def d2_target_d_params_finite(f_obs, xray_structure, eps=1.e-8):
result = flex.double()
scatterers = xray_structure.scatterers()
xray_structure_eps = xray_structure.deep_copy_scatterers()
scatterers_eps = xray_structure_eps.scatterers()
for i_scatterer in xrange(len(scatterers)):
if (not scatterers[i_scatterer].flags.use_u_aniso()):
np = 7
else:
np = 12
dx = []
for ix in xrange(np):
gs = []
for signed_eps in [eps, -eps]:
si_eps = scatterer_as_list(scatterers[i_scatterer])
si_eps[ix] += signed_eps
scatterers_eps[i_scatterer] = scatterer_from_list(si_eps)
sf = structure_factors(xray_structure=xray_structure_eps,
miller_set=f_obs)
dp = sf.d_target_d_params(f_obs=f_obs,
target_type=least_squares)
gs.append(dp)
result.extend((gs[0] - gs[1]) / (2 * eps))
scatterers_eps[i_scatterer] = scatterers[i_scatterer]
return result
def d_target_d_params_finite(f_obs, xray_structure, eps=1.e-8):
result = flex.double()
scatterers = xray_structure.scatterers()
xray_structure_eps = xray_structure.deep_copy_scatterers()
scatterers_eps = xray_structure_eps.scatterers()
for i_scatterer in xrange(len(scatterers)):
if (not scatterers[i_scatterer].flags.use_u_aniso()):
np = 7
else:
np = 12
dx = []
for ix in xrange(np):
ts = []
for signed_eps in [eps, -eps]:
si_eps = scatterer_as_list(scatterers[i_scatterer])
si_eps[ix] += signed_eps
scatterers_eps[i_scatterer] = scatterer_from_list(si_eps)
sf = structure_factors(xray_structure=xray_structure_eps,
miller_set=f_obs)
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()
ts.append(sum_target_f)
result.append((ts[0] - ts[1]) / (2 * eps))
scatterers_eps[i_scatterer] = scatterers[i_scatterer]
return result
def d_target_d_params_finite(f_obs, xray_structure, eps=1.e-8):
result = flex.double()
scatterers = xray_structure.scatterers()
xray_structure_eps = xray_structure.deep_copy_scatterers()
scatterers_eps = xray_structure_eps.scatterers()
for i_scatterer in xrange(len(scatterers)):
if (not scatterers[i_scatterer].flags.use_u_aniso()):
np = 7
else:
np = 12
dx = []
for ix in xrange(np):
ts = []
for signed_eps in [eps, -eps]:
si_eps = scatterer_as_list(scatterers[i_scatterer])
si_eps[ix] += signed_eps
scatterers_eps[i_scatterer] = scatterer_from_list(si_eps)
sf = structure_factors(
xray_structure=xray_structure_eps, miller_set=f_obs)
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()
ts.append(sum_target_f)
result.append((ts[0]-ts[1])/(2*eps))
scatterers_eps[i_scatterer] = scatterers[i_scatterer]
return result
def exercise(
space_group_info,
use_u_aniso,
anomalous_flag,
max_n_indices=5,
verbose=0):
if (not verbose):
out = StringIO()
else:
out = sys.stdout
for n_scatterers in xrange(3,3+1):
for i_trial in xrange(1):
xray_structure = random_structure.xray_structure(
space_group_info=space_group_info,
elements=["const"]*n_scatterers,
volume_per_atom=100,
general_positions_only=True,
random_f_prime_d_min=1,
random_f_double_prime=anomalous_flag,
use_u_aniso = use_u_aniso,
use_u_iso = (not use_u_aniso),
random_u_iso=True,
random_u_iso_scale=0.3,
random_occupancy=True)
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()))
compare_analytical_and_finite(
f_obs=f_obs,
xray_structure=xray_structure,
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,
out=out)
def exercise(space_group_info,
use_u_aniso,
anomalous_flag,
max_n_indices=5,
verbose=0):
if (not verbose):
out = StringIO()
else:
out = sys.stdout
for n_scatterers in xrange(3, 3 + 1):
for i_trial in xrange(1):
xray_structure = random_structure.xray_structure(
space_group_info=space_group_info,
elements=["const"] * n_scatterers,
volume_per_atom=100,
general_positions_only=True,
random_f_prime_d_min=1,
random_f_double_prime=anomalous_flag,
use_u_aniso=use_u_aniso,
use_u_iso=(not use_u_aniso),
random_u_iso=True,
random_u_iso_scale=0.3,
random_occupancy=True)
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()))
compare_analytical_and_finite(f_obs=f_obs,
xray_structure=xray_structure,
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,
out=out)
def compare_analytical_and_finite(f_obs, xray_structure, out):
grads_fin = d_target_d_params_finite(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)
flex.compare_derivatives(grads_ana, grads_fin)
curvs_fin = d2_target_d_params_finite(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)
print >> out
def compare_analytical_and_finite(f_obs, xray_structure, out):
grads_fin = d_target_d_params_finite(
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)
flex.compare_derivatives(grads_ana, grads_fin)
curvs_fin = d2_target_d_params_finite(
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)
print >> out
def d2_target_d_params_finite(f_obs, xray_structure, eps=1.e-8):
result = flex.double()
scatterers = xray_structure.scatterers()
xray_structure_eps = xray_structure.deep_copy_scatterers()
scatterers_eps = xray_structure_eps.scatterers()
for i_scatterer in xrange(len(scatterers)):
if (not scatterers[i_scatterer].flags.use_u_aniso()):
np = 7
else:
np = 12
dx = []
for ix in xrange(np):
gs = []
for signed_eps in [eps, -eps]:
si_eps = scatterer_as_list(scatterers[i_scatterer])
si_eps[ix] += signed_eps
scatterers_eps[i_scatterer] = scatterer_from_list(si_eps)
sf = structure_factors(
xray_structure=xray_structure_eps, miller_set=f_obs)
dp = sf.d_target_d_params(f_obs=f_obs, target_type=least_squares)
gs.append(dp)
result.extend((gs[0]-gs[1])/(2*eps))
scatterers_eps[i_scatterer] = scatterers[i_scatterer]
return result
