From 5f74f3e95e6a8c2b260930d7cd1d25b5d1e40fee Mon Sep 17 00:00:00 2001 From: Chen Zhang Date: Wed, 29 Jul 2015 19:23:06 +0000 Subject: [PATCH] add Cython version of orientation module to provide faster orientation calculation. --- Makefile | 10 +- lib/damask/__init__.py | 9 +- lib/damask/corientation.pyx | 1216 ++++++++++++++++++++++++++++++ lib/damask/setup_corientation.py | 16 + 4 files changed, 1247 insertions(+), 4 deletions(-) create mode 100644 lib/damask/corientation.pyx create mode 100644 lib/damask/setup_corientation.py diff --git a/Makefile b/Makefile index 0483f4a2c..b0613fc12 100755 --- a/Makefile +++ b/Makefile @@ -19,14 +19,20 @@ marc: .PHONY: processing processing: + @if hash cython 2>/dev/null; then \ + cd ./lib/damask; \ + python setup_corientation.py build_ext --inplace; \ + rm -rv build; \ + rm *.c; \ + fi @./installation/compile_CoreModule.py ${MAKEFLAGS} .PHONY: tidy -tidy: +tidy: @$(MAKE) tidy -C code >/dev/null .PHONY: clean -clean: +clean: @$(MAKE) clean -C code >/dev/null .PHONY: install diff --git a/lib/damask/__init__.py b/lib/damask/__init__.py index fd7f8df7f..29d890034 100644 --- a/lib/damask/__init__.py +++ b/lib/damask/__init__.py @@ -7,9 +7,13 @@ from .environment import Environment # only one class from .asciitable import ASCIItable # only one class from .config import Material # will be extended to debug and numerics from .colormaps import Colormap, Color -from .orientation import Quaternion, Rodrigues, Symmetry, Orientation +try: + from .corientation import Quaternion, Rodrigues, Symmetry, Orientation + print "Import Cython version of Orientation module" +except: + from .orientation import Quaternion, Rodrigues, Symmetry, Orientation #from .block import Block # only one class -from .result import Result # only one class +from .result import Result # only one class from .geometry import Geometry # one class with subclasses from .solver import Solver # one class with subclasses from .test import Test @@ -31,6 +35,7 @@ try: core.debug.init = core.debug.debug_init core.math.init = core.math.math_init core.math.periodicNearestNeighbor = core.math.math_periodicNearestNeighbor + core.math.barycentricInterpolate = core.math.math_barycentricInterpolate core.math.periodicNearestNeighborDistances = core.math.math_periodicNearestNeighborDistances core.math.tensorAvg = core.math.math_tensorAvg core.FEsolving.init = core.FEsolving.FE_init diff --git a/lib/damask/corientation.pyx b/lib/damask/corientation.pyx new file mode 100644 index 000000000..ed56be0a9 --- /dev/null +++ b/lib/damask/corientation.pyx @@ -0,0 +1,1216 @@ +#!/usr/bin/env python +# encoding: utf-8 +# filename: corientation.pyx + +# __ __ __________ ____ __ ____ ______ ____ +# / //_// ____/ __ \/ __ \/ //_/ / / / __ \/ __ \ +# / ,< / __/ / / / / / / / ,< / / / / / / / / / / +# / /| |/ /___/ /_/ / /_/ / /| / /_/ / /_/ / /_/ / +# /_/ |_/_____/_____/\____/_/ |_\____/_____/\____/ + + +###################################################### +# This is a Cython implementation of original DAMASK # +# orientation class, mainly for speed improvement. # +###################################################### + +import math, random, os +import numpy as np +#cimport numpy as np + + +## +# This Rodrigues class is odd, not sure if it will function +# properly or not +cdef class Rodrigues: + """Rodrigues representation of orientation """ + cdef public double[3] r + + def __init__(self, vector): + if isinstance(vector, Rodrigues): + self.r[0] = vector.r[0] + self.r[1] = vector.r[1] + self.r[2] = vector.r[2] + else: + self.r[0] = vector[0] + self.r[1] = vector[1] + self.r[2] = vector[2] + + def asQuaternion(self): + cdef double norm, halfAngle + cdef double[4] q + + norm = np.linalg.norm(self.vector) + halfAngle = np.arctan(norm) + q[0] = np.cos(halfAngle) + tmp = np.sin(halfAngle)*self.vector/norm + q[1],q[2],q[3] = tmp[0],tmp[1],tmp[2] + + return Quaternion(q) + + def asAngleAxis(self): + cdef double norm, halfAngle + + norm = np.linalg.norm(self.vector) + halfAngle = np.arctan(norm) + + return (2.0*halfAngle,self.vector/norm) + + +## +# The Quaternion class do the heavy lifting of orientation +# calculation +cdef class Quaternion: + """ Quaternion representation of orientation """ + # All methods and naming conventions based off + # http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions + cdef public double w,x,y,z + + def __init__(self, data): + """ copy constructor friendly """ + cdef double[4] q + + if isinstance(data, Quaternion): + q[0] = data.w + q[1] = data.x + q[2] = data.y + q[3] = data.z + else: + q[0] = data[0] + q[1] = data[1] + q[2] = data[2] + q[3] = data[3] + + self.Quaternion(q) + + cdef Quaternion(self, double* quatArray): + """ + @para: quatArray = + w is the real part, (x, y, z) are the imaginary parts + """ + if quatArray[0] < 0: + self.w = -quatArray[0] + self.x = -quatArray[1] + self.y = -quatArray[2] + self.z = -quatArray[3] + else: + self.w = quatArray[0] + self.x = quatArray[1] + self.y = quatArray[2] + self.z = quatArray[3] + + def __copy__(self): + cdef double[4] q = [self.w,self.x,self.y,self.z] + return Quaternion(q) + + copy = __copy__ + + def __iter__(self): + return iter([self.w,self.x,self.y,self.z]) + + def __repr__(self): + return 'Quaternion(real={:.4f},imag=<{:.4f},{:.4f}, {:.4f}>)'.format(self.w, + self.x, + self.y, + self.z) + + def __pow__(self, exponent, modulo): + # declare local var for speed gain + cdef double omega, vRescale + cdef double[4] q + + omega = math.acos(self.w) + vRescale = math.sin(exponent*omega)/math.sin(omega) + + q[0] = math.cos(exponent*omega) + q[1] = self.x*vRescale + q[2] = self.y*vRescale + q[3] = self.z*vRescale + return Quaternion(q) + + def __ipow__(self, exponent): + self = self.__pow__(self, exponent, 1.0) + return self + + def __mul__(self, other): + # declare local var for speed gain + cdef double Aw,Ax,Ay,Az,Bw,Bx,By,Bz + cdef double w,x,y,z,Vx,Vy,Vz + cdef double[4] q + + # quaternion * quaternion + try: + Aw = self.w + Ax = self.x + Ay = self.y + Az = self.z + Bw = other.w + Bx = other.x + By = other.y + Bz = other.z + q[0] = - Ax * Bx - Ay * By - Az * Bz + Aw * Bw + q[1] = + Ax * Bw + Ay * Bz - Az * By + Aw * Bx + q[2] = - Ax * Bz + Ay * Bw + Az * Bx + Aw * By + q[3] = + Ax * By - Ay * Bx + Az * Bw + Aw * Bz + return Quaternion(q) + except: + pass + # vector (perform active rotation, i.e. q*v*q.conjugated) + try: + w = self.w + x = self.x + y = self.y + z = self.z + Vx = other[0] + Vy = other[1] + Vz = other[2] + return np.array([\ + w * w * Vx + 2 * y * w * Vz - 2 * z * w * Vy + \ + x * x * Vx + 2 * y * x * Vy + 2 * z * x * Vz - \ + z * z * Vx - y * y * Vx, + 2 * x * y * Vx + y * y * Vy + 2 * z * y * Vz + \ + 2 * w * z * Vx - z * z * Vy + w * w * Vy - \ + 2 * x * w * Vz - x * x * Vy, + 2 * x * z * Vx + 2 * y * z * Vy + \ + z * z * Vz - 2 * w * y * Vx - y * y * Vz + \ + 2 * w * x * Vy - x * x * Vz + w * w * Vz ]) + except: + pass + # quaternion * scalar + try: + Q = self.copy() + Q.w *= other + Q.x *= other + Q.y *= other + Q.z *= other + return Q + except: + return self.copy() + + def __imul__(self, other): + if isinstance(other, Quaternion): + self = self.__mul__(other) + return self + else: + return NotImplemented + + def __div__(self, other): + cdef double[4] q + + if isinstance(other, (int,float,long)): + q[0] = self.w / other + q[1] = self.x / other + q[2] = self.y / other + q[3] = self.z / other + return Quaternion(q) + else: + NotImplemented + + def __idiv__(self, other): + self = self.__div__(other) + return self + + def __add__(self, other): + cdef double[4] q + + if isinstance(other, Quaternion): + q[0] = self.w + other.w + q[1] = self.x + other.x + q[2] = self.y + other.y + q[3] = self.z + other.z + return self.__class__(q) + else: + return NotImplemented + + def __iadd__(self, other): + self = self.__add__(other) + return self + + def __sub__(self, other): + cdef double[4] q + + if isinstance(other, Quaternion): + q[0] = self.w - other.w + q[1] = self.x - other.x + q[2] = self.y - other.y + q[3] = self.z - other.z + return self.__class__(q) + else: + return NotImplemented + + def __isub__(self, other): + self = self.__sub__(other) + return self + + def __neg__(self): + cdef double[4] q + + q[0] = -self.w + q[1] = -self.x + q[2] = -self.y + q[3] = -self.z + + return self.__class__(q) + + def __abs__(self): + cdef double tmp + + tmp = self.w**2 + self.x**2 + self.y**2 + self.z**2 + tmp = math.sqrt(tmp) + return tmp + + magnitude = __abs__ + + def __richcmp__(Quaternion self, Quaternion other, int op): + cdef bint tmp + + tmp = (abs(self.w-other.w) < 1e-8 and \ + abs(self.x-other.x) < 1e-8 and \ + abs(self.y-other.y) < 1e-8 and \ + abs(self.z-other.z) < 1e-8) \ + or \ + (abs(-self.w-other.w) < 1e-8 and \ + abs(-self.x-other.x) < 1e-8 and \ + abs(-self.y-other.y) < 1e-8 and \ + abs(-self.z-other.z) < 1e-8) + if op == 2: #__eq__ + return tmp + elif op ==3: #__ne__ + return not tmp + else: + return NotImplemented + + def __cmp__(self,other): + # not sure if this actually works or not + return cmp(self.Rodrigues(),other.Rodrigues()) + + def magnitude_squared(self): + cdef double tmp + + tmp = self.w**2 + self.x**2 + self.y**2 + self.z**2 + return tmp + + def identity(self): + self.w = 1.0 + self.x = 0.0 + self.y = 0.0 + self.z = 0.0 + return self + + def rotateBy_angleaxis(self, angle, axis): + self *= Quaternion.fromAngleAxis(angle, axis) + return self + + def rotateBy_Eulers(self, eulers): + self *= Quaternion.fromEulers(eulers, type) + return self + + def rotateBy_matrix(self, m): + self *= Quaternion.fromMatrix(m) + return self + + def normalize(self): + cdef double d + + d = self.magnitude() + if d > 0.0: + self /= d + return self + + def conjugate(self): + self.x = -self.x + self.y = -self.y + self.z = -self.z + return self + + def inverse(self): + cdef double d + + d = self.magnitude() + if d > 0.0: + self.conjugate() + self /= d + return self + + def homomorph(self): + if self.w < 0.0: + self.w = -self.w + self.x = -self.x + self.y = -self.y + self.z = -self.z + return self + + # return a copy of me + def normalized(self): + cdef Quaternion q + + q = Quaternion(self.normalize()) + return q + + def conjugated(self): + cdef Quaternion q + + q = Quaternion(self.conjugate()) + return q + + def asList(self): + cdef double[4] q = [self.w, self.x, self.y, self.z] + + return list(q) + + def asM(self): # to find Averaging Quaternions (see F. Landis Markley et al.) + return np.outer([i for i in self],[i for i in self]) + + def asMatrix(self): + return np.array([[1.0-2.0*(self.y*self.y+self.z*self.z), 2.0*(self.x*self.y-self.z*self.w), 2.0*(self.x*self.z+self.y*self.w)], + [ 2.0*(self.x*self.y+self.z*self.w), 1.0-2.0*(self.x*self.x+self.z*self.z), 2.0*(self.y*self.z-self.x*self.w)], + [ 2.0*(self.x*self.z-self.y*self.w), 2.0*(self.x*self.w+self.y*self.z), 1.0-2.0*(self.x*self.x+self.y*self.y)]]) + + def asAngleAxis(self): + cdef double s,x,y + + if self.w > 1: + self.normalize() + + s = math.sqrt(1. - self.w**2) + x = 2*self.w**2 - 1. + y = 2*self.w * s + + angle = math.atan2(y,x) + + return angle, np.array([1.0, 0.0, 0.0] if angle < 1e-3 else [self.x/s, self.y/s, self.z/s]) + + def asRodrigues(self): + if self.w != 0.0: + return np.array([self.x, self.y, self.z])/self.w + else: + return np.array([float('inf')]*3) + + def asEulers(self,type='bunge',degrees=False): + """conversion taken from: + Melcher, A.; Unser, A.; Reichhardt, M.; Nestler, B.; Pötschke, M.; Selzer, M. + Conversion of EBSD data by a quaternion based algorithm to be used for grain structure simulations + Technische Mechanik 30 (2010) pp 401--413 + """ + cdef double x,y + + angles = [0.0,0.0,0.0] + + if type.lower() == 'bunge' or type.lower() == 'zxz': + if abs(self.x - self.y) < 1e-8: + x = self.w**2 - self.z**2 + y = 2.*self.w*self.z + angles[0] = math.atan2(y,x) + elif abs(self.w - self.z) < 1e-8: + x = self.x**2 - self.y**2 + y = 2.*self.x*self.y + angles[0] = math.atan2(y,x) + angles[1] = math.pi + else: + chi = math.sqrt((self.w**2 + self.z**2)*(self.x**2 + self.y**2)) + + x = (self.w * self.x - self.y * self.z)/2./chi + y = (self.w * self.y + self.x * self.z)/2./chi + angles[0] = math.atan2(y,x) + + x = self.w**2 + self.z**2 - (self.x**2 + self.y**2) + y = 2.*chi + angles[1] = math.atan2(y,x) + + x = (self.w * self.x + self.y * self.z)/2./chi + y = (self.z * self.x - self.y * self.w)/2./chi + angles[2] = math.atan2(y,x) + + return np.degrees(angles) if degrees else angles + + @staticmethod + def fromIdentity(): + cdef double[4] q = [1.0, 0.0, 0.0, 0.0] + + return Quaternion(q) + + @staticmethod + def fromRandom(randomSeed=None): + cdef double r1,r2,r3 + cdef double[4] q + + if randomSeed == None: + randomSeed = int(os.urandom(4).encode('hex'), 16) + random.seed(randomSeed) + + r1 = random.random() + r2 = random.random() + r3 = random.random() + q[0] = math.cos(2.0*math.pi*r1)*math.sqrt(r3) + q[1] = math.sin(2.0*math.pi*r2)*math.sqrt(1.0-r3) + q[2] = math.cos(2.0*math.pi*r2)*math.sqrt(1.0-r3) + q[3] = math.sin(2.0*math.pi*r1)*math.sqrt(r3) + return Quaternion(q) + + @staticmethod + def fromRodrigues(cls, rodrigues): + if not isinstance(rodrigues, np.ndarray): rodrigues = np.array(rodrigues) + halfangle = math.atan(np.linalg.norm(rodrigues)) + c = math.cos(halfangle) + w = c + x,y,z = c*rodrigues + return cls([w,x,y,z]) + + @staticmethod + def fromAngleAxis(cls, angle, axis): + if not isinstance(axis, np.ndarray): axis = np.array(axis) + axis /= np.linalg.norm(axis) + s = math.sin(angle / 2.0) + w = math.cos(angle / 2.0) + x = axis[0] * s + y = axis[1] * s + z = axis[2] * s + return cls([w,x,y,z]) + + @staticmethod + def fromEulers(cls, eulers, type = 'Bunge'): + cdef double c1,s1,c2,s2,c3,s3 + cdef double[4] q + + eulers *= 0.5 # reduce to half angles + + c1 = math.cos(eulers[0]) + s1 = math.sin(eulers[0]) + c2 = math.cos(eulers[1]) + s2 = math.sin(eulers[1]) + c3 = math.cos(eulers[2]) + s3 = math.sin(eulers[2]) + + if type.lower() == 'bunge' or type.lower() == 'zxz': + q[0] = c1 * c2 * c3 - s1 * c2 * s3 + q[1] = c1 * s2 * c3 + s1 * s2 * s3 + q[2] = - c1 * s2 * s3 + s1 * s2 * c3 + q[3] = c1 * c2 * s3 + s1 * c2 * c3 + else: + q[0] = c1 * c2 * c3 - s1 * s2 * s3 + q[1] = s1 * s2 * c3 + c1 * c2 * s3 + q[2] = s1 * c2 * c3 + c1 * s2 * s3 + q[3] = c1 * s2 * c3 - s1 * c2 * s3 + return Quaternion(q) + + ## Modified Method to calculate Quaternion from Orientation Matrix, Source: http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/ + + @staticmethod + def fromMatrix(cls, m): + # This is a slow implementation + if m.shape != (3,3) and np.prod(m.shape) == 9: + m = m.reshape(3,3) + + tr=m[0,0]+m[1,1]+m[2,2] + if tr > 0.00000001: + s = math.sqrt(tr + 1.0)*2.0 + + return Quaternion( + [ s*0.25, + (m[2,1] - m[1,2])/s, + (m[0,2] - m[2,0])/s, + (m[1,0] - m[0,1])/s + ]) + + elif m[0,0] > m[1,1] and m[0,0] > m[2,2]: + t = m[0,0] - m[1,1] - m[2,2] + 1.0 + s = 2.0*math.sqrt(t) + + return cls( + [ (m[2,1] - m[1,2])/s, + s*0.25, + (m[0,1] + m[1,0])/s, + (m[2,0] + m[0,2])/s, + ]) + + elif m[1,1] > m[2,2]: + t = -m[0,0] + m[1,1] - m[2,2] + 1.0 + s = 2.0*math.sqrt(t) + + return cls( + [ (m[0,2] - m[2,0])/s, + (m[0,1] + m[1,0])/s, + s*0.25, + (m[1,2] + m[2,1])/s, + ]) + + else: + t = -m[0,0] - m[1,1] + m[2,2] + 1.0 + s = 2.0*math.sqrt(t) + + return cls( + [ (m[1,0] - m[0,1])/s, + (m[2,0] + m[0,2])/s, + (m[1,2] + m[2,1])/s, + s*0.25, + ]) + + @staticmethod + def new_interpolate(cls, q1, q2, t): + # see http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20070017872_2007014421.pdf for (another?) way to interpolate quaternions + + assert isinstance(q1, Quaternion) and isinstance(q2, Quaternion) + Q = Quaternion.fromIdentity() + + costheta = q1.w * q2.w + q1.x * q2.x + q1.y * q2.y + q1.z * q2.z + if costheta < 0.: + costheta = -costheta + q1 = q1.conjugated() + elif costheta > 1: + costheta = 1 + + theta = math.acos(costheta) + if abs(theta) < 0.01: + Q.w = q2.w + Q.x = q2.x + Q.y = q2.y + Q.z = q2.z + return Q + + sintheta = math.sqrt(1.0 - costheta * costheta) + if abs(sintheta) < 0.01: + Q.w = (q1.w + q2.w) * 0.5 + Q.x = (q1.x + q2.x) * 0.5 + Q.y = (q1.y + q2.y) * 0.5 + Q.z = (q1.z + q2.z) * 0.5 + return Q + + ratio1 = math.sin((1 - t) * theta) / sintheta + ratio2 = math.sin(t * theta) / sintheta + + Q.w = q1.w * ratio1 + q2.w * ratio2 + Q.x = q1.x * ratio1 + q2.x * ratio2 + Q.y = q1.y * ratio1 + q2.y * ratio2 + Q.z = q1.z * ratio1 + q2.z * ratio2 + return Q + +## +# Define lattice_type to make it easier for future +# development +cdef enum lattice_type: + NONE = 0 + ORTHORHOMBIC= 1 + TETRAGONAL = 2 + HEXAGONAL = 3 + CUBIC = 4 +## +# Symmetry class +cdef class Symmetry: + cdef public lattice_type lattice + # cdef enum LATTICES: + # NONE = 0 + # ORTHORHOMBIC= 1 + # TETRAGONAL = 2 + # HEXAGONAL = 3 + # CUBIC = 4 + + def __init__(self, int symmetry): + if symmetry == 0: + self.lattice = NONE + elif symmetry == 1: + self.lattice = ORTHORHOMBIC + elif symmetry == 2: + self.lattice = TETRAGONAL + elif symmetry == 3: + self.lattice = HEXAGONAL + elif symmetry == 4: + self.lattice = CUBIC + else: + self.lattice = NONE + # self.lattice = symmetry # use code here + + def __copy__(self): + return self.__class__(self.lattice) + + copy = __copy__ + + def __repr__(self): + return '{}'.format(self.lattice) + + def __richcmp__(Symmetry self, Symmetry other, int op): + cdef bint tmp + + tmp = self.lattice == other.lattice + if op == 2: #__eq__ + return tmp + elif op ==3: #__ne__ + return not tmp + else: + return NotImplemented + + def __cmp__(self,other): + return cmp(self.lattice,other.lattice) + + def equivalentQuaternions(self,quaternion): + ''' + List of symmetrically equivalent quaternions based on own symmetry. + ''' + if self.lattice == CUBIC: + symQuats = [ + [ 1.0,0.0,0.0,0.0 ], + [ 0.0,1.0,0.0,0.0 ], + [ 0.0,0.0,1.0,0.0 ], + [ 0.0,0.0,0.0,1.0 ], + [ 0.0, 0.0, 0.5*math.sqrt(2), 0.5*math.sqrt(2) ], + [ 0.0, 0.0, 0.5*math.sqrt(2),-0.5*math.sqrt(2) ], + [ 0.0, 0.5*math.sqrt(2), 0.0, 0.5*math.sqrt(2) ], + [ 0.0, 0.5*math.sqrt(2), 0.0,-0.5*math.sqrt(2) ], + [ 0.0, 0.5*math.sqrt(2),-0.5*math.sqrt(2), 0.0 ], + [ 0.0,-0.5*math.sqrt(2),-0.5*math.sqrt(2), 0.0 ], + [ 0.5, 0.5, 0.5, 0.5 ], + [-0.5, 0.5, 0.5, 0.5 ], + [-0.5, 0.5, 0.5,-0.5 ], + [-0.5, 0.5,-0.5, 0.5 ], + [-0.5,-0.5, 0.5, 0.5 ], + [-0.5,-0.5, 0.5,-0.5 ], + [-0.5,-0.5,-0.5, 0.5 ], + [-0.5, 0.5,-0.5,-0.5 ], + [-0.5*math.sqrt(2), 0.0, 0.0, 0.5*math.sqrt(2) ], + [ 0.5*math.sqrt(2), 0.0, 0.0, 0.5*math.sqrt(2) ], + [-0.5*math.sqrt(2), 0.0, 0.5*math.sqrt(2), 0.0 ], + [-0.5*math.sqrt(2), 0.0,-0.5*math.sqrt(2), 0.0 ], + [-0.5*math.sqrt(2), 0.5*math.sqrt(2), 0.0, 0.0 ], + [-0.5*math.sqrt(2),-0.5*math.sqrt(2), 0.0, 0.0 ], + ] + elif self.lattice == HEXAGONAL: + symQuats = [ + [ 1.0,0.0,0.0,0.0 ], + [ 0.0,1.0,0.0,0.0 ], + [ 0.0,0.0,1.0,0.0 ], + [ 0.0,0.0,0.0,1.0 ], + [-0.5*math.sqrt(3), 0.0, 0.0, 0.5 ], + [-0.5*math.sqrt(3), 0.0, 0.0,-0.5 ], + [ 0.0, 0.5*math.sqrt(3), 0.5, 0.0 ], + [ 0.0,-0.5*math.sqrt(3), 0.5, 0.0 ], + [ 0.0, 0.5,-0.5*math.sqrt(3), 0.0 ], + [ 0.0,-0.5,-0.5*math.sqrt(3), 0.0 ], + [ 0.5, 0.0, 0.0, 0.5*math.sqrt(3) ], + [-0.5, 0.0, 0.0, 0.5*math.sqrt(3) ], + ] + elif self.lattice == TETRAGONAL: + symQuats = [ + [ 1.0,0.0,0.0,0.0 ], + [ 0.0,1.0,0.0,0.0 ], + [ 0.0,0.0,1.0,0.0 ], + [ 0.0,0.0,0.0,1.0 ], + [ 0.0, 0.5*math.sqrt(2), 0.5*math.sqrt(2), 0.0 ], + [ 0.0,-0.5*math.sqrt(2), 0.5*math.sqrt(2), 0.0 ], + [ 0.5*math.sqrt(2), 0.0, 0.0, 0.5*math.sqrt(2) ], + [-0.5*math.sqrt(2), 0.0, 0.0, 0.5*math.sqrt(2) ], + ] + elif self.lattice == ORTHORHOMBIC: + symQuats = [ + [ 1.0,0.0,0.0,0.0 ], + [ 0.0,1.0,0.0,0.0 ], + [ 0.0,0.0,1.0,0.0 ], + [ 0.0,0.0,0.0,1.0 ], + ] + else: + symQuats = [ + [ 1.0,0.0,0.0,0.0 ], + ] + # due to the use of list comprehension, the speed grain is quite + # limited + return [quaternion*Quaternion(q) for q in symQuats] + + def inFZ(self,R): + ''' + Check whether given Rodrigues vector falls into fundamental zone of own symmetry. + ''' + if isinstance(R, Quaternion): R = R.asRodrigues() # translate accidentially passed quaternion + R = abs(R) # fundamental zone in Rodrigues space is point symmetric around origin + if self.lattice == CUBIC: + return math.sqrt(2.0)-1.0 >= R[0] \ + and math.sqrt(2.0)-1.0 >= R[1] \ + and math.sqrt(2.0)-1.0 >= R[2] \ + and 1.0 >= R[0] + R[1] + R[2] + elif self.lattice == HEXAGONAL: + return 1.0 >= R[0] and 1.0 >= R[1] and 1.0 >= R[2] \ + and 2.0 >= math.sqrt(3)*R[0] + R[1] \ + and 2.0 >= math.sqrt(3)*R[1] + R[0] \ + and 2.0 >= math.sqrt(3) + R[2] + elif self.lattice == TETRAGONAL: + return 1.0 >= R[0] and 1.0 >= R[1] \ + and math.sqrt(2.0) >= R[0] + R[1] \ + and math.sqrt(2.0) >= R[2] + 1.0 + elif self.lattice == ORTHORHOMBIC: + return 1.0 >= R[0] and 1.0 >= R[1] and 1.0 >= R[2] + else: + return True + + def inDisorientationSST(self,R): + ''' + Check whether given Rodrigues vector (of misorientation) falls into standard stereographic triangle of own symmetry. + Determination of disorientations follow the work of A. Heinz and P. Neumann: + Representation of Orientation and Disorientation Data for Cubic, Hexagonal, Tetragonal and Orthorhombic Crystals + Acta Cryst. (1991). A47, 780-789 + ''' + if isinstance(R, Quaternion): R = R.asRodrigues() # translate accidentally passed quaternion + + cdef double epsilon = 0.0 + + if self.lattice == CUBIC: + return R[0] >= R[1]+epsilon and R[1] >= R[2]+epsilon and R[2] >= epsilon and self.inFZ(R) + + elif self.lattice == HEXAGONAL: + return R[0] >= math.sqrt(3)*(R[1]+epsilon) and R[1] >= epsilon and R[2] >= epsilon and self.inFZ(R) + + elif self.lattice == TETRAGONAL: + return R[0] >= R[1]+epsilon and R[1] >= epsilon and R[2] >= epsilon and self.inFZ(R) + + elif self.lattice == ORTHORHOMBIC: + return R[0] >= epsilon and R[1] >= epsilon and R[2] >= epsilon and self.inFZ(R) + + else: + return True + + def inSST(self,vector,color = False): + ''' + Check whether given vector falls into standard stereographic triangle of own symmetry. + Return inverse pole figure color if requested. + ''' +# basis = {4 : np.linalg.inv(np.array([[0.,0.,1.], # direction of red +# [1.,0.,1.]/np.sqrt(2.), # direction of green +# [1.,1.,1.]/np.sqrt(3.)]).transpose()), # direction of blue +# 3 : np.linalg.inv(np.array([[0.,0.,1.], # direction of red +# [1.,0.,0.], # direction of green +# [np.sqrt(3.),1.,0.]/np.sqrt(4.)]).transpose()), # direction of blue +# 2 : np.linalg.inv(np.array([[0.,0.,1.], # direction of red +# [1.,0.,0.], # direction of green +# [1.,1.,0.]/np.sqrt(2.)]).transpose()), # direction of blue +# 1 : np.linalg.inv(np.array([[0.,0.,1.], # direction of red +# [1.,0.,0.], # direction of green +# [0.,1.,0.]]).transpose()), # direction of blue +# } + if self.lattice == CUBIC: + basis = np.array([ [-1. , 0. , 1. ], + [ np.sqrt(2.), -np.sqrt(2.), 0. ], + [ 0. , np.sqrt(3.), 0. ] ]) + elif self.lattice == HEXAGONAL: + basis = np.array([ [ 0. , 0. , 1. ], + [ 1. , -np.sqrt(3.), 0. ], + [ 0. , 2. , 0. ] ]) + elif self.lattice == TETRAGONAL: + basis = np.array([ [ 0. , 0. , 1. ], + [ 1. , -1. , 0. ], + [ 0. , np.sqrt(2.), 0. ] ]) + elif self.lattice == ORTHORHOMBIC: + basis = np.array([ [ 0., 0., 1.], + [ 1., 0., 0.], + [ 0., 1., 0.] ]) + else: + basis = np.zeros((3,3),dtype=float) + + if np.all(basis == 0.0): + theComponents = -np.ones(3,'d') + else: + theComponents = np.dot(basis,np.array([vector[0],vector[1],abs(vector[2])])) + + inSST = np.all(theComponents >= 0.0) + + if color: # have to return color array + if inSST: + rgb = np.power(theComponents/np.linalg.norm(theComponents),0.5) # smoothen color ramps + rgb = np.minimum(np.ones(3,'d'),rgb) # limit to maximum intensity + rgb /= max(rgb) # normalize to (HS)V = 1 + else: + rgb = np.zeros(3,'d') + return (inSST,rgb) + else: + return inSST + +# code derived from http://pyeuclid.googlecode.com/svn/trunk/euclid.py +# suggested reading: http://web.mit.edu/2.998/www/QuaternionReport1.pdf + + +## +# Orientation class is a composite class of Symmetry and Quaternion +cdef class Orientation: + cdef public Quaternion quaternion + cdef public Symmetry symmetry + + def __init__(self, + quaternion = Quaternion.fromIdentity(), + Rodrigues = None, + angleAxis = None, + matrix = None, + Eulers = None, + random = False, # put any integer to have a fixed seed or True for real random + symmetry = None, + ): + if random: # produce random orientation + if isinstance(random, bool ): + self.quaternion = Quaternion.fromRandom() + else: + self.quaternion = Quaternion.fromRandom(randomSeed=random) + elif isinstance(Eulers, np.ndarray) and Eulers.shape == (3,): # based on given Euler angles + self.quaternion = Quaternion.fromEulers(Eulers,'bunge') + elif isinstance(matrix, np.ndarray) : # based on given rotation matrix + self.quaternion = Quaternion.fromMatrix(matrix) + elif isinstance(angleAxis, np.ndarray) and angleAxis.shape == (4,): # based on given angle and rotation axis + self.quaternion = Quaternion.fromAngleAxis(angleAxis[0],angleAxis[1:4]) + elif isinstance(Rodrigues, np.ndarray) and Rodrigues.shape == (3,): # based on given Rodrigues vector + self.quaternion = Quaternion.fromRodrigues(Rodrigues) + elif isinstance(quaternion, Quaternion): # based on given quaternion + self.quaternion = quaternion.homomorph() + elif isinstance(quaternion, np.ndarray) and quaternion.shape == (4,): # based on given quaternion + self.quaternion = Quaternion(quaternion).homomorph() + + self.symmetry = Symmetry(symmetry) + + def __copy__(self): + return self.__class__(quaternion=self.quaternion,symmetry=self.symmetry.lattice) + + copy = __copy__ + + def __repr__(self): + return 'Symmetry: %s\n' % (self.symmetry) + \ + 'Quaternion: %s\n' % (self.quaternion) + \ + 'Matrix:\n%s\n' % ( '\n'.join(['\t'.join(map(str,self.asMatrix()[i,:])) for i in range(3)]) ) + \ + 'Bunge Eulers / deg: %s' % ('\t'.join(map(lambda x:str(np.degrees(x)),self.asEulers('bunge'))) ) + + def asQuaternion(self): + return self.quaternion.asList() + + def asEulers(self,type='bunge'): + return self.quaternion.asEulers(type) + + def asRodrigues(self): + return self.quaternion.asRodrigues() + + def asAngleAxis(self): + return self.quaternion.asAngleAxis() + + def asMatrix(self): + return self.quaternion.asMatrix() + + def inFZ(self): + return self.symmetry.inFZ(self.quaternion.asRodrigues()) + + def equivalentQuaternions(self): + return self.symmetry.equivalentQuaternions(self.quaternion) + + def equivalentOrientations(self): + return map(lambda q: Orientation(quaternion=q,symmetry=self.symmetry.lattice), + self.equivalentQuaternions()) + + + def reduced(self): + '''Transform orientation to fall into fundamental zone according to symmetry''' + for me in self.symmetry.equivalentQuaternions(self.quaternion): + if self.symmetry.inFZ(me.asRodrigues()): break + + return Orientation(quaternion=me,symmetry=self.symmetry.lattice) + + def disorientation(self,other): + ''' + Disorientation between myself and given other orientation + (either reduced according to my own symmetry or given one) + ''' + + lowerSymmetry = min(self.symmetry,other.symmetry) + breaker = False + + for me in self.symmetry.equivalentQuaternions(self.quaternion): + me.conjugate() + for they in other.symmetry.equivalentQuaternions(other.quaternion): + theQ = they * me + breaker = lowerSymmetry.inDisorientationSST(theQ.asRodrigues()) #\ +# or lowerSymmetry.inDisorientationSST(theQ.conjugated().asRodrigues()) + if breaker: break + if breaker: break + + return Orientation(quaternion=theQ,symmetry=self.symmetry.lattice) #, me.conjugated(), they + + def inversePole(self,axis,SST = True): + ''' + axis rotated according to orientation (using crystal symmetry to ensure location falls into SST) + ''' + + if SST: # pole requested to be within SST + for i,q in enumerate(self.symmetry.equivalentQuaternions(self.quaternion)): # test all symmetric equivalent quaternions + pole = q.conjugated()*axis # align crystal direction to axis + if self.symmetry.inSST(pole): break # found SST version + else: + pole = self.quaternion.conjugated()*axis # align crystal direction to axis + + return pole + + def IPFcolor(self,axis): + ''' TSL color of inverse pole figure for given axis ''' + color = np.zeros(3,'d') + for q in self.symmetry.equivalentQuaternions(self.quaternion): + pole = q.conjugated()*axis # align crystal direction to axis + inSST,color = self.symmetry.inSST(pole,color=True) + if inSST: break + + return color + + @staticmethod + def getAverageOrientation(cls, orientationList): + """ + RETURN THE AVERAGE ORIENTATION + ref: F. Landis Markley, Yang Cheng, John Lucas Crassidis, and Yaakov Oshman. + Averaging Quaternions, + Journal of Guidance, Control, and Dynamics, Vol. 30, No. 4 (2007), pp. 1193-1197. + doi: 10.2514/1.28949 + sample usage: + a = Orientation(Eulers=np.radians([10, 10, 0]), symmetry=3) + b = Orientation(Eulers=np.radians([20, 0, 0]), symmetry=3) + avg = Orientation.getAverageOrientation([a,b]) + """ + + if not all(isinstance(item, Orientation) for item in orientationList): + raise TypeError("Only instances of Orientation can be averaged.") + + N = len(orientationList) + M = orientationList.pop(0).quaternion.asM() + for o in orientationList: + M += o.quaternion.asM() + eig, vec = np.linalg.eig(M/N) + + return Orientation(quaternion = Quaternion(quatArray = vec.T[eig.argmax()])) + + def related(self, relationModel, direction, targetSymmetry = None): + + if relationModel not in ['KS','GT','GTdash','NW','Pitsch','Bain']: return None + if int(direction) == 0: return None + + # KS from S. Morito et al./Journal of Alloys and Compounds 5775 (2013) S587-S592 + # GT from Y. He et al./Journal of Applied Crystallography (2006). 39, 72-81 + # GT' from Y. He et al./Journal of Applied Crystallography (2006). 39, 72-81 + # NW from H. Kitahara et al./Materials Characterization 54 (2005) 378-386 + # Pitsch from Y. He et al./Acta Materialia 53 (2005) 1179-1190 + # Bain from Y. He et al./Journal of Applied Crystallography (2006). 39, 72-81 + + variant = int(abs(direction))-1 + (me,other) = (0,1) if direction > 0 else (1,0) + + planes = {'KS': \ + np.array([[[ 1, 1, 1],[ 0, 1, 1]],\ + [[ 1, 1, 1],[ 0, 1, 1]],\ + [[ 1, 1, 1],[ 0, 1, 1]],\ + [[ 1, 1, 1],[ 0, 1, 1]],\ + [[ 1, 1, 1],[ 0, 1, 1]],\ + [[ 1, 1, 1],[ 0, 1, 1]],\ + [[ 1, -1, 1],[ 0, 1, 1]],\ + [[ 1, -1, 1],[ 0, 1, 1]],\ + [[ 1, -1, 1],[ 0, 1, 1]],\ + [[ 1, -1, 1],[ 0, 1, 1]],\ + [[ 1, -1, 1],[ 0, 1, 1]],\ + [[ 1, -1, 1],[ 0, 1, 1]],\ + [[ -1, 1, 1],[ 0, 1, 1]],\ + [[ -1, 1, 1],[ 0, 1, 1]],\ + [[ -1, 1, 1],[ 0, 1, 1]],\ + [[ -1, 1, 1],[ 0, 1, 1]],\ + [[ -1, 1, 1],[ 0, 1, 1]],\ + [[ -1, 1, 1],[ 0, 1, 1]],\ + [[ 1, 1, -1],[ 0, 1, 1]],\ + [[ 1, 1, -1],[ 0, 1, 1]],\ + [[ 1, 1, -1],[ 0, 1, 1]],\ + [[ 1, 1, -1],[ 0, 1, 1]],\ + [[ 1, 1, -1],[ 0, 1, 1]],\ + [[ 1, 1, -1],[ 0, 1, 1]]]), + 'GT': \ + np.array([[[ 1, 1, 1],[ 1, 0, 1]],\ + [[ 1, 1, 1],[ 1, 1, 0]],\ + [[ 1, 1, 1],[ 0, 1, 1]],\ + [[ -1, -1, 1],[ -1, 0, 1]],\ + [[ -1, -1, 1],[ -1, -1, 0]],\ + [[ -1, -1, 1],[ 0, -1, 1]],\ + [[ -1, 1, 1],[ -1, 0, 1]],\ + [[ -1, 1, 1],[ -1, 1, 0]],\ + [[ -1, 1, 1],[ 0, 1, 1]],\ + [[ 1, -1, 1],[ 1, 0, 1]],\ + [[ 1, -1, 1],[ 1, -1, 0]],\ + [[ 1, -1, 1],[ 0, -1, 1]],\ + [[ 1, 1, 1],[ 1, 1, 0]],\ + [[ 1, 1, 1],[ 0, 1, 1]],\ + [[ 1, 1, 1],[ 1, 0, 1]],\ + [[ -1, -1, 1],[ -1, -1, 0]],\ + [[ -1, -1, 1],[ 0, -1, 1]],\ + [[ -1, -1, 1],[ -1, 0, 1]],\ + [[ -1, 1, 1],[ -1, 1, 0]],\ + [[ -1, 1, 1],[ 0, 1, 1]],\ + [[ -1, 1, 1],[ -1, 0, 1]],\ + [[ 1, -1, 1],[ 1, -1, 0]],\ + [[ 1, -1, 1],[ 0, -1, 1]],\ + [[ 1, -1, 1],[ 1, 0, 1]]]), + 'GTdash': \ + np.array([[[ 7, 17, 17],[ 12, 5, 17]],\ + [[ 17, 7, 17],[ 17, 12, 5]],\ + [[ 17, 17, 7],[ 5, 17, 12]],\ + [[ -7,-17, 17],[-12, -5, 17]],\ + [[-17, -7, 17],[-17,-12, 5]],\ + [[-17,-17, 7],[ -5,-17, 12]],\ + [[ 7,-17,-17],[ 12, -5,-17]],\ + [[ 17, -7,-17],[ 17,-12, -5]],\ + [[ 17,-17, -7],[ 5,-17,-12]],\ + [[ -7, 17,-17],[-12, 5,-17]],\ + [[-17, 7,-17],[-17, 12, -5]],\ + [[-17, 17, -7],[ -5, 17,-12]],\ + [[ 7, 17, 17],[ 12, 17, 5]],\ + [[ 17, 7, 17],[ 5, 12, 17]],\ + [[ 17, 17, 7],[ 17, 5, 12]],\ + [[ -7,-17, 17],[-12,-17, 5]],\ + [[-17, -7, 17],[ -5,-12, 17]],\ + [[-17,-17, 7],[-17, -5, 12]],\ + [[ 7,-17,-17],[ 12,-17, -5]],\ + [[ 17, -7,-17],[ 5, -12,-17]],\ + [[ 17,-17, 7],[ 17, -5,-12]],\ + [[ -7, 17,-17],[-12, 17, -5]],\ + [[-17, 7,-17],[ -5, 12,-17]],\ + [[-17, 17, -7],[-17, 5,-12]]]), + 'NW': \ + np.array([[[ 1, 1, 1],[ 0, 1, 1]],\ + [[ 1, 1, 1],[ 0, 1, 1]],\ + [[ 1, 1, 1],[ 0, 1, 1]],\ + [[ -1, 1, 1],[ 0, 1, 1]],\ + [[ -1, 1, 1],[ 0, 1, 1]],\ + [[ -1, 1, 1],[ 0, 1, 1]],\ + [[ 1, -1, 1],[ 0, 1, 1]],\ + [[ 1, -1, 1],[ 0, 1, 1]],\ + [[ 1, -1, 1],[ 0, 1, 1]],\ + [[ -1, -1, 1],[ 0, 1, 1]],\ + [[ -1, -1, 1],[ 0, 1, 1]],\ + [[ -1, -1, 1],[ 0, 1, 1]]]), + 'Pitsch': \ + np.array([[[ 0, 1, 0],[ -1, 0, 1]],\ + [[ 0, 0, 1],[ 1, -1, 0]],\ + [[ 1, 0, 0],[ 0, 1, -1]],\ + [[ 1, 0, 0],[ 0, -1, -1]],\ + [[ 0, 1, 0],[ -1, 0, -1]],\ + [[ 0, 0, 1],[ -1, -1, 0]],\ + [[ 0, 1, 0],[ -1, 0, -1]],\ + [[ 0, 0, 1],[ -1, -1, 0]],\ + [[ 1, 0, 0],[ 0, -1, -1]],\ + [[ 1, 0, 0],[ 0, -1, 1]],\ + [[ 0, 1, 0],[ 1, 0, -1]],\ + [[ 0, 0, 1],[ -1, 1, 0]]]), + 'Bain': \ + np.array([[[ 1, 0, 0],[ 1, 0, 0]],\ + [[ 0, 1, 0],[ 0, 1, 0]],\ + [[ 0, 0, 1],[ 0, 0, 1]]]), + } + + normals = {'KS': \ + np.array([[[ -1, 0, 1],[ -1, -1, 1]],\ + [[ -1, 0, 1],[ -1, 1, -1]],\ + [[ 0, 1, -1],[ -1, -1, 1]],\ + [[ 0, 1, -1],[ -1, 1, -1]],\ + [[ 1, -1, 0],[ -1, -1, 1]],\ + [[ 1, -1, 0],[ -1, 1, -1]],\ + [[ 1, 0, -1],[ -1, -1, 1]],\ + [[ 1, 0, -1],[ -1, 1, -1]],\ + [[ -1, -1, 0],[ -1, -1, 1]],\ + [[ -1, -1, 0],[ -1, 1, -1]],\ + [[ 0, 1, 1],[ -1, -1, 1]],\ + [[ 0, 1, 1],[ -1, 1, -1]],\ + [[ 0, -1, 1],[ -1, -1, 1]],\ + [[ 0, -1, 1],[ -1, 1, -1]],\ + [[ -1, 0, -1],[ -1, -1, 1]],\ + [[ -1, 0, -1],[ -1, 1, -1]],\ + [[ 1, 1, 0],[ -1, -1, 1]],\ + [[ 1, 1, 0],[ -1, 1, -1]],\ + [[ -1, 1, 0],[ -1, -1, 1]],\ + [[ -1, 1, 0],[ -1, 1, -1]],\ + [[ 0, -1, -1],[ -1, -1, 1]],\ + [[ 0, -1, -1],[ -1, 1, -1]],\ + [[ 1, 0, 1],[ -1, -1, 1]],\ + [[ 1, 0, 1],[ -1, 1, -1]]]), + 'GT': \ + np.array([[[ -5,-12, 17],[-17, -7, 17]],\ + [[ 17, -5,-12],[ 17,-17, -7]],\ + [[-12, 17, -5],[ -7, 17,-17]],\ + [[ 5, 12, 17],[ 17, 7, 17]],\ + [[-17, 5,-12],[-17, 17, -7]],\ + [[ 12,-17, -5],[ 7,-17,-17]],\ + [[ -5, 12,-17],[-17, 7,-17]],\ + [[ 17, 5, 12],[ 17, 17, 7]],\ + [[-12,-17, 5],[ -7,-17, 17]],\ + [[ 5,-12,-17],[ 17, -7,-17]],\ + [[-17, -5, 12],[-17,-17, 7]],\ + [[ 12, 17, 5],[ 7, 17, 17]],\ + [[ -5, 17,-12],[-17, 17, -7]],\ + [[-12, -5, 17],[ -7,-17, 17]],\ + [[ 17,-12, -5],[ 17, -7,-17]],\ + [[ 5,-17,-12],[ 17,-17, -7]],\ + [[ 12, 5, 17],[ 7, 17, 17]],\ + [[-17, 12, -5],[-17, 7,-17]],\ + [[ -5,-17, 12],[-17,-17, 7]],\ + [[-12, 5,-17],[ -7, 17,-17]],\ + [[ 17, 12, 5],[ 17, 7, 17]],\ + [[ 5, 17, 12],[ 17, 17, 7]],\ + [[ 12, -5,-17],[ 7,-17,-17]],\ + [[-17,-12, 5],[-17, 7, 17]]]), + 'GTdash': \ + np.array([[[ 0, 1, -1],[ 1, 1, -1]],\ + [[ -1, 0, 1],[ -1, 1, 1]],\ + [[ 1, -1, 0],[ 1, -1, 1]],\ + [[ 0, -1, -1],[ -1, -1, -1]],\ + [[ 1, 0, 1],[ 1, -1, 1]],\ + [[ 1, -1, 0],[ 1, -1, -1]],\ + [[ 0, 1, -1],[ -1, 1, -1]],\ + [[ 1, 0, 1],[ 1, 1, 1]],\ + [[ -1, -1, 0],[ -1, -1, 1]],\ + [[ 0, -1, -1],[ 1, -1, -1]],\ + [[ -1, 0, 1],[ -1, -1, 1]],\ + [[ -1, -1, 0],[ -1, -1, -1]],\ + [[ 0, -1, 1],[ 1, -1, 1]],\ + [[ 1, 0, -1],[ 1, 1, -1]],\ + [[ -1, 1, 0],[ -1, 1, 1]],\ + [[ 0, 1, 1],[ -1, 1, 1]],\ + [[ -1, 0, -1],[ -1, -1, -1]],\ + [[ -1, 1, 0],[ -1, 1, -1]],\ + [[ 0, -1, 1],[ -1, -1, 1]],\ + [[ -1, 0, -1],[ -1, 1, -1]],\ + [[ 1, 1, 0],[ 1, 1, 1]],\ + [[ 0, 1, 1],[ 1, 1, 1]],\ + [[ 1, 0, -1],[ 1, -1, -1]],\ + [[ 1, 1, 0],[ 1, 1, -1]]]), + 'NW': \ + np.array([[[ 2, -1, -1],[ 0, -1, 1]],\ + [[ -1, 2, -1],[ 0, -1, 1]],\ + [[ -1, -1, 2],[ 0, -1, 1]],\ + [[ -2, -1, -1],[ 0, -1, 1]],\ + [[ 1, 2, -1],[ 0, -1, 1]],\ + [[ 1, -1, 2],[ 0, -1, 1]],\ + [[ 2, 1, -1],[ 0, -1, 1]],\ + [[ -1, -2, -1],[ 0, -1, 1]],\ + [[ -1, 1, 2],[ 0, -1, 1]],\ + [[ -1, 2, 1],[ 0, -1, 1]],\ + [[ -1, 2, 1],[ 0, -1, 1]],\ + [[ -1, -1, -2],[ 0, -1, 1]]]), + 'Pitsch': \ + np.array([[[ 1, 0, 1],[ 1, -1, 1]],\ + [[ 1, 1, 0],[ 1, 1, -1]],\ + [[ 0, 1, 1],[ -1, 1, 1]],\ + [[ 0, 1, -1],[ -1, 1, -1]],\ + [[ -1, 0, 1],[ -1, -1, 1]],\ + [[ 1, -1, 0],[ 1, -1, -1]],\ + [[ 1, 0, -1],[ 1, -1, -1]],\ + [[ -1, 1, 0],[ -1, 1, -1]],\ + [[ 0, -1, 1],[ -1, -1, 1]],\ + [[ 0, 1, 1],[ -1, 1, 1]],\ + [[ 1, 0, 1],[ 1, -1, 1]],\ + [[ 1, 1, 0],[ 1, 1, -1]]]), + 'Bain': \ + np.array([[[ 0, 1, 0],[ 0, 1, 1]], + [[ 0, 0, 1],[ 1, 0, 1]], + [[ 1, 0, 0],[ 1, 1, 0]]]), + } + myPlane = [float(i) for i in planes[relationModel][variant,me]] # map(float, planes[...]) does not work in python 3 + myPlane /= np.linalg.norm(myPlane) + myNormal = [float(i) for i in normals[relationModel][variant,me]] # map(float, planes[...]) does not work in python 3 + myNormal /= np.linalg.norm(myNormal) + myMatrix = np.array([myPlane,myNormal,np.cross(myPlane,myNormal)]) + + otherPlane = [float(i) for i in planes[relationModel][variant,other]] # map(float, planes[...]) does not work in python 3 + otherPlane /= np.linalg.norm(otherPlane) + otherNormal = [float(i) for i in normals[relationModel][variant,other]] # map(float, planes[...]) does not work in python 3 + otherNormal /= np.linalg.norm(otherNormal) + otherMatrix = np.array([otherPlane,otherNormal,np.cross(otherPlane,otherNormal)]) + + rot=np.dot(otherMatrix.T,myMatrix) + + return Orientation(matrix=np.dot(rot,self.asMatrix())) # no symmetry information ?? \ No newline at end of file diff --git a/lib/damask/setup_corientation.py b/lib/damask/setup_corientation.py new file mode 100644 index 000000000..45570e316 --- /dev/null +++ b/lib/damask/setup_corientation.py @@ -0,0 +1,16 @@ +#!/usr/bin/env python +# -*- coding: UTF-8 no BOM -*- + +from distutils.core import setup +from distutils.extension import Extension +from Cython.Distutils import build_ext +import numpy as np + +ext = [Extension("corientation", ["corientation.pyx"])] + +setup( + name="corientation", + include_dirs=[np.get_include()], + cmdclass = {'build_ext': build_ext}, + ext_modules=ext +) \ No newline at end of file