def reeke_model_for_use_case(phi_beg, phi_end, margin):
"""Construct a reeke_model for the geometry of the Use Case Thaumatin
dataset, taken from the XDS XPARM. The values are hard-
coded here so that this module does not rely on the location of that
file."""
axis = matrix.col([0.0, 1.0, 0.0])
# original (unrotated) setting
ub = matrix.sqr([
-0.0133393674072, -0.00541609051856, -0.00367748834997,
0.00989309470346, 0.000574825936669, -0.0054505379664,
0.00475395109417, -0.0163935257377, 0.00102384915696
])
r_beg = matrix.sqr(
scitbx.math.r3_rotation_axis_and_angle_as_matrix(axis=self._axis,
angle=phi_beg,
deg=True))
r_osc = matrix.sqr(
scitbx.math.r3_rotation_axis_and_angle_as_matrix(axis=self._axis,
angle=(phi_end -
phi_beg),
deg=True))
ub_beg = r_beg * ub
ub_end = self._r_osc * ub_mid
s0 = matrix.col([0.00237878589035, 1.55544539299e-16, -1.09015329696])
dmin = 1.20117776325
return reeke_model(ub_beg, ub_end, axis, s0, dmin, margin)
def reeke_model_for_use_case(phi_beg, phi_end, margin):
"""Construct a reeke_model for the geometry of the Use Case Thaumatin
dataset, taken from the XDS XPARM. The values are hard-
coded here so that this module does not rely on the location of that
file."""
axis = matrix.col([0.0, 1.0, 0.0])
# original (unrotated) setting
ub = matrix.sqr(
[
-0.0133393674072,
-0.00541609051856,
-0.00367748834997,
0.00989309470346,
0.000574825936669,
-0.0054505379664,
0.00475395109417,
-0.0163935257377,
0.00102384915696,
]
)
r_beg = matrix.sqr(scitbx.math.r3_rotation_axis_and_angle_as_matrix(axis=self._axis, angle=phi_beg, deg=True))
r_osc = matrix.sqr(
scitbx.math.r3_rotation_axis_and_angle_as_matrix(axis=self._axis, angle=(phi_end - phi_beg), deg=True)
)
ub_beg = r_beg * ub
ub_end = self._r_osc * ub_mid
s0 = matrix.col([0.00237878589035, 1.55544539299e-16, -1.09015329696])
dmin = 1.20117776325
return reeke_model(ub_beg, ub_end, axis, s0, dmin, margin)
def generate_python(self, frame): from dials.algorithms.spot_prediction.reeke import reeke_model ub_beg, ub_end = self.get_ub(frame) r = reeke_model(ub_beg, ub_end, self.axis, self.s0, self.dmin, self.margin) hkl = r.generate_indices() hkl = [h for h in hkl if h != (0, 0, 0)] return sorted(hkl)
def regression_test():
"""Perform a regression test by comparing to indices generating
by the brute force method used in the Use Case."""
from rstbx.diffraction import rotation_angles
from rstbx.diffraction import full_sphere_indices
from cctbx.sgtbx import space_group, space_group_symbols
from cctbx.uctbx import unit_cell
# cubic, 50A cell, 1A radiation, 1 deg osciillation, everything ideal
a = 50.0
ub_beg = matrix.sqr(
(1.0 / a, 0.0, 0.0, 0.0, 1.0 / a, 0.0, 0.0, 0.0, 1.0 / a))
axis = matrix.col((0, 1, 0))
r_osc = matrix.sqr(
scitbx.math.r3_rotation_axis_and_angle_as_matrix(axis=axis,
angle=1.0,
deg=True))
ub_end = r_osc * ub_beg
uc = unit_cell((a, a, a, 90, 90, 90))
sg = space_group(space_group_symbols('P23').hall())
s0 = matrix.col((0, 0, 1))
wavelength = 1.0
dmin = 1.5
indices = full_sphere_indices(unit_cell=uc,
resolution_limit=dmin,
space_group=sg)
ra = rotation_angles(dmin, ub_beg, wavelength, axis)
obs_indices, obs_angles = ra.observed_indices_and_angles_from_angle_range(
phi_start_rad=0.0 * pi / 180.0,
phi_end_rad=1.0 * pi / 180.0,
indices=indices)
r = reeke_model(ub_beg, ub_end, axis, s0, dmin, 1.0)
reeke_indices = r.generate_indices()
#r.visualize_with_rgl()
for oi in obs_indices:
assert (tuple(map(int, oi)) in reeke_indices)
#TODO Tests for an oblique cell
print "OK"
def regression_test():
"""Perform a regression test by comparing to indices generating
by the brute force method used in the Use Case."""
from rstbx.diffraction import rotation_angles
from rstbx.diffraction import full_sphere_indices
from cctbx.sgtbx import space_group, space_group_symbols
from cctbx.uctbx import unit_cell
# cubic, 50A cell, 1A radiation, 1 deg osciillation, everything ideal
a = 50.0
ub_beg = matrix.sqr((1.0 / a, 0.0, 0.0, 0.0, 1.0 / a, 0.0, 0.0, 0.0, 1.0 / a))
axis = matrix.col((0, 1, 0))
r_osc = matrix.sqr(scitbx.math.r3_rotation_axis_and_angle_as_matrix(axis=axis, angle=1.0, deg=True))
ub_end = r_osc * ub_beg
uc = unit_cell((a, a, a, 90, 90, 90))
sg = space_group(space_group_symbols("P23").hall())
s0 = matrix.col((0, 0, 1))
wavelength = 1.0
dmin = 1.5
indices = full_sphere_indices(unit_cell=uc, resolution_limit=dmin, space_group=sg)
ra = rotation_angles(dmin, ub_beg, wavelength, axis)
obs_indices, obs_angles = ra.observed_indices_and_angles_from_angle_range(
phi_start_rad=0.0 * pi / 180.0, phi_end_rad=1.0 * pi / 180.0, indices=indices
)
r = reeke_model(ub_beg, ub_end, axis, s0, dmin, 1.0)
reeke_indices = r.generate_indices()
# r.visualize_with_rgl()
for oi in obs_indices:
assert tuple(map(int, oi)) in reeke_indices
# TODO Tests for an oblique cell
print "OK"
sys.exit(
"Expecting either 3 or 4 arguments: path/to/xparm.xds start_phi end_phi margin=3"
)
else:
# take an xparm.xds, phi_beg, phi_end and margin from the command arguments.
from rstbx.cftbx.coordinate_frame_converter import coordinate_frame_converter
cfc = coordinate_frame_converter(sys.argv[1])
phi_beg, phi_end = float(sys.argv[2]), float(sys.argv[3])
margin = int(sys.argv[4]) if len(sys.argv) == 5 else 3
# test run for development/debugging.
u, b = cfc.get_u_b()
ub = matrix.sqr(u * b)
axis = matrix.col(cfc.get("rotation_axis"))
rub_beg = axis.axis_and_angle_as_r3_rotation_matrix(phi_beg) * ub
rub_end = axis.axis_and_angle_as_r3_rotation_matrix(phi_end) * ub
wavelength = cfc.get("wavelength")
sample_to_source_vec = matrix.col(
cfc.get_c("sample_to_source").normalize())
s0 = (-1.0 / wavelength) * sample_to_source_vec
dmin = 1.20117776325
r = reeke_model(rub_beg, rub_end, axis, s0, dmin, margin)
indices = r.generate_indices()
for hkl in indices:
print("%4d %4d %4d" % hkl)
from libtbx.utils import Sorry
raise Sorry("Expecting either 3 or 4 arguments: path/to/xparm.xds start_phi end_phi margin=3")
else:
# take an xparm.xds, phi_beg, phi_end and margin from the command arguments.
from rstbx.cftbx.coordinate_frame_converter import coordinate_frame_converter
cfc = coordinate_frame_converter(sys.argv[1])
phi_beg, phi_end = float(sys.argv[2]), float(sys.argv[3])
margin = int(sys.argv[4]) if len(sys.argv) == 5 else 3
# test run for development/debugging.
u, b = cfc.get_u_b()
ub = matrix.sqr(u * b)
axis = matrix.col(cfc.get("rotation_axis"))
rub_beg = axis.axis_and_angle_as_r3_rotation_matrix(phi_beg) * ub
rub_end = axis.axis_and_angle_as_r3_rotation_matrix(phi_end) * ub
wavelength = cfc.get("wavelength")
sample_to_source_vec = matrix.col(cfc.get_c("sample_to_source").normalize())
s0 = (-1.0 / wavelength) * sample_to_source_vec
dmin = 1.20117776325
r = reeke_model(rub_beg, rub_end, axis, s0, dmin, margin)
indices = r.generate_indices()
for hkl in indices:
print "%4d %4d %4d" % hkl
def tst_use_in_stills_parameterisation_for_crystal(crystal_param=0):
# test use of analytical expression in stills prediction parameterisation
from scitbx import matrix
from math import pi, sqrt, atan2
import random
print
print "Test use of analytical expressions in stills prediction " + "parameterisation for crystal parameters"
# crystal model
from dxtbx.model.crystal import crystal_model
from dials.algorithms.refinement.parameterisation.crystal_parameters import (
CrystalOrientationParameterisation,
CrystalUnitCellParameterisation,
)
crystal = crystal_model((20, 0, 0), (0, 30, 0), (0, 0, 40), space_group_symbol="P 1")
# random reorientation
e = matrix.col((random.random(), random.random(), random.random())).normalize()
angle = random.random() * 180
crystal.rotate_around_origin(e, angle)
wl = 1.1
s0 = matrix.col((0, 0, 1 / wl))
s0u = s0.normalize()
# these are stills, but need a rotation axis for the Reeke algorithm
axis = matrix.col((1, 0, 0))
# crystal parameterisations
xlop = CrystalOrientationParameterisation(crystal)
xlucp = CrystalUnitCellParameterisation(crystal)
# Find some reflections close to the Ewald sphere
from dials.algorithms.spot_prediction.reeke import reeke_model
U = crystal.get_U()
B = crystal.get_B()
UB = U * B
dmin = 4
hkl = reeke_model(UB, UB, axis, s0, dmin, margin=1).generate_indices()
# choose first reflection for now, calc quantities relating to q
h = matrix.col(hkl[0])
q = UB * h
q0 = q.normalize()
q_scalar = q.length()
qq = q_scalar * q_scalar
# calculate the axis of closest rotation
e1 = q0.cross(s0u).normalize()
# calculate c0, a vector orthogonal to s0u and e1
c0 = s0u.cross(e1).normalize()
# calculate q1
q1 = q0.cross(e1).normalize()
# calculate DeltaPsi
a = 0.5 * qq * wl
b = sqrt(qq - a * a)
r = -1.0 * a * s0u + b * c0
DeltaPsi = -1.0 * atan2(r.dot(q1), r.dot(q0))
# Checks on the reflection prediction
from libtbx.test_utils import approx_equal
# 1. check r is on the Ewald sphere
s1 = s0 + r
assert approx_equal(s1.length(), s0.length())
# 2. check DeltaPsi is correct
tst = q.rotate_around_origin(e1, DeltaPsi)
assert approx_equal(tst, r)
# choose the derivative with respect to a particular parameter.
if crystal_param < 3:
dU_dp = xlop.get_ds_dp()[crystal_param]
dq = dU_dp * B * h
else:
dB_dp = xlucp.get_ds_dp()[crystal_param - 3]
dq = U * dB_dp * h
# NKS method of calculating d[q0]/dp
q_dot_dq = q.dot(dq)
dqq = 2.0 * q_dot_dq
dq_scalar = dqq / q_scalar
dq0_dp = (q_scalar * dq - (q_dot_dq * q0)) / qq
# orthogonal to q0, as expected.
print "NKS [q0].(d[q0]/dp) = {0} (should be 0.0)".format(q0.dot(dq0_dp))
# intuitive method of calculating d[q0]/dp, based on the fact that
# it must be orthogonal to q0, i.e. in the plane containing q1 and e1
scaled = dq / q.length()
dq0_dp = scaled.dot(q1) * q1 + scaled.dot(e1) * e1
# orthogonal to q0, as expected.
print "DGW [q0].(d[q0]/dp) = {0} (should be 0.0)".format(q0.dot(dq0_dp))
# So it doesn't matter which method I use to calculate d[q0]/dp, as
# both methods give the same results
# use the fact that -e1 == q0.cross(q1) to redefine the derivative d[e1]/dp
# from Sauter et al. (2014) (A.22)
de1_dp = -1.0 * dq0_dp.cross(q1)
# this *is* orthogonal to e1, as expected.
print "[e1].(d[e1]/dp) = {0} (should be 0.0)".format(e1.dot(de1_dp))
# calculate (d[r]/d[e1])(d[e1]/dp) analytically
from scitbx.array_family import flex
from dials_refinement_helpers_ext import dRq_de
dr_de1 = matrix.sqr(dRq_de(flex.double([DeltaPsi]), flex.vec3_double([e1]), flex.vec3_double([q]))[0])
print "Analytical calculation for (d[r]/d[e1])(d[e1]/dp):"
print dr_de1 * de1_dp
# now calculate using finite differences.
dp = 1.0e-8
del_e1 = de1_dp * dp
e1f = e1 + del_e1 * 0.5
rfwd = q.rotate_around_origin(e1f, DeltaPsi)
e1r = e1 - del_e1 * 0.5
rrev = q.rotate_around_origin(e1r, DeltaPsi)
print "Finite difference estimate for (d[r]/d[e1])(d[e1]/dp):"
print (rfwd - rrev) * (1 / dp)
print "These are essentially the same :-)"
def tst_use_in_stills_parameterisation_for_crystal(crystal_param=0):
# test use of analytical expression in stills prediction parameterisation
from scitbx import matrix
from math import pi, sqrt, atan2
import random
print()
print("Test use of analytical expressions in stills prediction " +
"parameterisation for crystal parameters")
# crystal model
from dxtbx.model.crystal import crystal_model
from dials.algorithms.refinement.parameterisation.crystal_parameters import (
CrystalOrientationParameterisation,
CrystalUnitCellParameterisation,
)
crystal = crystal_model((20, 0, 0), (0, 30, 0), (0, 0, 40),
space_group_symbol="P 1")
# random reorientation
e = matrix.col(
(random.random(), random.random(), random.random())).normalize()
angle = random.random() * 180
crystal.rotate_around_origin(e, angle)
wl = 1.1
s0 = matrix.col((0, 0, 1 / wl))
s0u = s0.normalize()
# these are stills, but need a rotation axis for the Reeke algorithm
axis = matrix.col((1, 0, 0))
# crystal parameterisations
xlop = CrystalOrientationParameterisation(crystal)
xlucp = CrystalUnitCellParameterisation(crystal)
# Find some reflections close to the Ewald sphere
from dials.algorithms.spot_prediction.reeke import reeke_model
U = crystal.get_U()
B = crystal.get_B()
UB = U * B
dmin = 4
hkl = reeke_model(UB, UB, axis, s0, dmin, margin=1).generate_indices()
# choose first reflection for now, calc quantities relating to q
h = matrix.col(hkl[0])
q = UB * h
q0 = q.normalize()
q_scalar = q.length()
qq = q_scalar * q_scalar
# calculate the axis of closest rotation
e1 = q0.cross(s0u).normalize()
# calculate c0, a vector orthogonal to s0u and e1
c0 = s0u.cross(e1).normalize()
# calculate q1
q1 = q0.cross(e1).normalize()
# calculate DeltaPsi
a = 0.5 * qq * wl
b = sqrt(qq - a * a)
r = -1.0 * a * s0u + b * c0
DeltaPsi = -1.0 * atan2(r.dot(q1), r.dot(q0))
# Checks on the reflection prediction
from libtbx.test_utils import approx_equal
# 1. check r is on the Ewald sphere
s1 = s0 + r
assert approx_equal(s1.length(), s0.length())
# 2. check DeltaPsi is correct
tst = q.rotate_around_origin(e1, DeltaPsi)
assert approx_equal(tst, r)
# choose the derivative with respect to a particular parameter.
if crystal_param < 3:
dU_dp = xlop.get_ds_dp()[crystal_param]
dq = dU_dp * B * h
else:
dB_dp = xlucp.get_ds_dp()[crystal_param - 3]
dq = U * dB_dp * h
# NKS method of calculating d[q0]/dp
q_dot_dq = q.dot(dq)
dqq = 2.0 * q_dot_dq
dq_scalar = dqq / q_scalar
dq0_dp = (q_scalar * dq - (q_dot_dq * q0)) / qq
# orthogonal to q0, as expected.
print("NKS [q0].(d[q0]/dp) = {0} (should be 0.0)".format(q0.dot(dq0_dp)))
# intuitive method of calculating d[q0]/dp, based on the fact that
# it must be orthogonal to q0, i.e. in the plane containing q1 and e1
scaled = dq / q.length()
dq0_dp = scaled.dot(q1) * q1 + scaled.dot(e1) * e1
# orthogonal to q0, as expected.
print("DGW [q0].(d[q0]/dp) = {0} (should be 0.0)".format(q0.dot(dq0_dp)))
# So it doesn't matter which method I use to calculate d[q0]/dp, as
# both methods give the same results
# use the fact that -e1 == q0.cross(q1) to redefine the derivative d[e1]/dp
# from Sauter et al. (2014) (A.22)
de1_dp = -1.0 * dq0_dp.cross(q1)
# this *is* orthogonal to e1, as expected.
print("[e1].(d[e1]/dp) = {0} (should be 0.0)".format(e1.dot(de1_dp)))
# calculate (d[r]/d[e1])(d[e1]/dp) analytically
from scitbx.array_family import flex
from dials_refinement_helpers_ext import dRq_de
dr_de1 = matrix.sqr(
dRq_de(flex.double([DeltaPsi]), flex.vec3_double([e1]),
flex.vec3_double([q]))[0])
print("Analytical calculation for (d[r]/d[e1])(d[e1]/dp):")
print(dr_de1 * de1_dp)
# now calculate using finite differences.
dp = 1.0e-8
del_e1 = de1_dp * dp
e1f = e1 + del_e1 * 0.5
rfwd = q.rotate_around_origin(e1f, DeltaPsi)
e1r = e1 - del_e1 * 0.5
rrev = q.rotate_around_origin(e1r, DeltaPsi)
print("Finite difference estimate for (d[r]/d[e1])(d[e1]/dp):")
print((rfwd - rrev) * (1 / dp))
print("These are essentially the same :-)")
