from __future__ import division, print_function, absolute_import

__all__ = ['fftshift', 'ifftshift', 'fftfreq', 'rfftfreq']

from numpy import arange
from numpy.fft.helper import fftshift, ifftshift, fftfreq


def rfftfreq(n, d=1.0):
    """DFT sample frequencies (for usage with rfft, irfft).

    The returned float array contains the frequency bins in
    cycles/unit (with zero at the start) given a window length `n` and a
    sample spacing `d`::

      f = [0,1,1,2,2,...,n/2-1,n/2-1,n/2]/(d*n)   if n is even
      f = [0,1,1,2,2,...,n/2-1,n/2-1,n/2,n/2]/(d*n)   if n is odd

    Parameters
    ----------
    n : int
        Window length.
    d : scalar, optional
        Sample spacing. Default is 1.

    Returns
    -------
    out : ndarray
        The array of length `n`, containing the sample frequencies.

    Examples
    --------
    >>> from scipy import fftpack
    >>> sig = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float)
    >>> sig_fft = fftpack.rfft(sig)
    >>> n = sig_fft.size
    >>> timestep = 0.1
    >>> freq = fftpack.rfftfreq(n, d=timestep)
    >>> freq
    array([ 0.  ,  1.25,  1.25,  2.5 ,  2.5 ,  3.75,  3.75,  5.  ])

    """
    if not isinstance(n, int) or n < 0:
        raise ValueError("n = %s is not valid.  n must be a nonnegative integer." % n)

    return (arange(1, n + 1, dtype=int) // 2) / float(n * d)