DAMASK_EICMD/python/tests/test_Rotation.py

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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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n = 1100
atol=1.e-4
scatter=1.e-2
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@pytest.fixture
def default():
"""A set of n random rotations."""
specials = np.array(
[np.array([ 1.0, 0.0, 0.0, 0.0]),
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#-----------------------------------------------
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]),
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#-----------------------------------------------
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.),
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#-----------------------------------------------
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.),
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#-----------------------------------------------
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.),
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#-----------------------------------------------
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.,
])
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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
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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))]
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@pytest.fixture
def reference_dir(reference_dir_base):
"""Directory containing reference results."""
return os.path.join(reference_dir_base,'Rotation')
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class TestRotation:
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def test_Eulers(self,default):
for rot in default:
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m = rot.as_quaternion()
o = Rotation.from_Eulers(rot.as_Eulers()).as_quaternion()
ok = np.allclose(m,o,atol=atol)
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if np.isclose(rot.as_quaternion()[0],0.0,atol=atol):
ok = ok or np.allclose(m*-1.,o,atol=atol)
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print(m,o,rot.as_quaternion())
assert ok and np.isclose(np.linalg.norm(o),1.0)
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def test_AxisAngle(self,default):
for rot in default:
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m = rot.as_Eulers()
o = Rotation.from_axis_angle(rot.as_axis_angle()).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)
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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()
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def test_Matrix(self,default):
for rot in default:
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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)
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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
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def test_Rodrigues(self,default):
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for rot in default:
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m = rot.as_matrix()
o = Rotation.from_Rodrigues(rot.as_Rodrigues()).as_matrix()
ok = np.allclose(m,o,atol=atol)
print(m,o)
assert ok and np.isclose(np.linalg.det(o),1.0)
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def test_Homochoric(self,default):
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()
o = Rotation.from_homochoric(rot.as_homochoric()).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)
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print(m,o,rot.as_quaternion())
assert ok and np.isclose(np.linalg.norm(o[:3]),1.0)
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def test_Cubochoric(self,default):
for rot in default:
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m = rot.as_homochoric()
o = Rotation.from_cubochoric(rot.as_cubochoric()).as_homochoric()
ok = np.allclose(m,o,atol=atol)
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print(m,o,rot.as_quaternion())
assert ok and np.linalg.norm(o) < (3.*np.pi/4.)**(1./3.) + 1.e-9
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def test_Quaternion(self,default):
for rot in default:
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m = rot.as_cubochoric()
o = Rotation.from_quaternion(rot.as_quaternion()).as_cubochoric()
ok = np.allclose(m,o,atol=atol)
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print(m,o,rot.as_quaternion())
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,
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)
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@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,
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Rotation.qu2ho,
Rotation.qu2cu
])
def test_quaternion_vectorization(self,default,conversion):
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qu = np.array([rot.as_quaternion() for rot in default])
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conversion(qu.reshape(qu.shape[0]//2,-1,4))
co = conversion(qu)
for q,c in zip(qu,co):
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print(q,c)
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assert np.allclose(conversion(q),c)
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@pytest.mark.parametrize('conversion',[Rotation.om2qu,
Rotation.om2eu,
Rotation.om2ax,
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Rotation.om2ro,
Rotation.om2ho,
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Rotation.om2cu
])
def test_matrix_vectorization(self,default,conversion):
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om = np.array([rot.as_matrix() for rot in default])
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conversion(om.reshape(om.shape[0]//2,-1,3,3))
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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,
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Rotation.eu2ho,
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Rotation.eu2cu
])
def test_Euler_vectorization(self,default,conversion):
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eu = np.array([rot.as_Eulers() for rot in default])
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conversion(eu.reshape(eu.shape[0]//2,-1,3))
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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,
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Rotation.ax2eu,
Rotation.ax2ro,
Rotation.ax2ho,
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Rotation.ax2cu
])
def test_axisAngle_vectorization(self,default,conversion):
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ax = np.array([rot.as_axis_angle() for rot in default])
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conversion(ax.reshape(ax.shape[0]//2,-1,4))
co = conversion(ax)
for a,c in zip(ax,co):
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print(a,c)
assert np.allclose(conversion(a),c)
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@pytest.mark.parametrize('conversion',[Rotation.ro2qu,
Rotation.ro2om,
Rotation.ro2eu,
Rotation.ro2ax,
Rotation.ro2ho,
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Rotation.ro2cu
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])
def test_Rodrigues_vectorization(self,default,conversion):
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ro = np.array([rot.as_Rodrigues() for rot in default])
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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)
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@pytest.mark.parametrize('conversion',[Rotation.ho2qu,
Rotation.ho2om,
Rotation.ho2eu,
Rotation.ho2ax,
Rotation.ho2ro,
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Rotation.ho2cu
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])
def test_homochoric_vectorization(self,default,conversion):
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ho = np.array([rot.as_homochoric() for rot in default])
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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)
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@pytest.mark.parametrize('conversion',[Rotation.cu2qu,
Rotation.cu2om,
Rotation.cu2eu,
Rotation.cu2ax,
Rotation.cu2ro,
Rotation.cu2ho
])
def test_cubochoric_vectorization(self,default,conversion):
cu = np.array([rot.as_cubochoric() for rot in default])
conversion(cu.reshape(cu.shape[0]//2,-1,3))
co = conversion(cu)
for u,c in zip(cu,co):
print(u,c)
assert np.allclose(conversion(u),c)
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@pytest.mark.parametrize('direction',['forward',
'backward'])
def test_pyramid_vectorization(self,direction):
p = np.random.rand(n,3)
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o = Rotation._get_pyramid_order(p,direction)
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for i,o_i in enumerate(o):
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assert np.all(o_i==Rotation._get_pyramid_order(p[i],direction))
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def test_pyramid_invariant(self):
a = np.random.rand(n,3)
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f = Rotation._get_pyramid_order(a,'forward')
b = Rotation._get_pyramid_order(a,'backward')
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assert np.all(np.take_along_axis(np.take_along_axis(a,f,-1),b,-1) == a)