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)
assert approx_equal(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)
assert approx_equal(curvs_ana, curvs_fin, 1.e-5)
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)
assert approx_equal(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)
assert approx_equal(curvs_ana, curvs_fin, 1.e-5)
print >> out
def exercise(args):
verbose = "--verbose" in args
if (not verbose):
out = StringIO()
else:
out = sys.stdout
crystal_symmetry = crystal.symmetry(
unit_cell=(8,9,10,83,97,113),
space_group_symbol="P1")
miller_set = miller.set(
crystal_symmetry=crystal_symmetry,
indices=flex.miller_index([(1,2,3), (2,3,4), (-1,3,-2)]),
anomalous_flag=False)
for n_scatterers in xrange(2,2+5):
for i_trial in xrange(5):
scatterers = flex.xray_scatterer()
for i in xrange(n_scatterers):
scatterers.append(xray.scatterer(
site=[random.random() for i in xrange(3)],
u=random.random()*0.1,
occupancy=random.random(),
scattering_type="const",
fp=(random.random()-0.5)*2,
fdp=(random.random()-0.5)*2))
xray_structure = xray.structure(
crystal_symmetry=crystal_symmetry,
scatterers=scatterers)
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()
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)
print "OK"
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)):
for ix in xrange(7):
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 exercise(args):
verbose = "--verbose" in args
if (not verbose):
out = StringIO()
else:
out = sys.stdout
crystal_symmetry = crystal.symmetry(unit_cell=(8, 9, 10, 83, 97, 113),
space_group_symbol="P1")
miller_set = miller.set(crystal_symmetry=crystal_symmetry,
indices=flex.miller_index([(1, 2, 3), (2, 3, 4),
(-1, 3, -2)]),
anomalous_flag=False)
for n_scatterers in xrange(2, 2 + 5):
for i_trial in xrange(5):
scatterers = flex.xray_scatterer()
for i in xrange(n_scatterers):
scatterers.append(
xray.scatterer(site=[random.random() for i in xrange(3)],
u=random.random() * 0.1,
occupancy=random.random(),
scattering_type="const",
fp=(random.random() - 0.5) * 2,
fdp=(random.random() - 0.5) * 2))
xray_structure = xray.structure(crystal_symmetry=crystal_symmetry,
scatterers=scatterers)
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()
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)
print "OK"
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)):
for ix in xrange(7):
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)):
dx = []
for ix in xrange(7):
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)):
dx = []
for ix in xrange(7):
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
