def exercise_ls_cycles(self):
xs = self.xray_structure.deep_copy_scatterers()
xs.shake_adp() # it must happen before the reparamtrisation is constructed
# because the ADP values are read then and only then.
connectivity_table = smtbx.utils.connectivity_table(xs)
reparametrisation = constraints.reparametrisation(
structure=xs,
constraints=[],
connectivity_table=connectivity_table)
ls = least_squares.crystallographic_ls(
self.fo_sq.as_xray_observations(), reparametrisation,
weighting_scheme=least_squares.unit_weighting(),
origin_fixing_restraints_type=oop.null())
cycles = normal_eqns_solving.naive_iterations(
ls,
n_max_iterations=10,
track_all=True)
assert approx_equal(ls.scale_factor(), 1, eps=1e-4)
assert approx_equal(ls.objective(), 0)
# skip next-to-last one to allow for no progress and rounding error
n = len(cycles.objective_history)
assert cycles.objective_history[0] > cycles.objective_history[n-1],\
cycles.objective_history
assert approx_equal(cycles.gradient_norm_history[-1], 0, eps=1e-6)
for sc0, sc1 in zip(self.xray_structure.scatterers(), xs.scatterers()):
assert approx_equal(sc0.u_star, sc1.u_star)
def exercise_ls_cycles(self):
xs = self.xray_structure.deep_copy_scatterers()
connectivity_table = smtbx.utils.connectivity_table(xs)
emma_ref = xs.as_emma_model()
# shaking must happen before the reparametrisation is constructed,
# otherwise the original values will prevail
xs.shake_sites_in_place(rms_difference=0.1)
reparametrisation = constraints.reparametrisation(
structure=xs,
constraints=[],
connectivity_table=connectivity_table)
ls = least_squares.crystallographic_ls(
self.fo_sq.as_xray_observations(), reparametrisation,
weighting_scheme=least_squares.unit_weighting(),
origin_fixing_restraints_type=
origin_fixing_restraints.atomic_number_weighting)
cycles = normal_eqns_solving.naive_iterations(
ls,
n_max_iterations=5,
track_all=True)
assert approx_equal(ls.scale_factor(), 1, eps=1e-5)
assert approx_equal(ls.objective(), 0)
# skip next-to-last one to allow for no progress and rounding error
assert (
cycles.objective_history[0]
>= cycles.objective_history[1]
>= cycles.objective_history[3]), numstr(cycles.objective_history)
assert approx_equal(cycles.gradient_norm_history[-1], 0, eps=5e-8)
match = emma.model_matches(emma_ref, xs.as_emma_model()).refined_matches[0]
assert match.rt.r == matrix.identity(3)
for pair in match.pairs:
assert approx_equal(match.calculate_shortest_dist(pair), 0, eps=1e-4)
def exercise(self, fixed_twin_fraction):
# Create a shaken structure xs ready for refinement
xs0 = self.structure
emma_ref = xs0.as_emma_model()
xs = xs0.deep_copy_scatterers()
xs.shake_sites_in_place(rms_difference=0.15)
xs.shake_adp()
for sc in xs.scatterers():
sc.flags.set_use_u_iso(False).set_use_u_aniso(True)
sc.flags.set_grad_site(True).set_grad_u_aniso(True)
# Setup L.S. problem
connectivity_table = smtbx.utils.connectivity_table(xs)
shaken_twin_fraction = (self.twin_fraction if fixed_twin_fraction else
self.twin_fraction +
0.1 * flex.random_double())
# 2nd domain in __init__
twin_components = (xray.twin_component(twin_law=self.twin_law.r(),
value=shaken_twin_fraction,
grad=not fixed_twin_fraction), )
reparametrisation = constraints.reparametrisation(
structure=xs,
constraints=[],
connectivity_table=connectivity_table,
twin_fractions=twin_components)
obs = self.fo_sq.as_xray_observations(twin_components=twin_components)
ls = least_squares.crystallographic_ls(
obs,
reparametrisation,
weighting_scheme=least_squares.unit_weighting(),
origin_fixing_restraints_type=origin_fixing_restraints.
atomic_number_weighting)
# Refine till we get back the original structure (so we hope)
cycles = normal_eqns_solving.levenberg_marquardt_iterations(
ls, gradient_threshold=1e-12, step_threshold=1e-6, track_all=True)
# Now let's start to check it all worked
assert ls.n_parameters == 63 if fixed_twin_fraction else 64
match = emma.model_matches(emma_ref,
xs.as_emma_model()).refined_matches[0]
assert match.rt.r == matrix.identity(3)
for pair in match.pairs:
assert approx_equal(match.calculate_shortest_dist(pair),
0,
eps=1e-4), pair
if fixed_twin_fraction:
assert ls.twin_fractions[0].value == self.twin_fraction
else:
assert approx_equal(ls.twin_fractions[0].value,
self.twin_fraction,
eps=1e-2)
assert approx_equal(ls.scale_factor(), 1, eps=1e-5)
assert approx_equal(ls.objective(), 0)
def exercise_weighting_schemes():
unit_weighting = least_squares.unit_weighting()
assert unit_weighting.type() == "unit"
assert str(unit_weighting) == "w=1"
shelx_weighting = least_squares.mainstream_shelx_weighting(0.1234, 0.5678)
assert shelx_weighting.type() == "calc"
assert not show_diff(
str(shelx_weighting),
"w=1/[\s^2^(Fo^2^)+(0.1234P)^2^+0.5678P] where P=(Fo^2^+2Fc^2^)/3")
def exercise(self, fixed_twin_fraction):
# Create a shaken structure xs ready for refinement
xs0 = self.structure
emma_ref = xs0.as_emma_model()
xs = xs0.deep_copy_scatterers()
xs.shake_sites_in_place(rms_difference=0.15)
xs.shake_adp()
for sc in xs.scatterers():
sc.flags.set_use_u_iso(False).set_use_u_aniso(True)
sc.flags.set_grad_site(True).set_grad_u_aniso(True)
# Setup L.S. problem
connectivity_table = smtbx.utils.connectivity_table(xs)
shaken_twin_fraction = (
self.twin_fraction if fixed_twin_fraction else
self.twin_fraction + 0.1*flex.random_double())
# 2nd domain in __init__
twin_components = (xray.twin_component(
twin_law=self.twin_law.r(), value=shaken_twin_fraction,
grad=not fixed_twin_fraction),)
reparametrisation = constraints.reparametrisation(
structure=xs,
constraints=[],
connectivity_table=connectivity_table,
twin_fractions=twin_components)
obs = self.fo_sq.as_xray_observations(twin_components=twin_components)
ls = least_squares.crystallographic_ls(
obs, reparametrisation,
weighting_scheme=least_squares.unit_weighting(),
origin_fixing_restraints_type=
origin_fixing_restraints.atomic_number_weighting)
# Refine till we get back the original structure (so we hope)
cycles = normal_eqns_solving.levenberg_marquardt_iterations(
ls,
gradient_threshold=1e-12,
step_threshold=1e-6,
track_all=True)
# Now let's start to check it all worked
assert ls.n_parameters == 63 if fixed_twin_fraction else 64
match = emma.model_matches(emma_ref, xs.as_emma_model()).refined_matches[0]
assert match.rt.r == matrix.identity(3)
for pair in match.pairs:
assert approx_equal(match.calculate_shortest_dist(pair), 0, eps=1e-4), pair
if fixed_twin_fraction:
assert ls.twin_fractions[0].value == self.twin_fraction
else:
assert approx_equal(ls.twin_fractions[0].value, self.twin_fraction,
eps=1e-2)
assert approx_equal(ls.scale_factor(), 1, eps=1e-5)
assert approx_equal(ls.objective(), 0)
def exercise_weighting_schemes():
unit_weighting = least_squares.unit_weighting()
assert unit_weighting.type() == "unit"
assert str(unit_weighting) == "w=1"
shelx_weighting = least_squares.mainstream_shelx_weighting(0.1234, 0.5678)
assert shelx_weighting.type() == "calc"
assert not show_diff(
str(shelx_weighting),
"w=1/[\s^2^(Fo^2^)+(0.1234P)^2^+0.5678P] where P=(Fo^2^+2Fc^2^)/3")
try:
shelx_weighting(fo_sq=1, sigma=1, fc_sq=1, scale_factor=None)
except RuntimeError, e:
assert 'SMTBX_ASSERT' in str(e)
def exercise_weighting_schemes():
unit_weighting = least_squares.unit_weighting()
assert unit_weighting.type() == "unit"
assert str(unit_weighting) == "w=1"
shelx_weighting = least_squares.mainstream_shelx_weighting(0.1234, 0.5678)
assert shelx_weighting.type() == "calc"
assert not show_diff(
str(shelx_weighting),
"w=1/[\s^2^(Fo^2^)+(0.1234P)^2^+0.5678P] where P=(Fo^2^+2Fc^2^)/3")
try:
shelx_weighting(fo_sq=1, sigma=1, fc_sq=1, scale_factor=None)
except RuntimeError, e:
assert 'SMTBX_ASSERT' in str(e)
def exercise_floating_origin_dynamic_weighting(verbose=False):
from cctbx import covariance
import scitbx.math
worst_condition_number_acceptable = 10
# light elements only
xs0 = random_structure.xray_structure(elements=['C', 'C', 'C', 'O', 'N'],
use_u_aniso=True)
msg = "light elements in %s ..." % (
xs0.space_group_info().type().hall_symbol())
if verbose:
print(msg, end=' ')
fo_sq = xs0.structure_factors(d_min=0.8).f_calc().norm()
fo_sq = fo_sq.customized_copy(sigmas=flex.double(fo_sq.size(), 1.))
xs = xs0.deep_copy_scatterers()
xs.shake_adp()
xs.shake_sites_in_place(rms_difference=0.1)
for sc in xs.scatterers():
sc.flags.set_grad_site(True).set_grad_u_aniso(True)
ls = least_squares.crystallographic_ls(
fo_sq.as_xray_observations(),
constraints.reparametrisation(
structure=xs,
constraints=[],
connectivity_table=smtbx.utils.connectivity_table(xs)),
weighting_scheme=least_squares.unit_weighting(),
origin_fixing_restraints_type=
origin_fixing_restraints.atomic_number_weighting)
ls.build_up()
lambdas = eigensystem.real_symmetric(
ls.normal_matrix_packed_u().matrix_packed_u_as_symmetric()).values()
# assert the restrained L.S. problem is not too ill-conditionned
cond = math.log10(lambdas[0]/lambdas[-1])
if verbose:
print("normal matrix condition: %.1f" % cond)
assert cond < worst_condition_number_acceptable, msg
# one heavy element
xs0 = random_structure.xray_structure(
space_group_info=sgtbx.space_group_info('hall: P 2yb'),
elements=['Zn', 'C', 'C', 'C', 'O', 'N'],
use_u_aniso=True)
msg = "one heavy element + light elements (synthetic data) in %s ..." % (
xs0.space_group_info().type().hall_symbol())
if verbose:
print(msg, end=' ')
fo_sq = xs0.structure_factors(d_min=0.8).f_calc().norm()
fo_sq = fo_sq.customized_copy(sigmas=flex.double(fo_sq.size(), 1.))
xs = xs0.deep_copy_scatterers()
xs.shake_adp()
xs.shake_sites_in_place(rms_difference=0.1)
for sc in xs.scatterers():
sc.flags.set_grad_site(True).set_grad_u_aniso(True)
ls = least_squares.crystallographic_ls(
fo_sq.as_xray_observations(),
constraints.reparametrisation(
structure=xs,
constraints=[],
connectivity_table=smtbx.utils.connectivity_table(xs)),
weighting_scheme=least_squares.mainstream_shelx_weighting(),
origin_fixing_restraints_type=
origin_fixing_restraints.atomic_number_weighting)
ls.build_up()
lambdas = eigensystem.real_symmetric(
ls.normal_matrix_packed_u().matrix_packed_u_as_symmetric()).values()
# assert the restrained L.S. problem is not too ill-conditionned
cond = math.log10(lambdas[0]/lambdas[-1])
if verbose:
print("normal matrix condition: %.1f" % cond)
assert cond < worst_condition_number_acceptable, msg
# are esd's for x,y,z coordinates of the same order of magnitude?
var_cart = covariance.orthogonalize_covariance_matrix(
ls.covariance_matrix(),
xs.unit_cell(),
xs.parameter_map())
var_site_cart = covariance.extract_covariance_matrix_for_sites(
flex.size_t_range(len(xs.scatterers())),
var_cart,
xs.parameter_map())
site_esds = var_site_cart.matrix_packed_u_diagonal()
indicators = flex.double()
for i in xrange(0, len(site_esds), 3):
stats = scitbx.math.basic_statistics(site_esds[i:i+3])
indicators.append(stats.bias_corrected_standard_deviation/stats.mean)
assert indicators.all_lt(2)
# especially troublesome structure with one heavy element
# (contributed by Jonathan Coome)
xs0 = xray.structure(
crystal_symmetry=crystal.symmetry(
unit_cell=(8.4519, 8.4632, 18.7887, 90, 96.921, 90),
space_group_symbol="hall: P 2yb"),
scatterers=flex.xray_scatterer([
xray.scatterer( #0
label="ZN1",
site=(-0.736683, -0.313978, -0.246902),
u=(0.000302, 0.000323, 0.000054,
0.000011, 0.000015, -0.000004)),
xray.scatterer( #1
label="N3B",
site=(-0.721014, -0.313583, -0.134277),
u=(0.000268, 0.000237, 0.000055,
-0.000027, 0.000005, 0.000006)),
xray.scatterer( #2
label="N3A",
site=(-0.733619, -0.290423, -0.357921),
u=(0.000229, 0.000313, 0.000053,
0.000022, 0.000018, -0.000018)),
xray.scatterer( #3
label="C9B",
site=(-1.101537, -0.120157, -0.138063),
u=(0.000315, 0.000345, 0.000103,
0.000050, 0.000055, -0.000017)),
xray.scatterer( #4
label="N5B",
site=(-0.962032, -0.220345, -0.222045),
u=(0.000274, 0.000392, 0.000060,
-0.000011, -0.000001, -0.000002)),
xray.scatterer( #5
label="N1B",
site=(-0.498153, -0.402742, -0.208698),
u=(0.000252, 0.000306, 0.000063,
0.000000, 0.000007, 0.000018)),
xray.scatterer( #6
label="C3B",
site=(-0.322492, -0.472610, -0.114594),
u=(0.000302, 0.000331, 0.000085,
0.000016, -0.000013, 0.000037)),
xray.scatterer( #7
label="C4B",
site=(-0.591851, -0.368163, -0.094677),
u=(0.000262, 0.000255, 0.000073,
-0.000034, 0.000027, -0.000004)),
xray.scatterer( #8
label="N4B",
site=(-0.969383, -0.204624, -0.150014),
u=(0.000279, 0.000259, 0.000070,
-0.000009, 0.000039, 0.000000)),
xray.scatterer( #9
label="N2B",
site=(-0.470538, -0.414572, -0.135526),
u=(0.000277, 0.000282, 0.000065,
0.000003, 0.000021, -0.000006)),
xray.scatterer( #10
label="C8A",
site=(-0.679889, -0.158646, -0.385629),
u=(0.000209, 0.000290, 0.000078,
0.000060, 0.000006, 0.000016)),
xray.scatterer( #11
label="N5A",
site=(-0.649210, -0.075518, -0.263412),
u=(0.000307, 0.000335, 0.000057,
-0.000002, 0.000016, -0.000012)),
xray.scatterer( #12
label="C6B",
site=(-0.708620, -0.325965, 0.011657),
u=(0.000503, 0.000318, 0.000053,
-0.000058, 0.000032, -0.000019)),
xray.scatterer( #13
label="C10B",
site=(-1.179332, -0.083184, -0.202815),
u=(0.000280, 0.000424, 0.000136,
0.000094, 0.000006, 0.000013)),
xray.scatterer( #14
label="N1A",
site=(-0.838363, -0.532191, -0.293213),
u=(0.000312, 0.000323, 0.000060,
0.000018, 0.000011, -0.000008)),
xray.scatterer( #15
label="C3A",
site=(-0.915414, -0.671031, -0.393826),
u=(0.000319, 0.000384, 0.000078,
-0.000052, -0.000001, -0.000020)),
xray.scatterer( #16
label="C1A",
site=(-0.907466, -0.665419, -0.276011),
u=(0.000371, 0.000315, 0.000079,
0.000006, 0.000036, 0.000033)),
xray.scatterer( #17
label="C1B",
site=(-0.365085, -0.452753, -0.231927),
u=(0.000321, 0.000253, 0.000087,
-0.000024, 0.000047, -0.000034)),
xray.scatterer( #18
label="C11A",
site=(-0.598622, 0.053343, -0.227354),
u=(0.000265, 0.000409, 0.000084,
0.000088, -0.000018, -0.000030)),
xray.scatterer( #19
label="C2A",
site=(-0.958694, -0.755645, -0.337016),
u=(0.000394, 0.000350, 0.000106,
-0.000057, 0.000027, -0.000005)),
xray.scatterer( #20
label="C4A",
site=(-0.784860, -0.407601, -0.402050),
u=(0.000238, 0.000296, 0.000064,
0.000002, 0.000011, -0.000016)),
xray.scatterer( #21
label="C5A",
site=(-0.784185, -0.399716, -0.475491),
u=(0.000310, 0.000364, 0.000062,
0.000044, -0.000011, -0.000017)),
xray.scatterer( #22
label="N4A",
site=(-0.630284, -0.043981, -0.333143),
u=(0.000290, 0.000275, 0.000074,
0.000021, 0.000027, 0.000013)),
xray.scatterer( #23
label="C10A",
site=(-0.545465, 0.166922, -0.272829),
u=(0.000369, 0.000253, 0.000117,
0.000015, -0.000002, -0.000008)),
xray.scatterer( #24
label="C9A",
site=(-0.567548, 0.102272, -0.339923),
u=(0.000346, 0.000335, 0.000103,
-0.000016, 0.000037, 0.000023)),
xray.scatterer( #25
label="C11B",
site=(-1.089943, -0.146930, -0.253779),
u=(0.000262, 0.000422, 0.000102,
-0.000018, -0.000002, 0.000029)),
xray.scatterer( #26
label="N2A",
site=(-0.843385, -0.537780, -0.366515),
u=(0.000273, 0.000309, 0.000055,
-0.000012, -0.000005, -0.000018)),
xray.scatterer( #27
label="C7A",
site=(-0.674021, -0.136086, -0.457790),
u=(0.000362, 0.000378, 0.000074,
0.000043, 0.000034, 0.000016)),
xray.scatterer( #28
label="C8B",
site=(-0.843625, -0.264182, -0.102023),
u=(0.000264, 0.000275, 0.000072,
-0.000025, 0.000019, -0.000005)),
xray.scatterer( #29
label="C6A",
site=(-0.726731, -0.261702, -0.502366),
u=(0.000339, 0.000472, 0.000064,
0.000062, -0.000003, 0.000028)),
xray.scatterer( #30
label="C5B",
site=(-0.577197, -0.376753, -0.020800),
u=(0.000349, 0.000353, 0.000066,
-0.000082, -0.000022, 0.000014)),
xray.scatterer( #31
label="C2B",
site=(-0.252088, -0.497338, -0.175057),
u=(0.000251, 0.000342, 0.000119,
0.000020, 0.000034, -0.000018)),
xray.scatterer( #32
label="C7B",
site=(-0.843956, -0.268811, -0.028080),
u=(0.000344, 0.000377, 0.000078,
-0.000029, 0.000059, -0.000007)),
xray.scatterer( #33
label="F4B",
site=(-0.680814, -0.696808, -0.115056),
u=(0.000670, 0.000408, 0.000109,
-0.000099, 0.000139, -0.000031)),
xray.scatterer( #34
label="F1B",
site=(-0.780326, -0.921249, -0.073962),
u=(0.000687, 0.000357, 0.000128,
-0.000152, -0.000011, 0.000021)),
xray.scatterer( #35
label="B1B",
site=(-0.795220, -0.758128, -0.075955),
u=(0.000413, 0.000418, 0.000075,
0.000054, 0.000045, 0.000023)),
xray.scatterer( #36
label="F2B",
site=(-0.945140, -0.714626, -0.105820),
u=(0.000584, 0.001371, 0.000108,
0.000420, 0.000067, 0.000134)),
xray.scatterer( #37
label="F3B",
site=(-0.768914, -0.701660, -0.005161),
u=(0.000678, 0.000544, 0.000079,
-0.000000, 0.000090, -0.000021)),
xray.scatterer( #38
label="F1A",
site=(-0.109283, -0.252334, -0.429288),
u=(0.000427, 0.001704, 0.000125,
0.000407, 0.000041, 0.000035)),
xray.scatterer( #39
label="F4A",
site=(-0.341552, -0.262864, -0.502023),
u=(0.000640, 0.000557, 0.000081,
-0.000074, 0.000042, -0.000052)),
xray.scatterer( #40
label="F3A",
site=(-0.324533, -0.142292, -0.393215),
u=(0.000471, 0.001203, 0.000134,
0.000333, -0.000057, -0.000220)),
xray.scatterer( #41
label="F2A",
site=(-0.312838, -0.405405, -0.400231),
u=(0.002822, 0.000831, 0.000092,
-0.000648, 0.000115, 0.000027)),
xray.scatterer( #42
label="B1A",
site=(-0.271589, -0.268874, -0.430724),
u=(0.000643, 0.000443, 0.000079,
0.000040, 0.000052, -0.000034)),
xray.scatterer( #43
label="H5B",
site=(-0.475808, -0.413802, 0.004402),
u=0.005270),
xray.scatterer( #44
label="H6B",
site=(-0.699519, -0.326233, 0.062781),
u=0.019940),
xray.scatterer( #45
label="H3B",
site=(-0.283410, -0.484757, -0.063922),
u=0.029990),
xray.scatterer( #46
label="H1B",
site=(-0.357103, -0.451819, -0.284911),
u=0.031070),
xray.scatterer( #47
label="H10A",
site=(-0.495517, 0.268296, -0.256187),
u=0.027610),
xray.scatterer( #48
label="H2B",
site=(-0.147129, -0.535141, -0.174699),
u=0.017930),
xray.scatterer( #49
label="H7A",
site=(-0.643658, -0.031387, -0.475357),
u=0.020200),
xray.scatterer( #50
label="H1A",
site=(-0.912757, -0.691043, -0.227554),
u=0.033320),
xray.scatterer( #51
label="H7B",
site=(-0.933670, -0.241189, -0.010263),
u=0.021310),
xray.scatterer( #52
label="H11B",
site=(-1.107736, -0.155470, -0.311996),
u=0.041500),
xray.scatterer( #53
label="H9A",
site=(-0.539908, 0.139753, -0.382281),
u=0.007130),
xray.scatterer( #54
label="H10B",
site=(-1.265944, -0.029610, -0.212398),
u=0.030910),
xray.scatterer( #55
label="H3A",
site=(-0.934728, -0.691149, -0.450551),
u=0.038950),
xray.scatterer( #56
label="H5A",
site=(-0.833654, -0.487479, -0.508239),
u=0.031150),
xray.scatterer( #57
label="H6A",
site=(-0.742871, -0.242269, -0.558157),
u=0.050490),
xray.scatterer( #58
label="H9B",
site=(-1.120150, -0.093752, -0.090706),
u=0.039310),
xray.scatterer( #59
label="H11A",
site=(-0.593074, 0.054973, -0.180370),
u=0.055810),
xray.scatterer( #60
label="H2A",
site=(-0.999576, -0.842158, -0.340837),
u=0.057030)
]))
fo_sq = xs0.structure_factors(d_min=0.8).f_calc().norm()
fo_sq = fo_sq.customized_copy(sigmas=flex.double(fo_sq.size(), 1.))
for hydrogen_flag in (True, False):
xs = xs0.deep_copy_scatterers()
if not hydrogen_flag:
xs.select_inplace(~xs.element_selection('H'))
xs.shake_adp()
xs.shake_sites_in_place(rms_difference=0.1)
for sc in xs.scatterers():
sc.flags.set_grad_site(True).set_grad_u_aniso(False)
ls = least_squares.crystallographic_ls(
fo_sq.as_xray_observations(),
constraints.reparametrisation(
structure=xs,
constraints=[],
connectivity_table=smtbx.utils.connectivity_table(xs)),
weighting_scheme=least_squares.unit_weighting(),
origin_fixing_restraints_type=
origin_fixing_restraints.atomic_number_weighting)
ls.build_up()
lambdas = eigensystem.real_symmetric(
ls.normal_matrix_packed_u().matrix_packed_u_as_symmetric()).values()
# assert the restrained L.S. problem is not too ill-conditionned
cond = math.log10(lambdas[0]/lambdas[-1])
msg = ("one heavy element + light elements (real data) %s Hydrogens: %.1f"
% (['without', 'with'][hydrogen_flag], cond))
if verbose: print(msg)
assert cond < worst_condition_number_acceptable, msg
# are esd's for x,y,z coordinates of the same order of magnitude?
var_cart = covariance.orthogonalize_covariance_matrix(
ls.covariance_matrix(),
xs.unit_cell(),
xs.parameter_map())
var_site_cart = covariance.extract_covariance_matrix_for_sites(
flex.size_t_range(len(xs.scatterers())),
var_cart,
xs.parameter_map())
site_esds = var_site_cart.matrix_packed_u_diagonal()
indicators = flex.double()
for i in xrange(0, len(site_esds), 3):
stats = scitbx.math.basic_statistics(site_esds[i:i+3])
indicators.append(stats.bias_corrected_standard_deviation/stats.mean)
assert indicators.all_lt(1)
def exercise(self):
xs0 = self.structure
xs = xs0.deep_copy_scatterers()
k1, s1, li1, o1, o2 = xs.scatterers()
self.shake_point_group_3(k1)
self.shake_point_group_3(s1)
self.shake_point_group_3(li1)
self.shake_point_group_3(o1)
o2.site = tuple(
[ x*(1 + random.uniform(-self.delta_site, self.delta_site))
for x in o2.site])
o2.u_star = tuple(
[ u*(1 + random.uniform(-self.delta_u_star, self.delta_u_star))
for u in o2.u_star])
for sc in xs.scatterers():
sc.flags.set_use_u_iso(False).set_use_u_aniso(True)
sc.flags.set_grad_site(True).set_grad_u_aniso(True)
connectivity_table = smtbx.utils.connectivity_table(xs)
reparametrisation = constraints.reparametrisation(
structure=xs,
constraints=[],
connectivity_table=connectivity_table)
ls = least_squares.crystallographic_ls(
self.fo_sq.as_xray_observations(), reparametrisation,
weighting_scheme=least_squares.unit_weighting(),
origin_fixing_restraints_type=
origin_fixing_restraints.atomic_number_weighting)
cycles = normal_eqns_solving.levenberg_marquardt_iterations(
ls,
gradient_threshold=1e-12,
step_threshold=1e-7,
track_all=True)
## Test whether refinement brought back the shaked structure to its
## original state
match = emma.model_matches(xs0.as_emma_model(),
xs.as_emma_model()).refined_matches[0]
assert match.rt.r == matrix.identity(3)
assert not match.singles1 and not match.singles2
assert match.rms < 1e-6
delta_u_carts= ( xs.scatterers().extract_u_cart(xs.unit_cell())
- xs0.scatterers().extract_u_cart(xs.unit_cell())).norms()
assert flex.abs(delta_u_carts) < 1e-6
assert approx_equal(ls.scale_factor(), 1, eps=1e-4)
## Test covariance matrix
jac_tr = reparametrisation.jacobian_transpose_matching_grad_fc()
cov = ls.covariance_matrix(
jacobian_transpose=jac_tr, normalised_by_goof=False)\
.matrix_packed_u_as_symmetric()
m, n = cov.accessor().focus()
# x,y for point group 3 sites are fixed: no variance or correlation
for i in (0, 9, 18, 27,):
assert cov.matrix_copy_block(i, 0, 2, n) == 0
# u_star coefficients u13 and u23 for point group 3 sites are fixed
# to 0: again no variance or correlation with any other param
for i in (7, 16, 25, 34,):
assert cov.matrix_copy_block(i, 0, 2, n).as_1d()\
.all_approx_equal(0., 1e-20)
# u_star coefficients u11, u22 and u12 for point group 3 sites
# are totally correlated, with variances in ratios 1:1:1/2
for i in (3, 12, 21, 30,):
assert cov[i, i] != 0
assert approx_equal(cov[i, i], cov[i+1, i+1], eps=1e-15)
assert approx_equal(cov[i, i+1]/cov[i, i], 1, eps=1e-12)
assert approx_equal(cov[i, i+3]/cov[i, i], 0.5, eps=1e-12)
def exercise_floating_origin_restraints(self):
n = self.n_independent_params
eps_zero_rhs = 1e-6
connectivity_table = smtbx.utils.connectivity_table(self.xray_structure)
reparametrisation = constraints.reparametrisation(
structure=self.xray_structure,
constraints=[],
connectivity_table=connectivity_table)
obs = self.fo_sq.as_xray_observations()
ls = least_squares.crystallographic_ls(
obs, reparametrisation,
weighting_scheme=least_squares.unit_weighting(),
origin_fixing_restraints_type=oop.null())
ls.build_up()
unrestrained_normal_matrix = ls.normal_matrix_packed_u()
assert len(unrestrained_normal_matrix) == n*(n+1)//2
ev = eigensystem.real_symmetric(
unrestrained_normal_matrix.matrix_packed_u_as_symmetric())
unrestrained_eigenval = ev.values()
unrestrained_eigenvec = ev.vectors()
ls = least_squares.crystallographic_ls(
obs,
reparametrisation,
weighting_scheme=least_squares.unit_weighting(),
origin_fixing_restraints_type=
origin_fixing_restraints.homogeneous_weighting)
ls.build_up()
# Let's check that the computed singular directions span the same
# space as the expected ones
singular_test = flex.double()
jac = ls.reparametrisation.jacobian_transpose_matching_grad_fc()
m = 0
for s in ls.origin_fixing_restraint.singular_directions:
assert s.norm() != 0
singular_test.extend(jac*s)
m += 1
for s in self.continuous_origin_shift_basis:
singular_test.extend(flex.double(s))
m += 1
singular_test.reshape(flex.grid(m, n))
assert self.rank(singular_test) == len(self.continuous_origin_shift_basis)
assert ls.opposite_of_gradient()\
.all_approx_equal(0, eps_zero_rhs),\
list(ls.gradient())
restrained_normal_matrix = ls.normal_matrix_packed_u()
assert len(restrained_normal_matrix) == n*(n+1)//2
ev = eigensystem.real_symmetric(
restrained_normal_matrix.matrix_packed_u_as_symmetric())
restrained_eigenval = ev.values()
restrained_eigenvec = ev.vectors()
# The eigendecomposition of the normal matrix
# for the unrestrained problem is:
# A = sum_{0 <= i < n-p-1} lambda_i v_i^T v_i
# where the eigenvalues lambda_i are sorted in decreasing order
# and p is the dimension of the continous origin shift space.
# In particular A v_i = 0, n-p <= i < n.
# In the restrained case, it becomes:
# A' = A + sum_{n-p <= i < n} mu v_i^T v_i
p = len(self.continuous_origin_shift_basis)
assert approx_equal(restrained_eigenval[p:], unrestrained_eigenval[:-p],
eps=1e-12)
assert unrestrained_eigenval[-p]/unrestrained_eigenval[-p-1] < 1e-12
if p > 1:
# eigenvectors are stored by rows
unrestrained_null_space = unrestrained_eigenvec.matrix_copy_block(
i_row=n-p, i_column=0,
n_rows=p, n_columns=n)
assert self.rank(unrestrained_null_space) == p
restrained_space = restrained_eigenvec.matrix_copy_block(
i_row=0, i_column=0,
n_rows=p, n_columns=n)
assert self.rank(restrained_space) == p
singular = flex.double(
self.continuous_origin_shift_basis)
assert self.rank(singular) == p
rank_finder = flex.double(n*3*p)
rank_finder.resize(flex.grid(3*p, n))
rank_finder.matrix_paste_block_in_place(unrestrained_null_space,
i_row=0, i_column=0)
rank_finder.matrix_paste_block_in_place(restrained_space,
i_row=p, i_column=0)
rank_finder.matrix_paste_block_in_place(singular,
i_row=2*p, i_column=0)
assert self.rank(rank_finder) == p
else:
# this branch handles the case p=1
# it's necessary to work around a bug in the svd module
# ( nx1 matrices crashes the code )
assert approx_equal(
restrained_eigenvec[0:n].angle(
unrestrained_eigenvec[-n:]) % math.pi, 0)
assert approx_equal(
unrestrained_eigenvec[-n:].angle(
flex.double(self.continuous_origin_shift_basis[0])) % math.pi, 0)
# Do the floating origin restraints prevent the structure from floating?
xs = self.xray_structure.deep_copy_scatterers()
ls = least_squares.crystallographic_ls(
obs,
reparametrisation,
weighting_scheme=least_squares.unit_weighting(),
origin_fixing_restraints_type=
origin_fixing_restraints.atomic_number_weighting
)
barycentre_0 = xs.sites_frac().mean()
while True:
xs.shake_sites_in_place(rms_difference=0.15)
xs.apply_symmetry_sites()
barycentre_1 = xs.sites_frac().mean()
delta = matrix.col(barycentre_1) - matrix.col(barycentre_0)
moved_far_enough = 0
for singular in self.continuous_origin_shift_basis:
e = matrix.col(singular[:3])
if not approx_equal(delta.dot(e), 0, eps=0.01, out=None):
moved_far_enough += 1
if moved_far_enough: break
# one refinement cycle
ls.build_up()
ls.solve()
shifts = ls.step()
# That's what floating origin restraints are for!
# Note that in the presence of special position, that's different
# from the barycentre not moving along the continuous shift directions.
# TODO: typeset notes about that subtlety.
for singular in self.continuous_origin_shift_basis:
assert approx_equal(shifts.dot(flex.double(singular)), 0, eps=1e-12)
def exercise_floating_origin_dynamic_weighting(verbose=False):
from cctbx import covariance
import scitbx.math
worst_condition_number_acceptable = 10
# light elements only
xs0 = random_structure.xray_structure(elements=['C', 'C', 'C', 'O', 'N'],
use_u_aniso=True)
fo_sq = xs0.structure_factors(d_min=0.8).f_calc().norm()
fo_sq = fo_sq.customized_copy(sigmas=flex.double(fo_sq.size(), 1.))
xs = xs0.deep_copy_scatterers()
xs.shake_adp()
xs.shake_sites_in_place(rms_difference=0.1)
for sc in xs.scatterers():
sc.flags.set_grad_site(True).set_grad_u_aniso(True)
ls = least_squares.crystallographic_ls(
fo_sq.as_xray_observations(),
constraints.reparametrisation(
structure=xs,
constraints=[],
connectivity_table=smtbx.utils.connectivity_table(xs)),
weighting_scheme=least_squares.unit_weighting(),
origin_fixing_restraints_type=
origin_fixing_restraints.atomic_number_weighting)
ls.build_up()
lambdas = eigensystem.real_symmetric(
ls.normal_matrix_packed_u().matrix_packed_u_as_symmetric()).values()
# assert the restrained L.S. problem is not too ill-conditionned
cond = math.log10(lambdas[0]/lambdas[-1])
msg = "light elements: %.1f" % cond
if verbose: print msg
assert cond < worst_condition_number_acceptable, msg
# one heavy element
xs0 = random_structure.xray_structure(
space_group_info=sgtbx.space_group_info('hall: P 2yb'),
elements=['Zn', 'C', 'C', 'C', 'O', 'N'],
use_u_aniso=True)
fo_sq = xs0.structure_factors(d_min=0.8).f_calc().norm()
fo_sq = fo_sq.customized_copy(sigmas=flex.double(fo_sq.size(), 1.))
xs = xs0.deep_copy_scatterers()
xs.shake_adp()
xs.shake_sites_in_place(rms_difference=0.1)
for sc in xs.scatterers():
sc.flags.set_grad_site(True).set_grad_u_aniso(True)
ls = least_squares.crystallographic_ls(
fo_sq.as_xray_observations(),
constraints.reparametrisation(
structure=xs,
constraints=[],
connectivity_table=smtbx.utils.connectivity_table(xs)),
weighting_scheme=least_squares.mainstream_shelx_weighting(),
origin_fixing_restraints_type=
origin_fixing_restraints.atomic_number_weighting)
ls.build_up()
lambdas = eigensystem.real_symmetric(
ls.normal_matrix_packed_u().matrix_packed_u_as_symmetric()).values()
# assert the restrained L.S. problem is not too ill-conditionned
cond = math.log10(lambdas[0]/lambdas[-1])
msg = "one heavy element + light elements (synthetic data): %.1f" % cond
if verbose: print msg
assert cond < worst_condition_number_acceptable, msg
# are esd's for x,y,z coordinates of the same order of magnitude?
var_cart = covariance.orthogonalize_covariance_matrix(
ls.covariance_matrix(),
xs.unit_cell(),
xs.parameter_map())
var_site_cart = covariance.extract_covariance_matrix_for_sites(
flex.size_t_range(len(xs.scatterers())),
var_cart,
xs.parameter_map())
site_esds = var_site_cart.matrix_packed_u_diagonal()
indicators = flex.double()
for i in xrange(0, len(site_esds), 3):
stats = scitbx.math.basic_statistics(site_esds[i:i+3])
indicators.append(stats.bias_corrected_standard_deviation/stats.mean)
assert indicators.all_lt(1)
# especially troublesome structure with one heavy element
# (contributed by Jonathan Coome)
xs0 = xray.structure(
crystal_symmetry=crystal.symmetry(
unit_cell=(8.4519, 8.4632, 18.7887, 90, 96.921, 90),
space_group_symbol="hall: P 2yb"),
scatterers=flex.xray_scatterer([
xray.scatterer( #0
label="ZN1",
site=(-0.736683, -0.313978, -0.246902),
u=(0.000302, 0.000323, 0.000054,
0.000011, 0.000015, -0.000004)),
xray.scatterer( #1
label="N3B",
site=(-0.721014, -0.313583, -0.134277),
u=(0.000268, 0.000237, 0.000055,
-0.000027, 0.000005, 0.000006)),
xray.scatterer( #2
label="N3A",
site=(-0.733619, -0.290423, -0.357921),
u=(0.000229, 0.000313, 0.000053,
0.000022, 0.000018, -0.000018)),
xray.scatterer( #3
label="C9B",
site=(-1.101537, -0.120157, -0.138063),
u=(0.000315, 0.000345, 0.000103,
0.000050, 0.000055, -0.000017)),
xray.scatterer( #4
label="N5B",
site=(-0.962032, -0.220345, -0.222045),
u=(0.000274, 0.000392, 0.000060,
-0.000011, -0.000001, -0.000002)),
xray.scatterer( #5
label="N1B",
site=(-0.498153, -0.402742, -0.208698),
u=(0.000252, 0.000306, 0.000063,
0.000000, 0.000007, 0.000018)),
xray.scatterer( #6
label="C3B",
site=(-0.322492, -0.472610, -0.114594),
u=(0.000302, 0.000331, 0.000085,
0.000016, -0.000013, 0.000037)),
xray.scatterer( #7
label="C4B",
site=(-0.591851, -0.368163, -0.094677),
u=(0.000262, 0.000255, 0.000073,
-0.000034, 0.000027, -0.000004)),
xray.scatterer( #8
label="N4B",
site=(-0.969383, -0.204624, -0.150014),
u=(0.000279, 0.000259, 0.000070,
-0.000009, 0.000039, 0.000000)),
xray.scatterer( #9
label="N2B",
site=(-0.470538, -0.414572, -0.135526),
u=(0.000277, 0.000282, 0.000065,
0.000003, 0.000021, -0.000006)),
xray.scatterer( #10
label="C8A",
site=(-0.679889, -0.158646, -0.385629),
u=(0.000209, 0.000290, 0.000078,
0.000060, 0.000006, 0.000016)),
xray.scatterer( #11
label="N5A",
site=(-0.649210, -0.075518, -0.263412),
u=(0.000307, 0.000335, 0.000057,
-0.000002, 0.000016, -0.000012)),
xray.scatterer( #12
label="C6B",
site=(-0.708620, -0.325965, 0.011657),
u=(0.000503, 0.000318, 0.000053,
-0.000058, 0.000032, -0.000019)),
xray.scatterer( #13
label="C10B",
site=(-1.179332, -0.083184, -0.202815),
u=(0.000280, 0.000424, 0.000136,
0.000094, 0.000006, 0.000013)),
xray.scatterer( #14
label="N1A",
site=(-0.838363, -0.532191, -0.293213),
u=(0.000312, 0.000323, 0.000060,
0.000018, 0.000011, -0.000008)),
xray.scatterer( #15
label="C3A",
site=(-0.915414, -0.671031, -0.393826),
u=(0.000319, 0.000384, 0.000078,
-0.000052, -0.000001, -0.000020)),
xray.scatterer( #16
label="C1A",
site=(-0.907466, -0.665419, -0.276011),
u=(0.000371, 0.000315, 0.000079,
0.000006, 0.000036, 0.000033)),
xray.scatterer( #17
label="C1B",
site=(-0.365085, -0.452753, -0.231927),
u=(0.000321, 0.000253, 0.000087,
-0.000024, 0.000047, -0.000034)),
xray.scatterer( #18
label="C11A",
site=(-0.598622, 0.053343, -0.227354),
u=(0.000265, 0.000409, 0.000084,
0.000088, -0.000018, -0.000030)),
xray.scatterer( #19
label="C2A",
site=(-0.958694, -0.755645, -0.337016),
u=(0.000394, 0.000350, 0.000106,
-0.000057, 0.000027, -0.000005)),
xray.scatterer( #20
label="C4A",
site=(-0.784860, -0.407601, -0.402050),
u=(0.000238, 0.000296, 0.000064,
0.000002, 0.000011, -0.000016)),
xray.scatterer( #21
label="C5A",
site=(-0.784185, -0.399716, -0.475491),
u=(0.000310, 0.000364, 0.000062,
0.000044, -0.000011, -0.000017)),
xray.scatterer( #22
label="N4A",
site=(-0.630284, -0.043981, -0.333143),
u=(0.000290, 0.000275, 0.000074,
0.000021, 0.000027, 0.000013)),
xray.scatterer( #23
label="C10A",
site=(-0.545465, 0.166922, -0.272829),
u=(0.000369, 0.000253, 0.000117,
0.000015, -0.000002, -0.000008)),
xray.scatterer( #24
label="C9A",
site=(-0.567548, 0.102272, -0.339923),
u=(0.000346, 0.000335, 0.000103,
-0.000016, 0.000037, 0.000023)),
xray.scatterer( #25
label="C11B",
site=(-1.089943, -0.146930, -0.253779),
u=(0.000262, 0.000422, 0.000102,
-0.000018, -0.000002, 0.000029)),
xray.scatterer( #26
label="N2A",
site=(-0.843385, -0.537780, -0.366515),
u=(0.000273, 0.000309, 0.000055,
-0.000012, -0.000005, -0.000018)),
xray.scatterer( #27
label="C7A",
site=(-0.674021, -0.136086, -0.457790),
u=(0.000362, 0.000378, 0.000074,
0.000043, 0.000034, 0.000016)),
xray.scatterer( #28
label="C8B",
site=(-0.843625, -0.264182, -0.102023),
u=(0.000264, 0.000275, 0.000072,
-0.000025, 0.000019, -0.000005)),
xray.scatterer( #29
label="C6A",
site=(-0.726731, -0.261702, -0.502366),
u=(0.000339, 0.000472, 0.000064,
0.000062, -0.000003, 0.000028)),
xray.scatterer( #30
label="C5B",
site=(-0.577197, -0.376753, -0.020800),
u=(0.000349, 0.000353, 0.000066,
-0.000082, -0.000022, 0.000014)),
xray.scatterer( #31
label="C2B",
site=(-0.252088, -0.497338, -0.175057),
u=(0.000251, 0.000342, 0.000119,
0.000020, 0.000034, -0.000018)),
xray.scatterer( #32
label="C7B",
site=(-0.843956, -0.268811, -0.028080),
u=(0.000344, 0.000377, 0.000078,
-0.000029, 0.000059, -0.000007)),
xray.scatterer( #33
label="F4B",
site=(-0.680814, -0.696808, -0.115056),
u=(0.000670, 0.000408, 0.000109,
-0.000099, 0.000139, -0.000031)),
xray.scatterer( #34
label="F1B",
site=(-0.780326, -0.921249, -0.073962),
u=(0.000687, 0.000357, 0.000128,
-0.000152, -0.000011, 0.000021)),
xray.scatterer( #35
label="B1B",
site=(-0.795220, -0.758128, -0.075955),
u=(0.000413, 0.000418, 0.000075,
0.000054, 0.000045, 0.000023)),
xray.scatterer( #36
label="F2B",
site=(-0.945140, -0.714626, -0.105820),
u=(0.000584, 0.001371, 0.000108,
0.000420, 0.000067, 0.000134)),
xray.scatterer( #37
label="F3B",
site=(-0.768914, -0.701660, -0.005161),
u=(0.000678, 0.000544, 0.000079,
-0.000000, 0.000090, -0.000021)),
xray.scatterer( #38
label="F1A",
site=(-0.109283, -0.252334, -0.429288),
u=(0.000427, 0.001704, 0.000125,
0.000407, 0.000041, 0.000035)),
xray.scatterer( #39
label="F4A",
site=(-0.341552, -0.262864, -0.502023),
u=(0.000640, 0.000557, 0.000081,
-0.000074, 0.000042, -0.000052)),
xray.scatterer( #40
label="F3A",
site=(-0.324533, -0.142292, -0.393215),
u=(0.000471, 0.001203, 0.000134,
0.000333, -0.000057, -0.000220)),
xray.scatterer( #41
label="F2A",
site=(-0.312838, -0.405405, -0.400231),
u=(0.002822, 0.000831, 0.000092,
-0.000648, 0.000115, 0.000027)),
xray.scatterer( #42
label="B1A",
site=(-0.271589, -0.268874, -0.430724),
u=(0.000643, 0.000443, 0.000079,
0.000040, 0.000052, -0.000034)),
xray.scatterer( #43
label="H5B",
site=(-0.475808, -0.413802, 0.004402),
u=0.005270),
xray.scatterer( #44
label="H6B",
site=(-0.699519, -0.326233, 0.062781),
u=0.019940),
xray.scatterer( #45
label="H3B",
site=(-0.283410, -0.484757, -0.063922),
u=0.029990),
xray.scatterer( #46
label="H1B",
site=(-0.357103, -0.451819, -0.284911),
u=0.031070),
xray.scatterer( #47
label="H10A",
site=(-0.495517, 0.268296, -0.256187),
u=0.027610),
xray.scatterer( #48
label="H2B",
site=(-0.147129, -0.535141, -0.174699),
u=0.017930),
xray.scatterer( #49
label="H7A",
site=(-0.643658, -0.031387, -0.475357),
u=0.020200),
xray.scatterer( #50
label="H1A",
site=(-0.912757, -0.691043, -0.227554),
u=0.033320),
xray.scatterer( #51
label="H7B",
site=(-0.933670, -0.241189, -0.010263),
u=0.021310),
xray.scatterer( #52
label="H11B",
site=(-1.107736, -0.155470, -0.311996),
u=0.041500),
xray.scatterer( #53
label="H9A",
site=(-0.539908, 0.139753, -0.382281),
u=0.007130),
xray.scatterer( #54
label="H10B",
site=(-1.265944, -0.029610, -0.212398),
u=0.030910),
xray.scatterer( #55
label="H3A",
site=(-0.934728, -0.691149, -0.450551),
u=0.038950),
xray.scatterer( #56
label="H5A",
site=(-0.833654, -0.487479, -0.508239),
u=0.031150),
xray.scatterer( #57
label="H6A",
site=(-0.742871, -0.242269, -0.558157),
u=0.050490),
xray.scatterer( #58
label="H9B",
site=(-1.120150, -0.093752, -0.090706),
u=0.039310),
xray.scatterer( #59
label="H11A",
site=(-0.593074, 0.054973, -0.180370),
u=0.055810),
xray.scatterer( #60
label="H2A",
site=(-0.999576, -0.842158, -0.340837),
u=0.057030)
]))
fo_sq = xs0.structure_factors(d_min=0.8).f_calc().norm()
fo_sq = fo_sq.customized_copy(sigmas=flex.double(fo_sq.size(), 1.))
for hydrogen_flag in (True, False):
xs = xs0.deep_copy_scatterers()
if not hydrogen_flag:
xs.select_inplace(~xs.element_selection('H'))
xs.shake_adp()
xs.shake_sites_in_place(rms_difference=0.1)
for sc in xs.scatterers():
sc.flags.set_grad_site(True).set_grad_u_aniso(False)
ls = least_squares.crystallographic_ls(
fo_sq.as_xray_observations(),
constraints.reparametrisation(
structure=xs,
constraints=[],
connectivity_table=smtbx.utils.connectivity_table(xs)),
weighting_scheme=least_squares.unit_weighting(),
origin_fixing_restraints_type=
origin_fixing_restraints.atomic_number_weighting)
ls.build_up()
lambdas = eigensystem.real_symmetric(
ls.normal_matrix_packed_u().matrix_packed_u_as_symmetric()).values()
# assert the restrained L.S. problem is not too ill-conditionned
cond = math.log10(lambdas[0]/lambdas[-1])
msg = ("one heavy element + light elements (real data) %s Hydrogens: %.1f"
% (['without', 'with'][hydrogen_flag], cond))
if verbose: print msg
assert cond < worst_condition_number_acceptable, msg
# are esd's for x,y,z coordinates of the same order of magnitude?
var_cart = covariance.orthogonalize_covariance_matrix(
ls.covariance_matrix(),
xs.unit_cell(),
xs.parameter_map())
var_site_cart = covariance.extract_covariance_matrix_for_sites(
flex.size_t_range(len(xs.scatterers())),
var_cart,
xs.parameter_map())
site_esds = var_site_cart.matrix_packed_u_diagonal()
indicators = flex.double()
for i in xrange(0, len(site_esds), 3):
stats = scitbx.math.basic_statistics(site_esds[i:i+3])
indicators.append(stats.bias_corrected_standard_deviation/stats.mean)
assert indicators.all_lt(1)
def exercise_floating_origin_restraints(self):
n = self.n_independent_params
eps_zero_rhs = 1e-6
connectivity_table = smtbx.utils.connectivity_table(self.xray_structure)
reparametrisation = constraints.reparametrisation(
structure=self.xray_structure,
constraints=[],
connectivity_table=connectivity_table)
obs = self.fo_sq.as_xray_observations()
ls = least_squares.crystallographic_ls(
obs, reparametrisation,
weighting_scheme=least_squares.unit_weighting(),
origin_fixing_restraints_type=oop.null())
ls.build_up()
unrestrained_normal_matrix = ls.normal_matrix_packed_u()
assert len(unrestrained_normal_matrix) == n*(n+1)//2
ev = eigensystem.real_symmetric(
unrestrained_normal_matrix.matrix_packed_u_as_symmetric())
unrestrained_eigenval = ev.values()
unrestrained_eigenvec = ev.vectors()
ls = least_squares.crystallographic_ls(
obs,
reparametrisation,
weighting_scheme=least_squares.unit_weighting(),
origin_fixing_restraints_type=
origin_fixing_restraints.homogeneous_weighting)
ls.build_up()
# Let's check that the computed singular directions span the same
# space as the expected ones
singular_test = flex.double()
jac = ls.reparametrisation.jacobian_transpose_matching_grad_fc()
m = 0
for s in ls.origin_fixing_restraint.singular_directions:
assert s.norm() != 0
singular_test.extend(jac*s)
m += 1
for s in self.continuous_origin_shift_basis:
singular_test.extend(flex.double(s))
m += 1
singular_test.reshape(flex.grid(m, n))
assert self.rank(singular_test) == len(self.continuous_origin_shift_basis)
assert ls.opposite_of_gradient()\
.all_approx_equal(0, eps_zero_rhs),\
list(ls.gradient())
restrained_normal_matrix = ls.normal_matrix_packed_u()
assert len(restrained_normal_matrix) == n*(n+1)//2
ev = eigensystem.real_symmetric(
restrained_normal_matrix.matrix_packed_u_as_symmetric())
restrained_eigenval = ev.values()
restrained_eigenvec = ev.vectors()
# The eigendecomposition of the normal matrix
# for the unrestrained problem is:
# A = sum_{0 <= i < n-p-1} lambda_i v_i^T v_i
# where the eigenvalues lambda_i are sorted in decreasing order
# and p is the dimension of the continous origin shift space.
# In particular A v_i = 0, n-p <= i < n.
# In the restrained case, it becomes:
# A' = A + sum_{n-p <= i < n} mu v_i^T v_i
p = len(self.continuous_origin_shift_basis)
assert approx_equal(restrained_eigenval[p:], unrestrained_eigenval[:-p],
eps=1e-12)
assert unrestrained_eigenval[-p]/unrestrained_eigenval[-p-1] < 1e-12
if p > 1:
# eigenvectors are stored by rows
unrestrained_null_space = unrestrained_eigenvec.matrix_copy_block(
i_row=n-p, i_column=0,
n_rows=p, n_columns=n)
assert self.rank(unrestrained_null_space) == p
restrained_space = restrained_eigenvec.matrix_copy_block(
i_row=0, i_column=0,
n_rows=p, n_columns=n)
assert self.rank(restrained_space) == p
singular = flex.double(
self.continuous_origin_shift_basis)
assert self.rank(singular) == p
rank_finder = flex.double(n*3*p)
rank_finder.resize(flex.grid(3*p, n))
rank_finder.matrix_paste_block_in_place(unrestrained_null_space,
i_row=0, i_column=0)
rank_finder.matrix_paste_block_in_place(restrained_space,
i_row=p, i_column=0)
rank_finder.matrix_paste_block_in_place(singular,
i_row=2*p, i_column=0)
assert self.rank(rank_finder) == p
else:
# this branch handles the case p=1
# it's necessary to work around a bug in the svd module
# ( nx1 matrices crashes the code )
assert approx_equal(
restrained_eigenvec[0:n].angle(
unrestrained_eigenvec[-n:]) % math.pi, 0)
assert approx_equal(
unrestrained_eigenvec[-n:].angle(
flex.double(self.continuous_origin_shift_basis[0])) % math.pi, 0)
# Do the floating origin restraints prevent the structure from floating?
xs = self.xray_structure.deep_copy_scatterers()
ls = least_squares.crystallographic_ls(
obs,
reparametrisation,
weighting_scheme=least_squares.unit_weighting(),
origin_fixing_restraints_type=
origin_fixing_restraints.atomic_number_weighting
)
barycentre_0 = xs.sites_frac().mean()
while 1:
xs.shake_sites_in_place(rms_difference=0.15)
xs.apply_symmetry_sites()
barycentre_1 = xs.sites_frac().mean()
delta = matrix.col(barycentre_1) - matrix.col(barycentre_0)
moved_far_enough = 0
for singular in self.continuous_origin_shift_basis:
e = matrix.col(singular[:3])
if not approx_equal(delta.dot(e), 0, eps=0.01, out=None):
moved_far_enough += 1
if moved_far_enough: break
# one refinement cycle
ls.build_up()
ls.solve()
shifts = ls.step()
# That's what floating origin restraints are for!
# Note that in the presence of special position, that's different
# from the barycentre not moving along the continuous shift directions.
# TODO: typeset notes about that subtlety.
for singular in self.continuous_origin_shift_basis:
assert approx_equal(shifts.dot(flex.double(singular)), 0, eps=1e-12)
def exercise(self):
xs0 = self.structure
xs = xs0.deep_copy_scatterers()
k1, s1, li1, o1, o2 = xs.scatterers()
self.shake_point_group_3(k1)
self.shake_point_group_3(s1)
self.shake_point_group_3(li1)
self.shake_point_group_3(o1)
o2.site = tuple(
[ x*(1 + random.uniform(-self.delta_site, self.delta_site))
for x in o2.site])
o2.u_star = tuple(
[ u*(1 + random.uniform(-self.delta_u_star, self.delta_u_star))
for u in o2.u_star])
for sc in xs.scatterers():
sc.flags.set_use_u_iso(False).set_use_u_aniso(True)
sc.flags.set_grad_site(True).set_grad_u_aniso(True)
connectivity_table = smtbx.utils.connectivity_table(xs)
reparametrisation = constraints.reparametrisation(
structure=xs,
constraints=[],
connectivity_table=connectivity_table)
ls = least_squares.crystallographic_ls(
self.fo_sq.as_xray_observations(), reparametrisation,
weighting_scheme=least_squares.unit_weighting(),
origin_fixing_restraints_type=
origin_fixing_restraints.atomic_number_weighting)
cycles = normal_eqns_solving.naive_iterations(
ls,
gradient_threshold=1e-6,
step_threshold=1e-6,
track_all=True)
## Test whether refinement brought back the shaked structure to its
## original state
match = emma.model_matches(xs0.as_emma_model(),
xs.as_emma_model()).refined_matches[0]
assert match.rt.r == matrix.identity(3)
assert not match.singles1 and not match.singles2
assert match.rms < 1e-6
delta_u_carts= ( xs.scatterers().extract_u_cart(xs.unit_cell())
- xs0.scatterers().extract_u_cart(xs.unit_cell())).norms()
assert flex.abs(delta_u_carts) < 1e-6
assert approx_equal(ls.scale_factor(), 1, eps=1e-4)
## Test covariance matrix
jac_tr = reparametrisation.jacobian_transpose_matching_grad_fc()
cov = ls.covariance_matrix(
jacobian_transpose=jac_tr, normalised_by_goof=False)\
.matrix_packed_u_as_symmetric()
m, n = cov.accessor().focus()
# x,y for point group 3 sites are fixed: no variance or correlation
for i in (0, 9, 18, 27,):
assert cov.matrix_copy_block(i, 0, 2, n) == 0
# u_star coefficients u13 and u23 for point group 3 sites are fixed
# to 0: again no variance or correlation with any other param
for i in (7, 16, 25, 34,):
assert cov.matrix_copy_block(i, 0, 2, n).as_1d()\
.all_approx_equal(0., 1e-20)
# u_star coefficients u11, u22 and u12 for point group 3 sites
# are totally correlated, with variances in ratios 1:1:1/2
for i in (3, 12, 21, 30,):
assert cov[i, i] != 0
assert approx_equal(cov[i, i], cov[i+1, i+1], eps=1e-15)
assert approx_equal(cov[i, i+1]/cov[i, i], 1, eps=1e-12)
assert approx_equal(cov[i, i+3]/cov[i, i], 0.5, eps=1e-12)
def exercise(self):
xs0 = self.structure
xs = xs0.deep_copy_scatterers()
xs.shake_sites_in_place(rms_difference=0.15)
xs.shake_adp()
for sc in xs.scatterers():
sc.flags.set_use_u_iso(False).set_use_u_aniso(True)
sc.flags.set_grad_site(True).set_grad_u_aniso(True)
connectivity_table = smtbx.utils.connectivity_table(xs)
if self.twin_fractions[0] < 0.5:
twin_fractions = self.twin_fractions.deep_copy() + 0.1
else:
twin_fractions = self.twin_fractions.deep_copy() - 0.1
twin_components = tuple(
[xray.twin_component(law, fraction, grad=True)
for law, fraction in zip(self.twin_laws, twin_fractions)])
reparametrisation = constraints.reparametrisation(
structure=xs,
constraints=[],
connectivity_table=connectivity_table,
twin_fractions=twin_components)
obs = self.fo_sq.as_xray_observations(twin_components=twin_components)
normal_eqns = least_squares.crystallographic_ls(
obs, reparametrisation,
weighting_scheme=least_squares.unit_weighting(),
origin_fixing_restraints_type=
origin_fixing_restraints.atomic_number_weighting)
cycles = normal_eqns_solving.naive_iterations(
normal_eqns,
n_max_iterations=10,
track_all=True)
assert approx_equal(
[twin.value for twin in normal_eqns.twin_fractions],
self.twin_fractions, eps=1e-2)
assert approx_equal(normal_eqns.objective(), 0, eps=1e-5)
assert normal_eqns.n_parameters == 64
# now with fixed twin fraction
xs.shake_sites_in_place(rms_difference=0.15)
xs.shake_adp()
twin_components = tuple(
[xray.twin_component(law, fraction, grad=False)
for law, fraction in zip(self.twin_laws, twin_fractions)])
#change the twin_components of the observations...
obs = observations.customized_copy(obs, twin_components=twin_components)
reparametrisation = constraints.reparametrisation(
structure=xs,
constraints=[],
connectivity_table=connectivity_table,
twin_fractions=twin_components)
normal_eqns = least_squares.crystallographic_ls(
obs, reparametrisation,
weighting_scheme=least_squares.unit_weighting(),
origin_fixing_restraints_type=
origin_fixing_restraints.atomic_number_weighting)
cycles = normal_eqns_solving.naive_iterations(
normal_eqns,
n_max_iterations=10,
track_all=True)
assert approx_equal(
[twin.value for twin in normal_eqns.twin_fractions],
twin_fractions)
assert normal_eqns.objective() != 0 # since the twin fraction is not refined
assert normal_eqns.n_parameters == 63
