# pylint:  disable=too-many-lines
# (Yes, it has a point!)

from __future__ import division, absolute_import, print_function

__copyright__ = "Copyright (C) 2009-2013 Andreas Kloeckner"

__license__ = """
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 functools import reduce
import operator
import sys
import logging
from typing import (
        Any, Callable, Dict, Iterable, List, Optional, Set, Tuple, TypeVar)


import six
from six.moves import range, zip, intern, input


decorator_module = __import__("decorator", level=0)
my_decorator = decorator_module.decorator

__doc__ = """
A Collection of Utilities
=========================

Math
----

.. autofunction:: levi_civita
.. autofunction:: perm
.. autofunction:: comb

Assertive accessors
-------------------

.. autofunction:: one
.. autofunction:: is_single_valued
.. autofunction:: all_roughly_equal
.. autofunction:: single_valued

Memoization
-----------

.. autofunction:: memoize
.. autofunction:: memoize_on_first_arg
.. autofunction:: memoize_method
.. autofunction:: memoize_in
.. autofunction:: keyed_memoize_on_first_arg
.. autofunction:: keyed_memoize_method

Argmin/max
----------

.. autofunction:: argmin2
.. autofunction:: argmax2
.. autofunction:: argmin
.. autofunction:: argmax

Cartesian products
------------------
.. autofunction:: cartesian_product
.. autofunction:: distinct_pairs

Permutations, Tuples, Integer sequences
---------------------------------------

.. autofunction:: wandering_element
.. autofunction:: generate_nonnegative_integer_tuples_below
.. autofunction:: generate_nonnegative_integer_tuples_summing_to_at_most
.. autofunction:: generate_all_nonnegative_integer_tuples
.. autofunction:: generate_all_integer_tuples_below
.. autofunction:: generate_all_integer_tuples
.. autofunction:: generate_permutations
.. autofunction:: generate_unique_permutations

Formatting
----------

.. autoclass:: Table
.. autofunction:: string_histogram
.. autofunction:: word_wrap

Debugging
---------

.. autofunction:: typedump
.. autofunction:: invoke_editor

Progress bars
-------------

.. autoclass:: ProgressBar

Name generation
---------------

.. autofunction:: generate_unique_names
.. autofunction:: generate_numbered_unique_names
.. autoclass:: UniqueNameGenerator

Functions for dealing with (large) auxiliary files
--------------------------------------------------

.. autofunction:: download_from_web_if_not_present

Helpers for :mod:`numpy`
------------------------

.. autofunction:: reshaped_view


Timing data
-----------

.. data:: SUPPORTS_PROCESS_TIME

   A :class:`bool` indicating whether :class:`ProcessTimer` measures elapsed
   process time (available on Python 3.3+).

.. autoclass:: ProcessTimer

Log utilities
-------------

.. autoclass:: ProcessLogger
.. autoclass:: DebugProcessLogger
.. autoclass:: log_process

Sorting in natural order
------------------------

.. autofunction:: natorder
.. autofunction:: natsorted
"""

# {{{ type variables

T = TypeVar("T")
F = TypeVar('F', bound=Callable[..., Any])

# }}}


# {{{ math --------------------------------------------------------------------

def delta(x, y):
    if x == y:
        return 1
    else:
        return 0


def levi_civita(tup):
    """Compute an entry of the Levi-Civita tensor for the indices *tuple*."""
    if len(tup) == 2:
        i, j = tup
        return j-i
    if len(tup) == 3:
        i, j, k = tup
        return (j-i)*(k-i)*(k-j)/2
    else:
        raise NotImplementedError


def factorial(n):
    from operator import mul
    assert n == int(n)
    return reduce(mul, (i for i in range(1, n+1)), 1)


def perm(n, k):
    """Return P(n, k), the number of permutations of length k drawn from n
    choices.
    """
    result = 1
    assert k > 0
    while k:
        result *= n
        n -= 1
        k -= 1

    return result


def comb(n, k):
    """Return C(n, k), the number of combinations (subsets)
    of length k drawn from n choices.
    """
    return perm(n, k)//factorial(k)


def norm_1(iterable):
    return sum(abs(x) for x in iterable)


def norm_2(iterable):
    return sum(x**2 for x in iterable)**0.5


def norm_inf(iterable):
    return max(abs(x) for x in iterable)


def norm_p(iterable, p):
    return sum(i**p for i in iterable)**(1/p)


class Norm(object):
    def __init__(self, p):
        self.p = p

    def __call__(self, iterable):
        return sum(i**self.p for i in iterable)**(1/self.p)

# }}}


# {{{ data structures

# {{{ record

class RecordWithoutPickling(object):
    """An aggregate of named sub-variables. Assumes that each record sub-type
    will be individually derived from this class.
    """

    __slots__: List[str] = []

    def __init__(self, valuedict=None, exclude=None, **kwargs):
        assert self.__class__ is not Record

        if exclude is None:
            exclude = ["self"]

        try:
            fields = self.__class__.fields
        except AttributeError:
            self.__class__.fields = fields = set()

        if valuedict is not None:
            kwargs.update(valuedict)

        for key, value in six.iteritems(kwargs):
            if key not in exclude:
                fields.add(key)
                setattr(self, key, value)

    def get_copy_kwargs(self, **kwargs):
        for f in self.__class__.fields:
            if f not in kwargs:
                try:
                    kwargs[f] = getattr(self, f)
                except AttributeError:
                    pass
        return kwargs

    def copy(self, **kwargs):
        return self.__class__(**self.get_copy_kwargs(**kwargs))

    def __repr__(self):
        return "%s(%s)" % (
                self.__class__.__name__,
                ", ".join("%s=%r" % (fld, getattr(self, fld))
                    for fld in self.__class__.fields
                    if hasattr(self, fld)))

    def register_fields(self, new_fields):
        try:
            fields = self.__class__.fields
        except AttributeError:
            self.__class__.fields = fields = set()

        fields.update(new_fields)

    def __getattr__(self, name):
        # This method is implemented to avoid pylint 'no-member' errors for
        # attribute access.
        raise AttributeError(
                "'%s' object has no attribute '%s'" % (
                    self.__class__.__name__, name))


class Record(RecordWithoutPickling):
    __slots__: List[str] = []

    def __getstate__(self):
        return dict(
                (key, getattr(self, key))
                for key in self.__class__.fields
                if hasattr(self, key))

    def __setstate__(self, valuedict):
        try:
            fields = self.__class__.fields
        except AttributeError:
            self.__class__.fields = fields = set()

        for key, value in six.iteritems(valuedict):
            fields.add(key)
            setattr(self, key, value)

    def __eq__(self, other):
        return (self.__class__ == other.__class__
                and self.__getstate__() == other.__getstate__())

    def __ne__(self, other):
        return not self.__eq__(other)


class ImmutableRecordWithoutPickling(RecordWithoutPickling):
    "Hashable record. Does not explicitly enforce immutability."
    def __init__(self, *args, **kwargs):
        RecordWithoutPickling.__init__(self, *args, **kwargs)
        self._cached_hash = None

    def __hash__(self):
        if self._cached_hash is None:
            self._cached_hash = hash(
                (type(self),) + tuple(getattr(self, field)
                    for field in self.__class__.fields))

        return self._cached_hash