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 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 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 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 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 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 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 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
# 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 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)
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 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 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 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 = int(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)
f._delta_t = delta_t
return f
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 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 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 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 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_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 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 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)
hp_size = len(hp)
hp.resize(time_duration * f_sample)
psd = noise.psd(4)
psd = interpolate(psd, hp.delta_f)
sigma = matchedfilter.sigma(hp, psd=psd, low_frequency_cutoff=f_min)
Amplitude = snr / (sigma)
hp *= Amplitude
hp.resize(hp_size)
merger_time = 69
merger_index = int(69 / delta_t) + 1
start_index = merger_index + len(hp)
waveform = TimeSeries(numpy.zeros(len(noise)), delta_t=delta_t, \
dtype=real_same_precision_as(noise))
waveform[merger_index:start_index] = hp
signal = noise + waveform
pylab.figure(figsize=(10, 5))
pylab.plot(signal.sample_times, signal, label='Waveform + Noise')
pylab.plot(waveform.sample_times, waveform, label='Waveform')
pylab.legend()
pylab.xlabel('Time (s)')
pylab.ylabel('Strain')
pylab.title('Injected Waveform')
zoom_signal = signal.time_slice(merger_time - 0.5, merger_time + 0.5)
def compress_waveform(htilde,
sample_points,
tolerance,
interpolation,
precision,
decomp_scratch=None,
psd=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, a
PSD may be 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.
precision : str
The precision being used to generate and store the compressed waveform
points.
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`.
psd : {None, FrequencySeries}
The psd to use for calculating the overlap between the decompressed
waveform and the original full waveform.
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
hdecomp = fd_decompress(comp_amp,
comp_phase,
sample_points,
out=decomp_scratch,
df=outdf,
f_lower=fmin,
interpolation=interpolation)
kmax = min(len(htilde), len(hdecomp))
htilde = htilde[:kmax]
hdecomp = hdecomp[:kmax]
mismatch = 1. - filter.overlap(
hdecomp, htilde, psd=psd, 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, psd=psd)
# 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(round(add_freq / df))
# ensure that only new points are added
if addidx in sample_index:
diffidx = vecdiffs.argsort()
addpt = -1
while addidx in sample_index:
addpt -= 1
try:
minpt = diffidx[addpt]
except IndexError:
raise ValueError("unable to compress to desired tolerance")
add_freq = sample_points[[minpt, minpt + 1]].mean()
addidx = int(round(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)
hdecomp = hdecomp[:kmax]
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],
psd=psd)
vecdiffs = new_vecdiffs
mismatch = 1. - filter.overlap(
hdecomp, htilde, psd=psd, 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,
mismatch=mismatch,
precision=precision)
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 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)
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 power_chisq_from_precomputed(corr,
snr,
snr_norm,
bins,
indices=None,
return_bins=False):
"""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.
return_bins: {boolean, False}, optional
Return a list of the SNRs for each chisq bin.
Returns
-------
chisq: TimeSeries
"""
# Get workspace memory
global _q_l, _qtilde_l, _chisq_l
bin_snrs = []
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 return_bins:
bin_snrs.append(
TimeSeries(q * snr_norm * num_bins**0.5,
delta_t=snr.delta_t,
epoch=snr.start_time))
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 None:
chisq = TimeSeries(chisq,
delta_t=snr.delta_t,
epoch=snr.start_time,
copy=False)
if return_bins:
return chisq, bin_snrs
else:
return chisq
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 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)
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,
mismatch=mismatch)
