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shortened from_fiber_component algorithm

This commit is contained in:
Philip Eisenlohr 2020-09-15 16:34:19 -04:00
parent 3f823ca717
commit d6378ec9bc
1 changed files with 23 additions and 43 deletions
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66
python/damask/_rotation.py
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@ -434,10 +434,11 @@ class Rotation:
if P == 1: ax[...,0:3] *= -1 if P == 1: ax[...,0:3] *= -1
if degrees: ax[..., 3] = np.radians(ax[...,3]) if degrees: ax[..., 3] = np.radians(ax[...,3])
if normalize: ax[...,0:3] /= np.linalg.norm(ax[...,0:3],axis=-1) if normalize: ax[...,0:3] /= np.linalg.norm(ax[...,0:3],axis=-1,keepdims=True)
if np.any(ax[...,3] < 0.0) or np.any(ax[...,3] > np.pi): if np.any(ax[...,3] < 0.0) or np.any(ax[...,3] > np.pi):
raise ValueError('Axis angle rotation angle outside of [0..π].') raise ValueError('Axis angle rotation angle outside of [0..π].')
if not np.all(np.isclose(np.linalg.norm(ax[...,0:3],axis=-1), 1.0)): if not np.all(np.isclose(np.linalg.norm(ax[...,0:3],axis=-1), 1.0)):
print(np.linalg.norm(ax[...,0:3],axis=-1))
raise ValueError('Axis angle rotation axis is not of unit length.') raise ValueError('Axis angle rotation axis is not of unit length.')
return Rotation(Rotation._ax2qu(ax)) return Rotation(Rotation._ax2qu(ax))
@ -516,7 +517,7 @@ class Rotation:
raise ValueError('P ∉ {-1,1}') raise ValueError('P ∉ {-1,1}')
if P == 1: ro[...,0:3] *= -1 if P == 1: ro[...,0:3] *= -1
if normalize: ro[...,0:3] /= np.linalg.norm(ro[...,0:3],axis=-1) if normalize: ro[...,0:3] /= np.linalg.norm(ro[...,0:3],axis=-1,keepdims=True)
if np.any(ro[...,3] < 0.0): if np.any(ro[...,3] < 0.0):
raise ValueError('Rodrigues vector rotation angle not positive.') raise ValueError('Rodrigues vector rotation angle not positive.')
if not np.all(np.isclose(np.linalg.norm(ro[...,0:3],axis=-1), 1.0)): if not np.all(np.isclose(np.linalg.norm(ro[...,0:3],axis=-1), 1.0)):
@ -686,7 +687,7 @@ class Rotation:
@staticmethod @staticmethod
def from_fiber_component(alpha,beta,FWHM,N_samples=500,degrees=True,seed=None): def from_fiber_component(alpha,beta,FWHM=0.0,N=500,degrees=True,seed=None):
""" """
Calculate set of rotations with Gaussian distribution around direction. Calculate set of rotations with Gaussian distribution around direction.
@ -701,8 +702,9 @@ class Rotation:
tbd. tbd.
beta : numpy.ndarray of size 2 beta : numpy.ndarray of size 2
tbd. tbd.
FWHM : float FWHM : float, optional
Full width at half maximum of the Gaussian distribution. Full width at half maximum of the Gaussian distribution.
Defaults to 0.
N_samples : int, optional N_samples : int, optional
Number of samples, defaults to 500. Number of samples, defaults to 500.
degrees : boolean, optional degrees : boolean, optional
@ -713,48 +715,26 @@ class Rotation:
""" """
rng = np.random.default_rng(seed) rng = np.random.default_rng(seed)
FWHM_,alpha_,beta_ = np.radians((FWHM,alpha,beta)) if degrees else (FWHM,alpha,beta) FWHM_,alpha_,beta_ = map(np.radians,(FWHM,alpha,beta)) if degrees else (FWHM,alpha,beta)
f_in_C = np.array([np.sin(alpha_[0])*np.cos(alpha_[1]), np.sin(alpha_[0])*np.sin(alpha_[1]), np.cos(alpha_[0])]) d_cr = np.array([np.sin(alpha_[0])*np.cos(alpha_[1]), np.sin(alpha_[0])*np.sin(alpha_[1]), np.cos(alpha_[0])])
f_in_S = 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 = np.append(np.cross(f_in_C,f_in_S), - np.arccos(np.dot(f_in_C,f_in_S))) ax_align = np.append(np.cross(d_lab,d_cr), np.arccos(np.dot(d_lab,d_cr)))
R_align = 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 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
rotations = [] u,v,b = (np.random.random((N,3)) * 2 * np.array([1,np.pi,np.pi]) - np.array([1,0,np.pi])).T
for i in range(N_samples): a = abs(np.random.normal(scale=FWHM_,size=N))
rnd = rng.random(3) p = np.vstack((np.sqrt(1-u**2)*np.cos(v),
ax = np.append(f_in_S,rnd[0]*np.pi*2.0) np.sqrt(1-u**2)*np.sin(v),
if ax[3] > np.pi: ax = np.append(ax[:3]*-1,np.pi*2-ax[3]) u,
R = R_align @ Rotation.from_axis_angle(ax) # rotation (0..360deg) perpendicular to fiber axis a)).T
if FWHM_ > np.radians(0.1): f = np.hstack((np.broadcast_to(d_cr,(N,3)),b.reshape(N,1)))
f[f[:,3]<0] *= -1.
i_smallest = np.argmin(np.abs(f_in_S)) return Rotation.from_axis_angle(p) \
i_non_smallest = list(filter(lambda x: x!=i_smallest, [0,1,2])) * Rotation.from_axis_angle(f) \
* R_align
s = f_in_S[i_smallest]
a = f_in_S[i_non_smallest]
x = np.sum(a**2)
u = np.empty(3)
while True: # rejection sampling
angle = (rnd[1] - 0.5)*4 *FWHM_
# solve cos(angle) = dot_product(fInS,u) for u. This is underdetermined, hence assume that
# they share the smallest component.
c = np.cos(angle) - s**2
u[i_non_smallest[1]] = -(2.0*c*a[1] + np.sqrt(4*((c*a[1])**2.0-x*(c**2.0-a[0]**2*(1.0-s**2)))))/(2*x)
u[i_non_smallest[0]] = np.sqrt(1.0-u[i_non_smallest[1]]**2.0-s**2.0)
u[i_smallest] = s
if (rnd[2] <= np.exp(-4.0*np.log(2.0)*(angle/FWHM_)**2)):
ax = np.append(np.cross(u,f_in_S),angle)
R = R @ Rotation.from_axis_angle(ax if ax[3] > 0.0 else ax*-1.0,normalize=True) # tilt around direction of smallest component
break
else:
rnd = rng.random(3)
rotations.append(R.as_quaternion())
return Rotation.from_quaternion(rotations)