hexrd.transforms.old_xfcapi module

hexrd.transforms.old_xfcapi.anglesToDVec(angs, bHat_l=array([[-0.], [-0.], [-1.]]), eHat_l=array([[1.], [0.], [0.]]), chi=0.0, rMat_c=array([[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]]))

from ‘eta’ frame out to lab (with handy kwargs to go to crystal or sample)

• setting omega to zero in ang imput and omitting rMat_c leaves in the lab frame in accordance with beam frame specs.

hexrd.transforms.old_xfcapi.anglesToGVec(angs, bHat_l=array([[-0.], [-0.], [-1.]]), eHat_l=array([[1.], [0.], [0.]]), chi=0.0, rMat_c=array([[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]]))

from ‘eta’ frame out to lab (with handy kwargs to go to crystal or sample)

• setting omega to zero in ang imput and omitting rMat_c leaves in the lab frame in accordance with beam frame specs.

hexrd.transforms.old_xfcapi.angularDifference(angList0, angList1, units='radians')

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

*) Default angular range is [-pi, pi]

hexrd.transforms.old_xfcapi.arccosSafe(temp)

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

hexrd.transforms.old_xfcapi.columnNorm(a)

normalize array of column vectors (hstacked, axis = 0)

hexrd.transforms.old_xfcapi.detectorXYToGvec(xy_det, rMat_d, rMat_s, tVec_d, tVec_s, tVec_c, beamVec=array([[-0.], [-0.], [-1.]]), etaVec=array([[1.], [0.], [0.]]))

Takes a list cartesian (x, y) pairs in the detector coordinates and calculates the associated reciprocal lattice (G) vectors and (bragg angle, azimuth) pairs with respect to the specified beam and azimth (eta) reference directions

Required Arguments: xy_det – (n, 2) ndarray or list-like input of n detector (x, y) points rMat_d – (3, 3) ndarray, the COB taking DETECTOR FRAME components

to LAB FRAME

rMat_s – (3, 3) ndarray, the COB taking SAMPLE FRAME components

to LAB FRAME

tVec_d – (3, 1) ndarray, the translation vector connecting

LAB to DETECTOR in LAB

tVec_s – (3, 1) ndarray, the translation vector connecting

LAB to SAMPLE in LAB

tVec_c – (3, 1) ndarray, the translation vector connecting

SAMPLE to CRYSTAL in SAMPLE

Optional Keyword Arguments: beamVec – (3, 1) mdarray containing the incident beam direction

components in the LAB FRAME

etaVec – (3, 1) mdarray containing the reference azimuth direction

components in the LAB FRAME

Outputs: (n, 2) ndarray containing the (tTh, eta) pairs associated with each (x, y) (n, 3) ndarray containing the associated G vector directions in the LAB FRAME associated with gVecs

hexrd.transforms.old_xfcapi.detectorXYToGvecArray(xy_det, rMat_d, rMat_s, tVec_d, tVec_s, tVec_c, beamVec=array([[-0.], [-0.], [-1.]]), etaVec=array([[1.], [0.], [0.]]))

Takes a list cartesian (x, y) pairs in the detector coordinates and calculates the associated reciprocal lattice (G) vectors and (bragg angle, azimuth) pairs with respect to the specified beam and azimth (eta) reference directions

Required Arguments: xy_det – (n, 2) ndarray or list-like input of n detector (x, y) points rMat_d – (3, 3) ndarray, the COB taking DETECTOR FRAME components

to LAB FRAME

rMat_s – (n, 3, 3) ndarray, the COB taking SAMPLE FRAME components

to LAB FRAME

tVec_d – (3, 1) ndarray, the translation vector connecting

LAB to DETECTOR in LAB

tVec_s – (3, 1) ndarray, the translation vector connecting

LAB to SAMPLE in LAB

tVec_c – (3, 1) ndarray, the translation vector connecting

SAMPLE to CRYSTAL in SAMPLE

Optional Keyword Arguments: beamVec – (3, 1) mdarray containing the incident beam direction

components in the LAB FRAME

etaVec – (3, 1) mdarray containing the reference azimuth direction

components in the LAB FRAME

Outputs: (n, 2) ndarray containing the (tTh, eta) pairs associated with each (x, y) (n, 3) ndarray containing the associated G vector directions in the LAB FRAME associated with gVecs

hexrd.transforms.old_xfcapi.gvecToDetectorXY(gVec_c, rMat_d, rMat_s, rMat_c, tVec_d, tVec_s, tVec_c, beamVec=array([[-0.], [-0.], [-1.]]))

Takes a list of unit reciprocal lattice vectors in crystal frame to the specified detector-relative frame, subject to the conditions:

1. the reciprocal lattice vector must be able to satisfy a bragg condition

2. the associated diffracted beam must intersect the detector plane

Required Arguments: gVec_c – (n, 3) ndarray of n reciprocal lattice vector components

in the CRYSTAL FRAME

rMat_d – (3, 3) ndarray, the COB taking DETECTOR FRAME components

to LAB FRAME

rMat_s – (3, 3) ndarray, the COB taking SAMPLE FRAME components

to LAB FRAME

rMat_c – (3, 3) ndarray, the COB taking CRYSTAL FRAME components

to SAMPLE FRAME

tVec_d – (3, 1) ndarray, the translation vector connecting

LAB to DETECTOR

tVec_s – (3, 1) ndarray, the translation vector connecting

LAB to SAMPLE

tVec_c – (3, 1) ndarray, the translation vector connecting

SAMPLE to CRYSTAL

Outputs: (m, 2) ndarray containing the intersections of m <= n diffracted beams associated with gVecs

hexrd.transforms.old_xfcapi.gvecToDetectorXYArray(gVec_c, rMat_d, rMat_s, rMat_c, tVec_d, tVec_s, tVec_c, beamVec=array([[-0.], [-0.], [-1.]]))

Takes a list of unit reciprocal lattice vectors in crystal frame to the specified detector-relative frame, subject to the conditions:

1. the reciprocal lattice vector must be able to satisfy a bragg condition

2. the associated diffracted beam must intersect the detector plane

Required Arguments: gVec_c – (n, 3) ndarray of n reciprocal lattice vector components

in the CRYSTAL FRAME

rMat_d – (3, 3) ndarray, the COB taking DETECTOR FRAME components

to LAB FRAME

rMat_s – (n, 3, 3) ndarray of n COB taking SAMPLE FRAME components

to LAB FRAME

rMat_c – (3, 3) ndarray, the COB taking CRYSTAL FRAME components

to SAMPLE FRAME

tVec_d – (3, 1) ndarray, the translation vector connecting

LAB to DETECTOR in LAB

tVec_s – (3, 1) ndarray, the translation vector connecting

LAB to SAMPLE in LAB

tVec_c – (3, 1) ndarray, the translation vector connecting

SAMPLE to CRYSTAL in SAMPLE

Outputs: (m, 2) ndarray containing the intersections of m <= n diffracted beams associated with gVecs

hexrd.transforms.old_xfcapi.homochoricOfQuat(quats)

Compute homochoric parameters of unit quaternions

quats is (4, n)

hexrd.transforms.old_xfcapi.makeBinaryRotMat(axis)

hexrd.transforms.old_xfcapi.makeDetectorRotMat(tiltAngles)

Form the (3, 3) tilt rotations from the tilt angle list:

tiltAngles = [gamma_Xl, gamma_Yl, gamma_Zl] in radians

hexrd.transforms.old_xfcapi.makeEtaFrameRotMat(bHat_l, eHat_l)

hexrd.transforms.old_xfcapi.makeGVector(hkl, bMat)

take a CRYSTAL RELATIVE B matrix onto a list of hkls to output unit reciprocal lattice vectors (a.k.a. lattice plane normals)

Required Arguments: hkls – (3, n) ndarray of n hstacked reciprocal lattice vector component

triplets

bMat – (3, 3) ndarray representing the matirix taking reciprocal lattice

vectors to the crystal reference frame

Output: gVecs – (3, n) ndarray of n unit reciprocal lattice vectors

(a.k.a. lattice plane normals)

To Do: * might benefit from some assert statements to catch improperly shaped

input.

hexrd.transforms.old_xfcapi.makeOscillRotMat(oscillAngles)

oscillAngles = [chi, ome]

hexrd.transforms.old_xfcapi.makeOscillRotMatArray(chi, omeArray)

Applies makeOscillAngles multiple times, for one chi value and an array of omega values.

hexrd.transforms.old_xfcapi.makeRotMatOfExpMap(expMap)

make a rotation matrix from an exponential map

hexrd.transforms.old_xfcapi.makeRotMatOfQuat(quats)

make rotation matrix from vstacked unit quaternions

hexrd.transforms.old_xfcapi.mapAngle(ang, *args, **kwargs)

Utility routine to map an angle into a specified period

hexrd.transforms.old_xfcapi.oscillAnglesOfHKLs(hkls, chi, rMat_c, bMat, wavelength, vInv=None, beamVec=array([[-0.], [-0.], [-1.]]), etaVec=array([[1.], [0.], [0.]]))

Takes a list of unit reciprocal lattice vectors in crystal frame to the specified detector-relative frame, subject to the conditions:

1. the reciprocal lattice vector must be able to satisfy a bragg condition

2. the associated diffracted beam must intersect the detector plane

Required Arguments: hkls – (n, 3) ndarray of n reciprocal lattice vectors

in the CRYSTAL FRAME

chi – float representing the inclination angle of the

oscillation axis (std coords)

rMat_c – (3, 3) ndarray, the COB taking CRYSTAL FRAME components

to SAMPLE FRAME

bMat – (3, 3) ndarray, the COB taking RECIPROCAL LATTICE components

to CRYSTAL FRAME

wavelength – float representing the x-ray wavelength in Angstroms

Optional Keyword Arguments: beamVec – (3, 1) mdarray containing the incident beam direction

components in the LAB FRAME

etaVec – (3, 1) mdarray containing the reference azimuth direction

components in the LAB FRAME

Outputs: ome0 – (n, 3) ndarray containing the feasible (tTh, eta, ome) triplets

for each input hkl (first solution)

ome1 – (n, 3) ndarray containing the feasible (tTh, eta, ome) triplets

for each input hkl (second solution)

Notes:

The reciprocal lattice vector, G, will satisfy the the Bragg condition when:

b.T * G / ||G|| = -sin(theta)

where b is the incident beam direction (k_i) and theta is the Bragg angle consistent with G and the specified wavelength. The components of G in the lab frame in this case are obtained using the crystal orientation, Rc, and the single-parameter oscillation matrix, Rs(ome):

Rs(ome) * Rc * G / ||G||

The equation above can be rearranged to yield an expression of the form:

a*sin(ome) + b*cos(ome) = c

which is solved using the relation:

a*sin(x) + b*cos(x) = sqrt(a**2 + b**2) * sin(x + alpha)

—> sin(x + alpha) = c / sqrt(a**2 + b**2)

where:

alpha = atan2(b, a)

The solutions are:

/ | arcsin(c / sqrt(a**2 + b**2)) - alpha

x = <

pi - arcsin(c / sqrt(a**2 + b**2)) - alpha

There is a double root in the case the reflection is tangent to the Debye-Scherrer cone (c**2 = a**2 + b**2), and no solution if the Laue condition cannot be satisfied (filled with NaNs in the results array here)

hexrd.transforms.old_xfcapi.quat_distance(q1, q2, qsym)

qsym coming from hexrd.crystallogray.PlaneData.getQSym() is C-contiguous

hexrd.transforms.old_xfcapi.rotate_vecs_about_axis(angle, axis, vecs)

hexrd.transforms.old_xfcapi.rowNorm(a)

normalize array of row vectors (vstacked, axis = 1)

hexrd.transforms.old_xfcapi.unitRowVector(vecIn)

hexrd.transforms.old_xfcapi.validateAngleRanges(angList, angMin, angMax, ccw=True)