def create_filter_bank(delta_f,flow,band,nchan,psd,spec_corr,fmin=0,fmax=None):
"""
Create filter bank. The construction of a filter bank is fairly simple. For
each channel, a frequency domain channel filter function will be created using
the `CreateExcessPowerFilter <http://software.ligo.org/docs/lalsuite/lalburst/group___e_p_search__h.html#ga899990cbd45111ba907772650c265ec9>`_ module from the ``lalburst`` package. Each channel
filter is divided by the square root of the PSD frequency series prior to
normalization, which has the effect of de-emphasizing frequency bins with high
noise content, and is called `over whitening`. The data and metadata are finally
stored in the ``filter_fseries`` and ``filter_bank`` arrays respectively.
Finally, we store on a final array, called ``np_filters`` the all time-series
generated from each filter so that we can plot them afterwards.
Parameters
----------
delta_f : float
Bandwidth of each filter
flow : float
Lowest frequency of the filter bank
band :
"""
print "|- Create filter..."
lal_psd = psd.lal()
lal_filters, np_filters = [], []
for i in range(nchan):
lal_filter = lalburst.CreateExcessPowerFilter(flow + i*band, band, lal_psd, spec_corr)
np_filters.append(Spectrum.from_lal(lal_filter))
lal_filters.append(lal_filter)
return lal_filters, np_filters
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"))
