def candidate_orientation_matrices(basis_vectors, max_combinations=None):
# select unique combinations of input vectors to test
# the order of combinations is such that combinations comprising vectors
# nearer the beginning of the input list will appear before combinations
# comprising vectors towards the end of the list
n = len(basis_vectors)
# hardcoded limit on number of vectors, fixes issue #72
# https://github.com/dials/dials/issues/72
n = min(n, 100)
basis_vectors = basis_vectors[:n]
combinations = flex.vec3_int(flex.nested_loop((n, n, n)))
combinations = combinations.select(
flex.sort_permutation(combinations.as_vec3_double().norms()))
# select only those combinations where j > i and k > j
i, j, k = combinations.as_vec3_double().parts()
sel = flex.bool(len(combinations), True)
sel &= j > i
sel &= k > j
combinations = combinations.select(sel)
if max_combinations is not None and max_combinations < len(combinations):
combinations = combinations[:max_combinations]
half_pi = 0.5 * math.pi
min_angle = 20 / 180 * math.pi # 20 degrees, arbitrary cutoff
for i, j, k in combinations:
a = basis_vectors[i]
b = basis_vectors[j]
angle = a.angle(b)
if angle < min_angle or (math.pi - angle) < min_angle:
continue
a_cross_b = a.cross(b)
gamma = a.angle(b)
if gamma < half_pi:
# all angles obtuse if possible please
b = -b
a_cross_b = -a_cross_b
c = basis_vectors[k]
if abs(half_pi - a_cross_b.angle(c)) < min_angle:
continue
alpha = b.angle(c, deg=True)
if alpha < half_pi:
c = -c
if a_cross_b.dot(c) < 0:
# we want right-handed basis set, therefore invert all vectors
a = -a
b = -b
c = -c
model = Crystal(a, b, c, space_group_symbol="P 1")
uc = model.get_unit_cell()
cb_op_to_niggli = uc.change_of_basis_op_to_niggli_cell()
model = model.change_basis(cb_op_to_niggli)
uc = model.get_unit_cell()
params = uc.parameters()
if uc.volume() > (params[0] * params[1] * params[2] / 100):
# unit cell volume cutoff from labelit 2004 paper
yield model
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 apply_symmetry(self, crystal_model):
if not (self.target_symmetry_primitive
and self.target_symmetry_primitive.space_group()):
return crystal, sgtbx.change_of_basis_op()
target_space_group = self.target_symmetry_primitive.space_group()
A = crystal_model.get_A()
max_delta = self._max_delta
items = iotbx_converter(crystal_model.get_unit_cell(),
max_delta=max_delta)
target_sg_ref = target_space_group.info().reference_setting().group()
best_angular_difference = 1e8
best_subgroup = None
for item in items:
if bravais_lattice(group=target_sg_ref) != bravais_lattice(
group=item["ref_subsym"].space_group()):
continue
if item["max_angular_difference"] < best_angular_difference:
best_angular_difference = item["max_angular_difference"]
best_subgroup = item
if best_subgroup is None:
return None, None
cb_op_inp_best = best_subgroup["cb_op_inp_best"]
orient = crystal_orientation(A, True)
orient_best = orient.change_basis(
scitbx.matrix.sqr(
cb_op_inp_best.c().as_double_array()[0:9]).transpose())
constrain_orient = orient_best.constrain(best_subgroup["system"])
best_subsym = best_subgroup["best_subsym"]
cb_op_best_ref = best_subsym.change_of_basis_op_to_reference_setting()
target_sg_best = target_sg_ref.change_basis(cb_op_best_ref.inverse())
ref_subsym = best_subsym.change_basis(cb_op_best_ref)
cb_op_ref_primitive = ref_subsym.change_of_basis_op_to_primitive_setting(
)
cb_op_best_primitive = cb_op_ref_primitive * cb_op_best_ref
cb_op_inp_primitive = cb_op_ref_primitive * cb_op_best_ref * cb_op_inp_best
direct_matrix = constrain_orient.direct_matrix()
a = scitbx.matrix.col(direct_matrix[:3])
b = scitbx.matrix.col(direct_matrix[3:6])
c = scitbx.matrix.col(direct_matrix[6:9])
model = Crystal(a, b, c, space_group=target_sg_best)
assert target_sg_best.is_compatible_unit_cell(model.get_unit_cell())
model = model.change_basis(cb_op_best_primitive)
return model, cb_op_inp_primitive
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 test_crystal_model():
real_space_a = matrix.col((10, 0, 0))
real_space_b = matrix.col((0, 11, 0))
real_space_c = matrix.col((0, 0, 12))
model = Crystal(
real_space_a=(10, 0, 0),
real_space_b=(0, 11, 0),
real_space_c=(0, 0, 12),
space_group_symbol="P 1",
)
# This doesn't work as python class uctbx.unit_cell(uctbx_ext.unit_cell)
# so C++ and python classes are different types
# assert isinstance(model.get_unit_cell(), uctbx.unit_cell)
assert model.get_unit_cell().parameters() == (10.0, 11.0, 12.0, 90.0, 90.0,
90.0)
assert approx_equal(model.get_A(),
(1 / 10, 0, 0, 0, 1 / 11, 0, 0, 0, 1 / 12))
assert approx_equal(
matrix.sqr(model.get_A()).inverse(), (10, 0, 0, 0, 11, 0, 0, 0, 12))
assert approx_equal(model.get_B(), model.get_A())
assert approx_equal(model.get_U(), (1, 0, 0, 0, 1, 0, 0, 0, 1))
assert approx_equal(model.get_real_space_vectors(),
(real_space_a, real_space_b, real_space_c))
assert (model.get_crystal_symmetry().unit_cell().parameters() ==
model.get_unit_cell().parameters())
assert model.get_crystal_symmetry().space_group() == model.get_space_group(
)
model2 = Crystal(
real_space_a=(10, 0, 0),
real_space_b=(0, 11, 0),
real_space_c=(0, 0, 12),
space_group_symbol="P 1",
)
assert model == model2
model2a = Crystal(model.get_A(), model.get_space_group())
assert model == model2a
model2b = Crystal(
matrix.sqr(model.get_A()).inverse().elems,
model.get_space_group().type().lookup_symbol(),
reciprocal=False,
)
assert model == model2b
# rotate 45 degrees about x-axis
R1 = matrix.sqr((
1,
0,
0,
0,
math.cos(math.pi / 4),
-math.sin(math.pi / 4),
0,
math.sin(math.pi / 4),
math.cos(math.pi / 4),
))
# rotate 30 degrees about y-axis
R2 = matrix.sqr((
math.cos(math.pi / 6),
0,
math.sin(math.pi / 6),
0,
1,
0,
-math.sin(math.pi / 6),
0,
math.cos(math.pi / 6),
))
# rotate 60 degrees about z-axis
R3 = matrix.sqr((
math.cos(math.pi / 3),
-math.sin(math.pi / 3),
0,
math.sin(math.pi / 3),
math.cos(math.pi / 3),
0,
0,
0,
1,
))
R = R1 * R2 * R3
model.set_U(R)
# B is unchanged
assert approx_equal(model.get_B(),
(1 / 10, 0, 0, 0, 1 / 11, 0, 0, 0, 1 / 12))
assert approx_equal(model.get_U(), R)
assert approx_equal(model.get_A(),
matrix.sqr(model.get_U()) * matrix.sqr(model.get_B()))
a_, b_, c_ = model.get_real_space_vectors()
assert approx_equal(a_, R * real_space_a)
assert approx_equal(b_, R * real_space_b)
assert approx_equal(c_, R * real_space_c)
assert (str(model).replace("-0.0000", " 0.0000") == """\
Crystal:
Unit cell: (10.000, 11.000, 12.000, 90.000, 90.000, 90.000)
Space group: P 1
U matrix: {{ 0.4330, -0.7500, 0.5000},
{ 0.7891, 0.0474, -0.6124},
{ 0.4356, 0.6597, 0.6124}}
B matrix: {{ 0.1000, 0.0000, 0.0000},
{ 0.0000, 0.0909, 0.0000},
{ 0.0000, 0.0000, 0.0833}}
A = UB: {{ 0.0433, -0.0682, 0.0417},
{ 0.0789, 0.0043, -0.0510},
{ 0.0436, 0.0600, 0.0510}}
""")
model.set_B((1 / 12, 0, 0, 0, 1 / 12, 0, 0, 0, 1 / 12))
assert approx_equal(model.get_unit_cell().parameters(),
(12, 12, 12, 90, 90, 90))
U = matrix.sqr((0.3455, -0.2589, -0.9020, 0.8914, 0.3909, 0.2293, 0.2933,
-0.8833, 0.3658))
B = matrix.sqr((1 / 13, 0, 0, 0, 1 / 13, 0, 0, 0, 1 / 13))
model.set_A(U * B)
assert approx_equal(model.get_A(), U * B)
assert approx_equal(model.get_U(), U, 1e-4)
assert approx_equal(model.get_B(), B, 1e-5)
model3 = Crystal(
real_space_a=(10, 0, 0),
real_space_b=(0, 11, 0),
real_space_c=(0, 0, 12),
space_group=sgtbx.space_group_info("P 222").group(),
)
assert model3.get_space_group().type().hall_symbol() == " P 2 2"
assert model != model3
#
sgi_ref = sgtbx.space_group_info(number=230)
model_ref = Crystal(
real_space_a=(44, 0, 0),
real_space_b=(0, 44, 0),
real_space_c=(0, 0, 44),
space_group=sgi_ref.group(),
)
assert approx_equal(model_ref.get_U(), (1, 0, 0, 0, 1, 0, 0, 0, 1))
assert approx_equal(model_ref.get_B(),
(1 / 44, 0, 0, 0, 1 / 44, 0, 0, 0, 1 / 44))
assert approx_equal(model_ref.get_A(), model_ref.get_B())
assert approx_equal(model_ref.get_unit_cell().parameters(),
(44, 44, 44, 90, 90, 90))
a_ref, b_ref, c_ref = map(matrix.col, model_ref.get_real_space_vectors())
cb_op_to_primitive = sgi_ref.change_of_basis_op_to_primitive_setting()
model_primitive = model_ref.change_basis(cb_op_to_primitive)
cb_op_to_reference = (model_primitive.get_space_group().info().
change_of_basis_op_to_reference_setting())
a_prim, b_prim, c_prim = map(matrix.col,
model_primitive.get_real_space_vectors())
assert (cb_op_to_primitive.as_abc() ==
"-1/2*a+1/2*b+1/2*c,1/2*a-1/2*b+1/2*c,1/2*a+1/2*b-1/2*c")
assert approx_equal(a_prim, -1 / 2 * a_ref + 1 / 2 * b_ref + 1 / 2 * c_ref)
assert approx_equal(b_prim, 1 / 2 * a_ref - 1 / 2 * b_ref + 1 / 2 * c_ref)
assert approx_equal(c_prim, 1 / 2 * a_ref + 1 / 2 * b_ref - 1 / 2 * c_ref)
assert cb_op_to_reference.as_abc() == "b+c,a+c,a+b"
assert approx_equal(a_ref, b_prim + c_prim)
assert approx_equal(b_ref, a_prim + c_prim)
assert approx_equal(c_ref, a_prim + b_prim)
assert approx_equal(
model_primitive.get_U(),
[
-0.5773502691896258,
0.40824829046386285,
0.7071067811865476,
0.5773502691896257,
-0.4082482904638631,
0.7071067811865476,
0.5773502691896257,
0.8164965809277259,
0.0,
],
)
assert approx_equal(
model_primitive.get_B(),
[
0.0262431940540739,
0.0,
0.0,
0.00927837023781507,
0.02783511071344521,
0.0,
0.01607060866333063,
0.01607060866333063,
0.03214121732666125,
],
)
assert approx_equal(
model_primitive.get_A(),
(0, 1 / 44, 1 / 44, 1 / 44, 0, 1 / 44, 1 / 44, 1 / 44, 0),
)
assert approx_equal(
model_primitive.get_unit_cell().parameters(),
[
38.1051177665153,
38.1051177665153,
38.1051177665153,
109.47122063449069,
109.47122063449069,
109.47122063449069,
],
)
assert model_ref != model_primitive
model_ref_recycled = model_primitive.change_basis(cb_op_to_reference)
assert approx_equal(model_ref.get_U(), model_ref_recycled.get_U())
assert approx_equal(model_ref.get_B(), model_ref_recycled.get_B())
assert approx_equal(model_ref.get_A(), model_ref_recycled.get_A())
assert approx_equal(
model_ref.get_unit_cell().parameters(),
model_ref_recycled.get_unit_cell().parameters(),
)
assert model_ref == model_ref_recycled
uc = uctbx.unit_cell(
(58.2567, 58.1264, 39.7093, 46.9077, 46.8612, 62.1055))
sg = sgtbx.space_group_info(symbol="P1").group()
cs = crystal.symmetry(unit_cell=uc, space_group=sg)
cb_op_to_minimum = cs.change_of_basis_op_to_minimum_cell()
# the reciprocal matrix
B = matrix.sqr(uc.fractionalization_matrix()).transpose()
U = random_rotation()
direct_matrix = (U * B).inverse()
model = Crystal(direct_matrix[:3],
direct_matrix[3:6],
direct_matrix[6:9],
space_group=sg)
assert uc.is_similar_to(model.get_unit_cell())
uc_minimum = uc.change_basis(cb_op_to_minimum)
model_minimum = model.change_basis(cb_op_to_minimum)
assert uc_minimum.is_similar_to(model_minimum.get_unit_cell())
assert model_minimum != model
model_minimum.update(model)
assert model_minimum == model # lgtm
A_static = matrix.sqr(model.get_A())
A_as_scan_points = [A_static]
num_scan_points = 11
for i in range(num_scan_points - 1):
A_as_scan_points.append(
A_as_scan_points[-1] *
matrix.sqr(euler_angles.xyz_matrix(0.1, 0.2, 0.3)))
model.set_A_at_scan_points(A_as_scan_points)
model_minimum = model.change_basis(cb_op_to_minimum)
assert model.num_scan_points == model_minimum.num_scan_points == num_scan_points
M = matrix.sqr(cb_op_to_minimum.c_inv().r().transpose().as_double())
M_inv = M.inverse()
for i in range(num_scan_points):
A_orig = matrix.sqr(model.get_A_at_scan_point(i))
A_min = matrix.sqr(model_minimum.get_A_at_scan_point(i))
assert approx_equal(A_min, A_orig * M_inv)
assert model.get_unit_cell().parameters() == pytest.approx(
(58.2567, 58.1264, 39.7093, 46.9077, 46.8612, 62.1055))
uc = uctbx.unit_cell((10, 11, 12, 91, 92, 93))
model.set_unit_cell(uc)
assert model.get_unit_cell().parameters() == pytest.approx(uc.parameters())
def apply_symmetry(self, crystal_model):
"""Apply symmetry constraints to a crystal model.
Returns the crystal model (with symmetry constraints applied) in the same
setting as provided as input. The cb_op returned by the method is
that necessary to transform that model to the user-provided
target symmetry.
Args:
crystal_model (dxtbx.model.Crystal): The input crystal model to which to
apply symmetry constraints.
Returns: (dxtbx.model.Crystal, cctbx.sgtbx.change_of_basis_op):
The crystal model with symmetry constraints applied, and the change_of_basis_op
that transforms the returned model to the user-specified target symmetry.
"""
if not (
self.target_symmetry_primitive
and self.target_symmetry_primitive.space_group()
):
return crystal, sgtbx.change_of_basis_op()
target_space_group = self.target_symmetry_primitive.space_group()
A = crystal_model.get_A()
max_delta = self._max_delta
items = iotbx_converter(crystal_model.get_unit_cell(), max_delta=max_delta)
target_sg_ref = target_space_group.info().reference_setting().group()
best_angular_difference = 1e8
best_subgroup = None
for item in items:
if bravais_lattice(group=target_sg_ref) != item["bravais"]:
continue
if item["max_angular_difference"] < best_angular_difference:
best_angular_difference = item["max_angular_difference"]
best_subgroup = item
if best_subgroup is None:
return None, None
cb_op_inp_best = best_subgroup["cb_op_inp_best"]
best_subsym = best_subgroup["best_subsym"]
ref_subsym = best_subgroup["ref_subsym"]
cb_op_ref_best = ref_subsym.change_of_basis_op_to_best_cell()
cb_op_best_ref = cb_op_ref_best.inverse()
cb_op_inp_ref = cb_op_best_ref * cb_op_inp_best
cb_op_ref_inp = cb_op_inp_ref.inverse()
orient = crystal_orientation(A, True)
orient_ref = orient.change_basis(
scitbx.matrix.sqr((cb_op_inp_ref).c().as_double_array()[0:9]).transpose()
)
constrain_orient = orient_ref.constrain(best_subgroup["system"])
direct_matrix = constrain_orient.direct_matrix()
a = scitbx.matrix.col(direct_matrix[:3])
b = scitbx.matrix.col(direct_matrix[3:6])
c = scitbx.matrix.col(direct_matrix[6:9])
model = Crystal(a, b, c, space_group=target_sg_ref)
assert target_sg_ref.is_compatible_unit_cell(model.get_unit_cell())
model = model.change_basis(cb_op_ref_inp)
if self.cb_op_inp_best is not None:
# Then the unit cell has been provided: this is the cb_op to map to the
# user-provided input unit cell
return model, self.cb_op_inp_best.inverse() * cb_op_inp_best
if not self.cb_op_ref_inp.is_identity_op():
if self.target_symmetry_inp.space_group() == best_subsym.space_group():
# Handle where e.g. the user has requested I2 instead of the reference C2
return model, cb_op_inp_best
# The user has specified a setting that is not the reference setting
return model, self.cb_op_ref_inp * cb_op_inp_ref
# Default to reference setting
# This change of basis op will ensure that we get the best beta angle without
# changing the centring (e.g. from C2 to I2)
cb_op_ref_best = ref_subsym.change_of_basis_op_to_best_cell(
best_monoclinic_beta=False
)
return model, cb_op_ref_best * cb_op_inp_ref
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
""")
uctbx.unit_cell(
ucell).orthogonalization_matrix()).transpose().as_list_of_lists()
C = Crystal(a_real, b_real, c_real, symbol)
nbr = NBcrystal()
nbr.dxtbx_crystal = C
S = sim_data.SimData(use_default_crystal=True)
S.crystal = nbr
S.instantiate_diffBragg(auto_set_spotscale=True)
S.D.add_diffBragg_spots()
img = S.D.raw_pixels.as_numpy_array()
# simulate the primitive cell directly
to_p1 = C.get_space_group().info().change_of_basis_op_to_primitive_setting()
Cp1 = C.change_basis(to_p1)
nbr2 = NBcrystal()
nbr2.dxtbx_crystal = Cp1
S2 = sim_data.SimData()
S2.crystal = nbr2
S2.instantiate_diffBragg(auto_set_spotscale=True)
S2.D.add_diffBragg_spots()
img2 = S2.D.raw_pixels.as_numpy_array()
# rescale because currently volume is computed incorrectly
img2 = img2 * S.D.spot_scale / S2.D.spot_scale
assert S.D.Omatrix == tuple(to_p1.c_inv().r().transpose().as_double())
assert S2.D.Omatrix == (1, 0, 0, 0, 1, 0, 0, 0, 1)
assert np.allclose(img, img2)
