Python FrequencySeries.to_timeseries方法代碼示例

# 需要導入模塊: from pycbc.types import FrequencySeries [as 別名]
# 或者: from pycbc.types.FrequencySeries import to_timeseries [as 別名]
 def _shift_and_ifft(self, fdsinx, tshift, fseries=None):
     """Calls apply_fd_time_shift, and iFFTs to the time domain.
     """
     start_time = self.time_series.start_time
     tdshift = apply_fd_time_shift(fdsinx, start_time+tshift,
                                   fseries=fseries)
     if not isinstance(tdshift, FrequencySeries):
         # cast to FrequencySeries so time series will work
         tdshift = FrequencySeries(tdshift, delta_f=fdsinx.delta_f,
                                   epoch=fdsinx.epoch)
     return tdshift.to_timeseries()

# 需要導入模塊: from pycbc.types import FrequencySeries [as 別名]
# 或者: from pycbc.types.FrequencySeries import to_timeseries [as 別名]
def calculate_acf(data, delta_t=1.0, unbiased=False):
    """ Calculates the autocorrelation function (ACF) and returns the one-sided
    ACF.

    The ACF is defined as the autocovariance divided by the variance. The ACF
    can be estimated using

        \hat{R}(k) = \frac{1}{\left( n \sigma^{2}} \right) \sum_{t=1}^{n-k} \left( X_{t} - \mu \right) \left( X_{t+k} - \mu \right) 

    Where \hat{R}(k) is the ACF, X_{t} is the data series at time t, \mu is the
    mean of X_{t}, and \sigma^{2} is the variance of X_{t}.

    Parameters
    -----------
    data : {TimeSeries, numpy.array}
        A TimeSeries or numpy.array of data.
    delta_t : float
        The time step of the data series if it is not a TimeSeries instance.
    unbiased : bool
        If True the normalization of the autocovariance function is n-k
        instead of n. This is called the unbiased estimation of the
        autocovariance. Note that this does not mean the ACF is unbiased.

    Returns
    -------
    acf : numpy.array
        If data is a TimeSeries then acf will be a TimeSeries of the
        one-sided ACF. Else acf is a numpy.array.
    """

    # if given a TimeSeries instance then get numpy.array
    if isinstance(data, TimeSeries):
        y = data.numpy()
        delta_t = data.delta_t
    else:
        y = data

    # FFT data minus the mean
    fdata = TimeSeries(y-y.mean(), delta_t=delta_t).to_frequencyseries()

    # correlate
    # do not need to give the congjugate since correlate function does it
    cdata = FrequencySeries(zeros(len(fdata), dtype=numpy.complex64),
                           delta_f=fdata.delta_f, copy=False)
    correlate(fdata, fdata, cdata)

    # IFFT correlated data to get unnormalized autocovariance time series
    acf = cdata.to_timeseries()

    # normalize the autocovariance
    # note that dividing by acf[0] is the same as ( y.var() * len(acf) )
    if unbiased:
        acf /= ( y.var() * numpy.arange(len(acf), 0, -1) )
    else:
        acf /= acf[0]

    # return input datatype
    if isinstance(data, TimeSeries):
        return TimeSeries(acf, delta_t=delta_t)
    else:
        return acf

# 需要導入模塊: from pycbc.types import FrequencySeries [as 別名]
# 或者: from pycbc.types.FrequencySeries import to_timeseries [as 別名]
def calculate_acf(data, delta_t=1.0, unbiased=False):
    r"""Calculates the one-sided autocorrelation function.

    Calculates the autocorrelation function (ACF) and returns the one-sided
    ACF. The ACF is defined as the autocovariance divided by the variance. The
    ACF can be estimated using

    .. math::

        \hat{R}(k) = \frac{1}{n \sigma^{2}} \sum_{t=1}^{n-k} \left( X_{t} - \mu \right) \left( X_{t+k} - \mu \right)

    Where :math:`\hat{R}(k)` is the ACF, :math:`X_{t}` is the data series at
    time t, :math:`\mu` is the mean of :math:`X_{t}`, and :math:`\sigma^{2}` is
    the variance of :math:`X_{t}`.

    Parameters
    -----------
    data : TimeSeries or numpy.array
        A TimeSeries or numpy.array of data.
    delta_t : float
        The time step of the data series if it is not a TimeSeries instance.
    unbiased : bool
        If True the normalization of the autocovariance function is n-k
        instead of n. This is called the unbiased estimation of the
        autocovariance. Note that this does not mean the ACF is unbiased.

    Returns
    -------
    acf : numpy.array
        If data is a TimeSeries then acf will be a TimeSeries of the
        one-sided ACF. Else acf is a numpy.array.
    """

    # if given a TimeSeries instance then get numpy.array
    if isinstance(data, TimeSeries):
        y = data.numpy()
        delta_t = data.delta_t
    else:
        y = data

    # Zero mean
    y = y - y.mean()
    ny_orig = len(y)

    npad = 1
    while npad < 2*ny_orig:
        npad = npad << 1
    ypad = numpy.zeros(npad)
    ypad[:ny_orig] = y

    # FFT data minus the mean
    fdata = TimeSeries(ypad, delta_t=delta_t).to_frequencyseries()

    # correlate
    # do not need to give the congjugate since correlate function does it
    cdata = FrequencySeries(zeros(len(fdata), dtype=fdata.dtype),
                           delta_f=fdata.delta_f, copy=False)
    correlate(fdata, fdata, cdata)

    # IFFT correlated data to get unnormalized autocovariance time series
    acf = cdata.to_timeseries()
    acf = acf[:ny_orig]

    # normalize the autocovariance
    # note that dividing by acf[0] is the same as ( y.var() * len(acf) )
    if unbiased:
        acf /= ( y.var() * numpy.arange(len(acf), 0, -1) )
    else:
        acf /= acf[0]

    # return input datatype
    if isinstance(data, TimeSeries):
        return TimeSeries(acf, delta_t=delta_t)
    else:
        return acf