from __future__ import division
import math
from lnt.external.stats.stats import mannwhitneyu as mannwhitneyu_large
from functools import reduce


def safe_min(values):
    """Calculate min, but if given an empty list return None."""
    values = list(values)  # In case this is a complex type, get a simple list.
    if not values:
        return None
    else:
        return min(values)


def safe_max(values):
    """Calculate max, but if given an empty list return None."""
    values = list(values)  # In case this is a complex type, get a simple list.
    if not values:
        return None
    else:
        return max(values)


def mean(values):
    if values:
        return sum(values) / len(values)
    else:
        return None


def geometric_mean(l):
    iPow = 1. / len(l)
    return reduce(lambda a, b: a * b, [v ** iPow for v in l])


def agg_mean(pairs):
    """Aggregation function in views.py receives input via enumerate and
       produces a tuple.
       Input: (value, index)
       Output: (mean, 0), or (None, None) on invalid input.
    """
    if not pairs:
        return None, None
    my_sum = 0.0
    counter = 0
    for item in pairs:
        my_sum += item[0]
        counter += 1
    if counter > 0:
        return my_sum / counter, 0
    return None, None


def median(values):
    if not values:
        return None
    values = sorted(values)
    N = len(values)
    return (values[(N - 1) // 2] + values[N // 2]) * .5


def median_absolute_deviation(values, med=None):
    if med is None:
        med = median(values)
    return median([abs(x - med) for x in values])


def standard_deviation(values):
    m = mean(values)
    means_sqrd = sum([(v - m) ** 2 for v in values]) / len(values)
    rms = math.sqrt(means_sqrd)
    return rms


def mannwhitneyu(a, b, sigLevel=.05):
    """
    Determine if sample a and b are the same at given significance level.
    """
    if len(a) <= 20 and len(b) <= 20:
        return mannwhitneyu_small(a, b, sigLevel)
    else:
        try:
            # MWU in SciPy is one-sided, multiply by 2 to get two-sided.
            p = mannwhitneyu_large(a, b) * 2
            return p >= sigLevel
        except ValueError:
            return True


def mannwhitneyu_small(a, b, sigLevel):
    """
    Determine if sample a and b are the same.
    Sample size must be less than 20.
    """
    assert len(a) <= 20, "Sample size must be less than 20."
    assert len(b) <= 20, "Sample size must be less than 20."

    if sigLevel not in SIGN_TABLES:
        raise ValueError("Do not have according significance table.")

    # Calculate U value for sample groups using method described on Wikipedia.
    flip = len(a) > len(b)
    x = a if not flip else b
    y = b if not flip else a

    Ux = 0.
    for xe in x:
        for ye in y:
            if xe < ye:
                Ux += 1
            elif xe == ye:
                Ux += .5
    Uy = len(a) * len(b) - Ux
    Ua = Ux if not flip else Uy
    Ub = Uy if not flip else Ux

    U = abs(Ua - Ub)

    same = U <= SIGN_TABLES[sigLevel][len(a) - 1][len(b) - 1]
    return same


# Table for .10 significance level.
TABLE_0_10 = [
    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4],
    [0, 0, 0, 0, 1, 2, 2, 3, 4, 4, 5, 5, 6, 7, 7, 8, 9, 9, 10, 11],
    [0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18],
    [0, 0, 1, 2, 4, 5, 6, 8, 9, 11, 12, 13, 15, 16, 18, 19, 20, 22, 23,
     25],
    [0, 0, 2, 3, 5, 7, 8, 10, 12, 14, 16, 17, 19, 21, 23, 25, 26, 28, 30,
     32],
    [0, 0, 2, 4, 6, 8, 11, 13, 15, 17, 19, 21, 24, 26, 28, 30, 33, 35, 37,
     39],
    [0, 1, 3, 5, 8, 10, 13, 15, 18, 20, 23, 26, 28, 31, 33, 36, 39, 41, 44,
     47],
    [0, 1, 4, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51,
     54],
    [0, 1, 4, 7, 11, 14, 17, 20, 24, 27, 31, 34, 37, 41, 44, 48, 51, 55,
     58, 62],
    [0, 1, 5, 8, 12, 16, 19, 23, 27, 31, 34, 38, 42, 46, 50, 54, 57, 61,
     65, 69],
    [0, 2, 5, 9, 13, 17, 21, 26, 30, 34, 38, 42, 47, 51, 55, 60, 64, 68,
     72, 77],
    [0, 2, 6, 10, 15, 19, 24, 28, 33, 37, 42, 47, 51, 56, 61, 65, 70, 75,
     80, 89],
    [0, 3, 7, 11, 16, 21, 26, 31, 36, 41, 46, 51, 56, 61, 66, 71, 77, 82,
     87, 92],
    [0, 3, 7, 12, 18, 23, 28, 33, 39, 44, 50, 55, 61, 66, 72, 77, 83, 88,
     94, 100],
    [0, 3, 8, 14, 19, 25, 30, 36, 42, 48, 54, 60, 65, 71, 77, 83, 89, 95,
     101, 107],
    [0, 3, 9, 15, 20, 26, 33, 39, 45, 51, 57, 64, 70, 77, 83, 89, 96, 102,
     109, 115],
    [0, 4, 9, 16, 22, 28, 35, 41, 48, 55, 61, 68, 75, 82, 88, 95, 102, 109,
     116, 123],
    [0, 4, 10, 17, 23, 30, 37, 44, 51, 58, 65, 72, 80, 87, 94, 101, 109,
     116, 123, 130],
    [0, 4, 11, 18, 25, 32, 39, 47, 54, 62, 69, 77, 89, 92, 100, 107, 115,
     123, 130, 138]
]

# Table for .05 significance level.
TABLE_0_05 = [
    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2],
    [0, 0, 0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8],
    [0, 0, 0, 0, 1, 2, 3, 4, 4, 5, 6, 7, 8, 9, 10, 11, 11, 12, 13, 13],
    [0, 0, 0, 1, 2, 3, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 17, 18, 19, 20],
    [0, 0, 1, 2, 3, 5, 6, 8, 10, 11, 13, 14, 16, 17, 19, 21, 22, 24, 25,
     27],
    [0, 0, 1, 3, 5, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32,
     34],
    [0, 0, 2, 4, 6, 8, 10, 13, 15, 17, 19, 22, 24, 26, 29, 31, 34, 36, 38,
     41],
    [0, 0, 2, 4, 7, 10, 12, 15, 17, 20, 23, 26, 28, 31, 34, 37, 39, 42, 45,
     48],
    [0, 0, 3, 5, 8, 11, 14, 17, 20, 23, 26, 29, 33, 36, 39, 42, 45, 48, 52,
     55],
    [0, 0, 3, 6, 9, 13, 16, 19, 23, 26, 30, 33, 37, 40, 44, 47, 51, 55, 58,
     62],
    [0, 1, 4, 7, 11, 14, 18, 22, 26, 29, 33, 37, 41, 45, 49, 53, 57, 61,
     65, 69],
    [0, 1, 4, 8, 12, 16, 20, 24, 28, 33, 37, 41, 45, 50, 54, 59, 63, 67,
     72, 76],
    [0, 1, 5, 9, 13, 17, 22, 26, 31, 36, 40, 45, 50, 55, 59, 64, 67, 74,
     78, 83],
    [0, 1, 5, 10, 14, 19, 24, 29, 34, 39, 44, 49, 54, 59, 64, 70, 75, 80,
     85, 90],
    [0, 1, 6, 11, 15, 21, 26, 31, 37, 42, 47, 53, 59, 64, 70, 75, 81, 86,
     92, 98],
    [0, 2, 6, 11, 17, 22, 28, 34, 39, 45, 51, 57, 63, 67, 75, 81, 87, 93,
     99, 105],
    [0, 2, 7, 12, 18, 24, 30, 36, 42, 48, 55, 61, 67, 74, 80, 86, 93, 99,
     106, 112],
    [0, 2, 7, 13, 19, 25, 32, 38, 45, 52, 58, 65, 72, 78, 85, 92, 99, 106,
     113, 119],
    [0, 2, 8, 13, 20, 27, 34, 41, 48, 55, 62, 69, 76, 83, 90, 98, 105, 112,
     119, 127]
]

# Table for .01 significance level.
TABLE_0_01 = [
    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 3, 3],
    [0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 6, 7, 8],
    [0, 0, 0, 0, 0, 1, 1, 2, 3, 4, 5, 6, 7, 7, 8, 9, 10, 11, 12, 13],
    [0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 15, 16, 17, 18],
    [0, 0, 0, 0, 1, 3, 4, 6, 7, 9, 10, 12, 13, 15, 16, 18, 19, 21, 22, 24],
    [0, 0, 0, 1, 2, 4, 6, 7, 9, 11, 13, 15, 17, 18, 20, 22, 24, 26, 28,
     30],
    [0, 0, 0, 1, 3, 5, 7, 9, 11, 13, 16, 18, 20, 22, 24, 27, 29, 31, 33,
     36],
    [0, 0, 0, 2, 4, 6, 9, 11, 13, 16, 18, 21, 24, 26, 29, 31, 34, 37, 39,
     42],
    [0, 0, 0, 2, 5, 7, 10, 13, 16, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45,
     46],
    [0, 0, 1, 3, 6, 9, 12, 15, 18, 21, 24, 27, 31, 34, 37, 41, 44, 47, 51,
     54],
    [0, 0, 1, 3, 7, 10, 13, 17, 20, 24, 27, 31, 34, 38, 42, 45, 49, 53, 56,
     60],
    [0, 0, 1, 4, 7, 11, 15, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 63,
     67],
    [0, 0, 2, 5, 8, 12, 16, 20, 24, 29, 33, 37, 42, 46, 51, 55, 60, 64, 69,
     73],
    [0, 0, 2, 5, 9, 13, 18, 22, 27, 31, 36, 41, 45, 50, 55, 60, 65, 70, 74,
     79],
    [0, 0, 2, 6, 10, 15, 19, 24, 29, 34, 39, 44, 49, 54, 60, 65, 70, 75,
     81, 86],
    [0, 0, 2, 6, 11, 16, 21, 26, 31, 37, 42, 47, 53, 58, 64, 70, 75, 81,
     87, 92],
    [0, 0, 3, 7, 12, 17, 22, 28, 33, 39, 45, 51, 56, 63, 69, 74, 81, 87,
     93, 99],
    [0, 0, 3, 8, 13, 18, 24, 30, 36, 42, 46, 54, 60, 67, 73, 79, 86, 92,
     99, 105]
]

SIGN_TABLES = {.10: TABLE_0_10, .05: TABLE_0_05, .01: TABLE_0_01}