tools.py

#!/usr/bin/env python

"""@namespace IMP.pmi.tools
   Miscellaneous utilities.
"""

import IMP
import IMP.algebra
import IMP.isd
import IMP.pmi
import IMP.pmi.topology
from collections.abc import MutableSet
import itertools
import math
import ast
from time import process_time
import RMF
import IMP.rmf
from collections import defaultdict, OrderedDict
import warnings
import numpy


def _get_system_for_hier(hier):
    """Given a hierarchy, return the System that created it, or None"""
    # If we are given the raw particle, get the corresponding Hierarchy
    # decorator if available
    if hier and not hasattr(hier, 'get_parent'):
        if IMP.atom.Hierarchy.get_is_setup(hier):
            hier = IMP.atom.Hierarchy(hier)
        else:
            return None
    while hier:
        # See if we labeled the Python object directly with the System
        if hasattr(hier, '_pmi2_system'):
            h = hier._pmi2_system()
            if h:
                return h
        # Otherwise (maybe we got a new Python wrapper around the same C++
        # object), try all extant systems
        for s in IMP.pmi.topology.System._all_systems:
            if s.hier == hier:
                return s
        # Try the next level up in the hierarchy
        hier = hier.get_parent()


def _all_protocol_outputs(hier):
    """Iterate over all (ProtocolOutput, State) pairs for the
       given hierarchy"""
    system = _get_system_for_hier(hier)
    if system:
        for state in system.states:
            for p in state._protocol_output:
                yield p


def _add_pmi_provenance(p):
    """Tag the given particle as being created by the current version
       of PMI."""
    IMP.core.add_imp_provenance(p)
    IMP.core.add_software_provenance(
        p, name="IMP PMI module", version=IMP.pmi.get_module_version(),
        location="https://integrativemodeling.org")
    IMP.core.add_script_provenance(p)


def _get_restraint_set_keys():
    if not hasattr(_get_restraint_set_keys, 'pmi_rs_key'):
        _get_restraint_set_keys.pmi_rs_key = IMP.ModelKey("PMI restraints")
        _get_restraint_set_keys.rmf_rs_key = IMP.ModelKey("RMF restraints")
    return (_get_restraint_set_keys.pmi_rs_key,
            _get_restraint_set_keys.rmf_rs_key)


def _add_restraint_sets(model, mk, mk_rmf):
    rs = IMP.RestraintSet(model, "All PMI restraints")
    rs_rmf = IMP.RestraintSet(model, "All PMI RMF restraints")
    model.add_data(mk, rs)
    model.add_data(mk_rmf, rs_rmf)
    return rs, rs_rmf


def add_restraint_to_model(model, restraint, add_to_rmf=False):
    """Add a PMI restraint to the model.
       Since Model.add_restraint() no longer exists (in modern IMP restraints
       should be added to a ScoringFunction instead) store them instead in
       a RestraintSet, and keep a reference to it in the Model.

       If `add_to_rmf` is True, also add the restraint to a separate list
       of restraints that will be written out to RMF files (by default, most
       PMI restraints are not)."""
    mk, mk_rmf = _get_restraint_set_keys()
    if model.get_has_data(mk):
        rs = IMP.RestraintSet.get_from(model.get_data(mk))
        rs_rmf = IMP.RestraintSet.get_from(model.get_data(mk_rmf))
    else:
        rs, rs_rmf = _add_restraint_sets(model, mk, mk_rmf)
    rs.add_restraint(restraint)
    if add_to_rmf:
        rs_rmf.add_restraint(restraint)


def get_restraint_set(model, rmf=False):
    """Get a RestraintSet containing all PMI restraints added to the model.
       If `rmf` is True, return only the subset of these restraints that
       should be written out to RMF files."""
    mk, mk_rmf = _get_restraint_set_keys()
    if not model.get_has_data(mk):
        warnings.warn("no restraints added to model yet",
                      IMP.pmi.ParameterWarning)
        _add_restraint_sets(model, mk, mk_rmf)
    if rmf:
        return IMP.RestraintSet.get_from(model.get_data(mk_rmf))
    else:
        return IMP.RestraintSet.get_from(model.get_data(mk))


class Stopwatch:
    """Collect timing information.
       Add an instance of this class to outputobjects to get timing information
       in a stat file."""

    def __init__(self, isdelta=True):
        """Constructor.
           @param isdelta if True (the default) then report the time since the
                  last use of this class; if False, report cumulative time."""
        self.starttime = process_time()
        self.label = "None"
        self.isdelta = isdelta

    def set_label(self, labelstr):
        self.label = labelstr

    def get_output(self):
        output = {}
        if self.isdelta:
            newtime = process_time()
            output["Stopwatch_" + self.label + "_delta_seconds"] \
                = str(newtime - self.starttime)
            self.starttime = newtime
        else:
            output["Stopwatch_" + self.label + "_elapsed_seconds"] \
                    = str(process_time() - self.starttime)
        return output


class SetupNuisance:

    def __init__(self, m, initialvalue, minvalue, maxvalue, isoptimized=True,
                 name=None):

        p = IMP.Particle(m)
        if name:
            p.set_name(name)
        nuisance = IMP.isd.Scale.setup_particle(p, initialvalue)
        if minvalue:
            nuisance.set_lower(minvalue)
        if maxvalue:
            nuisance.set_upper(maxvalue)

        # m.add_score_state(IMP.core.SingletonConstraint(IMP.isd.NuisanceRangeModifier(),None,nuisance))
        nuisance.set_is_optimized(nuisance.get_nuisance_key(), isoptimized)
        self.nuisance = nuisance

    def get_particle(self):
        return self.nuisance


class SetupWeight:

    def __init__(self, m, isoptimized=True, nweights_or_weights=None):
        pw = IMP.Particle(m)
        if isinstance(nweights_or_weights, int):
            self.weight = IMP.isd.Weight.setup_particle(
                pw, nweights_or_weights
            )
        else:
            try:
                nweights_or_weights = list(nweights_or_weights)
                self.weight = IMP.isd.Weight.setup_particle(
                    pw, nweights_or_weights
                )
            except (TypeError, IMP.UsageException):
                self.weight = IMP.isd.Weight.setup_particle(pw)
            self.weight.set_weights_are_optimized(isoptimized)

    def get_particle(self):
        return self.weight


class SetupSurface:

    def __init__(self, m, center, normal, isoptimized=True):
        p = IMP.Particle(m)
        self.surface = IMP.core.Surface.setup_particle(p, center, normal)
        self.surface.set_coordinates_are_optimized(isoptimized)
        self.surface.set_normal_is_optimized(isoptimized)

    def get_particle(self):
        return self.surface


def get_cross_link_data(directory, filename, dist, omega, sigma,
                        don=None, doff=None, prior=0, type_of_profile="gofr"):

    (distmin, distmax, ndist) = dist
    (omegamin, omegamax, nomega) = omega
    (sigmamin, sigmamax, nsigma) = sigma

    filen = IMP.isd.get_data_path("CrossLinkPMFs.dict")
    with open(filen) as xlpot:
        dictionary = ast.literal_eval(xlpot.readline())

    xpot = dictionary[directory][filename]["distance"]
    pot = dictionary[directory][filename][type_of_profile]

    dist_grid = get_grid(distmin, distmax, ndist, False)
    omega_grid = get_log_grid(omegamin, omegamax, nomega)
    sigma_grid = get_log_grid(sigmamin, sigmamax, nsigma)

    if don is not None and doff is not None:
        xlmsdata = IMP.isd.CrossLinkData(
            dist_grid,
            omega_grid,
            sigma_grid,
            xpot,
            pot,
            don,
            doff,
            prior)
    else:
        xlmsdata = IMP.isd.CrossLinkData(
            dist_grid,
            omega_grid,
            sigma_grid,
            xpot,
            pot)
    return xlmsdata


def get_grid(gmin, gmax, ngrid, boundaries):
    grid = []
    dx = (gmax - gmin) / float(ngrid)
    for i in range(0, ngrid + 1):
        if not boundaries and i == 0:
            continue
        if not boundaries and i == ngrid:
            continue
        grid.append(gmin + float(i) * dx)
    return grid


def get_log_grid(gmin, gmax, ngrid):
    grid = []
    for i in range(0, ngrid + 1):
        grid.append(gmin * math.exp(float(i) / ngrid * math.log(gmax / gmin)))
    return grid


def cross_link_db_filter_parser(inputstring):
    '''
    example '"{ID_Score}" > 28 AND "{Sample}" ==
     "%10_1%" OR ":Sample}" == "%10_2%" OR ":Sample}"
    == "%10_3%" OR ":Sample}" == "%8_1%" OR ":Sample}" == "%8_2%"'
    '''

    import pyparsing as pp

    operator = pp.Regex(">=|<=|!=|>|<|==|in").setName("operator")
    value = pp.QuotedString(
        '"') | pp.Regex(
        r"[+-]?\d+(:?\.\d*)?(:?[eE][+-]?\d+)?")
    identifier = pp.Word(pp.alphas, pp.alphanums + "_")
    comparison_term = identifier | value
    condition = pp.Group(comparison_term + operator + comparison_term)

    expr = pp.operatorPrecedence(condition, [
                                ("OR", 2, pp.opAssoc.LEFT, ),
        ("AND", 2, pp.opAssoc.LEFT, ),
    ])

    parsedstring = str(expr.parseString(inputstring)) \
        .replace("[", "(") \
        .replace("]", ")") \
        .replace(",", " ") \
        .replace("'", " ") \
        .replace("%", "'") \
        .replace("{", "float(entry['") \
        .replace("}", "'])") \
        .replace(":", "str(entry['") \
        .replace("}", "'])") \
        .replace("AND", "and") \
        .replace("OR", "or")
    return parsedstring


def open_file_or_inline_text(filename):
    try:
        fl = open(filename, "r")
    except IOError:
        fl = filename.split("\n")
    return fl


def get_ids_from_fasta_file(fastafile):
    ids = []
    with open(fastafile) as ff:
        for line in ff:
            if line[0] == ">":
                ids.append(line[1:-1])
    return ids


def get_closest_residue_position(hier, resindex, terminus="N"):
    '''
    this function works with plain hierarchies, as read from the pdb,
    no multi-scale hierarchies
    '''
    p = []
    niter = 0
    while len(p) == 0:
        niter += 1
        sel = IMP.atom.Selection(hier, residue_index=resindex,
                                 atom_type=IMP.atom.AT_CA)

        if terminus == "N":
            resindex += 1
        if terminus == "C":
            resindex -= 1

        if niter >= 10000:
            print("get_closest_residue_position: exiting while loop "
                  "without result")
            break
        p = sel.get_selected_particles()

    if len(p) == 1:
        return IMP.core.XYZ(p[0]).get_coordinates()
    elif len(p) == 0:
        print("get_closest_residue_position: got NO residues for hierarchy "
              "%s and residue %i" % (hier, resindex))
        raise Exception(
            "get_closest_residue_position: got NO residues for hierarchy "
            "%s and residue %i" % (hier, resindex))
    else:
        raise ValueError(
            "got multiple residues for hierarchy %s and residue %i; the list "
            "of particles is %s"
            % (hier, resindex, str([pp.get_name() for pp in p])))


def get_residue_gaps_in_hierarchy(hierarchy, start, end):
    '''
    Return the residue index gaps and contiguous segments in the hierarchy.

    @param hierarchy hierarchy to examine
    @param start first residue index
    @param end last residue index

    @return A list of lists of the form
            [[1,100,"cont"],[101,120,"gap"],[121,200,"cont"]]
    '''
    gaps = []
    for n, rindex in enumerate(range(start, end + 1)):
        sel = IMP.atom.Selection(hierarchy, residue_index=rindex,
                                 atom_type=IMP.atom.AT_CA)

        if len(sel.get_selected_particles()) == 0:
            if n == 0:
                # set the initial condition
                rindexgap = start
                rindexcont = start - 1
            if rindexgap == rindex - 1:
                # residue is contiguous with the previously discovered gap
                gaps[-1][1] += 1
            else:
                # residue is not contiguous with the previously discovered gap
                # hence create a new gap tuple
                gaps.append([rindex, rindex, "gap"])
            # update the index of the last residue gap
            rindexgap = rindex
        else:
            if n == 0:
                # set the initial condition
                rindexgap = start - 1
                rindexcont = start
            if rindexcont == rindex - 1:
                # residue is contiguous with the previously discovered
                # continuous part
                gaps[-1][1] += 1
            else:
                # residue is not contiguous with the previously discovered
                # continuous part, hence create a new cont tuple
                gaps.append([rindex, rindex, "cont"])
            # update the index of the last residue gap
            rindexcont = rindex
    return gaps


class map:

    def __init__(self):
        self.map = {}

    def set_map_element(self, xvalue, yvalue):
        self.map[xvalue] = yvalue

    def get_map_element(self, invalue):
        if isinstance(invalue, float):
            n = 0
            mindist = 1
            for x in self.map:
                dist = (invalue - x) * (invalue - x)

                if n == 0:
                    mindist = dist
                    minx = x
                if dist < mindist:
                    mindist = dist
                    minx = x
                n += 1
            return self.map[minx]
        elif isinstance(invalue, str):
            return self.map[invalue]
        else:
            raise TypeError("wrong type for map")


def select_by_tuple_2(hier, tuple_selection, resolution):
    """New tuple format: molname OR (start,stop,molname,copynum,statenum)
    Copy and state are optional. Can also use 'None' for them which will
    get all. You can also pass -1 for stop which will go to the end.
    Returns the particles
    """
    kwds = {}  # going to accumulate keywords
    kwds['resolution'] = resolution
    if isinstance(tuple_selection, str):
        kwds['molecule'] = tuple_selection
    elif isinstance(tuple_selection, tuple):
        rbegin = tuple_selection[0]
        rend = tuple_selection[1]
        kwds['molecule'] = tuple_selection[2]
        try:
            copynum = tuple_selection[3]
            if copynum is not None:
                kwds['copy_index'] = copynum
        except:  # noqa: E722
            pass
        try:
            statenum = tuple_selection[4]
            if statenum is not None:
                kwds['state_index'] = statenum
        except:  # noqa: E722
            pass
        if rend == -1:
            if rbegin > 1:
                s = IMP.atom.Selection(hier, **kwds)
                s -= IMP.atom.Selection(hier,
                                        residue_indexes=range(1, rbegin),
                                        **kwds)
                return s.get_selected_particles()
        else:
            kwds['residue_indexes'] = range(rbegin, rend+1)
    s = IMP.atom.Selection(hier, **kwds)
    return s.get_selected_particles()


def get_db_from_csv(csvfilename, encoding=None):
    import csv
    outputlist = []
    with open(csvfilename, encoding=encoding) as fh:
        csvr = csv.DictReader(fh)
        for ls in csvr:
            outputlist.append(ls)
    return outputlist


def get_prot_name_from_particle(p, list_of_names):
    '''Return the component name provided a particle and a list of names'''
    root = p
    protname = root.get_name()
    is_a_bead = False
    while protname not in list_of_names:
        root0 = root.get_parent()
        if root0 == IMP.atom.Hierarchy():
            return (None, None)
        protname = root0.get_name()

        # check if that is a bead
        # this piece of code might be dangerous if
        # the hierarchy was called Bead :)
        if "Beads" in protname:
            is_a_bead = True
        root = root0
    return (protname, is_a_bead)


def get_residue_indexes(hier):
    '''
    Retrieve the residue indexes for the given particle.

    The particle must be an instance of Fragment,Residue, Atom or Molecule
    or else returns an empty list
    '''
    resind = []
    if IMP.atom.Fragment.get_is_setup(hier):
        resind = IMP.atom.Fragment(hier).get_residue_indexes()
    elif IMP.atom.Residue.get_is_setup(hier):
        resind = [IMP.atom.Residue(hier).get_index()]
    elif IMP.atom.Atom.get_is_setup(hier):
        a = IMP.atom.Atom(hier)
        resind = [IMP.atom.Residue(a.get_parent()).get_index()]
    elif IMP.atom.Molecule.get_is_setup(hier):
        resind_tmp = IMP.pmi.tools.OrderedSet()
        for lv in IMP.atom.get_leaves(hier):
            if IMP.atom.Fragment.get_is_setup(lv) or \
               IMP.atom.Residue.get_is_setup(lv) or \
               IMP.atom.Atom.get_is_setup(lv):
                for ind in get_residue_indexes(lv):
                    resind_tmp.add(ind)
        resind = list(resind_tmp)
    else:
        resind = []
    return resind


def sort_by_residues(particles):
    particles_residues = [(p, list(IMP.pmi.tools.get_residue_indexes(p)))
                          for p in particles]
    sorted_particles_residues = sorted(
        particles_residues,
        key=lambda tup: tup[1])
    particles = [p[0] for p in sorted_particles_residues]
    return particles

#
# Parallel Computation
#


def scatter_and_gather(data):
    """Synchronize data over a parallel run"""
    from mpi4py import MPI
    comm = MPI.COMM_WORLD
    rank = comm.Get_rank()
    number_of_processes = comm.size
    comm.Barrier()
    if rank != 0:
        comm.send(data, dest=0, tag=11)

    elif rank == 0:
        for i in range(1, number_of_processes):
            data_tmp = comm.recv(source=i, tag=11)
            if isinstance(data, list):
                data += data_tmp
            elif isinstance(data, dict):
                data.update(data_tmp)
            else:
                raise TypeError("data not supported, use list or dictionaries")

        for i in range(1, number_of_processes):
            comm.send(data, dest=i, tag=11)

    if rank != 0:
        data = comm.recv(source=0, tag=11)
    return data

#
# Lists and iterators
#


def sublist_iterator(ls, lmin=1, lmax=None):
    '''
    Yield all sublists of length >= lmin and <= lmax
    '''
    if lmax is None:
        lmax = len(ls)
    n = len(ls)
    for i in range(n):
        for j in range(i + lmin, min(n + 1, i + 1 + lmax)):
            yield ls[i:j]


def flatten_list(ls):
    return [item for sublist in ls for item in sublist]


def list_chunks_iterator(list, length):
    """ Yield successive length-sized chunks from a list.
    """
    for i in range(0, len(list), length):
        yield list[i:i + length]


def chunk_list_into_segments(seq, num):
    seq = list(seq)
    avg = len(seq) / float(num)
    out = []
    last = 0.0

    while last < len(seq):
        out.append(seq[int(last):int(last + avg)])
        last += avg

    return out


class Segments:

    ''' This class stores integers
    in ordered compact lists eg:
    [[1,2,3],[6,7,8]]
    the methods help splitting and merging the internal lists
    Example:
    s=Segments([1,2,3]) is [[1,2,3]]
    s.add(4) is [[1,2,3,4]] (add right)
    s.add(3) is [[1,2,3,4]] (item already existing)
    s.add(7) is [[1,2,3,4],[7]] (new list)
    s.add([8,9]) is [[1,2,3,4],[7,8,9]]  (add item right)
    s.add([5,6]) is [[1,2,3,4,5,6,7,8,9]]  (merge)
    s.remove(3) is [[1,2],[4,5,6,7,8,9]]  (split)
    etc.
    '''

    def __init__(self, index):
        '''index can be a integer or a list of integers '''
        if isinstance(index, int):
            self.segs = [[index]]
        elif isinstance(index, list):
            self.segs = [[index[0]]]
            for i in index[1:]:
                self.add(i)
        else:
            raise TypeError("index must be an int or list of ints")

    def add(self, index):
        '''index can be a integer or a list of integers '''
        if isinstance(index, (int, numpy.int32, numpy.int64)):
            mergeleft = None
            mergeright = None
            for n, s in enumerate(self.segs):
                if index in s:
                    return 0
                else:
                    if s[0]-index == 1:
                        mergeleft = n
                    if index-s[-1] == 1:
                        mergeright = n
            if mergeright is None and mergeleft is None:
                self.segs.append([index])
            if mergeright is not None and mergeleft is None:
                self.segs[mergeright].append(index)
            if mergeleft is not None and mergeright is None:
                self.segs[mergeleft] = [index]+self.segs[mergeleft]
            if mergeleft is not None and mergeright is not None:
                self.segs[mergeright] = \
                    self.segs[mergeright]+[index]+self.segs[mergeleft]
                del self.segs[mergeleft]

            for n in range(len(self.segs)):
                self.segs[n].sort()

            self.segs.sort(key=lambda tup: tup[0])

        elif isinstance(index, list):
            for i in index:
                self.add(i)
        else:
            raise TypeError("index must be an int or list of ints")

    def remove(self, index):
        '''index can be a integer'''
        for n, s in enumerate(self.segs):
            if index in s:
                if s[0] == index:
                    self.segs[n] = s[1:]
                elif s[-1] == index:
                    self.segs[n] = s[:-1]
                else:
                    i = self.segs[n].index(index)
                    self.segs[n] = s[:i]
                    self.segs.append(s[i+1:])
        for n in range(len(self.segs)):
            self.segs[n].sort()
            if len(self.segs[n]) == 0:
                del self.segs[n]
        self.segs.sort(key=lambda tup: tup[0])

    def get_flatten(self):
        ''' Returns a flatten list '''
        return [item for sublist in self.segs for item in sublist]

    def __repr__(self):
        ret_tmp = "["
        for seg in self.segs:
            ret_tmp += str(seg[0])+"-"+str(seg[-1])+","
        ret = ret_tmp[:-1]+"]"
        return ret

#
# Tools to simulate data
#


def normal_density_function(expected_value, sigma, x):
    return (
        1 / math.sqrt(2 * math.pi) / sigma *
        math.exp(-(x - expected_value) ** 2 / 2 / sigma / sigma)
    )


def log_normal_density_function(expected_value, sigma, x):
    return (
        1 / math.sqrt(2 * math.pi) / sigma / x *
        math.exp(-(math.log(x / expected_value) ** 2 / 2 / sigma / sigma))
    )


def print_multicolumn(list_of_strings, ncolumns=2, truncate=40):

    ls = list_of_strings

    cols = ncolumns
    # add empty entries after ls
    for i in range(len(ls) % cols):
        ls.append(" ")

    split = [ls[i:i + len(ls) // cols]
             for i in range(0, len(ls), len(ls) // cols)]
    for row in zip(*split):
        print("".join(str.ljust(i, truncate) for i in row))


class ColorChange:
    '''Change color code to hexadecimal to rgb'''
    def __init__(self):
        self._NUMERALS = '0123456789abcdefABCDEF'
        self._HEXDEC = dict((v, int(v, 16)) for v in
                            (x+y for x in self._NUMERALS
                            for y in self._NUMERALS))
        self.LOWERCASE, self.UPPERCASE = 'x', 'X'

    def rgb(self, triplet):
        return (float(self._HEXDEC[triplet[0:2]]),
                float(self._HEXDEC[triplet[2:4]]),
                float(self._HEXDEC[triplet[4:6]]))

    def triplet(self, rgb, lettercase=None):
        if lettercase is None:
            lettercase = self.LOWERCASE
        return format(rgb[0] << 16 | rgb[1] << 8 | rgb[2], '06'+lettercase)


# -------------- Collections --------------- #
class OrderedSet(MutableSet):

    def __init__(self, iterable=None):
        self.end = end = []
        end += [None, end, end]         # sentinel node for doubly linked list
        self.map = {}                   # key --> [key, prev, next]
        if iterable is not None:
            self |= iterable

    def __len__(self):
        return len(self.map)

    def __contains__(self, key):
        return key in self.map

    def add(self, key):
        if key not in self.map:
            end = self.end
            curr = end[1]
            curr[2] = end[1] = self.map[key] = [key, curr, end]

    def discard(self, key):
        if key in self.map:
            key, prev, next = self.map.pop(key)
            prev[2] = next
            next[1] = prev

    def __iter__(self):
        end = self.end
        curr = end[2]
        while curr is not end:
            yield curr[0]
            curr = curr[2]

    def __reversed__(self):
        end = self.end
        curr = end[1]
        while curr is not end:
            yield curr[0]
            curr = curr[1]

    def pop(self, last=True):
        if not self:
            raise KeyError('set is empty')
        if last:
            key = self.end[1][0]
        else:
            key = self.end[2][0]
        self.discard(key)
        return key

    def __repr__(self):
        if not self:
            return '%s()' % (self.__class__.__name__,)
        return '%s(%r)' % (self.__class__.__name__, list(self))

    def __eq__(self, other):
        if isinstance(other, OrderedSet):
            return len(self) == len(other) and list(self) == list(other)
        return set(self) == set(other)


class OrderedDefaultDict(OrderedDict):
    """Store objects in order they were added, but with default type.
    Source: http://stackoverflow.com/a/4127426/2608793
    """
    def __init__(self, *args, **kwargs):
        if not args:
            self.default_factory = None
        else:
            if not (args[0] is None or callable(args[0])):
                raise TypeError('first argument must be callable or None')
            self.default_factory = args[0]
            args = args[1:]
        super().__init__(*args, **kwargs)

    def __missing__(self, key):
        if self.default_factory is None:
            raise KeyError(key)
        self[key] = default = self.default_factory()
        return default

    def __reduce__(self):  # optional, for pickle support
        args = (self.default_factory,) if self.default_factory else ()
        return self.__class__, args, None, None, self.items()


# -------------- PMI2 Tools --------------- #

def set_coordinates_from_rmf(hier, rmf_fn, frame_num=0):
    """Extract frame from RMF file and fill coordinates. Must be identical
    topology.

    @param hier The (System) hierarchy to fill (e.g. after you've built it)
    @param rmf_fn The file to extract from
    @param frame_num The frame number to extract
    """
    rh = RMF.open_rmf_file_read_only(rmf_fn)
    IMP.rmf.link_hierarchies(rh, [hier])
    IMP.rmf.load_frame(rh, RMF.FrameID(frame_num))
    del rh


def input_adaptor(stuff, pmi_resolution=0, flatten=False, selection_tuple=None,
                  warn_about_slices=True):
    """Adapt things for PMI (degrees of freedom, restraints, ...)
    Returns list of list of hierarchies, separated into Molecules if possible.
    The input can be a list, or a list of lists (iterable of ^1 or
    iterable of ^2)
    (iterable of ^2) Hierarchy -> returns input as list of list of hierarchies,
        only one entry, not grouped by molecules.
    (iterable of ^2) PMI::System/State/Molecule/TempResidue ->
        returns residue hierarchies, grouped in molecules, at requested
    resolution

    @param stuff Can be one of the following inputs:
           IMP Hierarchy, PMI System/State/Molecule/TempResidue, or a
           list/set (of list/set) of them.
           Must be uniform input, however. No mixing object types.
    @param pmi_resolution For selecting, only does it if you pass PMI
          objects. Set it to "all" if you want all resolutions!
    @param flatten Set to True if you just want all hierarchies in one list.
    @param warn_about_slices Print a warning if you are requesting only part
           of a bead. Sometimes you just don't care!
    @note since this relies on IMP::atom::Selection, this will not return
          any objects if they weren't built! But there should be no problem
          if you request unbuilt residues - they should be ignored.
    """

    if stuff is None:
        return stuff

    if hasattr(stuff, '__iter__'):
        if len(stuff) == 0:
            return stuff
        thelist = list(stuff)

        # iter of iter of should be ok
        if all(hasattr(el, '__iter__') for el in thelist):
            thelist = [i for sublist in thelist for i in sublist]
        elif any(hasattr(el, '__iter__') for el in thelist):
            raise Exception('input_adaptor: input_object must be a list '
                            'or a list of lists')

        stuff = thelist
    else:
        stuff = [stuff]

    # check that it is a hierarchy homogeneously:
    try:
        is_hierarchy = all(IMP.atom.Hierarchy.get_is_setup(s) for s in stuff)
    except (NotImplementedError, TypeError):
        is_hierarchy = False
    # get the other types homogeneously
    is_system = all(isinstance(s, IMP.pmi.topology.System) for s in stuff)
    is_state = all(isinstance(s, IMP.pmi.topology.State) for s in stuff)
    is_molecule = all(isinstance(s, IMP.pmi.topology.Molecule) for s in stuff)
    is_temp_residue = all(isinstance(s, IMP.pmi.topology.TempResidue)
                          for s in stuff)

    # now that things are ok, do selection if requested
    hier_list = []
    pmi_input = False
    if is_system or is_state or is_molecule or is_temp_residue:
        # if PMI, perform selection using gathered indexes
        pmi_input = True
        # key is Molecule object, value are residues
        indexes_per_mol = OrderedDefaultDict(list)
        if is_system:
            for system in stuff:
                for state in system.get_states():
                    mdict = state.get_molecules()
                    for molname in mdict:
                        for copy in mdict[molname]:
                            indexes_per_mol[copy] += \
                                [r.get_index() for r in copy.get_residues()]
        elif is_state:
            for state in stuff:
                mdict = state.get_molecules()
                for molname in mdict:
                    for copy in mdict[molname]:
                        indexes_per_mol[copy] += [r.get_index()
                                                  for r in copy.get_residues()]
        elif is_molecule:
            for molecule in stuff:
                indexes_per_mol[molecule] += [r.get_index()
                                              for r in molecule.get_residues()]
        else:  # is_temp_residue
            for tempres in stuff:
                indexes_per_mol[tempres.get_molecule()].append(
                    tempres.get_index())
        for mol in indexes_per_mol:
            if pmi_resolution == 'all':
                # because you select from the molecule,
                #  this will start the search from the base resolution
                ps = select_at_all_resolutions(
                    mol.get_hierarchy(), residue_indexes=indexes_per_mol[mol])
            else:
                sel = IMP.atom.Selection(mol.get_hierarchy(),
                                         resolution=pmi_resolution,
                                         residue_indexes=indexes_per_mol[mol])
                ps = sel.get_selected_particles()

            # check that you don't have any incomplete fragments!
            if warn_about_slices:
                rset = set(indexes_per_mol[mol])
                for p in ps:
                    if IMP.atom.Fragment.get_is_setup(p):
                        fset = set(IMP.atom.Fragment(p).get_residue_indexes())
                        if not fset <= rset:
                            minset = min(fset)
                            maxset = max(fset)
                            found = fset & rset
                            minf = min(found)
                            maxf = max(found)
                            resbreak = maxf if minf == minset else minset-1
                            warnings.warn(
                                'You are trying to select only part of the '
                                'bead %s:%i-%i. The residues you requested '
                                'are %i-%i. You can fix this by: '
                                '1) requesting the whole bead/none of it; or'
                                '2) break the bead up by passing '
                                'bead_extra_breaks=[\'%i\'] in '
                                'molecule.add_representation()'
                                % (mol.get_name(), minset, maxset, minf, maxf,
                                   resbreak), IMP.pmi.ParameterWarning)
            hier_list.append([IMP.atom.Hierarchy(p) for p in ps])
    elif is_hierarchy:
        # check
        ps = []
        if pmi_resolution == 'all':
            for h in stuff:
                ps += select_at_all_resolutions(h)
        else:
            for h in stuff:
                ps += IMP.atom.Selection(
                    h, resolution=pmi_resolution).get_selected_particles()
        hier_list = [IMP.atom.Hierarchy(p) for p in ps]
        if not flatten:
            hier_list = [hier_list]
    else:
        raise Exception('input_adaptor: you passed something of wrong type '
                        'or a list with mixed types')

    if flatten and pmi_input:
        return [h for sublist in hier_list for h in sublist]
    else:
        return hier_list


def get_sorted_segments(mol):
    """Returns sequence-sorted segments array, each containing the first
    particle the last particle and the first residue index."""

    from operator import itemgetter
    hiers = IMP.pmi.tools.input_adaptor(mol)
    if len(hiers) > 1:
        raise ValueError("only pass stuff from one Molecule, please")
    hiers = hiers[0]
    segs = []
    for h in hiers:
        try:
            start = IMP.atom.Hierarchy(h).get_children()[0]
        except IndexError:
            start = IMP.atom.Hierarchy(h)

        try:
            end = IMP.atom.Hierarchy(h).get_children()[-1]
        except IndexError:
            end = IMP.atom.Hierarchy(h)

        startres = IMP.pmi.tools.get_residue_indexes(start)[0]
        segs.append((start, end, startres))
    return sorted(segs, key=itemgetter(2))


def display_bonds(mol):
    """Decorate the sequence-consecutive particles from a PMI2 molecule
    with a bond, so that they appear connected in the rmf file"""
    SortedSegments = get_sorted_segments(mol)
    for x in range(len(SortedSegments) - 1):

        last = SortedSegments[x][1]
        first = SortedSegments[x + 1][0]

        p1 = last.get_particle()
        p2 = first.get_particle()
        if not IMP.atom.Bonded.get_is_setup(p1):
            IMP.atom.Bonded.setup_particle(p1)
        if not IMP.atom.Bonded.get_is_setup(p2):
            IMP.atom.Bonded.setup_particle(p2)

        if not IMP.atom.get_bond(IMP.atom.Bonded(p1), IMP.atom.Bonded(p2)):
            IMP.atom.create_bond(
                IMP.atom.Bonded(p1),
                IMP.atom.Bonded(p2), 1)


def get_all_leaves(list_of_hs):
    """ Just get the leaves from a list of hierarchies """
    lvs = list(itertools.chain.from_iterable(
        IMP.atom.get_leaves(item) for item in list_of_hs))
    return lvs


def select_at_all_resolutions(hier=None, hiers=None, **kwargs):
    """Perform selection using the usual keywords but return ALL
    resolutions (BEADS and GAUSSIANS).
    Returns in flat list!
    """

    if hiers is None:
        hiers = []
    if hier is not None:
        hiers.append(hier)
    if len(hiers) == 0:
        warnings.warn("You passed nothing to select_at_all_resolutions()",
                      IMP.pmi.ParameterWarning)
        return []
    ret = OrderedSet()
    for hsel in hiers:
        try:
            htest = IMP.atom.Hierarchy.get_is_setup(hsel)
        except:  # noqa: E722
            raise Exception('select_at_all_resolutions: you have to pass '
                            'an IMP Hierarchy')
        if not htest:
            raise Exception('select_at_all_resolutions: you have to pass '
                            'an IMP Hierarchy')
        if 'resolution' in kwargs or 'representation_type' in kwargs:
            raise Exception("don't pass resolution or representation_type "
                            "to this function")
        selB = IMP.atom.Selection(hsel, resolution=IMP.atom.ALL_RESOLUTIONS,
                                  representation_type=IMP.atom.BALLS,
                                  **kwargs)
        selD = IMP.atom.Selection(hsel, resolution=IMP.atom.ALL_RESOLUTIONS,
                                  representation_type=IMP.atom.DENSITIES,
                                  **kwargs)
        ret |= OrderedSet(selB.get_selected_particles())
        ret |= OrderedSet(selD.get_selected_particles())
    return list(ret)


def get_particles_within_zone(hier,
                              target_ps,
                              sel_zone,
                              entire_residues,
                              exclude_backbone):
    """Utility to retrieve particles from a hierarchy within a
    zone around a set of ps.
    @param hier The hierarchy in which to look for neighbors
    @param target_ps The particles for zoning
    @param sel_zone The maximum distance
    @param entire_residues If True, will grab entire residues
    @param exclude_backbone If True, will only return sidechain particles
    """

    test_sel = IMP.atom.Selection(hier)
    backbone_types = ['C', 'N', 'CB', 'O']
    if exclude_backbone:
        test_sel -= IMP.atom.Selection(
            hier, atom_types=[IMP.atom.AtomType(n) for n in backbone_types])
    test_ps = test_sel.get_selected_particles()
    nn = IMP.algebra.NearestNeighbor3D([IMP.core.XYZ(p).get_coordinates()
                                        for p in test_ps])
    zone = set()
    for target in target_ps:
        zone |= set(nn.get_in_ball(IMP.core.XYZ(target).get_coordinates(),
                                   sel_zone))
    zone_ps = [test_ps[z] for z in zone]
    if entire_residues:
        final_ps = set()
        for z in zone_ps:
            final_ps |= set(IMP.atom.Hierarchy(z).get_parent().get_children())
        zone_ps = [h.get_particle() for h in final_ps]
    return zone_ps


def get_rbs_and_beads(hiers):
    """Returns unique objects in original order"""
    rbs = set()
    beads = []
    rbs_ordered = []
    if not hasattr(hiers, '__iter__'):
        hiers = [hiers]
    for p in get_all_leaves(hiers):
        if IMP.core.RigidMember.get_is_setup(p):
            rb = IMP.core.RigidMember(p).get_rigid_body()
            if rb not in rbs:
                rbs.add(rb)
                rbs_ordered.append(rb)
        elif IMP.core.NonRigidMember.get_is_setup(p):
            rb = IMP.core.NonRigidMember(p).get_rigid_body()
            if rb not in rbs:
                rbs.add(rb)
                rbs_ordered.append(rb)
            beads.append(p)
        else:
            beads.append(p)
    return rbs_ordered, beads


def get_molecules(input_objects):
    "This function returns the parent molecule hierarchies of given objects"
    stuff = input_adaptor(input_objects, pmi_resolution='all', flatten=True)
    molecules = set()
    for h in stuff:
        is_root = False
        is_molecule = False
        while not (is_molecule or is_root):
            root = IMP.atom.get_root(h)
            if root == h:
                is_root = True
            is_molecule = IMP.atom.Molecule.get_is_setup(h)
            if is_molecule:
                molecules.add(IMP.atom.Molecule(h))
            h = h.get_parent()
    return list(molecules)


def get_molecules_dictionary(input_objects):
    moldict = defaultdict(list)
    for mol in IMP.pmi.tools.get_molecules(input_objects):
        name = mol.get_name()
        moldict[name].append(mol)

    for mol in moldict:
        moldict[mol].sort(key=lambda x: IMP.atom.Copy(x).get_copy_index())
    return moldict


def get_molecules_dictionary_by_copy(input_objects):
    moldict = defaultdict(dict)
    for mol in IMP.pmi.tools.get_molecules(input_objects):
        name = mol.get_name()
        c = IMP.atom.Copy(mol).get_copy_index()
        moldict[name][c] = mol
    return moldict


def get_selections_dictionary(input_objects):
    moldict = IMP.pmi.tools.get_molecules_dictionary(input_objects)
    seldict = defaultdict(list)
    for name, mols in moldict.items():
        for m in mols:
            seldict[name].append(IMP.atom.Selection(m))
    return seldict


def get_densities(input_objects):
    """Given a list of PMI objects, returns all density hierarchies within
    these objects.  The output of this function can be inputted into
    things such as EM restraints. This function is intended to gather
    density particles appended to molecules (and not other hierarchies
    which might have been appended to the root node directly).
    """
    # Note that Densities can only be selected at the Root or Molecule
    # level and not at the Leaves level.
    # we'll first get all molecule hierarchies corresponding to the leaves.
    molecules = get_molecules(input_objects)
    densities = []
    for i in molecules:
        densities += IMP.atom.Selection(
            i, representation_type=IMP.atom.DENSITIES).get_selected_particles()
    return densities


def shuffle_configuration(objects,
                          max_translation=300., max_rotation=2.0 * math.pi,
                          avoidcollision_rb=True, avoidcollision_fb=False,
                          cutoff=10.0, niterations=100,
                          bounding_box=None,
                          excluded_rigid_bodies=[],
                          hierarchies_excluded_from_collision=[],
                          hierarchies_included_in_collision=[],
                          verbose=False,
                          return_debug=False):
    """Shuffle particles. Used to restart the optimization.
    The configuration of the system is initialized by placing each
    rigid body and each bead randomly in a box. If `bounding_box` is
    specified, the particles are placed inside this box; otherwise, each
    particle is displaced by up to max_translation angstroms, and randomly
    rotated. Effort is made to place particles far enough from each other to
    prevent any steric clashes.
    @param objects Can be one of the following inputs:
               IMP Hierarchy, PMI System/State/Molecule/TempResidue, or
               a list/set of them
    @param max_translation Max translation (rbs and flexible beads)
    @param max_rotation Max rotation (rbs only)
    @param avoidcollision_rb check if the particle/rigid body was
           placed close to another particle; uses the optional
           arguments cutoff and niterations
    @param avoidcollision_fb Advanced. Generally you want this False because
           it's hard to shuffle beads.
    @param cutoff Distance less than this is a collision
    @param niterations How many times to try avoiding collision
    @param bounding_box Only shuffle particles within this box.
           Defined by ((x1,y1,z1),(x2,y2,z2)).
    @param excluded_rigid_bodies Don't shuffle these rigid body objects
    @param hierarchies_excluded_from_collision Don't count collision
           with these bodies
    @param hierarchies_included_in_collision Hierarchies that are not
           shuffled, but should be included in collision calculation
           (for fixed regions)
    @param verbose Give more output
    @note Best to only call this function after you've set up degrees
          of freedom
    For debugging purposes, returns: <shuffled indexes>,
    <collision avoided indexes>
    """

    # checking input
    hierarchies = IMP.pmi.tools.input_adaptor(objects,
                                              pmi_resolution='all',
                                              flatten=True)
    rigid_bodies, flexible_beads = get_rbs_and_beads(hierarchies)
    if len(rigid_bodies) > 0:
        mdl = rigid_bodies[0].get_model()
    elif len(flexible_beads) > 0:
        mdl = flexible_beads[0].get_model()
    else:
        raise Exception("Could not find any particles in the hierarchy")
    if len(rigid_bodies) == 0:
        print("shuffle_configuration: rigid bodies were not initialized")

    # gather all particles
    gcpf = IMP.core.GridClosePairsFinder()
    gcpf.set_distance(cutoff)

    # Add particles from excluded hierarchies to excluded list
    collision_excluded_hierarchies = IMP.pmi.tools.input_adaptor(
        hierarchies_excluded_from_collision, pmi_resolution='all',
        flatten=True)

    collision_included_hierarchies = IMP.pmi.tools.input_adaptor(
        hierarchies_included_in_collision, pmi_resolution='all', flatten=True)

    collision_excluded_idxs = set(
        leaf.get_particle().get_index()
        for h in collision_excluded_hierarchies
        for leaf in IMP.core.get_leaves(h))

    collision_included_idxs = set(
        leaf.get_particle().get_index()
        for h in collision_included_hierarchies
        for leaf in IMP.core.get_leaves(h))

    # Excluded collision with Gaussians
    all_idxs = []  # expand to representations?
    for p in IMP.pmi.tools.get_all_leaves(hierarchies):
        if IMP.core.XYZ.get_is_setup(p):
            all_idxs.append(p.get_particle_index())
        if IMP.core.Gaussian.get_is_setup(p):
            collision_excluded_idxs.add(p.get_particle_index())

    if bounding_box is not None:
        ((x1, y1, z1), (x2, y2, z2)) = bounding_box
        ub = IMP.algebra.Vector3D(x1, y1, z1)
        lb = IMP.algebra.Vector3D(x2, y2, z2)
        bb = IMP.algebra.BoundingBox3D(ub, lb)

    all_idxs = set(all_idxs) | collision_included_idxs
    all_idxs = all_idxs - collision_excluded_idxs
    debug = []
    print('shuffling', len(rigid_bodies), 'rigid bodies')
    for rb in rigid_bodies:
        if rb not in excluded_rigid_bodies:
            # gather particles to avoid with this transform
            if avoidcollision_rb:
                rb_idxs = set(rb.get_member_particle_indexes()) - \
                          collision_excluded_idxs
                other_idxs = all_idxs - rb_idxs

            debug.append([rb, other_idxs if avoidcollision_rb else set()])
            # iterate, trying to avoid collisions
            niter = 0
            while niter < niterations:
                rbxyz = (rb.get_x(), rb.get_y(), rb.get_z())

                # local transform
                if bounding_box:
                    translation = IMP.algebra.get_random_vector_in(bb)
                    # First move to origin
                    transformation_orig = IMP.algebra.Transformation3D(
                        IMP.algebra.get_identity_rotation_3d(),
                        -IMP.core.XYZ(rb).get_coordinates())
                    IMP.core.transform(rb, transformation_orig)
                    rotation = IMP.algebra.get_random_rotation_3d()
                    transformation = IMP.algebra.Transformation3D(rotation,
                                                                  translation)

                else:
                    transformation = \
                        IMP.algebra.get_random_local_transformation(
                            rbxyz, max_translation, max_rotation)

                IMP.core.transform(rb, transformation)

                # check collisions
                if avoidcollision_rb and other_idxs:
                    mdl.update()
                    npairs = len(gcpf.get_close_pairs(mdl,
                                                      list(other_idxs),
                                                      list(rb_idxs)))
                    if npairs == 0:
                        break
                    else:
                        niter += 1
                        if verbose:
                            print("shuffle_configuration: rigid body placed "
                                  "close to other %d particles, trying "
                                  "again..." % npairs)
                            print("shuffle_configuration: rigid body name: "
                                  + rb.get_name())
                        if niter == niterations:
                            raise ValueError(
                                "tried the maximum number of iterations to "
                                "avoid collisions, increase the distance "
                                "cutoff")
                else:
                    break

    print('shuffling', len(flexible_beads), 'flexible beads')
    for fb in flexible_beads:
        # gather particles to avoid
        if avoidcollision_fb:
            fb_idxs = set(IMP.get_indexes([fb]))
            other_idxs = all_idxs - fb_idxs
            if not other_idxs:
                continue

        # iterate, trying to avoid collisions
        niter = 0
        while niter < niterations:
            if bounding_box:
                translation = IMP.algebra.get_random_vector_in(bb)
                transformation = IMP.algebra.Transformation3D(translation)
            else:
                fbxyz = IMP.core.XYZ(fb).get_coordinates()
                transformation = IMP.algebra.get_random_local_transformation(
                    fbxyz, max_translation, max_rotation)

            # For gaussians, treat this fb as an rb
            if IMP.core.NonRigidMember.get_is_setup(fb):
                memb = IMP.core.NonRigidMember(fb)
                xyz = memb.get_internal_coordinates()
                if bounding_box:
                    # 'translation' is the new desired position in global
                    # coordinates; we need to convert that to internal
                    # coordinates first using the rigid body's ref frame
                    rf = memb.get_rigid_body().get_reference_frame()
                    glob_to_int = rf.get_transformation_from()
                    memb.set_internal_coordinates(
                            glob_to_int.get_transformed(translation))
                else:
                    xyz_transformed = transformation.get_transformed(xyz)
                    memb.set_internal_coordinates(xyz_transformed)
                if niter == 0:
                    debug.append(
                        [xyz, other_idxs if avoidcollision_fb else set()])
            else:
                d = IMP.core.XYZ(fb)
                if bounding_box:
                    # Translate to origin first
                    if IMP.core.RigidBody.get_is_setup(fb.get_particle()):
                        IMP.core.transform(
                            IMP.core.RigidBody(fb.get_particle()),
                            -d.get_coordinates())
                    else:
                        IMP.core.transform(d, -d.get_coordinates())
                    d = IMP.core.XYZ(fb)
                if niter == 0:
                    debug.append(
                        [d, other_idxs if avoidcollision_fb else set()])
                if IMP.core.RigidBody.get_is_setup(fb.get_particle()):
                    IMP.core.transform(
                        IMP.core.RigidBody(fb.get_particle()), transformation)
                else:
                    IMP.core.transform(d, transformation)

            if avoidcollision_fb:
                mdl.update()
                npairs = len(gcpf.get_close_pairs(mdl,
                                                  list(other_idxs),
                                                  list(fb_idxs)))

                if npairs == 0:
                    break
                else:
                    niter += 1
                    print("shuffle_configuration: floppy body placed close "
                          "to other %d particles, trying again..." % npairs)
                    if niter == niterations:
                        raise ValueError(
                            "tried the maximum number of iterations to avoid "
                            "collisions, increase the distance cutoff")
            else:
                break
    if return_debug:
        return debug


class ColorHierarchy:

    def __init__(self, hier):
        import matplotlib as mpl
        mpl.use('Agg')
        import matplotlib.pyplot as plt
        self.mpl = mpl
        self.plt = plt

        hier.ColorHierarchy = self
        self.hier = hier
        mols = IMP.pmi.tools.get_molecules(IMP.atom.get_leaves(self.hier))
        self.mols = [IMP.pmi.topology.PMIMoleculeHierarchy(mol)
                     for mol in mols]
        self.method = self.nochange
        self.scheme = None
        self.first = None
        self.last = None

    def nochange(self):
        pass

    def get_color(self, fl):
        return IMP.display.Color(*self.scheme(fl)[0:3])

    def get_log_scale(self, fl):
        import math
        eps = 1.0
        return math.log(fl+eps)

    def color_by_resid(self):
        self.method = self.color_by_resid
        self.scheme = self.mpl.cm.rainbow
        for mol in self.mols:
            self.first = 1
            self.last = len(IMP.pmi.topology.PMIMoleculeHierarchy(
                mol).get_residue_indexes())
            for p in IMP.atom.get_leaves(mol):
                if IMP.atom.Residue.get_is_setup(p):
                    ri = IMP.atom.Residue(p).get_index()
                    c = self.get_color(float(ri)/self.last)
                    IMP.display.Colored(p).set_color(c)
                if IMP.atom.Fragment.get_is_setup(p):
                    ris = IMP.atom.Fragment(p).get_residue_indexes()
                    avr = sum(ris)/len(ris)
                    c = self.get_color(float(avr)/self.last)
                    IMP.display.Colored(p).set_color(c)

    def color_by_uncertainty(self):
        self.method = self.color_by_uncertainty
        self.scheme = self.mpl.cm.jet
        ps = IMP.atom.get_leaves(self.hier)
        unc_dict = {}
        for p in ps:
            if IMP.pmi.Uncertainty.get_is_setup(p):
                u = IMP.pmi.Uncertainty(p).get_uncertainty()
                unc_dict[p] = u
        self.first = self.get_log_scale(1.0)
        self.last = self.get_log_scale(100.0)
        for p in unc_dict:
            value = self.get_log_scale(unc_dict[p])
            if value >= self.last:
                value = self.last
            if value <= self.first:
                value = self.first
            c = self.get_color((value-self.first) / (self.last-self.first))
            IMP.display.Colored(p).set_color(c)

    def get_color_bar(self, filename):
        import matplotlib as mpl
        mpl.use('Agg')
        import matplotlib.pyplot as plt
        plt.clf()
        fig = plt.figure(figsize=(8, 3))
        ax1 = fig.add_axes([0.05, 0.80, 0.9, 0.15])

        cmap = self.scheme
        norm = mpl.colors.Normalize(vmin=0.0, vmax=1.0)

        if self.method == self.color_by_uncertainty:
            angticks = [1.0, 2.5, 5.0, 10.0, 25.0, 50.0, 100.0]
            vvalues = []
            marks = []
            for at in angticks:
                vvalue = (self.get_log_scale(at)-self.first) \
                          / (self.last-self.first)
                if vvalue <= 1.0 and vvalue >= 0.0:
                    vvalues.append(vvalue)
                    marks.append(str(at))
            cb1 = mpl.colorbar.ColorbarBase(
                ax1, cmap=cmap, norm=norm, ticks=vvalues,
                orientation='horizontal')
            print(self.first, self.last, marks, vvalues)
            cb1.ax.set_xticklabels(marks)
            cb1.set_label('Angstorm')
            plt.savefig(filename, dpi=150, transparent=True)
            plt.show()


def color2rgb(colorname):
    """Given a Chimera color name or hex color value, return RGB"""
    d = {'aquamarine': (0.4980392156862745, 1.0, 0.8313725490196079),
         'black': (0.0, 0.0, 0.0),
         'blue': (0.0, 0.0, 1.0),
         'brown': (0.6470588235, 0.16470588235294117, 0.16470588235294117),
         'chartreuse': (0.4980392156862745, 1.0, 0.0),
         'coral': (1.0, 0.4980392156862745, 0.3137254901960784),
         'cornflower blue': (0.39215686, 0.58431372549, 0.9294117647058824),
         'cyan': (0.0, 1.0, 1.0),
         'dark cyan': (0.0, 0.5450980392156862, 0.5450980392156862),
         'dark gray': (0.6627450980, 0.6627450980392157, 0.6627450980392157),
         'dark green': (0.0, 0.39215686274509803, 0.0),
         'dark khaki': (0.74117647, 0.7176470588235294, 0.4196078431372549),
         'dark magenta': (0.5450980392156862, 0.0, 0.5450980392156862),
         'dark olive green': (0.333333333, 0.419607843, 0.1843137254901961),
         'dark red': (0.5450980392156862, 0.0, 0.0),
         'dark slate blue': (0.28235294, 0.239215686, 0.5450980392156862),
         'dark slate gray': (0.1843137, 0.30980392, 0.30980392156862746),
         'deep pink': (1.0, 0.0784313725490196, 0.5764705882352941),
         'deep sky blue': (0.0, 0.7490196078431373, 1.0),
         'dim gray': (0.41176470, 0.4117647058823529, 0.4117647058823529),
         'dodger blue': (0.11764705882352941, 0.5647058823529412, 1.0),
         'firebrick': (0.6980392, 0.13333333333333333, 0.13333333333333333),
         'forest green': (0.13333333, 0.5450980392156862, 0.13333333333333333),
         'gold': (1.0, 0.8431372549019608, 0.0),
         'goldenrod': (0.85490196, 0.6470588235294118, 0.12549019607843137),
         'gray': (0.7450980392156863, 0.7450980392156863, 0.7450980392156863),
         'green': (0.0, 1.0, 0.0),
         'hot pink': (1.0, 0.4117647058823529, 0.7058823529411765),
         'khaki': (0.9411764705882353, 0.9019607843137255, 0.5490196078431373),
         'light blue': (0.67843137, 0.8470588235294118, 0.9019607843137255),
         'light gray': (0.82745098, 0.8274509803921568, 0.8274509803921568),
         'light green': (0.56470588, 0.9333333333333333, 0.5647058823529412),
         'light sea green': (0.125490, 0.6980392156862745, 0.6666666666666666),
         'lime green': (0.1960784, 0.803921568627451, 0.19607843137254902),
         'magenta': (1.0, 0.0, 1.0),
         'medium blue': (0.1960784, 0.19607843137254902, 0.803921568627451),
         'medium purple': (0.57647, 0.4392156862745098, 0.8588235294117647),
         'navy blue': (0.0, 0.0, 0.5019607843137255),
         'olive drab': (0.4196078, 0.5568627450980392, 0.13725490196078433),
         'orange red': (1.0, 0.27058823529411763, 0.0),
         'orange': (1.0, 0.4980392156862745, 0.0),
         'orchid': (0.85490196, 0.4392156862745098, 0.8392156862745098),
         'pink': (1.0, 0.7529411764705882, 0.796078431372549),
         'plum': (0.8666666666666667, 0.6274509803921569, 0.8666666666666667),
         'purple': (0.62745098, 0.12549019607843137, 0.9411764705882353),
         'red': (1.0, 0.0, 0.0),
         'rosy brown': (0.7372549, 0.5607843137254902, 0.5607843137254902),
         'salmon': (0.980392, 0.5019607843137255, 0.4470588235294118),
         'sandy brown': (0.956862745, 0.6431372549019608, 0.3764705882352941),
         'sea green': (0.18039, 0.5450980392156862, 0.3411764705882353),
         'sienna': (0.6274509, 0.3215686274509804, 0.17647058823529413),
         'sky blue': (0.52941176, 0.807843137254902, 0.9215686274509803),
         'slate gray': (0.439215686, 0.50196078, 0.5647058823529412),
         'spring green': (0.0, 1.0, 0.4980392156862745),
         'steel blue': (0.2745098, 0.50980392, 0.70588235),
         'tan': (0.8235294117647058, 0.7058823529411765, 0.5490196078431373),
         'turquoise': (0.25098039, 0.87843137, 0.81568627),
         'violet red': (0.81568627, 0.125490196, 0.56470588235),
         'white': (1.0, 1.0, 1.0),
         'yellow': (1.0, 1.0, 0.0)}
    if colorname.startswith('#'):
        return tuple(int(colorname[i:i+2], 16) / 255. for i in (1, 3, 5))
    else:
        return d[colorname]