Beispiel #1
0
def exercise_chirality(verbose=0):
    # monomer library: CA N CB C
    sites = [
        col(site)
        for site in [(27.660, 9.903,
                      2.078), (28.049, 9.675,
                               3.486), (28.183, 11.269,
                                        1.625), (28.085, 8.759, 1.165)]
    ]
    chir = geometry_restraints.chirality(sites=sites,
                                         volume_ideal=-2.48,
                                         both_signs=False,
                                         weight=1)
    assert approx_equal(chir.volume_model, -2.411548478)
    assert approx_equal(chir.residual(), 0.00468561086412)
    dih = geometry_restraints.dihedral(sites=improper_permutation(sites),
                                       angle_ideal=35.26439,
                                       weight=1)
    assert approx_equal(dih.angle_model, 32.2587249641)
    assert approx_equal(dih.residual(), 9.03402230782)
    if (verbose):
        dump_pdb("sites.pdb", sites)
        print("volume_ideal:", chir.volume_ideal)
        print("volume_model:", chir.volume_model)
        print("angle_ideal:", dih.angle_ideal)
        print("angle model:", dih.angle_model)
    for i_trial in range(50):
        volume_ideal = chir.volume_ideal
        for both_signs in [False, True]:
            sites_mod = []
            for site in sites:
                shift = col([random.uniform(-.5, .5) for i in range(3)])
                sites_mod.append(site + shift)
            if (both_signs): volume_ideal = abs(volume_ideal)
            c = geometry_restraints.chirality(sites=sites_mod,
                                              volume_ideal=volume_ideal,
                                              both_signs=both_signs,
                                              weight=500 * 1 / 0.2**2)
            residual_obj = residual_functor(
                restraint_type=geometry_restraints.chirality,
                volume_ideal=c.volume_ideal,
                both_signs=c.both_signs,
                weight=c.weight)
            fg = flex.vec3_double(finite_differences(
                sites_mod, residual_obj)).as_double()
            ag = flex.vec3_double(c.gradients()).as_double()
            scale = max(1, flex.mean(flex.abs(fg)))
            assert approx_equal(ag / scale, fg / scale)
            d = geometry_restraints.dihedral(
                sites=improper_permutation(sites_mod),
                angle_ideal=dih.angle_ideal,
                weight=750)
            ag_dih = dih.gradients()
            if (verbose and i_trial == 0 and not both_signs):
                dump_pdb("sites_mod.pdb", sites_mod)
                max_g_len = 0
                for g in ag_dih:
                    max_g_len = max(max_g_len, abs(col(g)))
                for g in flex.vec3_double(fg):
                    max_g_len = max(max_g_len, abs(col(g)))
                sticks = []
                for site, g in zip(improper_permutation(sites_mod), ag_dih):
                    sticks.append(
                        pml_stick(begin=site,
                                  end=site + col(g) / max_g_len,
                                  colors=[[1, 0, 0]] * 2,
                                  width=0.01))
                pml_write(f=open("dih.pml", "w"), label="dih", sticks=sticks)
                sticks = []
                for site, g in zip(sites_mod, flex.vec3_double(fg)):
                    sticks.append(
                        pml_stick(begin=site,
                                  end=site + col(g) / max_g_len,
                                  colors=[[0, 1, 0]] * 2,
                                  width=0.01))
                pml_write(f=open("chir.pml", "w"), label="chir", sticks=sticks)
def exercise_chirality(verbose=0):
  # monomer library: CA N CB C
  sites = [col(site) for site in [
    (27.660, 9.903, 2.078),
    (28.049, 9.675, 3.486),
    (28.183, 11.269, 1.625),
    (28.085, 8.759, 1.165)]]
  chir = geometry_restraints.chirality(
    sites=sites,
    volume_ideal=-2.48,
    both_signs=False,
    weight=1)
  assert approx_equal(chir.volume_model, -2.411548478)
  assert approx_equal(chir.residual(), 0.00468561086412)
  dih = geometry_restraints.dihedral(
    sites=improper_permutation(sites),
    angle_ideal=35.26439,
    weight=1)
  assert approx_equal(dih.angle_model, 32.2587249641)
  assert approx_equal(dih.residual(), 9.03402230782)
  if (verbose):
    dump_pdb("sites.pdb", sites)
    print "volume_ideal:", chir.volume_ideal
    print "volume_model:", chir.volume_model
    print "angle_ideal:", dih.angle_ideal
    print "angle model:", dih.angle_model
  for i_trial in xrange(50):
    volume_ideal = chir.volume_ideal
    for both_signs in [False, True]:
      sites_mod = []
      for site in sites:
        shift = col([random.uniform(-.5,.5) for i in xrange(3)])
        sites_mod.append(site+shift)
      if (both_signs): volume_ideal = abs(volume_ideal)
      c = geometry_restraints.chirality(
        sites=sites_mod,
        volume_ideal=volume_ideal,
        both_signs=both_signs,
        weight=500*1/0.2**2)
      residual_obj = residual_functor(
        restraint_type=geometry_restraints.chirality,
        volume_ideal=c.volume_ideal,
        both_signs=c.both_signs,
        weight=c.weight)
      fg = flex.vec3_double(
        finite_differences(sites_mod, residual_obj)).as_double()
      ag = flex.vec3_double(
        c.gradients()).as_double()
      scale = max(1, flex.mean(flex.abs(fg)))
      assert approx_equal(ag/scale, fg/scale)
      d = geometry_restraints.dihedral(
        sites=improper_permutation(sites_mod),
        angle_ideal=dih.angle_ideal,
        weight=750)
      ag_dih = dih.gradients()
      if (verbose and i_trial == 0 and not both_signs):
        dump_pdb("sites_mod.pdb", sites_mod)
        max_g_len = 0
        for g in ag_dih:
          max_g_len = max(max_g_len, abs(col(g)))
        for g in flex.vec3_double(fg):
          max_g_len = max(max_g_len, abs(col(g)))
        sticks = []
        for site,g in zip(improper_permutation(sites_mod),ag_dih):
          sticks.append(
            pml_stick(
              begin=site,
              end=site+col(g)/max_g_len,
              colors=[[1,0,0]]*2,
              width=0.01))
        pml_write(f=open("dih.pml", "w"), label="dih", sticks=sticks)
        sticks = []
        for site,g in zip(sites_mod,flex.vec3_double(fg)):
          sticks.append(
            pml_stick(
              begin=site,
              end=site+col(g)/max_g_len,
              colors=[[0,1,0]]*2,
              width=0.01))
        pml_write(f=open("chir.pml", "w"), label="chir", sticks=sticks)
Beispiel #3
0
def exercise(verbose=0):
    distance_ideal = 1.8
    default_vdw_distance = 3.6
    vdw_1_4_factor = 3.5 / 3.6
    sites_cart_manual = flex.vec3_double([(1, 3, 0), (2, 3, 0), (3, 2, 0),
                                          (3, 1, 0), (4, 1, 0), (3, 4, 0),
                                          (4, 3, 0), (5, 3, 0), (6, 2, 0),
                                          (7, 2, 0), (8, 3, 0), (7, 4, 0),
                                          (6, 4, 0), (7, 5, 0), (6, 6, 0),
                                          (8, 6, 0)])
    bond_proxies = geometry_restraints.bond_sorted_asu_proxies(
        asu_mappings=None)
    for i_seqs in [(0, 1), (1, 2), (2, 3), (3, 4), (1, 5), (2, 6), (5, 6),
                   (6, 7), (7, 8), (8, 9), (9, 10), (10, 11), (11, 12),
                   (12, 7), (11, 13), (13, 14), (14, 15), (15, 13)]:
        bond_proxies.process(
            geometry_restraints.bond_simple_proxy(
                i_seqs=i_seqs, distance_ideal=distance_ideal, weight=100))
    angle_proxies = geometry_restraints.shared_angle_proxy()
    for i_seqs, angle_ideal in [[(0, 1, 2), 135], [(0, 1, 5), 135],
                                [(1, 2, 3), 135], [(3, 2, 6), 135],
                                [(2, 3, 4), 120], [(1, 2, 6), 90],
                                [(2, 6, 5), 90], [(6, 5, 1), 90],
                                [(5, 1, 2), 90], [(2, 6, 7), 135],
                                [(5, 6, 7), 135], [(6, 7, 8), 120],
                                [(6, 7, 12), 120], [(7, 8, 9), 120],
                                [(8, 9, 10), 120], [(9, 10, 11), 120],
                                [(10, 11, 12), 120], [(11, 12, 7), 120],
                                [(12, 7, 8), 120], [(10, 11, 13), 120],
                                [(12, 11, 13), 120], [(11, 13, 15), 150],
                                [(11, 13, 14), 150], [(13, 15, 14), 60],
                                [(15, 14, 13), 60], [(14, 13, 15), 60]]:
        angle_proxies.append(
            geometry_restraints.angle_proxy(i_seqs=i_seqs,
                                            angle_ideal=angle_ideal,
                                            weight=1))
    if (0 or verbose):
        dump_pdb(file_name="manual.pdb", sites_cart=sites_cart_manual)
    for traditional_convergence_test in [True, False]:
        for sites_cart_selection in [True, False]:
            sites_cart = sites_cart_manual.deep_copy()
            if sites_cart_selection:
                sites_cart_selection = flex.bool(sites_cart.size(), True)
                sites_cart_selection[1] = False
            assert bond_proxies.asu.size() == 0
            bond_params_table = geometry_restraints.extract_bond_params(
                n_seq=sites_cart.size(),
                bond_simple_proxies=bond_proxies.simple)
            manager = geometry_restraints.manager.manager(
                bond_params_table=bond_params_table,
                angle_proxies=angle_proxies)
            minimized = geometry_restraints.lbfgs.lbfgs(
                sites_cart=sites_cart,
                geometry_restraints_manager=manager,
                lbfgs_termination_params=scitbx.lbfgs.termination_parameters(
                    traditional_convergence_test=traditional_convergence_test,
                    drop_convergence_test_max_drop_eps=1.e-20,
                    drop_convergence_test_iteration_coefficient=1,
                    max_iterations=1000),
                sites_cart_selection=sites_cart_selection,
            )
            assert minimized.minimizer.iter() > 100
            sites_cart_minimized_1 = sites_cart.deep_copy()
            if (0 or verbose):
                dump_pdb(file_name="minimized_1.pdb",
                         sites_cart=sites_cart_minimized_1)
            bond_deltas = geometry_restraints.bond_deltas(
                sites_cart=sites_cart_minimized_1, proxies=bond_proxies.simple)
            angle_deltas = geometry_restraints.angle_deltas(
                sites_cart=sites_cart_minimized_1, proxies=angle_proxies)
            if (0 or verbose):
                for proxy, delta in zip(bond_proxies.simple, bond_deltas):
                    print "bond:", proxy.i_seqs, delta
                for proxy, delta in zip(angle_proxies, angle_deltas):
                    print "angle:", proxy.i_seqs, delta
            assert is_below_limit(value=flex.max(flex.abs(bond_deltas)),
                                  limit=0,
                                  eps=1.e-6)
            assert is_below_limit(value=flex.max(flex.abs(angle_deltas)),
                                  limit=0,
                                  eps=2.e-6)
    sites_cart += matrix.col((1, 1, 0)) - matrix.col(sites_cart.min())
    unit_cell_lengths = list(
        matrix.col(sites_cart.max()) + matrix.col((1, -1.2, 4)))
    unit_cell_lengths[1] *= 2
    unit_cell_lengths[2] *= 2
    xray_structure = xray.structure(crystal_symmetry=crystal.symmetry(
        unit_cell=unit_cell_lengths, space_group_symbol="P112"))
    for serial, site in zip(count(1), sites_cart):
        xray_structure.add_scatterer(
            xray.scatterer(
                label="C%02d" % serial,
                site=xray_structure.unit_cell().fractionalize(site)))
    if (0 or verbose):
        xray_structure.show_summary().show_scatterers()
    p1_structure = (xray_structure.apply_shift(
        (-.5, -.5, 0)).expand_to_p1().apply_shift((.5, .5, 0)))
    for shift in [(1, 0, 0), (0, 1, 0), (0, 0, 1)]:
        p1_structure.add_scatterers(
            p1_structure.apply_shift(shift).scatterers())
    if (0 or verbose):
        open("p1_structure.pdb", "w").write(p1_structure.as_pdb_file())
    nonbonded_cutoff = 6.5
    asu_mappings = xray_structure.asu_mappings(
        buffer_thickness=nonbonded_cutoff)
    bond_asu_table = crystal.pair_asu_table(asu_mappings=asu_mappings)
    geometry_restraints.add_pairs(bond_asu_table, bond_proxies.simple)
    shell_asu_tables = crystal.coordination_sequences.shell_asu_tables(
        pair_asu_table=bond_asu_table, max_shell=3)
    shell_sym_tables = [
        shell_asu_table.extract_pair_sym_table()
        for shell_asu_table in shell_asu_tables
    ]
    bond_params_table = geometry_restraints.extract_bond_params(
        n_seq=sites_cart.size(), bond_simple_proxies=bond_proxies.simple)
    atom_energy_types = flex.std_string(sites_cart.size(), "Default")
    nonbonded_params = geometry_restraints.nonbonded_params(
        factor_1_4_interactions=vdw_1_4_factor,
        const_shrink_1_4_interactions=0,
        default_distance=default_vdw_distance)
    nonbonded_params.distance_table.setdefault(
        "Default")["Default"] = default_vdw_distance
    pair_proxies = geometry_restraints.pair_proxies(
        bond_params_table=bond_params_table,
        shell_asu_tables=shell_asu_tables,
        model_indices=None,
        conformer_indices=None,
        nonbonded_params=nonbonded_params,
        nonbonded_types=atom_energy_types,
        nonbonded_distance_cutoff_plus_buffer=nonbonded_cutoff)
    if (0 or verbose):
        print "pair_proxies.bond_proxies.n_total():", \
               pair_proxies.bond_proxies.n_total(),
        print "simple:", pair_proxies.bond_proxies.simple.size(),
        print "sym:", pair_proxies.bond_proxies.asu.size()
        print "pair_proxies.nonbonded_proxies.n_total():", \
               pair_proxies.nonbonded_proxies.n_total(),
        print "simple:", pair_proxies.nonbonded_proxies.simple.size(),
        print "sym:", pair_proxies.nonbonded_proxies.asu.size()
        print "min_distance_nonbonded: %.2f" % flex.min(
            geometry_restraints.nonbonded_deltas(
                sites_cart=sites_cart,
                sorted_asu_proxies=pair_proxies.nonbonded_proxies))
    s = StringIO()
    pair_proxies.bond_proxies.show_histogram_of_model_distances(
        sites_cart=sites_cart, f=s, prefix="[]")
    assert s.getvalue().splitlines()[0] == "[]Histogram of bond lengths:"
    assert s.getvalue().splitlines()[5].startswith("[]      1.80 -     1.80:")
    s = StringIO()
    pair_proxies.bond_proxies.show_histogram_of_deltas(sites_cart=sites_cart,
                                                       f=s,
                                                       prefix="][")
    assert s.getvalue().splitlines()[0] == "][Histogram of bond deltas:"
    assert s.getvalue().splitlines()[5].startswith("][     0.000 -    0.000:")
    s = StringIO()
    pair_proxies.bond_proxies.show_sorted(by_value="residual",
                                          sites_cart=sites_cart,
                                          max_items=3,
                                          f=s,
                                          prefix=":;")
    l = s.getvalue().splitlines()
    assert l[0] == ":;Bond restraints: 18"
    assert l[1] == ":;Sorted by residual:"
    assert l[2].startswith(":;bond ")
    assert l[3].startswith(":;     ")
    assert l[4] == ":;  ideal  model  delta    sigma   weight residual"
    for i in [5, -2]:
        assert l[i].startswith(":;  1.800  1.800 ")
    assert l[-1] == ":;... (remaining 15 not shown)"
    s = StringIO()
    pair_proxies.nonbonded_proxies.show_histogram_of_model_distances(
        sites_cart=sites_cart, f=s, prefix="]^")
    assert not show_diff(
        s.getvalue(), """\
]^Histogram of nonbonded interaction distances:
]^      2.16 -     3.03: 3
]^      3.03 -     3.89: 12
]^      3.89 -     4.75: 28
]^      4.75 -     5.61: 44
]^      5.61 -     6.48: 54
""")
    s = StringIO()
    pair_proxies.nonbonded_proxies.show_sorted(by_value="delta",
                                               sites_cart=sites_cart,
                                               max_items=7,
                                               f=s,
                                               prefix=">,")
    assert not show_diff(s.getvalue(),
                         """\
>,Nonbonded interactions: 141
>,Sorted by model distance:
>,nonbonded 15
>,          15
>,   model   vdw sym.op.
>,   2.164 3.600 -x+2,-y+1,z
...
>,nonbonded 4
>,          8
>,   model   vdw
>,   3.414 3.600
>,... (remaining 134 not shown)
""",
                         selections=[range(6), range(-5, 0)])
    vdw_1_sticks = []
    vdw_2_sticks = []
    for proxy in pair_proxies.nonbonded_proxies.simple:
        if (proxy.vdw_distance == default_vdw_distance):
            vdw_1_sticks.append(
                pml_stick(begin=sites_cart[proxy.i_seqs[0]],
                          end=sites_cart[proxy.i_seqs[1]]))
        else:
            vdw_2_sticks.append(
                pml_stick(begin=sites_cart[proxy.i_seqs[0]],
                          end=sites_cart[proxy.i_seqs[1]]))
    mps = asu_mappings.mappings()
    for proxy in pair_proxies.nonbonded_proxies.asu:
        if (proxy.vdw_distance == default_vdw_distance):
            vdw_1_sticks.append(
                pml_stick(begin=mps[proxy.i_seq][0].mapped_site(),
                          end=mps[proxy.j_seq][proxy.j_sym].mapped_site()))
        else:
            vdw_2_sticks.append(
                pml_stick(begin=mps[proxy.i_seq][0].mapped_site(),
                          end=mps[proxy.j_seq][proxy.j_sym].mapped_site()))
    if (0 or verbose):
        pml_write(f=open("vdw_1.pml", "w"), label="vdw_1", sticks=vdw_1_sticks)
        pml_write(f=open("vdw_2.pml", "w"), label="vdw_2", sticks=vdw_2_sticks)
    #
    i_pdb = count(2)
    for use_crystal_symmetry in [False, True]:
        if (not use_crystal_symmetry):
            crystal_symmetry = None
            site_symmetry_table = None
        else:
            crystal_symmetry = xray_structure
            site_symmetry_table = xray_structure.site_symmetry_table()
        for sites_cart in [
                sites_cart_manual.deep_copy(),
                sites_cart_minimized_1.deep_copy()
        ]:
            manager = geometry_restraints.manager.manager(
                crystal_symmetry=crystal_symmetry,
                site_symmetry_table=site_symmetry_table,
                nonbonded_params=nonbonded_params,
                nonbonded_types=atom_energy_types,
                nonbonded_function=geometry_restraints.
                prolsq_repulsion_function(),
                bond_params_table=bond_params_table,
                shell_sym_tables=shell_sym_tables,
                nonbonded_distance_cutoff=nonbonded_cutoff,
                nonbonded_buffer=1,
                angle_proxies=angle_proxies,
                plain_pairs_radius=5)
            manager = manager.select(
                selection=flex.bool(sites_cart.size(), True))
            manager = manager.select(iselection=flex.size_t_range(
                stop=sites_cart.size()))
            pair_proxies = manager.pair_proxies(sites_cart=sites_cart)
            minimized = geometry_restraints.lbfgs.lbfgs(
                sites_cart=sites_cart,
                geometry_restraints_manager=manager,
                lbfgs_termination_params=scitbx.lbfgs.termination_parameters(
                    max_iterations=1000))
            if (0 or verbose):
                minimized.final_target_result.show()
                print "number of function evaluations:", minimized.minimizer.nfun(
                )
                print "n_updates_pair_proxies:", manager.n_updates_pair_proxies
            if (not use_crystal_symmetry):
                assert minimized.final_target_result.bond_residual_sum < 1.e-3
                assert minimized.final_target_result.nonbonded_residual_sum < 0.1
            else:
                assert minimized.final_target_result.bond_residual_sum < 1.e-2
                assert minimized.final_target_result.nonbonded_residual_sum < 0.1
            assert minimized.final_target_result.angle_residual_sum < 1.e-3
            if (0 or verbose):
                pdb_file_name = "minimized_%d.pdb" % i_pdb.next()
                print "Writing file:", pdb_file_name
                dump_pdb(file_name=pdb_file_name, sites_cart=sites_cart)
            if (manager.site_symmetry_table is None):
                additional_site_symmetry_table = None
            else:
                additional_site_symmetry_table = sgtbx.site_symmetry_table()
            assert manager.new_including_isolated_sites(
              n_additional_sites=0,
              site_symmetry_table=additional_site_symmetry_table,
              nonbonded_types=flex.std_string()).plain_pairs_radius \
                == manager.plain_pairs_radius
            if (crystal_symmetry is not None):
                assert len(manager.plain_pair_sym_table) == 16
                if (0 or verbose):
                    manager.plain_pair_sym_table.show()
    #
    xray_structure.set_u_iso(values=flex.double([
        0.77599982480241358, 0.38745781137212021, 0.20667558236418682,
        0.99759840171302094, 0.8917287406687805, 0.64780251325379845,
        0.24878590382983534, 0.59480621182194615, 0.58695637792905142,
        0.33997130213653637, 0.51258699130743735, 0.79760289141276675,
        0.39996577657875021, 0.4329328819341467, 0.70422156561726479,
        0.87260110626999332
    ]))

    class parameters:
        pass

    parameters.sphere_radius = 5
    parameters.distance_power = 0.7
    parameters.average_power = 0.9
    parameters.wilson_b_weight = 1.3952
    parameters.wilson_b_weight_auto = False
    adp_energies = adp_restraints.energies_iso(
        geometry_restraints_manager=manager,
        xray_structure=xray_structure,
        parameters=parameters,
        wilson_b=None,
        use_hd=False,
        use_u_local_only=False,
        compute_gradients=False,
        gradients=None,
        normalization=False,
        collect=True)
    assert adp_energies.number_of_restraints == 69
    assert approx_equal(adp_energies.residual_sum, 6.24865382467)
    assert adp_energies.gradients is None
    assert adp_energies.u_i.size() == adp_energies.number_of_restraints
    assert adp_energies.u_j.size() == adp_energies.number_of_restraints
    assert adp_energies.r_ij.size() == adp_energies.number_of_restraints
    for wilson_b in [None, 10, 100]:
        finite_difference_gradients = flex.double()
        eps = 1.e-6
        for i_scatterer in xrange(xray_structure.scatterers().size()):
            rs = []
            for signed_eps in [eps, -eps]:
                xray_structure_eps = xray_structure.deep_copy_scatterers()
                xray_structure_eps.scatterers(
                )[i_scatterer].u_iso += signed_eps
                adp_energies = adp_restraints.energies_iso(
                    geometry_restraints_manager=manager,
                    xray_structure=xray_structure_eps,
                    parameters=parameters,
                    wilson_b=wilson_b,
                    use_u_local_only=False,
                    use_hd=False,
                    compute_gradients=True,
                    gradients=None,
                    normalization=False,
                    collect=False)
                rs.append(adp_energies.residual_sum)
                assert adp_energies.gradients.size() \
                    == xray_structure.scatterers().size()
                assert adp_energies.u_i == None
                assert adp_energies.u_j == None
                assert adp_energies.r_ij == None
            finite_difference_gradients.append((rs[0] - rs[1]) / (2 * eps))
        sel = flex.bool(xray_structure.scatterers().size(), True)
        xray_structure.scatterers().flags_set_grad_u_iso(sel.iselection())
        adp_energies = adp_restraints.energies_iso(
            geometry_restraints_manager=manager,
            xray_structure=xray_structure,
            parameters=parameters,
            wilson_b=wilson_b,
            use_u_local_only=False,
            use_hd=False,
            compute_gradients=True,
            gradients=None,
            normalization=False,
            collect=False)
        assert approx_equal(adp_energies.gradients,
                            finite_difference_gradients)
    print "OK"
def exercise(verbose=0):
  distance_ideal = 1.8
  default_vdw_distance = 3.6
  vdw_1_4_factor = 3.5/3.6
  sites_cart_manual = flex.vec3_double([
    (1,3,0), (2,3,0), (3,2,0), (3,1,0), (4,1,0), (3,4,0), (4,3,0), (5,3,0),
    (6,2,0), (7,2,0), (8,3,0), (7,4,0), (6,4,0), (7,5,0), (6,6,0), (8,6,0)])
  bond_proxies = geometry_restraints.bond_sorted_asu_proxies(asu_mappings=None)
  for i_seqs in [(0,1),(1,2),(2,3),(3,4),(1,5),(2,6),(5,6),
                 (6,7),(7,8),(8,9),(9,10),(10,11),(11,12),
                 (12,7),(11,13),(13,14),(14,15),(15,13)]:
    bond_proxies.process(geometry_restraints.bond_simple_proxy(
      i_seqs=i_seqs, distance_ideal=distance_ideal, weight=100))
  angle_proxies = geometry_restraints.shared_angle_proxy()
  for i_seqs,angle_ideal in [[(0,1,2),135],
                             [(0,1,5),135],
                             [(1,2,3),135],
                             [(3,2,6),135],
                             [(2,3,4),120],
                             [(1,2,6),90],
                             [(2,6,5),90],
                             [(6,5,1),90],
                             [(5,1,2),90],
                             [(2,6,7),135],
                             [(5,6,7),135],
                             [(6,7,8),120],
                             [(6,7,12),120],
                             [(7,8,9),120],
                             [(8,9,10),120],
                             [(9,10,11),120],
                             [(10,11,12),120],
                             [(11,12,7),120],
                             [(12,7,8),120],
                             [(10,11,13),120],
                             [(12,11,13),120],
                             [(11,13,15),150],
                             [(11,13,14),150],
                             [(13,15,14),60],
                             [(15,14,13),60],
                             [(14,13,15),60]]:
    angle_proxies.append(geometry_restraints.angle_proxy(
      i_seqs=i_seqs, angle_ideal=angle_ideal, weight=1))
  if (0 or verbose):
    dump_pdb(file_name="manual.pdb", sites_cart=sites_cart_manual)
  for traditional_convergence_test in [True,False]:
    for sites_cart_selection in [True, False]:
      sites_cart = sites_cart_manual.deep_copy()
      if sites_cart_selection:
        sites_cart_selection = flex.bool(sites_cart.size(), True)
        sites_cart_selection[1] = False
      assert bond_proxies.asu.size() == 0
      bond_params_table = geometry_restraints.extract_bond_params(
        n_seq=sites_cart.size(),
        bond_simple_proxies=bond_proxies.simple)
      manager = geometry_restraints.manager.manager(
        bond_params_table=bond_params_table,
        angle_proxies=angle_proxies)
      minimized = geometry_restraints.lbfgs.lbfgs(
        sites_cart=sites_cart,
        geometry_restraints_manager=manager,
        lbfgs_termination_params=scitbx.lbfgs.termination_parameters(
          traditional_convergence_test=traditional_convergence_test,
          drop_convergence_test_max_drop_eps=1.e-20,
          drop_convergence_test_iteration_coefficient=1,
          max_iterations=1000),
        sites_cart_selection=sites_cart_selection,
        )
      assert minimized.minimizer.iter() > 100
      sites_cart_minimized_1 = sites_cart.deep_copy()
      if (0 or verbose):
        dump_pdb(
          file_name="minimized_1.pdb", sites_cart=sites_cart_minimized_1)
      bond_deltas = geometry_restraints.bond_deltas(
        sites_cart=sites_cart_minimized_1,
        proxies=bond_proxies.simple)
      angle_deltas = geometry_restraints.angle_deltas(
        sites_cart=sites_cart_minimized_1,
        proxies=angle_proxies)
      if (0 or verbose):
        for proxy,delta in zip(bond_proxies.simple, bond_deltas):
          print "bond:", proxy.i_seqs, delta
        for proxy,delta in zip(angle_proxies, angle_deltas):
          print "angle:", proxy.i_seqs, delta
      assert is_below_limit(
        value=flex.max(flex.abs(bond_deltas)), limit=0, eps=1.e-6)
      assert is_below_limit(
        value=flex.max(flex.abs(angle_deltas)), limit=0, eps=2.e-6)
  sites_cart += matrix.col((1,1,0)) - matrix.col(sites_cart.min())
  unit_cell_lengths = list(  matrix.col(sites_cart.max())
                           + matrix.col((1,-1.2,4)))
  unit_cell_lengths[1] *= 2
  unit_cell_lengths[2] *= 2
  xray_structure = xray.structure(
    crystal_symmetry=crystal.symmetry(
      unit_cell=unit_cell_lengths,
      space_group_symbol="P112"))
  for serial,site in zip(count(1), sites_cart):
    xray_structure.add_scatterer(xray.scatterer(
      label="C%02d"%serial,
      site=xray_structure.unit_cell().fractionalize(site)))
  if (0 or verbose):
    xray_structure.show_summary().show_scatterers()
  p1_structure = (xray_structure
    .apply_shift((-.5,-.5,0))
    .expand_to_p1()
    .apply_shift((.5,.5,0)))
  for shift in [(1,0,0), (0,1,0), (0,0,1)]:
    p1_structure.add_scatterers(p1_structure.apply_shift(shift).scatterers())
  if (0 or verbose):
    open("p1_structure.pdb", "w").write(p1_structure.as_pdb_file())
  nonbonded_cutoff = 6.5
  asu_mappings = xray_structure.asu_mappings(
    buffer_thickness=nonbonded_cutoff)
  bond_asu_table = crystal.pair_asu_table(asu_mappings=asu_mappings)
  geometry_restraints.add_pairs(bond_asu_table, bond_proxies.simple)
  shell_asu_tables = crystal.coordination_sequences.shell_asu_tables(
    pair_asu_table=bond_asu_table,
    max_shell=3)
  shell_sym_tables = [shell_asu_table.extract_pair_sym_table()
    for shell_asu_table in shell_asu_tables]
  bond_params_table = geometry_restraints.extract_bond_params(
    n_seq=sites_cart.size(),
    bond_simple_proxies=bond_proxies.simple)
  atom_energy_types = flex.std_string(sites_cart.size(), "Default")
  nonbonded_params = geometry_restraints.nonbonded_params(
    factor_1_4_interactions=vdw_1_4_factor,
    const_shrink_1_4_interactions=0,
    default_distance=default_vdw_distance)
  nonbonded_params.distance_table.setdefault(
    "Default")["Default"] = default_vdw_distance
  pair_proxies = geometry_restraints.pair_proxies(
    bond_params_table=bond_params_table,
    shell_asu_tables=shell_asu_tables,
    model_indices=None,
    conformer_indices=None,
    nonbonded_params=nonbonded_params,
    nonbonded_types=atom_energy_types,
    nonbonded_distance_cutoff_plus_buffer=nonbonded_cutoff)
  if (0 or verbose):
    print "pair_proxies.bond_proxies.n_total():", \
           pair_proxies.bond_proxies.n_total(),
    print "simple:", pair_proxies.bond_proxies.simple.size(),
    print "sym:", pair_proxies.bond_proxies.asu.size()
    print "pair_proxies.nonbonded_proxies.n_total():", \
           pair_proxies.nonbonded_proxies.n_total(),
    print "simple:", pair_proxies.nonbonded_proxies.simple.size(),
    print "sym:", pair_proxies.nonbonded_proxies.asu.size()
    print "min_distance_nonbonded: %.2f" % flex.min(
      geometry_restraints.nonbonded_deltas(
        sites_cart=sites_cart,
        sorted_asu_proxies=pair_proxies.nonbonded_proxies))
  s = StringIO()
  pair_proxies.bond_proxies.show_histogram_of_model_distances(
    sites_cart=sites_cart,
    f=s,
    prefix="[]")
  assert s.getvalue().splitlines()[0] == "[]Histogram of bond lengths:"
  assert s.getvalue().splitlines()[5].startswith("[]      1.80 -     1.80:")
  s = StringIO()
  pair_proxies.bond_proxies.show_histogram_of_deltas(
    sites_cart=sites_cart,
    f=s,
    prefix="][")
  assert s.getvalue().splitlines()[0] == "][Histogram of bond deltas:"
  assert s.getvalue().splitlines()[5].startswith("][     0.000 -    0.000:")
  s = StringIO()
  pair_proxies.bond_proxies.show_sorted(
    by_value="residual",
    sites_cart=sites_cart,
    max_items=3,
    f=s,
    prefix=":;")
  l = s.getvalue().splitlines()
  assert l[0] == ":;Bond restraints: 18"
  assert l[1] == ":;Sorted by residual:"
  assert l[2].startswith(":;bond ")
  assert l[3].startswith(":;     ")
  assert l[4] == ":;  ideal  model  delta    sigma   weight residual"
  for i in [5,-2]:
    assert l[i].startswith(":;  1.800  1.800 ")
  assert l[-1] == ":;... (remaining 15 not shown)"
  s = StringIO()
  pair_proxies.nonbonded_proxies.show_histogram_of_model_distances(
    sites_cart=sites_cart,
    f=s,
    prefix="]^")
  assert not show_diff(s.getvalue(), """\
]^Histogram of nonbonded interaction distances:
]^      2.16 -     3.03: 3
]^      3.03 -     3.89: 12
]^      3.89 -     4.75: 28
]^      4.75 -     5.61: 44
]^      5.61 -     6.48: 54
""")
  s = StringIO()
  pair_proxies.nonbonded_proxies.show_sorted(
    by_value="delta",
    sites_cart=sites_cart,
    max_items=7,
    f=s,
    prefix=">,")
  assert not show_diff(s.getvalue(), """\
>,Nonbonded interactions: 141
>,Sorted by model distance:
>,nonbonded 15
>,          15
>,   model   vdw sym.op.
>,   2.164 3.600 -x+2,-y+1,z
...
>,nonbonded 4
>,          8
>,   model   vdw
>,   3.414 3.600
>,... (remaining 134 not shown)
""",
    selections=[range(6), range(-5,0)])
  vdw_1_sticks = []
  vdw_2_sticks = []
  for proxy in pair_proxies.nonbonded_proxies.simple:
    if (proxy.vdw_distance == default_vdw_distance):
      vdw_1_sticks.append(pml_stick(
        begin=sites_cart[proxy.i_seqs[0]],
        end=sites_cart[proxy.i_seqs[1]]))
    else:
      vdw_2_sticks.append(pml_stick(
        begin=sites_cart[proxy.i_seqs[0]],
        end=sites_cart[proxy.i_seqs[1]]))
  mps = asu_mappings.mappings()
  for proxy in pair_proxies.nonbonded_proxies.asu:
    if (proxy.vdw_distance == default_vdw_distance):
      vdw_1_sticks.append(pml_stick(
        begin=mps[proxy.i_seq][0].mapped_site(),
        end=mps[proxy.j_seq][proxy.j_sym].mapped_site()))
    else:
      vdw_2_sticks.append(pml_stick(
        begin=mps[proxy.i_seq][0].mapped_site(),
        end=mps[proxy.j_seq][proxy.j_sym].mapped_site()))
  if (0 or verbose):
    pml_write(f=open("vdw_1.pml", "w"), label="vdw_1", sticks=vdw_1_sticks)
    pml_write(f=open("vdw_2.pml", "w"), label="vdw_2", sticks=vdw_2_sticks)
  #
  i_pdb = count(2)
  for use_crystal_symmetry in [False, True]:
    if (not use_crystal_symmetry):
      crystal_symmetry = None
      site_symmetry_table = None
    else:
      crystal_symmetry = xray_structure
      site_symmetry_table = xray_structure.site_symmetry_table()
    for sites_cart in [sites_cart_manual.deep_copy(),
                       sites_cart_minimized_1.deep_copy()]:
      manager = geometry_restraints.manager.manager(
        crystal_symmetry=crystal_symmetry,
        site_symmetry_table=site_symmetry_table,
        nonbonded_params=nonbonded_params,
        nonbonded_types=atom_energy_types,
        nonbonded_function=geometry_restraints.prolsq_repulsion_function(),
        bond_params_table=bond_params_table,
        shell_sym_tables=shell_sym_tables,
        nonbonded_distance_cutoff=nonbonded_cutoff,
        nonbonded_buffer=1,
        angle_proxies=angle_proxies,
        plain_pairs_radius=5)
      manager = manager.select(selection=flex.bool(sites_cart.size(), True))
      manager = manager.select(
        iselection=flex.size_t_range(stop=sites_cart.size()))
      pair_proxies = manager.pair_proxies(sites_cart=sites_cart)
      minimized = geometry_restraints.lbfgs.lbfgs(
        sites_cart=sites_cart,
        geometry_restraints_manager=manager,
        lbfgs_termination_params=scitbx.lbfgs.termination_parameters(
          max_iterations=1000))
      if (0 or verbose):
        minimized.final_target_result.show()
        print "number of function evaluations:", minimized.minimizer.nfun()
        print "n_updates_pair_proxies:", manager.n_updates_pair_proxies
      if (not use_crystal_symmetry):
        assert minimized.final_target_result.bond_residual_sum < 1.e-3
        assert minimized.final_target_result.nonbonded_residual_sum < 0.1
      else:
        assert minimized.final_target_result.bond_residual_sum < 1.e-2
        assert minimized.final_target_result.nonbonded_residual_sum < 0.1
      assert minimized.final_target_result.angle_residual_sum < 1.e-3
      if (0 or verbose):
        pdb_file_name = "minimized_%d.pdb" % i_pdb.next()
        print "Writing file:", pdb_file_name
        dump_pdb(file_name=pdb_file_name, sites_cart=sites_cart)
      if (manager.site_symmetry_table is None):
        additional_site_symmetry_table = None
      else:
        additional_site_symmetry_table = sgtbx.site_symmetry_table()
      assert manager.new_including_isolated_sites(
        n_additional_sites=0,
        site_symmetry_table=additional_site_symmetry_table,
        nonbonded_types=flex.std_string()).plain_pairs_radius \
          == manager.plain_pairs_radius
      if (crystal_symmetry is not None):
        assert len(manager.plain_pair_sym_table) == 16
        if (0 or verbose):
          manager.plain_pair_sym_table.show()
  #
  xray_structure.set_u_iso(values=flex.double([
    0.77599982480241358, 0.38745781137212021, 0.20667558236418682,
    0.99759840171302094, 0.8917287406687805, 0.64780251325379845,
    0.24878590382983534, 0.59480621182194615, 0.58695637792905142,
    0.33997130213653637, 0.51258699130743735, 0.79760289141276675,
    0.39996577657875021, 0.4329328819341467, 0.70422156561726479,
    0.87260110626999332]))
  class parameters: pass
  parameters.sphere_radius = 5
  parameters.distance_power = 0.7
  parameters.average_power = 0.9
  parameters.wilson_b_weight = 1.3952
  parameters.wilson_b_weight_auto = False
  adp_energies = adp_restraints.energies_iso(
    geometry_restraints_manager=manager,
    xray_structure=xray_structure,
    parameters=parameters,
    wilson_b=None,
    use_hd=False,
    use_u_local_only = False,
    compute_gradients=False,
    gradients=None,
    normalization=False,
    collect=True)
  assert adp_energies.number_of_restraints == 69
  assert approx_equal(adp_energies.residual_sum, 6.24865382467)
  assert adp_energies.gradients is None
  assert adp_energies.u_i.size() == adp_energies.number_of_restraints
  assert adp_energies.u_j.size() == adp_energies.number_of_restraints
  assert adp_energies.r_ij.size() == adp_energies.number_of_restraints
  for wilson_b in [None, 10, 100]:
    finite_difference_gradients = flex.double()
    eps = 1.e-6
    for i_scatterer in xrange(xray_structure.scatterers().size()):
      rs = []
      for signed_eps in [eps, -eps]:
        xray_structure_eps = xray_structure.deep_copy_scatterers()
        xray_structure_eps.scatterers()[i_scatterer].u_iso += signed_eps
        adp_energies = adp_restraints.energies_iso(
          geometry_restraints_manager=manager,
          xray_structure=xray_structure_eps,
          parameters=parameters,
          wilson_b=wilson_b,
          use_u_local_only = False,
          use_hd=False,
          compute_gradients=True,
          gradients=None,
          normalization=False,
          collect=False)
        rs.append(adp_energies.residual_sum)
        assert adp_energies.gradients.size() \
            == xray_structure.scatterers().size()
        assert adp_energies.u_i == None
        assert adp_energies.u_j == None
        assert adp_energies.r_ij == None
      finite_difference_gradients.append((rs[0]-rs[1])/(2*eps))
    sel = flex.bool(xray_structure.scatterers().size(), True)
    xray_structure.scatterers().flags_set_grad_u_iso(sel.iselection())
    adp_energies = adp_restraints.energies_iso(
      geometry_restraints_manager=manager,
      xray_structure=xray_structure,
      parameters=parameters,
      wilson_b=wilson_b,
      use_u_local_only = False,
      use_hd=False,
      compute_gradients=True,
      gradients=None,
      normalization=False,
      collect=False)
    assert approx_equal(adp_energies.gradients, finite_difference_gradients)
  print "OK"