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DAMASK_EICMD
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Merge branch 'development' into state-integration-cleaning

This commit is contained in:
Martin Diehl 2020-04-17 07:46:40 +02:00
parent 5fca7c4369 875b3b6321
commit 84d6521183
18 changed files with 1057 additions and 622 deletions
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2
PRIVATE

@ -1 +1 @@
Subproject commit aa0b9fe992ce0bfc172989ab006893ddb8939c1e
Subproject commit 232a094c715bcbbd1c6652c4dc4a4a50d402b82f

2
VERSION
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@ -1 +1 @@
v2.0.3-2245-gc7508d85
v2.0.3-2303-g2a6132b7

34
python/damask/_Lambert.py
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@ -51,19 +51,18 @@ def cube_to_ball(cube):
https://doi.org/10.1088/0965-0393/22/7/075013
"""
if np.abs(np.max(cube))>np.pi**(2./3.) * 0.5:
raise ValueError
cube_ = np.clip(cube,None,np.pi**(2./3.) * 0.5) if np.isclose(np.abs(np.max(cube)),np.pi**(2./3.) * 0.5,atol=1e-6) else cube
# transform to the sphere grid via the curved square, and intercept the zero point
if np.allclose(cube,0.0,rtol=0.0,atol=1.0e-300):
if np.allclose(cube_,0.0,rtol=0.0,atol=1.0e-16):
ball = np.zeros(3)
else:
# get pyramide and scale by grid parameter ratio
p = _get_order(cube)
XYZ = cube[p] * sc
p = _get_order(cube_)
XYZ = cube_[p[0]] * sc
# intercept all the points along the z-axis
if np.allclose(XYZ[0:2],0.0,rtol=0.0,atol=1.0e-300):
if np.allclose(XYZ[0:2],0.0,rtol=0.0,atol=1.0e-16):
ball = np.array([0.0, 0.0, np.sqrt(6.0/np.pi) * XYZ[2]])
else:
order = [1,0] if np.abs(XYZ[1]) <= np.abs(XYZ[0]) else [0,1]
@ -82,7 +81,7 @@ def cube_to_ball(cube):
ball = np.array([ T[order[1]] * q, T[order[0]] * q, np.sqrt(6.0/np.pi) * XYZ[2] - c ])
# reverse the coordinates back to the regular order according to the original pyramid number
ball = ball[p]
ball = ball[p[1]]
return ball
@ -102,15 +101,14 @@ def ball_to_cube(ball):
https://doi.org/10.1088/0965-0393/22/7/075013
"""
rs = np.linalg.norm(ball)
if rs > R1:
raise ValueError
ball_ = ball/np.linalg.norm(ball)*R1 if np.isclose(np.linalg.norm(ball),R1,atol=1e-6) else ball
rs = np.linalg.norm(ball_)
if np.allclose(ball,0.0,rtol=0.0,atol=1.0e-300):
if np.allclose(ball_,0.0,rtol=0.0,atol=1.0e-16):
cube = np.zeros(3)
else:
p = _get_order(ball)
xyz3 = ball[p]
p = _get_order(ball_)
xyz3 = ball_[p[0]]
# inverse M_3
xyz2 = xyz3[0:2] * np.sqrt( 2.0*rs/(rs+np.abs(xyz3[2])) )
@ -118,7 +116,7 @@ def ball_to_cube(ball):
# inverse M_2
qxy = np.sum(xyz2**2)
if np.isclose(qxy,0.0,rtol=0.0,atol=1.0e-300):
if np.isclose(qxy,0.0,rtol=0.0,atol=1.0e-16):
Tinv = np.zeros(2)
else:
q2 = qxy + np.max(np.abs(xyz2))**2
@ -132,7 +130,7 @@ def ball_to_cube(ball):
# inverse M_1
cube = np.array([ Tinv[0], Tinv[1], (-1.0 if xyz3[2] < 0.0 else 1.0) * rs / np.sqrt(6.0/np.pi) ]) /sc
# reverse the coordinates back to the regular order according to the original pyramid number
cube = cube[p]
cube = cube[p[1]]
return cube
@ -157,10 +155,10 @@ def _get_order(xyz):
"""
if (abs(xyz[0])<= xyz[2]) and (abs(xyz[1])<= xyz[2]) or \
(abs(xyz[0])<=-xyz[2]) and (abs(xyz[1])<=-xyz[2]):
return [0,1,2]
return [[0,1,2],[0,1,2]]
elif (abs(xyz[2])<= xyz[0]) and (abs(xyz[1])<= xyz[0]) or \
(abs(xyz[2])<=-xyz[0]) and (abs(xyz[1])<=-xyz[0]):
return [1,2,0]
return [[1,2,0],[2,0,1]]
elif (abs(xyz[0])<= xyz[1]) and (abs(xyz[2])<= xyz[1]) or \
(abs(xyz[0])<=-xyz[1]) and (abs(xyz[2])<=-xyz[1]):
return [2,0,1]
return [[2,0,1],[1,2,0]]

2
python/damask/__init__.py
View File

@ -6,7 +6,7 @@ name = 'damask'
with open(_os.path.join(_os.path.dirname(__file__),'VERSION')) as _f:
version = _re.sub(r'^v','',_f.readline().strip())
# classes
# make classes directly accessible as damask.Class
from ._environment import Environment # noqa
from ._table import Table # noqa
from ._vtk import VTK # noqa

4
python/damask/_geom.py
View File

@ -291,7 +291,7 @@ class Geom:
comments = []
for i,line in enumerate(content[:header_length]):
items = line.lower().strip().split()
items = line.split('#')[0].lower().strip().split()
key = items[0] if items else ''
if key == 'grid':
grid = np.array([ int(dict(zip(items[1::2],items[2::2]))[i]) for i in ['a','b','c']])
@ -307,7 +307,7 @@ class Geom:
microstructure = np.empty(grid.prod()) # initialize as flat array
i = 0
for line in content[header_length:]:
items = line.split()
items = line.split('#')[0].split()
if len(items) == 3:
if items[1].lower() == 'of':
items = np.ones(int(items[0]))*float(items[2])

364
python/damask/_rotation.py
View File

@ -2,7 +2,7 @@ import numpy as np
from ._Lambert import ball_to_cube, cube_to_ball
P = -1
_P = -1
def iszero(a):
return np.isclose(a,0.0,atol=1.0e-12,rtol=0.0)
@ -89,7 +89,7 @@ class Rotation:
other_q = other.quaternion[0]
other_p = other.quaternion[1:]
R = self.__class__(np.append(self_q*other_q - np.dot(self_p,other_p),
self_q*other_p + other_q*self_p + P * np.cross(self_p,other_p)))
self_q*other_p + other_q*self_p + _P * np.cross(self_p,other_p)))
return R.standardize()
elif isinstance(other, (tuple,np.ndarray)):
if isinstance(other,tuple) or other.shape == (3,): # rotate a single (3)-vector or meshgrid
@ -97,7 +97,7 @@ class Rotation:
B = 2.0 * ( self.quaternion[1]*other[0]
+ self.quaternion[2]*other[1]
+ self.quaternion[3]*other[2])
C = 2.0 * P*self.quaternion[0]
C = 2.0 * _P*self.quaternion[0]
return np.array([
A*other[0] + B*self.quaternion[1] + C*(self.quaternion[2]*other[2] - self.quaternion[3]*other[1]),
@ -206,7 +206,7 @@ class Rotation:
"""
ax = Rotation.qu2ax(self.quaternion)
if degrees: ax[3] = np.degrees(ax[3])
return (ax[:3],np.degrees(ax[3])) if pair else ax
return (ax[:3],ax[3]) if pair else ax
def asMatrix(self):
"""Rotation matrix."""
@ -262,9 +262,9 @@ class Rotation:
if acceptHomomorph:
qu *= -1.
else:
raise ValueError('Quaternion has negative first component.\n{}'.format(qu[0]))
raise ValueError('Quaternion has negative first component: {}.'.format(qu[0]))
if not np.isclose(np.linalg.norm(qu), 1.0):
raise ValueError('Quaternion is not of unit length.\n{} {} {} {}'.format(*qu))
raise ValueError('Quaternion is not of unit length: {} {} {} {}.'.format(*qu))
return Rotation(qu)
@ -276,7 +276,7 @@ class Rotation:
else np.array(eulers,dtype=float)
eu = np.radians(eu) if degrees else eu
if np.any(eu < 0.0) or np.any(eu > 2.0*np.pi) or eu[1] > np.pi:
raise ValueError('Euler angles outside of [0..2π],[0..π],[0..2π].\n{} {} {}.'.format(*eu))
raise ValueError('Euler angles outside of [0..2π],[0..π],[0..2π]: {} {} {}.'.format(*eu))
return Rotation(Rotation.eu2qu(eu))
@ -292,9 +292,9 @@ class Rotation:
if degrees: ax[ 3] = np.radians(ax[3])
if normalise: ax[0:3] /= np.linalg.norm(ax[0:3])
if ax[3] < 0.0 or ax[3] > np.pi:
raise ValueError('Axis angle rotation angle outside of [0..π].\n{}'.format(ax[3]))
raise ValueError('Axis angle rotation angle outside of [0..π]: {}.'.format(ax[3]))
if not np.isclose(np.linalg.norm(ax[0:3]), 1.0):
raise ValueError('Axis angle rotation axis is not of unit length.\n{} {} {}'.format(*ax[0:3]))
raise ValueError('Axis angle rotation axis is not of unit length: {} {} {}.'.format(*ax[0:3]))
return Rotation(Rotation.ax2qu(ax))
@ -312,11 +312,11 @@ class Rotation:
(U,S,Vh) = np.linalg.svd(om) # singular value decomposition
om = np.dot(U,Vh)
if not np.isclose(np.linalg.det(om),1.0):
raise ValueError('matrix is not a proper rotation.\n{}'.format(om))
raise ValueError('matrix is not a proper rotation: {}.'.format(om))
if not np.isclose(np.dot(om[0],om[1]), 0.0) \
or not np.isclose(np.dot(om[1],om[2]), 0.0) \
or not np.isclose(np.dot(om[2],om[0]), 0.0):
raise ValueError('matrix is not orthogonal.\n{}'.format(om))
raise ValueError('matrix is not orthogonal: {}.'.format(om))
return Rotation(Rotation.om2qu(om))
@ -336,9 +336,9 @@ class Rotation:
if P > 0: ro[0:3] *= -1 # convert from P=1 to P=-1
if normalise: ro[0:3] /= np.linalg.norm(ro[0:3])
if not np.isclose(np.linalg.norm(ro[0:3]), 1.0):
raise ValueError('Rodrigues rotation axis is not of unit length.\n{} {} {}'.format(*ro[0:3]))
raise ValueError('Rodrigues rotation axis is not of unit length: {} {} {}.'.format(*ro[0:3]))
if ro[3] < 0.0:
raise ValueError('Rodrigues rotation angle not positive.\n{}'.format(ro[3]))
raise ValueError('Rodrigues rotation angle not positive: {}.'.format(ro[3]))
return Rotation(Rotation.ro2qu(ro))
@ -350,6 +350,9 @@ class Rotation:
else np.array(homochoric,dtype=float)
if P > 0: ho *= -1 # convert from P=1 to P=-1
if np.linalg.norm(ho) > (3.*np.pi/4.)**(1./3.)+1e-9:
raise ValueError('Coordinate outside of the sphere: {} {} {}.'.format(ho))
return Rotation(Rotation.ho2qu(ho))
@staticmethod
@ -358,6 +361,10 @@ class Rotation:
cu = cubochoric if isinstance(cubochoric, np.ndarray) and cubochoric.dtype == np.dtype(float) \
else np.array(cubochoric,dtype=float)
if np.abs(np.max(cu))>np.pi**(2./3.) * 0.5+1e-9:
raise ValueError('Coordinate outside of the cube: {} {} {}.'.format(*cu))
ho = Rotation.cu2ho(cu)
if P > 0: ho *= -1 # convert from P=1 to P=-1
@ -383,7 +390,7 @@ class Rotation:
"""
if not all(isinstance(item, Rotation) for item in rotations):
raise TypeError("Only instances of Rotation can be averaged.")
raise TypeError('Only instances of Rotation can be averaged.')
N = len(rotations)
if not weights:
@ -441,34 +448,69 @@ class Rotation:
#---------- Quaternion ----------
@staticmethod
def qu2om(qu):
if len(qu.shape) == 1:
"""Quaternion to rotation matrix."""
qq = qu[0]**2-(qu[1]**2 + qu[2]**2 + qu[3]**2)
om = np.diag(qq + 2.0*np.array([qu[1],qu[2],qu[3]])**2)
om[1,0] = 2.0*(qu[2]*qu[1]+qu[0]*qu[3])
om[0,1] = 2.0*(qu[1]*qu[2]-qu[0]*qu[3])
om[2,1] = 2.0*(qu[3]*qu[2]+qu[0]*qu[1])
om[1,2] = 2.0*(qu[2]*qu[3]-qu[0]*qu[1])
om[0,2] = 2.0*(qu[1]*qu[3]+qu[0]*qu[2])
om[2,0] = 2.0*(qu[3]*qu[1]-qu[0]*qu[2])
return om if P > 0.0 else om.T
om[0,1] = 2.0*(qu[2]*qu[1]+qu[0]*qu[3])
om[1,0] = 2.0*(qu[1]*qu[2]-qu[0]*qu[3])
om[1,2] = 2.0*(qu[3]*qu[2]+qu[0]*qu[1])
om[2,1] = 2.0*(qu[2]*qu[3]-qu[0]*qu[1])
om[2,0] = 2.0*(qu[1]*qu[3]+qu[0]*qu[2])
om[0,2] = 2.0*(qu[3]*qu[1]-qu[0]*qu[2])
else:
qq = qu[...,0:1]**2-(qu[...,1:2]**2 + qu[...,2:3]**2 + qu[...,3:4]**2)
om = np.block([qq + 2.0*qu[...,1:2]**2,
2.0*(qu[...,2:3]*qu[...,1:2]+qu[...,0:1]*qu[...,3:4]),
2.0*(qu[...,3:4]*qu[...,1:2]-qu[...,0:1]*qu[...,2:3]),
2.0*(qu[...,1:2]*qu[...,2:3]-qu[...,0:1]*qu[...,3:4]),
qq + 2.0*qu[...,2:3]**2,
2.0*(qu[...,3:4]*qu[...,2:3]+qu[...,0:1]*qu[...,1:2]),
2.0*(qu[...,1:2]*qu[...,3:4]+qu[...,0:1]*qu[...,2:3]),
2.0*(qu[...,2:3]*qu[...,3:4]-qu[...,0:1]*qu[...,1:2]),
qq + 2.0*qu[...,3:4]**2,
]).reshape(qu.shape[:-1]+(3,3))
return om if _P < 0.0 else np.swapaxes(om,(-1,-2))
@staticmethod
def qu2eu(qu):
"""Quaternion to Bunge-Euler angles."""
if len(qu.shape) == 1:
q03 = qu[0]**2+qu[3]**2
q12 = qu[1]**2+qu[2]**2
chi = np.sqrt(q03*q12)
if iszero(chi):
eu = np.array([np.arctan2(-P*2.0*qu[0]*qu[3],qu[0]**2-qu[3]**2), 0.0, 0.0]) if iszero(q12) else \
np.array([np.arctan2(2.0*qu[1]*qu[2],qu[1]**2-qu[2]**2), np.pi, 0.0])
if np.abs(q12) < 1.e-8:
eu = np.array([np.arctan2(-_P*2.0*qu[0]*qu[3],qu[0]**2-qu[3]**2), 0.0, 0.0])
elif np.abs(q03) < 1.e-8:
eu = np.array([np.arctan2( 2.0*qu[1]*qu[2],qu[1]**2-qu[2]**2), np.pi, 0.0])
else:
eu = np.array([np.arctan2((-P*qu[0]*qu[2]+qu[1]*qu[3])*chi, (-P*qu[0]*qu[1]-qu[2]*qu[3])*chi ),
eu = np.array([np.arctan2((-_P*qu[0]*qu[2]+qu[1]*qu[3])*chi, (-_P*qu[0]*qu[1]-qu[2]*qu[3])*chi ),
np.arctan2( 2.0*chi, q03-q12 ),
np.arctan2(( P*qu[0]*qu[2]+qu[1]*qu[3])*chi, (-P*qu[0]*qu[1]+qu[2]*qu[3])*chi )])
np.arctan2(( _P*qu[0]*qu[2]+qu[1]*qu[3])*chi, (-_P*qu[0]*qu[1]+qu[2]*qu[3])*chi )])
else:
q02 = qu[...,0:1]*qu[...,2:3]
q13 = qu[...,1:2]*qu[...,3:4]
q01 = qu[...,0:1]*qu[...,1:2]
q23 = qu[...,2:3]*qu[...,3:4]
q03_s = qu[...,0:1]**2+qu[...,3:4]**2
q12_s = qu[...,1:2]**2+qu[...,2:3]**2
chi = np.sqrt(q03_s*q12_s)
# reduce Euler angles to definition range, i.e a lower limit of 0.0
eu = np.where(np.abs(q12_s) < 1.0e-8,
np.block([np.arctan2(-_P*2.0*qu[...,0:1]*qu[...,3:4],qu[...,0:1]**2-qu[...,3:4]**2),
np.zeros(qu.shape[:-1]+(2,))]),
np.where(np.abs(q03_s) < 1.0e-8,
np.block([np.arctan2( 2.0*qu[...,1:2]*qu[...,2:3],qu[...,1:2]**2-qu[...,2:3]**2),
np.broadcast_to(np.pi,qu.shape[:-1]+(1,)),
np.zeros(qu.shape[:-1]+(1,))]),
np.block([np.arctan2((-_P*q02+q13)*chi, (-_P*q01-q23)*chi),
np.arctan2( 2.0*chi, q03_s-q12_s ),
np.arctan2(( _P*q02+q13)*chi, (-_P*q01+q23)*chi)])
)
)
# reduce Euler angles to definition range
eu[np.abs(eu)<1.e-6] = 0.0
eu = np.where(eu<0, (eu+2.0*np.pi)%np.array([2.0*np.pi,np.pi,2.0*np.pi]),eu)
return eu
@ -479,38 +521,65 @@ class Rotation:
Modified version of the original formulation, should be numerically more stable
"""
if iszero(qu[1]**2+qu[2]**2+qu[3]**2): # set axis to [001] if the angle is 0/360
ax = [ 0.0, 0.0, 1.0, 0.0 ]
elif not iszero(qu[0]):
if len(qu.shape) == 1:
if np.abs(np.sum(qu[1:4]**2)) < 1.e-6: # set axis to [001] if the angle is 0/360
ax = np.array([ 0.0, 0.0, 1.0, 0.0 ])
elif qu[0] > 1.e-6:
s = np.sign(qu[0])/np.sqrt(qu[1]**2+qu[2]**2+qu[3]**2)
omega = 2.0 * np.arccos(np.clip(qu[0],-1.0,1.0))
ax = [ qu[1]*s, qu[2]*s, qu[3]*s, omega ]
ax = ax = np.array([ qu[1]*s, qu[2]*s, qu[3]*s, omega ])
else:
ax = [ qu[1], qu[2], qu[3], np.pi]
return np.array(ax)
ax = ax = np.array([ qu[1], qu[2], qu[3], np.pi])
else:
with np.errstate(invalid='ignore',divide='ignore'):
s = np.sign(qu[...,0:1])/np.sqrt(qu[...,1:2]**2+qu[...,2:3]**2+qu[...,3:4]**2)
omega = 2.0 * np.arccos(np.clip(qu[...,0:1],-1.0,1.0))
ax = np.where(np.broadcast_to(qu[...,0:1] < 1.0e-6,qu.shape),
np.block([qu[...,1:4],np.broadcast_to(np.pi,qu.shape[:-1]+(1,))]),
np.block([qu[...,1:4]*s,omega]))
ax[np.sum(np.abs(qu[...,1:4])**2,axis=-1) < 1.0e-6,] = [0.0, 0.0, 1.0, 0.0]
return ax
@staticmethod
def qu2ro(qu):
"""Quaternion to Rodrigues-Frank vector."""
if len(qu.shape) == 1:
if iszero(qu[0]):
ro = [qu[1], qu[2], qu[3], np.inf]
ro = np.array([qu[1], qu[2], qu[3], np.inf])
else:
s = np.linalg.norm([qu[1],qu[2],qu[3]])
ro = [0.0,0.0,P,0.0] if iszero(s) else \
[ qu[1]/s, qu[2]/s, qu[3]/s, np.tan(np.arccos(np.clip(qu[0],-1.0,1.0)))]
return np.array(ro)
s = np.linalg.norm(qu[1:4])
ro = np.array([0.0,0.0,_P,0.0] if iszero(s) else \
[ qu[1]/s, qu[2]/s, qu[3]/s, np.tan(np.arccos(np.clip(qu[0],-1.0,1.0)))])
else:
with np.errstate(invalid='ignore',divide='ignore'):
s = np.linalg.norm(qu[...,1:4],axis=-1,keepdims=True)
ro = np.where(np.broadcast_to(np.abs(qu[...,0:1]) < 1.0e-12,qu.shape),
np.block([qu[...,1:2], qu[...,2:3], qu[...,3:4], np.broadcast_to(np.inf,qu.shape[:-1]+(1,))]),
np.block([qu[...,1:2]/s,qu[...,2:3]/s,qu[...,3:4]/s,
np.tan(np.arccos(np.clip(qu[...,0:1],-1.0,1.0)))
])
)
ro[np.abs(s).squeeze(-1) < 1.0e-12] = [0.0,0.0,_P,0.0]
return ro
@staticmethod
def qu2ho(qu):
"""Quaternion to homochoric vector."""
if len(qu.shape) == 1:
omega = 2.0 * np.arccos(np.clip(qu[0],-1.0,1.0))
if iszero(omega):
ho = np.array([ 0.0, 0.0, 0.0 ])
if np.abs(omega) < 1.0e-12:
ho = np.zeros(3)
else:
ho = np.array([qu[1], qu[2], qu[3]])
f = 0.75 * ( omega - np.sin(omega) )
ho = ho/np.linalg.norm(ho) * f**(1./3.)
else:
with np.errstate(invalid='ignore'):
omega = 2.0 * np.arccos(np.clip(qu[...,0:1],-1.0,1.0))
ho = np.where(np.abs(omega) < 1.0e-12,
np.zeros(3),
qu[...,1:4]/np.linalg.norm(qu[...,1:4],axis=-1,keepdims=True) \
* (0.75*(omega - np.sin(omega)))**(1./3.))
return ho
@staticmethod
@ -532,37 +601,71 @@ class Rotation:
@staticmethod
def om2eu(om):
"""Rotation matrix to Bunge-Euler angles."""
if abs(om[2,2]) < 1.0:
if len(om.shape) == 2:
if not np.isclose(np.abs(om[2,2]),1.0,1.e-4):
zeta = 1.0/np.sqrt(1.0-om[2,2]**2)
eu = np.array([np.arctan2(om[2,0]*zeta,-om[2,1]*zeta),
np.arccos(om[2,2]),
np.arctan2(om[0,2]*zeta, om[1,2]*zeta)])
else:
eu = np.array([np.arctan2( om[0,1],om[0,0]), np.pi*0.5*(1-om[2,2]),0.0]) # following the paper, not the reference implementation
# reduce Euler angles to definition range, i.e a lower limit of 0.0
else:
with np.errstate(invalid='ignore',divide='ignore'):
zeta = 1.0/np.sqrt(1.0-om[...,2,2:3]**2)
eu = np.where(np.isclose(np.abs(om[...,2,2:3]),1.0,1e-4),
np.block([np.arctan2(om[...,0,1:2],om[...,0,0:1]),
np.pi*0.5*(1-om[...,2,2:3]),
np.zeros(om.shape[:-2]+(1,)),
]),
np.block([np.arctan2(om[...,2,0:1]*zeta,-om[...,2,1:2]*zeta),
np.arccos(om[...,2,2:3]),
np.arctan2(om[...,0,2:3]*zeta,+om[...,1,2:3]*zeta)
])
)
eu[np.abs(eu)<1.e-6] = 0.0
eu = np.where(eu<0, (eu+2.0*np.pi)%np.array([2.0*np.pi,np.pi,2.0*np.pi]),eu)
return eu
@staticmethod
def om2ax(om):
"""Rotation matrix to axis angle pair."""
if len(om.shape) == 2:
ax=np.empty(4)
# first get the rotation angle
t = 0.5*(om.trace() -1.0)
ax[3] = np.arccos(np.clip(t,-1.0,1.0))
if iszero(ax[3]):
ax = [ 0.0, 0.0, 1.0, 0.0]
if np.abs(ax[3])<1.e-6:
ax = np.array([ 0.0, 0.0, 1.0, 0.0])
else:
w,vr = np.linalg.eig(om)
# next, find the eigenvalue (1,0j)
i = np.where(np.isclose(w,1.0+0.0j))[0][0]
ax[0:3] = np.real(vr[0:3,i])
diagDelta = np.array([om[1,2]-om[2,1],om[2,0]-om[0,2],om[0,1]-om[1,0]])
ax[0:3] = np.where(iszero(diagDelta), ax[0:3],np.abs(ax[0:3])*np.sign(-P*diagDelta))
return np.array(ax)
diagDelta = -_P*np.array([om[1,2]-om[2,1],om[2,0]-om[0,2],om[0,1]-om[1,0]])
diagDelta[np.abs(diagDelta)<1.e-6] = 1.0
ax[0:3] = np.where(np.abs(diagDelta)<0, ax[0:3],np.abs(ax[0:3])*np.sign(diagDelta))
else:
diag_delta = -_P*np.block([om[...,1,2:3]-om[...,2,1:2],
om[...,2,0:1]-om[...,0,2:3],
om[...,0,1:2]-om[...,1,0:1]
])
diag_delta[np.abs(diag_delta)<1.e-6] = 1.0
t = 0.5*(om.trace(axis2=-2,axis1=-1) -1.0).reshape(om.shape[:-2]+(1,))
w,vr = np.linalg.eig(om)
# mask duplicated real eigenvalues
w[np.isclose(w[...,0],1.0+0.0j),1:] = 0.
w[np.isclose(w[...,1],1.0+0.0j),2:] = 0.
vr = np.swapaxes(vr,-1,-2)
ax = np.where(np.abs(diag_delta)<0,
np.real(vr[np.isclose(w,1.0+0.0j)]).reshape(om.shape[:-2]+(3,)),
np.abs(np.real(vr[np.isclose(w,1.0+0.0j)]).reshape(om.shape[:-2]+(3,))) \
*np.sign(diag_delta))
ax = np.block([ax,np.arccos(np.clip(t,-1.0,1.0))])
ax[np.abs(ax[...,3])<1.e-6] = [ 0.0, 0.0, 1.0, 0.0]
return ax
@staticmethod
def om2ro(om):
@ -584,32 +687,57 @@ class Rotation:
@staticmethod
def eu2qu(eu):
"""Bunge-Euler angles to quaternion."""
if len(eu.shape) == 1:
ee = 0.5*eu
cPhi = np.cos(ee[1])
sPhi = np.sin(ee[1])
qu = np.array([ cPhi*np.cos(ee[0]+ee[2]),
-P*sPhi*np.cos(ee[0]-ee[2]),
-P*sPhi*np.sin(ee[0]-ee[2]),
-P*cPhi*np.sin(ee[0]+ee[2]) ])
-_P*sPhi*np.cos(ee[0]-ee[2]),
-_P*sPhi*np.sin(ee[0]-ee[2]),
-_P*cPhi*np.sin(ee[0]+ee[2]) ])
if qu[0] < 0.0: qu*=-1
else:
ee = 0.5*eu
cPhi = np.cos(ee[...,1:2])
sPhi = np.sin(ee[...,1:2])
qu = np.block([ cPhi*np.cos(ee[...,0:1]+ee[...,2:3]),
-_P*sPhi*np.cos(ee[...,0:1]-ee[...,2:3]),
-_P*sPhi*np.sin(ee[...,0:1]-ee[...,2:3]),
-_P*cPhi*np.sin(ee[...,0:1]+ee[...,2:3])])
qu[qu[...,0]<0.0]*=-1
return qu
@staticmethod
def eu2om(eu):
"""Bunge-Euler angles to rotation matrix."""
if len(eu.shape) == 1:
c = np.cos(eu)
s = np.sin(eu)
om = np.array([[+c[0]*c[2]-s[0]*s[2]*c[1], +s[0]*c[2]+c[0]*s[2]*c[1], +s[2]*s[1]],
[-c[0]*s[2]-s[0]*c[2]*c[1], -s[0]*s[2]+c[0]*c[2]*c[1], +c[2]*s[1]],
[+s[0]*s[1], -c[0]*s[1], +c[1] ]])
om[np.where(iszero(om))] = 0.0
else:
c = np.cos(eu)
s = np.sin(eu)
om = np.block([+c[...,0:1]*c[...,2:3]-s[...,0:1]*s[...,2:3]*c[...,1:2],
+s[...,0:1]*c[...,2:3]+c[...,0:1]*s[...,2:3]*c[...,1:2],
+s[...,2:3]*s[...,1:2],
-c[...,0:1]*s[...,2:3]-s[...,0:1]*c[...,2:3]*c[...,1:2],
-s[...,0:1]*s[...,2:3]+c[...,0:1]*c[...,2:3]*c[...,1:2],
+c[...,2:3]*s[...,1:2],
+s[...,0:1]*s[...,1:2],
-c[...,0:1]*s[...,1:2],
+c[...,1:2]
]).reshape(eu.shape[:-1]+(3,3))
om[np.abs(om)<1.e-12] = 0.0
return om
@staticmethod
def eu2ax(eu):
"""Bunge-Euler angles to axis angle pair."""
if len(eu.shape) == 1:
t = np.tan(eu[1]*0.5)
sigma = 0.5*(eu[0]+eu[2])
delta = 0.5*(eu[0]-eu[2])
@ -617,24 +745,45 @@ class Rotation:
alpha = np.pi if iszero(np.cos(sigma)) else \
2.0*np.arctan(tau/np.cos(sigma))
if iszero(alpha):
if np.abs(alpha)<1.e-6:
ax = np.array([ 0.0, 0.0, 1.0, 0.0 ])
else:
ax = -P/tau * np.array([ t*np.cos(delta), t*np.sin(delta), np.sin(sigma) ]) # passive axis angle pair so a minus sign in front
ax = -_P/tau * np.array([ t*np.cos(delta), t*np.sin(delta), np.sin(sigma) ]) # passive axis angle pair so a minus sign in front
ax = np.append(ax,alpha)
if alpha < 0.0: ax *= -1.0 # ensure alpha is positive
else:
t = np.tan(eu[...,1:2]*0.5)
sigma = 0.5*(eu[...,0:1]+eu[...,2:3])
delta = 0.5*(eu[...,0:1]-eu[...,2:3])
tau = np.linalg.norm(np.block([t,np.sin(sigma)]),axis=-1,keepdims=True)
alpha = np.where(np.abs(np.cos(sigma))<1.e-12,np.pi,2.0*np.arctan(tau/np.cos(sigma)))
with np.errstate(invalid='ignore',divide='ignore'):
ax = np.where(np.broadcast_to(np.abs(alpha)<1.0e-12,eu.shape[:-1]+(4,)),
[0.0,0.0,1.0,0.0],
np.block([-_P/tau*t*np.cos(delta),
-_P/tau*t*np.sin(delta),
-_P/tau* np.sin(sigma),
alpha
]))
ax[(alpha<0.0).squeeze()] *=-1
return ax
@staticmethod
def eu2ro(eu):
"""Bunge-Euler angles to Rodrigues-Frank vector."""
if len(eu.shape) == 1:
ro = Rotation.eu2ax(eu) # convert to axis angle pair representation
if ro[3] >= np.pi: # Differs from original implementation. check convention 5
ro[3] = np.inf
elif iszero(ro[3]):
ro = np.array([ 0.0, 0.0, P, 0.0 ])
ro = np.array([ 0.0, 0.0, _P, 0.0 ])
else:
ro[3] = np.tan(ro[3]*0.5)
else:
ax = Rotation.eu2ax(eu)
ro = np.block([ax[...,:3],np.tan(ax[...,3:4]*.5)])
ro[ax[...,3]>=np.pi,3] = np.inf
ro[np.abs(ax[...,3])<1.e-16] = [ 0.0, 0.0, _P, 0.0 ]
return ro
@staticmethod
@ -652,17 +801,24 @@ class Rotation:
@staticmethod
def ax2qu(ax):
"""Axis angle pair to quaternion."""
if iszero(ax[3]):
if len(ax.shape) == 1:
if np.abs(ax[3])<1.e-6:
qu = np.array([ 1.0, 0.0, 0.0, 0.0 ])
else:
c = np.cos(ax[3]*0.5)
s = np.sin(ax[3]*0.5)
qu = np.array([ c, ax[0]*s, ax[1]*s, ax[2]*s ])
return qu
else:
c = np.cos(ax[...,3:4]*.5)
s = np.sin(ax[...,3:4]*.5)
qu = np.where(np.abs(ax[...,3:4])<1.e-6,[1.0, 0.0, 0.0, 0.0],np.block([c, ax[...,:3]*s]))
return qu
@staticmethod
def ax2om(ax):
"""Axis angle pair to rotation matrix."""
if len(ax.shape) == 1:
c = np.cos(ax[3])
s = np.sin(ax[3])
omc = 1.0-c
@ -672,7 +828,20 @@ class Rotation:
q = omc*ax[idx[0]] * ax[idx[1]]
om[idx[0],idx[1]] = q + s*ax[idx[2]]
om[idx[1],idx[0]] = q - s*ax[idx[2]]
return om if P < 0.0 else om.T
else:
c = np.cos(ax[...,3:4])
s = np.sin(ax[...,3:4])
omc = 1. -c
om = np.block([c+omc*ax[...,0:1]**2,
omc*ax[...,0:1]*ax[...,1:2] + s*ax[...,2:3],
omc*ax[...,0:1]*ax[...,2:3] - s*ax[...,1:2],
omc*ax[...,0:1]*ax[...,1:2] - s*ax[...,2:3],
c+omc*ax[...,1:2]**2,
omc*ax[...,1:2]*ax[...,2:3] + s*ax[...,0:1],
omc*ax[...,0:1]*ax[...,2:3] + s*ax[...,1:2],
omc*ax[...,1:2]*ax[...,2:3] - s*ax[...,0:1],
c+omc*ax[...,2:3]**2]).reshape(ax.shape[:-1]+(3,3))
return om if _P < 0.0 else np.swapaxes(om,(-1,-2))
@staticmethod
def ax2eu(ax):
@ -682,21 +851,35 @@ class Rotation:
@staticmethod
def ax2ro(ax):
"""Axis angle pair to Rodrigues-Frank vector."""
if iszero(ax[3]):
ro = [ 0.0, 0.0, P, 0.0 ]
if len(ax.shape) == 1:
if np.abs(ax[3])<1.e-6:
ro = [ 0.0, 0.0, _P, 0.0 ]
else:
ro = [ax[0], ax[1], ax[2]]
# 180 degree case
ro += [np.inf] if np.isclose(ax[3],np.pi,atol=1.0e-15,rtol=0.0) else \
[np.tan(ax[3]*0.5)]
return np.array(ro)
else:
ro = np.block([ax[...,:3],
np.where(np.isclose(ax[...,3:4],np.pi,atol=1.e-15,rtol=.0),
np.inf,
np.tan(ax[...,3:4]*0.5))
])
ro[np.abs(ax[...,3])<1.e-6] = [.0,.0,_P,.0]
return ro
@staticmethod
def ax2ho(ax):
"""Axis angle pair to homochoric vector."""
if len(ax.shape) == 1:
f = (0.75 * ( ax[3] - np.sin(ax[3]) ))**(1.0/3.0)
ho = ax[0:3] * f
return ho
else:
f = (0.75 * ( ax[...,3:4] - np.sin(ax[...,3:4]) ))**(1.0/3.0)
ho = ax[...,:3] * f
return ho
@staticmethod
def ax2cu(ax):
@ -723,27 +906,38 @@ class Rotation:
@staticmethod
def ro2ax(ro):
"""Rodrigues-Frank vector to axis angle pair."""
ta = ro[3]
if iszero(ta):
ax = [ 0.0, 0.0, 1.0, 0.0 ]
elif not np.isfinite(ta):
ax = [ ro[0], ro[1], ro[2], np.pi ]
if len(ro.shape) == 1:
if np.abs(ro[3]) < 1.e-6:
ax = np.array([ 0.0, 0.0, 1.0, 0.0 ])
elif not np.isfinite(ro[3]):
ax = np.array([ ro[0], ro[1], ro[2], np.pi ])
else:
angle = 2.0*np.arctan(ta)
ta = 1.0/np.linalg.norm(ro[0:3])
ax = [ ro[0]/ta, ro[1]/ta, ro[2]/ta, angle ]
return np.array(ax)
angle = 2.0*np.arctan(ro[3])
ta = np.linalg.norm(ro[0:3])
ax = np.array([ ro[0]*ta, ro[1]*ta, ro[2]*ta, angle ])
else:
with np.errstate(invalid='ignore',divide='ignore'):
ax = np.where(np.isfinite(ro[...,3:4]),
np.block([ro[...,0:3]*np.linalg.norm(ro[...,0:3],axis=-1,keepdims=True),2.*np.arctan(ro[...,3:4])]),
np.block([ro[...,0:3],np.broadcast_to(np.pi,ro[...,3:4].shape)]))
ax[np.abs(ro[...,3]) < 1.e-6] = np.array([ 0.0, 0.0, 1.0, 0.0 ])
return ax
@staticmethod
def ro2ho(ro):
"""Rodrigues-Frank vector to homochoric vector."""
if iszero(np.sum(ro[0:3]**2.0)):
ho = [ 0.0, 0.0, 0.0 ]
if len(ro.shape) == 1:
if np.sum(ro[0:3]**2.0) < 1.e-6:
ho = np.zeros(3)
else:
f = 2.0*np.arctan(ro[3]) -np.sin(2.0*np.arctan(ro[3])) if np.isfinite(ro[3]) else np.pi
ho = ro[0:3] * (0.75*f)**(1.0/3.0)
return np.array(ho)
else:
f = np.where(np.isfinite(ro[...,3:4]),2.0*np.arctan(ro[...,3:4]) -np.sin(2.0*np.arctan(ro[...,3:4])),np.pi)
ho = np.where(np.broadcast_to(np.sum(ro[...,0:3]**2.0,axis=-1,keepdims=True) < 1.e-6,ro[...,0:3].shape),
np.zeros(3), ro[...,0:3]* (0.75*f)**(1.0/3.0))
return ho
@staticmethod
def ro2cu(ro):
@ -778,6 +972,7 @@ class Rotation:
+0.0001703481934140054, -0.00012062065004116828,
+0.000059719705868660826, -0.00001980756723965647,
+0.000003953714684212874, -0.00000036555001439719544])
if len(ho.shape) == 1:
# normalize h and store the magnitude
hmag_squared = np.sum(ho**2.)
if iszero(hmag_squared):
@ -791,6 +986,17 @@ class Rotation:
hm *= hmag_squared
s += tfit[i] * hm
ax = np.append(ho/np.sqrt(hmag_squared),2.0*np.arccos(np.clip(s,-1.0,1.0)))
else:
hmag_squared = np.sum(ho**2.,axis=-1,keepdims=True)
hm = hmag_squared.copy()
s = tfit[0] + tfit[1] * hmag_squared
for i in range(2,16):
hm *= hmag_squared
s += tfit[i] * hm
with np.errstate(invalid='ignore'):
ax = np.where(np.broadcast_to(np.abs(hmag_squared)<1.e-6,ho.shape[:-1]+(4,)),
[ 0.0, 0.0, 1.0, 0.0 ],
np.block([ho/np.sqrt(hmag_squared),2.0*np.arccos(np.clip(s,-1.0,1.0))]))
return ax
@staticmethod
@ -801,7 +1007,10 @@ class Rotation:
@staticmethod
def ho2cu(ho):
"""Homochoric vector to cubochoric vector."""
if len(ho.shape) == 1:
return ball_to_cube(ho)
else:
raise NotImplementedError
#---------- Cubochoric ----------
@ -833,4 +1042,7 @@ class Rotation:
@staticmethod
def cu2ho(cu):
"""Cubochoric vector to homochoric vector."""
if len(cu.shape) == 1:
return cube_to_ball(cu)
else:
raise NotImplementedError

142
python/damask/grid_filters.py
View File

@ -1,5 +1,5 @@
from scipy import spatial
import numpy as np
from scipy import spatial as _spatial
import numpy as _np
def _ks(size,grid,first_order=False):
"""
@ -11,16 +11,16 @@ def _ks(size,grid,first_order=False):
physical size of the periodic field.
"""
k_sk = np.where(np.arange(grid[0])>grid[0]//2,np.arange(grid[0])-grid[0],np.arange(grid[0]))/size[0]
k_sk = _np.where(_np.arange(grid[0])>grid[0]//2,_np.arange(grid[0])-grid[0],_np.arange(grid[0]))/size[0]
if grid[0]%2 == 0 and first_order: k_sk[grid[0]//2] = 0 # Nyquist freq=0 for even grid (Johnson, MIT, 2011)
k_sj = np.where(np.arange(grid[1])>grid[1]//2,np.arange(grid[1])-grid[1],np.arange(grid[1]))/size[1]
k_sj = _np.where(_np.arange(grid[1])>grid[1]//2,_np.arange(grid[1])-grid[1],_np.arange(grid[1]))/size[1]
if grid[1]%2 == 0 and first_order: k_sj[grid[1]//2] = 0 # Nyquist freq=0 for even grid (Johnson, MIT, 2011)
k_si = np.arange(grid[2]//2+1)/size[2]
k_si = _np.arange(grid[2]//2+1)/size[2]
kk, kj, ki = np.meshgrid(k_sk,k_sj,k_si,indexing = 'ij')
return np.concatenate((ki[:,:,:,None],kj[:,:,:,None],kk[:,:,:,None]),axis = 3)
kk, kj, ki = _np.meshgrid(k_sk,k_sj,k_si,indexing = 'ij')
return _np.concatenate((ki[:,:,:,None],kj[:,:,:,None],kk[:,:,:,None]),axis = 3)
def curl(size,field):
@ -33,18 +33,18 @@ def curl(size,field):
physical size of the periodic field.
"""
n = np.prod(field.shape[3:])
n = _np.prod(field.shape[3:])
k_s = _ks(size,field.shape[:3],True)
e = np.zeros((3, 3, 3))
e = _np.zeros((3, 3, 3))
e[0, 1, 2] = e[1, 2, 0] = e[2, 0, 1] = +1.0 # Levi-Civita symbol
e[0, 2, 1] = e[2, 1, 0] = e[1, 0, 2] = -1.0
field_fourier = np.fft.rfftn(field,axes=(0,1,2))
curl_ = (np.einsum('slm,ijkl,ijkm ->ijks', e,k_s,field_fourier)*2.0j*np.pi if n == 3 else # vector, 3 -> 3
np.einsum('slm,ijkl,ijknm->ijksn',e,k_s,field_fourier)*2.0j*np.pi) # tensor, 3x3 -> 3x3
field_fourier = _np.fft.rfftn(field,axes=(0,1,2))
curl_ = (_np.einsum('slm,ijkl,ijkm ->ijks', e,k_s,field_fourier)*2.0j*_np.pi if n == 3 else # vector, 3 -> 3
_np.einsum('slm,ijkl,ijknm->ijksn',e,k_s,field_fourier)*2.0j*_np.pi) # tensor, 3x3 -> 3x3
return np.fft.irfftn(curl_,axes=(0,1,2),s=field.shape[:3])
return _np.fft.irfftn(curl_,axes=(0,1,2),s=field.shape[:3])
def divergence(size,field):
@ -57,14 +57,14 @@ def divergence(size,field):
physical size of the periodic field.
"""
n = np.prod(field.shape[3:])
n = _np.prod(field.shape[3:])
k_s = _ks(size,field.shape[:3],True)
field_fourier = np.fft.rfftn(field,axes=(0,1,2))
div_ = (np.einsum('ijkl,ijkl ->ijk', k_s,field_fourier)*2.0j*np.pi if n == 3 else # vector, 3 -> 1
np.einsum('ijkm,ijklm->ijkl',k_s,field_fourier)*2.0j*np.pi) # tensor, 3x3 -> 3
field_fourier = _np.fft.rfftn(field,axes=(0,1,2))
div_ = (_np.einsum('ijkl,ijkl ->ijk', k_s,field_fourier)*2.0j*_np.pi if n == 3 else # vector, 3 -> 1
_np.einsum('ijkm,ijklm->ijkl',k_s,field_fourier)*2.0j*_np.pi) # tensor, 3x3 -> 3
return np.fft.irfftn(div_,axes=(0,1,2),s=field.shape[:3])
return _np.fft.irfftn(div_,axes=(0,1,2),s=field.shape[:3])
def gradient(size,field):
@ -77,17 +77,17 @@ def gradient(size,field):
physical size of the periodic field.
"""
n = np.prod(field.shape[3:])
n = _np.prod(field.shape[3:])
k_s = _ks(size,field.shape[:3],True)
field_fourier = np.fft.rfftn(field,axes=(0,1,2))
grad_ = (np.einsum('ijkl,ijkm->ijkm', field_fourier,k_s)*2.0j*np.pi if n == 1 else # scalar, 1 -> 3
np.einsum('ijkl,ijkm->ijklm',field_fourier,k_s)*2.0j*np.pi) # vector, 3 -> 3x3
field_fourier = _np.fft.rfftn(field,axes=(0,1,2))
grad_ = (_np.einsum('ijkl,ijkm->ijkm', field_fourier,k_s)*2.0j*_np.pi if n == 1 else # scalar, 1 -> 3
_np.einsum('ijkl,ijkm->ijklm',field_fourier,k_s)*2.0j*_np.pi) # vector, 3 -> 3x3
return np.fft.irfftn(grad_,axes=(0,1,2),s=field.shape[:3])
return _np.fft.irfftn(grad_,axes=(0,1,2),s=field.shape[:3])
def cell_coord0(grid,size,origin=np.zeros(3)):
def cell_coord0(grid,size,origin=_np.zeros(3)):
"""
Cell center positions (undeformed).
@ -103,7 +103,7 @@ def cell_coord0(grid,size,origin=np.zeros(3)):
"""
start = origin + size/grid*.5
end = origin + size - size/grid*.5
return np.mgrid[start[0]:end[0]:grid[0]*1j,start[1]:end[1]:grid[1]*1j,start[2]:end[2]:grid[2]*1j].T
return _np.mgrid[start[0]:end[0]:grid[0]*1j,start[1]:end[1]:grid[1]*1j,start[2]:end[2]:grid[2]*1j].T
def cell_displacement_fluct(size,F):
@ -118,19 +118,19 @@ def cell_displacement_fluct(size,F):
deformation gradient field.
"""
integrator = 0.5j*size/np.pi
integrator = 0.5j*size/_np.pi
k_s = _ks(size,F.shape[:3],False)
k_s_squared = np.einsum('...l,...l',k_s,k_s)
k_s_squared = _np.einsum('...l,...l',k_s,k_s)
k_s_squared[0,0,0] = 1.0
displacement = -np.einsum('ijkml,ijkl,l->ijkm',
np.fft.rfftn(F,axes=(0,1,2)),
displacement = -_np.einsum('ijkml,ijkl,l->ijkm',
_np.fft.rfftn(F,axes=(0,1,2)),
k_s,
integrator,
) / k_s_squared[...,np.newaxis]
) / k_s_squared[...,_np.newaxis]
return np.fft.irfftn(displacement,axes=(0,1,2),s=F.shape[:3])
return _np.fft.irfftn(displacement,axes=(0,1,2),s=F.shape[:3])
def cell_displacement_avg(size,F):
@ -145,8 +145,8 @@ def cell_displacement_avg(size,F):
deformation gradient field.
"""
F_avg = np.average(F,axis=(0,1,2))
return np.einsum('ml,ijkl->ijkm',F_avg-np.eye(3),cell_coord0(F.shape[:3][::-1],size))
F_avg = _np.average(F,axis=(0,1,2))
return _np.einsum('ml,ijkl->ijkm',F_avg-_np.eye(3),cell_coord0(F.shape[:3][::-1],size))
def cell_displacement(size,F):
@ -164,7 +164,7 @@ def cell_displacement(size,F):
return cell_displacement_avg(size,F) + cell_displacement_fluct(size,F)
def cell_coord(size,F,origin=np.zeros(3)):
def cell_coord(size,F,origin=_np.zeros(3)):
"""
Cell center positions.
@ -193,17 +193,17 @@ def cell_coord0_gridSizeOrigin(coord0,ordered=True):
expect coord0 data to be ordered (x fast, z slow).
"""
coords = [np.unique(coord0[:,i]) for i in range(3)]
mincorner = np.array(list(map(min,coords)))
maxcorner = np.array(list(map(max,coords)))
grid = np.array(list(map(len,coords)),'i')
size = grid/np.maximum(grid-1,1) * (maxcorner-mincorner)
coords = [_np.unique(coord0[:,i]) for i in range(3)]
mincorner = _np.array(list(map(min,coords)))
maxcorner = _np.array(list(map(max,coords)))
grid = _np.array(list(map(len,coords)),'i')
size = grid/_np.maximum(grid-1,1) * (maxcorner-mincorner)
delta = size/grid
origin = mincorner - delta*.5
# 1D/2D: size/origin combination undefined, set origin to 0.0
size [np.where(grid==1)] = origin[np.where(grid==1)]*2.
origin[np.where(grid==1)] = 0.0
size [_np.where(grid==1)] = origin[_np.where(grid==1)]*2.
origin[_np.where(grid==1)] = 0.0
if grid.prod() != len(coord0):
raise ValueError('Data count {} does not match grid {}.'.format(len(coord0),grid))
@ -211,13 +211,13 @@ def cell_coord0_gridSizeOrigin(coord0,ordered=True):
start = origin + delta*.5
end = origin - delta*.5 + size
if not np.allclose(coords[0],np.linspace(start[0],end[0],grid[0])) and \
np.allclose(coords[1],np.linspace(start[1],end[1],grid[1])) and \
np.allclose(coords[2],np.linspace(start[2],end[2],grid[2])):
if not _np.allclose(coords[0],_np.linspace(start[0],end[0],grid[0])) and \
_np.allclose(coords[1],_np.linspace(start[1],end[1],grid[1])) and \
_np.allclose(coords[2],_np.linspace(start[2],end[2],grid[2])):
raise ValueError('Regular grid spacing violated.')
if ordered and not np.allclose(coord0.reshape(tuple(grid[::-1])+(3,)),cell_coord0(grid,size,origin)):
raise ValueError('Input data is not a regular grid.')
if ordered and not _np.allclose(coord0.reshape(tuple(grid[::-1])+(3,)),cell_coord0(grid,size,origin)):
raise ValueError('I_nput data is not a regular grid.')
return (grid,size,origin)
@ -235,7 +235,7 @@ def coord0_check(coord0):
cell_coord0_gridSizeOrigin(coord0,ordered=True)
def node_coord0(grid,size,origin=np.zeros(3)):
def node_coord0(grid,size,origin=_np.zeros(3)):
"""
Nodal positions (undeformed).
@ -249,7 +249,7 @@ def node_coord0(grid,size,origin=np.zeros(3)):
physical origin of the periodic field. Defaults to [0.0,0.0,0.0].
"""
return np.mgrid[origin[0]:size[0]+origin[0]:(grid[0]+1)*1j,
return _np.mgrid[origin[0]:size[0]+origin[0]:(grid[0]+1)*1j,
origin[1]:size[1]+origin[1]:(grid[1]+1)*1j,
origin[2]:size[2]+origin[2]:(grid[2]+1)*1j].T
@ -281,8 +281,8 @@ def node_displacement_avg(size,F):
deformation gradient field.
"""
F_avg = np.average(F,axis=(0,1,2))
return np.einsum('ml,ijkl->ijkm',F_avg-np.eye(3),node_coord0(F.shape[:3][::-1],size))
F_avg = _np.average(F,axis=(0,1,2))
return _np.einsum('ml,ijkl->ijkm',F_avg-_np.eye(3),node_coord0(F.shape[:3][::-1],size))
def node_displacement(size,F):
@ -300,7 +300,7 @@ def node_displacement(size,F):
return node_displacement_avg(size,F) + node_displacement_fluct(size,F)
def node_coord(size,F,origin=np.zeros(3)):
def node_coord(size,F,origin=_np.zeros(3)):
"""
Nodal positions.
@ -319,18 +319,18 @@ def node_coord(size,F,origin=np.zeros(3)):
def cell_2_node(cell_data):
"""Interpolate periodic cell data to nodal data."""
n = ( cell_data + np.roll(cell_data,1,(0,1,2))
+ np.roll(cell_data,1,(0,)) + np.roll(cell_data,1,(1,)) + np.roll(cell_data,1,(2,))
+ np.roll(cell_data,1,(0,1)) + np.roll(cell_data,1,(1,2)) + np.roll(cell_data,1,(2,0)))*0.125
n = ( cell_data + _np.roll(cell_data,1,(0,1,2))
+ _np.roll(cell_data,1,(0,)) + _np.roll(cell_data,1,(1,)) + _np.roll(cell_data,1,(2,))
+ _np.roll(cell_data,1,(0,1)) + _np.roll(cell_data,1,(1,2)) + _np.roll(cell_data,1,(2,0)))*0.125
return np.pad(n,((0,1),(0,1),(0,1))+((0,0),)*len(cell_data.shape[3:]),mode='wrap')
return _np.pad(n,((0,1),(0,1),(0,1))+((0,0),)*len(cell_data.shape[3:]),mode='wrap')
def node_2_cell(node_data):
"""Interpolate periodic nodal data to cell data."""
c = ( node_data + np.roll(node_data,1,(0,1,2))
+ np.roll(node_data,1,(0,)) + np.roll(node_data,1,(1,)) + np.roll(node_data,1,(2,))
+ np.roll(node_data,1,(0,1)) + np.roll(node_data,1,(1,2)) + np.roll(node_data,1,(2,0)))*0.125
c = ( node_data + _np.roll(node_data,1,(0,1,2))
+ _np.roll(node_data,1,(0,)) + _np.roll(node_data,1,(1,)) + _np.roll(node_data,1,(2,))
+ _np.roll(node_data,1,(0,1)) + _np.roll(node_data,1,(1,2)) + _np.roll(node_data,1,(2,0)))*0.125
return c[:-1,:-1,:-1]
@ -347,23 +347,23 @@ def node_coord0_gridSizeOrigin(coord0,ordered=False):
expect coord0 data to be ordered (x fast, z slow).
"""
coords = [np.unique(coord0[:,i]) for i in range(3)]
mincorner = np.array(list(map(min,coords)))
maxcorner = np.array(list(map(max,coords)))
grid = np.array(list(map(len,coords)),'i') - 1
coords = [_np.unique(coord0[:,i]) for i in range(3)]
mincorner = _np.array(list(map(min,coords)))
maxcorner = _np.array(list(map(max,coords)))
grid = _np.array(list(map(len,coords)),'i') - 1
size = maxcorner-mincorner
origin = mincorner
if (grid+1).prod() != len(coord0):
raise ValueError('Data count {} does not match grid {}.'.format(len(coord0),grid))
if not np.allclose(coords[0],np.linspace(mincorner[0],maxcorner[0],grid[0]+1)) and \
np.allclose(coords[1],np.linspace(mincorner[1],maxcorner[1],grid[1]+1)) and \
np.allclose(coords[2],np.linspace(mincorner[2],maxcorner[2],grid[2]+1)):
if not _np.allclose(coords[0],_np.linspace(mincorner[0],maxcorner[0],grid[0]+1)) and \
_np.allclose(coords[1],_np.linspace(mincorner[1],maxcorner[1],grid[1]+1)) and \
_np.allclose(coords[2],_np.linspace(mincorner[2],maxcorner[2],grid[2]+1)):
raise ValueError('Regular grid spacing violated.')
if ordered and not np.allclose(coord0.reshape(tuple((grid+1)[::-1])+(3,)),node_coord0(grid,size,origin)):
raise ValueError('Input data is not a regular grid.')
if ordered and not _np.allclose(coord0.reshape(tuple((grid+1)[::-1])+(3,)),node_coord0(grid,size,origin)):
raise ValueError('I_nput data is not a regular grid.')
return (grid,size,origin)
@ -386,10 +386,10 @@ def regrid(size,F,new_grid):
+ cell_displacement_avg(size,F) \
+ cell_displacement_fluct(size,F)
outer = np.dot(np.average(F,axis=(0,1,2)),size)
outer = _np.dot(_np.average(F,axis=(0,1,2)),size)
for d in range(3):
c[np.where(c[:,:,:,d]<0)] += outer[d]
c[np.where(c[:,:,:,d]>outer[d])] -= outer[d]
c[_np.where(c[:,:,:,d]<0)] += outer[d]
c[_np.where(c[:,:,:,d]>outer[d])] -= outer[d]
tree = spatial.cKDTree(c.reshape(-1,3),boxsize=outer)
tree = _spatial.cKDTree(c.reshape(-1,3),boxsize=outer)
return tree.query(cell_coord0(new_grid,outer))[1].flatten()

76
python/damask/mechanics.py
View File

@ -1,4 +1,4 @@
import numpy as np
import numpy as _np
def Cauchy(P,F):
"""
@ -14,10 +14,10 @@ def Cauchy(P,F):
First Piola-Kirchhoff stress.
"""
if np.shape(F) == np.shape(P) == (3,3):
sigma = 1.0/np.linalg.det(F) * np.dot(P,F.T)
if _np.shape(F) == _np.shape(P) == (3,3):
sigma = 1.0/_np.linalg.det(F) * _np.dot(P,F.T)
else:
sigma = np.einsum('i,ijk,ilk->ijl',1.0/np.linalg.det(F),P,F)
sigma = _np.einsum('i,ijk,ilk->ijl',1.0/_np.linalg.det(F),P,F)
return symmetric(sigma)
@ -31,8 +31,8 @@ def deviatoric_part(T):
Tensor of which the deviatoric part is computed.
"""
return T - np.eye(3)*spherical_part(T) if np.shape(T) == (3,3) else \
T - np.einsum('ijk,i->ijk',np.broadcast_to(np.eye(3),[T.shape[0],3,3]),spherical_part(T))
return T - _np.eye(3)*spherical_part(T) if _np.shape(T) == (3,3) else \
T - _np.einsum('ijk,i->ijk',_np.broadcast_to(_np.eye(3),[T.shape[0],3,3]),spherical_part(T))
def eigenvalues(T_sym):
@ -48,7 +48,7 @@ def eigenvalues(T_sym):
Symmetric tensor of which the eigenvalues are computed.
"""
return np.linalg.eigvalsh(symmetric(T_sym))
return _np.linalg.eigvalsh(symmetric(T_sym))
def eigenvectors(T_sym,RHS=False):
@ -65,13 +65,13 @@ def eigenvectors(T_sym,RHS=False):
Enforce right-handed coordinate system. Default is False.
"""
(u,v) = np.linalg.eigh(symmetric(T_sym))
(u,v) = _np.linalg.eigh(symmetric(T_sym))
if RHS:
if np.shape(T_sym) == (3,3):
if np.linalg.det(v) < 0.0: v[:,2] *= -1.0
if _np.shape(T_sym) == (3,3):
if _np.linalg.det(v) < 0.0: v[:,2] *= -1.0
else:
v[np.linalg.det(v) < 0.0,:,2] *= -1.0
v[_np.linalg.det(v) < 0.0,:,2] *= -1.0
return v
@ -99,7 +99,7 @@ def maximum_shear(T_sym):
"""
w = eigenvalues(T_sym)
return (w[0] - w[2])*0.5 if np.shape(T_sym) == (3,3) else \
return (w[0] - w[2])*0.5 if _np.shape(T_sym) == (3,3) else \
(w[:,0] - w[:,2])*0.5
@ -141,10 +141,10 @@ def PK2(P,F):
Deformation gradient.
"""
if np.shape(F) == np.shape(P) == (3,3):
S = np.dot(np.linalg.inv(F),P)
if _np.shape(F) == _np.shape(P) == (3,3):
S = _np.dot(_np.linalg.inv(F),P)
else:
S = np.einsum('ijk,ikl->ijl',np.linalg.inv(F),P)
S = _np.einsum('ijk,ikl->ijl',_np.linalg.inv(F),P)
return symmetric(S)
@ -187,14 +187,14 @@ def spherical_part(T,tensor=False):
"""
if T.shape == (3,3):
sph = np.trace(T)/3.0
return sph if not tensor else np.eye(3)*sph
sph = _np.trace(T)/3.0
return sph if not tensor else _np.eye(3)*sph
else:
sph = np.trace(T,axis1=1,axis2=2)/3.0
sph = _np.trace(T,axis1=1,axis2=2)/3.0
if not tensor:
return sph
else:
return np.einsum('ijk,i->ijk',np.broadcast_to(np.eye(3),(T.shape[0],3,3)),sph)
return _np.einsum('ijk,i->ijk',_np.broadcast_to(_np.eye(3),(T.shape[0],3,3)),sph)
def strain_tensor(F,t,m):
@ -216,22 +216,22 @@ def strain_tensor(F,t,m):
"""
F_ = F.reshape(1,3,3) if F.shape == (3,3) else F
if t == 'V':
B = np.matmul(F_,transpose(F_))
w,n = np.linalg.eigh(B)
B = _np.matmul(F_,transpose(F_))
w,n = _np.linalg.eigh(B)
elif t == 'U':
C = np.matmul(transpose(F_),F_)
w,n = np.linalg.eigh(C)
C = _np.matmul(transpose(F_),F_)
w,n = _np.linalg.eigh(C)
if m > 0.0:
eps = 1.0/(2.0*abs(m)) * (+ np.matmul(n,np.einsum('ij,ikj->ijk',w**m,n))
- np.broadcast_to(np.eye(3),[F_.shape[0],3,3]))
eps = 1.0/(2.0*abs(m)) * (+ _np.matmul(n,_np.einsum('ij,ikj->ijk',w**m,n))
- _np.broadcast_to(_np.eye(3),[F_.shape[0],3,3]))
elif m < 0.0:
eps = 1.0/(2.0*abs(m)) * (- np.matmul(n,np.einsum('ij,ikj->ijk',w**m,n))
+ np.broadcast_to(np.eye(3),[F_.shape[0],3,3]))
eps = 1.0/(2.0*abs(m)) * (- _np.matmul(n,_np.einsum('ij,ikj->ijk',w**m,n))
+ _np.broadcast_to(_np.eye(3),[F_.shape[0],3,3]))
else:
eps = np.matmul(n,np.einsum('ij,ikj->ijk',0.5*np.log(w),n))
eps = _np.matmul(n,_np.einsum('ij,ikj->ijk',0.5*_np.log(w),n))
return eps.reshape(3,3) if np.shape(F) == (3,3) else \
return eps.reshape(3,3) if _np.shape(F) == (3,3) else \
eps
@ -258,8 +258,8 @@ def transpose(T):
Tensor of which the transpose is computed.
"""
return T.T if np.shape(T) == (3,3) else \
np.transpose(T,(0,2,1))
return T.T if _np.shape(T) == (3,3) else \
_np.transpose(T,(0,2,1))
def _polar_decomposition(T,requested):
@ -275,17 +275,17 @@ def _polar_decomposition(T,requested):
‘V’ for left stretch tensor and ‘U’ for right stretch tensor.
"""
u, s, vh = np.linalg.svd(T)
R = np.dot(u,vh) if np.shape(T) == (3,3) else \
np.einsum('ijk,ikl->ijl',u,vh)
u, s, vh = _np.linalg.svd(T)
R = _np.dot(u,vh) if _np.shape(T) == (3,3) else \
_np.einsum('ijk,ikl->ijl',u,vh)
output = []
if 'R' in requested:
output.append(R)
if 'V' in requested:
output.append(np.dot(T,R.T) if np.shape(T) == (3,3) else np.einsum('ijk,ilk->ijl',T,R))
output.append(_np.dot(T,R.T) if _np.shape(T) == (3,3) else _np.einsum('ijk,ilk->ijl',T,R))
if 'U' in requested:
output.append(np.dot(R.T,T) if np.shape(T) == (3,3) else np.einsum('ikj,ikl->ijl',R,T))
output.append(_np.dot(R.T,T) if _np.shape(T) == (3,3) else _np.einsum('ikj,ikl->ijl',R,T))
return tuple(output)
@ -303,5 +303,5 @@ def _Mises(T_sym,s):
"""
d = deviatoric_part(T_sym)
return np.sqrt(s*(np.sum(d**2.0))) if np.shape(T_sym) == (3,3) else \
np.sqrt(s*np.einsum('ijk->i',d**2.0))
return _np.sqrt(s*(_np.sum(d**2.0))) if _np.shape(T_sym) == (3,3) else \
_np.sqrt(s*_np.einsum('ijk->i',d**2.0))

153
python/damask/util.py
View File

@ -9,37 +9,22 @@ from optparse import Option
import numpy as np
class bcolors:
"""
ASCII Colors.
https://svn.blender.org/svnroot/bf-blender/trunk/blender/build_files/scons/tools/bcolors.py
https://stackoverflow.com/questions/287871
"""
HEADER = '\033[95m'
OKBLUE = '\033[94m'
OKGREEN = '\033[92m'
WARNING = '\033[93m'
FAIL = '\033[91m'
ENDC = '\033[0m'
BOLD = '\033[1m'
DIM = '\033[2m'
UNDERLINE = '\033[4m'
CROSSOUT = '\033[9m'
def disable(self):
self.HEADER = ''
self.OKBLUE = ''
self.OKGREEN = ''
self.WARNING = ''
self.FAIL = ''
self.ENDC = ''
self.BOLD = ''
self.UNDERLINE = ''
self.CROSSOUT = ''
# limit visibility
__all__=[
'srepr',
'croak',
'report',
'emph','deemph','delete','strikeout',
'execute',
'show_progress',
'scale_to_coprime',
'return_message',
'extendableOption',
]
####################################################################################################
# Functions
####################################################################################################
def srepr(arg,glue = '\n'):
r"""
Join arguments as individual lines.
@ -144,6 +129,52 @@ def execute(cmd,
return out,error
def show_progress(iterable,N_iter=None,prefix='',bar_length=50):
"""
Decorate a loop with a status bar.
Use similar like enumerate.
Parameters
----------
iterable : iterable/function with yield statement
Iterable (or function with yield statement) to be decorated.
N_iter : int
Total # of iterations. Needed if number of iterations can not be obtained as len(iterable).
prefix : str, optional.
Prefix string.
bar_length : int, optional
Character length of bar. Defaults to 50.
"""
status = _ProgressBar(N_iter if N_iter else len(iterable),prefix,bar_length)
for i,item in enumerate(iterable):
yield item
status.update(i)
def scale_to_coprime(v):
"""Scale vector to co-prime (relatively prime) integers."""
MAX_DENOMINATOR = 1000
def get_square_denominator(x):
"""Denominator of the square of a number."""
return fractions.Fraction(x ** 2).limit_denominator(MAX_DENOMINATOR).denominator
def lcm(a, b):
"""Least common multiple."""
return a * b // np.gcd(a, b)
denominators = [int(get_square_denominator(i)) for i in v]
s = reduce(lcm, denominators) ** 0.5
m = (np.array(v)*s).astype(np.int)
return m//reduce(np.gcd,m)
####################################################################################################
# Classes
####################################################################################################
class extendableOption(Option):
"""
Used for definition of new option parser action 'extend', which enables to take multiple option arguments.
@ -215,47 +246,36 @@ class _ProgressBar:
sys.stderr.write('\n')
sys.stderr.flush()
def show_progress(iterable,N_iter=None,prefix='',bar_length=50):
class bcolors:
"""
Decorate a loop with a status bar.
Use similar like enumerate.
Parameters
----------
iterable : iterable/function with yield statement
Iterable (or function with yield statement) to be decorated.
N_iter : int
Total # of iterations. Needed if number of iterations can not be obtained as len(iterable).
prefix : str, optional.
Prefix string.
bar_length : int, optional
Character length of bar. Defaults to 50.
ASCII Colors.
https://svn.blender.org/svnroot/bf-blender/trunk/blender/build_files/scons/tools/bcolors.py
https://stackoverflow.com/questions/287871
"""
status = _ProgressBar(N_iter if N_iter else len(iterable),prefix,bar_length)
for i,item in enumerate(iterable):
yield item
status.update(i)
HEADER = '\033[95m'
OKBLUE = '\033[94m'
OKGREEN = '\033[92m'
WARNING = '\033[93m'
FAIL = '\033[91m'
ENDC = '\033[0m'
BOLD = '\033[1m'
DIM = '\033[2m'
UNDERLINE = '\033[4m'
CROSSOUT = '\033[9m'
def scale_to_coprime(v):
"""Scale vector to co-prime (relatively prime) integers."""
MAX_DENOMINATOR = 1000
def get_square_denominator(x):
"""Denominator of the square of a number."""
return fractions.Fraction(x ** 2).limit_denominator(MAX_DENOMINATOR).denominator
def lcm(a, b):
"""Least common multiple."""
return a * b // np.gcd(a, b)
denominators = [int(get_square_denominator(i)) for i in v]
s = reduce(lcm, denominators) ** 0.5
m = (np.array(v)*s).astype(np.int)
return m//reduce(np.gcd,m)
def disable(self):
self.HEADER = ''
self.OKBLUE = ''
self.OKGREEN = ''
self.WARNING = ''
self.FAIL = ''
self.ENDC = ''
self.BOLD = ''
self.UNDERLINE = ''
self.CROSSOUT = ''
class return_message:
@ -276,4 +296,3 @@ class return_message:
def __repr__(self):
"""Return message suitable for interactive shells."""
return srepr(self.message)

220
python/tests/test_Rotation.py
View File

@ -5,12 +5,82 @@ import numpy as np
from damask import Rotation
n = 1000
n = 1100
atol=1.e-4
scatter=1.e-2
@pytest.fixture
def default():
"""A set of n random rotations."""
return [Rotation.fromRandom() for r in range(n)]
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):
@ -22,35 +92,151 @@ class TestRotation:
def test_Eulers(self,default):
for rot in default:
assert np.allclose(rot.asQuaternion(),
Rotation.fromEulers(rot.asEulers()).asQuaternion())
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:
assert np.allclose(rot.asEulers(),
Rotation.fromAxisAngle(rot.asAxisAngle()).asEulers())
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:
assert np.allclose(rot.asAxisAngle(),
Rotation.fromMatrix(rot.asMatrix()).asAxisAngle())
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_Rodriques(self,default):
def test_Rodrigues(self,default):
for rot in default:
assert np.allclose(rot.asMatrix(),
Rotation.fromRodrigues(rot.asRodrigues()).asMatrix())
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:
assert np.allclose(rot.asRodrigues(),
Rotation.fromHomochoric(rot.asHomochoric()).asRodrigues(),rtol=1.e-4)
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:
assert np.allclose(rot.asHomochoric(),
Rotation.fromCubochoric(rot.asCubochoric()).asHomochoric())
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:
assert np.allclose(rot.asCubochoric(),
Rotation.fromQuaternion(rot.asQuaternion()).asCubochoric())
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('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)

24
python/tests/test_grid_filters.py
View File

@ -24,7 +24,7 @@ class TestGridFilters:
n = grid_filters.node_coord0(grid,size) + size/grid*.5
assert np.allclose(c,n)
@pytest.mark.parametrize('mode',[('cell'),('node')])
@pytest.mark.parametrize('mode',['cell','node'])
def test_grid_DNA(self,mode):
"""Ensure that xx_coord0_gridSizeOrigin is the inverse of xx_coord0."""
grid = np.random.randint(8,32,(3))
@ -49,7 +49,7 @@ class TestGridFilters:
assert np.allclose(grid_filters.node_coord(size,F) [1:-1,1:-1,1:-1],grid_filters.cell_2_node(
grid_filters.cell_coord(size,F))[1:-1,1:-1,1:-1])
@pytest.mark.parametrize('mode',[('cell'),('node')])
@pytest.mark.parametrize('mode',['cell','node'])
def test_coord0_origin(self,mode):
origin= np.random.random(3)
size = np.random.random(3) # noqa
@ -61,22 +61,24 @@ class TestGridFilters:
elif mode == 'node':
assert np.allclose(shifted,unshifted+np.broadcast_to(origin,tuple(grid[::-1]+1)+(3,)))
@pytest.mark.parametrize('mode',[('cell'),('node')])
def test_displacement_avg_vanishes(self,mode):
@pytest.mark.parametrize('function',[grid_filters.cell_displacement_avg,
grid_filters.node_displacement_avg])
def test_displacement_avg_vanishes(self,function):
"""Ensure that random fluctuations in F do not result in average displacement."""
size = np.random.random(3) # noqa
size = np.random.random(3)
grid = np.random.randint(8,32,(3))
F = np.random.random(tuple(grid)+(3,3))
F += np.eye(3) - np.average(F,axis=(0,1,2))
assert np.allclose(eval('grid_filters.{}_displacement_avg(size,F)'.format(mode)),0.0)
assert np.allclose(function(size,F),0.0)
@pytest.mark.parametrize('mode',[('cell'),('node')])
def test_displacement_fluct_vanishes(self,mode):
@pytest.mark.parametrize('function',[grid_filters.cell_displacement_fluct,
grid_filters.node_displacement_fluct])
def test_displacement_fluct_vanishes(self,function):
"""Ensure that constant F does not result in fluctuating displacement."""
size = np.random.random(3) # noqa
size = np.random.random(3)
grid = np.random.randint(8,32,(3))
F = np.broadcast_to(np.random.random((3,3)), tuple(grid)+(3,3)) # noqa
assert np.allclose(eval('grid_filters.{}_displacement_fluct(size,F)'.format(mode)),0.0)
F = np.broadcast_to(np.random.random((3,3)), tuple(grid)+(3,3))
assert np.allclose(function(size,F),0.0)
def test_regrid(self):
size = np.random.random(3)

59
src/LAPACK_interface.f90 Normal file
View File

@ -0,0 +1,59 @@
!--------------------------------------------------------------------------------------------------
!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
!> @brief Fortran interfaces for LAPACK routines
!> @details https://www.netlib.org/lapack/
!--------------------------------------------------------------------------------------------------
module LAPACK_interface
interface
subroutine dgeev(jobvl,jobvr,n,a,lda,wr,wi,vl,ldvl,vr,ldvr,work,lwork,info)
use prec
character, intent(in) :: jobvl,jobvr
integer, intent(in) :: n,lda,ldvl,ldvr,lwork
real(pReal), intent(inout), dimension(lda,n) :: a
real(pReal), intent(out), dimension(n) :: wr,wi
real(pReal), intent(out), dimension(ldvl,n) :: vl
real(pReal), intent(out), dimension(ldvr,n) :: vr
real(pReal), intent(out), dimension(max(1,lwork)) :: work
integer, intent(out) :: info
end subroutine dgeev
subroutine dgesv(n,nrhs,a,lda,ipiv,b,ldb,info)
use prec
integer, intent(in) :: n,nrhs,lda,ldb
real(pReal), intent(inout), dimension(lda,n) :: a
integer, intent(out), dimension(n) :: ipiv
real(pReal), intent(out), dimension(ldb,nrhs) :: b
integer, intent(out) :: info
end subroutine dgesv
subroutine dgetrf(m,n,a,lda,ipiv,info)
use prec
integer, intent(in) :: m,n,lda
real(pReal), intent(inout), dimension(lda,n) :: a
integer, intent(out), dimension(min(m,n)) :: ipiv
integer, intent(out) :: info
end subroutine dgetrf
subroutine dgetri(n,a,lda,ipiv,work,lwork,info)
use prec
integer, intent(in) :: n,lda,lwork
real(pReal), intent(inout), dimension(lda,n) :: a
integer, intent(out), dimension(n) :: ipiv
real(pReal), intent(out), dimension(max(1,lwork)) :: work
integer, intent(out) :: info
end subroutine dgetri
subroutine dsyev(jobz,uplo,n,a,lda,w,work,lwork,info)
use prec
character, intent(in) :: jobz,uplo
integer, intent(in) :: n,lda,lwork
real(pReal), intent(inout), dimension(lda,n) :: a
real(pReal), intent(out), dimension(n) :: w
real(pReal), intent(out), dimension(max(1,lwork)) :: work
integer, intent(out) :: info
end subroutine dsyev
end interface
end module LAPACK_interface

20
src/Lambert.f90
View File

@ -75,7 +75,7 @@ pure function Lambert_CubeToBall(cube) result(ball)
real(pReal), dimension(2) :: T
real(pReal) :: c, s, q
real(pReal), parameter :: eps = 1.0e-8_pReal
integer, dimension(3) :: p
integer, dimension(3,2) :: p
integer, dimension(2) :: order
if (maxval(abs(cube)) > AP/2.0+eps) then
@ -89,7 +89,7 @@ pure function Lambert_CubeToBall(cube) result(ball)
else center
! get pyramide and scale by grid parameter ratio
p = GetPyramidOrder(cube)
XYZ = cube(p) * sc
XYZ = cube(p(:,1)) * sc
! intercept all the points along the z-axis
special: if (all(dEq0(XYZ(1:2)))) then
@ -112,7 +112,7 @@ pure function Lambert_CubeToBall(cube) result(ball)
endif special
! reverse the coordinates back to order according to the original pyramid number
ball = LamXYZ(p)
ball = LamXYZ(p(:,2))
endif center
@ -130,7 +130,7 @@ pure function Lambert_BallToCube(xyz) result(cube)
real(pReal), dimension(3) :: cube, xyz1, xyz3
real(pReal), dimension(2) :: Tinv, xyz2
real(pReal) :: rs, qxy, q2, sq2, q, tt
integer, dimension(3) :: p
integer, dimension(3,2) :: p
rs = norm2(xyz)
if (rs > R1) then
@ -142,7 +142,7 @@ pure function Lambert_BallToCube(xyz) result(cube)
cube = 0.0_pReal
else center
p = GetPyramidOrder(xyz)
xyz3 = xyz(p)
xyz3 = xyz(p(:,1))
! inverse M_3
xyz2 = xyz3(1:2) * sqrt( 2.0*rs/(rs+abs(xyz3(3))) )
@ -166,7 +166,7 @@ pure function Lambert_BallToCube(xyz) result(cube)
xyz1 = [ Tinv(1), Tinv(2), sign(1.0_pReal,xyz3(3)) * rs / pref ] /sc
! reverse the coordinates back to order according to the original pyramid number
cube = xyz1(p)
cube = xyz1(p(:,2))
endif center
@ -181,17 +181,17 @@ end function Lambert_BallToCube
pure function GetPyramidOrder(xyz)
real(pReal),intent(in),dimension(3) :: xyz
integer, dimension(3) :: GetPyramidOrder
integer, dimension(3,2) :: GetPyramidOrder
if (((abs(xyz(1)) <= xyz(3)).and.(abs(xyz(2)) <= xyz(3))) .or. &
((abs(xyz(1)) <= -xyz(3)).and.(abs(xyz(2)) <= -xyz(3)))) then
GetPyramidOrder = [1,2,3]
GetPyramidOrder = reshape([[1,2,3],[1,2,3]],[3,2])
else if (((abs(xyz(3)) <= xyz(1)).and.(abs(xyz(2)) <= xyz(1))) .or. &
((abs(xyz(3)) <= -xyz(1)).and.(abs(xyz(2)) <= -xyz(1)))) then
GetPyramidOrder = [2,3,1]
GetPyramidOrder = reshape([[2,3,1],[3,1,2]],[3,2])
else if (((abs(xyz(1)) <= xyz(2)).and.(abs(xyz(3)) <= xyz(2))) .or. &
((abs(xyz(1)) <= -xyz(2)).and.(abs(xyz(3)) <= -xyz(2)))) then
GetPyramidOrder = [3,1,2]
GetPyramidOrder = reshape([[3,1,2],[2,3,1]],[3,2])
else
GetPyramidOrder = -1 ! should be impossible, but might simplify debugging
end if

1
src/commercialFEM_fileList.f90
View File

@ -9,6 +9,7 @@
#include "list.f90"
#include "future.f90"
#include "config.f90"
#include "LAPACK_interface.f90"
#include "math.f90"
#include "quaternions.f90"
#include "Lambert.f90"

2
src/crystallite.f90
View File

@ -838,8 +838,6 @@ function integrateStress(ipc,ip,el,timeFraction) result(broken)
jacoCounterLp, &
jacoCounterLi ! counters to check for Jacobian update
logical :: error,broken
external :: &
dgesv
broken = .true.

201
src/homogenization.f90
View File

@ -27,30 +27,19 @@ module homogenization
implicit none
private
!--------------------------------------------------------------------------------------------------
! General variables for the homogenization at a material point
logical, public :: &
terminallyIll = .false. !< at least one material point is terminally ill
!--------------------------------------------------------------------------------------------------
! General variables for the homogenization at a material point
real(pReal), dimension(:,:,:,:), allocatable, public :: &
materialpoint_F0, & !< def grad of IP at start of FE increment
materialpoint_F, & !< def grad of IP to be reached at end of FE increment
materialpoint_F !< def grad of IP to be reached at end of FE increment
real(pReal), dimension(:,:,:,:), allocatable, public, protected :: &
materialpoint_P !< first P--K stress of IP
real(pReal), dimension(:,:,:,:,:,:), allocatable, public :: &
real(pReal), dimension(:,:,:,:,:,:), allocatable, public, protected :: &
materialpoint_dPdF !< tangent of first P--K stress at IP
real(pReal), dimension(:,:,:,:), allocatable :: &
materialpoint_subF0, & !< def grad of IP at beginning of homogenization increment
materialpoint_subF !< def grad of IP to be reached at end of homog inc
real(pReal), dimension(:,:), allocatable :: &
materialpoint_subFrac, &
materialpoint_subStep, &
materialpoint_subdt
logical, dimension(:,:), allocatable :: &
materialpoint_requested, &
materialpoint_converged
logical, dimension(:,:,:), allocatable :: &
materialpoint_doneAndHappy
type :: tNumerics
integer :: &
nMPstate !< materialpoint state loop limit
@ -161,15 +150,7 @@ subroutine homogenization_init
allocate(materialpoint_dPdF(3,3,3,3,discretization_nIP,discretization_nElem), source=0.0_pReal)
materialpoint_F0 = spread(spread(math_I3,3,discretization_nIP),4,discretization_nElem) ! initialize to identity
materialpoint_F = materialpoint_F0 ! initialize to identity
allocate(materialpoint_subF0(3,3,discretization_nIP,discretization_nElem), source=0.0_pReal)
allocate(materialpoint_subF(3,3,discretization_nIP,discretization_nElem), source=0.0_pReal)
allocate(materialpoint_P(3,3,discretization_nIP,discretization_nElem), source=0.0_pReal)
allocate(materialpoint_subFrac(discretization_nIP,discretization_nElem), source=0.0_pReal)
allocate(materialpoint_subStep(discretization_nIP,discretization_nElem), source=0.0_pReal)
allocate(materialpoint_subdt(discretization_nIP,discretization_nElem), source=0.0_pReal)
allocate(materialpoint_requested(discretization_nIP,discretization_nElem), source=.false.)
allocate(materialpoint_converged(discretization_nIP,discretization_nElem), source=.true.)
allocate(materialpoint_doneAndHappy(2,discretization_nIP,discretization_nElem), source=.true.)
write(6,'(/,a)') ' <<<+- homogenization init -+>>>'; flush(6)
@ -203,6 +184,16 @@ subroutine materialpoint_stressAndItsTangent(updateJaco,dt)
e, & !< element number
mySource, &
myNgrains
real(pReal), dimension(3,3) :: &
subF
real(pReal), dimension(discretization_nIP,discretization_nElem) :: &
subFrac, &
subStep
logical, dimension(discretization_nIP,discretization_nElem) :: &
requested, &
converged
logical, dimension(2,discretization_nIP,discretization_nElem) :: &
doneAndHappy
#ifdef DEBUG
if (iand(debug_level(debug_homogenization), debug_levelBasic) /= 0) then
@ -216,7 +207,7 @@ subroutine materialpoint_stressAndItsTangent(updateJaco,dt)
#endif
!--------------------------------------------------------------------------------------------------
! initialize restoration points of ...
! initialize restoration points
do e = FEsolving_execElem(1),FEsolving_execElem(2)
myNgrains = homogenization_Ngrains(material_homogenizationAt(e))
do i = FEsolving_execIP(1),FEsolving_execIP(2);
@ -238,74 +229,60 @@ subroutine materialpoint_stressAndItsTangent(updateJaco,dt)
enddo
materialpoint_subF0(1:3,1:3,i,e) = materialpoint_F0(1:3,1:3,i,e)
materialpoint_subFrac(i,e) = 0.0_pReal
materialpoint_subStep(i,e) = 1.0_pReal/num%subStepSizeHomog ! <<added to adopt flexibility in cutback size>>
materialpoint_converged(i,e) = .false. ! pretend failed step of twice the required size
materialpoint_requested(i,e) = .true. ! everybody requires calculation
subFrac(i,e) = 0.0_pReal
converged(i,e) = .false. ! pretend failed step ...
subStep(i,e) = 1.0_pReal/num%subStepSizeHomog ! ... larger then the requested calculation
requested(i,e) = .true. ! everybody requires calculation
if (homogState(material_homogenizationAt(e))%sizeState > 0) &
homogState(material_homogenizationAt(e))%subState0(:,material_homogenizationMemberAt(i,e)) = &
homogState(material_homogenizationAt(e))%State0( :,material_homogenizationMemberAt(i,e)) ! ...internal homogenization state
homogState(material_homogenizationAt(e))%State0( :,material_homogenizationMemberAt(i,e))
if (thermalState(material_homogenizationAt(e))%sizeState > 0) &
thermalState(material_homogenizationAt(e))%subState0(:,material_homogenizationMemberAt(i,e)) = &
thermalState(material_homogenizationAt(e))%State0( :,material_homogenizationMemberAt(i,e)) ! ...internal thermal state
thermalState(material_homogenizationAt(e))%State0( :,material_homogenizationMemberAt(i,e))
if (damageState(material_homogenizationAt(e))%sizeState > 0) &
damageState(material_homogenizationAt(e))%subState0(:,material_homogenizationMemberAt(i,e)) = &
damageState(material_homogenizationAt(e))%State0( :,material_homogenizationMemberAt(i,e)) ! ...internal damage state
damageState(material_homogenizationAt(e))%State0( :,material_homogenizationMemberAt(i,e))
enddo
enddo
NiterationHomog = 0
cutBackLooping: do while (.not. terminallyIll .and. &
any(materialpoint_subStep(:,FEsolving_execELem(1):FEsolving_execElem(2)) > num%subStepMinHomog))
any(subStep(:,FEsolving_execELem(1):FEsolving_execElem(2)) > num%subStepMinHomog))
!$OMP PARALLEL DO PRIVATE(myNgrains)
elementLooping1: do e = FEsolving_execElem(1),FEsolving_execElem(2)
myNgrains = homogenization_Ngrains(material_homogenizationAt(e))
IpLooping1: do i = FEsolving_execIP(1),FEsolving_execIP(2)
converged: if (materialpoint_converged(i,e)) then
if (converged(i,e)) then
#ifdef DEBUG
if (iand(debug_level(debug_homogenization), debug_levelExtensive) /= 0 &
.and. ((e == debug_e .and. i == debug_i) &
.or. .not. iand(debug_level(debug_homogenization),debug_levelSelective) /= 0)) then
write(6,'(a,1x,f12.8,1x,a,1x,f12.8,1x,a,i8,1x,i2/)') '<< HOMOG >> winding forward from', &
materialpoint_subFrac(i,e), 'to current materialpoint_subFrac', &
materialpoint_subFrac(i,e)+materialpoint_subStep(i,e),'in materialpoint_stressAndItsTangent at el ip',e,i
subFrac(i,e), 'to current subFrac', &
subFrac(i,e)+subStep(i,e),'in materialpoint_stressAndItsTangent at el ip',e,i
endif
#endif
!---------------------------------------------------------------------------------------------------
! calculate new subStep and new subFrac
materialpoint_subFrac(i,e) = materialpoint_subFrac(i,e) + materialpoint_subStep(i,e)
materialpoint_subStep(i,e) = min(1.0_pReal-materialpoint_subFrac(i,e), &
num%stepIncreaseHomog*materialpoint_subStep(i,e)) ! introduce flexibility for step increase/acceleration
subFrac(i,e) = subFrac(i,e) + subStep(i,e)
subStep(i,e) = min(1.0_pReal-subFrac(i,e),num%stepIncreaseHomog*subStep(i,e)) ! introduce flexibility for step increase/acceleration
steppingNeeded: if (materialpoint_subStep(i,e) > num%subStepMinHomog) then
steppingNeeded: if (subStep(i,e) > num%subStepMinHomog) then
! wind forward grain starting point of...
crystallite_partionedF0 (1:3,1:3,1:myNgrains,i,e) = &
crystallite_partionedF(1:3,1:3,1:myNgrains,i,e)
crystallite_partionedFp0 (1:3,1:3,1:myNgrains,i,e) = &
crystallite_Fp (1:3,1:3,1:myNgrains,i,e)
crystallite_partionedLp0 (1:3,1:3,1:myNgrains,i,e) = &
crystallite_Lp (1:3,1:3,1:myNgrains,i,e)
crystallite_partionedFi0 (1:3,1:3,1:myNgrains,i,e) = &
crystallite_Fi (1:3,1:3,1:myNgrains,i,e)
crystallite_partionedLi0 (1:3,1:3,1:myNgrains,i,e) = &
crystallite_Li (1:3,1:3,1:myNgrains,i,e)
crystallite_partionedS0 (1:3,1:3,1:myNgrains,i,e) = &
crystallite_S (1:3,1:3,1:myNgrains,i,e)
! wind forward grain starting point
crystallite_partionedF0 (1:3,1:3,1:myNgrains,i,e) = crystallite_partionedF(1:3,1:3,1:myNgrains,i,e)
crystallite_partionedFp0(1:3,1:3,1:myNgrains,i,e) = crystallite_Fp (1:3,1:3,1:myNgrains,i,e)
crystallite_partionedLp0(1:3,1:3,1:myNgrains,i,e) = crystallite_Lp (1:3,1:3,1:myNgrains,i,e)
crystallite_partionedFi0(1:3,1:3,1:myNgrains,i,e) = crystallite_Fi (1:3,1:3,1:myNgrains,i,e)
crystallite_partionedLi0(1:3,1:3,1:myNgrains,i,e) = crystallite_Li (1:3,1:3,1:myNgrains,i,e)
crystallite_partionedS0 (1:3,1:3,1:myNgrains,i,e) = crystallite_S (1:3,1:3,1:myNgrains,i,e)
do g = 1,myNgrains
plasticState (material_phaseAt(g,e))%partionedState0(:,material_phasememberAt(g,i,e)) = &
@ -326,15 +303,12 @@ subroutine materialpoint_stressAndItsTangent(updateJaco,dt)
damageState(material_homogenizationAt(e))%subState0(:,material_homogenizationMemberAt(i,e)) = &
damageState(material_homogenizationAt(e))%State (:,material_homogenizationMemberAt(i,e))
materialpoint_subF0(1:3,1:3,i,e) = materialpoint_subF(1:3,1:3,i,e)
endif steppingNeeded
else converged
if ( (myNgrains == 1 .and. materialpoint_subStep(i,e) <= 1.0 ) .or. & ! single grain already tried internal subStepping in crystallite
num%subStepSizeHomog * materialpoint_subStep(i,e) <= num%subStepMinHomog ) then ! would require too small subStep
else
if ( (myNgrains == 1 .and. subStep(i,e) <= 1.0 ) .or. & ! single grain already tried internal subStepping in crystallite
num%subStepSizeHomog * subStep(i,e) <= num%subStepMinHomog ) then ! would require too small subStep
! cutback makes no sense
!$OMP FLUSH(terminallyIll)
if (.not. terminallyIll) then ! so first signals terminally ill...
!$OMP CRITICAL (write2out)
write(6,*) 'Integration point ', i,' at element ', e, ' terminally ill'
@ -342,32 +316,27 @@ subroutine materialpoint_stressAndItsTangent(updateJaco,dt)
endif
terminallyIll = .true. ! ...and kills all others
else ! cutback makes sense
materialpoint_subStep(i,e) = num%subStepSizeHomog * materialpoint_subStep(i,e) ! crystallite had severe trouble, so do a significant cutback
subStep(i,e) = num%subStepSizeHomog * subStep(i,e) ! crystallite had severe trouble, so do a significant cutback
#ifdef DEBUG
if (iand(debug_level(debug_homogenization), debug_levelExtensive) /= 0 &
.and. ((e == debug_e .and. i == debug_i) &
.or. .not. iand(debug_level(debug_homogenization), debug_levelSelective) /= 0)) then
write(6,'(a,1x,f12.8,a,i8,1x,i2/)') &
'<< HOMOG >> cutback step in materialpoint_stressAndItsTangent with new materialpoint_subStep:',&
materialpoint_subStep(i,e),' at el ip',e,i
'<< HOMOG >> cutback step in materialpoint_stressAndItsTangent with new subStep:',&
subStep(i,e),' at el ip',e,i
endif
#endif
!--------------------------------------------------------------------------------------------------
! restore...
if (materialpoint_subStep(i,e) < 1.0_pReal) then ! protect against fake cutback from \Delta t = 2 to 1. Maybe that "trick" is not necessary anymore at all? I.e. start with \Delta t = 1
crystallite_Lp(1:3,1:3,1:myNgrains,i,e) = &
crystallite_partionedLp0(1:3,1:3,1:myNgrains,i,e)
crystallite_Li(1:3,1:3,1:myNgrains,i,e) = &
crystallite_partionedLi0(1:3,1:3,1:myNgrains,i,e)
! restore
if (subStep(i,e) < 1.0_pReal) then ! protect against fake cutback from \Delta t = 2 to 1. Maybe that "trick" is not necessary anymore at all? I.e. start with \Delta t = 1
crystallite_Lp(1:3,1:3,1:myNgrains,i,e) = crystallite_partionedLp0(1:3,1:3,1:myNgrains,i,e)
crystallite_Li(1:3,1:3,1:myNgrains,i,e) = crystallite_partionedLi0(1:3,1:3,1:myNgrains,i,e)
endif ! maybe protecting everything from overwriting (not only L) makes even more sense
crystallite_Fp(1:3,1:3,1:myNgrains,i,e) = &
crystallite_partionedFp0(1:3,1:3,1:myNgrains,i,e)
crystallite_Fi(1:3,1:3,1:myNgrains,i,e) = &
crystallite_partionedFi0(1:3,1:3,1:myNgrains,i,e)
crystallite_S(1:3,1:3,1:myNgrains,i,e) = &
crystallite_partionedS0(1:3,1:3,1:myNgrains,i,e)
crystallite_Fp(1:3,1:3,1:myNgrains,i,e) = crystallite_partionedFp0(1:3,1:3,1:myNgrains,i,e)
crystallite_Fi(1:3,1:3,1:myNgrains,i,e) = crystallite_partionedFi0(1:3,1:3,1:myNgrains,i,e)
crystallite_S (1:3,1:3,1:myNgrains,i,e) = crystallite_partionedS0 (1:3,1:3,1:myNgrains,i,e)
do g = 1, myNgrains
plasticState (material_phaseAt(g,e))%state( :,material_phasememberAt(g,i,e)) = &
plasticState (material_phaseAt(g,e))%partionedState0(:,material_phasememberAt(g,i,e))
@ -386,15 +355,11 @@ subroutine materialpoint_stressAndItsTangent(updateJaco,dt)
damageState(material_homogenizationAt(e))%State( :,material_homogenizationMemberAt(i,e)) = &
damageState(material_homogenizationAt(e))%subState0(:,material_homogenizationMemberAt(i,e))
endif
endif converged
endif
if (materialpoint_subStep(i,e) > num%subStepMinHomog) then
materialpoint_requested(i,e) = .true.
materialpoint_subF(1:3,1:3,i,e) = materialpoint_subF0(1:3,1:3,i,e) &
+ materialpoint_subStep(i,e) * (materialpoint_F(1:3,1:3,i,e) &
- materialpoint_F0(1:3,1:3,i,e))
materialpoint_subdt(i,e) = materialpoint_subStep(i,e) * dt
materialpoint_doneAndHappy(1:2,i,e) = [.false.,.true.]
if (subStep(i,e) > num%subStepMinHomog) then
requested(i,e) = .true.
doneAndHappy(1:2,i,e) = [.false.,.true.]
endif
enddo IpLooping1
enddo elementLooping1
@ -403,8 +368,8 @@ subroutine materialpoint_stressAndItsTangent(updateJaco,dt)
NiterationMPstate = 0
convergenceLooping: do while (.not. terminallyIll .and. &
any( materialpoint_requested(:,FEsolving_execELem(1):FEsolving_execElem(2)) &
.and. .not. materialpoint_doneAndHappy(1,:,FEsolving_execELem(1):FEsolving_execElem(2)) &
any( requested(:,FEsolving_execELem(1):FEsolving_execElem(2)) &
.and. .not. doneAndHappy(1,:,FEsolving_execELem(1):FEsolving_execElem(2)) &
) .and. &
NiterationMPstate < num%nMPstate)
NiterationMPstate = NiterationMPstate + 1
@ -413,14 +378,15 @@ subroutine materialpoint_stressAndItsTangent(updateJaco,dt)
! deformation partitioning
! based on materialpoint_subF0,.._subF,crystallite_partionedF0, and homogenization_state,
! results in crystallite_partionedF
!$OMP PARALLEL DO PRIVATE(myNgrains)
!$OMP PARALLEL DO PRIVATE(myNgrains,subF)
elementLooping2: do e = FEsolving_execElem(1),FEsolving_execElem(2)
myNgrains = homogenization_Ngrains(material_homogenizationAt(e))
IpLooping2: do i = FEsolving_execIP(1),FEsolving_execIP(2)
if ( materialpoint_requested(i,e) .and. & ! process requested but...
.not. materialpoint_doneAndHappy(1,i,e)) then ! ...not yet done material points
call partitionDeformation(i,e) ! partition deformation onto constituents
crystallite_dt(1:myNgrains,i,e) = materialpoint_subdt(i,e) ! propagate materialpoint dt to grains
if(requested(i,e) .and. .not. doneAndHappy(1,i,e)) then ! requested but not yet done
subF = materialpoint_F0(1:3,1:3,i,e) &
+ (materialpoint_F(1:3,1:3,i,e)-materialpoint_F0(1:3,1:3,i,e))*(subStep(i,e)+subFrac(i,e))
call partitionDeformation(subF,i,e) ! partition deformation onto constituents
crystallite_dt(1:myNgrains,i,e) = dt*subStep(i,e) ! propagate materialpoint dt to grains
crystallite_requested(1:myNgrains,i,e) = .true. ! request calculation for constituents
else
crystallite_requested(1:myNgrains,i,e) = .false. ! calculation for constituents not required anymore
@ -434,20 +400,21 @@ subroutine materialpoint_stressAndItsTangent(updateJaco,dt)
! based on crystallite_partionedF0,.._partionedF
! incrementing by crystallite_dt
materialpoint_converged = crystallite_stress() !ToDo: MD not sure if that is the best logic
converged = crystallite_stress() !ToDo: MD not sure if that is the best logic
!--------------------------------------------------------------------------------------------------
! state update
!$OMP PARALLEL DO
!$OMP PARALLEL DO PRIVATE(subF)
elementLooping3: do e = FEsolving_execElem(1),FEsolving_execElem(2)
IpLooping3: do i = FEsolving_execIP(1),FEsolving_execIP(2)
if ( materialpoint_requested(i,e) .and. &
.not. materialpoint_doneAndHappy(1,i,e)) then
if (.not. materialpoint_converged(i,e)) then
materialpoint_doneAndHappy(1:2,i,e) = [.true.,.false.]
if (requested(i,e) .and. .not. doneAndHappy(1,i,e)) then
if (.not. converged(i,e)) then
doneAndHappy(1:2,i,e) = [.true.,.false.]
else
materialpoint_doneAndHappy(1:2,i,e) = updateState(i,e)
materialpoint_converged(i,e) = all(materialpoint_doneAndHappy(1:2,i,e)) ! converged if done and happy
subF = materialpoint_F0(1:3,1:3,i,e) &
+ (materialpoint_F(1:3,1:3,i,e)-materialpoint_F0(1:3,1:3,i,e))*(subStep(i,e)+subFrac(i,e))
doneAndHappy(1:2,i,e) = updateState(dt*subStep(i,e),subF,i,e)
converged(i,e) = all(doneAndHappy(1:2,i,e)) ! converged if done and happy
endif
endif
enddo IpLooping3
@ -481,8 +448,10 @@ end subroutine materialpoint_stressAndItsTangent
!--------------------------------------------------------------------------------------------------
!> @brief partition material point def grad onto constituents
!--------------------------------------------------------------------------------------------------
subroutine partitionDeformation(ip,el)
subroutine partitionDeformation(subF,ip,el)
real(pReal), intent(in), dimension(3,3) :: &
subF
integer, intent(in) :: &
ip, & !< integration point
el !< element number
@ -490,17 +459,17 @@ subroutine partitionDeformation(ip,el)
chosenHomogenization: select case(homogenization_type(material_homogenizationAt(el)))
case (HOMOGENIZATION_NONE_ID) chosenHomogenization
crystallite_partionedF(1:3,1:3,1,ip,el) = materialpoint_subF(1:3,1:3,ip,el)
crystallite_partionedF(1:3,1:3,1,ip,el) = subF
case (HOMOGENIZATION_ISOSTRAIN_ID) chosenHomogenization
call mech_isostrain_partitionDeformation(&
crystallite_partionedF(1:3,1:3,1:homogenization_Ngrains(material_homogenizationAt(el)),ip,el), &
materialpoint_subF(1:3,1:3,ip,el))
subF)
case (HOMOGENIZATION_RGC_ID) chosenHomogenization
call mech_RGC_partitionDeformation(&
crystallite_partionedF(1:3,1:3,1:homogenization_Ngrains(material_homogenizationAt(el)),ip,el), &
materialpoint_subF(1:3,1:3,ip,el),&
subF,&
ip, &
el)
end select chosenHomogenization
@ -512,8 +481,12 @@ end subroutine partitionDeformation
!> @brief update the internal state of the homogenization scheme and tell whether "done" and
!> "happy" with result
!--------------------------------------------------------------------------------------------------
function updateState(ip,el)
function updateState(subdt,subF,ip,el)
real(pReal), intent(in) :: &
subdt !< current time step
real(pReal), intent(in), dimension(3,3) :: &
subF
integer, intent(in) :: &
ip, & !< integration point
el !< element number
@ -527,8 +500,8 @@ function updateState(ip,el)
mech_RGC_updateState(crystallite_P(1:3,1:3,1:homogenization_Ngrains(material_homogenizationAt(el)),ip,el), &
crystallite_partionedF(1:3,1:3,1:homogenization_Ngrains(material_homogenizationAt(el)),ip,el), &
crystallite_partionedF0(1:3,1:3,1:homogenization_Ngrains(material_homogenizationAt(el)),ip,el),&
materialpoint_subF(1:3,1:3,ip,el),&
materialpoint_subdt(ip,el), &
subF,&
subdt, &
crystallite_dPdF(1:3,1:3,1:3,1:3,1:homogenization_Ngrains(material_homogenizationAt(el)),ip,el), &
ip, &
el)
@ -538,7 +511,7 @@ function updateState(ip,el)
case (THERMAL_adiabatic_ID) chosenThermal
updateState = &
updateState .and. &
thermal_adiabatic_updateState(materialpoint_subdt(ip,el), &
thermal_adiabatic_updateState(subdt, &
ip, &
el)
end select chosenThermal
@ -547,7 +520,7 @@ function updateState(ip,el)
case (DAMAGE_local_ID) chosenDamage
updateState = &
updateState .and. &
damage_local_updateState(materialpoint_subdt(ip,el), &
damage_local_updateState(subdt, &
ip, &
el)
end select chosenDamage

20
src/math.f90
View File

@ -9,6 +9,7 @@ module math
use prec
use IO
use numerics
use LAPACK_interface
implicit none
public
@ -487,16 +488,12 @@ function math_invSym3333(A)
integer, dimension(6) :: ipiv6
real(pReal), dimension(6,6) :: temp66
real(pReal), dimension(6*(64+2)) :: work
real(pReal), dimension(6*6) :: work
integer :: ierr_i, ierr_f
external :: &
dgetrf, &
dgetri
temp66 = math_sym3333to66(A)
call dgetrf(6,6,temp66,6,ipiv6,ierr_i)
call dgetri(6,temp66,6,ipiv6,work,size(work,1),ierr_f)
if (ierr_i /= 0 .or. ierr_f /= 0) then
call IO_error(400, ext_msg = 'math_invSym3333')
else
@ -516,11 +513,8 @@ subroutine math_invert(InvA, error, A)
logical, intent(out) :: error
integer, dimension(size(A,1)) :: ipiv
real(pReal), dimension(size(A,1)*(64+2)) :: work
real(pReal), dimension(size(A,1)**2) :: work
integer :: ierr
external :: &
dgetrf, &
dgetri
invA = A
call dgetrf(size(A,1),size(A,1),invA,size(A,1),ipiv,ierr)
@ -884,9 +878,7 @@ subroutine math_eigh(m,w,v,error)
logical, intent(out) :: error
integer :: ierr
real(pReal), dimension((64+2)*size(m,1)) :: work ! block size of 64 taken from http://www.netlib.org/lapack/double/dsyev.f
external :: &
dsyev
real(pReal), dimension(size(m,1)**2) :: work
v = m ! copy matrix to input (doubles as output) array
call dsyev('V','U',size(m,1),v,size(m,1),w,work,size(work,1),ierr)
@ -1041,9 +1033,7 @@ function math_eigvalsh(m)
real(pReal), dimension(size(m,1),size(m,1)) :: m_
integer :: ierr
real(pReal), dimension((64+2)*size(m,1)) :: work ! block size of 64 taken from http://www.netlib.org/lapack/double/dsyev.f
external :: &
dsyev
real(pReal), dimension(size(m,1)**2) :: work
m_= m ! copy matrix to input (will be destroyed)
call dsyev('N','U',size(m,1),m_,size(m,1),math_eigvalsh,work,size(work,1),ierr)

13
src/rotations.f90
View File

@ -432,18 +432,17 @@ pure function qu2eu(qu) result(eu)
real(pReal), intent(in), dimension(4) :: qu
real(pReal), dimension(3) :: eu
real(pReal) :: q12, q03, chi, chiInv
real(pReal) :: q12, q03, chi
q03 = qu(1)**2+qu(4)**2
q12 = qu(2)**2+qu(3)**2
chi = sqrt(q03*q12)
degenerated: if (dEq0(chi)) then
eu = merge([atan2(-P*2.0_pReal*qu(1)*qu(4),qu(1)**2-qu(4)**2), 0.0_pReal, 0.0_pReal], &
[atan2( 2.0_pReal*qu(2)*qu(3),qu(2)**2-qu(3)**2), PI, 0.0_pReal], &
dEq0(q12))
degenerated: if (dEq0(q12)) then
eu = [atan2(-P*2.0_pReal*qu(1)*qu(4),qu(1)**2-qu(4)**2), 0.0_pReal, 0.0_pReal]
elseif (dEq0(q03)) then
eu = [atan2( 2.0_pReal*qu(2)*qu(3),qu(2)**2-qu(3)**2), PI, 0.0_pReal]
else degenerated
chiInv = 1.0_pReal/chi
eu = [atan2((-P*qu(1)*qu(3)+qu(2)*qu(4))*chi, (-P*qu(1)*qu(2)-qu(3)*qu(4))*chi ), &
atan2( 2.0_pReal*chi, q03-q12 ), &
atan2(( P*qu(1)*qu(3)+qu(2)*qu(4))*chi, (-P*qu(1)*qu(2)+qu(3)*qu(4))*chi )]
@ -596,8 +595,6 @@ function om2ax(om) result(ax)
real(pReal), dimension(3,3) :: VR, devNull, om_
integer :: ierr, i
external :: dgeev
om_ = om
! first get the rotation angle