Module: xrd.rotations

20 Functions

hexrd.xrd.rotations.arccosSafe(temp)

Protect against numbers slightly larger than 1 in magnitude due to round-off

hexrd.xrd.rotations.fixQuat(q)

flip to positive q0 and normalize

hexrd.xrd.rotations.invertQuat(q)

silly little routine for inverting a quaternion

hexrd.xrd.rotations.misorientation(q1, q2, *args)

sym is a tuple (crystal_symmetry, *sample_symmetry) generally coded, may split up special cases for no symmetry or crystal/sample only...

hexrd.xrd.rotations.quatProduct(q1, q2)

Product of two unit quaternions.

qp = quatProduct(q2, q1)

q2, q1 are 4 x n, arrays whose columns are

quaternion parameters

qp is 4 x n, an array whose columns are the

quaternion parameters of the product; the first component of qp is nonnegative

If R(q) is the rotation corresponding to the quaternion parameters q, then

R(qp) = R(q2) R(q1)

hexrd.xrd.rotations.quatProductMatrix(quats, mult='right')

Form 4 x 4 arrays to perform the quaternion product

USAGE

qmats = quatProductMatrix(quats, mult=’right’)

INPUTS

1. quats is (4, n), a numpy ndarray array of n quaternions horizontally concatenated

2. mult is a keyword arg, either ‘left’ or ‘right’, denoting the sense of the multiplication:

   / quatProductMatrix(h, mult=’right’) * q

   q * h –> <

   quatProductMatrix(q, mult=’left’) * h

OUTPUTS

1. qmats is (n, 4, 4), the left or right quaternion product operator

NOTES

*) This function is intended to replace a cross-product based

routine for products of quaternions with large arrays of quaternions (e.g. applying symmetries to a large set of orientations).

hexrd.xrd.rotations.quatOfAngleAxis(angle, rotaxis)

make an hstacked array of quaternions from arrays of angle/axis pairs

hexrd.xrd.rotations.quatOfExpMap(expMap)

hexrd.xrd.rotations.quatOfRotMat(R)

hexrd.xrd.rotations.rotMatOfExpMap_opt(expMap)

Optimized version of rotMatOfExpMap

hexrd.xrd.rotations.rotMatOfExpMap_orig(expMap)

Original rotMatOfExpMap, used for comparison to optimized version

hexrd.xrd.rotations.rotMatOfQuat(quat)

Take an array of n quats (numpy ndarray, 4 x n) and generate an array of rotation matrices (n x 3 x 3)

Uses the truncated series expansion for the exponential map; didvide-by-zero is checked using the global ‘tinyRotAng’

hexrd.xrd.rotations.angleAxisOfRotMat(R)

hexrd.xrd.rotations.distanceToFiber(c, s, q, qsym, **kwargs)

discreteFiber(c, s, B=array([[ 1., 0., 0.],

[ 0., 1., 0.],

[ 0., 0., 1.]]), ndiv=120, invert=False, csym=None, ssym=None)

hexrd.xrd.rotations.mapAngle(ang, *args, **kwargs)

Utility routine to map an angle into a specified period

hexrd.xrd.rotations.angularDifference_orig(angList0, angList1, units='radians')

Do the proper (acute) angular difference in the context of a branch cut.

*) Default angular range in the code is [-pi, pi] *) ... maybe more efficient not to vectorize?

hexrd.xrd.rotations.angularDifference_opt(angList0, angList1, units='radians')

Do the proper (acute) angular difference in the context of a branch cut.

*) Default angular range in the code is [-pi, pi]

hexrd.xrd.rotations.printTestName(num, name)

hexrd.xrd.rotations.testRotMatOfExpMap(numpts)

Test rotation matrix from axial vector