def contained_in_sst(vectors, vertices_ccw):
"""
checks hstack array of unit vectors
!!! inputs must both be unit vectors
!!! vertices must be CCW
"""
# column-wise normals to the spherical triangle edges
sst_normals = np.array([
np.cross(vertices_ccw[:, i[0]], vertices_ccw[:, i[1]])
for i in [(0, 1), (1, 2), (2, 0)]
]).T
sst_normals_unit = mutil.unitVector(sst_normals)
angles = np.arcsin(mutil.columnNorm(sst_normals))
edges = []
for i, ang in enumerate(angles):
sub_ang = np.linspace(0, ang, endpoint=True)
for j in sub_ang:
rm = rot.rotMatOfExpMap(j * sst_normals_unit[:, i].reshape(3, 1))
edges.append(np.dot(vertices_ccw[:, i], rm.T))
edges.append(np.nan * np.ones(3))
dim, n = vectors.shape
contained = []
for v in vectors.T:
d0 = np.dot(sst_normals_unit[:, 0], v)
d1 = np.dot(sst_normals_unit[:, 1], v)
d2 = np.dot(sst_normals_unit[:, 2], v)
contained.append(np.all([d0 > 0, d1 > 0, d2 > 0]))
return contained, np.vstack(edges)
def post_process_stress(grain_data, c_mat_C, schmid_T_list=None):
num_grains = grain_data.shape[0]
stress_S = np.zeros([num_grains, 6])
stress_C = np.zeros([num_grains, 6])
hydrostatic = np.zeros([num_grains, 1])
pressure = np.zeros([num_grains, 1])
von_mises = np.zeros([num_grains, 1])
if schmid_T_list is not None:
num_slip_systems = schmid_T_list.shape[0]
RSS = np.zeros([num_grains, num_slip_systems])
for jj in np.arange(num_grains):
expMap = np.atleast_2d(grain_data[jj, 3:6]).T
strainTmp = np.atleast_2d(grain_data[jj, 15:21]).T
#Turn exponential map into an orientation matrix
Rsc = rot.rotMatOfExpMap(expMap)
strainTenS = np.zeros((3, 3), dtype='float64')
strainTenS[0, 0] = strainTmp[0]
strainTenS[1, 1] = strainTmp[1]
strainTenS[2, 2] = strainTmp[2]
strainTenS[1, 2] = strainTmp[3]
strainTenS[0, 2] = strainTmp[4]
strainTenS[0, 1] = strainTmp[5]
strainTenS[2, 1] = strainTmp[3]
strainTenS[2, 0] = strainTmp[4]
strainTenS[1, 0] = strainTmp[5]
strainTenC = np.dot(np.dot(Rsc.T, strainTenS), Rsc)
strainVecC = mutil.strainTenToVec(strainTenC)
#Calculate stress
stressVecC = np.dot(c_mat_C, strainVecC)
stressTenC = mutil.stressVecToTen(stressVecC)
stressTenS = np.dot(np.dot(Rsc, stressTenC), Rsc.T)
stressVecS = mutil.stressTenToVec(stressTenS)
#Calculate hydrostatic stress
hydrostaticStress = (stressVecS[:3].sum() / 3)
#Calculate Von Mises Stress
devStressS = stressTenS - hydrostaticStress * np.identity(3)
vonMisesStress = np.sqrt((3 / 2) * (devStressS**2).sum())
#Project on to slip systems
if schmid_T_list is not None:
for ii in np.arange(num_slip_systems):
RSS[jj, ii] = np.abs(
(stressTenC * schmid_T_list[ii, :, :]).sum())
stress_S[jj, :] = stressVecS.flatten()
stress_C[jj, :] = stressVecC.flatten()
hydrostatic[jj, 0] = hydrostaticStress
pressure[jj, 0] = -hydrostaticStress
von_mises[jj, 0] = vonMisesStress
stress_data = dict()
stress_data['stress_S'] = stress_S
stress_data['stress_C'] = stress_C
stress_data['hydrostatic'] = hydrostatic
stress_data['pressure'] = pressure
stress_data['von_mises'] = von_mises
if schmid_T_list is not None:
stress_data['RSS'] = RSS
return stress_data
quats_final = rot.quatOfExpMap(
(grain_data['scan%d' % no_load_scans[-1]][:, 3:6].T))
expmaps_final = grain_data['scan111'][:, 3:6].T
grainlist = []
for i in range(ngrains):
mis = rot.misorientation(quats_init[:, i:i + 1], quats_final[:, i:i + 1],
(crystal_symmetry, ))[0]
mis_deg = np.degrees(mis)
if mis_deg > 0.05:
grainlist.append(i)
#%%
rmats_init = rot.rotMatOfExpMap(np.array(expmaps_init)[:, grainlist])
rmats_final = rot.rotMatOfExpMap(np.array(expmaps_final)[:, grainlist])
# getting symmetry group directly here; could also grab from planeData object
# qsym = symm.quatOfLaueGroup('d6h')
plane_data = load_pdata(
'/Users/rachellim/Documents/Research/CHESS_Jun17/2020-08-03/materials2.hexrd',
'ti7al')
qsym = plane_data.getQSym()
bmat = plane_data.latVecOps['B']
# this was for 001 triangle
# sst_vertices = mutil.unitVector(matfuncs.triu(np.ones((3, 3))).T)
# this if for the standard triangle
# sst_vertices = mutil.unitVector(matfuncs.triu(np.ones((3, 3))))
sst_vertices = mutil.unitVector(
def getFriedelPair(tth0, eta0, *ome0, **kwargs):
"""
Get the diffractometer angular coordinates in degrees for
the Friedel pair of a given reflection (min angular distance).
AUTHORS:
J. V. Bernier -- 10 Nov 2009
USAGE:
ome1, eta1 = getFriedelPair(tth0, eta0, *ome0,
display=False,
units='degrees',
convention='hexrd')
INPUTS:
1) tth0 is a list (or ndarray) of 1 or n the bragg angles (2theta) for
the n reflections (tiled to match eta0 if only 1 is given).
2) eta0 is a list (or ndarray) of 1 or n azimuthal coordinates for the n
reflections (tiled to match tth0 if only 1 is given).
3) ome0 is a list (or ndarray) of 1 or n reference oscillation
angles for the n reflections (denoted omega in [1]). This argument
is optional.
4) Keyword arguments may be one of the following:
Keyword Values|{default} Action
-------------- -------------- --------------
'display' True|{False} toggles display info to cmd line
'units' 'radians'|{'degrees'} sets units for input angles
'convention' 'fable'|{'hexrd'} sets conventions defining
the angles (see below)
'chiTilt' None the inclination (about Xlab) of
the oscillation axis
OUTPUTS:
1) ome1 contains the oscialltion angle coordinates of the
Friedel pairs associated with the n input reflections, relative to ome0
(i.e. ome1 = <result> + ome0). Output is in DEGREES!
2) eta1 contains the azimuthal coordinates of the Friedel
pairs associated with the n input reflections. Output units are
controlled via the module variable 'outputDegrees'
NOTES:
JVB) The ouputs ome1, eta1 are written using the selected convention, but the
units are alway degrees. May change this to work with Nathan's global...
JVB) In the 'fable' convention [1], {XYZ} form a RHON basis where X is
downstream, Z is vertical, and eta is CCW with +Z defining eta = 0.
JVB) In the 'hexrd' convention [2], {XYZ} form a RHON basis where Z is upstream,
Y is vertical, and eta is CCW with +X defining eta = 0.
REFERENCES:
[1] E. M. Lauridsen, S. Schmidt, R. M. Suter, and H. F. Poulsen,
``Tracking: a method for structural characterization of grains in
powders or polycrystals''. J. Appl. Cryst. (2001). 34, 744--750
[2] J. V. Bernier, M. P. Miller, J. -S. Park, and U. Lienert,
``Quantitative Stress Analysis of Recrystallized OFHC Cu Subject
to Deformed In Situ'', J. Eng. Mater. Technol. (2008). 130.
DOI:10.1115/1.2870234
"""
dispFlag = False
fableFlag = False
chi = None
c1 = 1.0
c2 = pi / 180.0
zTol = 1.0e-7
# cast to arrays (in case they aren't)
if num.isscalar(eta0):
eta0 = [eta0]
if num.isscalar(tth0):
tth0 = [tth0]
if num.isscalar(ome0):
ome0 = [ome0]
eta0 = num.asarray(eta0)
tth0 = num.asarray(tth0)
ome0 = num.asarray(ome0)
if eta0.ndim != 1:
raise RuntimeError, "your azimuthal input was not 1-D, so I do not know what you expect me to do"
npts = len(eta0)
if tth0.ndim != 1:
raise RuntimeError, "your Bragg angle input was not 1-D, so I do not know what you expect me to do"
else:
if len(tth0) != npts:
if len(tth0) == 1:
tth0 = tth0 * num.ones(npts)
elif npts == 1:
npts = len(tth0)
eta0 = eta0 * num.ones(npts)
else:
raise RuntimeError, "the azimuthal and Bragg angle inputs are inconsistent"
if len(ome0) == 0:
ome0 = num.zeros(npts) # dummy ome0
elif len(ome0) == 1 and npts > 1:
ome0 = ome0 * num.ones(npts)
else:
if len(ome0) != npts:
raise RuntimeError(
"your oscialltion angle input is inconsistent; "
+ "it has length %d while it should be %d" % (len(ome0), npts)
)
# keyword args processing
kwarglen = len(kwargs)
if kwarglen > 0:
argkeys = kwargs.keys()
for i in range(kwarglen):
if argkeys[i] == "display":
dispFlag = kwargs[argkeys[i]]
elif argkeys[i] == "convention":
if kwargs[argkeys[i]].lower() == "fable":
fableFlag = True
elif argkeys[i] == "units":
if kwargs[argkeys[i]] == "radians":
c1 = 180.0 / pi
c2 = 1.0
elif argkeys[i] == "chiTilt":
if kwargs[argkeys[i]] is not None:
chi = kwargs[argkeys[i]]
# a little talkback...
if dispFlag:
if fableFlag:
print "\nUsing Fable angle convention\n"
else:
print "\nUsing image-based angle convention\n"
# mapped eta input
# - in DEGREES, thanks to c1
eta0 = mapAngle(c1 * eta0, [-180, 180], units="degrees")
if fableFlag:
eta0 = 90 - eta0
# must put args into RADIANS
# - eta0 is in DEGREES,
# - the others are in whatever was entered, hence c2
eta0 = d2r * eta0
tht0 = c2 * tth0 / 2
if chi is not None:
chi = c2 * chi
else:
chi = 0
# ---------------------
# SYSTEM SOLVE
#
#
# cos(chi)cos(eta)cos(theta)sin(x) - cos(chi)sin(theta)cos(x) = sin(theta) - sin(chi)sin(eta)cos(theta)
#
#
# Identity: a sin x + b cos x = sqrt(a**2 + b**2) sin (x + alfa)
#
# /
# | atan(b/a) for a > 0
# alfa <
# | pi + atan(b/a) for a < 0
# \
#
# => sin (x + alfa) = c / sqrt(a**2 + b**2)
#
# must use both branches for sin(x) = n: x = u (+ 2k*pi) | x = pi - u (+ 2k*pi)
#
cchi = num.cos(chi)
schi = num.sin(chi)
ceta = num.cos(eta0)
seta = num.sin(eta0)
ctht = num.cos(tht0)
stht = num.sin(tht0)
nchi = num.c_[0.0, cchi, schi].T
gHat0_l = -num.vstack([ceta * ctht, seta * ctht, stht])
a = cchi * ceta * ctht
b = -cchi * stht
c = stht + schi * seta * ctht
# form solution
abMag = num.sqrt(a * a + b * b)
assert num.all(abMag > 0), "Beam vector specification is infeasible!"
phaseAng = num.arctan2(b, a)
rhs = c / abMag
rhs[abs(rhs) > 1.0] = num.nan
rhsAng = num.arcsin(rhs)
# write ome angle output arrays (NaNs persist here)
ome1 = rhsAng - phaseAng
ome2 = num.pi - rhsAng - phaseAng
ome1 = mapAngle(ome1, [-num.pi, num.pi], units="radians")
ome2 = mapAngle(ome2, [-num.pi, num.pi], units="radians")
ome_stack = num.vstack([ome1, ome2])
min_idx = num.argmin(abs(ome_stack), axis=0)
ome_min = ome_stack[min_idx, range(len(ome1))]
eta_min = num.nan * num.ones_like(ome_min)
# mark feasible reflections
goodOnes = -num.isnan(ome_min)
numGood = sum(goodOnes)
tmp_eta = num.empty(numGood)
tmp_gvec = gHat0_l[:, goodOnes]
for i in range(numGood):
come = num.cos(ome_min[goodOnes][i])
some = num.sin(ome_min[goodOnes][i])
rchi = rotMatOfExpMap(num.tile(ome_min[goodOnes][i], (3, 1)) * nchi)
gHat_l = num.dot(rchi, tmp_gvec[:, i].reshape(3, 1))
tmp_eta[i] = num.arctan2(gHat_l[1], gHat_l[0])
pass
eta_min[goodOnes] = tmp_eta
# everybody back to DEGREES!
# - ome1 is in RADIANS here
# - convert and put into [-180, 180]
ome1 = mapAngle(mapAngle(r2d * ome_min, [-180, 180], units="degrees") + c1 * ome0, [-180, 180], units="degrees")
# put eta1 in [-180, 180]
eta1 = mapAngle(r2d * eta_min, [-180, 180], units="degrees")
if not outputDegrees:
ome1 = d2r * ome1
eta1 = d2r * eta1
return ome1, eta1
from hexrd.xrd import transforms as xf
from hexrd.xrd import transforms_CAPI as xfcapi
if xrdbase.haveMultiProc:
multiprocessing = xrdbase.multiprocessing # formerly import
# module vars
piby2 = num.pi * 0.5
r2d = 180. / num.pi
d2r = num.pi / 180.
Xl = num.c_[1, 0, 0].T
Yl = num.c_[0, 1, 0].T
Zl = num.c_[0, 0, 1].T
fableSampCOB = num.dot( rotMatOfExpMap(piby2*Zl),
rotMatOfExpMap(piby2*Yl) )
# global vars for multiproc paintGrid method
planeData_MP = None
omeMin_MP = None
omeMax_MP = None
etaMin_MP = None
etaMax_MP = None
hklList_MP = None
hklIDs_MP = None
etaOmeMaps_MP = None
bMat_MP = None
threshold_MP = None
class GrainSpotter:
from hexrd.xrd.symmetry import toFundamentalRegion
from hexrd.xrd import xrdbase
if xrdbase.haveMultiProc:
multiprocessing = xrdbase.multiprocessing # formerly import
# module vars
piby2 = num.pi * 0.5
r2d = 180. / num.pi
d2r = num.pi / 180.
Xl = num.c_[1, 0, 0].T
Yl = num.c_[0, 1, 0].T
Zl = num.c_[0, 0, 1].T
fableSampCOB = num.dot(rotMatOfExpMap(piby2 * Zl), rotMatOfExpMap(piby2 * Yl))
# global vars for multiproc paintGrid method
planeData_MP = None
omeMin_MP = None
omeMax_MP = None
etaMin_MP = None
etaMax_MP = None
hklList_MP = None
hklIDs_MP = None
etaOmeMaps_MP = None
bMat_MP = None
threshold_MP = None
class GrainSpotter:
from hexrd import matrixutil as mutil
from hexrd.xrd import rotations as rot
from hexrd.xrd.transforms import detectorXYToGvec
d2r = np.pi / 180.
r2d = 180. / np.pi
Xl = np.c_[1, 0, 0].T
Yl = np.c_[0, 1, 0].T
Zl = np.c_[0, 0, 1].T
eVec = Xl.flatten()
chi_b = 15
ome_b = 5
rMat_b = np.dot(rot.rotMatOfExpMap(d2r * chi_b * Xl),
rot.rotMatOfExpMap(d2r * ome_b * Yl))
bVec = np.dot(rMat_b, -Zl)
beam_len = 10
tVec_d = np.c_[-5.0, 3.0, -10.0].T
tVec_s = np.c_[3.0, 0.2, -1.5].T
tVec_c = np.c_[2.0, 0.8, -0.7].T
rMat_d = rot.rotMatOfExpMap(d2r * 21 * mutil.unitVector(np.c_[2, 3, 1].T))
chi = 21 * d2r
ome = 67 * d2r
rMat_s = np.dot(rot.rotMatOfExpMap(chi * Xl), rot.rotMatOfExpMap(ome * Yl))
rMat_c = rot.rotMatOfExpMap(d2r * 36 * mutil.unitVector(np.c_[1, 2, 3].T))
def gen_trial_exp_data(grain_out_file,det_file,mat_file, x_ray_energy, mat_name, max_tth, comp_thresh, chi2_thresh, misorientation_bnd, \
misorientation_spacing,ome_range_deg, nframes, beam_stop_width):
print('Loading Grain Data.....')
#gen_grain_data
ff_data = np.loadtxt(grain_out_file)
#ff_data=np.atleast_2d(ff_data[2,:])
exp_maps = ff_data[:, 3:6]
t_vec_ds = ff_data[:, 6:9]
#
completeness = ff_data[:, 1]
chi2 = ff_data[:, 2]
n_grains = exp_maps.shape[0]
rMat_c = rot.rotMatOfExpMap(exp_maps.T)
cut = np.where(
np.logical_and(completeness > comp_thresh, chi2 < chi2_thresh))[0]
exp_maps = exp_maps[cut, :]
t_vec_ds = t_vec_ds[cut, :]
chi2 = chi2[cut]
# Add Misorientation
mis_amt = misorientation_bnd * np.pi / 180.
spacing = misorientation_spacing * np.pi / 180.
mis_steps = int(misorientation_bnd / misorientation_spacing)
ori_pts = np.arange(-mis_amt, (mis_amt + (spacing * 0.999)), spacing)
num_ori_grid_pts = ori_pts.shape[0]**3
num_oris = exp_maps.shape[0]
XsO, YsO, ZsO = np.meshgrid(ori_pts, ori_pts, ori_pts)
grid0 = np.vstack([XsO.flatten(), YsO.flatten(), ZsO.flatten()]).T
exp_maps_expanded = np.zeros([num_ori_grid_pts * num_oris, 3])
t_vec_ds_expanded = np.zeros([num_ori_grid_pts * num_oris, 3])
for ii in np.arange(num_oris):
pts_to_use = np.arange(num_ori_grid_pts) + ii * num_ori_grid_pts
exp_maps_expanded[pts_to_use, :] = grid0 + np.r_[exp_maps[ii, :]]
t_vec_ds_expanded[pts_to_use, :] = np.r_[t_vec_ds[ii, :]]
exp_maps = exp_maps_expanded
t_vec_ds = t_vec_ds_expanded
n_grains = exp_maps.shape[0]
rMat_c = rot.rotMatOfExpMap(exp_maps.T)
print('Loading Instrument Data.....')
instr_cfg = yaml.load(open(det_file, 'r'))
tiltAngles = instr_cfg['detector']['transform']['tilt_angles']
tVec_d = np.array(instr_cfg['detector']['transform']['t_vec_d']).reshape(
3, 1)
#tVec_d[0] = -0.05
chi = instr_cfg['oscillation_stage']['chi']
tVec_s = np.array(instr_cfg['oscillation_stage']['t_vec_s']).reshape(3, 1)
rMat_d = makeDetectorRotMat(tiltAngles)
rMat_s = makeOscillRotMat([chi, 0.])
pixel_size = instr_cfg['detector']['pixels']['size']
nrows = instr_cfg['detector']['pixels']['rows']
ncols = instr_cfg['detector']['pixels']['columns']
# row_dim = pixel_size[0]*nrows # in mm
# col_dim = pixel_size[1]*ncols # in mm
x_col_edges = pixel_size[1] * (np.arange(ncols + 1) - 0.5 * ncols)
y_row_edges = pixel_size[0] * (np.arange(nrows + 1) - 0.5 * nrows)[::-1]
panel_dims = [(-0.5 * ncols * pixel_size[1], -0.5 * nrows * pixel_size[0]),
(0.5 * ncols * pixel_size[1], 0.5 * nrows * pixel_size[0])]
# a bit overkill, but grab max two-theta from all pixel transforms
rx, ry = np.meshgrid(x_col_edges, y_row_edges)
gcrds = detectorXYToGvec(
np.vstack([rx.flatten(), ry.flatten()]).T, rMat_d, rMat_s, tVec_d,
tVec_s, np.zeros(3))
pixel_tth = gcrds[0][0]
detector_params = np.hstack(
[tiltAngles, tVec_d.flatten(), chi,
tVec_s.flatten()])
ome_period_deg = (ome_range_deg[0][0], (ome_range_deg[0][0] + 360.)
) #degrees
ome_step_deg = (ome_range_deg[0][1] -
ome_range_deg[0][0]) / nframes #degrees
ome_period = (ome_period_deg[0] * np.pi / 180.,
ome_period_deg[1] * np.pi / 180.)
ome_range = [(ome_range_deg[0][0] * np.pi / 180.,
ome_range_deg[0][1] * np.pi / 180.)]
ome_step = ome_step_deg * np.pi / 180.
ome_edges = np.arange(nframes +
1) * ome_step + ome_range[0][0] #fixed 2/26/17
base = np.array([x_col_edges[0], y_row_edges[0], ome_edges[0]])
deltas = np.array([
x_col_edges[1] - x_col_edges[0], y_row_edges[1] - y_row_edges[0],
ome_edges[1] - ome_edges[0]
])
inv_deltas = 1.0 / deltas
clip_vals = np.array([ncols, nrows])
print('Loading Material Data.....')
#Load Material Data
materials = cpl.load(open(mat_file, "rb"))
check = np.zeros(len(materials))
for ii in np.arange(len(materials)):
#print materials[ii].name
check[ii] = materials[ii].name == mat_name
mat_used = materials[np.where(check)[0][0]]
#niti_mart.beamEnergy = valunits.valWUnit("wavelength","ENERGY",61.332,"keV")
mat_used.beamEnergy = valunits.valWUnit("wavelength", "ENERGY",
x_ray_energy, "keV")
mat_used.planeData.exclusions = np.zeros(len(
mat_used.planeData.exclusions),
dtype=bool)
if max_tth > 0.:
mat_used.planeData.tThMax = np.amax(np.radians(max_tth))
else:
mat_used.planeData.tThMax = np.amax(pixel_tth)
pd = mat_used.planeData
print('Final Assembly.....')
experiment = argparse.Namespace()
# grains related information
experiment.n_grains = n_grains # this can be derived from other values...
experiment.rMat_c = rMat_c # n_grains rotation matrices (one per grain)
experiment.exp_maps = exp_maps # n_grains exp_maps -angle * rotation axis- (one per grain)
experiment.plane_data = pd
experiment.detector_params = detector_params
experiment.pixel_size = pixel_size
experiment.ome_range = ome_range
experiment.ome_period = ome_period
experiment.x_col_edges = x_col_edges
experiment.y_row_edges = y_row_edges
experiment.ome_edges = ome_edges
experiment.ncols = ncols
experiment.nrows = nrows
experiment.nframes = nframes # used only in simulate...
experiment.rMat_d = rMat_d
experiment.tVec_d = np.atleast_2d(detector_params[3:6]).T
experiment.chi = detector_params[
6] # note this is used to compute S... why is it needed?
experiment.tVec_s = np.atleast_2d(detector_params[7:]).T
experiment.rMat_c = rMat_c
experiment.distortion = None
experiment.panel_dims = panel_dims # used only in simulate...
experiment.base = base
experiment.inv_deltas = inv_deltas
experiment.clip_vals = clip_vals
experiment.bsw = beam_stop_width
if mis_steps == 0:
nf_to_ff_id_map = cut
else:
nf_to_ff_id_map = np.tile(cut, 27 * mis_steps)
return experiment, nf_to_ff_id_map
def getFriedelPair(tth0, eta0, *ome0, **kwargs):
"""
Get the diffractometer angular coordinates in degrees for
the Friedel pair of a given reflection (min angular distance).
AUTHORS:
J. V. Bernier -- 10 Nov 2009
USAGE:
ome1, eta1 = getFriedelPair(tth0, eta0, *ome0,
display=False,
units='degrees',
convention='hexrd')
INPUTS:
1) tth0 is a list (or ndarray) of 1 or n the bragg angles (2theta) for
the n reflections (tiled to match eta0 if only 1 is given).
2) eta0 is a list (or ndarray) of 1 or n azimuthal coordinates for the n
reflections (tiled to match tth0 if only 1 is given).
3) ome0 is a list (or ndarray) of 1 or n reference oscillation
angles for the n reflections (denoted omega in [1]). This argument
is optional.
4) Keyword arguments may be one of the following:
Keyword Values|{default} Action
-------------- -------------- --------------
'display' True|{False} toggles display info to cmd line
'units' 'radians'|{'degrees'} sets units for input angles
'convention' 'fable'|{'hexrd'} sets conventions defining
the angles (see below)
'chiTilt' None the inclination (about Xlab) of
the oscillation axis
OUTPUTS:
1) ome1 contains the oscialltion angle coordinates of the
Friedel pairs associated with the n input reflections, relative to ome0
(i.e. ome1 = <result> + ome0). Output is in DEGREES!
2) eta1 contains the azimuthal coordinates of the Friedel
pairs associated with the n input reflections. Output units are
controlled via the module variable 'outputDegrees'
NOTES:
JVB) The ouputs ome1, eta1 are written using the selected convention, but the
units are alway degrees. May change this to work with Nathan's global...
JVB) In the 'fable' convention [1], {XYZ} form a RHON basis where X is
downstream, Z is vertical, and eta is CCW with +Z defining eta = 0.
JVB) In the 'hexrd' convention [2], {XYZ} form a RHON basis where Z is upstream,
Y is vertical, and eta is CCW with +X defining eta = 0.
REFERENCES:
[1] E. M. Lauridsen, S. Schmidt, R. M. Suter, and H. F. Poulsen,
``Tracking: a method for structural characterization of grains in
powders or polycrystals''. J. Appl. Cryst. (2001). 34, 744--750
[2] J. V. Bernier, M. P. Miller, J. -S. Park, and U. Lienert,
``Quantitative Stress Analysis of Recrystallized OFHC Cu Subject
to Deformed In Situ'', J. Eng. Mater. Technol. (2008). 130.
DOI:10.1115/1.2870234
"""
dispFlag = False
fableFlag = False
chi = None
c1 = 1.
c2 = pi/180.
zTol = 1.e-7
# cast to arrays (in case they aren't)
if num.isscalar(eta0):
eta0 = [eta0]
if num.isscalar(tth0):
tth0 = [tth0]
if num.isscalar(ome0):
ome0 = [ome0]
eta0 = num.asarray(eta0)
tth0 = num.asarray(tth0)
ome0 = num.asarray(ome0)
if eta0.ndim != 1:
raise RuntimeError, 'your azimuthal input was not 1-D, so I do not know what you expect me to do'
npts = len(eta0)
if tth0.ndim != 1:
raise RuntimeError, 'your Bragg angle input was not 1-D, so I do not know what you expect me to do'
else:
if len(tth0) != npts:
if len(tth0) == 1:
tth0 = tth0*num.ones(npts)
elif npts == 1:
npts = len(tth0)
eta0 = eta0*num.ones(npts)
else:
raise RuntimeError, 'the azimuthal and Bragg angle inputs are inconsistent'
if len(ome0) == 0:
ome0 = num.zeros(npts) # dummy ome0
elif len(ome0) == 1 and npts > 1:
ome0 = ome0*num.ones(npts)
else:
if len(ome0) != npts:
raise RuntimeError('your oscialltion angle input is inconsistent; ' \
+ 'it has length %d while it should be %d' % (len(ome0), npts) )
# keyword args processing
kwarglen = len(kwargs)
if kwarglen > 0:
argkeys = kwargs.keys()
for i in range(kwarglen):
if argkeys[i] == 'display':
dispFlag = kwargs[argkeys[i]]
elif argkeys[i] == 'convention':
if kwargs[argkeys[i]].lower() == 'fable':
fableFlag = True
elif argkeys[i] == 'units':
if kwargs[argkeys[i]] == 'radians':
c1 = 180./pi
c2 = 1.
elif argkeys[i] == 'chiTilt':
if kwargs[argkeys[i]] is not None:
chi = kwargs[argkeys[i]]
# a little talkback...
if dispFlag:
if fableFlag:
print '\nUsing Fable angle convention\n'
else:
print '\nUsing image-based angle convention\n'
# mapped eta input
# - in DEGREES, thanks to c1
eta0 = mapAngle(c1*eta0, [-180, 180], units='degrees')
if fableFlag:
eta0 = 90 - eta0
# must put args into RADIANS
# - eta0 is in DEGREES,
# - the others are in whatever was entered, hence c2
eta0 = d2r*eta0
tht0 = c2*tth0/2
if chi is not None:
chi = c2*chi
else:
chi = 0
# ---------------------
# SYSTEM SOLVE
#
#
# cos(chi)cos(eta)cos(theta)sin(x) - cos(chi)sin(theta)cos(x) = sin(theta) - sin(chi)sin(eta)cos(theta)
#
#
# Identity: a sin x + b cos x = sqrt(a**2 + b**2) sin (x + alfa)
#
# /
# | atan(b/a) for a > 0
# alfa <
# | pi + atan(b/a) for a < 0
# \
#
# => sin (x + alfa) = c / sqrt(a**2 + b**2)
#
# must use both branches for sin(x) = n: x = u (+ 2k*pi) | x = pi - u (+ 2k*pi)
#
cchi = num.cos(chi); schi = num.sin(chi)
ceta = num.cos(eta0); seta = num.sin(eta0)
ctht = num.cos(tht0); stht = num.sin(tht0)
nchi = num.c_[0., cchi, schi].T
gHat0_l = num.vstack([ceta * ctht,
seta * ctht,
stht])
a = cchi*ceta*ctht
b = cchi*schi*seta*ctht + schi*schi*stht - stht
c = stht + cchi*schi*seta*ctht + schi*schi*stht
# form solution
abMag = num.sqrt(a*a + b*b); assert num.all(abMag > 0), "Beam vector specification is infealible!"
phaseAng = num.arctan2(b, a)
rhs = c / abMag; rhs[abs(rhs) > 1.] = num.nan
rhsAng = num.arcsin(rhs)
# write ome angle output arrays (NaNs persist here)
ome1 = rhsAng - phaseAng
ome2 = num.pi - rhsAng - phaseAng
ome1 = mapAngle(ome1, [-num.pi, num.pi], units='radians')
ome2 = mapAngle(ome2, [-num.pi, num.pi], units='radians')
ome_stack = num.vstack([ome1, ome2])
min_idx = num.argmin(abs(ome_stack), axis=0)
ome_min = ome_stack[min_idx, range(len(ome1))]
eta_min = num.nan * num.ones_like(ome_min)
# mark feasible reflections
goodOnes = -num.isnan(ome_min)
numGood = sum(goodOnes)
tmp_eta = num.empty(numGood)
tmp_gvec = gHat0_l[:, goodOnes]
for i in range(numGood):
come = num.cos(ome_min[goodOnes][i])
some = num.sin(ome_min[goodOnes][i])
rchi = rotMatOfExpMap( num.tile(ome_min[goodOnes][i], (3, 1)) * nchi )
gHat_l = num.dot(rchi, tmp_gvec[:, i].reshape(3, 1))
tmp_eta[i] = num.arctan2(gHat_l[1], gHat_l[0])
pass
eta_min[goodOnes] = tmp_eta
# everybody back to DEGREES!
# - ome1 is in RADIANS here
# - convert and put into [-180, 180]
ome1 = mapAngle( mapAngle(r2d*ome_min, [-180, 180], units='degrees') + c1*ome0, [-180, 180], units='degrees')
# put eta1 in [-180, 180]
eta1 = mapAngle(r2d*eta_min, [-180, 180], units='degrees')
if not outputDegrees:
ome1 = d2r * ome1
eta1 = d2r * eta1
return ome1, eta1
def post_process_stress(grain_data,c_mat_C,schmid_T_list=None):
num_grains=grain_data.shape[0]
stress_S=np.zeros([num_grains,6])
stress_C=np.zeros([num_grains,6])
hydrostatic=np.zeros([num_grains,1])
pressure=np.zeros([num_grains,1])
von_mises=np.zeros([num_grains,1])
if schmid_T_list is not None:
num_slip_systems=schmid_T_list.shape[0]
RSS=np.zeros([num_grains,num_slip_systems])
for jj in np.arange(num_grains):
expMap=np.atleast_2d(grain_data[jj,3:6]).T
strainTmp=np.atleast_2d(grain_data[jj,15:21]).T
#Turn exponential map into an orientation matrix
Rsc=rot.rotMatOfExpMap(expMap)
strainTenS = np.zeros((3, 3), dtype='float64')
strainTenS[0, 0] = strainTmp[0]
strainTenS[1, 1] = strainTmp[1]
strainTenS[2, 2] = strainTmp[2]
strainTenS[1, 2] = strainTmp[3]
strainTenS[0, 2] = strainTmp[4]
strainTenS[0, 1] = strainTmp[5]
strainTenS[2, 1] = strainTmp[3]
strainTenS[2, 0] = strainTmp[4]
strainTenS[1, 0] = strainTmp[5]
strainTenC=np.dot(np.dot(Rsc.T,strainTenS),Rsc)
strainVecC = mutil.strainTenToVec(strainTenC)
#Calculate stress
stressVecC=np.dot(c_mat_C,strainVecC)
stressTenC = mutil.stressVecToTen(stressVecC)
stressTenS = np.dot(np.dot(Rsc,stressTenC),Rsc.T)
stressVecS = mutil.stressTenToVec(stressTenS)
#Calculate hydrostatic stress
hydrostaticStress=(stressVecS[:3].sum()/3)
#Calculate Von Mises Stress
devStressS=stressTenS-hydrostaticStress*np.identity(3)
vonMisesStress=np.sqrt((3/2)*(devStressS**2).sum())
#Project on to slip systems
if schmid_T_list is not None:
for ii in np.arange(num_slip_systems):
RSS[jj,ii]=np.abs((stressTenC*schmid_T_list[ii,:,:]).sum())
stress_S[jj,:]=stressVecS.flatten()
stress_C[jj,:]=stressVecC.flatten()
hydrostatic[jj,0]=hydrostaticStress
pressure[jj,0]=-hydrostaticStress
von_mises[jj,0]=vonMisesStress
stress_data=dict()
stress_data['stress_S']=stress_S
stress_data['stress_C']=stress_C
stress_data['hydrostatic']=hydrostatic
stress_data['pressure']=pressure
stress_data['von_mises']=von_mises
if schmid_T_list is not None:
stress_data['RSS']=RSS
return stress_data
def gen_trial_exp_data(grain_out_file,det_file,mat_file, x_ray_energy, mat_name, max_tth, comp_thresh, chi2_thresh, misorientation_bnd, \
misorientation_spacing,ome_range_deg, nframes, beam_stop_width):
print('Loading Grain Data.....')
#gen_grain_data
ff_data=np.loadtxt(grain_out_file)
#ff_data=np.atleast_2d(ff_data[2,:])
exp_maps=ff_data[:,3:6]
t_vec_ds=ff_data[:,6:9]
#
completeness=ff_data[:,1]
chi2=ff_data[:,2]
n_grains=exp_maps.shape[0]
rMat_c = rot.rotMatOfExpMap(exp_maps.T)
cut=np.where(np.logical_and(completeness>comp_thresh,chi2<chi2_thresh))[0]
exp_maps=exp_maps[cut,:]
t_vec_ds=t_vec_ds[cut,:]
chi2=chi2[cut]
# Add Misorientation
mis_amt=misorientation_bnd*np.pi/180.
spacing=misorientation_spacing*np.pi/180.
ori_pts = np.arange(-mis_amt, (mis_amt+(spacing*0.999)),spacing)
num_ori_grid_pts=ori_pts.shape[0]**3
num_oris=exp_maps.shape[0]
XsO, YsO, ZsO = np.meshgrid(ori_pts, ori_pts, ori_pts)
grid0 = np.vstack([XsO.flatten(), YsO.flatten(), ZsO.flatten()]).T
exp_maps_expanded=np.zeros([num_ori_grid_pts*num_oris,3])
t_vec_ds_expanded=np.zeros([num_ori_grid_pts*num_oris,3])
for ii in np.arange(num_oris):
pts_to_use=np.arange(num_ori_grid_pts)+ii*num_ori_grid_pts
exp_maps_expanded[pts_to_use,:]=grid0+np.r_[exp_maps[ii,:] ]
t_vec_ds_expanded[pts_to_use,:]=np.r_[t_vec_ds[ii,:] ]
exp_maps=exp_maps_expanded
t_vec_ds=t_vec_ds_expanded
n_grains=exp_maps.shape[0]
rMat_c = rot.rotMatOfExpMap(exp_maps.T)
print('Loading Instrument Data.....')
instr_cfg = yaml.load(open(det_file, 'r'))
tiltAngles = instr_cfg['detector']['transform']['tilt_angles']
tVec_d = np.array(instr_cfg['detector']['transform']['t_vec_d']).reshape(3, 1)
#tVec_d[0] = -0.05
chi = instr_cfg['oscillation_stage']['chi']
tVec_s = np.array(instr_cfg['oscillation_stage']['t_vec_s']).reshape(3, 1)
rMat_d = makeDetectorRotMat(tiltAngles)
rMat_s = makeOscillRotMat([chi, 0.])
pixel_size = instr_cfg['detector']['pixels']['size']
nrows = instr_cfg['detector']['pixels']['rows']
ncols = instr_cfg['detector']['pixels']['columns']
# row_dim = pixel_size[0]*nrows # in mm
# col_dim = pixel_size[1]*ncols # in mm
x_col_edges = pixel_size[1]*(np.arange(ncols+1) - 0.5*ncols)
y_row_edges = pixel_size[0]*(np.arange(nrows+1) - 0.5*nrows)[::-1]
panel_dims = [(-0.5*ncols*pixel_size[1],
-0.5*nrows*pixel_size[0]),
( 0.5*ncols*pixel_size[1],
0.5*nrows*pixel_size[0])]
# a bit overkill, but grab max two-theta from all pixel transforms
rx, ry = np.meshgrid(x_col_edges, y_row_edges)
gcrds = detectorXYToGvec(np.vstack([rx.flatten(), ry.flatten()]).T,
rMat_d, rMat_s,
tVec_d, tVec_s, np.zeros(3))
pixel_tth = gcrds[0][0]
detector_params = np.hstack([tiltAngles, tVec_d.flatten(), chi, tVec_s.flatten()])
ome_period_deg=(ome_range_deg[0][0], (ome_range_deg[0][0]+360.)) #degrees
ome_step_deg=(ome_range_deg[0][1]-ome_range_deg[0][0])/nframes #degrees
ome_period = (ome_period_deg[0]*np.pi/180.,ome_period_deg[1]*np.pi/180.)
ome_range = [(ome_range_deg[0][0]*np.pi/180.,ome_range_deg[0][1]*np.pi/180.)]
ome_step = ome_step_deg*np.pi/180.
ome_edges = np.arange(nframes+1)*ome_step+ome_range[0][0]#fixed 2/26/17
base = np.array([x_col_edges[0],
y_row_edges[0],
ome_edges[0]])
deltas = np.array([x_col_edges[1] - x_col_edges[0],
y_row_edges[1] - y_row_edges[0],
ome_edges[1] - ome_edges[0]])
inv_deltas = 1.0/deltas
clip_vals = np.array([ncols, nrows])
print('Loading Material Data.....')
#Load Material Data
materials=cpl.load(open( mat_file, "rb" ))
check=np.zeros(len(materials))
for ii in np.arange(len(materials)):
#print materials[ii].name
check[ii]=materials[ii].name==mat_name
mat_used=materials[np.where(check)[0][0]]
#niti_mart.beamEnergy = valunits.valWUnit("wavelength","ENERGY",61.332,"keV")
mat_used.beamEnergy = valunits.valWUnit("wavelength","ENERGY",x_ray_energy,"keV")
mat_used.planeData.exclusions = np.zeros(len(mat_used.planeData.exclusions), dtype=bool)
if max_tth>0.:
mat_used.planeData.tThMax = np.amax(np.radians(max_tth))
else:
mat_used.planeData.tThMax = np.amax(pixel_tth)
pd=mat_used.planeData
print('Final Assembly.....')
experiment = argparse.Namespace()
# grains related information
experiment.n_grains = n_grains # this can be derived from other values...
experiment.rMat_c = rMat_c # n_grains rotation matrices (one per grain)
experiment.exp_maps = exp_maps # n_grains exp_maps -angle * rotation axis- (one per grain)
experiment.plane_data = pd
experiment.detector_params = detector_params
experiment.pixel_size = pixel_size
experiment.ome_range = ome_range
experiment.ome_period = ome_period
experiment.x_col_edges = x_col_edges
experiment.y_row_edges = y_row_edges
experiment.ome_edges = ome_edges
experiment.ncols = ncols
experiment.nrows = nrows
experiment.nframes = nframes# used only in simulate...
experiment.rMat_d = rMat_d
experiment.tVec_d = np.atleast_2d(detector_params[3:6]).T
experiment.chi = detector_params[6] # note this is used to compute S... why is it needed?
experiment.tVec_s = np.atleast_2d(detector_params[7:]).T
experiment.rMat_c = rMat_c
experiment.distortion = None
experiment.panel_dims = panel_dims # used only in simulate...
experiment.base = base
experiment.inv_deltas = inv_deltas
experiment.clip_vals = clip_vals
experiment.bsw = beam_stop_width
nf_to_ff_id_map=cut
return experiment, nf_to_ff_id_map
Eulers_grain = np.zeros([len(scanIDs), 3])
for i in range(len(scanIDs)):
q108 = rot.quatOfExpMap(grain_data['scan%d' % scanIDs[i]][:, 3:6].T)
expmaps_grain.append(grain_data['scan%d' % scanIDs[i]][grain, 3:6])
mis = rot.misorientation(quats_init[:, grain:grain + 1],
q108[:, grain:grain + 1], (crystal_symmetry, ))[0]
mis_ang.append(mis)
# rotmats_grain.append(rot.rotMatOfExpMap(grain_data['scan%d'%no_load_scans[i]][grain,3:6].T))
# Eulers_grain[i,:] = rot.angles_from_rmat_zxz(rot.rotMatOfExpMap(expmaps_grain))
mis_ang_deg = np.degrees(np.array(mis_ang))
#%%
rmats = rot.rotMatOfExpMap(np.array(expmaps_grain).T)
# getting symmetry group directly here; could also grab from planeData object
# qsym = symm.quatOfLaueGroup('d6h')
plane_data = load_pdata(
'/Users/rachellim/Documents/Research/CHESS_Jun17/2020-08-03/materials2.hexrd',
'ti7al')
qsym = plane_data.getQSym()
bmat = plane_data.latVecOps['B']
# this was for 001 triangle
# sst_vertices = mutil.unitVector(matfuncs.triu(np.ones((3, 3))).T)
# this if for the standard triangle
# sst_vertices = mutil.unitVector(matfuncs.triu(np.ones((3, 3))))
sst_vertices = mutil.unitVector(
np.dot(bmat,
for v in vectors.T:
d0 = np.dot(sst_normals_unit[:, 0], v)
d1 = np.dot(sst_normals_unit[:, 1], v)
d2 = np.dot(sst_normals_unit[:, 2], v)
contained.append(np.all([d0 > 0, d1 > 0, d2 > 0]))
return contained, np.vstack(edges)
# =============================================================================
# %% TRANSFORM GRAINS.OUT DATA
# =============================================================================
gt = np.loadtxt(
'/Users/rachellim/Documents/Research/Dye_CHESS_Jan20/fd1-q-1_filtered/filtered_scan_0067_grains.out',
ndmin=2)
rmats = rot.rotMatOfExpMap(gt[:, 3:6].T)
# getting symmetry group directly here; could also grab from planeData object
# qsym = symm.quatOfLaueGroup('d6h')
plane_data = load_pdata(
'/Users/rachellim/Documents/Research/CHESS_Jun17/2020-08-03/materials2.hexrd',
'ti7al')
qsym = plane_data.getQSym()
bmat = plane_data.latVecOps['B']
# this was for 001 triangle
# sst_vertices = mutil.unitVector(matfuncs.triu(np.ones((3, 3))).T)
# this if for the standard triangle
# sst_vertices = mutil.unitVector(matfuncs.triu(np.ones((3, 3))))
sst_vertices = mutil.unitVector(
np.dot(bmat,
from hexrd import matrixutil as mutil
from hexrd.xrd import rotations as rot
from hexrd.xrd.transforms import detectorXYToGvec
d2r = np.pi / 180.
r2d = 180. / np.pi
Xl = np.c_[1, 0, 0].T
Yl = np.c_[0, 1, 0].T
Zl = np.c_[0, 0, 1].T
eVec = Xl.flatten()
chi_b = 15
ome_b = 5
rMat_b = np.dot(rot.rotMatOfExpMap(d2r * chi_b * Xl),
rot.rotMatOfExpMap(d2r * ome_b * Yl))
bVec = np.dot(rMat_b, -Zl)
beam_len = 10
tVec_d = np.c_[ -5.0, 3.0, -10.0].T
tVec_s = np.c_[ 3.0, 0.2, -1.5].T
tVec_c = np.c_[ 2.0, 0.8, -0.7].T
rMat_d = rot.rotMatOfExpMap(d2r*21*mutil.unitVector(np.c_[2, 3, 1].T))
chi = 21 * d2r
ome = 67 * d2r
rMat_s = np.dot(rot.rotMatOfExpMap(chi * Xl),
rot.rotMatOfExpMap(ome * Yl))
