def convertUToRotMat(Urows, U0, symTag='Oh', display=False):
"""
Takes GrainSpotter gff ouput in rows
U11 U12 U13 U21 U22 U23 U13 U23 U33
and takes it into the hexrd/APS frame of reference
Urows comes from grainspotter's gff output
U0 comes from xrd.crystallography.latticeVectors.U0
"""
numU, testDim = Urows.shape
assert testDim == 9, "Your input must have 9 columns; yours has %d" % (testDim)
qin = quatOfRotMat(Urows.reshape(numU, 3, 3))
qout = num.dot( quatProductMatrix( quatOfRotMat(fableSampCOB), mult='left' ), \
num.dot( quatProductMatrix( quatOfRotMat(U0.T), mult='right'), \
qin ).squeeze() ).squeeze()
if qout.ndim == 1:
qout = toFundamentalRegion(qout.reshape(4, 1), crysSym=symTag, sampSym=None)
else:
qout = toFundamentalRegion(qout, crysSym=symTag, sampSym=None)
if display:
print "quaternions in (Fable convention):"
print qin.T
print "quaternions out (hexrd convention, symmetrically reduced)"
print qout.T
pass
Uout = rotMatOfQuat(qout)
return Uout
def convertRotMatToFableU(rMats, U0=num.eye(3), symTag='Oh', display=False):
"""
Makes GrainSpotter gff ouput
U11 U12 U13 U21 U22 U23 U13 U23 U33
and takes it into the hexrd/APS frame of reference
Urows comes from grainspotter's gff output
U0 comes from xrd.crystallography.latticeVectors.U0
"""
numU = num.shape(num.atleast_3d(rMats))[0]
qin = quatOfRotMat(num.atleast_3d(rMats))
qout = num.dot( quatProductMatrix( quatOfRotMat(fableSampCOB.T), mult='left' ), \
num.dot( quatProductMatrix( quatOfRotMat(U0), mult='right'), \
qin ).squeeze() ).squeeze()
if qout.ndim == 1:
qout = toFundamentalRegion(qout.reshape(4, 1), crysSym=symTag, sampSym=None)
else:
qout = toFundamentalRegion(qout, crysSym=symTag, sampSym=None)
if display:
print "quaternions in (hexrd convention):"
print qin.T
print "quaternions out (Fable convention, symmetrically reduced)"
print qout.T
pass
Uout = rotMatOfQuat(qout)
return Uout
def convertRotMatToFableU(rMats, U0=num.eye(3), symTag='Oh', display=False):
"""
Makes GrainSpotter gff ouput
U11 U12 U13 U21 U22 U23 U13 U23 U33
and takes it into the hexrd/APS frame of reference
Urows comes from grainspotter's gff output
U0 comes from xrd.crystallography.latticeVectors.U0
"""
numU = num.shape(num.atleast_3d(rMats))[0]
qin = quatOfRotMat(num.atleast_3d(rMats))
qout = num.dot( quatProductMatrix( quatOfRotMat(fableSampCOB.T), mult='left' ), \
num.dot( quatProductMatrix( quatOfRotMat(U0), mult='right'), \
qin ).squeeze() ).squeeze()
if qout.ndim == 1:
qout = toFundamentalRegion(qout.reshape(4, 1),
crysSym=symTag,
sampSym=None)
else:
qout = toFundamentalRegion(qout, crysSym=symTag, sampSym=None)
if display:
print "quaternions in (hexrd convention):"
print qin.T
print "quaternions out (Fable convention, symmetrically reduced)"
print qout.T
pass
Uout = rotMatOfQuat(qout)
return Uout
def convertUToRotMat(Urows, U0, symTag='Oh', display=False):
"""
Takes GrainSpotter gff ouput in rows
U11 U12 U13 U21 U22 U23 U13 U23 U33
and takes it into the hexrd/APS frame of reference
Urows comes from grainspotter's gff output
U0 comes from xrd.crystallography.latticeVectors.U0
"""
numU, testDim = Urows.shape
assert testDim == 9, "Your input must have 9 columns; yours has %d" % (
testDim)
qin = quatOfRotMat(Urows.reshape(numU, 3, 3))
qout = num.dot( quatProductMatrix( quatOfRotMat(fableSampCOB), mult='left' ), \
num.dot( quatProductMatrix( quatOfRotMat(U0.T), mult='right'), \
qin ).squeeze() ).squeeze()
if qout.ndim == 1:
qout = toFundamentalRegion(qout.reshape(4, 1),
crysSym=symTag,
sampSym=None)
else:
qout = toFundamentalRegion(qout, crysSym=symTag, sampSym=None)
if display:
print "quaternions in (Fable convention):"
print qin.T
print "quaternions out (hexrd convention, symmetrically reduced)"
print qout.T
pass
Uout = rotMatOfQuat(qout)
return Uout
def quaternion_ball(qref, radius, num=500):
"""
Makes a ball of randomly sampled quaternions within the specified misorientation of the supplied reference.
Parameters
----------
qref : array_like, (4,)
Unit quaternion defining the reference orientation.
radius : scalar
Maximum misorientation in degrees.
num : int, optional
The number of orientations to generate. The default is 500.
Returns
-------
The (4, num) array of quaternions around qref.
"""
# make random angle/axis pairs
rand_angs = np.radians(radius) * np.random.rand(num)
rand_axes = mutil.unitVector(np.random.randn(3, num))
# form quats
qball = rot.quatOfAngleAxis(rand_angs, rand_axes)
# recenter around reference orientation
qref_mat = rot.quatProductMatrix(np.atleast_1d(qref).reshape(4, 1),
mult='right').squeeze()
return np.dot(qref_mat, qball)
