import numpy as np
import scipy.stats as ss


class Xi:
    """
    x and y are the data vectors
    """

    def __init__(self, x, y):

        self.x = x
        self.y = y

    @property
    def sample_size(self):
        return len(self.x)

    @property
    def x_ordered_rank(self):
        # PI is the rank vector for x, with ties broken at random
        # Not mine: source (https://stackoverflow.com/a/47430384/1628971)
        # random shuffling of the data - reason to use random.choice is that
        # pd.sample(frac=1) uses the same randomizing algorithm
        len_x = len(self.x)
        randomized_indices = np.random.choice(np.arange(len_x), len_x, replace=False)
        randomized = [self.x[idx] for idx in randomized_indices]
        # same as pandas rank method 'first'
        rankdata = ss.rankdata(randomized, method="ordinal")
        # Reindexing based on pairs of indices before and after
        unrandomized = [
            rankdata[j] for i, j in sorted(zip(randomized_indices, range(len_x)))
        ]
        return unrandomized

    @property
    def y_rank_max(self):
        # f[i] is number of j s.t. y[j] <= y[i], divided by n.
        return ss.rankdata(self.y, method="max") / self.sample_size

    @property
    def g(self):
        # g[i] is number of j s.t. y[j] >= y[i], divided by n.
        return ss.rankdata([-i for i in self.y], method="max") / self.sample_size

    @property
    def x_ordered(self):
        # order of the x's, ties broken at random.
        return np.argsort(self.x_ordered_rank)

    @property
    def x_rank_max_ordered(self):
        # Rearrange f according to ord.
        return [self.y_rank_max[i] for i in self.x_ordered]

    @property
    def mean_absolute(self):
        return (
            np.mean(
                np.abs(
                    [
                        x - y
                        for x, y in zip(
                            self.x_rank_max_ordered[0 : (self.sample_size - 1)],
                            self.x_rank_max_ordered[1 : self.sample_size],
                        )
                    ]
                )
            )
            * (self.sample_size - 1)
            / (2 * self.sample_size)
        )

    @property
    def inverse_g_mean(self):
        return np.mean(self.g * (1 - self.g))

    @property
    def correlation(self):
        """xi correlation"""
        return 1 - self.mean_absolute / self.inverse_g_mean

    @classmethod
    def xi(cls, x, y):
        return cls(x, y)

    def pval_asymptotic(self, ties=False, nperm=1000):
        """
        Returns p values of the correlation

        Args:
            ties: boolean
                If ties is true, the algorithm assumes that the data has ties
                and employs the more elaborated theory for calculating
                the P-value. Otherwise, it uses the simpler theory. There is
                no harm in setting tiles True, even if there are no ties.
            nperm: int
                The number of permutations for the permutation test, if needed.
                default 1000

        Returns:
            p value
        """
        # If there are no ties, return xi and theoretical P-value:

        if ties:
            return 1 - ss.norm.cdf(
                np.sqrt(self.sample_size) * self.correlation / np.sqrt(2 / 5)
            )

        # If there are ties, and the theoretical method
        # is to be used for calculation P-values:
        # The following steps calculate the theoretical variance
        # in the presence of ties:
        sorted_ordered_x_rank = sorted(self.x_rank_max_ordered)

        ind = [i + 1 for i in range(self.sample_size)]
        ind2 = [2 * self.sample_size - 2 * ind[i - 1] + 1 for i in ind]

        a = (
            np.mean([i * j * j for i, j in zip(ind2, sorted_ordered_x_rank)])
            / self.sample_size
        )

        c = (
            np.mean([i * j for i, j in zip(ind2, sorted_ordered_x_rank)])
            / self.sample_size
        )

        cq = np.cumsum(sorted_ordered_x_rank)

        m = [
            (i + (self.sample_size - j) * k) / self.sample_size
            for i, j, k in zip(cq, ind, sorted_ordered_x_rank)
        ]

        b = np.mean([np.square(i) for i in m])
        v = (a - 2 * b + np.square(c)) / np.square(self.inverse_g_mean)

        return 1 - ss.norm.cdf(
            np.sqrt(self.sample_size) * self.correlation / np.sqrt(v)
        )

import numpy as np
import scipy.stats as ss


class Xi:
    """
    x and y are the data vectors
    """

    def __init__(self, x, y):

        self.x = x
        self.y = y

    @property
    def sample_size(self):
        return len(self.x)

    @property
    def x_ordered_rank(self):
        # PI is the rank vector for x, with ties broken at random
        # Not mine: source (https://stackoverflow.com/a/47430384/1628971)
        # random shuffling of the data - reason to use random.choice is that
        # pd.sample(frac=1) uses the same randomizing algorithm
        len_x = len(self.x)
        randomized_indices = np.random.choice(np.arange(len_x), len_x, replace=False)
        randomized = [self.x[idx] for idx in randomized_indices]
        # same as pandas rank method 'first'
        rankdata = ss.rankdata(randomized, method="ordinal")
        # Reindexing based on pairs of indices before and after
        unrandomized = [
            rankdata[j] for i, j in sorted(zip(randomized_indices, range(len_x)))
        ]
        return unrandomized

    @property
    def y_rank_max(self):
        # f[i] is number of j s.t. y[j] <= y[i], divided by n.
        return ss.rankdata(self.y, method="max") / self.sample_size

    @property
    def g(self):
        # g[i] is number of j s.t. y[j] >= y[i], divided by n.
        return ss.rankdata([-i for i in self.y], method="max") / self.sample_size

    @property
    def x_ordered(self):
        # order of the x's, ties broken at random.
        return np.argsort(self.x_ordered_rank)

    @property
    def x_rank_max_ordered(self):
        # Rearrange f according to ord.
        return [self.y_rank_max[i] for i in self.x_ordered]

    @property
    def mean_absolute(self):
        return (
            np.mean(
                np.abs(
                    [
                        x - y
                        for x, y in zip(
                            self.x_rank_max_ordered[0 : (self.sample_size - 1)],
                            self.x_rank_max_ordered[1 : self.sample_size],
                        )
                    ]
                )
            )
            * (self.sample_size - 1)
            / (2 * self.sample_size)
        )

    @property
    def inverse_g_mean(self):
        return np.mean(self.g * (1 - self.g))

    @property
    def correlation(self):
        """xi correlation"""
        return 1 - self.mean_absolute / self.inverse_g_mean

    @classmethod
    def xi(cls, x, y):
        return cls(x, y)

    def pval_asymptotic(self, ties=False, nperm=1000):
        """
        Returns p values of the correlation

        Args:
            ties: boolean
                If ties is true, the algorithm assumes that the data has ties
                and employs the more elaborated theory for calculating
                the P-value. Otherwise, it uses the simpler theory. There is
                no harm in setting tiles True, even if there are no ties.
            nperm: int
                The number of permutations for the permutation test, if needed.
                default 1000

        Returns:
            p value
        """
        # If there are no ties, return xi and theoretical P-value:

        if ties:
            return 1 - ss.norm.cdf(
                np.sqrt(self.sample_size) * self.correlation / np.sqrt(2 / 5)
            )

        # If there are ties, and the theoretical method
        # is to be used for calculation P-values:
        # The following steps calculate the theoretical variance
        # in the presence of ties:
        sorted_ordered_x_rank = sorted(self.x_rank_max_ordered)

        ind = [i + 1 for i in range(self.sample_size)]
        ind2 = [2 * self.sample_size - 2 * ind[i - 1] + 1 for i in ind]

        a = (
            np.mean([i * j * j for i, j in zip(ind2, sorted_ordered_x_rank)])
            / self.sample_size
        )

        c = (
            np.mean([i * j for i, j in zip(ind2, sorted_ordered_x_rank)])
            / self.sample_size
        )

        cq = np.cumsum(sorted_ordered_x_rank)

        m = [
            (i + (self.sample_size - j) * k) / self.sample_size
            for i, j, k in zip(cq, ind, sorted_ordered_x_rank)
        ]

        b = np.mean([np.square(i) for i in m])
        v = (a - 2 * b + np.square(c)) / np.square(self.inverse_g_mean)

        return 1 - ss.norm.cdf(
            np.sqrt(self.sample_size) * self.correlation / np.sqrt(v)
        )

x and y are the data vectors # PI is the rank vector for x, with ties broken at random # Not mine: source (https://stackoverflow.com/a/47430384/1628971) # random shuffling of the data - reason to use random.choice is that # pd.sample(frac=1) uses the same randomizing algorithm # same as pandas rank method 'first' # Reindexing based on pairs of indices before and after # f[i] is number of j s.t. y[j] <= y[i], divided by n. # g[i] is number of j s.t. y[j] >= y[i], divided by n. # order of the x's, ties broken at random. # Rearrange f according to ord. xi correlation Returns p values of the correlation          Args:             ties: boolean                 If ties is true, the algorithm assumes that the data has ties                 and employs the more elaborated theory for calculating                 the P-value. Otherwise, it uses the simpler theory. There is                 no harm in setting tiles True, even if there are no ties.             nperm: int                 The number of permutations for the permutation test, if needed.                 default 1000          Returns:             p value # If there are no ties, return xi and theoretical P-value: # If there are ties, and the theoretical method # is to be used for calculation P-values: # The following steps calculate the theoretical variance # in the presence of ties: