From 3567f6f1bdb3ad40e3072f158cd36a4cfd3361ac Mon Sep 17 00:00:00 2001 From: Avi Vajpeyi Date: Tue, 9 Jul 2024 12:36:27 +0100 Subject: [PATCH 1/5] add example --- examples/common.py | 103 +++++++++++++++++++++++ examples/lisa_wdb_snr.py | 140 ++++++++++++++++++++++++++++++++ examples/lvk_cbc_snr.pdf | Bin 0 -> 850021 bytes examples/lvk_cbc_snr.py | 171 +++++++++++++++++++++++++++++++++++++++ 4 files changed, 414 insertions(+) create mode 100644 examples/common.py create mode 100644 examples/lisa_wdb_snr.py create mode 100644 examples/lvk_cbc_snr.pdf create mode 100644 examples/lvk_cbc_snr.py diff --git a/examples/common.py b/examples/common.py new file mode 100644 index 0000000..df0585a --- /dev/null +++ b/examples/common.py @@ -0,0 +1,103 @@ +from typing import Optional, Tuple, Union + +import bilby +import matplotlib.pyplot as plt +import numpy as np +from scipy.interpolate import interp1d + + + + +def compute_wavelet_snr(h: "Wavelet", PSD: "Wavelet") -> float: + """Compute the SNR of a model h[ti,fi] given data d[ti,fi] and PSD[ti,fi]. + + SNR(h) = Sum_{ti,fi} [ h_hat[ti,fi] d[ti,fi] / PSD[ti,fi] + + Parameters + ---------- + h : np.ndarray + The model in the wavelet domain (binned in [ti,fi]). + d : np.ndarray + The data in the wavelet domain (binned in [ti,fi]). + PSD : np.ndarray + The PSD in the wavelet domain (binned in [ti,fi]). + + Returns + ------- + float + The SNR of the model h given data d and PSD. + + """ + snr_sqrd = np.nansum((h * h) / PSD) + return np.sqrt(snr_sqrd) + + +def compute_frequency_optimal_snr(h_freq, psd, duration)-> float: + """ + A18 from Veitch et al. 2009 + https://arxiv.org/abs/0911.3820 + """ + snr_sqrd = __noise_weighted_inner_product( + aa=h_freq, bb=h_freq, power_spectral_density=psd, duration=duration + ).real + return np.sqrt(snr_sqrd) + + +def __noise_weighted_inner_product(aa, bb, power_spectral_density, duration): + integrand = np.conj(aa) * bb / power_spectral_density + return (4 / duration) * np.sum(integrand) + +def evolutionary_psd_from_stationary_psd( + psd: np.ndarray, + psd_f: np.ndarray, + f_grid, + t_grid, +) -> "Wavelet": + """ + PSD[ti,fi] = PSD[fi] * delta_f + """ + + Nt = len(t_grid) + delta_F = f_grid[1] - f_grid[0] + delta_T = t_grid[1] - t_grid[0] + + freq_data = psd + nan_val = np.max(freq_data) + psd_grid = ( + interp1d( + psd_f, + freq_data, + kind="nearest", + fill_value=nan_val, + bounds_error=False, + )(f_grid) + * delta_F + ) + + # repeat the PSD for each time bin + psd_grid = np.repeat(psd_grid[None, :], Nt, axis=0) + return psd_grid + + + +def get_wavelet_bins(duration, data_len, Nf, Nt): + """Get the bins for the wavelet transform + Eq 4-6 in Wavelets paper + """ + T = duration + N = data_len + fs = N / T + fmax = fs / 2 + + delta_t = T / Nt + delta_f = 1 / (2 * delta_t) + + # assert delta_f == fmax / Nf, f"delta_f={delta_f} != fmax/Nf={fmax/Nf}" + + f_bins = np.arange(0, Nf) * delta_f + t_bins = np.arange(0, Nt) * delta_t + + + return t_bins, f_bins + + diff --git a/examples/lisa_wdb_snr.py b/examples/lisa_wdb_snr.py new file mode 100644 index 0000000..1d0183c --- /dev/null +++ b/examples/lisa_wdb_snr.py @@ -0,0 +1,140 @@ +from typing import Tuple + +import matplotlib.pyplot as plt +import numpy as np +from scipy.signal.windows import tukey +from common import compute_frequency_optimal_snr, evolutionary_psd_from_stationary_psd, compute_wavelet_snr, plot, \ + get_wavelet_bins +from WDMWaveletTransforms.wavelet_transforms import transform_wavelet_time + +from collections import namedtuple + +TIMESERIES = namedtuple("TimeSeries", ["data", "time"]) + + +def lisa_psd_func(f): + """ + PSD obtained from: + Robson et al 2018, "LISA Sensitivity Curves" + https://arxiv.org/pdf/1803.01944.pdf + + Removed galactic confusion noise. Non stationary effect. + + The power spectrum -- not the TDI + + """ + + L = 2.5 * 10 ** 9 # Length of LISA arm + f0 = 19.09 * 10 ** -3 + + # Eq 10 + Poms = ((1.5 * 10 ** -11) ** 2) * ( + 1 + ((2 * 10 ** -3) / f) ** 4 + ) # Optical Metrology Sensor + + # Eq 11 + Pacc = ( + (3 * 10 ** -15) ** 2 + * (1 + (4 * 10 ** -3 / (10 * f)) ** 2) + * (1 + (f / (8 * 10 ** -3)) ** 4) + ) # Acceleration Noise + + # Eq 13 + PSD = ( + (10 / (3 * L ** 2)) + * (Poms + (4 * Pacc) / ((2 * np.pi * f)) ** 4) + * (1 + 0.6 * (f / f0) ** 2) + ) # PSD + + return PSD + + +def waveform(a: float, f: float, fdot: float, t: np.ndarray, eps=0): + """ + This is a function. It takes in a value of the amplitude $a$, frequency $f$ and frequency derivative $\dot{f} + and a time vector $t$ and spits out whatever is in the return function. Modify amplitude to improve SNR. + Modify frequency range to also affect SNR but also to see if frequencies of the signal are important + for the windowing method. We aim to estimate the parameters $a$, $f$ and $\dot{f}$. + + h = a * sin(2 * pi * (ft + 0.5 * fdot * t^2)) + Quadratic chirp signal. + + """ + + return a * (np.sin((2 * np.pi) * (f * t + 0.5 * fdot * t ** 2))) + + +def get_lisa_data(): + """ + This function is used to generate the data for the LISA detector. We use the waveform function to generate + the signal and then use the freq_PSD function to generate the PSD. We then use the FFT function to generate + the frequency domain waveform. We then compute the optimal SNR. + """ + + a_true = 5e-21 + f_true = 1e-3 + fdot_true = 1e-8 + + fs = 2 * f_true # Sampling rate + delta_t = np.floor( + 0.01 / fs + ) # Sampling interval -- largely oversampling here. + tmax = 120 * 60 * 60 # 120 hours + t = np.arange(0, tmax, delta_t) + ND = int( + 2 ** (np.ceil(np.log2(len(t)))) + ) # Round length of time series to a power of two. + t = np.arange(0, ND) * delta_t + + h_signal_t = waveform(a_true, f_true, fdot_true, t) + freq = np.fft.fftfreq(ND, delta_t)[: ND // 2] + psd_f = lisa_psd_func(freq) + h_signal_f = np.fft.fft(h_signal_t)[: ND // 2] + duration = delta_t * ND + + # skip first element to avoid division by zero + freq = freq[1:] + psd_f = psd_f[1:] + h_signal_f = h_signal_f[1:] + + snr = compute_frequency_optimal_snr(h_signal_f, psd_f, duration) + return h_signal_t, t, h_signal_f, h_signal_f, psd_f, snr + + +def main(): + np.random.seed(1234) + + h_signal_t, t, h_signal_f, f, psd_f, snr = get_lisa_data() + ND = len(t) + Nf = 256 + Nt = ND // Nf + duration = ND * t[1] + + h_time = TIMESERIES(h_signal_t, t) + h_wavelet = transform_wavelet_time(h_time.data, Nf=Nf, Nt=Nt) + time_grid, freq_grid = get_wavelet_bins(duration, ND, Nf, Nt) + + # h_wavelet = from_time_to_wavelet(h_time, Nt=Nt) + psd_wavelet = evolutionary_psd_from_stationary_psd( + psd=psd_f, + psd_f=f, + f_grid=freq_grid, + t_grid=time_grid, + ) + + compute_frequency_optimal_snr( + h_freq=h_signal_f, psd=psd_f, duration=duration + ) + wavelet_snr = compute_wavelet_snr(h_wavelet, psd_wavelet) + + print(f"SNR in time domain (ND:{ND}): {snr:.2f}") + print(f"SNR in wavelet domain (Nf{Nf}xNt{Nt}): {wavelet_snr:.2f}") + + fig, axes = plt.subplots(2,1, figsize=(12, 10)) + axes[0].loglog(f, np.abs(h_signal_f)) + axes[0].loglog(f, psd_f) + axes[0].set_title("Frequency domain signal") + + +if __name__ == "__main__": + main() diff --git a/examples/lvk_cbc_snr.pdf b/examples/lvk_cbc_snr.pdf new file mode 100644 index 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Generate a CBC signal with a given SNR in LVK 04 noise +2. Perform a wavelet transform on the signal +3. Compute the SNR of the wavelet transform +4. Plot the wavelet transform + time domain signal + + +REQUIRES: +- WDMWaveletTransforms, bilby[gw], numba +""" + +from WDMWaveletTransforms.wavelet_transforms import transform_wavelet_time +import bilby +from typing import Tuple +import numpy as np +from common import compute_wavelet_snr, evolutionary_psd_from_stationary_psd, get_wavelet_bins + +import matplotlib.pyplot as plt +import matplotlib.colors as colors + +from collections import namedtuple +TIMESERIES = namedtuple("TimeSeries", ["data", "time"]) + +from scipy.interpolate import interp1d + + + +DURATION = 8 +SAMPLING_FREQUENCY = 4096 +DT = 1 / SAMPLING_FREQUENCY +MINIMUM_FREQUENCY = 20 +MAXIMUM_FREQUENCY = 256 + +CBC_GENERATOR = bilby.gw.WaveformGenerator( + duration=DURATION, + sampling_frequency=SAMPLING_FREQUENCY, + frequency_domain_source_model=bilby.gw.source.lal_binary_black_hole, + parameter_conversion=bilby.gw.conversion.convert_to_lal_binary_black_hole_parameters, + waveform_arguments=dict( + waveform_approximant="IMRPhenomD", + reference_frequency=20.0, + minimum_frequency=MINIMUM_FREQUENCY, + maximum_frequency=MAXIMUM_FREQUENCY, + ), +) + +GW_PARMS = dict( + mass_1=30, + mass_2=30, # 2 mass parameters + a_1=0.1, + a_2=0.1, + tilt_1=0.0, + tilt_2=0.0, + phi_12=0.0, + phi_jl=0.0, # 6 spin parameters + ra=1.375, + dec=-1.2108, + luminosity_distance=2000.0, + theta_jn=0.0, # 7 extrinsic parameters + psi=2.659, + phase=1.3, + geocent_time=0, +) + + +def _get_ifo(t0=0.0, noise=True): + ifos = bilby.gw.detector.InterferometerList(["H1"]) # design sensitivity + if noise: + ifos.set_strain_data_from_power_spectral_densities( + sampling_frequency=SAMPLING_FREQUENCY, + duration=DURATION, + start_time=t0, + ) + else: + ifos.set_strain_data_from_zero_noise( + sampling_frequency=SAMPLING_FREQUENCY, + duration=DURATION, + start_time=t0, + ) + return ifos + + +def inject_signal_in_noise( + mc, q=1, distance=1000.0, noise=True +) -> Tuple[TIMESERIES, float]: + injection_parameters = GW_PARMS.copy() + ( + injection_parameters["mass_1"], + injection_parameters["mass_2"], + ) = bilby.gw.conversion.chirp_mass_and_mass_ratio_to_component_masses( + mc, q + ) + injection_parameters["luminosity_distance"] = distance + + ifos = _get_ifo(injection_parameters["geocent_time"] + 1.5, noise=noise) + ifos.inject_signal( + waveform_generator=CBC_GENERATOR, parameters=injection_parameters + ) + ifo: bilby.gw.detector.Interferometer = ifos[0] + + snr = ifo.meta_data["matched_filter_SNR"] + + ifo.time_array = np.linspace(0, DURATION, int(DURATION * SAMPLING_FREQUENCY)) + data = TIMESERIES(ifo.strain_data.time_domain_strain, ifo.time_array) + return data, np.abs(snr) + + +def get_lvk_psd(): + ifo: bilby.gw.detector.Interferometer = _get_ifo()[0] + psd = ifo.power_spectral_density.psd_array + psd_f = ifo.power_spectral_density.frequency_array + return psd, psd_f + + +def get_lvk_psd_function(): + psd, psd_f = get_lvk_psd() + return interp1d(psd_f, psd, bounds_error=False, fill_value=max(psd)) + + + +def plot(signal_t, optimal_snr_ht, psd_f, psd, signal_wavelet, time_grid, freq_grid, psd_wavelet, snr_wavelet, DURATION, MINIMUM_FREQUENCY): + # plot Timeseries, wavelet signal and PSD + fig, ax = plt.subplots(2, 2, figsize=(12, 10)) + ax[0, 0].plot(signal_t.time, signal_t.data) + ax[0, 0].set_xlim(0,DURATION) + ax[0, 0].set_xlabel("Time [s]") + ax[0, 0].set_ylabel("Strain") + ax[0, 0].set_title("Time domain signal") + # ANNOTATE SNR + ax[0, 0].text(0.1, 0.85, f"SNR: {optimal_snr_ht:.2f}", transform=ax[0, 0].transAxes, fontsize='x-large') + ax[0, 1].loglog(psd_f, psd) + ax[0, 1].set_title("PSD in frequency domain") + + ax[1, 0].pcolor(time_grid, freq_grid, signal_wavelet.T, cmap="RdBu", norm=colors.TwoSlopeNorm( vcenter=0)) + ax[1, 0].set_ylim(MINIMUM_FREQUENCY, 512) + ax[1, 0].set_xlabel("Time [s]") + ax[1, 0].set_ylabel("Frequency [Hz]") + ax[1, 0].set_title("Wavelet transform") + ax[1, 0].text(0.1, 0.85, f"SNR: {snr_wavelet:.2f}", transform=ax[1, 0].transAxes, fontsize='x-large') + ax[1,1].pcolor(time_grid, freq_grid, psd_wavelet.T, cmap="viridis", norm='log') + ax[1,1].set_yscale('log') + ax[1,1].set_ylim(MINIMUM_FREQUENCY, 512) + ax[1,1].set_title("PSD in wavelet domain") + ax[1,1].set_xlabel("Time [s]") + ax[1,1].set_ylabel("Frequency [Hz]") + return fig + +def main(): + signal_t, optimal_snr_ht = inject_signal_in_noise(mc=30, noise=False) + psd, psd_f = get_lvk_psd() + ND = len(signal_t.time) + Nt = 128 + Nf = ND // Nt + signal_wavelet = transform_wavelet_time(signal_t.data, Nf, Nt) + time_grid, freq_grid = get_wavelet_bins(DURATION, ND, Nf, Nt) + psd_wavelet = evolutionary_psd_from_stationary_psd(psd, psd_f, freq_grid, time_grid) + snr_wavelet = compute_wavelet_snr(signal_wavelet, psd_wavelet) + print("SNR in time domain:", optimal_snr_ht) + print(f"ND: {ND}, Nt: {Nt}, Nf: {Nf}") + print("SNR in wavelet domain:", snr_wavelet) + plot( + signal_t, optimal_snr_ht, + psd_f, psd, + signal_wavelet, time_grid, freq_grid, + psd_wavelet, snr_wavelet, + DURATION, MINIMUM_FREQUENCY + ).savefig('lvk_cbc_snr.pdf', dpi=300) + + +if __name__ == "__main__": + main() From f38e3c111cd1c7f32ab133bd7f771235ae728784 Mon Sep 17 00:00:00 2001 From: Avi Vajpeyi Date: Tue, 9 Jul 2024 17:26:59 +0100 Subject: [PATCH 2/5] add more examples --- examples/lisa_wdb_snr.pdf | Bin 0 -> 2200865 bytes examples/lisa_wdb_snr.py | 38 +++++++++++----- examples/toy_model_snr.pdf | Bin 0 -> 74626 bytes examples/toy_model_snr.py | 88 +++++++++++++++++++++++++++++++++++++ 4 files changed, 114 insertions(+), 12 deletions(-) create mode 100644 examples/lisa_wdb_snr.pdf create mode 100644 examples/toy_model_snr.pdf create mode 100644 examples/toy_model_snr.py diff --git a/examples/lisa_wdb_snr.pdf b/examples/lisa_wdb_snr.pdf new file mode 100644 index 0000000000000000000000000000000000000000..a800f705ab5921c6d4715d70e53768ca38e4a236 GIT binary patch literal 2200865 zcmZTvc|26@`zA>tO4+iOB-ujtJw>Td_G}3$`#ua~NzrP{QkFrIol@4ZQ+6Z!zK^jE 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