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# Licensed under a 3-clause BSD style license - see LICENSE |
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"""Methods for synthetic generation of light curves.""" |
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import logging |
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import numpy as np |
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import nfft |
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import scipy.signal as scipy_signal |
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from numba import jit |
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__all__ = [ |
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"lc_gen_samp", |
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"lc_gen_psd_nft", |
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"lc_gen_ou", |
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"lc_gen_psd_lombscargle", |
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"lc_gen_psd_fft", |
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"lc_gen_psd_c", |
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"fgen_wrapper", |
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] |
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log = logging.getLogger(__name__) |
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def fgen_wrapper(fgen, t, y, fgen_params): |
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"""Wrapper for all lc_gen_* functions, so as not to duplicate code.""" |
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if fgen == "lc_gen_samp": |
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y2 = lc_gen_samp(y) |
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elif fgen == "lc_gen_psd_fft": |
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y2 = lc_gen_psd_fft(y) |
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elif fgen == "lc_gen_psd_nft": |
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y2 = lc_gen_psd_nft(t, y) |
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elif fgen == "lc_gen_psd_lombscargle": |
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y2 = lc_gen_psd_lombscargle(t, y) |
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elif fgen == "lc_gen_psd_c": |
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y2 = lc_gen_psd_c(t, y, t) |
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elif fgen == "lc_gen_ou": |
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if (fgen_params is None) or not ('theta' in fgen_params or 'mu' in fgen_params or 'sigma' in fgen_params): |
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raise Exception("You need to set the parameters for the signal") |
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y2 = lc_gen_ou(times=t, **fgen_params) |
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else: |
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raise Exception(f"Unknown fgen method {fgen}") |
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return y2 |
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def lc_gen_samp(signs): |
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"""Generation by sampling np.random.choice with same mean and std""" |
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return np.random.choice(signs, signs.size) |
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@jit(nopython=True) |
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def lc_gen_ou(theta, mu, sigma, times, scale=None, loc=None): |
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"""Generation from an OU process integrating the stochastic differential equation.""" |
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width = 100 * times.size |
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dt = (max(times) - min(times)) / width |
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s2 = np.empty(times.size) |
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s2[0] = mu # should get it from OU.rvs()!!!! |
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for i in range(1, times.size): |
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ti = times[i - 1] |
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y = s2[i - 1] |
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while ti < times[i]: |
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y = y + dt * (theta * (mu - y) + sigma * y * np.random.randn() / np.sqrt(dt)) |
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ti = ti + dt |
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s2[i] = y |
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if scale is not None: |
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s2 = scale * s2 / np.std(s2) |
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if loc is not None: |
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s2 = s2 - np.mean(s2) + loc |
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return s2 |
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def lc_gen_psd_c(ts, values, times): |
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"""Generation using interpolated PSD for light curves with similar PSD, mean and std.""" |
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f, p = scipy_signal.welch(values, nperseg=ts.size / 2) |
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fp = np.linspace(min(f), max(f), times.size // 2 + 1) |
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pp = np.interp(fp, f, p) |
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fft = np.sqrt(2 * pp * pp.size) * np.exp(1j * 2 * np.pi * np.random.random(pp.size)) |
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s2 = np.fft.irfft(fft, n=values.size) |
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a = values.std() / s2.std() |
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b = values.mean() - a * s2.mean() |
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s2 = a * s2 + b |
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return s2 |
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def lc_gen_psd_fft(values): |
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"""Generation using Welch algorithm and the FFT, of synthetic signals with similar PSD, mean and std. |
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Generates synthetic light curves using Lomb-Scargle algorithm |
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to compute the power spectral density and the non-uniform fft |
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to generate the signal.""" |
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# this is not valid for non-uniform times (see PSD tests for a comparison) |
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f, pxx = scipy_signal.welch(values) |
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# fft2 = np.sqrt(2*Pxx*Pxx.size)*np.exp(1j*2*pi*np.random.randn(Pxx.size)) |
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fft2 = np.sqrt(2 * pxx * pxx.size) * np.exp(1j * 2 * np.pi * np.random.random(pxx.size)) |
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s2 = np.fft.irfft(fft2, n=values.size) |
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a = values.std() / s2.std() |
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b = values.mean() - a * s2.mean() |
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s2 = a * s2 + b |
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return s2 |
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def lc_gen_psd_lombscargle(times, values): |
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"""Generation using Lomb-Scargle algorithm and the non-uniform FFT, of synthetic signals with similar PSD, mean and std. |
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Generates synthetic light curves using Lomb-Scargle algorithm |
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to compute the power spectral density and the non-uniform fft |
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to reconstruct the randomised signal.""" |
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if values.size % 2 != 0: |
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sigp = values[:-1] |
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tp = times[:-1] |
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else: |
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sigp = values |
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tp = times |
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offset = 1e-6 |
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n = sigp.size |
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# k = np.arange(-n/2, n/2) no bc scipy_signal.lombscargle does not support freq zero |
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k = np.linspace(-n / 2, n / 2 - 1 + offset, n) |
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freqs = k / 2 / np.pi |
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pxx = scipy_signal.lombscargle(tp, sigp, freqs) |
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# build random phase to get real signal |
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phase = np.random.random(pxx.size // 2) |
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phase = np.concatenate((-np.flip(phase), [0], phase[:-1])) |
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fft2 = np.sqrt(2 * pxx * pxx.size) * np.exp(1j * 2 * np.pi * phase) |
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s2 = ( |
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nfft.nfft((times - (times.max() + times.min()) / 2) / np.ptp(times), fft2, n, use_fft=True) |
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/ n |
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) |
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# fix small deviations |
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a = values.std() / s2.std() |
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b = values.mean() - a * s2.mean() |
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s2 = a * s2 + b |
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s2 = np.real(s2) |
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s2 = np.asarray(s2, dtype=float, order='C') # workaround for some bug in scipy lombscargle... |
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return s2 |
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def lc_gen_psd_nft(times, values): |
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"""Generation using the non-uniform FFT of synthetic signals with similar PSD, mean and std. |
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Generates synthetic light curves using the non-uniform FFT to |
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compute the power spectral density and to reconstruct the |
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randomised signal.""" |
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k = np.arange(-times.size // 2, times.size / 2) |
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n = k.size |
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nft = nfft.nfft_adjoint( |
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(times - (times.max() + times.min()) / 2) / np.ptp(times), values, n, use_fft=True |
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) |
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# build random phase to get real signal |
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phase = np.random.random(n // 2) |
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phase = np.concatenate((-np.flip(phase), [0], phase[:-1])) |
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fft2 = np.abs(nft) * np.exp(1j * 2 * np.pi * phase) |
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s2 = ( |
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nfft.nfft((times - (times.max() + times.min()) / 2) / np.ptp(times), fft2, use_fft=True) / n |
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) |
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s2 = np.real(s2) # np.real to fix small imaginary part from numerical error |
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# fix small mean, std difference from numerical error |
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a = values.std() / s2.std() |
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b = values.mean() - a * s2.mean() |
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s2 = a * s2 + b |
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return s2 |
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IAA-CSIC /
MUTIS
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