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DAMASK_EICMD
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fixed fiber component sampling and testing

This commit is contained in:
Philip Eisenlohr 2020-09-15 18:14:15 -04:00
parent d6378ec9bc
commit 0a34e342e4
2 changed files with 27 additions and 34 deletions
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40
python/damask/_rotation.py
View File

@ -687,55 +687,49 @@ class Rotation:
@staticmethod
def from_fiber_component(alpha,beta,FWHM=0.0,N=500,degrees=True,seed=None):
def from_fiber_component(alpha,beta,sigma=0.0,N=500,degrees=True,seed=None):
"""
Calculate set of rotations with Gaussian distribution around direction.
References
----------
K. Helming, Texturapproximation durch Modellkomponenten
Cuvillier Verlag, 1996
Parameters
----------
alpha : numpy.ndarray of size 2
tbd.
Polar coordinates (phi from x,theta from z) of fiber direction in crystal frame.
beta : numpy.ndarray of size 2
tbd.
FWHM : float, optional
Full width at half maximum of the Gaussian distribution.
Polar coordinates (phi from x,theta from z) of fiber direction in sample frame.
sigma : float, optional
Standard deviation of (Gaussian) misorientation distribution.
Defaults to 0.
N_samples : int, optional
N : int, optional
Number of samples, defaults to 500.
degrees : boolean, optional
FWHM, alpha, and beta are given in degrees.
sigma, alpha, and beta are given in degrees.
seed : {None, int, array_like[ints], SeedSequence, BitGenerator, Generator}, optional
A seed to initialize the BitGenerator. Defaults to None.
If None, then fresh, unpredictable entropy will be pulled from the OS.
A seed to initialize the BitGenerator. Defaults to None, i.e. unpredictable entropy
will be pulled from the OS.
"""
rng = np.random.default_rng(seed)
FWHM_,alpha_,beta_ = map(np.radians,(FWHM,alpha,beta)) if degrees else (FWHM,alpha,beta)
sigma_,alpha_,beta_ = map(np.radians,(sigma,alpha,beta)) if degrees else (sigma,alpha,beta)
d_cr = np.array([np.sin(alpha_[0])*np.cos(alpha_[1]), np.sin(alpha_[0])*np.sin(alpha_[1]), np.cos(alpha_[0])])
d_lab = np.array([np.sin(beta_[0] )*np.cos(beta_[1] ), np.sin(beta_[0] )*np.sin(beta_[1] ), np.cos(beta_[0] )])
d_lab = np.array([np.sin( beta_[0])*np.cos( beta_[1]), np.sin( beta_[0])*np.sin( beta_[1]), np.cos( beta_[0])])
ax_align = np.append(np.cross(d_lab,d_cr), np.arccos(np.dot(d_lab,d_cr)))
if np.isclose(ax_align[3],0.0): ax_align[:3] = np.array([1,0,0])
R_align = Rotation.from_axis_angle(ax_align if ax_align[3] > 0.0 else -ax_align,normalize=True) # rotation to align fiber axis in crystal and sample system
u,v,b = (np.random.random((N,3)) * 2 * np.array([1,np.pi,np.pi]) - np.array([1,0,np.pi])).T
a = abs(np.random.normal(scale=FWHM_,size=N))
a = abs(np.random.normal(scale=sigma_,size=N))
p = np.vstack((np.sqrt(1-u**2)*np.cos(v),
np.sqrt(1-u**2)*np.sin(v),
u,
a)).T
f = np.hstack((np.broadcast_to(d_cr,(N,3)),b.reshape(N,1)))
p[:,:3] = np.einsum('ij,...j->...i',np.eye(3)-np.outer(d_lab,d_lab),p[:,:3])
f = np.hstack((np.broadcast_to(d_lab,(N,3)),b.reshape(N,1)))
f[f[:,3]<0] *= -1.
return Rotation.from_axis_angle(p) \
* Rotation.from_axis_angle(f) \
* R_align
return R_align.broadcast_to(N) \
@ Rotation.from_axis_angle(p,normalize=True) \
@ Rotation.from_axis_angle(f)
####################################################################################################

21
python/tests/test_Rotation.py
View File

@ -925,14 +925,14 @@ class TestRotation:
dist = angles * (np.random.randint(0,2,N_samples)*2-1)
p = stats.normaltest(dist)[1]
FWHM_out = np.std(dist) * (2*np.sqrt(2*np.log(2)))
FWHM_out = np.std(dist) # * (2*np.sqrt(2*np.log(2)))
print(f'\np: {p}, FWHM ratio {FWHM/FWHM_out}')
assert (.9 < FWHM/FWHM_out < 1.1) and p > 0.001
@pytest.mark.parametrize('FWHM',[10,15,20])
@pytest.mark.parametrize('N_samples',[500,1000,2000])
def test_from_fiber_component(self,N_samples,FWHM):
@pytest.mark.parametrize('sigma',[5,10,15,20])
@pytest.mark.parametrize('N',[1000,10000,100000])
def test_from_fiber_component(self,N,sigma):
"""https://en.wikipedia.org/wiki/Full_width_at_half_maximum."""
alpha = np.random.random(2)*np.pi
beta = np.random.random(2)*np.pi
@ -942,12 +942,11 @@ class TestRotation:
ax = np.append(np.cross(f_in_C,f_in_S), - np.arccos(np.dot(f_in_C,f_in_S)))
n = Rotation.from_axis_angle(ax if ax[3] > 0.0 else ax*-1.0 ,normalize=True) # rotation to align fiber axis in crystal and sample system
o = Rotation.from_fiber_component(alpha,beta,np.radians(FWHM),N_samples,False)
angles=[np.arccos(np.clip(np.dot(n@f_in_S,o[i]@f_in_S),-1,1)) for i in range(N_samples)]
dist = np.array(angles) * (np.random.randint(0,2,N_samples)*2-1)
o = Rotation.from_fiber_component(alpha,beta,np.radians(sigma),N,False)
angles = np.arccos(np.clip(np.dot(o@np.broadcast_to(f_in_S,(N,3)),n@f_in_S),-1,1))
dist = np.array(angles) * (np.random.randint(0,2,N)*2-1)
p = stats.normaltest(dist)[1]
FWHM_out = np.degrees(np.std(dist)) * (2*np.sqrt(2*np.log(2)))
print(f'\np: {p}, FWHM ratio {FWHM/FWHM_out}')
assert (.85 < FWHM/FWHM_out < 1.15) and p > 0.001
sigma_out = np.degrees(np.std(dist))
print(f'\np: {p}, sigma ratio {sigma/sigma_out}')
assert (.85 < sigma/sigma_out < 1.15) and p > 0.001