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.mainstream_shelx_weighting(a=0),
      origin_fixing_restraints_type=
      origin_fixing_restraints.atomic_number_weighting)

    cycles = normal_eqns_solving.naive_iterations(
      ls,
      gradient_threshold=1e-12,
      step_threshold=1e-7,
      track_all=True)

    assert approx_equal(ls.scale_factor(), 1, eps=1e-5), ls.scale_factor()
    assert approx_equal(ls.objective(), 0), ls.objective()

    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 make_shelx_weighting_scheme(self, a, b, c=0, d=0, e=0, f=1/3):
   assert f == 1/3, "Non-Wilsonian ShelX weighting not supported"
   if c == 0 and d == 0 and e == 0:
     self.weighting_scheme = \
         least_squares.mainstream_shelx_weighting(a, b)
   else:
     raise NotImplementedError(
       "ShelX weighting scheme with non-zero parameter c, d or 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")
def exercise_optimise_shelxl_weights():
  def calc_goof(fo2, fc, w, k, n_params):
    fc2 = fc.as_intensity_array()
    w = w(fo2.data(), fo2.sigmas(), fc2.data(), k)
    return math.sqrt(flex.sum(
      w * flex.pow2(fo2.data() - k*fc2.data()))/(fo2.size() - n_params))
  xs = smtbx.development.sucrose()
  k = 0.05 + 10 * flex.random_double()
  fc = xs.structure_factors(anomalous_flag=False, d_min=0.7).f_calc()
  fo = fc.as_amplitude_array()
  fo = fo.customized_copy(data=fo.data()*math.sqrt(k))
  fo = fo.customized_copy(sigmas=0.03*fo.data())
  sigmas = fo.sigmas()
  for i in range(fo.size()):
    fo.data()[i] += 2 * scitbx.random.variate(
      scitbx.random.normal_distribution(sigma=sigmas[i]))() \
      + 0.5*random.random()
  fo2 = fo.as_intensity_array()
  fc2 = fc.as_intensity_array()
  w = least_squares.mainstream_shelx_weighting(a=0.1)
  s = calc_goof(fo2, fc, w, k, xs.n_parameters())
  w2 = w.optimise_parameters(fo2, fc2, k, xs.n_parameters())
  s2 = calc_goof(fo2, fc, w2, k, xs.n_parameters())
  # sort data and setup binning by fc/fc_max
  fc_sq = fc.as_intensity_array()
  fc_sq_over_fc_sq_max = fc_sq.data()/flex.max(fc_sq.data())
  permutation = flex.sort_permutation(fc_sq_over_fc_sq_max)
  fc_sq_over_fc_sq_max = fc_sq.customized_copy(
    data=fc_sq_over_fc_sq_max).select(permutation)
  fc_sq = fc_sq.select(permutation)
  fo_sq = fo2.select(permutation)
  n_bins = 10
  bin_max = 0
  bin_limits = flex.size_t(1, 0)
  bin_count = flex.size_t()
  for i in range(n_bins):
    bin_limits.append(int(math.ceil((i+1) * fc_sq.size()/n_bins)))
    bin_count.append(bin_limits[i+1] - bin_limits[i])
  goofs_w = flex.double()
  goofs_w2 = flex.double()
  for i_bin in range(n_bins):
    sel = flex.size_t_range(bin_limits[i_bin], bin_limits[i_bin+1])
    goofs_w2.append(calc_goof(fo_sq.select(sel),
                              fc_sq.select(sel),
                              w2, k, xs.n_parameters()))
    goofs_w.append(calc_goof(fo_sq.select(sel),
                              fc_sq.select(sel),
                              w, k, xs.n_parameters()))
  a = flex.mean_and_variance(goofs_w).unweighted_sample_variance()
  b = flex.mean_and_variance(goofs_w2).unweighted_sample_variance()
  assert a > b or abs(1-s) > abs(1-s2)
  assert a > b # flat analysis of variance
  assert abs(1-s) > abs(1-s2) # GooF close to 1
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 check_refinement_stability(self):
    if not self.shall_refine_thermal_displacements:
      for sc in self.xray_structure.scatterers():
        sc.flags.set_grad_site(True)
        if sc.flags.use_u_aniso(): sc.flags.set_grad_u_aniso(False)
        if sc.flags.use_u_iso(): sc.flags.set_grad_u_iso(False)

    xs = self.xray_structure
    xs0 = self.reference_xray_structure = xs.deep_copy_scatterers()
    mi = xs0.build_miller_set(anomalous_flag=False, d_min=0.5)
    fo_sq = mi.structure_factors_from_scatterers(
      xs0, algorithm="direct").f_calc().norm()
    fo_sq = fo_sq.customized_copy(sigmas=flex.double(fo_sq.size(), 1))

    xs.shake_sites_in_place(rms_difference=0.1)
    if self.shall_refine_thermal_displacements:
      # a spread of 10 for u_iso's would be enormous for our low temperature
      # test structures if those u_iso's were not constrained
      xs.shake_adp(spread=10, # absolute
                   aniso_spread=0.2) # relative

    self.reparametrisation = constraints.reparametrisation(
      xs, self.constraints, self.connectivity_table,
      temperature=self.t_celsius)
    obs = fo_sq.as_xray_observations()
    ls = least_squares.crystallographic_ls(
      obs,
      self.reparametrisation,
      weighting_scheme=least_squares.mainstream_shelx_weighting())
    self.cycles = self.normal_eqns_solving_method(ls)
    print ("%i %s iterations to recover from shaking"
           % (self.cycles.n_iterations,
              self.cycles))
    if 0:
      from crys3d.qttbx.xray_structure_viewer import display
      display(xray_structure=xs)

    diff = xray.meaningful_site_cart_differences(xs0, xs)
    assert diff.max_absolute() < self.site_refinement_tolerance,\
           self.__class__.__name__

    if self.shall_refine_thermal_displacements:
      delta_u = []
      for sc, sc0 in itertools.izip(xs.scatterers(), xs0.scatterers()):
        if not sc.flags.use_u_aniso() or not sc0.flags.use_u_aniso(): continue
        delta_u.extend(matrix.col(sc.u_star) - matrix.col(sc0.u_star))
      delta_u = flex.double(delta_u)

      assert flex.max_absolute(delta_u) < self.u_star_refinement_tolerance,\
             self.__class__.__name__
  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.mainstream_shelx_weighting(a=0),
      origin_fixing_restraints_type=oop.null())

    try:
      cycles = normal_eqns_solving.naive_iterations(
        ls,
        gradient_threshold=1e-12,
        track_all=True)

      assert approx_equal(ls.scale_factor(), 1, eps=1e-4)
      assert approx_equal(ls.objective(), 0)
      assert cycles.gradient_norm_history[-1] < cycles.gradient_threshold

      for sc0, sc1 in zip(self.xray_structure.scatterers(), xs.scatterers()):
        assert approx_equal(sc0.u_star, sc1.u_star)
    except RuntimeError, err:
      import re
      m = re.search(
        r'^cctbx::adptbx::debye_waller_factor_exp: \s* arg_limit \s+ exceeded'
        '.* arg \s* = \s* ([\d.eE+-]+)', str(err), re.X)
      assert m is not None, eval
      print "Warning: refinement of ADP's diverged"
      print '         argument to debye_waller_factor_exp reached %s' % m.group(1)
      print 'Here is the failing structure'
      xs.show_summary()
      xs.show_scatterers()
      raise self.refinement_diverged()
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)