def difference_rotation_matrix_and_euler_angles(crystal_a, crystal_b):
from cctbx import sgtbx
#assert crystal_a.get_space_group() == crystal_b.get_space_group()
space_group = crystal_b.get_space_group()
min_sum_euler_angles = 1e8
best_R_ab = None
best_cb_op = None
# iterate over space group ops to find smallest differences
for i_op, op in enumerate(space_group.build_derived_laue_group().all_ops()):
if op.r().determinant() < 0:
continue
elif not op.t().is_zero():
continue
cb_op = sgtbx.change_of_basis_op(op.inverse())
crystal_b_sym = crystal_b.change_basis(cb_op)
U_a = crystal_a.get_U()
U_b = crystal_b_sym.get_U()
assert U_a.is_r3_rotation_matrix()
assert U_b.is_r3_rotation_matrix()
# the rotation matrix to transform from U_a to U_b
R_ab = U_b * U_a.transpose()
euler_angles = euler.xyz_angles(R_ab)
sum_euler_angles = sum(abs(ea) for ea in euler_angles)
if sum_euler_angles < min_sum_euler_angles:
min_sum_euler_angles = sum_euler_angles
best_R_ab = R_ab
best_cb_op = cb_op
best_euler_angles = euler.xyz_angles(best_R_ab)
return best_R_ab, best_euler_angles, best_cb_op
def exercise():
from dials.algorithms.indexing import compare_orientation_matrices
from dxtbx.model import Crystal
from cctbx import sgtbx
from scitbx import matrix
from scitbx.math import euler_angles as euler
# try and see if we can get back the original rotation matrix and euler angles
real_space_a = matrix.col((10, 0, 0))
real_space_b = matrix.col((0, 10, 10))
real_space_c = matrix.col((0, 0, 10))
euler_angles = (1.3, 5.6, 7.8)
R = matrix.sqr(
euler.xyz_matrix(euler_angles[0], euler_angles[1], euler_angles[2]))
crystal_a = Crystal(real_space_a,
real_space_b,
real_space_c,
space_group=sgtbx.space_group('P 1'))
crystal_b = Crystal(R * real_space_a,
R * real_space_b,
R * real_space_c,
space_group=sgtbx.space_group('P 1'))
assert approx_equal(
matrix.sqr(crystal_b.get_U()) *
matrix.sqr(crystal_a.get_U()).transpose(), R)
best_R_ab, best_axis, best_angle, best_cb_op = \
compare_orientation_matrices.difference_rotation_matrix_axis_angle(
crystal_a,
crystal_b)
best_euler_angles = euler.xyz_angles(best_R_ab)
assert approx_equal(best_euler_angles, euler_angles)
assert best_cb_op.is_identity_op()
assert approx_equal(best_R_ab, R)
# now see if we can deconvolute the original euler angles after applying
# a change of basis to one of the crystals
crystal_a = Crystal(real_space_a,
real_space_b,
real_space_c,
space_group=sgtbx.space_group('I 2 3'))
crystal_b = Crystal(R * real_space_a,
R * real_space_b,
R * real_space_c,
space_group=sgtbx.space_group('I 2 3'))
cb_op = sgtbx.change_of_basis_op('z,x,y')
crystal_b = crystal_b.change_basis(cb_op)
best_R_ab, best_axis, best_angle, best_cb_op = \
compare_orientation_matrices.difference_rotation_matrix_axis_angle(
crystal_a,
crystal_b)
best_euler_angles = euler.xyz_angles(best_R_ab)
assert approx_equal(best_euler_angles, euler_angles)
assert best_cb_op.c() == cb_op.inverse().c()
assert approx_equal(best_R_ab, R)
def exercise():
from dials.algorithms.indexing import compare_orientation_matrices
from dxtbx.model.crystal import crystal_model
from cctbx import sgtbx
from scitbx import matrix
from scitbx.math import euler_angles as euler
# try and see if we can get back the original rotation matrix and euler angles
real_space_a = matrix.col((10,0,0))
real_space_b = matrix.col((0,10,10))
real_space_c = matrix.col((0,0,10))
euler_angles = (1.3, 5.6, 7.8)
R = matrix.sqr(
euler.xyz_matrix(euler_angles[0], euler_angles[1], euler_angles[2]))
crystal_a = crystal_model(real_space_a,
real_space_b,
real_space_c,
space_group=sgtbx.space_group('P 1'))
crystal_b = crystal_model(R * real_space_a,
R * real_space_b,
R * real_space_c,
space_group=sgtbx.space_group('P 1'))
assert approx_equal(crystal_b.get_U() * crystal_a.get_U().transpose(), R)
best_R_ab, best_axis, best_angle, best_cb_op = \
compare_orientation_matrices.difference_rotation_matrix_axis_angle(
crystal_a,
crystal_b)
best_euler_angles = euler.xyz_angles(best_R_ab)
assert approx_equal(best_euler_angles, euler_angles)
assert best_cb_op.is_identity_op()
assert approx_equal(best_R_ab, R)
# now see if we can deconvolute the original euler angles after applying
# a change of basis to one of the crystals
crystal_a = crystal_model(real_space_a,
real_space_b,
real_space_c,
space_group=sgtbx.space_group('I 2 3'))
crystal_b = crystal_model(R * real_space_a,
R * real_space_b,
R * real_space_c,
space_group=sgtbx.space_group('I 2 3'))
cb_op = sgtbx.change_of_basis_op('z,x,y')
crystal_b = crystal_b.change_basis(cb_op)
best_R_ab, best_axis, best_angle, best_cb_op = \
compare_orientation_matrices.difference_rotation_matrix_axis_angle(
crystal_a,
crystal_b)
best_euler_angles = euler.xyz_angles(best_R_ab)
assert approx_equal(best_euler_angles, euler_angles)
assert best_cb_op.c() == cb_op.inverse().c()
assert approx_equal(best_R_ab, R)
def test_compare_orientation_matrices():
# try and see if we can get back the original rotation matrix and euler angles
real_space_a = matrix.col((10, 0, 0))
real_space_b = matrix.col((0, 10, 10))
real_space_c = matrix.col((0, 0, 10))
euler_angles = (1.3, 5.6, 7.8)
R = matrix.sqr(
euler.xyz_matrix(euler_angles[0], euler_angles[1], euler_angles[2]))
crystal_a = Crystal(real_space_a,
real_space_b,
real_space_c,
space_group=sgtbx.space_group('P 1'))
crystal_b = Crystal(R * real_space_a,
R * real_space_b,
R * real_space_c,
space_group=sgtbx.space_group('P 1'))
assert (matrix.sqr(crystal_b.get_U()) *
matrix.sqr(crystal_a.get_U()).transpose()).elems == pytest.approx(
R.elems)
best_R_ab, best_axis, best_angle, best_cb_op = \
compare_orientation_matrices.difference_rotation_matrix_axis_angle(
crystal_a,
crystal_b)
best_euler_angles = euler.xyz_angles(best_R_ab)
assert best_euler_angles == pytest.approx(euler_angles)
assert best_cb_op.is_identity_op()
assert best_R_ab.elems == pytest.approx(R.elems)
# now see if we can deconvolute the original euler angles after applying
# a change of basis to one of the crystals
crystal_a = Crystal(real_space_a,
real_space_b,
real_space_c,
space_group=sgtbx.space_group('I 2 3'))
crystal_b = Crystal(R * real_space_a,
R * real_space_b,
R * real_space_c,
space_group=sgtbx.space_group('I 2 3'))
cb_op = sgtbx.change_of_basis_op('z,x,y')
crystal_b = crystal_b.change_basis(cb_op)
best_R_ab, best_axis, best_angle, best_cb_op = \
compare_orientation_matrices.difference_rotation_matrix_axis_angle(
crystal_a,
crystal_b)
best_euler_angles = euler.xyz_angles(best_R_ab)
assert best_euler_angles == pytest.approx(euler_angles)
assert best_cb_op.c() == cb_op.inverse().c()
assert best_R_ab.elems == pytest.approx(R.elems)
def ersatz_misset(integrate_lp):
a_s = []
b_s = []
c_s = []
for record in open(integrate_lp):
if 'COORDINATES OF UNIT CELL A-AXIS' in record:
a = map(float, record.split()[-3:])
a_s.append(matrix.col(a))
elif 'COORDINATES OF UNIT CELL B-AXIS' in record:
b = map(float, record.split()[-3:])
b_s.append(matrix.col(b))
elif 'COORDINATES OF UNIT CELL C-AXIS' in record:
c = map(float, record.split()[-3:])
c_s.append(matrix.col(c))
assert(len(a_s) == len(b_s) == len(c_s))
ub0 = matrix.sqr(a_s[0].elems + b_s[0].elems + c_s[0].elems).inverse()
for j in range(len(a_s)):
ub = matrix.sqr(a_s[j].elems + b_s[j].elems + c_s[j].elems).inverse()
print '%7.3f %7.3f %7.3f' % tuple(xyz_angles(ub.inverse() * ub0))
return
def ersatz_misset(integrate_lp):
a_s = []
b_s = []
c_s = []
for record in open(integrate_lp):
if 'COORDINATES OF UNIT CELL A-AXIS' in record:
a = map(float, record.split()[-3:])
a_s.append(matrix.col(a))
elif 'COORDINATES OF UNIT CELL B-AXIS' in record:
b = map(float, record.split()[-3:])
b_s.append(matrix.col(b))
elif 'COORDINATES OF UNIT CELL C-AXIS' in record:
c = map(float, record.split()[-3:])
c_s.append(matrix.col(c))
assert (len(a_s) == len(b_s) == len(c_s))
ub0 = matrix.sqr(a_s[0].elems + b_s[0].elems + c_s[0].elems).inverse()
for j in range(len(a_s)):
ub = matrix.sqr(a_s[j].elems + b_s[j].elems + c_s[j].elems).inverse()
print '%7.3f %7.3f %7.3f' % tuple(xyz_angles(ub.inverse() * ub0))
return
def missets(self, phi):
"""Calculate the missetting angles for the given rotation angle."""
P = self._z.axis_and_angle_as_r3_rotation_matrix(phi, deg=True)
R = self._r.axis_and_angle_as_r3_rotation_matrix(phi, deg=True)
M = P.inverse() * R * self._M0
return xyz_angles(M)
def missets(self, phi):
'''Calculate the missetting angles for the given rotation angle.'''
P = self._z.axis_and_angle_as_r3_rotation_matrix(phi, deg = True)
R = self._r.axis_and_angle_as_r3_rotation_matrix(phi, deg = True)
M = P.inverse() * R * self._M0
return xyz_angles(M)
def dump_mtz_orientation(mtz_file):
from iotbx import mtz
from scitbx import matrix
from scitbx.math.euler_angles import xyz_angles
m = mtz.object(mtz_file)
for b in m.batches():
rxyz = tuple(xyz_angles(matrix.sqr(b.umat())))
print(b.num(), '%7.4f %7.4f %7.4f' % rxyz)
def dump_mtz_orientation(mtz_file):
from iotbx import mtz
from scitbx import matrix
from scitbx.math.euler_angles import xyz_angles
import os.path
m = mtz.object(mtz_file)
for b in m.batches():
rxyz = tuple(xyz_angles(matrix.sqr(b.umat())))
print b.num(), '%7.4f %7.4f %7.4f' % rxyz
return
def test_compare_orientation_matrices():
# try and see if we can get back the original rotation matrix and euler angles
real_space_a = matrix.col((10, 0, 0))
real_space_b = matrix.col((0, 10, 10))
real_space_c = matrix.col((0, 0, 10))
euler_angles = (1.3, 5.6, 7.8)
R = matrix.sqr(
euler.xyz_matrix(euler_angles[0], euler_angles[1], euler_angles[2]))
crystal_a = Crystal(real_space_a,
real_space_b,
real_space_c,
space_group=sgtbx.space_group("P 1"))
crystal_b = Crystal(
R * real_space_a,
R * real_space_b,
R * real_space_c,
space_group=sgtbx.space_group("P 1"),
)
assert (matrix.sqr(crystal_b.get_U()) *
matrix.sqr(crystal_a.get_U()).transpose()).elems == pytest.approx(
R.elems)
(
best_R_ab,
best_axis,
best_angle,
best_cb_op,
) = compare_orientation_matrices.difference_rotation_matrix_axis_angle(
crystal_a, crystal_b)
best_euler_angles = euler.xyz_angles(best_R_ab)
assert best_euler_angles == pytest.approx(euler_angles)
assert best_cb_op.is_identity_op()
assert best_R_ab.elems == pytest.approx(R.elems)
# now see if we can deconvolute the original euler angles after applying
# a change of basis to one of the crystals
crystal_a = Crystal(real_space_a,
real_space_b,
real_space_c,
space_group=sgtbx.space_group("I 2 3"))
cb_op = sgtbx.change_of_basis_op("z,x,y")
crystal_b = Crystal(
R * real_space_a,
R * real_space_b,
R * real_space_c,
space_group=sgtbx.space_group("I 2 3"),
).change_basis(cb_op)
(
best_R_ab,
best_axis,
best_angle,
best_cb_op,
) = compare_orientation_matrices.difference_rotation_matrix_axis_angle(
crystal_a, crystal_b)
best_euler_angles = euler.xyz_angles(best_R_ab)
assert best_euler_angles == pytest.approx(euler_angles)
assert best_cb_op.c() == cb_op.inverse().c()
assert best_R_ab.elems == pytest.approx(R.elems)
crystal_c = crystal_b.change_basis(sgtbx.change_of_basis_op("-y,-z,x"))
assert crystal_c != crystal_b
s = compare_orientation_matrices.rotation_matrix_differences(
[crystal_a, crystal_b, crystal_c], comparison="pairwise")
s = "\n".join(s.splitlines()[:-1]).replace("-0.000", "0.000")
print(s)
assert (s == """\
Change of basis op: b,c,a
Rotation matrix to transform crystal 1 to crystal 2:
{{0.986, -0.135, 0.098},
{0.138, 0.990, -0.023},
{-0.094, 0.036, 0.995}}
Rotation of 9.738 degrees about axis (0.172, 0.565, 0.807)
Change of basis op: -a,-b,c
Rotation matrix to transform crystal 1 to crystal 3:
{{0.986, -0.135, 0.098},
{0.138, 0.990, -0.023},
{-0.094, 0.036, 0.995}}
Rotation of 9.738 degrees about axis (0.172, 0.565, 0.807)
Change of basis op: c,-a,-b
Rotation matrix to transform crystal 2 to crystal 3:
{{1.000, 0.000, 0.000},
{0.000, 1.000, 0.000},
{0.000, 0.000, 1.000}}""")
s = compare_orientation_matrices.rotation_matrix_differences(
[crystal_a, crystal_b, crystal_c], comparison="sequential")
s = "\n".join(s.splitlines()[:-1]).replace("-0.000", "0.000")
print(s)
assert (s == """\
Change of basis op: b,c,a
Rotation matrix to transform crystal 1 to crystal 2:
{{0.986, -0.135, 0.098},
{0.138, 0.990, -0.023},
{-0.094, 0.036, 0.995}}
Rotation of 9.738 degrees about axis (0.172, 0.565, 0.807)
Change of basis op: c,-a,-b
Rotation matrix to transform crystal 2 to crystal 3:
{{1.000, 0.000, 0.000},
{0.000, 1.000, 0.000},
{0.000, 0.000, 1.000}}""")
s = compare_orientation_matrices.rotation_matrix_differences(
(crystal_a, crystal_b), miller_indices=((1, 0, 0), (1, 1, 0)))
assert (s == """\
Change of basis op: b,c,a
Rotation matrix to transform crystal 1 to crystal 2:
{{0.986, -0.135, 0.098},
{0.138, 0.990, -0.023},
{-0.094, 0.036, 0.995}}
Rotation of 9.738 degrees about axis (0.172, 0.565, 0.807)
(1,0,0): 15.26 deg
(1,1,0): 9.12 deg
""")
def ersatz_misset_predict(xparm_xds, spot_xds):
'''As well as possible, try to predict the misorientation angles as a
function of frame # from the indexed spots from the XDS IDXREF step.
Calculation will be performed in CBF coordinae frame.'''
cfc = coordinate_frame_converter(xparm_xds)
axis = cfc.get_c('rotation_axis')
wavelength = cfc.get('wavelength')
beam = (1.0 / wavelength) * cfc.get_c('sample_to_source').normalize()
U, B = cfc.get_u_b()
UB = U * B
detector_origin = cfc.get_c('detector_origin')
detector_fast = cfc.get_c('detector_fast')
detector_slow = cfc.get_c('detector_slow')
pixel_size_fast, pixel_size_slow = cfc.get('detector_pixel_size_fast_slow')
size_fast, size_slow = cfc.get('detector_size_fast_slow')
img_start, osc_start, osc_range = parse_xds_xparm_scan_info(xparm_xds)
rx_s = {}
ry_s = {}
rz_s = {}
for record in open(spot_xds):
values = map(float, record.split())
if len(values) != 7:
continue
hkl = tuple(map(nint, values[-3:]))
if hkl == (0, 0, 0):
continue
x, y, f = values[:3]
phi = ((f - img_start + 1) * osc_range + osc_start) * math.pi / 180.0
lab_xyz = detector_origin + \
detector_fast * x * pixel_size_fast + \
detector_slow * y * pixel_size_slow
rec_xyz = ((1.0 / wavelength) * lab_xyz.normalize() + beam).rotate(
axis, - phi)
calc_xyz = UB * hkl
# now compute vector and angle to overlay calculated position on
# observed position, then convert this to a matrix
shift_axis = calc_xyz.cross(rec_xyz)
shift_angle = calc_xyz.angle(rec_xyz)
M = matrix.sqr(r3_rotation_axis_and_angle_as_matrix(
shift_axis, shift_angle))
rx, ry, rz = xyz_angles(M)
j = int(f)
if not j in rx_s:
rx_s[j] = []
if not j in ry_s:
ry_s[j] = []
if not j in rz_s:
rz_s[j] = []
rx_s[j].append(rx)
ry_s[j].append(ry)
rz_s[j].append(rz)
j = min(rx_s)
ms_x0 = meansd(rx_s[j])[0]
ms_y0 = meansd(ry_s[j])[0]
ms_z0 = meansd(rz_s[j])[0]
for j in sorted(rx_s)[1:]:
ms_x = meansd(rx_s[j])
ms_y = meansd(ry_s[j])
ms_z = meansd(rz_s[j])
print '%4d %6.3f %6.3f %6.3f' % \
(j, ms_x[0] - ms_x0, ms_y[0] - ms_y0, ms_z[0] - ms_z0)
def ersatz_misset_predict(xparm_xds, spot_xds):
'''As well as possible, try to predict the misorientation angles as a
function of frame # from the indexed spots from the XDS IDXREF step.
Calculation will be performed in CBF coordinae frame.'''
cfc = coordinate_frame_converter(xparm_xds)
axis = cfc.get_c('rotation_axis')
wavelength = cfc.get('wavelength')
beam = (1.0 / wavelength) * cfc.get_c('sample_to_source').normalize()
U, B = cfc.get_u_b()
UB = U * B
detector_origin = cfc.get_c('detector_origin')
detector_fast = cfc.get_c('detector_fast')
detector_slow = cfc.get_c('detector_slow')
pixel_size_fast, pixel_size_slow = cfc.get('detector_pixel_size_fast_slow')
size_fast, size_slow = cfc.get('detector_size_fast_slow')
img_start, osc_start, osc_range = parse_xds_xparm_scan_info(xparm_xds)
rx_s = {}
ry_s = {}
rz_s = {}
for record in open(spot_xds):
values = map(float, record.split())
if len(values) != 7:
continue
hkl = tuple(map(nint, values[-3:]))
if hkl == (0, 0, 0):
continue
x, y, f = values[:3]
phi = ((f - img_start + 1) * osc_range + osc_start) * math.pi / 180.0
lab_xyz = detector_origin + \
detector_fast * x * pixel_size_fast + \
detector_slow * y * pixel_size_slow
rec_xyz = ((1.0 / wavelength) * lab_xyz.normalize() + beam).rotate(
axis, -phi)
calc_xyz = UB * hkl
# now compute vector and angle to overlay calculated position on
# observed position, then convert this to a matrix
shift_axis = calc_xyz.cross(rec_xyz)
shift_angle = calc_xyz.angle(rec_xyz)
M = matrix.sqr(
r3_rotation_axis_and_angle_as_matrix(shift_axis, shift_angle))
rx, ry, rz = xyz_angles(M)
j = int(f)
if not j in rx_s:
rx_s[j] = []
if not j in ry_s:
ry_s[j] = []
if not j in rz_s:
rz_s[j] = []
rx_s[j].append(rx)
ry_s[j].append(ry)
rz_s[j].append(rz)
j = min(rx_s)
ms_x0 = meansd(rx_s[j])[0]
ms_y0 = meansd(ry_s[j])[0]
ms_z0 = meansd(rz_s[j])[0]
for j in sorted(rx_s)[1:]:
ms_x = meansd(rx_s[j])
ms_y = meansd(ry_s[j])
ms_z = meansd(rz_s[j])
print '%4d %6.3f %6.3f %6.3f' % \
(j, ms_x[0] - ms_x0, ms_y[0] - ms_y0, ms_z[0] - ms_z0)
def run():
random_seed = 35
flex.set_random_seed(random_seed)
random.seed(random_seed)
data = merge_close_spots.merge_close_spots()
# unit cell and space group for lysozyme
known_symmetry = crystal.symmetry("78,78,37,90,90,90", "P43212")
sim = data.two_color_sim
merged_spot_info = data.spot_proximity(sim)
merged_refl = merged_spot_info[0]
detector = data.detector
beams = data.beams
# to make sure input crystal and indexed crystal model are the same
# orientation before using the refiner
A = sim['input_orientation']
A_inv = A.inverse()
a = A_inv[:3]
b = A_inv[3:6]
c = A_inv[6:]
crystinp = Crystal(a, b, c, space_group=known_symmetry.space_group())
result = index(merged_refl, detector, known_symmetry, beams)
print("RESULTS ARE IN")
cm = result.refined_experiments.crystals()[0]
R, best_axis, best_angle, change_of_basis = difference_rotation_matrix_axis_angle(
crystal_a=cm, crystal_b=crystinp)
euler_angles = euler.xyz_angles(R)
print "input crystal: %s" % crystinp
print "Indexed crystal: %s" % cm
print "rotation of: %s" % R
print "euler angles:", euler_angles
print "change of basis:", change_of_basis.as_hkl()
# cmd_line = command_line.argument_interpreter(master_params=master_phil_scope)
# working_phil = cmd_line.process_and_fetch(args=[])
params = master_phil_scope.extract()
params.refinement.parameterisation.beam.fix = "all"
params.refinement.parameterisation.detector.fix = "all"
params.indexing.known_symmetry.space_group = known_symmetry.space_group_info(
)
params.refinement.verbosity = 3
params.indexing.refinement_protocol.d_min_start = 3
params.indexing.refinement_protocol.n_macro_cycles = 1
params.indexing.known_symmetry.unit_cell = known_symmetry.unit_cell()
params.indexing.multiple_lattice_search.max_lattices = 1
params.indexing.debug = True
params.indexing.known_symmetry.absolute_angle_tolerance = 5.0
params.indexing.known_symmetry.relative_length_tolerance = 0.3
expts = copy.deepcopy(result.refined_experiments)
expts.crystals()[0].change_basis(change_of_basis)
print(expts.crystals()[0])
refined = refine(params, result.reflections, expts, verbosity=1)
print(refined[0].get_experiments().crystals()[0])
# from annlib_ext import AnnAdaptor
# ann = AnnAdaptor(merged_refl['xyzobs.px.value'].as_double(), dim=3, k=1)
# ann.query(result.reflections['xyzobs.px.value'].as_double()+1e-6)
indices_sim = change_of_basis.apply(merged_refl['set_miller_index'])
id_sim = merged_refl['set_id']
# only get those that refined:
idx = align_merged_and_refined_refl(merged_refl,
result.refined_reflections)
indices_sim = flex.miller_index([indices_sim[i] for i in idx])
id_sim = flex.int([id_sim[i] for i in idx])
indices_result = result.refined_reflections['miller_index']
id_result = result.refined_reflections['id']
correct_ind = (indices_sim == indices_result)
wrong_wavelength = (id_sim != id_result) & (id_sim != 2)
wrong_index = (indices_sim != indices_result)
correct_wavelength = (id_sim == id_result) | (id_sim == 2)
correct = correct_ind & correct_wavelength
print "Correct index and wavelength: %i/%i" % (correct.count(True),
len(correct))
print "Correct index but wrong wavelength: %i/%i" % (
wrong_wavelength.count(True), len(wrong_wavelength))
print "Wrong index but correct wavelength: %i/%i" % (
wrong_index.count(True), len(correct_wavelength))
