# -*- coding: utf-8 -*-

from __future__ import division, print_function

import numpy as np

__all__ = ["function", "integrated_time", "AutocorrError"]


def function(x, axis=0, fast=False):
    """Estimate the autocorrelation function of a time series using the FFT.

    Args:
        x: The time series. If multidimensional, set the time axis using the
            ``axis`` keyword argument and the function will be computed for
            every other axis.
        axis (Optional[int]): The time axis of ``x``. Assumed to be the first
            axis if not specified.
        fast (Optional[bool]): If ``True``, only use the first ``2^n`` (for
            the largest power) entries for efficiency. (default: False)

    Returns:
        array: The autocorrelation function of the time series.

    """
    x = np.atleast_1d(x)
    m = [slice(None), ] * len(x.shape)

    # For computational efficiency, crop the chain to the largest power of
    # two if requested.
    if fast:
        n = int(2**np.floor(np.log2(x.shape[axis])))
        m[axis] = slice(0, n)
        x = x
    else:
        n = x.shape[axis]

    # Compute the FFT and then (from that) the auto-correlation function.
    f = np.fft.fft(x - np.mean(x, axis=axis), n=2*n, axis=axis)
    m[axis] = slice(0, n)
    acf = np.fft.ifft(f * np.conjugate(f), axis=axis)[m].real
    m[axis] = 0
    return acf / acf[m]


def integrated_time(x, low=10, high=None, step=1, c=10, full_output=False,
                    axis=0, fast=False):
    """Estimate the integrated autocorrelation time of a time series.

    This estimate uses the iterative procedure described on page 16 of `Sokal's
    notes <http://www.stat.unc.edu/faculty/cji/Sokal.pdf>`_ to determine a
    reasonable window size.

    Args:
        x: The time series. If multidimensional, set the time axis using the
            ``axis`` keyword argument and the function will be computed for
            every other axis.
        low (Optional[int]): The minimum window size to test. (default: ``10``)
        high (Optional[int]): The maximum window size to test. (default:
            ``x.shape[axis] / (2*c)``)
        step (Optional[int]): The step size for the window search. (default: 
            ``1``)
        c (Optional[float]): The minimum number of autocorrelation times
            needed to trust the estimate. (default: ``10``)
        full_output (Optional[bool]): Return the final window size as well as
            the autocorrelation time. (default: ``False``)
        axis (Optional[int]): The time axis of ``x``. Assumed to be the first
            axis if not specified.
        fast (Optional[bool]): If ``True``, only use the first ``2^n`` (for
            the largest power) entries for efficiency. (default: False)

    Returns:
        float or array: An estimate of the integrated autocorrelation time of
            the time series ``x`` computed along the axis ``axis``.
        Optional[int]: The final window size that was used. Only returned if
            ``full_output`` is ``True``.

    Raises
        AutocorrError: If the autocorrelation time can't be reliably estimated
            from the chain. This normally means that the chain is too short.

    """
    size = 0.5 * x.shape[axis]
    if int(c * low) >= size:
        raise AutocorrError("The chain is too short")

    # Compute the autocorrelation function.
    f = function(x, axis=axis, fast=fast)

    # Check the dimensions of the array.
    oned = len(f.shape) == 1
    m = [slice(None), ] * len(f.shape)

    # Loop over proposed window sizes until convergence is reached.
    if high is None:
        high = int(size / c)

    if oned:
        acl_ests = 2.0*np.cumsum(f) - 1.0
    else:
        acl_ests = 2.0*np.cumsum(f, axis=axis) - 1.0

    for M in np.arange(low, high, step).astype(int):
        # Compute the autocorrelation time with the given window.
        if oned:
            # Special case 1D for simplicity.
            tau = acl_ests[M]
        else:
            # N-dimensional case.
            m[axis] = M
            tau = acl_ests[m]        
        
        # Accept the window size if it satisfies the convergence criterion.
        if np.all(tau > 1.0) and M > c * tau.max():
            if full_output:
                return tau, M
            return tau

        # If the autocorrelation time is too long to be estimated reliably
        # from the chain, it should fail.
        if c * tau.max() >= size:
            break

    raise AutocorrError("The chain is too short to reliably estimate "
                        "the autocorrelation time")


class AutocorrError(Exception):
    """Raised if the chain is too short to estimate an autocorrelation time.

    """
    pass
