def theoretical_spectrum_func(channel, scale=1.0):
"""
Parameters
----------
channel : str
channel in {A, E, T}
scale : float
scale factor applied to the data, such that
data_rescaled = data * scale
Returns
-------
psd_fn : callable
PSD function in the requested channel
[rescaled Fractional Frequency / Hz]
"""
if channel == 'a_mat':
psd_fn = lambda x: tdi.noisepsd_AE(x, model='SciRDv1') * scale ** 2
elif channel == 'E':
psd_fn = lambda x: tdi.noisepsd_AE(x, model='SciRDv1') * scale ** 2
elif channel == 'T':
psd_fn = lambda x: tdi.noisepsd_T(x, model='SciRDv1') * scale ** 2
return psd_fn
def psd_fn(self, x):
if self.channel == 'A':
return tdi.noisepsd_AE(x, model='SciRDv1') * self.scale ** 2
elif self.channel == 'E':
return tdi.noisepsd_AE(x, model='SciRDv1') * self.scale ** 2
elif self.channel == 'T':
return tdi.noisepsd_T(x, model='SciRDv1') * self.scale ** 2
def generate_noise_AE(freq):
psd_j = tdi.noisepsd_AE(freq[1:])
# Gererate ramdom realisation of the noise
n_real = np.random.normal(loc=0.0, scale=np.sqrt(psd_j / 2))
n_imag = np.random.normal(loc=0.0, scale=np.sqrt(psd_j / 2))
n_real = np.insert(n_real, 0, 0., axis=0)
n_imag = np.insert(n_imag, 0, 0., axis=0)
return n_real + 1j * n_imag
def test_waveform_freq(self,
config_file="../configs/config_ldc.ini",
plot=True):
config = configparser.ConfigParser()
config.read(config_file)
fftwisdom.load_wisdom()
# Unpacking the hdf5 file and getting data and source parameters
p, td = loadings.load_ldc_data(config["InputData"]["FilePath"])
# Pre-processing data: anti-aliasing and filtering
tm, xd, yd, zd, q, t_offset, tobs, del_t, p_sampl = preprocess.preprocess_ldc_data(
p, td, config)
# Frequencies
freq_d = np.fft.fftfreq(len(tm), del_t * q)
# Restrict the frequency band to high SNR region
inds = np.where(
(float(config['Model']['MinimumFrequency']) <= freq_d)
& (freq_d <= float(config['Model']['MaximumFrequency'])))[0]
# Theoretical PSD
sa = tdi.noisepsd_AE(freq_d[inds], model='Proposal', includewd=None)
# Convert Michelson TDI to A, E, T (time domain)
ad, ed, td = ldctools.convert_XYZ_to_AET(xd, yd, zd)
# Transform to frequency domain
wd = np.ones(ad.shape[0])
wd_full = wd[:]
mask = wd[:]
a_df, e_df, t_df = preprocess.time_to_frequency(ad,
ed,
td,
wd,
del_t,
q,
compensate_window=True)
# Instantiate likelihood class
ll_cls = likelihoodmodel.LogLike(
[mask * ad, mask * ed],
sa,
inds,
tobs,
del_t * q,
normalized=config['Model'].getboolean('normalized'),
t_offset=t_offset,
channels=[1, 2],
scale=config["InputData"].getfloat("rescale"),
model_cls=None,
psd_cls=None,
wd=wd,
wd_full=wd_full)
t1 = time.time()
if config['Model'].getboolean('reduced'):
i_sampl_intr = [0, 1, 2, 3, 4, 7, 8]
aft, eft = ll_cls.compute_signal_reduced(p_sampl[i_sampl_intr])
else:
aft, eft = ll_cls.compute_signal(p_sampl)
t2 = time.time()
print('Waveform Calculated in ' + str(t2 - t1) + ' seconds.')
rms = rms_error(aft, a_df[inds], relative=True)
print("Cumulative relative error is " + str(rms))
self.assertLess(
rms, 1e-3,
"Cumulative relative error sould be less than 0.02 (2 percents)")
# Plotting
if plot:
from plottools import presets
presets.plotconfig(ctype='time', lbsize=16, lgsize=14)
# Frequency plot
fig1, ax1 = plt.subplots(nrows=2, sharex=True, sharey=True)
ax1[0].semilogx(freq_d[inds], np.real(a_df[inds]))
ax1[0].semilogx(freq_d[inds], np.real(aft), '--')
ax1[0].set_ylabel("Fractional frequency")
# ax1[0].legend()
ax1[1].semilogx(freq_d[inds], np.imag(a_df[inds]))
ax1[1].semilogx(freq_d[inds], np.imag(aft), '--')
ax1[1].set_xlabel("Frequency [Hz]")
ax1[1].set_ylabel("Fractional frequency")
# ax1[1].legend()
plt.show()
ldc=False,
tref=0)
freq_signal_sym3 = [
np.concatenate(
(sf[0:n_pos3 + 1], np.conjugate(sf[1:n_pos3 + 2][::-1])))
for sf in [af3, ef3, tf3]
]
time_signal3 = [ifft(sf_sym)[0:n3] for sf_sym in freq_signal_sym3]
t_vect3 = np.arange(t_start, t_end, del_t)
# ==================================================================================================================
# Generate noise
# ==================================================================================================================
freq_psd = np.fft.fftfreq(2 * N) * fs
freq_psd[0] = freq_psd[1]
psd_ae = tdi.noisepsd_AE(np.abs(freq_psd), model='SciRDv1')
psd_t = tdi.noisepsd_T(np.abs(freq_psd), model='SciRDv1')
a_noise = datamodel.generate_noise_from_psd(np.sqrt(psd_ae),
fs,
myseed=np.int(1234))[0:N]
e_noise = datamodel.generate_noise_from_psd(np.sqrt(psd_ae),
fs,
myseed=np.int(5678))[0:N]
t_noise = datamodel.generate_noise_from_psd(np.sqrt(psd_t),
fs,
myseed=np.int(9101))[0:N]
# ==================================================================================================================
# Form data
# ==================================================================================================================
a_meas = np.real(a_noise + time_signal[0])
def test_likelihood_with_gaps(
self,
config_file="../configs/config_ldc_single_gap.ini",
plot=True):
config = configparser.ConfigParser()
config.read(config_file)
fftwisdom.load_wisdom()
# Unpacking the hdf5 file and getting data and source parameters
p, td = loadings.load_ldc_data(config["InputData"]["FilePath"])
# Pre-processing data: anti-aliasing and filtering
tm, xd, yd, zd, q, t_offset, tobs, del_t, p_sampl = preprocess.preprocess_ldc_data(
p, td, config)
# Introducing gaps if requested
wd, wd_full, mask = loadings.load_gaps(config, tm)
print("Ideal decay number: " + str(
np.int((config["InputData"].getfloat("EndTime") - p_sampl[2]) /
(2 * del_t))))
# Now we get extract the data and transform it to frequency domain
freq_d = np.fft.fftfreq(len(tm), del_t * q)
# Convert Michelson TDI to A, E, T (time domain)
ad, ed, td = ldctools.convert_XYZ_to_AET(xd, yd, zd)
# Restrict the frequency band to high SNR region, and exclude distorted frequencies due to gaps
if (config["TimeWindowing"].getboolean('gaps')) & (
not config["Imputation"].getboolean('imputation')):
f1, f2 = physics.find_distorted_interval(mask,
p_sampl,
t_offset,
del_t,
margin=0.4)
f1 = np.max([f1, 0])
f2 = np.min([f2, 1 / (2 * del_t)])
inds = np.where(
(float(config['Model']['MinimumFrequency']) <= freq_d)
& (freq_d <= float(config['Model']['MaximumFrequency']))
& ((freq_d <= f1) | (freq_d >= f2)))[0]
else:
inds = np.where(
(float(config['Model']['MinimumFrequency']) <= freq_d)
& (freq_d <= float(config['Model']['MaximumFrequency'])))[0]
# Restriction of sampling parameters to instrinsic ones Mc, q, tc, chi1, chi2, np.sin(bet), lam
i_sampl_intr = [0, 1, 2, 3, 4, 7, 8]
print(
"================================================================="
)
fftwisdom.save_wisdom()
# Auxiliary parameter classes
psd_cls = None
# One-sided PSD
sa = tdi.noisepsd_AE(freq_d[inds], model='Proposal', includewd=None)
data_cls = None
# Instantiate likelihood class
ll_cls = likelihoodmodel.LogLike(
[mask * ad, mask * ed],
sa,
inds,
tobs,
del_t * q,
normalized=config['Model'].getboolean('normalized'),
t_offset=t_offset,
channels=[1, 2],
scale=config["InputData"].getfloat("rescale"),
model_cls=data_cls,
psd_cls=psd_cls,
wd=wd,
wd_full=wd_full)
# # Waveform generation in the Frequency domain
# t1 = time.time()
# if config['Model'].getboolean('reduced'):
# i_sampl_intr = [0, 1, 2, 3, 4, 7, 8]
# aft, eft = ll_cls.compute_signal_reduced(p_sampl[i_sampl_intr])
# else:
# aft, eft = ll_cls.compute_signal(p_sampl)
# t2 = time.time()
# print('Waveform Calculated in ' + str(t2 - t1) + ' seconds.')
# Get the windowed discrete Fourier transform used in the likelihood
a_df_like, e_df_like = ll_cls.data_dft
# Compare to the DFT of the complete data set
a_df = fft(
ad * wd_full) * del_t * q * wd_full.shape[0] / np.sum(wd_full)
e_df = fft(
ed * wd_full) * del_t * q * wd_full.shape[0] / np.sum(wd_full)
# Plotting
if plot:
from plottools import presets
presets.plotconfig(ctype='time', lbsize=16, lgsize=14)
# Time plot
fig0, ax0 = plt.subplots(nrows=1)
ax0.semilogx(tm, ad, 'k')
ax0.semilogx(tm, wd * np.max(ad), 'r')
ax0.semilogx(tm, mask * np.max(ad), 'gray')
# Frequency plot
fig1, ax1 = plt.subplots(nrows=2, sharex=True, sharey=True)
ax1[0].semilogx(freq_d[inds], np.real(a_df[inds]))
ax1[0].semilogx(freq_d[inds], np.real(a_df_like), '--')
ax1[0].set_ylabel("Fractional frequency", fontsize=16)
# ax1[0].legend()
ax1[1].semilogx(freq_d[inds], np.imag(a_df[inds]))
ax1[1].semilogx(freq_d[inds], np.imag(a_df_like), '--')
ax1[1].set_xlabel("Frequency [Hz]", fontsize=16)
ax1[1].set_ylabel("Fractional frequency", fontsize=16)
# ax1[1].legend()
for i in range(len(ax1)):
ax1[i].axvline(x=f1,
ymin=0,
ymax=np.max(np.real(a_df[inds])),
color='r',
linestyle='--')
ax1[i].axvline(x=f2,
ymin=0,
ymax=np.max(np.real(a_df[inds])),
color='r',
linestyle='--')
plt.show()
rms = rms_error(a_df_like, a_df[inds], relative=True)
print("Cumulative relative error is " + str(rms))
self.assertLess(
rms, 5e-2,
"Cumulative relative error sould be less than 0.05 (5 percents)")
print("Reduced-model signal computation time: " + str(t2 - t1))
print("=================================================================")
# Verification of parameters compatibility m1, m2, chi1, chi2, Deltat, dist, inc, phi, lambd, beta, psi
params0 = physics.like_to_waveform(p_sampl)
# # Testing the right offset
# offsets = np.linspace(50.60, 53, 50)
# results = [lisabeta_template(params, freqD, tobs, tref=0, toffset=toffset) for toffset in offsets]
# rms = np.array([np.sum(np.abs(ADf - res[0])**2) for res in results])
fftwisdom.save_wisdom()
# ==================================================================================================================
# Comparing log-likelihoood
# ==================================================================================================================
# One-sided PSD
SA = tdi.noisepsd_AE(freqD[inds], model='Proposal', includewd=None)
# Consider only A and E TDI data in frequency domain
dataAE = [ADf[inds], EDf[inds]]
# And in time domain
data_ae_time = [ad, ed]
templateAE = [aft, eft]
llA1, llE1 = SimpleLogLik(dataAE, templateAE, SA, df, tdi='AET')
llA2, llE2 = SimpleLogLik(dataAE, dataAE, SA, df, tdi='AET')
llA3, llE3 = SimpleLogLik(templateAE, templateAE, SA, df, tdi='AET')
print('compare A', llA1, llA2, llA3)
print('compare E', llE1, llE2, llE3)
print('total lloglik', llA1 + llE1, llA2 + llE2, llA3 + llE3)
# Full computation of likelihood
ll_cls = likelihoodmodel.LogLike(data_ae_time,
SA,
freqD[inds],
if __name__ == '__main__':
from matplotlib import pyplot as plt
import tdi
fftwisdom.load_wisdom()
N = 2**19
t = np.arange(0, N)
f = np.fft.fftfreq(N)
f[0] = f[1]
scale = 1e-21
S = tdi.noisepsd_AE(np.abs(f), model='Proposal') / scale**2
f2N = np.fft.fftfreq(2 * N)
f2N[0] = f2N[1]
S_2N = tdi.noisepsd_AE(np.abs(f2N), model='Proposal') / scale**2
# ==========================================================================
# Generate data
print("Generating data...")
b, S, Noise_TF = noise.generateNoiseFromDSP(np.sqrt(S[0:N]),
fs,
myseed=1354561)
y = np.real(b[0:N])
print("Data generated")
N_est = 100
PSD = PSD_estimate(N_est, N)
