def exercise(xray_structure, anomalous_flag, max_n_indices, out):
xray_structure.show_summary(f=out).show_scatterers(f=out)
miller_set = miller.build_set(
crystal_symmetry=xray_structure,
anomalous_flag=anomalous_flag,
d_min=max(1,
min(xray_structure.unit_cell().parameters()[:3]) / 2.5))
n_indices = miller_set.indices().size()
if (n_indices > max_n_indices):
miller_set = miller_set.select(
flex.random_size_t(size=max_n_indices) % n_indices)
sf = structure_factors(xray_structure=xray_structure,
miller_set=miller_set)
f_calc = miller_set.structure_factors_from_scatterers(
xray_structure=xray_structure, algorithm="direct",
cos_sin_table=False).f_calc()
f_calc.show_summary(f=out)
assert approx_equal(sf.fs(), f_calc.data())
f_obs = miller_set.array(data=flex.abs(sf.fs()))
noise_fin = compare_analytical_and_finite(f_obs=f_obs,
xray_structure=xray_structure,
gradients_should_be_zero=True,
eps=1.e-5,
out=out)
compare_analytical_and_finite(f_obs=f_obs.customized_copy(
data=f_obs.data() * (flex.random_double(size=f_obs.size()) + 0.5)),
xray_structure=xray_structure,
gradients_should_be_zero=False,
eps=max(1.e-5, noise_fin),
out=out)
def compare_analytical_and_finite(
f_obs,
xray_structure,
gradients_should_be_zero,
eps,
out):
grads_fin = d_target_d_params_finite(
d_order=1, f_obs=f_obs, xray_structure=xray_structure)
print >> out, "grads_fin:", list(grads_fin)
sf = structure_factors(
xray_structure=xray_structure, miller_set=f_obs)
grads_ana = sf.d_target_d_params(f_obs=f_obs, target_type=least_squares)
print >> out, "grads_ana:", list(grads_ana)
if (gradients_should_be_zero):
flex.compare_derivatives(grads_ana, flex.double(grads_ana.size(), 0), eps)
else:
flex.compare_derivatives(grads_ana, grads_fin, eps)
curvs_fin = d_target_d_params_finite(
d_order=2, f_obs=f_obs, xray_structure=xray_structure)
print >> out, "curvs_fin:", list(curvs_fin)
curvs_ana = sf.d2_target_d_params(f_obs=f_obs, target_type=least_squares)
print >> out, "curvs_ana:", list(curvs_ana)
flex.compare_derivatives(curvs_ana.as_1d(), curvs_fin, eps)
assert curvs_ana.matrix_is_symmetric(relative_epsilon=1e-10)
print >> out
#
for i_method,curvs_method in enumerate([
sf.d2_target_d_params_diag,
sf.d2_target_d_params_diag_cpp]):
curvs_diag_ana = curvs_method(f_obs=f_obs, target_type=least_squares)
if (i_method != 0):
flex.compare_derivatives(grads_ana, curvs_diag_ana.grads, eps=1e-12)
curvs_diag_ana = curvs_diag_ana.curvs
assert curvs_diag_ana.size() == curvs_ana.focus()[0]
flex.compare_derivatives(
curvs_ana.matrix_diagonal().as_1d(), curvs_diag_ana, eps=1e-12)
#
if (gradients_should_be_zero):
return flex.max(flex.abs(grads_fin))
def exercise(
xray_structure,
anomalous_flag,
max_n_indices,
out):
xray_structure.show_summary(f=out).show_scatterers(f=out)
miller_set = miller.build_set(
crystal_symmetry=xray_structure,
anomalous_flag=anomalous_flag,
d_min=max(1, min(xray_structure.unit_cell().parameters()[:3])/2.5))
n_indices = miller_set.indices().size()
if (n_indices > max_n_indices):
miller_set = miller_set.select(
flex.random_size_t(size=max_n_indices) % n_indices)
sf = structure_factors(
xray_structure=xray_structure,
miller_set=miller_set)
f_calc = miller_set.structure_factors_from_scatterers(
xray_structure=xray_structure,
algorithm="direct",
cos_sin_table=False).f_calc()
f_calc.show_summary(f=out)
assert approx_equal(sf.fs(), f_calc.data())
f_obs = miller_set.array(data=flex.abs(sf.fs()))
noise_fin = compare_analytical_and_finite(
f_obs=f_obs,
xray_structure=xray_structure,
gradients_should_be_zero=True,
eps=1.e-5,
out=out)
compare_analytical_and_finite(
f_obs=f_obs.customized_copy(
data=f_obs.data()*(flex.random_double(size=f_obs.size())+0.5)),
xray_structure=xray_structure,
gradients_should_be_zero=False,
eps=max(1.e-5, noise_fin),
out=out)
def d_target_d_params_finite(d_order, f_obs, xray_structure, eps=1.e-8):
assert d_order in [1,2]
result = flex.double()
scatterers = xray_structure.scatterers()
site_symmetry_table = xray_structure.site_symmetry_table()
xray_structure_eps = xray_structure.deep_copy_scatterers()
scatterers_eps = xray_structure_eps.scatterers()
for i_scatterer,scatterer in enumerate(scatterers):
if (not site_symmetry_table.is_special_position(i_scatterer)):
site_symmetry_ops = None
if (not scatterer.flags.use_u_aniso()):
ips = range(7)
else:
ips = range(12)
else:
site_symmetry_ops = site_symmetry_table.get(i_scatterer)
site_constraints = site_symmetry_ops.site_constraints()
ips = list(site_constraints.independent_indices)
if (not scatterer.flags.use_u_aniso()):
ips.extend(range(3,7))
else:
adp_constraints = site_symmetry_ops.adp_constraints()
ips.extend([i+3 for i in adp_constraints.independent_indices])
ips.extend(range(9,12))
dx = []
for ip in ips:
vs = []
for signed_eps in [eps, -eps]:
si_eps = scatterer_as_list(scatterer)
si_eps[ip] += signed_eps
if (site_symmetry_ops is not None):
if (ip < 3):
all_params = site_constraints.all_params(
independent_params=site_constraints.independent_params(
all_params=si_eps[:3]))
si_eps = list(all_params) + si_eps[3:]
elif (scatterer.flags.use_u_aniso() and ip < 9):
all_params = adp_constraints.all_params(
independent_params=adp_constraints.independent_params(
all_params=si_eps[3:9]))
si_eps = si_eps[:3] + list(all_params) + si_eps[9:]
scatterers_eps[i_scatterer] = scatterer_from_list(si_eps)
scatterers_eps[i_scatterer].scattering_type = scatterer.scattering_type
xray_structure_eps.re_apply_symmetry(i_scatterer)
sf = structure_factors(
xray_structure=xray_structure_eps, miller_set=f_obs)
if (d_order == 1):
sum_target_f = 0
for obs,f in zip(f_obs.data(), sf.fs()):
target = least_squares(obs=obs, calc=f)
sum_target_f += target.f()
vs.append(sum_target_f)
else:
dp = sf.d_target_d_params(f_obs=f_obs, target_type=least_squares)
vs.append(dp)
diff = (vs[0]-vs[1])/(2*eps)
if (d_order == 1):
result.append(diff)
else:
result.extend(diff)
scatterers_eps[i_scatterer] = scatterer
return result
