def exercise_geometry():
xs = quartz()
uc = xs.unit_cell()
flags = xs.scatterer_flags()
for f in flags:
f.set_grad_site(True)
xs.set_scatterer_flags(flags)
cov = flex.double(
(1e-8, 1e-9, 2e-9, 3e-9, 4e-9, 5e-9, 2e-8, 1e-9, 2e-9, 3e-9, 4e-9,
3e-8, 1e-9, 2e-9, 3e-9, 2e-8, 1e-9, 2e-9, 3e-8, 1e-9, 4e-8))
cell_vcv = flex.double((3e-2, 3e-2, 0, 0, 0, 0, 3e-2, 0, 0, 0, 0, 4e-2, 0,
0, 0, 0, 0, 0, 0, 0, 0))
param_map = xs.parameter_map()
cov_cart = covariance.orthogonalize_covariance_matrix(cov, uc, param_map)
O = matrix.sqr(uc.orthogonalization_matrix())
F = matrix.sqr(uc.fractionalization_matrix())
sites_cart = xs.sites_cart()
sites_frac = xs.sites_frac()
# distances
rt_mx_ji = sgtbx.rt_mx('-y,x-y,z-1/3')
sites = (sites_cart[0], uc.orthogonalize(rt_mx_ji * sites_frac[1]))
d = geometry.distance(sites)
assert approx_equal(d.distance_model, 1.6159860469110217)
v = matrix.col(sites[1]) - matrix.col(sites[0])
r_inv_cart = (O * matrix.sqr(rt_mx_ji.r().inverse().as_double()) * F)
g = d.d_distance_d_sites()
g = matrix.row(g[0] + tuple(r_inv_cart * matrix.col(g[1])))
f = g * matrix.sqr(cov_cart.matrix_packed_u_as_symmetric()) * g.transpose()
assert approx_equal(d.variance(cov_cart, uc, rt_mx_ji), f[0], eps=1e-15)
assert approx_equal(0.0018054494791580823,
d.variance(cov_cart, cell_vcv, uc, rt_mx_ji))
rt_mx_ji = sgtbx.rt_mx('x+1,y,z')
sites = (sites_cart[0], uc.orthogonalize(rt_mx_ji * sites_frac[0]))
d = geometry.distance(sites)
assert approx_equal(d.distance_model, uc.parameters()[0])
assert approx_equal(cell_vcv.matrix_packed_u_diagonal()[0],
d.variance(cov_cart, cell_vcv, uc, rt_mx_ji))
# angles
rt_mx_ji = sgtbx.rt_mx('x-y,x,z-2/3')
rt_mx_ki = sgtbx.rt_mx('-y,x-y,z-1/3')
r_inv_cart_ji = (O * matrix.sqr(rt_mx_ji.r().inverse().as_double()) * F)
r_inv_cart_ki = (O * matrix.sqr(rt_mx_ki.r().inverse().as_double()) * F)
cov_a = covariance.extract_covariance_matrix_for_sites(
flex.size_t([1, 0, 1]), cov_cart, param_map)
sites = (uc.orthogonalize(rt_mx_ji * sites_frac[1]), sites_cart[0],
uc.orthogonalize(rt_mx_ki * sites_frac[1]))
a = geometry.angle(sites)
assert approx_equal(a.angle_model, 101.30738566828551)
g = a.d_angle_d_sites()
g = matrix.row(
tuple(r_inv_cart_ji * matrix.col(g[0])) + g[1] +
tuple(r_inv_cart_ki * matrix.col(g[2])))
f = g * matrix.sqr(cov_a.matrix_packed_u_as_symmetric()) * g.transpose()
assert approx_equal(a.variance(cov_a, uc,
(rt_mx_ji, sgtbx.rt_mx(), rt_mx_ki)),
f[0],
eps=1e-15)
assert approx_equal(
0.0042632511984529199,
a.variance(cov_a, cell_vcv, uc, (rt_mx_ji, sgtbx.rt_mx(), rt_mx_ki)))
def calc_distance(metrical_matrix=None): xs = quartz_p1(metrical_matrix=metrical_matrix) uc = xs.unit_cell() sites_cart = xs.sites_cart() sites = (sites_cart[0], sites_cart[5]) d = geometry.distance(sites) return d.distance_model
def exercise_grad_metrical_matrix():
def calc_distance(metrical_matrix=None):
xs = quartz_p1(metrical_matrix=metrical_matrix)
uc = xs.unit_cell()
sites_cart = xs.sites_cart()
sites = (sites_cart[0], sites_cart[5])
d = geometry.distance(sites)
return d.distance_model
def calc_angle(metrical_matrix=None):
xs = quartz_p1(metrical_matrix=metrical_matrix)
uc = xs.unit_cell()
sites_cart = xs.sites_cart()
sites = (sites_cart[4], sites_cart[0], sites_cart[5])
a = geometry.angle(sites)
return a.angle_model*(math.pi/180)
xs = quartz_p1()
uc = xs.unit_cell()
sites_cart = xs.sites_cart()
# distances
sites = (sites_cart[0], sites_cart[5])
d = geometry.distance(sites)
grads = d.d_distance_d_metrical_matrix(uc)
fd_grads = finite_differences(calc_distance, xs.unit_cell())
assert approx_equal(grads, fd_grads)
# angles
sites = (sites_cart[4], sites_cart[0], sites_cart[5])
a = geometry.angle(sites)
grads = a.d_angle_d_metrical_matrix(uc)
fd_grads = finite_differences(calc_angle, xs.unit_cell())
assert approx_equal(grads, fd_grads)
def __init__(self,
hbonds,
pair_asu_table,
site_labels,
sites_frac=None,
sites_cart=None,
min_dha_angle=150, # degrees
max_da_distance=2.9, # angstrom
covariance_matrix=None,
cell_covariance_matrix=None,
parameter_map=None,
eps=2e-16):
assert [sites_frac, sites_cart].count(None) == 1
fmt_a = "%.1f"
pair_asu_table = pair_asu_table
asu_mappings = pair_asu_table.asu_mappings()
space_group_info = sgtbx.space_group_info(group=asu_mappings.space_group())
self.unit_cell = asu_mappings.unit_cell()
if sites_cart is not None:
sites_frac = self.unit_cell.fractionalize(sites_cart)
if sites_frac is not None:
sites_cart = self.unit_cell.orthogonalize(sites_frac)
if covariance_matrix is not None:
assert parameter_map is not None
self.covariance_matrix_cart = covariance.orthogonalize_covariance_matrix(
covariance_matrix, self.unit_cell, parameter_map)
else: self.covariance_matrix_cart = None
self.cell_covariance_matrix = cell_covariance_matrix
self.eps = eps
self.parameter_map = parameter_map
self.loop = model.loop(header=(
"_geom_hbond_atom_site_label_D",
"_geom_hbond_atom_site_label_H",
"_geom_hbond_atom_site_label_A",
"_geom_hbond_distance_DH",
"_geom_hbond_distance_HA",
"_geom_hbond_distance_DA",
"_geom_hbond_angle_DHA",
"_geom_hbond_site_symmetry_A",
))
for hbond in hbonds:
d_seq, a_seq = hbond.d_seq, hbond.a_seq
site_cart_d = sites_cart[d_seq]
if hbond.rt_mx is not None:
site_frac_a = sites_frac[a_seq]
site_frac_a = hbond.rt_mx * site_frac_a
site_cart_a = self.unit_cell.orthogonalize(site_frac_a)
else:
site_cart_a = sites_cart[a_seq]
distance_da = geometry.distance((site_cart_d, site_cart_a))
for h_seq, h_sym_groups in pair_asu_table.table()[hbond.d_seq].items():
if site_labels[h_seq][0] not in ('H','D'):
# XXX better to pass scattering types instead?
continue
site_cart_h = sites_cart[h_seq]
distance_dh = geometry.distance((site_cart_d, site_cart_h))
distance_ha = geometry.distance((site_cart_h, site_cart_a))
angle_dha = geometry.angle((site_cart_d, site_cart_h, site_cart_a))
if (angle_dha.angle_model < min_dha_angle or
distance_da.distance_model > max_da_distance):
continue
if hbond.rt_mx is not None:
sym_code = space_group_info.cif_symmetry_code(hbond.rt_mx)
else: sym_code = '.'
self.loop.add_row((
site_labels[d_seq],
site_labels[h_seq],
site_labels[a_seq],
self.formatted_distance(d_seq, h_seq, distance_dh, unit_mx),
self.formatted_distance(h_seq, a_seq, distance_ha, unit_mx),
self.formatted_distance(d_seq, a_seq, distance_da, hbond.rt_mx),
self.formatted_angle(d_seq, h_seq, a_seq, angle_dha, hbond.rt_mx),
sym_code
))
