def bandlimited_interpolate(series, delta_f):
    """Return a new PSD that has been interpolated to the desired delta_f.

    Parameters
    ----------
    series : FrequencySeries
        Frequency series to be interpolated.
    delta_f : float
        The desired delta_f of the output

    Returns
    -------
    interpolated series : FrequencySeries
        A new FrequencySeries that has been interpolated.
    """
    series = FrequencySeries(series, dtype=complex_same_precision_as(series), delta_f=series.delta_f)

    N = (len(series) - 1) * 2
    delta_t = 1.0 / series.delta_f / N

    new_N = int(1.0 / (delta_t * delta_f))
    new_n = new_N / 2 + 1

    series_in_time = TimeSeries(zeros(N), dtype=real_same_precision_as(series), delta_t=delta_t)
    ifft(series, series_in_time)

    padded_series_in_time = TimeSeries(zeros(new_N), dtype=series_in_time.dtype, delta_t=delta_t)
    padded_series_in_time[0:N/2] = series_in_time[0:N/2]
    padded_series_in_time[new_N-N/2:new_N] = series_in_time[N/2:N]

    interpolated_series = FrequencySeries(zeros(new_n), dtype=series.dtype, delta_f=delta_f)
    fft(padded_series_in_time, interpolated_series)

    return interpolated_series

def make_padded_frequency_series(vec,filter_N=None):
    """Pad a TimeSeries with a length of zeros greater than its length, such
    that the total length is the closest power of 2. This prevents the effects 
    of wraparound.
    """
    if filter_N is None:
        power = ceil(log(len(vec),2))+1
        N = 2 ** power
    else:
        N = filter_N
    n = N/2+1    
    
   
    if isinstance(vec,FrequencySeries):
        vectilde = FrequencySeries(zeros(n, dtype=complex_same_precision_as(vec)),
                                   delta_f=1.0,copy=False)
	if len(vectilde) < len(vec):
	    cplen = len(vectilde)
        else:
            cplen = len(vec)
        vectilde[0:cplen] = vec[0:cplen]  
        delta_f = vec.delta_f
    
        
    if isinstance(vec,TimeSeries):  
        vec_pad = TimeSeries(zeros(N),delta_t=vec.delta_t,
                         dtype=real_same_precision_as(vec))
        vec_pad[0:len(vec)] = vec   
        delta_f = 1.0/(vec.delta_t*N)
        vectilde = FrequencySeries(zeros(n),delta_f=1.0, 
                               dtype=complex_same_precision_as(vec))
        fft(vec_pad,vectilde)
        
    vectilde = FrequencySeries(vectilde * DYN_RANGE_FAC,delta_f=delta_f,dtype=complex64)
    return vectilde

def phase_from_polarizations(h_plus, h_cross, remove_start_phase=True):
    """Return gravitational wave phase

    Return the gravitation-wave phase from the h_plus and h_cross
    polarizations of the waveform. The returned phase is always
    positive and increasing with an initial phase of 0.

    Parameters
    ----------
    h_plus : TimeSeries
        An PyCBC TmeSeries vector that contains the plus polarization of the
        gravitational waveform.
    h_cross : TimeSeries
        A PyCBC TmeSeries vector that contains the cross polarization of the
        gravitational waveform.

    Returns
    -------
    GWPhase : TimeSeries
        A TimeSeries containing the gravitational wave phase.

    Examples
    --------s
    >>> from pycbc.waveform import get_td_waveform, phase_from_polarizations
    >>> hp, hc = get_td_waveform(approximant="TaylorT4", mass1=10, mass2=10,
                         f_lower=30, delta_t=1.0/4096)
    >>> phase = phase_from_polarizations(hp, hc)

    """
    p = numpy.unwrap(numpy.arctan2(h_cross.data, h_plus.data)).astype(
        real_same_precision_as(h_plus))
    if remove_start_phase:
        p += -p[0]
    return TimeSeries(p, delta_t=h_plus.delta_t, epoch=h_plus.start_time,
        copy=False)

def shift_sum(v1, shifts, bins):
    real_type = real_same_precision_as(v1)
    shifts = numpy.array(shifts, dtype=real_type)
    
    bins = numpy.array(bins, dtype=numpy.uint32)
    blen = len(bins) - 1
    v1 = numpy.array(v1.data, copy=False)
    slen = len(v1)

    if v1.dtype.name == 'complex64':
        code = point_chisq_code_single
    else:
        code = point_chisq_code_double
    
    n = int(len(shifts))
    
    # Create some output memory
    chisq =  numpy.zeros(n, dtype=real_type)
    
    inline(code, ['v1', 'n', 'chisq', 'slen', 'shifts', 'bins', 'blen'],
                    extra_compile_args=[WEAVE_FLAGS] + omp_flags,
                    libraries=omp_libs
          )
          
    return  chisq

def td_waveform_to_fd_waveform(waveform, out=None, length=None,
                               buffer_length=100):
    """ Convert a time domain into a frequency domain waveform by FFT.
        As a waveform is assumed to "wrap" in the time domain one must be
        careful to ensure the waveform goes to 0 at both "boundaries". To
        ensure this is done correctly the waveform must have the epoch set such
        the merger time is at t=0 and the length of the waveform should be
        shorter than the desired length of the FrequencySeries (times 2 - 1)
        so that zeroes can be suitably pre- and post-pended before FFTing.
        If given, out is a memory array to be used as the output of the FFT.
        If not given memory is allocated internally.
        If present the length of the returned FrequencySeries is determined
        from the length out. If out is not given the length can be provided
        expicitly, or it will be chosen as the nearest power of 2. If choosing
        length explicitly the waveform length + buffer_length is used when
        choosing the nearest binary number so that some zero padding is always
        added.
    """
    # Figure out lengths and set out if needed
    if out is None:
        if length is None:
            N = pnutils.nearest_larger_binary_number(len(waveform) + \
                                                     buffer_length)
            n = int(N//2) + 1
        else:
            n = length
            N = (n-1)*2
        out = zeros(n, dtype=complex_same_precision_as(waveform))
    else:
        n = len(out)
        N = (n-1)*2
    delta_f =  1. / (N * waveform.delta_t)

    # total duration of the waveform
    tmplt_length = len(waveform) * waveform.delta_t
    if len(waveform) > N:
        err_msg = "The time domain template is longer than the intended "
        err_msg += "duration in the frequency domain. This situation is "
        err_msg += "not supported in this function. Please shorten the "
        err_msg += "waveform appropriately before calling this function or "
        err_msg += "increase the allowed waveform length. "
        err_msg += "Waveform length (in samples): {}".format(len(waveform))
        err_msg += ". Intended length: {}.".format(N)
        raise ValueError(err_msg)
    # for IMR templates the zero of time is at max amplitude (merger)
    # thus the start time is minus the duration of the template from
    # lower frequency cutoff to merger, i.e. minus the 'chirp time'
    tChirp = - float( waveform.start_time )  # conversion from LIGOTimeGPS
    waveform.resize(N)
    k_zero = int(waveform.start_time / waveform.delta_t)
    waveform.roll(k_zero)
    htilde = FrequencySeries(out, delta_f=delta_f, copy=False)
    fft(waveform.astype(real_same_precision_as(htilde)), htilde)
    htilde.length_in_time = tmplt_length
    htilde.chirp_length = tChirp
    return htilde

def get_waveform_filter(out, template=None, **kwargs):
    """Return a frequency domain waveform filter for the specified approximant
    """
    n = len(out)

    input_params = props(template, **kwargs)

    if input_params['approximant'] in filter_approximants(_scheme.mgr.state):
        wav_gen = filter_wav[type(_scheme.mgr.state)]
        htilde = wav_gen[input_params['approximant']](out=out, **input_params)
        htilde.resize(n)
        htilde.chirp_length = get_waveform_filter_length_in_time(**input_params)
        htilde.length_in_time = htilde.chirp_length
        return htilde

    if input_params['approximant'] in fd_approximants(_scheme.mgr.state):
        wav_gen = fd_wav[type(_scheme.mgr.state)]
        hp, hc = wav_gen[input_params['approximant']](**input_params)
        hp.resize(n)
        out[0:len(hp)] = hp[:]
        hp = FrequencySeries(out, delta_f=hp.delta_f, copy=False)
        hp.chirp_length = get_waveform_filter_length_in_time(**input_params)
        hp.length_in_time = hp.chirp_length
        return hp

    elif input_params['approximant'] in td_approximants(_scheme.mgr.state):
        # N: number of time samples required
        N = (n-1)*2
        delta_f = 1.0 / (N * input_params['delta_t'])
        wav_gen = td_wav[type(_scheme.mgr.state)]
        hp, hc = wav_gen[input_params['approximant']](**input_params)
        # taper the time series hp if required
        if ('taper' in input_params.keys() and \
            input_params['taper'] is not None):
            hp = wfutils.taper_timeseries(hp, input_params['taper'],
                                          return_lal=False)
        # total duration of the waveform
        tmplt_length = len(hp) * hp.delta_t
        # for IMR templates the zero of time is at max amplitude (merger)
        # thus the start time is minus the duration of the template from
        # lower frequency cutoff to merger, i.e. minus the 'chirp time'
        tChirp = - float( hp.start_time )  # conversion from LIGOTimeGPS
        hp.resize(N)
        k_zero = int(hp.start_time / hp.delta_t)
        hp.roll(k_zero)
        htilde = FrequencySeries(out, delta_f=delta_f, copy=False)
        fft(hp.astype(real_same_precision_as(htilde)), htilde)
        htilde.length_in_time = tmplt_length
        htilde.chirp_length = tChirp
        return htilde

    else:
        raise ValueError("Approximant %s not available" %
                            (input_params['approximant']))

def abs_arg_max(self):
    if self.kind == 'real':
        return _np.argmax(abs(self.data))
    else:
        data = _np.array(self._data, # pylint:disable=unused-variable
                         copy=False).view(real_same_precision_as(self))
        loc = _np.array([0])
        N = len(self) # pylint:disable=unused-variable
        inline(code_abs_arg_max, ['data', 'loc', 'N'], libraries=omp_libs,
               extra_compile_args=code_flags)
        return loc[0]

def time_from_frequencyseries(htilde, sample_frequencies=None,
        discont_threshold=0.99*numpy.pi):
    """Computes time as a function of frequency from the given
    frequency-domain waveform. This assumes the stationary phase
    approximation. Any frequencies lower than the first non-zero value in
    htilde are assigned the time at the first non-zero value. Times for any
    frequencies above the next-to-last non-zero value in htilde will be
    assigned the time of the next-to-last non-zero value.

    .. note::
        Some waveform models (e.g., `SEOBNRv2_ROM_DoubleSpin`) can have
        discontinuities in the phase towards the end of the waveform due to
        numerical error. We therefore exclude any points that occur after a
        discontinuity in the phase, as the time estimate becomes untrustworthy
        beyond that point. What determines a discontinuity in the phase is set
        by the `discont_threshold`. To turn this feature off, just set
        `discont_threshold` to a value larger than pi (due to the unwrapping
        of the phase, no two points can have a difference > pi).

    Parameters
    ----------
    htilde : FrequencySeries
        The waveform to get the time evolution of; must be complex.
    sample_frequencies : {None, array}
        The frequencies at which the waveform is sampled. If None, will
        retrieve from ``htilde.sample_frequencies``.
    discont_threshold : {0.99*pi, float}
        If the difference in the phase changes by more than this threshold,
        it is considered to be a discontinuity. Default is 0.99*pi.

    Returns
    -------
    FrequencySeries
        The time evolution of the waveform as a function of frequency.
    """
    if sample_frequencies is None:
        sample_frequencies = htilde.sample_frequencies.numpy()
    phase = phase_from_frequencyseries(htilde).data
    dphi = numpy.diff(phase)
    time = -dphi / (2.*numpy.pi*numpy.diff(sample_frequencies))
    nzidx = numpy.nonzero(abs(htilde.data))[0]
    kmin, kmax = nzidx[0], nzidx[-2]
    # exclude everything after a discontinuity
    discont_idx = numpy.where(abs(dphi[kmin:]) >= discont_threshold)[0]
    if discont_idx.size != 0:
        kmax = min(kmax, kmin + discont_idx[0]-1)
    time[:kmin] = time[kmin]
    time[kmax:] = time[kmax]
    return FrequencySeries(time.astype(real_same_precision_as(htilde)),
        delta_f=htilde.delta_f, epoch=htilde.epoch,
        copy=False)

def amplitude_from_frequencyseries(htilde):
    """Returns the amplitude of the given frequency-domain waveform as a
    FrequencySeries.

    Parameters
    ----------
    htilde : FrequencySeries
        The waveform to get the amplitude of.

    Returns
    -------
    FrequencySeries
        The amplitude of the waveform as a function of frequency.
    """
    amp = abs(htilde.data).astype(real_same_precision_as(htilde))
    return FrequencySeries(amp, delta_f=htilde.delta_f, epoch=htilde.epoch,
        copy=False)

def interpolate_complex_frequency(series, delta_f, zeros_offset=0, side='right'):
    """Interpolate complex frequency series to desired delta_f.

    Return a new complex frequency series that has been interpolated to the
    desired delta_f.

    Parameters
    ----------
    series : FrequencySeries
        Frequency series to be interpolated.
    delta_f : float
        The desired delta_f of the output
    zeros_offset : optional, {0, int}
        Number of sample to delay the start of the zero padding
    side : optional, {'right', str}
        The side of the vector to zero pad
        
    Returns
    -------
    interpolated series : FrequencySeries
        A new FrequencySeries that has been interpolated.
    """
    new_n = int( (len(series)-1) * series.delta_f / delta_f + 1)
    samples = numpy.arange(0, new_n) * delta_f
    old_N = int( (len(series)-1) * 2 )
    new_N = int( (new_n - 1) * 2 )
    time_series = TimeSeries(zeros(old_N), delta_t =1.0/(series.delta_f*old_N),
                             dtype=real_same_precision_as(series))
                             
    ifft(series, time_series)

    time_series.roll(-zeros_offset)
    time_series.resize(new_N)
    
    if side == 'left':
        time_series.roll(zeros_offset + new_N - old_N)
    elif side == 'right':
        time_series.roll(zeros_offset)

    out_series = FrequencySeries(zeros(new_n), epoch=series.epoch,
                           delta_f=delta_f, dtype=series.dtype)
    fft(time_series, out_series)

    return out_series

    def to_timeseries(self, delta_t=None):
        """ Return the Fourier transform of this time series.

        Note that this assumes even length time series!
        
        Parameters
        ----------
        delta_t : {None, float}, optional
            The time resolution of the returned series. By default the 
        resolution is determined by length and delta_f of this frequency 
        series.
        
        Returns
        -------        
        TimeSeries: 
            The inverse fourier transform of this frequency series. 
        """
        from pycbc.fft import ifft
        from pycbc.types import TimeSeries, real_same_precision_as
        nat_delta_t =  1.0 / ((len(self)-1)*2) / self.delta_f
        if not delta_t:
            delta_t = nat_delta_t

        # add 0.5 to round integer
        tlen  = int(1.0 / self.delta_f / delta_t + 0.5)
        flen = tlen / 2 + 1
        
        if flen < len(self):
            raise ValueError("The value of delta_t (%s) would be "
                             "undersampled. Maximum delta_t "
                             "is %s." % (delta_t, nat_delta_t))
        if not delta_t:
            tmp = self
        else:
            tmp = FrequencySeries(zeros(flen, dtype=self.dtype), 
                             delta_f=self.delta_f, epoch=self.epoch)
            tmp[:len(self)] = self[:]
        
        f = TimeSeries(zeros(tlen, 
                           dtype=real_same_precision_as(self)),
                           delta_t=delta_t)
        ifft(tmp, f)
        return f

def sigmasq_series(htilde, psd=None, low_frequency_cutoff=None,
            high_frequency_cutoff=None):
    """Return a cumulative sigmasq frequency series. 

    Return a frequency series containing the accumulated power in the input 
    up to that frequency. 
    
    Parameters
    ----------
    htilde : TimeSeries or FrequencySeries 
        The input vector 
    psd : {None, FrequencySeries}, optional
        The psd used to weight the accumulated power.
    low_frequency_cutoff : {None, float}, optional
        The frequency to begin accumulating power. If None, start at the beginning
        of the vector.
    high_frequency_cutoff : {None, float}, optional
        The frequency to stop considering accumulated power. If None, continue 
        until the end of the input vector.

    Returns
    -------
    Frequency Series: FrequencySeries
        A frequency series containing the cumulative sigmasq.
    """
    htilde = make_frequency_series(htilde)
    N = (len(htilde)-1) * 2 
    norm = 4.0 * htilde.delta_f
    kmin, kmax = get_cutoff_indices(low_frequency_cutoff,
                                   high_frequency_cutoff, htilde.delta_f, N)  
   
    sigma_vec = FrequencySeries(zeros(len(htilde), dtype=real_same_precision_as(htilde)), 
                                delta_f = htilde.delta_f, copy=False)
    
    mag = htilde.squared_norm()
    
    if psd is not None:
        mag /= psd

    sigma_vec[kmin:kmax] = mag[kmin:kmax].cumsum()
        
    return sigma_vec*norm

def phase_from_frequencyseries(htilde, remove_start_phase=True):
    """Returns the phase from the given frequency-domain waveform. This assumes
    that the waveform has been sampled finely enough that the phase cannot
    change by more than pi radians between each step.

    Parameters
    ----------
    htilde : FrequencySeries
        The waveform to get the phase for; must be a complex frequency series.
    remove_start_phase : {True, bool}
        Subtract the initial phase before returning.

    Returns
    -------
    FrequencySeries
        The phase of the waveform as a function of frequency.
    """
    p = numpy.unwrap(numpy.angle(htilde.data)).astype(
            real_same_precision_as(htilde))
    if remove_start_phase:
        p += -p[0]
    return FrequencySeries(p, delta_f=htilde.delta_f, epoch=htilde.epoch,
        copy=False)

def frequency_from_polarizations(h_plus, h_cross):
    """Return gravitational wave frequency

    Return the gravitation-wave frequency as a function of time
    from the h_plus and h_cross polarizations of the waveform.
    It is 1 bin shorter than the input vectors and the sample times
    are advanced half a bin.

    Parameters
    ----------
    h_plus : TimeSeries
        A PyCBC TimeSeries vector that contains the plus polarization of the
        gravitational waveform.
    h_cross : TimeSeries
        A PyCBC TimeSeries vector that contains the cross polarization of the
        gravitational waveform.

    Returns
    -------
    GWFrequency : TimeSeries
        A TimeSeries containing the gravitational wave frequency as a function
        of time.

    Examples
    --------
    >>> from pycbc.waveform import get_td_waveform, phase_from_polarizations
    >>> hp, hc = get_td_waveform(approximant="TaylorT4", mass1=10, mass2=10,
                         f_lower=30, delta_t=1.0/4096)
    >>> freq = frequency_from_polarizations(hp, hc)

    """
    phase = phase_from_polarizations(h_plus, h_cross)
    freq = numpy.diff(phase) / ( 2 * lal.PI * phase.delta_t )
    start_time = phase.start_time + phase.delta_t / 2
    return TimeSeries(freq.astype(real_same_precision_as(h_plus)),
        delta_t=phase.delta_t, epoch=start_time)

def inverse_spectrum_truncation(psd, max_filter_len, low_frequency_cutoff=None, trunc_method=None):
    """Modify a PSD such that the impulse response associated with its inverse
    square root is no longer than `max_filter_len` time samples. In practice
    this corresponds to a coarse graining or smoothing of the PSD.

    Parameters
    ----------
    psd : FrequencySeries
        PSD whose inverse spectrum is to be truncated.
    max_filter_len : int
        Maximum length of the time-domain filter in samples.
    low_frequency_cutoff : {None, int}
        Frequencies below `low_frequency_cutoff` are zeroed in the output.
    trunc_method : {None, 'hann'}
        Function used for truncating the time-domain filter.
        None produces a hard truncation at `max_filter_len`.

    Returns
    -------
    psd : FrequencySeries
        PSD whose inverse spectrum has been truncated.

    Raises
    ------
    ValueError
        For invalid types or values of `max_filter_len` and `low_frequency_cutoff`.

    Notes
    -----
    See arXiv:gr-qc/0509116 for details.
    """
    # sanity checks
    if type(max_filter_len) is not int or max_filter_len <= 0:
        raise ValueError('max_filter_len must be a positive integer')
    if low_frequency_cutoff is not None and low_frequency_cutoff < 0 \
        or low_frequency_cutoff > psd.sample_frequencies[-1]:
        raise ValueError('low_frequency_cutoff must be within the bandwidth of the PSD')

    N = (len(psd)-1)*2

    inv_asd = FrequencySeries((1. / psd)**0.5, delta_f=psd.delta_f, \
        dtype=complex_same_precision_as(psd))
        
    inv_asd[0] = 0
    inv_asd[N/2] = 0
    q = TimeSeries(numpy.zeros(N), delta_t=(N / psd.delta_f), \
        dtype=real_same_precision_as(psd))

    if low_frequency_cutoff:
        kmin = int(low_frequency_cutoff / psd.delta_f)
        inv_asd[0:kmin] = 0

    ifft(inv_asd, q)
    
    trunc_start = max_filter_len / 2
    trunc_end = N - max_filter_len / 2

    if trunc_method == 'hann':
        trunc_window = Array(numpy.hanning(max_filter_len), dtype=q.dtype)
        q[0:trunc_start] *= trunc_window[max_filter_len/2:max_filter_len]
        q[trunc_end:N] *= trunc_window[0:max_filter_len/2]

    q[trunc_start:trunc_end] = 0
    psd_trunc = FrequencySeries(numpy.zeros(len(psd)), delta_f=psd.delta_f, \
                                dtype=complex_same_precision_as(psd))
    fft(q, psd_trunc)
    psd_trunc *= psd_trunc.conj()
    psd_out = 1. / abs(psd_trunc)

    return psd_out

def power_chisq_from_precomputed(corr, snr, snr_norm, bins, indices=None):
    """Calculate the chisq timeseries from precomputed values

    This function calculates the chisq at all times by performing an
    inverse FFT of each bin.

    Parameters
    ----------

    corr: FrequencySeries
        The produce of the template and data in the frequency domain.
    snr: TimeSeries
        The unnormalized snr time series.
    snr_norm:
        The snr normalization factor (true snr = snr * snr_norm) EXPLAINME - define 'true snr'?
    bins: List of integers
        The edges of the chisq bins.
    indices: {Array, None}, optional
        Index values into snr that indicate where to calculate
        chisq values. If none, calculate chisq for all possible indices.

    Returns
    -------
    chisq: TimeSeries
    """
    # Get workspace memory
    global _q_l, _qtilde_l, _chisq_l

    if _q_l is None or len(_q_l) != len(snr):
        q = zeros(len(snr), dtype=complex_same_precision_as(snr))
        qtilde = zeros(len(snr), dtype=complex_same_precision_as(snr))
        _q_l = q
        _qtilde_l = qtilde
    else:
        q = _q_l
        qtilde = _qtilde_l

    if indices is not None:
        snr = snr.take(indices)

    if _chisq_l is None or len(_chisq_l) < len(snr):
        chisq = zeros(len(snr), dtype=real_same_precision_as(snr))
        _chisq_l = chisq
    else:
        chisq = _chisq_l[0:len(snr)]
        chisq.clear()

    num_bins = len(bins) - 1

    for j in range(num_bins):
        k_min = int(bins[j])
        k_max = int(bins[j+1])

        qtilde[k_min:k_max] = corr[k_min:k_max]
        pycbc.fft.ifft(qtilde, q)
        qtilde[k_min:k_max].clear()

        if indices is not None:
            chisq_accum_bin(chisq, q.take(indices))
        else:
            chisq_accum_bin(chisq, q)

    chisq = (chisq * num_bins - snr.squared_norm()) * (snr_norm ** 2.0)

    if indices is not None:
        return chisq
    else:
        return TimeSeries(chisq, delta_t=snr.delta_t, epoch=snr.start_time, copy=False)

def get_two_pol_waveform_filter(outplus, outcross, template, **kwargs):
    """Return a frequency domain waveform filter for the specified approximant.
    Unlike get_waveform_filter this function returns both h_plus and h_cross
    components of the waveform, which are needed for searches where h_plus
    and h_cross are not related by a simple phase shift.
    """
    n = len(outplus)

    # If we don't have an inclination column alpha3 might be used
    if not hasattr(template, 'inclination') and 'inclination' not in kwargs:
        if hasattr(template, 'alpha3'):
            kwargs['inclination'] = template.alpha3

    input_params = props(template, **kwargs)

    if input_params['approximant'] in fd_approximants(_scheme.mgr.state):
        wav_gen = fd_wav[type(_scheme.mgr.state)]
        hp, hc = wav_gen[input_params['approximant']](**input_params)
        hp.resize(n)
        hc.resize(n)
        outplus[0:len(hp)] = hp[:]
        hp = FrequencySeries(outplus, delta_f=hp.delta_f, copy=False)
        outcross[0:len(hc)] = hc[:]
        hc = FrequencySeries(outcross, delta_f=hc.delta_f, copy=False)
        hp.chirp_length = get_waveform_filter_length_in_time(**input_params)
        hp.length_in_time = hp.chirp_length
        hc.chirp_length = hp.chirp_length
        hc.length_in_time = hp.length_in_time
        return hp, hc
    elif input_params['approximant'] in td_approximants(_scheme.mgr.state):
        # N: number of time samples required
        N = (n-1)*2
        delta_f = 1.0 / (N * input_params['delta_t'])
        wav_gen = td_wav[type(_scheme.mgr.state)]
        hp, hc = wav_gen[input_params['approximant']](**input_params)
        # taper the time series hp if required
        if 'taper' in input_params.keys() and \
                input_params['taper'] is not None:
            hp = wfutils.taper_timeseries(hp, input_params['taper'],
                                          return_lal=False)
            hc = wfutils.taper_timeseries(hc, input_params['taper'],
                                          return_lal=False)
        # total duration of the waveform
        tmplt_length = len(hp) * hp.delta_t
        # for IMR templates the zero of time is at max amplitude (merger)
        # thus the start time is minus the duration of the template from
        # lower frequency cutoff to merger, i.e. minus the 'chirp time'
        tChirp = - float( hp.start_time )  # conversion from LIGOTimeGPS
        hp.resize(N)
        hc.resize(N)
        k_zero = int(hp.start_time / hp.delta_t)
        hp.roll(k_zero)
        hc.roll(k_zero)
        hp_tilde = FrequencySeries(outplus, delta_f=delta_f, copy=False)
        hc_tilde = FrequencySeries(outcross, delta_f=delta_f, copy=False)
        fft(hp.astype(real_same_precision_as(hp_tilde)), hp_tilde)
        fft(hc.astype(real_same_precision_as(hc_tilde)), hc_tilde)
        hp_tilde.length_in_time = tmplt_length
        hp_tilde.chirp_length = tChirp
        hc_tilde.length_in_time = tmplt_length
        hc_tilde.chirp_length = tChirp
        return hp_tilde, hc_tilde
    else:
        raise ValueError("Approximant %s not available" %
                            (input_params['approximant']))

def compress_waveform(htilde, sample_points, tolerance, interpolation,
        decomp_scratch=None):
    """Retrieves the amplitude and phase at the desired sample points, and adds
    frequency points in order to ensure that the interpolated waveform
    has a mismatch with the full waveform that is <= the desired tolerance. The
    mismatch is computed by finding 1-overlap between `htilde` and the
    decompressed waveform; no maximimization over phase/time is done, nor is
    any PSD used.
    
    .. note::
        The decompressed waveform is only garaunteed to have a true mismatch
        <= the tolerance for the given `interpolation` and for no PSD.
        However, since no maximization over time/phase is performed when
        adding points, the actual mismatch between the decompressed waveform
        and `htilde` is better than the tolerance, using no PSD. Using a PSD
        does increase the mismatch, and can lead to mismatches > than the
        desired tolerance, but typically by only a factor of a few worse.

    Parameters
    ----------
    htilde : FrequencySeries
        The waveform to compress.
    sample_points : array
        The frequencies at which to store the amplitude and phase. More points
        may be added to this, depending on the desired tolerance.
    tolerance : float
        The maximum mismatch to allow between a decompressed waveform and
        `htilde`.
    interpolation : str
        The interpolation to use for decompressing the waveform when computing
        overlaps.
    decomp_scratch : {None, FrequencySeries}
        Optionally provide scratch space for decompressing the waveform. The
        provided frequency series must have the same `delta_f` and length
        as `htilde`.

    Returns
    -------
    CompressedWaveform
        The compressed waveform data; see `CompressedWaveform` for details.
    """
    fmin = sample_points.min()
    df = htilde.delta_f
    sample_index = (sample_points / df).astype(int)
    amp = utils.amplitude_from_frequencyseries(htilde)
    phase = utils.phase_from_frequencyseries(htilde)

    comp_amp = amp.take(sample_index)
    comp_phase = phase.take(sample_index)
    if decomp_scratch is None:
        outdf = df
    else:
        outdf = None
    out = decomp_scratch
    hdecomp = fd_decompress(comp_amp, comp_phase, sample_points,
        out=decomp_scratch, df=outdf, f_lower=fmin,
        interpolation=interpolation)
    mismatch = 1. - filter.overlap(hdecomp, htilde, low_frequency_cutoff=fmin)
    if mismatch > tolerance:
        # we'll need the difference in the waveforms as a function of frequency
        vecdiffs = vecdiff(htilde, hdecomp, sample_points)

    # We will find where in the frequency series the interpolated waveform
    # has the smallest overlap with the full waveform, add a sample point
    # there, and re-interpolate. We repeat this until the overall mismatch
    # is > than the desired tolerance 
    added_points = []
    while mismatch > tolerance:
        minpt = vecdiffs.argmax()
        # add a point at the frequency halfway between minpt and minpt+1
        add_freq = sample_points[[minpt, minpt+1]].mean()
        addidx = int(add_freq/df)
        new_index = numpy.zeros(sample_index.size+1, dtype=int)
        new_index[:minpt+1] = sample_index[:minpt+1]
        new_index[minpt+1] = addidx
        new_index[minpt+2:] = sample_index[minpt+1:]
        sample_index = new_index
        sample_points = (sample_index * df).astype(
            real_same_precision_as(htilde))
        # get the new compressed points
        comp_amp = amp.take(sample_index)
        comp_phase = phase.take(sample_index)
        # update the vecdiffs and mismatch
        hdecomp = fd_decompress(comp_amp, comp_phase, sample_points,
            out=decomp_scratch, df=outdf, f_lower=fmin,
            interpolation=interpolation)
        new_vecdiffs = numpy.zeros(vecdiffs.size+1)
        new_vecdiffs[:minpt] = vecdiffs[:minpt]
        new_vecdiffs[minpt+2:] = vecdiffs[minpt+1:]
        new_vecdiffs[minpt:minpt+2] = vecdiff(htilde, hdecomp,
            sample_points[minpt:minpt+2])
        vecdiffs = new_vecdiffs
        mismatch = 1. - filter.overlap(hdecomp, htilde,
            low_frequency_cutoff=fmin)
        added_points.append(addidx)
    logging.info("mismatch: %f, N points: %i (%i added)" %(mismatch,
        len(comp_amp), len(added_points)))
    
    return CompressedWaveform(sample_points, comp_amp, comp_phase,
                interpolation=interpolation, tolerance=tolerance,
#.........这里部分代码省略.........

def bank_chisq_from_filters(tmplt_snr, tmplt_norm, bank_snrs, bank_norms,
        tmplt_bank_matches, indices=None):
    """ This function calculates and returns a TimeSeries object containing the
    bank veto calculated over a segment.

    Parameters
    ----------
    tmplt_snr: TimeSeries
        The SNR time series from filtering the segment against the current
        search template
    tmplt_norm: float
        The normalization factor for the search template
    bank_snrs: list of TimeSeries
        The precomputed list of SNR time series between each of the bank veto
        templates and the segment
    bank_norms: list of floats
        The normalization factors for the list of bank veto templates
        (usually this will be the same for all bank veto templates)
    tmplt_bank_matches: list of floats
        The complex overlap between the search template and each
        of the bank templates
    indices: {None, Array}, optional
        Array of indices into the snr time series. If given, the bank chisq
        will only be calculated at these values.

    Returns
    -------
    bank_chisq: TimeSeries of the bank vetos
    """
    if indices is not None:
        tmplt_snr = Array(tmplt_snr, copy=False)
        bank_snrs_tmp = []
        for bank_snr in bank_snrs:
            bank_snrs_tmp.append(bank_snr.take(indices))
        bank_snrs=bank_snrs_tmp

    # Initialise bank_chisq as 0s everywhere
    bank_chisq = zeros(len(tmplt_snr), dtype=real_same_precision_as(tmplt_snr))

    # Loop over all the bank templates
    for i in range(len(bank_snrs)):
        bank_match = tmplt_bank_matches[i]
        if (abs(bank_match) > 0.99):
            # Not much point calculating bank_chisquared if the bank template
            # is very close to the filter template. Can also hit numerical
            # error due to approximations made in this calculation.
            # The value of 2 is the expected addition to the chisq for this
            # template
            bank_chisq += 2.
            continue
        bank_norm = sqrt((1 - bank_match*bank_match.conj()).real)

        bank_SNR = bank_snrs[i] * (bank_norms[i] / bank_norm)
        tmplt_SNR = tmplt_snr * (bank_match.conj() * tmplt_norm / bank_norm)

        bank_SNR = Array(bank_SNR, copy=False)
        tmplt_SNR = Array(tmplt_SNR, copy=False)

        bank_chisq += (bank_SNR - tmplt_SNR).squared_norm()

    if indices is not None:
        return bank_chisq
    else:
        return TimeSeries(bank_chisq, delta_t=tmplt_snr.delta_t,
                          epoch=tmplt_snr.start_time, copy=False)