nest.py

# -*- coding: utf-8 -*-
# Copyright 2016 The TensorFlow Authors. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ==============================================================================

"""## Functions for working with arbitrarily nested sequences of elements.

This module can perform operations on nested structures. A nested structure is a
Python sequence, tuple (including `namedtuple`), or dict that can contain
further sequences, tuples, and dicts.

The utilities here assume (and do not check) that the nested structures form a
'tree', i.e., no references in the structure of the input of these functions
should be recursive.

Example structures: `((3, 4), 5, (6, 7, (9, 10), 8))`, `(np.array(0),
  (np.array([3, 4]), tf.constant([3, 4])))`
"""

import collections as _collections

import six as _six


def _sorted(dict_):
    """Returns a sorted list of the dict keys, with error if keys not sortable."""
    try:
        return sorted(_six.iterkeys(dict_))
    except TypeError:
        raise TypeError("nest only supports dicts with sortable keys.")


def _sequence_like(instance, args):
    """Converts the sequence `args` to the same type as `instance`.

    Args:
      instance: an instance of `tuple`, `list`, `namedtuple`, `dict`, or
          `collections.OrderedDict`.
      args: elements to be converted to the `instance` type.

    Returns:
      `args` with the type of `instance`.
    """
    if isinstance(instance, dict):
        # Pack dictionaries in a deterministic order by sorting the keys.
        # Notice this means that we ignore the original order of `OrderedDict`
        # instances. This is intentional, to avoid potential bugs caused by mixing
        # ordered and plain dicts (e.g., flattening a dict but using a
        # corresponding `OrderedDict` to pack it back).
        result = dict(zip(_sorted(instance), args))
        return type(instance)((key, result[key]) for key in _six.iterkeys(instance))
    elif (isinstance(instance, tuple) and
          hasattr(instance, "_fields") and
          isinstance(instance._fields, _collections.Sequence) and
          all(isinstance(f, _six.string_types) for f in instance._fields)):
        # This is a namedtuple
        return type(instance)(*args)
    else:
        # Not a namedtuple
        return type(instance)(args)


def _yield_value(iterable):
    if isinstance(iterable, dict):
        # Iterate through dictionaries in a deterministic order by sorting the
        # keys. Notice this means that we ignore the original order of `OrderedDict`
        # instances. This is intentional, to avoid potential bugs caused by mixing
        # ordered and plain dicts (e.g., flattening a dict but using a
        # corresponding `OrderedDict` to pack it back).
        for key in _sorted(iterable):
            yield iterable[key]
    else:
        for value in iterable:
            yield value


def _yield_flat_nest(nest):
    for n in _yield_value(nest):
        if is_sequence(n):
            for ni in _yield_flat_nest(n):
                yield ni
        else:
            yield n


# Used by `_warn_once` to remember which warning messages have been given.
_ALREADY_WARNED = {}


def _warn_once(message):
    """Logs a warning message, once per unique string."""
    if message not in _ALREADY_WARNED:
        _ALREADY_WARNED[message] = True


def is_sequence(seq):
    """Returns a true if its input is a collections.Sequence (except strings).

    Args:
      seq: an input sequence.

    Returns:
      True if the sequence is a not a string and is a collections.Sequence or a
      dict.
    """
    if isinstance(seq, dict):
        return True
    if isinstance(seq, set):
        _warn_once("Sets are not currently considered sequences, but this may "
                   "change in the future, so consider avoiding using them.")
    return (isinstance(seq, _collections.Sequence)
            and not isinstance(seq, _six.string_types))


def flatten(nest):
    """Returns a flat list from a given nested structure.

    If `nest` is not a sequence, tuple, or dict, then returns a single-element
    list: `[nest]`.

    In the case of dict instances, the sequence consists of the values, sorted by
    key to ensure deterministic behavior. This is true also for `OrderedDict`
    instances: their sequence order is ignored, the sorting order of keys is
    used instead. The same convention is followed in `pack_sequence_as`. This
    correctly repacks dicts and `OrderedDict`s after they have been flattened,
    and also allows flattening an `OrderedDict` and then repacking it back using
    a correponding plain dict, or vice-versa.
    Dictionaries with non-sortable keys cannot be flattened.

    Args:
      nest: an arbitrarily nested structure or a scalar object. Note, numpy
          arrays are considered scalars.

    Returns:
      A Python list, the flattened version of the input.

    Raises:
      TypeError: The nest is or contains a dict with non-sortable keys.
    """
    if is_sequence(nest):
        return list(_yield_flat_nest(nest))
    else:
        return [nest]


def _recursive_assert_same_structure(nest1, nest2, check_types):
    """Helper function for `assert_same_structure`."""
    is_sequence_nest1 = is_sequence(nest1)
    if is_sequence_nest1 != is_sequence(nest2):
        raise ValueError(
            "The two structures don't have the same nested structure.\n\n"
            "First structure: %s\n\nSecond structure: %s." % (nest1, nest2))

    if not is_sequence_nest1:
        return  # finished checking

    if check_types:
        type_nest1 = type(nest1)
        type_nest2 = type(nest2)
        if type_nest1 != type_nest2:
            raise TypeError(
                "The two structures don't have the same sequence type. First "
                "structure has type %s, while second structure has type %s."
                % (type_nest1, type_nest2))

        if isinstance(nest1, dict):
            keys1 = set(_six.iterkeys(nest1))
            keys2 = set(_six.iterkeys(nest2))
            if keys1 != keys2:
                raise ValueError(
                    "The two dictionaries don't have the same set of keys. First "
                    "structure has keys {}, while second structure has keys {}."
                        .format(keys1, keys2))

    nest1_as_sequence = [n for n in _yield_value(nest1)]
    nest2_as_sequence = [n for n in _yield_value(nest2)]
    for n1, n2 in zip(nest1_as_sequence, nest2_as_sequence):
        _recursive_assert_same_structure(n1, n2, check_types)


def assert_same_structure(nest1, nest2, check_types=True):
    """Asserts that two structures are nested in the same way.

    Args:
      nest1: an arbitrarily nested structure.
      nest2: an arbitrarily nested structure.
      check_types: if `True` (default) types of sequences are checked as
          well, including the keys of dictionaries. If set to `False`, for example
          a list and a tuple of objects will look the same if they have the same
          size.

    Raises:
      ValueError: If the two structures do not have the same number of elements or
        if the two structures are not nested in the same way.
      TypeError: If the two structures differ in the type of sequence in any of
        their substructures. Only possible if `check_types` is `True`.
    """
    len_nest1 = len(flatten(nest1)) if is_sequence(nest1) else 1
    len_nest2 = len(flatten(nest2)) if is_sequence(nest2) else 1
    if len_nest1 != len_nest2:
        raise ValueError("The two structures don't have the same number of "
                         "elements.\n\nFirst structure (%i elements): %s\n\n"
                         "Second structure (%i elements): %s"
                         % (len_nest1, nest1, len_nest2, nest2))
    _recursive_assert_same_structure(nest1, nest2, check_types)


def flatten_dict_items(dictionary):
    """Returns a dictionary with flattened keys and values.

    This function flattens the keys and values of a dictionary, which can be
    arbitrarily nested structures, and returns the flattened version of such
    structures:

    ```python
    example_dictionary = {(4, 5, (6, 8)): ("a", "b", ("c", "d"))}
    result = {4: "a", 5: "b", 6: "c", 8: "d"}
    flatten_dict_items(example_dictionary) == result
    ```

    The input dictionary must satisfy two properties:

    1. Its keys and values should have the same exact nested structure.
    2. The set of all flattened keys of the dictionary must not contain repeated
       keys.

    Args:
      dictionary: the dictionary to zip

    Returns:
      The zipped dictionary.

    Raises:
      TypeError: If the input is not a dictionary.
      ValueError: If any key and value have not the same structure, or if keys are
        not unique.
    """
    if not isinstance(dictionary, dict):
        raise TypeError("input must be a dictionary")
    flat_dictionary = {}
    for i, v in _six.iteritems(dictionary):
        if not is_sequence(i):
            if i in flat_dictionary:
                raise ValueError(
                    "Could not flatten dictionary: key %s is not unique." % i)
            flat_dictionary[i] = v
        else:
            flat_i = flatten(i)
            flat_v = flatten(v)
            if len(flat_i) != len(flat_v):
                raise ValueError(
                    "Could not flatten dictionary. Key had %d elements, but value had "
                    "%d elements. Key: %s, value: %s."
                    % (len(flat_i), len(flat_v), flat_i, flat_v))
            for new_i, new_v in zip(flat_i, flat_v):
                if new_i in flat_dictionary:
                    raise ValueError(
                        "Could not flatten dictionary: key %s is not unique."
                        % (new_i))
                flat_dictionary[new_i] = new_v
    return flat_dictionary


def _packed_nest_with_indices(structure, flat, index):
    """Helper function for pack_sequence_as.

    Args:
      structure: Substructure (list / tuple / dict) to mimic.
      flat: Flattened values to output substructure for.
      index: Index at which to start reading from flat.

    Returns:
      The tuple (new_index, child), where:
        * new_index - the updated index into `flat` having processed `structure`.
        * packed - the subset of `flat` corresponding to `structure`,
                   having started at `index`, and packed into the same nested
                   format.

    Raises:
      ValueError: if `structure` contains more elements than `flat`
        (assuming indexing starts from `index`).
    """
    packed = []
    for s in _yield_value(structure):
        if is_sequence(s):
            new_index, child = _packed_nest_with_indices(s, flat, index)
            packed.append(_sequence_like(s, child))
            index = new_index
        else:
            packed.append(flat[index])
            index += 1
    return index, packed


def pack_sequence_as(structure, flat_sequence):
    """Returns a given flattened sequence packed into a given structure.

    If `structure` is a scalar, `flat_sequence` must be a single-element list;
    in this case the return value is `flat_sequence[0]`.

    If `structure` is or contains a dict instance, the keys will be sorted to
    pack the flat sequence in deterministic order. This is true also for
    `OrderedDict` instances: their sequence order is ignored, the sorting order of
    keys is used instead. The same convention is followed in `pack_sequence_as`.
    This correctly repacks dicts and `OrderedDict`s after they have been
    flattened, and also allows flattening an `OrderedDict` and then repacking it
    back using a correponding plain dict, or vice-versa.
    Dictionaries with non-sortable keys cannot be flattened.

    Args:
      structure: Nested structure, whose structure is given by nested lists,
          tuples, and dicts. Note: numpy arrays and strings are considered
          scalars.
      flat_sequence: flat sequence to pack.

    Returns:
      packed: `flat_sequence` converted to have the same recursive structure as
        `structure`.

    Raises:
      ValueError: If `flat_sequence` and `structure` have different
        element counts.
      TypeError: `structure` is or contains a dict with non-sortable keys.
    """
    if not is_sequence(flat_sequence):
        raise TypeError("flat_sequence must be a sequence")

    if not is_sequence(structure):
        if len(flat_sequence) != 1:
            raise ValueError("Structure is a scalar but len(flat_sequence) == %d > 1"
                             % len(flat_sequence))
        return flat_sequence[0]

    flat_structure = flatten(structure)
    if len(flat_structure) != len(flat_sequence):
        raise ValueError(
            "Could not pack sequence. Structure had %d elements, but flat_sequence "
            "had %d elements.  Structure: %s, flat_sequence: %s."
            % (len(flat_structure), len(flat_sequence), structure, flat_sequence))

    _, packed = _packed_nest_with_indices(structure, flat_sequence, 0)
    return _sequence_like(structure, packed)


def map_structure(func, *structure, **check_types_dict):
    """Applies `func` to each entry in `structure` and returns a new structure.

    Applies `func(x[0], x[1], ...)` where x[i] is an entry in
    `structure[i]`.  All structures in `structure` must have the same arity,
    and the return value will contain the results in the same structure.

    Args:
      func: A callable that accepts as many arguments as there are structures.
      *structure: scalar, or tuple or list of constructed scalars and/or other
        tuples/lists, or scalars.  Note: numpy arrays are considered as scalars.
      **check_types_dict: only valid keyword argument is `check_types`. If set to
        `True` (default) the types of iterables within the structures have to be
        same (e.g. `map_structure(func, [1], (1,))` raises a `TypeError`
        exception). To allow this set this argument to `False`.

    Returns:
      A new structure with the same arity as `structure`, whose values correspond
      to `func(x[0], x[1], ...)` where `x[i]` is a value in the corresponding
      location in `structure[i]`. If there are different sequence types and
      `check_types` is `False` the sequence types of the first structure will be
      used.

    Raises:
      TypeError: If `func` is not callable or if the structures do not match
        each other by depth tree.
      ValueError: If no structure is provided or if the structures do not match
        each other by type.
      ValueError: If wrong keyword arguments are provided.
    """
    if not callable(func):
        raise TypeError("func must be callable, got: %s" % func)

    if not structure:
        raise ValueError("Must provide at least one structure")

    if check_types_dict:
        if "check_types" not in check_types_dict or len(check_types_dict) > 1:
            raise ValueError("Only valid keyword argument is check_types")
        check_types = check_types_dict["check_types"]
    else:
        check_types = True

    for other in structure[1:]:
        assert_same_structure(structure[0], other, check_types=check_types)

    flat_structure = [flatten(s) for s in structure]
    entries = zip(*flat_structure)

    return pack_sequence_as(
        structure[0], [func(*x) for x in entries])


def _yield_flat_up_to(shallow_tree, input_tree):
    """Yields elements `input_tree` partially flattened up to `shallow_tree`."""
    if is_sequence(shallow_tree):
        for shallow_branch, input_branch in zip(_yield_value(shallow_tree),
                                                _yield_value(input_tree)):
            for input_leaf in _yield_flat_up_to(shallow_branch, input_branch):
                yield input_leaf
    else:
        yield input_tree


def assert_shallow_structure(shallow_tree, input_tree, check_types=True):
    """Asserts that `shallow_tree` is a shallow structure of `input_tree`.

    That is, this function tests if the `input_tree` structure can be created from
    the `shallow_tree` structure by replacing its leaf nodes with deeper
    tree structures.

    Examples:

    The following code will raise an exception:
    ```python
      shallow_tree = ["a", "b"]
      input_tree = ["c", ["d", "e"], "f"]
      assert_shallow_structure(shallow_tree, input_tree)
    ```

    The following code will not raise an exception:
    ```python
      shallow_tree = ["a", "b"]
      input_tree = ["c", ["d", "e"]]
      assert_shallow_structure(shallow_tree, input_tree)
    ```

    Args:
      shallow_tree: an arbitrarily nested structure.
      input_tree: an arbitrarily nested structure.
      check_types: if `True` (default) the sequence types of `shallow_tree` and
        `input_tree` have to be the same.

    Raises:
      TypeError: If `shallow_tree` is a sequence but `input_tree` is not.
      TypeError: If the sequence types of `shallow_tree` are different from
        `input_tree`. Only raised if `check_types` is `True`.
      ValueError: If the sequence lengths of `shallow_tree` are different from
        `input_tree`.
    """
    if is_sequence(shallow_tree):
        if not is_sequence(input_tree):
            raise TypeError(
                "If shallow structure is a sequence, input must also be a sequence. "
                "Input has type: %s." % type(input_tree))

        if check_types and not isinstance(input_tree, type(shallow_tree)):
            raise TypeError(
                "The two structures don't have the same sequence type. Input "
                "structure has type %s, while shallow structure has type %s."
                % (type(input_tree), type(shallow_tree)))

        if len(input_tree) != len(shallow_tree):
            raise ValueError(
                "The two structures don't have the same sequence length. Input "
                "structure has length %s, while shallow structure has length %s."
                % (len(input_tree), len(shallow_tree)))

        for shallow_branch, input_branch in zip(shallow_tree, input_tree):
            assert_shallow_structure(shallow_branch, input_branch,
                                     check_types=check_types)


def flatten_up_to(shallow_tree, input_tree):
    """Flattens `input_tree` up to `shallow_tree`.

    Any further depth in structure in `input_tree` is retained as elements in the
    partially flatten output.

    If `shallow_tree` and `input_tree` are not sequences, this returns a
    single-element list: `[input_tree]`.

    Use Case:

    Sometimes we may wish to partially flatten a nested sequence, retaining some
    of the nested structure. We achieve this by specifying a shallow structure,
    `shallow_tree`, we wish to flatten up to.

    The input, `input_tree`, can be thought of as having the same structure as
    `shallow_tree`, but with leaf nodes that are themselves tree structures.

    Examples:

    ```python
    input_tree = [[[2, 2], [3, 3]], [[4, 9], [5, 5]]]
    shallow_tree = [[True, True], [False, True]]

    flattened_input_tree = flatten_up_to(shallow_tree, input_tree)
    flattened_shallow_tree = flatten_up_to(shallow_tree, shallow_tree)

    # Output is:
    # [[2, 2], [3, 3], [4, 9], [5, 5]]
    # [True, True, False, True]
    ```

    ```python
    input_tree = [[('a', 1), [('b', 2), [('c', 3), [('d', 4)]]]]]
    shallow_tree = [['level_1', ['level_2', ['level_3', ['level_4']]]]]

    input_tree_flattened_as_shallow_tree = flatten_up_to(shallow_tree, input_tree)
    input_tree_flattened = flatten(input_tree)

    # Output is:
    # [('a', 1), ('b', 2), ('c', 3), ('d', 4)]
    # ['a', 1, 'b', 2, 'c', 3, 'd', 4]
    ```

    Non-Sequence Edge Cases:

    ```python
    flatten_up_to(0, 0)  # Output: [0]
    flatten_up_to(0, [0, 1, 2])  # Output: [[0, 1, 2]]
    flatten_up_to([0, 1, 2], 0)  # Output: TypeError
    flatten_up_to([0, 1, 2], [0, 1, 2])  # Output: [0, 1, 2]
    ```

    Args:
      shallow_tree: a possibly pruned structure of input_tree.
      input_tree: an arbitrarily nested structure or a scalar object.
        Note, numpy arrays are considered scalars.

    Returns:
      A Python list, the partially flattened version of `input_tree` according to
      the structure of `shallow_tree`.

    Raises:
      TypeError: If `shallow_tree` is a sequence but `input_tree` is not.
      TypeError: If the sequence types of `shallow_tree` are different from
        `input_tree`.
      ValueError: If the sequence lengths of `shallow_tree` are different from
        `input_tree`.
    """
    assert_shallow_structure(shallow_tree, input_tree)
    return list(_yield_flat_up_to(shallow_tree, input_tree))


def map_structure_up_to(shallow_tree, func, *inputs):
    """Applies a function or op to a number of partially flattened inputs.

    The `inputs` are flattened up to `shallow_tree` before being mapped.

    Use Case:

    Sometimes we wish to apply a function to a partially flattened
    sequence (for example when the function itself takes sequence inputs). We
    achieve this by specifying a shallow structure, `shallow_tree` we wish to
    flatten up to.

    The `inputs`, can be thought of as having the same structure as
    `shallow_tree`, but with leaf nodes that are themselves tree structures.

    This function therefore will return something with the same base structure as
    `shallow_tree`.

    Examples:

    ```python
    ab_tuple = collections.namedtuple("ab_tuple", "a, b")
    op_tuple = collections.namedtuple("op_tuple", "add, mul")
    inp_val = ab_tuple(a=2, b=3)
    inp_ops = ab_tuple(a=op_tuple(add=1, mul=2), b=op_tuple(add=2, mul=3))
    out = map_structure_up_to(inp_val, lambda val, ops: (val + ops.add) * ops.mul,
                              inp_val, inp_ops)

    # Output is: ab_tuple(a=6, b=15)
    ```

    ```python
    data_list = [[2, 4, 6, 8], [[1, 3, 5, 7, 9], [3, 5, 7]]]
    name_list = ['evens', ['odds', 'primes']]
    out = map_structure_up_to(
        name_list,
        lambda name, sec: "first_{}_{}".format(len(sec), name),
        name_list, data_list)

    # Output is: ['first_4_evens', ['first_5_odds', 'first_3_primes']]
    ```

    Args:
      shallow_tree: a shallow tree, common to all the inputs.
      func: callable which will be applied to each input individually.
      *inputs: arbitrarily nested combination of objects that are compatible with
          shallow_tree. The function `func` is applied to corresponding
          partially flattened elements of each input, so the function must support
          arity of `len(inputs)`.

    Raises:
      TypeError: If `shallow_tree` is a sequence but `input_tree` is not.
      TypeError: If the sequence types of `shallow_tree` are different from
        `input_tree`.
      ValueError: If the sequence lengths of `shallow_tree` are different from
        `input_tree`.

    Returns:
      result of repeatedly applying `func`, with same structure as
      `shallow_tree`.
    """
    if not inputs:
        raise ValueError("Cannot map over no sequences")
    for input_tree in inputs:
        assert_shallow_structure(shallow_tree, input_tree)

    # Flatten each input separately, apply the function to corresponding elements,
    # then repack based on the structure of the first input.
    all_flattened_up_to = [flatten_up_to(shallow_tree, input_tree)
                           for input_tree in inputs]
    results = [func(*tensors) for tensors in zip(*all_flattened_up_to)]
    return pack_sequence_as(structure=shallow_tree, flat_sequence=results)


def get_traverse_shallow_structure(traverse_fn, structure):
    """Generates a shallow structure from a `traverse_fn` and `structure`.

    `traverse_fn` must accept any possible subtree of `structure` and return
    a depth=1 structure containing `True` or `False` values, describing which
    of the top-level subtrees may be traversed.  It may also
    return scalar `True` or `False` "traversal is OK / not OK for all subtrees."

    Examples are available in the unit tests (nest_test.py).

    Args:
      traverse_fn: Function taking a substructure and returning either a scalar
        `bool` (whether to traverse that substructure or not) or a depth=1
        shallow structure of the same type, describing which parts of the
        substructure to traverse.
      structure: The structure to traverse.

    Returns:
      A shallow structure containing python bools, which can be passed to
      `map_structure_up_to` and `flatten_up_to`.

    Raises:
      TypeError: if `traverse_fn` returns a sequence for a non-sequence input,
        or a structure with depth higher than 1 for a sequence input,
        or if any leaf values in the returned structure or scalar are not type
        `bool`.
    """
    to_traverse = traverse_fn(structure)
    if not is_sequence(structure):
        if not isinstance(to_traverse, bool):
            raise TypeError("traverse_fn returned structure: %s for non-structure: %s"
                            % (to_traverse, structure))
        return to_traverse
    level_traverse = []
    if isinstance(to_traverse, bool):
        if not to_traverse:
            # Do not traverse this substructure at all.  Exit early.
            return False
        else:
            # Traverse the entire substructure.
            for branch in _yield_value(structure):
                level_traverse.append(
                    get_traverse_shallow_structure(traverse_fn, branch))
    elif not is_sequence(to_traverse):
        raise TypeError("traverse_fn returned a non-bool scalar: %s for input: %s"
                        % (to_traverse, structure))
    else:
        # Traverse some subset of this substructure.
        assert_shallow_structure(to_traverse, structure)
        for t, branch in zip(_yield_value(to_traverse), _yield_value(structure)):
            if not isinstance(t, bool):
                raise TypeError(
                    "traverse_fn didn't return a depth=1 structure of bools.  saw: %s "
                    " for structure: %s" % (to_traverse, structure))
            if t:
                level_traverse.append(
                    get_traverse_shallow_structure(traverse_fn, branch))
            else:
                level_traverse.append(False)
    return _sequence_like(structure, level_traverse)