This file is indexed.

/usr/lib/python2.7/dist-packages/objgraph.py is in python-objgraph 3.4.0-1.

This file is owned by root:root, with mode 0o644.

The actual contents of the file can be viewed below.

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"""
Tools for drawing Python object reference graphs with graphviz.

You can find documentation online at https://mg.pov.lt/objgraph/

Copyright (c) 2008-2017 Marius Gedminas <marius@pov.lt> and contributors

Released under the MIT licence.
"""
# Permission is hereby granted, free of charge, to any person obtaining a
# copy of this software and associated documentation files (the "Software"),
# to deal in the Software without restriction, including without limitation
# the rights to use, copy, modify, merge, publish, distribute, sublicense,
# and/or sell copies of the Software, and to permit persons to whom the
# Software is furnished to do so, subject to the following conditions:
#
# The above copyright notice and this permission notice shall be included in
# all copies or substantial portions of the Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
# FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
# DEALINGS IN THE SOFTWARE.

from __future__ import print_function

import codecs
import collections
import gc
import re
import inspect
import types
import operator
import os
import subprocess
import tempfile
import sys
import itertools

try:
    # Python 2.x compatibility
    from StringIO import StringIO
except ImportError:
    from io import StringIO

try:
    from types import InstanceType
except ImportError:
    # Python 3.x compatibility
    InstanceType = None


__author__ = "Marius Gedminas (marius@gedmin.as)"
__copyright__ = "Copyright (c) 2008-2017 Marius Gedminas and contributors"
__license__ = "MIT"
__version__ = '3.4.0'
__date__ = '2018-02-13'


try:
    basestring
except NameError:
    # Python 3.x compatibility
    basestring = str

try:
    iteritems = dict.iteritems
except AttributeError:
    # Python 3.x compatibility
    iteritems = dict.items

IS_INTERACTIVE = False
try:  # pragma: nocover
    import graphviz
    if get_ipython().__class__.__name__ != 'TerminalInteractiveShell':
        IS_INTERACTIVE = True
except (NameError, ImportError):
    pass


def _isinstance(object, classinfo):
    """Return whether an object is an instance of a class or its subclass.

    Differs from the builtin isinstance() implementation in that it does not
    depend on the ``__class__`` attribute which is proxied by
    mock.Mock(spec=...).
    """
    return issubclass(type(object), classinfo)


def count(typename, objects=None):
    """Count objects tracked by the garbage collector with a given class name.

    The class name can optionally be fully qualified.

    Example:

        >>> count('dict')
        42
        >>> count('mymodule.MyClass')
        2

    .. note::

        The Python garbage collector does not track simple
        objects like int or str.  See
        https://docs.python.org/3/library/gc.html#gc.is_tracked
        for more information.

    Instead of looking through all objects tracked by the GC, you may
    specify your own collection, e.g.

        >>> count('MyClass', get_leaking_objects())
        3

    See also: :func:`get_leaking_objects`.

    .. versionchanged:: 1.7
       New parameter: ``objects``.

    .. versionchanged:: 1.8
       Accepts fully-qualified type names (i.e. 'package.module.ClassName')
       as well as short type names (i.e. 'ClassName').

    """
    if objects is None:
        objects = gc.get_objects()
    try:
        if '.' in typename:
            return sum(1 for o in objects if _long_typename(o) == typename)
        else:
            return sum(1 for o in objects if _short_typename(o) == typename)
    finally:
        del objects  # clear cyclic references to frame


def typestats(objects=None, shortnames=True, filter=None):
    """Count the number of instances for each type tracked by the GC.

    Note that the GC does not track simple objects like int or str.

    Note that classes with the same name but defined in different modules
    will be lumped together if ``shortnames`` is True.

    If ``filter`` is specified, it should be a function taking one argument and
    returning a boolean. Objects for which ``filter(obj)`` returns ``False``
    will be ignored.

    Example:

        >>> typestats()
        {'list': 12041, 'tuple': 10245, ...}
        >>> typestats(get_leaking_objects())
        {'MemoryError': 1, 'tuple': 2795, 'RuntimeError': 1, 'list': 47, ...}

    .. versionadded:: 1.1

    .. versionchanged:: 1.7
       New parameter: ``objects``.

    .. versionchanged:: 1.8
       New parameter: ``shortnames``.

    .. versionchanged:: 3.1.3
       New parameter: ``filter``.

    """
    if objects is None:
        objects = gc.get_objects()
    try:
        if shortnames:
            typename = _short_typename
        else:
            typename = _long_typename
        stats = {}
        for o in objects:
            if filter and not filter(o):
                continue
            n = typename(o)
            stats[n] = stats.get(n, 0) + 1
        return stats
    finally:
        del objects  # clear cyclic references to frame


def most_common_types(limit=10, objects=None, shortnames=True, filter=None):
    """Count the names of types with the most instances.

    Returns a list of (type_name, count), sorted most-frequent-first.

    Limits the return value to at most ``limit`` items.  You may set ``limit``
    to None to avoid that.

    If ``filter`` is specified, it should be a function taking one argument and
    returning a boolean. Objects for which ``filter(obj)`` returns ``False``
    will be ignored.

    The caveats documented in :func:`typestats` apply.

    Example:

        >>> most_common_types(limit=2)
        [('list', 12041), ('tuple', 10245)]

    .. versionadded:: 1.4

    .. versionchanged:: 1.7
       New parameter: ``objects``.

    .. versionchanged:: 1.8
       New parameter: ``shortnames``.

    .. versionchanged:: 3.1.3
       New parameter: ``filter``.

    """
    stats = sorted(
        typestats(objects, shortnames=shortnames, filter=filter).items(),
        key=operator.itemgetter(1), reverse=True)
    if limit:
        stats = stats[:limit]
    return stats


def show_most_common_types(
        limit=10,
        objects=None,
        shortnames=True,
        file=None,
        filter=None):
    """Print the table of types of most common instances.

    If ``filter`` is specified, it should be a function taking one argument and
    returning a boolean. Objects for which ``filter(obj)`` returns ``False``
    will be ignored.

    The caveats documented in :func:`typestats` apply.

    Example:

        >>> show_most_common_types(limit=5)
        tuple                      8959
        function                   2442
        wrapper_descriptor         1048
        dict                       953
        builtin_function_or_method 800

    .. versionadded:: 1.1

    .. versionchanged:: 1.7
       New parameter: ``objects``.

    .. versionchanged:: 1.8
       New parameter: ``shortnames``.

    .. versionchanged:: 3.0
       New parameter: ``file``.

    .. versionchanged:: 3.1.3
       New parameter: ``filter``.

    """
    if file is None:
        file = sys.stdout
    stats = most_common_types(limit, objects, shortnames=shortnames,
                              filter=filter)
    width = max(len(name) for name, count in stats)
    for name, count in stats:
        file.write('%-*s %i\n' % (width, name, count))


def growth(limit=10, peak_stats={}, shortnames=True, filter=None):
    """Count the increase in peak object since last call.

    Returns a list of (type_name, total_count, increase_delta),
    descending order by increase_delta.

    Limits the output to ``limit`` largest deltas.  You may set ``limit`` to
    None to see all of them.

    Uses and updates ``peak_stats``, a dictionary from type names to previously
    seen peak object counts.  Usually you don't need to pay attention to this
    argument.

    If ``filter`` is specified, it should be a function taking one argument and
    returning a boolean. Objects for which ``filter(obj)`` returns ``False``
    will be ignored.

    The caveats documented in :func:`typestats` apply.

    Example:

        >>> growth(2)
        [(tuple, 12282, 10), (dict, 1922, 7)]

    .. versionadded:: 3.3.0

    """
    gc.collect()
    stats = typestats(shortnames=shortnames, filter=filter)
    deltas = {}
    for name, count in iteritems(stats):
        old_count = peak_stats.get(name, 0)
        if count > old_count:
            deltas[name] = count - old_count
            peak_stats[name] = count
    deltas = sorted(deltas.items(), key=operator.itemgetter(1),
                    reverse=True)
    if limit:
        deltas = deltas[:limit]

    return [(name, stats[name], delta) for name, delta in deltas]


def show_growth(limit=10, peak_stats=None, shortnames=True, file=None,
                filter=None):
    """Show the increase in peak object counts since last call.

    if ``peak_stats`` is None, peak object counts will recorded in
    func `growth`, and your can record the counts by yourself with set
    ``peak_stats`` to a dictionary.

    The caveats documented in :func:`growth` apply.

    Example:

        >>> show_growth()
        wrapper_descriptor       970       +14
        tuple                  12282       +10
        dict                    1922        +7
        ...

    .. versionadded:: 1.5

    .. versionchanged:: 1.8
       New parameter: ``shortnames``.

    .. versionchanged:: 2.1
       New parameter: ``file``.

    .. versionchanged:: 3.1.3
       New parameter: ``filter``.

    """
    if peak_stats is None:
        result = growth(limit, shortnames=shortnames, filter=filter)
    else:
        result = growth(limit, peak_stats, shortnames, filter)
    if result:
        if file is None:
            file = sys.stdout
        width = max(len(name) for name, _, _ in result)
        for name, count, delta in result:
            file.write('%-*s%9d %+9d\n' % (width, name, count, delta))


def get_new_ids(skip_update=False, limit=10, sortby='deltas',
                shortnames=None, file=None, _state={}):
    """Find and display new objects allocated since last call.

    Shows the increase in object counts since last call to this
    function and returns the memory address ids for new objects.

    Returns a dictionary mapping object type names to sets of object IDs
    that have been created since the last time this function was called.

    ``skip_update`` (bool): If True, returns the same dictionary that
    was returned during the previous call without updating the internal
    state or examining the objects currently in memory.

    ``limit`` (int): The maximum number of rows that you want to print
    data for.  Use 0 to suppress the printing.  Use None to print everything.

    ``sortby`` (str): This is the column that you want to sort by in
    descending order.  Possible values are: 'old', 'current', 'new',
    'deltas'

    ``shortnames`` (bool): If True, classes with the same name but
    defined in different modules will be lumped together.  If False,
    all type names will be qualified with the module name.  If None (default),
    ``get_new_ids`` will remember the value from previous calls, so it's
    enough to prime this once.  By default the primed value is True.

    ``_state`` (dict): Stores old, current, and new_ids in memory.
    It is used by the function to store the internal state between calls.
    Never pass in this argument unless you know what you're doing.

    The caveats documented in :func:`growth` apply.

    When one gets new_ids from :func:`get_new_ids`, one can use
    :func:`at_addrs` to get a list of those objects. Then one can iterate over
    the new objects, print out what they are, and call :func:`show_backrefs` or
    :func:`show_chain` to see where they are referenced.

    Example:

        >>> _ = get_new_ids() # store current objects in _state
        >>> _ = get_new_ids() # current_ids become old_ids in _state
        >>> a = [0, 1, 2] # list we don't know about
        >>> b = [3, 4, 5] # list we don't know about
        >>> new_ids = get_new_ids(limit=3) # we see new lists
        ======================================================================
        Type                    Old_ids  Current_ids      New_ids Count_Deltas
        ======================================================================
        list                        324          326           +3           +2
        dict                       1125         1125           +0           +0
        wrapper_descriptor         1001         1001           +0           +0
        ======================================================================
        >>> new_lists = at_addrs(new_ids['list'])
        >>> a in new_lists
        True
        >>> b in new_lists
        True

    .. versionadded:: 3.4
    """
    if not _state:
        _state['old'] = collections.defaultdict(set)
        _state['current'] = collections.defaultdict(set)
        _state['new'] = collections.defaultdict(set)
        _state['shortnames'] = True
    new_ids = _state['new']
    if skip_update:
        return new_ids
    old_ids = _state['old']
    current_ids = _state['current']
    if shortnames is None:
        shortnames = _state['shortnames']
    else:
        _state['shortnames'] = shortnames
    gc.collect()
    objects = gc.get_objects()
    for class_name in old_ids:
        old_ids[class_name].clear()
    for class_name, ids_set in current_ids.items():
        old_ids[class_name].update(ids_set)
    for class_name in current_ids:
        current_ids[class_name].clear()
    for o in objects:
        if shortnames:
            class_name = _short_typename(o)
        else:
            class_name = _long_typename(o)
        id_number = id(o)
        current_ids[class_name].add(id_number)
    for class_name in new_ids:
        new_ids[class_name].clear()
    rows = []
    keys_to_remove = []
    for class_name in current_ids:
        num_old = len(old_ids[class_name])
        num_current = len(current_ids[class_name])
        if num_old == 0 and num_current == 0:
            # remove the key from our dicts if we don't have any old or
            # current class_name objects
            keys_to_remove.append(class_name)
            continue
        new_ids_set = current_ids[class_name] - old_ids[class_name]
        new_ids[class_name].update(new_ids_set)
        num_new = len(new_ids_set)
        num_delta = num_current - num_old
        row = (class_name, num_old, num_current, num_new, num_delta)
        rows.append(row)
    for key in keys_to_remove:
        del old_ids[key]
        del current_ids[key]
        del new_ids[key]
    index_by_sortby = {'old': 1, 'current': 2, 'new': 3, 'deltas': 4}
    rows.sort(key=operator.itemgetter(index_by_sortby[sortby], 0),
              reverse=True)
    if limit is not None:
        rows = rows[:limit]
    if not rows:
        return new_ids
    if file is None:
        file = sys.stdout
    width = max(len(row[0]) for row in rows)
    print('='*(width+13*4), file=file)
    print('%-*s%13s%13s%13s%13s' %
          (width, 'Type', 'Old_ids', 'Current_ids', 'New_ids', 'Count_Deltas'),
          file=file)
    print('='*(width+13*4), file=file)
    for row_class, old, current, new, delta in rows:
        print('%-*s%13d%13d%+13d%+13d' %
              (width, row_class, old, current, new, delta), file=file)
    print('='*(width+13*4), file=file)
    return new_ids


def get_leaking_objects(objects=None):
    """Return objects that do not have any referents.

    These could indicate reference-counting bugs in C code.  Or they could
    be legitimate.

    Note that the GC does not track simple objects like int or str.

    .. versionadded:: 1.7
    """
    if objects is None:
        gc.collect()
        objects = gc.get_objects()
    try:
        ids = set(id(i) for i in objects)
        for i in objects:
            ids.difference_update(id(j) for j in gc.get_referents(i))
        # this then is our set of objects without referrers
        return [i for i in objects if id(i) in ids]
    finally:
        del objects, i  # clear cyclic references to frame


def by_type(typename, objects=None):
    """Return objects tracked by the garbage collector with a given class name.

    Example:

        >>> by_type('MyClass')
        [<mymodule.MyClass object at 0x...>]

    Note that the GC does not track simple objects like int or str.

    .. versionchanged:: 1.7
       New parameter: ``objects``.

    .. versionchanged:: 1.8
       Accepts fully-qualified type names (i.e. 'package.module.ClassName')
       as well as short type names (i.e. 'ClassName').

    """
    if objects is None:
        objects = gc.get_objects()
    try:
        if '.' in typename:
            return [o for o in objects if _long_typename(o) == typename]
        else:
            return [o for o in objects if _short_typename(o) == typename]
    finally:
        del objects  # clear cyclic references to frame


def at(addr):
    """Return an object at a given memory address.

    The reverse of id(obj):

        >>> at(id(obj)) is obj
        True

    Note that this function does not work on objects that are not tracked by
    the GC (e.g. ints or strings).
    """
    for o in gc.get_objects():
        if id(o) == addr:
            return o
    return None


def at_addrs(address_set):
    """Return a list of objects for a given set of memory addresses.

    The reverse of [id(obj1), id(obj2), ...].  Note that objects are returned
    in an arbitrary order.

    When one gets ``new_ids`` from :func:`get_new_ids`, one can use this
    function to get a list of those objects.  Then one can iterate over the new
    objects, print out what they are, and call :func:`show_backrefs` or
    :func:`show_chain` to see where they are referenced.

        >>> a = [0, 1, 2]
        >>> new_ids = get_new_ids()
        >>> new_lists = at_addrs(new_ids['list'])
        >>> a in new_lists
        True

    Note that this function does not work on objects that are not tracked
    by the GC (e.g. ints or strings).

    .. versionadded:: 3.4
    """
    res = []
    for o in gc.get_objects():
        if id(o) in address_set:
            res.append(o)
    return res


def find_ref_chain(obj, predicate, max_depth=20, extra_ignore=()):
    """Find a shortest chain of references leading from obj.

    The end of the chain will be some object that matches your predicate.

    ``predicate`` is a function taking one argument and returning a boolean.

    ``max_depth`` limits the search depth.

    ``extra_ignore`` can be a list of object IDs to exclude those objects from
    your search.

    Example:

        >>> find_ref_chain(obj, lambda x: isinstance(x, MyClass))
        [obj, ..., <MyClass object at ...>]

    Returns ``[obj]`` if such a chain could not be found.

    .. versionadded:: 1.7
    """
    return _find_chain(obj, predicate, gc.get_referents,
                       max_depth=max_depth, extra_ignore=extra_ignore)[::-1]


def find_backref_chain(obj, predicate, max_depth=20, extra_ignore=()):
    """Find a shortest chain of references leading to obj.

    The start of the chain will be some object that matches your predicate.

    ``predicate`` is a function taking one argument and returning a boolean.

    ``max_depth`` limits the search depth.

    ``extra_ignore`` can be a list of object IDs to exclude those objects from
    your search.

    Example:

        >>> find_backref_chain(obj, is_proper_module)
        [<module ...>, ..., obj]

    Returns ``[obj]`` if such a chain could not be found.

    .. versionchanged:: 1.5
       Returns ``obj`` instead of ``None`` when a chain could not be found.

    """
    return _find_chain(obj, predicate, gc.get_referrers,
                       max_depth=max_depth, extra_ignore=extra_ignore)


def show_backrefs(objs, max_depth=3, extra_ignore=(), filter=None, too_many=10,
                  highlight=None, filename=None, extra_info=None,
                  refcounts=False, shortnames=True, output=None):
    """Generate an object reference graph ending at ``objs``.

    The graph will show you what objects refer to ``objs``, directly and
    indirectly.

    ``objs`` can be a single object, or it can be a list of objects.  If
    unsure, wrap the single object in a new list.

    ``filename`` if specified, can be the name of a .dot or a image
    file, whose extension indicates the desired output format; note
    that output to a specific format is entirely handled by GraphViz:
    if the desired format is not supported, you just get the .dot
    file.  If ``filename`` and ``output`` are not specified, ``show_backrefs``
    will try to display the graph inline (if you're using IPython), otherwise
    it'll try to produce a .dot file and spawn a viewer (xdot).  If xdot is
    not available, ``show_backrefs`` will convert the .dot file to a
    .png and print its name.

    ``output`` if specified, the GraphViz output will be written to this
    file object. ``output`` and ``filename`` should not both be specified.

    Use ``max_depth`` and ``too_many`` to limit the depth and breadth of the
    graph.

    Use ``filter`` (a predicate) and ``extra_ignore`` (a list of object IDs) to
    remove undesired objects from the graph.

    Use ``highlight`` (a predicate) to highlight certain graph nodes in blue.

    Use ``extra_info`` (a function taking one argument and returning a
    string) to report extra information for objects.

    Specify ``refcounts=True`` if you want to see reference counts.
    These will mostly match the number of arrows pointing to an object,
    but can be different for various reasons.

    Specify ``shortnames=False`` if you want to see fully-qualified type
    names ('package.module.ClassName').  By default you get to see only the
    class name part.

    Examples:

        >>> show_backrefs(obj)
        >>> show_backrefs([obj1, obj2])
        >>> show_backrefs(obj, max_depth=5)
        >>> show_backrefs(obj, filter=lambda x: not inspect.isclass(x))
        >>> show_backrefs(obj, highlight=inspect.isclass)
        >>> show_backrefs(obj, extra_ignore=[id(locals())])

    .. versionchanged:: 1.3
       New parameters: ``filename``, ``extra_info``.

    .. versionchanged:: 1.5
       New parameter: ``refcounts``.

    .. versionchanged:: 1.8
       New parameter: ``shortnames``.

    .. versionchanged:: 2.0
       New parameter: ``output``.

    """
    # For show_backrefs(), it makes sense to stop when reaching a
    # module because you'll end up in sys.modules and explode the
    # graph with useless clutter.  That's why we're specifying
    # cull_func here, but not in show_graph().
    return _show_graph(objs, max_depth=max_depth, extra_ignore=extra_ignore,
                       filter=filter, too_many=too_many, highlight=highlight,
                       edge_func=gc.get_referrers, swap_source_target=False,
                       filename=filename, output=output, extra_info=extra_info,
                       refcounts=refcounts, shortnames=shortnames,
                       cull_func=is_proper_module)


def show_refs(objs, max_depth=3, extra_ignore=(), filter=None, too_many=10,
              highlight=None, filename=None, extra_info=None,
              refcounts=False, shortnames=True, output=None):
    """Generate an object reference graph starting at ``objs``.

    The graph will show you what objects are reachable from ``objs``, directly
    and indirectly.

    ``objs`` can be a single object, or it can be a list of objects.  If
    unsure, wrap the single object in a new list.

    ``filename`` if specified, can be the name of a .dot or a image
    file, whose extension indicates the desired output format; note
    that output to a specific format is entirely handled by GraphViz:
    if the desired format is not supported, you just get the .dot
    file.  If ``filename`` and ``output`` is not specified, ``show_refs`` will
    try to display the graph inline (if you're using IPython), otherwise it'll
    try to produce a .dot file and spawn a viewer (xdot).  If xdot is
    not available, ``show_refs`` will convert the .dot file to a
    .png and print its name.

    ``output`` if specified, the GraphViz output will be written to this
    file object. ``output`` and ``filename`` should not both be specified.

    Use ``max_depth`` and ``too_many`` to limit the depth and breadth of the
    graph.

    Use ``filter`` (a predicate) and ``extra_ignore`` (a list of object IDs) to
    remove undesired objects from the graph.

    Use ``highlight`` (a predicate) to highlight certain graph nodes in blue.

    Use ``extra_info`` (a function returning a string) to report extra
    information for objects.

    Specify ``refcounts=True`` if you want to see reference counts.

    Examples:

        >>> show_refs(obj)
        >>> show_refs([obj1, obj2])
        >>> show_refs(obj, max_depth=5)
        >>> show_refs(obj, filter=lambda x: not inspect.isclass(x))
        >>> show_refs(obj, highlight=inspect.isclass)
        >>> show_refs(obj, extra_ignore=[id(locals())])

    .. versionadded:: 1.1

    .. versionchanged:: 1.3
       New parameters: ``filename``, ``extra_info``.

    .. versionchanged:: 1.5
       Follows references from module objects instead of stopping.
       New parameter: ``refcounts``.

    .. versionchanged:: 1.8
       New parameter: ``shortnames``.

    .. versionchanged:: 2.0
       New parameter: ``output``.
    """
    return _show_graph(objs, max_depth=max_depth, extra_ignore=extra_ignore,
                       filter=filter, too_many=too_many, highlight=highlight,
                       edge_func=gc.get_referents, swap_source_target=True,
                       filename=filename, extra_info=extra_info,
                       refcounts=refcounts, shortnames=shortnames,
                       output=output)


def show_chain(*chains, **kw):
    """Show a chain (or several chains) of object references.

    Useful in combination with :func:`find_ref_chain` or
    :func:`find_backref_chain`, e.g.

        >>> show_chain(find_backref_chain(obj, is_proper_module))

    You can specify if you want that chain traced backwards or forwards
    by passing a ``backrefs`` keyword argument, e.g.

        >>> show_chain(find_ref_chain(obj, is_proper_module),
        ...            backrefs=False)

    Ideally this shouldn't matter, but for some objects
    :func:`gc.get_referrers` and :func:`gc.get_referents` are not perfectly
    symmetrical.

    You can specify ``highlight``, ``extra_info``, ``refcounts``,
    ``shortnames``, ``filename`` or ``output`` arguments like for
    :func:`show_backrefs` or :func:`show_refs`.

    .. versionadded:: 1.5

    .. versionchanged:: 1.7
       New parameter: ``backrefs``.

    .. versionchanged:: 2.0
       New parameter: ``output``.

    """
    backrefs = kw.pop('backrefs', True)
    chains = [chain for chain in chains if chain]  # remove empty ones

    def in_chains(x, ids=set(map(id, itertools.chain(*chains)))):
        return id(x) in ids
    max_depth = max(map(len, chains)) - 1
    if backrefs:
        show_backrefs([chain[-1] for chain in chains], max_depth=max_depth,
                      filter=in_chains, **kw)
    else:
        show_refs([chain[0] for chain in chains], max_depth=max_depth,
                  filter=in_chains, **kw)


def is_proper_module(obj):
    """
    Returns ``True`` if ``obj`` can be treated like a garbage collector root.

    That is, if ``obj`` is a module that is in ``sys.modules``.

    >>> import types
    >>> is_proper_module([])
    False
    >>> is_proper_module(types)
    True
    >>> is_proper_module(types.ModuleType('foo'))
    False

    .. versionadded:: 1.8
    """
    return (inspect.ismodule(obj) and
            obj is sys.modules.get(getattr(obj, '__name__', None)))


#
# Internal helpers
#

def _find_chain(obj, predicate, edge_func, max_depth=20, extra_ignore=()):
    queue = [obj]
    depth = {id(obj): 0}
    parent = {id(obj): None}
    ignore = set(extra_ignore)
    ignore.add(id(extra_ignore))
    ignore.add(id(queue))
    ignore.add(id(depth))
    ignore.add(id(parent))
    ignore.add(id(ignore))
    ignore.add(id(sys._getframe()))   # this function
    ignore.add(id(sys._getframe(1)))  # find_chain/find_backref_chain
    gc.collect()
    while queue:
        target = queue.pop(0)
        if predicate(target):
            chain = [target]
            while parent[id(target)] is not None:
                target = parent[id(target)]
                chain.append(target)
            return chain
        tdepth = depth[id(target)]
        if tdepth < max_depth:
            referrers = edge_func(target)
            ignore.add(id(referrers))
            for source in referrers:
                if id(source) in ignore:
                    continue
                if id(source) not in depth:
                    depth[id(source)] = tdepth + 1
                    parent[id(source)] = target
                    queue.append(source)
    return [obj]  # not found


def _show_graph(objs, edge_func, swap_source_target,
                max_depth=3, extra_ignore=(), filter=None, too_many=10,
                highlight=None, filename=None, extra_info=None,
                refcounts=False, shortnames=True, output=None,
                cull_func=None):
    if not _isinstance(objs, (list, tuple)):
        objs = [objs]

    is_interactive = False
    if filename and output:
        raise ValueError('Cannot specify both output and filename.')
    elif output:
        f = output
    elif filename and filename.endswith('.dot'):
        f = codecs.open(filename, 'w', encoding='utf-8')
        dot_filename = filename
    elif IS_INTERACTIVE:
        is_interactive = True
        f = StringIO()
    else:
        fd, dot_filename = tempfile.mkstemp(prefix='objgraph-',
                                            suffix='.dot', text=True)
        f = os.fdopen(fd, "w")
        if getattr(f, 'encoding', None):
            # Python 3 will wrap the file in the user's preferred encoding
            # Re-wrap it for utf-8
            import io
            f = io.TextIOWrapper(f.detach(), 'utf-8')
    f.write('digraph ObjectGraph {\n'
            '  node[shape=box, style=filled, fillcolor=white];\n')
    queue = []
    depth = {}
    ignore = set(extra_ignore)
    ignore.add(id(objs))
    ignore.add(id(extra_ignore))
    ignore.add(id(queue))
    ignore.add(id(depth))
    ignore.add(id(ignore))
    ignore.add(id(sys._getframe()))   # this function
    ignore.add(id(sys._getframe().f_locals))
    ignore.add(id(sys._getframe(1)))  # show_refs/show_backrefs
    ignore.add(id(sys._getframe(1).f_locals))
    for obj in objs:
        f.write('  %s[fontcolor=red];\n' % (_obj_node_id(obj)))
        depth[id(obj)] = 0
        queue.append(obj)
        del obj
    gc.collect()
    nodes = 0
    while queue:
        nodes += 1
        # The names "source" and "target" are reversed here because
        # originally there was just show_backrefs() and we were
        # traversing the reference graph backwards.
        target = queue.pop(0)
        tdepth = depth[id(target)]
        f.write('  %s[label="%s"];\n' % (_obj_node_id(target),
                                         _obj_label(target, extra_info,
                                                    refcounts, shortnames)))
        h, s, v = _gradient((0, 0, 1), (0, 0, .3), tdepth, max_depth)
        if inspect.ismodule(target):
            h = .3
            s = 1
        if highlight and highlight(target):
            h = .6
            s = .6
            v = 0.5 + v * 0.5
        f.write('  %s[fillcolor="%g,%g,%g"];\n'
                % (_obj_node_id(target), h, s, v))
        if v < 0.5:
            f.write('  %s[fontcolor=white];\n' % (_obj_node_id(target)))
        if hasattr(getattr(target, '__class__', None), '__del__'):
            f.write('  %s->%s_has_a_del[color=red,style=dotted,'
                    'len=0.25,weight=10];\n' % (_obj_node_id(target),
                                                _obj_node_id(target)))
            f.write('  %s_has_a_del[label="__del__",shape=doublecircle,'
                    'height=0.25,color=red,fillcolor="0,.5,1",fontsize=6];\n'
                    % (_obj_node_id(target)))
        if tdepth >= max_depth:
            continue
        if cull_func is not None and cull_func(target):
            continue
        neighbours = edge_func(target)
        ignore.add(id(neighbours))
        n = 0
        skipped = 0
        for source in neighbours:
            if id(source) in ignore:
                continue
            if filter and not filter(source):
                continue
            if n >= too_many:
                skipped += 1
                continue
            if swap_source_target:
                srcnode, tgtnode = target, source
            else:
                srcnode, tgtnode = source, target
            elabel = _edge_label(srcnode, tgtnode, shortnames)
            f.write('  %s -> %s%s;\n' % (_obj_node_id(srcnode),
                                         _obj_node_id(tgtnode), elabel))
            if id(source) not in depth:
                depth[id(source)] = tdepth + 1
                queue.append(source)
            n += 1
            del source
        del neighbours
        if skipped > 0:
            h, s, v = _gradient((0, 1, 1), (0, 1, .3), tdepth + 1, max_depth)
            if swap_source_target:
                label = "%d more references" % skipped
                edge = "%s->too_many_%s" % (_obj_node_id(target),
                                            _obj_node_id(target))
            else:
                label = "%d more backreferences" % skipped
                edge = "too_many_%s->%s" % (_obj_node_id(target),
                                            _obj_node_id(target))
            f.write('  %s[color=red,style=dotted,len=0.25,weight=10];\n'
                    % edge)
            f.write('  too_many_%s[label="%s",shape=box,height=0.25,'
                    'color=red,fillcolor="%g,%g,%g",fontsize=6];\n'
                    % (_obj_node_id(target), label, h, s, v))
            f.write('  too_many_%s[fontcolor=white];\n'
                    % (_obj_node_id(target)))
    f.write("}\n")

    if output:
        return

    if is_interactive:
        return graphviz.Source(f.getvalue())
    else:
        # The file should only be closed if this function was in charge of
        # opening the file.
        f.close()
        print("Graph written to %s (%d nodes)" % (dot_filename, nodes))
        _present_graph(dot_filename, filename)


def _present_graph(dot_filename, filename=None):
    """Present a .dot file to the user in the requested fashion.

    If ``filename`` is provided, runs ``dot`` to convert the .dot file
    into the desired format, determined by the filename extension.

    If ``filename`` is not provided, tries to launch ``xdot``, a
    graphical .dot file viewer.  If ``xdot`` is not present on the system,
    converts the graph to a PNG.
    """
    if filename == dot_filename:
        # nothing to do, the user asked for a .dot file and got it
        return
    if not filename and _program_in_path('xdot'):
        print("Spawning graph viewer (xdot)")
        subprocess.Popen(['xdot', dot_filename], close_fds=True)
    elif _program_in_path('dot'):
        if not filename:
            print("Graph viewer (xdot) not found, generating a png instead")
            filename = dot_filename[:-4] + '.png'
        stem, ext = os.path.splitext(filename)
        cmd = ['dot', '-T' + ext[1:], '-o' + filename, dot_filename]
        dot = subprocess.Popen(cmd, close_fds=False)
        dot.wait()
        if dot.returncode != 0:
            # XXX: shouldn't this go to stderr or a log?
            print('dot failed (exit code %d) while executing "%s"'
                  % (dot.returncode, ' '.join(cmd)))
        else:
            print("Image generated as %s" % filename)
    else:
        if not filename:
            print("Graph viewer (xdot) and image renderer (dot) not found,"
                  " not doing anything else")
        else:
            print("Image renderer (dot) not found, not doing anything else")


def _obj_node_id(obj):
    return ('o%d' % id(obj)).replace('-', '_')


def _obj_label(obj, extra_info=None, refcounts=False, shortnames=True):
    if shortnames:
        label = [_short_typename(obj)]
    else:
        label = [_long_typename(obj)]
    if refcounts:
        label[0] += ' [%d]' % (sys.getrefcount(obj) - 4)
        # Why -4?  To ignore the references coming from
        #   obj_label's frame (obj)
        #   show_graph's frame (target variable)
        #   sys.getrefcount()'s argument
        #   something else that doesn't show up in gc.get_referrers()
    label.append(_safe_repr(obj))
    if extra_info:
        label.append(str(extra_info(obj)))
    return _quote('\n'.join(label))


def _quote(s):
    return (s.replace("\\", "\\\\")
             .replace("\"", "\\\"")
             .replace("\n", "\\n")
             .replace("\0", "\\\\0"))


def _get_obj_type(obj):
    objtype = type(obj)
    if type(obj) == InstanceType:
        objtype = obj.__class__
    return objtype


def _short_typename(obj):
    return _get_obj_type(obj).__name__


def _long_typename(obj):
    objtype = _get_obj_type(obj)
    name = objtype.__name__
    module = getattr(objtype, '__module__', None)
    if module:
        return '%s.%s' % (module, name)
    else:
        return name


def _safe_repr(obj):
    try:
        return _short_repr(obj)
    except Exception:
        return '(unrepresentable)'


def _name_or_repr(value):
    try:
        result = value.__name__
    except AttributeError:
        result = repr(value)[:40]

    if _isinstance(result, basestring):
        return result
    else:
        return repr(value)[:40]


def _short_repr(obj):
    if _isinstance(obj, (type, types.ModuleType, types.BuiltinMethodType,
                         types.BuiltinFunctionType)):
        return _name_or_repr(obj)
    if _isinstance(obj, types.MethodType):
        name = _name_or_repr(obj.__func__)
        if obj.__self__:
            return name + ' (bound)'
        else:
            return name
    # NB: types.LambdaType is an alias for types.FunctionType!
    if _isinstance(obj, types.LambdaType) and obj.__name__ == '<lambda>':
        return 'lambda: %s:%s' % (os.path.basename(obj.__code__.co_filename),
                                  obj.__code__.co_firstlineno)
    if _isinstance(obj, types.FrameType):
        return '%s:%s' % (obj.f_code.co_filename, obj.f_lineno)
    if _isinstance(obj, (tuple, list, dict, set)):
        return '%d items' % len(obj)
    return repr(obj)[:40]


def _gradient(start_color, end_color, depth, max_depth):
    if max_depth == 0:
        # avoid division by zero
        return start_color
    h1, s1, v1 = start_color
    h2, s2, v2 = end_color
    f = float(depth) / max_depth
    h = h1 * (1-f) + h2 * f
    s = s1 * (1-f) + s2 * f
    v = v1 * (1-f) + v2 * f
    return h, s, v


def _edge_label(source, target, shortnames=True):
    if (_isinstance(target, dict) and
            target is getattr(source, '__dict__', None)):
        return ' [label="__dict__",weight=10]'
    if _isinstance(source, types.FrameType):
        if target is source.f_locals:
            return ' [label="f_locals",weight=10]'
        if target is source.f_globals:
            return ' [label="f_globals",weight=10]'
    if _isinstance(source, types.MethodType):
        try:
            if target is source.__self__:
                return ' [label="__self__",weight=10]'
            if target is source.__func__:
                return ' [label="__func__",weight=10]'
        except AttributeError:  # pragma: nocover
            # Python < 2.6 compatibility
            if target is source.im_self:
                return ' [label="im_self",weight=10]'
            if target is source.im_func:
                return ' [label="im_func",weight=10]'
    if _isinstance(source, types.FunctionType):
        for k in dir(source):
            if target is getattr(source, k):
                return ' [label="%s",weight=10]' % _quote(k)
    if _isinstance(source, dict):
        for k, v in iteritems(source):
            if v is target:
                if _isinstance(k, basestring) and _is_identifier(k):
                    return ' [label="%s",weight=2]' % _quote(k)
                else:
                    if shortnames:
                        tn = _short_typename(k)
                    else:
                        tn = _long_typename(k)
                    return ' [label="%s"]' % _quote(tn + "\n" + _safe_repr(k))
    return ''


_is_identifier = re.compile('[a-zA-Z_][a-zA-Z_0-9]*$').match


def _program_in_path(program):
    # XXX: Consider using distutils.spawn.find_executable or shutil.which
    path = os.environ.get("PATH", os.defpath).split(os.pathsep)
    path = [os.path.join(dir, program) for dir in path]
    path = [True for file in path
            if os.path.isfile(file) or os.path.isfile(file + '.exe')]
    return bool(path)