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)