hexrd.rotations module
- class hexrd.rotations.RotMatEuler(angles, axes_order, extrinsic=True, units='radians')[source]
Bases:
object- property angles
- property axes_order
- property exponential_map
The matrix invariants of self.rmat as exponential map parameters
Returns
- np.ndarray
The (3, ) array representing the exponential map parameters of the encoded rotation (self.rmat).
- property extrinsic
- property rmat
Return the rotation matrix.
As calculated from angles, axes_order, and convention.
Returns
- numpy.ndarray
The (3, 3) proper orthogonal matrix according to the specification.
- property units
- hexrd.rotations.angleAxisOfRotMat(R)[source]
Extracts angle and axis invariants from rotation matrices.
Parameters
- Rnumpy.ndarray
The (3, 3) or (n, 3, 3) array of rotation matrices. Note that these are assumed to be proper orthogonal.
Raises
- RuntimeError
If R is not an shape is not (3, 3) or (n, 3, 3).
Returns
- phinumpy.ndarray
The (n, ) array of rotation angles for the n input rotation matrices.
- nnumpy.ndarray
The (3, n) array of unit rotation axes for the n input rotation matrices.
- hexrd.rotations.angles_from_rmat_xyz(rmat)[source]
Calculate passive x-y-z Euler angles from a rotation matrix.
Parameters
- rmatTYPE
DESCRIPTION.
Returns
- rxTYPE
DESCRIPTION.
- ryTYPE
DESCRIPTION.
- rzTYPE
DESCRIPTION.
- hexrd.rotations.angles_from_rmat_zxz(rmat)[source]
Calculate active z-x-z Euler angles from a rotation matrix.
Parameters
- rmatTYPE
DESCRIPTION.
Returns
- alphaTYPE
DESCRIPTION.
- betaTYPE
DESCRIPTION.
- gammaTYPE
DESCRIPTION.
- hexrd.rotations.angularDifference(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.rotations.angularDifference_opt(angList0, angList1, units='radians')[source]
Do the proper (acute) angular difference in the context of a branch cut.
*) Default angular range in the code is [-pi, pi]
- hexrd.rotations.angularDifference_orig(angList0, angList1, units='radians')[source]
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.rotations.applySym(vec, qsym, csFlag=False, cullPM=False, tol=1.4901161193847656e-08)[source]
Apply symmetry group to a single 3-vector (columnar) argument.
csFlag : centrosymmetry flag cullPM : cull +/- flag
- hexrd.rotations.arccosSafe(temp)[source]
Protect against numbers slightly larger than 1 in magnitude due to round-off
- hexrd.rotations.discreteFiber(c, s, B=array([[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]]), ndiv=120, invert=False, csym=None, ssym=None)[source]
Generate symmetrically reduced discrete orientation fiber.
Parameters
- cTYPE
DESCRIPTION.
- sTYPE
DESCRIPTION.
- BTYPE, optional
DESCRIPTION. The default is I3.
- ndivTYPE, optional
DESCRIPTION. The default is 120.
- invertTYPE, optional
DESCRIPTION. The default is False.
- csymTYPE, optional
DESCRIPTION. The default is None.
- ssymTYPE, optional
DESCRIPTION. The default is None.
Raises
- RuntimeError
DESCRIPTION.
Returns
- retvalTYPE
DESCRIPTION.
- hexrd.rotations.distanceToFiber(c, s, q, qsym, **kwargs)[source]
Calculate symmetrically reduced distance to orientation fiber.
Parameters
- cTYPE
DESCRIPTION.
- sTYPE
DESCRIPTION.
- qTYPE
DESCRIPTION.
- qsymTYPE
DESCRIPTION.
- **kwargsTYPE
DESCRIPTION.
Raises
- RuntimeError
DESCRIPTION.
Returns
- dTYPE
DESCRIPTION.
- hexrd.rotations.expMapOfQuat(quats)[source]
Return the exponential map parameters for an array of unit quaternions
Parameters
- quatsarray_like
The (4, ) or (4, n) array of hstacked unit quaternions. The convention is [q0, q] where q0 is the scalar part and q is the vector part.
Returns
- expmapsarray_like
The (3, ) or (3, n) array of exponential map parameters associated with the input quaternions.
- hexrd.rotations.ltypeOfLaueGroup(tag)[source]
Yield lattice type of input tag.
Parameters
- tagTYPE
DESCRIPTION.
Raises
- RuntimeError
DESCRIPTION.
Returns
- ltypeTYPE
DESCRIPTION.
- hexrd.rotations.make_rmat_euler(tilt_angles, axes_order, extrinsic=True)[source]
Generate rotation matrix from Euler angles.
Parameters
- tilt_anglesarray_like
The (3, ) list of Euler angles in RADIANS.
- axes_orderstr
The axes order specification (case-insensitive). This must be one of the following: ‘xyz’, ‘zyx’
‘zxy’, ‘yxz’ ‘yzx’, ‘xzy’ ‘xyx’, ‘xzx’ ‘yxy’, ‘yzy’ ‘zxz’, ‘zyz’
- extrinsicbool, optional
Flag denoting the convention. If True, the convention is extrinsic (passive); if False, the convention is instrinsic (active). The default is True.
Returns
- numpy.ndarray
The (3, 3) rotation matrix corresponding to the input specification.
TODO: add kwarg for unit selection for tilt_angles TODO: input checks
- hexrd.rotations.mapAngle(ang, *args, **kwargs)[source]
Utility routine to map an angle into a specified period
- hexrd.rotations.misorientation(q1, q2, *args)[source]
sym is a tuple (crystal_symmetry, *sample_symmetry) generally coded.
!!! may split up special cases for no symmetry or crystal/sample only…
- hexrd.rotations.quatOfAngleAxis(angle, rotaxis)[source]
make an hstacked array of quaternions from arrays of angle/axis pairs
- hexrd.rotations.quatOfExpMap(expMaps)[source]
Returns the unit quaternions associated with exponential map parameters.
Parameters
- expMapsarray_like
The (3,) or (3, n) list of hstacked exponential map parameters to convert.
Returns
- quatsarray_like
The (4,) or (4, n) array of unit quaternions.
Notes
be aware that the output will always have non-negative q0; recall the antipodal symmetry of unit quaternions
- hexrd.rotations.quatOfLaueGroup(tag)[source]
Return quaternion representation of requested symmetry group.
Parameters
- tagstr
A case-insensitive string representing the Schoenflies symbol for the desired Laue group. The 14 available choices are:
Class Symbol N
Triclinic Ci (S2) 1 Monoclinic C2h 2 Orthorhombic D2h (Vh) 4 Tetragonal C4h 4
D4h 8
- Trigonal C3i (S6) 3
D3d 6
- Hexagonal C6h 6
D6h 12
- Cubic Th 12
Oh 24
Raises
- RuntimeError
For invalid symmetry group tag.
Returns
- qsym(4, N) ndarray
the quaterions associated with each element of the chosen symmetry group having n elements (dep. on group – see INPUTS list above).
Notes
The conventions used for assigning a RHON basis, {x1, x2, x3}, to each point group are consistent with those published in Appendix B of [1]_.
References
[1] Nye, J. F., ``Physical Properties of Crystals: Their Representation by Tensors and Matrices’’, Oxford University Press, 1985. ISBN 0198511655
- hexrd.rotations.quatProduct(q1, q2)[source]
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.rotations.quatProductMatrix(quats, mult='right')[source]
Form 4 x 4 arrays to perform the quaternion product
- USAGE
qmats = quatProductMatrix(quats, mult=’right’)
- INPUTS
quats is (4, n), a numpy ndarray array of n quaternions horizontally concatenated
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
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.rotations.rotMatOfExpMap(expMap)
Optimized version of rotMatOfExpMap
- hexrd.rotations.rotMatOfExpMap_orig(expMap)[source]
Original rotMatOfExpMap, used for comparison to optimized version
- hexrd.rotations.rotMatOfQuat(quat)[source]
Convert quaternions to rotation matrices.
Take an array of n quats (numpy ndarray, 4 x n) and generate an array of rotation matrices (n x 3 x 3)
Parameters
- quatTYPE
DESCRIPTION.
Raises
- RuntimeError
DESCRIPTION.
Returns
- rmatTYPE
DESCRIPTION.
Notes
Uses the truncated series expansion for the exponential map; didvide-by-zero is checked using the global ‘cnst.epsf’
- hexrd.rotations.toFundamentalRegion(q, crysSym='Oh', sampSym=None)[source]
Map quaternions to fundamental region.
Parameters
- qTYPE
DESCRIPTION.
- crysSymTYPE, optional
DESCRIPTION. The default is ‘Oh’.
- sampSymTYPE, optional
DESCRIPTION. The default is None.
Raises
- NotImplementedError
DESCRIPTION.
Returns
- qrTYPE
DESCRIPTION.