Пример #1
0
def generate_analytic_waveform(mass_rat,
                               eccentricity,
                               approximant='TaylorF2Ecc',
                               total_m=50,
                               f_lower=20.,
                               delta_f=0.1):
    mass1, mass2 = q_to_masses(mass_rat, total_m)
    hp, hc = hp, hc = get_fd_waveform(mass1=mass1,
                                      mass2=mass2,
                                      delta_f=delta_f,
                                      f_lower=f_lower,
                                      approximant=approximant,
                                      eccentricity=eccentricity)
    hs = hp + hc * 1j
    amp = amplitude_from_frequencyseries(
        types.FrequencySeries(hs, delta_f=delta_f))
    phase = phase_from_frequencyseries(
        types.FrequencySeries(hs, delta_f=delta_f))
    return hp.sample_frequencies.data, np.real(hp.data), np.real(
        hc.data), np.imag(hp.data), np.imag(hc.data), amp.data, phase.data
Пример #2
0
def fmoment(n, htilde, psd, frange):
    """
    Compute the n-th moment of frequency
    """

    # Get frequency series of waveform
    f  = htilde.get_sample_frequencies()

    fhtilde = types.FrequencySeries(initial_array=htilde.data * f.data**n,
            delta_f=htilde.delta_f)

    snrsq = sigmasq(htilde=htilde, psd=psd, low_frequency_cutoff=frange[0],
            high_frequency_cutoff=frange[1])

    return (1.0/snrsq) * overlap(fhtilde, htilde, psd=psd,
            low_frequency_cutoff=frange[0], high_frequency_cutoff=frange[1],
            normalized=False)
Пример #3
0
    def to_pycbc(self, copy=True):
        """Convert this `FrequencySeries` into a
        `~pycbc.types.frequencyseries.FrequencySeries`

        Parameters
        ----------
        copy : `bool`, optional, default: `True`
            if `True`, copy these data to a new array

        Returns
        -------
        frequencyseries : `pycbc.types.frequencyseries.FrequencySeries`
            a PyCBC representation of this `FrequencySeries`
        """
        from pycbc import types

        if self.epoch is None:
            epoch = None
        else:
            epoch = self.epoch.gps
        return types.FrequencySeries(self.value,
                                     delta_f=self.df.to('Hz').value,
                                     epoch=epoch, copy=copy)
Пример #4
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def create_tf_plane(fd_psd,nchans,seg_len,filter_bank,band,fs_data):
    """
    Create time-frequency map

    Parameters
    ----------
    fd_psd : array
      Power Spectrum Density
    """
    print "|-- Create time-frequency plane for current block"
    # Return the complex snr, along with its associated normalization of the template,
    # matched filtered against the data
    #filter.matched_filter_core(types.FrequencySeries(tmp_filter_bank,delta_f=fd_psd.delta_f),fs_data,h_norm=1,psd=fd_psd,low_frequency_cutoff=filter_bank[0].f0,high_frequency_cutoff=filter_bank[0].f0+2*band)
    print "|-- Filtering all %d channels..." % nchans
    # Initialise 2D zero array 
    tmp_filter_bank = numpy.zeros(len(fd_psd), dtype=numpy.complex128)
    # Initialise 2D zero array for time-frequency map
    tf_map = numpy.zeros((nchans, seg_len), dtype=numpy.complex128)
    # Loop over all the channels
    for i in range(nchans):
        # Reset filter bank series
        tmp_filter_bank *= 0.0
        # Index of starting frequency
        f1 = int(filter_bank[i].f0/fd_psd.delta_f)
        # Index of ending frequency
        f2 = int((filter_bank[i].f0 + 2*band)/fd_psd.delta_f)+1
        # (FIXME: Why is there a factor of 2 here?)
        tmp_filter_bank[f1:f2] = filter_bank[i].data.data * 2
        # Define the template to filter the frequency series with
        template = types.FrequencySeries(tmp_filter_bank, delta_f=fd_psd.delta_f, copy=False)
        # Create filtered series
        filtered_series = filter.matched_filter_core(template,fs_data,h_norm=None,psd=None,
                                                     low_frequency_cutoff=filter_bank[i].f0,
                                                     high_frequency_cutoff=filter_bank[i].f0+2*band)
        # Include filtered series in the map
        tf_map[i,:] = filtered_series[0].numpy()
    return tf_map
Пример #5
0
def excess_power2(
    ts_data,  # Time series from magnetic field data
    psd_segment_length,  # Length of each segment in seconds
    psd_segment_stride,  # Separation between 2 consecutive segments in seconds
    psd_estimation,  # Average method
    window_fraction,  # Withening window fraction
    tile_fap,  # Tile false alarm probability threshold in Gaussian noise.
    station,  # Station
    nchans=None,  # Total number of channels
    band=None,  # Channel bandwidth
    fmin=0,  # Lowest frequency of the filter bank.
    fmax=None,  # Highest frequency of the filter bank.
    max_duration=None,  # Maximum duration of the tile
    wtype='tukey'):  # Whitening type, can tukey or hann
    """
    Perform excess-power search analysis on magnetic field data.
    This method will produce a bunch of time-frequency plots for every
    tile duration and bandwidth analysed as well as a XML file identifying
    all the triggers found in the selected data within the user-defined
    time range.

    Parameters
    ----------
    ts_data : TimeSeries
      Time Series from magnetic field data
    psd_segment_length : float
      Length of each segment in seconds
    psd_segment_stride : float
      Separation between 2 consecutive segments in seconds
    psd_estimation : string
      Average method
    window_fraction : float
      Withening window fraction
    tile_fap : float
      Tile false alarm probability threshold in Gaussian noise.
    nchans : int
      Total number of channels
    band : float
      Channel bandwidth
    fmin : float
      Lowest frequency of the filter bank.
    fmax : float
      Highest frequency of the filter bank
    """
    # Determine sampling rate based on extracted time series
    sample_rate = ts_data.sample_rate
    # Check if tile maximum frequency is not defined
    if fmax is None or fmax > sample_rate / 2.:
        # Set the tile maximum frequency equal to the Nyquist frequency
        # (i.e. half the sampling rate)
        fmax = sample_rate / 2.0
    # Check whether or not tile bandwidth and channel are defined
    if band is None and nchans is None:
        # Exit program with error message
        exit("Either bandwidth or number of channels must be specified...")
    else:
        # Check if tile maximum frequency larger than its minimum frequency
        assert fmax >= fmin
        # Define spectral band of data
        data_band = fmax - fmin
        # Check whether tile bandwidth or channel is defined
        if band is not None:
            # Define number of possible filter bands
            nchans = int(data_band / band) - 1
        elif nchans is not None:
            # Define filter bandwidth
            band = data_band / nchans
            nchans = nchans - 1
        # Check if number of channels is superior than unity
        assert nchans > 1
    # Print segment information
    print '|- Estimating PSD from segments of time',
    print '%.2f s in length, with %.2f s stride...' % (psd_segment_length,
                                                       psd_segment_stride)
    # Convert time series as array of float
    data = ts_data.astype(numpy.float64)
    # Define segment length for PSD estimation in sample unit
    seg_len = int(psd_segment_length * sample_rate)
    # Define separation between consecutive segments in sample unit
    seg_stride = int(psd_segment_stride * sample_rate)
    # Calculate the overall PSD from individual PSD segments
    fd_psd = psd.welch(data,
                       avg_method=psd_estimation,
                       seg_len=seg_len,
                       seg_stride=seg_stride)
    # We need this for the SWIG functions...
    lal_psd = fd_psd.lal()
    # Plot the power spectral density
    plot_spectrum(fd_psd)
    # Create whitening window
    print "|- Whitening window and spectral correlation..."
    if wtype == 'hann':
        window = lal.CreateHannREAL8Window(seg_len)
    elif wtype == 'tukey':
        window = lal.CreateTukeyREAL8Window(seg_len, window_fraction)
    else:
        raise ValueError("Can't handle window type %s" % wtype)
    # Create FFT plan
    fft_plan = lal.CreateForwardREAL8FFTPlan(len(window.data.data), 1)
    # Perform two point spectral correlation
    spec_corr = lal.REAL8WindowTwoPointSpectralCorrelation(window, fft_plan)
    # Initialise filter bank
    print "|- Create filter..."
    filter_bank, fdb = [], []
    # Loop for each channels
    for i in range(nchans):
        channel_flow = fmin + band / 2 + i * band
        channel_width = band
        # Create excess power filter
        lal_filter = lalburst.CreateExcessPowerFilter(channel_flow,
                                                      channel_width, lal_psd,
                                                      spec_corr)
        filter_bank.append(lal_filter)
        fdb.append(Spectrum.from_lal(lal_filter))
    # Calculate the minimum bandwidth
    min_band = (len(filter_bank[0].data.data) - 1) * filter_bank[0].deltaF / 2
    # Plot filter bank
    plot_bank(fdb)
    # Convert filter bank from frequency to time domain
    print "|- Convert all the frequency domain to the time domain..."
    tdb = []
    # Loop for each filter's spectrum
    for fdt in fdb:
        zero_padded = numpy.zeros(int((fdt.f0 / fdt.df).value) + len(fdt))
        st = int((fdt.f0 / fdt.df).value)
        zero_padded[st:st + len(fdt)] = numpy.real_if_close(fdt.value)
        n_freq = int(sample_rate / 2 / fdt.df.value) * 2
        tdt = numpy.fft.irfft(zero_padded, n_freq) * math.sqrt(sample_rate)
        tdt = numpy.roll(tdt, len(tdt) / 2)
        tdt = TimeSeries(tdt,
                         name="",
                         epoch=fdt.epoch,
                         sample_rate=sample_rate)
        tdb.append(tdt)
    # Plot time series filter
    plot_filters(tdb, fmin, band)
    # Compute the renormalization for the base filters up to a given bandwidth.
    mu_sq_dict = {}
    # Loop through powers of 2 up to number of channels
    for nc_sum in range(0, int(math.log(nchans, 2))):
        nc_sum = 2**nc_sum - 1
        print "|- Calculating renormalization for resolution level containing %d %fHz channels" % (
            nc_sum + 1, min_band)
        mu_sq = (nc_sum + 1) * numpy.array([
            lalburst.ExcessPowerFilterInnerProduct(f, f, spec_corr, None)
            for f in filter_bank
        ])
        # Uncomment to get all possible frequency renormalizations
        #for n in xrange(nc_sum, nchans): # channel position index
        for n in xrange(nc_sum, nchans, nc_sum + 1):  # channel position index
            for k in xrange(0, nc_sum):  # channel sum index
                # FIXME: We've precomputed this, so use it instead
                mu_sq[n] += 2 * lalburst.ExcessPowerFilterInnerProduct(
                    filter_bank[n - k], filter_bank[n - 1 - k], spec_corr,
                    None)
        #print mu_sq[nc_sum::nc_sum+1]
        mu_sq_dict[nc_sum] = mu_sq
    # Create an event list where all the triggers will be stored
    event_list = lsctables.New(lsctables.SnglBurstTable, [
        'start_time', 'start_time_ns', 'peak_time', 'peak_time_ns', 'duration',
        'bandwidth', 'central_freq', 'chisq_dof', 'confidence', 'snr',
        'amplitude', 'channel', 'ifo', 'process_id', 'event_id', 'search',
        'stop_time', 'stop_time_ns'
    ])
    # Create repositories to save TF and time series plots
    os.system('mkdir -p segments/time-frequency')
    os.system('mkdir -p segments/time-series')
    # Define time edges
    t_idx_min, t_idx_max = 0, seg_len
    while t_idx_max <= len(ts_data):
        # Define starting and ending time of the segment in seconds
        start_time = ts_data.start_time + t_idx_min / float(
            ts_data.sample_rate)
        end_time = ts_data.start_time + t_idx_max / float(ts_data.sample_rate)
        print "\n|-- Analyzing block %i to %i (%.2f percent)" % (
            start_time, end_time, 100 * float(t_idx_max) / len(ts_data))
        # Model a withen time series for the block
        tmp_ts_data = types.TimeSeries(ts_data[t_idx_min:t_idx_max] *
                                       window.data.data,
                                       delta_t=1. / ts_data.sample_rate,
                                       epoch=start_time)
        # Save time series in relevant repository
        segfolder = 'segments/%i-%i' % (start_time, end_time)
        os.system('mkdir -p ' + segfolder)
        plot_ts(tmp_ts_data,
                fname='segments/time-series/%i-%i.png' %
                (start_time, end_time))
        # Convert times series to frequency series
        fs_data = tmp_ts_data.to_frequencyseries()
        print "|-- Frequency series data has variance: %s" % fs_data.data.std(
        )**2
        # Whitening (FIXME: Whiten the filters, not the data)
        fs_data.data /= numpy.sqrt(fd_psd) / numpy.sqrt(2 * fd_psd.delta_f)
        print "|-- Whitened frequency series data has variance: %s" % fs_data.data.std(
        )**2
        print "|-- Create time-frequency plane for current block"
        # Return the complex snr, along with its associated normalization of the template,
        # matched filtered against the data
        #filter.matched_filter_core(types.FrequencySeries(tmp_filter_bank,delta_f=fd_psd.delta_f),
        #                           fs_data,h_norm=1,psd=fd_psd,low_frequency_cutoff=filter_bank[0].f0,
        #                           high_frequency_cutoff=filter_bank[0].f0+2*band)
        print "|-- Filtering all %d channels..." % nchans
        # Initialise 2D zero array
        tmp_filter_bank = numpy.zeros(len(fd_psd), dtype=numpy.complex128)
        # Initialise 2D zero array for time-frequency map
        tf_map = numpy.zeros((nchans, seg_len), dtype=numpy.complex128)
        # Loop over all the channels
        for i in range(nchans):
            # Reset filter bank series
            tmp_filter_bank *= 0.0
            # Index of starting frequency
            f1 = int(filter_bank[i].f0 / fd_psd.delta_f)
            # Index of ending frequency
            f2 = int((filter_bank[i].f0 + 2 * band) / fd_psd.delta_f) + 1
            # (FIXME: Why is there a factor of 2 here?)
            tmp_filter_bank[f1:f2] = filter_bank[i].data.data * 2
            # Define the template to filter the frequency series with
            template = types.FrequencySeries(tmp_filter_bank,
                                             delta_f=fd_psd.delta_f,
                                             copy=False)
            # Create filtered series
            filtered_series = filter.matched_filter_core(
                template,
                fs_data,
                h_norm=None,
                psd=None,
                low_frequency_cutoff=filter_bank[i].f0,
                high_frequency_cutoff=filter_bank[i].f0 + 2 * band)
            # Include filtered series in the map
            tf_map[i, :] = filtered_series[0].numpy()
        # Plot spectrogram
        plot_spectrogram(numpy.abs(tf_map).T,
                         tmp_ts_data.delta_t,
                         band,
                         ts_data.sample_rate,
                         start_time,
                         end_time,
                         fname='segments/time-frequency/%i-%i.png' %
                         (start_time, end_time))
        # Loop through all summed channels
        for nc_sum in range(0, int(math.log(nchans, 2)))[::-1]:
            nc_sum = 2**nc_sum - 1
            mu_sq = mu_sq_dict[nc_sum]
            # Clip the boundaries to remove window corruption
            clip_samples = int(psd_segment_length * window_fraction *
                               ts_data.sample_rate / 2)
            # Constructing tile and calculate their energy
            print "\n|--- Constructing tile with %d summed channels..." % (
                nc_sum + 1)
            # Current bandwidth of the time-frequency map tiles
            df = band * (nc_sum + 1)
            dt = 1.0 / (2 * df)
            # How much each "step" is in the time domain -- under sampling rate
            us_rate = int(round(dt / ts_data.delta_t))
            print "|--- Undersampling rate for this level: %f" % (
                ts_data.sample_rate / us_rate)
            print "|--- Calculating tiles..."
            # Making independent tiles
            # because [0:-0] does not give the full array
            tf_map_temp = tf_map[:,clip_samples:-clip_samples:us_rate] \
                          if clip_samples > 0 else tf_map[:,::us_rate]
            tiles = tf_map_temp.copy()
            # Here's the deal: we're going to keep only the valid output and
            # it's *always* going to exist in the lowest available indices
            stride = nc_sum + 1
            for i in xrange(tiles.shape[0] / stride):
                numpy.absolute(tiles[stride * i:stride * (i + 1)].sum(axis=0),
                               tiles[stride * (i + 1) - 1])
            tiles = tiles[nc_sum::nc_sum + 1].real**2 / mu_sq[nc_sum::nc_sum +
                                                              1].reshape(
                                                                  -1, 1)
            print "|--- TF-plane is %dx%s samples" % tiles.shape
            print "|--- Tile energy mean %f, var %f" % (numpy.mean(tiles),
                                                        numpy.var(tiles))
            # Define maximum number of degrees of freedom and check it larger or equal to 2
            max_dof = 32 if max_duration == None else 2 * max_duration * df
            assert max_dof >= 2
            # Loop through multiple degrees of freedom
            for j in [2**l for l in xrange(0, int(math.log(max_dof, 2)))]:
                # Duration is fixed by the NDOF and bandwidth
                duration = j * dt
                print "\n|----- Explore signal duration of %f s..." % duration
                print "|----- Summing DOF = %d ..." % (2 * j)
                tlen = tiles.shape[1] - 2 * j + 1 + 1
                dof_tiles = numpy.zeros((tiles.shape[0], tlen))
                sum_filter = numpy.array([1, 0] * (j - 1) + [1])
                for f in range(tiles.shape[0]):
                    # Sum and drop correlate tiles
                    dof_tiles[f] = fftconvolve(tiles[f], sum_filter, 'valid')
                print "|----- Summed tile energy mean: %f, var %f" % (
                    numpy.mean(dof_tiles), numpy.var(dof_tiles))
                plot_spectrogram(
                    dof_tiles.T,
                    dt,
                    df,
                    ts_data.sample_rate,
                    start_time,
                    end_time,
                    fname='segments/%i-%i/tf_%02ichans_%02idof.png' %
                    (start_time, end_time, nc_sum + 1, 2 * j))
                threshold = scipy.stats.chi2.isf(tile_fap, j)
                print "|------ Threshold for this level: %f" % threshold
                spant, spanf = dof_tiles.shape[1] * dt, dof_tiles.shape[0] * df
                print "|------ Processing %.2fx%.2f time-frequency map." % (
                    spant, spanf)
                # Since we clip the data, the start time needs to be adjusted accordingly
                window_offset_epoch = fs_data.epoch + psd_segment_length * window_fraction / 2
                window_offset_epoch = LIGOTimeGPS(float(window_offset_epoch))
                for i, j in zip(*numpy.where(dof_tiles > threshold)):
                    event = event_list.RowType()
                    # The points are summed forward in time and thus a `summed point' is the
                    # sum of the previous N points. If this point is above threshold, it
                    # corresponds to a tile which spans the previous N points. However, the
                    # 0th point (due to the convolution specifier 'valid') is actually
                    # already a duration from the start time. All of this means, the +
                    # duration and the - duration cancels, and the tile 'start' is, by
                    # definition, the start of the time frequency map if j = 0
                    # FIXME: I think this needs a + dt/2 to center the tile properly
                    event.set_start(window_offset_epoch + float(j * dt))
                    event.set_stop(window_offset_epoch + float(j * dt) +
                                   duration)
                    event.set_peak(event.get_start() + duration / 2)
                    event.central_freq = filter_bank[
                        0].f0 + band / 2 + i * df + 0.5 * df
                    event.duration = duration
                    event.bandwidth = df
                    event.chisq_dof = 2 * duration * df
                    event.snr = math.sqrt(dof_tiles[i, j] / event.chisq_dof -
                                          1)
                    # FIXME: Magic number 0.62 should be determine empircally
                    event.confidence = -lal.LogChisqCCDF(
                        event.snr * 0.62, event.chisq_dof * 0.62)
                    event.amplitude = None
                    event.process_id = None
                    event.event_id = event_list.get_next_id()
                    event_list.append(event)
                for event in event_list[::-1]:
                    if event.amplitude != None:
                        continue
                    etime_min_idx = float(event.get_start()) - float(
                        fs_data.epoch)
                    etime_min_idx = int(etime_min_idx / tmp_ts_data.delta_t)
                    etime_max_idx = float(event.get_start()) - float(
                        fs_data.epoch) + event.duration
                    etime_max_idx = int(etime_max_idx / tmp_ts_data.delta_t)
                    # (band / 2) to account for sin^2 wings from finest filters
                    flow_idx = int((event.central_freq - event.bandwidth / 2 -
                                    (df / 2) - fmin) / df)
                    fhigh_idx = int((event.central_freq + event.bandwidth / 2 +
                                     (df / 2) - fmin) / df)
                    # TODO: Check that the undersampling rate is always commensurate
                    # with the indexing: that is to say that
                    # mod(etime_min_idx, us_rate) == 0 always
                    z_j_b = tf_map[flow_idx:fhigh_idx,
                                   etime_min_idx:etime_max_idx:us_rate]
                    event.amplitude = 0
                print "|------ Total number of events: %d" % len(event_list)
        t_idx_min += int(seg_len * (1 - window_fraction))
        t_idx_max += int(seg_len * (1 - window_fraction))
    setname = "MagneticFields"
    __program__ = 'pyburst_excesspower'
    start_time = LIGOTimeGPS(int(ts_data.start_time))
    end_time = LIGOTimeGPS(int(ts_data.end_time))
    inseg = segment(start_time, end_time)
    xmldoc = ligolw.Document()
    xmldoc.appendChild(ligolw.LIGO_LW())
    ifo = 'H1'  #channel_name.split(":")[0]
    straindict = psd.insert_psd_option_group.__dict__
    proc_row = register_to_xmldoc(xmldoc,
                                  __program__,
                                  straindict,
                                  ifos=[ifo],
                                  version=git_version.id,
                                  cvs_repository=git_version.branch,
                                  cvs_entry_time=git_version.date)
    dt_stride = psd_segment_length
    sample_rate = ts_data.sample_rate
    # Amount to overlap successive blocks so as not to lose data
    window_overlap_samples = window_fraction * sample_rate
    outseg = inseg.contract(window_fraction * dt_stride / 2)
    # With a given dt_stride, we cannot process the remainder of this data
    remainder = math.fmod(abs(outseg), dt_stride * (1 - window_fraction))
    # ...so make an accounting of it
    outseg = segment(outseg[0], outseg[1] - remainder)
    ss = append_search_summary(xmldoc,
                               proc_row,
                               ifos=(station, ),
                               inseg=inseg,
                               outseg=outseg)
    for sb in event_list:
        sb.process_id = proc_row.process_id
        sb.search = proc_row.program
        sb.ifo, sb.channel = station, setname
    xmldoc.childNodes[0].appendChild(event_list)
    fname = 'excesspower.xml.gz'
    utils.write_filename(xmldoc, fname, gz=fname.endswith("gz"))
Пример #6
0
def get_waveform(approximant,
                 phase_order,
                 amplitude_order,
                 spin_order,
                 template_params,
                 start_frequency,
                 sample_rate,
                 length,
                 datafile=None,
                 verbose=False):
    delta_t = 1. / sample_rate
    delta_f = 1. / length
    filter_N = int(length)
    filter_n = filter_N / 2 + 1
    if approximant in waveform.fd_approximants(
    ) and 'Eccentric' not in approximant:
        print("NORMAL FD WAVEFORM for", approximant)
        delta_f = sample_rate / length
        hplus, hcross = waveform.get_fd_waveform(
            template_params,
            approximant=approximant,
            spin_order=spin_order,
            phase_order=phase_order,
            delta_f=delta_f,
            f_lower=start_frequency,
            amplitude_order=amplitude_order)
    elif approximant in waveform.td_approximants(
    ) and 'Eccentric' not in approximant:
        print("NORMAL TD WAVEFORM for", approximant)
        hplus, hcross = waveform.get_td_waveform(
            template_params,
            approximant=approximant,
            spin_order=spin_order,
            phase_order=phase_order,
            delta_t=1.0 / sample_rate,
            f_lower=start_frequency,
            amplitude_order=amplitude_order)
    elif 'EccentricIMR' in approximant:
        # {{{
        # Legacy support
        import sys
        sys.path.append('/home/kuma/grav/kuma/src/Eccentric_IMR/Codes/Python/')
        import EccentricIMR as Ecc
        try:
            mass1 = getattr(template_params, 'mass1')
            mass2 = getattr(template_params, 'mass2')
        except:
            raise RuntimeError("template_params does not have mass1 or mass2!")
        try:
            ecc = getattr(template_params, 'alpha1')
            if 'E0' in approximant:
                ecc = 0
            anom = getattr(template_params, 'alpha2')
            inc = getattr(template_params, 'inclination')
            rtrans = getattr(template_params, 'alpha')
            beta = 0
        except:
            raise RuntimeError(
                "template_params does not have alpha{,1,2} or inclination")
        tol = 1.e-16
        fmin = start_frequency
        sample_rate = sample_rate
        #
        print(" Using phase order: %d" % phase_order, file=sys.stdout)
        sys.stdout.flush()
        hplus, hcross = Ecc.generate_eccentric_waveform(
            mass1,
            mass2,
            ecc,
            anom,
            inc,
            beta,
            tol,
            r_transition=rtrans,
            phase_order=phase_order,
            fmin=fmin,
            sample_rate=sample_rate,
            inspiral_only=False)
        # }}}
    elif 'EccentricInspiral' in approximant:
        # {{{
        # Legacy support
        import sys
        sys.path.append('/home/kuma/grav/kuma/src/Eccentric_IMR/Codes/Python/')
        import EccentricIMR as Ecc
        try:
            mass1 = getattr(template_params, 'mass1')
            mass2 = getattr(template_params, 'mass2')
        except:
            raise RuntimeError("template_params does not have mass1 or mass2!")
        try:
            ecc = getattr(template_params, 'alpha1')
            if 'E0' in approximant:
                ecc = 0
            anom = getattr(template_params, 'alpha2')
            inc = getattr(template_params, 'inclination')
            beta = getattr(template_params, 'alpha')
        except:
            raise RuntimeError(
                "template_params does not have alpha{,1,2} or inclination")
        tol = 1.e-16
        fmin = start_frequency
        sample_rate = sample_rate
        #
        hplus, hcross = Ecc.generate_eccentric_waveform(
            mass1,
            mass2,
            ecc,
            anom,
            inc,
            beta,
            tol,
            phase_order=phase_order,
            fmin=fmin,
            sample_rate=sample_rate,
            inspiral_only=True)
        # }}}
    elif 'EccentricFD' in approximant:
        # {{{
        # Legacy support
        import lalsimulation as ls
        import lal
        delta_f = sample_rate / length
        try:
            mass1 = getattr(template_params, 'mass1')
            mass2 = getattr(template_params, 'mass2')
        except:
            raise RuntimeError("template_params does not have mass1 or mass2!")
        try:
            ecc = getattr(template_params, 'alpha1')
            if 'E0' in approximant:
                ecc = 0
            anom = getattr(template_params, 'alpha2')
            inc = getattr(template_params, 'inclination')
        except:
            raise RuntimeError(
                "template_params does not have alpha{1,2} or inclination")
        eccPar = ls.SimInspiralCreateTestGRParam("inclination_azimuth", inc)
        ls.SimInspiralAddTestGRParam(eccPar, "e_min", ecc)
        fmin = start_frequency
        fmax = sample_rate / 2
        #
        thp, thc = ls.SimInspiralChooseFDWaveform(
            0, delta_f, mass1 * lal.MSUN_SI, mass2 * lal.MSUN_SI, 0, 0, 0, 0,
            0, 0, fmin, fmax, 0, 1.e6 * lal.PC_SI, inc, 0, 0, None, eccPar, -1,
            7, ls.EccentricFD)
        hplus = types.FrequencySeries(thp.data.data[:],
                                      delta_f=thp.deltaF,
                                      epoch=thp.epoch)
        hcross = types.FrequencySeries(thc.data.data[:],
                                       delta_f=thc.deltaF,
                                       epoch=thc.epoch)
        # }}}
    elif 'FromDataFile' in approximant:
        # {{{
        # Legacy support
        if not os.path.exists(datafile):
            raise IOError("File %s not found!" % datafile)
        if verbose:
            print("Reading from data file %s" % datafile)

        # Figure out waveform parameters from filename
        #q_value, M_value, w_value, _, _ = EA.get_q_m_e_pn_o_from_filename(datafile)
        q_value, M_value, w_value = EA.get_q_m_e_from_filename(datafile)

        # Read data, down-sample (assume data file is more finely sampled than
        # needed, i.e. interpolation is NOT supported, nor will be)
        data = np.loadtxt(datafile)
        dt = data[1, 0] - data[0, 0]
        delta_t = 1. / sample_rate
        downsample_ratio = delta_t / dt
        if not approx_equal(downsample_ratio, np.int(downsample_ratio)):
            raise RuntimeError(
                "Cannot handling resampling at a fractional factor = %e" %
                downsample_ratio)
        elif verbose:
            print("Downsampling by a factor of %d" % int(downsample_ratio))
        h_real = types.TimeSeries(data[::int(downsample_ratio), 1] /
                                  DYN_RANGE_FAC,
                                  delta_t=delta_t)
        h_imag = types.TimeSeries(data[::int(downsample_ratio), 2] /
                                  DYN_RANGE_FAC,
                                  delta_t=delta_t)

        if verbose:
            print("max, min,len of h_real = ", max(h_real.data),
                  min(h_real.data), len(h_real.data))

        # Compute Strain
        tmplt_pars = template_params
        wav = generate_detector_strain(tmplt_pars, h_real, h_imag)
        wav = extend_waveform_TimeSeries(wav, filter_N)

        # Return TimeSeries with (m1, m2, w_value)
        m1, m2 = mtotal_eta_to_mass1_mass2(M_value,
                                           q_value / (1. + q_value)**2)
        htilde = make_frequency_series(wav)
        htilde = extend_waveform_FrequencySeries(htilde, filter_n)

        if verbose:
            print("ISNAN(htilde from file) = ", np.any(np.isnan(htilde.data)))
        return htilde, [m1, m2, w_value, dt]
        # }}}
    else:
        raise IOError(".. APPROXIMANT %s not found.." % approximant)
    ##
    hvec = hplus
    htilde = make_frequency_series(hvec)
    htilde = extend_waveform_FrequencySeries(htilde, filter_n)

    if any(isnan(hplus.data)) or any(isnan(hcross.data)):
        print("..### %s hplus or hcross have NANS!!" % approximant)
    if any(isinf(hplus.data)) or any(isinf(hcross.data)):
        print("..### %s hplus or hcross have INFS!!" % approximant)
    if any(isnan(htilde.data)):
        print("..### %s Fourier transform htilde has NANS!!" % approximant)
    if any(isinf(htilde.data)):
        print("..### %s Fourier transform htilde has INFS!!" % approximant)
    return htilde
Пример #7
0
def excess_power(
    ts_data,  # Time series from magnetic field data 
    band=None,  # Channel bandwidth
    channel_name='channel-name',  # Channel name
    fmin=0,  # Lowest frequency of the filter bank.
    fmax=None,  # Highest frequency of the filter bank.
    impulse=False,  # Impulse response
    make_plot=True,  # Condition to produce plots
    max_duration=None,  # Maximum duration of the tile
    nchans=256,  # Total number of channels
    psd_estimation='median-mean',  # Average method
    psd_segment_length=60,  # Length of each segment in seconds
    psd_segment_stride=30,  # Separation between 2 consecutive segments in seconds
    station='station-name',  # Station name
    tile_fap=1e-7,  # Tile false alarm probability threshold in Gaussian noise.
    verbose=True,  # Print details
    window_fraction=0,  # Withening window fraction
    wtype='tukey'):  # Whitening type, can tukey or hann
    '''
    Perform excess-power search analysis on magnetic field data.
    This method will produce a bunch of time-frequency plots for every
    tile duration and bandwidth analysed as well as a XML file identifying
    all the triggers found in the selected data within the user-defined
    time range.

    Parameters
    ----------
    ts_data : TimeSeries
      Time Series from magnetic field data
    psd_segment_length : float
      Length of each segment in seconds
    psd_segment_stride : float
      Separation between 2 consecutive segments in seconds
    psd_estimation : string
      Average method
    window_fraction : float
      Withening window fraction
    tile_fap : float
      Tile false alarm probability threshold in Gaussian noise.
    nchans : int
      Total number of channels
    band : float
      Channel bandwidth
    fmin : float
      Lowest frequency of the filter bank.
    fmax : float
      Highest frequency of the filter bank

    Examples
    --------
    The program can be ran as an executable by using the ``excesspower`` command
    line as follows::

      excesspower --station "mainz01" \\
                  --start-time "2017-04-15-17-1" \\
                  --end-time "2017-04-15-18" \\
                  --rep "/Users/vincent/ASTRO/data/GNOME/GNOMEDrive/gnome/serverdata/" \\
                  --resample 512 \\
                  --verbose

    '''
    # Determine sampling rate based on extracted time series
    sample_rate = ts_data.sample_rate
    # Check if tile maximum frequency is not defined
    if fmax is None or fmax > sample_rate / 2.:
        # Set the tile maximum frequency equal to the Nyquist frequency
        # (i.e. half the sampling rate)
        fmax = sample_rate / 2.0
    # Check whether or not tile bandwidth and channel are defined
    if band is None and nchans is None:
        # Exit program with error message
        exit("Either bandwidth or number of channels must be specified...")
    else:
        # Check if tile maximum frequency larger than its minimum frequency
        assert fmax >= fmin
        # Define spectral band of data
        data_band = fmax - fmin
        # Check whether tile bandwidth or channel is defined
        if band is not None:
            # Define number of possible filter bands
            nchans = int(data_band / band)
        elif nchans is not None:
            # Define filter bandwidth
            band = data_band / nchans
            nchans -= 1
        # Check if number of channels is superior than unity
        assert nchans > 1
    # Print segment information
    if verbose: print '|- Estimating PSD from segments of',
    if verbose:
        print '%.2f s, with %.2f s stride...' % (psd_segment_length,
                                                 psd_segment_stride)
    # Convert time series as array of float
    data = ts_data.astype(numpy.float64)
    # Define segment length for PSD estimation in sample unit
    seg_len = int(psd_segment_length * sample_rate)
    # Define separation between consecutive segments in sample unit
    seg_stride = int(psd_segment_stride * sample_rate)
    # Minimum frequency of detectable signal in a segment
    delta_f = 1. / psd_segment_length
    # Calculate PSD length counting the zero frequency element
    fd_len = fmax / delta_f + 1
    # Calculate the overall PSD from individual PSD segments
    if impulse:
        # Produce flat data
        flat_data = numpy.ones(int(fd_len)) * 2. / fd_len
        # Create PSD frequency series
        fd_psd = types.FrequencySeries(flat_data, 1. / psd_segment_length,
                                       ts_data.start_time)
    else:
        # Create overall PSD using Welch's method
        fd_psd = psd.welch(data,
                           avg_method=psd_estimation,
                           seg_len=seg_len,
                           seg_stride=seg_stride)
    if make_plot:
        # Plot the power spectral density
        plot_spectrum(fd_psd)
    # We need this for the SWIG functions
    lal_psd = fd_psd.lal()
    # Create whitening window
    if verbose: print "|- Whitening window and spectral correlation..."
    if wtype == 'hann': window = lal.CreateHannREAL8Window(seg_len)
    elif wtype == 'tukey':
        window = lal.CreateTukeyREAL8Window(seg_len, window_fraction)
    else:
        raise ValueError("Can't handle window type %s" % wtype)
    # Create FFT plan
    fft_plan = lal.CreateForwardREAL8FFTPlan(len(window.data.data), 1)
    # Perform two point spectral correlation
    spec_corr = lal.REAL8WindowTwoPointSpectralCorrelation(window, fft_plan)
    # Determine length of individual filters
    filter_length = int(2 * band / fd_psd.delta_f) + 1
    # Initialise filter bank
    if verbose:
        print "|- Create bank of %i filters of %i Hz bandwidth..." % (
            nchans, filter_length)
    # Initialise array to store filter's frequency series and metadata
    lal_filters = []
    # Initialise array to store filter's time series
    fdb = []
    # Loop over the channels
    for i in range(nchans):
        # Define central position of the filter
        freq = fmin + band / 2 + i * band
        # Create excess power filter
        lal_filter = lalburst.CreateExcessPowerFilter(freq, band, lal_psd,
                                                      spec_corr)
        # Testing spectral correlation on filter
        #print lalburst.ExcessPowerFilterInnerProduct(lal_filter, lal_filter, spec_corr, None)
        # Append entire filter structure
        lal_filters.append(lal_filter)
        # Append filter's spectrum
        fdb.append(FrequencySeries.from_lal(lal_filter))
        #print fdb[0].frequencies
        #print fdb[0]
    if make_plot:
        # Plot filter bank
        plot_bank(fdb)
        # Convert filter bank from frequency to time domain
        if verbose:
            print "|- Convert all the frequency domain to the time domain..."
        tdb = []
        # Loop for each filter's spectrum
        for fdt in fdb:
            zero_padded = numpy.zeros(int((fdt.f0 / fdt.df).value) + len(fdt))
            st = int((fdt.f0 / fdt.df).value)
            zero_padded[st:st + len(fdt)] = numpy.real_if_close(fdt.value)
            n_freq = int(sample_rate / 2 / fdt.df.value) * 2
            tdt = numpy.fft.irfft(zero_padded, n_freq) * math.sqrt(sample_rate)
            tdt = numpy.roll(tdt, len(tdt) / 2)
            tdt = TimeSeries(tdt,
                             name="",
                             epoch=fdt.epoch,
                             sample_rate=sample_rate)
            tdb.append(tdt)
        # Plot time series filter
        plot_filters(tdb, fmin, band)
    # Computer whitened inner products of input filters with themselves
    #white_filter_ip = numpy.array([lalburst.ExcessPowerFilterInnerProduct(f, f, spec_corr, None) for f in lal_filters])
    # Computer unwhitened inner products of input filters with themselves
    #unwhite_filter_ip = numpy.array([lalburst.ExcessPowerFilterInnerProduct(f, f, spec_corr, lal_psd) for f in lal_filters])
    # Computer whitened filter inner products between input adjacent filters
    #white_ss_ip = numpy.array([lalburst.ExcessPowerFilterInnerProduct(f1, f2, spec_corr, None) for f1, f2 in zip(lal_filters[:-1], lal_filters[1:])])
    # Computer unwhitened filter inner products between input adjacent filters
    #unwhite_ss_ip = numpy.array([lalburst.ExcessPowerFilterInnerProduct(f1, f2, spec_corr, lal_psd) for f1, f2 in zip(lal_filters[:-1], lal_filters[1:])])
    # Check filter's bandwidth is equal to user defined channel bandwidth
    min_band = (len(lal_filters[0].data.data) - 1) * lal_filters[0].deltaF / 2
    assert min_band == band
    # Create an event list where all the triggers will be stored
    event_list = lsctables.New(lsctables.SnglBurstTable, [
        'start_time', 'start_time_ns', 'peak_time', 'peak_time_ns', 'duration',
        'bandwidth', 'central_freq', 'chisq_dof', 'confidence', 'snr',
        'amplitude', 'channel', 'ifo', 'process_id', 'event_id', 'search',
        'stop_time', 'stop_time_ns'
    ])
    # Create repositories to save TF and time series plots
    os.system('mkdir -p segments/time-frequency')
    os.system('mkdir -p segments/time-series')
    # Define time edges
    t_idx_min, t_idx_max = 0, seg_len
    # Loop over each segment
    while t_idx_max <= len(ts_data):
        # Define first and last timestamps of the block
        start_time = ts_data.start_time + t_idx_min / float(
            ts_data.sample_rate)
        end_time = ts_data.start_time + t_idx_max / float(ts_data.sample_rate)
        if verbose:
            print "\n|- Analyzing block %i to %i (%.2f percent)" % (
                start_time, end_time, 100 * float(t_idx_max) / len(ts_data))
        # Debug for impulse response
        if impulse:
            for i in range(t_idx_min, t_idx_max):
                ts_data[i] = 1000. if i == (t_idx_max + t_idx_min) / 2 else 0.
        # Model a withen time series for the block
        tmp_ts_data = types.TimeSeries(ts_data[t_idx_min:t_idx_max] *
                                       window.data.data,
                                       delta_t=1. / ts_data.sample_rate,
                                       epoch=start_time)
        # Save time series in relevant repository
        os.system('mkdir -p segments/%i-%i' % (start_time, end_time))
        if make_plot:
            # Plot time series
            plot_ts(tmp_ts_data,
                    fname='segments/time-series/%i-%i.png' %
                    (start_time, end_time))
        # Convert times series to frequency series
        fs_data = tmp_ts_data.to_frequencyseries()
        if verbose:
            print "|- Frequency series data has variance: %s" % fs_data.data.std(
            )**2
        # Whitening (FIXME: Whiten the filters, not the data)
        fs_data.data /= numpy.sqrt(fd_psd) / numpy.sqrt(2 * fd_psd.delta_f)
        if verbose:
            print "|- Whitened frequency series data has variance: %s" % fs_data.data.std(
            )**2
        if verbose: print "|- Create time-frequency plane for current block"
        # Return the complex snr, along with its associated normalization of the template,
        # matched filtered against the data
        #filter.matched_filter_core(types.FrequencySeries(tmp_filter_bank,delta_f=fd_psd.delta_f),
        #                           fs_data,h_norm=1,psd=fd_psd,low_frequency_cutoff=lal_filters[0].f0,
        #                           high_frequency_cutoff=lal_filters[0].f0+2*band)
        if verbose: print "|- Filtering all %d channels...\n" % nchans,
        # Initialise 2D zero array
        tmp_filter_bank = numpy.zeros(len(fd_psd), dtype=numpy.complex128)
        # Initialise 2D zero array for time-frequency map
        tf_map = numpy.zeros((nchans, seg_len), dtype=numpy.complex128)
        # Loop over all the channels
        for i in range(nchans):
            # Reset filter bank series
            tmp_filter_bank *= 0.0
            # Index of starting frequency
            f1 = int(lal_filters[i].f0 / fd_psd.delta_f)
            # Index of last frequency bin
            f2 = int((lal_filters[i].f0 + 2 * band) / fd_psd.delta_f) + 1
            # (FIXME: Why is there a factor of 2 here?)
            tmp_filter_bank[f1:f2] = lal_filters[i].data.data * 2
            # Define the template to filter the frequency series with
            template = types.FrequencySeries(tmp_filter_bank,
                                             delta_f=fd_psd.delta_f,
                                             copy=False)
            # Create filtered series
            filtered_series = filter.matched_filter_core(
                template,
                fs_data,
                h_norm=None,
                psd=None,
                low_frequency_cutoff=lal_filters[i].f0,
                high_frequency_cutoff=lal_filters[i].f0 + 2 * band)
            # Include filtered series in the map
            tf_map[i, :] = filtered_series[0].numpy()
        if make_plot:
            # Plot spectrogram
            plot_spectrogram(numpy.abs(tf_map).T,
                             dt=tmp_ts_data.delta_t,
                             df=band,
                             ymax=ts_data.sample_rate / 2.,
                             t0=start_time,
                             t1=end_time,
                             fname='segments/time-frequency/%i-%i.png' %
                             (start_time, end_time))
            plot_tiles_ts(numpy.abs(tf_map),
                          2,
                          1,
                          sample_rate=ts_data.sample_rate,
                          t0=start_time,
                          t1=end_time,
                          fname='segments/%i-%i/ts.png' %
                          (start_time, end_time))
            #plot_tiles_tf(numpy.abs(tf_map),2,1,ymax=ts_data.sample_rate/2,
            #              sample_rate=ts_data.sample_rate,t0=start_time,t1=end_time,
            #              fname='segments/%i-%i/tf.png'%(start_time,end_time))
        # Loop through powers of 2 up to number of channels
        for nc_sum in range(0, int(math.log(nchans, 2)))[::-1]:
            # Calculate total number of summed channels
            nc_sum = 2**nc_sum
            if verbose:
                print "\n\t|- Contructing tiles containing %d narrow band channels" % nc_sum
            # Compute full bandwidth of virtual channel
            df = band * nc_sum
            # Compute minimal signal's duration in virtual channel
            dt = 1.0 / (2 * df)
            # Compute under sampling rate
            us_rate = int(round(dt / ts_data.delta_t))
            if verbose:
                print "\t|- Undersampling rate for this level: %f" % (
                    ts_data.sample_rate / us_rate)
            if verbose: print "\t|- Calculating tiles..."
            # Clip the boundaries to remove window corruption
            clip_samples = int(psd_segment_length * window_fraction *
                               ts_data.sample_rate / 2)
            # Undersample narrow band channel's time series
            # Apply clipping condition because [0:-0] does not give the full array
            tf_map_temp = tf_map[:,clip_samples:-clip_samples:us_rate] \
                          if clip_samples > 0 else tf_map[:,::us_rate]
            # Initialise final tile time-frequency map
            tiles = numpy.zeros(((nchans + 1) / nc_sum, tf_map_temp.shape[1]))
            # Loop over tile index
            for i in xrange(len(tiles)):
                # Sum all inner narrow band channels
                ts_tile = numpy.absolute(tf_map_temp[nc_sum * i:nc_sum *
                                                     (i + 1)].sum(axis=0))
                # Define index of last narrow band channel for given tile
                n = (i + 1) * nc_sum - 1
                n = n - 1 if n == len(lal_filters) else n
                # Computer withened inner products of each input filter with itself
                mu_sq = nc_sum * lalburst.ExcessPowerFilterInnerProduct(
                    lal_filters[n], lal_filters[n], spec_corr, None)
                #kmax = nc_sum-1 if n==len(lal_filters) else nc_sum-2
                # Loop over the inner narrow band channels
                for k in xrange(0, nc_sum - 1):
                    # Computer whitened filter inner products between input adjacent filters
                    mu_sq += 2 * lalburst.ExcessPowerFilterInnerProduct(
                        lal_filters[n - k], lal_filters[n - 1 - k], spec_corr,
                        None)
                # Normalise tile's time series
                tiles[i] = ts_tile.real**2 / mu_sq
            if verbose: print "\t|- TF-plane is %dx%s samples" % tiles.shape
            if verbose:
                print "\t|- Tile energy mean %f, var %f" % (numpy.mean(tiles),
                                                            numpy.var(tiles))
            # Define maximum number of degrees of freedom and check it larger or equal to 2
            max_dof = 32 if max_duration == None else int(max_duration / dt)
            assert max_dof >= 2
            # Loop through multiple degrees of freedom
            for j in [2**l for l in xrange(0, int(math.log(max_dof, 2)))]:
                # Duration is fixed by the NDOF and bandwidth
                duration = j * dt
                if verbose: print "\n\t\t|- Summing DOF = %d ..." % (2 * j)
                if verbose:
                    print "\t\t|- Explore signal duration of %f s..." % duration
                # Construct filter
                sum_filter = numpy.array([1, 0] * (j - 1) + [1])
                # Calculate length of filtered time series
                tlen = tiles.shape[1] - sum_filter.shape[0] + 1
                # Initialise filtered time series array
                dof_tiles = numpy.zeros((tiles.shape[0], tlen))
                # Loop over tiles
                for f in range(tiles.shape[0]):
                    # Sum and drop correlate tiles
                    dof_tiles[f] = fftconvolve(tiles[f], sum_filter, 'valid')
                if verbose:
                    print "\t\t|- Summed tile energy mean: %f" % (
                        numpy.mean(dof_tiles))
                if verbose:
                    print "\t\t|- Variance tile energy: %f" % (
                        numpy.var(dof_tiles))
                if make_plot:
                    plot_spectrogram(
                        dof_tiles.T,
                        dt,
                        df,
                        ymax=ts_data.sample_rate / 2,
                        t0=start_time,
                        t1=end_time,
                        fname='segments/%i-%i/%02ichans_%02idof.png' %
                        (start_time, end_time, nc_sum, 2 * j))
                    plot_tiles_ts(
                        dof_tiles,
                        2 * j,
                        df,
                        sample_rate=ts_data.sample_rate / us_rate,
                        t0=start_time,
                        t1=end_time,
                        fname='segments/%i-%i/%02ichans_%02idof_ts.png' %
                        (start_time, end_time, nc_sum, 2 * j))
                    plot_tiles_tf(
                        dof_tiles,
                        2 * j,
                        df,
                        ymax=ts_data.sample_rate / 2,
                        sample_rate=ts_data.sample_rate / us_rate,
                        t0=start_time,
                        t1=end_time,
                        fname='segments/%i-%i/%02ichans_%02idof_tf.png' %
                        (start_time, end_time, nc_sum, 2 * j))
                threshold = scipy.stats.chi2.isf(tile_fap, j)
                if verbose:
                    print "\t\t|- Threshold for this level: %f" % threshold
                spant, spanf = dof_tiles.shape[1] * dt, dof_tiles.shape[0] * df
                if verbose:
                    print "\t\t|- Processing %.2fx%.2f time-frequency map." % (
                        spant, spanf)
                # Since we clip the data, the start time needs to be adjusted accordingly
                window_offset_epoch = fs_data.epoch + psd_segment_length * window_fraction / 2
                window_offset_epoch = LIGOTimeGPS(float(window_offset_epoch))
                for i, j in zip(*numpy.where(dof_tiles > threshold)):
                    event = event_list.RowType()
                    # The points are summed forward in time and thus a `summed point' is the
                    # sum of the previous N points. If this point is above threshold, it
                    # corresponds to a tile which spans the previous N points. However, the
                    # 0th point (due to the convolution specifier 'valid') is actually
                    # already a duration from the start time. All of this means, the +
                    # duration and the - duration cancels, and the tile 'start' is, by
                    # definition, the start of the time frequency map if j = 0
                    # FIXME: I think this needs a + dt/2 to center the tile properly
                    event.set_start(window_offset_epoch + float(j * dt))
                    event.set_stop(window_offset_epoch + float(j * dt) +
                                   duration)
                    event.set_peak(event.get_start() + duration / 2)
                    event.central_freq = lal_filters[
                        0].f0 + band / 2 + i * df + 0.5 * df
                    event.duration = duration
                    event.bandwidth = df
                    event.chisq_dof = 2 * duration * df
                    event.snr = math.sqrt(dof_tiles[i, j] / event.chisq_dof -
                                          1)
                    # FIXME: Magic number 0.62 should be determine empircally
                    event.confidence = -lal.LogChisqCCDF(
                        event.snr * 0.62, event.chisq_dof * 0.62)
                    event.amplitude = None
                    event.process_id = None
                    event.event_id = event_list.get_next_id()
                    event_list.append(event)
                for event in event_list[::-1]:
                    if event.amplitude != None:
                        continue
                    etime_min_idx = float(event.get_start()) - float(
                        fs_data.epoch)
                    etime_min_idx = int(etime_min_idx / tmp_ts_data.delta_t)
                    etime_max_idx = float(event.get_start()) - float(
                        fs_data.epoch) + event.duration
                    etime_max_idx = int(etime_max_idx / tmp_ts_data.delta_t)
                    # (band / 2) to account for sin^2 wings from finest filters
                    flow_idx = int((event.central_freq - event.bandwidth / 2 -
                                    (df / 2) - fmin) / df)
                    fhigh_idx = int((event.central_freq + event.bandwidth / 2 +
                                     (df / 2) - fmin) / df)
                    # TODO: Check that the undersampling rate is always commensurate
                    # with the indexing: that is to say that
                    # mod(etime_min_idx, us_rate) == 0 always
                    z_j_b = tf_map[flow_idx:fhigh_idx,
                                   etime_min_idx:etime_max_idx:us_rate]
                    # FIXME: Deal with negative hrss^2 -- e.g. remove the event
                    try:
                        event.amplitude = measure_hrss(
                            z_j_b, unwhite_filter_ip[flow_idx:fhigh_idx],
                            unwhite_ss_ip[flow_idx:fhigh_idx - 1],
                            white_ss_ip[flow_idx:fhigh_idx - 1],
                            fd_psd.delta_f, tmp_ts_data.delta_t,
                            len(lal_filters[0].data.data), event.chisq_dof)
                    except ValueError:
                        event.amplitude = 0
                if verbose:
                    print "\t\t|- Total number of events: %d" % len(event_list)
        t_idx_min += int(seg_len * (1 - window_fraction))
        t_idx_max += int(seg_len * (1 - window_fraction))
    setname = "MagneticFields"
    __program__ = 'pyburst_excesspower_gnome'
    start_time = LIGOTimeGPS(int(ts_data.start_time))
    end_time = LIGOTimeGPS(int(ts_data.end_time))
    inseg = segment(start_time, end_time)
    xmldoc = ligolw.Document()
    xmldoc.appendChild(ligolw.LIGO_LW())
    ifo = channel_name.split(":")[0]
    straindict = psd.insert_psd_option_group.__dict__
    proc_row = register_to_xmldoc(xmldoc,
                                  __program__,
                                  straindict,
                                  ifos=[ifo],
                                  version=git_version.id,
                                  cvs_repository=git_version.branch,
                                  cvs_entry_time=git_version.date)
    dt_stride = psd_segment_length
    sample_rate = ts_data.sample_rate
    # Amount to overlap successive blocks so as not to lose data
    window_overlap_samples = window_fraction * sample_rate
    outseg = inseg.contract(window_fraction * dt_stride / 2)
    # With a given dt_stride, we cannot process the remainder of this data
    remainder = math.fmod(abs(outseg), dt_stride * (1 - window_fraction))
    # ...so make an accounting of it
    outseg = segment(outseg[0], outseg[1] - remainder)
    ss = append_search_summary(xmldoc,
                               proc_row,
                               ifos=(station, ),
                               inseg=inseg,
                               outseg=outseg)
    for sb in event_list:
        sb.process_id = proc_row.process_id
        sb.search = proc_row.program
        sb.ifo, sb.channel = station, setname
    xmldoc.childNodes[0].appendChild(event_list)
    ifostr = ifo if isinstance(ifo, str) else "".join(ifo)
    st_rnd, end_rnd = int(math.floor(inseg[0])), int(math.ceil(inseg[1]))
    dur = end_rnd - st_rnd
    fname = "%s-excesspower-%d-%d.xml.gz" % (ifostr, st_rnd, dur)
    utils.write_filename(xmldoc, fname, gz=fname.endswith("gz"))
    plot_triggers(fname)