def align_waveforms_suboptimally(hplus1, hcross1, hplus2, hcross2, psd='aLIGOZeroDetHighPower', low_frequency_cutoff=None, high_frequency_cutoff=None, tsign=1, phsign=1, verify=True, trim_leading=False, trim_trailing=False, verbose=False): # Cast into time-series h_plus1 = TimeSeries(hplus1, epoch=hplus1._epoch, delta_t=hplus1.delta_t, dtype=hplus1.dtype) h_cross1 = TimeSeries(hcross1, epoch=hplus1._epoch, delta_t=hplus1.delta_t, dtype=hplus1.dtype) h_plus2 = TimeSeries(hplus2, epoch=hplus2._epoch, delta_t=hplus2.delta_t, dtype=hplus2.dtype) h_cross2 = TimeSeries(hcross2, epoch=hplus2._epoch, delta_t=hplus2.delta_t, dtype=hplus2.dtype) # # Ensure both input hplus vectors are equal in length if len(hplus2) > len(hplus1): h_plus1.append_zeros(len(hplus2) - len(hplus1)) h_cross1.append_zeros(len(hplus2) - len(hplus1)) elif len(hplus2) < len(hplus1): h_plus2.append_zeros(len(hplus1) - len(hplus2)) h_cross2.append_zeros(len(hplus1) - len(hplus2)) # htilde = make_frequency_series(h_plus1) stilde = make_frequency_series(h_plus2) # if high_frequency_cutoff == None: high_frequency_cutoff = 1. / h_plus1.delta_t / 2. # if psd == None: raise IOError("Need compatible psd [or name] as input!") elif type(psd) == str: psd_name = psd psd = from_string(psd_name, len(htilde), htilde.delta_f, low_frequency_cutoff) # # Determine the phase and time shifts for optimal match snr, corr, snr_norm = matched_filter_core( htilde, stilde, # h_plus1, h_plus2, psd, low_frequency_cutoff, high_frequency_cutoff, None) max_snr, max_id = snr.abs_max_loc() if max_id != 0: t_shift = snr.delta_t * (len(snr) - max_id) else: t_shift = snr.delta_t * max_id ph_shift = np.angle(snr[max_id]) - 0.24850315030 - 0.0465881735639 # if verbose: print(("max_id = %d, id_shift = %d" % (max_id, int(t_shift / snr.delta_t)))) print(("t_shift = %f,\n ph_shift = %f" % (t_shift, ph_shift))) # # print(OVERLAPS if verbose: print(("Overlap BEFORE ALIGNMENT:", overlap_cplx(h_plus1, h_plus2, psd=psd, low_frequency_cutoff=low_frequency_cutoff, high_frequency_cutoff=high_frequency_cutoff, normalized=True))) print(("Match BEFORE ALIGNMENT:", match(h_plus1, h_plus2, psd=psd, low_frequency_cutoff=low_frequency_cutoff, high_frequency_cutoff=high_frequency_cutoff))) # Shift whichever needs to be shifted to future time. # Shifting back in time is tricky. if t_shift >= 0: hp2, hc2 = shift_waveform_phase_time(h_plus2, h_cross2, tsign * t_shift, phsign * ph_shift, verbose=verbose) else: hp2, hc2 = shift_waveform_phase_time(h_plus2, h_cross2, tsign * t_shift, phsign * ph_shift, verbose=verbose) # # Ensure both input hplus vectors are equal in length if len(h_plus1) > len(hp2): hp2.append_zeros(len(h_plus1) - len(hp2)) elif len(h_plus1) < len(hp2): h_plus1.append_zeros(len(hp2) - len(h_plus1)) if verbose: htilde = make_frequency_series(h_plus1) psd = from_string(psd_name, len(htilde), htilde.delta_f, low_frequency_cutoff) print(("Overlap AFTER ALIGNMENT:", overlap_cplx(h_plus1, hp2, psd=psd, low_frequency_cutoff=low_frequency_cutoff, high_frequency_cutoff=high_frequency_cutoff, normalized=True))) print(("Match AFTER ALIGNMENT:", match(h_plus1, hp2, psd=psd, low_frequency_cutoff=low_frequency_cutoff, high_frequency_cutoff=high_frequency_cutoff))) if verify: # print("Verifying time alignment...") # Determine the phase and time shifts for optimal match snr, corr, snr_norm = matched_filter_core( # htilde, stilde, h_plus1, hp2, psd, low_frequency_cutoff, high_frequency_cutoff, None) max_snr, max_id = snr.abs_max_loc() print(("Post-Alignment Index of MAX SNR (should be 0 or 1 or %d): %d" % (len(snr) - 1, max_id))) print(("Length of whole SNR time-series: ", len(snr))) if max_id != 0 and max_id != 1 and max_id != ( len(snr) - 1) and max_id != (len(snr) - 2): # raise RuntimeError( "Warning: ALIGNMENT NOT CORRECT (see above)" ) print("Warning: ALIGNMENT NOT CORRECT (see above)") else: print("Alignment in time correct..") # print("Verifying phase alignment...") ph_shift = np.angle(snr[max_id]) if ph_shift != 0: print("Warning: Phasing alignment possibly incorrect.") print(("dphi, dphi+pi, dphi-pi: ", ph_shift, ph_shift + np.pi, ph_shift - np.pi)) print(("dphi/pi, dphi*pi: ", ph_shift / np.pi, ph_shift * np.pi)) # # if trim_trailing: hp1 = trim_trailing_zeros(hp1) hc1 = trim_trailing_zeros(hc1) hp2 = trim_trailing_zeros(hp2) hc2 = trim_trailing_zeros(hc2) if trim_leading: hp1 = trim_leading_zeros(hp1) hc1 = trim_leading_zeros(hc1) hp2 = trim_leading_zeros(hp2) hc2 = trim_leading_zeros(hc2) # return hplus1, hcross1, hp2, hc2
def shift_waveform_phase_time(hp, hc, t_shift, ph_shift, shift_epochs_only=True, trim_leading=False, trim_trailing=True, verbose=False): """ Input: hp, hc, where h = hp(t) + i hx(t) = Amp(t) * exp(-i * Phi(t)) Output: hp, hc, where h = Amp(t - t_c) * exp( -i * [Phi(t - t_c) + phi_c] ) """ hpnew = TimeSeries(hp, epoch=hp._epoch, delta_t=hp.delta_t, dtype=hp.dtype, copy=True) hcnew = TimeSeries(hc, epoch=hc._epoch, delta_t=hc.delta_t, dtype=hc.dtype, copy=True) # First apply phase shift if ph_shift != 0.: amplitude = amplitude_from_polarizations(hpnew, hcnew) phase = phase_from_polarizations(hpnew, hcnew) if verbose: print(("shifting by %f radians" % ph_shift)) phase = phase + ph_shift hpnew = TimeSeries(amplitude * np.cos(phase + np.pi), epoch=hpnew._epoch, delta_t=hpnew.delta_t, dtype=hpnew.dtype) hcnew = TimeSeries(amplitude * np.sin(phase + np.pi), epoch=hcnew._epoch, delta_t=hcnew.delta_t, dtype=hcnew.dtype) # Now apply time shift # Only positive time shifts can be applied by rolling forward data # if negative time shifts are asked for, we can only shift epochs if shift_epochs_only or t_shift <= 0: hpnew._epoch += t_shift hcnew._epoch += t_shift else: hpnewI = InterpolatedUnivariateSpline(hpnew.get_sample_times(), hpnew.data) hcnewI = InterpolatedUnivariateSpline(hcnew.get_sample_times(), hcnew.data) time_vals = hpnew.get_sample_times() shifted_time_vals = np.arange( time_vals[0], # start of new timeseries time_vals[-1] + t_shift + 0 * hpnew.delta_t, # end of it hpnew.delta_t) mask_times_to_reevaluate = [ (shifted_time_vals - t_shift >= time_vals[0]) & (shifted_time_vals - t_shift <= time_vals[-1]) ] hp_shifted = np.zeros(len(shifted_time_vals)) hp_shifted[mask_times_to_reevaluate] = hpnewI( shifted_time_vals[mask_times_to_reevaluate] - t_shift) hpnew = TimeSeries(hp_shifted, epoch=hpnew._epoch + t_shift, delta_t=hpnew.delta_t) hc_shifted = np.zeros(len(shifted_time_vals)) hc_shifted[mask_times_to_reevaluate] = hcnewI( shifted_time_vals[mask_times_to_reevaluate] - t_shift) hcnew = TimeSeries(hc_shifted, epoch=hcnew._epoch + t_shift, delta_t=hcnew.delta_t) if trim_trailing: hpnew = trim_trailing_zeros(hpnew) hcnew = trim_trailing_zeros(hcnew) if trim_leading: hpnew = trim_leading_zeros(hpnew) hcnew = trim_leading_zeros(hcnew) return hpnew, hcnew
def align_waveforms_at_frequency(hplus1, hcross1, hplus2, hcross2, falign, trim_leading=False, trim_trailing=True, verbose=False): # # Find amplitude peaks # hp1 = TimeSeries(hplus1) hc1 = TimeSeries(hcross1) hp2 = TimeSeries(hplus2) hc2 = TimeSeries(hcross2) # # Get time at flign for wave 1 # freq1 = frequency_from_polarizations(hp1, hc1) obj_func = np.abs(np.abs(freq1.data) - falign) f1I = InterpolatedUnivariateSpline(freq1.sample_times, obj_func) id_start = np.where(obj_func == np.min(obj_func))[0][0] for idx in range(id_start, len(freq1)): if freq1[idx] > 2 * falign and freq1[idx + 1] > 2 * falign: break tmp = minimize_scalar(f1I, freq1.sample_times[id_start], method='bounded', bounds=(freq1.sample_times[id_start], freq1.sample_times[idx])) f1_align_time = tmp['x'] # # Get time at flign for wave 2 # freq2 = frequency_from_polarizations(hp2, hc2) obj_func = np.abs(np.abs(freq2.data) - falign) f2I = InterpolatedUnivariateSpline(freq2.sample_times, obj_func) id_start = np.where(obj_func == np.min(obj_func))[0][0] for idx in range(id_start, len(freq2)): if freq2[idx] > 2 * falign and freq2[idx + 1] > 2 * falign: break tmp = minimize_scalar(f2I, freq2.sample_times[id_start], method='bounded', bounds=(freq2.sample_times[id_start], freq2.sample_times[idx])) f2_align_time = tmp['x'] # t1 = f1_align_time t2 = f2_align_time t_shift = t1 - t2 if verbose: print(("time shift = %f to be added to waveform 2" % t_shift)) # # Find phase shift at the time # phs1 = phase_from_polarizations(hp1, hc1) phs2 = phase_from_polarizations(hp2, hc2) phs1I = InterpolatedUnivariateSpline(phs1.sample_times, phs1.data) phs2I = InterpolatedUnivariateSpline(phs2.sample_times, phs2.data) ph1 = phs1I(f1_align_time) ph2 = phs2I(f2_align_time) ph_shift = (ph1 - ph2) * 1 if verbose: print(("time @ f1 = %f : %f" % (falign, f1_align_time))) print(("time @ f2 = %f : %f" % (falign, f2_align_time))) print(("ph1 = %f, ph2 = %f" % (ph1, ph2))) print(("phase shift = %f, time shift = %f" % (ph_shift, t_shift))) print(("type of ph_shift, t_shift: ", type(ph_shift), type(t_shift))) # # Shift whichever needs to be shifted to future time. # Shifting back in time is tricky. hp2, hc2 = shift_waveform_phase_time(hp2, hc2, t_shift, ph_shift, verbose=verbose) # if trim_trailing: hp1 = trim_trailing_zeros(hp1) hc1 = trim_trailing_zeros(hc1) hp2 = trim_trailing_zeros(hp2) hc2 = trim_trailing_zeros(hc2) if trim_leading: hp1 = trim_leading_zeros(hp1) hc1 = trim_leading_zeros(hc1) hp2 = trim_leading_zeros(hp2) hc2 = trim_leading_zeros(hc2) # return hp1, hc1, hp2, hc2
def align_waveforms_optimally(hplus1, hcross1, hplus2, hcross2, psd='aLIGOZeroDetHighPower', low_frequency_cutoff=None, high_frequency_cutoff=None, tsign=1, phsign=-1, verify=True, phase_tolerance=1e-3, overlap_tolerance=1e-3, trim_leading=False, trim_trailing=False, verbose=False): """ Align waveforms such that their inner product (noise weighted) is optimal without requiring any phase or time shift. The appropriate time and phase shifts are determined iteratively and applied to the second set of (hplus, hcross) vectors. """ ############################################################################# # First copy over data into local memory, ensure lengths of time and # frequency domain vectors are consistent, and compute the maximized overlap # # 1) Cast into time-series h_plus1 = TimeSeries(hplus1, epoch=hplus1._epoch, delta_t=hplus1.delta_t, dtype=hplus1.dtype, copy=True) h_cross1 = TimeSeries(hcross1, epoch=hplus1._epoch, delta_t=hplus1.delta_t, dtype=hplus1.dtype, copy=True) h_plus2 = TimeSeries(hplus2, epoch=hplus2._epoch, delta_t=hplus2.delta_t, dtype=hplus2.dtype, copy=True) h_cross2 = TimeSeries(hcross2, epoch=hplus2._epoch, delta_t=hplus2.delta_t, dtype=hplus2.dtype, copy=True) # # 2) Ensure both input hplus vectors are equal in length if len(hplus2) > len(hplus1): h_plus1.append_zeros(len(hplus2) - len(hplus1)) h_cross1.append_zeros(len(hplus2) - len(hplus1)) elif len(hplus2) < len(hplus1): h_plus2.append_zeros(len(hplus1) - len(hplus2)) h_cross2.append_zeros(len(hplus1) - len(hplus2)) # # 3) Set the upper frequency cutoff to Nyquist if not set by User if high_frequency_cutoff == None: high_frequency_cutoff = 1. / h_plus1.delta_t / 2. # # 4) Compute LIGO noise psd if psd == None: raise IOError("Need compatible psd [or name] as input!") elif type(psd) == str: htilde = make_frequency_series(h_plus1) psd_name = psd psd = from_string(psd_name, len(htilde), htilde.delta_f, low_frequency_cutoff) ## # 5) Calculate Overlap (maximized) before alignment m = match(h_plus1, h_plus2, psd=psd, low_frequency_cutoff=low_frequency_cutoff, high_frequency_cutoff=high_frequency_cutoff) optimal_overlap = m[0] # FIXME if verbose: print(("Overlap BEFORE ALIGNMENT:", overlap_cplx(h_plus1, h_plus2, psd=psd, low_frequency_cutoff=low_frequency_cutoff, high_frequency_cutoff=high_frequency_cutoff, normalized=True))) print(("Match BEFORE ALIGNMENT:", m)) ############################################################################# # Iterate to obtain the correct phase and time shifts, using which we # align the two waveforms such that their unmaximized and maximized overlaps # agree. # # 1) Initialize phase/time offset counters t_shift_counter = 0 ph_shift_counter = 0 # # 2) Initialize initial garbage values to enter the while loop idx = 0 ph_shift = t_shift = 1e9 olap = 0 + 0j # # 3) Iteration begins # >>>>>> while np.abs(ph_shift) > phase_tolerance or \ np.abs(t_shift) > h_plus1.delta_t or \ np.abs(np.abs(olap.real) - optimal_overlap) > overlap_tolerance: if idx == 0: hp2, hc2 = h_plus2, h_cross2 # # 1) Determine the phase and time shifts for optimal match # by comparing hplus1/hcross1 with hp2/hc2 which is phase/time shifted # in previous iteration snr, corr, snr_norm = matched_filter_core(h_plus1, hp2, psd, low_frequency_cutoff, high_frequency_cutoff, None) max_snr, max_id = snr.abs_max_loc() if max_id != 0: t_shift = snr.delta_t * (len(snr) - max_id) else: t_shift = snr.delta_t * max_id ph_shift = np.angle(snr[max_id]) # # 2) Add them to running time/phase offset counter t_shift_counter += t_shift ph_shift_counter += ph_shift # if verbose: print((" >> Iteration %d\n" % (idx + 1))) print(("max_id = %d, id_shift = %d" % (max_id, int(t_shift / snr.delta_t)))) print(("t_shift = %f,\n ph_shift = %f" % (t_shift, ph_shift))) # #### # 3) Shift the second hp/hc pair (ORIGINAL) by cumulative phase/time offset hp2, hc2 = shift_waveform_phase_time(h_plus2, h_cross2, tsign * t_shift_counter, phsign * ph_shift_counter, verbose=verbose) # ### # 4) As time shifting can change array lengths, equalize again, compute psd ## if len(h_plus1) > len(hp2): hp2.append_zeros(len(h_plus1) - len(hp2)) htilde = make_frequency_series(h_plus1) psd = from_string(psd_name, len(htilde), htilde.delta_f, low_frequency_cutoff) elif len(h_plus1) < len(hp2): h_plus1.append_zeros(len(hp2) - len(h_plus1)) htilde = make_frequency_series(h_plus1) psd = from_string(psd_name, len(htilde), htilde.delta_f, low_frequency_cutoff) # # 5) Compute UNMAXIMIZED overlap. olap = overlap_cplx(h_plus1, hp2, psd=psd, low_frequency_cutoff=low_frequency_cutoff, high_frequency_cutoff=high_frequency_cutoff, normalized=True) if verbose: print(("Overlap AFTER ALIGNMENT = ", olap)) print(("Optimal Overlap = ", optimal_overlap)) # idx += 1 if verbose: print("\n") # >>>>>> # 3) Iteration ended. ############################################################################# # Verify the alignment ### if verify: # print("Verifying time alignment...") # # 1) Determine the phase and time shifts for optimal match snr, corr, snr_norm = matched_filter_core(h_plus1, hp2, psd, low_frequency_cutoff, high_frequency_cutoff, None) max_snr, max_id = snr.abs_max_loc() if verbose: print( ("Post-Alignment Index of MAX SNR (should be 0 or 1 or %d): %d" % (len(snr) - 1, max_id))) print(("Length of whole SNR time-series: ", len(snr))) # # 2) Test if current time shift is within tolerance if max_id != 0 and max_id != 1 and \ max_id != (len(snr)-1) and max_id != (len(snr)-2): raise RuntimeError("Warning: ALIGNMENT NOT CORRECT (see above)") else: print("Alignment in time correct..") # # 3) Test if current phase shift is within tolerance print("Verifying phase alignment...") ph_shift = np.angle(snr[max_id]) if np.abs(ph_shift) > phase_tolerance: if verbose: print(("dphi, dphi+pi, dphi-pi: ", ph_shift, ph_shift + np.pi, ph_shift - np.pi)) print( ("dphi/pi, dphi*pi: ", ph_shift / np.pi, ph_shift * np.pi)) raise RuntimeError( "Warning: Phasing alignment possibly incorrect.") else: if verbose: print(("Post-Alignmend Phase shift (should be < %.2e): %.2e" % (phase_tolerance, np.abs(ph_shift)))) print(("Alignment in phasing correct.. (within tol %.2e)" % phase_tolerance)) # ############################################################################# # TRIM the output arrays and return if trim_trailing: hp2 = trim_trailing_zeros(hp2) hc2 = trim_trailing_zeros(hc2) if trim_leading: hp2 = trim_leading_zeros(hp2) hc2 = trim_leading_zeros(hc2) # return hplus1, hcross1, hp2, hc2
def align_waveforms_amplitude_peak(hplus1, hcross1, hplus2, hcross2, shift_epochs_only=True, trim_leading=False, trim_trailing=True, verbose=False): """ Align the two waveforms, shifting only one of the two. - AT the Amplitude PEAK """ _dt = 1.0 if type(hplus1) == TimeSeries: _dt = hplus1.delta_t elif type(hplus2) == TimeSeries: _dt = hplus2.delta_t if type(hcross1) != TimeSeries: _dt = hcross1.delta_t if type(hcross2) != TimeSeries: _dt = hcross2.delta_t hp1 = TimeSeries(hplus1, delta_t=_dt, copy=True) hc1 = TimeSeries(hcross1, delta_t=_dt, copy=True) hp2 = TimeSeries(hplus2, delta_t=_dt, copy=True) hc2 = TimeSeries(hcross2, delta_t=_dt, copy=True) # Get amplitude peak for 1st set of polarizations amp1 = amplitude_from_polarizations(hp1, hc1) amp1I = InterpolatedUnivariateSpline(amp1.sample_times, -1 * amp1.data) x0 = np.float64( amp1.sample_times[np.where(amp1.data == max(amp1.data))[0][0]]) tmp = minimize_scalar(amp1I, x0, method='bounded', bounds=(x0 - 10 * amp1.delta_t, x0 + 10 * amp1.delta_t)) h1_max_amp_time = tmp['x'] h1_max_amp = -1 * tmp['fun'] # Get amplitude peak for 1st set of polarizations amp2 = amplitude_from_polarizations(hp2, hc2) amp2I = InterpolatedUnivariateSpline(amp2.sample_times, -1 * amp2.data) x0 = np.float64( amp2.sample_times[(np.where(amp2.data == max(amp2.data))[0][0])]) tmp = minimize_scalar(amp2I, x0, method='bounded', bounds=(x0 - 10 * amp2.delta_t, x0 + 10 * amp2.delta_t)) h2_max_amp_time = tmp['x'] h2_max_amp = -1 * tmp['fun'] if verbose: print(("h1 max time = %f, epoch = %f" % (h1_max_amp_time, float(hp1._epoch)))) print(("h2 max time = %f, epoch = %f" % (h2_max_amp_time, float(hp2._epoch)))) # Amplitude location from the start t1 = h1_max_amp_time t2 = h2_max_amp_time t_shift = t1 - t2 if verbose: print(("time shift = %f to be added to waveform 2" % t_shift)) # Find phase shift phs1 = phase_from_polarizations(hp1, hc1) phs2 = phase_from_polarizations(hp2, hc2) phs1I = InterpolatedUnivariateSpline(phs1.sample_times, phs1.data) phs2I = InterpolatedUnivariateSpline(phs2.sample_times, phs2.data) ph1 = phs1I(h1_max_amp_time) ph2 = phs2I(h2_max_amp_time) ph_shift = np.float64(ph1 - ph2) if verbose: print(("phase1 at peak idx = %d, = %f" % (int(np.round(t1 / hp1.delta_t)), ph1))) print(("phase2 at peak idx = %d, = %f" % (int(np.round(t2 / hp2.delta_t)), ph2))) print(("phase shift = %f, time shift = %f" % (ph_shift, t_shift))) # # Shift whichever needs to be shifted to future time. # Shifting back in time is tricky. if shift_epochs_only: hp2, hc2 = shift_waveform_phase_time(hp2, hc2, t_shift, ph_shift, shift_epochs_only=True, verbose=verbose) # Finally, shift everything's peak to t=0 hp1._epoch -= h1_max_amp_time hc1._epoch -= h1_max_amp_time hp2._epoch -= h1_max_amp_time hc2._epoch -= h1_max_amp_time # Trim leading zeros. If time shifts are actual shifts of data along the # array, the leading zeros have meaning and cannot be trimmed. if trim_leading and shift_epochs_only: hp1 = trim_leading_zeros(hp1) hc1 = trim_leading_zeros(hc1) hp2 = trim_leading_zeros(hp2) hc2 = trim_leading_zeros(hc2) else: t_shift += (amp2.sample_times[0] - amp1.sample_times[0]) if verbose: print("phase shift is actually = {}, time shift = {}".format( ph_shift, t_shift)) if t_shift >= 0: hp2, hc2 = shift_waveform_phase_time(hp2, hc2, t_shift, ph_shift, shift_epochs_only=False, verbose=verbose) hp1._epoch -= h1_max_amp_time hc1._epoch -= h1_max_amp_time hp2._epoch = hp1._epoch hc2._epoch = hc1._epoch else: hp1, hc1 = shift_waveform_phase_time(hp1, hc1, -1 * t_shift, ph_shift, shift_epochs_only=False, verbose=verbose) hp2._epoch -= h2_max_amp_time hc2._epoch -= h2_max_amp_time hp1._epoch = hp2._epoch hc1._epoch = hc2._epoch # Trim any trailing zeros if trim_trailing: hp1 = trim_trailing_zeros(hp1) hc1 = trim_trailing_zeros(hc1) hp2 = trim_trailing_zeros(hp2) hc2 = trim_trailing_zeros(hc2) return hp1, hc1, hp2, hc2