def exercise_ellipsoid(n_trials=100, n_sub_trials=10):
from gltbx import quadrics
rnd = random.Random(0)
for i in range(n_trials):
centre = matrix.col([rnd.random() for k in range(3)])
half_lengths = matrix.col([0.1 + rnd.random() for k in range(3)])
r = scitbx.math.euler_angles_as_matrix(
[rnd.uniform(0, 360) for i in range(3)], deg=True)
metrics = r * matrix.diag([x**2 for x in half_lengths]) * r.transpose()
t = quadrics.ellipsoid_to_sphere_transform(centre,
metrics.as_sym_mat3())
assert approx_equal(t.translation_part(), centre)
m = matrix.sqr(t.linear_part())
assert m.determinant() > 0
for j in range(n_sub_trials):
y = matrix.col([rnd.random() for k in range(3)])
c_y = y.transpose() * y
x = m * y
c_x = x.transpose() * metrics.inverse() * x
assert approx_equal(c_x, c_y)
r = scitbx.math.euler_angles_as_matrix((30, 115, 260), deg=True)
centre = matrix.col((-1, 2, 3))
metrics = r * matrix.diag((-1, 0.1, 1)) * r.transpose()
t = quadrics.ellipsoid_to_sphere_transform(centre, metrics.as_sym_mat3())
assert t.non_positive_definite()
x = r * matrix.col((1, 0, 0))
assert x.transpose() * metrics.inverse() * x > 0
def exercise_ellipsoid(n_trials=100, n_sub_trials=10):
from gltbx import quadrics
rnd = random.Random(0)
for i in xrange(n_trials):
centre = matrix.col([ rnd.random() for k in xrange(3) ])
half_lengths = matrix.col([ 0.1 + rnd.random() for k in xrange(3) ])
r = scitbx.math.euler_angles_as_matrix(
[ rnd.uniform(0, 360) for i in xrange(3) ], deg=True)
metrics = r * matrix.diag([ x**2 for x in half_lengths ]) * r.transpose()
t = quadrics.ellipsoid_to_sphere_transform(centre, metrics.as_sym_mat3())
assert approx_equal(t.translation_part(), centre)
m = matrix.sqr(t.linear_part())
assert m.determinant() > 0
for j in xrange(n_sub_trials):
y = matrix.col([ rnd.random() for k in xrange(3) ])
c_y = y.transpose() * y
x = m*y
c_x = x.transpose() * metrics.inverse() * x
assert approx_equal(c_x, c_y)
r = scitbx.math.euler_angles_as_matrix((30, 115, 260), deg=True)
centre = matrix.col((-1, 2, 3))
metrics = r * matrix.diag((-1, 0.1, 1)) * r.transpose()
t = quadrics.ellipsoid_to_sphere_transform(centre, metrics.as_sym_mat3())
assert t.non_positive_definite()
x = r * matrix.col((1,0,0))
assert x.transpose() * metrics.inverse() * x > 0
def __init__(self, xray_structure, name='??',
**kwds):
super(xray_structure_viewer, self).__init__(
unit_cell=xray_structure.unit_cell(),
orthographic=True,
light_position=(-1, 1, 1, 0),
**kwds)
assert self.bonding in ("covalent", "all")
assert self.bonding != "all" or self.distance_cutoff is not None
self.xray_structure = xs = xray_structure
self.setWindowTitle("%s in %s" % (name,
xs.space_group().type().hall_symbol()))
sites_frac = xs.sites_frac()
self.set_extent(sites_frac.min(), sites_frac.max())
self.is_unit_cell_shown = False
sites_cart = self.sites_cart = xs.sites_cart()
thermal_tensors = xs.extract_u_cart_plus_u_iso()
self.ellipsoid_to_sphere_transforms = {}
self.scatterer_indices = flex.std_string()
self.scatterer_labels = flex.std_string()
for i, (sc, site, u_cart) in enumerate(itertools.izip(xs.scatterers(),
sites_cart,
thermal_tensors)):
t = quadrics.ellipsoid_to_sphere_transform(site, u_cart)
self.ellipsoid_to_sphere_transforms.setdefault(
sc.element_symbol(),
quadrics.shared_ellipsoid_to_sphere_transforms()).append(t)
self.scatterer_indices.append("# %i" % i)
self.scatterer_labels.append(sc.label)
self.labels = None
self.label_font = QtGui.QFont("Arial Black", pointSize=18)
if self.bonding == "covalent":
radii = [
covalent_radii.table(elt).radius()
for elt in xs.scattering_type_registry().type_index_pairs_as_dict() ]
buffer_thickness = 2*max(radii) + self.covalent_bond_tolerance
asu_mappings = xs.asu_mappings(buffer_thickness=buffer_thickness)
bond_table = crystal.pair_asu_table(asu_mappings)
bond_table.add_covalent_pairs(xs.scattering_types(),
tolerance=self.covalent_bond_tolerance)
elif self.bonding == "all":
asu_mappings = xs.asu_mappings(buffer_thickness=self.distance_cutoff)
bond_table = crystal.pair_asu_table(asu_mappings)
bond_table.add_all_pairs(self.distance_cutoff)
pair_sym_table = bond_table.extract_pair_sym_table(
all_interactions_from_inside_asu=True)
self.bonds = flex.vec3_double()
self.bonds.reserve(len(xs.scatterers()))
uc = self.xray_structure.unit_cell()
frac = mat.rec(uc.fractionalization_matrix(), (3,3))
inv_frac = frac.inverse()
site_symms = xs.site_symmetry_table()
scatt = self.xray_structure.scatterers()
for i, neighbours in enumerate(pair_sym_table):
x0 = sites_cart[i]
sc0 = scatt[i]
for j, ops in neighbours.items():
sc1 = scatt[j]
if sc0.scattering_type == 'H' and sc1.scattering_type == 'H':
continue
for op in ops:
if op.is_unit_mx():
x1 = sites_cart[j]
else:
x1 = uc.orthogonalize(op*sites_frac[j])
op_cart = inv_frac*mat.rec(op.r().as_double(), (3,3))*frac
u1 = (op_cart
*mat.sym(sym_mat3=thermal_tensors[j])
*op_cart.transpose())
t = quadrics.ellipsoid_to_sphere_transform(x1, u1.as_sym_mat3())
self.ellipsoid_to_sphere_transforms[sc1.element_symbol()].append(t)
self.sites_cart.append(x1)
op_lbl = (" [%s]" % op).lower()
self.scatterer_indices.append("# %i%s" % (j, op_lbl))
self.scatterer_labels.append("%s%s" % (sc1.label, op_lbl))
self.bonds.append(x0)
self.bonds.append(x1)
def __init__(self, xray_structure, name='??', **kwds):
super(xray_structure_viewer,
self).__init__(unit_cell=xray_structure.unit_cell(),
orthographic=True,
light_position=(-1, 1, 1, 0),
**kwds)
assert self.bonding in ("covalent", "all")
assert self.bonding != "all" or self.distance_cutoff is not None
self.xray_structure = xs = xray_structure
self.setWindowTitle("%s in %s" %
(name, xs.space_group().type().hall_symbol()))
sites_frac = xs.sites_frac()
self.set_extent(sites_frac.min(), sites_frac.max())
self.is_unit_cell_shown = False
sites_cart = self.sites_cart = xs.sites_cart()
thermal_tensors = xs.extract_u_cart_plus_u_iso()
self.ellipsoid_to_sphere_transforms = {}
self.scatterer_indices = flex.std_string()
self.scatterer_labels = flex.std_string()
for i, (sc, site, u_cart) in enumerate(
zip(xs.scatterers(), sites_cart, thermal_tensors)):
t = quadrics.ellipsoid_to_sphere_transform(site, u_cart)
self.ellipsoid_to_sphere_transforms.setdefault(
sc.element_symbol(),
quadrics.shared_ellipsoid_to_sphere_transforms()).append(t)
self.scatterer_indices.append("# %i" % i)
self.scatterer_labels.append(sc.label)
self.labels = None
self.label_font = QtGui.QFont("Arial Black", pointSize=18)
if self.bonding == "covalent":
radii = [
covalent_radii.table(elt).radius() for elt in
xs.scattering_type_registry().type_index_pairs_as_dict()
]
buffer_thickness = 2 * max(radii) + self.covalent_bond_tolerance
asu_mappings = xs.asu_mappings(buffer_thickness=buffer_thickness)
bond_table = crystal.pair_asu_table(asu_mappings)
bond_table.add_covalent_pairs(
xs.scattering_types(), tolerance=self.covalent_bond_tolerance)
elif self.bonding == "all":
asu_mappings = xs.asu_mappings(
buffer_thickness=self.distance_cutoff)
bond_table = crystal.pair_asu_table(asu_mappings)
bond_table.add_all_pairs(self.distance_cutoff)
pair_sym_table = bond_table.extract_pair_sym_table(
all_interactions_from_inside_asu=True)
self.bonds = flex.vec3_double()
self.bonds.reserve(len(xs.scatterers()))
uc = self.xray_structure.unit_cell()
frac = mat.rec(uc.fractionalization_matrix(), (3, 3))
inv_frac = frac.inverse()
site_symms = xs.site_symmetry_table()
scatt = self.xray_structure.scatterers()
for i, neighbours in enumerate(pair_sym_table):
x0 = sites_cart[i]
sc0 = scatt[i]
for j, ops in neighbours.items():
sc1 = scatt[j]
if sc0.scattering_type == 'H' and sc1.scattering_type == 'H':
continue
for op in ops:
if op.is_unit_mx():
x1 = sites_cart[j]
else:
x1 = uc.orthogonalize(op * sites_frac[j])
op_cart = inv_frac * mat.rec(op.r().as_double(),
(3, 3)) * frac
u1 = (op_cart * mat.sym(sym_mat3=thermal_tensors[j]) *
op_cart.transpose())
t = quadrics.ellipsoid_to_sphere_transform(
x1, u1.as_sym_mat3())
self.ellipsoid_to_sphere_transforms[
sc1.element_symbol()].append(t)
self.sites_cart.append(x1)
op_lbl = (" [%s]" % op).lower()
self.scatterer_indices.append("# %i%s" % (j, op_lbl))
self.scatterer_labels.append("%s%s" %
(sc1.label, op_lbl))
self.bonds.append(x0)
self.bonds.append(x1)