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                # Licensed under a 3-clause BSD style license - see LICENSE  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                """Synthetic generation of light curves."""  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                import logging  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                import matplotlib.pyplot as plt  | 
            
                            
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                import numpy as np  | 
            
                            
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                import scipy.optimize as scipy_optimize  | 
            
                            
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                import scipy.signal as scipy_signal  | 
            
                            
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                import scipy.special as scipy_special  | 
            
                            
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                import scipy.stats as scipy_stats  | 
            
                            
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                from matplotlib.offsetbox import AnchoredText  | 
            
                            
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                from mutis.lib.signal import *  | 
            
                            
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                __all__ = ["Signal"]  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                log = logging.getLogger(__name__)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                class Signal:  | 
            
                            
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                    """Analysis and generation of a signal.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    Description goes here.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    Parameters  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    ----------  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    times : :class:`numpy.ndarray` or :class:`pandas.Series`  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        Values of the time axis.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    values : :class:`numpy.ndarray` or :class:`pandas.Series`  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        Values of the signal axis.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    fgen : :class:`str`  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        Method used to generate the synthetic signal.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    def __init__(self, times, values, dvalues=None, fgen=None):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        self.times = np.array(times)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        self.values = np.array(values)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        self.fgen = fgen  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        self.dvalues = np.array(dvalues) if dvalues is not None else None  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        self.synth = None  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        # TODO make attributes below specific of OU method / not the entire class  | 
            
                            
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                        self.OU_theta = None  | 
            
                            
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                        self.OU_mu = None  | 
            
                            
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                        self.OU_sigma = None  | 
            
                            
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                    def plot(self, ax=None):  | 
            
                            
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                        if ax is None:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                            ax = plt.gca()  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        return ax.plot(self.times, self.values, ".-", lw=1, alpha=0.7)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    def gen_synth(self, samples):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        """Description goes here."""  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        self.synth = np.empty((samples, self.times.size))  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        for n in range(samples):  | 
            
                            
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                            self.synth[n] = fgen_wrapper(fgen=self.fgen, t=self.times, y=self.values,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                         fgen_params={'theta':self.OU_theta, 'mu':self.OU_mu, 'sigma':self.OU_sigma}) | 
            
                            
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                    def OU_fit(self, bins=None, rang=None, a=1e-5, b=100):  | 
            
                            
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                        """Fit the signal to an OU stochastic process, using several statistical approaches.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        This function tries to fit the signal to an OU stochastic  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        process using both basic curve fitting and the Maximum  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        Likelihood Estimation method, and returns some plots of  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        the signals and its properties, and the estimated parameters.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        # TODO: make a generic fit method  | 
            
                            
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                        res = dict()  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        y = self.values  | 
            
                            
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                        t = self.times  | 
            
                            
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                        dy = np.diff(y)  | 
            
                            
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                        dt = np.diff(t)  | 
            
                            
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                        # estimate sigma  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        try:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                            sigma_est = (np.nanmean(dy ** 2 / y[:-1] ** 2 / dt)) ** 0.5  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                            res["sigma_est"] = sigma_est  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        except Exception as e:  | 
            
                            
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                            log.error(f"Could not estimate sigma: {e}") | 
            
                            
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                        # plot histogram  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        if bins is None:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                            bins = np.int(y.size ** 0.5 / 1.5)  # bins='auto'  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        if rang is None:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                            rang = (np.percentile(y, 0), np.percentile(y, 99))  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        p, x = np.histogram(y, density=True, bins=bins, range=rang)  # bins='sqrt')  | 
            
                            
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                        x = (x + np.roll(x, -1))[:-1] / 2.0  | 
            
                            
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                        plt.subplots()  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        plt.hist(y, density=True, alpha=0.75, bins=bins, range=rang)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        plt.plot(x, p, "r-", alpha=0.5)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        anchored_text = AnchoredText(  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                            f"mean    {np.mean(y):.2g} \n " | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                            f"median  {np.median(y):.2g} \n " | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                            f"mode    {scipy_stats.mode(y)[0][0]:.2g} \n " | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                            f"std     {np.std(y):.2g} \n " | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                            f"var     {np.var(y):.2g}", | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                            loc="upper right",  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        )  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    110
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                                                     | 
                
                 | 
                        plt.gca().add_artist(anchored_text)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    111
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    112
                 | 
                                    
                                                     | 
                
                 | 
                        # curve_fit  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    113
                 | 
                                    
                                                     | 
                
                 | 
                        try:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    114
                 | 
                                    
                                                     | 
                
                 | 
                            popt, pcov = scipy_optimize.curve_fit(f=self.pdf, xdata=x, ydata=p)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    115
                 | 
                                    
                                                     | 
                
                 | 
                            # print('curve_fit: (l, mu)') | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    116
                 | 
                                    
                                                     | 
                
                 | 
                            # print('popt: ') | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    117
                 | 
                                    
                                                     | 
                
                 | 
                            # print(popt)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    118
                 | 
                                    
                                                     | 
                
                 | 
                            # print('pcov: ') | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    119
                 | 
                                    
                                                     | 
                
                 | 
                            # print(np.sqrt(np.diag(pcov)))  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    120
                 | 
                                    
                                                     | 
                
                 | 
                            x_c = np.linspace(1e-5, 1.1 * np.max(x), 1000)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    121
                 | 
                                    
                                                     | 
                
                 | 
                            plt.plot(x_c, self.pdf(x_c, *popt), "k-", label="curve_fit", alpha=0.8)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    122
                 | 
                                    
                                                     | 
                
                 | 
                            res["curve_fit"] = (popt, np.sqrt(np.diag(pcov)))  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    123
                 | 
                                    
                                                     | 
                
                 | 
                        except Exception as e:  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                                                                        
                        
                         
                                                                                        
                                                                                            
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    124
                 | 
                                    
                                                     | 
                
                 | 
                            log.error(f"Some error fitting with curve_fit {e}") | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    125
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    126
                 | 
                                    
                                                     | 
                
                 | 
                        # fit pdf with MLE  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    127
                 | 
                                    
                                                     | 
                
                 | 
                        # TODO: place outside as a helper class  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    128
                 | 
                                    
                                                     | 
                
                 | 
                        #       mu here is different than self.mu  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    129
                 | 
                                    
                                                     | 
                
                 | 
                        class OU(scipy_stats.rv_continuous):  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    130
                 | 
                                    
                                                     | 
                
                 | 
                            def _pdf(self, x, l, mu):  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                                                                                                                                                                                
                        
                         
                                                                                        
                                                                                            
                                                                                            
                                                                                            
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    131
                 | 
                                    
                                                     | 
                
                 | 
                                return (  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    132
                 | 
                                    
                                                     | 
                
                 | 
                                    (l * mu) ** (1 + l)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    133
                 | 
                                    
                                                     | 
                
                 | 
                                    / scipy_special.gamma(1 + l)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    134
                 | 
                                    
                                                     | 
                
                 | 
                                    * np.exp(-l * mu / x)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    135
                 | 
                                    
                                                     | 
                
                 | 
                                    / x ** (l + 2)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    136
                 | 
                                    
                                                     | 
                
                 | 
                                )  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    137
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    138
                 | 
                                    
                                                     | 
                
                 | 
                        try:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    139
                 | 
                                    
                                                     | 
                
                 | 
                            fit = OU(a=a, b=np.percentile(y, b)).fit(y, 1, 1, floc=0, fscale=1)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    140
                 | 
                                    
                                                     | 
                
                 | 
                            # print('MLE fit: (l, mu)') | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    141
                 | 
                                    
                                                     | 
                
                 | 
                            # print(fit)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    142
                 | 
                                    
                                                     | 
                
                 | 
                            x_c = np.linspace(0, 1.1 * np.max(x), 1000)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    143
                 | 
                                    
                                                     | 
                
                 | 
                            plt.plot(x_c, self.pdf(x_c, fit[0], fit[1]), "k-.", label="MLE", alpha=0.8)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    144
                 | 
                                    
                                                     | 
                
                 | 
                            res["MLE_fit"] = fit[:-2]  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    145
                 | 
                                    
                                                     | 
                
                 | 
                        except Exception as e:  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                                                                        
                        
                         
                                                                                        
                                                                                            
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    146
                 | 
                                    
                                                     | 
                
                 | 
                            log.error(f"Some error fitting with MLE {e}") | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    147
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    148
                 | 
                                    
                                                     | 
                
                 | 
                        plt.legend(loc="lower right")  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    149
                 | 
                                    
                                                     | 
                
                 | 
                        # plt.show()  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    150
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    151
                 | 
                                    
                                                     | 
                
                 | 
                        # estimate theta (from curve_fit)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    152
                 | 
                                    
                                                     | 
                
                 | 
                        try:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    153
                 | 
                                    
                                                     | 
                
                 | 
                            res["th_est1"] = fit[0] * sigma_est ** 2 / 2  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    154
                 | 
                                    
                                                     | 
                
                 | 
                        except NameError as e:  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    155
                 | 
                                    
                                                     | 
                
                 | 
                            res["th_est1"] = None  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    156
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    157
                 | 
                                    
                                                     | 
                
                 | 
                        # estimate theta (from MLE)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    158
                 | 
                                    
                                                     | 
                
                 | 
                        try:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    159
                 | 
                                    
                                                     | 
                
                 | 
                            res["th_est2"] = popt[0] * sigma_est ** 2 / 2  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    160
                 | 
                                    
                                                     | 
                
                 | 
                        except NameError as e:  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    161
                 | 
                                    
                                                     | 
                
                 | 
                            res["th_est2"] = None  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    162
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    163
                 | 
                                    
                                                     | 
                
                 | 
                        return res  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    164
                 | 
                                    
                                                     | 
                
                 | 
                          | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    165
                 | 
                                    
                                                     | 
                
                 | 
                          | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    166
                 | 
                                    
                                                     | 
                
                 | 
                    def check_gen(self, fgen=None, fgen_params=None, fpsd="lombscargle", **axes):  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    167
                 | 
                                    
                                                     | 
                
                 | 
                        """Check the generation of synthetic signals.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    168
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    169
                 | 
                                    
                                                     | 
                
                 | 
                        This function checks the generation of a synthetic light curve.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    170
                 | 
                                    
                                                     | 
                
                 | 
                          | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    171
                 | 
                                    
                                                     | 
                
                 | 
                        Parameters:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    172
                 | 
                                    
                                                     | 
                
                 | 
                        -----------  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    173
                 | 
                                    
                                                     | 
                
                 | 
                        fgen: :str:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    174
                 | 
                                    
                                                     | 
                
                 | 
                            A valid fgen method name.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    175
                 | 
                                    
                                                     | 
                
                 | 
                        fgen_params: :dict:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    176
                 | 
                                    
                                                     | 
                
                 | 
                            Parameters for fgen (e.g. for fgen='lc_gen_ou', a dict containing  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    177
                 | 
                                    
                                                     | 
                
                 | 
                            values for theta, mu and sigma).  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    178
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    179
                 | 
                                    
                                                     | 
                
                 | 
                        Returns:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    180
                 | 
                                    
                                                     | 
                
                 | 
                        --------  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    181
                 | 
                                    
                                                     | 
                
                 | 
                        axes: :tuple:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    182
                 | 
                                    
                                                     | 
                
                 | 
                            Tuple of three axes, on which:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    183
                 | 
                                    
                                                     | 
                
                 | 
                            - The first plot show both the original signal and the synthetic one.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    184
                 | 
                                    
                                                     | 
                
                 | 
                            - The second plot shows the histogram of the values taken by both signals.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    185
                 | 
                                    
                                                     | 
                
                 | 
                            - The third plot shows their PSD.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    186
                 | 
                                    
                                                     | 
                
                 | 
                        """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    187
                 | 
                                    
                                                     | 
                
                 | 
                          | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    188
                 | 
                                    
                                                     | 
                
                 | 
                        t, y = self.times, self.values  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                                                                        
                        
                         
                                                                                        
                                                                                            
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    189
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    190
                 | 
                                    
                                                     | 
                
                 | 
                        y2 = fgen_wrapper(fgen=fgen, t=t, y=y, fgen_params=fgen_params)  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    191
                 | 
                                    
                                                     | 
                
                 | 
                          | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    192
                 | 
                                    
                                                     | 
                
                 | 
                          | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    193
                 | 
                                    
                                                     | 
                
                 | 
                        if ("ax1" not in axes) or ("ax2" not in axes) or ("ax3" not in axes): | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    194
                 | 
                                    
                                                     | 
                
                 | 
                            fig, (axes["ax1"], axes["ax2"], axes["ax3"]) = plt.subplots(  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    195
                 | 
                                    
                                                     | 
                
                 | 
                                nrows=1, ncols=3, figsize=(20, 4)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    196
                 | 
                                    
                                                     | 
                
                 | 
                            )  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    197
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    198
                 | 
                                    
                                                     | 
                
                 | 
                        # plot the two signals  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    199
                 | 
                                    
                                                     | 
                
                 | 
                        axes["ax1"].plot(t, y, "b-", label="orig", lw=0.5, alpha=0.8)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    200
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    201
                 | 
                                    
                                                     | 
                
                 | 
                        # ax1p = ax1.twinx()  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    202
                 | 
                                    
                                                     | 
                
                 | 
                        axes["ax1"].plot(t, y2, "r-", label="gen", lw=0.5, alpha=0.8)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    203
                 | 
                                    
                                                     | 
                
                 | 
                        axes["ax1"].set_title("light curves") | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    204
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    205
                 | 
                                    
                                                     | 
                
                 | 
                        # plot their histogram  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    206
                 | 
                                    
                                                     | 
                
                 | 
                        bins = "auto"  # bins = np.int(y.size**0.5/1.5) #  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    207
                 | 
                                    
                                                     | 
                
                 | 
                        rang = (np.percentile(y, 0), np.percentile(y, 99))  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    208
                 | 
                                    
                                                     | 
                
                 | 
                        axes["ax2"].hist(y, density=True, color="b", alpha=0.4, bins=bins, range=rang)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    209
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    210
                 | 
                                    
                                                     | 
                
                 | 
                        # ax2p = ax2.twinx()  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    211
                 | 
                                    
                                                     | 
                
                 | 
                        bins = "auto"  # bins = np.int(y.size**0.5/1.5) #  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    212
                 | 
                                    
                                                     | 
                
                 | 
                        rang = (np.percentile(y2, 0), np.percentile(y2, 99))  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    213
                 | 
                                    
                                                     | 
                
                 | 
                        axes["ax2"].hist(y2, density=True, color="r", alpha=0.4, bins=bins, range=rang)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    214
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    215
                 | 
                                    
                                                     | 
                
                 | 
                        axes["ax2"].set_title("pdf") | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    216
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    217
                 | 
                                    
                                                     | 
                
                 | 
                        # plot their PSD  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    218
                 | 
                                    
                                                     | 
                
                 | 
                        if fpsd == "lombscargle":  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    219
                 | 
                                    
                                                     | 
                
                 | 
                            k = np.linspace(1e-3, self.values.size / 2, self.values.size // 2)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    220
                 | 
                                    
                                                     | 
                
                 | 
                            freqs = k / 2 / np.pi  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    221
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    222
                 | 
                                    
                                                     | 
                
                 | 
                            pxx = scipy_signal.lombscargle(t, y, freqs, normalize=True)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    223
                 | 
                                    
                                                     | 
                
                 | 
                            axes["ax3"].plot(freqs, pxx, "b-", lw=1, alpha=0.5)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    224
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                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    225
                 | 
                                    
                                                     | 
                
                 | 
                            pxx2 = scipy_signal.lombscargle(t, y2, freqs, normalize=True)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    226
                 | 
                                    
                                                     | 
                
                 | 
                            axes["ax3"].plot(freqs, pxx2, "r-", lw=1, alpha=0.5)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    227
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                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    228
                 | 
                                    
                                                     | 
                
                 | 
                            axes["ax3"].set_xscale("log") | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    229
                 | 
                                    
                                                     | 
                
                 | 
                            # ax3.set_yscale('log') | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    230
                 | 
                                    
                                                     | 
                
                 | 
                        else:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    231
                 | 
                                    
                                                     | 
                
                 | 
                            axes["ax3"].psd(y, color="b", lw=1, alpha=0.5)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    232
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    233
                 | 
                                    
                                                     | 
                
                 | 
                            ax3p = axes["ax3"].twinx()  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    234
                 | 
                                    
                                                     | 
                
                 | 
                            ax3p.psd(y2, color="r", lw=1, alpha=0.5)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    235
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    236
                 | 
                                    
                                                     | 
                
                 | 
                        axes["ax3"].set_title("PSD") | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    237
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    238
                 | 
                                    
                                                     | 
                
                 | 
                        return axes  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    239
                 | 
                                    
                                                     | 
                
                 | 
                      | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    240
                 | 
                                    
                                                     | 
                
                 | 
                      | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    241
                 | 
                                    
                                                     | 
                
                 | 
                          | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                                                                
            
                                    
            
            
                | 
                    242
                 | 
                                    
                                                     | 
                
                 | 
                    @staticmethod  | 
            
            
                                                        
            
                                    
            
            
                | 
                    243
                 | 
                                    
                                                     | 
                
                 | 
                    def pdf(xx, ll, mu):  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                                                                                                                            
                        
                         
                                                                                        
                                                                                            
                                                                                            
                                                                                     
                     | 
                
            
                                                        
            
                                    
            
            
                | 
                    244
                 | 
                                    
                                                     | 
                
                 | 
                        """Helper func to fit pdf as a curve."""  | 
            
            
                                                        
            
                                    
            
            
                | 
                    245
                 | 
                                    
                                                     | 
                
                 | 
                        return (  | 
            
            
                                                        
            
                                    
            
            
                | 
                    246
                 | 
                                    
                                                     | 
                
                 | 
                            (ll * mu) ** (1 + ll)  | 
            
            
                                                        
            
                                    
            
            
                | 
                    247
                 | 
                                    
                                                     | 
                
                 | 
                            / scipy_special.gamma(1 + ll)  | 
            
            
                                                        
            
                                    
            
            
                | 
                    248
                 | 
                                    
                                                     | 
                
                 | 
                            * np.exp(-ll * mu / xx)  | 
            
            
                                                        
            
                                    
            
            
                | 
                    249
                 | 
                                    
                                                     | 
                
                 | 
                            / xx ** (ll + 2)  | 
            
            
                                                        
            
                                    
            
            
                | 
                    250
                 | 
                                    
                                                     | 
                
                 | 
                        )  | 
            
            
                                                        
            
                                    
            
            
                | 
                    251
                 | 
                                    
                                                     | 
                
                 | 
                 |