def rotMatrixFromCrystalVectors(cvs1=None, cvs2=None, cvs3=None):
"""\
Make a rotation matrix in the RotationParameterization convention
from components of crystal vectors that are along given sample directions
"""
mat = zeros([3,3], dtype='float64')
if cvs1 == None:
if ((cvs2 == None) or (cvs3 == None)):
print >> sys.stderr, "need more inputs"
raise RuntimeError, "unrecoverable error"
cvs1 = cross(cvs2,cvs3)
cvs1 = normalized(cvs1)
if cvs2 == None:
if ((cvs1 == None) or (cvs3 == None)):
print >> sys.stderr, "need more inputs"
raise RuntimeError, "unrecoverable error"
cvs2 = cross(cvs1,cvs3)
cvs2 = normalized(cvs2)
if cvs3 == None:
if ((cvs1 == None) or (cvs2 == None)):
print >> sys.stderr, "need more inputs"
raise RuntimeError, "unrecoverable error"
cvs3 = cross(cvs1,cvs2)
cvs3 = normalized(cvs3)
mat[0,:] = cvs1[:]
mat[1,:] = cvs2[:]
mat[2,:] = cvs3[:]
det = determinant3(mat)
if (abs(det-1.0) < 1e-12):
return mat
elif (abs(det+1.0) < 1e-12):
mat = -mat
return mat
else:
print >> sys.stderr, "vectors not close enough to orthonormal"
raise RuntimeError, "unrecoverable error"
def __init__(self, *args):
if isinstance(args[0], str):
a = args[0]
if a == 'rand':
if len(args) > 1:
if hasattr(args[1], '__len__'):
thetaScale = args[1]
if len(thetaScale) == 3:
self.n = zeros(3, dtype='float64')
self.n[0] = RotInv.__rvNorm() * thetaScale[0]
self.n[1] = RotInv.__rvNorm() * thetaScale[1]
self.n[2] = RotInv.__rvNorm() * thetaScale[2]
mag = normvec3(self.n)
if mag > 0.:
self.n[:] = self.n[:] / mag
self.theta = mag
else:
newInv = Quat('rand').toInv()
self.n[:] = newInv.n[:]
self.theta = mag
else:
raise RuntimeError, "unrecoverable error: bad thetaScale length"
else:
newInv = Quat('rand').toInv()
self.n = newInv.n
thetaScale = float(args[1])
self.theta = RotInv.__rvNorm() * thetaScale
else:
newInv = Quat('rand').toInv()
self.n = newInv.n
self.theta = newInv.theta
elif a == 'align':
# align given crystal vector with given sample vector
vl = num.array(args[1])
vs = num.array(args[2])
# normalize
mag = normvec3(vl)
vl /= mag
mag = normvec3(vs)
vs /= mag
self.theta = math.acos(num.dot(vs,vl)) # arccosine
w = cross(vl,vs)
mag = normvec3(w)
if mag > 1e-14:
self.n = w / mag
else:
sqr3i = 1./sqrt(3.)
self.n = num.array([sqr3i, sqr3i, sqr3i])
else:
print >> sys.stderr, "bad string"
raise RuntimeError, "unrecoverable error"
elif len(args) == 1:
a = args[0]
if (hasattr(a,"toInv")):
"use direct conversion, assuming it is more efficient"
newInv = a.toInv()
self.theta = newInv.theta
self.n = newInv.n
elif isinstance(a,RotationParameterization):
"from 3x3 matrix of components"
(self.theta, self.n) = matToThetaN(a.toMatrix())
else:
a = num.atleast_1d(args[0])
if size(shape(a)) == 2:
"from 3x3 matrix of components"
assert a.shape[0] == 3 and a.shape[1] == 3, 'wrong shape for matrix'
(self.theta, self.n) = matToThetaN(a)
elif size(shape(a)) == 1:
"exponential map parameters"
assert a.shape[0] == 3, 'wrong shape for exp map parameters'
self.n = a
self.theta = sqrt(sum(self.n[:] * self.n[:]))
if self.theta > 0.:
self.n = self.n / self.theta
else:
self.n = num.array([1.,0.,0.]) # n not really well defined
else:
print >> sys.stderr, "wrong shape of args[0]", shape(a)
raise RuntimeError, "unrecoverable error"
elif len(args) == 2:
"from theta and normal vector (not necessarily normalized)"
self.theta = float(args[0])
self.n = zeros(3, dtype='float64')
self.n[:] = args[1]
mag = sqrt(sum(self.n[:] * self.n[:]))
self.n[:] = self.n[:] / mag
elif len(args) == 4:
"from theta and normal vector (not necessarily normalized)"
self.theta = float(args[0])
self.n = zeros(3, dtype='float64')
self.n[:] = args[1:4]
mag = sqrt(sum(self.n[:] * self.n[:]))
self.n[:] = self.n[:] / mag
else:
print >> sys.stderr, "wrong number of args %g" % len(args)
raise RuntimeError, "unrecoverable error"