------------------------------------------
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np.array([0.0, 1.0, 1.0, 1.0])/np.sqrt(3.),
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np.array([0.0, 1.0,-1.0, 1.0])/np.sqrt(3.),
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np.array([0.0, 1.0, 1.0,-1.0])/np.sqrt(3.),
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np.array([0.0,-1.0, 1.0, 1.0])/np.sqrt(3.),
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np.array([0.0,-1.0,-1.0, 1.0])/np.sqrt(3.),
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np.array([0.0,-1.0, 1.0,-1.0])/np.sqrt(3.),
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np.array([0.0,-1.0,-1.0,-1.0])/np.sqrt(3.),
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#-----------------------------------------------
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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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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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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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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_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.from_quaternion(s) for s in specials] + \
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[Rotation.from_quaternion(s) for s in specials_scatter] + \
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[Rotation.from_random() for _ in range(n-len(specials)-len(specials_scatter))]
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@pytest.fixture
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def reference_dir(reference_dir_base):
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"""Directory containing reference results."""
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return os.path.join(reference_dir_base,'Rotation')
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class TestRotation:
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@pytest.mark.parametrize('forward,backward',[(Rotation.qu2om,Rotation.om2qu),
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(Rotation.qu2eu,Rotation.eu2qu),
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(Rotation.qu2ax,Rotation.ax2qu),
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(Rotation.qu2ro,Rotation.ro2qu),
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(Rotation.qu2ho,Rotation.ho2qu),
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(Rotation.qu2cu,Rotation.cu2qu)])
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def test_quaternion_internal(self,default,forward,backward):
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for rot in default:
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m = rot.as_quaternion()
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o = backward(forward(m))
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ok = np.allclose(m,o,atol=atol)
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if np.isclose(rot.as_quaternion()[0],0.0,atol=atol):
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ok = ok or np.allclose(m*-1.,o,atol=atol)
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print(m,o,rot.as_quaternion())
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assert ok and np.isclose(np.linalg.norm(o),1.0)
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@pytest.mark.parametrize('forward,backward',[(Rotation.om2qu,Rotation.qu2om),
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(Rotation.om2eu,Rotation.eu2om),
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(Rotation.om2ax,Rotation.ax2om),
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(Rotation.om2ro,Rotation.ro2om),
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(Rotation.om2ho,Rotation.ho2om),
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(Rotation.om2cu,Rotation.cu2om)])
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def test_matrix_internal(self,default,forward,backward):
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for rot in default:
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m = rot.as_matrix()
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o = backward(forward(m))
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ok = np.allclose(m,o,atol=atol)
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print(m,o,rot.as_quaternion())
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assert ok and np.isclose(np.linalg.det(o),1.0)
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@pytest.mark.parametrize('forward,backward',[(Rotation.eu2qu,Rotation.qu2eu),
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(Rotation.eu2om,Rotation.om2eu),
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(Rotation.eu2ax,Rotation.ax2eu),
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(Rotation.eu2ro,Rotation.ro2eu),
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(Rotation.eu2ho,Rotation.ho2eu),
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(Rotation.eu2cu,Rotation.cu2eu)])
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def test_Eulers_internal(self,default,forward,backward):
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for rot in default:
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m = rot.as_Eulers()
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o = backward(forward(m))
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u = np.array([np.pi*2,np.pi,np.pi*2])
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ok = np.allclose(m,o,atol=atol)
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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)
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if np.isclose(m[1],0.0,atol=atol) or np.isclose(m[1],np.pi,atol=atol):
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sum_phi = np.unwrap([m[0]+m[2],o[0]+o[2]])
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ok = ok or np.isclose(sum_phi[0],sum_phi[1],atol=atol)
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print(m,o,rot.as_quaternion())
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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()
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@pytest.mark.parametrize('forward,backward',[(Rotation.ax2qu,Rotation.qu2ax),
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(Rotation.ax2om,Rotation.om2ax),
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(Rotation.ax2eu,Rotation.eu2ax),
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(Rotation.ax2ro,Rotation.ro2ax),
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(Rotation.ax2ho,Rotation.ho2ax),
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(Rotation.ax2cu,Rotation.cu2ax)])
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def test_axis_angle_internal(self,default,forward,backward):
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for rot in default:
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m = rot.as_axis_angle()
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o = backward(forward(m))
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ok = np.allclose(m,o,atol=atol)
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if np.isclose(m[3],np.pi,atol=atol):
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ok = ok or np.allclose(m*np.array([-1.,-1.,-1.,1.]),o,atol=atol)
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print(m,o,rot.as_quaternion())
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assert ok and np.isclose(np.linalg.norm(o[:3]),1.0) and o[3]<=np.pi+1.e-7
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@pytest.mark.parametrize('degrees',[True,False])
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def test_Eulers(self,default,degrees):
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for rot in default:
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m = rot.as_quaternion()
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o = Rotation.from_Eulers(rot.as_Eulers(degrees),degrees).as_quaternion()
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ok = np.allclose(m,o,atol=atol)
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if np.isclose(rot.as_quaternion()[0],0.0,atol=atol):
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ok = ok or np.allclose(m*-1.,o,atol=atol)
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print(m,o,rot.as_quaternion())
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assert ok and np.isclose(np.linalg.norm(o),1.0)
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@pytest.mark.parametrize('P',[1,-1])
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@pytest.mark.parametrize('normalise',[True,False])
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@pytest.mark.parametrize('degrees',[True,False])
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def test_AxisAngle(self,default,degrees,normalise,P):
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c = np.array([P*-1,P*-1,P*-1,1.])
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for rot in default:
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m = rot.as_Eulers()
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o = Rotation.from_axis_angle(rot.as_axis_angle(degrees)*c,degrees,normalise,P).as_Eulers()
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u = np.array([np.pi*2,np.pi,np.pi*2])
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ok = np.allclose(m,o,atol=atol)
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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)
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if np.isclose(m[1],0.0,atol=atol) or np.isclose(m[1],np.pi,atol=atol):
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sum_phi = np.unwrap([m[0]+m[2],o[0]+o[2]])
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ok = ok or np.isclose(sum_phi[0],sum_phi[1],atol=atol)
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print(m,o,rot.as_quaternion())
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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()
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def test_Matrix(self,default):
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for rot in default:
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m = rot.as_axis_angle()
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o = Rotation.from_axis_angle(rot.as_axis_angle()).as_axis_angle()
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ok = np.allclose(m,o,atol=atol)
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if np.isclose(m[3],np.pi,atol=atol):
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ok = ok or np.allclose(m*np.array([-1.,-1.,-1.,1.]),o,atol=atol)
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print(m,o,rot.as_quaternion())
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assert ok and np.isclose(np.linalg.norm(o[:3]),1.0) and o[3]<=np.pi+1.e-7
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@pytest.mark.parametrize('P',[1,-1])
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@pytest.mark.parametrize('normalise',[True,False])
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def test_Rodrigues(self,default,normalise,P):
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c = np.array([P*-1,P*-1,P*-1,1.])
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for rot in default:
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m = rot.as_matrix()
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o = Rotation.from_Rodrigues(rot.as_Rodrigues()*c,normalise,P).as_matrix()
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ok = np.allclose(m,o,atol=atol)
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print(m,o)
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assert ok and np.isclose(np.linalg.det(o),1.0)
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@pytest.mark.parametrize('P',[1,-1])
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def test_Homochoric(self,default,P):
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cutoff = np.tan(np.pi*.5*(1.-1e-4))
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for rot in default:
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m = rot.as_Rodrigues()
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o = Rotation.from_homochoric(rot.as_homochoric()*P*-1,P).as_Rodrigues()
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ok = np.allclose(np.clip(m,None,cutoff),np.clip(o,None,cutoff),atol=atol)
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ok = ok or np.isclose(m[3],0.0,atol=atol)
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print(m,o,rot.as_quaternion())
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assert ok and np.isclose(np.linalg.norm(o[:3]),1.0)
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@pytest.mark.parametrize('P',[1,-1])
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def test_Cubochoric(self,default,P):
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for rot in default:
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m = rot.as_homochoric()
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o = Rotation.from_cubochoric(rot.as_cubochoric()*P*-1,P).as_homochoric()
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ok = np.allclose(m,o,atol=atol)
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print(m,o,rot.as_quaternion())
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assert ok and np.linalg.norm(o) < (3.*np.pi/4.)**(1./3.) + 1.e-9
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@pytest.mark.parametrize('P',[1,-1])
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def test_Quaternion(self,default,P):
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c = np.array([1,P*-1,P*-1,P*-1])
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for rot in default:
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m = rot.as_cubochoric()
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o = Rotation.from_quaternion(rot.as_quaternion()*c,False,P).as_cubochoric()
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ok = np.allclose(m,o,atol=atol)
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print(m,o,rot.as_quaternion())
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assert ok and o.max() < np.pi**(2./3.)*0.5+1.e-9
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@pytest.mark.parametrize('function',[Rotation.from_quaternion,
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Rotation.from_Eulers,
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Rotation.from_axis_angle,
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Rotation.from_matrix,
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Rotation.from_Rodrigues,
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Rotation.from_homochoric])
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def test_invalid_shape(self,function):
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invalid_shape = np.random.random(np.random.randint(8,32,(3)))
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with pytest.raises(ValueError):
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function(invalid_shape)
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@pytest.mark.parametrize('function,invalid',[(Rotation.from_quaternion, np.array([-1,0,0,0])),
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(Rotation.from_quaternion, np.array([1,1,1,0])),
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(Rotation.from_Eulers, np.array([1,4,0])),
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(Rotation.from_axis_angle, np.array([1,0,0,4])),
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(Rotation.from_axis_angle, np.array([1,1,0,1])),
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(Rotation.from_matrix, np.random.rand(3,3)),
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(Rotation.from_Rodrigues, np.array([1,0,0,-1])),
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(Rotation.from_Rodrigues, np.array([1,1,0,1])),
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(Rotation.from_homochoric, np.array([2,2,2])) ])
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def test_invalid_value(self,function,invalid):
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with pytest.raises(ValueError):
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function(invalid)
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@pytest.mark.parametrize('vectorized, single',[(Rotation.qu2om,rotation_conversion.qu2om),
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(Rotation.qu2eu,rotation_conversion.qu2eu),
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(Rotation.qu2ax,rotation_conversion.qu2ax),
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(Rotation.qu2ro,rotation_conversion.qu2ro),
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(Rotation.qu2ho,rotation_conversion.qu2ho)])
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def test_quaternion_vectorization(self,default,vectorized,single):
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qu = np.array([rot.as_quaternion() for rot in default])
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vectorized(qu.reshape(qu.shape[0]//2,-1,4))
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co = vectorized(qu)
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for q,c in zip(qu,co):
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print(q,c)
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assert np.allclose(single(q),c) and np.allclose(single(q),vectorized(q))
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@pytest.mark.parametrize('vectorized, single',[(Rotation.om2qu,rotation_conversion.om2qu),
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(Rotation.om2eu,rotation_conversion.om2eu),
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(Rotation.om2ax,rotation_conversion.om2ax)])
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def test_matrix_vectorization(self,default,vectorized,single):
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om = np.array([rot.as_matrix() for rot in default])
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vectorized(om.reshape(om.shape[0]//2,-1,3,3))
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co = vectorized(om)
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for o,c in zip(om,co):
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print(o,c)
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assert np.allclose(single(o),c) and np.allclose(single(o),vectorized(o))
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@pytest.mark.parametrize('vectorized, single',[(Rotation.eu2qu,rotation_conversion.eu2qu),
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(Rotation.eu2om,rotation_conversion.eu2om),
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(Rotation.eu2ax,rotation_conversion.eu2ax),
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(Rotation.eu2ro,rotation_conversion.eu2ro)])
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def test_Euler_vectorization(self,default,vectorized,single):
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eu = np.array([rot.as_Eulers() for rot in default])
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vectorized(eu.reshape(eu.shape[0]//2,-1,3))
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co = vectorized(eu)
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for e,c in zip(eu,co):
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print(e,c)
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assert np.allclose(single(e),c) and np.allclose(single(e),vectorized(e))
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@pytest.mark.parametrize('vectorized, single',[(Rotation.ax2qu,rotation_conversion.ax2qu),
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(Rotation.ax2om,rotation_conversion.ax2om),
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(Rotation.ax2ro,rotation_conversion.ax2ro),
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(Rotation.ax2ho,rotation_conversion.ax2ho)])
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def test_axisAngle_vectorization(self,default,vectorized,single):
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ax = np.array([rot.as_axis_angle() for rot in default])
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vectorized(ax.reshape(ax.shape[0]//2,-1,4))
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co = vectorized(ax)
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for a,c in zip(ax,co):
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print(a,c)
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assert np.allclose(single(a),c) and np.allclose(single(a),vectorized(a))
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@pytest.mark.parametrize('vectorized, single',[(Rotation.ro2ax,rotation_conversion.ro2ax),
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(Rotation.ro2ho,rotation_conversion.ro2ho)])
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def test_Rodrigues_vectorization(self,default,vectorized,single):
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ro = np.array([rot.as_Rodrigues() for rot in default])
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vectorized(ro.reshape(ro.shape[0]//2,-1,4))
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co = vectorized(ro)
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for r,c in zip(ro,co):
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print(r,c)
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assert np.allclose(single(r),c) and np.allclose(single(r),vectorized(r))
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@pytest.mark.parametrize('vectorized, single',[(Rotation.ho2ax,rotation_conversion.ho2ax),
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(Rotation.ho2cu,rotation_conversion.ho2cu)])
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def test_homochoric_vectorization(self,default,vectorized,single):
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ho = np.array([rot.as_homochoric() for rot in default])
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vectorized(ho.reshape(ho.shape[0]//2,-1,3))
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co = vectorized(ho)
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for h,c in zip(ho,co):
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print(h,c)
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assert np.allclose(single(h),c) and np.allclose(single(h),vectorized(h))
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@pytest.mark.parametrize('vectorized, single',[(Rotation.cu2ho,rotation_conversion.cu2ho)])
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def test_cubochoric_vectorization(self,default,vectorized,single):
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cu = np.array([rot.as_cubochoric() for rot in default])
|
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vectorized(cu.reshape(cu.shape[0]//2,-1,3))
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co = vectorized(cu)
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|
for u,c in zip(cu,co):
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|
print(u,c)
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|
assert np.allclose(single(u),c) and np.allclose(single(u),vectorized(u))
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|
|
|
@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(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
|