def exercise_py_LS(obs, f_calc, weighting, verbose):
weighting.computing_derivatives_wrt_f_c = True
r = xray.unified_least_squares_residual(obs, weighting=weighting)
rt = r(f_calc, compute_derivatives=True)
if obs.is_xray_amplitude_array():
assert(isinstance(rt, xray.targets_least_squares_residual))
elif obs.is_xray_intensity_array():
assert(isinstance(rt, xray.targets_least_squares_residual_for_intensity))
scale_factor = rt.scale_factor()
gr_ana = rt.derivatives()
K = scale_factor
w = weighting.weights
if w is not None: w = w.deep_copy()
dw_dfc = weighting.derivatives_wrt_f_c
if dw_dfc is not None: dw_dfc = dw_dfc.deep_copy()
y_o = obs.data()
if w is None: w = flex.double(obs.size(), 1)
sum_w_y_o_sqr = flex.sum(w * y_o * y_o)
f_c = f_calc.data().deep_copy()
if obs.is_xray_amplitude_array():
y_c = flex.abs(f_c)
der = f_c * (1/y_c)
elif obs.is_xray_intensity_array():
y_c = flex.norm(f_c)
der = 2 * f_c
gr_explicit = w*2*K*(K*y_c - y_o) * der / sum_w_y_o_sqr
sum_w_squares = flex.sum(w*flex.pow2(K*y_c - y_o))
assert approx_equal(gr_ana, gr_explicit)
gr_fin = flex.complex_double()
eps = 1.e-6
for i_refl in xrange(obs.size()):
gc = []
for i_part in [0,1]:
fc0 = f_calc.data()[i_refl]
ts = []
for signed_eps in [eps,-eps]:
if (i_part == 0):
f_calc.data()[i_refl] = complex(fc0.real + signed_eps, fc0.imag)
else:
f_calc.data()[i_refl] = complex(fc0.real, fc0.imag + signed_eps)
rt = r(f_calc, compute_derivatives=False, scale_factor=scale_factor)
ts.append(rt.target())
f_calc.data()[i_refl] = fc0
gc.append((ts[0]-ts[1])/(2*eps))
gr_fin.append(complex(*gc))
if (verbose):
print "ana:", list(gr_ana)
print "fin:", list(gr_fin)
if dw_dfc is None:
assert approx_equal(gr_fin, gr_ana)
else:
gr_total_ana = ( gr_ana
+ dw_dfc*(flex.pow2(K*y_c - y_o)/sum_w_y_o_sqr
- sum_w_squares*flex.pow2(y_o)/sum_w_y_o_sqr**2) )
assert approx_equal(gr_fin, gr_total_ana)
anomalous_flag=False,
d_min=0.8)
structure = random_structure.xray_structure(indices.space_group_info(),
elements=['C']*6 + ['O']*2 + ['N'],
volume_per_atom=18.6,
random_u_iso=True)
f_ideal = structure.structure_factors(d_min=indices.d_min()).f_calc()
f_obs = f_ideal.amplitudes()
f_obs *= 2
f_obs.set_observation_type_xray_amplitude()
f_obs_square = f_ideal.norm()
f_obs_square *= 3
f_obs_square.set_observation_type_xray_intensity()
ls_against_f = xray.unified_least_squares_residual(f_obs)
ls_against_f_square = xray.unified_least_squares_residual(f_obs_square)
residuals = ls_against_f(f_ideal, compute_derivatives=True)
print "against F: value=%.3f, scale=%.3f" % (residuals.target(),
residuals.scale_factor())
residuals = ls_against_f_square(f_ideal, compute_derivatives=True)
print "against F^2: value=%.3f, scale=%.3f" % (residuals.target(),
residuals.scale_factor())
perturbed_structure = structure.random_shift_sites(max_shift_cart=0.2)
for s in perturbed_structure.scatterers():
s.flags.set_grad_site(True)
refining_structure = perturbed_structure.deep_copy_scatterers()
optimiser = xray.lbfgs(
d_min=0.8)
structure = random_structure.xray_structure(indices.space_group_info(),
elements=['C'] * 6 + ['O'] * 2 +
['N'],
volume_per_atom=18.6,
random_u_iso=True)
f_ideal = structure.structure_factors(d_min=indices.d_min()).f_calc()
f_obs = f_ideal.amplitudes()
f_obs *= 2
f_obs.set_observation_type_xray_amplitude()
f_obs_square = f_ideal.norm()
f_obs_square *= 3
f_obs_square.set_observation_type_xray_intensity()
ls_against_f = xray.unified_least_squares_residual(f_obs)
ls_against_f_square = xray.unified_least_squares_residual(f_obs_square)
residuals = ls_against_f(f_ideal, compute_derivatives=True)
print("against F: value=%.3f, scale=%.3f" %
(residuals.target(), residuals.scale_factor()))
residuals = ls_against_f_square(f_ideal, compute_derivatives=True)
print("against F^2: value=%.3f, scale=%.3f" %
(residuals.target(), residuals.scale_factor()))
perturbed_structure = structure.random_shift_sites(max_shift_cart=0.2)
for s in perturbed_structure.scatterers():
s.flags.set_grad_site(True)
refining_structure = perturbed_structure.deep_copy_scatterers()
optimiser = xray.lbfgs(target_functor=ls_against_f_square,
def exercise_py_LS(obs, f_calc, weighting, verbose):
weighting.computing_derivatives_wrt_f_c = True
r = xray.unified_least_squares_residual(obs, weighting=weighting)
rt = r(f_calc, compute_derivatives=True)
if obs.is_xray_amplitude_array():
assert (isinstance(rt, xray.targets_least_squares_residual))
elif obs.is_xray_intensity_array():
assert (isinstance(rt,
xray.targets_least_squares_residual_for_intensity))
scale_factor = rt.scale_factor()
gr_ana = rt.derivatives()
K = scale_factor
w = weighting.weights
if w is not None: w = w.deep_copy()
dw_dfc = weighting.derivatives_wrt_f_c
if dw_dfc is not None: dw_dfc = dw_dfc.deep_copy()
y_o = obs.data()
if w is None: w = flex.double(obs.size(), 1)
sum_w_y_o_sqr = flex.sum(w * y_o * y_o)
f_c = f_calc.data().deep_copy()
if obs.is_xray_amplitude_array():
y_c = flex.abs(f_c)
der = f_c * (1 / y_c)
elif obs.is_xray_intensity_array():
y_c = flex.norm(f_c)
der = 2 * f_c
gr_explicit = w * 2 * K * (K * y_c - y_o) * der / sum_w_y_o_sqr
sum_w_squares = flex.sum(w * flex.pow2(K * y_c - y_o))
assert approx_equal(gr_ana, gr_explicit)
gr_fin = flex.complex_double()
eps = 1.e-6
for i_refl in xrange(obs.size()):
gc = []
for i_part in [0, 1]:
fc0 = f_calc.data()[i_refl]
ts = []
for signed_eps in [eps, -eps]:
if (i_part == 0):
f_calc.data()[i_refl] = complex(fc0.real + signed_eps,
fc0.imag)
else:
f_calc.data()[i_refl] = complex(fc0.real,
fc0.imag + signed_eps)
rt = r(f_calc,
compute_derivatives=False,
scale_factor=scale_factor)
ts.append(rt.target())
f_calc.data()[i_refl] = fc0
gc.append((ts[0] - ts[1]) / (2 * eps))
gr_fin.append(complex(*gc))
if (verbose):
print "ana:", list(gr_ana)
print "fin:", list(gr_fin)
if dw_dfc is None:
assert approx_equal(gr_fin, gr_ana)
else:
gr_total_ana = (gr_ana + dw_dfc *
(flex.pow2(K * y_c - y_o) / sum_w_y_o_sqr -
sum_w_squares * flex.pow2(y_o) / sum_w_y_o_sqr**2))
assert approx_equal(gr_fin, gr_total_ana)
