def exercise_similarity():
model_1 = Crystal(real_space_a=(10, 0, 0),
real_space_b=(0, 11, 0),
real_space_c=(0, 0, 12),
space_group_symbol="P 1")
model_1.set_mosaicity(0.5)
model_2 = Crystal(real_space_a=(10, 0, 0),
real_space_b=(0, 11, 0),
real_space_c=(0, 0, 12),
space_group_symbol="P 1")
model_2.set_mosaicity(0.5)
assert model_1.is_similar_to(model_2)
model_1.set_mosaicity(-1)
model_2.set_mosaicity(-0.5)
assert model_1.is_similar_to(model_2) # test ignores negative mosaicity
model_1.set_mosaicity(0.5)
model_2.set_mosaicity(0.63) # outside tolerance
assert not model_1.is_similar_to(model_2)
model_2.set_mosaicity(0.62) #just inside tolerance
# orientation tests
R = matrix.sqr(model_2.get_U())
dr1 = matrix.col((1, 0, 0)).axis_and_angle_as_r3_rotation_matrix(0.0101,
deg=True)
dr2 = matrix.col((1, 0, 0)).axis_and_angle_as_r3_rotation_matrix(0.0099,
deg=True)
model_2.set_U(dr1 * R)
assert not model_1.is_similar_to(model_2) # outside tolerance
model_2.set_U(dr2 * R)
assert model_1.is_similar_to(model_2) # inside tolerance
# unit_cell.is_similar_to is tested elsewhere
return
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())
class Simulation(object):
def __init__(self, override_fdp=None):
# Set up detector
distance = 100
pixel_size = 0.1
image_size = (1000, 1000)
beam_centre_mm = (
pixel_size * image_size[0] / 2,
pixel_size * image_size[1] / 2,
)
self.detector = DetectorFactory().simple(
"CCD",
distance,
beam_centre_mm,
"+x",
"-y",
(pixel_size, pixel_size),
image_size,
)
# Set up beam
self.beam = BeamFactory().simple(wavelength=1)
# Set up scan
sequence_width = 90.0
osc_start = 0.0
image_width = 0.2
oscillation = (osc_start, image_width)
nframes = int(math.ceil(sequence_width / image_width))
image_range = (1, nframes)
exposure_times = 0.0
epochs = [0] * nframes
self.scan = ScanFactory().make_scan(
image_range, exposure_times, oscillation, epochs, deg=True
)
# Set up goniometer
self.goniometer = GoniometerFactory.known_axis(self.detector[0].get_fast_axis())
# Set up simulated structure factors
self.sfall = self.fcalc_from_pdb(
resolution=1.6, algorithm="direct", override_fdp=override_fdp
)
# Set up crystal
self.crystal = Crystal(
real_space_a=(50, 0, 0),
real_space_b=(0, 60, 0),
real_space_c=(0, 0, 70),
space_group_symbol="P1",
)
axis = matrix.col(
elems=(-0.14480368275412925, -0.6202131724405818, -0.7709523423610766)
)
self.crystal.set_U(
axis.axis_and_angle_as_r3_rotation_matrix(angle=0.625126343998969)
)
def fcalc_from_pdb(self, resolution, algorithm=None, override_fdp=None):
pdb_inp = pdb.input(source_info=None, lines=_pdb_lines)
xray_structure = pdb_inp.xray_structure_simple()
wavelength = self.beam.get_wavelength()
#
# take a detour to calculate anomalous contribution of every atom
scatterers = xray_structure.scatterers()
for sc in scatterers:
expected_henke = henke.table(sc.element_symbol()).at_angstrom(wavelength)
sc.fp = expected_henke.fp()
sc.fdp = override_fdp if override_fdp is not None else expected_henke.fdp()
# how do we do bulk solvent?
primitive_xray_structure = xray_structure.primitive_setting()
P1_primitive_xray_structure = primitive_xray_structure.expand_to_p1()
fcalc = P1_primitive_xray_structure.structure_factors(
d_min=resolution, anomalous_flag=True, algorithm=algorithm
).f_calc()
return fcalc.amplitudes()
def set_varying_beam(self, along="fast", npixels_drift=5):
assert along in ["fast", "slow", "both"]
num_scan_points = self.scan.get_num_images() + 1
s0 = matrix.col(self.beam.get_s0())
beam_centre_px = self.detector[0].get_beam_centre_px(s0)
if along == "fast":
start_beam_centre = (
beam_centre_px[0] - npixels_drift / 2,
beam_centre_px[1],
)
end_beam_centre = (beam_centre_px[0] + npixels_drift / 2, beam_centre_px[1])
elif along == "slow":
start_beam_centre = (
beam_centre_px[0],
beam_centre_px[1] - npixels_drift / 2,
)
end_beam_centre = (beam_centre_px[0], beam_centre_px[1] + npixels_drift / 2)
elif along == "both":
offset = math.sqrt(2.0) * npixels_drift / 4.0
start_beam_centre = (beam_centre_px[0] - offset, beam_centre_px[1] - offset)
end_beam_centre = (beam_centre_px[0] + offset, beam_centre_px[1] + offset)
start_lab = matrix.col(self.detector[0].get_pixel_lab_coord(start_beam_centre))
end_lab = matrix.col(self.detector[0].get_pixel_lab_coord(end_beam_centre))
axis = start_lab.cross(end_lab).normalize()
full_angle = start_lab.angle(end_lab)
angle_step = full_angle / self.scan.get_num_images()
angles = [e * angle_step for e in range(num_scan_points)]
start_s0 = start_lab.normalize() * s0.length()
s0_list = [start_s0.rotate_around_origin(axis=axis, angle=e) for e in angles]
self.beam.set_s0_at_scan_points(s0_list)