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diff --git a/.venv/lib/python3.12/site-packages/setuptools/_vendor/more_itertools/recipes.py b/.venv/lib/python3.12/site-packages/setuptools/_vendor/more_itertools/recipes.py new file mode 100644 index 00000000..b32fa955 --- /dev/null +++ b/.venv/lib/python3.12/site-packages/setuptools/_vendor/more_itertools/recipes.py @@ -0,0 +1,1046 @@ +"""Imported from the recipes section of the itertools documentation. + +All functions taken from the recipes section of the itertools library docs +[1]_. +Some backward-compatible usability improvements have been made. + +.. [1] http://docs.python.org/library/itertools.html#recipes + +""" + +import math +import operator + +from collections import deque +from collections.abc import Sized +from functools import partial, reduce +from itertools import ( + chain, + combinations, + compress, + count, + cycle, + groupby, + islice, + product, + repeat, + starmap, + tee, + zip_longest, +) +from random import randrange, sample, choice +from sys import hexversion + +__all__ = [ + 'all_equal', + 'batched', + 'before_and_after', + 'consume', + 'convolve', + 'dotproduct', + 'first_true', + 'factor', + 'flatten', + 'grouper', + 'iter_except', + 'iter_index', + 'matmul', + 'ncycles', + 'nth', + 'nth_combination', + 'padnone', + 'pad_none', + 'pairwise', + 'partition', + 'polynomial_eval', + 'polynomial_from_roots', + 'polynomial_derivative', + 'powerset', + 'prepend', + 'quantify', + 'reshape', + 'random_combination_with_replacement', + 'random_combination', + 'random_permutation', + 'random_product', + 'repeatfunc', + 'roundrobin', + 'sieve', + 'sliding_window', + 'subslices', + 'sum_of_squares', + 'tabulate', + 'tail', + 'take', + 'totient', + 'transpose', + 'triplewise', + 'unique', + 'unique_everseen', + 'unique_justseen', +] + +_marker = object() + + +# zip with strict is available for Python 3.10+ +try: + zip(strict=True) +except TypeError: + _zip_strict = zip +else: + _zip_strict = partial(zip, strict=True) + +# math.sumprod is available for Python 3.12+ +_sumprod = getattr(math, 'sumprod', lambda x, y: dotproduct(x, y)) + + +def take(n, iterable): + """Return first *n* items of the iterable as a list. + + >>> take(3, range(10)) + [0, 1, 2] + + If there are fewer than *n* items in the iterable, all of them are + returned. + + >>> take(10, range(3)) + [0, 1, 2] + + """ + return list(islice(iterable, n)) + + +def tabulate(function, start=0): + """Return an iterator over the results of ``func(start)``, + ``func(start + 1)``, ``func(start + 2)``... + + *func* should be a function that accepts one integer argument. + + If *start* is not specified it defaults to 0. It will be incremented each + time the iterator is advanced. + + >>> square = lambda x: x ** 2 + >>> iterator = tabulate(square, -3) + >>> take(4, iterator) + [9, 4, 1, 0] + + """ + return map(function, count(start)) + + +def tail(n, iterable): + """Return an iterator over the last *n* items of *iterable*. + + >>> t = tail(3, 'ABCDEFG') + >>> list(t) + ['E', 'F', 'G'] + + """ + # If the given iterable has a length, then we can use islice to get its + # final elements. Note that if the iterable is not actually Iterable, + # either islice or deque will throw a TypeError. This is why we don't + # check if it is Iterable. + if isinstance(iterable, Sized): + yield from islice(iterable, max(0, len(iterable) - n), None) + else: + yield from iter(deque(iterable, maxlen=n)) + + +def consume(iterator, n=None): + """Advance *iterable* by *n* steps. If *n* is ``None``, consume it + entirely. + + Efficiently exhausts an iterator without returning values. Defaults to + consuming the whole iterator, but an optional second argument may be + provided to limit consumption. + + >>> i = (x for x in range(10)) + >>> next(i) + 0 + >>> consume(i, 3) + >>> next(i) + 4 + >>> consume(i) + >>> next(i) + Traceback (most recent call last): + File "<stdin>", line 1, in <module> + StopIteration + + If the iterator has fewer items remaining than the provided limit, the + whole iterator will be consumed. + + >>> i = (x for x in range(3)) + >>> consume(i, 5) + >>> next(i) + Traceback (most recent call last): + File "<stdin>", line 1, in <module> + StopIteration + + """ + # Use functions that consume iterators at C speed. + if n is None: + # feed the entire iterator into a zero-length deque + deque(iterator, maxlen=0) + else: + # advance to the empty slice starting at position n + next(islice(iterator, n, n), None) + + +def nth(iterable, n, default=None): + """Returns the nth item or a default value. + + >>> l = range(10) + >>> nth(l, 3) + 3 + >>> nth(l, 20, "zebra") + 'zebra' + + """ + return next(islice(iterable, n, None), default) + + +def all_equal(iterable, key=None): + """ + Returns ``True`` if all the elements are equal to each other. + + >>> all_equal('aaaa') + True + >>> all_equal('aaab') + False + + A function that accepts a single argument and returns a transformed version + of each input item can be specified with *key*: + + >>> all_equal('AaaA', key=str.casefold) + True + >>> all_equal([1, 2, 3], key=lambda x: x < 10) + True + + """ + return len(list(islice(groupby(iterable, key), 2))) <= 1 + + +def quantify(iterable, pred=bool): + """Return the how many times the predicate is true. + + >>> quantify([True, False, True]) + 2 + + """ + return sum(map(pred, iterable)) + + +def pad_none(iterable): + """Returns the sequence of elements and then returns ``None`` indefinitely. + + >>> take(5, pad_none(range(3))) + [0, 1, 2, None, None] + + Useful for emulating the behavior of the built-in :func:`map` function. + + See also :func:`padded`. + + """ + return chain(iterable, repeat(None)) + + +padnone = pad_none + + +def ncycles(iterable, n): + """Returns the sequence elements *n* times + + >>> list(ncycles(["a", "b"], 3)) + ['a', 'b', 'a', 'b', 'a', 'b'] + + """ + return chain.from_iterable(repeat(tuple(iterable), n)) + + +def dotproduct(vec1, vec2): + """Returns the dot product of the two iterables. + + >>> dotproduct([10, 10], [20, 20]) + 400 + + """ + return sum(map(operator.mul, vec1, vec2)) + + +def flatten(listOfLists): + """Return an iterator flattening one level of nesting in a list of lists. + + >>> list(flatten([[0, 1], [2, 3]])) + [0, 1, 2, 3] + + See also :func:`collapse`, which can flatten multiple levels of nesting. + + """ + return chain.from_iterable(listOfLists) + + +def repeatfunc(func, times=None, *args): + """Call *func* with *args* repeatedly, returning an iterable over the + results. + + If *times* is specified, the iterable will terminate after that many + repetitions: + + >>> from operator import add + >>> times = 4 + >>> args = 3, 5 + >>> list(repeatfunc(add, times, *args)) + [8, 8, 8, 8] + + If *times* is ``None`` the iterable will not terminate: + + >>> from random import randrange + >>> times = None + >>> args = 1, 11 + >>> take(6, repeatfunc(randrange, times, *args)) # doctest:+SKIP + [2, 4, 8, 1, 8, 4] + + """ + if times is None: + return starmap(func, repeat(args)) + return starmap(func, repeat(args, times)) + + +def _pairwise(iterable): + """Returns an iterator of paired items, overlapping, from the original + + >>> take(4, pairwise(count())) + [(0, 1), (1, 2), (2, 3), (3, 4)] + + On Python 3.10 and above, this is an alias for :func:`itertools.pairwise`. + + """ + a, b = tee(iterable) + next(b, None) + return zip(a, b) + + +try: + from itertools import pairwise as itertools_pairwise +except ImportError: + pairwise = _pairwise +else: + + def pairwise(iterable): + return itertools_pairwise(iterable) + + pairwise.__doc__ = _pairwise.__doc__ + + +class UnequalIterablesError(ValueError): + def __init__(self, details=None): + msg = 'Iterables have different lengths' + if details is not None: + msg += (': index 0 has length {}; index {} has length {}').format( + *details + ) + + super().__init__(msg) + + +def _zip_equal_generator(iterables): + for combo in zip_longest(*iterables, fillvalue=_marker): + for val in combo: + if val is _marker: + raise UnequalIterablesError() + yield combo + + +def _zip_equal(*iterables): + # Check whether the iterables are all the same size. + try: + first_size = len(iterables[0]) + for i, it in enumerate(iterables[1:], 1): + size = len(it) + if size != first_size: + raise UnequalIterablesError(details=(first_size, i, size)) + # All sizes are equal, we can use the built-in zip. + return zip(*iterables) + # If any one of the iterables didn't have a length, start reading + # them until one runs out. + except TypeError: + return _zip_equal_generator(iterables) + + +def grouper(iterable, n, incomplete='fill', fillvalue=None): + """Group elements from *iterable* into fixed-length groups of length *n*. + + >>> list(grouper('ABCDEF', 3)) + [('A', 'B', 'C'), ('D', 'E', 'F')] + + The keyword arguments *incomplete* and *fillvalue* control what happens for + iterables whose length is not a multiple of *n*. + + When *incomplete* is `'fill'`, the last group will contain instances of + *fillvalue*. + + >>> list(grouper('ABCDEFG', 3, incomplete='fill', fillvalue='x')) + [('A', 'B', 'C'), ('D', 'E', 'F'), ('G', 'x', 'x')] + + When *incomplete* is `'ignore'`, the last group will not be emitted. + + >>> list(grouper('ABCDEFG', 3, incomplete='ignore', fillvalue='x')) + [('A', 'B', 'C'), ('D', 'E', 'F')] + + When *incomplete* is `'strict'`, a subclass of `ValueError` will be raised. + + >>> it = grouper('ABCDEFG', 3, incomplete='strict') + >>> list(it) # doctest: +IGNORE_EXCEPTION_DETAIL + Traceback (most recent call last): + ... + UnequalIterablesError + + """ + args = [iter(iterable)] * n + if incomplete == 'fill': + return zip_longest(*args, fillvalue=fillvalue) + if incomplete == 'strict': + return _zip_equal(*args) + if incomplete == 'ignore': + return zip(*args) + else: + raise ValueError('Expected fill, strict, or ignore') + + +def roundrobin(*iterables): + """Yields an item from each iterable, alternating between them. + + >>> list(roundrobin('ABC', 'D', 'EF')) + ['A', 'D', 'E', 'B', 'F', 'C'] + + This function produces the same output as :func:`interleave_longest`, but + may perform better for some inputs (in particular when the number of + iterables is small). + + """ + # Algorithm credited to George Sakkis + iterators = map(iter, iterables) + for num_active in range(len(iterables), 0, -1): + iterators = cycle(islice(iterators, num_active)) + yield from map(next, iterators) + + +def partition(pred, iterable): + """ + Returns a 2-tuple of iterables derived from the input iterable. + The first yields the items that have ``pred(item) == False``. + The second yields the items that have ``pred(item) == True``. + + >>> is_odd = lambda x: x % 2 != 0 + >>> iterable = range(10) + >>> even_items, odd_items = partition(is_odd, iterable) + >>> list(even_items), list(odd_items) + ([0, 2, 4, 6, 8], [1, 3, 5, 7, 9]) + + If *pred* is None, :func:`bool` is used. + + >>> iterable = [0, 1, False, True, '', ' '] + >>> false_items, true_items = partition(None, iterable) + >>> list(false_items), list(true_items) + ([0, False, ''], [1, True, ' ']) + + """ + if pred is None: + pred = bool + + t1, t2, p = tee(iterable, 3) + p1, p2 = tee(map(pred, p)) + return (compress(t1, map(operator.not_, p1)), compress(t2, p2)) + + +def powerset(iterable): + """Yields all possible subsets of the iterable. + + >>> list(powerset([1, 2, 3])) + [(), (1,), (2,), (3,), (1, 2), (1, 3), (2, 3), (1, 2, 3)] + + :func:`powerset` will operate on iterables that aren't :class:`set` + instances, so repeated elements in the input will produce repeated elements + in the output. + + >>> seq = [1, 1, 0] + >>> list(powerset(seq)) + [(), (1,), (1,), (0,), (1, 1), (1, 0), (1, 0), (1, 1, 0)] + + For a variant that efficiently yields actual :class:`set` instances, see + :func:`powerset_of_sets`. + """ + s = list(iterable) + return chain.from_iterable(combinations(s, r) for r in range(len(s) + 1)) + + +def unique_everseen(iterable, key=None): + """ + Yield unique elements, preserving order. + + >>> list(unique_everseen('AAAABBBCCDAABBB')) + ['A', 'B', 'C', 'D'] + >>> list(unique_everseen('ABBCcAD', str.lower)) + ['A', 'B', 'C', 'D'] + + Sequences with a mix of hashable and unhashable items can be used. + The function will be slower (i.e., `O(n^2)`) for unhashable items. + + Remember that ``list`` objects are unhashable - you can use the *key* + parameter to transform the list to a tuple (which is hashable) to + avoid a slowdown. + + >>> iterable = ([1, 2], [2, 3], [1, 2]) + >>> list(unique_everseen(iterable)) # Slow + [[1, 2], [2, 3]] + >>> list(unique_everseen(iterable, key=tuple)) # Faster + [[1, 2], [2, 3]] + + Similarly, you may want to convert unhashable ``set`` objects with + ``key=frozenset``. For ``dict`` objects, + ``key=lambda x: frozenset(x.items())`` can be used. + + """ + seenset = set() + seenset_add = seenset.add + seenlist = [] + seenlist_add = seenlist.append + use_key = key is not None + + for element in iterable: + k = key(element) if use_key else element + try: + if k not in seenset: + seenset_add(k) + yield element + except TypeError: + if k not in seenlist: + seenlist_add(k) + yield element + + +def unique_justseen(iterable, key=None): + """Yields elements in order, ignoring serial duplicates + + >>> list(unique_justseen('AAAABBBCCDAABBB')) + ['A', 'B', 'C', 'D', 'A', 'B'] + >>> list(unique_justseen('ABBCcAD', str.lower)) + ['A', 'B', 'C', 'A', 'D'] + + """ + if key is None: + return map(operator.itemgetter(0), groupby(iterable)) + + return map(next, map(operator.itemgetter(1), groupby(iterable, key))) + + +def unique(iterable, key=None, reverse=False): + """Yields unique elements in sorted order. + + >>> list(unique([[1, 2], [3, 4], [1, 2]])) + [[1, 2], [3, 4]] + + *key* and *reverse* are passed to :func:`sorted`. + + >>> list(unique('ABBcCAD', str.casefold)) + ['A', 'B', 'c', 'D'] + >>> list(unique('ABBcCAD', str.casefold, reverse=True)) + ['D', 'c', 'B', 'A'] + + The elements in *iterable* need not be hashable, but they must be + comparable for sorting to work. + """ + return unique_justseen(sorted(iterable, key=key, reverse=reverse), key=key) + + +def iter_except(func, exception, first=None): + """Yields results from a function repeatedly until an exception is raised. + + Converts a call-until-exception interface to an iterator interface. + Like ``iter(func, sentinel)``, but uses an exception instead of a sentinel + to end the loop. + + >>> l = [0, 1, 2] + >>> list(iter_except(l.pop, IndexError)) + [2, 1, 0] + + Multiple exceptions can be specified as a stopping condition: + + >>> l = [1, 2, 3, '...', 4, 5, 6] + >>> list(iter_except(lambda: 1 + l.pop(), (IndexError, TypeError))) + [7, 6, 5] + >>> list(iter_except(lambda: 1 + l.pop(), (IndexError, TypeError))) + [4, 3, 2] + >>> list(iter_except(lambda: 1 + l.pop(), (IndexError, TypeError))) + [] + + """ + try: + if first is not None: + yield first() + while 1: + yield func() + except exception: + pass + + +def first_true(iterable, default=None, pred=None): + """ + Returns the first true value in the iterable. + + If no true value is found, returns *default* + + If *pred* is not None, returns the first item for which + ``pred(item) == True`` . + + >>> first_true(range(10)) + 1 + >>> first_true(range(10), pred=lambda x: x > 5) + 6 + >>> first_true(range(10), default='missing', pred=lambda x: x > 9) + 'missing' + + """ + return next(filter(pred, iterable), default) + + +def random_product(*args, repeat=1): + """Draw an item at random from each of the input iterables. + + >>> random_product('abc', range(4), 'XYZ') # doctest:+SKIP + ('c', 3, 'Z') + + If *repeat* is provided as a keyword argument, that many items will be + drawn from each iterable. + + >>> random_product('abcd', range(4), repeat=2) # doctest:+SKIP + ('a', 2, 'd', 3) + + This equivalent to taking a random selection from + ``itertools.product(*args, **kwarg)``. + + """ + pools = [tuple(pool) for pool in args] * repeat + return tuple(choice(pool) for pool in pools) + + +def random_permutation(iterable, r=None): + """Return a random *r* length permutation of the elements in *iterable*. + + If *r* is not specified or is ``None``, then *r* defaults to the length of + *iterable*. + + >>> random_permutation(range(5)) # doctest:+SKIP + (3, 4, 0, 1, 2) + + This equivalent to taking a random selection from + ``itertools.permutations(iterable, r)``. + + """ + pool = tuple(iterable) + r = len(pool) if r is None else r + return tuple(sample(pool, r)) + + +def random_combination(iterable, r): + """Return a random *r* length subsequence of the elements in *iterable*. + + >>> random_combination(range(5), 3) # doctest:+SKIP + (2, 3, 4) + + This equivalent to taking a random selection from + ``itertools.combinations(iterable, r)``. + + """ + pool = tuple(iterable) + n = len(pool) + indices = sorted(sample(range(n), r)) + return tuple(pool[i] for i in indices) + + +def random_combination_with_replacement(iterable, r): + """Return a random *r* length subsequence of elements in *iterable*, + allowing individual elements to be repeated. + + >>> random_combination_with_replacement(range(3), 5) # doctest:+SKIP + (0, 0, 1, 2, 2) + + This equivalent to taking a random selection from + ``itertools.combinations_with_replacement(iterable, r)``. + + """ + pool = tuple(iterable) + n = len(pool) + indices = sorted(randrange(n) for i in range(r)) + return tuple(pool[i] for i in indices) + + +def nth_combination(iterable, r, index): + """Equivalent to ``list(combinations(iterable, r))[index]``. + + The subsequences of *iterable* that are of length *r* can be ordered + lexicographically. :func:`nth_combination` computes the subsequence at + sort position *index* directly, without computing the previous + subsequences. + + >>> nth_combination(range(5), 3, 5) + (0, 3, 4) + + ``ValueError`` will be raised If *r* is negative or greater than the length + of *iterable*. + ``IndexError`` will be raised if the given *index* is invalid. + """ + pool = tuple(iterable) + n = len(pool) + if (r < 0) or (r > n): + raise ValueError + + c = 1 + k = min(r, n - r) + for i in range(1, k + 1): + c = c * (n - k + i) // i + + if index < 0: + index += c + + if (index < 0) or (index >= c): + raise IndexError + + result = [] + while r: + c, n, r = c * r // n, n - 1, r - 1 + while index >= c: + index -= c + c, n = c * (n - r) // n, n - 1 + result.append(pool[-1 - n]) + + return tuple(result) + + +def prepend(value, iterator): + """Yield *value*, followed by the elements in *iterator*. + + >>> value = '0' + >>> iterator = ['1', '2', '3'] + >>> list(prepend(value, iterator)) + ['0', '1', '2', '3'] + + To prepend multiple values, see :func:`itertools.chain` + or :func:`value_chain`. + + """ + return chain([value], iterator) + + +def convolve(signal, kernel): + """Convolve the iterable *signal* with the iterable *kernel*. + + >>> signal = (1, 2, 3, 4, 5) + >>> kernel = [3, 2, 1] + >>> list(convolve(signal, kernel)) + [3, 8, 14, 20, 26, 14, 5] + + Note: the input arguments are not interchangeable, as the *kernel* + is immediately consumed and stored. + + """ + # This implementation intentionally doesn't match the one in the itertools + # documentation. + kernel = tuple(kernel)[::-1] + n = len(kernel) + window = deque([0], maxlen=n) * n + for x in chain(signal, repeat(0, n - 1)): + window.append(x) + yield _sumprod(kernel, window) + + +def before_and_after(predicate, it): + """A variant of :func:`takewhile` that allows complete access to the + remainder of the iterator. + + >>> it = iter('ABCdEfGhI') + >>> all_upper, remainder = before_and_after(str.isupper, it) + >>> ''.join(all_upper) + 'ABC' + >>> ''.join(remainder) # takewhile() would lose the 'd' + 'dEfGhI' + + Note that the first iterator must be fully consumed before the second + iterator can generate valid results. + """ + it = iter(it) + transition = [] + + def true_iterator(): + for elem in it: + if predicate(elem): + yield elem + else: + transition.append(elem) + return + + # Note: this is different from itertools recipes to allow nesting + # before_and_after remainders into before_and_after again. See tests + # for an example. + remainder_iterator = chain(transition, it) + + return true_iterator(), remainder_iterator + + +def triplewise(iterable): + """Return overlapping triplets from *iterable*. + + >>> list(triplewise('ABCDE')) + [('A', 'B', 'C'), ('B', 'C', 'D'), ('C', 'D', 'E')] + + """ + for (a, _), (b, c) in pairwise(pairwise(iterable)): + yield a, b, c + + +def sliding_window(iterable, n): + """Return a sliding window of width *n* over *iterable*. + + >>> list(sliding_window(range(6), 4)) + [(0, 1, 2, 3), (1, 2, 3, 4), (2, 3, 4, 5)] + + If *iterable* has fewer than *n* items, then nothing is yielded: + + >>> list(sliding_window(range(3), 4)) + [] + + For a variant with more features, see :func:`windowed`. + """ + it = iter(iterable) + window = deque(islice(it, n - 1), maxlen=n) + for x in it: + window.append(x) + yield tuple(window) + + +def subslices(iterable): + """Return all contiguous non-empty subslices of *iterable*. + + >>> list(subslices('ABC')) + [['A'], ['A', 'B'], ['A', 'B', 'C'], ['B'], ['B', 'C'], ['C']] + + This is similar to :func:`substrings`, but emits items in a different + order. + """ + seq = list(iterable) + slices = starmap(slice, combinations(range(len(seq) + 1), 2)) + return map(operator.getitem, repeat(seq), slices) + + +def polynomial_from_roots(roots): + """Compute a polynomial's coefficients from its roots. + + >>> roots = [5, -4, 3] # (x - 5) * (x + 4) * (x - 3) + >>> polynomial_from_roots(roots) # x^3 - 4 * x^2 - 17 * x + 60 + [1, -4, -17, 60] + """ + factors = zip(repeat(1), map(operator.neg, roots)) + return list(reduce(convolve, factors, [1])) + + +def iter_index(iterable, value, start=0, stop=None): + """Yield the index of each place in *iterable* that *value* occurs, + beginning with index *start* and ending before index *stop*. + + + >>> list(iter_index('AABCADEAF', 'A')) + [0, 1, 4, 7] + >>> list(iter_index('AABCADEAF', 'A', 1)) # start index is inclusive + [1, 4, 7] + >>> list(iter_index('AABCADEAF', 'A', 1, 7)) # stop index is not inclusive + [1, 4] + + The behavior for non-scalar *values* matches the built-in Python types. + + >>> list(iter_index('ABCDABCD', 'AB')) + [0, 4] + >>> list(iter_index([0, 1, 2, 3, 0, 1, 2, 3], [0, 1])) + [] + >>> list(iter_index([[0, 1], [2, 3], [0, 1], [2, 3]], [0, 1])) + [0, 2] + + See :func:`locate` for a more general means of finding the indexes + associated with particular values. + + """ + seq_index = getattr(iterable, 'index', None) + if seq_index is None: + # Slow path for general iterables + it = islice(iterable, start, stop) + for i, element in enumerate(it, start): + if element is value or element == value: + yield i + else: + # Fast path for sequences + stop = len(iterable) if stop is None else stop + i = start - 1 + try: + while True: + yield (i := seq_index(value, i + 1, stop)) + except ValueError: + pass + + +def sieve(n): + """Yield the primes less than n. + + >>> list(sieve(30)) + [2, 3, 5, 7, 11, 13, 17, 19, 23, 29] + """ + if n > 2: + yield 2 + start = 3 + data = bytearray((0, 1)) * (n // 2) + limit = math.isqrt(n) + 1 + for p in iter_index(data, 1, start, limit): + yield from iter_index(data, 1, start, p * p) + data[p * p : n : p + p] = bytes(len(range(p * p, n, p + p))) + start = p * p + yield from iter_index(data, 1, start) + + +def _batched(iterable, n, *, strict=False): + """Batch data into tuples of length *n*. If the number of items in + *iterable* is not divisible by *n*: + * The last batch will be shorter if *strict* is ``False``. + * :exc:`ValueError` will be raised if *strict* is ``True``. + + >>> list(batched('ABCDEFG', 3)) + [('A', 'B', 'C'), ('D', 'E', 'F'), ('G',)] + + On Python 3.13 and above, this is an alias for :func:`itertools.batched`. + """ + if n < 1: + raise ValueError('n must be at least one') + it = iter(iterable) + while batch := tuple(islice(it, n)): + if strict and len(batch) != n: + raise ValueError('batched(): incomplete batch') + yield batch + + +if hexversion >= 0x30D00A2: + from itertools import batched as itertools_batched + + def batched(iterable, n, *, strict=False): + return itertools_batched(iterable, n, strict=strict) + +else: + batched = _batched + + batched.__doc__ = _batched.__doc__ + + +def transpose(it): + """Swap the rows and columns of the input matrix. + + >>> list(transpose([(1, 2, 3), (11, 22, 33)])) + [(1, 11), (2, 22), (3, 33)] + + The caller should ensure that the dimensions of the input are compatible. + If the input is empty, no output will be produced. + """ + return _zip_strict(*it) + + +def reshape(matrix, cols): + """Reshape the 2-D input *matrix* to have a column count given by *cols*. + + >>> matrix = [(0, 1), (2, 3), (4, 5)] + >>> cols = 3 + >>> list(reshape(matrix, cols)) + [(0, 1, 2), (3, 4, 5)] + """ + return batched(chain.from_iterable(matrix), cols) + + +def matmul(m1, m2): + """Multiply two matrices. + + >>> list(matmul([(7, 5), (3, 5)], [(2, 5), (7, 9)])) + [(49, 80), (41, 60)] + + The caller should ensure that the dimensions of the input matrices are + compatible with each other. + """ + n = len(m2[0]) + return batched(starmap(_sumprod, product(m1, transpose(m2))), n) + + +def factor(n): + """Yield the prime factors of n. + + >>> list(factor(360)) + [2, 2, 2, 3, 3, 5] + """ + for prime in sieve(math.isqrt(n) + 1): + while not n % prime: + yield prime + n //= prime + if n == 1: + return + if n > 1: + yield n + + +def polynomial_eval(coefficients, x): + """Evaluate a polynomial at a specific value. + + Example: evaluating x^3 - 4 * x^2 - 17 * x + 60 at x = 2.5: + + >>> coefficients = [1, -4, -17, 60] + >>> x = 2.5 + >>> polynomial_eval(coefficients, x) + 8.125 + """ + n = len(coefficients) + if n == 0: + return x * 0 # coerce zero to the type of x + powers = map(pow, repeat(x), reversed(range(n))) + return _sumprod(coefficients, powers) + + +def sum_of_squares(it): + """Return the sum of the squares of the input values. + + >>> sum_of_squares([10, 20, 30]) + 1400 + """ + return _sumprod(*tee(it)) + + +def polynomial_derivative(coefficients): + """Compute the first derivative of a polynomial. + + Example: evaluating the derivative of x^3 - 4 * x^2 - 17 * x + 60 + + >>> coefficients = [1, -4, -17, 60] + >>> derivative_coefficients = polynomial_derivative(coefficients) + >>> derivative_coefficients + [3, -8, -17] + """ + n = len(coefficients) + powers = reversed(range(1, n)) + return list(map(operator.mul, coefficients, powers)) + + +def totient(n): + """Return the count of natural numbers up to *n* that are coprime with *n*. + + >>> totient(9) + 6 + >>> totient(12) + 4 + """ + # The itertools docs use unique_justseen instead of set; see + # https://github.com/more-itertools/more-itertools/issues/823 + for p in set(factor(n)): + n = n // p * (p - 1) + + return n |