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Merge branch 'development' into vectorize_rotation

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Martin Diehl 2020-05-15 23:25:36 +02:00
parent ef4a4dad4a 45e608e71b
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14 changed files with 2011 additions and 724 deletions
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2
VERSION
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@ -1 +1 @@
v2.0.3-2402-gb88f5ec0
v2.0.3-2464-g90f93d23

164
python/damask/_Lambert.py
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@ -1,164 +0,0 @@
####################################################################################################
# Code below available according to the following conditions on
# https://github.com/MarDiehl/3Drotations
####################################################################################################
# Copyright (c) 2017-2019, Martin Diehl/Max-Planck-Institut für Eisenforschung GmbH
# Copyright (c) 2013-2014, Marc De Graef/Carnegie Mellon University
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without modification, are
# permitted provided that the following conditions are met:
#
# - Redistributions of source code must retain the above copyright notice, this list
# of conditions and the following disclaimer.
# - Redistributions in binary form must reproduce the above copyright notice, this
# list of conditions and the following disclaimer in the documentation and/or
# other materials provided with the distribution.
# - Neither the names of Marc De Graef, Carnegie Mellon University nor the names
# of its contributors may be used to endorse or promote products derived from
# this software without specific prior written permission.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
# ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
# LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
# DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
# SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
# CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
# OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
# USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
####################################################################################################
import numpy as np
sc = np.pi**(1./6.)/6.**(1./6.)
beta = np.pi**(5./6.)/6.**(1./6.)/2.
R1 = (3.*np.pi/4.)**(1./3.)
def cube_to_ball(cube):
"""
Map a point in a uniform refinable cubical grid to a point on a uniform refinable grid on a ball.
Parameters
----------
cube : numpy.ndarray
coordinates of a point in a uniform refinable cubical grid.
References
----------
D. Roşca et al., Modelling and Simulation in Materials Science and Engineering 22:075013, 2014
https://doi.org/10.1088/0965-0393/22/7/075013
"""
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-16):
ball = np.zeros(3)
else:
# get pyramide and scale by grid parameter ratio
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-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]
q = np.pi/12.0 * XYZ[order[0]]/XYZ[order[1]]
c = np.cos(q)
s = np.sin(q)
q = R1*2.0**0.25/beta * XYZ[order[1]] / np.sqrt(np.sqrt(2.0)-c)
T = np.array([ (np.sqrt(2.0)*c - 1.0), np.sqrt(2.0) * s]) * q
# transform to sphere grid (inverse Lambert)
# note that there is no need to worry about dividing by zero, since XYZ[2] can not become zero
c = np.sum(T**2)
s = c * np.pi/24.0 /XYZ[2]**2
c = c * np.sqrt(np.pi/24.0)/XYZ[2]
q = np.sqrt( 1.0 - s )
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[1]]
return ball
def ball_to_cube(ball):
"""
Map a point on a uniform refinable grid on a ball to a point in a uniform refinable cubical grid.
Parameters
----------
ball : numpy.ndarray
coordinates of a point on a uniform refinable grid on a ball.
References
----------
D. Roşca et al., Modelling and Simulation in Materials Science and Engineering 22:075013, 2014
https://doi.org/10.1088/0965-0393/22/7/075013
"""
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-16):
cube = np.zeros(3)
else:
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])) )
# inverse M_2
qxy = np.sum(xyz2**2)
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
sq2 = np.sqrt(q2)
q = (beta/np.sqrt(2.0)/R1) * np.sqrt(q2*qxy/(q2-np.max(np.abs(xyz2))*sq2))
tt = np.clip((np.min(np.abs(xyz2))**2+np.max(np.abs(xyz2))*sq2)/np.sqrt(2.0)/qxy,-1.0,1.0)
Tinv = np.array([1.0,np.arccos(tt)/np.pi*12.0]) if np.abs(xyz2[1]) <= np.abs(xyz2[0]) else \
np.array([np.arccos(tt)/np.pi*12.0,1.0])
Tinv = q * np.where(xyz2<0.0,-Tinv,Tinv)
# 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[1]]
return cube
def _get_order(xyz):
"""
Get order of the coordinates.
Depending on the pyramid in which the point is located, the order need to be adjusted.
Parameters
----------
xyz : numpy.ndarray
coordinates of a point on a uniform refinable grid on a ball or
in a uniform refinable cubical grid.
References
----------
D. Roşca et al., Modelling and Simulation in Materials Science and Engineering 22:075013, 2014
https://doi.org/10.1088/0965-0393/22/7/075013
"""
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],[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],[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],[1,2,0]]

189
python/damask/_rotation.py
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@ -1,10 +1,14 @@
import numpy as np
from ._Lambert import ball_to_cube, cube_to_ball
from . import mechanics
_P = -1
# parameters for conversion from/to cubochoric
_sc = np.pi**(1./6.)/6.**(1./6.)
_beta = np.pi**(5./6.)/6.**(1./6.)/2.
_R1 = (3.*np.pi/4.)**(1./3.)
def iszero(a):
return np.isclose(a,0.0,atol=1.0e-12,rtol=0.0)
@ -288,7 +292,7 @@ class Rotation:
"""Homochoric vector: (h_1, h_2, h_3)."""
return Rotation.qu2ho(self.quaternion)
def asCubochoric(self):
def as_cubochoric(self):
"""Cubochoric vector: (c_1, c_2, c_3)."""
return Rotation.qu2cu(self.quaternion)
@ -312,6 +316,7 @@ class Rotation:
asMatrix = as_matrix
asRodrigues = as_Rodrigues
asHomochoric = as_homochoric
asCubochoric = as_cubochoric
################################################################################################
# Static constructors. The input data needs to follow the conventions, options allow to
@ -433,7 +438,7 @@ class Rotation:
return Rotation(Rotation.ho2qu(ho))
@staticmethod
def fromCubochoric(cubochoric,
def from_cubochoric(cubochoric,
P = -1):
cu = np.array(cubochoric,dtype=float)
@ -508,6 +513,7 @@ class Rotation:
fromMatrix = from_matrix
fromRodrigues = from_Rodrigues
fromHomochoric = from_homochoric
fromCubochoric = from_cubochoric
fromRandom = from_random
####################################################################################################
@ -1098,12 +1104,71 @@ class Rotation:
@staticmethod
def ho2cu(ho):
"""Homochoric vector to cubochoric vector."""
if len(ho.shape) == 1:
return ball_to_cube(ho)
else:
raise NotImplementedError('Support for multiple rotations missing')
"""
Homochoric vector to cubochoric vector.
References
----------
D. Roşca et al., Modelling and Simulation in Materials Science and Engineering 22:075013, 2014
https://doi.org/10.1088/0965-0393/22/7/075013
"""
if len(ho.shape) == 1:
rs = np.linalg.norm(ho)
if np.allclose(ho,0.0,rtol=0.0,atol=1.0e-16):
cu = np.zeros(3)
else:
xyz3 = ho[Rotation._get_pyramid_order(ho,'forward')]
# inverse M_3
xyz2 = xyz3[0:2] * np.sqrt( 2.0*rs/(rs+np.abs(xyz3[2])) )
# inverse M_2
qxy = np.sum(xyz2**2)
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
sq2 = np.sqrt(q2)
q = (_beta/np.sqrt(2.0)/_R1) * np.sqrt(q2*qxy/(q2-np.max(np.abs(xyz2))*sq2))
tt = np.clip((np.min(np.abs(xyz2))**2+np.max(np.abs(xyz2))*sq2)/np.sqrt(2.0)/qxy,-1.0,1.0)
Tinv = np.array([1.0,np.arccos(tt)/np.pi*12.0]) if np.abs(xyz2[1]) <= np.abs(xyz2[0]) else \
np.array([np.arccos(tt)/np.pi*12.0,1.0])
Tinv = q * np.where(xyz2<0.0,-Tinv,Tinv)
# inverse M_1
cu = np.array([ Tinv[0], Tinv[1], (-1.0 if xyz3[2] < 0.0 else 1.0) * rs / np.sqrt(6.0/np.pi) ]) /_sc
cu = cu[Rotation._get_pyramid_order(ho,'backward')]
else:
rs = np.linalg.norm(ho,axis=-1,keepdims=True)
xyz3 = np.take_along_axis(ho,Rotation._get_pyramid_order(ho,'forward'),-1)
with np.errstate(invalid='ignore',divide='ignore'):
# inverse M_3
xyz2 = xyz3[...,0:2] * np.sqrt( 2.0*rs/(rs+np.abs(xyz3[...,2:3])) )
qxy = np.sum(xyz2**2,axis=-1,keepdims=True)
q2 = qxy + np.max(np.abs(xyz2),axis=-1,keepdims=True)**2
sq2 = np.sqrt(q2)
q = (_beta/np.sqrt(2.0)/_R1) * np.sqrt(q2*qxy/(q2-np.max(np.abs(xyz2),axis=-1,keepdims=True)*sq2))
tt = np.clip((np.min(np.abs(xyz2),axis=-1,keepdims=True)**2\
+np.max(np.abs(xyz2),axis=-1,keepdims=True)*sq2)/np.sqrt(2.0)/qxy,-1.0,1.0)
T_inv = np.where(np.abs(xyz2[...,1:2]) <= np.abs(xyz2[...,0:1]),
np.block([np.ones_like(tt),np.arccos(tt)/np.pi*12.0]),
np.block([np.arccos(tt)/np.pi*12.0,np.ones_like(tt)]))*q
T_inv[xyz2<0.0] *= -1.0
T_inv[np.broadcast_to(np.isclose(qxy,0.0,rtol=0.0,atol=1.0e-12),T_inv.shape)] = 0.0
cu = np.block([T_inv, np.where(xyz3[...,2:3]<0.0,-np.ones_like(xyz3[...,2:3]),np.ones_like(xyz3[...,2:3])) \
* rs/np.sqrt(6.0/np.pi),
])/ _sc
cu[np.isclose(np.sum(np.abs(ho),axis=-1),0.0,rtol=0.0,atol=1.0e-16)] = 0.0
cu = np.take_along_axis(cu,Rotation._get_pyramid_order(ho,'backward'),-1)
return cu
#---------- Cubochoric ----------
@staticmethod
@ -1133,8 +1198,110 @@ class Rotation:
@staticmethod
def cu2ho(cu):
"""Cubochoric vector to homochoric vector."""
"""
Cubochoric vector to homochoric vector.
References
----------
D. Roşca et al., Modelling and Simulation in Materials Science and Engineering 22:075013, 2014
https://doi.org/10.1088/0965-0393/22/7/075013
"""
if len(cu.shape) == 1:
return cube_to_ball(cu)
# transform to the sphere grid via the curved square, and intercept the zero point
if np.allclose(cu,0.0,rtol=0.0,atol=1.0e-16):
ho = np.zeros(3)
else:
# get pyramide and scale by grid parameter ratio
XYZ = cu[Rotation._get_pyramid_order(cu,'forward')] * _sc
# intercept all the points along the z-axis
if np.allclose(XYZ[0:2],0.0,rtol=0.0,atol=1.0e-16):
ho = 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]
q = np.pi/12.0 * XYZ[order[0]]/XYZ[order[1]]
c = np.cos(q)
s = np.sin(q)
q = _R1*2.0**0.25/_beta * XYZ[order[1]] / np.sqrt(np.sqrt(2.0)-c)
T = np.array([ (np.sqrt(2.0)*c - 1.0), np.sqrt(2.0) * s]) * q
# transform to sphere grid (inverse Lambert)
# note that there is no need to worry about dividing by zero, since XYZ[2] can not become zero
c = np.sum(T**2)
s = c * np.pi/24.0 /XYZ[2]**2
c = c * np.sqrt(np.pi/24.0)/XYZ[2]
q = np.sqrt( 1.0 - s )
ho = np.array([ T[order[1]] * q, T[order[0]] * q, np.sqrt(6.0/np.pi) * XYZ[2] - c ])
ho = ho[Rotation._get_pyramid_order(cu,'backward')]
else:
raise NotImplementedError('Support for multiple rotations missing')
with np.errstate(invalid='ignore',divide='ignore'):
# get pyramide and scale by grid parameter ratio
XYZ = np.take_along_axis(cu,Rotation._get_pyramid_order(cu,'forward'),-1) * _sc
order = np.abs(XYZ[...,1:2]) <= np.abs(XYZ[...,0:1])
q = np.pi/12.0 * np.where(order,XYZ[...,1:2],XYZ[...,0:1]) \
/ np.where(order,XYZ[...,0:1],XYZ[...,1:2])
c = np.cos(q)
s = np.sin(q)
q = _R1*2.0**0.25/_beta/ np.sqrt(np.sqrt(2.0)-c) \
* np.where(order,XYZ[...,0:1],XYZ[...,1:2])
T = np.block([ (np.sqrt(2.0)*c - 1.0), np.sqrt(2.0) * s]) * q
# transform to sphere grid (inverse Lambert)
c = np.sum(T**2,axis=-1,keepdims=True)
s = c * np.pi/24.0 /XYZ[...,2:3]**2
c = c * np.sqrt(np.pi/24.0)/XYZ[...,2:3]
q = np.sqrt( 1.0 - s)
ho = np.where(np.isclose(np.sum(np.abs(XYZ[...,0:2]),axis=-1,keepdims=True),0.0,rtol=0.0,atol=1.0e-16),
np.block([np.zeros_like(XYZ[...,0:2]),np.sqrt(6.0/np.pi) *XYZ[...,2:3]]),
np.block([np.where(order,T[...,0:1],T[...,1:2])*q,
np.where(order,T[...,1:2],T[...,0:1])*q,
np.sqrt(6.0/np.pi) * XYZ[...,2:3] - c])
)
ho[np.isclose(np.sum(np.abs(cu),axis=-1),0.0,rtol=0.0,atol=1.0e-16)] = 0.0
ho = np.take_along_axis(ho,Rotation._get_pyramid_order(cu,'backward'),-1)
return ho
@staticmethod
def _get_pyramid_order(xyz,direction=None):
"""
Get order of the coordinates.
Depending on the pyramid in which the point is located, the order need to be adjusted.
Parameters
----------
xyz : numpy.ndarray
coordinates of a point on a uniform refinable grid on a ball or
in a uniform refinable cubical grid.
References
----------
D. Roşca et al., Modelling and Simulation in Materials Science and Engineering 22:075013, 2014
https://doi.org/10.1088/0965-0393/22/7/075013
"""
order = {'forward':np.array([[0,1,2],[1,2,0],[2,0,1]]),
'backward':np.array([[0,1,2],[2,0,1],[1,2,0]])}
if len(xyz.shape) == 1:
if np.maximum(abs(xyz[0]),abs(xyz[1])) <= xyz[2] or \
np.maximum(abs(xyz[0]),abs(xyz[1])) <=-xyz[2]:
p = 0
elif np.maximum(abs(xyz[1]),abs(xyz[2])) <= xyz[0] or \
np.maximum(abs(xyz[1]),abs(xyz[2])) <=-xyz[0]:
p = 1
elif np.maximum(abs(xyz[2]),abs(xyz[0])) <= xyz[1] or \
np.maximum(abs(xyz[2]),abs(xyz[0])) <=-xyz[1]:
p = 2
else:
p = np.where(np.maximum(np.abs(xyz[...,0]),np.abs(xyz[...,1])) <= np.abs(xyz[...,2]),0,
np.where(np.maximum(np.abs(xyz[...,1]),np.abs(xyz[...,2])) <= np.abs(xyz[...,0]),1,2))
return order[direction][p]

98
python/tests/test_Rotation.py
View File

@ -78,9 +78,9 @@ def default():
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))]
return [Rotation.from_quaternion(s) for s in specials] + \
[Rotation.from_quaternion(s) for s in specials_scatter] + \
[Rotation.from_random() for _ in range(n-len(specials)-len(specials_scatter))]
@pytest.fixture
def reference_dir(reference_dir_base):
@ -92,41 +92,41 @@ class TestRotation:
def test_Eulers(self,default):
for rot in default:
m = rot.asQuaternion()
o = Rotation.fromEulers(rot.asEulers()).asQuaternion()
m = rot.as_quaternion()
o = Rotation.from_Eulers(rot.as_Eulers()).as_quaternion()
ok = np.allclose(m,o,atol=atol)
if np.isclose(rot.asQuaternion()[0],0.0,atol=atol):
if np.isclose(rot.as_quaternion()[0],0.0,atol=atol):
ok = ok or np.allclose(m*-1.,o,atol=atol)
print(m,o,rot.asQuaternion())
print(m,o,rot.as_quaternion())
assert ok and np.isclose(np.linalg.norm(o),1.0)
def test_AxisAngle(self,default):
for rot in default:
m = rot.asEulers()
o = Rotation.fromAxisAngle(rot.asAxisAngle()).asEulers()
m = rot.as_Eulers()
o = Rotation.from_axis_angle(rot.as_axis_angle()).as_Eulers()
u = np.array([np.pi*2,np.pi,np.pi*2])
ok = np.allclose(m,o,atol=atol)
ok = ok or np.allclose(np.where(np.isclose(m,u),m-u,m),np.where(np.isclose(o,u),o-u,o),atol=atol)
if np.isclose(m[1],0.0,atol=atol) or np.isclose(m[1],np.pi,atol=atol):
sum_phi = np.unwrap([m[0]+m[2],o[0]+o[2]])
ok = ok or np.isclose(sum_phi[0],sum_phi[1],atol=atol)
print(m,o,rot.asQuaternion())
print(m,o,rot.as_quaternion())
assert ok and (np.zeros(3)-1.e-9 <= o).all() and (o <= np.array([np.pi*2.,np.pi,np.pi*2.])+1.e-9).all()
def test_Matrix(self,default):
for rot in default:
m = rot.asAxisAngle()
o = Rotation.fromAxisAngle(rot.asAxisAngle()).asAxisAngle()
m = rot.as_axis_angle()
o = Rotation.from_axis_angle(rot.as_axis_angle()).as_axis_angle()
ok = np.allclose(m,o,atol=atol)
if np.isclose(m[3],np.pi,atol=atol):
ok = ok or np.allclose(m*np.array([-1.,-1.,-1.,1.]),o,atol=atol)
print(m,o,rot.asQuaternion())
print(m,o,rot.as_quaternion())
assert ok and np.isclose(np.linalg.norm(o[:3]),1.0) and o[3]<=np.pi++1.e-9
def test_Rodrigues(self,default):
for rot in default:
m = rot.asMatrix()
o = Rotation.fromRodrigues(rot.asRodrigues()).asMatrix()
m = rot.as_matrix()
o = Rotation.from_Rodrigues(rot.as_Rodrigues()).as_matrix()
ok = np.allclose(m,o,atol=atol)
print(m,o)
assert ok and np.isclose(np.linalg.det(o),1.0)
@ -134,27 +134,27 @@ class TestRotation:
def test_Homochoric(self,default):
cutoff = np.tan(np.pi*.5*(1.-1e-4))
for rot in default:
m = rot.asRodrigues()
o = Rotation.fromHomochoric(rot.asHomochoric()).asRodrigues()
m = rot.as_Rodrigues()
o = Rotation.from_homochoric(rot.as_homochoric()).as_Rodrigues()
ok = np.allclose(np.clip(m,None,cutoff),np.clip(o,None,cutoff),atol=atol)
ok = ok or np.isclose(m[3],0.0,atol=atol)
print(m,o,rot.asQuaternion())
print(m,o,rot.as_quaternion())
assert ok and np.isclose(np.linalg.norm(o[:3]),1.0)
def test_Cubochoric(self,default):
for rot in default:
m = rot.asHomochoric()
o = Rotation.fromCubochoric(rot.asCubochoric()).asHomochoric()
m = rot.as_homochoric()
o = Rotation.from_cubochoric(rot.as_cubochoric()).as_homochoric()
ok = np.allclose(m,o,atol=atol)
print(m,o,rot.asQuaternion())
print(m,o,rot.as_quaternion())
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:
m = rot.asCubochoric()
o = Rotation.fromQuaternion(rot.asQuaternion()).asCubochoric()
m = rot.as_cubochoric()
o = Rotation.from_quaternion(rot.as_quaternion()).as_cubochoric()
ok = np.allclose(m,o,atol=atol)
print(m,o,rot.asQuaternion())
print(m,o,rot.as_quaternion())
assert ok and o.max() < np.pi**(2./3.)*0.5+1.e-9
@pytest.mark.parametrize('function',[Rotation.from_quaternion,
@ -185,9 +185,11 @@ class TestRotation:
Rotation.qu2eu,
Rotation.qu2ax,
Rotation.qu2ro,
Rotation.qu2ho])
Rotation.qu2ho,
Rotation.qu2cu
])
def test_quaternion_vectorization(self,default,conversion):
qu = np.array([rot.asQuaternion() for rot in default])
qu = np.array([rot.as_quaternion() for rot in default])
conversion(qu.reshape(qu.shape[0]//2,-1,4))
co = conversion(qu)
for q,c in zip(qu,co):
@ -199,9 +201,10 @@ class TestRotation:
Rotation.om2ax,
Rotation.om2ro,
Rotation.om2ho,
Rotation.om2cu
])
def test_matrix_vectorization(self,default,conversion):
om = np.array([rot.asMatrix() for rot in default])
om = np.array([rot.as_matrix() for rot in default])
conversion(om.reshape(om.shape[0]//2,-1,3,3))
co = conversion(om)
for o,c in zip(om,co):
@ -213,9 +216,10 @@ class TestRotation:
Rotation.eu2ax,
Rotation.eu2ro,
Rotation.eu2ho,
Rotation.eu2cu
])
def test_Euler_vectorization(self,default,conversion):
eu = np.array([rot.asEulers() for rot in default])
eu = np.array([rot.as_Eulers() for rot in default])
conversion(eu.reshape(eu.shape[0]//2,-1,3))
co = conversion(eu)
for e,c in zip(eu,co):
@ -227,9 +231,10 @@ class TestRotation:
Rotation.ax2eu,
Rotation.ax2ro,
Rotation.ax2ho,
Rotation.ax2cu
])
def test_axisAngle_vectorization(self,default,conversion):
ax = np.array([rot.asAxisAngle() for rot in default])
ax = np.array([rot.as_axis_angle() for rot in default])
conversion(ax.reshape(ax.shape[0]//2,-1,4))
co = conversion(ax)
for a,c in zip(ax,co):
@ -242,9 +247,10 @@ class TestRotation:
Rotation.ro2eu,
Rotation.ro2ax,
Rotation.ro2ho,
Rotation.ro2cu
])
def test_Rodrigues_vectorization(self,default,conversion):
ro = np.array([rot.asRodrigues() for rot in default])
ro = np.array([rot.as_Rodrigues() for rot in default])
conversion(ro.reshape(ro.shape[0]//2,-1,4))
co = conversion(ro)
for r,c in zip(ro,co):
@ -256,11 +262,41 @@ class TestRotation:
Rotation.ho2eu,
Rotation.ho2ax,
Rotation.ho2ro,
Rotation.ho2cu
])
def test_homochoric_vectorization(self,default,conversion):
ho = np.array([rot.asHomochoric() for rot in default])
ho = np.array([rot.as_homochoric() 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)
@pytest.mark.parametrize('conversion',[Rotation.cu2qu,
Rotation.cu2om,
Rotation.cu2eu,
Rotation.cu2ax,
Rotation.cu2ro,
Rotation.cu2ho
])
def test_cubochoric_vectorization(self,default,conversion):
cu = np.array([rot.as_cubochoric() for rot in default])
conversion(cu.reshape(cu.shape[0]//2,-1,3))
co = conversion(cu)
for u,c in zip(cu,co):
print(u,c)
assert np.allclose(conversion(u),c)
@pytest.mark.parametrize('direction',['forward',
'backward'])
def test_pyramid_vectorization(self,direction):
p = np.random.rand(n,3)
o = Rotation._get_pyramid_order(p,direction)
for i,o_i in enumerate(o):
assert np.all(o_i==Rotation._get_pyramid_order(p[i],direction))
def test_pyramid_invariant(self):
a = np.random.rand(n,3)
f = Rotation._get_pyramid_order(a,'forward')
b = Rotation._get_pyramid_order(a,'backward')
assert np.all(np.take_along_axis(np.take_along_axis(a,f,-1),b,-1) == a)

184
python/tests/test_grid_filters.py
View File

@ -101,6 +101,7 @@ class TestGridFilters:
with pytest.raises(ValueError):
function(uneven)
@pytest.mark.parametrize('mode',[True,False])
@pytest.mark.parametrize('function',[grid_filters.node_coord0_gridSizeOrigin,
grid_filters.cell_coord0_gridSizeOrigin])
@ -120,3 +121,186 @@ class TestGridFilters:
grid = np.random.randint(8,32,(3))
F = np.broadcast_to(np.eye(3), tuple(grid)+(3,3))
assert all(grid_filters.regrid(size,F,grid) == np.arange(grid.prod()))
@pytest.mark.parametrize('differential_operator',[grid_filters.curl,
grid_filters.divergence,
grid_filters.gradient])
def test_differential_operator_constant(self,differential_operator):
size = np.random.random(3)+1.0
grid = np.random.randint(8,32,(3))
shapes = {
grid_filters.curl: [(3,),(3,3)],
grid_filters.divergence:[(3,),(3,3)],
grid_filters.gradient: [(1,),(3,)]
}
for shape in shapes[differential_operator]:
field = np.ones(tuple(grid)+shape)*np.random.random()*1.0e5
assert np.allclose(differential_operator(size,field),0.0)
grad_test_data = [
(['np.sin(np.pi*2*nodes[...,0]/size[0])', '0.0', '0.0'],
['np.cos(np.pi*2*nodes[...,0]/size[0])*np.pi*2/size[0]', '0.0', '0.0',
'0.0', '0.0', '0.0',
'0.0', '0.0', '0.0']),
(['0.0', 'np.cos(np.pi*2*nodes[...,1]/size[1])', '0.0' ],
['0.0', '0.0', '0.0',
'0.0', '-np.pi*2/size[1]*np.sin(np.pi*2*nodes[...,1]/size[1])', '0.0',
'0.0', '0.0', '0.0' ]),
(['1.0', '0.0', '2.0*np.cos(np.pi*2*nodes[...,2]/size[2])'],
['0.0', '0.0', '0.0',
'0.0', '0.0', '0.0',
'0.0', '0.0', '-2.0*np.pi*2/size[2]*np.sin(np.pi*2*nodes[...,2]/size[2])']),
(['np.cos(np.pi*2*nodes[...,2]/size[2])', '3.0', 'np.sin(np.pi*2*nodes[...,2]/size[2])'],
['0.0', '0.0', '-np.sin(np.pi*2*nodes[...,2]/size[2])*np.pi*2/size[2]',
'0.0', '0.0', '0.0',
'0.0', '0.0', ' np.cos(np.pi*2*nodes[...,2]/size[2])*np.pi*2/size[2]']),
(['np.sin(np.pi*2*nodes[...,0]/size[0])',
'np.sin(np.pi*2*nodes[...,1]/size[1])',
'np.sin(np.pi*2*nodes[...,2]/size[2])'],
['np.cos(np.pi*2*nodes[...,0]/size[0])*np.pi*2/size[0]', '0.0', '0.0',
'0.0', 'np.cos(np.pi*2*nodes[...,1]/size[1])*np.pi*2/size[1]', '0.0',
'0.0', '0.0', 'np.cos(np.pi*2*nodes[...,2]/size[2])*np.pi*2/size[2]']),
(['np.sin(np.pi*2*nodes[...,0]/size[0])'],
['np.cos(np.pi*2*nodes[...,0]/size[0])*np.pi*2/size[0]', '0.0', '0.0']),
(['8.0'],
['0.0', '0.0', '0.0' ])
]
@pytest.mark.parametrize('field_def,grad_def',grad_test_data)
def test_grad(self,field_def,grad_def):
size = np.random.random(3)+1.0
grid = np.random.randint(8,32,(3))
nodes = grid_filters.cell_coord0(grid,size)
my_locals = locals() # needed for list comprehension
field = np.stack([np.broadcast_to(eval(f,globals(),my_locals),grid) for f in field_def],axis=-1)
field = field.reshape(tuple(grid) + ((3,) if len(field_def)==3 else (1,)))
grad = np.stack([np.broadcast_to(eval(c,globals(),my_locals),grid) for c in grad_def], axis=-1)
grad = grad.reshape(tuple(grid) + ((3,3) if len(grad_def)==9 else (3,)))
assert np.allclose(grad,grid_filters.gradient(size,field))
curl_test_data = [
(['np.sin(np.pi*2*nodes[...,2]/size[2])', '0.0', '0.0',
'0.0', '0.0', '0.0',
'0.0', '0.0', '0.0'],
['0.0' , '0.0', '0.0',
'np.cos(np.pi*2*nodes[...,2]/size[2])*np.pi*2/size[2]', '0.0', '0.0',
'0.0', '0.0', '0.0']),
(['np.cos(np.pi*2*nodes[...,1]/size[1])', '0.0', '0.0',
'0.0', '0.0', '0.0',
'np.cos(np.pi*2*nodes[...,0]/size[0])', '0.0', '0.0'],
['0.0', '0.0', '0.0',
'0.0', '0.0', '0.0',
'np.sin(np.pi*2*nodes[...,1]/size[1])*np.pi*2/size[1]', '0.0', '0.0']),
(['np.sin(np.pi*2*nodes[...,0]/size[0])','np.cos(np.pi*2*nodes[...,1]/size[1])','np.sin(np.pi*2*nodes[...,2]/size[2])',
'np.sin(np.pi*2*nodes[...,0]/size[0])','np.cos(np.pi*2*nodes[...,1]/size[1])','np.sin(np.pi*2*nodes[...,2]/size[2])',
'np.sin(np.pi*2*nodes[...,0]/size[0])','np.cos(np.pi*2*nodes[...,1]/size[1])','np.sin(np.pi*2*nodes[...,2]/size[2])'],
['0.0', '0.0', '0.0',
'0.0', '0.0', '0.0',
'0.0', '0.0', '0.0']),
(['5.0', '0.0', '0.0',
'0.0', '0.0', '0.0',
'0.0', '0.0', '2*np.cos(np.pi*2*nodes[...,1]/size[1])'],
['0.0', '0.0', '-2*np.pi*2/size[1]*np.sin(np.pi*2*nodes[...,1]/size[1])',
'0.0', '0.0', '0.0',
'0.0', '0.0', '0.0']),
([ '4*np.sin(np.pi*2*nodes[...,2]/size[2])',
'8*np.sin(np.pi*2*nodes[...,0]/size[0])',
'16*np.sin(np.pi*2*nodes[...,1]/size[1])'],
['16*np.pi*2/size[1]*np.cos(np.pi*2*nodes[...,1]/size[1])',
'4*np.pi*2/size[2]*np.cos(np.pi*2*nodes[...,2]/size[2])',
'8*np.pi*2/size[0]*np.cos(np.pi*2*nodes[...,0]/size[0])']),
(['0.0',
'np.cos(np.pi*2*nodes[...,0]/size[0])+5*np.cos(np.pi*2*nodes[...,2]/size[2])',
'0.0'],
['5*np.sin(np.pi*2*nodes[...,2]/size[2])*np.pi*2/size[2]',
'0.0',
'-np.sin(np.pi*2*nodes[...,0]/size[0])*np.pi*2/size[0]'])
]
@pytest.mark.parametrize('field_def,curl_def',curl_test_data)
def test_curl(self,field_def,curl_def):
size = np.random.random(3)+1.0
grid = np.random.randint(8,32,(3))
nodes = grid_filters.cell_coord0(grid,size)
my_locals = locals() # needed for list comprehension
field = np.stack([np.broadcast_to(eval(f,globals(),my_locals),grid) for f in field_def],axis=-1)
field = field.reshape(tuple(grid) + ((3,3) if len(field_def)==9 else (3,)))
curl = np.stack([np.broadcast_to(eval(c,globals(),my_locals),grid) for c in curl_def], axis=-1)
curl = curl.reshape(tuple(grid) + ((3,3) if len(curl_def)==9 else (3,)))
assert np.allclose(curl,grid_filters.curl(size,field))
div_test_data =[
(['np.sin(np.pi*2*nodes[...,0]/size[0])', '0.0', '0.0',
'0.0' , '0.0', '0.0',
'0.0' , '0.0', '0.0'],
['np.cos(np.pi*2*nodes[...,0]/size[0])*np.pi*2/size[0]','0.0', '0.0']),
(['0.0', '0.0', '0.0',
'0.0', 'np.cos(np.pi*2*nodes[...,1]/size[1])', '0.0',
'0.0', '0.0', '0.0'],
['0.0', '-np.sin(np.pi*2*nodes[...,1]/size[1])*np.pi*2/size[1]', '0.0']),
(['1.0', '0.0', '0.0',
'0.0', '0.0', '0.0',
'0.0', '0.0', '2*np.cos(np.pi*2*nodes[...,2]/size[2])' ],
['0.0', '0.0', '-2.0*np.pi*2/size[2]*np.sin(np.pi*2*nodes[...,2]/size[2])']
),
([ '23.0', '0.0', 'np.sin(np.pi*2*nodes[...,2]/size[2])',
'0.0', '100.0', 'np.sin(np.pi*2*nodes[...,2]/size[2])',
'0.0', '0.0', 'np.sin(np.pi*2*nodes[...,2]/size[2])'],
['np.cos(np.pi*2*nodes[...,2]/size[2])*np.pi*2/size[2]',\
'np.cos(np.pi*2*nodes[...,2]/size[2])*np.pi*2/size[2]', \
'np.cos(np.pi*2*nodes[...,2]/size[2])*np.pi*2/size[2]']),
(['400.0', '0.0', '0.0',
'np.sin(np.pi*2*nodes[...,0]/size[0])', 'np.sin(np.pi*2*nodes[...,1]/size[1])', 'np.sin(np.pi*2*nodes[...,2]/size[2])',
'0.0', '10.0', '6.0'],
['0.0','np.sum(np.cos(np.pi*2*nodes/size)*np.pi*2/size,axis=-1)', '0.0' ]),
(['np.sin(np.pi*2*nodes[...,0]/size[0])', '0.0', '0.0'],
['np.cos(np.pi*2*nodes[...,0]/size[0])*np.pi*2/size[0]',]),
(['0.0', 'np.cos(np.pi*2*nodes[...,1]/size[1])', '0.0' ],
['-np.sin(np.pi*2*nodes[...,1]/size[1])*np.pi*2/size[1]'])
]
@pytest.mark.parametrize('field_def,div_def',div_test_data)
def test_div(self,field_def,div_def):
size = np.random.random(3)+1.0
grid = np.random.randint(8,32,(3))
nodes = grid_filters.cell_coord0(grid,size)
my_locals = locals() # needed for list comprehension
field = np.stack([np.broadcast_to(eval(f,globals(),my_locals),grid) for f in field_def],axis=-1)
field = field.reshape(tuple(grid) + ((3,3) if len(field_def)==9 else (3,)))
div = np.stack([np.broadcast_to(eval(c,globals(),my_locals),grid) for c in div_def], axis=-1)
if len(div_def)==3:
div = div.reshape(tuple(grid) + ((3,)))
else:
div=div.reshape(tuple(grid))
assert np.allclose(div,grid_filters.divergence(size,field))

2
src/CPFEM.f90
View File

@ -10,6 +10,7 @@ module CPFEM
use FEsolving
use math
use rotations
use YAML_types
use discretization_marc
use material
use config
@ -82,6 +83,7 @@ subroutine CPFEM_initAll(el,ip)
call config_init
call math_init
call rotations_init
call YAML_types_init
call HDF5_utilities_init
call results_init
call discretization_marc_init(ip, el)

2
src/CPFEM2.f90
View File

@ -11,6 +11,7 @@ module CPFEM2
use FEsolving
use math
use rotations
use YAML_types
use material
use lattice
use IO
@ -50,6 +51,7 @@ subroutine CPFEM_initAll
call config_init
call math_init
call rotations_init
call YAML_types_init
call lattice_init
call HDF5_utilities_init
call results_init

174
src/IO.f90
View File

@ -29,9 +29,13 @@ module IO
IO_getTag, &
IO_stringPos, &
IO_stringValue, &
IO_floatValue, &
IO_intValue, &
IO_floatValue, &
IO_lc, &
IO_rmComment, &
IO_stringAsInt, &
IO_stringAsFloat, &
IO_stringAsBool, &
IO_error, &
IO_warning
@ -250,7 +254,7 @@ integer function IO_intValue(string,chunkPos,myChunk)
integer, dimension(:), intent(in) :: chunkPos !< positions of start and end of each tag/chunk in given string
integer, intent(in) :: myChunk !< position number of desired chunk
IO_intValue = verifyIntValue(IO_stringValue(string,chunkPos,myChunk))
IO_intValue = IO_stringAsInt(IO_stringValue(string,chunkPos,myChunk))
end function IO_intValue
@ -264,7 +268,7 @@ real(pReal) function IO_floatValue(string,chunkPos,myChunk)
integer, dimension(:), intent(in) :: chunkPos !< positions of start and end of each tag/chunk in given string
integer, intent(in) :: myChunk !< position number of desired chunk
IO_floatValue = verifyFloatValue(IO_stringValue(string,chunkPos,myChunk))
IO_floatValue = IO_stringAsFloat(IO_stringValue(string,chunkPos,myChunk))
end function IO_floatValue
@ -294,6 +298,88 @@ pure function IO_lc(string)
end function IO_lc
!--------------------------------------------------------------------------------------------------
! @brief Remove comments (characters beyond '#') and trailing space
! ToDo: Discuss name (the trim aspect is not clear)
!--------------------------------------------------------------------------------------------------
function IO_rmComment(line)
character(len=*), intent(in) :: line
character(len=:), allocatable :: IO_rmComment
integer :: split
split = index(line,IO_COMMENT)
if (split == 0) then
IO_rmComment = trim(line)
else
IO_rmComment = trim(line(:split-1))
endif
end function IO_rmComment
!--------------------------------------------------------------------------------------------------
!> @brief return verified integer value in given string
!--------------------------------------------------------------------------------------------------
integer function IO_stringAsInt(string)
character(len=*), intent(in) :: string !< string for conversion to int value
integer :: readStatus
character(len=*), parameter :: VALIDCHARS = '0123456789+- '
valid: if (verify(string,VALIDCHARS) == 0) then
read(string,*,iostat=readStatus) IO_stringAsInt
if (readStatus /= 0) call IO_error(111,ext_msg=string)
else valid
IO_stringAsInt = 0
call IO_error(111,ext_msg=string)
endif valid
end function IO_stringAsInt
!--------------------------------------------------------------------------------------------------
!> @brief return verified float value in given string
!--------------------------------------------------------------------------------------------------
real(pReal) function IO_stringAsFloat(string)
character(len=*), intent(in) :: string !< string for conversion to float value
integer :: readStatus
character(len=*), parameter :: VALIDCHARS = '0123456789eE.+- '
valid: if (verify(string,VALIDCHARS) == 0) then
read(string,*,iostat=readStatus) IO_stringAsFloat
if (readStatus /= 0) call IO_error(112,ext_msg=string)
else valid
IO_stringAsFloat = 0.0_pReal
call IO_error(112,ext_msg=string)
endif valid
end function IO_stringAsFloat
!--------------------------------------------------------------------------------------------------
!> @brief return verified logical value in given string
!--------------------------------------------------------------------------------------------------
logical function IO_stringAsBool(string)
character(len=*), intent(in) :: string !< string for conversion to int value
if (trim(adjustl(string)) == 'True') then
IO_stringAsBool = .true.
elseif (trim(adjustl(string)) == 'False') then
IO_stringAsBool = .false.
else
IO_stringAsBool = .false.
call IO_error(113,ext_msg=string)
endif
end function IO_stringAsBool
!--------------------------------------------------------------------------------------------------
!> @brief write error statements to standard out and terminate the Marc/spectral run with exit #9xxx
!--------------------------------------------------------------------------------------------------
@ -335,7 +421,8 @@ subroutine IO_error(error_ID,el,ip,g,instance,ext_msg)
msg = 'invalid character for int:'
case (112)
msg = 'invalid character for float:'
case (113)
msg = 'invalid character for logical:'
!--------------------------------------------------------------------------------------------------
! lattice error messages
case (130)
@ -606,51 +693,6 @@ subroutine IO_warning(warning_ID,el,ip,g,ext_msg)
end subroutine IO_warning
!--------------------------------------------------------------------------------------------------
! internal helper functions
!--------------------------------------------------------------------------------------------------
!> @brief returns verified integer value in given string
!--------------------------------------------------------------------------------------------------
integer function verifyIntValue(string)
character(len=*), intent(in) :: string !< string for conversion to int value
integer :: readStatus
character(len=*), parameter :: VALIDCHARS = '0123456789+- '
valid: if (verify(string,VALIDCHARS) == 0) then
read(string,*,iostat=readStatus) verifyIntValue
if (readStatus /= 0) call IO_error(111,ext_msg=string)
else valid
verifyIntValue = 0
call IO_error(111,ext_msg=string)
endif valid
end function verifyIntValue
!--------------------------------------------------------------------------------------------------
!> @brief returns verified float value in given string
!--------------------------------------------------------------------------------------------------
real(pReal) function verifyFloatValue(string)
character(len=*), intent(in) :: string !< string for conversion to float value
integer :: readStatus
character(len=*), parameter :: VALIDCHARS = '0123456789eE.+- '
valid: if (verify(string,VALIDCHARS) == 0) then
read(string,*,iostat=readStatus) verifyFloatValue
if (readStatus /= 0) call IO_error(112,ext_msg=string)
else valid
verifyFloatValue = 0.0_pReal
call IO_error(112,ext_msg=string)
endif valid
end function verifyFloatValue
!--------------------------------------------------------------------------------------------------
!> @brief check correctness of some IO functions
!--------------------------------------------------------------------------------------------------
@ -659,14 +701,19 @@ subroutine unitTest
integer, dimension(:), allocatable :: chunkPos
character(len=:), allocatable :: str
if(dNeq(1.0_pReal, verifyFloatValue('1.0'))) call IO_error(0,ext_msg='verifyFloatValue')
if(dNeq(1.0_pReal, verifyFloatValue('1e0'))) call IO_error(0,ext_msg='verifyFloatValue')
if(dNeq(0.1_pReal, verifyFloatValue('1e-1'))) call IO_error(0,ext_msg='verifyFloatValue')
if(dNeq(1.0_pReal, IO_stringAsFloat('1.0'))) call IO_error(0,ext_msg='IO_stringAsFloat')
if(dNeq(1.0_pReal, IO_stringAsFloat('1e0'))) call IO_error(0,ext_msg='IO_stringAsFloat')
if(dNeq(0.1_pReal, IO_stringAsFloat('1e-1'))) call IO_error(0,ext_msg='IO_stringAsFloat')
if(3112019 /= verifyIntValue( '3112019')) call IO_error(0,ext_msg='verifyIntValue')
if(3112019 /= verifyIntValue(' 3112019')) call IO_error(0,ext_msg='verifyIntValue')
if(-3112019 /= verifyIntValue('-3112019')) call IO_error(0,ext_msg='verifyIntValue')
if(3112019 /= verifyIntValue('+3112019 ')) call IO_error(0,ext_msg='verifyIntValue')
if(3112019 /= IO_stringAsInt( '3112019')) call IO_error(0,ext_msg='IO_stringAsInt')
if(3112019 /= IO_stringAsInt(' 3112019')) call IO_error(0,ext_msg='IO_stringAsInt')
if(-3112019 /= IO_stringAsInt('-3112019')) call IO_error(0,ext_msg='IO_stringAsInt')
if(3112019 /= IO_stringAsInt('+3112019 ')) call IO_error(0,ext_msg='IO_stringAsInt')
if(.not. IO_stringAsBool(' True')) call IO_error(0,ext_msg='IO_stringAsBool')
if(.not. IO_stringAsBool(' True ')) call IO_error(0,ext_msg='IO_stringAsBool')
if( IO_stringAsBool(' False')) call IO_error(0,ext_msg='IO_stringAsBool')
if( IO_stringAsBool('False')) call IO_error(0,ext_msg='IO_stringAsBool')
if(any([1,1,1] /= IO_stringPos('a'))) call IO_error(0,ext_msg='IO_stringPos')
if(any([2,2,3,5,5] /= IO_stringPos(' aa b'))) call IO_error(0,ext_msg='IO_stringPos')
@ -683,6 +730,21 @@ subroutine unitTest
if(.not. IO_isBlank(' #isBlank')) call IO_error(0,ext_msg='IO_isBlank/2')
if( IO_isBlank(' i#s')) call IO_error(0,ext_msg='IO_isBlank/3')
str = IO_rmComment('#')
if (str /= '' .or. len(str) /= 0) call IO_error(0,ext_msg='IO_rmComment/1')
str = IO_rmComment(' #')
if (str /= '' .or. len(str) /= 0) call IO_error(0,ext_msg='IO_rmComment/2')
str = IO_rmComment(' # ')
if (str /= '' .or. len(str) /= 0) call IO_error(0,ext_msg='IO_rmComment/3')
str = IO_rmComment(' # a')
if (str /= '' .or. len(str) /= 0) call IO_error(0,ext_msg='IO_rmComment/4')
str = IO_rmComment(' # a')
if (str /= '' .or. len(str) /= 0) call IO_error(0,ext_msg='IO_rmComment/5')
str = IO_rmComment(' a#')
if (str /= ' a' .or. len(str) /= 2) call IO_error(0,ext_msg='IO_rmComment/6')
str = IO_rmComment(' ab #')
if (str /= ' ab'.or. len(str) /= 3) call IO_error(0,ext_msg='IO_rmComment/7')
end subroutine unitTest
end module IO

201
src/Lambert.f90
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@ -1,201 +0,0 @@
! ###################################################################
! Copyright (c) 2013-2015, Marc De Graef/Carnegie Mellon University
! Modified 2017-2019, Martin Diehl/Max-Planck-Institut für Eisenforschung GmbH
! All rights reserved.
!
! Redistribution and use in source and binary forms, with or without modification, are
! permitted provided that the following conditions are met:
!
! - Redistributions of source code must retain the above copyright notice, this list
! of conditions and the following disclaimer.
! - Redistributions in binary form must reproduce the above copyright notice, this
! list of conditions and the following disclaimer in the documentation and/or
! other materials provided with the distribution.
! - Neither the names of Marc De Graef, Carnegie Mellon University nor the names
! of its contributors may be used to endorse or promote products derived from
! this software without specific prior written permission.
!
! THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
! AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
! IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
! ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
! LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
! DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
! SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
! CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
! OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
! USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
! ###################################################################
!--------------------------------------------------------------------------
!> @author Marc De Graef, Carnegie Mellon University
!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
!> @brief Mapping homochoric <-> cubochoric
!
!> @details
!> D. Rosca, A. Morawiec, and M. De Graef. “A new method of constructing a grid
!> in the space of 3D rotations and its applications to texture analysis”.
!> Modeling and Simulations in Materials Science and Engineering 22, 075013 (2014).
!--------------------------------------------------------------------------
module Lambert
use prec
use math
implicit none
private
real(pReal), parameter :: &
SPI = sqrt(PI), &
PREF = sqrt(6.0_pReal/PI), &
A = PI**(5.0_pReal/6.0_pReal)/6.0_pReal**(1.0_pReal/6.0_pReal), &
AP = PI**(2.0_pReal/3.0_pReal), &
SC = A/AP, &
BETA = A/2.0_pReal, &
R1 = (3.0_pReal*PI/4.0_pReal)**(1.0_pReal/3.0_pReal), &
R2 = sqrt(2.0_pReal), &
PI12 = PI/12.0_pReal, &
PREK = R1 * 2.0_pReal**(1.0_pReal/4.0_pReal)/BETA
public :: &
Lambert_CubeToBall, &
Lambert_BallToCube
contains
!--------------------------------------------------------------------------
!> @author Marc De Graef, Carnegie Mellon University
!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
!> @brief map from 3D cubic grid to 3D ball
!--------------------------------------------------------------------------
pure function Lambert_CubeToBall(cube) result(ball)
real(pReal), intent(in), dimension(3) :: cube
real(pReal), dimension(3) :: ball, LamXYZ, XYZ
real(pReal), dimension(2) :: T
real(pReal) :: c, s, q
real(pReal), parameter :: eps = 1.0e-8_pReal
integer, dimension(3,2) :: p
integer, dimension(2) :: order
if (maxval(abs(cube)) > AP/2.0+eps) then
ball = IEEE_value(cube,IEEE_positive_inf)
return
end if
! transform to the sphere grid via the curved square, and intercept the zero point
center: if (all(dEq0(cube))) then
ball = 0.0_pReal
else center
! get pyramide and scale by grid parameter ratio
p = GetPyramidOrder(cube)
XYZ = cube(p(:,1)) * sc
! intercept all the points along the z-axis
special: if (all(dEq0(XYZ(1:2)))) then
LamXYZ = [ 0.0_pReal, 0.0_pReal, pref * XYZ(3) ]
else special
order = merge( [2,1], [1,2], abs(XYZ(2)) <= abs(XYZ(1))) ! order of absolute values of XYZ
q = PI12 * XYZ(order(1))/XYZ(order(2)) ! smaller by larger
c = cos(q)
s = sin(q)
q = prek * XYZ(order(2))/ sqrt(R2-c)
T = [ (R2*c - 1.0), R2 * s] * q
! transform to sphere grid (inverse Lambert)
! [note that there is no need to worry about dividing by zero, since XYZ(3) can not become zero]
c = sum(T**2)
s = Pi * c/(24.0*XYZ(3)**2)
c = sPi * c / sqrt(24.0_pReal) / XYZ(3)
q = sqrt( 1.0 - s )
LamXYZ = [ T(order(2)) * q, T(order(1)) * q, pref * XYZ(3) - c ]
endif special
! reverse the coordinates back to order according to the original pyramid number
ball = LamXYZ(p(:,2))
endif center
end function Lambert_CubeToBall
!--------------------------------------------------------------------------
!> @author Marc De Graef, Carnegie Mellon University
!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
!> @brief map from 3D ball to 3D cubic grid
!--------------------------------------------------------------------------
pure function Lambert_BallToCube(xyz) result(cube)
real(pReal), intent(in), dimension(3) :: xyz
real(pReal), dimension(3) :: cube, xyz1, xyz3
real(pReal), dimension(2) :: Tinv, xyz2
real(pReal) :: rs, qxy, q2, sq2, q, tt
integer, dimension(3,2) :: p
rs = norm2(xyz)
if (rs > R1) then
cube = IEEE_value(cube,IEEE_positive_inf)
return
endif
center: if (all(dEq0(xyz))) then
cube = 0.0_pReal
else center
p = GetPyramidOrder(xyz)
xyz3 = xyz(p(:,1))
! inverse M_3
xyz2 = xyz3(1:2) * sqrt( 2.0*rs/(rs+abs(xyz3(3))) )
! inverse M_2
qxy = sum(xyz2**2)
special: if (dEq0(qxy)) then
Tinv = 0.0_pReal
else special
q2 = qxy + maxval(abs(xyz2))**2
sq2 = sqrt(q2)
q = (beta/R2/R1) * sqrt(q2*qxy/(q2-maxval(abs(xyz2))*sq2))
tt = (minval(abs(xyz2))**2+maxval(abs(xyz2))*sq2)/R2/qxy
Tinv = q * sign(1.0_pReal,xyz2) * merge([ 1.0_pReal, acos(math_clip(tt,-1.0_pReal,1.0_pReal))/PI12], &
[ acos(math_clip(tt,-1.0_pReal,1.0_pReal))/PI12, 1.0_pReal], &
abs(xyz2(2)) <= abs(xyz2(1)))
endif special
! inverse M_1
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(:,2))
endif center
end function Lambert_BallToCube
!--------------------------------------------------------------------------
!> @author Marc De Graef, Carnegie Mellon University
!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
!> @brief determine to which pyramid a point in a cubic grid belongs
!--------------------------------------------------------------------------
pure function GetPyramidOrder(xyz)
real(pReal),intent(in),dimension(3) :: xyz
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 = 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 = 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 = reshape([[3,1,2],[2,3,1]],[3,2])
else
GetPyramidOrder = -1 ! should be impossible, but might simplify debugging
end if
end function GetPyramidOrder
end module Lambert

1044
src/YAML_types.f90 Normal file
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File diff suppressed because it is too large Load Diff

2
src/commercialFEM_fileList.f90
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@ -7,12 +7,12 @@
#include "numerics.f90"
#include "debug.f90"
#include "list.f90"
#include "YAML_types.f90"
#include "future.f90"
#include "config.f90"
#include "LAPACK_interface.f90"
#include "math.f90"
#include "quaternions.f90"
#include "Lambert.f90"
#include "rotations.f90"
#include "FEsolving.f90"
#include "element.f90"

300
src/constitutive_plastic_nonlocal.f90
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@ -962,39 +962,24 @@ module subroutine plastic_nonlocal_dotState(Mp, F, Fp, Temperature,timestep, &
integer :: &
ph, &
neighbor_instance, & !< instance of my neighbor's plasticity
ns, & !< short notation for the total number of active slip systems
c, & !< character of dislocation
n, & !< index of my current neighbor
neighbor_el, & !< element number of my neighbor
neighbor_ip, & !< integration point of my neighbor
neighbor_n, & !< neighbor index pointing to me when looking from my neighbor
opposite_neighbor, & !< index of my opposite neighbor
opposite_ip, & !< ip of my opposite neighbor
opposite_el, & !< element index of my opposite neighbor
opposite_n, & !< neighbor index pointing to me when looking from my opposite neighbor
t, & !< type of dislocation
no,& !< neighbor offset shortcut
np,& !< neighbor phase shortcut
topp, & !< type of dislocation with opposite sign to t
s !< index of my current slip system
real(pReal), dimension(param(instance)%sum_N_sl,10) :: &
rho, &
rho0, & !< dislocation density at beginning of time step
rhoDot, & !< density evolution
rhoDotMultiplication, & !< density evolution by multiplication
rhoDotFlux, & !< density evolution by flux
rhoDotSingle2DipoleGlide, & !< density evolution by dipole formation (by glide)
rhoDotAthermalAnnihilation, & !< density evolution by athermal annihilation
rhoDotThermalAnnihilation !< density evolution by thermal annihilation
real(pReal), dimension(param(instance)%sum_N_sl,8) :: &
rhoSgl, & !< current single dislocation densities (positive/negative screw and edge without dipoles)
neighbor_rhoSgl0, & !< current single dislocation densities of neighboring ip (positive/negative screw and edge without dipoles)
my_rhoSgl0 !< single dislocation densities of central ip (positive/negative screw and edge without dipoles)
real(pReal), dimension(param(instance)%sum_N_sl,4) :: &
v, & !< current dislocation glide velocity
v0, &
neighbor_v0, & !< dislocation glide velocity of enighboring ip
gdot !< shear rates
real(pReal), dimension(param(instance)%sum_N_sl) :: &
tau, & !< current resolved shear stress
@ -1003,23 +988,7 @@ module subroutine plastic_nonlocal_dotState(Mp, F, Fp, Temperature,timestep, &
rhoDip, & !< current dipole dislocation densities (screw and edge dipoles)
dLower, & !< minimum stable dipole distance for edges and screws
dUpper !< current maximum stable dipole distance for edges and screws
real(pReal), dimension(3,param(instance)%sum_N_sl,4) :: &
m !< direction of dislocation motion
real(pReal), dimension(3,3) :: &
my_F, & !< my total deformation gradient
neighbor_F, & !< total deformation gradient of my neighbor
my_Fe, & !< my elastic deformation gradient
neighbor_Fe, & !< elastic deformation gradient of my neighbor
Favg !< average total deformation gradient of me and my neighbor
real(pReal), dimension(3) :: &
normal_neighbor2me, & !< interface normal pointing from my neighbor to me in neighbor's lattice configuration
normal_neighbor2me_defConf, & !< interface normal pointing from my neighbor to me in shared deformed configuration
normal_me2neighbor, & !< interface normal pointing from me to my neighbor in my lattice configuration
normal_me2neighbor_defConf !< interface normal pointing from me to my neighbor in shared deformed configuration
real(pReal) :: &
area, & !< area of the current interface
transmissivity, & !< overall transmissivity of dislocation flux to neighboring material point
lineLength, & !< dislocation line length leaving the current interface
selfDiffusion !< self diffusion
ph = material_phaseAt(1,el)
@ -1092,6 +1061,172 @@ module subroutine plastic_nonlocal_dotState(Mp, F, Fp, Temperature,timestep, &
* sqrt(stt%rho_forest(:,of)) / prm%lambda0 / prm%burgers, 2, 4)
endif isBCC
forall (s = 1:ns, t = 1:4) v0(s,t) = plasticState(ph)%state0(iV(s,t,instance),of)
!****************************************************************************
!*** calculate dipole formation and annihilation
!*** formation by glide
do c = 1,2
rhoDotSingle2DipoleGlide(:,2*c-1) = -2.0_pReal * dUpper(:,c) / prm%burgers &
* ( rhoSgl(:,2*c-1) * abs(gdot(:,2*c)) & ! negative mobile --> positive mobile
+ rhoSgl(:,2*c) * abs(gdot(:,2*c-1)) & ! positive mobile --> negative mobile
+ abs(rhoSgl(:,2*c+4)) * abs(gdot(:,2*c-1))) ! positive mobile --> negative immobile
rhoDotSingle2DipoleGlide(:,2*c) = -2.0_pReal * dUpper(:,c) / prm%burgers &
* ( rhoSgl(:,2*c-1) * abs(gdot(:,2*c)) & ! negative mobile --> positive mobile
+ rhoSgl(:,2*c) * abs(gdot(:,2*c-1)) & ! positive mobile --> negative mobile
+ abs(rhoSgl(:,2*c+3)) * abs(gdot(:,2*c))) ! negative mobile --> positive immobile
rhoDotSingle2DipoleGlide(:,2*c+3) = -2.0_pReal * dUpper(:,c) / prm%burgers &
* rhoSgl(:,2*c+3) * abs(gdot(:,2*c)) ! negative mobile --> positive immobile
rhoDotSingle2DipoleGlide(:,2*c+4) = -2.0_pReal * dUpper(:,c) / prm%burgers &
* rhoSgl(:,2*c+4) * abs(gdot(:,2*c-1)) ! positive mobile --> negative immobile
rhoDotSingle2DipoleGlide(:,c+8) = abs(rhoDotSingle2DipoleGlide(:,2*c+3)) &
+ abs(rhoDotSingle2DipoleGlide(:,2*c+4)) &
- rhoDotSingle2DipoleGlide(:,2*c-1) &
- rhoDotSingle2DipoleGlide(:,2*c)
enddo
!*** athermal annihilation
rhoDotAthermalAnnihilation = 0.0_pReal
forall (c=1:2) &
rhoDotAthermalAnnihilation(:,c+8) = -2.0_pReal * dLower(:,c) / prm%burgers &
* ( 2.0_pReal * (rhoSgl(:,2*c-1) * abs(gdot(:,2*c)) + rhoSgl(:,2*c) * abs(gdot(:,2*c-1))) & ! was single hitting single
+ 2.0_pReal * (abs(rhoSgl(:,2*c+3)) * abs(gdot(:,2*c)) + abs(rhoSgl(:,2*c+4)) * abs(gdot(:,2*c-1))) & ! was single hitting immobile single or was immobile single hit by single
+ rhoDip(:,c) * (abs(gdot(:,2*c-1)) + abs(gdot(:,2*c)))) ! single knocks dipole constituent
! annihilated screw dipoles leave edge jogs behind on the colinear system
if (lattice_structure(ph) == LATTICE_fcc_ID) &
forall (s = 1:ns, prm%colinearSystem(s) > 0) &
rhoDotAthermalAnnihilation(prm%colinearSystem(s),1:2) = - rhoDotAthermalAnnihilation(s,10) &
* 0.25_pReal * sqrt(stt%rho_forest(s,of)) * (dUpper(s,2) + dLower(s,2)) * prm%edgeJogFactor
!*** thermally activated annihilation of edge dipoles by climb
rhoDotThermalAnnihilation = 0.0_pReal
selfDiffusion = prm%Dsd0 * exp(-prm%selfDiffusionEnergy / (kB * Temperature))
vClimb = prm%atomicVolume * selfDiffusion * prm%mu &
/ ( kB * Temperature * PI * (1.0_pReal-prm%nu) * (dUpper(:,1) + dLower(:,1)))
forall (s = 1:ns, dUpper(s,1) > dLower(s,1)) &
rhoDotThermalAnnihilation(s,9) = max(- 4.0_pReal * rhoDip(s,1) * vClimb(s) / (dUpper(s,1) - dLower(s,1)), &
- rhoDip(s,1) / timestep - rhoDotAthermalAnnihilation(s,9) &
- rhoDotSingle2DipoleGlide(s,9)) ! make sure that we do not annihilate more dipoles than we have
rhoDot = rhoDotFlux(F,Fp,timestep, instance,of,ip,el) &
+ rhoDotMultiplication &
+ rhoDotSingle2DipoleGlide &
+ rhoDotAthermalAnnihilation &
+ rhoDotThermalAnnihilation
if ( any(rho(:,mob) + rhoDot(:,1:4) * timestep < -prm%atol_rho) &
.or. any(rho(:,dip) + rhoDot(:,9:10) * timestep < -prm%atol_rho)) then
#ifdef DEBUG
if (iand(debug_level(debug_constitutive),debug_levelExtensive) /= 0) then
write(6,'(a,i5,a,i2)') '<< CONST >> evolution rate leads to negative density at el ',el,' ip ',ip
write(6,'(a)') '<< CONST >> enforcing cutback !!!'
endif
#endif
plasticState(ph)%dotState = IEEE_value(1.0_pReal,IEEE_quiet_NaN)
else
dot%rho(:,of) = pack(rhoDot,.true.)
dot%gamma(:,of) = sum(gdot,2)
endif
end associate
end subroutine plastic_nonlocal_dotState
!---------------------------------------------------------------------------------------------------
!> @brief calculates the rate of change of microstructure
!---------------------------------------------------------------------------------------------------
function rhoDotFlux(F,Fp,timestep, instance,of,ip,el)
real(pReal), dimension(3,3,homogenization_maxNgrains,discretization_nIP,discretization_nElem), intent(in) :: &
F, & !< elastic deformation gradient
Fp !< plastic deformation gradient
real(pReal), intent(in) :: &
timestep !< substepped crystallite time increment
integer, intent(in) :: &
instance, &
of, &
ip, & !< current integration point
el !< current element number
integer :: &
ph, &
neighbor_instance, & !< instance of my neighbor's plasticity
ns, & !< short notation for the total number of active slip systems
c, & !< character of dislocation
n, & !< index of my current neighbor
neighbor_el, & !< element number of my neighbor
neighbor_ip, & !< integration point of my neighbor
neighbor_n, & !< neighbor index pointing to me when looking from my neighbor
opposite_neighbor, & !< index of my opposite neighbor
opposite_ip, & !< ip of my opposite neighbor
opposite_el, & !< element index of my opposite neighbor
opposite_n, & !< neighbor index pointing to me when looking from my opposite neighbor
t, & !< type of dislocation
no,& !< neighbor offset shortcut
np,& !< neighbor phase shortcut
topp, & !< type of dislocation with opposite sign to t
s !< index of my current slip system
real(pReal), dimension(param(instance)%sum_N_sl,10) :: &
rho, &
rho0, & !< dislocation density at beginning of time step
rhoDotFlux !< density evolution by flux
real(pReal), dimension(param(instance)%sum_N_sl,8) :: &
rhoSgl, & !< current single dislocation densities (positive/negative screw and edge without dipoles)
neighbor_rhoSgl0, & !< current single dislocation densities of neighboring ip (positive/negative screw and edge without dipoles)
my_rhoSgl0 !< single dislocation densities of central ip (positive/negative screw and edge without dipoles)
real(pReal), dimension(param(instance)%sum_N_sl,4) :: &
v, & !< current dislocation glide velocity
v0, &
neighbor_v0, & !< dislocation glide velocity of enighboring ip
gdot !< shear rates
real(pReal), dimension(3,param(instance)%sum_N_sl,4) :: &
m !< direction of dislocation motion
real(pReal), dimension(3,3) :: &
my_F, & !< my total deformation gradient
neighbor_F, & !< total deformation gradient of my neighbor
my_Fe, & !< my elastic deformation gradient
neighbor_Fe, & !< elastic deformation gradient of my neighbor
Favg !< average total deformation gradient of me and my neighbor
real(pReal), dimension(3) :: &
normal_neighbor2me, & !< interface normal pointing from my neighbor to me in neighbor's lattice configuration
normal_neighbor2me_defConf, & !< interface normal pointing from my neighbor to me in shared deformed configuration
normal_me2neighbor, & !< interface normal pointing from me to my neighbor in my lattice configuration
normal_me2neighbor_defConf !< interface normal pointing from me to my neighbor in shared deformed configuration
real(pReal) :: &
area, & !< area of the current interface
transmissivity, & !< overall transmissivity of dislocation flux to neighboring material point
lineLength !< dislocation line length leaving the current interface
ph = material_phaseAt(1,el)
associate(prm => param(instance), &
dst => microstructure(instance), &
dot => dotState(instance), &
stt => state(instance))
ns = prm%sum_N_sl
gdot = 0.0_pReal
rho = getRho(instance,of,ip,el)
rhoSgl = rho(:,sgl)
rho0 = getRho0(instance,of,ip,el)
my_rhoSgl0 = rho0(:,sgl)
forall (s = 1:ns, t = 1:4) v(s,t) = plasticState(ph)%state(iV(s,t,instance),of) !ToDo: MD: I think we should use state0 here
gdot = rhoSgl(:,1:4) * v * spread(prm%burgers,2,4)
forall (s = 1:ns, t = 1:4) v0(s,t) = plasticState(ph)%state0(iV(s,t,instance),of)
!****************************************************************************
@ -1114,7 +1249,7 @@ module subroutine plastic_nonlocal_dotState(Mp, F, Fp, Temperature,timestep, &
write(6,'(a)') '<< CONST >> enforcing cutback !!!'
endif
#endif
plasticState(ph)%dotState = IEEE_value(1.0_pReal,IEEE_quiet_NaN) ! -> return NaN and, hence, enforce cutback
rhoDotFlux = IEEE_value(1.0_pReal,IEEE_quiet_NaN) ! enforce cutback
return
endif
@ -1240,108 +1375,9 @@ module subroutine plastic_nonlocal_dotState(Mp, F, Fp, Temperature,timestep, &
enddo neighbors
endif
!****************************************************************************
!*** calculate dipole formation and annihilation
!*** formation by glide
do c = 1,2
rhoDotSingle2DipoleGlide(:,2*c-1) = -2.0_pReal * dUpper(:,c) / prm%burgers &
* ( rhoSgl(:,2*c-1) * abs(gdot(:,2*c)) & ! negative mobile --> positive mobile
+ rhoSgl(:,2*c) * abs(gdot(:,2*c-1)) & ! positive mobile --> negative mobile
+ abs(rhoSgl(:,2*c+4)) * abs(gdot(:,2*c-1))) ! positive mobile --> negative immobile
rhoDotSingle2DipoleGlide(:,2*c) = -2.0_pReal * dUpper(:,c) / prm%burgers &
* ( rhoSgl(:,2*c-1) * abs(gdot(:,2*c)) & ! negative mobile --> positive mobile
+ rhoSgl(:,2*c) * abs(gdot(:,2*c-1)) & ! positive mobile --> negative mobile
+ abs(rhoSgl(:,2*c+3)) * abs(gdot(:,2*c))) ! negative mobile --> positive immobile
rhoDotSingle2DipoleGlide(:,2*c+3) = -2.0_pReal * dUpper(:,c) / prm%burgers &
* rhoSgl(:,2*c+3) * abs(gdot(:,2*c)) ! negative mobile --> positive immobile
rhoDotSingle2DipoleGlide(:,2*c+4) = -2.0_pReal * dUpper(:,c) / prm%burgers &
* rhoSgl(:,2*c+4) * abs(gdot(:,2*c-1)) ! positive mobile --> negative immobile
rhoDotSingle2DipoleGlide(:,c+8) = abs(rhoDotSingle2DipoleGlide(:,2*c+3)) &
+ abs(rhoDotSingle2DipoleGlide(:,2*c+4)) &
- rhoDotSingle2DipoleGlide(:,2*c-1) &
- rhoDotSingle2DipoleGlide(:,2*c)
enddo
!*** athermal annihilation
rhoDotAthermalAnnihilation = 0.0_pReal
forall (c=1:2) &
rhoDotAthermalAnnihilation(:,c+8) = -2.0_pReal * dLower(:,c) / prm%burgers &
* ( 2.0_pReal * (rhoSgl(:,2*c-1) * abs(gdot(:,2*c)) + rhoSgl(:,2*c) * abs(gdot(:,2*c-1))) & ! was single hitting single
+ 2.0_pReal * (abs(rhoSgl(:,2*c+3)) * abs(gdot(:,2*c)) + abs(rhoSgl(:,2*c+4)) * abs(gdot(:,2*c-1))) & ! was single hitting immobile single or was immobile single hit by single
+ rhoDip(:,c) * (abs(gdot(:,2*c-1)) + abs(gdot(:,2*c)))) ! single knocks dipole constituent
! annihilated screw dipoles leave edge jogs behind on the colinear system
if (lattice_structure(ph) == LATTICE_fcc_ID) &
forall (s = 1:ns, prm%colinearSystem(s) > 0) &
rhoDotAthermalAnnihilation(prm%colinearSystem(s),1:2) = - rhoDotAthermalAnnihilation(s,10) &
* 0.25_pReal * sqrt(stt%rho_forest(s,of)) * (dUpper(s,2) + dLower(s,2)) * prm%edgeJogFactor
!*** thermally activated annihilation of edge dipoles by climb
rhoDotThermalAnnihilation = 0.0_pReal
selfDiffusion = prm%Dsd0 * exp(-prm%selfDiffusionEnergy / (kB * Temperature))
vClimb = prm%atomicVolume * selfDiffusion * prm%mu &
/ ( kB * Temperature * PI * (1.0_pReal-prm%nu) * (dUpper(:,1) + dLower(:,1)))
forall (s = 1:ns, dUpper(s,1) > dLower(s,1)) &
rhoDotThermalAnnihilation(s,9) = max(- 4.0_pReal * rhoDip(s,1) * vClimb(s) / (dUpper(s,1) - dLower(s,1)), &
- rhoDip(s,1) / timestep - rhoDotAthermalAnnihilation(s,9) &
- rhoDotSingle2DipoleGlide(s,9)) ! make sure that we do not annihilate more dipoles than we have
rhoDot = rhoDotFlux &
+ rhoDotMultiplication &
+ rhoDotSingle2DipoleGlide &
+ rhoDotAthermalAnnihilation &
+ rhoDotThermalAnnihilation
#ifdef DEBUG
if (iand(debug_level(debug_constitutive),debug_levelExtensive) /= 0 &
.and. ((debug_e == el .and. debug_i == ip)&
.or. .not. iand(debug_level(debug_constitutive),debug_levelSelective) /= 0 )) then
write(6,'(a,/,4(12x,12(e12.5,1x),/))') '<< CONST >> dislocation multiplication', &
rhoDotMultiplication(:,1:4) * timestep
write(6,'(a,/,8(12x,12(e12.5,1x),/))') '<< CONST >> dislocation flux', &
rhoDotFlux(:,1:8) * timestep
write(6,'(a,/,10(12x,12(e12.5,1x),/))') '<< CONST >> dipole formation by glide', &
rhoDotSingle2DipoleGlide * timestep
write(6,'(a,/,10(12x,12(e12.5,1x),/))') '<< CONST >> athermal dipole annihilation', &
rhoDotAthermalAnnihilation * timestep
write(6,'(a,/,2(12x,12(e12.5,1x),/))') '<< CONST >> thermally activated dipole annihilation', &
rhoDotThermalAnnihilation(:,9:10) * timestep
write(6,'(a,/,10(12x,12(e12.5,1x),/))') '<< CONST >> total density change', &
rhoDot * timestep
write(6,'(a,/,10(12x,12(f12.5,1x),/))') '<< CONST >> relative density change', &
rhoDot(:,1:8) * timestep / (abs(stt%rho(:,sgl))+1.0e-10), &
rhoDot(:,9:10) * timestep / (stt%rho(:,dip)+1.0e-10)
write(6,*)
endif
#endif
if ( any(rho(:,mob) + rhoDot(:,1:4) * timestep < -prm%atol_rho) &
.or. any(rho(:,dip) + rhoDot(:,9:10) * timestep < -prm%atol_rho)) then
#ifdef DEBUG
if (iand(debug_level(debug_constitutive),debug_levelExtensive) /= 0) then
write(6,'(a,i5,a,i2)') '<< CONST >> evolution rate leads to negative density at el ',el,' ip ',ip
write(6,'(a)') '<< CONST >> enforcing cutback !!!'
endif
#endif
plasticState(ph)%dotState = IEEE_value(1.0_pReal,IEEE_quiet_NaN)
else
dot%rho(:,of) = pack(rhoDot,.true.)
dot%gamma(:,of) = sum(gdot,2)
endif
end associate
end subroutine plastic_nonlocal_dotState
end function rhoDotFlux
!--------------------------------------------------------------------------------------------------

4
src/grid/grid_mech_FEM.f90
View File

@ -132,11 +132,11 @@ subroutine grid_mech_FEM_init
[grid(1)],[grid(2)],localK, &
mech_grid,ierr)
CHKERRQ(ierr)
call DMDASetUniformCoordinates(mech_grid,0.0_pReal,geomSize(1),0.0_pReal,geomSize(2),0.0_pReal,geomSize(3),ierr)
CHKERRQ(ierr)
call SNESSetDM(mech_snes,mech_grid,ierr); CHKERRQ(ierr)
call DMsetFromOptions(mech_grid,ierr); CHKERRQ(ierr)
call DMsetUp(mech_grid,ierr); CHKERRQ(ierr)
call DMDASetUniformCoordinates(mech_grid,0.0_pReal,geomSize(1),0.0_pReal,geomSize(2),0.0_pReal,geomSize(3),ierr)
CHKERRQ(ierr)
call DMCreateGlobalVector(mech_grid,solution_current,ierr); CHKERRQ(ierr)
call DMCreateGlobalVector(mech_grid,solution_lastInc,ierr); CHKERRQ(ierr)
call DMCreateGlobalVector(mech_grid,solution_rate ,ierr); CHKERRQ(ierr)

369
src/rotations.f90
View File

@ -3,27 +3,27 @@
! Modified 2017-2020, Martin Diehl/Max-Planck-Institut für Eisenforschung GmbH
! All rights reserved.
!
! Redistribution and use in source and binary forms, with or without modification, are
! Redistribution and use in source and binary forms, with or without modification, are
! permitted provided that the following conditions are met:
!
! - Redistributions of source code must retain the above copyright notice, this list
! - Redistributions of source code must retain the above copyright notice, this list
! of conditions and the following disclaimer.
! - Redistributions in binary form must reproduce the above copyright notice, this
! list of conditions and the following disclaimer in the documentation and/or
! - Redistributions in binary form must reproduce the above copyright notice, this
! list of conditions and the following disclaimer in the documentation and/or
! other materials provided with the distribution.
! - Neither the names of Marc De Graef, Carnegie Mellon University nor the names
! of its contributors may be used to endorse or promote products derived from
! - Neither the names of Marc De Graef, Carnegie Mellon University nor the names
! of its contributors may be used to endorse or promote products derived from
! this software without specific prior written permission.
!
! THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
! AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
! IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
! ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
! LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
! DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
! SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
! CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
! OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
! THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
! AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
! IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
! ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
! LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
! DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
! SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
! CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
! OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
! USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
! ###################################################################
@ -31,7 +31,7 @@
!> @author Marc De Graef, Carnegie Mellon University
!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
!> @brief rotation storage and conversion
!> @details: rotation is internally stored as quaternion. It can be inialized from different
!> @details: rotation is internally stored as quaternion. It can be inialized from different
!> representations and also returns itself in different representations.
!
! All methods and naming conventions based on Rowenhorst_etal2015
@ -50,9 +50,8 @@ module rotations
use prec
use IO
use math
use Lambert
use quaternions
implicit none
private
@ -80,7 +79,19 @@ module rotations
procedure, public :: misorientation
procedure, public :: standardize
end type rotation
real(pReal), parameter :: &
SPI = sqrt(PI), &
PREF = sqrt(6.0_pReal/PI), &
A = PI**(5.0_pReal/6.0_pReal)/6.0_pReal**(1.0_pReal/6.0_pReal), &
AP = PI**(2.0_pReal/3.0_pReal), &
SC = A/AP, &
BETA = A/2.0_pReal, &
R1 = (3.0_pReal*PI/4.0_pReal)**(1.0_pReal/3.0_pReal), &
R2 = sqrt(2.0_pReal), &
PI12 = PI/12.0_pReal, &
PREK = R1 * 2.0_pReal**(1.0_pReal/4.0_pReal)/BETA
public :: &
rotations_init, &
eu2om
@ -106,16 +117,16 @@ pure function asQuaternion(self)
class(rotation), intent(in) :: self
real(pReal), dimension(4) :: asQuaternion
asQuaternion = self%q%asArray()
end function asQuaternion
!---------------------------------------------------------------------------------------------------
pure function asEulers(self)
class(rotation), intent(in) :: self
real(pReal), dimension(3) :: asEulers
asEulers = qu2eu(self%q%asArray())
end function asEulers
@ -124,16 +135,16 @@ pure function asAxisAngle(self)
class(rotation), intent(in) :: self
real(pReal), dimension(4) :: asAxisAngle
asAxisAngle = qu2ax(self%q%asArray())
end function asAxisAngle
!---------------------------------------------------------------------------------------------------
pure function asMatrix(self)
class(rotation), intent(in) :: self
real(pReal), dimension(3,3) :: asMatrix
asMatrix = qu2om(self%q%asArray())
end function asMatrix
@ -142,20 +153,20 @@ pure function asRodrigues(self)
class(rotation), intent(in) :: self
real(pReal), dimension(4) :: asRodrigues
asRodrigues = qu2ro(self%q%asArray())
end function asRodrigues
!---------------------------------------------------------------------------------------------------
pure function asHomochoric(self)
class(rotation), intent(in) :: self
real(pReal), dimension(3) :: asHomochoric
asHomochoric = qu2ho(self%q%asArray())
end function asHomochoric
!---------------------------------------------------------------------------------------------------
! Initialize rotation from different representations
!---------------------------------------------------------------------------------------------------
@ -207,7 +218,7 @@ subroutine fromAxisAngle(self,ax,degrees,P)
else
angle = merge(ax(4)*INRAD,ax(4),degrees)
endif
if (.not. present(P)) then
axis = ax(1:3)
else
@ -217,7 +228,7 @@ subroutine fromAxisAngle(self,ax,degrees,P)
if(dNeq(norm2(axis),1.0_pReal) .or. angle < 0.0_pReal .or. angle > PI) &
call IO_error(402,ext_msg='fromAxisAngle')
self%q = ax2qu([axis,angle])
end subroutine fromAxisAngle
@ -240,10 +251,10 @@ end subroutine fromMatrix
!> @brief: Rotate a rotation
!---------------------------------------------------------------------------------------------------
pure elemental function rotRot__(self,R) result(rRot)
type(rotation) :: rRot
class(rotation), intent(in) :: self,R
rRot = rotation(self%q*R%q)
call rRot%standardize()
@ -251,12 +262,12 @@ end function rotRot__
!---------------------------------------------------------------------------------------------------
!> @brief quaternion representation with positive q
!> @brief quaternion representation with positive q
!---------------------------------------------------------------------------------------------------
pure elemental subroutine standardize(self)
class(rotation), intent(inout) :: self
if (real(self%q) < 0.0_pReal) self%q = self%q%homomorphed()
end subroutine standardize
@ -267,22 +278,22 @@ end subroutine standardize
!> @brief rotate a vector passively (default) or actively
!---------------------------------------------------------------------------------------------------
pure function rotVector(self,v,active) result(vRot)
real(pReal), dimension(3) :: vRot
class(rotation), intent(in) :: self
real(pReal), intent(in), dimension(3) :: v
logical, intent(in), optional :: active
real(pReal), dimension(3) :: v_normed
type(quaternion) :: q
logical :: passive
if (present(active)) then
passive = .not. active
else
passive = .true.
endif
if (dEq0(norm2(v))) then
vRot = v
else
@ -304,12 +315,12 @@ end function rotVector
!> @details: rotation is based on rotation matrix
!---------------------------------------------------------------------------------------------------
pure function rotTensor2(self,T,active) result(tRot)
real(pReal), dimension(3,3) :: tRot
class(rotation), intent(in) :: self
real(pReal), intent(in), dimension(3,3) :: T
logical, intent(in), optional :: active
logical :: passive
if (present(active)) then
@ -317,7 +328,7 @@ pure function rotTensor2(self,T,active) result(tRot)
else
passive = .true.
endif
if (passive) then
tRot = matmul(matmul(self%asMatrix(),T),transpose(self%asMatrix()))
else
@ -339,7 +350,7 @@ pure function rotTensor4(self,T,active) result(tRot)
class(rotation), intent(in) :: self
real(pReal), intent(in), dimension(3,3,3,3) :: T
logical, intent(in), optional :: active
real(pReal), dimension(3,3) :: R
integer :: i,j,k,l,m,n,o,p
@ -370,7 +381,7 @@ pure function rotTensor4sym(self,T,active) result(tRot)
class(rotation), intent(in) :: self
real(pReal), intent(in), dimension(6,6) :: T
logical, intent(in), optional :: active
if (present(active)) then
tRot = math_sym3333to66(rotTensor4(self,math_66toSym3333(T),active))
else
@ -384,10 +395,10 @@ end function rotTensor4sym
!> @brief misorientation
!---------------------------------------------------------------------------------------------------
pure elemental function misorientation(self,other)
type(rotation) :: misorientation
class(rotation), intent(in) :: self, other
misorientation%q = other%q * conjg(self%q)
end function misorientation
@ -401,7 +412,7 @@ pure function qu2om(qu) result(om)
real(pReal), intent(in), dimension(4) :: qu
real(pReal), dimension(3,3) :: om
real(pReal) :: qq
qq = qu(1)**2-sum(qu(2:4)**2)
@ -431,13 +442,13 @@ pure function qu2eu(qu) result(eu)
real(pReal), intent(in), dimension(4) :: qu
real(pReal), dimension(3) :: eu
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(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
@ -460,7 +471,7 @@ pure function qu2ax(qu) result(ax)
real(pReal), intent(in), dimension(4) :: qu
real(pReal), dimension(4) :: ax
real(pReal) :: omega, s
if (dEq0(sum(qu(2:4)**2))) then
@ -481,13 +492,13 @@ end function qu2ax
!> @brief convert unit quaternion to Rodrigues vector
!---------------------------------------------------------------------------------------------------
pure function qu2ro(qu) result(ro)
real(pReal), intent(in), dimension(4) :: qu
real(pReal), dimension(4) :: ro
real(pReal) :: s
real(pReal), parameter :: thr = 1.0e-8_pReal
if (abs(qu(1)) < thr) then
ro = [qu(2), qu(3), qu(4), IEEE_value(1.0_pReal,IEEE_positive_inf)]
else
@ -497,7 +508,7 @@ pure function qu2ro(qu) result(ro)
else
ro = [qu(2)/s,qu(3)/s,qu(4)/s, tan(acos(math_clip(qu(1),-1.0_pReal,1.0_pReal)))]
endif
end if
end function qu2ro
@ -511,12 +522,12 @@ pure function qu2ho(qu) result(ho)
real(pReal), intent(in), dimension(4) :: qu
real(pReal), dimension(3) :: ho
real(pReal) :: omega, f
omega = 2.0 * acos(math_clip(qu(1),-1.0_pReal,1.0_pReal))
if (dEq0(omega)) then
if (dEq0(omega,tol=1.e-5_pReal)) then
ho = [ 0.0_pReal, 0.0_pReal, 0.0_pReal ]
else
ho = qu(2:4)
@ -532,7 +543,7 @@ end function qu2ho
!> @brief convert unit quaternion to cubochoric
!---------------------------------------------------------------------------------------------------
pure function qu2cu(qu) result(cu)
real(pReal), intent(in), dimension(4) :: qu
real(pReal), dimension(3) :: cu
@ -565,18 +576,18 @@ pure function om2eu(om) result(eu)
real(pReal), intent(in), dimension(3,3) :: om
real(pReal), dimension(3) :: eu
real(pReal) :: zeta
if (abs(om(3,3)) < 1.0_pReal) then
zeta = 1.0_pReal/sqrt(1.0_pReal-om(3,3)**2.0_pReal)
eu = [atan2(om(3,1)*zeta,-om(3,2)*zeta), &
acos(om(3,3)), &
atan2(om(1,3)*zeta, om(2,3)*zeta)]
else
else
eu = [atan2(om(1,2),om(1,1)), 0.5_pReal*PI*(1.0_pReal-om(3,3)),0.0_pReal ]
end if
where(eu<0.0_pReal) eu = mod(eu+2.0_pReal*PI,[2.0_pReal*PI,PI,2.0_pReal*PI])
end function om2eu
@ -588,19 +599,19 @@ function om2ax(om) result(ax)
real(pReal), intent(in), dimension(3,3) :: om
real(pReal), dimension(4) :: ax
real(pReal) :: t
real(pReal), dimension(3) :: Wr, Wi
real(pReal), dimension((64+2)*3) :: work
real(pReal), dimension(3,3) :: VR, devNull, om_
integer :: ierr, i
om_ = om
! first get the rotation angle
t = 0.5_pReal * (math_trace33(om) - 1.0_pReal)
ax(4) = acos(math_clip(t,-1.0_pReal,1.0_pReal))
if (dEq0(ax(4))) then
ax(1:3) = [ 0.0_pReal, 0.0_pReal, 1.0_pReal ]
else
@ -674,7 +685,7 @@ pure function eu2qu(eu) result(qu)
real(pReal) :: cPhi, sPhi
ee = 0.5_pReal*eu
cPhi = cos(ee(2))
sPhi = sin(ee(2))
@ -692,15 +703,15 @@ end function eu2qu
!> @brief Euler angles to orientation matrix
!---------------------------------------------------------------------------------------------------
pure function eu2om(eu) result(om)
real(pReal), intent(in), dimension(3) :: eu
real(pReal), dimension(3,3) :: om
real(pReal), dimension(3) :: c, s
real(pReal), dimension(3) :: c, s
c = cos(eu)
s = sin(eu)
om(1,1) = c(1)*c(3)-s(1)*s(3)*c(2)
om(1,2) = s(1)*c(3)+c(1)*s(3)*c(2)
om(1,3) = s(3)*s(2)
@ -710,7 +721,7 @@ pure function eu2om(eu) result(om)
om(3,1) = s(1)*s(2)
om(3,2) = -c(1)*s(2)
om(3,3) = c(2)
where(dEq0(om)) om = 0.0_pReal
end function eu2om
@ -721,19 +732,19 @@ end function eu2om
!> @brief convert euler to axis angle
!---------------------------------------------------------------------------------------------------
pure function eu2ax(eu) result(ax)
real(pReal), intent(in), dimension(3) :: eu
real(pReal), dimension(4) :: ax
real(pReal) :: t, delta, tau, alpha, sigma
t = tan(eu(2)*0.5_pReal)
sigma = 0.5_pReal*(eu(1)+eu(3))
delta = 0.5_pReal*(eu(1)-eu(3))
tau = sqrt(t**2+sin(sigma)**2)
alpha = merge(PI, 2.0_pReal*atan(tau/cos(sigma)), dEq(sigma,PI*0.5_pReal,tol=1.0e-15_pReal))
if (dEq0(alpha)) then ! return a default identity axis-angle pair
ax = [ 0.0_pReal, 0.0_pReal, 1.0_pReal, 0.0_pReal ]
else
@ -741,7 +752,7 @@ pure function eu2ax(eu) result(ax)
ax(4) = alpha
if (alpha < 0.0_pReal) ax = -ax ! ensure alpha is positive
end if
end function eu2ax
@ -753,7 +764,7 @@ pure function eu2ro(eu) result(ro)
real(pReal), intent(in), dimension(3) :: eu
real(pReal), dimension(4) :: ro
ro = eu2ax(eu)
if (ro(4) >= PI) then
ro(4) = IEEE_value(ro(4),IEEE_positive_inf)
@ -762,7 +773,7 @@ pure function eu2ro(eu) result(ro)
else
ro(4) = tan(ro(4)*0.5_pReal)
end if
end function eu2ro
@ -799,7 +810,7 @@ end function eu2cu
!> @brief convert axis angle pair to quaternion
!---------------------------------------------------------------------------------------------------
pure function ax2qu(ax) result(qu)
real(pReal), intent(in), dimension(4) :: ax
real(pReal), dimension(4) :: qu
@ -825,7 +836,7 @@ pure function ax2om(ax) result(om)
real(pReal), intent(in), dimension(4) :: ax
real(pReal), dimension(3,3) :: om
real(pReal) :: q, c, s, omc
c = cos(ax(4))
@ -839,11 +850,11 @@ pure function ax2om(ax) result(om)
q = omc*ax(1)*ax(2)
om(1,2) = q + s*ax(3)
om(2,1) = q - s*ax(3)
q = omc*ax(2)*ax(3)
om(2,3) = q + s*ax(1)
om(3,2) = q - s*ax(1)
q = omc*ax(3)*ax(1)
om(3,1) = q + s*ax(2)
om(1,3) = q - s*ax(2)
@ -875,12 +886,12 @@ pure function ax2ro(ax) result(ro)
real(pReal), intent(in), dimension(4) :: ax
real(pReal), dimension(4) :: ro
real(pReal), parameter :: thr = 1.0e-7_pReal
if (dEq0(ax(4))) then
ro = [ 0.0_pReal, 0.0_pReal, P, 0.0_pReal ]
else
else
ro(1:3) = ax(1:3)
! we need to deal with the 180 degree case
ro(4) = merge(IEEE_value(ro(4),IEEE_positive_inf),tan(ax(4)*0.5_pReal),abs(ax(4)-PI) < thr)
@ -897,9 +908,9 @@ pure function ax2ho(ax) result(ho)
real(pReal), intent(in), dimension(4) :: ax
real(pReal), dimension(3) :: ho
real(pReal) :: f
f = 0.75_pReal * ( ax(4) - sin(ax(4)) )
f = f**(1.0_pReal/3.0_pReal)
ho = ax(1:3) * f
@ -916,7 +927,7 @@ function ax2cu(ax) result(cu)
real(pReal), intent(in), dimension(4) :: ax
real(pReal), dimension(3) :: cu
cu = ho2cu(ax2ho(ax))
cu = ho2cu(ax2ho(ax))
end function ax2cu
@ -929,7 +940,7 @@ pure function ro2qu(ro) result(qu)
real(pReal), intent(in), dimension(4) :: ro
real(pReal), dimension(4) :: qu
qu = ax2qu(ro2ax(ro))
end function ro2qu
@ -957,7 +968,7 @@ pure function ro2eu(ro) result(eu)
real(pReal), intent(in), dimension(4) :: ro
real(pReal), dimension(3) :: eu
eu = om2eu(ro2om(ro))
end function ro2eu
@ -971,14 +982,14 @@ pure function ro2ax(ro) result(ax)
real(pReal), intent(in), dimension(4) :: ro
real(pReal), dimension(4) :: ax
real(pReal) :: ta, angle
ta = ro(4)
if (.not. IEEE_is_finite(ta)) then
ax = [ ro(1), ro(2), ro(3), PI ]
elseif (dEq0(ta)) then
elseif (dEq0(ta)) then
ax = [ 0.0_pReal, 0.0_pReal, 1.0_pReal, 0.0_pReal ]
else
angle = 2.0_pReal*atan(ta)
@ -997,9 +1008,9 @@ pure function ro2ho(ro) result(ho)
real(pReal), intent(in), dimension(4) :: ro
real(pReal), dimension(3) :: ho
real(pReal) :: f
if (dEq0(norm2(ro(1:3)))) then
ho = [ 0.0_pReal, 0.0_pReal, 0.0_pReal ]
else
@ -1074,26 +1085,26 @@ pure function ho2ax(ho) result(ax)
real(pReal), intent(in), dimension(3) :: ho
real(pReal), dimension(4) :: ax
integer :: i
real(pReal) :: hmag_squared, s, hm
real(pReal), parameter, dimension(16) :: &
tfit = [ 1.0000000000018852_pReal, -0.5000000002194847_pReal, &
-0.024999992127593126_pReal, -0.003928701544781374_pReal, &
-0.0008152701535450438_pReal, -0.0002009500426119712_pReal, &
-0.00002397986776071756_pReal, -0.00008202868926605841_pReal, &
+0.00012448715042090092_pReal, -0.0001749114214822577_pReal, &
+0.0001703481934140054_pReal, -0.00012062065004116828_pReal, &
+0.000059719705868660826_pReal, -0.00001980756723965647_pReal, &
tfit = [ 1.0000000000018852_pReal, -0.5000000002194847_pReal, &
-0.024999992127593126_pReal, -0.003928701544781374_pReal, &
-0.0008152701535450438_pReal, -0.0002009500426119712_pReal, &
-0.00002397986776071756_pReal, -0.00008202868926605841_pReal, &
+0.00012448715042090092_pReal, -0.0001749114214822577_pReal, &
+0.0001703481934140054_pReal, -0.00012062065004116828_pReal, &
+0.000059719705868660826_pReal, -0.00001980756723965647_pReal, &
+0.000003953714684212874_pReal, -0.00000036555001439719544_pReal ]
! normalize h and store the magnitude
hmag_squared = sum(ho**2.0_pReal)
if (dEq0(hmag_squared)) then
ax = [ 0.0_pReal, 0.0_pReal, 1.0_pReal, 0.0_pReal ]
else
hm = hmag_squared
! convert the magnitude to the rotation angle
s = tfit(1) + tfit(2) * hmag_squared
do i=3,16
@ -1120,16 +1131,56 @@ pure function ho2ro(ho) result(ro)
end function ho2ro
!---------------------------------------------------------------------------------------------------
!--------------------------------------------------------------------------
!> @author Marc De Graef, Carnegie Mellon University
!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
!> @brief convert homochoric to cubochoric
!---------------------------------------------------------------------------------------------------
!--------------------------------------------------------------------------
pure function ho2cu(ho) result(cu)
real(pReal), intent(in), dimension(3) :: ho
real(pReal), dimension(3) :: cu
real(pReal), intent(in), dimension(3) :: ho
real(pReal), dimension(3) :: cu, xyz1, xyz3
real(pReal), dimension(2) :: Tinv, xyz2
real(pReal) :: rs, qxy, q2, sq2, q, tt
integer, dimension(3,2) :: p
cu = Lambert_BallToCube(ho)
rs = norm2(ho)
if (rs > R1+1.e-6_pReal) then
cu = IEEE_value(cu,IEEE_positive_inf)
return
endif
center: if (all(dEq0(ho))) then
cu = 0.0_pReal
else center
p = GetPyramidOrder(ho)
xyz3 = ho(p(:,1))
! inverse M_3
xyz2 = xyz3(1:2) * sqrt( 2.0*rs/(rs+abs(xyz3(3))) )
! inverse M_2
qxy = sum(xyz2**2)
special: if (dEq0(qxy)) then
Tinv = 0.0_pReal
else special
q2 = qxy + maxval(abs(xyz2))**2
sq2 = sqrt(q2)
q = (beta/R2/R1) * sqrt(q2*qxy/(q2-maxval(abs(xyz2))*sq2))
tt = (minval(abs(xyz2))**2+maxval(abs(xyz2))*sq2)/R2/qxy
Tinv = q * sign(1.0_pReal,xyz2) * merge([ 1.0_pReal, acos(math_clip(tt,-1.0_pReal,1.0_pReal))/PI12], &
[ acos(math_clip(tt,-1.0_pReal,1.0_pReal))/PI12, 1.0_pReal], &
abs(xyz2(2)) <= abs(xyz2(1)))
endif special
! inverse M_1
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
cu = xyz1(p(:,2))
endif center
end function ho2cu
@ -1204,25 +1255,93 @@ pure function cu2ro(cu) result(ro)
end function cu2ro
!---------------------------------------------------------------------------------------------------
!--------------------------------------------------------------------------
!> @author Marc De Graef, Carnegie Mellon University
!> @brief convert cubochoric to homochoric
!---------------------------------------------------------------------------------------------------
!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
!> @brief map from 3D cubic grid to 3D ball
!--------------------------------------------------------------------------
pure function cu2ho(cu) result(ho)
real(pReal), intent(in), dimension(3) :: cu
real(pReal), dimension(3) :: ho
real(pReal), intent(in), dimension(3) :: cu
real(pReal), dimension(3) :: ho, LamXYZ, XYZ
real(pReal), dimension(2) :: T
real(pReal) :: c, s, q
real(pReal), parameter :: eps = 1.0e-8_pReal
integer, dimension(3,2) :: p
integer, dimension(2) :: order
ho = Lambert_CubeToBall(cu)
if (maxval(abs(cu)) > AP/2.0+eps) then
ho = IEEE_value(cu,IEEE_positive_inf)
return
end if
! transform to the sphere grid via the curved square, and intercept the zero point
center: if (all(dEq0(cu))) then
ho = 0.0_pReal
else center
! get pyramide and scale by grid parameter ratio
p = GetPyramidOrder(cu)
XYZ = cu(p(:,1)) * sc
! intercept all the points along the z-axis
special: if (all(dEq0(XYZ(1:2)))) then
LamXYZ = [ 0.0_pReal, 0.0_pReal, pref * XYZ(3) ]
else special
order = merge( [2,1], [1,2], abs(XYZ(2)) <= abs(XYZ(1))) ! order of absolute values of XYZ
q = PI12 * XYZ(order(1))/XYZ(order(2)) ! smaller by larger
c = cos(q)
s = sin(q)
q = prek * XYZ(order(2))/ sqrt(R2-c)
T = [ (R2*c - 1.0), R2 * s] * q
! transform to sphere grid (inverse Lambert)
! [note that there is no need to worry about dividing by zero, since XYZ(3) can not become zero]
c = sum(T**2)
s = Pi * c/(24.0*XYZ(3)**2)
c = sPi * c / sqrt(24.0_pReal) / XYZ(3)
q = sqrt( 1.0 - s )
LamXYZ = [ T(order(2)) * q, T(order(1)) * q, pref * XYZ(3) - c ]
endif special
! reverse the coordinates back to order according to the original pyramid number
ho = LamXYZ(p(:,2))
endif center
end function cu2ho
!--------------------------------------------------------------------------
!> @author Marc De Graef, Carnegie Mellon University
!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
!> @brief determine to which pyramid a point in a cubic grid belongs
!--------------------------------------------------------------------------
pure function GetPyramidOrder(xyz)
real(pReal),intent(in),dimension(3) :: xyz
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 = 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 = 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 = reshape([[3,1,2],[2,3,1]],[3,2])
else
GetPyramidOrder = -1 ! should be impossible, but might simplify debugging
end if
end function GetPyramidOrder
!--------------------------------------------------------------------------------------------------
!> @brief check correctness of some rotations functions
!--------------------------------------------------------------------------------------------------
subroutine unitTest
type(rotation) :: R
real(pReal), dimension(4) :: qu, ax, ro
real(pReal), dimension(3) :: x, eu, ho, v3
@ -1233,7 +1352,7 @@ subroutine unitTest
integer :: i
do i=1,10
msg = ''
#if defined(__GFORTRAN__) && __GNUC__<9
@ -1307,15 +1426,15 @@ subroutine unitTest
#endif
call R%fromMatrix(om)
call random_number(v3)
if(all(dNeq(R%rotVector(R%rotVector(v3),active=.true.),v3,1.0e-12_pReal))) &
msg = trim(msg)//'rotVector,'
call random_number(t33)
if(all(dNeq(R%rotTensor2(R%rotTensor2(t33),active=.true.),t33,1.0e-12_pReal))) &
msg = trim(msg)//'rotTensor2,'
call random_number(t3333)
if(all(dNeq(R%rotTensor4(R%rotTensor4(t3333),active=.true.),t3333,1.0e-12_pReal))) &
msg = trim(msg)//'rotTensor4,'