Function _rank

Lib/statistics.py:1651–1702

Rank order a dataset. The lowest value has rank 1. Ties are averaged so that equal values receive the same rank: >>> data = [31, 56, 31, 25, 75, 18] >>> _rank(data) [3.5, 5.0, 3.5, 2.0, 6.0, 1.0] The operation is idempotent: >>> _rank([3.5, 5.0, 3.5, 2.0,

(data, /, *, key=None, reverse=False, ties='average', start=1)

def _rank(data, /, *, key=None, reverse=False, ties='average', start=1) -> list[float]:
    """Rank order a dataset. The lowest value has rank 1.

    Ties are averaged so that equal values receive the same rank:

        >>> data = [31, 56, 31, 25, 75, 18]
        >>> _rank(data)
        [3.5, 5.0, 3.5, 2.0, 6.0, 1.0]

    The operation is idempotent:

        >>> _rank([3.5, 5.0, 3.5, 2.0, 6.0, 1.0])
        [3.5, 5.0, 3.5, 2.0, 6.0, 1.0]

    It is possible to rank the data in reverse order so that the
    highest value has rank 1.  Also, a key-function can extract
    the field to be ranked:

        >>> goals = [('eagles', 45), ('bears', 48), ('lions', 44)]
        >>> _rank(goals, key=itemgetter(1), reverse=True)
        [2.0, 1.0, 3.0]

    Ranks are conventionally numbered starting from one; however,
    setting *start* to zero allows the ranks to be used as array indices:

        >>> prize = ['Gold', 'Silver', 'Bronze', 'Certificate']
        >>> scores = [8.1, 7.3, 9.4, 8.3]
        >>> [prize[int(i)] for i in _rank(scores, start=0, reverse=True)]
        ['Bronze', 'Certificate', 'Gold', 'Silver']

    """
    # If this function becomes public at some point, more thought
    # needs to be given to the signature.  A list of ints is
    # plausible when ties is "min" or "max".  When ties is "average",
    # either list[float] or list[Fraction] is plausible.

    # Default handling of ties matches scipy.stats.mstats.spearmanr.
    if ties != 'average':
        raise ValueError(f'Unknown tie resolution method: {ties!r}')
    if key is not None:
        data = map(key, data)
    val_pos = sorted(zip(data, count()), reverse=reverse)
    i = start - 1
    result = [0] * len(val_pos)
    for _, g in groupby(val_pos, key=itemgetter(0)):
        group = list(g)
        size = len(group)
        rank = i + (size + 1) / 2
        for value, orig_pos in group:
            result[orig_pos] = rank
        i += size
    return result


def _integer_sqrt_of_frac_rto(n: int, m: int) -> int: