Merge branch 'development' into misc-improvements
This commit is contained in:
Martin Diehl
commit
a279785149
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@ -1,164 +0,0 @@
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####################################################################################################
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# Code below available according to the following conditions on
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# https://github.com/MarDiehl/3Drotations
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####################################################################################################
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# Copyright (c) 2017-2019, Martin Diehl/Max-Planck-Institut für Eisenforschung GmbH
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# Copyright (c) 2013-2014, Marc De Graef/Carnegie Mellon University
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# All rights reserved.
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#
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# Redistribution and use in source and binary forms, with or without modification, are
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# permitted provided that the following conditions are met:
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#
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# - Redistributions of source code must retain the above copyright notice, this list
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# of conditions and the following disclaimer.
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# - Redistributions in binary form must reproduce the above copyright notice, this
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# list of conditions and the following disclaimer in the documentation and/or
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# other materials provided with the distribution.
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# - Neither the names of Marc De Graef, Carnegie Mellon University nor the names
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# of its contributors may be used to endorse or promote products derived from
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# this software without specific prior written permission.
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#
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# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
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# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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# ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
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# LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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# DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
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# SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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# CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
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# OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
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# USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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####################################################################################################
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import numpy as np
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sc = np.pi**(1./6.)/6.**(1./6.)
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beta = np.pi**(5./6.)/6.**(1./6.)/2.
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R1 = (3.*np.pi/4.)**(1./3.)
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def cube_to_ball(cube):
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"""
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Map a point in a uniform refinable cubical grid to a point on a uniform refinable grid on a ball.
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Parameters
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----------
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cube : numpy.ndarray
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coordinates of a point in a uniform refinable cubical grid.
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References
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----------
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D. Roşca et al., Modelling and Simulation in Materials Science and Engineering 22:075013, 2014
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https://doi.org/10.1088/0965-0393/22/7/075013
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"""
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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
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# transform to the sphere grid via the curved square, and intercept the zero point
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if np.allclose(cube_,0.0,rtol=0.0,atol=1.0e-16):
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ball = np.zeros(3)
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else:
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# get pyramide and scale by grid parameter ratio
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p = _get_order(cube_)
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XYZ = cube_[p[0]] * sc
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# intercept all the points along the z-axis
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if np.allclose(XYZ[0:2],0.0,rtol=0.0,atol=1.0e-16):
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ball = np.array([0.0, 0.0, np.sqrt(6.0/np.pi) * XYZ[2]])
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else:
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order = [1,0] if np.abs(XYZ[1]) <= np.abs(XYZ[0]) else [0,1]
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q = np.pi/12.0 * XYZ[order[0]]/XYZ[order[1]]
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c = np.cos(q)
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s = np.sin(q)
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q = R1*2.0**0.25/beta * XYZ[order[1]] / np.sqrt(np.sqrt(2.0)-c)
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T = np.array([ (np.sqrt(2.0)*c - 1.0), np.sqrt(2.0) * s]) * q
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# transform to sphere grid (inverse Lambert)
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# note that there is no need to worry about dividing by zero, since XYZ[2] can not become zero
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c = np.sum(T**2)
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s = c * np.pi/24.0 /XYZ[2]**2
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c = c * np.sqrt(np.pi/24.0)/XYZ[2]
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q = np.sqrt( 1.0 - s )
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ball = np.array([ T[order[1]] * q, T[order[0]] * q, np.sqrt(6.0/np.pi) * XYZ[2] - c ])
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# reverse the coordinates back to the regular order according to the original pyramid number
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ball = ball[p[1]]
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return ball
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def ball_to_cube(ball):
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"""
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Map a point on a uniform refinable grid on a ball to a point in a uniform refinable cubical grid.
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Parameters
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----------
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ball : numpy.ndarray
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coordinates of a point on a uniform refinable grid on a ball.
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References
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----------
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D. Roşca et al., Modelling and Simulation in Materials Science and Engineering 22:075013, 2014
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https://doi.org/10.1088/0965-0393/22/7/075013
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"""
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ball_ = ball/np.linalg.norm(ball)*R1 if np.isclose(np.linalg.norm(ball),R1,atol=1e-6) else ball
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rs = np.linalg.norm(ball_)
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if np.allclose(ball_,0.0,rtol=0.0,atol=1.0e-16):
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cube = np.zeros(3)
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else:
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p = _get_order(ball_)
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xyz3 = ball_[p[0]]
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# inverse M_3
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xyz2 = xyz3[0:2] * np.sqrt( 2.0*rs/(rs+np.abs(xyz3[2])) )
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# inverse M_2
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qxy = np.sum(xyz2**2)
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if np.isclose(qxy,0.0,rtol=0.0,atol=1.0e-16):
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Tinv = np.zeros(2)
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else:
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q2 = qxy + np.max(np.abs(xyz2))**2
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sq2 = np.sqrt(q2)
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q = (beta/np.sqrt(2.0)/R1) * np.sqrt(q2*qxy/(q2-np.max(np.abs(xyz2))*sq2))
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tt = np.clip((np.min(np.abs(xyz2))**2+np.max(np.abs(xyz2))*sq2)/np.sqrt(2.0)/qxy,-1.0,1.0)
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Tinv = np.array([1.0,np.arccos(tt)/np.pi*12.0]) if np.abs(xyz2[1]) <= np.abs(xyz2[0]) else \
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np.array([np.arccos(tt)/np.pi*12.0,1.0])
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Tinv = q * np.where(xyz2<0.0,-Tinv,Tinv)
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# inverse M_1
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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
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# reverse the coordinates back to the regular order according to the original pyramid number
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cube = cube[p[1]]
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return cube
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def _get_order(xyz):
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"""
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Get order of the coordinates.
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Depending on the pyramid in which the point is located, the order need to be adjusted.
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Parameters
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----------
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xyz : numpy.ndarray
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coordinates of a point on a uniform refinable grid on a ball or
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in a uniform refinable cubical grid.
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References
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----------
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D. Roşca et al., Modelling and Simulation in Materials Science and Engineering 22:075013, 2014
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https://doi.org/10.1088/0965-0393/22/7/075013
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"""
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if (abs(xyz[0])<= xyz[2]) and (abs(xyz[1])<= xyz[2]) or \
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(abs(xyz[0])<=-xyz[2]) and (abs(xyz[1])<=-xyz[2]):
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return [[0,1,2],[0,1,2]]
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elif (abs(xyz[2])<= xyz[0]) and (abs(xyz[1])<= xyz[0]) or \
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(abs(xyz[2])<=-xyz[0]) and (abs(xyz[1])<=-xyz[0]):
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return [[1,2,0],[2,0,1]]
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elif (abs(xyz[0])<= xyz[1]) and (abs(xyz[2])<= xyz[1]) or \
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(abs(xyz[0])<=-xyz[1]) and (abs(xyz[2])<=-xyz[1]):
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return [[2,0,1],[1,2,0]]
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@ -1,10 +1,14 @@
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import numpy as np
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from ._Lambert import ball_to_cube, cube_to_ball
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from . import mechanics
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_P = -1
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# parameters for conversion from/to cubochoric
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_sc = np.pi**(1./6.)/6.**(1./6.)
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_beta = np.pi**(5./6.)/6.**(1./6.)/2.
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_R1 = (3.*np.pi/4.)**(1./3.)
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def iszero(a):
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return np.isclose(a,0.0,atol=1.0e-12,rtol=0.0)
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@ -237,7 +241,7 @@ class Rotation:
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"""Homochoric vector: (h_1, h_2, h_3)."""
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return Rotation.qu2ho(self.quaternion)
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def asCubochoric(self):
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def as_cubochoric(self):
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"""Cubochoric vector: (c_1, c_2, c_3)."""
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return Rotation.qu2cu(self.quaternion)
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@ -261,6 +265,7 @@ class Rotation:
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asMatrix = as_matrix
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asRodrigues = as_Rodrigues
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asHomochoric = as_homochoric
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asCubochoric = as_cubochoric
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################################################################################################
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# Static constructors. The input data needs to follow the conventions, options allow to
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@ -382,7 +387,7 @@ class Rotation:
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return Rotation(Rotation.ho2qu(ho))
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@staticmethod
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def fromCubochoric(cubochoric,
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def from_cubochoric(cubochoric,
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P = -1):
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cu = np.array(cubochoric,dtype=float)
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@ -457,6 +462,7 @@ class Rotation:
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fromMatrix = from_matrix
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fromRodrigues = from_Rodrigues
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fromHomochoric = from_homochoric
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fromCubochoric = from_cubochoric
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fromRandom = from_random
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####################################################################################################
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@ -1047,12 +1053,71 @@ class Rotation:
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@staticmethod
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def ho2cu(ho):
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"""Homochoric vector to cubochoric vector."""
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if len(ho.shape) == 1:
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return ball_to_cube(ho)
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else:
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raise NotImplementedError('Support for multiple rotations missing')
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"""
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Homochoric vector to cubochoric vector.
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References
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----------
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D. Roşca et al., Modelling and Simulation in Materials Science and Engineering 22:075013, 2014
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https://doi.org/10.1088/0965-0393/22/7/075013
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"""
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if len(ho.shape) == 1:
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rs = np.linalg.norm(ho)
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if np.allclose(ho,0.0,rtol=0.0,atol=1.0e-16):
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cu = np.zeros(3)
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else:
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xyz3 = ho[Rotation._get_pyramid_order(ho,'forward')]
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# inverse M_3
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xyz2 = xyz3[0:2] * np.sqrt( 2.0*rs/(rs+np.abs(xyz3[2])) )
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# inverse M_2
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qxy = np.sum(xyz2**2)
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if np.isclose(qxy,0.0,rtol=0.0,atol=1.0e-16):
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Tinv = np.zeros(2)
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else:
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q2 = qxy + np.max(np.abs(xyz2))**2
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sq2 = np.sqrt(q2)
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q = (_beta/np.sqrt(2.0)/_R1) * np.sqrt(q2*qxy/(q2-np.max(np.abs(xyz2))*sq2))
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tt = np.clip((np.min(np.abs(xyz2))**2+np.max(np.abs(xyz2))*sq2)/np.sqrt(2.0)/qxy,-1.0,1.0)
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Tinv = np.array([1.0,np.arccos(tt)/np.pi*12.0]) if np.abs(xyz2[1]) <= np.abs(xyz2[0]) else \
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np.array([np.arccos(tt)/np.pi*12.0,1.0])
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Tinv = q * np.where(xyz2<0.0,-Tinv,Tinv)
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# inverse M_1
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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
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cu = cu[Rotation._get_pyramid_order(ho,'backward')]
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else:
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rs = np.linalg.norm(ho,axis=-1,keepdims=True)
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xyz3 = np.take_along_axis(ho,Rotation._get_pyramid_order(ho,'forward'),-1)
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with np.errstate(invalid='ignore',divide='ignore'):
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# inverse M_3
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xyz2 = xyz3[...,0:2] * np.sqrt( 2.0*rs/(rs+np.abs(xyz3[...,2:3])) )
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qxy = np.sum(xyz2**2,axis=-1,keepdims=True)
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q2 = qxy + np.max(np.abs(xyz2),axis=-1,keepdims=True)**2
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sq2 = np.sqrt(q2)
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q = (_beta/np.sqrt(2.0)/_R1) * np.sqrt(q2*qxy/(q2-np.max(np.abs(xyz2),axis=-1,keepdims=True)*sq2))
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tt = np.clip((np.min(np.abs(xyz2),axis=-1,keepdims=True)**2\
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+np.max(np.abs(xyz2),axis=-1,keepdims=True)*sq2)/np.sqrt(2.0)/qxy,-1.0,1.0)
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T_inv = np.where(np.abs(xyz2[...,1:2]) <= np.abs(xyz2[...,0:1]),
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np.block([np.ones_like(tt),np.arccos(tt)/np.pi*12.0]),
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np.block([np.arccos(tt)/np.pi*12.0,np.ones_like(tt)]))*q
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T_inv[xyz2<0.0] *= -1.0
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T_inv[np.broadcast_to(np.isclose(qxy,0.0,rtol=0.0,atol=1.0e-12),T_inv.shape)] = 0.0
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cu = np.block([T_inv, np.where(xyz3[...,2:3]<0.0,-np.ones_like(xyz3[...,2:3]),np.ones_like(xyz3[...,2:3])) \
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* rs/np.sqrt(6.0/np.pi),
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])/ _sc
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cu[np.isclose(np.sum(np.abs(ho),axis=-1),0.0,rtol=0.0,atol=1.0e-16)] = 0.0
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cu = np.take_along_axis(cu,Rotation._get_pyramid_order(ho,'backward'),-1)
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return cu
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#---------- Cubochoric ----------
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@staticmethod
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@ -1082,8 +1147,110 @@ class Rotation:
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@staticmethod
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def cu2ho(cu):
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"""Cubochoric vector to homochoric vector."""
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"""
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Cubochoric vector to homochoric vector.
|
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References
|
||||
----------
|
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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
|
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|
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"""
|
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if len(cu.shape) == 1:
|
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return cube_to_ball(cu)
|
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# 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)
|
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else:
|
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raise NotImplementedError('Support for multiple rotations missing')
|
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# 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]])
|
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else:
|
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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:
|
||||
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]
|
||||
|
|
|
|||
|
|
@ -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)
|
||||
|
|
|
|||
|
|
@ -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))
|
||||
|
|
|
|||
|
|
@ -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(.false.)
|
||||
call discretization_marc_init(ip, el)
|
||||
|
|
|
|||
|
|
@ -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(restart=interface_restartInc>0)
|
||||
|
|
|
|||
174
src/IO.f90
174
src/IO.f90
|
|
@ -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
201
src/Lambert.f90
|
|
@ -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
|
||||
File diff suppressed because it is too large
Load Diff
|
|
@ -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"
|
||||
|
|
|
|||
|
|
@ -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)
|
||||
|
|
|
|||
|
|
@ -50,7 +50,6 @@ module rotations
|
|||
use prec
|
||||
use IO
|
||||
use math
|
||||
use Lambert
|
||||
use quaternions
|
||||
|
||||
implicit none
|
||||
|
|
@ -81,6 +80,18 @@ module rotations
|
|||
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
|
||||
|
|
@ -516,7 +527,7 @@ pure function qu2ho(qu) result(ho)
|
|||
|
||||
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)
|
||||
|
|
@ -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), 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
|
||||
|
||||
|
|
@ -1204,20 +1255,88 @@ 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), 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
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!--------------------------------------------------------------------------------------------------
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Reference in New Issue