import numpy

def hurst(X):

    """ Compute the Hurst exponent of X. If the output H=0.5,the behavior

    of the time-series is similar to random walk. If H<0.5, the time-series

    cover less "distance" than a random walk, vice verse.

    Parameters

    ----------

    X

        list

        a time series

    Returns

    -------

    H

        float

        Hurst exponent

    Notes

    --------

    Author of this function is Xin Liu

    Examples

    --------

    >>> import pyeeg

    >>> from numpy.random import randn

    >>> a = randn(4096)

    >>> pyeeg.hurst(a)

    0.5057444

    """

    X = numpy.array(X)

    N = X.size

    T = numpy.arange(1, N + 1)

    Y = numpy.cumsum(X)

    Ave_T = Y / T

    S_T = numpy.zeros(N)

    R_T = numpy.zeros(N)

    for i in range(N):

        S_T[i] = numpy.std(X[:i + 1])

        X_T = Y - T * Ave_T[i]

        R_T[i] = numpy.ptp(X_T[:i + 1])

    R_S = R_T / S_T

    R_S = numpy.log(R_S)[1:]

    n = numpy.log(T)[1:]

    A = numpy.column_stack((n, numpy.ones(n.size)))

    [m, c] = numpy.linalg.lstsq(A, R_S)[0]

    H = m

    return H